%------------------------------------------------------------------------------ % File : SPASS---3.9 % Problem : NUM149-1 : TPTP v8.1.0. Bugfixed v2.1.0. % Transfm : none % Format : tptp % Command : run_spass %d %s % Computer : n007.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 14:24:21 EDT 2022 % Result : Timeout 299.95s 300.39s % Output : None % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----No solution output by system %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : NUM149-1 : TPTP v8.1.0. Bugfixed v2.1.0. % 0.12/0.13 % Command : run_spass %d %s % 0.13/0.34 % Computer : n007.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 600 % 0.13/0.35 % DateTime : Wed Jul 6 01:03:28 EDT 2022 % 0.13/0.35 % CPUTime : % 299.95/300.39 % 299.95/300.39 SPASS V 3.9 % 299.95/300.39 SPASS beiseite: Ran out of time. % 299.95/300.39 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p % 299.95/300.39 SPASS derived 197366 clauses, backtracked 21255 clauses, performed 77 splits and kept 80694 clauses. % 299.95/300.39 SPASS allocated 248222 KBytes. % 299.95/300.39 SPASS spent 0:05:00.04 on the problem. % 299.95/300.39 0:00:00.05 for the input. % 299.95/300.39 0:00:00.00 for the FLOTTER CNF translation. % 299.95/300.39 0:00:03.59 for inferences. % 299.95/300.39 0:00:09.65 for the backtracking. % 299.95/300.39 0:4:42.76 for the reduction. % 299.95/300.39 % 299.95/300.39 % 299.95/300.39 The set of clauses at termination is : % 299.95/300.39 168592[19:Rew:166997.0,80860.1] || well_ordering(u,universal_class) -> equal(symmetric_difference(v,w),ordinal_numbers) member(least(u,symmetric_difference(v,w)),union(v,w))*. % 299.95/300.39 227961[18:MRR:227937.0,227937.2,36583.1,19.0] || member(u,v) member(v,cantor(u))* -> . % 299.95/300.39 252948[19:Res:220180.1,167211.1] inductive(complement(complement(u))) || subclass(u,ordinal_numbers)* -> . % 299.95/300.39 253057[20:MRR:253011.1,175557.0] || subclass(inverse(ordinal_numbers),complement(symmetrization_of(ordinal_numbers)))* -> . % 299.95/300.39 252894[19:SpR:167191.0,220180.1] || subclass(inverse(ordinal_numbers),u) -> subclass(symmetrization_of(ordinal_numbers),u)*. % 299.95/300.39 56455[2:MRR:56453.2,5260.0] || well_ordering(u,universal_class) subclass(singleton(least(u,v)),v) -> section(u,singleton(least(u,v)),v)*. % 299.95/300.39 220180[0:SpR:149012.1,218971.0] || subclass(u,v) -> subclass(complement(complement(u)),v)*. % 299.95/300.39 250112[19:Res:248806.0,190819.0] || -> subclass(singleton(not_subclass_element(u,ordinal_numbers)),u)* subclass(u,ordinal_numbers). % 299.95/300.39 252735[19:Res:249272.0,167211.1] inductive(complement(union(complement(complement(complement(ordinal_numbers))),u))) || -> . % 299.95/300.39 249272[0:Res:248817.0,219712.0] || -> subclass(complement(union(complement(complement(complement(u))),v)),u)*. % 299.95/300.39 125121[8:Rew:124836.0,42810.0] || member(u,cantor(v)) subclass(rest_of(v),w) -> member(ordered_pair(u,restrict(v,u,universal_class)),w)*. % 299.95/300.39 252487[19:Res:249106.0,167211.1] inductive(complement(union(u,complement(complement(complement(ordinal_numbers)))))) || -> . % 299.95/300.39 249106[0:Res:248816.0,219712.0] || -> subclass(complement(union(u,complement(complement(complement(v))))),v)*. % 299.95/300.39 252342[19:Res:248812.0,167211.1] inductive(complement(complement(intersection(complement(complement(ordinal_numbers)),u)))) || -> . % 299.95/300.39 248812[0:Res:218971.0,219712.0] || -> subclass(complement(complement(intersection(complement(complement(u)),v))),u)*. % 299.95/300.39 27879[0:Rew:4125.0,27806.0] || -> subclass(symmetric_difference(complement(u),complement(v)),w) member(not_subclass_element(symmetric_difference(complement(u),complement(v)),w),union(u,v))*. % 299.95/300.39 252027[19:Res:248810.0,167211.1] inductive(complement(complement(intersection(u,complement(complement(ordinal_numbers)))))) || -> . % 299.95/300.39 248810[0:Res:217853.0,219712.0] || -> subclass(complement(complement(intersection(u,complement(complement(v))))),v)*. % 299.95/300.39 251891[19:Res:248798.0,167211.1] inductive(intersection(u,complement(complement(complement(complement(ordinal_numbers)))))) || -> . % 299.95/300.39 248798[0:Res:219700.0,219712.0] || -> subclass(intersection(u,complement(complement(complement(complement(v))))),v)*. % 299.95/300.39 36863[0:MRR:35128.0,36682.1] || -> member(not_subclass_element(u,intersection(complement(v),complement(w))),union(v,w))* subclass(u,intersection(complement(v),complement(w))). % 299.95/300.39 251567[19:Res:248783.0,167211.1] inductive(intersection(complement(complement(complement(complement(ordinal_numbers)))),u)) || -> . % 299.95/300.39 248783[0:Res:218920.0,219712.0] || -> subclass(intersection(complement(complement(complement(complement(u)))),v),u)*. % 299.95/300.39 248778[19:Res:238770.1,219712.0] || equal(complement(complement(u)),universal_class)**+ -> subclass(v,u)*. % 299.95/300.39 250124[19:Res:248806.0,203417.1] || subclass(complement(u),ordinal_numbers)* -> subclass(singleton(ordinal_numbers),u). % 299.95/300.39 237458[0:Rew:237384.0,16892.0] || member(u,symmetric_difference(symmetrization_of(v),complement(intersection(v,inverse(v)))))* -> member(u,complement(symmetric_difference(v,inverse(v)))). % 299.95/300.39 250085[19:Res:248806.0,203420.1] || subclass(complement(u),ordinal_numbers)* -> subclass(singleton(omega),u). % 299.95/300.39 248975[19:Res:248819.0,167311.1] inductive(complement(symmetrization_of(complement(u)))) || -> member(ordinal_numbers,u)*. % 299.95/300.39 248972[19:SpR:204449.1,248819.0] || equal(symmetrization_of(complement(u)),ordinal_numbers)** -> subclass(universal_class,u). % 299.95/300.39 248858[19:Res:248818.0,167311.1] inductive(complement(successor(complement(u)))) || -> member(ordinal_numbers,u)*. % 299.95/300.39 207765[0:SpR:206407.0,978.1] || member(u,universal_class) -> member(u,intersection(complement(v),power_class(w)))* member(u,union(v,complement(power_class(w)))). % 299.95/300.39 250947[19:Res:248811.0,167211.1] inductive(complement(complement(complement(complement(complement(complement(ordinal_numbers))))))) || -> . % 299.95/300.39 248811[0:Res:219703.0,219712.0] || -> subclass(complement(complement(complement(complement(complement(complement(u)))))),u)*. % 299.95/300.39 250609[19:Obv:250605.1] || equal(successor(union(complement(symmetrization_of(ordinal_numbers)),u)),ordinal_numbers)** -> . % 299.95/300.39 250368[19:Obv:250364.1] || equal(successor(union(u,complement(symmetrization_of(ordinal_numbers)))),ordinal_numbers)** -> . % 299.95/300.39 207750[0:SpR:206407.0,978.1] || member(u,universal_class) -> member(u,intersection(power_class(v),complement(w)))* member(u,union(complement(power_class(v)),w)). % 299.95/300.39 250643[19:MRR:250631.1,167338.0] inductive(complement(union(complement(symmetrization_of(ordinal_numbers)),u))) || -> . % 299.95/300.39 249267[19:Res:248817.0,219089.0] || -> subclass(complement(union(complement(symmetrization_of(ordinal_numbers)),u)),inverse(ordinal_numbers))*. % 299.95/300.39 249266[19:Res:248817.0,239702.0] || equal(complement(union(complement(symmetrization_of(ordinal_numbers)),u)),universal_class)** -> . % 299.95/300.39 249220[19:SpR:167191.0,248817.0] || -> subclass(complement(union(symmetrization_of(ordinal_numbers),u)),complement(inverse(ordinal_numbers)))*. % 299.95/300.39 176259[19:Rew:176206.1,158756.2] || member(u,universal_class) subclass(domain_relation,restrict(v,w,x))*+ -> member(ordered_pair(u,ordinal_numbers),cross_product(w,x))*. % 299.95/300.39 250532[19:MRR:250520.1,167338.0] inductive(complement(union(u,complement(symmetrization_of(ordinal_numbers))))) || -> . % 299.95/300.39 249101[19:Res:248816.0,219089.0] || -> subclass(complement(union(u,complement(symmetrization_of(ordinal_numbers)))),inverse(ordinal_numbers))*. % 299.95/300.39 250475[19:SpL:236669.0,250367.0] || equal(union(complement(symmetrization_of(ordinal_numbers)),u),ordinal_numbers)** -> . % 299.95/300.39 250367[19:Obv:250365.1] || equal(union(u,complement(symmetrization_of(ordinal_numbers))),ordinal_numbers)** -> . % 299.95/300.39 167719[19:Rew:166997.0,80600.2] || member(u,universal_class) subclass(u,intersection(v,w))*+ -> equal(u,ordinal_numbers) member(apply(choice,u),w)*. % 299.95/300.39 249100[19:Res:248816.0,239702.0] || equal(complement(union(u,complement(symmetrization_of(ordinal_numbers)))),universal_class)** -> . % 299.95/300.39 250315[20:SpL:236669.0,250183.0] || equal(successor(union(symmetrization_of(ordinal_numbers),u)),ordinal_numbers)** -> . % 299.95/300.39 250183[20:MRR:250166.1,176136.0] || equal(successor(union(u,symmetrization_of(ordinal_numbers))),ordinal_numbers)** -> . % 299.95/300.39 250188[20:SpL:236669.0,250181.0] || equal(union(symmetrization_of(ordinal_numbers),u),ordinal_numbers)** -> . % 299.95/300.39 167718[19:Rew:166997.0,80601.2] || member(u,universal_class) subclass(u,intersection(v,w))*+ -> equal(u,ordinal_numbers) member(apply(choice,u),v)*. % 299.95/300.39 250181[20:MRR:250167.1,176136.0] || equal(union(u,symmetrization_of(ordinal_numbers)),ordinal_numbers)** -> . % 299.95/300.39 249055[19:SpR:167191.0,248816.0] || -> subclass(complement(union(u,symmetrization_of(ordinal_numbers))),complement(inverse(ordinal_numbers)))*. % 299.95/300.39 250113[19:Res:248806.0,197071.0] || -> subclass(singleton(not_subclass_element(element_relation,ordinal_numbers)),compose(element_relation,universal_class))*. % 299.95/300.39 248806[0:Res:95593.1,219712.0] || -> member(u,complement(v))* subclass(singleton(u),v). % 299.95/300.39 167716[19:Rew:166997.0,80611.2] || subclass(u,intersection(complement(v),complement(w)))* member(regular(u),union(v,w)) -> equal(u,ordinal_numbers). % 299.95/300.39 249862[19:Res:248999.0,167211.1] inductive(complement(symmetrization_of(complement(complement(complement(ordinal_numbers)))))) || -> . % 299.95/300.39 248999[0:Res:248819.0,219712.0] || -> subclass(complement(symmetrization_of(complement(complement(complement(u))))),u)*. % 299.95/300.39 249745[19:Res:248882.0,167211.1] inductive(complement(successor(complement(complement(complement(ordinal_numbers)))))) || -> . % 299.95/300.39 248882[0:Res:248818.0,219712.0] || -> subclass(complement(successor(complement(complement(complement(u))))),u)*. % 299.95/300.39 42928[0:Res:5.0,9836.1] || member(u,universal_class)*+ well_ordering(v,universal_class) -> member(u,w)* member(least(v,complement(w)),complement(w))*. % 299.95/300.39 248786[0:Res:52.1,219712.0] inductive(complement(complement(u))) || -> subclass(omega,u)*. % 299.95/300.39 249488[19:Obv:249485.1] || equal(successor(symmetrization_of(complement(symmetrization_of(ordinal_numbers)))),ordinal_numbers)** -> . % 299.95/300.39 249414[19:Obv:249411.1] || equal(successor(successor(complement(symmetrization_of(ordinal_numbers)))),ordinal_numbers)** -> . % 299.95/300.39 249509[19:MRR:249501.1,167338.0] inductive(complement(symmetrization_of(complement(symmetrization_of(ordinal_numbers))))) || -> . % 299.95/300.39 160283[8:MRR:80670.0,160281.0] || -> equal(apply(choice,ordered_pair(u,v)),unordered_pair(u,singleton(v)))** equal(apply(choice,ordered_pair(u,v)),singleton(u)). % 299.95/300.39 248994[19:Res:248819.0,219089.0] || -> subclass(complement(symmetrization_of(complement(symmetrization_of(ordinal_numbers)))),inverse(ordinal_numbers))*. % 299.95/300.39 248993[19:Res:248819.0,239702.0] || equal(complement(symmetrization_of(complement(symmetrization_of(ordinal_numbers)))),universal_class)** -> . % 299.95/300.39 249461[20:MRR:249447.1,176136.0] || equal(successor(symmetrization_of(symmetrization_of(ordinal_numbers))),ordinal_numbers)** -> . % 299.95/300.39 249459[20:MRR:249448.1,176136.0] || equal(symmetrization_of(symmetrization_of(ordinal_numbers)),ordinal_numbers)** -> . % 299.95/300.39 36582[0:Res:63.1,7972.2] function(intersection(u,v)) || member(w,v)* member(w,u)* -> member(w,cross_product(universal_class,universal_class))*. % 299.95/300.39 248958[19:SpR:167191.0,248819.0] || -> subclass(complement(symmetrization_of(symmetrization_of(ordinal_numbers))),complement(inverse(ordinal_numbers)))*. % 299.95/300.39 249435[19:MRR:249427.1,167338.0] inductive(complement(successor(complement(symmetrization_of(ordinal_numbers))))) || -> . % 299.95/300.39 248877[19:Res:248818.0,219089.0] || -> subclass(complement(successor(complement(symmetrization_of(ordinal_numbers)))),inverse(ordinal_numbers))*. % 299.95/300.39 248876[19:Res:248818.0,239702.0] || equal(complement(successor(complement(symmetrization_of(ordinal_numbers)))),universal_class)** -> . % 299.95/300.39 34754[0:Res:6521.3,22.0] function(u) || member(v,universal_class) subclass(universal_class,intersection(w,x))*+ -> member(image(u,v),w)*. % 299.95/300.39 249340[20:MRR:249327.1,176136.0] || equal(successor(successor(symmetrization_of(ordinal_numbers))),ordinal_numbers)** -> . % 299.95/300.39 248841[19:SpR:167191.0,248818.0] || -> subclass(complement(successor(symmetrization_of(ordinal_numbers))),complement(inverse(ordinal_numbers)))*. % 299.95/300.39 249286[19:Res:248817.0,167211.1] inductive(complement(union(complement(ordinal_numbers),u))) || -> . % 299.95/300.39 248817[0:Res:220194.0,219712.0] || -> subclass(complement(union(complement(u),v)),u)*. % 299.95/300.39 34755[0:Res:6521.3,23.0] function(u) || member(v,universal_class) subclass(universal_class,intersection(w,x))*+ -> member(image(u,v),x)*. % 299.95/300.39 249120[19:Res:248816.0,167211.1] inductive(complement(union(u,complement(ordinal_numbers)))) || -> . % 299.95/300.39 248816[0:Res:218022.0,219712.0] || -> subclass(complement(union(u,complement(v))),v)*. % 299.95/300.39 249013[19:Res:248819.0,167211.1] inductive(complement(symmetrization_of(complement(ordinal_numbers)))) || -> . % 299.95/300.39 248819[0:Res:220427.0,219712.0] || -> subclass(complement(symmetrization_of(complement(u))),u)*. % 299.95/300.39 15080[0:Res:2483.2,9.0] || member(u,universal_class)* subclass(universal_class,unordered_pair(v,w))*+ -> equal(power_class(u),w)* equal(power_class(u),v)*. % 299.95/300.39 248896[19:Res:248818.0,167211.1] inductive(complement(successor(complement(ordinal_numbers)))) || -> . % 299.95/300.39 248818[0:Res:220426.0,219712.0] || -> subclass(complement(successor(complement(u))),u)*. % 299.95/300.39 219712[0:SpR:149012.1,218920.0] || subclass(u,complement(complement(v)))* -> subclass(u,v). % 299.95/300.39 218724[0:SpR:4105.0,217850.0] || -> subclass(intersection(u,symmetric_difference(v,inverse(v))),symmetrization_of(v))*. % 299.95/300.39 9652[0:SpL:946.0,34.0] || member(ordered_pair(singleton(singleton(singleton(u))),v),rotate(w))*+ -> member(ordered_pair(ordered_pair(u,v),singleton(u)),w)*. % 299.95/300.39 217958[0:SpR:160.0,217853.0] || -> subclass(complement(complement(symmetric_difference(u,v))),union(u,v))*. % 299.95/300.39 217784[0:SpR:4105.0,217683.0] || -> subclass(intersection(symmetric_difference(u,inverse(u)),v),symmetrization_of(u))*. % 299.95/300.39 246509[25:SpL:234134.1,204472.0] function(u) || equal(complement(u),successor(u))** -> . % 299.95/300.39 246387[25:SpR:234134.1,219703.0] function(u) || -> subclass(complement(complement(successor(u))),u)*. % 299.95/300.39 9607[0:SpL:946.0,37.0] || member(ordered_pair(singleton(singleton(singleton(u))),v),flip(w))*+ -> member(ordered_pair(ordered_pair(u,singleton(u)),v),w)*. % 299.95/300.39 246385[25:SpR:234134.1,190268.0] function(u) || -> equal(symmetric_difference(u,successor(u)),ordinal_numbers)**. % 299.95/300.39 245621[19:Res:7.1,224470.0] || equal(cross_product(u,v),composition_function)** -> member(ordinal_numbers,u). % 299.95/300.39 245391[19:Res:7.1,215211.0] || equal(intersection(u,v),kind_1_ordinals)** -> member(ordinal_numbers,v). % 299.95/300.39 248149[19:SpL:235538.0,245337.0] || equal(u,kind_1_ordinals) -> member(ordinal_numbers,u)*. % 299.95/300.39 27142[0:Res:2523.2,2.0] || member(u,universal_class)+ subclass(rest_relation,v)* subclass(v,w)* -> member(ordered_pair(u,rest_of(u)),w)*. % 299.95/300.39 245337[19:Res:7.1,215210.0] || equal(intersection(u,v),kind_1_ordinals)** -> member(ordinal_numbers,u). % 299.95/300.39 248123[19:Obv:248122.1] || equal(inverse(u),universal_class) -> connected(u,v)*. % 299.95/300.39 247536[19:SpR:238841.1,114.0] || equal(inverse(u),universal_class) -> equal(symmetrization_of(u),universal_class)**. % 299.95/300.39 247534[19:SpR:238841.1,44.0] || equal(singleton(u),universal_class) -> equal(successor(u),universal_class)**. % 299.95/300.39 27157[0:Res:2523.2,4127.0] || member(u,universal_class) subclass(rest_relation,symmetric_difference(v,w)) -> member(ordered_pair(u,rest_of(u)),union(v,w))*. % 299.95/300.39 247573[19:SpR:238841.1,167022.0] || equal(image(successor_relation,ordinal_numbers),universal_class)** -> equal(kind_1_ordinals,universal_class). % 299.95/300.39 238841[19:Rew:167055.0,238047.1,167140.0,238047.1,234692.0,238047.1] || equal(u,universal_class) -> equal(union(v,u),universal_class)**. % 299.95/300.39 238829[19:Rew:167055.0,237999.1,167140.0,237999.1] || equal(u,universal_class) -> equal(union(u,v),universal_class)**. % 299.95/300.40 238772[19:Rew:167055.0,238068.1] || equal(intersection(u,v),universal_class)** -> subclass(universal_class,u). % 299.95/300.40 27192[0:MRR:27181.1,145.0] || member(u,universal_class) equal(compose(v,u),rest_of(u)) -> member(ordered_pair(u,rest_of(u)),compose_class(v))*. % 299.95/300.40 247103[19:MRR:247065.1,160285.0] || equal(restrict(u,v,w),universal_class)** -> . % 299.95/300.40 247161[23:Res:229698.1,247121.0] || equal(successor(complement(rest_of(u))),ordinal_numbers)** -> . % 299.95/300.40 247123[23:Res:12015.1,247104.0] || equal(complement(complement(rest_of(u))),universal_class)** -> . % 299.95/300.40 247121[23:Res:203424.1,247104.0] || subclass(complement(rest_of(u)),ordinal_numbers)* -> . % 299.95/300.40 15114[0:Res:2482.2,9.0] || member(u,universal_class)* subclass(universal_class,unordered_pair(v,w))*+ -> equal(sum_class(u),w)* equal(sum_class(u),v)*. % 299.95/300.40 247104[23:MRR:184035.1,247103.0] || member(singleton(singleton(ordinal_numbers)),rest_of(u))* -> . % 299.95/300.40 238771[19:Rew:167055.0,238067.1] || equal(intersection(u,v),universal_class)** -> subclass(universal_class,v). % 299.95/300.40 247053[25:SoR:246596.0,72.1] one_to_one(successor_relation) || equal(complement(successor(successor_relation)),ordinal_numbers)** -> . % 299.95/300.40 246596[25:SpL:234134.1,221858.0] function(successor_relation) || equal(complement(successor(successor_relation)),ordinal_numbers)** -> . % 299.95/300.40 167615[19:Rew:166997.0,80514.1] || asymmetric(cross_product(u,v),universal_class) -> equal(image(restrict(inverse(cross_product(u,v)),u,v),universal_class),range_of(ordinal_numbers))**. % 299.95/300.40 246893[25:SoR:246601.0,72.1] one_to_one(domain_relation) || equal(successor(domain_relation),universal_class)** -> . % 299.95/300.40 246890[25:SoR:246599.0,72.1] one_to_one(rest_relation) || equal(successor(rest_relation),universal_class)** -> . % 299.95/300.40 246887[25:SoR:246595.0,72.1] one_to_one(successor_relation) || equal(successor(successor_relation),universal_class)** -> . % 299.95/300.40 246738[25:SoR:246594.0,72.1] one_to_one(successor_relation) || equal(successor(successor_relation),domain_relation)** -> . % 299.95/300.40 168602[19:Rew:166997.0,80870.1] || member(regular(intersection(complement(u),complement(v))),union(u,v))* -> equal(intersection(complement(u),complement(v)),ordinal_numbers). % 299.95/300.40 246735[25:SoR:246593.0,72.1] one_to_one(successor_relation) || subclass(domain_relation,successor(successor_relation))* -> . % 299.95/300.40 246601[25:SpL:234134.1,184098.0] function(domain_relation) || equal(successor(domain_relation),universal_class)** -> . % 299.95/300.40 246599[25:SpL:234134.1,184106.0] function(rest_relation) || equal(successor(rest_relation),universal_class)** -> . % 299.95/300.40 246595[25:SpL:234134.1,184187.0] function(successor_relation) || equal(successor(successor_relation),universal_class)** -> . % 299.95/300.40 168451[19:Rew:166997.0,80853.1] || member(regular(complement(complement(intersection(u,v)))),symmetric_difference(u,v))* -> equal(complement(complement(intersection(u,v))),ordinal_numbers). % 299.95/300.40 246594[25:SpL:234134.1,163181.0] function(successor_relation) || equal(successor(successor_relation),domain_relation)** -> . % 299.95/300.40 246593[25:SpL:234134.1,163180.0] function(successor_relation) || subclass(domain_relation,successor(successor_relation))* -> . % 299.95/300.40 246381[25:SpR:234134.1,135236.0] function(u) || -> subclass(successor(u),u)*. % 299.95/300.40 234134[25:Rew:233390.0,193301.1] function(u) || -> equal(complement(complement(u)),successor(u))**. % 299.95/300.40 168370[19:Rew:166997.0,84841.2] || subclass(omega,intersection(complement(u),complement(v)))*+ member(w,union(u,v))* -> equal(integer_of(w),ordinal_numbers). % 299.95/300.40 229753[19:Obv:229458.1] || equal(successor(inverse(u)),ordinal_numbers)**+ -> asymmetric(u,v)*. % 299.95/300.40 246082[22:Res:177171.1,229738.1] || subclass(omega,u)* equal(successor(u),ordinal_numbers) -> . % 299.95/300.40 246079[19:Res:214528.1,229738.1] || subclass(kind_1_ordinals,u)* equal(successor(u),ordinal_numbers) -> . % 299.95/300.40 229738[19:MRR:229216.2,36583.1] || equal(successor(u),ordinal_numbers) member(v,u)* -> . % 299.95/300.40 167717[19:Rew:166997.0,80602.3] || member(u,universal_class) subclass(u,complement(v)) member(apply(choice,u),v)* -> equal(u,ordinal_numbers). % 299.95/300.40 229660[19:Rew:142500.0,228978.1] || equal(successor(complement(u)),ordinal_numbers)**+ -> subclass(v,u)*. % 299.95/300.40 225704[19:Res:220544.1,48402.0] || equal(symmetrization_of(unordered_pair(unordered_pair(u,v),w)),ordinal_numbers)** -> . % 299.95/300.40 225703[19:Res:220544.1,48618.0] || equal(symmetrization_of(unordered_pair(ordered_pair(u,v),w)),ordinal_numbers)** -> . % 299.95/300.40 225701[19:Res:220544.1,48401.0] || equal(symmetrization_of(unordered_pair(u,unordered_pair(v,w))),ordinal_numbers)** -> . % 299.95/300.40 104246[12:SpL:43.0,99366.2] || member(u,universal_class)* member(restrict(v,w,universal_class),universal_class)*+ equal(sum_class(image(v,w)),u)* -> . % 299.95/300.40 225700[19:Res:220544.1,48587.0] || equal(symmetrization_of(unordered_pair(u,ordered_pair(v,w))),ordinal_numbers)** -> . % 299.95/300.40 225036[19:Res:220510.1,48402.0] || equal(successor(unordered_pair(unordered_pair(u,v),w)),ordinal_numbers)** -> . % 299.95/300.40 225035[19:Res:220510.1,48618.0] || equal(successor(unordered_pair(ordered_pair(u,v),w)),ordinal_numbers)** -> . % 299.95/300.40 225033[19:Res:220510.1,48401.0] || equal(successor(unordered_pair(u,unordered_pair(v,w))),ordinal_numbers)** -> . % 299.95/300.40 34746[0:Res:6521.3,25.1] function(u) || member(v,universal_class) subclass(universal_class,complement(w)) member(image(u,v),w)* -> . % 299.95/300.40 225032[19:Res:220510.1,48587.0] || equal(successor(unordered_pair(u,ordered_pair(v,w))),ordinal_numbers)** -> . % 299.95/300.40 224470[19:MRR:224464.0,99.0] || subclass(composition_function,cross_product(u,v))* -> member(ordinal_numbers,u). % 299.95/300.40 221567[19:Res:219766.1,151723.0] || equal(complement(complement(u)),ordinal_numbers)**+ -> subclass(u,v)*. % 299.95/300.40 40606[0:MRR:40597.1,170.0] || member(u,universal_class) equal(compose(v,singleton(u)),u) -> member(singleton(singleton(singleton(u))),compose_class(v))*. % 299.95/300.40 217960[0:SpR:4105.0,217853.0] || -> subclass(complement(complement(symmetric_difference(u,inverse(u)))),symmetrization_of(u))*. % 299.95/300.40 215211[19:Res:214528.1,23.0] || subclass(kind_1_ordinals,intersection(u,v))* -> member(ordinal_numbers,v). % 299.95/300.40 215210[19:Res:214528.1,22.0] || subclass(kind_1_ordinals,intersection(u,v))* -> member(ordinal_numbers,u). % 299.95/300.40 82309[0:Res:2478.1,7963.1] || subclass(universal_class,complement(intersection(u,v)))* member(omega,union(u,v)) -> member(omega,symmetric_difference(u,v)). % 299.95/300.40 243847[19:Res:7.1,242435.0] || equal(u,complement(symmetrization_of(ordinal_numbers)))*+ -> member(ordinal_numbers,u)*. % 299.95/300.40 243742[19:Res:7.1,239702.0] || equal(symmetrization_of(ordinal_numbers),u)* equal(u,universal_class) -> . % 299.95/300.40 244638[19:Rew:142500.0,244410.1,234692.0,244410.1,167055.0,244410.1] || equal(u,universal_class) -> equal(symmetrization_of(u),universal_class)**. % 299.95/300.40 244637[19:Obv:244593.1] || equal(u,universal_class) -> connected(u,v)*. % 299.95/300.40 207436[0:Rew:206400.0,206879.1] || member(not_subclass_element(power_class(complement(power_class(u))),v),image(element_relation,power_class(u)))* -> subclass(power_class(complement(power_class(u))),v). % 299.95/300.40 242818[19:Res:238042.1,167211.1] inductive(complement(symmetrization_of(u))) || equal(u,universal_class)* -> . % 299.95/300.40 244056[19:Rew:142500.0,243878.1,234692.0,243878.1,167055.0,243878.1] || equal(u,universal_class) -> equal(successor(u),universal_class)**. % 299.95/300.40 204404[19:Rew:204394.1,204383.2] || member(u,universal_class)* subclass(universal_class,ordered_pair(v,w))*+ -> equal(sum_class(u),omega) equal(sum_class(u),ordinal_numbers). % 299.95/300.40 242722[19:Res:238041.1,167211.1] inductive(complement(successor(u))) || equal(u,universal_class)* -> . % 299.95/300.40 242435[19:Res:242417.0,2.0] || subclass(complement(symmetrization_of(ordinal_numbers)),u)* -> member(ordinal_numbers,u). % 299.95/300.40 242348[19:Res:7.1,232073.0] || equal(u,kind_1_ordinals) equal(symmetrization_of(u),ordinal_numbers)** -> . % 299.95/300.40 242249[19:Res:7.1,228026.0] || equal(rest_of(regular(u)),composition_function)** -> equal(u,ordinal_numbers). % 299.95/300.40 204403[19:Rew:204394.1,204382.2] || member(u,universal_class)* subclass(universal_class,ordered_pair(v,w))*+ -> equal(power_class(u),omega) equal(power_class(u),ordinal_numbers). % 299.95/300.40 242228[19:Res:7.1,228025.0] || equal(rest_of(u),composition_function)** -> equal(singleton(u),ordinal_numbers). % 299.95/300.40 239881[19:Res:238770.1,205984.1] || equal(rotate(u),universal_class)** equal(ordinal_numbers,u) -> . % 299.95/300.40 239873[19:Res:238770.1,205983.1] || equal(flip(u),universal_class)** equal(ordinal_numbers,u) -> . % 299.95/300.40 239702[19:SpL:149012.1,238793.0] || subclass(u,symmetrization_of(ordinal_numbers))* equal(u,universal_class) -> . % 299.95/300.40 79963[0:Res:2523.2,158.0] || member(u,universal_class) subclass(rest_relation,omega) -> equal(integer_of(ordered_pair(u,rest_of(u))),ordered_pair(u,rest_of(u)))**. % 299.95/300.40 239302[19:SoR:228539.0,238779.1] || equal(intersection(intersection(symmetrization_of(ordinal_numbers),u),v),universal_class)** -> . % 299.95/300.40 239300[19:SoR:228710.0,238779.1] || equal(intersection(intersection(u,symmetrization_of(ordinal_numbers)),v),universal_class)** -> . % 299.95/300.40 239286[19:SoR:228647.0,238779.1] || equal(intersection(u,intersection(symmetrization_of(ordinal_numbers),v)),universal_class)** -> . % 299.95/300.40 239284[19:SoR:228810.0,238779.1] || equal(intersection(u,intersection(v,symmetrization_of(ordinal_numbers))),universal_class)** -> . % 299.95/300.40 207289[19:Rew:206400.0,168270.1] || member(power_class(u),universal_class) member(apply(choice,power_class(u)),complement(power_class(u)))* -> equal(power_class(u),ordinal_numbers). % 299.95/300.40 243467[25:SoR:243466.0,72.1] one_to_one(power_class(u)) || equal(u,universal_class)* -> . % 299.95/300.40 243466[25:SoR:243200.0,5484.1] function(power_class(u)) || equal(u,universal_class)* -> . % 299.95/300.40 243200[25:MRR:243199.2,192574.0] single_valued_class(power_class(u)) || equal(u,universal_class)* -> . % 299.95/300.40 243117[19:Obv:243003.2] inductive(power_class(u)) || equal(u,universal_class)* -> . % 299.95/300.40 177429[19:Res:940.0,168644.0] || subclass(universal_class,u)+ well_ordering(omega,u)* -> equal(integer_of(ordered_pair(ordered_pair(v,w),least(omega,universal_class))),ordinal_numbers)**. % 299.95/300.40 243093[19:Rew:167049.0,242965.1] || equal(u,universal_class) -> equal(power_class(u),ordinal_numbers)**. % 299.95/300.40 177428[19:Res:12.0,168644.0] || subclass(universal_class,u)+ well_ordering(omega,u)* -> equal(integer_of(ordered_pair(unordered_pair(v,w),least(omega,universal_class))),ordinal_numbers)**. % 299.95/300.40 168182[19:Rew:166997.0,80685.2] || member(complement(complement(u)),universal_class) -> member(apply(choice,complement(complement(u))),u)* equal(complement(complement(u)),ordinal_numbers). % 299.95/300.40 235552[19:Rew:235538.0,228972.1] || equal(successor(complement(u)),ordinal_numbers)** -> equal(u,universal_class). % 299.95/300.40 242441[19:Res:242417.0,169221.1] || equal(complement(complement(symmetrization_of(ordinal_numbers))),singleton(ordinal_numbers))** -> . % 299.95/300.40 242442[22:Res:242417.0,177998.1] || equal(complement(complement(symmetrization_of(ordinal_numbers))),omega)** -> . % 299.95/300.40 242439[19:Res:242417.0,217129.1] || equal(complement(complement(symmetrization_of(ordinal_numbers))),kind_1_ordinals)** -> . % 299.95/300.40 169567[19:Rew:166997.0,167670.1,166997.0,167670.0] || member(not_subclass_element(u,ordinal_numbers),element_relation) member(not_subclass_element(u,ordinal_numbers),complement(compose(element_relation,universal_class)))* -> subclass(u,ordinal_numbers). % 299.95/300.40 242438[19:Res:242417.0,225687.1] || equal(symmetrization_of(complement(symmetrization_of(ordinal_numbers))),ordinal_numbers)** -> . % 299.95/300.40 242440[19:Res:242417.0,203417.1] || subclass(complement(symmetrization_of(ordinal_numbers)),ordinal_numbers)* -> . % 299.95/300.40 242417[19:MRR:242384.0,167337.0] || -> member(ordinal_numbers,complement(symmetrization_of(ordinal_numbers)))*. % 299.95/300.40 234130[19:Rew:233390.0,188588.1] || member(ordinal_numbers,u) -> member(ordinal_numbers,complement(complement(u)))*. % 299.95/300.40 161073[8:Res:158049.1,5426.1] function(complement(complement(symmetrization_of(u)))) || connected(u,universal_class) -> equal(complement(complement(symmetrization_of(u))),cross_product(universal_class,universal_class))**. % 299.95/300.40 232443[19:Res:7.1,225688.1] || equal(u,domain_relation) equal(symmetrization_of(u),ordinal_numbers)** -> . % 299.95/300.40 232076[22:Res:177171.1,225687.1] || subclass(omega,u)* equal(symmetrization_of(u),ordinal_numbers) -> . % 299.95/300.40 232075[22:Res:178902.1,225687.1] || equal(u,omega) equal(symmetrization_of(u),ordinal_numbers)** -> . % 299.95/300.40 232073[19:Res:214528.1,225687.1] || subclass(kind_1_ordinals,u)* equal(symmetrization_of(u),ordinal_numbers) -> . % 299.95/300.40 158715[8:Rew:157840.0,30677.2] function(union(identity_relation,symmetrization_of(u))) || connected(u,universal_class) -> equal(complement(complement(symmetrization_of(u))),cross_product(universal_class,universal_class))**. % 299.95/300.40 229730[19:Obv:229140.2] || equal(successor(u),ordinal_numbers)** equal(u,domain_relation) -> . % 299.95/300.40 229729[22:Obv:229139.2] || equal(successor(u),ordinal_numbers)** equal(u,omega) -> . % 299.95/300.40 229728[19:Obv:229130.1] || equal(successor(u),ordinal_numbers)** equal(u,kind_1_ordinals) -> . % 299.95/300.40 228219[19:Res:7.1,223780.0] || equal(u,kind_1_ordinals) equal(complement(u),kind_1_ordinals)** -> . % 299.95/300.40 16467[0:Res:2526.2,896.0] || subclass(u,restrict(v,w,x))*+ -> subclass(u,y) member(not_subclass_element(u,y),cross_product(w,x))*. % 299.95/300.40 228026[19:MRR:227988.2,167057.0] || subclass(composition_function,rest_of(regular(u)))* -> equal(u,ordinal_numbers). % 299.95/300.40 228025[19:MRR:227976.2,167057.0] || subclass(composition_function,rest_of(u))* -> equal(singleton(u),ordinal_numbers). % 299.95/300.40 227746[27:Res:7.1,221235.0] || equal(u,image(successor_relation,ordinal_numbers))*+ -> member(ordinal_numbers,u)*. % 299.95/300.40 225693[19:Res:220544.1,148626.0] || equal(symmetrization_of(complement(u)),ordinal_numbers)** -> member(omega,u). % 299.95/300.40 40491[0:Obv:40461.0] || -> equal(not_subclass_element(unordered_pair(u,v),w),u)** subclass(unordered_pair(u,v),w) member(v,unordered_pair(u,v))*. % 299.95/300.40 225692[19:Res:220544.1,167093.0] || equal(symmetrization_of(complement(u)),ordinal_numbers)** -> member(ordinal_numbers,u). % 299.95/300.40 225691[19:Res:220544.1,9715.1] || equal(symmetrization_of(u),ordinal_numbers) subclass(universal_class,u)* -> . % 299.95/300.40 239294[19:SoR:224412.0,238779.1] || equal(intersection(complement(complement(symmetrization_of(ordinal_numbers))),u),universal_class)** -> . % 299.95/300.40 239282[19:SoR:224449.0,238779.1] || equal(intersection(u,complement(complement(symmetrization_of(ordinal_numbers)))),universal_class)** -> . % 299.95/300.40 40490[0:Obv:40469.0] || -> equal(not_subclass_element(unordered_pair(u,v),w),v)** subclass(unordered_pair(u,v),w) member(u,unordered_pair(u,v))*. % 299.95/300.40 241734[19:Res:7.1,241037.0] || equal(intersection(singleton(ordinal_numbers),singleton(singleton(ordinal_numbers))),kind_1_ordinals)** -> . % 299.95/300.40 241042[19:Res:167104.1,241002.0] || subclass(universal_class,intersection(singleton(ordinal_numbers),singleton(singleton(ordinal_numbers))))* -> . % 299.95/300.40 241040[22:Res:177171.1,241002.0] || subclass(omega,intersection(singleton(ordinal_numbers),singleton(singleton(ordinal_numbers))))* -> . % 299.95/300.40 241039[22:Res:178902.1,241002.0] || equal(intersection(singleton(ordinal_numbers),singleton(singleton(ordinal_numbers))),omega)** -> . % 299.95/300.40 168568[19:Rew:166997.0,80844.0] || -> equal(intersection(restrict(u,v,w),x),ordinal_numbers) member(regular(intersection(restrict(u,v,w),x)),u)*. % 299.95/300.40 241037[19:Res:214528.1,241002.0] || subclass(kind_1_ordinals,intersection(singleton(ordinal_numbers),singleton(singleton(ordinal_numbers))))* -> . % 299.95/300.40 241020[19:MRR:240999.1,167057.0] || equal(intersection(singleton(ordinal_numbers),singleton(singleton(ordinal_numbers))),universal_class)** -> . % 299.95/300.40 241044[19:Res:167106.1,241002.0] inductive(intersection(singleton(ordinal_numbers),singleton(singleton(ordinal_numbers)))) || -> . % 299.95/300.40 241054[19:Res:169181.1,241045.0] || equal(singleton(singleton(ordinal_numbers)),singleton(ordinal_numbers))** -> . % 299.95/300.40 168566[19:Rew:166997.0,80842.0] || -> equal(intersection(u,restrict(v,w,x)),ordinal_numbers) member(regular(intersection(u,restrict(v,w,x))),v)*. % 299.95/300.40 241051[19:Res:205391.1,241045.0] || equal(complement(singleton(singleton(ordinal_numbers))),ordinal_numbers)** -> . % 299.95/300.40 241332[19:Res:7.1,241050.0] || equal(singleton(singleton(ordinal_numbers)),kind_1_ordinals)** -> . % 299.95/300.40 241056[19:Res:167087.1,241045.0] || equal(singleton(singleton(ordinal_numbers)),universal_class)** -> . % 299.95/300.40 241055[19:Res:167104.1,241045.0] || subclass(universal_class,singleton(singleton(ordinal_numbers)))* -> . % 299.95/300.40 236817[0:SpR:234713.0,4126.1] || member(u,symmetric_difference(union(v,w),complement(intersection(v,w))))* -> member(u,complement(symmetric_difference(v,w))). % 299.95/300.40 241053[22:Res:177171.1,241045.0] || subclass(omega,singleton(singleton(ordinal_numbers)))* -> . % 299.95/300.40 241052[22:Res:178902.1,241045.0] || equal(singleton(singleton(ordinal_numbers)),omega)** -> . % 299.95/300.40 241050[19:Res:214528.1,241045.0] || subclass(kind_1_ordinals,singleton(singleton(ordinal_numbers)))* -> . % 299.95/300.40 241057[19:Res:167106.1,241045.0] inductive(singleton(singleton(ordinal_numbers))) || -> . % 299.95/300.40 234704[0:Rew:234692.0,207712.0] || -> equal(intersection(union(power_class(u),complement(v)),union(complement(power_class(u)),v)),symmetric_difference(power_class(u),complement(v)))**. % 299.95/300.40 241045[19:MRR:241035.1,167277.0] || member(ordinal_numbers,singleton(singleton(ordinal_numbers)))* -> . % 299.95/300.40 241002[19:Res:240703.0,25.1] || member(ordinal_numbers,intersection(singleton(ordinal_numbers),singleton(singleton(ordinal_numbers))))* -> . % 299.95/300.40 240703[19:Res:237678.0,214682.0] || -> member(ordinal_numbers,complement(intersection(singleton(ordinal_numbers),singleton(singleton(ordinal_numbers)))))*. % 299.95/300.40 240866[19:MRR:240858.1,167176.0] || equal(choice,universal_class)** -> . % 299.95/300.40 237637[19:Rew:237493.0,237470.1] || member(u,symmetric_difference(successor(v),complement(intersection(v,singleton(v)))))* -> member(u,complement(successor(v))). % 299.95/300.40 236254[0:SpR:234692.0,16276.0] || -> subclass(symmetric_difference(u,v),complement(intersection(v,u)))*. % 299.95/300.40 238827[19:Obv:238693.1] || equal(symmetrization_of(u),universal_class) -> connected(u,v)*. % 299.95/300.40 237678[19:SpR:237493.0,16276.0] || -> subclass(successor(u),complement(intersection(u,singleton(u))))*. % 299.95/300.40 239132[19:SpL:237603.0,23.0] || member(u,successor(v)) -> member(u,complement(intersection(v,singleton(v))))*. % 299.95/300.40 239914[19:Res:238770.1,196698.0] || equal(u,universal_class) -> member(regular(element_relation),u)*. % 299.95/300.40 239742[19:Res:238770.1,9780.0] || equal(u,universal_class) -> section(element_relation,u,universal_class)*. % 299.95/300.40 238828[19:Obv:238748.1] || equal(rotate(domain_relation),universal_class)**+ -> equal(ordinal_numbers,u)*. % 299.95/300.40 237138[0:Rew:237023.0,236673.0] || -> equal(intersection(complement(symmetric_difference(u,v)),union(union(u,v),complement(intersection(u,v)))),symmetric_difference(union(u,v),complement(intersection(u,v))))**. % 299.95/300.40 239377[20:SoR:213085.0,238779.1] || equal(singleton(not_subclass_element(symmetrization_of(ordinal_numbers),ordinal_numbers)),universal_class)** -> . % 299.95/300.40 239376[20:SoR:196618.0,238779.1] || equal(singleton(not_subclass_element(inverse(ordinal_numbers),ordinal_numbers)),universal_class)** -> . % 299.95/300.40 238770[19:Rew:142500.0,238009.1,167055.0,238009.1] || equal(u,universal_class) -> subclass(v,u)*. % 299.95/300.40 238793[19:Obv:238334.1] || equal(intersection(symmetrization_of(ordinal_numbers),u),universal_class)** -> . % 299.95/300.40 234711[0:Rew:234692.0,4105.0] || -> equal(intersection(symmetrization_of(u),complement(intersection(u,inverse(u)))),symmetric_difference(u,inverse(u)))**. % 299.95/300.40 238792[19:Obv:238327.1] || equal(intersection(u,symmetrization_of(ordinal_numbers)),universal_class)** -> . % 299.95/300.40 239375[20:SoR:187487.0,238779.1] || equal(singleton(regular(symmetrization_of(ordinal_numbers))),universal_class)** -> . % 299.95/300.40 238803[19:Obv:238747.1] || equal(rotate(cross_product(universal_class,universal_class)),universal_class)** -> . % 299.95/300.40 238779[19:Obv:238282.1] || equal(u,universal_class) -> inductive(u)*. % 299.95/300.40 236997[19:Rew:142500.0,236861.0,234692.0,236861.0,167055.0,236861.0] || -> equal(symmetric_difference(element_relation,complement(compose(element_relation,universal_class))),union(element_relation,complement(compose(element_relation,universal_class))))**. % 299.95/300.40 238768[19:Obv:238746.1] || equal(rotate(element_relation),universal_class)** -> . % 299.95/300.40 238767[19:Obv:238745.1] || equal(rotate(ordinal_numbers),universal_class)** -> . % 299.95/300.40 238766[19:Obv:238744.1] || equal(flip(successor_relation),universal_class)** -> . % 299.95/300.40 238765[19:Obv:238743.1] || equal(flip(element_relation),universal_class)** -> . % 299.95/300.40 237603[19:Rew:237493.0,234712.0] || -> equal(intersection(successor(u),complement(intersection(u,singleton(u)))),successor(u))**. % 299.95/300.40 238764[19:Obv:238742.1] || equal(flip(ordinal_numbers),universal_class)** -> . % 299.95/300.40 238753[19:Obv:238660.1] || equal(omega,universal_class)** -> . % 299.95/300.40 237974[19:Res:7.1,235555.0] || equal(u,universal_class) -> equal(complement(u),ordinal_numbers)**. % 299.95/300.40 235555[19:Rew:235542.0,167361.1] || subclass(universal_class,u)* -> equal(complement(u),ordinal_numbers). % 299.95/300.40 234710[27:Rew:234692.0,220931.0] || -> equal(intersection(kind_1_ordinals,complement(intersection(singleton(ordinal_numbers),image(successor_relation,ordinal_numbers)))),ordinal_numbers)**. % 299.95/300.40 237384[0:Rew:236846.0,237233.0] || -> equal(symmetric_difference(u,v),symmetric_difference(v,u))*. % 299.95/300.40 237218[0:SpR:236669.0,16403.0] || -> subclass(symmetric_difference(u,v),union(v,u))*. % 299.95/300.40 237493[19:MRR:237492.0,5.0] || -> equal(symmetric_difference(u,singleton(u)),successor(u))**. % 299.95/300.40 236669[0:Rew:27.0,236250.0] || -> equal(union(u,v),union(v,u))*. % 299.95/300.40 234713[0:Rew:234692.0,160.0] || -> equal(intersection(union(u,v),complement(intersection(u,v))),symmetric_difference(u,v))**. % 299.95/300.40 234692[0:MRR:233329.0,233022.0] || -> equal(intersection(u,v),intersection(v,u))*. % 299.95/300.40 234127[19:Rew:233390.0,167229.0] || -> equal(symmetric_difference(u,ordinal_numbers),complement(complement(u)))**. % 299.95/300.40 233390[19:Rew:233350.0,167227.0] || -> equal(union(u,ordinal_numbers),complement(complement(u)))**. % 299.95/300.40 235542[2:Rew:235538.0,233386.0] || -> equal(symmetric_difference(u,universal_class),complement(u))**. % 299.95/300.40 234709[19:Rew:234692.0,167159.0] || -> equal(intersection(element_relation,complement(compose(element_relation,universal_class))),ordinal_numbers)**. % 299.95/300.40 233350[2:MRR:144819.0,233349.0] || -> equal(symmetric_difference(universal_class,u),complement(u))**. % 299.95/300.40 235538[0:MRR:235358.0,16254.0] || -> equal(intersection(u,universal_class),u)**. % 299.95/300.40 233022[0:Obv:233007.0] || -> subclass(intersection(u,v),intersection(v,u))*. % 299.95/300.40 42077[0:Obv:42066.1] || member(not_subclass_element(intersection(u,v),intersection(w,u)),w)* -> subclass(intersection(u,v),intersection(w,u)). % 299.95/300.40 232835[19:MRR:232808.0,53.0] || equal(symmetrization_of(unordered_pair(u,omega)),ordinal_numbers)** -> . % 299.95/300.40 232834[19:MRR:232807.0,53.0] || equal(symmetrization_of(unordered_pair(omega,u)),ordinal_numbers)** -> . % 299.95/300.40 225690[19:Res:220544.1,2532.0] || equal(symmetrization_of(u),ordinal_numbers) member(omega,u)* -> . % 299.95/300.40 42076[0:Obv:42069.1] || member(not_subclass_element(intersection(u,v),intersection(w,v)),w)* -> subclass(intersection(u,v),intersection(w,v)). % 299.95/300.40 232446[19:Res:99.0,225688.1] || equal(symmetrization_of(cross_product(universal_class,universal_class)),ordinal_numbers)** -> . % 299.95/300.40 225688[19:Res:220544.1,164453.1] || equal(symmetrization_of(u),ordinal_numbers) subclass(domain_relation,u)* -> . % 299.95/300.40 232080[19:Res:167106.1,225687.1] inductive(u) || equal(symmetrization_of(u),ordinal_numbers)** -> . % 299.95/300.40 232088[19:Res:214498.0,225687.1] || equal(symmetrization_of(union(singleton(ordinal_numbers),u)),ordinal_numbers)** -> . % 299.95/300.40 42073[0:Obv:42070.2] || subclass(u,v) member(not_subclass_element(u,intersection(w,v)),w)* -> subclass(u,intersection(w,v)). % 299.95/300.40 232087[19:Res:215454.0,225687.1] || equal(symmetrization_of(union(u,singleton(ordinal_numbers))),ordinal_numbers)** -> . % 299.95/300.40 232097[27:Res:221200.0,225687.1] || equal(symmetrization_of(image(successor_relation,ordinal_numbers)),ordinal_numbers)** -> . % 299.95/300.40 232094[19:Res:214502.0,225687.1] || equal(symmetrization_of(successor(singleton(ordinal_numbers))),ordinal_numbers)** -> . % 299.95/300.40 232089[19:Res:214503.0,225687.1] || equal(symmetrization_of(symmetrization_of(singleton(ordinal_numbers))),ordinal_numbers)** -> . % 299.95/300.40 36578[0:Res:7.1,7972.2] || equal(u,intersection(v,w))*+ member(x,w)* member(x,v)* -> member(x,u)*. % 299.95/300.40 232096[19:Res:214509.0,225687.1] || equal(symmetrization_of(kind_1_ordinals),ordinal_numbers)** -> . % 299.95/300.40 232082[22:Res:177170.0,225687.1] || equal(symmetrization_of(omega),ordinal_numbers)** -> . % 299.95/300.40 225687[19:Res:220544.1,167096.0] || equal(symmetrization_of(u),ordinal_numbers) member(ordinal_numbers,u)* -> . % 299.95/300.40 225681[19:Res:220544.1,1063.0] || equal(symmetrization_of(u),ordinal_numbers)** -> equal(complement(u),universal_class). % 299.95/300.40 177306[19:MRR:177305.0,12.0] || -> equal(apply(choice,unordered_pair(u,v)),u)** equal(unordered_pair(u,v),ordinal_numbers) member(v,unordered_pair(u,v))*. % 299.95/300.40 225025[19:Res:220510.1,148626.0] || equal(successor(complement(u)),ordinal_numbers)** -> member(omega,u). % 299.95/300.40 225024[19:Res:220510.1,167093.0] || equal(successor(complement(u)),ordinal_numbers)** -> member(ordinal_numbers,u). % 299.95/300.40 225023[19:Res:220510.1,9715.1] || equal(successor(u),ordinal_numbers) subclass(universal_class,u)* -> . % 299.95/300.40 177304[19:MRR:177303.0,12.0] || -> equal(apply(choice,unordered_pair(u,v)),v)** equal(unordered_pair(u,v),ordinal_numbers) member(u,unordered_pair(u,v))*. % 299.95/300.40 225020[19:Res:220510.1,164453.1] || equal(successor(u),ordinal_numbers) subclass(domain_relation,u)* -> . % 299.95/300.40 229743[19:Obv:229379.1] || equal(successor(complement(complement(singleton(singleton(u))))),ordinal_numbers)** -> . % 299.95/300.40 229727[19:MRR:229093.1,167196.0] || equal(successor(union(complement(inverse(ordinal_numbers)),u)),ordinal_numbers)** -> . % 299.95/300.40 229726[19:MRR:229092.1,180092.0] || equal(successor(union(complement(singleton(ordinal_numbers)),u)),ordinal_numbers)** -> . % 299.95/300.40 168570[19:Rew:166997.0,80846.0] || -> equal(intersection(u,symmetric_difference(v,w)),ordinal_numbers) member(regular(intersection(u,symmetric_difference(v,w))),union(v,w))*. % 299.95/300.40 229725[19:MRR:229090.1,167196.0] || equal(successor(union(u,complement(inverse(ordinal_numbers)))),ordinal_numbers)** -> . % 299.95/300.40 229724[19:MRR:229089.1,180092.0] || equal(successor(union(u,complement(singleton(ordinal_numbers)))),ordinal_numbers)** -> . % 299.95/300.40 229722[19:MRR:229003.1,167186.0] || equal(successor(complement(intersection(symmetrization_of(ordinal_numbers),u))),ordinal_numbers)** -> . % 299.95/300.40 229721[19:MRR:229002.1,167186.0] || equal(successor(complement(intersection(u,symmetrization_of(ordinal_numbers)))),ordinal_numbers)** -> . % 299.95/300.40 168569[19:Rew:166997.0,80845.0] || -> equal(intersection(symmetric_difference(u,v),w),ordinal_numbers) member(regular(intersection(symmetric_difference(u,v),w)),union(u,v))*. % 299.95/300.40 229747[19:Obv:229399.1] || equal(successor(image(successor_relation,kind_1_ordinals)),ordinal_numbers)** -> inductive(kind_1_ordinals). % 299.95/300.40 229720[19:MRR:228997.1,167186.0] || equal(successor(complement(complement(complement(symmetrization_of(ordinal_numbers))))),ordinal_numbers)** -> . % 299.95/300.40 231178[19:Res:229698.1,202966.0] || equal(successor(u),ordinal_numbers) -> asymmetric(u,v)*. % 299.95/300.40 229698[19:MRR:229178.1,5.0] || equal(successor(u),ordinal_numbers) -> subclass(u,v)*. % 299.95/300.40 168559[19:Rew:166997.0,80834.0] || -> equal(second(not_subclass_element(restrict(cross_product(singleton(u),v),w,x),ordinal_numbers)),range__dfg(cross_product(w,x),u,v))**. % 299.95/300.40 229697[19:Obv:229141.2] inductive(u) || equal(successor(u),ordinal_numbers)** -> . % 299.95/300.40 229640[19:Rew:142500.0,228894.1] || equal(successor(u),ordinal_numbers)** -> equal(u,ordinal_numbers). % 299.95/300.40 229708[19:Obv:229564.1] || equal(successor(union(singleton(ordinal_numbers),u)),ordinal_numbers)** -> . % 299.95/300.40 229707[19:Obv:229559.1] || equal(successor(union(u,singleton(ordinal_numbers))),ordinal_numbers)** -> . % 299.95/300.40 168558[19:Rew:166997.0,80833.0] || -> equal(first(not_subclass_element(restrict(cross_product(u,singleton(v)),w,x),ordinal_numbers)),domain__dfg(cross_product(w,x),u,v))**. % 299.95/300.40 229702[20:Obv:229383.1] || equal(successor(complement(complement(symmetrization_of(ordinal_numbers)))),ordinal_numbers)** -> . % 299.95/300.40 229695[19:MRR:229120.1,167196.0] || equal(successor(symmetrization_of(complement(inverse(ordinal_numbers)))),ordinal_numbers)** -> . % 299.95/300.40 229694[19:MRR:229119.1,180092.0] || equal(successor(symmetrization_of(complement(singleton(ordinal_numbers)))),ordinal_numbers)** -> . % 299.95/300.40 229693[19:MRR:229099.1,167196.0] || equal(successor(successor(complement(inverse(ordinal_numbers)))),ordinal_numbers)** -> . % 299.95/300.40 167722[19:Rew:166997.0,80613.1] || subclass(u,unordered_pair(v,w))* -> equal(u,ordinal_numbers) equal(regular(u),w) equal(regular(u),v). % 299.95/300.40 229692[19:MRR:229098.1,180092.0] || equal(successor(successor(complement(singleton(ordinal_numbers)))),ordinal_numbers)** -> . % 299.95/300.40 229670[19:Obv:229412.1] || equal(successor(unordered_pair(u,omega)),ordinal_numbers)** -> . % 299.95/300.40 229668[19:Obv:229400.1] || equal(successor(unordered_pair(omega,u)),ordinal_numbers)** -> . % 299.95/300.40 229677[19:Obv:229598.1] || equal(successor(symmetrization_of(singleton(ordinal_numbers))),ordinal_numbers)** -> . % 299.95/300.40 79427[2:MRR:74338.3,79425.0] || asymmetric(u,v)* member(w,cross_product(v,v))* member(w,intersection(u,inverse(u)))*+ -> . % 299.95/300.40 229676[19:Obv:229569.1] || equal(successor(successor(singleton(ordinal_numbers))),ordinal_numbers)** -> . % 299.95/300.40 229675[19:Obv:229502.1] || equal(successor(cross_product(universal_class,universal_class)),ordinal_numbers)** -> . % 299.95/300.40 229673[19:MRR:229446.1,5.0] || equal(successor(compose(element_relation,universal_class)),ordinal_numbers)** -> . % 299.95/300.40 229667[19:Obv:229395.1] || equal(successor(image(successor_relation,ordinal_numbers)),ordinal_numbers)** -> . % 299.95/300.40 1032[0:Rew:27.0,1021.1] || member(not_subclass_element(union(u,v),w),intersection(complement(u),complement(v)))* -> subclass(union(u,v),w). % 299.95/300.40 229661[19:MRR:228986.1,167186.0] || equal(successor(complement(symmetrization_of(ordinal_numbers))),ordinal_numbers)** -> . % 299.95/300.40 229650[20:Obv:229582.1] || equal(successor(symmetrization_of(ordinal_numbers)),ordinal_numbers)** -> . % 299.95/300.40 229648[23:Obv:229369.1] || equal(successor(complement(domain_relation)),ordinal_numbers)** -> . % 299.95/300.40 229647[23:Obv:229367.1] || equal(successor(complement(rest_relation)),ordinal_numbers)** -> . % 299.95/300.40 16109[0:Res:4126.1,4.0] || member(not_subclass_element(u,complement(intersection(v,w))),symmetric_difference(v,w))* -> subclass(u,complement(intersection(v,w))). % 299.95/300.40 229645[19:MRR:229361.1,5.0] || equal(successor(complement(successor_relation)),ordinal_numbers)** -> . % 299.95/300.40 229644[19:Obv:229329.1] || equal(successor(complement(element_relation)),ordinal_numbers)** -> . % 299.95/300.40 229638[19:Obv:229620.1] || equal(successor(composition_function),ordinal_numbers)** -> . % 299.95/300.40 229637[19:Obv:229615.1] || equal(successor(kind_1_ordinals),ordinal_numbers)** -> . % 299.95/300.40 229636[22:Obv:229547.1] || equal(successor(omega),ordinal_numbers)** -> . % 299.95/300.40 229633[19:Obv:229490.1] || equal(successor(element_relation),ordinal_numbers)** -> . % 299.95/300.40 225013[19:Res:220510.1,1063.0] || equal(successor(u),ordinal_numbers) -> equal(complement(u),universal_class)**. % 299.95/300.40 224744[19:MRR:224712.1,224712.2,53.0,167008.0] inductive(singleton(u)) || -> equal(apply(choice,omega),u)*. % 299.95/300.40 224579[19:SpL:30.0,224571.0] || equal(complement(restrict(symmetrization_of(ordinal_numbers),u,v)),ordinal_numbers)** -> . % 299.95/300.40 228810[19:MRR:228790.1,167338.0] inductive(intersection(u,intersection(v,symmetrization_of(ordinal_numbers)))) || -> . % 299.95/300.40 224152[19:Res:217850.0,219089.0] || -> subclass(intersection(u,intersection(v,symmetrization_of(ordinal_numbers))),inverse(ordinal_numbers))*. % 299.95/300.40 228710[19:MRR:228690.1,167338.0] inductive(intersection(intersection(u,symmetrization_of(ordinal_numbers)),v)) || -> . % 299.95/300.40 224140[19:Res:217683.0,219089.0] || -> subclass(intersection(intersection(u,symmetrization_of(ordinal_numbers)),v),inverse(ordinal_numbers))*. % 299.95/300.40 228647[19:MRR:228625.1,167338.0] inductive(intersection(u,intersection(symmetrization_of(ordinal_numbers),v))) || -> . % 299.95/300.40 224138[19:Res:218968.0,219089.0] || -> subclass(intersection(u,intersection(symmetrization_of(ordinal_numbers),v)),inverse(ordinal_numbers))*. % 299.95/300.40 228539[19:MRR:228517.1,167338.0] inductive(intersection(intersection(symmetrization_of(ordinal_numbers),u),v)) || -> . % 299.95/300.40 224124[19:Res:218280.0,219089.0] || -> subclass(intersection(intersection(symmetrization_of(ordinal_numbers),u),v),inverse(ordinal_numbers))*. % 299.95/300.40 228443[19:MRR:228355.2,167338.0] inductive(u) || equal(symmetrization_of(ordinal_numbers),u)* -> . % 299.95/300.40 228441[23:MRR:228390.1,167338.0] || equal(ordered_pair(universal_class,u),symmetrization_of(ordinal_numbers))** -> . % 299.95/300.40 228442[27:MRR:228430.1,167338.0] || equal(image(successor_relation,ordinal_numbers),symmetrization_of(ordinal_numbers))** -> . % 299.95/300.40 43071[0:Res:5.0,9842.1] || member(u,universal_class) well_ordering(v,universal_class) -> member(least(v,unordered_pair(w,u)),unordered_pair(w,u))*. % 299.95/300.40 228440[19:MRR:228388.1,167338.0] || equal(successor(singleton(ordinal_numbers)),symmetrization_of(ordinal_numbers))** -> . % 299.95/300.40 228439[19:MRR:228381.1,167338.0] || equal(symmetrization_of(singleton(ordinal_numbers)),symmetrization_of(ordinal_numbers))** -> . % 299.95/300.40 224120[19:Res:7.1,219089.0] || equal(symmetrization_of(ordinal_numbers),u) -> subclass(u,inverse(ordinal_numbers))*. % 299.95/300.40 43050[0:Res:5.0,9843.1] || member(u,universal_class) well_ordering(v,universal_class) -> member(least(v,unordered_pair(u,w)),unordered_pair(u,w))*. % 299.95/300.40 223783[22:Res:177171.1,217129.1] || subclass(omega,u)* equal(complement(u),kind_1_ordinals) -> . % 299.95/300.40 223782[22:Res:178902.1,217129.1] || equal(u,omega) equal(complement(u),kind_1_ordinals)** -> . % 299.95/300.40 35515[0:Res:63.1,9856.0] function(u) || well_ordering(v,cross_product(universal_class,universal_class))*+ -> subclass(u,w)* member(least(v,u),u)*. % 299.95/300.40 223780[19:Res:214528.1,217129.1] || subclass(kind_1_ordinals,u)* equal(complement(u),kind_1_ordinals) -> . % 299.95/300.40 228209[20:Res:7.1,228027.0] || equal(rest_of(regular(complement(complement(symmetrization_of(ordinal_numbers))))),composition_function)** -> . % 299.95/300.40 228187[19:Res:7.1,228011.0] || equal(rest_of(complement(cross_product(singleton(ordinal_numbers),universal_class))),composition_function)** -> . % 299.95/300.40 228027[20:MRR:227990.1,167057.0] || subclass(composition_function,rest_of(regular(complement(complement(symmetrization_of(ordinal_numbers))))))* -> . % 299.95/300.40 16161[0:Res:2483.2,896.0] || member(u,universal_class) subclass(universal_class,restrict(v,w,x))*+ -> member(power_class(u),cross_product(w,x))*. % 299.95/300.40 228011[19:Res:223552.1,192214.0] || subclass(composition_function,rest_of(complement(cross_product(singleton(ordinal_numbers),universal_class))))* -> . % 299.95/300.40 228164[19:Res:7.1,228024.0] || equal(rest_of(ordered_pair(u,v)),composition_function)** -> . % 299.95/300.40 228125[19:Res:7.1,228023.0] || equal(rest_of(unordered_pair(u,v)),composition_function)** -> . % 299.95/300.40 228024[19:MRR:227992.1,167057.0] || subclass(composition_function,rest_of(ordered_pair(u,v)))* -> . % 299.95/300.40 8667[0:SpR:946.0,17.2] || member(u,v) member(singleton(u),w) -> member(singleton(singleton(singleton(u))),cross_product(w,v))*. % 299.95/300.40 228023[19:MRR:227991.1,167057.0] || subclass(composition_function,rest_of(unordered_pair(u,v)))* -> . % 299.95/300.40 228111[20:Res:7.1,228022.0] || equal(rest_of(regular(symmetrization_of(ordinal_numbers))),composition_function)** -> . % 299.95/300.40 228022[20:MRR:227987.1,167057.0] || subclass(composition_function,rest_of(regular(symmetrization_of(ordinal_numbers))))* -> . % 299.95/300.40 228083[19:Res:7.1,228020.0] || equal(rest_of(singleton(u)),composition_function)** -> . % 299.95/300.40 27149[0:Res:2523.2,897.0] || member(u,universal_class) subclass(rest_relation,restrict(v,w,x))*+ -> member(ordered_pair(u,rest_of(u)),v)*. % 299.95/300.40 228020[19:MRR:227986.1,167057.0] || subclass(composition_function,rest_of(singleton(u)))* -> . % 299.95/300.40 228070[19:Res:7.1,228021.0] || equal(rest_of(regular(element_relation)),composition_function)** -> . % 299.95/300.40 228021[19:MRR:227989.1,167057.0] || subclass(composition_function,rest_of(regular(element_relation)))* -> . % 299.95/300.40 228047[19:Res:7.1,228019.0] || equal(rest_of(omega),composition_function)** -> . % 299.95/300.40 16162[0:Res:2482.2,896.0] || member(u,universal_class) subclass(universal_class,restrict(v,w,x))*+ -> member(sum_class(u),cross_product(w,x))*. % 299.95/300.40 228042[19:Res:7.1,228018.0] || equal(rest_of(ordinal_numbers),composition_function)** -> . % 299.95/300.40 228019[19:MRR:227985.1,167057.0] || subclass(composition_function,rest_of(omega))* -> . % 299.95/300.40 228018[19:MRR:227984.1,167057.0] || subclass(composition_function,rest_of(ordinal_numbers))* -> . % 299.95/300.40 223552[19:MRR:223546.0,99.0] || subclass(composition_function,rest_of(u)) -> member(ordinal_numbers,cantor(u))*. % 299.95/300.40 36606[0:MRR:36020.1,36583.1] || member(u,universal_class) member(v,u) subclass(element_relation,w) -> member(ordered_pair(v,u),w)*. % 299.95/300.40 221767[19:Res:219766.1,196698.0] || equal(complement(u),ordinal_numbers) -> member(regular(element_relation),u)*. % 299.95/300.40 221586[19:Res:219766.1,9780.0] || equal(complement(u),ordinal_numbers) -> section(element_relation,u,universal_class)*. % 299.95/300.40 221566[19:Res:219766.1,186989.0] || equal(complement(complement(u)),ordinal_numbers)** -> equal(u,ordinal_numbers). % 299.95/300.40 221235[27:Res:221200.0,2.0] || subclass(image(successor_relation,ordinal_numbers),u)* -> member(ordinal_numbers,u). % 299.95/300.40 207766[0:SpR:206407.0,481.0] || -> equal(complement(intersection(complement(u),union(v,complement(power_class(w))))),union(u,intersection(complement(v),power_class(w))))**. % 299.95/300.40 220547[19:Res:220427.0,167311.1] inductive(complement(symmetrization_of(u))) || -> member(ordinal_numbers,complement(u))*. % 299.95/300.40 227316[19:Res:53.0,225707.1] || equal(symmetrization_of(rest_relation),ordinal_numbers)** -> . % 299.95/300.40 225719[26:Res:220544.1,203596.0] || equal(symmetrization_of(compose(complement(element_relation),inverse(element_relation))),ordinal_numbers)** -> . % 299.95/300.40 207752[0:SpR:206407.0,4125.0] || -> equal(intersection(union(u,complement(power_class(v))),union(complement(u),power_class(v))),symmetric_difference(complement(u),power_class(v)))**. % 299.95/300.40 225702[19:Res:220544.1,9733.0] || equal(symmetrization_of(unordered_pair(singleton(u),v)),ordinal_numbers)** -> . % 299.95/300.40 225699[19:Res:220544.1,9732.0] || equal(symmetrization_of(unordered_pair(u,singleton(v))),ordinal_numbers)** -> . % 299.95/300.40 207751[0:SpR:206407.0,481.0] || -> equal(complement(intersection(complement(u),union(complement(power_class(v)),w))),union(u,intersection(power_class(v),complement(w))))**. % 299.95/300.40 225697[19:Res:220544.1,48400.0] || equal(symmetrization_of(singleton(unordered_pair(u,v))),ordinal_numbers)** -> . % 299.95/300.40 225696[19:Res:220544.1,48410.0] || equal(symmetrization_of(singleton(ordered_pair(u,v))),ordinal_numbers)** -> . % 299.95/300.40 225717[19:Res:220544.1,197178.0] || equal(symmetrization_of(unordered_pair(u,regular(element_relation))),ordinal_numbers)** -> . % 299.95/300.40 225715[19:Res:220544.1,197154.0] || equal(symmetrization_of(unordered_pair(regular(element_relation),u)),ordinal_numbers)** -> . % 299.95/300.40 207747[0:SpR:206407.0,480.0] || -> equal(complement(intersection(union(u,complement(power_class(v))),complement(w))),union(intersection(complement(u),power_class(v)),w))**. % 299.95/300.40 225722[20:Res:220544.1,211041.0] || equal(symmetrization_of(singleton(regular(symmetrization_of(ordinal_numbers)))),ordinal_numbers)** -> . % 299.95/300.40 225698[19:Res:220544.1,9712.0] || equal(symmetrization_of(ordered_pair(u,v)),ordinal_numbers)** -> . % 299.95/300.40 225716[23:Res:220544.1,183954.0] || equal(symmetrization_of(unordered_pair(u,ordinal_numbers)),ordinal_numbers)** -> . % 299.95/300.40 225714[23:Res:220544.1,183930.0] || equal(symmetrization_of(unordered_pair(ordinal_numbers,u)),ordinal_numbers)** -> . % 299.95/300.40 225695[19:Res:220544.1,9731.0] || equal(symmetrization_of(singleton(singleton(u))),ordinal_numbers)** -> . % 299.95/300.40 225721[19:Res:220544.1,197148.0] || equal(symmetrization_of(singleton(regular(element_relation))),ordinal_numbers)** -> . % 299.95/300.40 225723[19:Res:220544.1,204688.0] || equal(symmetrization_of(singleton(omega)),ordinal_numbers)** -> . % 299.95/300.40 225718[19:Res:220544.1,197146.0] || equal(symmetrization_of(regular(element_relation)),ordinal_numbers)** -> . % 299.95/300.40 207699[0:SpR:206407.0,480.0] || -> equal(complement(intersection(union(complement(power_class(u)),v),complement(w))),union(intersection(power_class(u),complement(v)),w))**. % 299.95/300.40 225712[20:Res:220544.1,176136.0] || equal(symmetrization_of(inverse(ordinal_numbers)),ordinal_numbers)** -> . % 299.95/300.40 225710[19:Res:220544.1,159745.0] || equal(symmetrization_of(domain_relation),ordinal_numbers)** -> . % 299.95/300.40 176255[19:Rew:176206.1,158692.2] || member(u,universal_class) subclass(domain_relation,symmetric_difference(v,w)) -> member(ordered_pair(u,ordinal_numbers),union(v,w))*. % 299.95/300.40 220513[19:Res:220426.0,167311.1] inductive(complement(successor(u))) || -> member(ordinal_numbers,complement(u))*. % 299.95/300.40 225456[19:Res:53.0,225039.1] || equal(successor(rest_relation),ordinal_numbers)** -> . % 299.95/300.40 225051[26:Res:220510.1,203596.0] || equal(successor(compose(complement(element_relation),inverse(element_relation))),ordinal_numbers)** -> . % 299.95/300.40 176248[19:Rew:176206.1,158695.3] || member(u,universal_class)+ subclass(domain_relation,v)* subclass(v,w)* -> member(ordered_pair(u,ordinal_numbers),w)*. % 299.95/300.40 225034[19:Res:220510.1,9733.0] || equal(successor(unordered_pair(singleton(u),v)),ordinal_numbers)** -> . % 299.95/300.40 225031[19:Res:220510.1,9732.0] || equal(successor(unordered_pair(u,singleton(v))),ordinal_numbers)** -> . % 299.95/300.40 169006[19:Rew:166997.0,84861.1] || subclass(omega,composition_function) -> equal(integer_of(ordered_pair(u,ordered_pair(v,w))),ordinal_numbers)** equal(compose(u,v),w). % 299.95/300.40 225029[19:Res:220510.1,48400.0] || equal(successor(singleton(unordered_pair(u,v))),ordinal_numbers)** -> . % 299.95/300.40 225028[19:Res:220510.1,48410.0] || equal(successor(singleton(ordered_pair(u,v))),ordinal_numbers)** -> . % 299.95/300.40 225049[19:Res:220510.1,197178.0] || equal(successor(unordered_pair(u,regular(element_relation))),ordinal_numbers)** -> . % 299.95/300.40 225047[19:Res:220510.1,197154.0] || equal(successor(unordered_pair(regular(element_relation),u)),ordinal_numbers)** -> . % 299.95/300.40 168561[19:Rew:166997.0,158643.1] || member(u,cantor(cross_product(v,w))) equal(restrict(cross_product(singleton(u),universal_class),v,w),ordinal_numbers)** -> . % 299.95/300.40 225054[20:Res:220510.1,211041.0] || equal(successor(singleton(regular(symmetrization_of(ordinal_numbers)))),ordinal_numbers)** -> . % 299.95/300.40 225030[19:Res:220510.1,9712.0] || equal(successor(ordered_pair(u,v)),ordinal_numbers)** -> . % 299.95/300.40 225048[23:Res:220510.1,183954.0] || equal(successor(unordered_pair(u,ordinal_numbers)),ordinal_numbers)** -> . % 299.95/300.40 225046[23:Res:220510.1,183930.0] || equal(successor(unordered_pair(ordinal_numbers,u)),ordinal_numbers)** -> . % 299.95/300.40 168557[19:Rew:166997.0,80831.0] || -> equal(symmetric_difference(complement(u),complement(v)),ordinal_numbers) member(regular(symmetric_difference(complement(u),complement(v))),union(u,v))*. % 299.95/300.40 225027[19:Res:220510.1,9731.0] || equal(successor(singleton(singleton(u))),ordinal_numbers)** -> . % 299.95/300.40 225053[19:Res:220510.1,197148.0] || equal(successor(singleton(regular(element_relation))),ordinal_numbers)** -> . % 299.95/300.40 225093[19:Res:219766.1,225056.0] || equal(complement(flip(successor_relation)),ordinal_numbers)** -> . % 299.95/300.40 225055[19:Res:220510.1,204688.0] || equal(successor(singleton(omega)),ordinal_numbers)** -> . % 299.95/300.40 168497[19:Rew:166997.0,84865.1] || subclass(omega,rest_of(u))+ -> equal(integer_of(ordered_pair(v,w)),ordinal_numbers)** equal(restrict(u,v,universal_class),w)*. % 299.95/300.40 225050[19:Res:220510.1,197146.0] || equal(successor(regular(element_relation)),ordinal_numbers)** -> . % 299.95/300.40 225044[20:Res:220510.1,176136.0] || equal(successor(inverse(ordinal_numbers)),ordinal_numbers)** -> . % 299.95/300.40 225094[19:Res:7.1,225056.0] || equal(flip(successor_relation),domain_relation)** -> . % 299.95/300.40 225056[19:MRR:184882.1,225030.0] || subclass(domain_relation,flip(successor_relation))* -> . % 299.95/300.40 169537[19:Rew:166997.0,167978.2] inductive(complement(intersection(u,v))) || member(ordinal_numbers,union(u,v)) -> member(ordinal_numbers,symmetric_difference(u,v))*. % 299.95/300.40 225042[19:Res:220510.1,159745.0] || equal(successor(domain_relation),ordinal_numbers)** -> . % 299.95/300.40 169529[19:Rew:166997.0,167765.0] || -> equal(cross_product(u,singleton(v)),ordinal_numbers) equal(domain__dfg(regular(cross_product(u,singleton(v))),u,v),single_valued3(ordinal_numbers))**. % 299.95/300.40 219799[19:Res:219690.0,167311.1] inductive(symmetric_difference(universal_class,complement(u))) || -> member(ordinal_numbers,u)*. % 299.95/300.40 224697[19:SoR:224670.0,189460.1] || equal(complement(complement(intersection(symmetrization_of(ordinal_numbers),u))),universal_class)** -> . % 299.95/300.40 224619[19:SoR:224572.0,189460.1] || equal(complement(complement(intersection(u,symmetrization_of(ordinal_numbers)))),universal_class)** -> . % 299.95/300.40 167723[19:Rew:166997.0,80603.2] || member(u,universal_class) subclass(u,singleton(v))* -> equal(u,ordinal_numbers) equal(apply(choice,u),v). % 299.95/300.40 224670[19:MRR:224647.1,167338.0] inductive(complement(complement(intersection(symmetrization_of(ordinal_numbers),u)))) || -> . % 299.95/300.40 224669[19:MRR:224643.1,167186.0] || equal(complement(intersection(symmetrization_of(ordinal_numbers),u)),ordinal_numbers)** -> . % 299.95/300.40 224159[19:Res:218971.0,219089.0] || -> subclass(complement(complement(intersection(symmetrization_of(ordinal_numbers),u))),inverse(ordinal_numbers))*. % 299.95/300.40 224572[19:MRR:224551.1,167338.0] inductive(complement(complement(intersection(u,symmetrization_of(ordinal_numbers))))) || -> . % 299.95/300.40 4728[0:SpL:946.0,97.0] || member(singleton(singleton(singleton(ordered_pair(u,v)))),composition_function)*+ -> equal(compose(singleton(ordered_pair(u,v)),u),v)**. % 299.95/300.40 224571[19:MRR:224547.1,167186.0] || equal(complement(intersection(u,symmetrization_of(ordinal_numbers))),ordinal_numbers)** -> . % 299.95/300.40 224157[19:Res:217853.0,219089.0] || -> subclass(complement(complement(intersection(u,symmetrization_of(ordinal_numbers)))),inverse(ordinal_numbers))*. % 299.95/300.40 41507[0:Res:9790.2,15.0] || member(ordered_pair(u,v),cross_product(universal_class,universal_class))*+ subclass(composition_function,cross_product(w,x))* -> member(u,w)*. % 299.95/300.40 224449[19:MRR:224440.1,167338.0] inductive(intersection(u,complement(complement(symmetrization_of(ordinal_numbers))))) || -> . % 299.95/300.40 224137[19:Res:219700.0,219089.0] || -> subclass(intersection(u,complement(complement(symmetrization_of(ordinal_numbers)))),inverse(ordinal_numbers))*. % 299.95/300.40 224412[19:MRR:224403.1,167338.0] inductive(intersection(complement(complement(symmetrization_of(ordinal_numbers))),u)) || -> . % 299.95/300.40 224123[19:Res:218920.0,219089.0] || -> subclass(intersection(complement(complement(symmetrization_of(ordinal_numbers))),u),inverse(ordinal_numbers))*. % 299.95/300.40 158652[8:Rew:157840.0,41401.1,157840.0,41401.0] || equal(cross_product(u,u),complement(complement(symmetrization_of(v))))* -> equal(complement(complement(symmetrization_of(v))),cross_product(u,u)). % 299.95/300.40 224358[19:SoR:224350.0,189460.1] || equal(complement(complement(complement(complement(symmetrization_of(ordinal_numbers))))),universal_class)** -> . % 299.95/300.40 224350[19:MRR:224339.1,167338.0] inductive(complement(complement(complement(complement(symmetrization_of(ordinal_numbers)))))) || -> . % 299.95/300.40 224347[19:MRR:224335.1,167186.0] || equal(complement(complement(complement(symmetrization_of(ordinal_numbers)))),ordinal_numbers)** -> . % 299.95/300.40 224158[19:Res:219703.0,219089.0] || -> subclass(complement(complement(complement(complement(symmetrization_of(ordinal_numbers))))),inverse(ordinal_numbers))*. % 299.95/300.40 79954[0:Res:315.1,158.0] || -> subclass(intersection(omega,u),v) equal(integer_of(not_subclass_element(intersection(omega,u),v)),not_subclass_element(intersection(omega,u),v))**. % 299.95/300.40 224151[20:Res:213073.0,219089.0] || -> subclass(singleton(not_subclass_element(symmetrization_of(ordinal_numbers),ordinal_numbers)),inverse(ordinal_numbers))*. % 299.95/300.40 224150[20:Res:196602.0,219089.0] || -> subclass(singleton(not_subclass_element(inverse(ordinal_numbers),ordinal_numbers)),inverse(ordinal_numbers))*. % 299.95/300.40 79959[0:Res:297.1,158.0] || -> subclass(intersection(u,omega),v) equal(integer_of(not_subclass_element(intersection(u,omega),v)),not_subclass_element(intersection(u,omega),v))**. % 299.95/300.40 224187[19:MRR:224181.1,167338.0] inductive(symmetric_difference(universal_class,complement(symmetrization_of(ordinal_numbers)))) || -> . % 299.95/300.40 224149[20:Res:181516.0,219089.0] || -> subclass(singleton(regular(symmetrization_of(ordinal_numbers))),inverse(ordinal_numbers))*. % 299.95/300.40 219089[19:SpR:149012.1,218952.0] || subclass(u,symmetrization_of(ordinal_numbers))* -> subclass(u,inverse(ordinal_numbers)). % 299.95/300.40 35242[2:Res:63.1,9859.1] function(u) inductive(u) || well_ordering(v,cross_product(universal_class,universal_class))*+ -> member(least(v,u),u)*. % 299.95/300.40 217231[22:Res:7.1,215256.0] || equal(u,kind_1_ordinals) equal(complement(u),omega)** -> . % 299.95/300.40 217156[19:Res:7.1,215201.0] || equal(complement(complement(u)),kind_1_ordinals)** -> member(ordinal_numbers,u). % 299.95/300.40 223787[19:Res:167106.1,217129.1] inductive(u) || equal(complement(u),kind_1_ordinals)** -> . % 299.95/300.40 224005[19:MRR:224001.1,223784.0] || equal(complement(regular(ordered_pair(ordinal_numbers,u))),kind_1_ordinals)** -> . % 299.95/300.40 34759[0:Res:6521.3,4178.0] function(u) || member(v,universal_class) subclass(universal_class,singleton(w))*+ -> equal(image(u,v),w)*. % 299.95/300.40 223793[19:Res:214498.0,217129.1] || equal(complement(union(singleton(ordinal_numbers),u)),kind_1_ordinals)** -> . % 299.95/300.40 223792[19:Res:215454.0,217129.1] || equal(complement(union(u,singleton(ordinal_numbers))),kind_1_ordinals)** -> . % 299.95/300.40 223807[19:MRR:223759.0,167011.0] || equal(complement(unordered_pair(u,ordinal_numbers)),kind_1_ordinals)** -> . % 299.95/300.40 223806[19:MRR:223758.0,167011.0] || equal(complement(unordered_pair(ordinal_numbers,u)),kind_1_ordinals)** -> . % 299.95/300.40 14972[0:SpL:27.0,282.0] || member(u,image(element_relation,union(v,w))) member(u,power_class(intersection(complement(v),complement(w))))* -> . % 299.95/300.40 223795[23:Res:183852.0,217129.1] || equal(complement(ordered_pair(universal_class,u)),kind_1_ordinals)** -> . % 299.95/300.40 223802[27:Res:221200.0,217129.1] || equal(complement(image(successor_relation,ordinal_numbers)),kind_1_ordinals)** -> . % 299.95/300.40 223799[19:Res:214502.0,217129.1] || equal(complement(successor(singleton(ordinal_numbers))),kind_1_ordinals)** -> . % 299.95/300.40 223794[19:Res:214503.0,217129.1] || equal(complement(symmetrization_of(singleton(ordinal_numbers))),kind_1_ordinals)** -> . % 299.95/300.40 223709[28:MRR:169536.2,223707.0] || subclass(compose(ordinal_numbers,ordinal_numbers),ordinal_numbers)*+ -> equal(cross_product(u,u),ordinal_numbers)**. % 299.95/300.40 223788[22:Res:177170.0,217129.1] || equal(complement(omega),kind_1_ordinals)** -> . % 299.95/300.40 217129[19:Res:7.1,215196.0] || equal(complement(u),kind_1_ordinals) member(ordinal_numbers,u)* -> . % 299.95/300.40 217001[19:Res:7.1,214694.0] || equal(u,symmetrization_of(singleton(ordinal_numbers)))*+ -> member(ordinal_numbers,u)*. % 299.95/300.40 216992[19:Res:7.1,214682.0] || equal(u,successor(singleton(ordinal_numbers)))*+ -> member(ordinal_numbers,u)*. % 299.95/300.40 223708[28:MRR:169534.2,223707.0] || equal(compose(ordinal_numbers,ordinal_numbers),ordinal_numbers)**+ -> equal(cross_product(u,u),ordinal_numbers)**. % 299.95/300.40 223713[28:Rew:167055.0,223712.1] || subclass(compose(ordinal_numbers,ordinal_numbers),ordinal_numbers)*+ -> transitive(universal_class,u)*. % 299.95/300.40 223733[28:Obv:223732.1] || equal(compose_class(ordinal_numbers),domain_relation) -> transitive(universal_class,u)*. % 299.95/300.40 223711[28:Rew:167055.0,223710.1] || equal(compose(ordinal_numbers,ordinal_numbers),ordinal_numbers)**+ -> transitive(universal_class,u)*. % 299.95/300.40 223692[19:SoR:223672.0,189460.1] || equal(complement(union(complement(inverse(ordinal_numbers)),u)),universal_class)** -> . % 299.95/300.40 223707[28:Spt:169535.0,169535.1] || transitive(regular(cross_product(u,u)),u)* -> equal(cross_product(u,u),ordinal_numbers). % 299.95/300.40 223495[19:SoR:223481.0,189460.1] || equal(complement(union(u,complement(inverse(ordinal_numbers)))),universal_class)** -> . % 299.95/300.40 221739[19:Res:219766.1,184983.0] || equal(complement(rotate(domain_relation)),ordinal_numbers)**+ -> equal(ordinal_numbers,u)*. % 299.95/300.40 223672[19:MRR:223656.1,187485.0] inductive(complement(union(complement(inverse(ordinal_numbers)),u))) || -> . % 299.95/300.40 223670[19:MRR:223653.1,167196.0] || equal(union(complement(inverse(ordinal_numbers)),u),ordinal_numbers)** -> . % 299.95/300.40 220412[19:SpR:167191.0,220194.0] || -> subclass(complement(union(complement(inverse(ordinal_numbers)),u)),symmetrization_of(ordinal_numbers))*. % 299.95/300.40 223618[19:MRR:223601.1,180092.0] || equal(union(complement(singleton(ordinal_numbers)),u),ordinal_numbers)** -> . % 299.95/300.40 220304[19:SpR:167191.0,219700.0] || -> subclass(intersection(u,complement(symmetrization_of(ordinal_numbers))),complement(inverse(ordinal_numbers)))*. % 299.95/300.40 125075[8:Rew:124836.0,41506.2] || member(ordered_pair(u,v),cross_product(universal_class,universal_class))*+ subclass(composition_function,rest_of(w)) -> member(u,cantor(w))*. % 299.95/300.40 219673[19:SpR:167191.0,218920.0] || -> subclass(intersection(complement(symmetrization_of(ordinal_numbers)),u),complement(inverse(ordinal_numbers)))*. % 299.95/300.40 223481[19:MRR:223465.1,187485.0] inductive(complement(union(u,complement(inverse(ordinal_numbers))))) || -> . % 299.95/300.40 223479[19:MRR:223462.1,167196.0] || equal(union(u,complement(inverse(ordinal_numbers))),ordinal_numbers)** -> . % 299.95/300.40 218381[19:SpR:167191.0,218022.0] || -> subclass(complement(union(u,complement(inverse(ordinal_numbers)))),symmetrization_of(ordinal_numbers))*. % 299.95/300.40 35240[2:Res:141.0,9859.1] inductive(rest_of(u)) || well_ordering(v,cross_product(universal_class,universal_class)) -> member(least(v,rest_of(u)),rest_of(u))*. % 299.95/300.40 223437[19:MRR:223421.1,180092.0] || equal(union(u,complement(singleton(ordinal_numbers))),ordinal_numbers)** -> . % 299.95/300.40 223392[20:Res:7.1,223003.0] || equal(complement(complement(symmetrization_of(ordinal_numbers))),complement(inverse(ordinal_numbers)))** -> . % 299.95/300.40 223021[20:Res:222998.0,177583.1] || equal(rest_of(regular(complement(complement(symmetrization_of(ordinal_numbers))))),rest_relation)** -> . % 299.95/300.40 35239[2:Res:93.0,9859.1] inductive(compose_class(u)) || well_ordering(v,cross_product(universal_class,universal_class)) -> member(least(v,compose_class(u)),compose_class(u))*. % 299.95/300.40 223015[20:Res:222998.0,205988.1] || equal(singleton(regular(complement(complement(symmetrization_of(ordinal_numbers))))),ordinal_numbers)** -> . % 299.95/300.40 223389[20:Res:188649.1,223003.0] || equal(complement(complement(complement(symmetrization_of(ordinal_numbers)))),universal_class)** -> . % 299.95/300.40 223003[20:MRR:223000.1,222900.0] || subclass(complement(complement(symmetrization_of(ordinal_numbers))),complement(inverse(ordinal_numbers)))* -> . % 299.95/300.40 221380[27:Res:221347.0,203417.1] || subclass(intersection(singleton(ordinal_numbers),image(successor_relation,ordinal_numbers)),ordinal_numbers)* -> . % 299.95/300.40 79384[0:Res:53.0,8669.0] || member(u,v)*+ -> equal(ordered_pair(first(ordered_pair(u,omega)),second(ordered_pair(u,omega))),ordered_pair(u,omega))**. % 299.95/300.40 221349[27:MRR:221334.1,214509.0] inductive(complement(intersection(singleton(ordinal_numbers),image(successor_relation,ordinal_numbers)))) || -> . % 299.95/300.40 221203[27:MRR:221202.1,214529.0] || equal(intersection(singleton(ordinal_numbers),image(successor_relation,ordinal_numbers)),ordinal_numbers)** -> . % 299.95/300.40 223022[20:Res:222998.0,176206.0] || -> equal(cantor(regular(complement(complement(symmetrization_of(ordinal_numbers))))),ordinal_numbers)**. % 299.95/300.40 223027[25:SoR:223017.0,72.1] one_to_one(regular(complement(complement(symmetrization_of(ordinal_numbers))))) || -> . % 299.95/300.40 208593[0:SpR:206408.0,206410.0] || -> equal(union(complement(power_class(u)),image(element_relation,power_class(v))),complement(intersection(power_class(u),power_class(complement(power_class(v))))))**. % 299.95/300.40 223017[25:Res:222998.0,193595.1] function(regular(complement(complement(symmetrization_of(ordinal_numbers))))) || -> . % 299.95/300.40 222998[20:Res:222901.0,36583.0] || -> member(regular(complement(complement(symmetrization_of(ordinal_numbers)))),universal_class)*. % 299.95/300.40 222901[20:MRR:183594.0,222900.0] || -> member(regular(complement(complement(symmetrization_of(ordinal_numbers)))),inverse(ordinal_numbers))*. % 299.95/300.40 222900[20:MRR:222888.1,176136.0] || equal(complement(complement(symmetrization_of(ordinal_numbers))),ordinal_numbers)** -> . % 299.95/300.40 208291[0:SpR:206408.0,206403.0] || -> equal(union(image(element_relation,power_class(u)),complement(power_class(v))),complement(intersection(power_class(complement(power_class(u))),power_class(v))))**. % 299.95/300.40 219943[19:SpR:167191.0,219703.0] || -> subclass(complement(complement(complement(symmetrization_of(ordinal_numbers)))),complement(inverse(ordinal_numbers)))*. % 299.95/300.40 222829[19:Res:218966.0,167211.1] inductive(restrict(intersection(ordinal_numbers,u),v,w)) || -> . % 299.95/300.40 218966[0:SpR:29.0,218280.0] || -> subclass(restrict(intersection(u,v),w,x),u)*. % 299.95/300.40 222702[19:Res:218740.0,167211.1] inductive(intersection(u,restrict(ordinal_numbers,v,w))) || -> . % 299.95/300.40 195079[25:Rew:195076.1,193838.2] one_to_one(flip(cross_product(u,universal_class))) || subclass(universal_class,v) -> maps(flip(cross_product(u,universal_class)),universal_class,v)*. % 299.95/300.40 218740[0:SpR:30.0,217850.0] || -> subclass(intersection(u,restrict(v,w,x)),v)*. % 299.95/300.40 222587[19:Res:217848.0,167211.1] inductive(restrict(intersection(u,ordinal_numbers),v,w)) || -> . % 299.95/300.40 217848[0:SpR:29.0,217683.0] || -> subclass(restrict(intersection(u,v),w,x),v)*. % 299.95/300.40 222460[19:Res:217800.0,167211.1] inductive(intersection(restrict(ordinal_numbers,u,v),w)) || -> . % 299.95/300.40 195053[25:Rew:195050.1,193840.2] one_to_one(restrict(element_relation,universal_class,u)) || subclass(universal_class,v) -> maps(restrict(element_relation,universal_class,u),universal_class,v)*. % 299.95/300.40 217800[0:SpR:30.0,217683.0] || -> subclass(intersection(restrict(u,v,w),x),u)*. % 299.95/300.40 222371[19:Res:219698.0,167211.1] inductive(restrict(complement(complement(ordinal_numbers)),u,v)) || -> . % 299.95/300.40 219698[0:SpR:29.0,218920.0] || -> subclass(restrict(complement(complement(u)),v,w),u)*. % 299.95/300.40 222282[19:Res:217976.0,167211.1] inductive(complement(complement(restrict(ordinal_numbers,u,v)))) || -> . % 299.95/300.40 4280[0:Res:130.2,1073.1] inductive(not_well_ordering(u,omega)) || connected(u,omega) -> well_ordering(u,omega) equal(not_well_ordering(u,omega),omega)**. % 299.95/300.40 217976[0:SpR:30.0,217853.0] || -> subclass(complement(complement(restrict(u,v,w))),u)*. % 299.95/300.40 221878[19:Res:219766.1,196830.0] || equal(complement(complement(cross_product(universal_class,universal_class))),ordinal_numbers)** -> . % 299.95/300.40 221854[19:Res:219766.1,160080.0] || equal(complement(complement(compose(element_relation,universal_class))),ordinal_numbers)** -> . % 299.95/300.40 207409[19:Rew:206400.0,206925.0] || member(regular(power_class(complement(power_class(u)))),image(element_relation,power_class(u)))* -> equal(power_class(complement(power_class(u))),ordinal_numbers). % 299.95/300.40 221738[19:Res:219766.1,184985.0] || equal(complement(rotate(cross_product(universal_class,universal_class))),ordinal_numbers)** -> . % 299.95/300.40 222016[19:MRR:221800.1,205391.1] || equal(complement(u),ordinal_numbers)** -> inductive(u). % 299.95/300.40 221858[19:Res:219766.1,163180.0] || equal(complement(complement(complement(successor_relation))),ordinal_numbers)** -> . % 299.95/300.40 177427[19:Res:170.0,168644.0] || subclass(universal_class,u)+ well_ordering(omega,u)* -> equal(integer_of(ordered_pair(singleton(v),least(omega,universal_class))),ordinal_numbers)**. % 299.95/300.40 221719[19:Res:219766.1,98608.0] || equal(complement(complement(complement(element_relation))),ordinal_numbers)** -> . % 299.95/300.40 222008[19:MRR:221643.1,221567.1] || equal(complement(complement(rest_relation)),ordinal_numbers)** -> . % 299.95/300.40 221740[19:Res:219766.1,185696.0] || equal(complement(rotate(element_relation)),ordinal_numbers)** -> . % 299.95/300.40 221737[19:Res:219766.1,184944.0] || equal(complement(rotate(ordinal_numbers)),ordinal_numbers)** -> . % 299.95/300.40 35657[0:Res:7.1,1066.0] || 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)). % 299.95/300.40 221731[19:Res:219766.1,184897.0] || equal(complement(flip(element_relation)),ordinal_numbers)** -> . % 299.95/300.40 221730[19:Res:219766.1,184866.0] || equal(complement(flip(ordinal_numbers)),ordinal_numbers)** -> . % 299.95/300.40 219766[19:Rew:142500.0,219685.1] || equal(complement(u),ordinal_numbers) -> subclass(v,u)*. % 299.95/300.40 35659[0:Res:7.1,1067.0] || 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)). % 299.95/300.40 221347[27:MRR:221326.0,214509.0] || -> member(ordinal_numbers,intersection(singleton(ordinal_numbers),image(successor_relation,ordinal_numbers)))*. % 299.95/300.40 221253[19:MRR:221247.1,167338.0] inductive(restrict(symmetrization_of(ordinal_numbers),u,v)) || -> . % 299.95/300.40 221036[27:MRR:220934.2,167057.0] || member(u,kind_1_ordinals) member(u,complement(intersection(singleton(ordinal_numbers),image(successor_relation,ordinal_numbers))))* -> . % 299.95/300.40 219075[19:SpR:29.0,218952.0] || -> subclass(restrict(symmetrization_of(ordinal_numbers),u,v),inverse(ordinal_numbers))*. % 299.95/300.40 221239[27:Res:221200.0,169221.1] || equal(complement(image(successor_relation,ordinal_numbers)),singleton(ordinal_numbers))** -> . % 299.95/300.40 221240[27:Res:221200.0,177998.1] || equal(complement(image(successor_relation,ordinal_numbers)),omega)** -> . % 299.95/300.40 221200[27:MRR:221199.1,214529.0] || -> member(ordinal_numbers,image(successor_relation,ordinal_numbers))*. % 299.95/300.40 221080[19:SoR:220927.0,189460.1] || equal(complement(symmetrization_of(complement(inverse(ordinal_numbers)))),universal_class)** -> . % 299.95/300.40 220891[19:SoR:220843.0,189460.1] || equal(complement(successor(complement(inverse(ordinal_numbers)))),universal_class)** -> . % 299.95/300.40 220927[19:MRR:220918.1,187485.0] inductive(complement(symmetrization_of(complement(inverse(ordinal_numbers))))) || -> . % 299.95/300.40 220926[19:MRR:220915.1,167196.0] || equal(symmetrization_of(complement(inverse(ordinal_numbers))),ordinal_numbers)** -> . % 299.95/300.40 220929[27:Spt:169524.0] || -> equal(symmetric_difference(singleton(ordinal_numbers),image(successor_relation,ordinal_numbers)),ordinal_numbers)**. % 299.95/300.40 220531[19:SpR:167191.0,220427.0] || -> subclass(complement(symmetrization_of(complement(inverse(ordinal_numbers)))),symmetrization_of(ordinal_numbers))*. % 299.95/300.40 220908[19:MRR:220895.1,180092.0] || equal(symmetrization_of(complement(singleton(ordinal_numbers))),ordinal_numbers)** -> . % 299.95/300.40 220843[19:MRR:220834.1,187485.0] inductive(complement(successor(complement(inverse(ordinal_numbers))))) || -> . % 299.95/300.40 16146[0:Res:3.1,896.0] || -> subclass(restrict(u,v,w),x) member(not_subclass_element(restrict(u,v,w),x),cross_product(v,w))*. % 299.95/300.40 220842[19:MRR:220831.1,167196.0] || equal(successor(complement(inverse(ordinal_numbers))),ordinal_numbers)** -> . % 299.95/300.40 220496[19:SpR:167191.0,220426.0] || -> subclass(complement(successor(complement(inverse(ordinal_numbers)))),symmetrization_of(ordinal_numbers))*. % 299.95/300.40 220824[19:MRR:220811.1,180092.0] || equal(successor(complement(singleton(ordinal_numbers))),ordinal_numbers)** -> . % 299.95/300.40 125327[8:Rew:124836.0,17190.1] || section(cross_product(u,v),w,x) -> subclass(cantor(restrict(cross_product(x,w),u,v)),w)*. % 299.95/300.40 220680[19:Res:218968.0,167211.1] inductive(intersection(u,intersection(ordinal_numbers,v))) || -> . % 299.95/300.40 218968[0:SpR:149318.0,218280.0] || -> subclass(intersection(u,intersection(v,w)),v)*. % 299.95/300.40 220427[0:SpR:114.0,220194.0] || -> subclass(complement(symmetrization_of(u)),complement(u))*. % 299.95/300.40 35494[0:Res:7.1,9856.0] || equal(u,v)*+ well_ordering(w,u)* -> subclass(v,x)* member(least(w,v),v)*. % 299.95/300.40 220426[0:SpR:44.0,220194.0] || -> subclass(complement(successor(u)),complement(u))*. % 299.95/300.40 220487[19:MRR:220479.1,167331.0] inductive(complement(kind_1_ordinals)) || -> . % 299.95/300.40 220439[19:SpR:167022.0,220194.0] || -> subclass(complement(kind_1_ordinals),complement(singleton(ordinal_numbers)))*. % 299.95/300.40 220194[0:SpR:27.0,218971.0] || -> subclass(complement(union(u,v)),complement(u))*. % 299.95/300.40 85328[2:SpR:30.0,80099.1] || asymmetric(cross_product(u,v),w) -> section(restrict(inverse(cross_product(u,v)),u,v),w,w)*. % 299.95/300.40 220375[19:Res:219700.0,167211.1] inductive(intersection(u,complement(complement(ordinal_numbers)))) || -> . % 299.95/300.40 219700[0:SpR:149318.0,218920.0] || -> subclass(intersection(u,complement(complement(v))),v)*. % 299.95/300.40 220233[19:Res:218971.0,167211.1] inductive(complement(complement(intersection(ordinal_numbers,u)))) || -> . % 299.95/300.40 218971[0:SpR:148172.0,218280.0] || -> subclass(complement(complement(intersection(u,v))),u)*. % 299.95/300.40 16462[0:Res:2526.2,2.0] || subclass(u,v)*+ subclass(v,w)* -> subclass(u,x) member(not_subclass_element(u,x),w)*. % 299.95/300.40 219997[19:Res:219703.0,167211.1] inductive(complement(complement(complement(complement(ordinal_numbers))))) || -> . % 299.95/300.40 219703[0:SpR:148172.0,218920.0] || -> subclass(complement(complement(complement(complement(u)))),u)*. % 299.95/300.40 219747[19:Res:218920.0,167211.1] inductive(intersection(complement(complement(ordinal_numbers)),u)) || -> . % 299.95/300.40 219829[19:Res:219690.0,167211.1] inductive(symmetric_difference(universal_class,complement(ordinal_numbers))) || -> . % 299.95/300.40 16475[0:Res:2526.2,4127.0] || subclass(u,symmetric_difference(v,w)) -> subclass(u,x) member(not_subclass_element(u,x),union(v,w))*. % 299.95/300.40 218920[0:SpR:148172.0,218280.0] || -> subclass(intersection(complement(complement(u)),v),u)*. % 299.95/300.40 219016[19:Res:218280.0,167211.1] inductive(intersection(intersection(ordinal_numbers,u),v)) || -> . % 299.95/300.40 219408[19:MRR:219398.1,167338.0] inductive(intersection(u,symmetrization_of(ordinal_numbers))) || -> . % 299.95/300.40 16361[0:Res:297.1,22.0] || -> subclass(intersection(u,intersection(v,w)),x) member(not_subclass_element(intersection(u,intersection(v,w)),x),v)*. % 299.95/300.40 219077[19:SpR:149318.0,218952.0] || -> subclass(intersection(u,symmetrization_of(ordinal_numbers)),inverse(ordinal_numbers))*. % 299.95/300.40 219376[19:MRR:219368.1,167338.0] inductive(complement(complement(symmetrization_of(ordinal_numbers)))) || -> . % 299.95/300.40 219080[19:SpR:148172.0,218952.0] || -> subclass(complement(complement(symmetrization_of(ordinal_numbers))),inverse(ordinal_numbers))*. % 299.95/300.40 219105[19:MRR:219095.1,167338.0] inductive(intersection(symmetrization_of(ordinal_numbers),u)) || -> . % 299.95/300.40 16362[0:Res:297.1,23.0] || -> subclass(intersection(u,intersection(v,w)),x) member(not_subclass_element(intersection(u,intersection(v,w)),x),w)*. % 299.95/300.40 218952[19:SpR:167193.0,218280.0] || -> subclass(intersection(symmetrization_of(ordinal_numbers),u),inverse(ordinal_numbers))*. % 299.95/300.40 218280[0:Obv:218263.0] || -> subclass(intersection(intersection(u,v),w),u)*. % 299.95/300.40 218840[19:Res:217850.0,167211.1] inductive(intersection(u,intersection(v,ordinal_numbers))) || -> . % 299.95/300.40 217850[0:SpR:149318.0,217683.0] || -> subclass(intersection(u,intersection(v,w)),w)*. % 299.95/300.40 16358[0:Res:297.1,2.0] || subclass(u,v) -> subclass(intersection(w,u),x) member(not_subclass_element(intersection(w,u),x),v)*. % 299.95/300.40 218396[0:SpR:114.0,218022.0] || -> subclass(complement(symmetrization_of(u)),complement(inverse(u)))*. % 299.95/300.40 218395[0:SpR:44.0,218022.0] || -> subclass(complement(successor(u)),complement(singleton(u)))*. % 299.95/300.40 218408[19:SpR:167022.0,218022.0] || -> subclass(complement(kind_1_ordinals),complement(image(successor_relation,ordinal_numbers)))*. % 299.95/300.40 218022[0:SpR:27.0,217853.0] || -> subclass(complement(union(u,v)),complement(v))*. % 299.95/300.40 16234[0:Res:315.1,22.0] || -> subclass(intersection(intersection(u,v),w),x) member(not_subclass_element(intersection(intersection(u,v),w),x),u)*. % 299.95/300.40 218060[19:Res:217853.0,167211.1] inductive(complement(complement(intersection(u,ordinal_numbers)))) || -> . % 299.95/300.40 217853[0:SpR:148172.0,217683.0] || -> subclass(complement(complement(intersection(u,v))),v)*. % 299.95/300.40 217898[19:Res:217683.0,167211.1] inductive(intersection(intersection(u,ordinal_numbers),v)) || -> . % 299.95/300.40 217683[0:Obv:217666.0] || -> subclass(intersection(intersection(u,v),w),v)*. % 299.95/300.40 16235[0:Res:315.1,23.0] || -> subclass(intersection(intersection(u,v),w),x) member(not_subclass_element(intersection(intersection(u,v),w),x),v)*. % 299.95/300.40 216465[19:Res:188649.1,216452.1] || equal(complement(u),universal_class)** equal(u,kind_1_ordinals) -> . % 299.95/300.40 216356[19:SpL:29.0,216181.0] || equal(restrict(complement(singleton(ordinal_numbers)),u,v),kind_1_ordinals)** -> . % 299.95/300.40 216163[19:SpL:29.0,215260.0] || subclass(kind_1_ordinals,restrict(complement(singleton(ordinal_numbers)),u,v))* -> . % 299.95/300.40 16231[0:Res:315.1,2.0] || subclass(u,v) -> subclass(intersection(u,w),x) member(not_subclass_element(intersection(u,w),x),v)*. % 299.95/300.40 215880[19:SpL:29.0,214492.0] || subclass(universal_class,restrict(complement(singleton(ordinal_numbers)),u,v))* -> . % 299.95/300.40 215848[22:SpL:29.0,214490.0] || subclass(omega,restrict(complement(singleton(ordinal_numbers)),u,v))* -> . % 299.95/300.40 215821[22:SpL:29.0,214489.0] || equal(restrict(complement(singleton(ordinal_numbers)),u,v),omega)** -> . % 299.95/300.40 215256[22:Res:214528.1,177998.1] || subclass(kind_1_ordinals,u)* equal(complement(u),omega) -> . % 299.95/300.40 40487[0:Obv:40476.1] || member(u,v) -> equal(not_subclass_element(unordered_pair(w,u),v),w)** subclass(unordered_pair(w,u),v). % 299.95/300.40 215252[19:Res:214528.1,188593.1] || subclass(kind_1_ordinals,u)* equal(complement(u),universal_class) -> . % 299.95/300.40 215201[19:Res:214528.1,148647.0] || subclass(kind_1_ordinals,complement(complement(u)))* -> member(ordinal_numbers,u). % 299.95/300.40 215196[19:Res:214528.1,25.1] || subclass(kind_1_ordinals,complement(u))* member(ordinal_numbers,u) -> . % 299.95/300.40 217020[23:SpR:183840.0,215063.0] || -> equal(regular(singleton(singleton(ordinal_numbers))),singleton(ordinal_numbers))**. % 299.95/300.40 40458[0:EqF:4174.1,4174.2] || equal(u,v) -> subclass(unordered_pair(v,u),w) equal(not_subclass_element(unordered_pair(v,u),w),v)**. % 299.95/300.40 215063[8:Rew:946.0,215062.0] || -> equal(regular(singleton(singleton(singleton(u)))),singleton(singleton(u)))**. % 299.95/300.40 214694[19:Res:214503.0,2.0] || subclass(symmetrization_of(singleton(ordinal_numbers)),u)* -> member(ordinal_numbers,u). % 299.95/300.40 214682[19:Res:214502.0,2.0] || subclass(successor(singleton(ordinal_numbers)),u)* -> member(ordinal_numbers,u). % 299.95/300.40 216935[19:Res:167106.1,214469.0] inductive(restrict(complement(singleton(ordinal_numbers)),u,v)) || -> . % 299.95/300.40 40485[0:Obv:40478.1] || member(u,v) -> equal(not_subclass_element(unordered_pair(u,w),v),w)** subclass(unordered_pair(u,w),v). % 299.95/300.40 214469[19:SpL:29.0,214449.0] || member(ordinal_numbers,restrict(complement(singleton(ordinal_numbers)),u,v))* -> . % 299.95/300.40 216545[19:SpL:149318.0,214439.0] || subclass(singleton(ordinal_numbers),intersection(u,complement(singleton(ordinal_numbers))))* -> . % 299.95/300.40 215627[19:Res:215454.0,169221.1] || equal(complement(union(u,singleton(ordinal_numbers))),singleton(ordinal_numbers))** -> . % 299.95/300.40 215448[19:Res:169181.1,214471.0] || equal(intersection(u,complement(singleton(ordinal_numbers))),singleton(ordinal_numbers))** -> . % 299.95/300.40 38094[0:MRR:38061.0,36583.1] || member(u,union(v,w)) -> member(u,intersection(v,w))* member(u,symmetric_difference(v,w)). % 299.95/300.40 215445[19:Res:205391.1,214471.0] || equal(complement(intersection(u,complement(singleton(ordinal_numbers)))),ordinal_numbers)** -> . % 299.95/300.40 215058[19:MRR:215022.1,180883.0] || equal(complement(regular(ordered_pair(ordinal_numbers,u))),singleton(ordinal_numbers))** -> . % 299.95/300.40 214519[19:Res:214498.0,169221.1] || equal(complement(union(singleton(ordinal_numbers),u)),singleton(ordinal_numbers))** -> . % 299.95/300.40 175988[19:Obv:175968.0] || -> equal(regular(unordered_pair(u,v)),u) equal(unordered_pair(u,v),ordinal_numbers) member(v,unordered_pair(u,v))*. % 299.95/300.40 214491[19:Res:169181.1,214449.0] || equal(intersection(complement(singleton(ordinal_numbers)),u),singleton(ordinal_numbers))** -> . % 299.95/300.40 214488[19:Res:205391.1,214449.0] || equal(complement(intersection(complement(singleton(ordinal_numbers)),u)),ordinal_numbers)** -> . % 299.95/300.40 214439[19:MRR:214358.1,167046.0] || subclass(singleton(ordinal_numbers),intersection(complement(singleton(ordinal_numbers)),u))* -> . % 299.95/300.40 216495[19:Res:7.1,215230.0] || equal(cantor(complement(cross_product(singleton(ordinal_numbers),universal_class))),kind_1_ordinals)** -> . % 299.95/300.40 175987[19:Obv:175976.0] || -> equal(regular(unordered_pair(u,v)),v) equal(unordered_pair(u,v),ordinal_numbers) member(u,unordered_pair(u,v))*. % 299.95/300.40 215414[19:Res:188649.1,214521.0] || equal(complement(image(successor_relation,kind_1_ordinals)),universal_class)** -> inductive(kind_1_ordinals). % 299.95/300.40 215230[19:Res:214528.1,192214.0] || subclass(kind_1_ordinals,cantor(complement(cross_product(singleton(ordinal_numbers),universal_class))))* -> . % 299.95/300.40 216452[19:Res:7.1,215254.0] || equal(u,kind_1_ordinals) subclass(u,ordinal_numbers)* -> . % 299.95/300.40 216442[19:Res:7.1,215251.0] || equal(u,kind_1_ordinals)* equal(ordinal_numbers,u) -> . % 299.95/300.40 168527[19:Rew:166997.0,81103.1] || subclass(u,v) -> equal(cross_product(v,u),ordinal_numbers) section(regular(cross_product(v,u)),u,v)*. % 299.95/300.40 216438[19:Res:7.1,215215.0] || equal(singleton(u),kind_1_ordinals)** -> equal(ordinal_numbers,u). % 299.95/300.40 215254[19:Res:214528.1,203417.1] || subclass(kind_1_ordinals,u)*+ subclass(u,ordinal_numbers)* -> . % 299.95/300.40 215251[19:Res:214528.1,205934.1] || subclass(kind_1_ordinals,u)* equal(ordinal_numbers,u) -> . % 299.95/300.40 215215[19:Res:214528.1,4178.0] || subclass(kind_1_ordinals,singleton(u))* -> equal(ordinal_numbers,u). % 299.95/300.40 167724[19:Rew:166997.0,80617.1] || subclass(u,restrict(v,w,x))*+ -> equal(u,ordinal_numbers) member(regular(u),cross_product(w,x))*. % 299.95/300.40 214524[19:Res:214509.0,11848.0] || subclass(kind_1_ordinals,u) well_ordering(universal_class,u)* -> . % 299.95/300.40 216207[19:Res:7.1,215444.0] || equal(intersection(u,complement(singleton(ordinal_numbers))),kind_1_ordinals)** -> . % 299.95/300.40 216181[19:Res:7.1,215260.0] || equal(intersection(complement(singleton(ordinal_numbers)),u),kind_1_ordinals)** -> . % 299.95/300.40 215628[22:Res:215454.0,177998.1] || equal(complement(union(u,singleton(ordinal_numbers))),omega)** -> . % 299.95/300.40 35221[2:Res:7.1,9859.1] inductive(u) || equal(v,u)*+ well_ordering(w,v)* -> member(least(w,u),u)*. % 299.95/300.40 215625[19:Res:215454.0,188593.1] || equal(complement(union(u,singleton(ordinal_numbers))),universal_class)** -> . % 299.95/300.40 215450[19:Res:167087.1,214471.0] || equal(intersection(u,complement(singleton(ordinal_numbers))),universal_class)** -> . % 299.95/300.40 215449[19:Res:167104.1,214471.0] || subclass(universal_class,intersection(u,complement(singleton(ordinal_numbers))))* -> . % 299.95/300.40 215447[22:Res:177171.1,214471.0] || subclass(omega,intersection(u,complement(singleton(ordinal_numbers))))* -> . % 299.95/300.40 6441[0:Res:2480.1,9.0] || subclass(universal_class,unordered_pair(u,v))*+ -> equal(unordered_pair(w,x),v)* equal(unordered_pair(w,x),u)*. % 299.95/300.40 215446[22:Res:178902.1,214471.0] || equal(intersection(u,complement(singleton(ordinal_numbers))),omega)** -> . % 299.95/300.40 215444[19:Res:214528.1,214471.0] || subclass(kind_1_ordinals,intersection(u,complement(singleton(ordinal_numbers))))* -> . % 299.95/300.40 215260[19:Res:214528.1,214449.0] || subclass(kind_1_ordinals,intersection(complement(singleton(ordinal_numbers)),u))* -> . % 299.95/300.40 215061[19:MRR:215029.1,182391.0] || well_ordering(universal_class,regular(ordered_pair(singleton(ordinal_numbers),u)))* -> . % 299.95/300.40 16107[0:Res:4126.1,2.0] || member(u,symmetric_difference(v,w))* subclass(complement(intersection(v,w)),x)*+ -> member(u,x)*. % 299.95/300.40 215057[22:MRR:215021.1,178289.0] || equal(complement(regular(ordered_pair(ordinal_numbers,u))),omega)** -> . % 299.95/300.40 214520[22:Res:214498.0,177998.1] || equal(complement(union(singleton(ordinal_numbers),u)),omega)** -> . % 299.95/300.40 214517[19:Res:214498.0,188593.1] || equal(complement(union(singleton(ordinal_numbers),u)),universal_class)** -> . % 299.95/300.40 177279[19:EqF:168360.1,168360.2] || equal(u,v) -> equal(unordered_pair(v,u),ordinal_numbers) equal(apply(choice,unordered_pair(v,u)),v)**. % 299.95/300.40 214493[19:Res:167087.1,214449.0] || equal(intersection(complement(singleton(ordinal_numbers)),u),universal_class)** -> . % 299.95/300.40 214492[19:Res:167104.1,214449.0] || subclass(universal_class,intersection(complement(singleton(ordinal_numbers)),u))* -> . % 299.95/300.40 214490[22:Res:177171.1,214449.0] || subclass(omega,intersection(complement(singleton(ordinal_numbers)),u))* -> . % 299.95/300.40 214489[22:Res:178902.1,214449.0] || equal(intersection(complement(singleton(ordinal_numbers)),u),omega)** -> . % 299.95/300.40 168521[19:Rew:166997.0,80820.1] || well_ordering(u,universal_class) -> equal(intersection(v,w),ordinal_numbers) member(least(u,intersection(v,w)),w)*. % 299.95/300.40 215626[19:Res:215454.0,203417.1] || subclass(union(u,singleton(ordinal_numbers)),ordinal_numbers)* -> . % 299.95/300.40 215624[19:Res:215454.0,205934.1] || equal(union(u,singleton(ordinal_numbers)),ordinal_numbers)** -> . % 299.95/300.40 215451[19:Res:167106.1,214471.0] inductive(intersection(u,complement(singleton(ordinal_numbers)))) || -> . % 299.95/300.40 215454[19:MRR:215442.0,167011.0] || -> member(ordinal_numbers,union(u,singleton(ordinal_numbers)))*. % 299.95/300.40 168520[19:Rew:166997.0,80821.1] || well_ordering(u,universal_class) -> equal(intersection(v,w),ordinal_numbers) member(least(u,intersection(v,w)),v)*. % 299.95/300.40 214471[19:SpL:149318.0,214449.0] || member(ordinal_numbers,intersection(u,complement(singleton(ordinal_numbers))))* -> . % 299.95/300.40 215415[19:Res:167219.1,214521.0] || equal(image(successor_relation,kind_1_ordinals),ordinal_numbers)** -> inductive(kind_1_ordinals). % 299.95/300.40 214698[19:Res:214503.0,169221.1] || equal(complement(symmetrization_of(singleton(ordinal_numbers))),singleton(ordinal_numbers))** -> . % 299.95/300.40 214686[19:Res:214502.0,169221.1] || equal(complement(successor(singleton(ordinal_numbers))),singleton(ordinal_numbers))** -> . % 299.95/300.40 168518[19:Rew:166997.0,80817.2] inductive(segment(u,v,w)) || section(u,singleton(w),v)* -> member(ordinal_numbers,singleton(w)). % 299.95/300.40 214521[19:MRR:168229.1,214509.0] || subclass(image(successor_relation,kind_1_ordinals),ordinal_numbers)* -> inductive(kind_1_ordinals). % 299.95/300.40 215389[19:Res:7.1,215262.0] || equal(cross_product(u,v),kind_1_ordinals)** -> . % 299.95/300.40 168434[19:Rew:166997.0,84842.1] || subclass(omega,restrict(u,v,w))*+ -> equal(integer_of(x),ordinal_numbers) member(x,cross_product(v,w))*. % 299.95/300.40 215391[19:SoR:215390.0,72.1] one_to_one(kind_1_ordinals) || -> . % 299.95/300.40 215390[19:Res:63.1,215262.0] function(kind_1_ordinals) || -> . % 299.95/300.40 215262[19:MRR:215227.1,167176.0] || subclass(kind_1_ordinals,cross_product(u,v))* -> . % 299.95/300.40 215368[19:Res:7.1,215253.0] || equal(complement(singleton(ordinal_numbers)),kind_1_ordinals)** -> . % 299.95/300.40 168373[19:Rew:166997.0,84845.1] || subclass(omega,unordered_pair(u,v))*+ -> equal(integer_of(w),ordinal_numbers)** equal(w,v)* equal(w,u)*. % 299.95/300.40 215253[19:Res:214528.1,167331.0] || subclass(kind_1_ordinals,complement(singleton(ordinal_numbers)))* -> . % 299.95/300.40 215363[19:Res:7.1,215259.0] || equal(symmetrization_of(ordinal_numbers),kind_1_ordinals)** -> . % 299.95/300.40 215268[19:Res:7.1,215257.0] || equal(inverse(ordinal_numbers),kind_1_ordinals)** -> . % 299.95/300.40 215259[19:Res:214528.1,187485.0] || subclass(kind_1_ordinals,symmetrization_of(ordinal_numbers))* -> . % 299.95/300.40 168249[19:Rew:166997.0,80696.3] || member(u,regular(v))*+ member(u,v) well_ordering(w,x)* -> equal(v,ordinal_numbers). % 299.95/300.40 215257[19:Res:214528.1,167338.0] || subclass(kind_1_ordinals,inverse(ordinal_numbers))* -> . % 299.95/300.40 214528[19:Res:214509.0,2.0] || subclass(kind_1_ordinals,u) -> member(ordinal_numbers,u)*. % 299.95/300.40 214518[19:Res:214498.0,203417.1] || subclass(union(singleton(ordinal_numbers),u),ordinal_numbers)* -> . % 299.95/300.40 214516[19:Res:214498.0,205934.1] || equal(union(singleton(ordinal_numbers),u),ordinal_numbers)** -> . % 299.95/300.40 168245[19:Rew:166997.0,80700.2] || well_ordering(u,universal_class) subclass(v,w) -> equal(v,ordinal_numbers) member(least(u,v),w)*. % 299.95/300.40 214494[19:Res:167106.1,214449.0] inductive(intersection(complement(singleton(ordinal_numbers)),u)) || -> . % 299.95/300.40 214699[22:Res:214503.0,177998.1] || equal(complement(symmetrization_of(singleton(ordinal_numbers))),omega)** -> . % 299.95/300.40 214696[19:Res:214503.0,188593.1] || equal(complement(symmetrization_of(singleton(ordinal_numbers))),universal_class)** -> . % 299.95/300.40 214687[22:Res:214502.0,177998.1] || equal(complement(successor(singleton(ordinal_numbers))),omega)** -> . % 299.95/300.40 160282[8:MRR:80671.0,160281.0] || -> equal(unordered_pair(u,singleton(v)),regular(ordered_pair(u,v)))** equal(regular(ordered_pair(u,v)),singleton(u)). % 299.95/300.40 214684[19:Res:214502.0,188593.1] || equal(complement(successor(singleton(ordinal_numbers))),universal_class)** -> . % 299.95/300.40 214697[19:Res:214503.0,203417.1] || subclass(symmetrization_of(singleton(ordinal_numbers)),ordinal_numbers)* -> . % 299.95/300.40 214695[19:Res:214503.0,205934.1] || equal(symmetrization_of(singleton(ordinal_numbers)),ordinal_numbers)** -> . % 299.95/300.40 214685[19:Res:214502.0,203417.1] || subclass(successor(singleton(ordinal_numbers)),ordinal_numbers)* -> . % 299.95/300.40 27258[0:Res:24.2,488.0] || member(u,complement(v)) member(u,complement(w)) member(u,union(w,v))* -> . % 299.95/300.40 214683[19:Res:214502.0,205934.1] || equal(successor(singleton(ordinal_numbers)),ordinal_numbers)** -> . % 299.95/300.40 214532[19:Res:214509.0,169221.1] || equal(complement(kind_1_ordinals),singleton(ordinal_numbers))** -> . % 299.95/300.40 214533[22:Res:214509.0,177998.1] || equal(complement(kind_1_ordinals),omega)** -> . % 299.95/300.40 214530[19:Res:214509.0,188593.1] || equal(complement(kind_1_ordinals),universal_class)** -> . % 299.95/300.40 207871[0:SpL:206407.0,488.0] || member(u,intersection(complement(v),power_class(w)))* member(u,union(v,complement(power_class(w)))) -> . % 299.95/300.40 214503[19:SpR:114.0,214498.0] || -> member(ordinal_numbers,symmetrization_of(singleton(ordinal_numbers)))*. % 299.95/300.40 214502[19:SpR:44.0,214498.0] || -> member(ordinal_numbers,successor(singleton(ordinal_numbers)))*. % 299.95/300.40 214531[19:Res:214509.0,203417.1] || subclass(kind_1_ordinals,ordinal_numbers)* -> . % 299.95/300.40 214529[19:Res:214509.0,205934.1] || equal(kind_1_ordinals,ordinal_numbers)** -> . % 299.95/300.40 207852[0:SpL:206407.0,488.0] || member(u,intersection(power_class(v),complement(w)))* member(u,union(complement(power_class(v)),w)) -> . % 299.95/300.40 214509[19:SpR:167022.0,214498.0] || -> member(ordinal_numbers,kind_1_ordinals)*. % 299.95/300.40 214498[19:MRR:214486.0,167011.0] || -> member(ordinal_numbers,union(singleton(ordinal_numbers),u))*. % 299.95/300.40 214449[19:MRR:214448.1,187474.0] || member(ordinal_numbers,intersection(complement(singleton(ordinal_numbers)),u))* -> . % 299.95/300.40 204401[19:Rew:204394.1,204388.1] || subclass(universal_class,ordered_pair(u,v))*+ -> equal(unordered_pair(w,x),omega)** equal(unordered_pair(w,x),ordinal_numbers). % 299.95/300.40 198938[19:SpR:167191.0,197702.0] || -> equal(intersection(symmetrization_of(ordinal_numbers),intersection(u,complement(inverse(ordinal_numbers)))),ordinal_numbers)**. % 299.95/300.40 198937[19:SpR:180103.0,197702.0] || -> equal(intersection(singleton(ordinal_numbers),intersection(u,complement(singleton(ordinal_numbers)))),ordinal_numbers)**. % 299.95/300.40 198291[19:SpR:167191.0,197499.0] || -> equal(intersection(symmetrization_of(ordinal_numbers),intersection(complement(inverse(ordinal_numbers)),u)),ordinal_numbers)**. % 299.95/300.40 198290[19:SpR:180103.0,197499.0] || -> equal(intersection(singleton(ordinal_numbers),intersection(complement(singleton(ordinal_numbers)),u)),ordinal_numbers)**. % 299.95/300.40 178410[19:SpR:168412.1,945.0] || -> equal(cross_product(u,v),ordinal_numbers) member(singleton(first(regular(cross_product(u,v)))),regular(cross_product(u,v)))*. % 299.95/300.40 196818[19:MRR:196808.2,167057.0] || member(u,universal_class)* subclass(rest_relation,rest_of(regular(element_relation)))*+ -> . % 299.95/300.40 213202[19:Res:7.1,204579.1] || equal(sum_class(ordinal_numbers),domain_relation)** equal(sum_class(ordinal_numbers),ordinal_numbers) -> . % 299.95/300.40 212976[19:Res:7.1,196865.0] || equal(cantor(complement(cross_product(singleton(regular(element_relation)),universal_class))),universal_class)** -> . % 299.95/300.40 211476[19:MRR:211471.0,170.0] || -> member(singleton(ordinal_numbers),cantor(choice)) section(element_relation,range_of(ordinal_numbers),universal_class)*. % 299.95/300.40 176242[19:Rew:176206.1,158626.2] || member(u,universal_class) subclass(domain_relation,restrict(v,w,x))*+ -> member(ordered_pair(u,ordinal_numbers),v)*. % 299.95/300.40 210205[26:Res:205520.1,203596.0] || equal(complement(complement(compose(complement(element_relation),inverse(element_relation)))),ordinal_numbers)** -> . % 299.95/300.40 209917[19:Res:180693.1,205934.1] || well_ordering(element_relation,range_of(ordinal_numbers))* equal(cantor(choice),ordinal_numbers) -> . % 299.95/300.40 209198[19:SpR:167191.0,206400.0] || -> equal(complement(power_class(complement(inverse(ordinal_numbers)))),image(element_relation,symmetrization_of(ordinal_numbers)))**. % 299.95/300.40 209197[19:SpR:180103.0,206400.0] || -> equal(complement(power_class(complement(singleton(ordinal_numbers)))),image(element_relation,singleton(ordinal_numbers)))**. % 299.95/300.40 169640[19:MRR:169076.2,167057.0] || equal(image(u,singleton(v)),apply(u,v)) well_ordering(element_relation,image(u,singleton(v)))* -> . % 299.95/300.40 208482[19:Res:205414.1,192214.0] || equal(complement(cantor(complement(cross_product(singleton(omega),universal_class)))),ordinal_numbers)** -> . % 299.95/300.40 207951[19:Res:205391.1,192214.0] || equal(complement(cantor(complement(cross_product(singleton(ordinal_numbers),universal_class)))),ordinal_numbers)** -> . % 299.95/300.40 169509[19:Rew:166997.0,168526.1] || -> equal(cross_product(u,singleton(v)),ordinal_numbers) equal(segment(regular(cross_product(u,singleton(v))),u,v),ordinal_numbers)**. % 299.95/300.40 206190[22:Res:167355.1,204538.1] || equal(sum_class(ordinal_numbers),ordinal_numbers) equal(sum_class(ordinal_numbers),omega)** -> . % 299.95/300.40 205042[19:Res:167355.1,203421.0] || equal(sum_class(ordinal_numbers),ordinal_numbers) subclass(universal_class,sum_class(ordinal_numbers))* -> . % 299.95/300.40 204658[19:Res:147404.1,203420.1] || member(omega,element_relation) subclass(compose(element_relation,universal_class),ordinal_numbers)* -> . % 299.95/300.40 204622[19:Res:167355.1,203419.0] || equal(sum_class(ordinal_numbers),ordinal_numbers) equal(sum_class(ordinal_numbers),universal_class)** -> . % 299.95/300.40 168498[19:Rew:166997.0,84868.1] || subclass(omega,compose_class(u))*+ -> equal(integer_of(ordered_pair(v,w)),ordinal_numbers)** equal(compose(u,v),w)*. % 299.95/300.40 204579[19:Res:167355.1,203418.0] || equal(sum_class(ordinal_numbers),ordinal_numbers) subclass(domain_relation,sum_class(ordinal_numbers))* -> . % 299.95/300.40 204526[19:Res:147404.1,203417.1] || member(ordinal_numbers,element_relation) subclass(compose(element_relation,universal_class),ordinal_numbers)* -> . % 299.95/300.40 204489[19:SpL:180125.0,204472.0] || equal(image(element_relation,singleton(ordinal_numbers)),power_class(complement(singleton(ordinal_numbers))))** -> . % 299.95/300.40 204488[19:SpL:167200.0,204472.0] || equal(image(element_relation,symmetrization_of(ordinal_numbers)),power_class(complement(inverse(ordinal_numbers))))** -> . % 299.95/300.40 168461[19:Rew:166997.0,80798.1] || member(regular(union(u,v)),intersection(complement(u),complement(v)))* -> equal(union(u,v),ordinal_numbers). % 299.95/300.40 201819[26:Rew:200916.0,201044.1] || equal(complement(sum_class(ordinal_numbers)),universal_class)** well_ordering(element_relation,ordinal_numbers) -> . % 299.95/300.40 213085[20:MRR:213078.1,187485.0] inductive(singleton(not_subclass_element(symmetrization_of(ordinal_numbers),ordinal_numbers))) || -> . % 299.95/300.40 213073[20:Res:169234.0,213033.0] || -> subclass(singleton(not_subclass_element(symmetrization_of(ordinal_numbers),ordinal_numbers)),symmetrization_of(ordinal_numbers))*. % 299.95/300.40 213033[20:Res:142678.1,200876.0] || member(not_subclass_element(symmetrization_of(ordinal_numbers),ordinal_numbers),complement(inverse(ordinal_numbers)))* -> . % 299.95/300.40 167955[19:Rew:166997.0,83650.1] || -> equal(not_subclass_element(unordered_pair(u,v),omega),u)** equal(integer_of(v),ordinal_numbers) subclass(unordered_pair(u,v),omega). % 299.95/300.40 197187[19:MRR:197168.1,196720.0] || equal(sum_class(range_of(first(regular(element_relation)))),second(regular(element_relation)))** -> . % 299.95/300.40 196924[19:MRR:196892.1,196718.0] || subclass(rest_relation,domain_relation) -> member(ordered_pair(regular(element_relation),ordinal_numbers),rest_relation)*. % 299.95/300.40 196874[19:Res:196731.1,158.0] || subclass(universal_class,omega) -> equal(integer_of(regular(element_relation)),regular(element_relation))**. % 299.95/300.40 167778[19:Rew:166997.0,83651.1] || -> equal(not_subclass_element(unordered_pair(u,v),omega),v)** equal(integer_of(u),ordinal_numbers) subclass(unordered_pair(u,v),omega). % 299.95/300.40 212979[25:SoR:212978.0,72.1] one_to_one(complement(cross_product(singleton(regular(element_relation)),universal_class))) || -> . % 299.95/300.40 212978[25:MRR:212973.1,289.0] function(complement(cross_product(singleton(regular(element_relation)),universal_class))) || -> . % 299.95/300.40 196865[19:Res:196731.1,192214.0] || subclass(universal_class,cantor(complement(cross_product(singleton(regular(element_relation)),universal_class))))* -> . % 299.95/300.40 15073[0:Res:2483.2,2.0] || member(u,universal_class)+ subclass(universal_class,v)* subclass(v,w)* -> member(power_class(u),w)*. % 299.95/300.40 198248[19:SpR:29.0,197499.0] || -> equal(intersection(complement(u),restrict(u,v,w)),ordinal_numbers)**. % 299.95/300.40 212592[19:Res:209033.1,202966.0] || equal(power_class(u),ordinal_numbers) -> asymmetric(power_class(u),v)*. % 299.95/300.40 209033[19:MRR:209013.1,36682.1] || equal(power_class(u),ordinal_numbers) -> subclass(power_class(u),v)*. % 299.95/300.40 205993[19:Obv:205732.1] || equal(complement(symmetrization_of(u)),ordinal_numbers)**+ -> connected(u,v)*. % 299.95/300.40 15085[0:Res:2483.2,4127.0] || member(u,universal_class) subclass(universal_class,symmetric_difference(v,w)) -> member(power_class(u),union(v,w))*. % 299.95/300.40 205991[19:MRR:205716.1,289.0] || equal(complement(u),ordinal_numbers) -> member(singleton(v),u)*. % 299.95/300.40 205897[19:Rew:142500.0,205475.1] || equal(ordinal_numbers,u) -> equal(intersection(v,u),ordinal_numbers)**. % 299.95/300.40 205896[19:Rew:142500.0,205474.1] || equal(ordinal_numbers,u) -> equal(intersection(u,v),ordinal_numbers)**. % 299.95/300.40 211666[19:Res:203424.1,182393.0] || subclass(complement(u),ordinal_numbers)* well_ordering(universal_class,u) -> . % 299.95/300.40 27264[0:Res:2480.1,488.0] || subclass(universal_class,intersection(complement(u),complement(v))) member(unordered_pair(w,x),union(u,v))* -> . % 299.95/300.40 211820[19:Res:211653.1,167057.0] || subclass(complement(element_relation),ordinal_numbers)* -> . % 299.95/300.40 211683[19:MRR:211615.1,203610.0] || subclass(complement(complement(singleton(singleton(u)))),ordinal_numbers)* -> . % 299.95/300.40 211665[23:Res:203424.1,184175.0] || subclass(complement(successor_relation),ordinal_numbers)* -> . % 299.95/300.40 27146[0:Res:2523.2,22.0] || member(u,universal_class) subclass(rest_relation,intersection(v,w))*+ -> member(ordered_pair(u,rest_of(u)),v)*. % 299.95/300.40 211664[23:Res:203424.1,184001.0] || subclass(complement(rest_relation),ordinal_numbers)* -> . % 299.95/300.40 211663[23:Res:203424.1,183982.0] || subclass(complement(domain_relation),ordinal_numbers)* -> . % 299.95/300.40 203424[19:Res:203242.1,9734.0] || subclass(complement(u),ordinal_numbers) -> member(singleton(v),u)*. % 299.95/300.40 211481[20:Res:7.1,210035.0] || equal(u,symmetrization_of(ordinal_numbers))* equal(ordinal_numbers,u) -> . % 299.95/300.40 27147[0:Res:2523.2,23.0] || member(u,universal_class) subclass(rest_relation,intersection(v,w))*+ -> member(ordered_pair(u,rest_of(u)),w)*. % 299.95/300.40 210982[19:Res:167115.1,205988.1] || equal(singleton(u),ordinal_numbers) -> equal(integer_of(u),ordinal_numbers)**. % 299.95/300.40 210036[20:Res:175570.1,205934.1] || subclass(inverse(ordinal_numbers),u)* equal(ordinal_numbers,u) -> . % 299.95/300.40 210035[20:Res:181635.1,205934.1] || subclass(symmetrization_of(ordinal_numbers),u)* equal(ordinal_numbers,u) -> . % 299.95/300.40 211454[19:MRR:211443.0,166995.0] || -> section(element_relation,image(choice,singleton(singleton(ordinal_numbers))),universal_class)*. % 299.95/300.40 9806[0:SpL:69.0,9780.0] || subclass(apply(u,v),image(u,singleton(v)))* -> section(element_relation,image(u,singleton(v)),universal_class). % 299.95/300.40 209972[19:Res:27189.1,205934.1] || subclass(rest_relation,rotate(u))* equal(ordinal_numbers,u) -> . % 299.95/300.40 209971[19:Res:27190.1,205934.1] || subclass(rest_relation,flip(u))* equal(ordinal_numbers,u) -> . % 299.95/300.40 208807[19:Res:205520.1,9733.0] || equal(complement(complement(unordered_pair(singleton(u),v))),ordinal_numbers)** -> . % 299.95/300.40 208804[19:Res:205520.1,9732.0] || equal(complement(complement(unordered_pair(u,singleton(v)))),ordinal_numbers)** -> . % 299.95/300.40 15098[0:SpR:69.0,2482.2] || member(image(u,singleton(v)),universal_class)*+ subclass(universal_class,w) -> member(apply(u,v),w)*. % 299.95/300.40 208802[19:Res:205520.1,48400.0] || equal(complement(complement(singleton(unordered_pair(u,v)))),ordinal_numbers)** -> . % 299.95/300.40 208801[19:Res:205520.1,48410.0] || equal(complement(complement(singleton(ordered_pair(u,v)))),ordinal_numbers)** -> . % 299.95/300.40 208468[19:Res:205414.1,4178.0] || equal(complement(singleton(u)),ordinal_numbers)** -> equal(omega,u). % 299.95/300.40 207937[19:Res:205391.1,4178.0] || equal(complement(singleton(u)),ordinal_numbers)** -> equal(ordinal_numbers,u). % 299.95/300.40 15107[0:Res:2482.2,2.0] || member(u,universal_class)+ subclass(universal_class,v)* subclass(v,w)* -> member(sum_class(u),w)*. % 299.95/300.40 205996[19:Obv:205844.1] || equal(rest_of(u),ordinal_numbers)** -> equal(cantor(u),ordinal_numbers). % 299.95/300.40 205992[19:Obv:205717.1] || equal(complement(u),ordinal_numbers) well_ordering(universal_class,u)* -> . % 299.95/300.40 205989[19:MRR:205709.1,5.0] || equal(singleton(regular(u)),ordinal_numbers)** -> equal(u,ordinal_numbers). % 299.95/300.40 211156[20:Res:7.1,211043.0] || equal(complement(singleton(regular(symmetrization_of(ordinal_numbers)))),inverse(ordinal_numbers))** -> . % 299.95/300.40 15119[0:Res:2482.2,4127.0] || member(u,universal_class) subclass(universal_class,symmetric_difference(v,w)) -> member(sum_class(u),union(v,w))*. % 299.95/300.40 211150[20:Res:7.1,211042.0] || equal(complement(singleton(regular(symmetrization_of(ordinal_numbers)))),symmetrization_of(ordinal_numbers))** -> . % 299.95/300.40 211055[20:Res:205520.1,211041.0] || equal(complement(complement(singleton(regular(symmetrization_of(ordinal_numbers))))),ordinal_numbers)** -> . % 299.95/300.40 211043[20:MRR:188283.1,210996.0] || subclass(inverse(ordinal_numbers),complement(singleton(regular(symmetrization_of(ordinal_numbers)))))* -> . % 299.95/300.40 211042[20:MRR:188282.1,210996.0] || subclass(symmetrization_of(ordinal_numbers),complement(singleton(regular(symmetrization_of(ordinal_numbers)))))* -> . % 299.95/300.40 206492[0:Rew:206400.0,975.2] || member(u,universal_class) -> member(u,image(element_relation,power_class(v)))* member(u,power_class(complement(power_class(v)))). % 299.95/300.40 211054[20:Res:7.1,211041.0] || equal(complement(singleton(regular(symmetrization_of(ordinal_numbers)))),universal_class)** -> . % 299.95/300.40 211041[20:MRR:188284.1,210996.0] || subclass(universal_class,complement(singleton(regular(symmetrization_of(ordinal_numbers)))))* -> . % 299.95/300.40 210996[20:Res:175569.0,205988.1] || equal(singleton(regular(symmetrization_of(ordinal_numbers))),ordinal_numbers)** -> . % 299.95/300.40 205988[19:Obv:205691.2] || equal(singleton(u),ordinal_numbers) member(u,universal_class)* -> . % 299.95/300.40 177022[19:Obv:177021.1] || member(u,universal_class)+ -> member(u,image(universal_class,singleton(u)))* asymmetric(cross_product(singleton(u),universal_class),v)*. % 299.95/300.40 205984[19:MRR:205633.2,5.0] || equal(ordinal_numbers,u) subclass(domain_relation,rotate(u))* -> . % 299.95/300.40 205983[19:MRR:205632.2,5.0] || equal(ordinal_numbers,u) subclass(domain_relation,flip(u))* -> . % 299.95/300.40 205980[19:Obv:205602.2] || equal(ordinal_numbers,u) equal(u,singleton(ordinal_numbers))* -> . % 299.95/300.40 205979[19:Obv:205601.1] || equal(ordinal_numbers,u) equal(flip(u),domain_relation)** -> . % 299.95/300.40 176326[19:Rew:176206.1,176251.1] || member(u,universal_class) equal(compose(v,u),ordinal_numbers) -> member(ordered_pair(u,ordinal_numbers),compose_class(v))*. % 299.95/300.40 205978[19:Obv:205600.1] || equal(ordinal_numbers,u) equal(rotate(u),domain_relation)** -> . % 299.95/300.40 205977[20:Obv:205598.2] || equal(ordinal_numbers,u) equal(u,inverse(ordinal_numbers))* -> . % 299.95/300.40 205976[19:Obv:205597.2] || equal(ordinal_numbers,u) equal(flip(u),rest_relation)** -> . % 299.95/300.40 205975[19:Obv:205596.2] || equal(ordinal_numbers,u) equal(rotate(u),rest_relation)** -> . % 299.95/300.40 167924[19:Rew:166997.0,80665.2] || asymmetric(u,v) transitive(intersection(u,inverse(u)),v)* -> equal(compose(ordinal_numbers,ordinal_numbers),ordinal_numbers). % 299.95/300.40 204540[19:Res:169181.1,203417.1] || equal(u,singleton(ordinal_numbers)) subclass(u,ordinal_numbers)* -> . % 299.95/300.40 203415[19:Res:203242.1,185656.1] || subclass(u,ordinal_numbers)* equal(flip(u),domain_relation) -> . % 299.95/300.40 167923[19:Rew:166997.0,80666.1] || asymmetric(u,v) equal(compose(ordinal_numbers,ordinal_numbers),ordinal_numbers) -> transitive(intersection(u,inverse(u)),v)*. % 299.95/300.40 203414[19:Res:203242.1,185733.1] || subclass(u,ordinal_numbers)* equal(rotate(u),domain_relation) -> . % 299.95/300.40 203413[19:Res:203242.1,195635.1] || subclass(u,ordinal_numbers)* equal(flip(u),rest_relation) -> . % 299.95/300.40 203412[19:Res:203242.1,195669.1] || subclass(u,ordinal_numbers)* equal(rotate(u),rest_relation) -> . % 299.95/300.40 31137[0:MRR:31135.1,145.0] || member(u,universal_class) equal(rest_of(u),successor(u)) -> member(ordered_pair(u,rest_of(u)),successor_relation)*. % 299.95/300.40 209817[0:Obv:209800.0] || member(u,universal_class)* subclass(rest_relation,complement(rest_relation))*+ -> . % 299.95/300.40 208879[19:Res:205520.1,197178.0] || equal(complement(complement(unordered_pair(u,regular(element_relation)))),ordinal_numbers)** -> . % 299.95/300.40 208877[19:Res:205520.1,197154.0] || equal(complement(complement(unordered_pair(regular(element_relation),u))),ordinal_numbers)** -> . % 299.95/300.40 203614[19:MRR:188248.1,203610.0] || equal(complement(complement(complement(singleton(singleton(u))))),universal_class)** -> . % 299.95/300.40 27837[0:SpR:114.0,4125.0] || -> equal(intersection(symmetrization_of(u),union(complement(u),complement(inverse(u)))),symmetric_difference(complement(u),complement(inverse(u))))**. % 299.95/300.40 210204[26:Res:7.1,203596.0] || equal(complement(compose(complement(element_relation),inverse(element_relation))),universal_class)** -> . % 299.95/300.40 210197[19:Res:182871.1,203482.0] || member(not_subclass_element(complement(inverse(ordinal_numbers)),ordinal_numbers),inverse(ordinal_numbers))* -> . % 299.95/300.40 203596[26:MRR:203589.1,196720.0] || subclass(universal_class,complement(compose(complement(element_relation),inverse(element_relation))))* -> . % 299.95/300.40 203482[19:MRR:191329.1,203481.0] || member(not_subclass_element(complement(inverse(ordinal_numbers)),ordinal_numbers),symmetrization_of(ordinal_numbers))* -> . % 299.95/300.40 27168[0:Res:2523.2,143.0] || member(u,universal_class) subclass(rest_relation,rest_of(v)) -> equal(restrict(v,u,universal_class),rest_of(u))**. % 299.95/300.40 205948[19:Obv:205772.1] || equal(unordered_pair(unordered_pair(u,v),w),ordinal_numbers)** -> . % 299.95/300.40 205947[19:Obv:205770.1] || equal(unordered_pair(ordered_pair(u,v),w),ordinal_numbers)** -> . % 299.95/300.40 205946[19:Obv:205760.1] || equal(unordered_pair(u,unordered_pair(v,w)),ordinal_numbers)** -> . % 299.95/300.40 205945[19:Obv:205756.1] || equal(unordered_pair(u,ordered_pair(v,w)),ordinal_numbers)** -> . % 299.95/300.40 28088[0:Res:63.1,2497.1] function(complement(u)) || member(v,universal_class) -> member(v,u)* member(v,cross_product(universal_class,universal_class))*. % 299.95/300.40 210020[22:Res:177171.1,205934.1] || subclass(omega,u)* equal(ordinal_numbers,u) -> . % 299.95/300.40 205934[19:MRR:205672.2,36583.1] || equal(ordinal_numbers,u) member(v,u)* -> . % 299.95/300.40 203434[19:Res:203242.1,48402.0] || subclass(unordered_pair(unordered_pair(u,v),w),ordinal_numbers)* -> . % 299.95/300.40 203433[19:Res:203242.1,48618.0] || subclass(unordered_pair(ordered_pair(u,v),w),ordinal_numbers)* -> . % 299.95/300.40 27138[0:Res:2523.2,25.1] || member(u,universal_class) subclass(rest_relation,complement(v)) member(ordered_pair(u,rest_of(u)),v)* -> . % 299.95/300.40 203431[19:Res:203242.1,48401.0] || subclass(unordered_pair(u,unordered_pair(v,w)),ordinal_numbers)* -> . % 299.95/300.40 203430[19:Res:203242.1,48587.0] || subclass(unordered_pair(u,ordered_pair(v,w)),ordinal_numbers)* -> . % 299.95/300.40 208286[0:SpR:206407.0,206403.0] || -> equal(union(complement(power_class(u)),complement(power_class(v))),complement(intersection(power_class(u),power_class(v))))**. % 299.95/300.40 208803[19:Res:205520.1,9712.0] || equal(complement(complement(ordered_pair(u,v))),ordinal_numbers)** -> . % 299.95/300.40 208786[19:Res:205520.1,1063.0] || equal(complement(u),ordinal_numbers)** -> equal(universal_class,u). % 299.95/300.40 206400[0:MRR:135346.0,206399.0] || -> equal(image(element_relation,complement(u)),complement(power_class(u)))**. % 299.95/300.40 205926[19:Obv:205604.2] || equal(ordinal_numbers,u) equal(u,domain_relation)* -> . % 299.95/300.40 206404[0:Rew:206400.0,927.1] || member(u,image(element_relation,power_class(v)))* member(u,power_class(complement(power_class(v)))) -> . % 299.95/300.40 205925[22:Obv:205603.2] || equal(ordinal_numbers,u) equal(u,omega)* -> . % 299.95/300.40 205892[19:Rew:167049.0,205434.1,96580.0,205434.1] || equal(ordinal_numbers,u) -> equal(power_class(u),ordinal_numbers)**. % 299.95/300.40 208878[23:Res:205520.1,183954.0] || equal(complement(complement(unordered_pair(u,ordinal_numbers))),ordinal_numbers)** -> . % 299.95/300.40 208876[23:Res:205520.1,183930.0] || equal(complement(complement(unordered_pair(ordinal_numbers,u))),ordinal_numbers)** -> . % 299.95/300.40 206414[0:Rew:206400.0,1030.0] || member(not_subclass_element(power_class(u),v),complement(power_class(u)))* -> subclass(power_class(u),v). % 299.95/300.40 208800[19:Res:205520.1,9731.0] || equal(complement(complement(singleton(singleton(u)))),ordinal_numbers)** -> . % 299.95/300.40 208882[19:Res:205520.1,197148.0] || equal(complement(complement(singleton(regular(element_relation)))),ordinal_numbers)** -> . % 299.95/300.40 208880[19:Res:205520.1,197146.0] || equal(complement(complement(regular(element_relation))),ordinal_numbers)** -> . % 299.95/300.40 206416[19:Rew:206400.0,168271.0] || member(regular(power_class(u)),complement(power_class(u)))* -> equal(power_class(u),ordinal_numbers). % 299.95/300.40 208856[19:Res:205520.1,158094.0] || equal(complement(rest_of(u)),ordinal_numbers)** -> . % 299.95/300.40 208872[19:Res:205520.1,159745.0] || equal(complement(complement(domain_relation)),ordinal_numbers)** -> . % 299.95/300.40 208860[19:Res:205520.1,8290.0] || equal(complement(composition_function),ordinal_numbers)** -> . % 299.95/300.40 206410[0:Rew:206400.0,485.0] || -> equal(complement(intersection(power_class(u),complement(v))),union(complement(power_class(u)),v))**. % 299.95/300.40 208501[19:MRR:208457.1,204685.0] || equal(complement(complement(singleton(omega))),ordinal_numbers)** -> . % 299.95/300.40 205414[19:Res:167219.1,203423.0] || equal(complement(u),ordinal_numbers) -> member(omega,u)*. % 299.95/300.40 208205[19:Res:7.1,208201.0] || equal(complement(symmetrization_of(ordinal_numbers)),inverse(ordinal_numbers))** -> . % 299.95/300.40 208203[19:Res:188649.1,208201.0] || equal(complement(complement(symmetrization_of(ordinal_numbers))),universal_class)** -> . % 299.95/300.40 206403[0:Rew:206400.0,483.0] || -> equal(complement(intersection(complement(u),power_class(v))),union(u,complement(power_class(v))))**. % 299.95/300.40 208201[19:MRR:208199.1,207974.0] || subclass(complement(symmetrization_of(ordinal_numbers)),inverse(ordinal_numbers))* -> . % 299.95/300.40 207976[19:MRR:182884.1,207974.0] || member(regular(complement(symmetrization_of(ordinal_numbers))),inverse(ordinal_numbers))* -> . % 299.95/300.40 207987[19:MRR:207948.1,167176.0] || equal(complement(cross_product(u,v)),ordinal_numbers)** -> . % 299.95/300.40 207993[19:SoR:207988.0,72.1] one_to_one(complement(cross_product(universal_class,universal_class))) || -> . % 299.95/300.40 206408[0:Rew:206400.0,188.0] || -> equal(complement(image(element_relation,power_class(u))),power_class(complement(power_class(u))))**. % 299.95/300.40 207988[19:MRR:168267.1,207987.0] function(complement(cross_product(universal_class,universal_class))) || -> . % 299.95/300.40 207974[19:Res:205391.1,187485.0] || equal(complement(symmetrization_of(ordinal_numbers)),ordinal_numbers)** -> . % 299.95/300.40 205391[19:Res:167219.1,203422.0] || equal(complement(u),ordinal_numbers) -> member(ordinal_numbers,u)*. % 299.95/300.40 206407[0:Rew:206400.0,56.0] || -> equal(complement(complement(power_class(u))),power_class(u))**. % 299.95/300.40 205036[19:Res:167219.1,203421.0] || equal(ordinal_numbers,u) subclass(universal_class,u)* -> . % 299.95/300.40 204616[19:Res:167219.1,203419.0] || equal(ordinal_numbers,u) equal(u,universal_class)* -> . % 299.95/300.40 204573[19:Res:167219.1,203418.0] || equal(ordinal_numbers,u) subclass(domain_relation,u)* -> . % 299.95/300.40 204539[22:Res:177171.1,203417.1] || subclass(omega,u)*+ subclass(u,ordinal_numbers)* -> . % 299.95/300.40 27838[0:SpR:44.0,4125.0] || -> equal(intersection(successor(u),union(complement(u),complement(singleton(u)))),symmetric_difference(complement(u),complement(singleton(u))))**. % 299.95/300.40 204538[22:Res:178902.1,203417.1] || equal(u,omega) subclass(u,ordinal_numbers)* -> . % 299.95/300.40 206001[26:MRR:206000.1,167161.0] || equal(compose(complement(element_relation),inverse(element_relation)),ordinal_numbers)** -> . % 299.95/300.40 205888[19:MRR:205780.1,5.0] || equal(compose(element_relation,universal_class),ordinal_numbers)** -> . % 299.95/300.40 205875[23:Obv:205740.1] || equal(complement(domain_relation),ordinal_numbers)** -> . % 299.95/300.40 205874[23:Obv:205739.1] || equal(complement(rest_relation),ordinal_numbers)** -> . % 299.95/300.40 205872[19:MRR:205734.1,5.0] || equal(complement(successor_relation),ordinal_numbers)** -> . % 299.95/300.40 37525[0:MRR:37517.1,170.0] || member(u,universal_class) equal(successor(singleton(u)),u) -> member(singleton(singleton(singleton(u))),successor_relation)*. % 299.95/300.40 205871[19:Obv:205723.1] || equal(complement(element_relation),ordinal_numbers)** -> . % 299.95/300.40 204449[19:Res:167219.1,203411.0] || equal(ordinal_numbers,u) -> equal(complement(u),universal_class)**. % 299.95/300.40 203423[19:Res:203242.1,148626.0] || subclass(complement(u),ordinal_numbers)* -> member(omega,u). % 299.95/300.40 203422[19:Res:203242.1,167093.0] || subclass(complement(u),ordinal_numbers)* -> member(ordinal_numbers,u). % 299.95/300.40 203421[19:Res:203242.1,9715.1] || subclass(u,ordinal_numbers)*+ subclass(universal_class,u)* -> . % 299.95/300.40 204718[19:Res:167219.1,204672.0] || equal(unordered_pair(u,omega),ordinal_numbers)** -> . % 299.95/300.40 204714[19:Res:167219.1,204671.0] || equal(unordered_pair(omega,u),ordinal_numbers)** -> . % 299.95/300.40 204672[19:MRR:204650.0,53.0] || subclass(unordered_pair(u,omega),ordinal_numbers)* -> . % 299.95/300.40 204671[19:MRR:204649.0,53.0] || subclass(unordered_pair(omega,u),ordinal_numbers)* -> . % 299.95/300.40 204688[19:MRR:188251.1,204685.0] || subclass(universal_class,complement(singleton(omega)))* -> . % 299.95/300.40 204685[19:Res:167219.1,204670.0] || equal(singleton(omega),ordinal_numbers)** -> . % 299.95/300.40 176258[19:Rew:176206.1,158699.2] || member(u,universal_class) subclass(domain_relation,omega) -> equal(integer_of(ordered_pair(u,ordinal_numbers)),ordered_pair(u,ordinal_numbers))**. % 299.95/300.40 204670[19:MRR:204645.0,53.0] || subclass(singleton(omega),ordinal_numbers)* -> . % 299.95/300.40 203420[19:Res:203242.1,2532.0] || subclass(u,ordinal_numbers) member(omega,u)* -> . % 299.95/300.40 203419[19:Res:203242.1,146229.1] || subclass(u,ordinal_numbers)* equal(u,universal_class) -> . % 299.95/300.40 204607[19:MRR:204605.0,99.0] || equal(sum_class(range_of(singleton(ordinal_numbers))),ordinal_numbers)** -> . % 299.95/300.40 99368[12:MRR:99332.2,80465.0] || equal(sum_class(range_of(singleton(u))),u) member(singleton(singleton(singleton(u))),cross_product(universal_class,universal_class))* -> . % 299.95/300.40 203418[19:Res:203242.1,164453.1] || subclass(u,ordinal_numbers)*+ subclass(domain_relation,u)* -> . % 299.95/300.40 203417[19:Res:203242.1,167096.0] || subclass(u,ordinal_numbers) member(ordinal_numbers,u)* -> . % 299.95/300.40 204394[19:MRR:204385.2,167008.0] || subclass(universal_class,ordered_pair(u,v))* -> equal(unordered_pair(u,singleton(v)),omega). % 299.95/300.40 204472[19:MRR:204471.1,9070.0] || equal(complement(u),u)** -> . % 299.95/300.40 203411[19:Res:203242.1,1063.0] || subclass(u,ordinal_numbers)* -> equal(complement(u),universal_class). % 299.95/300.40 204415[19:Res:167219.1,203432.0] || equal(unordered_pair(singleton(u),v),ordinal_numbers)** -> . % 299.95/300.40 204370[19:Res:167219.1,203429.0] || equal(unordered_pair(u,singleton(v)),ordinal_numbers)** -> . % 299.95/300.40 204373[19:MRR:169434.1,204370.0] inductive(ordered_pair(u,v)) || -> equal(singleton(u),ordinal_numbers)**. % 299.95/300.40 204039[19:Res:167219.1,203427.0] || equal(singleton(unordered_pair(u,v)),ordinal_numbers)** -> . % 299.95/300.40 204022[19:Res:167219.1,203426.0] || equal(singleton(ordered_pair(u,v)),ordinal_numbers)** -> . % 299.95/300.40 203432[19:Res:203242.1,9733.0] || subclass(unordered_pair(singleton(u),v),ordinal_numbers)* -> . % 299.95/300.40 203429[19:Res:203242.1,9732.0] || subclass(unordered_pair(u,singleton(v)),ordinal_numbers)* -> . % 299.95/300.40 203427[19:Res:203242.1,48400.0] || subclass(singleton(unordered_pair(u,v)),ordinal_numbers)* -> . % 299.95/300.40 203426[19:Res:203242.1,48410.0] || subclass(singleton(ordered_pair(u,v)),ordinal_numbers)* -> . % 299.95/300.40 203693[19:Res:167219.1,203447.0] || equal(unordered_pair(u,regular(element_relation)),ordinal_numbers)** -> . % 299.95/300.40 203688[19:Res:167219.1,203445.0] || equal(unordered_pair(regular(element_relation),u),ordinal_numbers)** -> . % 299.95/300.40 203447[19:Res:203242.1,197178.0] || subclass(unordered_pair(u,regular(element_relation)),ordinal_numbers)* -> . % 299.95/300.40 203445[19:Res:203242.1,197154.0] || subclass(unordered_pair(regular(element_relation),u),ordinal_numbers)* -> . % 299.95/300.40 203528[19:MRR:187099.1,203525.0] || subclass(complement(inverse(ordinal_numbers)),symmetrization_of(ordinal_numbers))* -> . % 299.95/300.40 203655[23:Res:167219.1,203446.0] || equal(unordered_pair(u,ordinal_numbers),ordinal_numbers)** -> . % 299.95/300.40 177417[19:Res:53.0,168644.0] || subclass(universal_class,u)+ well_ordering(omega,u)* -> equal(integer_of(ordered_pair(omega,least(omega,universal_class))),ordinal_numbers)**. % 299.95/300.40 203650[23:Res:167219.1,203444.0] || equal(unordered_pair(ordinal_numbers,u),ordinal_numbers)** -> . % 299.95/300.40 203610[19:Res:167219.1,203425.0] || equal(singleton(singleton(u)),ordinal_numbers)** -> . % 299.95/300.40 203446[23:Res:203242.1,183954.0] || subclass(unordered_pair(u,ordinal_numbers),ordinal_numbers)* -> . % 299.95/300.40 203444[23:Res:203242.1,183930.0] || subclass(unordered_pair(ordinal_numbers,u),ordinal_numbers)* -> . % 299.95/300.40 16468[0:Res:2526.2,897.0] || subclass(u,restrict(v,w,x))*+ -> subclass(u,y) member(not_subclass_element(u,y),v)*. % 299.95/300.40 203425[19:Res:203242.1,9731.0] || subclass(singleton(singleton(u)),ordinal_numbers)* -> . % 299.95/300.40 203525[19:Res:167219.1,203481.0] || equal(complement(inverse(ordinal_numbers)),ordinal_numbers)** -> . % 299.95/300.40 203519[19:Res:167219.1,203480.0] || equal(complement(singleton(ordinal_numbers)),ordinal_numbers)** -> . % 299.95/300.40 203513[19:Res:167219.1,203451.0] || equal(singleton(regular(element_relation)),ordinal_numbers)** -> . % 299.95/300.40 202277[26:MRR:201485.2,167057.0] || member(u,cross_product(universal_class,universal_class)) member(u,complement(compose(complement(element_relation),inverse(element_relation))))* -> . % 299.95/300.40 203481[19:MRR:203383.1,167196.0] || subclass(complement(inverse(ordinal_numbers)),ordinal_numbers)* -> . % 299.95/300.40 203480[19:MRR:203382.1,180092.0] || subclass(complement(singleton(ordinal_numbers)),ordinal_numbers)* -> . % 299.95/300.40 203451[19:Res:203242.1,197148.0] || subclass(singleton(regular(element_relation)),ordinal_numbers)* -> . % 299.95/300.40 202320[26:MRR:202319.1,166995.0] || transitive(complement(compose(complement(element_relation),inverse(element_relation))),universal_class)* -> equal(compose(ordinal_numbers,ordinal_numbers),ordinal_numbers). % 299.95/300.40 203007[19:Res:167355.1,202966.0] || equal(sum_class(ordinal_numbers),ordinal_numbers) -> asymmetric(sum_class(ordinal_numbers),u)*. % 299.95/300.40 200995[26:Rew:200916.0,153308.0] || equal(compose(ordinal_numbers,ordinal_numbers),ordinal_numbers) -> transitive(complement(compose(complement(element_relation),inverse(element_relation))),universal_class)*. % 299.95/300.40 203000[19:Res:167219.1,202966.0] || equal(ordinal_numbers,u) -> asymmetric(u,v)*. % 299.95/300.40 202966[19:Obv:202965.1] || subclass(u,ordinal_numbers)*+ -> asymmetric(u,v)*. % 299.95/300.40 197859[19:Res:168474.2,167057.0] || subclass(u,ordinal_numbers) -> equal(intersection(u,v),ordinal_numbers)**. % 299.95/300.40 202766[19:Res:167219.1,202732.0] || equal(inverse(u),ordinal_numbers) -> asymmetric(u,v)*. % 299.95/300.40 200993[26:Rew:200916.0,153307.0] || subclass(compose(ordinal_numbers,ordinal_numbers),ordinal_numbers) -> transitive(complement(compose(complement(element_relation),inverse(element_relation))),universal_class)*. % 299.95/300.40 202732[19:Obv:202731.1] || subclass(inverse(u),ordinal_numbers)*+ -> asymmetric(u,v)*. % 299.95/300.40 197295[19:Res:168469.2,167057.0] || subclass(u,ordinal_numbers) -> equal(intersection(v,u),ordinal_numbers)**. % 299.95/300.40 201795[26:Rew:200916.0,201043.1] || equal(sum_class(ordinal_numbers),ordinal_numbers) well_ordering(element_relation,ordinal_numbers)* -> . % 299.95/300.40 201793[26:Rew:200916.0,201041.1] || subclass(sum_class(ordinal_numbers),ordinal_numbers)* well_ordering(element_relation,ordinal_numbers) -> . % 299.95/300.40 200982[26:Rew:200916.0,153288.0] || -> equal(image(complement(compose(complement(element_relation),inverse(element_relation))),universal_class),range_of(ordinal_numbers))**. % 299.95/300.40 200988[26:Rew:200916.0,163274.1] inductive(compose(subset_relation,subset_relation)) || transitive(ordinal_numbers,universal_class)* -> . % 299.95/300.40 202521[26:SoR:202520.0,72.1] one_to_one(subset_relation) || -> . % 299.95/300.40 202520[26:SoR:201762.0,5484.1] function(subset_relation) || -> . % 299.95/300.40 201762[26:MRR:200917.1,192574.0] single_valued_class(subset_relation) || -> . % 299.95/300.40 200984[26:Rew:200916.0,153199.0] || -> equal(restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class),ordinal_numbers)**. % 299.95/300.40 200916[26:Spt:200907.0] || -> equal(subset_relation,ordinal_numbers)**. % 299.95/300.40 168349[19:Rew:166997.0,80763.0] || -> equal(restrict(u,v,w),ordinal_numbers) member(regular(restrict(u,v,w)),cross_product(v,w))*. % 299.95/300.40 125331[8:Rew:124836.0,17185.0] || -> equal(cantor(restrict(cross_product(u,singleton(v)),w,x)),segment(cross_product(w,x),u,v))**. % 299.95/300.40 16083[0:SpR:29.0,4126.1] || member(u,symmetric_difference(v,cross_product(w,x)))* -> member(u,complement(restrict(v,w,x))). % 299.95/300.40 200647[19:Res:167106.1,200628.0] inductive(symmetric_difference(universal_class,singleton(ordinal_numbers))) || -> . % 299.95/300.40 16086[0:SpR:30.0,4126.1] || member(u,symmetric_difference(cross_product(v,w),x))* -> member(u,complement(restrict(x,v,w))). % 299.95/300.40 16274[0:Rew:160.0,16201.0] || -> subclass(symmetric_difference(u,v),w) member(not_subclass_element(symmetric_difference(u,v),w),complement(intersection(u,v)))*. % 299.95/300.40 197180[19:SpL:196827.0,137176.0] || equal(u,regular(element_relation)) well_ordering(universal_class,u)* -> . % 299.95/300.40 197160[19:SpL:196827.0,135397.0] || subclass(regular(element_relation),u)* well_ordering(universal_class,u) -> . % 299.95/300.40 199565[25:SoR:197131.0,72.1] one_to_one(first(regular(element_relation))) || -> member(ordinal_numbers,regular(element_relation))*. % 299.95/300.40 175965[19:EqF:168361.1,168361.2] || equal(u,v) -> equal(unordered_pair(v,u),ordinal_numbers) equal(regular(unordered_pair(v,u)),v)**. % 299.95/300.40 197186[19:MRR:197165.0,196720.0] || member(second(regular(element_relation)),cantor(first(regular(element_relation))))* -> . % 299.95/300.40 197131[25:SpR:196827.0,193300.1] function(first(regular(element_relation))) || -> member(ordinal_numbers,regular(element_relation))*. % 299.95/300.40 168477[19:Rew:166997.0,80809.0] || -> equal(intersection(intersection(u,v),w),ordinal_numbers) member(regular(intersection(intersection(u,v),w)),v)*. % 299.95/300.40 197702[19:Obv:197679.0] || -> equal(intersection(complement(u),intersection(v,u)),ordinal_numbers)**. % 299.95/300.40 168476[19:Rew:166997.0,80810.0] || -> equal(intersection(intersection(u,v),w),ordinal_numbers) member(regular(intersection(intersection(u,v),w)),u)*. % 299.95/300.40 197499[19:Obv:197478.0] || -> equal(intersection(complement(u),intersection(u,v)),ordinal_numbers)**. % 299.95/300.40 168474[19:Rew:166997.0,80808.1] || subclass(u,v) -> equal(intersection(u,w),ordinal_numbers) member(regular(intersection(u,w)),v)*. % 299.95/300.40 197178[19:SpL:196827.0,48587.0] || subclass(universal_class,complement(unordered_pair(u,regular(element_relation))))* -> . % 299.95/300.40 197177[19:SpL:196827.0,48630.0] || equal(complement(unordered_pair(u,regular(element_relation))),universal_class)** -> . % 299.95/300.40 197154[19:SpL:196827.0,48618.0] || subclass(universal_class,complement(unordered_pair(regular(element_relation),u)))* -> . % 299.95/300.40 197153[19:SpL:196827.0,48663.0] || equal(complement(unordered_pair(regular(element_relation),u)),universal_class)** -> . % 299.95/300.40 168472[19:Rew:166997.0,80806.0] || -> equal(intersection(u,intersection(v,w)),ordinal_numbers) member(regular(intersection(u,intersection(v,w))),w)*. % 299.95/300.40 197148[19:SpL:196827.0,48410.0] || subclass(universal_class,complement(singleton(regular(element_relation))))* -> . % 299.95/300.40 197147[19:SpL:196827.0,48430.0] || equal(complement(singleton(regular(element_relation))),universal_class)** -> . % 299.95/300.40 197122[19:SpR:196827.0,945.0] || -> member(singleton(first(regular(element_relation))),regular(element_relation))*. % 299.95/300.40 168471[19:Rew:166997.0,80807.0] || -> equal(intersection(u,intersection(v,w)),ordinal_numbers) member(regular(intersection(u,intersection(v,w))),v)*. % 299.95/300.40 197146[19:SpL:196827.0,9712.0] || subclass(universal_class,complement(regular(element_relation)))* -> . % 299.95/300.40 197145[19:SpL:196827.0,9769.0] || equal(complement(regular(element_relation)),universal_class)** -> . % 299.95/300.40 197173[19:SpL:196827.0,167176.0] || equal(regular(element_relation),ordinal_numbers)** -> . % 299.95/300.40 197172[19:SpL:196827.0,167175.0] || subclass(regular(element_relation),ordinal_numbers)* -> . % 299.95/300.40 168469[19:Rew:166997.0,80805.1] || subclass(u,v) -> equal(intersection(w,u),ordinal_numbers) member(regular(intersection(w,u)),v)*. % 299.95/300.40 197163[19:SpL:196827.0,137177.0] || well_ordering(universal_class,regular(element_relation))* -> . % 299.95/300.40 196827[19:Res:196720.0,18.0] || -> equal(ordered_pair(first(regular(element_relation)),second(regular(element_relation))),regular(element_relation))**. % 299.95/300.40 196813[19:SpL:196737.0,182439.1] || subclass(rest_relation,rest_of(regular(element_relation)))* well_ordering(universal_class,ordinal_numbers) -> . % 299.95/300.40 168467[19:Rew:166997.0,80802.2] inductive(domain_of(restrict(u,v,w))) || section(u,w,v)* -> member(ordinal_numbers,w). % 299.95/300.40 197048[19:Res:7.1,196852.0] || equal(singleton(u),universal_class)**+ -> equal(regular(element_relation),u)*. % 299.95/300.40 197071[19:MRR:169315.1,197070.0] || member(not_subclass_element(element_relation,ordinal_numbers),complement(compose(element_relation,universal_class)))* -> . % 299.95/300.40 197070[19:MRR:197062.0,289.0] || subclass(element_relation,ordinal_numbers)* -> . % 299.95/300.40 168465[19:Rew:166997.0,163207.2] inductive(cantor(restrict(u,v,w))) || section(u,w,v)* -> member(ordinal_numbers,w). % 299.95/300.40 196852[19:Res:196731.1,4178.0] || subclass(universal_class,singleton(u))* -> equal(regular(element_relation),u). % 299.95/300.40 196735[19:Res:196718.0,176273.0] || subclass(domain_relation,rest_relation) -> equal(rest_of(regular(element_relation)),ordinal_numbers)**. % 299.95/300.40 168251[19:Rew:166997.0,80699.2] || member(u,regular(v))*+ member(u,v) -> equal(v,ordinal_numbers) member(u,w)*. % 299.95/300.40 196734[19:Res:196718.0,176274.0] || subclass(rest_relation,domain_relation) -> equal(rest_of(regular(element_relation)),ordinal_numbers)**. % 299.95/300.40 196731[19:Res:196718.0,2.0] || subclass(universal_class,u) -> member(regular(element_relation),u)*. % 299.95/300.40 196834[19:Res:7.1,196830.0] || equal(complement(cross_product(universal_class,universal_class)),element_relation)** -> . % 299.95/300.40 196830[19:MRR:196828.1,167005.0] || subclass(element_relation,complement(cross_product(universal_class,universal_class)))* -> . % 299.95/300.40 167812[19:Rew:166997.0,80633.3] inductive(not_well_ordering(u,v)) || connected(u,v) -> well_ordering(u,v)* member(ordinal_numbers,v). % 299.95/300.40 196736[19:Res:196718.0,177583.1] || equal(rest_of(regular(element_relation)),rest_relation)** -> . % 299.95/300.40 196720[19:Res:289.0,196698.0] || -> member(regular(element_relation),cross_product(universal_class,universal_class))*. % 299.95/300.40 196737[19:Res:196718.0,176206.0] || -> equal(cantor(regular(element_relation)),ordinal_numbers)**. % 299.95/300.40 196742[25:SoR:196732.0,72.1] one_to_one(regular(element_relation)) || -> . % 299.95/300.40 167729[19:Rew:166997.0,80621.1] || subclass(u,symmetric_difference(v,w)) -> equal(u,ordinal_numbers) member(regular(u),union(v,w))*. % 299.95/300.40 196732[25:Res:196718.0,193595.1] function(regular(element_relation)) || -> . % 299.95/300.40 196718[19:Res:5.0,196698.0] || -> member(regular(element_relation),universal_class)*. % 299.95/300.40 196698[19:MRR:196651.1,167005.0] || subclass(cross_product(universal_class,universal_class),u)* -> member(regular(element_relation),u). % 299.95/300.40 196618[20:MRR:196611.1,187485.0] inductive(singleton(not_subclass_element(inverse(ordinal_numbers),ordinal_numbers))) || -> . % 299.95/300.40 167728[19:Rew:166997.0,80622.2] || subclass(u,v)*+ subclass(v,w)* -> equal(u,ordinal_numbers) member(regular(u),w)*. % 299.95/300.40 196602[20:MRR:196597.1,181757.0] || -> subclass(singleton(not_subclass_element(inverse(ordinal_numbers),ordinal_numbers)),symmetrization_of(ordinal_numbers))*. % 299.95/300.40 190819[19:Rew:190665.0,190800.1] || member(not_subclass_element(u,ordinal_numbers),complement(u))* -> subclass(u,ordinal_numbers). % 299.95/300.40 189434[8:Res:188742.1,158050.0] || equal(complement(complement(symmetrization_of(u))),universal_class)**+ -> connected(u,v)*. % 299.95/300.40 189173[19:Res:188649.1,167174.0] || equal(complement(compose(u,inverse(u))),universal_class)** -> single_valued_class(u). % 299.95/300.40 79960[0:Res:2526.2,158.0] || subclass(u,omega) -> subclass(u,v) equal(integer_of(not_subclass_element(u,v)),not_subclass_element(u,v))**. % 299.95/300.40 189065[2:Res:188649.1,8596.1] single_valued_class(u) || equal(complement(u),universal_class)** -> function(u). % 299.95/300.40 196497[19:Obv:196496.1] || equal(complement(inverse(u)),universal_class)**+ -> asymmetric(u,v)*. % 299.95/300.40 188752[19:Res:167340.1,188593.1] || equal(complement(u),universal_class) -> equal(intersection(v,u),ordinal_numbers)**. % 299.95/300.40 196273[19:Obv:196272.1] || equal(complement(u),universal_class) -> asymmetric(u,v)*. % 299.95/300.40 28086[0:Res:7.1,2497.1] || equal(u,complement(v))*+ member(w,universal_class)* -> member(w,v)* member(w,u)*. % 299.95/300.40 188655[19:Res:167341.1,188593.1] || equal(complement(u),universal_class) -> equal(intersection(u,v),ordinal_numbers)**. % 299.95/300.40 196068[19:Res:7.1,195678.1] || equal(complement(u),domain_relation)** equal(rotate(u),rest_relation) -> . % 299.95/300.40 195719[19:Res:7.1,195563.1] || equal(flip(u),domain_relation) equal(complement(u),domain_relation)** -> . % 299.95/300.40 195678[19:Res:7.1,195414.0] || equal(rotate(u),rest_relation) subclass(domain_relation,complement(u))* -> . % 299.95/300.40 16351[0:Res:297.1,25.1] || member(not_subclass_element(intersection(u,complement(v)),w),v)* -> subclass(intersection(u,complement(v)),w). % 299.95/300.40 195673[2:Res:7.1,195406.0] || equal(rotate(u),rest_relation) equal(complement(u),universal_class)** -> . % 299.95/300.40 195669[0:Res:7.1,195397.0] || equal(rotate(u),rest_relation) subclass(universal_class,complement(u))* -> . % 299.95/300.40 195664[2:Res:7.1,195304.0] || equal(flip(u),rest_relation) equal(complement(u),universal_class)** -> . % 299.95/300.40 16224[0:Res:315.1,25.1] || member(not_subclass_element(intersection(complement(u),v),w),u)* -> subclass(intersection(complement(u),v),w). % 299.95/300.40 195635[0:Res:7.1,195297.0] || equal(flip(u),rest_relation) subclass(universal_class,complement(u))* -> . % 299.95/300.40 195630[19:Res:7.1,195218.1] || equal(rotate(u),domain_relation) equal(complement(u),domain_relation)** -> . % 299.95/300.40 195613[25:SoR:195048.0,72.1] one_to_one(cantor(u)) || equal(complement(rest_of(u)),universal_class)** -> . % 299.95/300.40 195563[19:Res:7.1,194014.1] || equal(complement(u),domain_relation) subclass(domain_relation,flip(u))* -> . % 299.95/300.40 195414[19:MRR:195405.1,940.0] || subclass(rest_relation,rotate(u))* subclass(domain_relation,complement(u)) -> . % 299.95/300.40 195406[2:Res:27189.1,188593.1] || subclass(rest_relation,rotate(u))* equal(complement(u),universal_class) -> . % 299.95/300.40 195397[0:Res:27189.1,6476.1] || subclass(rest_relation,rotate(u))* subclass(universal_class,complement(u)) -> . % 299.95/300.40 195304[2:Res:27190.1,188593.1] || subclass(rest_relation,flip(u))* equal(complement(u),universal_class) -> . % 299.95/300.40 16913[0:Rew:4105.0,16889.0] || -> subclass(symmetric_difference(u,inverse(u)),v) member(not_subclass_element(symmetric_difference(u,inverse(u)),v),symmetrization_of(u))*. % 299.95/300.40 195297[0:Res:27190.1,6476.1] || subclass(rest_relation,flip(u))* subclass(universal_class,complement(u)) -> . % 299.95/300.40 195218[19:Res:7.1,194013.1] || equal(complement(u),domain_relation) subclass(domain_relation,rotate(u))* -> . % 299.95/300.40 195076[25:SoR:193173.0,72.1] one_to_one(flip(cross_product(u,universal_class))) || -> equal(inverse(u),universal_class)**. % 299.95/300.40 195050[25:SoR:193168.0,72.1] one_to_one(restrict(element_relation,universal_class,u)) || -> equal(sum_class(u),universal_class)**. % 299.95/300.40 168375[19:Rew:166997.0,84838.2] || subclass(omega,u)*+ subclass(u,v)* -> equal(integer_of(w),ordinal_numbers) member(w,v)*. % 299.95/300.40 195048[25:SoR:192602.0,5484.1] function(cantor(u)) || equal(complement(rest_of(u)),universal_class)** -> . % 299.95/300.40 194014[19:MRR:194003.1,940.0] || subclass(domain_relation,flip(u)) subclass(domain_relation,complement(u))* -> . % 299.95/300.40 168374[19:Rew:166997.0,84849.1] || subclass(omega,symmetric_difference(u,v)) -> equal(integer_of(w),ordinal_numbers) member(w,union(u,v))*. % 299.95/300.40 195427[19:Res:7.1,195411.0] || equal(rotate(domain_relation),rest_relation)**+ -> equal(ordinal_numbers,u)*. % 299.95/300.40 15078[0:Res:2483.2,897.0] || member(u,universal_class) subclass(universal_class,restrict(v,w,x))*+ -> member(power_class(u),v)*. % 299.95/300.40 195411[19:Rew:176363.0,195403.1] || subclass(rest_relation,rotate(domain_relation))*+ -> equal(ordinal_numbers,u)*. % 299.95/300.40 195419[19:Res:7.1,195375.0] || equal(rotate(ordinal_numbers),rest_relation)** -> . % 299.95/300.40 195375[19:Res:27189.1,167057.0] || subclass(rest_relation,rotate(ordinal_numbers))* -> . % 299.95/300.40 27189[0:MRR:27183.0,940.0] || subclass(rest_relation,rotate(u)) -> member(ordered_pair(ordered_pair(v,rest_of(ordered_pair(w,v))),w),u)*. % 299.95/300.40 195314[19:Res:7.1,195278.0] || equal(flip(ordinal_numbers),rest_relation)** -> . % 299.95/300.40 195278[19:Res:27190.1,167057.0] || subclass(rest_relation,flip(ordinal_numbers))* -> . % 299.95/300.40 27190[0:MRR:27182.0,940.0] || subclass(rest_relation,flip(u)) -> member(ordered_pair(ordered_pair(v,w),rest_of(ordered_pair(w,v))),u)*. % 299.95/300.40 194013[19:MRR:193988.1,940.0] || subclass(domain_relation,rotate(u)) subclass(domain_relation,complement(u))* -> . % 299.95/300.40 193865[25:SpR:193832.1,146278.0] one_to_one(cross_product(u,universal_class)) || -> equal(image(universal_class,u),universal_class)**. % 299.95/300.40 193305[25:SpR:193223.1,946.0] function(u) || -> equal(ordered_pair(ordinal_numbers,u),singleton(singleton(ordinal_numbers)))**. % 299.95/300.40 193173[25:SpR:192881.1,125707.0] function(flip(cross_product(u,universal_class))) || -> equal(inverse(u),universal_class)**. % 299.95/300.40 15112[0:Res:2482.2,897.0] || member(u,universal_class) subclass(universal_class,restrict(v,w,x))*+ -> member(sum_class(u),v)*. % 299.95/300.40 193168[25:SpR:192881.1,125772.0] function(restrict(element_relation,universal_class,u)) || -> equal(sum_class(u),universal_class)**. % 299.95/300.40 192607[25:MRR:16139.2,192606.0] single_valued_class(singleton(u)) || member(u,cross_product(universal_class,universal_class))* -> . % 299.95/300.40 192602[25:MRR:183423.2,192574.0] single_valued_class(cantor(u)) || equal(complement(rest_of(u)),universal_class)** -> . % 299.95/300.40 176249[19:Rew:176206.1,158515.2] || member(u,universal_class) subclass(domain_relation,intersection(v,w))*+ -> member(ordered_pair(u,ordinal_numbers),w)*. % 299.95/300.40 190075[20:Res:7.1,188787.0] || equal(u,inverse(ordinal_numbers)) equal(complement(u),universal_class)** -> . % 299.95/300.40 190062[20:Res:7.1,188786.0] || equal(u,symmetrization_of(ordinal_numbers))*+ equal(complement(u),universal_class)** -> . % 299.95/300.40 176243[19:Rew:176206.1,158518.2] || member(u,universal_class) subclass(domain_relation,intersection(v,w))*+ -> member(ordered_pair(u,ordinal_numbers),v)*. % 299.95/300.40 189608[19:MRR:189564.2,189536.0] || equal(power_class(u),universal_class) well_ordering(element_relation,power_class(u))* -> . % 299.95/300.40 167580[19:Rew:166997.0,158454.2] || member(u,universal_class) -> member(u,cantor(v))* equal(apply(v,u),sum_class(range_of(ordinal_numbers))). % 299.95/300.40 192318[19:Res:2479.1,192214.0] || subclass(universal_class,cantor(complement(cross_product(singleton(singleton(u)),universal_class))))* -> . % 299.95/300.40 194332[25:SoR:193813.0,72.1] one_to_one(apply(choice,omega)) || -> equal(apply(choice,omega),ordinal_numbers)**. % 299.95/300.40 193813[25:SpR:193675.1,6468.0] function(apply(choice,omega)) || -> equal(apply(choice,omega),ordinal_numbers)**. % 299.95/300.40 169002[19:Rew:166997.0,81002.2] || well_ordering(u,universal_class) member(least(u,complement(v)),v)* -> equal(complement(v),ordinal_numbers). % 299.95/300.40 194275[25:SoR:194240.0,72.1] one_to_one(intersection(singleton(u),v)) || -> member(u,v)*. % 299.95/300.40 194272[25:SoR:194239.0,72.1] one_to_one(intersection(u,singleton(v))) || -> member(v,u)*. % 299.95/300.40 194240[25:SoR:192600.0,5484.1] function(intersection(singleton(u),v)) || -> member(u,v)*. % 299.95/300.40 194239[25:SoR:192599.0,5484.1] function(intersection(u,singleton(v))) || -> member(v,u)*. % 299.95/300.40 168502[19:Rew:166997.0,84893.1] || subclass(omega,u) -> equal(integer_of(not_subclass_element(complement(u),v)),ordinal_numbers)** subclass(complement(u),v). % 299.95/300.40 192600[25:MRR:167385.2,192574.0] single_valued_class(intersection(singleton(u),v)) || -> member(u,v)*. % 299.95/300.40 192599[25:MRR:167384.2,192574.0] single_valued_class(intersection(u,singleton(v))) || -> member(v,u)*. % 299.95/300.40 194168[25:SoR:193246.0,72.1] one_to_one(least(u,omega)) || well_ordering(u,omega)* -> . % 299.95/300.40 168499[19:Rew:166997.0,158416.1] || subclass(omega,rest_of(u))+ -> equal(integer_of(ordered_pair(v,w)),ordinal_numbers)** member(v,cantor(u))*. % 299.95/300.40 194165[25:SoR:193245.0,72.1] one_to_one(least(u,omega)) || well_ordering(u,universal_class)* -> . % 299.95/300.40 194162[25:SoR:193244.0,72.1] one_to_one(least(u,rest_relation)) || well_ordering(u,universal_class)* -> . % 299.95/300.40 194159[25:SoR:193243.0,72.1] one_to_one(least(u,rest_relation)) || well_ordering(u,rest_relation)* -> . % 299.95/300.40 194136[25:SoR:193242.0,72.1] one_to_one(least(u,universal_class)) || well_ordering(u,universal_class)* -> . % 299.95/300.40 193246[25:MRR:193195.2,9070.0] function(least(u,omega)) || well_ordering(u,omega)* -> . % 299.95/300.40 193245[25:MRR:193194.2,9070.0] function(least(u,omega)) || well_ordering(u,universal_class)* -> . % 299.95/300.40 193244[25:MRR:193193.2,9070.0] function(least(u,rest_relation)) || well_ordering(u,universal_class)* -> . % 299.95/300.40 193243[25:MRR:193192.2,9070.0] function(least(u,rest_relation)) || well_ordering(u,rest_relation)* -> . % 299.95/300.40 4727[0:SpL:946.0,97.0] || member(ordered_pair(u,singleton(singleton(singleton(v)))),composition_function)* -> equal(compose(u,singleton(v)),v). % 299.95/300.40 193242[25:MRR:193191.2,9070.0] function(least(u,universal_class)) || well_ordering(u,universal_class)* -> . % 299.95/300.40 192819[25:SoR:192606.0,167213.2] single_valued_class(singleton(u)) || equal(singleton(u),ordinal_numbers)** -> . % 299.95/300.40 194124[19:Res:7.1,194106.0] || equal(rest_of(u),domain_relation)** -> . % 299.95/300.40 194106[19:MRR:181826.1,194104.1] || subclass(domain_relation,rest_of(u))* -> . % 299.95/300.40 194044[23:Res:7.1,194010.1] || equal(complement(rest_relation),domain_relation) subclass(rest_relation,domain_relation)* -> . % 299.95/300.40 194037[25:SoR:193959.0,72.1] one_to_one(complement(kind_1_ordinals)) || equal(complement(kind_1_ordinals),ordinal_numbers)** -> . % 299.95/300.40 194010[23:MRR:193998.1,167011.0] || subclass(rest_relation,domain_relation) subclass(domain_relation,complement(rest_relation))* -> . % 299.95/300.40 193959[25:SoR:192601.0,5484.1] function(complement(kind_1_ordinals)) || equal(complement(kind_1_ordinals),ordinal_numbers)** -> . % 299.95/300.40 176244[19:Rew:176206.1,158517.2] || member(u,universal_class) subclass(domain_relation,complement(v)) member(ordered_pair(u,ordinal_numbers),v)* -> . % 299.95/300.40 192601[25:MRR:169165.2,192574.0] single_valued_class(complement(kind_1_ordinals)) || equal(complement(kind_1_ordinals),ordinal_numbers)** -> . % 299.95/300.40 193956[25:SoR:193239.0,72.1] one_to_one(not_subclass_element(u,v)) || -> subclass(u,v)*. % 299.95/300.40 193239[25:MRR:193189.2,9070.0] function(not_subclass_element(u,v)) || -> subclass(u,v)*. % 299.95/300.40 193934[25:SoR:193238.0,72.1] function(u) one_to_one(apply(u,v)) || -> . % 299.95/300.40 193844[25:Rew:193832.1,34661.2] one_to_one(u) || subclass(range_of(inverse(u)),v) -> maps(inverse(u),universal_class,v)*. % 299.95/300.40 193300[25:SpR:193223.1,945.0] function(u) || -> member(ordinal_numbers,ordered_pair(u,v))*. % 299.95/300.40 193238[25:MRR:193188.2,9070.0] function(apply(u,v)) function(u) || -> . % 299.95/300.40 193848[25:Rew:193833.1,193836.2] one_to_one(inverse(u)) || subclass(universal_class,v) -> maps(inverse(u),universal_class,v)*. % 299.95/300.40 193921[25:SoR:193235.0,72.1] one_to_one(rest_of(u)) || member(u,universal_class)* -> . % 299.95/300.40 193918[25:SoR:193234.0,72.1] one_to_one(power_class(u)) || member(u,universal_class)* -> . % 299.95/300.40 193884[25:SoR:193233.0,72.1] one_to_one(sum_class(u)) || member(u,universal_class)* -> . % 299.95/300.40 193833[25:SoR:193167.0,72.1] one_to_one(inverse(u)) || -> equal(range_of(u),universal_class)**. % 299.95/300.40 192935[25:Rew:192881.1,126279.2] 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)*. % 299.95/300.40 193235[25:MRR:193185.2,9070.0] function(rest_of(u)) || member(u,universal_class)* -> . % 299.95/300.40 193234[25:MRR:193184.2,9070.0] function(power_class(u)) || member(u,universal_class)* -> . % 299.95/300.40 192943[25:Rew:192881.1,126244.2] 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)))*. % 299.95/300.40 193233[25:MRR:193176.2,9070.0] function(sum_class(u)) || member(u,universal_class)* -> . % 299.95/300.40 193832[25:SoR:193167.0,73.1] one_to_one(u) || -> equal(range_of(u),universal_class)**. % 299.95/300.40 193167[25:SpR:192881.1,124908.0] function(inverse(u)) || -> equal(range_of(u),universal_class)**. % 299.95/300.40 193824[25:SoR:193247.0,72.1] one_to_one(complement(cross_product(singleton(singleton(u)),universal_class))) || -> . % 299.95/300.40 192938[25:Rew:192881.1,126180.2] 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))*. % 299.95/300.40 193247[25:Obv:193214.1] function(complement(cross_product(singleton(singleton(u)),universal_class))) || -> . % 299.95/300.40 193675[25:Res:167115.1,193595.1] function(u) || -> equal(integer_of(u),ordinal_numbers)**. % 299.95/300.40 193647[25:SoR:193232.0,72.1] one_to_one(regular(u)) || -> equal(u,ordinal_numbers)*. % 299.95/300.40 192939[25:Rew:192881.1,126153.2] function(u) || subclass(range_of(u),range_of(v)) equal(cantor(cantor(w)),universal_class) -> compatible(u,w,flip(cross_product(v,universal_class)))*. % 299.95/300.40 193595[25:MRR:193303.2,167057.0] function(u) || member(u,universal_class)* -> . % 299.95/300.40 193272[25:SoR:193067.1,72.1] function(u) one_to_one(cantor(u)) || -> . % 299.95/300.40 193232[25:MRR:193181.2,9070.0] function(regular(u)) || -> equal(u,ordinal_numbers)*. % 299.95/300.40 193223[25:MRR:193165.2,9070.0] function(u) || -> equal(singleton(u),ordinal_numbers)**. % 299.95/300.40 192940[25:Rew:192881.1,126142.2] function(u) || subclass(range_of(u),cantor(range_of(v)))*+ equal(cantor(cantor(w)),universal_class) -> compatible(u,w,inverse(v))*. % 299.95/300.40 193067[25:MRR:193066.2,160357.0] function(u) function(cantor(u)) || -> . % 299.95/300.40 193269[25:SoR:193222.0,72.1] one_to_one(ordered_pair(u,v)) || -> . % 299.95/300.40 193262[25:SoR:193221.0,72.1] one_to_one(unordered_pair(u,v)) || -> . % 299.95/300.40 193222[25:MRR:193183.1,9070.0] function(ordered_pair(u,v)) || -> . % 299.95/300.40 192941[25:Rew:192881.1,126130.2] function(u) || equal(cantor(cantor(v)),range_of(u)) equal(cantor(cantor(w)),universal_class) -> compatible(u,w,v)*. % 299.95/300.40 193221[25:MRR:193182.1,9070.0] function(unordered_pair(u,v)) || -> . % 299.95/300.40 193259[25:SoR:193220.0,72.1] one_to_one(regular(symmetrization_of(ordinal_numbers))) || -> . % 299.95/300.40 193220[25:MRR:193180.1,9070.0] function(regular(symmetrization_of(ordinal_numbers))) || -> . % 299.95/300.40 192881[25:Res:192616.1,1063.0] function(u) || -> equal(cantor(u),universal_class)**. % 299.95/300.40 192942[25:Rew:192881.1,126129.2] function(u) || subclass(range_of(u),cantor(cantor(v)))*+ equal(cantor(cantor(w)),universal_class) -> compatible(u,w,v)*. % 299.95/300.40 193103[25:SoR:192884.0,72.1] one_to_one(complement(cross_product(singleton(ordinal_numbers),universal_class))) || -> . % 299.95/300.40 193100[25:SoR:192883.0,72.1] one_to_one(complement(cross_product(singleton(omega),universal_class))) || -> . % 299.95/300.40 192884[25:Res:192616.1,192345.0] function(complement(cross_product(singleton(ordinal_numbers),universal_class))) || -> . % 299.95/300.40 192883[25:Res:192616.1,192320.0] function(complement(cross_product(singleton(omega),universal_class))) || -> . % 299.95/300.40 192937[25:Rew:192881.1,124944.2] function(u) || subclass(range_of(u),v) -> maps(u,universal_class,v)*. % 299.95/300.40 192915[25:MRR:87.1,192913.0] || homomorphism(u,v,w)* -> . % 299.95/300.40 192913[25:SSi:192882.0,79.1] operation(u) || -> . % 299.95/300.40 192596[25:MRR:167061.2,192574.0] single_valued_class(singleton(u)) || -> member(u,universal_class)*. % 299.95/300.40 192595[25:MRR:167069.1,192574.0] single_valued_class(intersection(subset_relation,inverse(subset_relation))) || -> . % 299.95/300.40 192594[25:MRR:167068.1,192574.0] function(intersection(subset_relation,inverse(subset_relation))) || -> . % 299.95/300.40 192593[25:MRR:167067.1,192574.0] one_to_one(intersection(subset_relation,inverse(subset_relation))) || -> . % 299.95/300.40 192816[25:SoR:192606.0,72.1] one_to_one(singleton(u)) || -> . % 299.95/300.40 192606[25:MRR:192597.1,192605.1] function(singleton(u)) || -> . % 299.95/300.40 192590[25:MRR:170804.1,192574.0] one_to_one(recursion_equation_functions(u)) || -> . % 299.95/300.40 192589[25:MRR:170803.1,192574.0] function(recursion_equation_functions(u)) || -> . % 299.95/300.40 192694[25:SoR:192574.0,72.1] one_to_one(ordinal_numbers) || -> . % 299.95/300.40 192586[25:MRR:170531.1,192574.0] one_to_one(identity_relation) || -> . % 299.95/300.40 192585[25:MRR:170285.1,192574.0] function(identity_relation) || -> . % 299.95/300.40 192584[25:MRR:169755.1,192574.0] single_valued_class(ordinal_numbers) || -> . % 299.95/300.40 192583[25:MRR:167081.1,192574.0] single_valued_class(singleton_relation) || -> . % 299.95/300.40 192582[25:MRR:167080.1,192574.0] single_valued_class(identity_relation) || -> . % 299.95/300.40 192588[25:MRR:170346.1,192574.0] single_valued_class(recursion_equation_functions(u)) || -> . % 299.95/300.40 192581[25:MRR:167079.1,192574.0] function(singleton_relation) || -> . % 299.95/300.40 192580[25:MRR:167078.1,192574.0] one_to_one(singleton_relation) || -> . % 299.95/300.40 192578[25:MRR:167076.1,192574.0] single_valued_class(union_of_range_map) || -> . % 299.95/300.40 192577[25:MRR:167075.1,192574.0] function(union_of_range_map) || -> . % 299.95/300.40 192576[25:MRR:167074.1,192574.0] one_to_one(union_of_range_map) || -> . % 299.95/300.40 192574[25:MRR:171074.1,192573.1] function(ordinal_numbers) || -> . % 299.95/300.40 192316[19:Res:144532.1,192214.0] || equal(cantor(complement(cross_product(singleton(singleton(u)),universal_class))),universal_class)** -> . % 299.95/300.40 192344[19:Res:169181.1,192214.0] || equal(cantor(complement(cross_product(singleton(ordinal_numbers),universal_class))),singleton(ordinal_numbers))** -> . % 299.95/300.40 192241[23:SpR:192178.0,183885.0] || -> equal(apply(complement(cross_product(ordinal_numbers,universal_class)),universal_class),sum_class(range_of(ordinal_numbers)))**. % 299.95/300.40 192346[19:Res:167087.1,192214.0] || equal(cantor(complement(cross_product(singleton(ordinal_numbers),universal_class))),universal_class)** -> . % 299.95/300.40 192345[19:Res:167104.1,192214.0] || subclass(universal_class,cantor(complement(cross_product(singleton(ordinal_numbers),universal_class))))* -> . % 299.95/300.40 192343[22:Res:177171.1,192214.0] || subclass(omega,cantor(complement(cross_product(singleton(ordinal_numbers),universal_class))))* -> . % 299.95/300.40 192342[22:Res:178902.1,192214.0] || equal(cantor(complement(cross_product(singleton(ordinal_numbers),universal_class))),omega)** -> . % 299.95/300.40 192320[19:Res:2478.1,192214.0] || subclass(universal_class,cantor(complement(cross_product(singleton(omega),universal_class))))* -> . % 299.95/300.40 168479[19:Rew:166997.0,81091.0] || -> equal(intersection(u,omega),ordinal_numbers) equal(integer_of(regular(intersection(u,omega))),regular(intersection(u,omega)))**. % 299.95/300.40 192319[19:Res:144531.1,192214.0] || equal(cantor(complement(cross_product(singleton(omega),universal_class))),universal_class)** -> . % 299.95/300.40 192347[19:Res:167106.1,192214.0] inductive(cantor(complement(cross_product(singleton(ordinal_numbers),universal_class)))) || -> . % 299.95/300.40 192312[23:SpL:183840.0,192214.0] || member(universal_class,cantor(complement(cross_product(ordinal_numbers,universal_class))))* -> . % 299.95/300.40 192214[19:Obv:192204.1] || member(u,cantor(complement(cross_product(singleton(u),universal_class))))* -> . % 299.95/300.40 168478[19:Rew:166997.0,81090.0] || -> equal(intersection(omega,u),ordinal_numbers) equal(integer_of(regular(intersection(omega,u))),regular(intersection(omega,u)))**. % 299.95/300.40 192178[19:SpR:190384.0,43.0] || -> equal(image(complement(cross_product(u,universal_class)),u),range_of(ordinal_numbers))**. % 299.95/300.40 190384[19:SpR:190219.0,30.0] || -> equal(restrict(complement(cross_product(u,v)),u,v),ordinal_numbers)**. % 299.95/300.40 167733[19:Rew:166997.0,80623.1] || subclass(u,restrict(v,w,x))* -> equal(u,ordinal_numbers) member(regular(u),v). % 299.95/300.40 190944[19:SpR:167191.0,190268.0] || -> equal(symmetric_difference(complement(inverse(ordinal_numbers)),complement(symmetrization_of(ordinal_numbers))),ordinal_numbers)**. % 299.95/300.40 190899[19:SpR:167191.0,190813.0] || -> equal(symmetric_difference(symmetrization_of(ordinal_numbers),complement(inverse(ordinal_numbers))),universal_class)**. % 299.95/300.40 190857[19:SpR:167191.0,190801.0] || -> equal(union(symmetrization_of(ordinal_numbers),complement(inverse(ordinal_numbers))),universal_class)**. % 299.95/300.40 190748[19:SpR:167191.0,190665.0] || -> equal(intersection(symmetrization_of(ordinal_numbers),complement(inverse(ordinal_numbers))),ordinal_numbers)**. % 299.95/300.40 168435[19:Rew:166997.0,84843.1] || subclass(omega,restrict(u,v,w))*+ -> equal(integer_of(x),ordinal_numbers) member(x,u)*. % 299.95/300.40 190955[19:SpR:167191.0,190268.0] || -> equal(symmetric_difference(inverse(ordinal_numbers),symmetrization_of(ordinal_numbers)),ordinal_numbers)**. % 299.95/300.40 168353[19:Rew:166997.0,80767.0] || -> equal(symmetric_difference(u,v),ordinal_numbers) member(regular(symmetric_difference(u,v)),complement(intersection(u,v)))*. % 299.95/300.40 190268[19:Rew:190220.0,148677.0] || -> equal(symmetric_difference(u,complement(complement(u))),ordinal_numbers)**. % 299.95/300.40 168419[19:Rew:166997.0,80786.1] || member(regular(intersection(complement(u),v)),u)* -> equal(intersection(complement(u),v),ordinal_numbers). % 299.95/300.40 190464[19:Rew:190453.0,190463.0] || -> equal(symmetric_difference(u,complement(u)),universal_class)**. % 299.95/300.40 190453[19:Rew:167055.0,190368.0] || -> equal(union(u,complement(u)),universal_class)**. % 299.95/300.40 190219[19:Obv:190211.0] || -> equal(intersection(u,complement(u)),ordinal_numbers)**. % 299.95/300.40 190220[19:Rew:190219.0,144766.0] || -> equal(symmetric_difference(u,u),ordinal_numbers)**. % 299.95/300.40 168418[19:Rew:166997.0,80785.1] || member(regular(intersection(u,complement(v))),v)* -> equal(intersection(u,complement(v)),ordinal_numbers). % 299.95/300.40 189466[19:MRR:189465.1,167011.0] || equal(complement(u),universal_class) well_ordering(element_relation,complement(u))* -> . % 299.95/300.40 189444[19:Res:188742.1,186996.0] || equal(complement(singleton(regular(u))),universal_class)** -> equal(u,ordinal_numbers). % 299.95/300.40 188916[2:Res:188649.1,9780.0] || equal(complement(sum_class(u)),universal_class) -> section(element_relation,u,universal_class)*. % 299.95/300.40 168240[19:Rew:166997.0,80692.1] || well_ordering(u,universal_class) -> equal(singleton(v),ordinal_numbers) equal(least(u,singleton(v)),v)**. % 299.95/300.40 188787[20:Res:175570.1,188593.1] || subclass(inverse(ordinal_numbers),u)* equal(complement(u),universal_class) -> . % 299.95/300.40 188786[20:Res:181635.1,188593.1] || subclass(symmetrization_of(ordinal_numbers),u)* equal(complement(u),universal_class) -> . % 299.95/300.40 188735[19:Res:176419.1,188593.1] || subclass(domain_relation,flip(u))* equal(complement(u),universal_class) -> . % 299.95/300.40 188716[19:Res:176420.1,188593.1] || subclass(domain_relation,rotate(u))* equal(complement(u),universal_class) -> . % 299.95/300.40 188629[2:Res:280.1,188593.1] || member(u,universal_class) equal(complement(singleton(u)),universal_class)** -> . % 299.95/300.40 176276[19:Rew:176206.1,158393.2] || member(u,universal_class) subclass(domain_relation,compose_class(v))*+ -> equal(compose(v,u),ordinal_numbers)**. % 299.95/300.40 176246[19:Rew:176206.1,158394.2] || member(u,universal_class) subclass(domain_relation,singleton(v))*+ -> equal(ordered_pair(u,ordinal_numbers),v)*. % 299.95/300.40 189174[19:Res:188649.1,169211.0] || equal(complement(compose(ordinal_numbers,ordinal_numbers)),universal_class)**+ -> transitive(ordinal_numbers,u)*. % 299.95/300.40 168191[19:Rew:166997.0,84869.1] || subclass(omega,rest_relation) -> equal(integer_of(ordered_pair(u,v)),ordinal_numbers)** equal(rest_of(u),v). % 299.95/300.40 189170[19:Res:188649.1,169324.0] || equal(complement(sum_class(kind_1_ordinals)),universal_class)** well_ordering(element_relation,kind_1_ordinals) -> . % 299.95/300.40 168190[19:Rew:166997.0,84873.1] || subclass(omega,successor_relation) -> equal(integer_of(ordered_pair(u,v)),ordinal_numbers)** equal(successor(u),v). % 299.95/300.40 189433[9:Res:188742.1,160080.0] || equal(complement(compose(element_relation,universal_class)),universal_class)** -> . % 299.95/300.40 189115[2:Res:188649.1,1.0] || equal(complement(image(successor_relation,ordinal_numbers)),universal_class)** -> . % 299.95/300.40 168189[19:Rew:166997.0,158318.1] || subclass(omega,domain_relation) -> equal(integer_of(ordered_pair(u,v)),ordinal_numbers)** equal(cantor(u),v). % 299.95/300.40 189190[19:Res:188649.1,184360.0] || equal(complement(composition_function),universal_class)** -> . % 299.95/300.40 189151[9:Res:188649.1,160080.0] || equal(complement(element_relation),universal_class)** -> . % 299.95/300.40 188649[2:Res:3.1,188593.1] || equal(complement(u),universal_class) -> subclass(u,v)*. % 299.95/300.40 188653[19:Res:167139.1,188593.1] || equal(complement(u),universal_class)** -> equal(u,ordinal_numbers). % 299.95/300.40 188789[20:Res:181628.0,188593.1] || equal(complement(symmetrization_of(ordinal_numbers)),universal_class)** -> . % 299.95/300.40 188593[2:MRR:188533.1,36583.1] || equal(complement(u),universal_class) member(v,u)* -> . % 299.95/300.40 188587[19:Res:167106.1,144545.0] inductive(symmetric_difference(universal_class,u)) || member(ordinal_numbers,u)* -> . % 299.95/300.40 176321[19:Rew:176206.1,176250.1] || member(u,universal_class) equal(successor(u),ordinal_numbers) -> member(ordered_pair(u,ordinal_numbers),successor_relation)*. % 299.95/300.40 188189[19:Res:7.1,186996.0] || equal(complement(singleton(regular(u))),u)** -> equal(u,ordinal_numbers). % 299.95/300.40 188107[19:Res:7.1,184877.0] || equal(flip(cross_product(u,v)),domain_relation)** -> member(ordinal_numbers,v). % 299.95/300.40 187914[19:Res:7.1,181823.0] || equal(cross_product(u,v),domain_relation)**+ -> member(singleton(ordinal_numbers),u)*. % 299.95/300.40 169372[19:Rew:166997.0,167596.0] || -> equal(cross_product(u,universal_class),ordinal_numbers) equal(image(regular(cross_product(u,universal_class)),u),range_of(ordinal_numbers))**. % 299.95/300.40 188292[19:Res:7.1,188285.0] || equal(complement(singleton(singleton(singleton(singleton(ordinal_numbers))))),domain_relation)** -> . % 299.95/300.40 188285[19:MRR:188253.1,167208.0] || subclass(domain_relation,complement(singleton(singleton(singleton(singleton(ordinal_numbers))))))* -> . % 299.95/300.40 187114[19:Res:16133.1,186989.0] || member(u,complement(singleton(u)))* -> equal(singleton(u),ordinal_numbers). % 299.95/300.40 169380[19:Rew:166997.0,167907.1] || subclass(omega,u) -> equal(integer_of(regular(complement(u))),ordinal_numbers)** equal(complement(u),ordinal_numbers). % 299.95/300.40 188196[19:MRR:188190.1,167008.0] inductive(complement(singleton(regular(omega)))) || -> . % 299.95/300.40 186996[19:MRR:186958.0,167137.1] || subclass(u,complement(singleton(regular(u))))* -> equal(u,ordinal_numbers). % 299.95/300.40 184877[19:Res:176419.1,16.0] || subclass(domain_relation,flip(cross_product(u,v)))* -> member(ordinal_numbers,v). % 299.95/300.40 183883[23:SpR:183840.0,14.0] || -> equal(unordered_pair(singleton(u),unordered_pair(u,ordinal_numbers)),ordered_pair(u,universal_class))**. % 299.95/300.40 181823[19:Res:176345.1,2997.0] || subclass(domain_relation,cross_product(u,v))* -> member(singleton(ordinal_numbers),u). % 299.95/300.40 167458[19:Rew:166997.0,80538.0] || -> equal(power_class(intersection(complement(singleton(ordinal_numbers)),complement(image(successor_relation,ordinal_numbers)))),complement(image(element_relation,kind_1_ordinals)))**. % 299.95/300.40 168350[19:Rew:166997.0,80764.0] || -> equal(restrict(u,v,w),ordinal_numbers) member(regular(restrict(u,v,w)),u)*. % 299.95/300.40 178140[18:Res:15058.1,177583.1] function(u) || equal(rest_of(apply(u,v)),rest_relation)** -> . % 299.95/300.40 168354[19:Rew:166997.0,80768.0] || -> equal(symmetric_difference(u,v),ordinal_numbers) member(regular(symmetric_difference(u,v)),union(u,v))*. % 299.95/300.40 177822[19:SpR:177036.0,945.0] || -> equal(range_of(u),ordinal_numbers) member(ordinal_numbers,ordered_pair(inverse(u),v))*. % 299.95/300.40 167737[19:Rew:166997.0,80626.1] || subclass(u,intersection(v,w))* -> equal(u,ordinal_numbers) member(regular(u),w). % 299.95/300.40 187492[19:MRR:182860.2,187485.0] inductive(singleton(u)) || member(u,inverse(ordinal_numbers))* -> . % 299.95/300.40 187491[19:MRR:174592.1,187485.0] inductive(symmetric_difference(complement(inverse(ordinal_numbers)),complement(inverse(ordinal_numbers)))) || -> . % 299.95/300.40 187490[19:MRR:172073.1,187485.0] inductive(symmetric_difference(inverse(ordinal_numbers),inverse(ordinal_numbers))) || -> . % 299.95/300.40 167736[19:Rew:166997.0,80627.1] || subclass(u,intersection(v,w))* -> equal(u,ordinal_numbers) member(regular(u),v). % 299.95/300.40 187489[19:MRR:168235.1,187485.0] inductive(symmetric_difference(universal_class,complement(inverse(identity_relation)))) || -> . % 299.95/300.40 187488[19:MRR:168234.1,187485.0] inductive(symmetric_difference(inverse(identity_relation),inverse(identity_relation))) || -> . % 299.95/300.40 187487[20:MRR:181621.1,187485.0] inductive(singleton(regular(symmetrization_of(ordinal_numbers)))) || -> . % 299.95/300.40 187485[19:Res:16133.1,187475.0] || member(ordinal_numbers,symmetrization_of(ordinal_numbers))* -> . % 299.95/300.40 168379[19:Rew:166997.0,84892.1] || subclass(omega,u) -> equal(integer_of(not_subclass_element(v,u)),ordinal_numbers)** subclass(v,u). % 299.95/300.40 187475[19:MRR:187458.1,167337.0] || subclass(singleton(ordinal_numbers),symmetrization_of(ordinal_numbers))* -> . % 299.95/300.40 187474[19:MRR:187465.1,167011.0] || subclass(singleton(ordinal_numbers),ordinal_numbers)* -> . % 299.95/300.40 186994[19:MRR:186946.2,167046.0] || subclass(singleton(ordinal_numbers),complement(u))* member(ordinal_numbers,u) -> . % 299.95/300.40 168377[19:Rew:166997.0,84839.1] || subclass(omega,intersection(u,v))*+ -> equal(integer_of(w),ordinal_numbers) member(w,u)*. % 299.95/300.40 168376[19:Rew:166997.0,84840.1] || subclass(omega,intersection(u,v))*+ -> equal(integer_of(w),ordinal_numbers) member(w,v)*. % 299.95/300.40 168356[19:Rew:166997.0,80769.0] || -> equal(intersection(singleton(u),v),ordinal_numbers) equal(regular(intersection(singleton(u),v)),u)**. % 299.95/300.40 187118[19:MRR:187111.1,167008.0] inductive(complement(omega)) || -> . % 299.95/300.40 186989[19:Obv:186972.1] || subclass(u,complement(u))* -> equal(u,ordinal_numbers). % 299.95/300.40 168351[19:Rew:166997.0,80765.0] || -> equal(intersection(u,singleton(v)),ordinal_numbers) equal(regular(intersection(u,singleton(v))),v)**. % 299.95/300.40 167734[19:Rew:166997.0,80629.2] || subclass(u,complement(v)) member(regular(u),v)* -> equal(u,ordinal_numbers). % 299.95/300.40 168194[19:Rew:166997.0,84874.1] || subclass(omega,element_relation) -> equal(integer_of(ordered_pair(u,v)),ordinal_numbers)** member(u,v). % 299.95/300.40 167982[19:Rew:166997.0,80676.1] inductive(intersection(complement(u),complement(v))) || member(ordinal_numbers,union(u,v))* -> . % 299.95/300.40 168950[19:Rew:166997.0,164570.1] || member(u,universal_class) -> member(ordinal_numbers,ordered_pair(range_of(u),v))*. % 299.95/300.40 168206[19:Rew:166997.0,163263.1] inductive(symmetric_difference(u,u)) || -> member(ordinal_numbers,complement(complement(u)))*. % 299.95/300.40 167996[19:Rew:166997.0,80459.1] inductive(symmetric_difference(u,inverse(u))) || -> member(ordinal_numbers,symmetrization_of(u))*. % 299.95/300.40 167991[19:Rew:166997.0,80458.1] inductive(symmetric_difference(u,singleton(u))) || -> member(ordinal_numbers,successor(u))*. % 299.95/300.40 167960[19:Rew:166997.0,84833.2] || subclass(omega,complement(u))*+ member(v,u)* -> equal(integer_of(v),ordinal_numbers). % 299.95/300.40 186353[19:SpR:148172.0,167777.1] || -> equal(integer_of(u),ordinal_numbers) subclass(complement(complement(singleton(u))),omega)*. % 299.95/300.40 167777[19:Rew:166997.0,162841.0] || -> equal(integer_of(u),ordinal_numbers) subclass(intersection(singleton(u),v),omega)*. % 299.95/300.40 167776[19:Rew:166997.0,162842.0] || -> equal(integer_of(u),ordinal_numbers) subclass(intersection(v,singleton(u)),omega)*. % 299.95/300.40 185772[19:Res:7.1,185733.1] || equal(complement(u),universal_class)** equal(rotate(u),domain_relation) -> . % 299.95/300.40 167738[19:Rew:166997.0,80579.1] || subclass(u,omega) -> equal(u,ordinal_numbers) equal(integer_of(regular(u)),regular(u))**. % 299.95/300.40 186287[19:MRR:186283.1,167176.0] || equal(rest_relation,successor_relation)** -> . % 299.95/300.40 166843[18:MRR:166831.2,80465.0] || member(ordered_pair(u,v),cross_product(universal_class,universal_class))* member(v,cantor(u)) -> . % 299.95/300.40 9833[0:Res:170.0,126.0] || subclass(universal_class,u)+ well_ordering(v,u)* -> member(least(v,universal_class),universal_class)*. % 299.95/300.40 169527[19:MRR:167614.1,169313.1] inductive(singleton(u)) || -> member(u,cantor(successor_relation)) subclass(range_of(ordinal_numbers),singleton(u))*. % 299.95/300.40 185861[19:Rew:180089.0,185826.1] || subclass(rest_relation,successor_relation)* -> equal(rest_of(ordinal_numbers),singleton(ordinal_numbers)). % 299.95/300.40 185805[0:Res:53.0,30589.0] || subclass(rest_relation,successor_relation)* -> equal(rest_of(omega),successor(omega)). % 299.95/300.40 30589[0:Res:2523.2,46.0] || member(u,universal_class)* subclass(rest_relation,successor_relation) -> equal(rest_of(u),successor(u)). % 299.95/300.40 185751[19:Res:7.1,185656.1] || equal(complement(u),universal_class)** equal(flip(u),domain_relation) -> . % 299.95/300.40 185733[19:Res:7.1,184965.0] || equal(rotate(u),domain_relation) subclass(universal_class,complement(u))* -> . % 299.95/300.40 185656[19:Res:7.1,184883.0] || equal(flip(u),domain_relation) subclass(universal_class,complement(u))* -> . % 299.95/300.40 184965[19:Res:176420.1,6476.1] || subclass(domain_relation,rotate(u))* subclass(universal_class,complement(u)) -> . % 299.95/300.40 185730[19:Res:7.1,185696.0] || equal(rotate(element_relation),domain_relation)** -> . % 299.95/300.40 185696[19:Res:184950.1,167057.0] || subclass(domain_relation,rotate(element_relation))* -> . % 299.95/300.40 167892[19:Rew:166997.0,164078.1] one_to_one(image(successor_relation,cross_product(universal_class,universal_class))) || member(ordinal_numbers,cross_product(universal_class,universal_class))* -> . % 299.95/300.40 184883[19:Res:176419.1,6476.1] || subclass(domain_relation,flip(u))* subclass(universal_class,complement(u)) -> . % 299.95/300.40 184522[19:Res:940.0,176274.0] || subclass(rest_relation,domain_relation) -> equal(rest_of(ordered_pair(u,v)),ordinal_numbers)**. % 299.95/300.40 184521[19:Res:12.0,176274.0] || subclass(rest_relation,domain_relation) -> equal(rest_of(unordered_pair(u,v)),ordinal_numbers)**. % 299.95/300.40 184390[19:Res:940.0,176273.0] || subclass(domain_relation,rest_relation) -> equal(rest_of(ordered_pair(u,v)),ordinal_numbers)**. % 299.95/300.40 184389[19:Res:12.0,176273.0] || subclass(domain_relation,rest_relation) -> equal(rest_of(unordered_pair(u,v)),ordinal_numbers)**. % 299.95/300.40 185358[23:SpR:183840.0,183856.0] || -> equal(unordered_pair(ordinal_numbers,unordered_pair(universal_class,ordinal_numbers)),ordered_pair(universal_class,universal_class))**. % 299.95/300.40 183856[23:SpR:183840.0,14.0] || -> equal(unordered_pair(ordinal_numbers,unordered_pair(universal_class,singleton(u))),ordered_pair(universal_class,u))**. % 299.95/300.40 168261[19:Rew:166997.0,80722.1] || well_ordering(u,v) -> equal(segment(u,v,least(u,v)),ordinal_numbers)**. % 299.95/300.40 185236[19:SpR:946.0,184704.1] || subclass(rest_relation,domain_relation) -> member(singleton(singleton(singleton(ordinal_numbers))),rest_relation)*. % 299.95/300.40 185244[19:Res:184704.1,6476.1] || subclass(rest_relation,domain_relation) subclass(universal_class,complement(rest_relation))* -> . % 299.95/300.40 185235[23:SpR:183840.0,184704.1] || subclass(rest_relation,domain_relation) -> member(ordered_pair(ordinal_numbers,ordinal_numbers),rest_relation)*. % 299.95/300.40 168252[19:Rew:166997.0,80705.1] || well_ordering(u,v) -> equal(v,ordinal_numbers) member(least(u,v),v)*. % 299.95/300.40 185245[19:MRR:185238.0,135384.2] || subclass(rest_relation,u) well_ordering(universal_class,u)* -> . % 299.95/300.40 184704[19:MRR:184655.1,170.0] || subclass(rest_relation,domain_relation) -> member(ordered_pair(singleton(u),ordinal_numbers),rest_relation)*. % 299.95/300.40 35222[2:Res:289.0,9859.1] inductive(u) || well_ordering(v,u) -> member(least(v,u),u)*. % 299.95/300.40 35493[0:Res:5.0,9856.0] || well_ordering(u,universal_class)+ -> subclass(v,w)* member(least(u,v),v)*. % 299.95/300.40 184540[20:Res:175569.0,176274.0] || subclass(rest_relation,domain_relation) -> equal(rest_of(regular(symmetrization_of(ordinal_numbers))),ordinal_numbers)**. % 299.95/300.40 185042[19:Res:7.1,184983.0] || equal(rotate(domain_relation),domain_relation)**+ -> equal(ordinal_numbers,u)*. % 299.95/300.40 167739[19:Rew:166997.0,80631.1] || subclass(u,singleton(v))* -> equal(u,ordinal_numbers) equal(regular(u),v). % 299.95/300.40 184983[19:Rew:176363.0,184975.1] || subclass(domain_relation,rotate(domain_relation))*+ -> equal(ordinal_numbers,u)*. % 299.95/300.40 35220[2:Res:5.0,9859.1] inductive(u) || well_ordering(v,universal_class) -> member(least(v,u),u)*. % 299.95/300.40 184992[19:Res:7.1,184985.0] || equal(rotate(cross_product(universal_class,universal_class)),domain_relation)** -> . % 299.95/300.40 184985[19:AED:184958.1] || subclass(domain_relation,rotate(cross_product(universal_class,universal_class)))* -> . % 299.95/300.40 184989[19:Res:7.1,184944.0] || equal(rotate(ordinal_numbers),domain_relation)** -> . % 299.95/300.40 184944[19:Res:176420.1,167057.0] || subclass(domain_relation,rotate(ordinal_numbers))* -> . % 299.95/300.40 176420[19:Rew:176363.0,158396.1] || subclass(domain_relation,rotate(u)) -> member(ordered_pair(ordered_pair(v,ordinal_numbers),w),u)*. % 299.95/300.40 184904[19:Res:7.1,184897.0] || equal(flip(element_relation),domain_relation)** -> . % 299.95/300.40 184901[19:Res:7.1,184866.0] || equal(flip(ordinal_numbers),domain_relation)** -> . % 299.95/300.40 184897[19:MRR:184872.1,167057.0] || subclass(domain_relation,flip(element_relation))* -> . % 299.95/300.40 184866[19:Res:176419.1,167057.0] || subclass(domain_relation,flip(ordinal_numbers))* -> . % 299.95/300.40 176419[19:Rew:176363.0,158395.1] || subclass(domain_relation,flip(u)) -> member(ordered_pair(ordered_pair(v,w),ordinal_numbers),u)*. % 299.95/300.40 184408[20:Res:175569.0,176273.0] || subclass(domain_relation,rest_relation) -> equal(rest_of(regular(symmetrization_of(ordinal_numbers))),ordinal_numbers)**. % 299.95/300.40 184758[23:Res:7.1,184751.0] || equal(omega,successor_relation) subclass(universal_class,omega)* -> . % 299.95/300.40 184759[23:Res:52.1,184751.0] inductive(successor_relation) || subclass(universal_class,omega)* -> . % 299.95/300.40 167961[19:Rew:166997.0,84844.1] || subclass(omega,singleton(u))*+ -> equal(integer_of(v),ordinal_numbers)** equal(v,u)*. % 299.95/300.40 184751[23:MRR:184746.2,182533.0] || subclass(omega,successor_relation)* subclass(universal_class,omega) -> . % 299.95/300.40 184189[23:Res:167339.2,184175.0] || subclass(omega,successor_relation) -> equal(integer_of(singleton(singleton(ordinal_numbers))),ordinal_numbers)**. % 299.95/300.40 184734[23:Res:7.1,184721.0] || equal(rest_relation,omega) subclass(universal_class,omega)* -> . % 299.95/300.40 184735[23:Res:52.1,184721.0] inductive(rest_relation) || subclass(universal_class,omega)* -> . % 299.95/300.40 184721[23:MRR:184717.2,182533.0] || subclass(omega,rest_relation)* subclass(universal_class,omega) -> . % 299.95/300.40 85602[8:MRR:85597.1,80463.0] || well_ordering(u,universal_class) -> equal(integer_of(least(u,omega)),least(u,omega))**. % 299.95/300.40 184108[23:Res:167339.2,184001.0] || subclass(omega,rest_relation) -> equal(integer_of(singleton(singleton(ordinal_numbers))),ordinal_numbers)**. % 299.95/300.40 184520[19:Res:170.0,176274.0] || subclass(rest_relation,domain_relation) -> equal(rest_of(singleton(u)),ordinal_numbers)**. % 299.95/300.40 956[0:SpL:946.0,46.0] || member(singleton(singleton(singleton(u))),successor_relation)* -> equal(successor(singleton(u)),u). % 299.95/300.40 184388[19:Res:170.0,176273.0] || subclass(domain_relation,rest_relation) -> equal(rest_of(singleton(u)),ordinal_numbers)**. % 299.95/300.40 184494[19:MRR:184452.1,53.0] || equal(rest_relation,domain_relation) -> member(ordered_pair(omega,ordinal_numbers),rest_relation)*. % 299.95/300.40 184538[19:Res:167011.0,176274.0] || subclass(rest_relation,domain_relation)* -> equal(rest_of(ordinal_numbers),ordinal_numbers). % 299.95/300.40 184519[19:Res:53.0,176274.0] || subclass(rest_relation,domain_relation)* -> equal(rest_of(omega),ordinal_numbers). % 299.95/300.40 176274[19:Rew:176206.1,158114.2] || member(u,universal_class)* subclass(rest_relation,domain_relation) -> equal(rest_of(u),ordinal_numbers). % 299.95/300.40 184450[19:Res:7.1,184387.0] || equal(rest_relation,domain_relation) -> equal(rest_of(omega),ordinal_numbers)**. % 299.95/300.40 184387[19:Res:53.0,176273.0] || subclass(domain_relation,rest_relation)* -> equal(rest_of(omega),ordinal_numbers). % 299.95/300.40 184367[23:Res:7.1,184341.0] || equal(domain_relation,omega) subclass(universal_class,omega)* -> . % 299.95/300.40 176273[19:Rew:176206.1,158115.2] || member(u,universal_class)* subclass(domain_relation,rest_relation) -> equal(rest_of(u),ordinal_numbers). % 299.95/300.40 184368[23:Res:52.1,184341.0] inductive(domain_relation) || subclass(universal_class,omega)* -> . % 299.95/300.40 184341[23:MRR:184338.2,182533.0] || subclass(omega,domain_relation)* subclass(universal_class,omega) -> . % 299.95/300.40 184360[19:MRR:184354.0,99.0] || subclass(composition_function,ordinal_numbers)* -> . % 299.95/300.40 184100[23:Res:167339.2,183982.0] || subclass(omega,domain_relation) -> equal(integer_of(singleton(singleton(ordinal_numbers))),ordinal_numbers)**. % 299.95/300.40 184280[23:Res:7.1,184082.0] || equal(u,ordered_pair(universal_class,v))*+ -> member(ordinal_numbers,u)*. % 299.95/300.40 184082[23:Res:183852.0,2.0] || subclass(ordered_pair(universal_class,u),v)* -> member(ordinal_numbers,v). % 299.95/300.40 184260[23:SpR:167060.0,183885.0] || -> equal(apply(element_relation,universal_class),sum_class(universal_class))**. % 299.95/300.40 183885[23:SpR:183840.0,69.0] || -> equal(sum_class(image(u,ordinal_numbers)),apply(u,universal_class))**. % 299.95/300.40 184084[23:Res:183852.0,169221.1] || equal(complement(ordered_pair(universal_class,u)),singleton(ordinal_numbers))** -> . % 299.95/300.40 183882[23:SpR:183840.0,947.0] || -> member(unordered_pair(u,ordinal_numbers),ordered_pair(u,universal_class))*. % 299.95/300.40 184085[23:Res:183852.0,177998.1] || equal(complement(ordered_pair(universal_class,u)),omega)** -> . % 299.95/300.40 183954[23:SpL:183840.0,9732.0] || subclass(universal_class,complement(unordered_pair(u,ordinal_numbers)))* -> . % 299.95/300.40 183930[23:SpL:183840.0,9733.0] || subclass(universal_class,complement(unordered_pair(ordinal_numbers,u)))* -> . % 299.95/300.40 184187[23:Res:12015.1,184175.0] || equal(complement(complement(successor_relation)),universal_class)** -> . % 299.95/300.40 184188[23:Res:2479.1,184175.0] || subclass(universal_class,successor_relation)* -> . % 299.95/300.40 184175[23:MRR:184174.1,180091.0] || member(singleton(singleton(ordinal_numbers)),successor_relation)* -> . % 299.95/300.40 169555[19:MRR:169072.2,167057.0] one_to_one(sum_class(cross_product(universal_class,universal_class))) || well_ordering(element_relation,cross_product(universal_class,universal_class))* -> . % 299.95/300.40 183857[23:SpR:183840.0,946.0] || -> equal(ordered_pair(ordinal_numbers,universal_class),singleton(singleton(ordinal_numbers)))**. % 299.95/300.40 184106[23:Res:12015.1,184001.0] || equal(complement(complement(rest_relation)),universal_class)** -> . % 299.95/300.40 184098[23:Res:12015.1,183982.0] || equal(complement(complement(domain_relation)),universal_class)** -> . % 299.95/300.40 184107[23:Res:2479.1,184001.0] || subclass(universal_class,rest_relation)* -> . % 299.95/300.40 184001[23:MRR:184000.1,160037.0] || member(singleton(singleton(ordinal_numbers)),rest_relation)* -> . % 299.95/300.40 184099[23:Res:2479.1,183982.0] || subclass(universal_class,domain_relation)* -> . % 299.95/300.40 183982[23:MRR:183910.1,9070.0] || member(singleton(singleton(ordinal_numbers)),domain_relation)* -> . % 299.95/300.40 168287[19:Rew:166997.0,81041.1] || member(complement(omega),universal_class) -> equal(integer_of(apply(choice,complement(omega))),ordinal_numbers)**. % 299.95/300.40 183852[23:SpR:183840.0,945.0] || -> member(ordinal_numbers,ordered_pair(universal_class,u))*. % 299.95/300.40 184068[23:Res:167115.1,183965.0] || -> equal(integer_of(universal_class),ordinal_numbers)**. % 299.95/300.40 183965[23:MRR:183855.1,167057.0] || member(universal_class,universal_class)* -> . % 299.95/300.40 183970[23:MRR:12331.1,183968.0] single_valued_class(element_relation) || -> . % 299.95/300.40 183968[23:MRR:97043.1,183965.0] function(element_relation) || -> . % 299.95/300.40 183967[23:MRR:97044.1,183965.0] one_to_one(element_relation) || -> . % 299.95/300.40 183840[23:Spt:183826.1] || -> equal(singleton(universal_class),ordinal_numbers)**. % 299.95/300.40 168260[19:Rew:166997.0,80708.1] inductive(restrict(u,v,w)) || -> member(ordinal_numbers,cross_product(v,w))*. % 299.95/300.40 169224[19:Rew:166997.0,167542.1] || equal(intersection(u,v),singleton(ordinal_numbers))** -> member(ordinal_numbers,u). % 299.95/300.40 169223[19:Rew:166997.0,167541.1] || equal(intersection(u,v),singleton(ordinal_numbers))** -> member(ordinal_numbers,v). % 299.95/300.40 168184[19:Rew:166997.0,80686.1] || -> member(regular(complement(complement(u))),u)* equal(complement(complement(u)),ordinal_numbers). % 299.95/300.40 168203[19:Rew:166997.0,80992.0] || -> equal(integer_of(not_subclass_element(complement(omega),u)),ordinal_numbers)** subclass(complement(omega),u). % 299.95/300.40 183405[19:Res:131984.1,169167.0] || equal(complement(rest_of(u)),universal_class)** -> equal(cantor(u),ordinal_numbers). % 299.95/300.40 183404[19:Res:131984.1,167211.1] inductive(cantor(u)) || equal(complement(rest_of(u)),universal_class)** -> . % 299.95/300.40 167920[19:Rew:166997.0,80658.1] inductive(image(element_relation,complement(u))) || member(ordinal_numbers,power_class(u))* -> . % 299.95/300.40 167895[19:Rew:166997.0,80650.2] function(u) inductive(u) || -> member(ordinal_numbers,cross_product(universal_class,universal_class))*. % 299.95/300.40 182463[19:Res:7.1,179771.0] || equal(u,singleton(singleton(ordinal_numbers))) -> member(singleton(ordinal_numbers),u)*. % 299.95/300.40 183043[19:SpL:176361.0,182439.1] || subclass(rest_relation,rest_of(singleton(u)))* well_ordering(universal_class,ordinal_numbers) -> . % 299.95/300.40 183042[19:SpL:176360.0,182439.1] || subclass(rest_relation,rest_of(omega))* well_ordering(universal_class,ordinal_numbers) -> . % 299.95/300.40 183041[19:SpL:167050.0,182439.1] || subclass(rest_relation,rest_of(ordinal_numbers))* well_ordering(universal_class,ordinal_numbers) -> . % 299.95/300.40 182439[19:MRR:182421.0,170.0] || subclass(rest_relation,rest_of(u)) well_ordering(universal_class,cantor(u))* -> . % 299.95/300.40 182427[19:Res:12015.1,182393.0] || equal(complement(complement(u)),universal_class)** well_ordering(universal_class,u) -> . % 299.95/300.40 182391[19:Res:7.1,179767.0] || equal(u,singleton(singleton(ordinal_numbers)))*+ well_ordering(universal_class,u)* -> . % 299.95/300.40 181775[20:Res:7.1,176112.0] || equal(singleton(u),universal_class)**+ -> equal(regular(symmetrization_of(ordinal_numbers)),u)*. % 299.95/300.40 168226[19:Rew:166997.0,80717.1] inductive(rotate(u)) || -> member(ordinal_numbers,cross_product(cross_product(universal_class,universal_class),universal_class))*. % 299.95/300.40 181715[19:Res:7.1,168068.0] || equal(u,complement(inverse(ordinal_numbers)))*+ well_ordering(universal_class,u)* -> . % 299.95/300.40 182938[20:Res:181635.1,167057.0] || subclass(symmetrization_of(ordinal_numbers),ordinal_numbers)* -> . % 299.95/300.40 181635[20:Res:181628.0,2.0] || subclass(symmetrization_of(ordinal_numbers),u) -> member(regular(symmetrization_of(ordinal_numbers)),u)*. % 299.95/300.40 182871[19:MRR:182868.1,36583.1] || member(u,inverse(ordinal_numbers)) -> member(u,symmetrization_of(ordinal_numbers))*. % 299.95/300.40 168225[19:Rew:166997.0,80718.1] inductive(flip(u)) || -> member(ordinal_numbers,cross_product(cross_product(universal_class,universal_class),universal_class))*. % 299.95/300.40 181489[19:Res:169234.0,25.1] || member(u,inverse(ordinal_numbers)) -> subclass(singleton(u),symmetrization_of(ordinal_numbers))*. % 299.95/300.40 166842[18:MRR:166826.2,80465.0] inductive(application_function) || well_ordering(u,cross_product(universal_class,cross_product(universal_class,universal_class)))* -> . % 299.95/300.40 180882[22:Res:177171.1,169221.1] || subclass(omega,u)* equal(complement(u),singleton(ordinal_numbers)) -> . % 299.95/300.40 180881[22:Res:178902.1,169221.1] || equal(u,omega) equal(complement(u),singleton(ordinal_numbers))** -> . % 299.95/300.40 167986[19:Rew:166997.0,80678.1] inductive(symmetric_difference(u,v)) || -> member(ordinal_numbers,union(u,v))*. % 299.95/300.40 179968[12:SoR:158500.0,72.1] one_to_one(range_of(u)) || equal(rest_of(inverse(u)),rest_relation)** -> . % 299.95/300.40 167817[19:Rew:166997.0,80635.2] inductive(u) || equal(v,u)*+ -> member(ordinal_numbers,v)*. % 299.95/300.40 167760[19:Rew:166997.0,80572.0] || -> equal(singleton(u),ordinal_numbers) equal(apply(choice,singleton(u)),u)**. % 299.95/300.40 182467[19:Res:95593.1,179771.0] || -> member(singleton(ordinal_numbers),u) member(singleton(ordinal_numbers),complement(u))*. % 299.95/300.40 179771[19:Res:179714.0,2.0] || subclass(singleton(singleton(ordinal_numbers)),u)* -> member(singleton(ordinal_numbers),u). % 299.95/300.40 182431[19:Res:180693.1,182393.0] || well_ordering(element_relation,range_of(ordinal_numbers))* well_ordering(universal_class,cantor(choice)) -> . % 299.95/300.40 182395[19:Res:95593.1,179767.0] || well_ordering(universal_class,complement(u))* -> member(singleton(ordinal_numbers),u). % 299.95/300.40 182426[19:Res:144532.1,182393.0] || equal(u,universal_class) well_ordering(universal_class,u)* -> . % 299.95/300.40 182438[19:MRR:182418.0,170.0] || well_ordering(universal_class,unordered_pair(u,singleton(ordinal_numbers)))* -> . % 299.95/300.40 182437[19:MRR:182417.0,170.0] || well_ordering(universal_class,unordered_pair(singleton(ordinal_numbers),u))* -> . % 299.95/300.40 182393[19:Res:16133.1,179767.0] || member(singleton(ordinal_numbers),u)* well_ordering(universal_class,u) -> . % 299.95/300.40 182396[19:Res:167113.1,179767.0] || well_ordering(universal_class,omega) -> equal(integer_of(singleton(ordinal_numbers)),ordinal_numbers)**. % 299.95/300.40 182392[19:Res:289.0,179767.0] || well_ordering(universal_class,singleton(singleton(ordinal_numbers)))* -> . % 299.95/300.40 179767[19:Res:179714.0,11848.0] || subclass(singleton(singleton(ordinal_numbers)),u)* well_ordering(universal_class,u) -> . % 299.95/300.40 178289[22:Res:169181.1,177998.1] || equal(u,singleton(ordinal_numbers)) equal(complement(u),omega)** -> . % 299.95/300.40 178148[18:Res:149603.1,177583.1] || member(u,universal_class) equal(rest_of(rest_of(u)),rest_relation)** -> . % 299.95/300.40 178139[18:Res:57.1,177583.1] || member(u,universal_class) equal(rest_of(power_class(u)),rest_relation)** -> . % 299.95/300.40 178138[18:Res:55.1,177583.1] || member(u,universal_class) equal(rest_of(sum_class(u)),rest_relation)** -> . % 299.95/300.40 176590[19:MRR:176569.2,167057.0] || member(u,universal_class)* subclass(rest_relation,rest_of(singleton(v)))*+ -> . % 299.95/300.40 168645[19:Rew:166997.0,80909.2] || 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))),ordinal_numbers) member(ordered_pair(w,apply(choice,image(u,image(v,singleton(w))))),compose(u,v))*. % 299.95/300.40 176410[19:Rew:176361.0,158042.1] || member(singleton(singleton(singleton(u))),domain_relation)* -> equal(ordinal_numbers,u). % 299.95/300.40 176375[21:Res:176155.1,176206.0] || well_ordering(u,universal_class) -> equal(cantor(least(u,omega)),ordinal_numbers)**. % 299.95/300.40 176374[21:Res:176162.1,176206.0] || well_ordering(u,omega) -> equal(cantor(least(u,omega)),ordinal_numbers)**. % 299.95/300.40 176373[19:Res:137620.1,176206.0] || well_ordering(u,rest_relation) -> equal(cantor(least(u,rest_relation)),ordinal_numbers)**. % 299.95/300.40 168482[19:Rew:166997.0,80796.2] || transitive(u,v) well_ordering(w,restrict(u,v,v)) -> equal(compose(restrict(u,v,v),restrict(u,v,v)),ordinal_numbers) member(least(w,compose(restrict(u,v,v),restrict(u,v,v))),compose(restrict(u,v,v),restrict(u,v,v)))*. % 299.95/300.40 176372[19:Res:137613.1,176206.0] || well_ordering(u,universal_class) -> equal(cantor(least(u,rest_relation)),ordinal_numbers)**. % 299.95/300.40 176371[19:Res:137890.1,176206.0] || well_ordering(u,universal_class) -> equal(cantor(least(u,universal_class)),ordinal_numbers)**. % 299.95/300.40 176345[19:Res:176340.0,2.0] || subclass(domain_relation,u) -> member(singleton(singleton(singleton(ordinal_numbers))),u)*. % 299.95/300.40 176272[19:Rew:176206.1,157942.1] || member(u,universal_class) equal(sum_class(range_of(u)),ordinal_numbers)** -> . % 299.95/300.40 176112[20:Res:175613.1,4178.0] || subclass(universal_class,singleton(u))* -> equal(regular(symmetrization_of(ordinal_numbers)),u). % 299.95/300.40 181761[20:Res:175570.1,175561.0] || subclass(inverse(ordinal_numbers),complement(inverse(ordinal_numbers)))* -> . % 299.95/300.40 181757[20:Res:175570.1,167057.0] || subclass(inverse(ordinal_numbers),ordinal_numbers)* -> . % 299.95/300.40 175570[20:Res:175558.0,2.0] || subclass(inverse(ordinal_numbers),u) -> member(regular(symmetrization_of(ordinal_numbers)),u)*. % 299.95/300.40 181716[19:Res:289.0,168068.0] || well_ordering(universal_class,complement(inverse(ordinal_numbers)))* -> . % 299.95/300.40 168068[19:Rew:166997.0,163343.0] || subclass(complement(inverse(ordinal_numbers)),u)* well_ordering(universal_class,u) -> . % 299.95/300.40 181674[20:SoR:181642.0,72.1] one_to_one(symmetrization_of(ordinal_numbers)) || well_ordering(universal_class,cross_product(universal_class,universal_class))* -> . % 299.95/300.40 181642[20:Res:63.1,181631.0] function(symmetrization_of(ordinal_numbers)) || well_ordering(universal_class,cross_product(universal_class,universal_class))* -> . % 299.95/300.40 181640[20:Res:7.1,181631.0] || equal(u,symmetrization_of(ordinal_numbers)) well_ordering(universal_class,u)* -> . % 299.95/300.40 11961[0:Res:3.1,60.0] || 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))*. % 299.95/300.40 181641[20:Res:289.0,181631.0] || well_ordering(universal_class,symmetrization_of(ordinal_numbers))* -> . % 299.95/300.40 181631[20:Res:181628.0,11848.0] || subclass(symmetrization_of(ordinal_numbers),u)* well_ordering(universal_class,u) -> . % 299.95/300.40 181628[20:MRR:181627.0,175569.0] || -> member(regular(symmetrization_of(ordinal_numbers)),symmetrization_of(ordinal_numbers))*. % 299.95/300.40 181516[20:Res:169234.0,175561.0] || -> subclass(singleton(regular(symmetrization_of(ordinal_numbers))),symmetrization_of(ordinal_numbers))*. % 299.95/300.40 168717[19:Rew:166997.0,80963.2] || 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)))),ordinal_numbers)**. % 299.95/300.40 169234[19:Rew:166997.0,168057.1] || -> member(u,complement(inverse(ordinal_numbers)))* subclass(singleton(u),symmetrization_of(ordinal_numbers)). % 299.95/300.40 168903[19:Rew:166997.0,163124.1] || subclass(rest_relation,rest_of(u))* -> equal(complement(cantor(u)),ordinal_numbers). % 299.95/300.40 168753[19:Rew:166997.0,160911.1] || member(u,universal_class) -> equal(integer_of(sum_class(range_of(u))),ordinal_numbers)**. % 299.95/300.40 168752[19:Rew:166997.0,160877.1] || member(u,universal_class) -> equal(singleton(sum_class(range_of(u))),ordinal_numbers)**. % 299.95/300.40 168001[19:Rew:166997.0,84252.1] || subclass(domain_relation,compose_class(u))* -> equal(compose(u,ordinal_numbers),ordinal_numbers). % 299.95/300.40 168000[19:Rew:166997.0,94497.1] || equal(compose_class(u),domain_relation) -> equal(compose(u,ordinal_numbers),ordinal_numbers)**. % 299.95/300.40 169049[19:Rew:166997.0,80964.1] || member(ordered_pair(u,regular(image(v,image(w,singleton(u))))),cross_product(universal_class,universal_class)) -> equal(image(v,image(w,singleton(u))),ordinal_numbers) member(ordered_pair(u,regular(image(v,image(w,singleton(u))))),compose(v,w))*. % 299.95/300.40 167896[19:Rew:166997.0,80417.1] inductive(compose(u,v)) || -> member(ordinal_numbers,cross_product(universal_class,universal_class))*. % 299.95/300.40 167784[19:Rew:166997.0,83728.1] single_valued_class(u) || -> equal(second(not_subclass_element(ordinal_numbers,ordinal_numbers)),single_valued2(u))*. % 299.95/300.40 167783[19:Rew:166997.0,83789.1] function(u) || -> equal(second(not_subclass_element(ordinal_numbers,ordinal_numbers)),single_valued2(u))*. % 299.95/300.40 167547[19:Rew:166997.0,164336.0] || equal(u,singleton(ordinal_numbers)) equal(complement(u),universal_class)** -> . % 299.95/300.40 169222[19:Rew:166997.0,167539.1] || equal(complement(complement(u)),singleton(ordinal_numbers))** -> member(ordinal_numbers,u). % 299.95/300.40 180886[19:Res:167106.1,169221.1] inductive(u) || equal(complement(u),singleton(ordinal_numbers))** -> . % 299.95/300.40 180893[19:MRR:180864.0,167011.0] || equal(complement(unordered_pair(u,ordinal_numbers)),singleton(ordinal_numbers))** -> . % 299.95/300.40 180892[19:MRR:180863.0,167011.0] || equal(complement(unordered_pair(ordinal_numbers,u)),singleton(ordinal_numbers))** -> . % 299.95/300.40 180888[22:Res:177170.0,169221.1] || equal(complement(omega),singleton(ordinal_numbers))** -> . % 299.95/300.40 169221[19:Rew:166997.0,167538.1] || equal(complement(u),singleton(ordinal_numbers)) member(ordinal_numbers,u)* -> . % 299.95/300.40 180852[19:MRR:180843.2,167057.0] || well_ordering(element_relation,range_of(ordinal_numbers))* -> equal(singleton(choice),ordinal_numbers). % 299.95/300.40 180693[19:MRR:180692.0,170.0] || well_ordering(element_relation,range_of(ordinal_numbers)) -> member(singleton(ordinal_numbers),cantor(choice))*. % 299.95/300.40 180125[19:Rew:180089.0,168799.0] || -> equal(complement(image(element_relation,singleton(ordinal_numbers))),power_class(complement(singleton(ordinal_numbers))))**. % 299.95/300.40 180664[19:MRR:180663.1,166995.0] || well_ordering(element_relation,image(choice,singleton(singleton(ordinal_numbers))))* -> . % 299.95/300.40 180649[19:Res:180365.0,4178.0] || -> equal(apply(choice,singleton(ordinal_numbers)),ordinal_numbers)**. % 299.95/300.40 180361[19:MRR:180137.1,167331.0] inductive(symmetric_difference(singleton(identity_relation),successor(identity_relation))) || -> . % 299.95/300.40 180360[19:MRR:180136.1,167331.0] inductive(symmetric_difference(singleton(ordinal_numbers),successor(ordinal_numbers))) || -> . % 299.95/300.40 180105[19:Rew:180089.0,167302.0] || subclass(singleton(ordinal_numbers),complement(singleton(ordinal_numbers)))* -> . % 299.95/300.40 180103[19:Rew:180089.0,167279.0] || -> equal(complement(complement(singleton(ordinal_numbers))),singleton(ordinal_numbers))**. % 299.95/300.40 180097[19:Rew:180089.0,167342.0] || -> equal(regular(singleton(ordinal_numbers)),ordinal_numbers)**. % 299.95/300.40 168409[19:Rew:166997.0,80771.1] || member(cross_product(u,v),universal_class) -> equal(cross_product(u,v),ordinal_numbers) equal(ordered_pair(first(apply(choice,cross_product(u,v))),second(apply(choice,cross_product(u,v)))),apply(choice,cross_product(u,v)))**. % 299.95/300.40 180092[19:Rew:180089.0,167285.0] || subclass(universal_class,singleton(ordinal_numbers))* -> . % 299.95/300.40 180091[19:Rew:180089.0,167278.0] || equal(singleton(ordinal_numbers),universal_class)** -> . % 299.95/300.40 180089[19:MRR:169273.0,180086.0] || -> equal(successor(ordinal_numbers),singleton(ordinal_numbers))**. % 299.95/300.40 168705[19:Rew:166997.0,159097.2] || section(u,v,w) well_ordering(x,v) -> equal(cantor(restrict(u,w,v)),ordinal_numbers) member(least(x,cantor(restrict(u,w,v))),cantor(restrict(u,w,v)))*. % 299.95/300.40 167406[19:Rew:166997.0,84232.1] || subclass(domain_relation,singleton(u))* -> equal(ordered_pair(ordinal_numbers,ordinal_numbers),u). % 299.95/300.40 167405[19:Rew:166997.0,94499.1] || equal(singleton(u),domain_relation)**+ -> equal(ordered_pair(ordinal_numbers,ordinal_numbers),u)*. % 299.95/300.40 158500[12:MRR:139659.2,99409.0] function(range_of(u)) || equal(rest_of(inverse(u)),rest_relation)** -> . % 299.95/300.40 12111[0:Res:17.2,35.1] || 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))*. % 299.95/300.40 12073[0:Res:17.2,38.1] || 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))*. % 299.95/300.40 168007[19:Rew:166997.0,80988.1] || subclass(universal_class,complement(omega))*+ -> equal(integer_of(singleton(u)),ordinal_numbers)**. % 299.95/300.40 179714[19:Res:53.0,167565.0] || -> member(singleton(ordinal_numbers),singleton(singleton(ordinal_numbers)))*. % 299.95/300.40 168682[19:Rew:166997.0,159021.2] || section(u,v,w) well_ordering(x,v) -> equal(segment(x,cantor(restrict(u,w,v)),least(x,cantor(restrict(u,w,v)))),ordinal_numbers)**. % 299.95/300.40 179578[20:SoR:176082.0,72.1] one_to_one(inverse(ordinal_numbers)) || well_ordering(universal_class,cross_product(universal_class,universal_class))* -> . % 299.95/300.40 179245[19:SoR:173516.0,72.1] one_to_one(successor(ordinal_numbers)) || well_ordering(universal_class,cross_product(universal_class,universal_class))* -> . % 299.95/300.40 168681[19:Rew:166997.0,159020.2] || connected(u,v)* well_ordering(w,complement(complement(symmetrization_of(u))))*+ -> equal(cross_product(v,v),ordinal_numbers) member(least(w,cross_product(v,v)),cross_product(v,v))*. % 299.95/300.40 179241[19:SoR:173290.0,72.1] one_to_one(complement(inverse(ordinal_numbers))) || -> member(ordinal_numbers,cross_product(universal_class,universal_class))*. % 299.95/300.40 178946[22:Res:178902.1,110865.0] || equal(rest_of(ordinal_numbers),omega) subclass(universal_class,complement(element_relation))* -> . % 299.95/300.40 177211[22:Res:177171.1,110865.0] || subclass(omega,rest_of(ordinal_numbers))* subclass(universal_class,complement(element_relation)) -> . % 299.95/300.40 169033[19:Rew:166997.0,80935.3] || 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))),ordinal_numbers)**. % 299.95/300.40 176082[20:Res:63.1,175566.0] function(inverse(ordinal_numbers)) || well_ordering(universal_class,cross_product(universal_class,universal_class))* -> . % 299.95/300.40 167200[19:Rew:166997.0,159490.0] || -> equal(complement(image(element_relation,symmetrization_of(ordinal_numbers))),power_class(complement(inverse(ordinal_numbers))))**. % 299.95/300.40 9843[0:Res:10.1,126.0] || 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))*. % 299.95/300.40 174574[19:SoR:167889.0,72.1] one_to_one(complement(inverse(identity_relation))) || -> member(ordinal_numbers,cross_product(universal_class,universal_class))*. % 299.95/300.40 9842[0:Res:11.1,126.0] || 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))*. % 299.95/300.40 174371[15:SoR:164971.0,72.1] one_to_one(successor(identity_relation)) || well_ordering(universal_class,cross_product(universal_class,universal_class))* -> . % 299.95/300.40 168666[19:Rew:166997.0,158962.2] || connected(u,v)* well_ordering(w,complement(complement(symmetrization_of(u))))*+ -> equal(segment(w,cross_product(v,v),least(w,cross_product(v,v))),ordinal_numbers)**. % 299.95/300.40 173516[19:Res:63.1,167288.0] function(successor(ordinal_numbers)) || well_ordering(universal_class,cross_product(universal_class,universal_class))* -> . % 299.95/300.40 173290[19:Res:63.1,169200.0] function(complement(inverse(ordinal_numbers))) || -> member(ordinal_numbers,cross_product(universal_class,universal_class))*. % 299.95/300.40 9836[0:Res:26.2,126.0] || member(u,universal_class)* subclass(complement(v),w)*+ well_ordering(x,w)* -> member(u,v)* member(least(x,complement(v)),complement(v))*. % 299.95/300.40 176369[19:Res:36682.1,176206.0] || -> subclass(u,v) equal(cantor(not_subclass_element(u,v)),ordinal_numbers)**. % 299.95/300.40 169657[19:Rew:166997.0,169038.2] inductive(image(u,image(v,singleton(w)))) || member(ordered_pair(w,ordinal_numbers),cross_product(universal_class,universal_class)) -> member(ordered_pair(w,ordinal_numbers),compose(u,v))*. % 299.95/300.40 178869[22:Res:7.1,177191.0] || equal(intersection(u,v),omega)** -> member(ordinal_numbers,v). % 299.95/300.40 178902[22:SpL:144658.0,178812.0] || equal(u,omega) -> member(ordinal_numbers,u)*. % 299.95/300.40 178812[22:Res:7.1,177190.0] || equal(intersection(u,v),omega)** -> member(ordinal_numbers,u). % 299.95/300.40 177191[22:Res:177171.1,23.0] || subclass(omega,intersection(u,v))* -> member(ordinal_numbers,v). % 299.95/300.40 177190[22:Res:177171.1,22.0] || subclass(omega,intersection(u,v))* -> member(ordinal_numbers,u). % 299.95/300.40 176368[19:Res:15058.1,176206.0] function(u) || -> equal(cantor(apply(u,v)),ordinal_numbers)**. % 299.95/300.40 178652[22:Res:7.1,178287.0] || equal(u,omega) equal(complement(u),omega)** -> . % 299.95/300.40 178287[22:Res:177171.1,177998.1] || subclass(omega,u)* equal(complement(u),omega) -> . % 299.95/300.40 178195[19:Res:167115.1,177916.0] || -> equal(integer_of(inverse(u)),ordinal_numbers)** equal(range_of(u),ordinal_numbers). % 299.95/300.40 178152[19:Res:167137.1,177583.1] || equal(rest_of(regular(u)),rest_relation)** -> equal(u,ordinal_numbers). % 299.95/300.40 178137[19:Res:167115.1,177583.1] || equal(rest_of(u),rest_relation) -> equal(integer_of(u),ordinal_numbers)**. % 299.95/300.40 178136[19:Res:167224.0,177583.1] || equal(rest_of(u),rest_relation)** -> equal(singleton(u),ordinal_numbers). % 299.95/300.40 168412[19:Rew:166997.0,80772.0] || -> equal(cross_product(u,v),ordinal_numbers) equal(ordered_pair(first(regular(cross_product(u,v))),second(regular(cross_product(u,v)))),regular(cross_product(u,v)))**. % 299.95/300.40 178038[22:Res:7.1,177220.0] || equal(u,omega) equal(complement(u),universal_class)** -> . % 299.95/300.40 178014[22:Res:7.1,177183.0] || equal(complement(complement(u)),omega)** -> member(ordinal_numbers,u). % 299.95/300.40 178292[22:Res:167106.1,177998.1] inductive(u) || equal(complement(u),omega)** -> . % 299.95/300.40 178299[22:MRR:178270.0,167011.0] || equal(complement(unordered_pair(u,ordinal_numbers)),omega)** -> . % 299.95/300.40 9790[0:Res:98.1,2.0] || 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)*. % 299.95/300.40 178298[22:MRR:178269.0,167011.0] || equal(complement(unordered_pair(ordinal_numbers,u)),omega)** -> . % 299.95/300.40 177998[22:Res:7.1,177179.0] || equal(complement(u),omega) member(ordinal_numbers,u)* -> . % 299.95/300.40 177916[19:MRR:177825.2,167057.0] || member(inverse(u),universal_class)* -> equal(range_of(u),ordinal_numbers). % 299.95/300.40 178135[18:Res:940.0,177583.1] || equal(rest_of(ordered_pair(u,v)),rest_relation)** -> . % 299.95/300.40 178134[18:Res:12.0,177583.1] || equal(rest_of(unordered_pair(u,v)),rest_relation)** -> . % 299.95/300.40 178153[20:Res:175569.0,177583.1] || equal(rest_of(regular(symmetrization_of(ordinal_numbers))),rest_relation)** -> . % 299.95/300.40 178133[18:Res:170.0,177583.1] || equal(rest_of(singleton(u)),rest_relation)** -> . % 299.95/300.40 177583[18:Res:7.1,176311.0] || equal(rest_of(u),rest_relation) member(u,universal_class)* -> . % 299.95/300.40 158909[8:Rew:157840.0,3132.2,157840.0,3132.1] || connected(u,v) subclass(complement(complement(symmetrization_of(u))),cross_product(v,v))* -> equal(complement(complement(symmetrization_of(u))),cross_product(v,v)). % 299.95/300.40 177220[22:Res:177171.1,167095.1] || subclass(omega,u)* equal(complement(u),universal_class) -> . % 299.95/300.40 168326[19:Rew:166997.0,80748.2] inductive(u) || well_ordering(v,u) -> equal(image(successor_relation,u),ordinal_numbers) member(least(v,image(successor_relation,u)),image(successor_relation,u))*. % 299.95/300.40 177183[22:Res:177171.1,148647.0] || subclass(omega,complement(complement(u)))* -> member(ordinal_numbers,u). % 299.95/300.40 177179[22:Res:177171.1,25.1] || subclass(omega,complement(u))* member(ordinal_numbers,u) -> . % 299.95/300.40 177036[19:SpR:176364.1,124908.0] || -> equal(singleton(inverse(u)),ordinal_numbers)** equal(range_of(u),ordinal_numbers). % 299.95/300.40 9765[2:MRR:9744.3,5298.1] || connected(u,v) well_ordering(w,v) -> well_ordering(u,v) member(least(w,not_well_ordering(u,v)),not_well_ordering(u,v))*. % 299.95/300.40 176376[19:Res:149603.1,176206.0] || member(u,universal_class) -> equal(cantor(rest_of(u)),ordinal_numbers)**. % 299.95/300.40 176367[19:Res:57.1,176206.0] || member(u,universal_class) -> equal(cantor(power_class(u)),ordinal_numbers)**. % 299.95/300.40 176366[19:Res:55.1,176206.0] || member(u,universal_class) -> equal(cantor(sum_class(u)),ordinal_numbers)**. % 299.95/300.40 176311[18:Con:176196.0] || subclass(rest_relation,rest_of(u))* member(u,universal_class) -> . % 299.95/300.40 168642[19:Rew:166997.0,80908.1] || well_ordering(u,cross_product(universal_class,universal_class)) -> equal(compose(v,w),ordinal_numbers) member(least(u,compose(v,w)),compose(v,w))*. % 299.95/300.40 177515[19:Res:53.0,177380.1] || equal(rest_of(omega),rest_relation)** -> . % 299.95/300.40 168644[19:Rew:166997.0,81042.3] || member(u,v)+ subclass(v,w)* well_ordering(omega,w)* -> equal(integer_of(ordered_pair(u,least(omega,v))),ordinal_numbers)**. % 299.95/300.40 176480[19:MRR:176460.2,167057.0] || member(u,universal_class)* subclass(rest_relation,rest_of(omega))*+ -> . % 299.95/300.40 177327[22:Res:7.1,177193.0] || equal(singleton(u),omega)** -> equal(ordinal_numbers,u). % 299.95/300.40 177193[22:Res:177171.1,4178.0] || subclass(omega,singleton(u))* -> equal(ordinal_numbers,u). % 299.95/300.40 177172[22:Res:177170.0,11848.0] || subclass(omega,u) well_ordering(universal_class,u)* -> . % 299.95/300.40 177315[22:Res:7.1,177225.0] || equal(cross_product(u,v),omega)** -> . % 299.95/300.40 177318[22:SoR:177317.0,72.1] one_to_one(omega) || -> . % 299.95/300.40 177317[22:Res:63.1,177225.0] function(omega) || -> . % 299.95/300.40 177225[22:MRR:177200.1,167176.0] || subclass(omega,cross_product(u,v))* -> . % 299.95/300.40 168360[19:Rew:166997.0,80753.0] || -> equal(unordered_pair(u,v),ordinal_numbers) equal(apply(choice,unordered_pair(u,v)),v)** equal(apply(choice,unordered_pair(u,v)),u)**. % 299.95/300.40 177277[22:Res:7.1,177219.0] || equal(complement(singleton(ordinal_numbers)),omega)** -> . % 299.95/300.40 177219[22:Res:177171.1,167331.0] || subclass(omega,complement(singleton(ordinal_numbers)))* -> . % 299.95/300.40 177259[22:Res:7.1,177223.0] || equal(symmetrization_of(ordinal_numbers),omega)** -> . % 299.95/300.40 177255[22:Res:7.1,177221.0] || equal(inverse(ordinal_numbers),omega)** -> . % 299.95/300.40 169023[19:Rew:166997.0,80904.2] inductive(u) || well_ordering(v,u) -> equal(segment(v,image(successor_relation,u),least(v,image(successor_relation,u))),ordinal_numbers)**. % 299.95/300.40 177223[22:MRR:177209.1,167338.0] || subclass(omega,symmetrization_of(ordinal_numbers))* -> . % 299.95/300.40 177221[22:Res:177171.1,167338.0] || subclass(omega,inverse(ordinal_numbers))* -> . % 299.95/300.40 177216[22:Res:177171.1,167057.0] || subclass(omega,ordinal_numbers)* -> . % 299.95/300.40 177171[22:MRR:177166.1,167008.0] || subclass(omega,u) -> member(ordinal_numbers,u)*. % 299.95/300.40 177178[22:Res:177170.0,167095.1] || equal(complement(omega),universal_class)** -> . % 299.95/300.40 168636[19:Rew:166997.0,80907.1] || well_ordering(u,cross_product(cross_product(universal_class,universal_class),universal_class))*+ -> equal(flip(v),ordinal_numbers) member(least(u,flip(v)),flip(v))*. % 299.95/300.40 177170[22:MRR:177163.0,167008.0] || -> member(ordinal_numbers,omega)*. % 299.95/300.40 177161[22:Spt:177104.1] || -> equal(regular(omega),ordinal_numbers)**. % 299.95/300.40 168635[19:Rew:166997.0,80906.1] || well_ordering(u,cross_product(cross_product(universal_class,universal_class),universal_class))*+ -> equal(rotate(v),ordinal_numbers) member(least(u,rotate(v)),rotate(v))*. % 299.95/300.40 176380[19:Res:167137.1,176206.0] || -> equal(u,ordinal_numbers) equal(cantor(regular(u)),ordinal_numbers)**. % 299.95/300.40 176365[19:Res:167115.1,176206.0] || -> equal(integer_of(u),ordinal_numbers)** equal(cantor(u),ordinal_numbers). % 299.95/300.40 176364[19:Res:167224.0,176206.0] || -> equal(singleton(u),ordinal_numbers) equal(cantor(u),ordinal_numbers)**. % 299.95/300.40 176231[19:Res:167106.1,175681.1] inductive(cantor(u)) || member(u,universal_class)* -> . % 299.95/300.40 168608[19:Rew:166997.0,80879.0] || equal(restrict(restrict(inverse(cross_product(u,v)),u,v),w,w),ordinal_numbers)** -> asymmetric(cross_product(u,v),w). % 299.95/300.40 168607[19:Rew:166997.0,80880.1] || asymmetric(cross_product(u,v),w) -> equal(restrict(restrict(inverse(cross_product(u,v)),u,v),w,w),ordinal_numbers)**. % 299.95/300.40 168610[19:Rew:166997.0,80882.1] || well_ordering(u,cross_product(universal_class,universal_class)) -> equal(segment(u,compose(v,w),least(u,compose(v,w))),ordinal_numbers)**. % 299.95/300.40 176363[19:Res:940.0,176206.0] || -> equal(cantor(ordered_pair(u,v)),ordinal_numbers)**. % 299.95/300.40 176362[19:Res:12.0,176206.0] || -> equal(cantor(unordered_pair(u,v)),ordinal_numbers)**. % 299.95/300.40 168223[19:Rew:166997.0,80683.1] || member(intersection(u,v),universal_class) -> equal(intersection(u,v),ordinal_numbers) member(apply(choice,intersection(u,v)),u)*. % 299.95/300.40 176381[20:Res:175569.0,176206.0] || -> equal(cantor(regular(symmetrization_of(ordinal_numbers))),ordinal_numbers)**. % 299.95/300.40 168222[19:Rew:166997.0,80684.1] || member(intersection(u,v),universal_class) -> equal(intersection(u,v),ordinal_numbers) member(apply(choice,intersection(u,v)),v)*. % 299.95/300.40 176361[19:Res:170.0,176206.0] || -> equal(cantor(singleton(u)),ordinal_numbers)**. % 299.95/300.40 176491[19:Res:7.1,176428.0] || equal(rest_relation,element_relation)** -> . % 299.95/300.40 176235[19:Rew:176206.1,158257.2] || member(u,universal_class) subclass(domain_relation,v) -> member(ordered_pair(u,ordinal_numbers),v)*. % 299.95/300.40 176428[19:MRR:176423.1,167057.0] || subclass(rest_relation,element_relation)* -> . % 299.95/300.40 176360[19:Res:53.0,176206.0] || -> equal(cantor(omega),ordinal_numbers)**. % 299.95/300.40 176206[19:Res:167139.1,175681.1] || member(u,universal_class)* -> equal(cantor(u),ordinal_numbers). % 299.95/300.40 176340[19:MRR:176332.0,170.0] || -> member(singleton(singleton(singleton(ordinal_numbers))),domain_relation)*. % 299.95/300.40 176234[19:Rew:176206.1,157887.1] || member(u,universal_class) -> member(ordered_pair(u,ordinal_numbers),domain_relation)*. % 299.95/300.40 176162[21:Res:175804.1,36583.0] || well_ordering(u,omega) -> member(least(u,omega),universal_class)*. % 299.95/300.40 176155[21:Res:175802.1,36583.0] || well_ordering(u,universal_class) -> member(least(u,omega),universal_class)*. % 299.95/300.40 176080[20:Res:7.1,175566.0] || equal(u,inverse(ordinal_numbers)) well_ordering(universal_class,u)* -> . % 299.95/300.40 167788[19:Rew:166997.0,80574.1] || asymmetric(u,singleton(v)) -> equal(range__dfg(intersection(u,inverse(u)),v,singleton(v)),second(not_subclass_element(ordinal_numbers,ordinal_numbers)))**. % 299.95/300.40 175804[21:Res:289.0,175799.0] || well_ordering(u,omega) -> member(least(u,omega),omega)*. % 299.95/300.40 175802[21:Res:5.0,175799.0] || well_ordering(u,universal_class) -> member(least(u,omega),omega)*. % 299.95/300.40 176150[20:Res:7.1,176136.0] || equal(complement(inverse(ordinal_numbers)),universal_class)** -> . % 299.95/300.40 176136[20:Res:175613.1,175561.0] || subclass(universal_class,complement(inverse(ordinal_numbers)))* -> . % 299.95/300.40 9914[0:Res:17.2,47.1] || member(u,universal_class) member(v,universal_class) equal(successor(v),u) -> member(ordered_pair(v,u),successor_relation)*. % 299.95/300.40 175613[20:Res:175569.0,2.0] || subclass(universal_class,u) -> member(regular(symmetrization_of(ordinal_numbers)),u)*. % 299.95/300.40 176096[20:MRR:176095.0,83157.0] || equal(inverse(ordinal_numbers),ordinal_numbers)** -> . % 299.95/300.40 168612[19:Rew:166997.0,80884.1] || well_ordering(u,cross_product(cross_product(universal_class,universal_class),universal_class)) -> equal(segment(u,flip(v),least(u,flip(v))),ordinal_numbers)**. % 299.95/300.40 176081[20:Res:289.0,175566.0] || well_ordering(universal_class,inverse(ordinal_numbers))* -> . % 299.95/300.40 175566[20:Res:175558.0,11848.0] || subclass(inverse(ordinal_numbers),u)* well_ordering(universal_class,u) -> . % 299.95/300.40 169198[19:Rew:166997.0,167088.0] || equal(u,complement(inverse(ordinal_numbers)))*+ -> member(ordinal_numbers,u)*. % 299.95/300.40 169200[19:Rew:166997.0,167090.0] || subclass(complement(inverse(ordinal_numbers)),u)* -> member(ordinal_numbers,u). % 299.95/300.40 168611[19:Rew:166997.0,80883.1] || well_ordering(u,cross_product(cross_product(universal_class,universal_class),universal_class)) -> equal(segment(u,rotate(v),least(u,rotate(v))),ordinal_numbers)**. % 299.95/300.40 169207[19:Rew:166997.0,167189.0] || member(u,symmetrization_of(ordinal_numbers))* -> member(u,inverse(ordinal_numbers)). % 299.95/300.40 169204[19:Rew:166997.0,167180.0] || equal(sum_class(ordinal_numbers),ordinal_numbers) -> subclass(sum_class(ordinal_numbers),u)*. % 299.95/300.40 168361[19:Rew:166997.0,80754.0] || -> equal(unordered_pair(u,v),ordinal_numbers) equal(regular(unordered_pair(u,v)),v)** equal(regular(unordered_pair(u,v)),u)**. % 299.95/300.40 169484[19:MRR:169483.2,169483.3,167011.0,167057.0] || connected(element_relation,ordinal_numbers)* equal(sum_class(ordinal_numbers),ordinal_numbers) -> . % 299.95/300.40 168539[19:Rew:166997.0,80827.2] function(u) || well_ordering(v,cross_product(universal_class,universal_class)) -> equal(segment(v,u,least(v,u)),ordinal_numbers)**. % 299.95/300.40 167721[19:Rew:166997.0,80614.2] function(u) || well_ordering(v,cross_product(universal_class,universal_class))*+ -> equal(u,ordinal_numbers) member(least(v,u),u)*. % 299.95/300.40 175561[20:MRR:169311.1,175557.0] || member(regular(symmetrization_of(ordinal_numbers)),complement(inverse(ordinal_numbers)))* -> . % 299.95/300.40 168564[19:Rew:166997.0,80840.1] || well_ordering(u,cross_product(universal_class,universal_class)) -> equal(rest_of(v),ordinal_numbers) member(least(u,rest_of(v)),rest_of(v))*. % 299.95/300.40 168563[19:Rew:166997.0,80839.1] || well_ordering(u,cross_product(universal_class,universal_class)) -> equal(compose_class(v),ordinal_numbers) member(least(u,compose_class(v)),compose_class(v))*. % 299.95/300.40 167193[19:Rew:166997.0,160531.0] || -> equal(intersection(inverse(ordinal_numbers),symmetrization_of(ordinal_numbers)),symmetrization_of(ordinal_numbers))**. % 299.95/300.40 167204[19:Rew:166997.0,81109.0] || -> equal(apply(ordinal_numbers,u),sum_class(range_of(ordinal_numbers)))**. % 299.95/300.40 175799[21:Spt:168372.0,168372.1,168372.3] || subclass(omega,u)+ well_ordering(v,u)* -> member(least(v,omega),omega)*. % 299.95/300.40 175560[20:MRR:169272.1,175557.0] || subclass(symmetrization_of(ordinal_numbers),complement(inverse(ordinal_numbers)))* -> . % 299.95/300.40 175559[20:MRR:169271.1,175557.0] || equal(complement(inverse(ordinal_numbers)),symmetrization_of(ordinal_numbers))** -> . % 299.95/300.40 167785[19:Rew:166997.0,158669.2] || member(u,universal_class) -> member(u,cantor(v)) equal(second(not_subclass_element(ordinal_numbers,ordinal_numbers)),range__dfg(v,u,universal_class))*. % 299.95/300.40 167191[19:Rew:166997.0,159937.0] || -> equal(complement(complement(inverse(ordinal_numbers))),symmetrization_of(ordinal_numbers))**. % 299.95/300.40 167165[19:Rew:166997.0,80485.0] || -> equal(image(ordinal_numbers,u),range_of(ordinal_numbers))**. % 299.95/300.40 167148[19:Rew:166997.0,99355.0] || equal(sum_class(range_of(ordinal_numbers)),ordinal_numbers)** -> . % 299.95/300.40 167188[19:Rew:166997.0,163350.0] || equal(inverse(ordinal_numbers),singleton(ordinal_numbers))** -> . % 299.95/300.40 167147[19:Rew:166997.0,158452.2] || member(u,universal_class) -> member(u,cantor(v)) equal(image(v,singleton(u)),range_of(ordinal_numbers))**. % 299.95/300.40 167198[19:Rew:166997.0,164561.0] || equal(symmetrization_of(ordinal_numbers),singleton(ordinal_numbers))** -> . % 299.95/300.40 175569[20:Res:175558.0,36583.0] || -> member(regular(symmetrization_of(ordinal_numbers)),universal_class)*. % 299.95/300.40 167186[19:Rew:166997.0,163351.0] || subclass(universal_class,inverse(ordinal_numbers))* -> . % 299.95/300.40 167146[19:Rew:166997.0,80393.1] || asymmetric(u,universal_class) -> equal(image(intersection(u,inverse(u)),universal_class),range_of(ordinal_numbers))**. % 299.95/300.40 167187[19:Rew:166997.0,163464.0] || equal(inverse(ordinal_numbers),universal_class)** -> . % 299.95/300.40 167338[19:Rew:166997.0,163342.0] || member(ordinal_numbers,inverse(ordinal_numbers))* -> . % 299.95/300.40 167337[19:Rew:166997.0,163341.0] || -> member(ordinal_numbers,complement(inverse(ordinal_numbers)))*. % 299.95/300.40 167192[19:Rew:166997.0,160530.0] || -> subclass(symmetrization_of(ordinal_numbers),inverse(ordinal_numbers))*. % 299.95/300.40 175557[20:Spt:175550.0,169235.0,174599.0] || equal(symmetrization_of(ordinal_numbers),ordinal_numbers)** -> . % 299.95/300.40 167196[19:Rew:166997.0,164303.0] || subclass(universal_class,symmetrization_of(ordinal_numbers))* -> . % 299.95/300.40 167197[19:Rew:166997.0,164315.0] || equal(symmetrization_of(ordinal_numbers),universal_class)** -> . % 299.95/300.40 175558[20:Spt:175550.0,169235.1] || -> member(regular(symmetrization_of(ordinal_numbers)),inverse(ordinal_numbers))*. % 299.95/300.40 168514[19:Rew:166997.0,80461.2] || equal(u,v)*+ well_ordering(w,u)* -> equal(segment(w,v,least(w,v)),ordinal_numbers)**. % 299.95/300.40 168250[19:Rew:166997.0,80449.2] || equal(u,v)*+ well_ordering(w,u)* -> equal(v,ordinal_numbers) member(least(w,v),v)*. % 299.95/300.40 167889[19:Rew:166997.0,164993.1] function(complement(inverse(identity_relation))) || -> member(ordinal_numbers,cross_product(universal_class,universal_class))*. % 299.95/300.40 169641[19:MRR:169077.2,167057.0] || well_ordering(element_relation,image(u,singleton(v))) subclass(apply(u,v),image(u,singleton(v)))* -> . % 299.95/300.40 167762[19:Rew:166997.0,84163.1] || asymmetric(u,singleton(v)) -> equal(domain__dfg(intersection(u,inverse(u)),singleton(v),v),single_valued3(ordinal_numbers))**. % 299.95/300.40 167454[19:Rew:166997.0,80534.0] || -> subclass(symmetric_difference(complement(singleton(ordinal_numbers)),complement(image(successor_relation,ordinal_numbers))),kind_1_ordinals)*. % 299.95/300.40 167380[19:Rew:166997.0,80986.1] inductive(composition_function) || -> member(ordinal_numbers,cross_product(universal_class,cross_product(universal_class,universal_class)))*. % 299.95/300.40 167379[19:Rew:166997.0,80987.1] inductive(application_function) || -> member(ordinal_numbers,cross_product(universal_class,cross_product(universal_class,universal_class)))*. % 299.95/300.40 167727[19:Rew:166997.0,80383.2] || member(u,universal_class) subclass(u,v) -> equal(u,ordinal_numbers) member(apply(choice,u),v)*. % 299.95/300.40 167257[19:Rew:166997.0,98592.1] || subclass(domain_relation,complement(complement(rest_relation)))* -> equal(rest_of(ordinal_numbers),ordinal_numbers). % 299.95/300.40 167256[19:Rew:166997.0,98651.1] || equal(complement(complement(rest_relation)),domain_relation)** -> equal(rest_of(ordinal_numbers),ordinal_numbers). % 299.95/300.40 164971[15:Res:63.1,163018.0] function(successor(identity_relation)) || well_ordering(universal_class,cross_product(universal_class,universal_class))* -> . % 299.95/300.40 167375[19:Rew:166997.0,166663.1] || -> member(u,v) equal(intersection(v,singleton(u)),ordinal_numbers)**. % 299.95/300.40 167374[19:Rew:166997.0,166474.1] || -> member(u,v) equal(intersection(singleton(u),v),ordinal_numbers)**. % 299.95/300.40 167371[19:Rew:166997.0,84181.0] || -> equal(range__dfg(ordinal_numbers,u,v),range__dfg(ordinal_numbers,w,x))*. % 299.95/300.40 167370[19:Rew:166997.0,82481.0] || equal(cross_product(u,u),ordinal_numbers)**+ -> connected(v,u)*. % 299.95/300.40 167082[19:Rew:166997.0,80369.1] inductive(restrict(u,v,w)) || -> member(ordinal_numbers,u)*. % 299.95/300.40 167355[19:Rew:166997.0,84386.0] || equal(sum_class(u),ordinal_numbers) -> subclass(sum_class(u),u)*. % 299.95/300.40 168513[19:Rew:166997.0,80457.1] || well_ordering(u,cross_product(universal_class,universal_class)) -> equal(segment(u,rest_of(v),least(u,rest_of(v))),ordinal_numbers)**. % 299.95/300.40 167332[19:Rew:166997.0,80442.1] || subclass(complement(u),u)* -> equal(complement(u),ordinal_numbers). % 299.95/300.40 167313[19:Rew:166997.0,163259.1] inductive(symmetric_difference(u,u)) || -> member(ordinal_numbers,complement(u))*. % 299.95/300.40 167310[19:Rew:166997.0,82387.1] || subclass(universal_class,intersection(u,v))* -> member(ordinal_numbers,v). % 299.95/300.40 168512[19:Rew:166997.0,80456.1] || well_ordering(u,cross_product(universal_class,universal_class)) -> equal(segment(u,compose_class(v),least(u,compose_class(v))),ordinal_numbers)**. % 299.95/300.40 167309[19:Rew:166997.0,84251.1] || subclass(domain_relation,cross_product(u,v))* -> member(ordinal_numbers,v). % 299.95/300.40 167308[19:Rew:166997.0,93588.1] || equal(intersection(u,v),universal_class)** -> member(ordinal_numbers,v). % 299.95/300.40 167307[19:Rew:166997.0,93600.1] || equal(cross_product(u,v),domain_relation)** -> member(ordinal_numbers,v). % 299.95/300.40 167222[19:Rew:166997.0,80404.0] || -> equal(singleton(u),ordinal_numbers) equal(regular(singleton(u)),u)**. % 299.95/300.40 167926[19:Rew:166997.0,80437.1] || asymmetric(u,v) subclass(compose(ordinal_numbers,ordinal_numbers),ordinal_numbers) -> transitive(intersection(u,inverse(u)),v)*. % 299.95/300.40 167213[19:Rew:166997.0,82515.1] single_valued_class(u) || equal(ordinal_numbers,u) -> function(u)*. % 299.95/300.40 167086[19:Rew:166997.0,82386.1] || subclass(universal_class,intersection(u,v))* -> member(ordinal_numbers,u). % 299.95/300.40 167085[19:Rew:166997.0,84250.1] || subclass(domain_relation,cross_product(u,v))* -> member(ordinal_numbers,u). % 299.95/300.40 167084[19:Rew:166997.0,93633.1] || equal(intersection(u,v),universal_class)** -> member(ordinal_numbers,u). % 299.95/300.40 167083[19:Rew:166997.0,93662.1] || equal(cross_product(u,v),domain_relation)** -> member(ordinal_numbers,u). % 299.95/300.40 167363[19:Rew:166997.0,160913.1] || member(u,universal_class) -> equal(integer_of(range_of(u)),ordinal_numbers)**. % 299.95/300.40 167362[19:Rew:166997.0,160879.1] || member(u,universal_class) -> equal(singleton(range_of(u)),ordinal_numbers)**. % 299.95/300.40 167356[19:Rew:166997.0,82465.0] || equal(sum_class(u),ordinal_numbers) -> section(element_relation,u,universal_class)*. % 299.95/300.40 167354[19:Rew:166997.0,81097.0] || -> equal(second(not_subclass_element(ordinal_numbers,ordinal_numbers)),range__dfg(ordinal_numbers,u,v))*. % 299.95/300.40 167906[19:Rew:166997.0,80440.2] || member(complement(u),universal_class) member(apply(choice,complement(u)),u)* -> equal(complement(u),ordinal_numbers). % 299.95/300.40 167353[19:Rew:166997.0,80439.1] inductive(cantor(inverse(u))) || -> member(ordinal_numbers,range_of(u))*. % 299.95/300.40 167314[19:Rew:166997.0,163216.1] inductive(symmetric_difference(universal_class,u)) || -> member(ordinal_numbers,complement(u))*. % 299.95/300.40 169008[19:Rew:166997.0,80455.1] || well_ordering(u,cross_product(universal_class,cross_product(universal_class,universal_class)))*+ -> equal(segment(u,composition_function,least(u,composition_function)),ordinal_numbers)**. % 299.95/300.40 167127[19:Rew:166997.0,81104.1] || subclass(domain_relation,u) -> member(ordered_pair(ordinal_numbers,ordinal_numbers),u)*. % 299.95/300.40 167096[19:Rew:166997.0,82380.1] || subclass(universal_class,complement(u))* member(ordinal_numbers,u) -> . % 299.95/300.40 167094[19:Rew:166997.0,85108.1] || equal(complement(complement(u)),universal_class)** -> member(ordinal_numbers,u). % 299.95/300.40 167093[19:Rew:166997.0,160952.1] || subclass(universal_class,complement(complement(u)))* -> member(ordinal_numbers,u). % 299.95/300.40 167367[19:Rew:166997.0,81102.1] || asymmetric(u,singleton(v)) -> equal(segment(intersection(u,inverse(u)),singleton(v),v),ordinal_numbers)**. % 299.95/300.40 167378[19:Rew:166997.0,81006.2] inductive(u) || well_ordering(v,u)*+ -> equal(segment(v,omega,least(v,omega)),ordinal_numbers)**. % 299.95/300.40 169197[19:Rew:166997.0,167041.1] || equal(singleton(u),singleton(ordinal_numbers))* -> equal(ordinal_numbers,u). % 299.95/300.40 167032[19:Rew:166997.0,164844.0] || equal(u,singleton(ordinal_numbers)) well_ordering(universal_class,u)* -> . % 299.95/300.40 167024[19:Rew:166997.0,162020.0] || subclass(singleton(ordinal_numbers),u)* well_ordering(universal_class,u) -> . % 299.95/300.40 169213[19:Rew:166997.0,167275.1] || transitive(ordinal_numbers,u)*+ -> equal(compose(ordinal_numbers,ordinal_numbers),ordinal_numbers)**. % 299.95/300.40 167324[19:Rew:166997.0,8595.0] || equal(compose(u,inverse(u)),ordinal_numbers)**+ subclass(u,cross_product(universal_class,universal_class))* -> function(u). % 299.95/300.40 169212[19:Rew:166997.0,167274.0] || equal(compose(ordinal_numbers,ordinal_numbers),ordinal_numbers)**+ -> transitive(ordinal_numbers,u)*. % 299.95/300.40 169211[19:Rew:166997.0,167273.0] || subclass(compose(ordinal_numbers,ordinal_numbers),ordinal_numbers)*+ -> transitive(ordinal_numbers,u)*. % 299.95/300.40 167238[19:Rew:166997.0,80418.1] inductive(rest_of(u)) || -> member(ordinal_numbers,cross_product(universal_class,universal_class))*. % 299.95/300.40 167237[19:Rew:166997.0,80419.1] inductive(compose_class(u)) || -> member(ordinal_numbers,cross_product(universal_class,universal_class))*. % 299.95/300.40 169365[19:Rew:166997.0,167364.1] || -> equal(cross_product(u,v),ordinal_numbers) equal(restrict(regular(cross_product(u,v)),u,v),ordinal_numbers)**. % 299.95/300.40 167124[19:Rew:166997.0,97527.0] || subclass(domain_relation,complement(unordered_pair(ordered_pair(ordinal_numbers,ordinal_numbers),u)))* -> . % 299.95/300.40 167123[19:Rew:166997.0,97541.0] || equal(complement(unordered_pair(ordered_pair(ordinal_numbers,ordinal_numbers),u)),domain_relation)** -> . % 299.95/300.40 167122[19:Rew:166997.0,97528.0] || subclass(domain_relation,complement(unordered_pair(u,ordered_pair(ordinal_numbers,ordinal_numbers))))* -> . % 299.95/300.40 167360[19:Rew:166997.0,80453.1] || well_ordering(u,cross_product(universal_class,universal_class)) -> equal(segment(u,rest_relation,least(u,rest_relation)),ordinal_numbers)**. % 299.95/300.40 167121[19:Rew:166997.0,97544.0] || equal(complement(unordered_pair(u,ordered_pair(ordinal_numbers,ordinal_numbers))),domain_relation)** -> . % 299.95/300.40 167109[19:Rew:166997.0,159368.1] || member(u,universal_class)* subclass(rest_relation,rest_of(ordinal_numbers))*+ -> . % 299.95/300.40 167359[19:Rew:166997.0,80452.1] || well_ordering(u,cross_product(universal_class,universal_class)) -> equal(segment(u,domain_relation,least(u,domain_relation)),ordinal_numbers)**. % 299.95/300.40 173021[19:SoR:172321.0,72.1] one_to_one(successor(ordinal_numbers)) || -> member(ordinal_numbers,cross_product(universal_class,universal_class))*. % 299.95/300.40 167358[19:Rew:166997.0,80451.1] || well_ordering(u,cross_product(universal_class,universal_class)) -> equal(segment(u,successor_relation,least(u,successor_relation)),ordinal_numbers)**. % 299.95/300.40 173002[19:Res:167219.1,169324.0] || equal(sum_class(kind_1_ordinals),ordinal_numbers) well_ordering(element_relation,kind_1_ordinals)* -> . % 299.95/300.40 172321[19:Res:63.1,169185.0] function(successor(ordinal_numbers)) || -> member(ordinal_numbers,cross_product(universal_class,universal_class))*. % 299.95/300.40 167357[19:Rew:166997.0,80450.1] || well_ordering(u,cross_product(universal_class,universal_class)) -> equal(segment(u,element_relation,least(u,element_relation)),ordinal_numbers)**. % 299.95/300.40 170250[19:Res:167106.1,110865.0] inductive(rest_of(ordinal_numbers)) || subclass(universal_class,complement(element_relation))* -> . % 299.95/300.40 170242[19:Res:167106.1,110991.0] inductive(cantor(ordinal_numbers)) || subclass(universal_class,complement(element_relation))* -> . % 299.95/300.40 169108[19:MRR:8686.3,167057.0] || equal(sum_class(u),u) member(u,universal_class) well_ordering(element_relation,u)* -> . % 299.95/300.40 169324[19:MRR:169069.2,167057.0] || subclass(sum_class(kind_1_ordinals),ordinal_numbers)* well_ordering(element_relation,kind_1_ordinals) -> . % 299.95/300.40 167236[19:Rew:166997.0,160292.1] function(image(successor_relation,cross_product(universal_class,universal_class))) || member(ordinal_numbers,cross_product(universal_class,universal_class))* -> . % 299.95/300.40 167373[19:Rew:166997.0,80721.1] || well_ordering(u,universal_class) -> equal(segment(u,v,least(u,v)),ordinal_numbers)**. % 299.95/300.40 167372[19:Rew:166997.0,80702.1] || well_ordering(u,universal_class) -> equal(v,ordinal_numbers) member(least(u,v),v)*. % 299.95/300.40 167130[19:Rew:166997.0,158355.0] || -> equal(u,ordinal_numbers) equal(symmetric_difference(u,regular(u)),union(u,regular(u)))**. % 299.95/300.40 167241[19:Rew:166997.0,163080.1] function(successor(identity_relation)) || -> member(ordinal_numbers,cross_product(universal_class,universal_class))*. % 299.95/300.40 167240[19:Rew:166997.0,163710.1] one_to_one(successor(identity_relation)) || -> member(ordinal_numbers,cross_product(universal_class,universal_class))*. % 299.95/300.40 169098[19:MRR:8655.3,167057.0] || equal(sum_class(u),u) well_ordering(element_relation,u)* -> equal(u,ordinal_numbers). % 299.95/300.40 167120[19:Rew:166997.0,84327.1] || equal(rest_relation,domain_relation) -> member(ordered_pair(ordinal_numbers,ordinal_numbers),rest_relation)*. % 299.95/300.40 167097[19:Rew:166997.0,80370.1] || equal(image(successor_relation,u),u)** member(ordinal_numbers,u) -> inductive(u). % 299.95/300.40 167319[19:Rew:166997.0,81098.1] || subclass(u,v) -> section(ordinal_numbers,u,v)*. % 299.95/300.40 167223[19:Rew:166997.0,80405.0] || -> equal(singleton(u),ordinal_numbers) member(u,singleton(u))*. % 299.95/300.40 167216[19:Rew:166997.0,80412.0] || equal(ordinal_numbers,u) -> equal(integer_of(u),u)**. % 299.95/300.40 169556[19:MRR:169074.2,167057.0] function(sum_class(cross_product(universal_class,universal_class))) || well_ordering(element_relation,cross_product(universal_class,universal_class))* -> . % 299.95/300.40 167305[19:Rew:166997.0,83824.1] inductive(domain_of(u)) || -> member(ordinal_numbers,cantor(u))*. % 299.95/300.40 167341[19:Rew:166997.0,80445.0] || -> equal(intersection(u,v),ordinal_numbers) member(regular(intersection(u,v)),u)*. % 299.95/300.40 167218[19:Rew:166997.0,82391.1] || subclass(universal_class,singleton(u))* -> equal(ordinal_numbers,u). % 299.95/300.40 167217[19:Rew:166997.0,83494.1] || equal(singleton(u),universal_class)** -> equal(ordinal_numbers,u). % 299.95/300.40 167340[19:Rew:166997.0,80446.0] || -> equal(intersection(u,v),ordinal_numbers) member(regular(intersection(u,v)),v)*. % 299.95/300.40 167182[19:Rew:166997.0,84165.1] function(u) || -> equal(single_valued3(ordinal_numbers),single_valued1(u))*. % 299.95/300.40 167181[19:Rew:166997.0,84166.1] single_valued_class(u) || -> equal(single_valued3(ordinal_numbers),single_valued1(u))*. % 299.95/300.40 167113[19:Rew:166997.0,83649.0] || -> equal(integer_of(u),ordinal_numbers) subclass(singleton(u),omega)*. % 299.95/300.40 167131[19:Rew:166997.0,80384.1] || subclass(u,v) -> equal(u,ordinal_numbers) member(regular(u),v)*. % 299.95/300.40 167102[19:Rew:166997.0,159676.1] inductive(complement(complement(u))) || -> member(ordinal_numbers,u)*. % 299.95/300.40 167092[19:Rew:166997.0,164846.0] || member(ordinal_numbers,u) well_ordering(universal_class,u)* -> . % 299.95/300.40 167339[19:Rew:166997.0,80990.1] || subclass(omega,u) -> equal(integer_of(v),ordinal_numbers) member(v,u)*. % 299.95/300.40 167091[19:Rew:166997.0,164848.1] || well_ordering(universal_class,complement(u))* -> member(ordinal_numbers,u). % 299.95/300.40 169181[19:Rew:166997.0,167033.1] || equal(u,singleton(ordinal_numbers)) -> member(ordinal_numbers,u)*. % 299.95/300.40 169179[19:Rew:166997.0,167025.1] || subclass(singleton(ordinal_numbers),u)* -> member(ordinal_numbers,u). % 299.95/300.40 169191[19:Rew:166997.0,167272.1] || equal(compose_class(ordinal_numbers),domain_relation) -> transitive(ordinal_numbers,u)*. % 299.95/300.40 169243[19:Rew:166997.0,167215.1] inductive(unordered_pair(u,v)) || -> equal(ordinal_numbers,v)* equal(ordinal_numbers,u)*. % 299.95/300.40 172114[19:MRR:172111.1,167331.0] inductive(complement(successor(ordinal_numbers))) || -> . % 299.95/300.40 172113[19:MRR:172091.1,167338.0] inductive(symmetrization_of(ordinal_numbers)) || -> . % 299.95/300.40 167311[19:Rew:166997.0,80433.2] inductive(u) || subclass(u,v)*+ -> member(ordinal_numbers,v)*. % 299.95/300.40 167382[19:Rew:166997.0,166840.0] || equal(cross_product(universal_class,cross_product(universal_class,universal_class)),ordinal_numbers)** -> . % 299.95/300.40 167334[19:Rew:166997.0,80443.1] || member(regular(complement(u)),u)* -> equal(complement(u),ordinal_numbers). % 299.95/300.40 167327[19:Rew:166997.0,5482.0] || equal(compose(u,inverse(u)),ordinal_numbers)** -> single_valued_class(u). % 299.95/300.40 167326[19:Rew:166997.0,81111.1] single_valued_class(u) || -> equal(compose(u,inverse(u)),ordinal_numbers)**. % 299.95/300.40 167259[19:Rew:166997.0,84253.1] || subclass(domain_relation,rest_relation)* -> equal(rest_of(ordinal_numbers),ordinal_numbers). % 299.95/300.40 167258[19:Rew:166997.0,84277.1] || equal(rest_relation,domain_relation) -> equal(rest_of(ordinal_numbers),ordinal_numbers)**. % 299.95/300.40 167325[19:Rew:166997.0,81112.1] function(u) || -> equal(compose(u,inverse(u)),ordinal_numbers)**. % 299.95/300.40 167251[19:Rew:166997.0,80420.1] inductive(rest_relation) || -> member(ordinal_numbers,cross_product(universal_class,universal_class))*. % 299.95/300.40 167250[19:Rew:166997.0,80421.1] inductive(domain_relation) || -> member(ordinal_numbers,cross_product(universal_class,universal_class))*. % 299.95/300.40 167249[19:Rew:166997.0,80422.1] inductive(successor_relation) || -> member(ordinal_numbers,cross_product(universal_class,universal_class))*. % 299.95/300.40 167248[19:Rew:166997.0,80647.1] inductive(union_of_range_map) || -> member(ordinal_numbers,cross_product(universal_class,universal_class))*. % 299.95/300.40 167320[19:Rew:166997.0,80985.0] || -> equal(integer_of(not_subclass_element(u,omega)),ordinal_numbers)** subclass(u,omega). % 299.95/300.40 167247[19:Rew:166997.0,80648.1] inductive(element_relation) || -> member(ordinal_numbers,cross_product(universal_class,universal_class))*. % 299.95/300.40 167312[19:Rew:166997.0,80434.1] inductive(intersection(u,v)) || -> member(ordinal_numbers,v)*. % 299.95/300.40 167112[19:Rew:166997.0,80376.0] || -> equal(integer_of(u),ordinal_numbers)** equal(integer_of(u),u)**. % 299.95/300.40 167119[19:Rew:166997.0,97526.0] || subclass(domain_relation,complement(singleton(ordered_pair(ordinal_numbers,ordinal_numbers))))* -> . % 299.95/300.40 167118[19:Rew:166997.0,97536.0] || equal(complement(singleton(ordered_pair(ordinal_numbers,ordinal_numbers))),domain_relation)** -> . % 299.95/300.40 167100[19:Rew:166997.0,80371.1] inductive(intersection(u,v)) || -> member(ordinal_numbers,u)*. % 299.95/300.40 167103[19:Rew:166997.0,80372.1] inductive(complement(u)) || member(ordinal_numbers,u)* -> . % 299.95/300.40 167219[19:Rew:166997.0,82438.0] || equal(ordinal_numbers,u) -> subclass(u,v)*. % 299.95/300.40 167210[19:Rew:166997.0,81012.0] || subclass(u,ordinal_numbers)*+ -> subclass(u,v)*. % 299.95/300.40 169313[19:MRR:168269.2,164.0] inductive(singleton(u)) || -> member(u,universal_class)*. % 299.95/300.40 167306[19:Rew:166997.0,80438.2] || connected(u,v) member(w,not_well_ordering(u,v)) equal(segment(u,not_well_ordering(u,v),w),ordinal_numbers)** -> well_ordering(u,v). % 299.95/300.40 167231[19:Rew:166997.0,157842.0] || -> equal(symmetric_difference(ordinal_numbers,u),complement(complement(u)))**. % 299.95/300.40 167230[19:Rew:166997.0,157840.0] || -> equal(union(ordinal_numbers,u),complement(complement(u)))**. % 299.95/300.40 167276[19:Rew:166997.0,80432.2] || subclass(u,v)*+ well_ordering(w,v)* -> equal(segment(w,u,least(w,u)),ordinal_numbers)**. % 299.95/300.40 167225[19:Rew:166997.0,84162.0] || -> equal(domain__dfg(ordinal_numbers,u,v),single_valued3(ordinal_numbers))**. % 299.95/300.40 167224[19:Rew:166997.0,80406.1] || -> member(u,universal_class)* equal(singleton(u),ordinal_numbers). % 299.95/300.40 167221[19:Rew:166997.0,80413.1] inductive(singleton(u)) || -> equal(ordinal_numbers,u)*. % 299.95/300.40 167220[19:Rew:166997.0,161080.1] inductive(u) || equal(ordinal_numbers,u)* -> . % 299.95/300.40 167133[19:Rew:166997.0,80385.2] || subclass(u,v)*+ well_ordering(w,v)* -> equal(u,ordinal_numbers) member(least(w,u),u)*. % 299.95/300.40 171310[19:Res:16280.0,167211.1] inductive(restrict(ordinal_numbers,u,v)) || -> . % 299.95/300.40 171315[19:Res:16381.0,167211.1] inductive(intersection(u,ordinal_numbers)) || -> . % 299.95/300.40 171308[19:Res:16254.0,167211.1] inductive(intersection(ordinal_numbers,u)) || -> . % 299.95/300.40 171312[19:Res:135236.0,167211.1] inductive(complement(complement(ordinal_numbers))) || -> . % 299.95/300.40 167252[19:Rew:166997.0,158405.2] || member(u,universal_class) -> member(u,cantor(v)) equal(restrict(v,singleton(u),universal_class),ordinal_numbers)**. % 299.95/300.40 167211[19:Rew:166997.0,159468.1] inductive(u) || subclass(u,ordinal_numbers)* -> . % 299.95/300.40 169177[19:Rew:166997.0,167162.1] || connected(u,ordinal_numbers) -> well_ordering(u,ordinal_numbers)*. % 299.95/300.40 167137[19:Rew:166997.0,80386.0] || -> equal(u,ordinal_numbers) member(regular(u),universal_class)*. % 299.95/300.40 169167[19:Rew:166997.0,167136.0] || subclass(u,ordinal_numbers)* -> equal(u,ordinal_numbers). % 299.95/300.40 167173[19:Rew:166997.0,65.1] || subclass(u,cross_product(universal_class,universal_class)) subclass(compose(u,inverse(u)),ordinal_numbers)* -> function(u). % 299.95/300.40 169159[19:Rew:166997.0,167134.0] || equal(ordinal_numbers,u)* -> equal(u,ordinal_numbers). % 299.95/300.40 167115[19:Rew:166997.0,81039.0] || -> equal(integer_of(u),ordinal_numbers) member(u,universal_class)*. % 299.95/300.40 167104[19:Rew:166997.0,80563.1] || subclass(universal_class,u) -> member(ordinal_numbers,u)*. % 299.95/300.40 169158[19:Rew:166997.0,167101.1] || -> member(ordinal_numbers,u) member(ordinal_numbers,complement(u))*. % 299.95/300.40 167271[19:Rew:166997.0,80423.0] || equal(restrict(intersection(u,inverse(u)),v,v),ordinal_numbers)** -> asymmetric(u,v). % 299.95/300.40 167087[19:Rew:166997.0,166041.1] || equal(u,universal_class) -> member(ordinal_numbers,u)*. % 299.95/300.40 167035[19:Rew:166997.0,162761.0] || equal(cross_product(u,v),singleton(ordinal_numbers))** -> . % 299.95/300.40 167270[19:Rew:166997.0,80424.1] || asymmetric(u,v) -> equal(restrict(intersection(u,inverse(u)),v,v),ordinal_numbers)**. % 299.95/300.40 167206[19:Rew:166997.0,85106.0] || equal(complement(unordered_pair(ordinal_numbers,u)),universal_class)** -> . % 299.95/300.40 167205[19:Rew:166997.0,85105.0] || equal(complement(unordered_pair(u,ordinal_numbers)),universal_class)** -> . % 299.95/300.40 167262[19:Rew:166997.0,80416.1] || connected(u,v) equal(not_well_ordering(u,v),ordinal_numbers)** -> well_ordering(u,v). % 299.95/300.40 167261[19:Rew:166997.0,80415.0] || -> equal(second(not_subclass_element(restrict(u,singleton(v),w),ordinal_numbers)),range__dfg(u,v,w))**. % 299.95/300.40 167183[19:Rew:166997.0,84160.0] || -> equal(first(not_subclass_element(ordinal_numbers,ordinal_numbers)),single_valued3(ordinal_numbers))**. % 299.95/300.40 167260[19:Rew:166997.0,80414.0] || -> equal(first(not_subclass_element(restrict(u,v,singleton(w)),ordinal_numbers)),domain__dfg(u,v,w))**. % 299.95/300.40 169099[19:MRR:137.3,167057.0] || member(u,universal_class) well_ordering(element_relation,u) subclass(sum_class(u),u)* -> . % 299.95/300.40 167176[19:Rew:166997.0,160281.0] || equal(ordered_pair(u,v),ordinal_numbers)** -> . % 299.95/300.40 167175[19:Rew:166997.0,159590.0] || subclass(ordered_pair(u,v),ordinal_numbers)* -> . % 299.95/300.40 167172[19:Rew:166997.0,80486.0] || -> equal(segment(ordinal_numbers,u,v),ordinal_numbers)**. % 299.95/300.40 167171[19:Rew:166997.0,80478.0] || -> equal(restrict(ordinal_numbers,u,v),ordinal_numbers)**. % 299.95/300.40 167253[19:Rew:166997.0,158119.1] || member(u,cantor(v)) equal(restrict(v,singleton(u),universal_class),ordinal_numbers)** -> . % 299.95/300.40 169097[19:MRR:138.3,167057.0] || well_ordering(element_relation,u) subclass(sum_class(u),u)* -> equal(u,ordinal_numbers). % 299.95/300.40 167135[19:Rew:166997.0,80389.1] || member(u,universal_class) -> equal(u,ordinal_numbers) member(apply(choice,u),u)*. % 299.95/300.40 167105[19:Rew:166997.0,80373.0] || member(ordinal_numbers,u) subclass(image(successor_relation,u),u)* -> inductive(u). % 299.95/300.40 167161[19:Rew:166997.0,157825.0] || equal(cross_product(universal_class,universal_class),ordinal_numbers)** -> . % 299.95/300.40 167158[19:Rew:166997.0,80462.0] || -> equal(integer_of(regular(complement(omega))),ordinal_numbers)**. % 299.95/300.40 167004[19:Rew:166997.0,99309.0] || -> equal(apply(recursion(u,successor_relation,ordinal_numbers),v),ordinal_add(u,v))**. % 299.95/300.40 167021[19:Rew:166997.0,163025.0] || subclass(universal_class,complement(singleton(ordinal_numbers)))* -> . % 299.95/300.40 167020[19:Rew:166997.0,85104.0] || equal(complement(singleton(ordinal_numbers)),universal_class)** -> . % 299.95/300.40 167141[19:Rew:166997.0,80470.0] || -> equal(intersection(u,ordinal_numbers),ordinal_numbers)**. % 299.95/300.40 167203[19:Rew:166997.0,102.0] || -> equal(first(not_subclass_element(compose(u,inverse(u)),ordinal_numbers)),single_valued1(u))**. % 299.95/300.40 167140[19:Rew:166997.0,80467.0] || -> equal(intersection(ordinal_numbers,u),ordinal_numbers)**. % 299.95/300.40 167202[19:Rew:166997.0,103.0] || -> equal(second(not_subclass_element(compose(u,inverse(u)),ordinal_numbers)),single_valued2(u))**. % 299.95/300.40 170256[19:Res:167106.1,167331.0] inductive(complement(singleton(ordinal_numbers))) || -> . % 299.95/300.40 170520[19:Res:167106.1,167338.0] inductive(inverse(ordinal_numbers)) || -> . % 299.95/300.40 167201[19:Rew:166997.0,99308.0] || -> equal(recursion(ordinal_numbers,apply(add_relation,u),ordinal_numbers),ordinal_multiply(u,v))*. % 299.95/300.40 167174[19:Rew:166997.0,62.0] || subclass(compose(u,inverse(u)),ordinal_numbers)* -> single_valued_class(u). % 299.95/300.40 169201[19:Rew:166997.0,167138.1] || -> equal(u,ordinal_numbers) equal(intersection(u,regular(u)),ordinal_numbers)**. % 299.95/300.40 167117[19:Rew:166997.0,80484.0] || -> member(ordered_pair(ordinal_numbers,ordinal_numbers),domain_relation)*. % 299.95/300.40 167110[19:Rew:166997.0,164161.0] || equal(rest_of(ordinal_numbers),rest_relation)** -> . % 299.95/300.40 167022[19:Rew:166997.0,80471.0] || -> equal(union(singleton(ordinal_numbers),image(successor_relation,ordinal_numbers)),kind_1_ordinals)**. % 299.95/300.40 170318[19:Res:167139.1,169102.0] || -> equal(recursion_equation_functions(u),ordinal_numbers)**. % 299.95/300.40 167139[19:Rew:166997.0,80391.0] || -> equal(u,ordinal_numbers) member(regular(u),u)*. % 299.95/300.40 167116[19:Rew:166997.0,80375.1] || -> member(u,omega)* equal(integer_of(u),ordinal_numbers). % 299.95/300.40 167106[19:Rew:166997.0,80374.1] inductive(u) || -> member(ordinal_numbers,u)*. % 299.95/300.40 167060[19:Rew:166997.0,96992.0] || -> equal(image(element_relation,ordinal_numbers),universal_class)**. % 299.95/300.40 167040[19:Rew:166997.0,164845.0] || well_ordering(universal_class,singleton(ordinal_numbers))* -> . % 299.95/300.40 167331[19:Rew:166997.0,163016.0] || member(ordinal_numbers,complement(singleton(ordinal_numbers)))* -> . % 299.95/300.40 167058[19:Rew:166997.0,85331.0] || -> section(ordinal_numbers,u,u)*. % 299.95/300.40 169176[19:MRR:167156.1,167057.0] inductive(recursion_equation_functions(u)) || -> . % 299.95/300.40 167057[19:Rew:166997.0,80465.0] || member(u,ordinal_numbers)* -> . % 299.95/300.40 169106[19:MRR:9071.1,167057.0] || well_ordering(element_relation,universal_class)* -> . % 299.95/300.40 167277[19:Rew:166997.0,162019.0] || -> member(ordinal_numbers,singleton(ordinal_numbers))*. % 299.95/300.40 167055[19:Rew:166997.0,82914.0] || -> equal(complement(ordinal_numbers),universal_class)**. % 299.95/300.40 167054[19:Rew:166997.0,82770.0] || equal(domain_relation,ordinal_numbers)** -> . % 299.95/300.40 167053[19:Rew:166997.0,82738.0] || subclass(domain_relation,ordinal_numbers)* -> . % 299.95/300.40 167052[19:Rew:166997.0,82704.0] || equal(rest_relation,ordinal_numbers)** -> . % 299.95/300.40 167046[19:Rew:166997.0,80472.0] || equal(singleton(ordinal_numbers),ordinal_numbers)** -> . % 299.95/300.40 167051[19:Rew:166997.0,82672.0] || subclass(rest_relation,ordinal_numbers)* -> . % 299.95/300.40 167050[19:Rew:166997.0,157777.0] || -> equal(cantor(ordinal_numbers),ordinal_numbers)**. % 299.95/300.40 167049[19:Rew:166997.0,80464.0] || -> equal(complement(universal_class),ordinal_numbers)**. % 299.95/300.40 167048[19:Rew:166997.0,80367.0] || -> equal(integer_of(ordinal_numbers),ordinal_numbers)**. % 299.95/300.40 167015[19:Rew:166997.0,80466.0] || equal(complement(omega),ordinal_numbers)** -> . % 299.95/300.40 167019[19:Rew:166997.0,80365.0] || subclass(universal_class,ordinal_numbers)* -> . % 299.95/300.40 167018[19:Rew:166997.0,94327.0] || -> equal(regular(universal_class),ordinal_numbers)**. % 299.95/300.40 167017[19:Rew:166997.0,96186.0] || -> equal(power_class(ordinal_numbers),ordinal_numbers)**. % 299.95/300.40 167016[19:Rew:166997.0,96632.0] || -> equal(power_class(universal_class),ordinal_numbers)**. % 299.95/300.40 167368[19:Rew:166997.0,165532.0] || equal(composition_function,ordinal_numbers)** -> . % 299.95/300.40 167013[19:Rew:166997.0,157775.0] || equal(ordinal_numbers,successor_relation)** -> . % 299.95/300.40 167014[19:Rew:166997.0,80468.0] || -> asymmetric(ordinal_numbers,u)*. % 299.95/300.40 166995[19:Res:166988.0,81012.0] || -> subclass(ordinal_numbers,u)*. % 299.95/300.40 169153[19:MRR:167157.1,167057.0] inductive(limit_ordinals) || -> . % 299.95/300.40 167008[19:Rew:166997.0,80463.0] || equal(omega,ordinal_numbers)** -> . % 299.95/300.40 167381[19:Rew:166997.0,166810.0] || -> equal(application_function,ordinal_numbers)**. % 299.95/300.40 167011[19:Rew:166997.0,80474.0] || -> member(ordinal_numbers,universal_class)*. % 299.95/300.40 167010[19:Rew:166997.0,80363.0] || -> equal(null_class,ordinal_numbers)**. % 299.95/300.40 167009[19:Rew:166997.0,80362.0] || -> equal(limit_ordinals,ordinal_numbers)**. % 299.95/300.40 167005[19:Rew:166997.0,92065.0] || equal(element_relation,ordinal_numbers)** -> . % 299.95/300.40 167007[19:Rew:166997.0,80361.0] || -> equal(singleton_relation,ordinal_numbers)**. % 299.95/300.40 167006[19:Rew:166997.0,99300.0] || -> equal(union_of_range_map,ordinal_numbers)**. % 299.95/300.40 166997[19:Res:166988.0,81378.0] || -> equal(identity_relation,ordinal_numbers)**. % 299.95/300.40 435[0:SpR:39.0,101.1] || member(flip(cross_product(u,universal_class)),universal_class) -> member(ordered_pair(flip(cross_product(u,universal_class)),inverse(u)),domain_relation)*. % 299.95/300.40 166844[18:MRR:166816.2,80465.0] || member(u,cantor(v)) member(ordered_pair(v,ordered_pair(u,w)),cross_product(universal_class,cross_product(universal_class,universal_class)))* -> . % 299.95/300.40 2127[0:SSi:2125.0,51.0] inductive(image(successor_relation,omega)) || -> equal(image(successor_relation,omega),omega)**. % 299.95/300.40 1065[0:Res:96.0,8.0] || 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). % 299.95/300.40 166662[8:Res:151370.0,159468.1] inductive(intersection(u,singleton(v))) || -> member(v,u)*. % 299.95/300.40 166605[8:Obv:166604.0] || -> member(u,inverse(singleton(u)))* asymmetric(singleton(u),v)*. % 299.95/300.40 166473[8:Res:150982.0,159468.1] inductive(intersection(singleton(u),v)) || -> member(u,v)*. % 299.95/300.40 9764[4:MRR:9741.2,5896.0] inductive(u) || well_ordering(v,u)*+ -> member(least(v,omega),omega)*. % 299.95/300.40 60[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)). % 299.95/300.40 95[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))*. % 299.95/300.40 47[0:Inp] || equal(successor(u),v) member(ordered_pair(u,v),cross_product(universal_class,universal_class))* -> member(ordered_pair(u,v),successor_relation). % 299.95/300.40 21[0:Inp] || member(u,v) member(ordered_pair(u,v),cross_product(universal_class,universal_class))* -> member(ordered_pair(u,v),element_relation). % 299.95/300.40 137606[0:Res:289.0,35668.0] || well_ordering(u,rest_relation) -> member(least(u,rest_relation),rest_relation)*. % 299.95/300.40 137603[0:Res:5.0,35668.0] || well_ordering(u,universal_class) -> member(least(u,rest_relation),rest_relation)*. % 299.95/300.40 137613[0:Res:137603.1,36583.0] || well_ordering(u,universal_class) -> member(least(u,rest_relation),universal_class)*. % 299.95/300.40 98[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)*. % 299.95/300.40 137620[0:Res:137606.1,36583.0] || well_ordering(u,rest_relation) -> member(least(u,rest_relation),universal_class)*. % 299.95/300.40 137890[0:Res:5.0,9833.0] || well_ordering(u,universal_class) -> member(least(u,universal_class),universal_class)*. % 299.95/300.40 99365[12:MRR:99310.2,80465.0] || equal(sum_class(range_of(u)),v) member(ordered_pair(u,v),cross_product(universal_class,universal_class))* -> . % 299.95/300.40 97[0:Inp] || member(ordered_pair(u,ordered_pair(v,w)),composition_function)* -> equal(compose(u,v),w). % 299.95/300.40 135412[0:Res:53.0,11848.0] || subclass(universal_class,u) well_ordering(universal_class,u)* -> . % 299.95/300.40 96[0:Inp] || -> subclass(composition_function,cross_product(universal_class,cross_product(universal_class,universal_class)))*. % 299.95/300.40 137174[0:Res:5.0,135397.0] || well_ordering(universal_class,universal_class)* -> . % 299.95/300.40 8290[0:MRR:8078.1,8287.1] || subclass(universal_class,composition_function)* -> . % 299.95/300.40 8297[0:Res:7.1,8290.0] || equal(composition_function,universal_class)** -> . % 299.95/300.40 165533[17:Spt:165530.0,81007.0,81007.2] || well_ordering(u,cross_product(universal_class,cross_product(universal_class,universal_class)))* -> member(least(u,composition_function),composition_function). % 299.95/300.40 434[0:SpR:54.0,101.1] || member(restrict(element_relation,universal_class,u),universal_class) -> member(ordered_pair(restrict(element_relation,universal_class,u),sum_class(u)),domain_relation)*. % 299.95/300.40 165106[8:Res:7.1,165014.1] || equal(u,domain_relation) equal(complement(u),universal_class)** -> . % 299.95/300.40 165108[8:Res:99.0,165014.1] || equal(complement(cross_product(universal_class,universal_class)),universal_class)** -> . % 299.95/300.40 165014[8:Res:7.1,164453.1] || equal(complement(u),universal_class) subclass(domain_relation,u)* -> . % 299.95/300.40 164520[12:SoR:158385.0,72.1] one_to_one(cantor(u)) || equal(rest_of(u),rest_relation)** -> . % 299.95/300.40 164453[8:Res:81104.1,6476.1] || subclass(domain_relation,u) subclass(universal_class,complement(u))* -> . % 299.95/300.40 1070[0:Res:49.1,8.0] inductive(u) || subclass(u,image(successor_relation,u))* -> equal(image(successor_relation,u),u). % 299.95/300.40 158385[12:MRR:138703.2,99409.0] function(cantor(u)) || equal(rest_of(u),rest_relation)** -> . % 299.95/300.40 158048[8:Rew:157840.0,3645.0] || equal(complement(complement(symmetrization_of(u))),cross_product(v,v))*+ -> connected(u,v)*. % 299.95/300.40 162887[8:Res:84327.1,6476.1] || equal(rest_relation,domain_relation) subclass(universal_class,complement(rest_relation))* -> . % 299.95/300.40 163352[16:Res:80374.1,163342.0] inductive(inverse(identity_relation)) || -> . % 299.95/300.40 163348[16:MRR:163238.1,163342.0] inductive(symmetrization_of(identity_relation)) || -> . % 299.95/300.40 5228[0:Res:45.0,8.0] || subclass(cross_product(universal_class,universal_class),successor_relation)* -> equal(cross_product(universal_class,universal_class),successor_relation). % 299.95/300.40 163181[15:MRR:98649.1,163171.0] || equal(complement(complement(successor_relation)),domain_relation)** -> . % 299.95/300.40 163273[15:MRR:163258.1,163016.0] inductive(complement(successor(identity_relation))) || -> . % 299.95/300.40 163180[15:MRR:98590.1,163171.0] || subclass(domain_relation,complement(complement(successor_relation)))* -> . % 299.95/300.40 163179[15:MRR:84257.1,163171.0] || subclass(domain_relation,successor_relation)* -> . % 299.95/300.40 163026[15:Res:80374.1,163016.0] inductive(complement(singleton(identity_relation))) || -> . % 299.95/300.40 162992[8:MRR:162986.1,85104.0] || equal(domain_relation,successor_relation)** -> . % 299.95/300.40 159703[8:Res:80374.1,110865.0] inductive(rest_of(identity_relation)) || subclass(universal_class,complement(element_relation))* -> . % 299.95/300.40 159695[8:Res:80374.1,110991.0] inductive(cantor(identity_relation)) || subclass(universal_class,complement(element_relation))* -> . % 299.95/300.40 97508[8:Res:84327.1,84221.1] || equal(rest_relation,domain_relation) subclass(domain_relation,complement(rest_relation))* -> . % 299.95/300.40 134784[3:Res:134636.1,9780.0] || subclass(sum_class(kind_1_ordinals),ordinal_numbers) -> section(element_relation,kind_1_ordinals,universal_class)*. % 299.95/300.40 159740[8:Res:80484.0,11848.0] || subclass(domain_relation,u) well_ordering(universal_class,u)* -> . % 299.95/300.40 6468[4:MRR:6465.0,6465.1,53.0,5896.0] || -> equal(integer_of(apply(choice,omega)),apply(choice,omega))**. % 299.95/300.40 158050[8:Rew:157840.0,118.0] || subclass(cross_product(u,u),complement(complement(symmetrization_of(v))))* -> connected(v,u). % 299.95/300.40 161087[8:Res:135236.0,159468.1] inductive(complement(complement(identity_relation))) || -> . % 299.95/300.40 158049[8:Rew:157840.0,117.1] || connected(u,v) -> subclass(cross_product(v,v),complement(complement(symmetrization_of(u))))*. % 299.95/300.40 160743[8:MRR:160725.1,80463.0] inductive(intersection(subset_relation,inverse(subset_relation))) || -> . % 299.95/300.40 46[0:Inp] || member(ordered_pair(u,v),successor_relation)* -> equal(successor(u),v). % 299.95/300.40 166[0:Res:132.1,1.0] || section(u,image(successor_relation,ordinal_numbers),ordinal_numbers)* -> . % 299.95/300.40 160585[9:Res:7.1,160080.0] || equal(complement(compose(element_relation,universal_class)),element_relation)** -> . % 299.95/300.40 160080[9:MRR:160052.1,92065.0] || subclass(element_relation,complement(compose(element_relation,universal_class)))* -> . % 299.95/300.40 160357[8:Res:7.1,160285.0] || equal(cross_product(u,v),universal_class)** -> . % 299.95/300.40 160285[8:MRR:82393.1,160281.0] || subclass(universal_class,cross_product(u,v))* -> . % 299.95/300.40 160284[8:MRR:80447.1,160281.0] inductive(cross_product(u,v)) || -> . % 299.95/300.40 159467[8:MRR:80428.1,159464.0] inductive(restrict(identity_relation,u,v)) || -> . % 299.95/300.40 49[0:Inp] inductive(u) || -> subclass(image(successor_relation,u),u)*. % 299.95/300.40 164[0:Res:7.1,1.0] || equal(image(successor_relation,ordinal_numbers),ordinal_numbers)** -> . % 299.95/300.40 160037[0:Res:7.1,158094.0] || equal(rest_of(u),universal_class)** -> . % 299.95/300.40 159466[8:MRR:80430.1,159464.0] inductive(intersection(identity_relation,u)) || -> . % 299.95/300.40 159465[8:MRR:80429.1,159464.0] inductive(intersection(u,identity_relation)) || -> . % 299.95/300.40 158094[0:MRR:110774.1,110765.1] || subclass(universal_class,rest_of(u))* -> . % 299.95/300.40 159791[8:Res:7.1,159745.0] || equal(complement(domain_relation),universal_class)** -> . % 299.95/300.40 159745[8:Res:80484.0,6476.1] || subclass(universal_class,complement(domain_relation))* -> . % 299.95/300.40 159707[8:Res:80374.1,159464.0] inductive(subset_relation) || -> . % 299.95/300.40 1[0:Inp] || subclass(image(successor_relation,ordinal_numbers),ordinal_numbers)* -> . % 299.95/300.40 12332[0:Res:45.0,8596.1] single_valued_class(successor_relation) || -> function(successor_relation)*. % 299.95/300.40 45[0:Inp] || -> subclass(successor_relation,cross_product(universal_class,universal_class))*. % 299.95/300.40 157776[13:Spt:157770.0,80994.0,80994.2] || well_ordering(u,cross_product(universal_class,universal_class))* -> member(least(u,successor_relation),successor_relation). % 299.95/300.40 27175[0:Res:2523.2,94.0] || member(u,universal_class) subclass(rest_relation,compose_class(v))*+ -> equal(compose(v,u),rest_of(u))**. % 299.95/300.40 4676[0:SpL:946.0,143.0] || member(singleton(singleton(singleton(u))),rest_of(v))* -> equal(restrict(v,singleton(u),universal_class),u). % 299.95/300.40 27150[0:Res:2523.2,4178.0] || member(u,universal_class) subclass(rest_relation,singleton(v))*+ -> equal(ordered_pair(u,rest_of(u)),v)*. % 299.95/300.40 36025[0:MRR:36018.1,170.0] || member(u,universal_class) member(singleton(u),u)*+ -> member(singleton(singleton(singleton(u))),element_relation)*. % 299.95/300.40 82994[8:Rew:82899.0,81260.1] || member(u,element_relation) member(u,complement(compose(element_relation,universal_class)))*+ well_ordering(v,w)* -> . % 299.95/300.40 149318[0:MRR:149273.0,16381.0] || -> equal(intersection(u,intersection(v,u)),intersection(v,u))**. % 299.95/300.40 149179[0:MRR:149142.0,16381.0] || -> equal(intersection(u,intersection(u,v)),intersection(u,v))**. % 299.95/300.40 905[0:Res:3.1,897.0] || -> subclass(restrict(u,v,w),x) member(not_subclass_element(restrict(u,v,w),x),u)*. % 299.95/300.40 16465[0:Res:2526.2,22.0] || subclass(u,intersection(v,w))*+ -> subclass(u,x) member(not_subclass_element(u,x),v)*. % 299.95/300.40 16466[0:Res:2526.2,23.0] || subclass(u,intersection(v,w))*+ -> subclass(u,x) member(not_subclass_element(u,x),w)*. % 299.95/300.40 12798[0:Res:3.1,4127.0] || -> subclass(symmetric_difference(u,v),w) member(not_subclass_element(symmetric_difference(u,v),w),union(u,v))*. % 299.95/300.40 151723[0:Obv:151712.1] || subclass(u,complement(u))*+ -> subclass(u,v)*. % 299.95/300.40 16455[0:Res:2526.2,25.1] || subclass(u,complement(v)) member(not_subclass_element(u,w),v)* -> subclass(u,w). % 299.95/300.40 16365[0:Res:297.1,4178.0] || -> subclass(intersection(u,singleton(v)),w) equal(not_subclass_element(intersection(u,singleton(v)),w),v)**. % 299.95/300.40 16238[0:Res:315.1,4178.0] || -> subclass(intersection(singleton(u),v),w) equal(not_subclass_element(intersection(singleton(u),v),w),u)**. % 299.95/300.40 16150[0:Res:2480.1,896.0] || subclass(universal_class,restrict(u,v,w))*+ -> member(unordered_pair(x,y),cross_product(v,w))*. % 299.95/300.40 149603[0:Res:145.0,27171.1] || member(u,universal_class) -> member(rest_of(u),universal_class)*. % 299.95/300.40 27171[0:Res:2523.2,16.0] || member(u,universal_class) subclass(rest_relation,cross_product(v,w))*+ -> member(rest_of(u),w)*. % 299.95/300.40 149012[0:MRR:148937.1,16381.0] || subclass(u,v) -> equal(intersection(v,u),u)**. % 299.95/300.40 148647[0:SpL:148172.0,22.0] || member(u,complement(complement(v)))* -> member(u,v). % 299.95/300.40 15076[0:Res:2483.2,22.0] || member(u,universal_class) subclass(universal_class,intersection(v,w))*+ -> member(power_class(u),v)*. % 299.95/300.40 148626[0:SpL:148172.0,2539.0] || subclass(universal_class,complement(complement(u)))* -> member(omega,u). % 299.95/300.40 15077[0:Res:2483.2,23.0] || member(u,universal_class) subclass(universal_class,intersection(v,w))*+ -> member(power_class(u),w)*. % 299.95/300.40 148172[0:MRR:148163.0,16381.0] || -> equal(intersection(u,complement(complement(u))),complement(complement(u)))**. % 299.95/300.40 144505[2:SpR:142500.0,80099.1] || asymmetric(universal_class,u) -> section(inverse(universal_class),u,u)*. % 299.95/300.40 3975[0:SpL:946.0,94.0] || member(singleton(singleton(singleton(u))),compose_class(v))* -> equal(compose(v,singleton(u)),u). % 299.95/300.40 40806[0:Rew:54.0,40796.2] || section(element_relation,u,universal_class)*+ subclass(u,sum_class(u))* -> equal(sum_class(u),u). % 299.95/300.40 15110[0:Res:2482.2,22.0] || member(u,universal_class) subclass(universal_class,intersection(v,w))*+ -> member(sum_class(u),v)*. % 299.95/300.40 15111[0:Res:2482.2,23.0] || member(u,universal_class) subclass(universal_class,intersection(v,w))*+ -> member(sum_class(u),w)*. % 299.95/300.40 147404[8:MRR:147403.0,36583.1] || member(u,element_relation) -> member(u,compose(element_relation,universal_class))*. % 299.95/300.40 15066[0:Res:2483.2,25.1] || member(u,universal_class) subclass(universal_class,complement(v)) member(power_class(u),v)* -> . % 299.95/300.40 15100[0:Res:2482.2,25.1] || member(u,universal_class) subclass(universal_class,complement(v)) member(sum_class(u),v)* -> . % 299.95/300.40 82995[8:Rew:82899.0,81261.1] || member(u,element_relation) member(u,complement(compose(element_relation,universal_class)))*+ -> member(u,v)*. % 299.95/300.40 82316[0:Res:2478.1,488.0] || subclass(universal_class,intersection(complement(u),complement(v)))* member(omega,union(u,v)) -> . % 299.95/300.40 79962[0:Res:2483.2,158.0] || member(u,universal_class) subclass(universal_class,omega) -> equal(integer_of(power_class(u)),power_class(u))**. % 299.95/300.40 79961[0:Res:2482.2,158.0] || member(u,universal_class) subclass(universal_class,omega) -> equal(integer_of(sum_class(u)),sum_class(u))**. % 299.95/300.40 26413[0:Res:7.1,5426.1] function(u) || equal(u,cross_product(universal_class,universal_class))* -> equal(cross_product(universal_class,universal_class),u). % 299.95/300.40 16469[0:Res:2526.2,4178.0] || subclass(u,singleton(v))*+ -> subclass(u,w) equal(not_subclass_element(u,w),v)*. % 299.95/300.40 146278[0:SpR:144504.0,43.0] || -> equal(range_of(cross_product(u,universal_class)),image(universal_class,u))**. % 299.95/300.40 144504[0:SpR:142500.0,29.0] || -> equal(restrict(universal_class,u,v),cross_product(u,v))**. % 299.95/300.40 144532[0:SpL:142500.0,15276.0] || equal(u,universal_class) -> member(singleton(v),u)*. % 299.95/300.40 144694[0:SpR:144658.0,27.0] || -> equal(union(u,u),complement(complement(u)))**. % 299.95/300.40 144531[0:SpL:142500.0,6310.0] || equal(u,universal_class) -> member(omega,u)*. % 299.95/300.40 144658[0:MRR:144600.0,16381.0] || -> equal(intersection(u,u),u)**. % 299.95/300.40 142500[0:MRR:142406.0,16381.0] || -> equal(intersection(universal_class,u),u)**. % 299.95/300.40 42071[0:Obv:42064.1] || member(not_subclass_element(u,intersection(v,u)),v)* -> subclass(u,intersection(v,u)). % 299.95/300.40 17187[0:SpR:902.0,43.0] || -> equal(range_of(restrict(cross_product(u,universal_class),v,w)),image(cross_product(v,w),u))**. % 299.95/300.40 35124[0:Res:978.1,22.0] || member(u,universal_class) -> member(u,union(v,w))* member(u,complement(v)). % 299.95/300.40 35125[0:Res:978.1,23.0] || member(u,universal_class) -> member(u,union(v,w))* member(u,complement(w)). % 299.95/300.40 6435[0:Res:2480.1,2.0] || subclass(universal_class,u)*+ subclass(u,v)* -> member(unordered_pair(w,x),v)*. % 299.95/300.40 12807[0:Res:2480.1,4127.0] || subclass(universal_class,symmetric_difference(u,v)) -> member(unordered_pair(w,x),union(u,v))*. % 299.95/300.40 17078[0:Res:7.1,2500.1] || equal(u,unordered_pair(v,w))*+ member(v,universal_class) -> member(v,u)*. % 299.95/300.40 17050[0:Res:7.1,2501.1] || equal(u,unordered_pair(v,w))*+ member(w,universal_class) -> member(w,u)*. % 299.95/300.40 16102[0:SpR:27.0,4126.1] || member(u,symmetric_difference(complement(v),complement(w)))* -> member(u,union(v,w)). % 299.95/300.40 139599[8:Res:138596.1,1063.0] || equal(rest_of(inverse(u)),rest_relation)** -> equal(range_of(u),universal_class). % 299.95/300.40 26887[0:Res:2524.2,15.0] || member(u,universal_class)* subclass(domain_relation,cross_product(v,w))*+ -> member(u,v)*. % 299.95/300.40 27170[0:Res:2523.2,15.0] || member(u,universal_class)* subclass(rest_relation,cross_product(v,w))*+ -> member(u,v)*. % 299.95/300.40 138645[8:Res:138594.1,1063.0] || equal(rest_of(u),rest_relation)** -> equal(cantor(u),universal_class). % 299.95/300.40 2997[0:SpL:946.0,15.0] || member(singleton(singleton(singleton(u))),cross_product(v,w))* -> member(singleton(u),v). % 299.95/300.40 138340[8:MRR:138325.0,36682.1] || subclass(rest_relation,rest_of(u))*+ -> subclass(v,cantor(u))*. % 299.95/300.40 125174[8:Rew:124836.0,1013.1] || member(singleton(singleton(singleton(u))),rest_of(v))* -> member(singleton(u),cantor(v)). % 299.95/300.40 125124[8:Rew:124836.0,27169.2] || member(u,universal_class) subclass(rest_relation,rest_of(v)) -> member(u,cantor(v))*. % 299.95/300.40 35668[0:Res:170.0,9851.0] || subclass(rest_relation,u)+ well_ordering(v,u)* -> member(least(v,rest_relation),rest_relation)*. % 299.95/300.40 15079[0:Res:2483.2,4178.0] || member(u,universal_class)* subclass(universal_class,singleton(v))*+ -> equal(power_class(u),v)*. % 299.95/300.40 15113[0:Res:2482.2,4178.0] || member(u,universal_class)* subclass(universal_class,singleton(v))*+ -> equal(sum_class(u),v)*. % 299.95/300.40 16825[0:SpR:114.0,479.0] || -> equal(power_class(intersection(complement(u),complement(inverse(u)))),complement(image(element_relation,symmetrization_of(u))))**. % 299.95/300.40 137176[0:Res:7.1,135397.0] || equal(u,ordered_pair(v,w))*+ well_ordering(universal_class,u)* -> . % 299.95/300.40 16826[0:SpR:44.0,479.0] || -> equal(power_class(intersection(complement(u),complement(singleton(u)))),complement(image(element_relation,successor(u))))**. % 299.95/300.40 137179[0:SpL:946.0,137177.0] || well_ordering(universal_class,singleton(singleton(singleton(u))))* -> . % 299.95/300.40 137177[0:Res:289.0,135397.0] || well_ordering(universal_class,ordered_pair(u,v))* -> . % 299.95/300.40 135397[0:Res:945.0,11848.0] || subclass(ordered_pair(u,v),w)* well_ordering(universal_class,w) -> . % 299.95/300.40 137026[0:SpR:114.0,135266.0] || -> subclass(complement(symmetrization_of(u)),intersection(complement(u),complement(inverse(u))))*. % 299.95/300.40 137025[0:SpR:44.0,135266.0] || -> subclass(complement(successor(u)),intersection(complement(u),complement(singleton(u))))*. % 299.95/300.40 135266[0:SpR:27.0,135236.0] || -> subclass(complement(union(u,v)),intersection(complement(u),complement(v)))*. % 299.95/300.40 16502[0:Res:7.1,5240.0] || equal(compose_class(u),cross_product(universal_class,universal_class))* -> equal(cross_product(universal_class,universal_class),compose_class(u)). % 299.95/300.40 16647[0:Res:7.1,5239.0] || equal(rest_of(u),cross_product(universal_class,universal_class))* -> equal(cross_product(universal_class,universal_class),rest_of(u)). % 299.95/300.40 35495[0:Res:289.0,9856.0] || well_ordering(u,v)+ -> subclass(v,w)* member(least(u,v),v)*. % 299.95/300.40 6439[0:Res:2480.1,897.0] || subclass(universal_class,restrict(u,v,w))*+ -> member(unordered_pair(x,y),u)*. % 299.95/300.40 2525[0:Res:947.0,2.0] || subclass(ordered_pair(u,v),w) -> member(unordered_pair(u,singleton(v)),w)*. % 299.95/300.40 16105[0:Res:4126.1,25.1] || member(u,symmetric_difference(v,w)) member(u,intersection(v,w))* -> . % 299.95/300.40 135284[0:Res:135236.0,1073.1] inductive(complement(complement(omega))) || -> equal(complement(complement(omega)),omega)**. % 299.95/300.40 11848[0:Res:940.0,128.3] || member(u,v)*+ subclass(v,w)* well_ordering(universal_class,w)* -> . % 299.95/300.40 2499[0:Res:280.1,2.0] || member(u,universal_class) subclass(singleton(u),v)* -> member(u,v). % 299.95/300.40 135236[0:Obv:135232.0] || -> subclass(complement(complement(u)),u)*. % 299.95/300.40 36865[0:MRR:1022.0,36682.1] || -> member(not_subclass_element(complement(complement(u)),v),u)* subclass(complement(complement(u)),v). % 299.95/300.40 2557[0:SpL:946.0,16.0] || member(singleton(singleton(singleton(u))),cross_product(v,w))* -> member(u,w). % 299.95/300.40 83043[8:Rew:82899.0,81340.1] || member(u,cantor(v))*+ subclass(universal_class,w) -> member(u,w)*. % 299.95/300.40 6446[0:Res:2480.1,158.0] || subclass(universal_class,omega) -> equal(integer_of(unordered_pair(u,v)),unordered_pair(u,v))**. % 299.95/300.40 5362[0:Res:2478.1,9.0] || subclass(universal_class,unordered_pair(u,v))* -> equal(omega,v) equal(omega,u). % 299.95/300.40 954[0:SpL:946.0,146.0] || member(singleton(singleton(singleton(u))),rest_relation)* -> equal(rest_of(singleton(u)),u). % 299.95/300.40 9810[0:Res:63.1,9780.0] function(sum_class(cross_product(universal_class,universal_class))) || -> section(element_relation,cross_product(universal_class,universal_class),universal_class)*. % 299.95/300.40 16910[0:SpL:4105.0,23.0] || member(u,symmetric_difference(v,inverse(v)))* -> member(u,symmetrization_of(v)). % 299.95/300.40 125926[8:Rew:124836.0,124925.0] || member(u,cantor(u)) -> member(ordered_pair(u,cantor(u)),element_relation)*. % 299.95/300.40 125116[8:Rew:124836.0,110891.0] || member(u,cantor(v))* subclass(universal_class,complement(rest_of(v)))*+ -> . % 299.95/300.40 124869[8:Rew:124836.0,11849.0] || 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)* -> . % 299.95/300.40 124870[8:Rew:124836.0,9935.0] || member(u,cantor(v)) equal(restrict(v,u,universal_class),w)*+ subclass(rest_of(v),x)* -> member(ordered_pair(u,w),x)*. % 299.95/300.40 128275[8:Res:63.1,124906.1] 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)*. % 299.95/300.40 126121[8:Rew:124836.0,124900.2] || section(u,v,w) subclass(v,cantor(restrict(u,w,v)))* -> equal(cantor(restrict(u,w,v)),v). % 299.95/300.40 110985[0:SpL:40.0,110864.0] || member(inverse(u),range_of(u))* subclass(universal_class,complement(element_relation)) -> . % 299.95/300.40 124903[8:Rew:124836.0,9777.0] || equal(cantor(restrict(u,v,w)),w)** subclass(w,v) -> section(u,w,v). % 299.95/300.40 124875[8:Rew:124836.0,144.0] || member(u,cantor(v)) equal(restrict(v,u,universal_class),w) -> member(ordered_pair(u,w),rest_of(v))*. % 299.95/300.40 124906[8:Rew:124836.0,134.1] || subclass(u,v) subclass(cantor(restrict(w,v,u)),u)* -> section(w,u,v). % 299.95/300.40 5466[0:Res:2479.1,158.0] || subclass(universal_class,omega) -> equal(integer_of(singleton(u)),singleton(u))**. % 299.95/300.40 124899[8:Rew:124836.0,133.1] || section(u,v,w) -> subclass(cantor(restrict(u,w,v)),v)*. % 299.95/300.40 124905[8:Rew:124836.0,123.0] || -> equal(cantor(restrict(u,v,singleton(w))),segment(u,v,w))**. % 299.95/300.40 125874[8:Rew:124836.0,124882.1] || compatible(u,v,w)*+ -> subclass(range_of(u),cantor(cantor(w)))*. % 299.95/300.40 124881[8:Rew:124836.0,142.1] || member(ordered_pair(u,v),rest_of(w))* -> member(u,cantor(w)). % 299.95/300.40 125873[8:Rew:124836.0,124864.1,124836.0,124864.1] || compatible(u,v,w)* -> equal(cantor(cantor(v)),cantor(u)). % 299.95/300.40 124911[8:Rew:124836.0,100.1] || member(ordered_pair(u,v),domain_relation)* -> equal(cantor(u),v). % 299.95/300.40 124912[8:Rew:124836.0,111.1] || maps(u,v,w)* -> equal(cantor(u),v). % 299.95/300.40 125772[8:Rew:125770.0,83024.0] || -> equal(cantor(restrict(element_relation,universal_class,u)),sum_class(u))**. % 299.95/300.40 125707[8:Rew:125705.0,83023.0] || -> equal(cantor(flip(cross_product(u,universal_class))),inverse(u))**. % 299.95/300.40 124908[8:Rew:124836.0,40.0] || -> equal(cantor(inverse(u)),range_of(u))**. % 299.95/300.40 124836[8:MRR:52651.0,124835.0] || -> equal(domain_of(u),cantor(u))**. % 299.95/300.40 6437[0:Res:2480.1,22.0] || subclass(universal_class,intersection(u,v))*+ -> member(unordered_pair(w,x),u)*. % 299.95/300.40 6438[0:Res:2480.1,23.0] || subclass(universal_class,intersection(u,v))*+ -> member(unordered_pair(w,x),v)*. % 299.95/300.40 6432[0:Res:2480.1,25.1] || subclass(universal_class,complement(u)) member(unordered_pair(v,w),u)* -> . % 299.95/300.40 2121[0:Res:7.1,1073.1] inductive(u) || equal(omega,u)* -> equal(u,omega). % 299.95/300.40 208[0:Res:3.1,158.0] || -> subclass(omega,u) equal(integer_of(not_subclass_element(omega,u)),not_subclass_element(omega,u))**. % 299.95/300.40 2527[0:Res:2478.1,158.0] || subclass(universal_class,omega)* -> equal(integer_of(omega),omega). % 299.95/300.40 158[0:Inp] || member(u,omega)* -> equal(integer_of(u),u). % 299.95/300.40 9858[0:Res:59.1,126.0] || 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))))*. % 299.95/300.40 11844[0:Res:24.2,128.3] || 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)* -> . % 299.95/300.40 11852[0:Res:59.1,128.3] || 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)* -> . % 299.95/300.40 11791[0:Res:119.1,8.0] || 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)). % 299.95/300.40 9854[0:Res:17.2,126.0] || 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))*. % 299.95/300.40 9839[0:Res:24.2,126.0] || member(u,v)* member(u,w)* subclass(intersection(w,v),x)*+ well_ordering(y,x)* -> member(least(y,intersection(w,v)),intersection(w,v))*. % 299.95/300.40 11850[0:Res:17.2,128.3] || member(least(cross_product(u,v),w),v)*+ member(x,u)* member(x,w)* subclass(w,y)* well_ordering(cross_product(u,v),y)* -> . % 299.95/300.40 5132[0:Res:3.1,18.0] || -> 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))**. % 299.95/300.40 8694[0:Res:59.1,4.0] || 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)))). % 299.95/300.40 110991[0:Res:912.1,110864.0] || member(u,cantor(u))* subclass(universal_class,complement(element_relation)) -> . % 299.95/300.40 110865[0:Res:36588.1,6476.1] || member(u,rest_of(u))* subclass(universal_class,complement(element_relation)) -> . % 299.95/300.40 7975[0:Res:24.2,4.0] || member(not_subclass_element(u,intersection(v,w)),w)*+ member(not_subclass_element(u,intersection(v,w)),v)* -> subclass(u,intersection(v,w)). % 299.95/300.40 11853[0:MRR:11842.0,940.0] || member(u,v) subclass(v,w)* well_ordering(complement(x),w)*+ -> member(ordered_pair(u,least(complement(x),v)),x)*. % 299.95/300.40 8669[0:Res:17.2,18.0] || member(u,v)*+ member(w,x)* -> equal(ordered_pair(first(ordered_pair(w,u)),second(ordered_pair(w,u))),ordered_pair(w,u))**. % 299.95/300.40 9779[0:Res:63.1,134.1] 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)*. % 299.95/300.40 8693[0:Res:59.1,2.0] || member(ordered_pair(u,v),compose(w,x))* subclass(image(w,image(x,singleton(u))),y)*+ -> member(v,y)*. % 299.95/300.40 1421[0:SpR:123.0,101.1] || member(restrict(u,v,singleton(w)),universal_class) -> member(ordered_pair(restrict(u,v,singleton(w)),segment(u,v,w)),domain_relation)*. % 299.95/300.40 11810[0:Res:17.2,95.1] || member(u,universal_class) member(v,universal_class) equal(compose(w,v),u) -> member(ordered_pair(v,u),compose_class(w))*. % 299.95/300.40 4174[0:Res:3.1,9.0] || -> 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)**. % 299.95/300.40 8668[0:Res:17.2,2.0] || member(u,v)* member(w,x)* subclass(cross_product(x,v),y)*+ -> member(ordered_pair(w,u),y)*. % 299.95/300.40 11772[0:Res:7.1,120.0] || equal(compose(restrict(u,v,v),restrict(u,v,v)),restrict(u,v,v))** -> transitive(u,v). % 299.95/300.40 4278[0:Res:130.2,8.0] || connected(u,v) subclass(v,not_well_ordering(u,v))* -> well_ordering(u,v) equal(not_well_ordering(u,v),v). % 299.95/300.40 9773[0:SpL:123.0,134.1] || subclass(singleton(u),v) subclass(segment(w,v,u),singleton(u))* -> section(w,singleton(u),v). % 299.95/300.40 4119[0:SpR:29.0,160.0] || -> equal(intersection(complement(restrict(u,v,w)),union(u,cross_product(v,w))),symmetric_difference(u,cross_product(v,w)))**. % 299.95/300.40 4121[0:SpR:30.0,160.0] || -> equal(intersection(complement(restrict(u,v,w)),union(cross_product(v,w),u)),symmetric_difference(cross_product(v,w),u))**. % 299.95/300.40 1066[0:Res:36.0,8.0] || 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)). % 299.95/300.40 110920[0:Res:53.0,110907.1] || equal(complement(rest_relation),universal_class)** -> . % 299.95/300.40 110861[0:Res:147.1,6476.1] || member(u,universal_class)* subclass(universal_class,complement(rest_relation))*+ -> . % 299.95/300.40 1067[0:Res:33.0,8.0] || 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)). % 299.95/300.40 6476[0:Res:2481.1,25.1] || subclass(universal_class,complement(u)) member(ordered_pair(v,w),u)* -> . % 299.95/300.40 36588[0:MRR:27191.0,36583.1] || member(u,rest_of(u)) -> member(ordered_pair(u,rest_of(u)),element_relation)*. % 299.95/300.40 9856[0:Res:3.1,126.0] || subclass(u,v)*+ well_ordering(w,v)* -> subclass(u,x)* member(least(w,u),u)*. % 299.95/300.40 84173[8:SpR:84165.1,84165.1] function(u) function(v) || -> equal(single_valued1(u),single_valued1(v))*. % 299.95/300.40 7968[0:SpR:29.0,24.2] || member(u,cross_product(v,w)) member(u,x) -> member(u,restrict(x,v,w))*. % 299.95/300.40 2534[0:Res:2478.1,2.0] || subclass(universal_class,u)*+ subclass(u,v)* -> member(omega,v)*. % 299.95/300.40 6303[0:SpL:160.0,2540.0] || subclass(universal_class,symmetric_difference(u,v)) -> member(omega,union(u,v))*. % 299.95/300.40 6403[0:SpL:160.0,6310.0] || equal(symmetric_difference(u,v),universal_class) -> member(omega,union(u,v))*. % 299.95/300.40 107104[12:SoR:99390.0,72.1] one_to_one(recursion(u,successor_relation,identity_relation)) || -> member(ordinal_add(u,v),universal_class)*. % 299.95/300.40 9859[2:Res:5266.1,126.0] inductive(u) || subclass(u,v)*+ well_ordering(w,v)* -> member(least(w,u),u)*. % 299.95/300.40 4165[0:SpL:14.0,9.0] || member(u,ordered_pair(v,w))* -> equal(u,unordered_pair(v,singleton(w))) equal(u,singleton(v)). % 299.95/300.40 978[0:SpR:27.0,26.2] || member(u,universal_class) -> member(u,intersection(complement(v),complement(w)))* member(u,union(v,w)). % 299.95/300.40 99390[12:SpR:99309.0,15058.1] function(recursion(u,successor_relation,identity_relation)) || -> member(ordinal_add(u,v),universal_class)*. % 299.95/300.40 99364[12:MRR:99339.2,80465.0] || member(u,universal_class) equal(sum_class(range_of(u)),rest_of(u))** -> . % 299.95/300.40 6521[0:Res:66.2,2.0] function(u) || member(v,universal_class) subclass(universal_class,w) -> member(image(u,v),w)*. % 299.95/300.40 82325[0:Res:2478.1,16910.0] || subclass(universal_class,symmetric_difference(u,inverse(u)))* -> member(omega,symmetrization_of(u)). % 299.95/300.40 85629[0:SpL:4105.0,6310.0] || equal(symmetric_difference(u,inverse(u)),universal_class)** -> member(omega,symmetrization_of(u)). % 299.95/300.40 12322[0:Res:7.1,8596.1] single_valued_class(u) || equal(cross_product(universal_class,universal_class),u)*+ -> function(u)*. % 299.95/300.40 12044[0:Res:12015.1,4178.0] || equal(complement(complement(singleton(u))),universal_class)**+ -> equal(singleton(v),u)*. % 299.95/300.40 2497[0:Res:26.2,2.0] || member(u,universal_class)* subclass(complement(v),w)*+ -> member(u,v)* member(u,w)*. % 299.95/300.40 5331[0:Res:58.0,8.0] || subclass(cross_product(universal_class,universal_class),compose(u,v))* -> equal(compose(u,v),cross_product(universal_class,universal_class)). % 299.95/300.40 105054[12:Res:55.1,104245.0] || member(range_of(u),universal_class)* member(u,universal_class) -> . % 299.95/300.40 104245[12:EqR:99366.2] || member(sum_class(range_of(u)),universal_class)* member(u,universal_class) -> . % 299.95/300.40 2523[0:Res:147.1,2.0] || member(u,universal_class) subclass(rest_relation,v) -> member(ordered_pair(u,rest_of(u)),v)*. % 299.95/300.40 99366[12:MRR:99340.3,80465.0] || member(u,universal_class)* member(v,universal_class) equal(sum_class(range_of(v)),u)*+ -> . % 299.95/300.40 5426[0:Res:63.1,8.0] function(u) || subclass(cross_product(universal_class,universal_class),u)* -> equal(cross_product(universal_class,universal_class),u). % 299.95/300.40 99417[12:MRR:94061.1,99409.0] one_to_one(symmetric_difference(universal_class,identity_relation)) || -> . % 299.95/300.40 99416[12:MRR:85430.1,99409.0] function(symmetric_difference(universal_class,identity_relation)) || -> . % 299.95/300.40 99414[12:MRR:83781.1,99409.0] one_to_one(successor(universal_class)) || -> . % 299.95/300.40 99413[12:MRR:83124.1,99409.0] function(successor(universal_class)) || -> . % 299.95/300.40 99412[12:MRR:5429.1,99409.0] one_to_one(universal_class) || -> . % 299.95/300.40 99410[12:Res:63.1,99407.0] function(universal_class) || -> . % 299.95/300.40 99359[12:MRR:99334.2,80465.0] inductive(union_of_range_map) || well_ordering(u,cross_product(universal_class,universal_class))* -> . % 299.95/300.40 47785[0:SoR:15059.0,72.1] one_to_one(recursion(u,successor_relation,union_of_range_map)) || -> member(ordinal_add(u,v),universal_class)*. % 299.95/300.40 15059[0:SpR:156.0,15058.1] function(recursion(u,successor_relation,union_of_range_map)) || -> member(ordinal_add(u,v),universal_class)*. % 300.04/300.40 953[0:SpL:946.0,20.0] || member(singleton(singleton(singleton(u))),element_relation)*+ -> member(singleton(u),u)*. % 300.04/300.40 902[0:SpR:29.0,30.0] || -> equal(restrict(cross_product(u,v),w,x),restrict(cross_product(w,x),u,v))*. % 300.04/300.40 4233[0:SpR:123.0,133.1] || section(u,singleton(v),w) -> subclass(segment(u,w,v),singleton(v))*. % 300.04/300.40 2501[0:Res:11.1,2.0] || member(u,universal_class) subclass(unordered_pair(v,u),w)* -> member(u,w). % 300.04/300.40 2500[0:Res:10.1,2.0] || member(u,universal_class) subclass(unordered_pair(u,v),w)* -> member(u,w). % 300.04/300.40 36585[0:MRR:9812.1,36583.1] || member(u,universal_class) member(v,u) -> member(ordered_pair(v,u),element_relation)*. % 300.04/300.40 479[0:SpR:27.0,56.0] || -> equal(complement(image(element_relation,union(u,v))),power_class(intersection(complement(u),complement(v))))**. % 300.04/300.40 98647[8:Res:7.1,98608.0] || equal(complement(complement(element_relation)),domain_relation)** -> . % 300.04/300.40 98608[8:MRR:98589.1,80465.0] || subclass(domain_relation,complement(complement(element_relation)))* -> . % 300.04/300.40 5240[0:Res:93.0,8.0] || subclass(cross_product(universal_class,universal_class),compose_class(u))* -> equal(cross_product(universal_class,universal_class),compose_class(u)). % 300.04/300.40 5239[0:Res:141.0,8.0] || subclass(cross_product(universal_class,universal_class),rest_of(u))* -> equal(cross_product(universal_class,universal_class),rest_of(u)). % 300.04/300.40 16808[0:Res:16283.0,8596.1] single_valued_class(restrict(u,universal_class,universal_class)) || -> function(restrict(u,universal_class,universal_class))*. % 300.04/300.40 896[0:SpL:30.0,22.0] || member(u,restrict(v,w,x))* -> member(u,cross_product(w,x)). % 300.04/300.40 2526[0:Res:3.1,2.0] || subclass(u,v) -> subclass(u,w) member(not_subclass_element(u,w),v)*. % 300.04/300.40 315[0:Res:3.1,22.0] || -> subclass(intersection(u,v),w) member(not_subclass_element(intersection(u,v),w),u)*. % 300.04/300.40 85194[8:SpL:56.0,85097.1] inductive(image(element_relation,complement(u))) || equal(power_class(u),universal_class)** -> . % 300.04/300.40 297[0:Res:3.1,23.0] || -> subclass(intersection(u,v),w) member(not_subclass_element(intersection(u,v),w),v)*. % 300.04/300.40 2483[0:Res:57.1,2.0] || member(u,universal_class) subclass(universal_class,v) -> member(power_class(u),v)*. % 300.04/300.40 277[0:SpR:69.0,55.1] || member(image(u,singleton(v)),universal_class)* -> member(apply(u,v),universal_class). % 300.04/300.40 2482[0:Res:55.1,2.0] || member(u,universal_class) subclass(universal_class,v) -> member(sum_class(u),v)*. % 300.04/300.40 97574[8:Res:7.1,97561.1] || equal(u,domain_relation) equal(complement(u),domain_relation)** -> . % 300.04/300.40 97576[8:Res:99.0,97561.1] || equal(complement(cross_product(universal_class,universal_class)),domain_relation)** -> . % 300.04/300.40 97561[8:Res:7.1,97509.1] || equal(complement(u),domain_relation) subclass(domain_relation,u)* -> . % 300.04/300.40 97509[8:Res:81104.1,84221.1] || subclass(domain_relation,u) subclass(domain_relation,complement(u))* -> . % 300.04/300.40 80099[2:MRR:9781.1,80077.0] || asymmetric(u,v) -> section(intersection(u,inverse(u)),v,v)*. % 300.04/300.40 97507[8:Res:80484.0,84221.1] || subclass(domain_relation,complement(domain_relation))* -> . % 300.04/300.40 284[0:Res:3.1,25.1] || member(not_subclass_element(complement(u),v),u)* -> subclass(complement(u),v). % 300.04/300.40 8596[0:Res:61.1,65.1] single_valued_class(u) || subclass(u,cross_product(universal_class,universal_class))* -> function(u). % 300.04/300.40 82772[8:MRR:81001.1,82770.0] || well_ordering(u,cross_product(universal_class,universal_class))* -> member(least(u,domain_relation),domain_relation). % 300.04/300.40 82706[8:MRR:81000.1,82704.0] || well_ordering(u,cross_product(universal_class,universal_class))* -> member(least(u,rest_relation),rest_relation). % 300.04/300.40 96580[10:Res:96567.0,1063.0] || -> equal(image(element_relation,universal_class),universal_class)**. % 300.04/300.40 38[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))*. % 300.04/300.40 35[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))*. % 300.04/300.40 5227[0:Res:99.0,8.0] || subclass(cross_product(universal_class,universal_class),domain_relation)* -> equal(cross_product(universal_class,universal_class),domain_relation). % 300.04/300.40 5226[0:Res:145.0,8.0] || subclass(cross_product(universal_class,universal_class),rest_relation)* -> equal(cross_product(universal_class,universal_class),rest_relation). % 300.04/300.40 5229[0:Res:19.0,8.0] || subclass(cross_product(universal_class,universal_class),element_relation)* -> equal(cross_product(universal_class,universal_class),element_relation). % 300.04/300.40 128[0:Inp] || member(u,v) subclass(v,w)* well_ordering(x,w)* member(ordered_pair(u,least(x,v)),x)*+ -> . % 300.04/300.40 119[0:Inp] || transitive(u,v) -> subclass(compose(restrict(u,v,v),restrict(u,v,v)),restrict(u,v,v))*. % 300.04/300.40 120[0:Inp] || subclass(compose(restrict(u,v,v),restrict(u,v,v)),restrict(u,v,v))* -> transitive(u,v). % 300.04/300.40 897[0:SpL:30.0,23.0] || member(u,restrict(v,w,x))* -> member(u,v). % 300.04/300.40 126[0:Inp] || member(u,v)*+ subclass(v,w)* well_ordering(x,w)* -> member(least(x,v),v)*. % 300.04/300.40 95593[0:Obv:95569.0] || -> member(u,v) subclass(singleton(u),complement(v))*. % 300.04/300.40 51413[0:MRR:36151.0,5.0] || -> member(not_subclass_element(u,complement(v)),v)* subclass(u,complement(v)). % 300.04/300.40 4577[0:Res:3.1,4178.0] || -> subclass(singleton(u),v) equal(not_subclass_element(singleton(u),v),u)**. % 300.04/300.40 16125[0:Res:7.1,2488.0] || equal(u,ordered_pair(v,w))*+ -> member(singleton(v),u)*. % 300.04/300.40 2488[0:Res:945.0,2.0] || subclass(ordered_pair(u,v),w)* -> member(singleton(u),w). % 300.04/300.40 2541[0:Res:2478.1,897.0] || subclass(universal_class,restrict(u,v,w))* -> member(omega,u). % 300.04/300.40 6504[0:Res:2481.1,94.0] || subclass(universal_class,compose_class(u))*+ -> equal(compose(u,v),w)*. % 300.04/300.40 12375[0:Res:7.1,6440.0] || equal(singleton(u),universal_class)**+ -> equal(unordered_pair(v,w),u)*. % 300.04/300.40 37[0:Inp] || member(ordered_pair(ordered_pair(u,v),w),flip(x))* -> member(ordered_pair(ordered_pair(v,u),w),x). % 300.04/300.40 6440[0:Res:2480.1,4178.0] || subclass(universal_class,singleton(u))*+ -> equal(unordered_pair(v,w),u)*. % 300.04/300.40 12435[0:Res:7.1,6484.0] || equal(singleton(u),universal_class)**+ -> equal(ordered_pair(v,w),u)*. % 300.04/300.40 6484[0:Res:2481.1,4178.0] || subclass(universal_class,singleton(u))*+ -> equal(ordered_pair(v,w),u)*. % 300.04/300.40 34[0:Inp] || member(ordered_pair(ordered_pair(u,v),w),rotate(x))* -> member(ordered_pair(ordered_pair(v,w),u),x). % 300.04/300.40 59[0:Inp] || member(ordered_pair(u,v),compose(w,x)) -> member(v,image(w,image(x,singleton(u))))*. % 300.04/300.40 12015[0:Res:7.1,9734.0] || equal(complement(complement(u)),universal_class) -> member(singleton(v),u)*. % 300.04/300.40 17[0:Inp] || member(u,v) member(w,x) -> member(ordered_pair(w,u),cross_product(x,v))*. % 300.04/300.40 18[0:Inp] || member(u,cross_product(v,w))*+ -> equal(ordered_pair(first(u),second(u)),u)**. % 300.04/300.40 94712[8:Res:12032.1,80465.0] || equal(complement(complement(element_relation)),universal_class)** -> . % 300.04/300.40 143[0:Inp] || member(ordered_pair(u,v),rest_of(w))* -> equal(restrict(w,u,universal_class),v). % 300.04/300.40 84011[0:Res:16381.0,1073.1] inductive(intersection(u,omega)) || -> equal(intersection(u,omega),omega)**. % 300.04/300.40 84002[0:Res:16254.0,1073.1] inductive(intersection(omega,u)) || -> equal(intersection(omega,u),omega)**. % 300.04/300.40 94326[8:Res:80374.1,94322.0] inductive(regular(universal_class)) || -> . % 300.04/300.40 94249[8:Obv:94231.1] inductive(intersection(universal_class,regular(universal_class))) || -> . % 300.04/300.40 104[0:Inp] || -> equal(domain__dfg(u,image(inverse(u),singleton(single_valued1(u))),single_valued2(u)),single_valued3(u))**. % 300.04/300.40 130[0:Inp] || connected(u,v) -> well_ordering(u,v) subclass(not_well_ordering(u,v),v)*. % 300.04/300.40 9[0:Inp] || member(u,unordered_pair(v,w))* -> equal(u,w) equal(u,v). % 300.04/300.40 94[0:Inp] || member(ordered_pair(u,v),compose_class(w))* -> equal(compose(w,u),v). % 300.04/300.40 12338[0:Res:58.0,8596.1] single_valued_class(compose(u,v)) || -> function(compose(u,v))*. % 300.04/300.40 2480[0:Res:12.0,2.0] || subclass(universal_class,u) -> member(unordered_pair(v,w),u)*. % 300.04/300.40 2481[0:Res:940.0,2.0] || subclass(universal_class,u) -> member(ordered_pair(v,w),u)*. % 300.04/300.40 66[0:Inp] function(u) || member(v,universal_class) -> member(image(u,v),universal_class)*. % 300.04/300.40 9820[0:Res:9808.1,4232.0] || equal(sum_class(u),u) -> subclass(sum_class(u),u)*. % 300.04/300.40 17082[0:SpR:114.0,16762.0] || -> subclass(symmetric_difference(complement(u),complement(inverse(u))),symmetrization_of(u))*. % 300.04/300.40 81434[8:MRR:80720.2,80465.0] single_valued_class(u) inductive(compose(u,inverse(u))) || -> . % 300.04/300.40 81433[8:MRR:80719.2,80465.0] function(u) inductive(compose(u,inverse(u))) || -> . % 300.04/300.40 48402[0:MRR:48382.0,12.0] || subclass(universal_class,complement(unordered_pair(unordered_pair(u,v),w)))* -> . % 300.04/300.40 48621[0:Res:7.1,48402.0] || equal(complement(unordered_pair(unordered_pair(u,v),w)),universal_class)** -> . % 300.04/300.40 48401[0:MRR:48381.0,12.0] || subclass(universal_class,complement(unordered_pair(u,unordered_pair(v,w))))* -> . % 300.04/300.40 15[0:Inp] || member(ordered_pair(u,v),cross_product(w,x))* -> member(u,w). % 300.04/300.40 48591[0:Res:7.1,48401.0] || equal(complement(unordered_pair(u,unordered_pair(v,w))),universal_class)** -> . % 300.04/300.40 48587[0:SpL:14.0,48401.0] || subclass(universal_class,complement(unordered_pair(u,ordered_pair(v,w))))* -> . % 300.04/300.40 16[0:Inp] || member(ordered_pair(u,v),cross_product(w,x))* -> member(v,x). % 300.04/300.40 48630[0:Res:7.1,48587.0] || equal(complement(unordered_pair(u,ordered_pair(v,w))),universal_class)** -> . % 300.04/300.40 946[0:Rew:13.0,944.0] || -> equal(ordered_pair(singleton(u),u),singleton(singleton(singleton(u))))**. % 300.04/300.40 48618[0:SpL:14.0,48402.0] || subclass(universal_class,complement(unordered_pair(ordered_pair(u,v),w)))* -> . % 300.04/300.40 48663[0:Res:7.1,48618.0] || equal(complement(unordered_pair(ordered_pair(u,v),w)),universal_class)** -> . % 300.04/300.40 9780[0:MRR:9774.0,5.0] || subclass(sum_class(u),u)*+ -> section(element_relation,u,universal_class)*. % 300.04/300.40 4232[0:SpR:54.0,133.1] || section(element_relation,u,universal_class)*+ -> subclass(sum_class(u),u)*. % 300.04/300.40 9808[0:Res:7.1,9780.0] || equal(sum_class(u),u) -> section(element_relation,u,universal_class)*. % 300.04/300.40 26[0:Inp] || member(u,universal_class) -> member(u,v) member(u,complement(v))*. % 300.04/300.40 14[0:Inp] || -> equal(unordered_pair(singleton(u),unordered_pair(u,singleton(v))),ordered_pair(u,v))**. % 300.04/300.40 30[0:Inp] || -> equal(intersection(cross_product(u,v),w),restrict(w,u,v))**. % 300.04/300.40 6422[0:MRR:6421.0,53.0] || equal(complement(complement(u)),universal_class)** -> member(omega,u). % 300.04/300.40 29[0:Inp] || -> equal(intersection(u,cross_product(v,w)),restrict(u,v,w))**. % 300.04/300.40 146[0:Inp] || member(ordered_pair(u,v),rest_relation)* -> equal(rest_of(u),v). % 300.04/300.40 147[0:Inp] || member(u,universal_class) -> member(ordered_pair(u,rest_of(u)),rest_relation)*. % 300.04/300.40 112[0:Inp] || maps(u,v,w)* -> subclass(range_of(u),w). % 300.04/300.40 12323[0:Res:289.0,8596.1] single_valued_class(cross_product(universal_class,universal_class)) || -> function(cross_product(universal_class,universal_class))*. % 300.04/300.40 4[0:Inp] || member(not_subclass_element(u,v),v)* -> subclass(u,v). % 300.04/300.40 43[0:Inp] || -> equal(range_of(restrict(u,v,universal_class)),image(u,v))**. % 300.04/300.40 11[0:Inp] || member(u,universal_class) -> member(u,unordered_pair(v,u))*. % 300.04/300.40 10[0:Inp] || member(u,universal_class) -> member(u,unordered_pair(u,v))*. % 300.04/300.40 69[0:Inp] || -> equal(sum_class(image(u,singleton(v))),apply(u,v))**. % 300.04/300.40 16283[0:SpR:30.0,16254.0] || -> subclass(restrict(u,v,w),cross_product(v,w))*. % 300.04/300.40 36682[0:Res:3.1,36583.0] || -> subclass(u,v) member(not_subclass_element(u,v),universal_class)*. % 300.04/300.40 947[0:MRR:942.0,12.0] || -> member(unordered_pair(u,singleton(v)),ordered_pair(u,v))*. % 300.04/300.40 20[0:Inp] || member(ordered_pair(u,v),element_relation)* -> member(u,v). % 300.04/300.40 280[0:SpR:13.0,11.1] || member(u,universal_class) -> member(u,singleton(u))*. % 300.04/300.40 15058[0:MRR:15056.1,170.0] function(u) || -> member(apply(u,v),universal_class)*. % 300.04/300.40 74[0:Inp] function(u) || function(inverse(u))* -> one_to_one(u). % 300.04/300.40 950[0:SpR:946.0,945.0] || -> member(singleton(singleton(u)),singleton(singleton(singleton(u))))*. % 300.04/300.40 9733[0:MRR:9723.0,170.0] || subclass(universal_class,complement(unordered_pair(singleton(u),v)))* -> . % 300.04/300.40 9787[0:Res:7.1,9733.0] || equal(complement(unordered_pair(singleton(u),v)),universal_class)** -> . % 300.04/300.40 48400[0:MRR:48380.0,12.0] || subclass(universal_class,complement(singleton(unordered_pair(u,v))))* -> . % 300.04/300.40 48413[0:Res:7.1,48400.0] || equal(complement(singleton(unordered_pair(u,v))),universal_class)** -> . % 300.04/300.40 9732[0:MRR:9722.0,170.0] || subclass(universal_class,complement(unordered_pair(u,singleton(v))))* -> . % 300.04/300.40 9784[0:Res:7.1,9732.0] || equal(complement(unordered_pair(u,singleton(v))),universal_class)** -> . % 300.04/300.40 48410[0:SpL:14.0,48400.0] || subclass(universal_class,complement(singleton(ordered_pair(u,v))))* -> . % 300.04/300.40 48430[0:Res:7.1,48410.0] || equal(complement(singleton(ordered_pair(u,v))),universal_class)** -> . % 300.04/300.40 3[0:Inp] || -> subclass(u,v) member(not_subclass_element(u,v),u)*. % 300.04/300.40 1417[0:SpR:123.0,54.0] || -> equal(segment(element_relation,universal_class,u),sum_class(singleton(u)))**. % 300.04/300.40 63[0:Inp] function(u) || -> subclass(u,cross_product(universal_class,universal_class))*. % 300.04/300.40 57[0:Inp] || member(u,universal_class) -> member(power_class(u),universal_class)*. % 300.04/300.40 55[0:Inp] || member(u,universal_class) -> member(sum_class(u),universal_class)*. % 300.04/300.40 36[0:Inp] || -> subclass(flip(u),cross_product(cross_product(universal_class,universal_class),universal_class))*. % 300.04/300.40 33[0:Inp] || -> subclass(rotate(u),cross_product(cross_product(universal_class,universal_class),universal_class))*. % 300.04/300.40 124[0:Inp] || well_ordering(u,v)* -> connected(u,v). % 300.04/300.40 16650[0:SpR:114.0,16403.0] || -> subclass(symmetric_difference(u,inverse(u)),symmetrization_of(u))*. % 300.04/300.40 36583[0:Con:36577.1] || member(u,v)*+ -> member(u,universal_class)*. % 300.04/300.40 114[0:Inp] || -> equal(union(u,inverse(u)),symmetrization_of(u))**. % 300.04/300.40 12337[0:Res:141.0,8596.1] single_valued_class(rest_of(u)) || -> function(rest_of(u))*. % 300.04/300.40 44[0:Inp] || -> equal(union(u,singleton(u)),successor(u))**. % 300.04/300.40 12336[0:Res:93.0,8596.1] single_valued_class(compose_class(u)) || -> function(compose_class(u))*. % 300.04/300.40 9712[0:Res:945.0,5467.1] || subclass(universal_class,complement(ordered_pair(u,v)))* -> . % 300.04/300.40 9769[0:Res:7.1,9712.0] || equal(complement(ordered_pair(u,v)),universal_class)** -> . % 300.04/300.40 58[0:Inp] || -> subclass(compose(u,v),cross_product(universal_class,universal_class))*. % 300.04/300.40 6257[0:MRR:6249.0,53.0] || equal(complement(unordered_pair(omega,u)),universal_class)** -> . % 300.04/300.40 6263[0:MRR:6262.0,53.0] || equal(complement(unordered_pair(u,omega)),universal_class)** -> . % 300.04/300.40 16280[0:SpR:29.0,16254.0] || -> subclass(restrict(u,v,w),u)*. % 300.04/300.40 13[0:Inp] || -> equal(unordered_pair(u,u),singleton(u))**. % 300.04/300.40 945[0:MRR:941.0,170.0] || -> member(singleton(u),ordered_pair(u,v))*. % 300.04/300.40 73[0:Inp] one_to_one(u) || -> function(inverse(u))*. % 300.04/300.40 93[0:Inp] || -> subclass(compose_class(u),cross_product(universal_class,universal_class))*. % 300.04/300.40 5484[0:Res:64.1,62.0] function(u) || -> single_valued_class(u)*. % 300.04/300.40 141[0:Inp] || -> subclass(rest_of(u),cross_product(universal_class,universal_class))*. % 300.04/300.40 940[0:SpR:14.0,12.0] || -> member(ordered_pair(u,v),universal_class)*. % 300.04/300.40 51379[0:MRR:15467.1,15933.1] || equal(compose_class(u),universal_class)** -> . % 300.04/300.40 12333[0:Res:99.0,8596.1] single_valued_class(domain_relation) || -> function(domain_relation)*. % 300.04/300.40 12334[0:Res:145.0,8596.1] single_valued_class(rest_relation) || -> function(rest_relation)*. % 300.04/300.40 12[0:Inp] || -> member(unordered_pair(u,v),universal_class)*. % 300.04/300.40 99[0:Inp] || -> subclass(domain_relation,cross_product(universal_class,universal_class))*. % 300.04/300.40 145[0:Inp] || -> subclass(rest_relation,cross_product(universal_class,universal_class))*. % 300.04/300.40 170[0:SpR:13.0,12.0] || -> member(singleton(u),universal_class)*. % 300.04/300.40 82908[2:Rew:82899.0,79860.0] || -> equal(symmetrization_of(universal_class),universal_class)**. % 300.04/300.40 19[0:Inp] || -> subclass(element_relation,cross_product(universal_class,universal_class))*. % 300.04/300.40 82899[2:Res:82873.0,1063.0] || -> equal(successor(universal_class),universal_class)**. % 300.04/300.40 7557[0:MRR:7354.1,7555.1] || equal(domain_relation,universal_class)** -> . % 300.04/300.40 84270[8:MRR:84258.1,80465.0] || subclass(domain_relation,element_relation)* -> . % 300.04/300.40 84275[8:Res:7.1,84270.0] || equal(domain_relation,element_relation)** -> . % 300.04/300.40 7248[0:MRR:7044.1,7244.1] || equal(rest_relation,universal_class)** -> . % 300.04/300.40 9807[0:Res:5.0,9780.0] || -> section(element_relation,universal_class,universal_class)*. % 300.04/300.40 53[0:Inp] || -> member(omega,universal_class)*. % 300.04/300.40 92066[9:Spt:91823.0,80993.0,80993.2] || well_ordering(u,cross_product(universal_class,universal_class))* -> member(least(u,element_relation),element_relation). % 300.04/300.40 2539[0:Res:2478.1,22.0] || subclass(universal_class,intersection(u,v))* -> member(omega,u). % 300.04/300.40 6300[0:Res:7.1,2539.0] || equal(intersection(u,v),universal_class)** -> member(omega,u). % 300.04/300.40 2540[0:Res:2478.1,23.0] || subclass(universal_class,intersection(u,v))* -> member(omega,v). % 300.04/300.40 6310[0:Res:7.1,2540.0] || equal(intersection(u,v),universal_class)** -> member(omega,v). % 300.04/300.40 85263[8:MRR:85234.1,80465.0] inductive(symmetric_difference(universal_class,universal_class)) || -> . % 300.04/300.40 85097[8:Res:80374.1,84384.1] inductive(u) || equal(complement(u),universal_class)** -> . % 300.04/300.40 2532[0:Res:2478.1,25.1] || subclass(universal_class,complement(u))* member(omega,u) -> . % 300.04/300.40 1073[0:Res:52.1,8.0] inductive(u) || subclass(u,omega)* -> equal(u,omega). % 300.04/300.40 83125[8:MRR:83002.1,80474.0] inductive(domain_of(intersection(u,identity_relation))) || -> . % 300.04/300.40 82912[2:Rew:82899.0,79849.0] || -> equal(union(u,universal_class),universal_class)**. % 300.04/300.40 82911[2:Rew:82899.0,79819.0] || -> equal(union(universal_class,u),universal_class)**. % 300.04/300.40 82913[8:Rew:82899.0,81308.0] || -> equal(diagonalise(u),universal_class)**. % 300.04/300.40 83157[2:MRR:83156.0,5.0] || -> connected(universal_class,u)*. % 300.04/300.40 82874[8:MRR:81229.0,82873.0] || -> irreflexive(u,v)*. % 300.04/300.40 5361[0:Res:2478.1,4178.0] || subclass(universal_class,singleton(u))* -> equal(omega,u). % 300.04/300.40 5447[0:Res:7.1,5361.0] || equal(singleton(u),universal_class)** -> equal(omega,u). % 300.04/300.40 2478[0:Res:53.0,2.0] || subclass(universal_class,u) -> member(omega,u)*. % 300.04/300.40 81911[8:Res:80374.1,80465.0] inductive(identity_relation) || -> . % 300.04/300.40 80084[2:Res:5266.1,80062.0] inductive(domain_of(singleton_relation)) || -> . % 300.04/300.40 79785[7:Spt:79768.0,79582.1] || -> inductive(universal_class)*. % 300.04/300.40 6256[0:MRR:6248.0,53.0] || equal(complement(singleton(omega)),universal_class)** -> . % 300.04/300.40 52[0:Inp] inductive(u) || -> subclass(omega,u)*. % 300.04/300.40 51[0:Inp] || -> inductive(omega)*. % 300.04/300.40 6320[0:Res:7.1,5475.0] || equal(singleton(u),universal_class)**+ -> equal(singleton(v),u)*. % 300.04/300.40 7963[0:SpR:160.0,24.2] || member(u,union(v,w)) member(u,complement(intersection(v,w)))* -> member(u,symmetric_difference(v,w)). % 300.04/300.40 7972[0:Res:24.2,2.0] || member(u,v)* member(u,w)* subclass(intersection(w,v),x)*+ -> member(u,x)*. % 300.04/300.40 4125[0:SpR:27.0,160.0] || -> equal(intersection(union(u,v),union(complement(u),complement(v))),symmetric_difference(complement(u),complement(v)))**. % 300.04/300.40 480[0:SpR:27.0,27.0] || -> equal(union(intersection(complement(u),complement(v)),w),complement(intersection(union(u,v),complement(w))))**. % 300.04/300.40 481[0:SpR:27.0,27.0] || -> equal(union(u,intersection(complement(v),complement(w))),complement(intersection(complement(u),union(v,w))))**. % 300.04/300.40 488[0:SpL:27.0,25.1] || member(u,intersection(complement(v),complement(w)))* member(u,union(v,w)) -> . % 300.04/300.40 6274[2:SpR:5291.0,5291.0] || -> equal(ordinal_multiply(u,v),ordinal_multiply(u,w))*. % 300.04/300.40 9731[0:MRR:9720.0,170.0] || subclass(universal_class,complement(singleton(singleton(u))))* -> . % 300.04/300.40 9767[0:Res:7.1,9731.0] || equal(complement(singleton(singleton(u))),universal_class)** -> . % 300.04/300.40 17083[0:SpR:44.0,16762.0] || -> subclass(symmetric_difference(complement(u),complement(singleton(u))),successor(u))*. % 300.04/300.40 16762[0:SpR:27.0,16276.0] || -> subclass(symmetric_difference(complement(u),complement(v)),union(u,v))*. % 300.04/300.40 16276[0:SpR:160.0,16254.0] || -> subclass(symmetric_difference(u,v),complement(intersection(u,v)))*. % 300.04/300.40 16403[0:SpR:160.0,16381.0] || -> subclass(symmetric_difference(u,v),union(u,v))*. % 300.04/300.40 16381[0:Obv:16377.0] || -> subclass(intersection(u,v),v)*. % 300.04/300.40 16254[0:Obv:16250.0] || -> subclass(intersection(u,v),u)*. % 300.04/300.40 16133[0:Obv:16130.1] || member(u,v) -> subclass(singleton(u),v)*. % 300.04/300.40 4126[0:SpL:160.0,22.0] || member(u,symmetric_difference(v,w)) -> member(u,complement(intersection(v,w)))*. % 300.04/300.40 15276[0:Res:7.1,5473.0] || equal(intersection(u,v),universal_class)**+ -> member(singleton(w),v)*. % 300.04/300.40 12446[0:Res:7.1,5472.0] || equal(intersection(u,v),universal_class)**+ -> member(singleton(w),u)*. % 300.04/300.40 5473[0:Res:2479.1,23.0] || subclass(universal_class,intersection(u,v))*+ -> member(singleton(w),v)*. % 300.04/300.40 4127[0:SpL:160.0,23.0] || member(u,symmetric_difference(v,w))* -> member(u,union(v,w)). % 300.04/300.40 5472[0:Res:2479.1,22.0] || subclass(universal_class,intersection(u,v))*+ -> member(singleton(w),u)*. % 300.04/300.40 9734[0:MRR:9716.0,170.0] || subclass(universal_class,complement(complement(u)))*+ -> member(singleton(v),u)*. % 300.04/300.40 5467[0:Res:2479.1,25.1] || subclass(universal_class,complement(u)) member(singleton(v),u)* -> . % 300.04/300.40 5475[0:Res:2479.1,4178.0] || subclass(universal_class,singleton(u))*+ -> equal(singleton(v),u)*. % 300.04/300.40 5456[0:Res:72.1,74.1] one_to_one(inverse(u)) function(u) || -> one_to_one(u)*. % 300.04/300.40 2479[0:Res:170.0,2.0] || subclass(universal_class,u) -> member(singleton(v),u)*. % 300.04/300.40 83[0:Inp] || compatible(u,v,w)* -> function(u). % 300.04/300.40 110[0:Inp] || maps(u,v,w)* -> function(u). % 300.04/300.40 72[0:Inp] one_to_one(u) || -> function(u)*. % 300.04/300.40 70[0:Inp] || -> function(choice)*. % 300.04/300.40 9776[0:Res:5.0,134.1] || subclass(universal_class,u) -> section(v,universal_class,u)*. % 300.04/300.40 1063[0:Res:5.0,8.0] || subclass(universal_class,u)* -> equal(universal_class,u). % 300.04/300.40 1083[0:Res:7.1,1063.0] || equal(u,universal_class)* -> equal(universal_class,u). % 300.04/300.40 6183[2:MRR:6177.0,7.1] || equal(element_relation,universal_class)** -> . % 300.04/300.40 6357[3:MRR:6323.1,6326.1] || subclass(universal_class,element_relation)* -> . % 300.04/300.40 6954[0:MRR:6745.1,6949.1] || equal(universal_class,successor_relation)** -> . % 300.04/300.40 9070[5:Spt:9004.0,8654.1,8697.0] || equal(universal_class,ordinal_numbers)** -> . % 300.04/300.40 5[0:Inp] || -> subclass(u,universal_class)*. % 300.04/300.40 24[0:Inp] || member(u,v) member(u,w) -> member(u,intersection(w,v))*. % 300.04/300.40 5899[4:MRR:5310.1,5896.0] inductive(singleton_relation) || -> . % 300.04/300.40 5898[4:MRR:5264.1,5896.0] inductive(null_class) || -> . % 300.04/300.40 4178[0:Obv:4164.1] || member(u,singleton(v))* -> equal(u,v). % 300.04/300.40 2[0:Inp] || member(u,v)*+ subclass(v,w)* -> member(u,w)*. % 300.04/300.40 27[0:Inp] || -> equal(complement(intersection(complement(u),complement(v))),union(u,v))**. % 300.04/300.40 22[0:Inp] || member(u,intersection(v,w))* -> member(u,v). % 300.04/300.40 23[0:Inp] || member(u,intersection(v,w))* -> member(u,w). % 300.04/300.40 25[0:Inp] || member(u,v) member(u,complement(v))* -> . % 300.04/300.40 8[0:Inp] || subclass(u,v)*+ subclass(v,u)* -> equal(v,u). % 300.04/300.40 289[0:Obv:287.0] || -> subclass(u,u)*. % 300.04/300.40 132[0:Inp] || section(u,v,w)* -> subclass(v,w). % 300.04/300.40 7[0:Inp] || equal(u,v) -> subclass(v,u)*. % 300.04/300.40 165[0:Res:49.1,1.0] inductive(ordinal_numbers) || -> .217397[0:Obv:217382.1] || subclass(u,v) -> subclass(intersection(u,w),v)*. % 300.04/300.40 217782[0:SpR:160.0,217683.0] || -> subclass(intersection(symmetric_difference(u,v),w),union(u,v))*. % 300.04/300.40 217862[0:SpR:149012.1,217683.0] || subclass(u,intersection(v,w))* -> subclass(u,w). % 300.04/300.40 218634[0:Obv:218619.1] || subclass(u,v) -> subclass(intersection(w,u),v)*. % 300.04/300.40 218722[0:SpR:160.0,217850.0] || -> subclass(intersection(u,symmetric_difference(v,w)),union(v,w))*. % 300.04/300.40 218980[0:SpR:149012.1,218280.0] || subclass(u,intersection(v,w))* -> subclass(u,v). % 300.04/300.40 222411[0:SpR:29.0,217800.0] || -> subclass(restrict(restrict(u,v,w),x,y),u)*. % 300.04/300.40 232656[0:Obv:232620.0] || -> subclass(intersection(intersection(u,v),w),intersection(v,w))*. % 300.04/300.40 232657[0:Obv:232621.0] || -> subclass(intersection(intersection(u,v),w),intersection(u,w))*. % 300.04/300.40 233044[0:Obv:233015.0] || -> subclass(intersection(u,intersection(v,w)),intersection(w,u))*. % 300.04/300.40 233045[0:Obv:233016.0] || -> subclass(intersection(u,intersection(v,w)),intersection(v,u))*. % 300.04/300.40 236358[0:SpR:234692.0,149012.1] || subclass(u,v) -> equal(intersection(u,v),u)**. % 300.04/300.40 237219[0:SpR:236669.0,16762.0] || -> subclass(symmetric_difference(complement(u),complement(v)),union(v,u))*. % 300.04/300.40 246386[25:SpR:234134.1,218920.0] function(u) || -> subclass(intersection(successor(u),v),u)*. % 300.04/300.40 246394[25:SpR:234134.1,219700.0] function(u) || -> subclass(intersection(v,successor(u)),u)*. % 300.04/300.40 248614[0:SpR:236669.0,217958.0] || -> subclass(complement(complement(symmetric_difference(u,v))),union(v,u))*. % 300.04/300.40 248780[0:Res:7.1,219712.0] || equal(complement(complement(u)),v)* -> subclass(v,u)*. % 300.04/300.40 248784[0:Res:218280.0,219712.0] || -> subclass(intersection(intersection(complement(complement(u)),v),w),u)*. % 300.04/300.40 248799[0:Res:218968.0,219712.0] || -> subclass(intersection(u,intersection(complement(complement(v)),w)),v)*. % 300.04/300.40 248801[0:Res:217683.0,219712.0] || -> subclass(intersection(intersection(u,complement(complement(v))),w),v)*. % 300.04/300.40 248807[0:Res:217850.0,219712.0] || -> subclass(intersection(u,intersection(v,complement(complement(w)))),w)*. % 300.04/300.40 253109[18:Res:144531.1,227961.1] || equal(cantor(u),universal_class) member(u,omega)* -> . % 300.04/300.40 253110[18:Res:2478.1,227961.1] || subclass(universal_class,cantor(u))* member(u,omega) -> . % 300.04/300.40 144710[0:SpR:144658.0,29.0] || -> equal(restrict(cross_product(u,v),u,v),cross_product(u,v))**. % 300.04/300.40 146281[8:SpR:144504.0,124905.0] || -> equal(cantor(cross_product(u,singleton(v))),segment(universal_class,u,v))**. % 300.04/300.40 149452[0:SpR:149012.1,16276.0] || subclass(u,v) -> subclass(symmetric_difference(v,u),complement(u))*. % 300.04/300.40 150995[0:Obv:150966.1] || member(u,v) -> subclass(intersection(singleton(u),w),v)*. % 300.04/300.40 150996[0:Obv:150936.0] || -> member(u,v) subclass(intersection(singleton(u),w),complement(v))*. % 300.04/300.40 151380[0:Obv:151354.1] || member(u,v) -> subclass(intersection(w,singleton(u)),v)*. % 300.04/300.40 151381[0:Obv:151326.0] || -> member(u,v) subclass(intersection(w,singleton(u)),complement(v))*. % 300.04/300.40 153081[0:SpR:149179.0,16276.0] || -> subclass(symmetric_difference(u,intersection(u,v)),complement(intersection(u,v)))*. % 300.04/300.40 153350[0:SpR:149318.0,16276.0] || -> subclass(symmetric_difference(u,intersection(v,u)),complement(intersection(v,u)))*. % 300.04/300.40 167661[19:Rew:166997.0,82390.1] || subclass(universal_class,restrict(u,v,w))* -> member(ordinal_numbers,u). % 300.04/300.40 167966[19:Rew:166997.0,94672.1] function(u) || -> equal(single_valued2(u),range__dfg(ordinal_numbers,v,w))*. % 300.04/300.40 167967[19:Rew:166997.0,94664.1] single_valued_class(u) || -> equal(single_valued2(u),range__dfg(ordinal_numbers,v,w))*. % 300.04/300.40 177207[22:Res:177171.1,897.0] || subclass(omega,restrict(u,v,w))* -> member(ordinal_numbers,u). % 300.04/300.40 178141[18:Res:36682.1,177583.1] || equal(rest_of(not_subclass_element(u,v)),rest_relation)** -> subclass(u,v). % 300.04/300.40 178882[22:SpL:29.0,178812.0] || equal(restrict(u,v,w),omega)** -> member(ordinal_numbers,u). % 300.04/300.40 183893[23:SpR:183840.0,124905.0] || -> equal(cantor(restrict(u,v,ordinal_numbers)),segment(u,v,universal_class))**. % 300.04/300.40 184955[19:Res:176420.1,16.0] || subclass(domain_relation,rotate(cross_product(u,v)))* -> member(w,v)*. % 300.04/300.40 187179[19:Obv:187137.0] || -> equal(intersection(singleton(u),singleton(v)),ordinal_numbers)** equal(u,v). % 300.04/300.40 189152[8:Res:188649.1,158050.0] || equal(complement(cross_product(u,u)),universal_class)** -> connected(v,u)*. % 300.04/300.40 190290[19:MRR:190256.2,167057.0] inductive(symmetric_difference(u,u)) || well_ordering(v,complement(u))* -> . % 300.04/300.40 192211[19:Rew:167050.0,192180.0] || -> equal(segment(complement(cross_product(u,singleton(v))),u,v),ordinal_numbers)**. % 300.04/300.40 192302[19:Obv:192298.0] || -> equal(intersection(omega,singleton(u)),ordinal_numbers)** equal(integer_of(u),u). % 300.04/300.40 193351[25:SpR:193223.1,947.0] function(u) || -> member(unordered_pair(v,ordinal_numbers),ordered_pair(v,u))*. % 300.04/300.40 193598[25:Rew:183885.0,193354.1] function(u) || -> equal(apply(v,universal_class),apply(v,u))*. % 300.04/300.40 193609[25:Rew:183883.0,193352.1] function(u) || -> equal(ordered_pair(v,universal_class),ordered_pair(v,u))*. % 300.04/300.40 193951[25:Res:193300.1,177998.1] function(u) || equal(complement(ordered_pair(u,v)),omega)** -> . % 300.04/300.40 195387[0:Res:27189.1,16.0] || subclass(rest_relation,rotate(cross_product(u,v)))* -> member(w,v)*. % 300.04/300.40 196699[19:MRR:196652.1,167052.0] || subclass(cross_product(universal_class,universal_class),u)* -> member(regular(rest_relation),u). % 300.04/300.40 196700[19:MRR:196653.1,167054.0] || subclass(cross_product(universal_class,universal_class),u)* -> member(regular(domain_relation),u). % 300.04/300.40 196701[19:MRR:196659.1,167013.0] || subclass(cross_product(universal_class,universal_class),u)* -> member(regular(successor_relation),u). % 300.04/300.40 196719[19:Res:7.1,196698.0] || equal(u,cross_product(universal_class,universal_class)) -> member(regular(element_relation),u)*. % 300.04/300.40 196822[19:Res:196720.0,11848.0] || subclass(cross_product(universal_class,universal_class),u)* well_ordering(universal_class,u) -> . % 300.04/300.40 196836[19:Res:196731.1,25.1] || subclass(universal_class,complement(u)) member(regular(element_relation),u)* -> . % 300.04/300.40 196840[19:Res:196731.1,148647.0] || subclass(universal_class,complement(complement(u)))* -> member(regular(element_relation),u). % 300.04/300.40 196849[19:Res:196731.1,22.0] || subclass(universal_class,intersection(u,v))* -> member(regular(element_relation),u). % 300.04/300.40 196850[19:Res:196731.1,23.0] || subclass(universal_class,intersection(u,v))* -> member(regular(element_relation),v). % 300.04/300.40 197318[19:Obv:197309.1] || subclass(u,v) -> equal(intersection(complement(v),u),ordinal_numbers)**. % 300.04/300.40 197881[19:Obv:197872.1] || subclass(u,v) -> equal(intersection(u,complement(v)),ordinal_numbers)**. % 300.04/300.40 198882[19:SpR:4105.0,197702.0] || -> equal(intersection(complement(symmetrization_of(u)),symmetric_difference(u,inverse(u))),ordinal_numbers)**. % 300.04/300.40 199436[19:SpR:160.0,199166.0] || -> equal(intersection(symmetric_difference(u,v),complement(union(u,v))),ordinal_numbers)**. % 300.04/300.40 202594[19:SpR:197295.1,30.0] || subclass(u,ordinal_numbers) -> equal(restrict(u,v,w),ordinal_numbers)**. % 300.04/300.40 202708[19:Rew:167055.0,202536.1] || subclass(complement(u),ordinal_numbers)* -> equal(union(v,u),universal_class)**. % 300.04/300.40 202839[19:SpR:197859.1,137025.0] || subclass(complement(u),ordinal_numbers) -> subclass(complement(successor(u)),ordinal_numbers)*. % 300.04/300.40 202841[19:SpR:197859.1,137026.0] || subclass(complement(u),ordinal_numbers) -> subclass(complement(symmetrization_of(u)),ordinal_numbers)*. % 300.04/300.40 202941[19:Rew:167055.0,202769.1] || subclass(complement(u),ordinal_numbers)* -> equal(union(u,v),universal_class)**. % 300.04/300.40 203439[19:Res:203242.1,125116.1] || subclass(rest_of(u),ordinal_numbers) member(v,cantor(u))* -> . % 300.04/300.40 204374[19:MRR:169487.1,204370.0] || equal(ordered_pair(u,v),universal_class)** -> equal(singleton(u),ordinal_numbers). % 300.04/300.40 204375[19:MRR:169488.1,204370.0] || subclass(universal_class,ordered_pair(u,v))* -> equal(singleton(u),ordinal_numbers). % 300.04/300.40 204377[22:MRR:177210.1,204370.0] || subclass(omega,ordered_pair(u,v))* -> equal(singleton(u),ordinal_numbers). % 300.04/300.40 204378[22:MRR:178945.1,204370.0] || equal(ordered_pair(u,v),omega)** -> equal(singleton(u),ordinal_numbers). % 300.04/300.40 204398[19:MRR:204397.2,197173.0] || subclass(universal_class,ordered_pair(u,v))* -> equal(regular(element_relation),omega). % 300.04/300.40 204478[19:SpL:27.0,204472.0] || equal(intersection(complement(u),complement(v)),union(u,v))** -> . % 300.04/300.40 204557[19:MRR:204515.0,167011.0] || subclass(union(u,v),ordinal_numbers)* -> member(ordinal_numbers,complement(u)). % 300.04/300.40 204558[19:MRR:204516.0,167011.0] || subclass(union(u,v),ordinal_numbers)* -> member(ordinal_numbers,complement(v)). % 300.04/300.40 204559[19:MRR:204521.0,167011.0] || subclass(rest_relation,rest_of(u)) subclass(cantor(u),ordinal_numbers)* -> . % 300.04/300.40 204677[19:MRR:204647.0,53.0] || subclass(union(u,v),ordinal_numbers)* -> member(omega,complement(u)). % 300.04/300.40 204678[19:MRR:204648.0,53.0] || subclass(union(u,v),ordinal_numbers)* -> member(omega,complement(v)). % 300.04/300.40 205970[19:MRR:205523.2,9070.0] || equal(complement(u),ordinal_numbers) equal(complement(u),universal_class)** -> . % 300.04/300.40 205972[19:MRR:205578.2,9070.0] || equal(power_class(u),ordinal_numbers) equal(power_class(u),universal_class)** -> . % 300.04/300.40 206002[19:Obv:205726.1] || equal(complement(singleton(u)),ordinal_numbers)** -> equal(singleton(v),u)*. % 300.04/300.40 206963[19:Rew:206400.0,204486.0] || equal(image(element_relation,power_class(u)),power_class(complement(power_class(u))))** -> . % 300.04/300.40 207245[19:Rew:206400.0,198293.0] || -> equal(intersection(power_class(u),intersection(complement(power_class(u)),v)),ordinal_numbers)**. % 300.04/300.40 207277[19:Rew:206400.0,168289.1] || well_ordering(universal_class,power_class(u)) -> member(ordinal_numbers,complement(power_class(u)))*. % 300.04/300.40 207320[19:Rew:206400.0,198940.0] || -> equal(intersection(power_class(u),intersection(v,complement(power_class(u)))),ordinal_numbers)**. % 300.04/300.40 207323[19:Rew:206400.0,203385.0] || subclass(complement(power_class(u)),ordinal_numbers)* -> subclass(universal_class,power_class(u)). % 300.04/300.40 207787[8:SpL:206407.0,85097.1] inductive(complement(power_class(u))) || equal(power_class(u),universal_class)** -> . % 300.04/300.40 207831[22:SpL:206407.0,178292.1] inductive(complement(power_class(u))) || equal(power_class(u),omega)** -> . % 300.04/300.40 207905[25:MRR:207904.2,192574.0] single_valued_class(complement(power_class(u))) || equal(power_class(u),universal_class)** -> . % 300.04/300.40 207920[19:Res:205391.1,25.1] || equal(complement(complement(u)),ordinal_numbers)** member(ordinal_numbers,u) -> . % 300.04/300.40 207925[19:Res:205391.1,148647.0] || equal(complement(complement(complement(u))),ordinal_numbers)** -> member(ordinal_numbers,u). % 300.04/300.40 207934[19:Res:205391.1,22.0] || equal(complement(intersection(u,v)),ordinal_numbers)** -> member(ordinal_numbers,u). % 300.04/300.40 207935[19:Res:205391.1,23.0] || equal(complement(intersection(u,v)),ordinal_numbers)** -> member(ordinal_numbers,v). % 300.04/300.40 207971[22:Res:205391.1,177998.1] || equal(complement(u),ordinal_numbers) equal(complement(u),omega)** -> . % 300.04/300.40 208451[19:Res:205414.1,25.1] || equal(complement(complement(u)),ordinal_numbers)** member(omega,u) -> . % 300.04/300.40 208456[19:Res:205414.1,148647.0] || equal(complement(complement(complement(u))),ordinal_numbers)** -> member(omega,u). % 300.04/300.40 208465[19:Res:205414.1,22.0] || equal(complement(intersection(u,v)),ordinal_numbers)** -> member(omega,u). % 300.04/300.40 208466[19:Res:205414.1,23.0] || equal(complement(intersection(u,v)),ordinal_numbers)** -> member(omega,v). % 300.04/300.40 208777[19:Res:205520.1,197067.1] || equal(complement(u),ordinal_numbers) equal(complement(u),element_relation)** -> . % 300.04/300.40 208784[19:Res:205520.1,97571.1] || equal(complement(u),ordinal_numbers) equal(complement(u),domain_relation)** -> . % 300.04/300.40 208793[19:Res:205520.1,164453.1] || equal(complement(complement(u)),ordinal_numbers)** subclass(domain_relation,u) -> . % 300.04/300.40 208805[19:Res:205520.1,48587.0] || equal(complement(complement(unordered_pair(u,ordered_pair(v,w)))),ordinal_numbers)** -> . % 300.04/300.40 208806[19:Res:205520.1,48401.0] || equal(complement(complement(unordered_pair(u,unordered_pair(v,w)))),ordinal_numbers)** -> . % 300.04/300.40 208808[19:Res:205520.1,48618.0] || equal(complement(complement(unordered_pair(ordered_pair(u,v),w))),ordinal_numbers)** -> . % 300.04/300.40 208809[19:Res:205520.1,48402.0] || equal(complement(complement(unordered_pair(unordered_pair(u,v),w))),ordinal_numbers)** -> . % 300.04/300.40 208815[19:Res:205520.1,196852.0] || equal(complement(singleton(u)),ordinal_numbers)** -> equal(regular(element_relation),u). % 300.04/300.40 209199[0:SpR:206407.0,206400.0] || -> equal(complement(power_class(complement(power_class(u)))),image(element_relation,power_class(u)))**. % 300.04/300.40 209695[25:SpR:209646.0,193301.1] function(power_class(u)) || -> equal(successor(power_class(u)),power_class(u))**. % 300.04/300.40 209818[0:MRR:209801.1,36583.1] || member(u,rest_of(u))* subclass(rest_relation,complement(element_relation)) -> . % 300.04/300.40 209821[19:MRR:209803.1,940.0] || subclass(domain_relation,rotate(u)) subclass(rest_relation,complement(u))* -> . % 300.04/300.40 209822[0:MRR:209811.1,940.0] || subclass(rest_relation,flip(u)) subclass(rest_relation,complement(u))* -> . % 300.04/300.40 209885[19:Res:10.1,205934.1] || member(u,universal_class) equal(unordered_pair(u,v),ordinal_numbers)** -> . % 300.04/300.40 209886[19:Res:11.1,205934.1] || member(u,universal_class) equal(unordered_pair(v,u),ordinal_numbers)** -> . % 300.04/300.40 209918[19:Res:182463.1,205934.1] || equal(u,singleton(singleton(ordinal_numbers)))* equal(ordinal_numbers,u) -> . % 300.04/300.40 210007[19:Res:2525.1,205934.1] || subclass(ordered_pair(u,v),w)* equal(ordinal_numbers,w) -> . % 300.04/300.40 210042[19:Res:168350.1,205934.1] || equal(ordinal_numbers,u) -> equal(restrict(u,v,w),ordinal_numbers)**. % 300.04/300.40 210983[19:Res:55.1,205988.1] || member(u,universal_class) equal(singleton(sum_class(u)),ordinal_numbers)** -> . % 300.04/300.40 210984[19:Res:57.1,205988.1] || member(u,universal_class) equal(singleton(power_class(u)),ordinal_numbers)** -> . % 300.04/300.40 210985[19:Res:15058.1,205988.1] function(u) || equal(singleton(apply(u,v)),ordinal_numbers)** -> . % 300.04/300.40 210986[19:Res:36682.1,205988.1] || equal(singleton(not_subclass_element(u,v)),ordinal_numbers)** -> subclass(u,v). % 300.04/300.40 210993[19:Res:149603.1,205988.1] || member(u,universal_class) equal(singleton(rest_of(u)),ordinal_numbers)** -> . % 300.04/300.40 211626[19:Res:203424.1,4178.0] || subclass(complement(singleton(u)),ordinal_numbers)* -> equal(singleton(v),u)*. % 300.04/300.40 211656[19:Res:203424.1,2557.0] || subclass(complement(cross_product(u,v)),ordinal_numbers)* -> member(w,v)*. % 300.04/300.40 211985[19:SpR:205896.1,137025.0] || equal(complement(u),ordinal_numbers) -> subclass(complement(successor(u)),ordinal_numbers)*. % 300.04/300.40 211987[19:SpR:205896.1,137026.0] || equal(complement(u),ordinal_numbers) -> subclass(complement(symmetrization_of(u)),ordinal_numbers)*. % 300.04/300.40 212097[19:Rew:167055.0,211912.1] || equal(complement(u),ordinal_numbers) -> equal(union(u,v),universal_class)**. % 300.04/300.40 212351[19:Rew:167055.0,212165.1] || equal(complement(u),ordinal_numbers) -> equal(union(v,u),universal_class)**. % 300.04/300.40 212463[19:Res:205991.1,5467.1] || equal(complement(u),ordinal_numbers) subclass(universal_class,complement(u))* -> . % 300.04/300.40 212587[22:Res:209033.1,204538.1] || equal(power_class(u),ordinal_numbers) equal(power_class(u),omega)** -> . % 300.04/300.40 212588[19:Res:209033.1,203421.0] || equal(power_class(u),ordinal_numbers) subclass(universal_class,power_class(u))* -> . % 300.04/300.40 212590[19:Res:209033.1,203418.0] || equal(power_class(u),ordinal_numbers) subclass(domain_relation,power_class(u))* -> . % 300.04/300.40 214483[19:SpL:149012.1,214449.0] || subclass(u,complement(singleton(ordinal_numbers)))* member(ordinal_numbers,u) -> . % 300.04/300.40 214500[19:SpR:481.0,214498.0] || -> member(ordinal_numbers,complement(intersection(complement(singleton(ordinal_numbers)),union(u,v))))*. % 300.04/300.40 214515[19:Res:214498.0,2.0] || subclass(union(singleton(ordinal_numbers),u),v)* -> member(ordinal_numbers,v). % 300.04/300.40 214678[19:Res:214502.0,11848.0] || subclass(successor(singleton(ordinal_numbers)),u)* well_ordering(universal_class,u) -> . % 300.04/300.40 214690[19:Res:214503.0,11848.0] || subclass(symmetrization_of(singleton(ordinal_numbers)),u)* well_ordering(universal_class,u) -> . % 300.04/300.40 215059[8:MRR:214968.1,135319.0] || member(u,universal_class) -> member(u,regular(ordered_pair(u,v)))*. % 300.04/300.40 215234[19:Res:214528.1,897.0] || subclass(kind_1_ordinals,restrict(u,v,w))* -> member(ordinal_numbers,u). % 300.04/300.40 215237[19:Res:214528.1,110865.0] || subclass(kind_1_ordinals,rest_of(ordinal_numbers))* subclass(universal_class,complement(element_relation)) -> . % 300.04/300.40 215255[19:Res:214528.1,169221.1] || subclass(kind_1_ordinals,u)* equal(complement(u),singleton(ordinal_numbers)) -> . % 300.04/300.40 215264[19:MRR:215236.1,204370.0] || subclass(kind_1_ordinals,ordered_pair(u,v))* -> equal(singleton(u),ordinal_numbers). % 300.04/300.40 215622[19:Res:215454.0,2.0] || subclass(union(u,singleton(ordinal_numbers)),v)* -> member(ordinal_numbers,v). % 300.04/300.40 215835[22:SpL:149012.1,214489.0] || subclass(u,complement(singleton(ordinal_numbers)))* equal(u,omega) -> . % 300.04/300.40 215862[22:SpL:149012.1,214490.0] || subclass(u,complement(singleton(ordinal_numbers)))* subclass(omega,u) -> . % 300.04/300.40 215894[19:SpL:149012.1,214492.0] || subclass(u,complement(singleton(ordinal_numbers)))* subclass(universal_class,u) -> . % 300.04/300.40 215926[19:SpL:149012.1,214493.0] || subclass(u,complement(singleton(ordinal_numbers)))* equal(u,universal_class) -> . % 300.04/300.40 216177[19:SpL:149012.1,215260.0] || subclass(u,complement(singleton(ordinal_numbers)))* subclass(kind_1_ordinals,u) -> . % 300.04/300.40 216370[19:SpL:149012.1,216181.0] || subclass(u,complement(singleton(ordinal_numbers)))* equal(u,kind_1_ordinals) -> . % 300.04/300.40 216543[19:SpL:29.0,214439.0] || subclass(singleton(ordinal_numbers),restrict(complement(singleton(ordinal_numbers)),u,v))* -> . % 300.04/300.40 216576[19:SpL:29.0,214488.0] || equal(complement(restrict(complement(singleton(ordinal_numbers)),u,v)),ordinal_numbers)** -> . % 300.04/300.40 216610[19:SpL:29.0,214491.0] || equal(restrict(complement(singleton(ordinal_numbers)),u,v),singleton(ordinal_numbers))** -> . % 300.04/300.40 216995[19:Res:63.1,214682.0] function(successor(singleton(ordinal_numbers))) || -> member(ordinal_numbers,cross_product(universal_class,universal_class))*. % 300.04/300.40 217004[19:Res:63.1,214694.0] function(symmetrization_of(singleton(ordinal_numbers))) || -> member(ordinal_numbers,cross_product(universal_class,universal_class))*. % 300.04/300.40 217795[0:SpR:29.0,217683.0] || -> subclass(intersection(restrict(u,v,w),x),cross_product(v,w))*. % 300.04/300.40 217866[19:Res:217683.0,167311.1] inductive(intersection(intersection(u,v),w)) || -> member(ordinal_numbers,v)*. % 300.04/300.40 217971[0:SpR:29.0,217853.0] || -> subclass(complement(complement(restrict(u,v,w))),cross_product(v,w))*. % 300.04/300.40 218025[19:SpR:204449.1,217853.0] || equal(complement(intersection(u,v)),ordinal_numbers)** -> subclass(universal_class,v). % 300.04/300.40 218028[19:Res:217853.0,167311.1] inductive(complement(complement(intersection(u,v)))) || -> member(ordinal_numbers,v)*. % 300.04/300.40 218414[19:SpR:204449.1,218022.0] || equal(union(u,v),ordinal_numbers)** -> subclass(universal_class,complement(v))*. % 300.04/300.40 218416[19:Res:218022.0,167311.1] inductive(complement(union(u,v))) || -> member(ordinal_numbers,complement(v))*. % 300.04/300.40 218463[19:SpR:204449.1,218395.0] || equal(successor(u),ordinal_numbers) -> subclass(universal_class,complement(singleton(u)))*. % 300.04/300.40 218465[19:Res:218395.0,167311.1] inductive(complement(successor(u))) || -> member(ordinal_numbers,complement(singleton(u)))*. % 300.04/300.40 218482[19:SpR:204449.1,218396.0] || equal(symmetrization_of(u),ordinal_numbers) -> subclass(universal_class,complement(inverse(u)))*. % 300.04/300.40 218484[19:Res:218396.0,167311.1] inductive(complement(symmetrization_of(u))) || -> member(ordinal_numbers,complement(inverse(u)))*. % 300.04/300.40 218735[0:SpR:29.0,217850.0] || -> subclass(intersection(u,restrict(v,w,x)),cross_product(w,x))*. % 300.04/300.40 218808[19:Res:217850.0,167311.1] inductive(intersection(u,intersection(v,w))) || -> member(ordinal_numbers,w)*. % 300.04/300.40 218900[0:SpR:160.0,218280.0] || -> subclass(intersection(symmetric_difference(u,v),w),complement(intersection(u,v)))*. % 300.04/300.40 218984[19:Res:218280.0,167311.1] inductive(intersection(intersection(u,v),w)) || -> member(ordinal_numbers,u)*. % 300.04/300.40 219715[19:Res:218920.0,167311.1] inductive(intersection(complement(complement(u)),v)) || -> member(ordinal_numbers,u)*. % 300.04/300.40 219965[19:Res:219703.0,167311.1] inductive(complement(complement(complement(complement(u))))) || -> member(ordinal_numbers,u)*. % 300.04/300.40 220130[0:SpR:160.0,218971.0] || -> subclass(complement(complement(symmetric_difference(u,v))),complement(intersection(u,v)))*. % 300.04/300.40 220197[19:SpR:204449.1,218971.0] || equal(complement(intersection(u,v)),ordinal_numbers)** -> subclass(universal_class,u). % 300.04/300.40 220201[19:Res:218971.0,167311.1] inductive(complement(complement(intersection(u,v)))) || -> member(ordinal_numbers,u)*. % 300.04/300.40 220343[19:Res:219700.0,167311.1] inductive(intersection(u,complement(complement(v)))) || -> member(ordinal_numbers,v)*. % 300.04/300.40 220445[19:SpR:204449.1,220194.0] || equal(union(u,v),ordinal_numbers)** -> subclass(universal_class,complement(u))*. % 300.04/300.40 220448[19:Res:220194.0,167311.1] inductive(complement(union(u,v))) || -> member(ordinal_numbers,complement(u))*. % 300.04/300.40 220561[0:SpR:160.0,218968.0] || -> subclass(intersection(u,symmetric_difference(v,w)),complement(intersection(v,w)))*. % 300.04/300.40 220648[19:Res:218968.0,167311.1] inductive(intersection(u,intersection(v,w))) || -> member(ordinal_numbers,v)*. % 300.04/300.40 221030[27:MRR:220950.1,214529.0] || subclass(kind_1_ordinals,complement(intersection(singleton(ordinal_numbers),image(successor_relation,ordinal_numbers))))* -> . % 300.04/300.40 221231[27:Res:221200.0,11848.0] || subclass(image(successor_relation,ordinal_numbers),u)* well_ordering(universal_class,u) -> . % 300.04/300.40 221350[27:MRR:221329.1,214509.0] || equal(complement(intersection(singleton(ordinal_numbers),image(successor_relation,ordinal_numbers))),omega)** -> . % 300.04/300.40 221351[27:MRR:221330.1,214509.0] || subclass(omega,complement(intersection(singleton(ordinal_numbers),image(successor_relation,ordinal_numbers))))* -> . % 300.04/300.40 221352[27:MRR:221332.1,214509.0] || subclass(universal_class,complement(intersection(singleton(ordinal_numbers),image(successor_relation,ordinal_numbers))))* -> . % 300.04/300.40 221353[27:MRR:221333.1,214509.0] || equal(complement(intersection(singleton(ordinal_numbers),image(successor_relation,ordinal_numbers))),universal_class)** -> . % 300.04/300.40 221726[19:Res:219766.1,205983.1] || equal(complement(flip(u)),ordinal_numbers)** equal(ordinal_numbers,u) -> . % 300.04/300.40 221733[19:Res:219766.1,205984.1] || equal(complement(rotate(u)),ordinal_numbers)** equal(ordinal_numbers,u) -> . % 300.04/300.40 222320[19:SpR:167191.0,219698.0] || -> subclass(restrict(complement(symmetrization_of(ordinal_numbers)),u,v),complement(inverse(ordinal_numbers)))*. % 300.04/300.40 222424[0:SpR:149012.1,217800.0] || subclass(u,restrict(v,w,x))* -> subclass(u,v). % 300.04/300.40 222489[0:SpR:160.0,217848.0] || -> subclass(restrict(symmetric_difference(u,v),w,x),union(u,v))*. % 300.04/300.40 222491[0:SpR:4105.0,217848.0] || -> subclass(restrict(symmetric_difference(u,inverse(u)),v,w),symmetrization_of(u))*. % 300.04/300.40 222781[0:SpR:149012.1,218966.0] || subclass(u,v) -> subclass(restrict(u,w,x),v)*. % 300.04/300.40 223640[19:Rew:180103.0,223626.0] || equal(complement(intersection(singleton(ordinal_numbers),union(u,v))),ordinal_numbers)** -> . % 300.04/300.40 223735[28:Res:188649.1,223713.0] || equal(complement(compose(ordinal_numbers,ordinal_numbers)),universal_class)** -> transitive(universal_class,u)*. % 300.04/300.40 223740[28:Obv:223739.1] || equal(compose_class(ordinal_numbers),domain_relation) -> equal(cross_product(u,u),ordinal_numbers)**. % 300.04/300.40 223784[19:Res:169181.1,217129.1] || equal(u,singleton(ordinal_numbers)) equal(complement(u),kind_1_ordinals)** -> . % 300.04/300.40 223798[25:Res:193300.1,217129.1] function(u) || equal(complement(ordered_pair(u,v)),kind_1_ordinals)** -> . % 300.04/300.40 223800[27:Res:221347.0,217129.1] || equal(complement(intersection(singleton(ordinal_numbers),image(successor_relation,ordinal_numbers))),kind_1_ordinals)** -> . % 300.04/300.40 224057[19:SpL:206407.0,223787.1] inductive(complement(power_class(u))) || equal(power_class(u),kind_1_ordinals)** -> . % 300.04/300.40 224125[19:Res:217800.0,219089.0] || -> subclass(intersection(restrict(symmetrization_of(ordinal_numbers),u,v),w),inverse(ordinal_numbers))*. % 300.04/300.40 224128[19:Res:219698.0,219089.0] || -> subclass(restrict(complement(complement(symmetrization_of(ordinal_numbers))),u,v),inverse(ordinal_numbers))*. % 300.04/300.40 224129[19:Res:218966.0,219089.0] || -> subclass(restrict(intersection(symmetrization_of(ordinal_numbers),u),v,w),inverse(ordinal_numbers))*. % 300.04/300.40 224135[19:Res:16133.1,219089.0] || member(u,symmetrization_of(ordinal_numbers)) -> subclass(singleton(u),inverse(ordinal_numbers))*. % 300.04/300.40 224139[19:Res:218740.0,219089.0] || -> subclass(intersection(u,restrict(symmetrization_of(ordinal_numbers),v,w)),inverse(ordinal_numbers))*. % 300.04/300.40 224144[19:Res:217848.0,219089.0] || -> subclass(restrict(intersection(u,symmetrization_of(ordinal_numbers)),v,w),inverse(ordinal_numbers))*. % 300.04/300.40 224160[19:Res:217976.0,219089.0] || -> subclass(complement(complement(restrict(symmetrization_of(ordinal_numbers),u,v))),inverse(ordinal_numbers))*. % 300.04/300.40 224689[19:SpL:149012.1,224669.0] || subclass(u,symmetrization_of(ordinal_numbers))* equal(complement(u),ordinal_numbers) -> . % 300.04/300.40 224754[19:SpL:30.0,224619.0] || equal(complement(complement(restrict(symmetrization_of(ordinal_numbers),u,v))),universal_class)** -> . % 300.04/300.40 225014[19:Res:220510.1,195669.1] || equal(successor(u),ordinal_numbers)** equal(rotate(u),rest_relation) -> . % 300.04/300.40 225015[19:Res:220510.1,195635.1] || equal(successor(u),ordinal_numbers)** equal(flip(u),rest_relation) -> . % 300.04/300.40 225016[19:Res:220510.1,185733.1] || equal(successor(u),ordinal_numbers)** equal(rotate(u),domain_relation) -> . % 300.04/300.40 225017[19:Res:220510.1,185656.1] || equal(successor(u),ordinal_numbers)** equal(flip(u),domain_relation) -> . % 300.04/300.40 225026[19:Res:220510.1,9734.0] || equal(successor(complement(u)),ordinal_numbers) -> member(singleton(v),u)*. % 300.04/300.40 225535[19:SoR:220513.0,189460.1] || equal(complement(successor(u)),universal_class) -> member(ordinal_numbers,complement(u))*. % 300.04/300.40 225682[19:Res:220544.1,195669.1] || equal(symmetrization_of(u),ordinal_numbers)** equal(rotate(u),rest_relation) -> . % 300.04/300.40 225683[19:Res:220544.1,195635.1] || equal(symmetrization_of(u),ordinal_numbers)** equal(flip(u),rest_relation) -> . % 300.04/300.40 225684[19:Res:220544.1,185733.1] || equal(symmetrization_of(u),ordinal_numbers)** equal(rotate(u),domain_relation) -> . % 300.04/300.40 225685[19:Res:220544.1,185656.1] || equal(symmetrization_of(u),ordinal_numbers)** equal(flip(u),domain_relation) -> . % 300.04/300.40 225694[19:Res:220544.1,9734.0] || equal(symmetrization_of(complement(u)),ordinal_numbers) -> member(singleton(v),u)*. % 300.04/300.40 225708[22:Res:220544.1,178946.1] || equal(symmetrization_of(element_relation),ordinal_numbers) equal(rest_of(ordinal_numbers),omega)** -> . % 300.04/300.40 227395[19:SoR:220547.0,189460.1] || equal(complement(symmetrization_of(u)),universal_class) -> member(ordinal_numbers,complement(u))*. % 300.04/300.40 227749[27:Res:63.1,221235.0] function(image(successor_relation,ordinal_numbers)) || -> member(ordinal_numbers,cross_product(universal_class,universal_class))*. % 300.04/300.40 227978[19:SpR:124908.0,223552.1] || subclass(composition_function,rest_of(inverse(u)))* -> member(ordinal_numbers,range_of(u)). % 300.04/300.40 228012[19:Res:223552.1,205934.1] || subclass(composition_function,rest_of(u))* equal(cantor(u),ordinal_numbers) -> . % 300.04/300.40 228015[19:Res:223552.1,203417.1] || subclass(composition_function,rest_of(u)) subclass(cantor(u),ordinal_numbers)* -> . % 300.04/300.40 228028[19:MRR:227983.2,167057.0] || member(u,universal_class) subclass(composition_function,rest_of(sum_class(u)))* -> . % 300.04/300.40 228029[19:MRR:227993.2,167057.0] || member(u,universal_class) subclass(composition_function,rest_of(power_class(u)))* -> . % 300.04/300.40 228030[19:MRR:227994.2,167057.0] || member(u,universal_class) subclass(composition_function,rest_of(rest_of(u)))* -> . % 300.04/300.40 228031[19:MRR:227995.2,167057.0] function(u) || subclass(composition_function,rest_of(apply(u,v)))* -> . % 300.04/300.40 228032[19:MRR:227996.2,167057.0] || subclass(composition_function,rest_of(not_subclass_element(u,v)))* -> subclass(u,v). % 300.04/300.40 229097[19:SpR:225013.1,220426.0] || equal(successor(successor(u)),ordinal_numbers) -> subclass(universal_class,complement(u))*. % 300.04/300.40 229106[19:SpR:225013.1,220427.0] || equal(successor(symmetrization_of(u)),ordinal_numbers) -> subclass(universal_class,complement(u))*. % 300.04/300.40 229681[19:Rew:96580.0,228868.1] || equal(successor(u),ordinal_numbers) -> equal(complement(power_class(u)),universal_class)**. % 300.04/300.40 229684[19:Rew:142500.0,228898.1] || equal(successor(u),ordinal_numbers) -> equal(intersection(u,v),ordinal_numbers)**. % 300.04/300.40 229685[19:Rew:142500.0,228899.1] || equal(successor(u),ordinal_numbers) -> equal(intersection(v,u),ordinal_numbers)**. % 300.04/300.40 229776[19:Obv:229131.2] single_valued_class(u) || equal(successor(u),ordinal_numbers)** -> function(u). % 300.04/300.40 229779[20:Obv:229134.2] || equal(successor(u),ordinal_numbers)** equal(u,inverse(ordinal_numbers)) -> . % 300.04/300.40 229782[19:Obv:229138.2] || equal(successor(u),ordinal_numbers)** equal(u,singleton(ordinal_numbers)) -> . % 300.04/300.40 229785[19:MRR:229168.2,5.0] || equal(successor(u),ordinal_numbers) subclass(domain_relation,flip(u))* -> . % 300.04/300.40 229786[19:MRR:229169.2,5.0] || equal(successor(u),ordinal_numbers) subclass(domain_relation,rotate(u))* -> . % 300.04/300.40 229790[19:Obv:229247.2] || equal(successor(singleton(u)),ordinal_numbers)** member(u,universal_class) -> . % 300.04/300.40 229791[19:MRR:229303.1,5.0] || equal(successor(singleton(regular(u))),ordinal_numbers)** -> equal(u,ordinal_numbers). % 300.04/300.40 229794[19:Obv:229320.1] || equal(successor(complement(u)),ordinal_numbers)** well_ordering(universal_class,u) -> . % 300.04/300.40 229795[19:Obv:229347.1] || equal(successor(complement(symmetrization_of(u))),ordinal_numbers)** -> connected(u,v)*. % 300.04/300.40 229796[19:Obv:229451.1] || equal(successor(compose(u,inverse(u))),ordinal_numbers)** -> single_valued_class(u). % 300.04/300.40 229797[19:Obv:229457.1] || equal(successor(compose(ordinal_numbers,ordinal_numbers)),ordinal_numbers)** -> transitive(ordinal_numbers,u)*. % 300.04/300.40 229798[19:Obv:229554.1] || equal(successor(rest_of(u)),ordinal_numbers)** -> equal(cantor(u),ordinal_numbers). % 300.04/300.40 229800[19:Obv:229622.1] || equal(successor(sum_class(kind_1_ordinals)),ordinal_numbers)** well_ordering(element_relation,kind_1_ordinals) -> . % 300.04/300.40 229801[26:Obv:229623.1] || equal(successor(sum_class(ordinal_numbers)),ordinal_numbers)** well_ordering(element_relation,ordinal_numbers) -> . % 300.04/300.40 229804[27:MRR:229803.1,214529.0] || equal(successor(intersection(singleton(ordinal_numbers),image(successor_relation,ordinal_numbers))),ordinal_numbers)** -> . % 300.04/300.40 230846[19:Res:229698.1,9780.0] || equal(successor(sum_class(u)),ordinal_numbers) -> section(element_relation,u,universal_class)*. % 300.04/300.40 231125[19:Res:229698.1,158050.0] || equal(successor(cross_product(u,u)),ordinal_numbers)** -> connected(v,u)*. % 300.04/300.40 231156[28:Res:229698.1,223713.0] || equal(successor(compose(ordinal_numbers,ordinal_numbers)),ordinal_numbers)** -> transitive(universal_class,u)*. % 300.04/300.40 231545[19:SpL:30.0,229721.0] || equal(successor(complement(restrict(symmetrization_of(ordinal_numbers),u,v))),ordinal_numbers)** -> . % 300.04/300.40 232077[19:Res:169181.1,225687.1] || equal(u,singleton(ordinal_numbers)) equal(symmetrization_of(u),ordinal_numbers)** -> . % 300.04/300.40 232095[27:Res:221347.0,225687.1] || equal(symmetrization_of(intersection(singleton(ordinal_numbers),image(successor_relation,ordinal_numbers))),ordinal_numbers)** -> . % 300.04/300.40 233324[19:Res:233022.0,167311.1] inductive(intersection(u,v)) || -> member(ordinal_numbers,intersection(v,u))*. % 300.04/300.40 233562[19:Rew:233350.0,209882.1] || member(u,complement(v))* equal(complement(v),ordinal_numbers) -> . % 300.04/300.40 233961[25:Rew:233350.0,225587.1] function(u) || -> subclass(complement(symmetrization_of(complement(u))),successor(u))*. % 300.04/300.40 233975[25:Rew:233350.0,224919.1] function(u) || -> subclass(complement(successor(complement(u))),successor(u))*. % 300.04/300.40 234089[25:Rew:233350.0,194208.1] function(u) || -> equal(intersection(successor(u),complement(u)),ordinal_numbers)**. % 300.04/300.40 234090[25:Rew:233350.0,194209.1] function(u) || -> equal(union(successor(u),complement(u)),universal_class)**. % 300.04/300.40 234091[25:Rew:233350.0,194210.1] function(u) || -> equal(symmetric_difference(successor(u),complement(u)),universal_class)**. % 300.04/300.40 234290[19:Rew:233390.0,204547.1] || member(ordinal_numbers,u) subclass(complement(complement(u)),ordinal_numbers)* -> . % 300.04/300.40 234695[19:Rew:234692.0,169229.1] || -> equal(singleton(u),ordinal_numbers) equal(intersection(u,singleton(u)),ordinal_numbers)**. % 300.04/300.40 236252[0:SpR:234692.0,135266.0] || -> subclass(complement(union(u,v)),intersection(complement(v),complement(u)))*. % 300.04/300.40 237743[19:Res:237218.0,167311.1] inductive(symmetric_difference(u,v)) || -> member(ordinal_numbers,union(v,u))*. % 300.04/300.40 239036[19:SpR:237603.0,217853.0] || -> subclass(complement(complement(successor(u))),complement(intersection(u,singleton(u))))*. % 300.04/300.40 239056[19:SpR:237603.0,217683.0] || -> subclass(intersection(successor(u),v),complement(intersection(u,singleton(u))))*. % 300.04/300.40 239065[19:SpR:237603.0,217850.0] || -> subclass(intersection(u,successor(v)),complement(intersection(v,singleton(v))))*. % 300.04/300.40 239370[19:SoR:224744.0,238779.1] || equal(singleton(u),universal_class)** -> equal(apply(choice,omega),u)*. % 300.04/300.40 239371[19:SoR:187492.0,238779.1] || member(u,inverse(ordinal_numbers))* equal(singleton(u),universal_class) -> . % 300.04/300.40 239874[19:Res:238770.1,195563.1] || equal(flip(u),universal_class) equal(complement(u),domain_relation)** -> . % 300.04/300.40 239875[19:Res:238770.1,188735.0] || equal(flip(u),universal_class) equal(complement(u),universal_class)** -> . % 300.04/300.40 239876[19:Res:238770.1,184883.0] || equal(flip(u),universal_class) subclass(universal_class,complement(u))* -> . % 300.04/300.40 239879[19:Res:238770.1,184877.0] || equal(flip(cross_product(u,v)),universal_class)** -> member(ordinal_numbers,v). % 300.04/300.40 239882[19:Res:238770.1,195218.1] || equal(rotate(u),universal_class) equal(complement(u),domain_relation)** -> . % 300.04/300.40 239883[19:Res:238770.1,188716.0] || equal(rotate(u),universal_class) equal(complement(u),universal_class)** -> . % 300.04/300.40 239884[19:Res:238770.1,184965.0] || equal(rotate(u),universal_class) subclass(universal_class,complement(u))* -> . % 300.04/300.40 239980[19:Res:238770.1,195414.0] || equal(rotate(u),universal_class) subclass(domain_relation,complement(u))* -> . % 300.04/300.40 240502[19:Res:239914.1,148647.0] || equal(complement(complement(u)),universal_class) -> member(regular(element_relation),u)*. % 300.04/300.40 240512[19:Res:239914.1,22.0] || equal(intersection(u,v),universal_class)** -> member(regular(element_relation),u)*. % 300.04/300.40 240513[19:Res:239914.1,23.0] || equal(intersection(u,v),universal_class)** -> member(regular(element_relation),v)*. % 300.04/300.40 240575[19:MRR:240574.2,197173.0] || equal(ordered_pair(u,v),universal_class)** -> equal(regular(element_relation),omega). % 300.04/300.40 240723[19:Res:238827.1,169484.0] || equal(symmetrization_of(element_relation),universal_class)** equal(sum_class(ordinal_numbers),ordinal_numbers) -> . % 300.04/300.40 240761[0:SpR:149012.1,236254.0] || subclass(u,v) -> subclass(symmetric_difference(u,v),complement(u))*. % 300.04/300.40 241011[19:Res:240703.0,205934.1] || equal(complement(intersection(singleton(ordinal_numbers),singleton(singleton(ordinal_numbers)))),ordinal_numbers)** -> . % 300.04/300.40 241015[19:Res:240703.0,203417.1] || subclass(complement(intersection(singleton(ordinal_numbers),singleton(singleton(ordinal_numbers)))),ordinal_numbers)* -> . % 300.04/300.40 241041[19:Res:169181.1,241002.0] || equal(intersection(singleton(ordinal_numbers),singleton(singleton(ordinal_numbers))),singleton(ordinal_numbers))** -> . % 300.04/300.40 242431[19:Res:242417.0,11848.0] || subclass(complement(symmetrization_of(ordinal_numbers)),u)* well_ordering(universal_class,u) -> . % 300.04/300.40 243503[19:SpL:30.0,239284.0] || equal(intersection(u,restrict(symmetrization_of(ordinal_numbers),v,w)),universal_class)** -> . % 300.04/300.40 243603[19:SpL:30.0,239300.0] || equal(intersection(restrict(symmetrization_of(ordinal_numbers),u,v),w),universal_class)** -> . % 300.04/300.40 243757[19:Res:16133.1,239702.0] || member(u,symmetrization_of(ordinal_numbers))* equal(singleton(u),universal_class) -> . % 300.04/300.40 243849[19:Res:63.1,242435.0] function(complement(symmetrization_of(ordinal_numbers))) || -> member(ordinal_numbers,cross_product(universal_class,universal_class))*. % 300.04/300.40 246016[19:Res:27190.1,229738.1] || subclass(rest_relation,flip(u))* equal(successor(u),ordinal_numbers) -> . % 300.04/300.40 246017[19:Res:27189.1,229738.1] || subclass(rest_relation,rotate(u))* equal(successor(u),ordinal_numbers) -> . % 300.04/300.40 246102[20:Res:181635.1,229738.1] || subclass(symmetrization_of(ordinal_numbers),u)* equal(successor(u),ordinal_numbers) -> . % 300.04/300.40 246103[20:Res:175570.1,229738.1] || subclass(inverse(ordinal_numbers),u)* equal(successor(u),ordinal_numbers) -> . % 300.04/300.40 246382[25:SpR:234134.1,148172.0] function(u) || -> equal(intersection(u,successor(u)),successor(u))**. % 300.04/300.40 246388[25:SpR:234134.1,219698.0] function(u) || -> subclass(restrict(successor(u),v,w),u)*. % 300.04/300.40 246393[25:SpR:234134.1,167191.0] function(inverse(ordinal_numbers)) || -> equal(successor(inverse(ordinal_numbers)),symmetrization_of(ordinal_numbers))**. % 300.04/300.40 246396[25:SpR:234134.1,219080.0] function(symmetrization_of(ordinal_numbers)) || -> subclass(successor(symmetrization_of(ordinal_numbers)),inverse(ordinal_numbers))*. % 300.04/300.40 246400[25:SpR:234134.1,222998.0] function(symmetrization_of(ordinal_numbers)) || -> member(regular(successor(symmetrization_of(ordinal_numbers))),universal_class)*. % 300.04/300.40 246575[25:SpL:234134.1,208203.0] function(symmetrization_of(ordinal_numbers)) || equal(successor(symmetrization_of(ordinal_numbers)),universal_class)** -> . % 300.04/300.40 246590[25:SpL:234134.1,242439.0] function(symmetrization_of(ordinal_numbers)) || equal(successor(symmetrization_of(ordinal_numbers)),kind_1_ordinals)** -> . % 300.04/300.40 246591[25:SpL:234134.1,242442.0] function(symmetrization_of(ordinal_numbers)) || equal(successor(symmetrization_of(ordinal_numbers)),omega)** -> . % 300.04/300.40 246696[25:Res:246381.1,167311.1] function(u) inductive(successor(u)) || -> member(ordinal_numbers,u)*. % 300.04/300.40 247197[25:SpL:234134.1,247123.0] function(rest_of(u)) || equal(successor(rest_of(u)),universal_class)** -> . % 300.04/300.40 248134[19:Res:248123.1,169484.0] || equal(inverse(element_relation),universal_class) equal(sum_class(ordinal_numbers),ordinal_numbers)** -> . % 300.04/300.40 248144[19:SpL:29.0,245337.0] || equal(restrict(u,v,w),kind_1_ordinals)** -> member(ordinal_numbers,u). % 300.04/300.40 248332[19:Res:248149.1,110865.0] || equal(rest_of(ordinal_numbers),kind_1_ordinals) subclass(universal_class,complement(element_relation))* -> . % 300.04/300.40 248359[19:Res:248149.1,169221.1] || equal(u,kind_1_ordinals) equal(complement(u),singleton(ordinal_numbers))** -> . % 300.04/300.40 248370[19:MRR:248331.1,204370.0] || equal(ordered_pair(u,v),kind_1_ordinals)** -> equal(singleton(u),ordinal_numbers). % 300.04/300.40 248779[19:Res:219766.1,219712.0] || equal(complement(complement(complement(u))),ordinal_numbers)** -> subclass(v,u)*. % 300.04/300.40 248785[0:Res:217800.0,219712.0] || -> subclass(intersection(restrict(complement(complement(u)),v,w),x),u)*. % 300.04/300.40 248788[0:Res:219698.0,219712.0] || -> subclass(restrict(complement(complement(complement(complement(u)))),v,w),u)*. % 300.04/300.40 248789[0:Res:218966.0,219712.0] || -> subclass(restrict(intersection(complement(complement(u)),v),w,x),u)*. % 300.04/300.40 248796[0:Res:16133.1,219712.0] || member(u,complement(complement(v)))* -> subclass(singleton(u),v). % 300.04/300.40 248800[0:Res:218740.0,219712.0] || -> subclass(intersection(u,restrict(complement(complement(v)),w,x)),v)*. % 300.04/300.40 248805[0:Res:217848.0,219712.0] || -> subclass(restrict(intersection(u,complement(complement(v))),w,x),v)*. % 300.04/300.40 248813[0:Res:217976.0,219712.0] || -> subclass(complement(complement(restrict(complement(complement(u)),v,w))),u)*. % 300.04/300.40 248815[8:Res:158049.1,219712.0] || connected(u,v) -> subclass(cross_product(v,v),symmetrization_of(u))*. % 300.04/300.40 248839[25:SpR:234134.1,248818.0] function(u) || -> subclass(complement(successor(successor(u))),complement(u))*. % 300.04/300.40 248854[19:SpR:225013.1,248818.0] || equal(successor(successor(complement(u))),ordinal_numbers)** -> subclass(universal_class,u). % 300.04/300.40 248956[25:SpR:234134.1,248819.0] function(u) || -> subclass(complement(symmetrization_of(successor(u))),complement(u))*. % 300.04/300.40 248971[19:SpR:225013.1,248819.0] || equal(successor(symmetrization_of(complement(u))),ordinal_numbers)** -> subclass(universal_class,u). % 300.04/300.40 249079[19:SpR:204449.1,248816.0] || equal(union(u,complement(v)),ordinal_numbers)** -> subclass(universal_class,v). % 300.04/300.40 249082[19:Res:248816.0,167311.1] inductive(complement(union(u,complement(v)))) || -> member(ordinal_numbers,v)*. % 300.04/300.40 249245[19:SpR:204449.1,248817.0] || equal(union(complement(u),v),ordinal_numbers)** -> subclass(universal_class,u). % 300.04/300.40 249248[19:Res:248817.0,167311.1] inductive(complement(union(complement(u),v))) || -> member(ordinal_numbers,u)*. % 300.04/300.40 249679[19:SpR:167191.0,248882.0] || -> subclass(complement(successor(complement(complement(symmetrization_of(ordinal_numbers))))),complement(inverse(ordinal_numbers)))*. % 300.04/300.40 249692[25:SpR:234134.1,248882.0] function(u) || -> subclass(complement(successor(complement(successor(u)))),u)*. % 300.04/300.40 249725[19:Res:248882.0,239702.0] || equal(complement(successor(complement(complement(complement(symmetrization_of(ordinal_numbers)))))),universal_class)** -> . % 300.04/300.40 249726[19:Res:248882.0,219089.0] || -> subclass(complement(successor(complement(complement(complement(symmetrization_of(ordinal_numbers)))))),inverse(ordinal_numbers))*. % 300.04/300.40 249731[0:Res:248882.0,219712.0] || -> subclass(complement(successor(complement(complement(complement(complement(complement(u))))))),u)*. % 300.04/300.40 249796[19:SpR:167191.0,248999.0] || -> subclass(complement(symmetrization_of(complement(complement(symmetrization_of(ordinal_numbers))))),complement(inverse(ordinal_numbers)))*. % 300.04/300.40 249809[25:SpR:234134.1,248999.0] function(u) || -> subclass(complement(symmetrization_of(complement(successor(u)))),u)*. % 300.04/300.40 249842[19:Res:248999.0,239702.0] || equal(complement(symmetrization_of(complement(complement(complement(symmetrization_of(ordinal_numbers)))))),universal_class)** -> . % 300.04/300.40 249843[19:Res:248999.0,219089.0] || -> subclass(complement(symmetrization_of(complement(complement(complement(symmetrization_of(ordinal_numbers)))))),inverse(ordinal_numbers))*. % 300.04/300.40 249848[0:Res:248999.0,219712.0] || -> subclass(complement(symmetrization_of(complement(complement(complement(complement(complement(u))))))),u)*. % 300.04/300.40 250058[19:SpR:167191.0,248806.0] || -> member(u,symmetrization_of(ordinal_numbers)) subclass(singleton(u),complement(inverse(ordinal_numbers)))*. % 300.04/300.40 250084[19:Res:248806.0,225690.1] || equal(symmetrization_of(complement(u)),ordinal_numbers) -> subclass(singleton(omega),u)*. % 300.04/300.40 250091[19:Res:248806.0,182393.0] || well_ordering(universal_class,complement(u)) -> subclass(singleton(singleton(ordinal_numbers)),u)*. % 300.04/300.40 250122[19:Res:248806.0,225687.1] || equal(symmetrization_of(complement(u)),ordinal_numbers) -> subclass(singleton(ordinal_numbers),u)*. % 300.04/300.40 250123[19:Res:248806.0,217129.1] || equal(complement(complement(u)),kind_1_ordinals) -> subclass(singleton(ordinal_numbers),u)*. % 300.04/300.40 250126[22:Res:248806.0,177998.1] || equal(complement(complement(u)),omega) -> subclass(singleton(ordinal_numbers),u)*. % 300.04/300.40 250291[19:MRR:250253.1,250253.2,53.0,167008.0] inductive(intersection(u,v)) || -> member(apply(choice,omega),u)*. % 300.04/300.40 250463[19:MRR:250425.1,250425.2,53.0,167008.0] inductive(intersection(u,v)) || -> member(apply(choice,omega),v)*. % 300.04/300.40 251158[19:SoR:248858.0,238779.1] || equal(complement(successor(complement(u))),universal_class)** -> member(ordinal_numbers,u). % 300.04/300.40 251187[19:SoR:248975.0,238779.1] || equal(complement(symmetrization_of(complement(u))),universal_class)** -> member(ordinal_numbers,u). % 300.04/300.40 252930[19:Res:220180.1,167332.0] || subclass(u,complement(u))* -> equal(complement(complement(u)),ordinal_numbers). % 300.04/300.40 253077[18:SpL:124908.0,227961.1] || member(inverse(u),v)* member(v,range_of(u))* -> . % 300.04/300.40 253105[18:Res:144532.1,227961.1] || equal(cantor(u),universal_class) member(u,singleton(v))* -> . % 300.04/300.40 253107[18:Res:2479.1,227961.1] || subclass(universal_class,cantor(u)) member(u,singleton(v))* -> . % 300.04/300.40 253108[19:Res:205414.1,227961.1] || equal(complement(cantor(u)),ordinal_numbers)** member(u,omega) -> . % 300.04/300.40 253115[19:Res:167139.1,227961.1] || member(u,regular(cantor(u)))* -> equal(cantor(u),ordinal_numbers). % 300.04/300.40 253122[19:Res:180693.1,227961.1] || well_ordering(element_relation,range_of(ordinal_numbers))* member(choice,singleton(ordinal_numbers)) -> . % 300.04/300.40 253176[19:Res:239914.1,227961.1] || equal(cantor(u),universal_class) member(u,regular(element_relation))* -> . % 300.04/300.40 253178[19:Res:196731.1,227961.1] || subclass(universal_class,cantor(u)) member(u,regular(element_relation))* -> . % 300.04/300.40 16302[0:Res:16254.0,8.0] || subclass(u,intersection(u,v))* -> equal(intersection(u,v),u). % 300.04/300.40 16429[0:Res:16381.0,8.0] || subclass(u,intersection(v,u))* -> equal(intersection(v,u),u). % 300.04/300.40 36684[0:Res:59.1,36583.0] || member(ordered_pair(u,v),compose(w,x))* -> member(v,universal_class). % 300.04/300.40 6482[0:Res:2481.1,23.0] || subclass(universal_class,intersection(u,v))* -> member(ordered_pair(w,x),v)*. % 300.04/300.40 6481[0:Res:2481.1,22.0] || subclass(universal_class,intersection(u,v))* -> member(ordered_pair(w,x),u)*. % 300.04/300.40 48403[0:MRR:48371.0,12.0] || subclass(universal_class,complement(complement(u))) -> member(unordered_pair(v,w),u)*. % 300.04/300.40 48707[0:Res:7.1,6437.0] || equal(intersection(u,v),universal_class)** -> member(unordered_pair(w,x),u)*. % 300.04/300.40 48763[0:Res:7.1,6438.0] || equal(intersection(u,v),universal_class)** -> member(unordered_pair(w,x),v)*. % 300.04/300.40 84177[8:SpR:84166.1,84165.1] single_valued_class(u) function(v) || -> equal(single_valued1(u),single_valued1(v))*. % 300.04/300.40 84176[8:SpR:84166.1,84166.1] single_valued_class(u) single_valued_class(v) || -> equal(single_valued1(u),single_valued1(v))*. % 300.04/300.40 5474[0:Res:2479.1,897.0] || subclass(universal_class,restrict(u,v,w))* -> member(singleton(x),u)*. % 300.04/300.40 16743[0:SpR:29.0,16276.0] || -> subclass(symmetric_difference(u,cross_product(v,w)),complement(restrict(u,v,w)))*. % 300.04/300.40 16746[0:SpR:30.0,16276.0] || -> subclass(symmetric_difference(cross_product(u,v),w),complement(restrict(w,u,v)))*. % 300.04/300.40 94665[8:SpR:83728.1,83728.1] single_valued_class(u) single_valued_class(v) || -> equal(single_valued2(u),single_valued2(v))*. % 300.04/300.40 94673[8:SpR:83789.1,83789.1] function(u) function(v) || -> equal(single_valued2(u),single_valued2(v))*. % 300.04/300.40 94674[8:SpR:83789.1,83728.1] function(u) single_valued_class(v) || -> equal(single_valued2(u),single_valued2(v))*. % 300.04/300.40 109268[0:Res:7.1,2534.0] || equal(u,universal_class) subclass(u,v)* -> member(omega,v)*. % 300.04/300.40 110890[0:MRR:110841.0,940.0] || subclass(universal_class,complement(complement(u))) -> member(ordered_pair(v,w),u)*. % 300.04/300.40 135144[0:Res:12015.1,2557.0] || equal(complement(complement(cross_product(u,v))),universal_class)** -> member(w,v)*. % 300.04/300.40 135283[0:Res:135236.0,8.0] || subclass(u,complement(complement(u)))* -> equal(complement(complement(u)),u). % 300.04/300.40 135384[0:Res:3.1,11848.0] || subclass(u,v)* well_ordering(universal_class,v)* -> subclass(u,w)*. % 300.04/300.40 135398[0:Res:950.0,11848.0] || subclass(singleton(singleton(singleton(u))),v)* well_ordering(universal_class,v) -> . % 300.04/300.40 135984[0:Res:2525.1,6432.1] || subclass(ordered_pair(u,v),w)* subclass(universal_class,complement(w)) -> . % 300.04/300.40 137274[0:SpL:946.0,137176.0] || equal(u,singleton(singleton(singleton(v))))* well_ordering(universal_class,u)* -> . % 300.04/300.40 140747[0:MRR:140727.0,53.0] || equal(complement(union(u,v)),universal_class)** -> member(omega,complement(v)). % 300.04/300.40 140841[0:MRR:140822.0,53.0] || equal(complement(union(u,v)),universal_class)** -> member(omega,complement(u)). % 300.04/300.40 140889[0:SpR:17187.0,43.0] || -> equal(image(cross_product(u,universal_class),v),image(cross_product(v,universal_class),u))*. % 300.04/300.40 142359[0:Obv:142301.1] || member(u,v) -> subclass(singleton(u),intersection(v,singleton(u)))*. % 300.04/300.40 142368[8:MRR:142318.0,36682.1] || subclass(rest_relation,rest_of(u)) -> subclass(v,intersection(cantor(u),v))*. % 300.04/300.40 146287[8:SpR:144504.0,124899.1] || section(universal_class,u,v) -> subclass(cantor(cross_product(v,u)),u)*. % 300.04/300.40 147464[0:MRR:147442.0,55.1] || member(u,universal_class) subclass(universal_class,complement(singleton(sum_class(u))))* -> . % 300.04/300.40 147595[0:MRR:147573.0,57.1] || member(u,universal_class) subclass(universal_class,complement(singleton(power_class(u))))* -> . % 300.04/300.40 148586[0:SpR:148172.0,27.0] || -> equal(union(u,complement(complement(u))),complement(complement(complement(complement(u)))))**. % 300.04/300.40 151729[0:MRR:151699.0,36682.1] || subclass(u,complement(singleton(not_subclass_element(u,v))))* -> subclass(u,v). % 300.04/300.40 153113[0:SpR:29.0,149179.0] || -> equal(intersection(u,restrict(u,v,w)),restrict(u,v,w))**. % 300.04/300.40 153374[0:SpR:160.0,149318.0] || -> equal(intersection(union(u,v),symmetric_difference(u,v)),symmetric_difference(u,v))**. % 300.04/300.40 159677[8:Res:80374.1,11848.0] inductive(u) || subclass(u,v)* well_ordering(universal_class,v)* -> . % 300.04/300.40 166451[0:SpR:149012.1,150982.0] || subclass(u,singleton(v))* -> subclass(u,w)* member(v,u). % 300.04/300.40 167396[19:Rew:166997.0,99102.1] || equal(intersection(u,v),domain_relation)** -> member(ordered_pair(ordinal_numbers,ordinal_numbers),u)*. % 300.04/300.40 167397[19:Rew:166997.0,84227.1] || subclass(domain_relation,intersection(u,v))* -> member(ordered_pair(ordinal_numbers,ordinal_numbers),u)*. % 300.04/300.40 167398[19:Rew:166997.0,97529.1] || subclass(domain_relation,complement(complement(u))) -> member(ordered_pair(ordinal_numbers,ordinal_numbers),u)*. % 300.04/300.40 167399[19:Rew:166997.0,84221.1] || subclass(domain_relation,complement(u)) member(ordered_pair(ordinal_numbers,ordinal_numbers),u)* -> . % 300.04/300.40 167410[19:Rew:166997.0,99021.1] || equal(intersection(u,v),domain_relation)** -> member(ordered_pair(ordinal_numbers,ordinal_numbers),v)*. % 300.04/300.40 167411[19:Rew:166997.0,84228.1] || subclass(domain_relation,intersection(u,v))* -> member(ordered_pair(ordinal_numbers,ordinal_numbers),v)*. % 300.04/300.40 167459[19:Rew:166997.0,160098.0] || -> subclass(complement(kind_1_ordinals),intersection(complement(singleton(ordinal_numbers)),complement(image(successor_relation,ordinal_numbers))))*. % 300.04/300.40 169250[19:Rew:166997.0,167544.1] || equal(restrict(u,v,w),singleton(ordinal_numbers))** -> member(ordinal_numbers,u). % 300.04/300.40 167545[19:Rew:166997.0,162749.0] || equal(rest_of(ordinal_numbers),singleton(ordinal_numbers)) subclass(universal_class,complement(element_relation))* -> . % 300.04/300.40 169254[19:Rew:166997.0,167651.2] || subclass(complement(u),v)* -> member(ordinal_numbers,u) member(ordinal_numbers,v). % 300.04/300.40 167658[19:Rew:166997.0,98599.1] || subclass(domain_relation,complement(complement(cross_product(u,v))))* -> member(ordinal_numbers,u). % 300.04/300.40 167696[19:Rew:166997.0,159799.2] || subclass(u,v)* well_ordering(universal_class,v)* -> equal(u,ordinal_numbers). % 300.04/300.40 167742[19:Rew:166997.0,166542.2] || subclass(u,singleton(v))* -> member(v,u) equal(ordinal_numbers,u). % 300.04/300.40 167750[19:Rew:166997.0,82462.0] || equal(ordinal_numbers,u) subclass(v,u)* -> equal(v,u). % 300.04/300.40 167809[19:Rew:166997.0,166059.2] || equal(u,universal_class) subclass(u,v)* -> member(ordinal_numbers,v)*. % 300.04/300.40 167814[19:Rew:166997.0,98600.1] || subclass(domain_relation,complement(complement(cross_product(u,v))))* -> member(ordinal_numbers,v). % 300.04/300.40 167815[19:Rew:166997.0,82385.2] || subclass(universal_class,u)* subclass(u,v)* -> member(ordinal_numbers,v)*. % 300.04/300.40 167816[19:Rew:166997.0,80634.2] inductive(singleton(u)) || member(u,v)* -> member(ordinal_numbers,v)*. % 300.04/300.40 167886[19:Rew:166997.0,157969.1] || equal(complement(complement(rest_of(u))),domain_relation)** -> member(ordinal_numbers,cantor(u)). % 300.04/300.40 167887[19:Rew:166997.0,157968.1] || subclass(domain_relation,complement(complement(rest_of(u))))* -> member(ordinal_numbers,cantor(u)). % 300.04/300.40 167963[19:Rew:166997.0,82425.1] || subclass(universal_class,u) -> equal(integer_of(v),ordinal_numbers) member(v,u)*. % 300.04/300.40 167984[19:Rew:166997.0,93805.1] || equal(symmetric_difference(u,v),universal_class) -> member(ordinal_numbers,union(u,v))*. % 300.04/300.40 167985[19:Rew:166997.0,82396.1] || subclass(universal_class,symmetric_difference(u,v)) -> member(ordinal_numbers,union(u,v))*. % 300.04/300.40 167994[19:Rew:166997.0,98845.1] || equal(symmetric_difference(u,inverse(u)),universal_class)** -> member(ordinal_numbers,symmetrization_of(u)). % 300.04/300.40 167995[19:Rew:166997.0,82397.1] || subclass(universal_class,symmetric_difference(u,inverse(u)))* -> member(ordinal_numbers,symmetrization_of(u)). % 300.04/300.40 168195[19:Rew:166997.0,97876.1] || subclass(universal_class,complement(omega)) -> equal(integer_of(ordered_pair(u,v)),ordinal_numbers)**. % 300.04/300.40 168200[19:Rew:166997.0,80709.1] inductive(cantor(restrict(element_relation,universal_class,u))) || -> member(ordinal_numbers,sum_class(u))*. % 300.04/300.40 168202[19:Rew:166997.0,80710.1] inductive(cantor(flip(cross_product(u,universal_class)))) || -> member(ordinal_numbers,inverse(u))*. % 300.04/300.40 168205[19:Rew:166997.0,81040.1] || subclass(universal_class,complement(omega)) -> equal(integer_of(unordered_pair(u,v)),ordinal_numbers)**. % 300.04/300.40 168213[19:Rew:166997.0,84152.1] inductive(symmetric_difference(domain_of(u),universal_class)) || -> member(ordinal_numbers,complement(cantor(u)))*. % 300.04/300.40 168216[19:Rew:166997.0,97497.1] || subclass(domain_relation,complement(omega)) -> equal(integer_of(ordered_pair(ordinal_numbers,ordinal_numbers)),ordinal_numbers)**. % 300.04/300.40 168238[19:Rew:166997.0,164357.1] || equal(complement(union(u,v)),universal_class)** -> member(ordinal_numbers,complement(v)). % 300.04/300.40 168239[19:Rew:166997.0,95611.2] inductive(singleton(u)) || -> member(u,v)* member(ordinal_numbers,complement(v))*. % 300.04/300.40 168243[19:Rew:166997.0,80693.1] || subclass(universal_class,u) -> equal(singleton(v),ordinal_numbers) member(v,u)*. % 300.04/300.40 168253[19:Rew:166997.0,80706.1] || subclass(universal_class,u) -> equal(v,ordinal_numbers) member(regular(v),u)*. % 300.04/300.40 168256[19:Rew:166997.0,80707.1] inductive(symmetric_difference(u,v)) || -> member(ordinal_numbers,complement(intersection(u,v)))*. % 300.04/300.40 168294[19:Rew:166997.0,158075.1] inductive(symmetric_difference(range_of(u),universal_class)) || -> member(ordinal_numbers,complement(range_of(u)))*. % 300.04/300.40 168423[19:Rew:166997.0,159682.1] inductive(intersection(u,v)) || member(ordinal_numbers,symmetric_difference(u,v))* -> . % 300.04/300.40 168741[19:Rew:166997.0,159739.0] || -> equal(integer_of(singleton(omega)),ordinal_numbers) member(singleton(singleton(singleton(omega))),element_relation)*. % 300.04/300.40 168757[19:Rew:166997.0,161569.1] || asymmetric(universal_class,u) -> equal(restrict(inverse(universal_class),u,u),ordinal_numbers)**. % 300.04/300.40 168758[19:Rew:166997.0,161503.0] || equal(restrict(inverse(universal_class),u,u),ordinal_numbers)** -> asymmetric(universal_class,u). % 300.04/300.40 168906[19:Rew:166997.0,164356.1] || equal(complement(union(u,v)),universal_class)** -> member(ordinal_numbers,complement(u)). % 300.04/300.40 170666[19:SpR:167004.0,15058.1] function(recursion(u,successor_relation,ordinal_numbers)) || -> member(ordinal_add(u,v),universal_class)*. % 300.04/300.40 169270[19:Rew:166997.0,168161.1] || subclass(inverse(ordinal_numbers),symmetrization_of(ordinal_numbers))* -> equal(symmetrization_of(ordinal_numbers),inverse(ordinal_numbers)). % 300.04/300.40 169269[19:Rew:166997.0,168149.1] || -> member(not_subclass_element(symmetrization_of(ordinal_numbers),u),inverse(ordinal_numbers))* subclass(symmetrization_of(ordinal_numbers),u). % 300.04/300.40 168140[19:Rew:166997.0,160520.0] || -> subclass(symmetric_difference(complement(u),symmetrization_of(ordinal_numbers)),union(u,complement(inverse(ordinal_numbers))))*. % 300.04/300.40 168139[19:Rew:166997.0,160502.0] || -> subclass(symmetric_difference(symmetrization_of(ordinal_numbers),complement(u)),union(complement(inverse(ordinal_numbers)),u))*. % 300.04/300.40 169266[19:Rew:166997.0,168064.1] || subclass(domain_relation,complement(inverse(ordinal_numbers)))* subclass(domain_relation,symmetrization_of(ordinal_numbers)) -> . % 300.04/300.40 169268[19:Rew:166997.0,168084.0] || subclass(domain_relation,symmetrization_of(ordinal_numbers)) -> member(ordered_pair(ordinal_numbers,ordinal_numbers),inverse(ordinal_numbers))*. % 300.04/300.40 169267[19:Rew:166997.0,168065.1] || equal(complement(inverse(ordinal_numbers)),domain_relation)** equal(symmetrization_of(ordinal_numbers),domain_relation) -> . % 300.04/300.40 169261[19:Rew:166997.0,168056.1] || member(u,complement(inverse(ordinal_numbers)))* member(u,symmetrization_of(ordinal_numbers)) -> . % 300.04/300.40 168093[19:Rew:166997.0,160501.0] || -> equal(intersection(complement(inverse(ordinal_numbers)),complement(symmetrization_of(ordinal_numbers))),complement(symmetrization_of(ordinal_numbers)))**. % 300.04/300.40 169264[19:Rew:166997.0,168062.0] || subclass(universal_class,complement(symmetrization_of(ordinal_numbers))) -> member(omega,complement(inverse(ordinal_numbers)))*. % 300.04/300.40 169260[19:Rew:166997.0,168055.0] || member(u,complement(symmetrization_of(ordinal_numbers)))* -> member(u,complement(inverse(ordinal_numbers))). % 300.04/300.40 167622[19:Rew:166997.0,164139.1] || asymmetric(universal_class,universal_class) -> equal(image(inverse(universal_class),universal_class),range_of(ordinal_numbers))**. % 300.04/300.40 175562[20:MRR:169447.1,175557.0] || well_ordering(u,universal_class) -> member(least(u,symmetrization_of(ordinal_numbers)),inverse(ordinal_numbers))*. % 300.04/300.40 176098[20:Res:175613.1,25.1] || subclass(universal_class,complement(u)) member(regular(symmetrization_of(ordinal_numbers)),u)* -> . % 300.04/300.40 176102[20:Res:175613.1,148647.0] || subclass(universal_class,complement(complement(u))) -> member(regular(symmetrization_of(ordinal_numbers)),u)*. % 300.04/300.40 176109[20:Res:175613.1,22.0] || subclass(universal_class,intersection(u,v))* -> member(regular(symmetrization_of(ordinal_numbers)),u)*. % 300.04/300.40 176110[20:Res:175613.1,23.0] || subclass(universal_class,intersection(u,v))* -> member(regular(symmetrization_of(ordinal_numbers)),v)*. % 300.04/300.40 176734[20:MRR:176715.2,167057.0] || member(u,universal_class)* subclass(rest_relation,rest_of(regular(symmetrization_of(ordinal_numbers))))* -> . % 300.04/300.40 176886[19:MRR:176865.2,167057.0] || member(u,universal_class)* subclass(rest_relation,rest_of(unordered_pair(v,w)))* -> . % 300.04/300.40 176927[19:MRR:176906.2,167057.0] || member(u,universal_class)* subclass(rest_relation,rest_of(ordered_pair(v,w)))* -> . % 300.04/300.40 177037[19:SpR:176364.1,125772.0] || -> equal(singleton(restrict(element_relation,universal_class,u)),ordinal_numbers)** equal(sum_class(u),ordinal_numbers). % 300.04/300.40 177040[19:SpR:176364.1,125707.0] || -> equal(singleton(flip(cross_product(u,universal_class))),ordinal_numbers)** equal(inverse(u),ordinal_numbers). % 300.04/300.40 177106[19:SpR:176365.0,6468.0] || -> equal(cantor(apply(choice,omega)),ordinal_numbers)** equal(apply(choice,omega),ordinal_numbers). % 300.04/300.40 177188[22:Res:177171.1,2.0] || subclass(omega,u)* subclass(u,v)* -> member(ordinal_numbers,v)*. % 300.04/300.40 177194[22:Res:177171.1,4127.0] || subclass(omega,symmetric_difference(u,v)) -> member(ordinal_numbers,union(u,v))*. % 300.04/300.40 177196[22:Res:177171.1,16910.0] || subclass(omega,symmetric_difference(u,inverse(u)))* -> member(ordinal_numbers,symmetrization_of(u)). % 300.04/300.40 178143[18:Res:137890.1,177583.1] || well_ordering(u,universal_class) equal(rest_of(least(u,universal_class)),rest_relation)** -> . % 300.04/300.40 178144[18:Res:137613.1,177583.1] || well_ordering(u,universal_class) equal(rest_of(least(u,rest_relation)),rest_relation)** -> . % 300.04/300.40 178145[18:Res:137620.1,177583.1] || well_ordering(u,rest_relation) equal(rest_of(least(u,rest_relation)),rest_relation)** -> . % 300.04/300.40 178146[21:Res:176162.1,177583.1] || well_ordering(u,omega) equal(rest_of(least(u,omega)),rest_relation)** -> . % 300.04/300.40 178147[21:Res:176155.1,177583.1] || well_ordering(u,universal_class) equal(rest_of(least(u,omega)),rest_relation)** -> . % 300.04/300.40 178272[22:Res:166605.0,177998.1] || equal(complement(inverse(singleton(ordinal_numbers))),omega)** -> asymmetric(singleton(ordinal_numbers),u)*. % 300.04/300.40 178277[22:Res:147404.1,177998.1] || member(ordinal_numbers,element_relation) equal(complement(compose(element_relation,universal_class)),omega)** -> . % 300.04/300.40 178300[22:MRR:178267.0,167011.0] || equal(complement(union(u,v)),omega)** -> member(ordinal_numbers,complement(u)). % 300.04/300.40 178301[22:MRR:178268.0,167011.0] || equal(complement(union(u,v)),omega)** -> member(ordinal_numbers,complement(v)). % 300.04/300.40 178382[22:SpL:56.0,178292.1] inductive(image(element_relation,complement(u))) || equal(power_class(u),omega)** -> . % 300.04/300.40 178904[22:SpL:149012.1,178812.0] || subclass(u,v)* equal(u,omega) -> member(ordinal_numbers,v)*. % 300.04/300.40 178929[22:Res:178902.1,4127.0] || equal(symmetric_difference(u,v),omega) -> member(ordinal_numbers,union(u,v))*. % 300.04/300.40 178931[22:Res:178902.1,16910.0] || equal(symmetric_difference(u,inverse(u)),omega)** -> member(ordinal_numbers,symmetrization_of(u)). % 300.04/300.40 180269[19:Rew:180089.0,168807.0] || -> subclass(symmetric_difference(singleton(ordinal_numbers),complement(u)),union(complement(singleton(ordinal_numbers)),u))*. % 300.04/300.40 180271[19:Rew:180089.0,168822.1] || well_ordering(u,universal_class) -> member(least(u,singleton(ordinal_numbers)),singleton(ordinal_numbers))*. % 300.04/300.40 180851[19:Res:180693.1,5467.1] || well_ordering(element_relation,range_of(ordinal_numbers)) subclass(universal_class,complement(cantor(choice)))* -> . % 300.04/300.40 180883[19:Res:169181.1,169221.1] || equal(u,singleton(ordinal_numbers)) equal(complement(u),singleton(ordinal_numbers))** -> . % 300.04/300.40 181274[19:SpR:168752.1,945.0] || member(u,universal_class) -> member(ordinal_numbers,ordered_pair(sum_class(range_of(u)),v))*. % 300.04/300.40 181717[19:Res:63.1,168068.0] function(complement(inverse(ordinal_numbers))) || well_ordering(universal_class,cross_product(universal_class,universal_class))* -> . % 300.04/300.40 181735[20:Res:175570.1,4178.0] || subclass(inverse(ordinal_numbers),singleton(u))* -> equal(regular(symmetrization_of(ordinal_numbers)),u). % 300.04/300.40 181796[19:Res:176345.1,4178.0] || subclass(domain_relation,singleton(u))* -> equal(singleton(singleton(singleton(ordinal_numbers))),u)*. % 300.04/300.40 181827[19:Res:176345.1,3975.0] || subclass(domain_relation,compose_class(u)) -> equal(compose(u,singleton(ordinal_numbers)),ordinal_numbers)**. % 300.04/300.40 182425[19:Res:147404.1,182393.0] || member(singleton(ordinal_numbers),element_relation) well_ordering(universal_class,compose(element_relation,universal_class))* -> . % 300.04/300.40 182440[19:MRR:182415.0,170.0] || well_ordering(universal_class,union(u,v))* -> member(singleton(ordinal_numbers),complement(u)). % 300.04/300.40 182441[19:MRR:182416.0,170.0] || well_ordering(universal_class,union(u,v))* -> member(singleton(ordinal_numbers),complement(v)). % 300.04/300.40 182472[19:SpR:167191.0,182467.1] || -> member(singleton(ordinal_numbers),complement(inverse(ordinal_numbers)))* member(singleton(ordinal_numbers),symmetrization_of(ordinal_numbers)). % 300.04/300.40 182916[20:Res:181635.1,4178.0] || subclass(symmetrization_of(ordinal_numbers),singleton(u))* -> equal(regular(symmetrization_of(ordinal_numbers)),u). % 300.04/300.40 183036[19:SpL:124908.0,182439.1] || subclass(rest_relation,rest_of(inverse(u)))* well_ordering(universal_class,range_of(u)) -> . % 300.04/300.40 183044[20:SpL:176381.0,182439.1] || subclass(rest_relation,rest_of(regular(symmetrization_of(ordinal_numbers))))* well_ordering(universal_class,ordinal_numbers) -> . % 300.04/300.40 183046[19:SpL:176362.0,182439.1] || subclass(rest_relation,rest_of(unordered_pair(u,v)))* well_ordering(universal_class,ordinal_numbers) -> . % 300.04/300.40 183047[19:SpL:176363.0,182439.1] || subclass(rest_relation,rest_of(ordered_pair(u,v)))* well_ordering(universal_class,ordinal_numbers) -> . % 300.04/300.40 183096[19:Res:182463.1,4178.0] || equal(singleton(u),singleton(singleton(ordinal_numbers)))* -> equal(singleton(ordinal_numbers),u). % 300.04/300.40 183119[19:Res:182463.1,5467.1] || equal(u,singleton(singleton(ordinal_numbers))) subclass(universal_class,complement(u))* -> . % 300.04/300.40 183245[19:Res:180693.1,146190.1] || well_ordering(element_relation,range_of(ordinal_numbers))* equal(complement(cantor(choice)),universal_class) -> . % 300.04/300.40 183247[19:Res:182463.1,146190.1] || equal(u,singleton(singleton(ordinal_numbers)))* equal(complement(u),universal_class)** -> . % 300.04/300.40 183362[8:SpR:124908.0,131984.1] || equal(complement(rest_of(inverse(u))),universal_class)** -> subclass(range_of(u),v)*. % 300.04/300.40 183884[23:SpR:183840.0,2525.1] || subclass(ordered_pair(u,universal_class),v) -> member(unordered_pair(u,ordinal_numbers),v)*. % 300.04/300.40 183903[23:SpL:183840.0,2557.0] || member(singleton(singleton(ordinal_numbers)),cross_product(u,v))* -> member(universal_class,v). % 300.04/300.40 183955[23:SpL:183840.0,277.0] || member(image(u,ordinal_numbers),universal_class) -> member(apply(u,universal_class),universal_class)*. % 300.04/300.40 183992[23:Rew:183893.0,169314.1] || section(u,ordinal_numbers,v) -> equal(segment(u,v,universal_class),ordinal_numbers)**. % 300.04/300.40 184013[23:Rew:183840.0,183902.1] || member(singleton(singleton(ordinal_numbers)),cross_product(u,v))* -> member(ordinal_numbers,u). % 300.04/300.40 184054[23:MRR:184053.0,166995.0] || subclass(segment(u,v,universal_class),ordinal_numbers)* -> section(u,ordinal_numbers,v). % 300.04/300.40 184768[19:Res:52.1,167961.0] inductive(singleton(u)) || -> equal(integer_of(v),ordinal_numbers)** equal(v,u)*. % 300.04/300.40 184873[19:Res:176419.1,146.0] || subclass(domain_relation,flip(rest_relation)) -> equal(rest_of(ordered_pair(u,v)),ordinal_numbers)**. % 300.04/300.40 184951[19:Res:176420.1,146.0] || subclass(domain_relation,rotate(rest_relation)) -> equal(rest_of(ordered_pair(u,ordinal_numbers)),v)*. % 300.04/300.40 184960[19:Res:176420.1,46.0] || subclass(domain_relation,rotate(successor_relation)) -> equal(successor(ordered_pair(u,ordinal_numbers)),v)*. % 300.04/300.40 185159[20:MRR:185113.1,175569.0] || subclass(rest_relation,domain_relation) -> member(ordered_pair(regular(symmetrization_of(ordinal_numbers)),ordinal_numbers),rest_relation)*. % 300.04/300.40 185593[19:MRR:185546.1,12.0] || subclass(rest_relation,domain_relation) -> member(ordered_pair(unordered_pair(u,v),ordinal_numbers),rest_relation)*. % 300.04/300.40 185648[19:MRR:185600.1,940.0] || subclass(rest_relation,domain_relation) -> member(ordered_pair(ordered_pair(u,v),ordinal_numbers),rest_relation)*. % 300.04/300.40 185808[0:Res:170.0,30589.0] || subclass(rest_relation,successor_relation) -> equal(rest_of(singleton(u)),successor(singleton(u)))**. % 300.04/300.40 186321[19:SpR:30.0,167776.1] || -> equal(integer_of(u),ordinal_numbers) subclass(restrict(singleton(u),v,w),omega)*. % 300.04/300.40 186999[20:MRR:186985.2,175557.0] || subclass(inverse(ordinal_numbers),u) subclass(symmetrization_of(ordinal_numbers),complement(u))* -> . % 300.04/300.40 187002[19:MRR:186961.0,167137.1] || subclass(u,complement(unordered_pair(regular(u),v)))* -> equal(u,ordinal_numbers). % 300.04/300.40 187003[19:MRR:186962.0,167137.1] || subclass(u,complement(unordered_pair(v,regular(u))))* -> equal(u,ordinal_numbers). % 300.04/300.40 188092[23:MRR:188089.1,12.0] || equal(u,ordered_pair(v,universal_class)) -> member(unordered_pair(v,ordinal_numbers),u)*. % 300.04/300.40 188633[2:Res:10.1,188593.1] || member(u,universal_class) equal(complement(unordered_pair(u,v)),universal_class)** -> . % 300.04/300.40 188634[2:Res:11.1,188593.1] || member(u,universal_class) equal(complement(unordered_pair(v,u)),universal_class)** -> . % 300.04/300.40 188759[2:Res:2525.1,188593.1] || subclass(ordered_pair(u,v),w)* equal(complement(w),universal_class) -> . % 300.04/300.40 188791[19:Res:168350.1,188593.1] || equal(complement(u),universal_class) -> equal(restrict(u,v,w),ordinal_numbers)**. % 300.04/300.40 189476[19:SoR:135284.0,189460.1] || equal(complement(complement(omega)),universal_class)** -> equal(complement(complement(omega)),omega). % 300.04/300.40 190292[19:MRR:190255.2,167057.0] inductive(symmetric_difference(u,u)) || well_ordering(v,complement(complement(u)))* -> . % 300.04/300.40 190301[19:Obv:190192.1] || member(u,v) -> equal(intersection(singleton(u),complement(v)),ordinal_numbers)**. % 300.04/300.40 190682[19:Obv:190637.1] || member(u,v) -> equal(intersection(complement(v),singleton(u)),ordinal_numbers)**. % 300.04/300.40 190745[19:SpR:27.0,190665.0] || -> equal(intersection(union(u,v),intersection(complement(u),complement(v))),ordinal_numbers)**. % 300.04/300.40 190753[19:SpR:167200.0,190665.0] || -> equal(intersection(power_class(complement(inverse(ordinal_numbers))),image(element_relation,symmetrization_of(ordinal_numbers))),ordinal_numbers)**. % 300.04/300.40 190754[19:SpR:180125.0,190665.0] || -> equal(intersection(power_class(complement(singleton(ordinal_numbers))),image(element_relation,singleton(ordinal_numbers))),ordinal_numbers)**. % 300.04/300.40 190862[19:SpR:167200.0,190801.0] || -> equal(union(power_class(complement(inverse(ordinal_numbers))),image(element_relation,symmetrization_of(ordinal_numbers))),universal_class)**. % 300.04/300.40 190863[19:SpR:180125.0,190801.0] || -> equal(union(power_class(complement(singleton(ordinal_numbers))),image(element_relation,singleton(ordinal_numbers))),universal_class)**. % 300.04/300.40 190896[19:SpR:27.0,190813.0] || -> equal(symmetric_difference(union(u,v),intersection(complement(u),complement(v))),universal_class)**. % 300.04/300.40 190904[19:SpR:167200.0,190813.0] || -> equal(symmetric_difference(power_class(complement(inverse(ordinal_numbers))),image(element_relation,symmetrization_of(ordinal_numbers))),universal_class)**. % 300.04/300.40 190905[19:SpR:180125.0,190813.0] || -> equal(symmetric_difference(power_class(complement(singleton(ordinal_numbers))),image(element_relation,singleton(ordinal_numbers))),universal_class)**. % 300.04/300.40 190979[19:Rew:190955.0,168164.0] || -> equal(intersection(complement(symmetrization_of(ordinal_numbers)),union(inverse(ordinal_numbers),symmetrization_of(ordinal_numbers))),ordinal_numbers)**. % 300.04/300.40 192213[19:Rew:167183.0,192181.0] || -> equal(domain__dfg(complement(cross_product(u,singleton(v))),u,v),single_valued3(ordinal_numbers))**. % 300.04/300.40 192218[19:MRR:192217.1,167219.1] || equal(ordinal_numbers,u) -> section(complement(cross_product(v,u)),u,v)*. % 300.04/300.40 192220[19:MRR:192219.1,166995.0] || subclass(u,v) -> section(complement(cross_product(v,u)),u,v)*. % 300.04/300.40 192237[19:SpR:192178.0,69.0] || -> equal(apply(complement(cross_product(singleton(u),universal_class)),u),sum_class(range_of(ordinal_numbers)))**. % 300.04/300.40 192321[19:Res:2480.1,192214.0] || subclass(universal_class,cantor(complement(cross_product(singleton(unordered_pair(u,v)),universal_class))))* -> . % 300.04/300.40 192325[19:Res:2481.1,192214.0] || subclass(universal_class,cantor(complement(cross_product(singleton(ordered_pair(u,v)),universal_class))))* -> . % 300.04/300.40 192328[19:Res:167127.1,192214.0] || subclass(domain_relation,cantor(complement(cross_product(singleton(ordered_pair(ordinal_numbers,ordinal_numbers)),universal_class))))* -> . % 300.04/300.40 192351[20:Res:175613.1,192214.0] || subclass(universal_class,cantor(complement(cross_product(singleton(regular(symmetrization_of(ordinal_numbers))),universal_class))))* -> . % 300.04/300.40 192448[23:SpR:192241.0,15058.1] function(complement(cross_product(ordinal_numbers,universal_class))) || -> member(sum_class(range_of(ordinal_numbers)),universal_class)*. % 300.04/300.40 192546[25:Res:192513.2,192214.0] function(complement(cross_product(singleton(u),universal_class))) || member(u,universal_class)* -> . % 300.04/300.40 192817[25:SoR:192606.0,12322.2] single_valued_class(singleton(u)) || equal(cross_product(universal_class,universal_class),singleton(u))* -> . % 300.04/300.40 193261[25:SoR:193220.0,167213.2] single_valued_class(regular(symmetrization_of(ordinal_numbers))) || equal(regular(symmetrization_of(ordinal_numbers)),ordinal_numbers)** -> . % 300.04/300.40 193264[25:SoR:193221.0,167213.2] single_valued_class(unordered_pair(u,v)) || equal(unordered_pair(u,v),ordinal_numbers)** -> . % 300.04/300.40 193457[25:SpL:193223.1,192214.0] function(u) || member(u,cantor(complement(cross_product(ordinal_numbers,universal_class))))* -> . % 300.04/300.40 193863[25:SpR:193832.1,43.0] one_to_one(restrict(u,v,universal_class)) || -> equal(image(u,v),universal_class)**. % 300.04/300.40 193950[25:Res:193300.1,169221.1] function(u) || equal(complement(ordered_pair(u,v)),singleton(ordinal_numbers))** -> . % 300.04/300.40 194201[25:SpR:193301.1,188588.1] function(u) || member(ordinal_numbers,u) -> member(ordinal_numbers,successor(u))*. % 300.04/300.40 194202[25:SpR:193301.1,188496.0] function(u) || -> member(ordinal_numbers,successor(u)) member(ordinal_numbers,complement(u))*. % 300.04/300.40 194311[19:MRR:194305.2,167015.0] || well_ordering(u,universal_class) -> equal(integer_of(least(u,complement(omega))),ordinal_numbers)**. % 300.04/300.40 194430[19:MRR:194378.1,167057.0] || member(u,universal_class) -> equal(apply(omega,u),sum_class(range_of(ordinal_numbers)))**. % 300.04/300.40 195308[19:Rew:176363.0,195303.1] || subclass(rest_relation,flip(domain_relation)) -> equal(rest_of(ordered_pair(u,v)),ordinal_numbers)**. % 300.04/300.40 196153[19:SpR:188655.1,137025.0] || equal(complement(complement(u)),universal_class) -> subclass(complement(successor(u)),ordinal_numbers)*. % 300.04/300.40 196155[19:SpR:188655.1,137026.0] || equal(complement(complement(u)),universal_class) -> subclass(complement(symmetrization_of(u)),ordinal_numbers)*. % 300.04/300.40 196254[19:Rew:167055.0,196097.1] || equal(complement(complement(u)),universal_class) -> equal(union(u,v),universal_class)**. % 300.04/300.40 196474[19:Rew:167055.0,196309.1] || equal(complement(complement(u)),universal_class) -> equal(union(v,u),universal_class)**. % 300.04/300.40 196533[25:MRR:196532.2,192574.0] single_valued_class(image(element_relation,complement(u))) || equal(power_class(u),universal_class)** -> . % 300.04/300.40 196724[19:Res:158049.1,196698.0] || connected(u,universal_class) -> member(regular(element_relation),complement(complement(symmetrization_of(u))))*. % 300.04/300.40 196733[19:Res:196718.0,30589.0] || subclass(rest_relation,successor_relation) -> equal(rest_of(regular(element_relation)),successor(regular(element_relation)))**. % 300.04/300.40 196743[25:SoR:196732.0,12322.2] single_valued_class(regular(element_relation)) || equal(cross_product(universal_class,universal_class),regular(element_relation))** -> . % 300.04/300.40 196869[19:Res:196731.1,897.0] || subclass(universal_class,restrict(u,v,w))* -> member(regular(element_relation),u). % 300.04/300.40 197123[19:SpR:196827.0,947.0] || -> member(unordered_pair(first(regular(element_relation)),singleton(second(regular(element_relation)))),regular(element_relation))*. % 300.04/300.40 197139[19:SpR:196827.0,176419.1] || subclass(domain_relation,flip(u)) -> member(ordered_pair(regular(element_relation),ordinal_numbers),u)*. % 300.04/300.40 197161[19:SpL:196827.0,2488.0] || subclass(regular(element_relation),u) -> member(singleton(first(regular(element_relation))),u)*. % 300.04/300.40 197181[19:SpL:196827.0,16125.0] || equal(u,regular(element_relation)) -> member(singleton(first(regular(element_relation))),u)*. % 300.04/300.40 197526[19:Obv:197426.0] || -> equal(intersection(singleton(u),intersection(v,w)),ordinal_numbers)** member(u,v). % 300.04/300.40 197728[19:Obv:197627.0] || -> equal(intersection(singleton(u),intersection(v,w)),ordinal_numbers)** member(u,w). % 300.04/300.40 198253[19:SpR:30.0,197499.0] || -> equal(intersection(complement(cross_product(u,v)),restrict(w,u,v)),ordinal_numbers)**. % 300.04/300.40 198349[19:MRR:198230.2,167057.0] || member(u,intersection(v,w))* member(u,complement(v)) -> . % 300.04/300.40 198535[19:Obv:198430.0] || -> equal(intersection(intersection(u,v),singleton(w)),ordinal_numbers)** member(w,u). % 300.04/300.40 199006[19:MRR:198872.2,167057.0] || member(u,intersection(v,w))* member(u,complement(w)) -> . % 300.04/300.40 199204[19:Obv:199094.0] || -> equal(intersection(intersection(u,v),singleton(w)),ordinal_numbers)** member(w,v). % 300.04/300.40 199249[19:SpR:198500.0,149012.1] || subclass(complement(u),intersection(u,v))* -> equal(complement(u),ordinal_numbers). % 300.04/300.40 199269[19:SpR:160.0,198500.0] || -> equal(intersection(symmetric_difference(u,v),complement(complement(intersection(u,v)))),ordinal_numbers)**. % 300.04/300.40 199416[19:SpR:199166.0,149012.1] || subclass(complement(u),intersection(v,u))* -> equal(complement(u),ordinal_numbers). % 300.04/300.40 199569[25:SpL:192881.1,197186.0] function(first(regular(element_relation))) || member(second(regular(element_relation)),universal_class)* -> . % 300.04/300.40 201875[26:Rew:200916.0,201395.1] || equal(compose(ordinal_numbers,ordinal_numbers),ordinal_numbers) -> subclass(compose(ordinal_numbers,ordinal_numbers),ordinal_numbers)*. % 300.04/300.40 202194[26:MRR:202193.2,160357.0] function(complement(subset_relation)) || subclass(cross_product(universal_class,universal_class),inverse(ordinal_numbers))* -> . % 300.04/300.40 202542[19:SpR:197295.1,160.0] || subclass(union(u,v),ordinal_numbers)* -> equal(symmetric_difference(u,v),ordinal_numbers). % 300.04/300.40 202544[19:SpR:197295.1,4105.0] || subclass(symmetrization_of(u),ordinal_numbers) -> equal(symmetric_difference(u,inverse(u)),ordinal_numbers)**. % 300.04/300.40 202605[19:SpR:197295.1,137025.0] || subclass(complement(singleton(u)),ordinal_numbers) -> subclass(complement(successor(u)),ordinal_numbers)*. % 300.04/300.40 202607[19:SpR:197295.1,137026.0] || subclass(complement(inverse(u)),ordinal_numbers) -> subclass(complement(symmetrization_of(u)),ordinal_numbers)*. % 300.04/300.40 202717[19:Rew:142500.0,202552.1,167055.0,202552.1] || subclass(u,ordinal_numbers) -> equal(symmetric_difference(v,u),union(v,u))**. % 300.04/300.40 202754[19:MRR:202753.2,166995.0] || subclass(u,ordinal_numbers) member(v,u)* -> member(v,w)*. % 300.04/300.40 202872[19:SpR:197859.1,149012.1] || subclass(u,ordinal_numbers)* subclass(v,u)* -> equal(ordinal_numbers,v). % 300.04/300.40 202956[19:Rew:142500.0,202785.1,167055.0,202785.1] || subclass(u,ordinal_numbers) -> equal(symmetric_difference(u,v),union(u,v))**. % 300.04/300.40 204028[19:MRR:188258.1,204022.0] || subclass(domain_relation,rotate(complement(singleton(ordered_pair(ordered_pair(u,ordinal_numbers),v)))))* -> . % 300.04/300.40 204030[19:MRR:188260.1,204022.0] || subclass(domain_relation,flip(complement(singleton(ordered_pair(ordered_pair(u,v),ordinal_numbers)))))* -> . % 300.04/300.40 204043[19:MRR:188272.1,204039.0] || subclass(ordered_pair(u,v),complement(singleton(unordered_pair(u,singleton(v)))))* -> . % 300.04/300.40 204376[19:MRR:169526.1,204370.0] || equal(ordered_pair(u,v),singleton(ordinal_numbers))** -> equal(singleton(u),ordinal_numbers). % 300.04/300.40 204392[23:MRR:204384.2,167008.0] || subclass(universal_class,ordered_pair(u,universal_class))* -> equal(unordered_pair(u,ordinal_numbers),omega). % 300.04/300.40 204400[19:MRR:204399.2,167176.0] || subclass(universal_class,ordered_pair(u,v))* -> equal(ordered_pair(w,x),omega)**. % 300.04/300.40 205824[23:SpL:204449.1,192312.0] || equal(cross_product(ordinal_numbers,universal_class),ordinal_numbers) member(universal_class,cantor(universal_class))* -> . % 300.04/300.40 205950[19:Rew:142500.0,205419.1] || equal(ordinal_numbers,u) -> equal(union(u,v),complement(complement(v)))**. % 300.04/300.40 206953[19:Rew:206400.0,190751.0] || -> equal(intersection(power_class(complement(power_class(u))),image(element_relation,power_class(u))),ordinal_numbers)**. % 300.04/300.40 206954[19:Rew:206400.0,190860.0] || -> equal(union(power_class(complement(power_class(u))),image(element_relation,power_class(u))),universal_class)**. % 300.04/300.40 206955[19:Rew:206400.0,190902.0] || -> equal(symmetric_difference(power_class(complement(power_class(u))),image(element_relation,power_class(u))),universal_class)**. % 300.04/300.40 206981[19:Rew:206400.0,197056.0] || subclass(universal_class,complement(power_class(u)))* subclass(element_relation,power_class(u)) -> . % 300.04/300.40 206996[19:Rew:206400.0,197104.0] || equal(complement(power_class(u)),universal_class)** equal(power_class(u),element_relation) -> . % 300.04/300.40 207272[22:Rew:206400.0,177991.1] || subclass(omega,power_class(u)) member(ordinal_numbers,complement(power_class(u)))* -> . % 300.04/300.40 207298[19:Rew:206400.0,182452.1] || well_ordering(universal_class,power_class(u)) -> member(singleton(ordinal_numbers),complement(power_class(u)))*. % 300.04/300.40 207710[0:SpR:206407.0,16762.0] || -> subclass(symmetric_difference(power_class(u),complement(v)),union(complement(power_class(u)),v))*. % 300.04/300.40 207749[0:SpR:206407.0,16762.0] || -> subclass(symmetric_difference(complement(u),power_class(v)),union(u,complement(power_class(v))))*. % 300.04/300.40 207769[19:SpR:167458.0,206407.0] || -> equal(complement(complement(complement(image(element_relation,kind_1_ordinals)))),complement(image(element_relation,kind_1_ordinals)))**. % 300.04/300.40 207834[19:SpL:206407.0,180886.1] inductive(complement(power_class(u))) || equal(power_class(u),singleton(ordinal_numbers))** -> . % 300.04/300.40 207954[19:Res:205391.1,897.0] || equal(complement(restrict(u,v,w)),ordinal_numbers)** -> member(ordinal_numbers,u). % 300.04/300.40 207970[19:Res:205391.1,169221.1] || equal(complement(u),ordinal_numbers) equal(complement(u),singleton(ordinal_numbers))** -> . % 300.04/300.40 207991[19:MRR:207956.1,204370.0] || equal(complement(ordered_pair(u,v)),ordinal_numbers)** -> equal(singleton(u),ordinal_numbers). % 300.04/300.40 208159[19:Rew:206407.0,208158.0] || -> equal(power_class(complement(complement(image(element_relation,kind_1_ordinals)))),power_class(image(element_relation,kind_1_ordinals)))**. % 300.04/300.40 208485[19:Res:205414.1,897.0] || equal(complement(restrict(u,v,w)),ordinal_numbers)** -> member(omega,u). % 300.04/300.40 208787[19:Res:205520.1,195669.1] || equal(complement(complement(u)),ordinal_numbers)** equal(rotate(u),rest_relation) -> . % 300.04/300.40 208788[19:Res:205520.1,195635.1] || equal(complement(complement(u)),ordinal_numbers)** equal(flip(u),rest_relation) -> . % 300.04/300.40 208789[19:Res:205520.1,185733.1] || equal(complement(complement(u)),ordinal_numbers)** equal(rotate(u),domain_relation) -> . % 300.04/300.40 208790[19:Res:205520.1,185656.1] || equal(complement(complement(u)),ordinal_numbers)** equal(flip(u),domain_relation) -> . % 300.04/300.40 208799[19:Res:205520.1,9734.0] || equal(complement(complement(complement(u))),ordinal_numbers)** -> member(singleton(v),u)*. % 300.04/300.40 208813[22:Res:205520.1,178946.1] || equal(complement(complement(element_relation)),ordinal_numbers)** equal(rest_of(ordinal_numbers),omega) -> . % 300.04/300.40 208816[20:Res:205520.1,176112.0] || equal(complement(singleton(u)),ordinal_numbers)** -> equal(regular(symmetrization_of(ordinal_numbers)),u). % 300.04/300.40 208818[19:Res:205520.1,6440.0] || equal(complement(singleton(u)),ordinal_numbers)** -> equal(unordered_pair(v,w),u)*. % 300.04/300.40 208819[19:Res:205520.1,6484.0] || equal(complement(singleton(u)),ordinal_numbers)** -> equal(ordered_pair(v,w),u)*. % 300.04/300.40 208830[19:Res:205520.1,5473.0] || equal(complement(intersection(u,v)),ordinal_numbers)** -> member(singleton(w),v)*. % 300.04/300.40 208831[19:Res:205520.1,5472.0] || equal(complement(intersection(u,v)),ordinal_numbers)** -> member(singleton(w),u)*. % 300.04/300.40 208843[19:Res:205520.1,6504.0] || equal(complement(compose_class(u)),ordinal_numbers) -> equal(compose(u,v),w)*. % 300.04/300.40 208859[19:Res:205520.1,192318.0] || equal(complement(cantor(complement(cross_product(singleton(singleton(u)),universal_class)))),ordinal_numbers)** -> . % 300.04/300.40 208875[19:Res:205520.1,168007.0] || equal(complement(complement(omega)),ordinal_numbers) -> equal(integer_of(singleton(u)),ordinal_numbers)**. % 300.04/300.40 209990[19:Res:2526.2,205934.1] || subclass(u,v)* equal(ordinal_numbers,v) -> subclass(u,w)*. % 300.04/300.40 209998[19:Res:167131.2,205934.1] || subclass(u,v)* equal(ordinal_numbers,v) -> equal(u,ordinal_numbers). % 300.04/300.40 210040[19:Res:168354.1,205934.1] || equal(union(u,v),ordinal_numbers) -> equal(symmetric_difference(u,v),ordinal_numbers)**. % 300.04/300.40 210427[25:SpR:203243.1,193301.1] function(u) || subclass(u,ordinal_numbers)* -> equal(successor(u),ordinal_numbers). % 300.04/300.40 210497[19:Res:167355.1,203412.0] || equal(sum_class(ordinal_numbers),ordinal_numbers) equal(rotate(sum_class(ordinal_numbers)),rest_relation)** -> . % 300.04/300.40 210520[19:Res:167355.1,203413.0] || equal(sum_class(ordinal_numbers),ordinal_numbers) equal(flip(sum_class(ordinal_numbers)),rest_relation)** -> . % 300.04/300.40 210543[19:Res:167355.1,203414.0] || equal(sum_class(ordinal_numbers),ordinal_numbers) equal(rotate(sum_class(ordinal_numbers)),domain_relation)** -> . % 300.04/300.40 210575[19:Res:167355.1,203415.0] || equal(sum_class(ordinal_numbers),ordinal_numbers) equal(flip(sum_class(ordinal_numbers)),domain_relation)** -> . % 300.04/300.40 210598[19:Res:167355.1,204540.1] || equal(sum_class(ordinal_numbers),ordinal_numbers) equal(sum_class(ordinal_numbers),singleton(ordinal_numbers))** -> . % 300.04/300.40 210988[19:Res:137890.1,205988.1] || well_ordering(u,universal_class) equal(singleton(least(u,universal_class)),ordinal_numbers)** -> . % 300.04/300.40 210989[19:Res:137613.1,205988.1] || well_ordering(u,universal_class) equal(singleton(least(u,rest_relation)),ordinal_numbers)** -> . % 300.04/300.40 210990[19:Res:137620.1,205988.1] || well_ordering(u,rest_relation) equal(singleton(least(u,rest_relation)),ordinal_numbers)** -> . % 300.04/300.40 210991[21:Res:176162.1,205988.1] || well_ordering(u,omega) equal(singleton(least(u,omega)),ordinal_numbers)** -> . % 300.04/300.40 210992[21:Res:176155.1,205988.1] || well_ordering(u,universal_class) equal(singleton(least(u,omega)),ordinal_numbers)** -> . % 300.04/300.40 211609[19:Res:203424.1,25.1] || subclass(complement(complement(u)),ordinal_numbers)* member(singleton(v),u)* -> . % 300.04/300.40 211614[19:Res:203424.1,148647.0] || subclass(complement(complement(complement(u))),ordinal_numbers)* -> member(singleton(v),u)*. % 300.04/300.40 211623[19:Res:203424.1,22.0] || subclass(complement(intersection(u,v)),ordinal_numbers)* -> member(singleton(w),u)*. % 300.04/300.40 211624[19:Res:203424.1,23.0] || subclass(complement(intersection(u,v)),ordinal_numbers)* -> member(singleton(w),v)*. % 300.04/300.40 211640[19:Res:203424.1,192214.0] || subclass(complement(cantor(complement(cross_product(singleton(singleton(u)),universal_class)))),ordinal_numbers)* -> . % 300.04/300.40 211648[19:Res:203424.1,158.0] || subclass(complement(omega),ordinal_numbers)* -> equal(integer_of(singleton(u)),singleton(u))**. % 300.04/300.40 211655[19:Res:203424.1,2997.0] || subclass(complement(cross_product(u,v)),ordinal_numbers)* -> member(singleton(w),u)*. % 300.04/300.40 212120[19:Rew:205950.1,212119.1] || equal(ordinal_numbers,u) -> equal(symmetric_difference(u,v),complement(complement(v)))**. % 300.04/300.40 212127[19:Rew:212120.1,212126.1] || equal(ordinal_numbers,u) -> equal(complement(complement(singleton(u))),successor(u))**. % 300.04/300.40 212129[19:Rew:212120.1,212128.1] || equal(ordinal_numbers,u) -> equal(complement(complement(inverse(u))),symmetrization_of(u))**. % 300.04/300.40 212174[19:SpR:205897.1,4105.0] || equal(symmetrization_of(u),ordinal_numbers) -> equal(symmetric_difference(u,inverse(u)),ordinal_numbers)**. % 300.04/300.40 212238[19:SpR:205897.1,137025.0] || equal(complement(singleton(u)),ordinal_numbers) -> subclass(complement(successor(u)),ordinal_numbers)*. % 300.04/300.40 212240[19:SpR:205897.1,137026.0] || equal(complement(inverse(u)),ordinal_numbers) -> subclass(complement(symmetrization_of(u)),ordinal_numbers)*. % 300.04/300.40 212421[19:Res:205991.1,25.1] || equal(complement(complement(u)),ordinal_numbers) member(singleton(v),u)* -> . % 300.04/300.40 212582[19:Res:209033.1,204540.1] || equal(power_class(u),ordinal_numbers) equal(power_class(u),singleton(ordinal_numbers))** -> . % 300.04/300.40 212583[19:Res:209033.1,203415.0] || equal(power_class(u),ordinal_numbers) equal(flip(power_class(u)),domain_relation)** -> . % 300.04/300.40 212584[19:Res:209033.1,203414.0] || equal(power_class(u),ordinal_numbers) equal(rotate(power_class(u)),domain_relation)** -> . % 300.04/300.40 212585[19:Res:209033.1,203413.0] || equal(power_class(u),ordinal_numbers) equal(flip(power_class(u)),rest_relation)** -> . % 300.04/300.40 212586[19:Res:209033.1,203412.0] || equal(power_class(u),ordinal_numbers) equal(rotate(power_class(u)),rest_relation)** -> . % 300.04/300.40 212665[19:SpR:180103.0,198248.0] || -> equal(intersection(singleton(ordinal_numbers),restrict(complement(singleton(ordinal_numbers)),u,v)),ordinal_numbers)**. % 300.04/300.40 212666[19:SpR:167191.0,198248.0] || -> equal(intersection(symmetrization_of(ordinal_numbers),restrict(complement(inverse(ordinal_numbers)),u,v)),ordinal_numbers)**. % 300.04/300.40 212667[19:SpR:206407.0,198248.0] || -> equal(intersection(power_class(u),restrict(complement(power_class(u)),v,w)),ordinal_numbers)**. % 300.04/300.40 212977[19:Res:205520.1,196865.0] || equal(complement(cantor(complement(cross_product(singleton(regular(element_relation)),universal_class)))),ordinal_numbers)** -> . % 300.04/300.40 213782[19:Res:211476.1,4232.0] || -> member(singleton(ordinal_numbers),cantor(choice)) subclass(sum_class(range_of(ordinal_numbers)),range_of(ordinal_numbers))*. % 300.04/300.40 214511[19:Res:214498.0,11848.0] || subclass(union(singleton(ordinal_numbers),u),v)* well_ordering(universal_class,v) -> . % 300.04/300.40 215182[19:SpL:481.0,214518.0] || subclass(complement(intersection(complement(singleton(ordinal_numbers)),union(u,v))),ordinal_numbers)* -> . % 300.04/300.40 215208[19:Res:214528.1,2.0] || subclass(kind_1_ordinals,u)* subclass(u,v)* -> member(ordinal_numbers,v)*. % 300.04/300.40 215216[19:Res:214528.1,4127.0] || subclass(kind_1_ordinals,symmetric_difference(u,v)) -> member(ordinal_numbers,union(u,v))*. % 300.04/300.40 215218[19:Res:214528.1,16910.0] || subclass(kind_1_ordinals,symmetric_difference(u,inverse(u)))* -> member(ordinal_numbers,symmetrization_of(u)). % 300.04/300.40 215345[19:MRR:215296.2,167005.0] || member(singleton(first(regular(element_relation))),element_relation)* well_ordering(u,v)* -> . % 300.04/300.40 215618[19:Res:215454.0,11848.0] || subclass(union(u,singleton(ordinal_numbers)),v)* well_ordering(universal_class,v) -> . % 300.04/300.40 216557[19:SpL:149012.1,214439.0] || subclass(u,complement(singleton(ordinal_numbers)))* subclass(singleton(ordinal_numbers),u) -> . % 300.04/300.40 216590[19:SpL:149012.1,214488.0] || subclass(u,complement(singleton(ordinal_numbers)))* equal(complement(u),ordinal_numbers) -> . % 300.04/300.40 216624[19:SpL:149012.1,214491.0] || subclass(u,complement(singleton(ordinal_numbers)))* equal(u,singleton(ordinal_numbers)) -> . % 300.04/300.40 217116[19:SpL:206407.0,215196.0] || subclass(kind_1_ordinals,power_class(u)) member(ordinal_numbers,complement(power_class(u)))* -> . % 300.04/300.40 218927[0:SpR:4125.0,218280.0] || -> subclass(intersection(symmetric_difference(complement(u),complement(v)),w),union(u,v))*. % 300.04/300.40 218928[0:SpR:27838.0,218280.0] || -> subclass(intersection(symmetric_difference(complement(u),complement(singleton(u))),v),successor(u))*. % 300.04/300.40 218929[0:SpR:27837.0,218280.0] || -> subclass(intersection(symmetric_difference(complement(u),complement(inverse(u))),v),symmetrization_of(u))*. % 300.04/300.40 219905[0:Obv:219893.1] || subclass(u,symmetric_difference(v,w))* -> subclass(u,union(v,w)). % 300.04/300.40 220157[0:SpR:4125.0,218971.0] || -> subclass(complement(complement(symmetric_difference(complement(u),complement(v)))),union(u,v))*. % 300.04/300.40 220158[0:SpR:27838.0,218971.0] || -> subclass(complement(complement(symmetric_difference(complement(u),complement(singleton(u))))),successor(u))*. % 300.04/300.40 220159[0:SpR:27837.0,218971.0] || -> subclass(complement(complement(symmetric_difference(complement(u),complement(inverse(u))))),symmetrization_of(u))*. % 300.04/300.40 220491[0:SpR:27.0,220426.0] || -> subclass(complement(successor(intersection(complement(u),complement(v)))),union(u,v))*. % 300.04/300.40 220500[19:SpR:167200.0,220426.0] || -> subclass(complement(successor(image(element_relation,symmetrization_of(ordinal_numbers)))),power_class(complement(inverse(ordinal_numbers))))*. % 300.04/300.40 220501[19:SpR:180125.0,220426.0] || -> subclass(complement(successor(image(element_relation,singleton(ordinal_numbers)))),power_class(complement(singleton(ordinal_numbers))))*. % 300.04/300.40 220502[0:SpR:206408.0,220426.0] || -> subclass(complement(successor(image(element_relation,power_class(u)))),power_class(complement(power_class(u))))*. % 300.04/300.40 220504[19:SpR:209197.0,220426.0] || -> subclass(complement(successor(power_class(complement(singleton(ordinal_numbers))))),image(element_relation,singleton(ordinal_numbers)))*. % 300.04/300.40 220505[19:SpR:209198.0,220426.0] || -> subclass(complement(successor(power_class(complement(inverse(ordinal_numbers))))),image(element_relation,symmetrization_of(ordinal_numbers)))*. % 300.04/300.40 220526[0:SpR:27.0,220427.0] || -> subclass(complement(symmetrization_of(intersection(complement(u),complement(v)))),union(u,v))*. % 300.04/300.40 220535[19:SpR:167200.0,220427.0] || -> subclass(complement(symmetrization_of(image(element_relation,symmetrization_of(ordinal_numbers)))),power_class(complement(inverse(ordinal_numbers))))*. % 300.04/300.40 220536[19:SpR:180125.0,220427.0] || -> subclass(complement(symmetrization_of(image(element_relation,singleton(ordinal_numbers)))),power_class(complement(singleton(ordinal_numbers))))*. % 300.04/300.40 220537[0:SpR:206408.0,220427.0] || -> subclass(complement(symmetrization_of(image(element_relation,power_class(u)))),power_class(complement(power_class(u))))*. % 300.04/300.40 220539[19:SpR:209197.0,220427.0] || -> subclass(complement(symmetrization_of(power_class(complement(singleton(ordinal_numbers))))),image(element_relation,singleton(ordinal_numbers)))*. % 300.04/300.40 220540[19:SpR:209198.0,220427.0] || -> subclass(complement(symmetrization_of(power_class(complement(inverse(ordinal_numbers))))),image(element_relation,symmetrization_of(ordinal_numbers)))*. % 300.04/300.40 220588[0:SpR:4125.0,218968.0] || -> subclass(intersection(u,symmetric_difference(complement(v),complement(w))),union(v,w))*. % 300.04/300.40 220589[0:SpR:27838.0,218968.0] || -> subclass(intersection(u,symmetric_difference(complement(v),complement(singleton(v)))),successor(v))*. % 300.04/300.40 220590[0:SpR:27837.0,218968.0] || -> subclass(intersection(u,symmetric_difference(complement(v),complement(inverse(v)))),symmetrization_of(v))*. % 300.04/300.40 221356[27:MRR:221328.1,214509.0] || equal(complement(complement(intersection(singleton(ordinal_numbers),image(successor_relation,ordinal_numbers)))),ordinal_numbers)** -> . % 300.04/300.40 221357[27:MRR:221331.1,214509.0] || equal(complement(intersection(singleton(ordinal_numbers),image(successor_relation,ordinal_numbers))),singleton(ordinal_numbers))** -> . % 300.04/300.40 221526[19:Res:218896.0,167311.1] inductive(intersection(symmetric_difference(universal_class,u),v)) || -> member(ordinal_numbers,complement(u))*. % 300.04/300.40 221714[19:Res:219766.1,194014.1] || equal(complement(complement(u)),ordinal_numbers) subclass(domain_relation,flip(u))* -> . % 300.04/300.40 221715[19:Res:219766.1,194013.1] || equal(complement(complement(u)),ordinal_numbers) subclass(domain_relation,rotate(u))* -> . % 300.04/300.40 221727[19:Res:219766.1,195563.1] || equal(complement(flip(u)),ordinal_numbers)** equal(complement(u),domain_relation) -> . % 300.04/300.40 221728[19:Res:219766.1,188735.0] || equal(complement(flip(u)),ordinal_numbers)** equal(complement(u),universal_class) -> . % 300.04/300.40 221729[19:Res:219766.1,184883.0] || equal(complement(flip(u)),ordinal_numbers) subclass(universal_class,complement(u))* -> . % 300.04/300.40 221732[19:Res:219766.1,184877.0] || equal(complement(flip(cross_product(u,v))),ordinal_numbers)** -> member(ordinal_numbers,v). % 300.04/300.40 221734[19:Res:219766.1,195218.1] || equal(complement(rotate(u)),ordinal_numbers)** equal(complement(u),domain_relation) -> . % 300.04/300.40 221735[19:Res:219766.1,188716.0] || equal(complement(rotate(u)),ordinal_numbers)** equal(complement(u),universal_class) -> . % 300.04/300.40 221736[19:Res:219766.1,184965.0] || equal(complement(rotate(u)),ordinal_numbers) subclass(universal_class,complement(u))* -> . % 300.04/300.40 221784[19:Res:219766.1,120.0] || equal(complement(restrict(u,v,v)),ordinal_numbers)** -> transitive(u,v). % 300.04/300.40 221830[19:Res:219766.1,195414.0] || equal(complement(rotate(u)),ordinal_numbers) subclass(domain_relation,complement(u))* -> . % 300.04/300.40 221855[19:Res:219766.1,158050.0] || equal(complement(complement(complement(symmetrization_of(u)))),ordinal_numbers)** -> connected(u,v)*. % 300.04/300.40 221859[19:Res:219766.1,167257.0] || equal(complement(complement(complement(rest_relation))),ordinal_numbers)** -> equal(rest_of(ordinal_numbers),ordinal_numbers). % 300.04/300.40 221866[19:Res:219766.1,186996.0] || equal(complement(complement(singleton(regular(u)))),ordinal_numbers)** -> equal(u,ordinal_numbers). % 300.04/300.40 222204[19:Res:220557.0,167311.1] inductive(intersection(u,symmetric_difference(universal_class,v))) || -> member(ordinal_numbers,complement(v))*. % 300.04/300.40 222246[19:SpR:204449.1,217976.0] || equal(complement(restrict(u,v,w)),ordinal_numbers)** -> subclass(universal_class,u). % 300.04/300.40 222250[19:Res:217976.0,167311.1] inductive(complement(complement(restrict(u,v,w)))) || -> member(ordinal_numbers,u)*. % 300.04/300.40 222341[19:Res:219698.0,167311.1] inductive(restrict(complement(complement(u)),v,w)) || -> member(ordinal_numbers,u)*. % 300.04/300.40 222428[19:Res:217800.0,167311.1] inductive(intersection(restrict(u,v,w),x)) || -> member(ordinal_numbers,u)*. % 300.04/300.40 222502[0:SpR:29.0,217848.0] || -> subclass(restrict(restrict(u,v,w),x,y),cross_product(v,w))*. % 300.04/300.40 222557[19:Res:217848.0,167311.1] inductive(restrict(intersection(u,v),w,x)) || -> member(ordinal_numbers,v)*. % 300.04/300.40 222670[19:Res:218740.0,167311.1] inductive(intersection(u,restrict(v,w,x))) || -> member(ordinal_numbers,v)*. % 300.04/300.40 222731[0:SpR:160.0,218966.0] || -> subclass(restrict(symmetric_difference(u,v),w,x),complement(intersection(u,v)))*. % 300.04/300.40 222799[19:Res:218966.0,167311.1] inductive(restrict(intersection(u,v),w,x)) || -> member(ordinal_numbers,u)*. % 300.04/300.40 223012[20:Res:222998.0,2.0] || subclass(universal_class,u) -> member(regular(complement(complement(symmetrization_of(ordinal_numbers)))),u)*. % 300.04/300.40 223519[19:SpR:149012.1,219673.0] || subclass(u,complement(symmetrization_of(ordinal_numbers)))* -> subclass(u,complement(inverse(ordinal_numbers))). % 300.04/300.40 223554[19:MRR:223538.0,196720.0] || subclass(composition_function,rest_of(u)) -> member(first(regular(element_relation)),cantor(u))*. % 300.04/300.40 223760[19:Res:166605.0,217129.1] || equal(complement(inverse(singleton(ordinal_numbers))),kind_1_ordinals)** -> asymmetric(singleton(ordinal_numbers),u)*. % 300.04/300.40 223767[19:Res:147404.1,217129.1] || member(ordinal_numbers,element_relation) equal(complement(compose(element_relation,universal_class)),kind_1_ordinals)** -> . % 300.04/300.40 223811[19:MRR:223755.0,167011.0] || equal(complement(union(u,v)),kind_1_ordinals)** -> member(ordinal_numbers,complement(u)). % 300.04/300.40 223812[19:MRR:223756.0,167011.0] || equal(complement(union(u,v)),kind_1_ordinals)** -> member(ordinal_numbers,complement(v)). % 300.04/300.40 224047[19:SpL:204449.1,224005.0] || equal(regular(ordered_pair(ordinal_numbers,u)),ordinal_numbers)** equal(kind_1_ordinals,universal_class) -> . % 300.04/300.40 224399[19:SpR:149012.1,224123.0] || subclass(u,complement(complement(symmetrization_of(ordinal_numbers))))* -> subclass(u,inverse(ordinal_numbers)). % 300.04/300.40 224413[19:Con:224410.0] || member(u,complement(complement(symmetrization_of(ordinal_numbers))))* -> member(u,inverse(ordinal_numbers)). % 300.04/300.40 224472[19:MRR:224456.0,196720.0] || subclass(composition_function,cross_product(u,v))* -> member(first(regular(element_relation)),u)*. % 300.04/300.40 224637[19:SpR:149012.1,224159.0] || subclass(u,symmetrization_of(ordinal_numbers)) -> subclass(complement(complement(u)),inverse(ordinal_numbers))*. % 300.04/300.40 224800[19:SpL:149012.1,224697.0] || subclass(u,symmetrization_of(ordinal_numbers))* equal(complement(complement(u)),universal_class) -> . % 300.04/300.40 225709[19:Res:220544.1,125116.1] || equal(symmetrization_of(rest_of(u)),ordinal_numbers) member(v,cantor(u))* -> . % 300.04/300.40 227789[19:Res:221767.1,25.1] || equal(complement(complement(u)),ordinal_numbers) member(regular(element_relation),u)* -> . % 300.04/300.40 227795[19:Res:221767.1,148647.0] || equal(complement(complement(complement(u))),ordinal_numbers)** -> member(regular(element_relation),u). % 300.04/300.40 227805[19:Res:221767.1,22.0] || equal(complement(intersection(u,v)),ordinal_numbers)** -> member(regular(element_relation),u). % 300.04/300.40 227806[19:Res:221767.1,23.0] || equal(complement(intersection(u,v)),ordinal_numbers)** -> member(regular(element_relation),v). % 300.04/300.40 227861[19:MRR:227860.2,197173.0] || equal(complement(ordered_pair(u,v)),ordinal_numbers)** -> equal(regular(element_relation),omega). % 300.04/300.40 228013[19:Res:223552.1,188593.1] || subclass(composition_function,rest_of(u))* equal(complement(cantor(u)),universal_class) -> . % 300.04/300.40 228014[19:Res:223552.1,217129.1] || subclass(composition_function,rest_of(u))* equal(complement(cantor(u)),kind_1_ordinals) -> . % 300.04/300.40 228017[22:Res:223552.1,177998.1] || subclass(composition_function,rest_of(u))* equal(complement(cantor(u)),omega) -> . % 300.04/300.40 228033[19:MRR:227997.2,167057.0] || well_ordering(u,universal_class) subclass(composition_function,rest_of(least(u,universal_class)))* -> . % 300.04/300.40 228034[19:MRR:227998.2,167057.0] || well_ordering(u,rest_relation) subclass(composition_function,rest_of(least(u,rest_relation)))* -> . % 300.04/300.40 228035[19:MRR:227999.2,167057.0] || well_ordering(u,universal_class) subclass(composition_function,rest_of(least(u,rest_relation)))* -> . % 300.04/300.40 228036[21:MRR:228000.2,167057.0] || well_ordering(u,universal_class) subclass(composition_function,rest_of(least(u,omega)))* -> . % 300.04/300.40 228037[21:MRR:228001.2,167057.0] || well_ordering(u,omega) subclass(composition_function,rest_of(least(u,omega)))* -> . % 300.04/300.40 228491[19:SpR:149012.1,224124.0] || subclass(u,symmetrization_of(ordinal_numbers)) -> subclass(intersection(u,v),inverse(ordinal_numbers))*. % 300.04/300.40 228513[19:SpR:149012.1,224124.0] || subclass(u,intersection(symmetrization_of(ordinal_numbers),v))* -> subclass(u,inverse(ordinal_numbers)). % 300.04/300.40 228540[19:Con:228524.0] || member(u,intersection(symmetrization_of(ordinal_numbers),v))* -> member(u,inverse(ordinal_numbers)). % 300.04/300.40 228598[19:SpR:149012.1,224138.0] || subclass(u,symmetrization_of(ordinal_numbers)) -> subclass(intersection(v,u),inverse(ordinal_numbers))*. % 300.04/300.40 228685[19:SpR:149012.1,224140.0] || subclass(u,intersection(v,symmetrization_of(ordinal_numbers)))* -> subclass(u,inverse(ordinal_numbers)). % 300.04/300.40 228711[19:Con:228697.0] || member(u,intersection(v,symmetrization_of(ordinal_numbers)))* -> member(u,inverse(ordinal_numbers)). % 300.04/300.40 229000[19:SpR:225013.1,217853.0] || equal(successor(complement(intersection(u,v))),ordinal_numbers)** -> subclass(universal_class,v). % 300.04/300.40 229001[19:SpR:225013.1,218971.0] || equal(successor(complement(intersection(u,v))),ordinal_numbers)** -> subclass(universal_class,u). % 300.04/300.40 229085[19:SpR:225013.1,218022.0] || equal(successor(union(u,v)),ordinal_numbers)** -> subclass(universal_class,complement(v)). % 300.04/300.40 229086[19:SpR:225013.1,220194.0] || equal(successor(union(u,v)),ordinal_numbers)** -> subclass(universal_class,complement(u)). % 300.04/300.40 229096[19:SpR:225013.1,218395.0] || equal(successor(successor(u)),ordinal_numbers) -> subclass(universal_class,complement(singleton(u)))*. % 300.04/300.40 229105[19:SpR:225013.1,218396.0] || equal(successor(symmetrization_of(u)),ordinal_numbers) -> subclass(universal_class,complement(inverse(u)))*. % 300.04/300.40 229714[19:Rew:142500.0,228904.1] || equal(successor(u),ordinal_numbers) -> equal(restrict(u,v,w),ordinal_numbers)**. % 300.04/300.40 229806[19:Obv:229333.1] || equal(successor(complement(singleton(u))),ordinal_numbers)** -> equal(singleton(v),u)*. % 300.04/300.40 231590[19:SpL:149012.1,229722.0] || subclass(u,symmetrization_of(ordinal_numbers))* equal(successor(complement(u)),ordinal_numbers) -> . % 300.04/300.40 231791[19:Rew:180103.0,231776.0] || equal(successor(complement(intersection(singleton(ordinal_numbers),union(u,v)))),ordinal_numbers)** -> . % 300.04/300.40 232053[19:Res:166605.0,225687.1] || equal(symmetrization_of(inverse(singleton(ordinal_numbers))),ordinal_numbers)** -> asymmetric(singleton(ordinal_numbers),u)*. % 300.04/300.40 232060[19:Res:147404.1,225687.1] || member(ordinal_numbers,element_relation) equal(symmetrization_of(compose(element_relation,universal_class)),ordinal_numbers)** -> . % 300.04/300.40 232081[19:Res:223552.1,225687.1] || subclass(composition_function,rest_of(u))* equal(symmetrization_of(cantor(u)),ordinal_numbers) -> . % 300.04/300.40 232101[19:MRR:232048.0,167011.0] || equal(symmetrization_of(union(u,v)),ordinal_numbers)** -> member(ordinal_numbers,complement(u)). % 300.04/300.40 232102[19:MRR:232049.0,167011.0] || equal(symmetrization_of(union(u,v)),ordinal_numbers)** -> member(ordinal_numbers,complement(v)). % 300.04/300.40 232103[19:MRR:232055.0,167011.0] || subclass(rest_relation,rest_of(u))* equal(symmetrization_of(cantor(u)),ordinal_numbers) -> . % 300.04/300.40 232178[0:MRR:232156.2,36583.1] || equal(u,v)* member(w,v)* -> member(w,u)*. % 300.04/300.40 232655[0:Obv:232619.1] || subclass(u,v) -> subclass(intersection(u,w),intersection(v,w))*. % 300.04/300.40 232809[19:Res:166605.0,225690.1] || equal(symmetrization_of(inverse(singleton(omega))),ordinal_numbers)** -> asymmetric(singleton(omega),u)*. % 300.04/300.40 232816[19:Res:147404.1,225690.1] || member(omega,element_relation) equal(symmetrization_of(compose(element_relation,universal_class)),ordinal_numbers)** -> . % 300.04/300.40 232836[19:MRR:232804.0,53.0] || equal(symmetrization_of(union(u,v)),ordinal_numbers)** -> member(omega,complement(u)). % 300.04/300.40 232837[19:MRR:232805.0,53.0] || equal(symmetrization_of(union(u,v)),ordinal_numbers)** -> member(omega,complement(v)). % 300.04/300.40 233043[0:Obv:233014.1] || subclass(u,v) -> subclass(intersection(w,u),intersection(v,w))*. % 300.04/300.40 233761[2:Rew:233350.0,219805.1] inductive(symmetric_difference(universal_class,complement(omega))) || -> equal(complement(complement(omega)),omega)**. % 300.04/300.40 233764[19:Rew:233350.0,225728.1] || equal(symmetrization_of(u),ordinal_numbers) -> equal(complement(complement(inverse(u))),ordinal_numbers)**. % 300.04/300.40 233772[19:Rew:233350.0,225061.1] || equal(successor(u),ordinal_numbers) -> equal(complement(complement(singleton(u))),ordinal_numbers)**. % 300.04/300.40 233890[19:Rew:233350.0,224846.1] inductive(symmetric_difference(universal_class,union(u,ordinal_numbers))) || -> member(ordinal_numbers,complement(u))*. % 300.04/300.40 234092[25:Rew:233350.0,194904.1] function(u) || -> equal(symmetric_difference(complement(u),complement(successor(u))),ordinal_numbers)**. % 300.04/300.40 234202[19:Rew:233390.0,205965.1] || equal(ordinal_numbers,u) -> equal(union(v,u),complement(complement(v)))**. % 300.04/300.40 234211[19:Rew:233390.0,188779.1] || member(ordinal_numbers,u) equal(complement(complement(complement(u))),universal_class)** -> . % 300.04/300.40 234216[22:Rew:233390.0,188618.1] || member(ordinal_numbers,u) equal(complement(complement(complement(u))),omega)** -> . % 300.04/300.40 234220[19:Rew:233390.0,223790.1] || member(ordinal_numbers,u) equal(complement(complement(complement(u))),kind_1_ordinals)** -> . % 300.04/300.40 234231[19:Rew:233390.0,168212.1] inductive(symmetric_difference(complement(u),universal_class)) || -> member(ordinal_numbers,complement(complement(u)))*. % 300.04/300.40 234236[25:Rew:233390.0,196531.1] single_valued_class(symmetric_difference(universal_class,u)) || equal(complement(complement(u)),universal_class)** -> . % 300.04/300.40 234239[19:Rew:233390.0,167827.1] inductive(symmetric_difference(universal_class,u)) || equal(complement(complement(u)),universal_class)** -> . % 300.04/300.40 234276[22:Rew:233390.0,178381.1] inductive(symmetric_difference(universal_class,u)) || equal(complement(complement(u)),omega)** -> . % 300.04/300.40 234292[19:Rew:233390.0,212379.1] || equal(singleton(u),ordinal_numbers) -> equal(complement(complement(u)),successor(u))**. % 300.04/300.40 234293[19:Rew:233390.0,212382.1] || equal(inverse(u),ordinal_numbers) -> equal(complement(complement(u)),symmetrization_of(u))**. % 300.04/300.40 234298[19:Rew:233390.0,224058.1] inductive(symmetric_difference(universal_class,u)) || equal(complement(complement(u)),kind_1_ordinals)** -> . % 300.04/300.40 234300[19:Rew:233390.0,232085.1] || member(ordinal_numbers,u) equal(symmetrization_of(complement(complement(u))),ordinal_numbers)** -> . % 300.04/300.40 234537[19:Rew:234202.1,212370.1] || equal(ordinal_numbers,u) -> equal(symmetric_difference(v,u),complement(complement(v)))**. % 300.04/300.40 235643[25:Rew:235542.0,235551.1] function(intersection(u,universal_class)) || -> equal(complement(complement(u)),successor(u))**. % 300.04/300.40 236268[19:SpR:234692.0,167340.1] || -> equal(intersection(u,v),ordinal_numbers) member(regular(intersection(v,u)),v)*. % 300.04/300.40 236269[19:SpR:234692.0,167341.1] || -> equal(intersection(u,v),ordinal_numbers) member(regular(intersection(v,u)),u)*. % 300.04/300.40 237222[0:SpR:236669.0,6303.1] || subclass(universal_class,symmetric_difference(u,v)) -> member(omega,union(v,u))*. % 300.04/300.40 237223[0:SpR:236669.0,6403.1] || equal(symmetric_difference(u,v),universal_class) -> member(omega,union(v,u))*. % 300.04/300.40 237450[19:Rew:237384.0,180268.0] || -> subclass(symmetric_difference(singleton(ordinal_numbers),complement(u)),union(u,complement(singleton(ordinal_numbers))))*. % 300.04/300.40 237803[0:SpL:237384.0,4127.0] || member(u,symmetric_difference(v,w))* -> member(u,union(w,v)). % 300.04/300.40 238056[19:SpR:237974.1,95593.1] || equal(u,universal_class) -> member(v,u)* subclass(singleton(v),ordinal_numbers)*. % 300.04/300.40 238894[19:Rew:167140.0,238069.1,234692.0,238069.1] || equal(intersection(u,v),universal_class)** -> equal(symmetric_difference(u,v),ordinal_numbers). % 300.04/300.40 239058[19:SpR:237603.0,217848.0] || -> subclass(restrict(successor(u),v,w),complement(intersection(u,singleton(u))))*. % 300.04/300.40 239166[19:Rew:234692.0,239082.0] || -> equal(intersection(successor(u),complement(complement(intersection(u,singleton(u))))),ordinal_numbers)**. % 300.04/300.40 239176[19:Rew:167140.0,239101.1,234692.0,239101.1] || equal(intersection(u,singleton(u)),universal_class)** -> equal(successor(u),ordinal_numbers). % 300.04/300.40 239245[19:EmS:2121.0,238779.1] || equal(omega,u)* equal(u,universal_class) -> equal(u,omega). % 300.04/300.40 239274[19:SoR:84011.0,238779.1] || equal(intersection(u,omega),universal_class)** -> equal(intersection(u,omega),omega). % 300.04/300.40 239289[19:SoR:84002.0,238779.1] || equal(intersection(omega,u),universal_class)** -> equal(intersection(omega,u),omega). % 300.04/300.40 239307[19:SoR:167896.0,238779.1] || equal(compose(u,v),universal_class)** -> member(ordinal_numbers,cross_product(universal_class,universal_class))*. % 300.04/300.40 239311[19:SoR:2127.0,238779.1] || equal(image(successor_relation,omega),universal_class)** -> equal(image(successor_relation,omega),omega). % 300.04/300.40 239716[19:Res:238770.1,8.0] || equal(u,universal_class) subclass(u,v)* -> equal(u,v). % 300.04/300.40 239741[19:Res:238770.1,169097.1] || equal(u,universal_class) well_ordering(element_relation,u)* -> equal(u,ordinal_numbers). % 300.04/300.40 240154[19:Con:239854.2] || equal(u,universal_class) member(v,w)* -> member(v,u)*. % 300.04/300.40 240665[19:Rew:16365.1,240636.0] || member(u,successor(u)) -> subclass(intersection(u,singleton(u)),ordinal_numbers)*. % 300.04/300.40 240688[19:SpR:149012.1,237678.0] || subclass(singleton(u),u) -> subclass(successor(u),complement(singleton(u)))*. % 300.04/300.40 240697[19:Res:237678.0,167311.1] inductive(successor(u)) || -> member(ordinal_numbers,complement(intersection(u,singleton(u))))*. % 300.04/300.40 240768[19:SpR:237974.1,236254.0] || equal(intersection(u,v),universal_class) -> subclass(symmetric_difference(v,u),ordinal_numbers)*. % 300.04/300.40 240774[0:SpR:206403.0,236254.0] || -> subclass(symmetric_difference(power_class(u),complement(v)),union(v,complement(power_class(u))))*. % 300.04/300.40 240777[0:SpR:206410.0,236254.0] || -> subclass(symmetric_difference(complement(u),power_class(v)),union(complement(power_class(v)),u))*. % 300.04/300.40 240796[19:Res:236254.0,167311.1] inductive(symmetric_difference(u,v)) || -> member(ordinal_numbers,complement(intersection(v,u)))*. % 300.04/300.40 241012[19:Res:240703.0,188593.1] || equal(complement(complement(intersection(singleton(ordinal_numbers),singleton(singleton(ordinal_numbers))))),universal_class)** -> . % 300.04/300.40 241013[19:Res:240703.0,225687.1] || equal(symmetrization_of(complement(intersection(singleton(ordinal_numbers),singleton(singleton(ordinal_numbers))))),ordinal_numbers)** -> . % 300.04/300.40 241014[19:Res:240703.0,217129.1] || equal(complement(complement(intersection(singleton(ordinal_numbers),singleton(singleton(ordinal_numbers))))),kind_1_ordinals)** -> . % 300.04/300.40 241017[22:Res:240703.0,177998.1] || equal(complement(complement(intersection(singleton(ordinal_numbers),singleton(singleton(ordinal_numbers))))),omega)** -> . % 300.04/300.40 242050[19:SpL:149012.1,239294.0] || subclass(u,complement(complement(symmetrization_of(ordinal_numbers))))* equal(u,universal_class) -> . % 300.04/300.40 243561[19:SpL:149012.1,239286.0] || subclass(u,symmetrization_of(ordinal_numbers))* equal(intersection(v,u),universal_class)** -> . % 300.04/300.40 243631[19:SpL:149012.1,239300.0] || subclass(u,intersection(v,symmetrization_of(ordinal_numbers)))* equal(u,universal_class) -> . % 300.04/300.40 243660[19:SpL:149012.1,239302.0] || subclass(u,symmetrization_of(ordinal_numbers))* equal(intersection(u,v),universal_class)** -> . % 300.04/300.40 243681[19:SpL:149012.1,239302.0] || subclass(u,intersection(symmetrization_of(ordinal_numbers),v))* equal(u,universal_class) -> . % 300.04/300.40 245421[19:Rew:167055.0,245399.1] || equal(symmetric_difference(u,inverse(u)),universal_class)** -> subclass(universal_class,symmetrization_of(u)). % 300.04/300.40 245587[19:SpL:206407.0,221567.0] || equal(complement(power_class(u)),ordinal_numbers) -> subclass(complement(power_class(u)),v)*. % 300.04/300.40 245922[19:Res:10.1,229738.1] || member(u,universal_class) equal(successor(unordered_pair(u,v)),ordinal_numbers)** -> . % 300.04/300.40 245923[19:Res:11.1,229738.1] || member(u,universal_class) equal(successor(unordered_pair(v,u)),ordinal_numbers)** -> . % 300.04/300.40 245960[19:Res:180693.1,229738.1] || well_ordering(element_relation,range_of(ordinal_numbers))* equal(successor(cantor(choice)),ordinal_numbers) -> . % 300.04/300.40 245961[19:Res:182463.1,229738.1] || equal(u,singleton(singleton(ordinal_numbers)))* equal(successor(u),ordinal_numbers)** -> . % 300.04/300.40 246059[19:Res:2525.1,229738.1] || subclass(ordered_pair(u,v),w)* equal(successor(w),ordinal_numbers) -> . % 300.04/300.40 246076[19:Res:234130.1,229738.1] || member(ordinal_numbers,u) equal(successor(complement(complement(u))),ordinal_numbers)** -> . % 300.04/300.40 246077[19:Res:240703.0,229738.1] || equal(successor(complement(intersection(singleton(ordinal_numbers),singleton(singleton(ordinal_numbers))))),ordinal_numbers)** -> . % 300.04/300.40 246087[19:Res:223552.1,229738.1] || subclass(composition_function,rest_of(u))* equal(successor(cantor(u)),ordinal_numbers) -> . % 300.04/300.40 246330[25:SpR:234134.1,218920.0] function(u) || -> subclass(intersection(complement(successor(u)),v),complement(u))*. % 300.04/300.40 246331[25:SpR:234134.1,219703.0] function(u) || -> subclass(complement(complement(complement(successor(u)))),complement(u))*. % 300.04/300.40 246359[25:SpR:234134.1,220194.0] function(u) || -> subclass(complement(union(complement(u),v)),successor(u))*. % 300.04/300.40 246376[25:SpR:234134.1,219700.0] function(u) || -> subclass(intersection(v,complement(successor(u))),complement(u))*. % 300.04/300.40 246378[25:SpR:234134.1,218022.0] function(u) || -> subclass(complement(union(v,complement(u))),successor(u))*. % 300.04/300.40 246399[25:SpR:234134.1,222901.0] function(symmetrization_of(ordinal_numbers)) || -> member(regular(successor(symmetrization_of(ordinal_numbers))),inverse(ordinal_numbers))*. % 300.04/300.40 246401[25:SpR:234134.1,223022.0] function(symmetrization_of(ordinal_numbers)) || -> equal(cantor(regular(successor(symmetrization_of(ordinal_numbers)))),ordinal_numbers)**. % 300.04/300.40 246406[25:SpR:234134.1,219703.0] function(complement(complement(u))) || -> subclass(successor(complement(complement(u))),u)*. % 300.04/300.40 246410[25:SpR:234134.1,217853.0] function(intersection(u,v)) || -> subclass(successor(intersection(u,v)),v)*. % 300.04/300.40 246411[25:SpR:234134.1,218971.0] function(intersection(u,v)) || -> subclass(successor(intersection(u,v)),u)*. % 300.04/300.40 246539[25:SpL:234134.1,167093.0] function(u) || subclass(universal_class,successor(u))* -> member(ordinal_numbers,u). % 300.04/300.40 246540[25:SpL:234134.1,148626.0] function(u) || subclass(universal_class,successor(u))* -> member(omega,u). % 300.04/300.40 246544[25:SpL:234134.1,167094.0] function(u) || equal(successor(u),universal_class) -> member(ordinal_numbers,u)*. % 300.04/300.40 246545[25:SpL:234134.1,6422.0] function(u) || equal(successor(u),universal_class) -> member(omega,u)*. % 300.04/300.40 246546[25:SpL:234134.1,177183.0] function(u) || subclass(omega,successor(u))* -> member(ordinal_numbers,u). % 300.04/300.40 246547[25:SpL:234134.1,178014.0] function(u) || equal(successor(u),omega) -> member(ordinal_numbers,u)*. % 300.04/300.40 246551[25:SpL:234134.1,215201.0] function(u) || subclass(kind_1_ordinals,successor(u))* -> member(ordinal_numbers,u). % 300.04/300.40 246552[25:SpL:234134.1,217156.0] function(u) || equal(successor(u),kind_1_ordinals) -> member(ordinal_numbers,u)*. % 300.04/300.40 246567[25:SpL:234134.1,148647.0] function(u) || member(v,successor(u))* -> member(v,u). % 300.04/300.40 246576[25:SpL:234134.1,223389.0] function(symmetrization_of(ordinal_numbers)) || equal(complement(successor(symmetrization_of(ordinal_numbers))),universal_class)** -> . % 300.04/300.40 246578[25:SpL:234134.1,224347.0] function(symmetrization_of(ordinal_numbers)) || equal(complement(successor(symmetrization_of(ordinal_numbers))),ordinal_numbers)** -> . % 300.04/300.40 246592[25:SpL:234134.1,242441.0] function(symmetrization_of(ordinal_numbers)) || equal(successor(symmetrization_of(ordinal_numbers)),singleton(ordinal_numbers))** -> . % 300.04/300.40 246635[25:Rew:167049.0,246422.2] function(u) || equal(ordinal_numbers,u) -> equal(successor(u),ordinal_numbers)**. % 300.04/300.40 247125[23:Res:167339.2,247104.0] || subclass(omega,rest_of(u))* -> equal(integer_of(singleton(singleton(ordinal_numbers))),ordinal_numbers)**. % 300.04/300.40 247313[19:SpL:234713.0,238772.0] || equal(symmetric_difference(u,v),universal_class) -> subclass(universal_class,union(u,v))*. % 300.04/300.40 247330[19:SpL:149012.1,238772.0] || subclass(u,v)* equal(u,universal_class) -> subclass(universal_class,v)*. % 300.04/300.40 248156[19:SpL:234713.0,245337.0] || equal(symmetric_difference(u,v),kind_1_ordinals) -> member(ordinal_numbers,union(u,v))*. % 300.04/300.40 248158[19:SpL:234711.0,245337.0] || equal(symmetric_difference(u,inverse(u)),kind_1_ordinals)** -> member(ordinal_numbers,symmetrization_of(u)). % 300.04/300.40 248173[19:SpL:149012.1,245337.0] || subclass(u,v)* equal(u,kind_1_ordinals) -> member(ordinal_numbers,v)*. % 300.04/300.40 248592[0:SpR:149012.1,217784.0] || subclass(u,symmetric_difference(v,inverse(v)))* -> subclass(u,symmetrization_of(v)). % 300.04/300.40 248771[25:SpL:234134.1,219712.0] function(u) || subclass(v,successor(u))* -> subclass(v,u). % 300.04/300.40 248832[0:SpR:27.0,248818.0] || -> subclass(complement(successor(union(u,v))),intersection(complement(u),complement(v)))*. % 300.04/300.40 248846[0:SpR:206408.0,248818.0] || -> subclass(complement(successor(power_class(complement(power_class(u))))),image(element_relation,power_class(u)))*. % 300.04/300.40 248949[0:SpR:27.0,248819.0] || -> subclass(complement(symmetrization_of(union(u,v))),intersection(complement(u),complement(v)))*. % 300.04/300.40 248963[0:SpR:206408.0,248819.0] || -> subclass(complement(symmetrization_of(power_class(complement(power_class(u))))),image(element_relation,power_class(u)))*. % 300.04/300.40 249053[25:SpR:234134.1,248816.0] function(u) || -> subclass(complement(union(v,successor(u))),complement(u))*. % 300.04/300.40 249078[19:SpR:225013.1,248816.0] || equal(successor(union(u,complement(v))),ordinal_numbers)** -> subclass(universal_class,v). % 300.04/300.40 249218[25:SpR:234134.1,248817.0] function(u) || -> subclass(complement(union(successor(u),v)),complement(u))*. % 300.04/300.40 249244[19:SpR:225013.1,248817.0] || equal(successor(union(complement(u),v)),ordinal_numbers)** -> subclass(universal_class,u). % 300.04/300.40 249699[25:SpR:234134.1,248882.0] function(complement(u)) || -> subclass(complement(successor(successor(complement(u)))),u)*. % 300.04/300.40 249707[19:Res:248882.0,167311.1] inductive(complement(successor(complement(complement(complement(u)))))) || -> member(ordinal_numbers,u)*. % 300.04/300.40 249816[25:SpR:234134.1,248999.0] function(complement(u)) || -> subclass(complement(symmetrization_of(successor(complement(u)))),u)*. % 300.04/300.40 249821[19:SpR:204449.1,248999.0] || equal(symmetrization_of(complement(complement(complement(u)))),ordinal_numbers)** -> subclass(universal_class,u). % 300.04/300.40 249824[19:Res:248999.0,167311.1] inductive(complement(symmetrization_of(complement(complement(complement(u)))))) || -> member(ordinal_numbers,u)*. % 300.04/300.40 250083[0:Res:248806.0,5467.1] || subclass(universal_class,complement(complement(u))) -> subclass(singleton(singleton(v)),u)*. % 300.04/300.40 250094[0:Res:248806.0,4.0] || -> subclass(singleton(not_subclass_element(u,complement(v))),v)* subclass(u,complement(v)). % 300.04/300.40 250130[19:Res:248806.0,206416.0] || -> subclass(singleton(regular(power_class(u))),power_class(u))* equal(power_class(u),ordinal_numbers). % 300.04/300.40 250141[19:Res:250113.0,167311.1] inductive(singleton(not_subclass_element(element_relation,ordinal_numbers))) || -> member(ordinal_numbers,compose(element_relation,universal_class))*. % 300.04/300.40 250196[20:Rew:234692.0,250189.0] || equal(complement(intersection(complement(symmetrization_of(ordinal_numbers)),union(u,v))),ordinal_numbers)** -> . % 300.04/300.40 250871[19:SpR:167191.0,248811.0] || -> subclass(complement(complement(complement(complement(complement(symmetrization_of(ordinal_numbers)))))),complement(inverse(ordinal_numbers)))*. % 300.04/300.40 250884[25:SpR:234134.1,248811.0] function(u) || -> subclass(complement(complement(complement(complement(successor(u))))),u)*. % 300.04/300.40 250927[19:Res:248811.0,239702.0] || equal(complement(complement(complement(complement(complement(complement(symmetrization_of(ordinal_numbers))))))),universal_class)** -> . % 300.04/300.40 250928[19:Res:248811.0,219089.0] || -> subclass(complement(complement(complement(complement(complement(complement(symmetrization_of(ordinal_numbers))))))),inverse(ordinal_numbers))*. % 300.04/300.40 250933[0:Res:248811.0,219712.0] || -> subclass(complement(complement(complement(complement(complement(complement(complement(complement(u)))))))),u)*. % 300.04/300.40 250974[19:Rew:167055.0,250896.1] || equal(complement(complement(complement(complement(u)))),universal_class)** -> subclass(universal_class,u). % 300.04/300.40 251453[25:SpL:234134.1,248778.0] function(u) || equal(successor(u),universal_class) -> subclass(v,u)*. % 300.04/300.40 251477[19:SpR:167191.0,248783.0] || -> subclass(intersection(complement(complement(complement(symmetrization_of(ordinal_numbers)))),u),complement(inverse(ordinal_numbers)))*. % 300.04/300.40 251490[25:SpR:234134.1,248783.0] function(u) || -> subclass(intersection(complement(complement(successor(u))),v),u)*. % 300.04/300.40 251522[0:SpR:149012.1,248783.0] || subclass(u,complement(complement(complement(complement(v)))))* -> subclass(u,v). % 300.04/300.40 251547[19:Res:248783.0,239702.0] || equal(intersection(complement(complement(complement(complement(symmetrization_of(ordinal_numbers))))),u),universal_class)** -> . % 300.04/300.40 251548[19:Res:248783.0,219089.0] || -> subclass(intersection(complement(complement(complement(complement(symmetrization_of(ordinal_numbers))))),u),inverse(ordinal_numbers))*. % 300.04/300.40 251553[0:Res:248783.0,219712.0] || -> subclass(intersection(complement(complement(complement(complement(complement(complement(u)))))),v),u)*. % 300.04/300.40 251591[19:Rew:142500.0,251499.1] || equal(successor(complement(complement(complement(u)))),ordinal_numbers)** -> subclass(v,u)*. % 300.04/300.40 251598[0:Con:251551.0] || member(u,complement(complement(complement(complement(v)))))* -> member(u,v). % 300.04/300.40 251807[19:SpR:167191.0,248798.0] || -> subclass(intersection(u,complement(complement(complement(symmetrization_of(ordinal_numbers))))),complement(inverse(ordinal_numbers)))*. % 300.04/300.40 251820[25:SpR:234134.1,248798.0] function(u) || -> subclass(intersection(v,complement(complement(successor(u)))),u)*. % 300.04/300.40 251871[19:Res:248798.0,239702.0] || equal(intersection(u,complement(complement(complement(complement(symmetrization_of(ordinal_numbers)))))),universal_class)** -> . % 300.04/300.40 251872[19:Res:248798.0,219089.0] || -> subclass(intersection(u,complement(complement(complement(complement(symmetrization_of(ordinal_numbers)))))),inverse(ordinal_numbers))*. % 300.04/300.40 251877[0:Res:248798.0,219712.0] || -> subclass(intersection(u,complement(complement(complement(complement(complement(complement(v))))))),v)*. % 300.04/300.40 251940[19:SpR:167191.0,248810.0] || -> subclass(complement(complement(intersection(u,complement(symmetrization_of(ordinal_numbers))))),complement(inverse(ordinal_numbers)))*. % 300.04/300.40 251953[25:SpR:234134.1,248810.0] function(u) || -> subclass(complement(complement(intersection(v,successor(u)))),u)*. % 300.04/300.40 252007[19:Res:248810.0,239702.0] || equal(complement(complement(intersection(u,complement(complement(symmetrization_of(ordinal_numbers)))))),universal_class)** -> . % 300.04/300.40 252008[19:Res:248810.0,219089.0] || -> subclass(complement(complement(intersection(u,complement(complement(symmetrization_of(ordinal_numbers)))))),inverse(ordinal_numbers))*. % 300.04/300.40 252013[0:Res:248810.0,219712.0] || -> subclass(complement(complement(intersection(u,complement(complement(complement(complement(v))))))),v)*. % 300.04/300.40 252066[19:Rew:167055.0,251973.1] || equal(intersection(u,complement(complement(v))),universal_class)** -> subclass(universal_class,v). % 300.04/300.40 252249[19:SpR:167191.0,248812.0] || -> subclass(complement(complement(intersection(complement(symmetrization_of(ordinal_numbers)),u))),complement(inverse(ordinal_numbers)))*. % 300.04/300.40 252262[25:SpR:234134.1,248812.0] function(u) || -> subclass(complement(complement(intersection(successor(u),v))),u)*. % 300.04/300.40 252286[0:SpR:149012.1,248812.0] || subclass(u,complement(complement(v))) -> subclass(complement(complement(u)),v)*. % 300.04/300.40 252322[19:Res:248812.0,239702.0] || equal(complement(complement(intersection(complement(complement(symmetrization_of(ordinal_numbers))),u))),universal_class)** -> . % 300.04/300.40 252323[19:Res:248812.0,219089.0] || -> subclass(complement(complement(intersection(complement(complement(symmetrization_of(ordinal_numbers))),u))),inverse(ordinal_numbers))*. % 300.04/300.40 252328[0:Res:248812.0,219712.0] || -> subclass(complement(complement(intersection(complement(complement(complement(complement(u)))),v))),u)*. % 300.04/300.40 252385[19:Rew:167055.0,252288.1] || equal(intersection(complement(complement(u)),v),universal_class)** -> subclass(universal_class,u). % 300.04/300.40 252411[19:SpR:167191.0,249106.0] || -> subclass(complement(union(u,complement(complement(symmetrization_of(ordinal_numbers))))),complement(inverse(ordinal_numbers)))*. % 300.04/300.40 252424[25:SpR:234134.1,249106.0] function(u) || -> subclass(complement(union(v,complement(successor(u)))),u)*. % 300.04/300.40 252467[19:Res:249106.0,239702.0] || equal(complement(union(u,complement(complement(complement(symmetrization_of(ordinal_numbers)))))),universal_class)** -> . % 300.04/300.40 252468[19:Res:249106.0,219089.0] || -> subclass(complement(union(u,complement(complement(complement(symmetrization_of(ordinal_numbers)))))),inverse(ordinal_numbers))*. % 300.04/300.40 252473[0:Res:249106.0,219712.0] || -> subclass(complement(union(u,complement(complement(complement(complement(complement(v))))))),v)*. % 300.04/300.40 252657[19:SpR:167191.0,249272.0] || -> subclass(complement(union(complement(complement(symmetrization_of(ordinal_numbers))),u)),complement(inverse(ordinal_numbers)))*. % 300.04/300.40 252670[25:SpR:234134.1,249272.0] function(u) || -> subclass(complement(union(complement(successor(u)),v)),u)*. % 300.04/300.40 252715[19:Res:249272.0,239702.0] || equal(complement(union(complement(complement(complement(symmetrization_of(ordinal_numbers)))),u)),universal_class)** -> . % 300.04/300.40 252716[19:Res:249272.0,219089.0] || -> subclass(complement(union(complement(complement(complement(symmetrization_of(ordinal_numbers)))),u)),inverse(ordinal_numbers))*. % 300.04/300.40 252721[0:Res:249272.0,219712.0] || -> subclass(complement(union(complement(complement(complement(complement(complement(u))))),v)),u)*. % 300.04/300.40 252879[19:SpR:167191.0,220180.1] || subclass(complement(inverse(ordinal_numbers)),u) -> subclass(complement(symmetrization_of(ordinal_numbers)),u)*. % 300.04/300.40 252892[25:SpR:234134.1,220180.1] function(u) || subclass(u,v) -> subclass(successor(u),v)*. % 300.04/300.40 253037[19:Res:252894.1,219712.0] || subclass(inverse(ordinal_numbers),complement(complement(u)))* -> subclass(symmetrization_of(ordinal_numbers),u). % 300.04/300.40 253076[25:SpL:192881.1,227961.1] function(u) || member(u,v)* member(v,universal_class)* -> . % 300.04/300.40 253103[19:Res:205991.1,227961.1] || equal(complement(cantor(u)),ordinal_numbers) member(u,singleton(v))* -> . % 300.04/300.40 253104[19:Res:203424.1,227961.1] || subclass(complement(cantor(u)),ordinal_numbers)* member(u,singleton(v))* -> . % 300.04/300.40 253111[18:Res:3.1,227961.1] || member(u,not_subclass_element(cantor(u),v))* -> subclass(cantor(u),v). % 300.04/300.40 253114[18:Res:2480.1,227961.1] || subclass(universal_class,cantor(u)) member(u,unordered_pair(v,w))* -> . % 300.04/300.40 253127[18:Res:2481.1,227961.1] || subclass(universal_class,cantor(u)) member(u,ordered_pair(v,w))* -> . % 300.04/300.40 253131[19:Res:167127.1,227961.1] || subclass(domain_relation,cantor(u)) member(u,ordered_pair(ordinal_numbers,ordinal_numbers))* -> . % 300.04/300.40 253174[20:Res:175613.1,227961.1] || subclass(universal_class,cantor(u)) member(u,regular(symmetrization_of(ordinal_numbers)))* -> . % 300.04/300.40 253177[19:Res:221767.1,227961.1] || equal(complement(cantor(u)),ordinal_numbers) member(u,regular(element_relation))* -> . % 300.04/300.40 5470[0:Res:2479.1,2.0] || subclass(universal_class,u)* subclass(u,v)* -> member(singleton(w),v)*. % 300.04/300.40 12804[0:Res:2479.1,4127.0] || subclass(universal_class,symmetric_difference(u,v)) -> member(singleton(w),union(u,v))*. % 300.04/300.40 16056[0:SpL:160.0,15276.0] || equal(symmetric_difference(u,v),universal_class) -> member(singleton(w),union(u,v))*. % 300.04/300.40 6385[0:SpL:160.0,6300.0] || equal(symmetric_difference(u,v),universal_class) -> member(omega,complement(intersection(u,v)))*. % 300.04/300.40 6293[0:SpL:160.0,2539.0] || subclass(universal_class,symmetric_difference(u,v)) -> member(omega,complement(intersection(u,v)))*. % 300.04/300.40 84010[0:Res:16133.1,1073.1] inductive(singleton(u)) || member(u,omega)* -> equal(singleton(u),omega). % 300.04/300.40 15062[0:Res:15058.1,2.0] function(u) || subclass(universal_class,v) -> member(apply(u,w),v)*. % 300.04/300.40 9608[0:Res:2481.1,37.0] || subclass(universal_class,flip(u)) -> member(ordered_pair(ordered_pair(v,w),x),u)*. % 300.04/300.40 9653[0:Res:2481.1,34.0] || subclass(universal_class,rotate(u)) -> member(ordered_pair(ordered_pair(v,w),x),u)*. % 300.04/300.40 6483[0:Res:2481.1,897.0] || subclass(universal_class,restrict(u,v,w))* -> member(ordered_pair(x,y),u)*. % 300.04/300.40 2489[0:Res:950.0,2.0] || subclass(singleton(singleton(singleton(u))),v)* -> member(singleton(singleton(u)),v). % 300.04/300.40 16141[0:SpL:946.0,16125.0] || equal(u,singleton(singleton(singleton(v)))) -> member(singleton(singleton(v)),u)*. % 300.04/300.40 37732[0:Res:36682.1,2.0] || subclass(universal_class,u) -> subclass(v,w) member(not_subclass_element(v,w),u)*. % 300.04/300.41 12033[0:Res:12015.1,25.1] || equal(complement(complement(complement(u))),universal_class)** member(singleton(v),u)* -> . % 300.04/300.41 12041[0:Res:12015.1,22.0] || equal(complement(complement(intersection(u,v))),universal_class)** -> member(singleton(w),u)*. % 300.04/300.41 12042[0:Res:12015.1,23.0] || equal(complement(complement(intersection(u,v))),universal_class)** -> member(singleton(w),v)*. % 300.04/300.41 16305[0:Rew:30.0,16304.1] single_valued_class(intersection(cross_product(universal_class,universal_class),u)) || -> function(restrict(u,universal_class,universal_class))*. % 300.04/300.41 16432[0:Rew:29.0,16431.1] single_valued_class(intersection(u,cross_product(universal_class,universal_class))) || -> function(restrict(u,universal_class,universal_class))*. % 300.04/300.41 6299[0:SpL:30.0,2539.0] || subclass(universal_class,restrict(u,v,w))* -> member(omega,cross_product(v,w)). % 300.04/300.41 84003[0:Res:16280.0,1073.1] inductive(restrict(omega,u,v)) || -> equal(restrict(omega,u,v),omega)**. % 300.04/300.41 16903[0:SpL:4105.0,15276.0] || equal(symmetric_difference(u,inverse(u)),universal_class)** -> member(singleton(v),symmetrization_of(u))*. % 300.04/300.41 16897[0:SpL:4105.0,5473.0] || subclass(universal_class,symmetric_difference(u,inverse(u)))* -> member(singleton(v),symmetrization_of(u))*. % 300.04/300.41 95577[0:Res:51413.0,4178.0] || -> subclass(u,complement(singleton(v))) equal(not_subclass_element(u,complement(singleton(v))),v)**. % 300.04/300.41 79950[0:Res:12015.1,158.0] || equal(complement(complement(omega)),universal_class) -> equal(integer_of(singleton(u)),singleton(u))**. % 300.04/300.41 6490[0:Res:2481.1,158.0] || subclass(universal_class,omega) -> equal(integer_of(ordered_pair(u,v)),ordered_pair(u,v))**. % 300.04/300.41 131962[8:SpL:124908.0,131613.1] || equal(complement(rest_of(inverse(u))),universal_class)** member(v,range_of(u))* -> . % 300.04/300.41 132756[0:SoR:9810.0,72.1] one_to_one(sum_class(cross_product(universal_class,universal_class))) || -> section(element_relation,cross_product(universal_class,universal_class),universal_class)*. % 300.04/300.41 134101[0:Res:7.1,5362.0] || equal(unordered_pair(u,v),universal_class)** -> equal(omega,v) equal(omega,u). % 300.04/300.41 135050[8:SpL:124908.0,83043.0] || member(u,range_of(v))* subclass(universal_class,w) -> member(u,w)*. % 300.04/300.41 135051[8:SpL:125772.0,83043.0] || member(u,sum_class(v))* subclass(universal_class,w) -> member(u,w)*. % 300.04/300.41 135054[8:SpL:125707.0,83043.0] || member(u,inverse(v))* subclass(universal_class,w) -> member(u,w)*. % 300.04/300.41 135319[0:Res:7.1,2499.1] || equal(u,singleton(v)) member(v,universal_class)* -> member(v,u)*. % 300.04/300.41 135381[0:Res:2479.1,11848.0] || subclass(universal_class,u)* subclass(u,v)* well_ordering(universal_class,v)* -> . % 300.04/300.41 135495[0:Res:51413.0,11848.0] || subclass(u,v)* well_ordering(universal_class,v)* -> subclass(w,complement(u))*. % 300.04/300.41 135886[0:Res:2478.1,16105.1] || subclass(universal_class,intersection(u,v)) member(omega,symmetric_difference(u,v))* -> . % 300.04/300.41 138597[8:SpR:125772.0,138594.1] || equal(rest_of(restrict(element_relation,universal_class,u)),rest_relation)** -> subclass(v,sum_class(u))*. % 300.04/300.41 138600[8:SpR:125707.0,138594.1] || equal(rest_of(flip(cross_product(u,universal_class))),rest_relation)** -> subclass(v,inverse(u))*. % 300.04/300.41 138758[0:Res:12015.1,2997.0] || equal(complement(complement(cross_product(u,v))),universal_class)** -> member(singleton(w),u)*. % 300.04/300.41 140029[0:MRR:140022.1,12.0] || equal(u,ordered_pair(v,w)) -> member(unordered_pair(v,singleton(w)),u)*. % 300.04/300.41 140753[0:MRR:140726.0,170.0] || subclass(universal_class,complement(union(u,v)))* -> member(singleton(w),complement(v))*. % 300.04/300.41 140802[0:SpR:44.0,35124.1] || member(u,universal_class) -> member(u,successor(v)) member(u,complement(v))*. % 300.04/300.41 140803[0:SpR:114.0,35124.1] || member(u,universal_class) -> member(u,symmetrization_of(v))* member(u,complement(v)). % 300.04/300.41 140845[0:MRR:140821.0,170.0] || subclass(universal_class,complement(union(u,v)))* -> member(singleton(w),complement(u))*. % 300.04/300.41 146198[0:Res:144532.1,2.0] || equal(u,universal_class) subclass(u,v)* -> member(singleton(w),v)*. % 300.04/300.41 146338[12:SpL:146278.0,105054.0] || member(image(universal_class,u),universal_class) member(cross_product(u,universal_class),universal_class)* -> . % 300.04/300.41 146480[0:Res:52.1,16469.0] inductive(singleton(u)) || -> subclass(omega,v) equal(not_subclass_element(omega,v),u)*. % 300.04/300.41 147465[0:MRR:147445.0,55.1] || member(u,universal_class) subclass(universal_class,complement(unordered_pair(sum_class(u),v)))* -> . % 300.04/300.41 147466[0:MRR:147446.0,55.1] || member(u,universal_class) subclass(universal_class,complement(unordered_pair(v,sum_class(u))))* -> . % 300.04/300.41 147596[0:MRR:147576.0,57.1] || member(u,universal_class) subclass(universal_class,complement(unordered_pair(power_class(u),v)))* -> . % 300.04/300.41 147597[0:MRR:147577.0,57.1] || member(u,universal_class) subclass(universal_class,complement(unordered_pair(v,power_class(u))))* -> . % 300.04/300.41 148014[8:Res:147404.1,5467.1] || member(singleton(u),element_relation)* subclass(universal_class,complement(compose(element_relation,universal_class)))* -> . % 300.04/300.41 148837[0:Res:12015.1,148647.0] || equal(complement(complement(complement(complement(u)))),universal_class)** -> member(singleton(v),u)*. % 300.04/300.41 149477[0:SpR:149012.1,30.0] || subclass(u,cross_product(v,w))* -> equal(restrict(u,v,w),u). % 300.04/300.41 149620[0:Res:149603.1,2.0] || member(u,universal_class) subclass(universal_class,v) -> member(rest_of(u),v)*. % 300.04/300.41 151728[0:Obv:151719.2] || subclass(u,v) subclass(u,complement(v))* -> subclass(u,w)*. % 300.04/300.41 151738[0:MRR:151702.0,36682.1] || subclass(u,complement(unordered_pair(not_subclass_element(u,v),w)))* -> subclass(u,v). % 300.04/300.41 151739[0:MRR:151703.0,36682.1] || subclass(u,complement(unordered_pair(v,not_subclass_element(u,w))))* -> subclass(u,w). % 300.04/300.41 153198[0:Rew:30.0,153116.0] || -> equal(restrict(restrict(u,v,w),v,w),restrict(u,v,w))**. % 300.04/300.41 153376[0:SpR:4105.0,149318.0] || -> equal(intersection(symmetrization_of(u),symmetric_difference(u,inverse(u))),symmetric_difference(u,inverse(u)))**. % 300.04/300.41 135318[3:Res:134636.1,2499.1] || subclass(singleton(u),ordinal_numbers)* member(u,universal_class) -> member(u,kind_1_ordinals). % 300.04/300.41 158092[8:Rew:157840.0,85192.1] inductive(intersection(universal_class,complement(u))) || equal(complement(complement(u)),universal_class)** -> . % 300.04/300.41 145454[0:Res:144531.1,11848.0] || equal(u,universal_class) subclass(u,v)* well_ordering(universal_class,v)* -> . % 300.04/300.41 158392[2:SSi:136376.0,51.0] || well_ordering(u,omega) -> equal(integer_of(least(u,omega)),least(u,omega))**. % 300.04/300.41 164408[8:Res:81104.1,11848.0] || subclass(domain_relation,u)* subclass(u,v)* well_ordering(universal_class,v)* -> . % 300.04/300.41 136343[2:Res:35222.2,36583.0] inductive(u) || well_ordering(v,u) -> member(least(v,u),universal_class)*. % 300.04/300.41 135700[2:Res:35220.2,36583.0] inductive(u) || well_ordering(v,universal_class) -> member(least(v,u),universal_class)*. % 300.04/300.41 166596[8:Rew:142500.0,166511.1,82914.0,166511.1] || -> member(u,v) equal(symmetric_difference(singleton(u),v),union(singleton(u),v))**. % 300.04/300.41 166761[8:Rew:142500.0,166691.1,82914.0,166691.1] || -> member(u,v) equal(symmetric_difference(v,singleton(u)),union(v,singleton(u)))**. % 300.04/300.41 167395[19:Rew:166997.0,84231.1] || subclass(domain_relation,restrict(u,v,w))* -> member(ordered_pair(ordinal_numbers,ordinal_numbers),u). % 300.04/300.41 167404[19:Rew:166997.0,98570.1] || subclass(domain_relation,complement(complement(singleton(u))))* -> equal(ordered_pair(ordinal_numbers,ordinal_numbers),u). % 300.04/300.41 167419[19:Rew:166997.0,84245.1] || subclass(domain_relation,omega) -> equal(integer_of(ordered_pair(ordinal_numbers,ordinal_numbers)),ordered_pair(ordinal_numbers,ordinal_numbers))**. % 300.04/300.41 169275[19:Rew:166997.0,167420.0] || equal(compose(u,ordinal_numbers),ordinal_numbers) -> member(ordered_pair(ordinal_numbers,ordinal_numbers),compose_class(u))*. % 300.04/300.41 167461[19:Rew:166997.0,160101.2] || member(u,universal_class) -> member(u,kind_1_ordinals) member(u,complement(singleton(ordinal_numbers)))*. % 300.04/300.41 169280[19:Rew:166997.0,167550.2] || equal(u,singleton(ordinal_numbers)) subclass(u,v)* -> member(ordinal_numbers,v)*. % 300.04/300.41 169281[19:Rew:166997.0,167551.1] || equal(symmetric_difference(u,v),singleton(ordinal_numbers)) -> member(ordinal_numbers,union(u,v))*. % 300.04/300.41 169283[19:Rew:166997.0,167553.1] || equal(symmetric_difference(u,inverse(u)),singleton(ordinal_numbers))** -> member(ordinal_numbers,symmetrization_of(u)). % 300.04/300.41 167650[19:Rew:166997.0,162681.2] || subclass(complement(u),v)* well_ordering(universal_class,v) -> member(ordinal_numbers,u). % 300.04/300.41 169289[19:Rew:166997.0,167657.0] || equal(image(successor_relation,u),ordinal_numbers)** member(ordinal_numbers,u) -> inductive(u). % 300.04/300.41 169293[19:Rew:166997.0,167695.2] || subclass(regular(u),u)* -> equal(u,ordinal_numbers) equal(regular(u),ordinal_numbers). % 300.04/300.41 167740[19:Rew:166997.0,80630.1] || member(u,universal_class) -> equal(u,ordinal_numbers) member(apply(choice,u),universal_class)*. % 300.04/300.41 169294[19:Rew:166997.0,167743.1] || equal(unordered_pair(u,v),universal_class)** -> equal(ordinal_numbers,v) equal(ordinal_numbers,u). % 300.04/300.41 169295[19:Rew:166997.0,167749.1] || subclass(universal_class,unordered_pair(u,v))* -> equal(ordinal_numbers,v) equal(ordinal_numbers,u). % 300.04/300.41 167759[19:Rew:166997.0,80571.1] || subclass(singleton(u),v)* -> equal(singleton(u),ordinal_numbers) member(u,v). % 300.04/300.41 167780[19:Rew:166997.0,84014.1] inductive(singleton(u)) || -> equal(integer_of(u),ordinal_numbers)** equal(singleton(u),omega). % 300.04/300.41 169303[19:Rew:166997.0,167976.0] || -> member(ordinal_numbers,intersection(complement(u),complement(v)))* member(ordinal_numbers,union(u,v)). % 300.04/300.41 167983[19:Rew:166997.0,80677.1] inductive(symmetric_difference(complement(u),complement(v))) || -> member(ordinal_numbers,union(u,v))*. % 300.04/300.41 167988[19:Rew:166997.0,80672.1] inductive(symmetric_difference(complement(u),complement(singleton(u)))) || -> member(ordinal_numbers,successor(u))*. % 300.04/300.41 167993[19:Rew:166997.0,80673.1] inductive(symmetric_difference(complement(u),complement(inverse(u)))) || -> member(ordinal_numbers,symmetrization_of(u))*. % 300.04/300.41 167999[19:Rew:166997.0,98604.1] || subclass(domain_relation,complement(complement(compose_class(u))))* -> equal(compose(u,ordinal_numbers),ordinal_numbers). % 300.04/300.41 168246[19:Rew:166997.0,80701.1] || well_ordering(u,universal_class) -> equal(v,ordinal_numbers) member(least(u,v),universal_class)*. % 300.04/300.41 168254[19:Rew:166997.0,93840.1] || equal(symmetric_difference(u,v),universal_class) -> member(ordinal_numbers,complement(intersection(u,v)))*. % 300.04/300.41 168255[19:Rew:166997.0,93613.1] || subclass(universal_class,symmetric_difference(u,v)) -> member(ordinal_numbers,complement(intersection(u,v)))*. % 300.04/300.41 168259[19:Rew:166997.0,82389.1] || subclass(universal_class,restrict(u,v,w))* -> member(ordinal_numbers,cross_product(v,w)). % 300.04/300.41 168268[19:Rew:166997.0,80727.0] || -> equal(singleton(image(u,singleton(v))),ordinal_numbers)** member(apply(u,v),universal_class). % 300.04/300.41 168274[19:Rew:166997.0,80737.1] || well_ordering(u,v)* -> equal(segment(u,ordinal_numbers,least(u,ordinal_numbers)),ordinal_numbers)**. % 300.04/300.41 168284[19:Rew:166997.0,161092.1] inductive(cantor(restrict(u,v,identity_relation))) || section(u,ordinal_numbers,v)* -> . % 300.04/300.41 168285[19:Rew:166997.0,159471.1] inductive(domain_of(restrict(u,v,identity_relation))) || section(u,ordinal_numbers,v)* -> . % 300.04/300.41 168288[19:Rew:166997.0,82432.0] || -> equal(integer_of(image(u,singleton(v))),ordinal_numbers)** member(apply(u,v),universal_class). % 300.04/300.41 168327[19:Rew:166997.0,166539.1] || -> member(u,complement(complement(singleton(u))))* equal(complement(complement(singleton(u))),ordinal_numbers). % 300.04/300.41 168355[19:Rew:166997.0,166531.1] || -> member(u,intersection(singleton(u),v))* equal(intersection(singleton(u),v),ordinal_numbers). % 300.04/300.41 168422[19:Rew:166997.0,160958.1] || subclass(universal_class,intersection(u,v)) member(ordinal_numbers,symmetric_difference(u,v))* -> . % 300.04/300.41 168455[19:Rew:166997.0,161347.1] || member(u,cantor(universal_class)) equal(cross_product(singleton(u),universal_class),ordinal_numbers)** -> . % 300.04/300.41 168755[19:Rew:166997.0,161421.0] || -> equal(first(not_subclass_element(cross_product(u,singleton(v)),ordinal_numbers)),domain__dfg(universal_class,u,v))**. % 300.04/300.41 168756[19:Rew:166997.0,161437.0] || -> equal(second(not_subclass_element(cross_product(singleton(u),v),ordinal_numbers)),range__dfg(universal_class,u,v))**. % 300.04/300.41 168959[19:Rew:166997.0,164604.1] || member(cross_product(u,universal_class),universal_class)* -> equal(singleton(image(universal_class,u)),ordinal_numbers). % 300.04/300.41 168974[19:Rew:166997.0,164708.1] || member(cross_product(u,universal_class),universal_class)* -> equal(integer_of(image(universal_class,u)),ordinal_numbers). % 300.04/300.41 169062[19:Rew:166997.0,166524.1] || -> member(u,cross_product(v,w)) equal(restrict(singleton(u),v,w),ordinal_numbers)**. % 300.04/300.41 169063[19:Rew:166997.0,166532.1] || -> member(u,intersection(v,singleton(u)))* equal(intersection(v,singleton(u)),ordinal_numbers). % 300.04/300.41 169438[19:MRR:167914.3,167057.0] || equal(sum_class(u),ordinal_numbers) well_ordering(element_relation,u)* -> equal(u,ordinal_numbers). % 300.04/300.41 171317[19:Res:124899.1,167211.1] inductive(cantor(restrict(u,v,ordinal_numbers))) || section(u,ordinal_numbers,v)* -> . % 300.04/300.41 169309[19:Rew:166997.0,168155.1] || -> member(not_subclass_element(u,symmetrization_of(ordinal_numbers)),complement(inverse(ordinal_numbers)))* subclass(u,symmetrization_of(ordinal_numbers)). % 300.04/300.41 168145[19:Rew:166997.0,160519.0] || -> subclass(complement(union(u,complement(inverse(ordinal_numbers)))),intersection(complement(u),symmetrization_of(ordinal_numbers)))*. % 300.04/300.41 168144[19:Rew:166997.0,160517.0] || -> equal(complement(intersection(complement(u),symmetrization_of(ordinal_numbers))),union(u,complement(inverse(ordinal_numbers))))**. % 300.04/300.41 168142[19:Rew:166997.0,160498.0] || -> subclass(complement(union(complement(inverse(ordinal_numbers)),u)),intersection(symmetrization_of(ordinal_numbers),complement(u)))*. % 300.04/300.41 168141[19:Rew:166997.0,160496.0] || -> equal(complement(intersection(symmetrization_of(ordinal_numbers),complement(u))),union(complement(inverse(ordinal_numbers)),u))**. % 300.04/300.41 169323[19:Rew:166997.0,169066.1] || -> member(ordinal_numbers,image(element_relation,symmetrization_of(ordinal_numbers)))* member(ordinal_numbers,power_class(complement(inverse(ordinal_numbers)))). % 300.04/300.41 169306[19:Rew:166997.0,168066.0] || subclass(universal_class,complement(symmetrization_of(ordinal_numbers))) -> member(singleton(u),complement(inverse(ordinal_numbers)))*. % 300.04/300.41 169609[19:MRR:169608.0,169608.3,167011.0,167057.0] || well_ordering(element_relation,range_of(ordinal_numbers)) subclass(sum_class(range_of(ordinal_numbers)),range_of(ordinal_numbers))* -> . % 300.04/300.41 169287[19:Rew:166997.0,167595.0] || member(ordered_pair(u,v),compose(ordinal_numbers,w))* -> member(v,range_of(ordinal_numbers)). % 300.04/300.41 175563[20:MRR:169499.1,175557.0] || well_ordering(u,inverse(ordinal_numbers)) -> member(least(u,symmetrization_of(ordinal_numbers)),symmetrization_of(ordinal_numbers))*. % 300.04/300.41 175564[20:MRR:169506.1,175557.0] || member(symmetrization_of(ordinal_numbers),universal_class) -> member(apply(choice,symmetrization_of(ordinal_numbers)),inverse(ordinal_numbers))*. % 300.04/300.41 175908[20:Res:167339.2,175561.0] || subclass(omega,complement(inverse(ordinal_numbers)))* -> equal(integer_of(regular(symmetrization_of(ordinal_numbers))),ordinal_numbers). % 300.04/300.41 176126[20:Res:175613.1,897.0] || subclass(universal_class,restrict(u,v,w))* -> member(regular(symmetrization_of(ordinal_numbers)),u). % 300.04/300.41 176131[20:Res:175613.1,158.0] || subclass(universal_class,omega) -> equal(integer_of(regular(symmetrization_of(ordinal_numbers))),regular(symmetrization_of(ordinal_numbers)))**. % 300.04/300.41 176192[18:SpL:125772.0,175681.1] || member(restrict(element_relation,universal_class,u),universal_class)* member(v,sum_class(u))* -> . % 300.04/300.41 176194[18:SpL:125707.0,175681.1] || member(flip(cross_product(u,universal_class)),universal_class)* member(v,inverse(u))* -> . % 300.04/300.41 177184[22:Res:177171.1,11848.0] || subclass(omega,u)* subclass(u,v)* well_ordering(universal_class,v)* -> . % 300.04/300.41 177189[22:Res:177171.1,16105.1] || subclass(omega,intersection(u,v)) member(ordinal_numbers,symmetric_difference(u,v))* -> . % 300.04/300.41 177199[22:Res:177171.1,9.0] || subclass(omega,unordered_pair(u,v))* -> equal(ordinal_numbers,v) equal(ordinal_numbers,u). % 300.04/300.41 177206[22:Res:177171.1,896.0] || subclass(omega,restrict(u,v,w))* -> member(ordinal_numbers,cross_product(v,w)). % 300.04/300.41 178441[19:SpL:168412.1,137177.0] || well_ordering(universal_class,regular(cross_product(u,v)))* -> equal(cross_product(u,v),ordinal_numbers). % 300.04/300.41 178449[19:SpL:168412.1,167175.0] || subclass(regular(cross_product(u,v)),ordinal_numbers)* -> equal(cross_product(u,v),ordinal_numbers). % 300.04/300.41 178450[19:SpL:168412.1,167176.0] || equal(regular(cross_product(u,v)),ordinal_numbers)** -> equal(cross_product(u,v),ordinal_numbers). % 300.04/300.41 178507[19:SpR:178137.1,6468.0] || equal(rest_of(apply(choice,omega)),rest_relation)** -> equal(apply(choice,omega),ordinal_numbers). % 300.04/300.41 178724[19:SpR:167004.0,176368.1] function(recursion(u,successor_relation,ordinal_numbers)) || -> equal(cantor(ordinal_add(u,v)),ordinal_numbers)**. % 300.04/300.41 178771[22:SpL:160.0,177190.0] || subclass(omega,symmetric_difference(u,v)) -> member(ordinal_numbers,complement(intersection(u,v)))*. % 300.04/300.41 178872[22:SpL:160.0,178812.0] || equal(symmetric_difference(u,v),omega) -> member(ordinal_numbers,complement(intersection(u,v)))*. % 300.04/300.41 178887[22:SpL:30.0,178812.0] || equal(restrict(u,v,w),omega)** -> member(ordinal_numbers,cross_product(v,w))*. % 300.04/300.41 178919[22:Res:178902.1,11848.0] || equal(u,omega) subclass(u,v)* well_ordering(universal_class,v)* -> . % 300.04/300.41 178924[22:Res:178902.1,16105.1] || equal(intersection(u,v),omega) member(ordinal_numbers,symmetric_difference(u,v))* -> . % 300.04/300.41 178934[22:Res:178902.1,9.0] || equal(unordered_pair(u,v),omega)** -> equal(ordinal_numbers,v) equal(ordinal_numbers,u). % 300.04/300.41 180205[19:Rew:180089.0,179098.0] || -> member(ordinal_numbers,image(element_relation,singleton(ordinal_numbers)))* member(ordinal_numbers,power_class(complement(singleton(ordinal_numbers)))). % 300.04/300.41 180274[19:Rew:180089.0,169279.1] || well_ordering(u,singleton(ordinal_numbers)) -> member(least(u,singleton(ordinal_numbers)),singleton(ordinal_numbers))*. % 300.04/300.41 180363[19:Rew:180089.0,180278.1] || -> member(not_subclass_element(u,singleton(ordinal_numbers)),complement(singleton(ordinal_numbers)))* subclass(u,singleton(ordinal_numbers)). % 300.04/300.41 180286[19:Rew:180089.0,168812.0] || -> subclass(complement(union(complement(singleton(ordinal_numbers)),u)),intersection(singleton(ordinal_numbers),complement(u)))*. % 300.04/300.41 180287[19:Rew:180089.0,168813.0] || -> equal(complement(intersection(singleton(ordinal_numbers),complement(u))),union(complement(singleton(ordinal_numbers)),u))**. % 300.04/300.41 180805[19:MRR:180753.0,167011.0] || -> member(ordinal_numbers,cantor(element_relation)) equal(power_class(complement(singleton(ordinal_numbers))),complement(range_of(ordinal_numbers)))**. % 300.04/300.41 180866[19:Res:166605.0,169221.1] || equal(complement(inverse(singleton(ordinal_numbers))),singleton(ordinal_numbers))** -> asymmetric(singleton(ordinal_numbers),u)*. % 300.04/300.41 180871[19:Res:147404.1,169221.1] || member(ordinal_numbers,element_relation) equal(complement(compose(element_relation,universal_class)),singleton(ordinal_numbers))** -> . % 300.04/300.41 180894[19:MRR:180861.0,167011.0] || equal(complement(union(u,v)),singleton(ordinal_numbers))** -> member(ordinal_numbers,complement(u)). % 300.04/300.41 180895[19:MRR:180862.0,167011.0] || equal(complement(union(u,v)),singleton(ordinal_numbers))** -> member(ordinal_numbers,complement(v)). % 300.04/300.41 180966[19:SpL:56.0,180886.1] inductive(image(element_relation,complement(u))) || equal(power_class(u),singleton(ordinal_numbers))** -> . % 300.04/300.41 181526[19:Rew:167191.0,181498.1,167191.0,181498.0] || -> subclass(singleton(not_subclass_element(symmetrization_of(ordinal_numbers),u)),symmetrization_of(ordinal_numbers))* subclass(symmetrization_of(ordinal_numbers),u). % 300.04/300.41 181720[20:Res:175570.1,25.1] || subclass(inverse(ordinal_numbers),complement(u)) member(regular(symmetrization_of(ordinal_numbers)),u)* -> . % 300.04/300.41 181724[20:Res:175570.1,148647.0] || subclass(inverse(ordinal_numbers),complement(complement(u)))* -> member(regular(symmetrization_of(ordinal_numbers)),u). % 300.04/300.41 181732[20:Res:175570.1,22.0] || subclass(inverse(ordinal_numbers),intersection(u,v))* -> member(regular(symmetrization_of(ordinal_numbers)),u). % 300.04/300.41 181733[20:Res:175570.1,23.0] || subclass(inverse(ordinal_numbers),intersection(u,v))* -> member(regular(symmetrization_of(ordinal_numbers)),v). % 300.04/300.41 181781[19:Res:176345.1,25.1] || subclass(domain_relation,complement(u)) member(singleton(singleton(singleton(ordinal_numbers))),u)* -> . % 300.04/300.41 181785[19:Res:176345.1,148647.0] || subclass(domain_relation,complement(complement(u))) -> member(singleton(singleton(singleton(ordinal_numbers))),u)*. % 300.04/300.41 181793[19:Res:176345.1,22.0] || subclass(domain_relation,intersection(u,v))* -> member(singleton(singleton(singleton(ordinal_numbers))),u)*. % 300.04/300.41 181794[19:Res:176345.1,23.0] || subclass(domain_relation,intersection(u,v))* -> member(singleton(singleton(singleton(ordinal_numbers))),v)*. % 300.04/300.41 181811[19:Res:176345.1,169207.0] || subclass(domain_relation,symmetrization_of(ordinal_numbers)) -> member(singleton(singleton(singleton(ordinal_numbers))),inverse(ordinal_numbers))*. % 300.04/300.41 182420[19:Res:166605.0,182393.0] || well_ordering(universal_class,inverse(singleton(singleton(ordinal_numbers))))* -> asymmetric(singleton(singleton(ordinal_numbers)),u)*. % 300.04/300.41 182880[19:Res:182871.1,5467.1] || member(singleton(u),inverse(ordinal_numbers))* subclass(universal_class,complement(symmetrization_of(ordinal_numbers))) -> . % 300.04/300.41 182890[19:Res:182871.1,4.0] || member(not_subclass_element(u,symmetrization_of(ordinal_numbers)),inverse(ordinal_numbers))* -> subclass(u,symmetrization_of(ordinal_numbers)). % 300.04/300.41 182901[20:Res:181635.1,25.1] || subclass(symmetrization_of(ordinal_numbers),complement(u)) member(regular(symmetrization_of(ordinal_numbers)),u)* -> . % 300.04/300.41 182905[20:Res:181635.1,148647.0] || subclass(symmetrization_of(ordinal_numbers),complement(complement(u)))* -> member(regular(symmetrization_of(ordinal_numbers)),u). % 300.04/300.41 182913[20:Res:181635.1,22.0] || subclass(symmetrization_of(ordinal_numbers),intersection(u,v))* -> member(regular(symmetrization_of(ordinal_numbers)),u). % 300.04/300.41 182914[20:Res:181635.1,23.0] || subclass(symmetrization_of(ordinal_numbers),intersection(u,v))* -> member(regular(symmetrization_of(ordinal_numbers)),v). % 300.04/300.41 183081[19:Res:182463.1,25.1] || equal(complement(u),singleton(singleton(ordinal_numbers))) member(singleton(ordinal_numbers),u)* -> . % 300.04/300.41 183085[19:Res:182463.1,148647.0] || equal(complement(complement(u)),singleton(singleton(ordinal_numbers))) -> member(singleton(ordinal_numbers),u)*. % 300.04/300.41 183093[19:Res:182463.1,22.0] || equal(intersection(u,v),singleton(singleton(ordinal_numbers)))** -> member(singleton(ordinal_numbers),u)*. % 300.04/300.41 183094[19:Res:182463.1,23.0] || equal(intersection(u,v),singleton(singleton(ordinal_numbers)))** -> member(singleton(ordinal_numbers),v)*. % 300.04/300.41 183111[19:Res:182463.1,169207.0] || equal(singleton(singleton(ordinal_numbers)),symmetrization_of(ordinal_numbers)) -> member(singleton(ordinal_numbers),inverse(ordinal_numbers))*. % 300.04/300.41 183260[0:MRR:183223.0,170.0] || equal(complement(union(u,v)),universal_class)** -> member(singleton(w),complement(u))*. % 300.04/300.41 183261[0:MRR:183224.0,170.0] || equal(complement(union(u,v)),universal_class)** -> member(singleton(w),complement(v))*. % 300.04/300.41 183777[19:SpR:169229.1,149012.1] || subclass(u,singleton(u))* -> equal(singleton(u),ordinal_numbers) equal(ordinal_numbers,u). % 300.04/300.41 183888[23:SpR:183840.0,167261.0] || -> equal(second(not_subclass_element(restrict(u,ordinal_numbers,v),ordinal_numbers)),range__dfg(u,universal_class,v))**. % 300.04/300.41 183894[23:SpR:183840.0,167260.0] || -> equal(first(not_subclass_element(restrict(u,v,ordinal_numbers),ordinal_numbers)),domain__dfg(u,v,universal_class))**. % 300.04/300.41 183941[23:SpL:183840.0,167253.1] || member(universal_class,cantor(u)) equal(restrict(u,ordinal_numbers,universal_class),ordinal_numbers)** -> . % 300.04/300.41 183975[23:Rew:183885.0,168960.1] || member(u,universal_class) -> equal(apply(v,range_of(u)),apply(v,universal_class))**. % 300.04/300.41 183976[23:Rew:183885.0,177848.1] || -> equal(range_of(u),ordinal_numbers) equal(apply(v,inverse(u)),apply(v,universal_class))**. % 300.04/300.41 183986[23:Rew:183883.0,168956.1] || member(u,universal_class) -> equal(ordered_pair(v,range_of(u)),ordered_pair(v,universal_class))**. % 300.04/300.41 183987[23:Rew:183883.0,177846.1] || -> equal(range_of(u),ordinal_numbers) equal(ordered_pair(v,inverse(u)),ordered_pair(v,universal_class))**. % 300.04/300.41 184023[23:Rew:183840.0,183907.1] || member(singleton(singleton(ordinal_numbers)),compose_class(u))* -> equal(compose(u,ordinal_numbers),universal_class). % 300.04/300.41 184257[23:SpR:183885.0,176366.1] || member(image(u,ordinal_numbers),universal_class)* -> equal(cantor(apply(u,universal_class)),ordinal_numbers). % 300.04/300.41 184391[19:Res:167224.0,176273.0] || subclass(domain_relation,rest_relation)* -> equal(singleton(u),ordinal_numbers) equal(rest_of(u),ordinal_numbers)**. % 300.04/300.41 184392[19:Res:167115.1,176273.0] || subclass(domain_relation,rest_relation)* -> equal(integer_of(u),ordinal_numbers)** equal(rest_of(u),ordinal_numbers). % 300.04/300.41 184407[19:Res:167137.1,176273.0] || subclass(domain_relation,rest_relation) -> equal(u,ordinal_numbers) equal(rest_of(regular(u)),ordinal_numbers)**. % 300.04/300.41 184523[19:Res:167224.0,176274.0] || subclass(rest_relation,domain_relation)* -> equal(singleton(u),ordinal_numbers) equal(rest_of(u),ordinal_numbers)**. % 300.04/300.41 184524[19:Res:167115.1,176274.0] || subclass(rest_relation,domain_relation)* -> equal(integer_of(u),ordinal_numbers)** equal(rest_of(u),ordinal_numbers). % 300.04/300.41 184539[19:Res:167137.1,176274.0] || subclass(rest_relation,domain_relation) -> equal(u,ordinal_numbers) equal(rest_of(regular(u)),ordinal_numbers)**. % 300.04/300.41 184767[19:Res:7.1,167961.0] || equal(singleton(u),omega)** -> equal(integer_of(v),ordinal_numbers)** equal(v,u)*. % 300.04/300.41 184827[23:SpR:183857.0,176419.1] || subclass(domain_relation,flip(u)) -> member(ordered_pair(singleton(singleton(ordinal_numbers)),ordinal_numbers),u)*. % 300.04/300.41 184874[19:Res:176419.1,124881.0] || subclass(domain_relation,flip(rest_of(u))) -> member(ordered_pair(v,w),cantor(u))*. % 300.04/300.41 184876[19:Res:176419.1,15.0] || subclass(domain_relation,flip(cross_product(u,v)))* -> member(ordered_pair(w,x),u)*. % 300.04/300.41 184952[19:Res:176420.1,124881.0] || subclass(domain_relation,rotate(rest_of(u))) -> member(ordered_pair(v,ordinal_numbers),cantor(u))*. % 300.04/300.41 184954[19:Res:176420.1,15.0] || subclass(domain_relation,rotate(cross_product(u,v)))* -> member(ordered_pair(w,ordinal_numbers),u)*. % 300.04/300.41 184963[19:Res:176420.1,97.0] || subclass(domain_relation,rotate(composition_function)) -> equal(compose(ordered_pair(u,ordinal_numbers),v),w)*. % 300.04/300.41 185089[19:Res:7.1,167739.0] || equal(singleton(u),v)* -> equal(v,ordinal_numbers) equal(regular(v),u)*. % 300.04/300.41 185256[19:Res:168252.2,36583.0] || well_ordering(u,v) -> equal(v,ordinal_numbers) member(least(u,v),universal_class)*. % 300.04/300.41 185290[20:MRR:185277.1,175557.0] || well_ordering(u,symmetrization_of(ordinal_numbers)) -> member(least(u,symmetrization_of(ordinal_numbers)),inverse(ordinal_numbers))*. % 300.04/300.41 186339[19:Con:186338.1] || member(u,singleton(v))* -> equal(integer_of(v),ordinal_numbers) member(u,omega). % 300.04/300.41 186357[19:SpR:149012.1,167777.1] || subclass(u,singleton(v))* -> equal(integer_of(v),ordinal_numbers) subclass(u,omega). % 300.04/300.41 186403[19:Res:52.1,167960.0] inductive(complement(u)) || member(v,u)* -> equal(integer_of(v),ordinal_numbers). % 300.04/300.41 186417[22:Res:168950.1,177998.1] || member(u,universal_class) equal(complement(ordered_pair(range_of(u),v)),omega)** -> . % 300.04/300.41 186998[19:Obv:186979.2] || subclass(u,v) subclass(u,complement(v))* -> equal(u,ordinal_numbers). % 300.04/300.41 187005[19:Obv:186974.1] || subclass(intersection(u,v),complement(u))* -> equal(intersection(u,v),ordinal_numbers). % 300.04/300.41 187007[19:Obv:186980.1] || subclass(intersection(u,v),complement(v))* -> equal(intersection(u,v),ordinal_numbers). % 300.04/300.41 187246[19:Res:52.1,168376.0] inductive(intersection(u,v)) || -> equal(integer_of(w),ordinal_numbers) member(w,v)*. % 300.04/300.41 187333[19:Res:52.1,168377.0] inductive(intersection(u,v)) || -> equal(integer_of(w),ordinal_numbers) member(w,u)*. % 300.04/300.41 187508[19:Obv:187503.1] || subclass(omega,u) -> equal(integer_of(v),ordinal_numbers) subclass(singleton(v),u)*. % 300.04/300.41 187581[19:Res:137025.0,167736.0] || -> equal(complement(successor(u)),ordinal_numbers) member(regular(complement(successor(u))),complement(u))*. % 300.04/300.41 187582[19:Res:137026.0,167736.0] || -> equal(complement(symmetrization_of(u)),ordinal_numbers) member(regular(complement(symmetrization_of(u))),complement(u))*. % 300.04/300.41 187699[22:Res:177822.1,177998.1] || equal(complement(ordered_pair(inverse(u),v)),omega)** -> equal(range_of(u),ordinal_numbers). % 300.04/300.41 188743[2:Res:2526.2,188593.1] || subclass(u,v)* equal(complement(v),universal_class) -> subclass(u,w)*. % 300.04/300.41 188751[19:Res:167131.2,188593.1] || subclass(u,v)* equal(complement(v),universal_class) -> equal(u,ordinal_numbers). % 300.04/300.41 188790[19:Res:168354.1,188593.1] || equal(complement(union(u,v)),universal_class)** -> equal(symmetric_difference(u,v),ordinal_numbers). % 300.04/300.41 188900[2:Res:188649.1,8.0] || equal(complement(u),universal_class) subclass(v,u)* -> equal(v,u). % 300.04/300.41 190166[19:Rew:27.0,190149.0] || equal(union(u,v),universal_class) well_ordering(element_relation,union(u,v))* -> . % 300.04/300.41 190295[19:MRR:190233.2,167057.0] inductive(symmetric_difference(singleton(identity_relation),singleton(identity_relation))) || well_ordering(u,singleton(ordinal_numbers))* -> . % 300.04/300.41 190296[19:MRR:190234.2,167057.0] inductive(symmetric_difference(singleton(ordinal_numbers),singleton(ordinal_numbers))) || well_ordering(u,singleton(ordinal_numbers))* -> . % 300.04/300.41 192233[19:MRR:192232.1,166995.0] || transitive(complement(cross_product(u,u)),u)* -> equal(compose(ordinal_numbers,ordinal_numbers),ordinal_numbers). % 300.04/300.41 192317[19:Res:12015.1,192214.0] || equal(complement(complement(cantor(complement(cross_product(singleton(singleton(u)),universal_class))))),universal_class)** -> . % 300.04/300.41 192322[19:Res:176345.1,192214.0] || subclass(domain_relation,cantor(complement(cross_product(singleton(singleton(singleton(singleton(ordinal_numbers)))),universal_class))))* -> . % 300.04/300.41 192324[19:Res:182463.1,192214.0] || equal(cantor(complement(cross_product(singleton(singleton(ordinal_numbers)),universal_class))),singleton(singleton(ordinal_numbers)))** -> . % 300.04/300.41 192349[20:Res:181635.1,192214.0] || subclass(symmetrization_of(ordinal_numbers),cantor(complement(cross_product(singleton(regular(symmetrization_of(ordinal_numbers))),universal_class))))* -> . % 300.04/300.41 192350[20:Res:175570.1,192214.0] || subclass(inverse(ordinal_numbers),cantor(complement(cross_product(singleton(regular(symmetrization_of(ordinal_numbers))),universal_class))))* -> . % 300.04/300.41 192450[23:SpR:192241.0,176368.1] function(complement(cross_product(ordinal_numbers,universal_class))) || -> equal(cantor(sum_class(range_of(ordinal_numbers))),ordinal_numbers)**. % 300.04/300.41 193335[25:SpR:193223.1,183883.0] function(u) || -> equal(unordered_pair(ordinal_numbers,unordered_pair(u,ordinal_numbers)),ordered_pair(u,universal_class))**. % 300.04/300.41 193610[25:Rew:183893.0,193364.1] function(u) || -> equal(segment(v,w,universal_class),segment(v,w,u))*. % 300.04/300.41 193611[25:Rew:193223.1,193402.2] function(u) || member(singleton(singleton(ordinal_numbers)),element_relation)* -> member(ordinal_numbers,u)*. % 300.04/300.41 193624[25:Rew:183888.0,193358.1] function(u) || -> equal(range__dfg(v,universal_class,w),range__dfg(v,u,w))*. % 300.04/300.41 193625[25:Rew:183894.0,193365.1] function(u) || -> equal(domain__dfg(v,w,universal_class),domain__dfg(v,w,u))*. % 300.04/300.41 193649[25:SoR:193232.0,167213.2] single_valued_class(regular(u)) || equal(regular(u),ordinal_numbers)** -> equal(u,ordinal_numbers). % 300.04/300.41 193680[25:Res:66.2,193595.1] function(u) function(image(u,v)) || member(v,universal_class)* -> . % 300.04/300.41 193727[25:MRR:193707.2,5.0] function(apply(choice,u)) || member(u,universal_class)* -> equal(u,ordinal_numbers). % 300.04/300.41 193855[25:SpR:193832.1,168752.1] one_to_one(u) || member(u,universal_class)* -> equal(singleton(sum_class(universal_class)),ordinal_numbers)**. % 300.04/300.41 193856[25:SpR:193832.1,168753.1] one_to_one(u) || member(u,universal_class)* -> equal(integer_of(sum_class(universal_class)),ordinal_numbers)**. % 300.04/300.41 193867[25:SpL:193832.1,104245.0] one_to_one(u) || member(sum_class(universal_class),universal_class)* member(u,universal_class)* -> . % 300.04/300.41 193869[25:SpL:193832.1,176272.1] one_to_one(u) || member(u,universal_class)* equal(sum_class(universal_class),ordinal_numbers) -> . % 300.04/300.41 193947[25:Res:193300.1,2.0] function(u) || subclass(ordered_pair(u,v),w)* -> member(ordinal_numbers,w). % 300.04/300.41 194019[19:MRR:193969.0,940.0] || member(u,universal_class) subclass(domain_relation,complement(singleton(ordered_pair(u,ordinal_numbers))))* -> . % 300.04/300.41 194203[25:SpR:193301.1,182706.1] function(u) || equal(complement(u),universal_class)** -> equal(successor(u),ordinal_numbers). % 300.04/300.41 194320[20:MRR:194319.2,175557.0] || well_ordering(u,universal_class) -> subclass(singleton(least(u,symmetrization_of(ordinal_numbers))),symmetrization_of(ordinal_numbers))*. % 300.04/300.41 194431[19:MRR:194379.1,167057.0] || member(u,universal_class) -> equal(apply(singleton(v),u),sum_class(range_of(ordinal_numbers)))**. % 300.04/300.41 195204[19:SpL:180103.0,194013.1] || subclass(domain_relation,rotate(complement(singleton(ordinal_numbers))))* subclass(domain_relation,singleton(ordinal_numbers)) -> . % 300.04/300.41 195205[19:SpL:167191.0,194013.1] || subclass(domain_relation,rotate(complement(inverse(ordinal_numbers))))* subclass(domain_relation,symmetrization_of(ordinal_numbers)) -> . % 300.04/300.41 195287[8:Res:27190.1,124881.0] || subclass(rest_relation,flip(rest_of(u))) -> member(ordered_pair(v,w),cantor(u))*. % 300.04/300.41 195289[0:Res:27190.1,15.0] || subclass(rest_relation,flip(cross_product(u,v)))* -> member(ordered_pair(w,x),u)*. % 300.04/300.41 195549[19:SpL:180103.0,194014.1] || subclass(domain_relation,flip(complement(singleton(ordinal_numbers))))* subclass(domain_relation,singleton(ordinal_numbers)) -> . % 300.04/300.41 195550[19:SpL:167191.0,194014.1] || subclass(domain_relation,flip(complement(inverse(ordinal_numbers))))* subclass(domain_relation,symmetrization_of(ordinal_numbers)) -> . % 300.04/300.41 195723[19:SpL:180103.0,195630.1] || equal(rotate(complement(singleton(ordinal_numbers))),domain_relation)** equal(singleton(ordinal_numbers),domain_relation) -> . % 300.04/300.41 195724[19:SpL:167191.0,195630.1] || equal(rotate(complement(inverse(ordinal_numbers))),domain_relation)** equal(symmetrization_of(ordinal_numbers),domain_relation) -> . % 300.04/300.41 196054[19:SpL:180103.0,195678.1] || equal(rotate(complement(singleton(ordinal_numbers))),rest_relation)** subclass(domain_relation,singleton(ordinal_numbers)) -> . % 300.04/300.41 196055[19:SpL:167191.0,195678.1] || equal(rotate(complement(inverse(ordinal_numbers))),rest_relation)** subclass(domain_relation,symmetrization_of(ordinal_numbers)) -> . % 300.04/300.41 196073[19:SpL:180103.0,195719.1] || equal(flip(complement(singleton(ordinal_numbers))),domain_relation)** equal(singleton(ordinal_numbers),domain_relation) -> . % 300.04/300.41 196074[19:SpL:167191.0,195719.1] || equal(flip(complement(inverse(ordinal_numbers))),domain_relation)** equal(symmetrization_of(ordinal_numbers),domain_relation) -> . % 300.04/300.41 196086[19:SpL:180103.0,196068.0] || equal(singleton(ordinal_numbers),domain_relation) equal(rotate(complement(singleton(ordinal_numbers))),rest_relation)** -> . % 300.04/300.41 196087[19:SpL:167191.0,196068.0] || equal(symmetrization_of(ordinal_numbers),domain_relation) equal(rotate(complement(inverse(ordinal_numbers))),rest_relation)** -> . % 300.04/300.41 196263[19:Rew:142500.0,196112.1,167055.0,196112.1] || equal(complement(u),universal_class) -> equal(symmetric_difference(u,v),union(u,v))**. % 300.04/300.41 196315[19:SpR:188752.1,4105.0] || equal(complement(symmetrization_of(u)),universal_class) -> equal(symmetric_difference(u,inverse(u)),ordinal_numbers)**. % 300.04/300.41 196365[19:SpR:188752.1,137025.0] || equal(complement(complement(singleton(u))),universal_class) -> subclass(complement(successor(u)),ordinal_numbers)*. % 300.04/300.41 196367[19:SpR:188752.1,137026.0] || equal(complement(complement(inverse(u))),universal_class) -> subclass(complement(symmetrization_of(u)),ordinal_numbers)*. % 300.04/300.41 196482[19:Rew:142500.0,196324.1,167055.0,196324.1] || equal(complement(u),universal_class) -> equal(symmetric_difference(v,u),union(v,u))**. % 300.04/300.41 196703[19:MRR:196660.1,167368.0] || subclass(cross_product(universal_class,cross_product(universal_class,universal_class)),u)* -> member(regular(composition_function),u). % 300.04/300.41 196786[19:MRR:196769.1,167046.0] || subclass(singleton(ordinal_numbers),symmetric_difference(u,v))* -> member(ordinal_numbers,union(u,v)). % 300.04/300.41 196819[19:MRR:196807.1,167057.0] || member(u,universal_class) -> equal(apply(regular(element_relation),u),sum_class(range_of(ordinal_numbers)))**. % 300.04/300.41 196847[19:Res:196731.1,2.0] || subclass(universal_class,u)* subclass(u,v)* -> member(regular(element_relation),v)*. % 300.04/300.41 196853[19:Res:196731.1,4127.0] || subclass(universal_class,symmetric_difference(u,v)) -> member(regular(element_relation),union(u,v))*. % 300.04/300.41 196855[19:Res:196731.1,16910.0] || subclass(universal_class,symmetric_difference(u,inverse(u)))* -> member(regular(element_relation),symmetrization_of(u)). % 300.04/300.41 197149[19:SpL:196827.0,20.0] || member(regular(element_relation),element_relation) -> member(first(regular(element_relation)),second(regular(element_relation)))*. % 300.04/300.41 197151[19:SpL:196827.0,124881.0] || member(regular(element_relation),rest_of(u)) -> member(first(regular(element_relation)),cantor(u))*. % 300.04/300.41 197155[19:SpL:196827.0,15.0] || member(regular(element_relation),cross_product(u,v))* -> member(first(regular(element_relation)),u). % 300.04/300.41 197156[19:SpL:196827.0,16.0] || member(regular(element_relation),cross_product(u,v))* -> member(second(regular(element_relation)),v). % 300.04/300.41 197189[19:MRR:197188.1,196720.0] || member(first(regular(element_relation)),second(regular(element_relation)))* -> member(regular(element_relation),element_relation). % 300.04/300.41 198258[19:SpR:4125.0,197499.0] || -> equal(intersection(complement(union(u,v)),symmetric_difference(complement(u),complement(v))),ordinal_numbers)**. % 300.04/300.41 199599[19:Obv:199576.1] || equal(u,v) -> equal(unordered_pair(v,u),ordinal_numbers)** member(v,universal_class). % 300.04/300.41 202575[19:SpR:197295.1,29.0] || subclass(cross_product(u,v),ordinal_numbers)* -> equal(restrict(w,u,v),ordinal_numbers)**. % 300.04/300.41 202764[19:MRR:202763.2,202763.4,166995.0,167057.0] || subclass(u,ordinal_numbers) member(v,u)* well_ordering(w,x)* -> . % 300.04/300.41 202775[19:SpR:197859.1,160.0] || subclass(complement(intersection(u,v)),ordinal_numbers)* -> equal(symmetric_difference(u,v),ordinal_numbers). % 300.04/300.41 202952[19:Rew:167017.0,202840.1] || subclass(complement(u),ordinal_numbers) -> equal(complement(image(element_relation,successor(u))),ordinal_numbers)**. % 300.04/300.41 202953[19:Rew:167017.0,202842.1] || subclass(complement(u),ordinal_numbers) -> equal(complement(image(element_relation,symmetrization_of(u))),ordinal_numbers)**. % 300.04/300.41 203671[19:Res:5.0,177417.0] || well_ordering(omega,universal_class) -> equal(integer_of(ordered_pair(omega,least(omega,universal_class))),ordinal_numbers)**. % 300.04/300.41 204393[19:MRR:204379.2,167008.0] || equal(ordered_pair(u,v),universal_class) -> equal(unordered_pair(u,singleton(v)),omega)**. % 300.04/300.41 204560[19:MRR:204520.0,167011.0] || subclass(cantor(u),ordinal_numbers)* -> equal(apply(u,ordinal_numbers),sum_class(range_of(ordinal_numbers))). % 300.04/300.41 204680[19:MRR:204652.0,53.0] || subclass(cantor(u),ordinal_numbers)* -> equal(apply(u,omega),sum_class(range_of(ordinal_numbers))). % 300.04/300.41 204702[19:MRR:204698.3,204698.4,167176.0,167057.0] || member(u,universal_class)* subclass(domain_relation,omega) subclass(omega,element_relation) -> . % 300.04/300.41 205571[19:SpR:204449.1,192178.0] || equal(cross_product(u,universal_class),ordinal_numbers)** -> equal(image(universal_class,u),range_of(ordinal_numbers)). % 300.04/300.41 205815[22:SpL:204449.1,192342.0] || equal(cross_product(singleton(ordinal_numbers),universal_class),ordinal_numbers)** equal(cantor(universal_class),omega) -> . % 300.04/300.41 205816[22:SpL:204449.1,192343.0] || equal(cross_product(singleton(ordinal_numbers),universal_class),ordinal_numbers)** subclass(omega,cantor(universal_class)) -> . % 300.04/300.41 205817[19:SpL:204449.1,192345.0] || equal(cross_product(singleton(ordinal_numbers),universal_class),ordinal_numbers)** subclass(universal_class,cantor(universal_class)) -> . % 300.04/300.41 205818[19:SpL:204449.1,192346.0] || equal(cross_product(singleton(ordinal_numbers),universal_class),ordinal_numbers)** equal(cantor(universal_class),universal_class) -> . % 300.04/300.41 205820[19:SpL:204449.1,192319.0] || equal(cross_product(singleton(omega),universal_class),ordinal_numbers)** equal(cantor(universal_class),universal_class) -> . % 300.04/300.41 205821[19:SpL:204449.1,192320.0] || equal(cross_product(singleton(omega),universal_class),ordinal_numbers)** subclass(universal_class,cantor(universal_class)) -> . % 300.04/300.41 206223[19:SpR:27838.0,197499.0] || -> equal(intersection(complement(successor(u)),symmetric_difference(complement(u),complement(singleton(u)))),ordinal_numbers)**. % 300.04/300.41 206663[0:Rew:206400.0,95596.0] || -> member(not_subclass_element(u,power_class(v)),complement(power_class(v)))* subclass(u,power_class(v)). % 300.04/300.41 206913[19:Rew:206400.0,169360.1] || -> member(ordinal_numbers,image(element_relation,power_class(u)))* member(ordinal_numbers,power_class(complement(power_class(u)))). % 300.04/300.41 206983[20:Rew:206400.0,187592.0] || subclass(universal_class,complement(power_class(u))) subclass(symmetrization_of(ordinal_numbers),power_class(u))* -> . % 300.04/300.41 207266[19:Rew:206400.0,187460.1] || subclass(singleton(ordinal_numbers),power_class(u)) member(ordinal_numbers,complement(power_class(u)))* -> . % 300.04/300.41 207301[19:Rew:206400.0,195552.0] || subclass(domain_relation,flip(complement(power_class(u))))* subclass(domain_relation,power_class(u)) -> . % 300.04/300.41 207303[19:Rew:206400.0,196076.0] || equal(flip(complement(power_class(u))),domain_relation)** equal(power_class(u),domain_relation) -> . % 300.04/300.41 207307[19:Rew:206400.0,195207.0] || subclass(domain_relation,rotate(complement(power_class(u))))* subclass(domain_relation,power_class(u)) -> . % 300.04/300.41 207309[19:Rew:206400.0,195726.0] || equal(rotate(complement(power_class(u))),domain_relation)** equal(power_class(u),domain_relation) -> . % 300.04/300.41 207312[19:Rew:206400.0,196089.1] || equal(power_class(u),domain_relation) equal(rotate(complement(power_class(u))),rest_relation)** -> . % 300.04/300.41 207313[19:Rew:206400.0,196057.0] || equal(rotate(complement(power_class(u))),rest_relation)** subclass(domain_relation,power_class(u)) -> . % 300.04/300.41 207700[0:SpR:206407.0,135266.0] || -> subclass(complement(union(complement(power_class(u)),v)),intersection(power_class(u),complement(v)))*. % 300.04/300.41 207748[0:SpR:206407.0,135266.0] || -> subclass(complement(union(u,complement(power_class(v)))),intersection(complement(u),power_class(v)))*. % 300.04/300.41 207932[19:Res:205391.1,2.0] || equal(complement(u),ordinal_numbers) subclass(u,v)* -> member(ordinal_numbers,v)*. % 300.04/300.41 207938[19:Res:205391.1,4127.0] || equal(complement(symmetric_difference(u,v)),ordinal_numbers) -> member(ordinal_numbers,union(u,v))*. % 300.04/300.41 207940[19:Res:205391.1,16910.0] || equal(complement(symmetric_difference(u,inverse(u))),ordinal_numbers)** -> member(ordinal_numbers,symmetrization_of(u)). % 300.04/300.41 207979[19:MRR:196692.1,207974.0] || subclass(complement(inverse(ordinal_numbers)),u) -> member(regular(complement(symmetrization_of(ordinal_numbers))),u)*. % 300.04/300.41 207990[19:Rew:27.0,207936.0] || equal(union(u,v),ordinal_numbers) member(ordinal_numbers,union(u,v))* -> . % 300.04/300.41 208372[19:SpL:206403.0,204472.0] || equal(intersection(complement(u),power_class(v)),union(u,complement(power_class(v))))** -> . % 300.04/300.41 208463[19:Res:205414.1,2.0] || equal(complement(u),ordinal_numbers) subclass(u,v)* -> member(omega,v)*. % 300.04/300.41 208469[19:Res:205414.1,4127.0] || equal(complement(symmetric_difference(u,v)),ordinal_numbers) -> member(omega,union(u,v))*. % 300.04/300.41 208471[19:Res:205414.1,16910.0] || equal(complement(symmetric_difference(u,inverse(u))),ordinal_numbers)** -> member(omega,symmetrization_of(u)). % 300.04/300.41 208505[19:Rew:27.0,208467.0] || equal(union(u,v),ordinal_numbers) member(omega,union(u,v))* -> . % 300.04/300.41 208682[19:SpL:206410.0,204472.0] || equal(intersection(power_class(u),complement(v)),union(complement(power_class(u)),v))** -> . % 300.04/300.41 208814[19:Res:205520.1,125116.1] || equal(complement(complement(rest_of(u))),ordinal_numbers)** member(v,cantor(u))* -> . % 300.04/300.41 208826[19:Res:205520.1,6437.0] || equal(complement(intersection(u,v)),ordinal_numbers)** -> member(unordered_pair(w,x),u)*. % 300.04/300.41 208827[19:Res:205520.1,6438.0] || equal(complement(intersection(u,v)),ordinal_numbers)** -> member(unordered_pair(w,x),v)*. % 300.04/300.41 209996[19:Res:2523.2,205934.1] || member(u,universal_class)* subclass(rest_relation,v)* equal(ordinal_numbers,v) -> . % 300.04/300.41 210041[19:Res:168353.1,205934.1] || equal(complement(intersection(u,v)),ordinal_numbers)** -> equal(symmetric_difference(u,v),ordinal_numbers). % 300.04/300.41 210052[19:Res:168349.1,205934.1] || equal(cross_product(u,v),ordinal_numbers) -> equal(restrict(w,u,v),ordinal_numbers)**. % 300.04/300.41 210230[19:SpR:27837.0,197499.0] || -> equal(intersection(complement(symmetrization_of(u)),symmetric_difference(complement(u),complement(inverse(u)))),ordinal_numbers)**. % 300.04/300.41 210888[19:Res:53.0,177022.0] || -> member(omega,image(universal_class,singleton(omega)))* asymmetric(cross_product(singleton(omega),universal_class),u)*. % 300.04/300.41 210907[19:Res:167011.0,177022.0] || -> member(ordinal_numbers,image(universal_class,singleton(ordinal_numbers)))* asymmetric(cross_product(singleton(ordinal_numbers),universal_class),u)*. % 300.04/300.41 211272[0:Res:53.0,15107.0] || subclass(universal_class,u)* subclass(u,v)* -> member(sum_class(omega),v)*. % 300.04/300.41 211291[19:Res:167011.0,15107.0] || subclass(universal_class,u)* subclass(u,v)* -> member(sum_class(ordinal_numbers),v)*. % 300.04/300.41 211528[19:SpR:210982.1,6468.0] || equal(singleton(apply(choice,omega)),ordinal_numbers)** -> equal(apply(choice,omega),ordinal_numbers). % 300.04/300.41 211644[19:Res:203424.1,897.0] || subclass(complement(restrict(u,v,w)),ordinal_numbers)* -> member(singleton(x),u)*. % 300.04/300.41 211660[19:Res:203424.1,3975.0] || subclass(complement(compose_class(u)),ordinal_numbers)* -> equal(compose(u,singleton(v)),v)**. % 300.04/300.41 212115[19:Rew:167017.0,211986.1] || equal(complement(u),ordinal_numbers) -> equal(complement(image(element_relation,successor(u))),ordinal_numbers)**. % 300.04/300.41 212116[19:Rew:167017.0,211988.1] || equal(complement(u),ordinal_numbers) -> equal(complement(image(element_relation,symmetrization_of(u))),ordinal_numbers)**. % 300.04/300.41 212456[19:Res:205991.1,897.0] || equal(complement(restrict(u,v,w)),ordinal_numbers)** -> member(singleton(x),u)*. % 300.04/300.41 212727[19:MRR:212641.2,167057.0] || member(u,restrict(v,w,x))* member(u,complement(v)) -> . % 300.04/300.41 212763[0:Res:53.0,15073.0] || subclass(universal_class,u)* subclass(u,v)* -> member(power_class(omega),v)*. % 300.04/300.41 212870[19:SpR:199281.0,149012.1] || subclass(complement(u),restrict(u,v,w))* -> equal(complement(u),ordinal_numbers). % 300.04/300.41 213000[19:Obv:212983.1] || -> equal(integer_of(u),ordinal_numbers) subclass(unordered_pair(u,v),omega)* member(v,universal_class). % 300.04/300.41 213032[25:SpL:193832.1,197187.0] one_to_one(first(regular(element_relation))) || equal(second(regular(element_relation)),sum_class(universal_class))** -> . % 300.04/300.41 213055[19:Obv:213037.1] || -> equal(integer_of(u),ordinal_numbers) subclass(unordered_pair(v,u),omega)* member(v,universal_class). % 300.04/300.41 213262[19:Rew:167165.0,213259.0,167204.0,213259.0] || equal(sum_class(range_of(ordinal_numbers)),range_of(ordinal_numbers)) well_ordering(element_relation,range_of(ordinal_numbers))* -> . % 300.04/300.41 213870[19:SpR:149012.1,198290.0] || subclass(u,complement(singleton(ordinal_numbers)))* -> equal(intersection(singleton(ordinal_numbers),u),ordinal_numbers). % 300.04/300.41 213999[19:SpR:149012.1,198291.0] || subclass(u,complement(inverse(ordinal_numbers)))* -> equal(intersection(symmetrization_of(ordinal_numbers),u),ordinal_numbers). % 300.04/300.41 214391[19:SpR:149012.1,199255.0] || subclass(u,complement(singleton(ordinal_numbers)))* -> equal(intersection(u,singleton(ordinal_numbers)),ordinal_numbers). % 300.04/300.41 214535[19:MRR:213180.1,214529.0] || member(regular(kind_1_ordinals),intersection(complement(singleton(ordinal_numbers)),complement(image(successor_relation,ordinal_numbers))))* -> . % 300.04/300.41 215152[25:MRR:215142.2,5.0] function(least(u,v)) || well_ordering(u,universal_class)* -> equal(v,ordinal_numbers)*. % 300.04/300.41 215204[19:Res:214528.1,11848.0] || subclass(kind_1_ordinals,u)* subclass(u,v)* well_ordering(universal_class,v)* -> . % 300.04/300.41 215209[19:Res:214528.1,16105.1] || subclass(kind_1_ordinals,intersection(u,v)) member(ordinal_numbers,symmetric_difference(u,v))* -> . % 300.04/300.41 215226[19:Res:214528.1,9.0] || subclass(kind_1_ordinals,unordered_pair(u,v))* -> equal(ordinal_numbers,v) equal(ordinal_numbers,u). % 300.04/300.41 215233[19:Res:214528.1,896.0] || subclass(kind_1_ordinals,restrict(u,v,w))* -> member(ordinal_numbers,cross_product(v,w)). % 300.04/300.41 215959[19:SpL:481.0,214517.0] || equal(complement(complement(intersection(complement(singleton(ordinal_numbers)),union(u,v)))),universal_class)** -> . % 300.04/300.41 215973[22:SpL:481.0,214520.0] || equal(complement(complement(intersection(complement(singleton(ordinal_numbers)),union(u,v)))),omega)** -> . % 300.04/300.41 216490[19:SpL:204449.1,215230.0] || equal(cross_product(singleton(ordinal_numbers),universal_class),ordinal_numbers)** subclass(kind_1_ordinals,cantor(universal_class)) -> . % 300.04/300.41 216531[19:SpL:204449.1,216495.0] || equal(cross_product(singleton(ordinal_numbers),universal_class),ordinal_numbers)** equal(cantor(universal_class),kind_1_ordinals) -> . % 300.04/300.41 216962[0:Obv:216937.1] || member(u,v) -> subclass(unordered_pair(u,w),v)* member(w,universal_class). % 300.04/300.41 217203[0:Obv:217176.1] || member(u,v) -> subclass(unordered_pair(w,u),v)* member(w,universal_class). % 300.04/300.41 217408[19:Obv:217388.1] || subclass(u,complement(intersection(u,v)))* -> subclass(intersection(u,v),ordinal_numbers). % 300.04/300.41 218385[19:SpR:167200.0,218022.0] || -> subclass(complement(union(u,image(element_relation,symmetrization_of(ordinal_numbers)))),power_class(complement(inverse(ordinal_numbers))))*. % 300.04/300.41 218386[19:SpR:180125.0,218022.0] || -> subclass(complement(union(u,image(element_relation,singleton(ordinal_numbers)))),power_class(complement(singleton(ordinal_numbers))))*. % 300.04/300.41 218387[0:SpR:206408.0,218022.0] || -> subclass(complement(union(u,image(element_relation,power_class(v)))),power_class(complement(power_class(v))))*. % 300.04/300.41 218389[19:SpR:209197.0,218022.0] || -> subclass(complement(union(u,power_class(complement(singleton(ordinal_numbers))))),image(element_relation,singleton(ordinal_numbers)))*. % 300.04/300.41 218390[19:SpR:209198.0,218022.0] || -> subclass(complement(union(u,power_class(complement(inverse(ordinal_numbers))))),image(element_relation,symmetrization_of(ordinal_numbers)))*. % 300.04/300.41 218647[19:Obv:218625.1] || subclass(u,complement(intersection(v,u)))* -> subclass(intersection(v,u),ordinal_numbers). % 300.04/300.41 219668[0:SpR:27.0,218920.0] || -> subclass(intersection(complement(union(u,v)),w),intersection(complement(u),complement(v)))*. % 300.04/300.41 219938[0:SpR:27.0,219703.0] || -> subclass(complement(complement(complement(union(u,v)))),intersection(complement(u),complement(v)))*. % 300.04/300.41 220299[0:SpR:27.0,219700.0] || -> subclass(intersection(u,complement(union(v,w))),intersection(complement(v),complement(w)))*. % 300.04/300.41 220416[19:SpR:167200.0,220194.0] || -> subclass(complement(union(image(element_relation,symmetrization_of(ordinal_numbers)),u)),power_class(complement(inverse(ordinal_numbers))))*. % 300.04/300.41 220417[19:SpR:180125.0,220194.0] || -> subclass(complement(union(image(element_relation,singleton(ordinal_numbers)),u)),power_class(complement(singleton(ordinal_numbers))))*. % 300.04/300.41 220418[0:SpR:206408.0,220194.0] || -> subclass(complement(union(image(element_relation,power_class(u)),v)),power_class(complement(power_class(u))))*. % 300.04/300.41 220420[19:SpR:209197.0,220194.0] || -> subclass(complement(union(power_class(complement(singleton(ordinal_numbers))),u)),image(element_relation,singleton(ordinal_numbers)))*. % 300.04/300.41 220421[19:SpR:209198.0,220194.0] || -> subclass(complement(union(power_class(complement(inverse(ordinal_numbers))),u)),image(element_relation,symmetrization_of(ordinal_numbers)))*. % 300.04/300.41 221038[27:MRR:220983.2,167057.0] inductive(symmetric_difference(singleton(ordinal_numbers),image(successor_relation,ordinal_numbers))) || well_ordering(u,kind_1_ordinals)* -> . % 300.04/300.41 221039[27:MRR:220984.2,167057.0] inductive(symmetric_difference(singleton(singleton_relation),image(successor_relation,ordinal_numbers))) || well_ordering(u,kind_1_ordinals)* -> . % 300.04/300.41 221040[27:MRR:220985.2,167057.0] inductive(symmetric_difference(singleton(identity_relation),image(successor_relation,ordinal_numbers))) || well_ordering(u,kind_1_ordinals)* -> . % 300.04/300.41 221045[27:MRR:221044.1,214531.0] || member(not_subclass_element(kind_1_ordinals,ordinal_numbers),complement(intersection(singleton(ordinal_numbers),image(successor_relation,ordinal_numbers))))* -> . % 300.04/300.41 221358[27:MRR:221265.0,36583.1] || member(u,kind_1_ordinals) -> member(u,intersection(singleton(ordinal_numbers),image(successor_relation,ordinal_numbers)))*. % 300.04/300.41 221374[27:Res:221347.0,2.0] || subclass(intersection(singleton(ordinal_numbers),image(successor_relation,ordinal_numbers)),u)* -> member(ordinal_numbers,u). % 300.04/300.41 221564[19:Res:219766.1,8.0] || equal(complement(u),ordinal_numbers) subclass(u,v)* -> equal(u,v). % 300.04/300.41 221585[19:Res:219766.1,169097.1] || equal(complement(u),ordinal_numbers) well_ordering(element_relation,u)* -> equal(u,ordinal_numbers). % 300.04/300.41 221766[19:Res:219766.1,5240.0] || equal(complement(compose_class(u)),ordinal_numbers)** -> equal(cross_product(universal_class,universal_class),compose_class(u))*. % 300.04/300.41 222022[19:Con:221708.2] || equal(complement(u),ordinal_numbers) member(v,w)* -> member(v,u)*. % 300.04/300.41 222758[0:SpR:4125.0,218966.0] || -> subclass(restrict(symmetric_difference(complement(u),complement(v)),w,x),union(u,v))*. % 300.04/300.41 222759[0:SpR:27838.0,218966.0] || -> subclass(restrict(symmetric_difference(complement(u),complement(singleton(u))),v,w),successor(u))*. % 300.04/300.41 222760[0:SpR:27837.0,218966.0] || -> subclass(restrict(symmetric_difference(complement(u),complement(inverse(u))),v,w),symmetrization_of(u))*. % 300.04/300.41 222902[20:MRR:219367.1,222900.0] || subclass(inverse(ordinal_numbers),u) -> member(regular(complement(complement(symmetrization_of(ordinal_numbers)))),u)*. % 300.04/300.41 223019[20:Res:222998.0,176274.0] || subclass(rest_relation,domain_relation) -> equal(rest_of(regular(complement(complement(symmetrization_of(ordinal_numbers))))),ordinal_numbers)**. % 300.04/300.41 223020[20:Res:222998.0,176273.0] || subclass(domain_relation,rest_relation) -> equal(rest_of(regular(complement(complement(symmetrization_of(ordinal_numbers))))),ordinal_numbers)**. % 300.04/300.41 223796[19:Res:168950.1,217129.1] || member(u,universal_class) equal(complement(ordered_pair(range_of(u),v)),kind_1_ordinals)** -> . % 300.04/300.41 223797[19:Res:177822.1,217129.1] || equal(complement(ordered_pair(inverse(u),v)),kind_1_ordinals)** -> equal(range_of(u),ordinal_numbers). % 300.04/300.41 223821[28:Res:188649.1,223709.0] || equal(complement(compose(ordinal_numbers,ordinal_numbers)),universal_class)** -> equal(cross_product(u,u),ordinal_numbers)**. % 300.04/300.41 224022[19:SpL:481.0,223793.0] || equal(complement(complement(intersection(complement(singleton(ordinal_numbers)),union(u,v)))),kind_1_ordinals)** -> . % 300.04/300.41 224130[19:Res:167355.1,219089.0] || equal(sum_class(symmetrization_of(ordinal_numbers)),ordinal_numbers) -> subclass(sum_class(symmetrization_of(ordinal_numbers)),inverse(ordinal_numbers))*. % 300.04/300.41 227828[19:Res:221767.1,897.0] || equal(complement(restrict(u,v,w)),ordinal_numbers)** -> member(regular(element_relation),u). % 300.04/300.41 227979[19:SpR:125772.0,223552.1] || subclass(composition_function,rest_of(restrict(element_relation,universal_class,u)))* -> member(ordinal_numbers,sum_class(u)). % 300.04/300.41 227982[19:SpR:125707.0,223552.1] || subclass(composition_function,rest_of(flip(cross_product(u,universal_class))))* -> member(ordinal_numbers,inverse(u)). % 300.04/300.41 228016[19:Res:223552.1,169221.1] || subclass(composition_function,rest_of(u))* equal(complement(cantor(u)),singleton(ordinal_numbers)) -> . % 300.04/300.41 228183[19:SpL:204449.1,228011.0] || equal(cross_product(singleton(ordinal_numbers),universal_class),ordinal_numbers)** subclass(composition_function,rest_of(universal_class)) -> . % 300.04/300.41 228211[19:SpL:204449.1,228187.0] || equal(cross_product(singleton(ordinal_numbers),universal_class),ordinal_numbers)** equal(rest_of(universal_class),composition_function) -> . % 300.04/300.41 228371[19:Res:224120.1,9780.0] || equal(sum_class(inverse(ordinal_numbers)),symmetrization_of(ordinal_numbers)) -> section(element_relation,inverse(ordinal_numbers),universal_class)*. % 300.04/300.41 228412[19:Res:224120.1,196698.0] || equal(cross_product(universal_class,universal_class),symmetrization_of(ordinal_numbers)) -> member(regular(element_relation),inverse(ordinal_numbers))*. % 300.04/300.41 228417[19:Res:224120.1,2488.0] || equal(ordered_pair(u,v),symmetrization_of(ordinal_numbers))** -> member(singleton(u),inverse(ordinal_numbers))*. % 300.04/300.41 228445[20:MRR:228370.2,176096.0] || equal(sum_class(inverse(ordinal_numbers)),symmetrization_of(ordinal_numbers)) well_ordering(element_relation,inverse(ordinal_numbers))* -> . % 300.04/300.41 229004[19:SpR:225013.1,217976.0] || equal(successor(complement(restrict(u,v,w))),ordinal_numbers)** -> subclass(universal_class,u). % 300.04/300.41 229524[23:SpL:225013.1,192312.0] || equal(successor(cross_product(ordinal_numbers,universal_class)),ordinal_numbers)** member(universal_class,cantor(universal_class)) -> . % 300.04/300.41 229614[19:SpL:225013.1,224005.0] || equal(successor(regular(ordered_pair(ordinal_numbers,u))),ordinal_numbers)** equal(kind_1_ordinals,universal_class) -> . % 300.04/300.41 229641[19:Rew:229640.1,225321.1] || equal(successor(regular(ordered_pair(u,v))),ordinal_numbers)** -> equal(singleton(u),ordinal_numbers). % 300.04/300.41 229756[19:Rew:142500.0,228848.1] || equal(successor(u),ordinal_numbers) -> equal(union(u,v),complement(complement(v)))**. % 300.04/300.41 230349[0:Obv:230323.1] || subclass(u,symmetric_difference(v,w)) -> subclass(u,complement(intersection(v,w)))*. % 300.04/300.41 230420[0:Obv:230332.0] || -> subclass(intersection(u,intersection(symmetric_difference(v,w),x)),complement(intersection(v,w)))*. % 300.04/300.41 230421[0:Obv:230331.0] || -> subclass(intersection(u,intersection(v,symmetric_difference(w,x))),complement(intersection(w,x)))*. % 300.04/300.41 230422[0:Obv:230329.0] || -> subclass(intersection(intersection(symmetric_difference(u,v),w),x),complement(intersection(u,v)))*. % 300.04/300.41 230423[0:Obv:230328.0] || -> subclass(intersection(intersection(u,symmetric_difference(v,w)),x),complement(intersection(v,w)))*. % 300.04/300.41 230781[19:SpL:481.0,229708.0] || equal(successor(complement(intersection(complement(singleton(ordinal_numbers)),union(u,v)))),ordinal_numbers)** -> . % 300.04/300.41 230820[19:Res:229698.1,8.0] || equal(successor(u),ordinal_numbers) subclass(v,u)* -> equal(v,u). % 300.04/300.41 231155[28:Res:229698.1,223709.0] || equal(successor(compose(ordinal_numbers,ordinal_numbers)),ordinal_numbers)** -> equal(cross_product(u,u),ordinal_numbers)**. % 300.04/300.41 232424[19:SpL:481.0,232088.0] || equal(symmetrization_of(complement(intersection(complement(singleton(ordinal_numbers)),union(u,v)))),ordinal_numbers)** -> . % 300.04/300.41 232677[0:Obv:232590.1] || member(u,v) -> subclass(intersection(singleton(u),w),intersection(v,w))*. % 300.04/300.41 233068[0:Obv:232983.1] || member(u,v) -> subclass(intersection(w,singleton(u)),intersection(v,w))*. % 300.04/300.41 234155[19:Rew:233390.0,177823.1] || -> equal(range_of(u),ordinal_numbers) equal(complement(complement(inverse(u))),successor(inverse(u)))**. % 300.04/300.41 234157[19:Rew:233390.0,168399.1] || member(u,universal_class) -> equal(complement(complement(range_of(u))),successor(range_of(u)))**. % 300.04/300.41 234201[19:Rew:233390.0,229764.1] || equal(successor(u),ordinal_numbers) -> equal(union(v,u),complement(complement(v)))**. % 300.04/300.41 234217[19:Rew:233390.0,188617.1] || member(ordinal_numbers,u) equal(complement(complement(complement(u))),singleton(ordinal_numbers))** -> . % 300.04/300.41 234221[19:Rew:233390.0,225611.1] inductive(complement(symmetrization_of(symmetric_difference(universal_class,u)))) || -> member(ordinal_numbers,complement(complement(u)))*. % 300.04/300.41 234222[19:Rew:233390.0,224943.1] inductive(complement(successor(symmetric_difference(universal_class,u)))) || -> member(ordinal_numbers,complement(complement(u)))*. % 300.04/300.41 234230[19:Rew:233390.0,168209.1] inductive(symmetric_difference(intersection(universal_class,u),identity_relation)) || -> member(ordinal_numbers,complement(complement(u)))*. % 300.04/300.41 234238[19:Rew:233390.0,167829.1] inductive(intersection(complement(u),universal_class)) || equal(complement(complement(u)),universal_class)** -> . % 300.04/300.41 234278[19:Rew:233390.0,180965.1] inductive(symmetric_difference(universal_class,u)) || equal(complement(complement(u)),singleton(ordinal_numbers))** -> . % 300.04/300.41 234800[0:Rew:234692.0,153103.0] || -> equal(intersection(symmetric_difference(u,v),complement(intersection(u,v))),symmetric_difference(u,v))**. % 300.04/300.41 234843[19:Rew:234692.0,180282.0] || -> subclass(complement(union(u,complement(singleton(ordinal_numbers)))),intersection(singleton(ordinal_numbers),complement(u)))*. % 300.04/300.41 234927[19:Rew:142500.0,234822.1] || equal(successor(singleton(u)),ordinal_numbers) -> equal(complement(complement(u)),successor(u))**. % 300.04/300.41 234929[19:Rew:142500.0,234826.1] || equal(successor(u),ordinal_numbers) -> equal(complement(complement(inverse(u))),symmetrization_of(u))**. % 300.04/300.41 234930[19:Rew:142500.0,234827.1] || equal(successor(inverse(u)),ordinal_numbers) -> equal(complement(complement(u)),symmetrization_of(u))**. % 300.04/300.41 235580[19:Rew:235542.0,168330.1] inductive(symmetric_difference(intersection(u,universal_class),identity_relation)) || -> member(ordinal_numbers,complement(complement(u)))*. % 300.04/300.41 236262[0:SpR:234692.0,297.1] || -> subclass(intersection(u,v),w) member(not_subclass_element(intersection(v,u),w),v)*. % 300.04/300.41 236263[0:SpR:234692.0,315.1] || -> subclass(intersection(u,v),w) member(not_subclass_element(intersection(v,u),w),u)*. % 300.04/300.41 236304[0:SpR:234692.0,4126.1] || member(u,symmetric_difference(v,w)) -> member(u,complement(intersection(w,v)))*. % 300.04/300.41 236521[0:SpL:234692.0,16105.1] || member(u,symmetric_difference(v,w)) member(u,intersection(w,v))* -> . % 300.04/300.41 236846[0:SpR:234692.0,234713.0] || -> equal(intersection(union(u,v),complement(intersection(v,u))),symmetric_difference(u,v))**. % 300.04/300.41 237437[19:Rew:237384.0,190941.0] || -> equal(symmetric_difference(complement(union(u,v)),intersection(complement(u),complement(v))),ordinal_numbers)**. % 300.04/300.41 237559[19:Rew:237493.0,237473.0] || -> subclass(symmetric_difference(successor(u),complement(intersection(u,singleton(u)))),complement(successor(u)))*. % 300.04/300.41 238850[19:Rew:237974.1,238055.2] || equal(u,universal_class) -> member(not_subclass_element(v,ordinal_numbers),u)* subclass(v,ordinal_numbers). % 300.04/300.41 238861[19:Rew:167055.0,238078.2] || equal(singleton(u),universal_class) -> equal(integer_of(u),ordinal_numbers)** subclass(universal_class,omega)*. % 300.04/300.41 238881[19:Rew:167055.0,238004.2,237974.1,238004.2,167055.0,238004.1] || equal(u,universal_class) -> member(not_subclass_element(universal_class,v),u)* subclass(universal_class,v). % 300.04/300.41 239079[19:SpR:237603.0,205897.1] || equal(complement(intersection(u,singleton(u))),ordinal_numbers)** -> equal(successor(u),ordinal_numbers). % 300.04/300.41 239080[19:SpR:237603.0,197295.1] || subclass(complement(intersection(u,singleton(u))),ordinal_numbers)* -> equal(successor(u),ordinal_numbers). % 300.04/300.41 239106[19:SpL:237603.0,167310.0] || subclass(universal_class,successor(u)) -> member(ordinal_numbers,complement(intersection(u,singleton(u))))*. % 300.04/300.41 239111[19:SpL:237603.0,2540.0] || subclass(universal_class,successor(u)) -> member(omega,complement(intersection(u,singleton(u))))*. % 300.04/300.41 239114[19:SpL:237603.0,167308.0] || equal(successor(u),universal_class) -> member(ordinal_numbers,complement(intersection(u,singleton(u))))*. % 300.04/300.41 239117[19:SpL:237603.0,6310.0] || equal(successor(u),universal_class) -> member(omega,complement(intersection(u,singleton(u))))*. % 300.04/300.41 239122[22:SpL:237603.0,177191.0] || subclass(omega,successor(u)) -> member(ordinal_numbers,complement(intersection(u,singleton(u))))*. % 300.04/300.41 239124[22:SpL:237603.0,178869.0] || equal(successor(u),omega) -> member(ordinal_numbers,complement(intersection(u,singleton(u))))*. % 300.04/300.41 239240[19:EmS:167895.0,167895.1,72.1,238779.1] one_to_one(u) || equal(u,universal_class)* -> member(ordinal_numbers,cross_product(universal_class,universal_class))*. % 300.04/300.41 239391[19:SoR:168225.0,238779.1] || equal(flip(u),universal_class)** -> member(ordinal_numbers,cross_product(cross_product(universal_class,universal_class),universal_class))*. % 300.04/300.41 239392[19:SoR:168226.0,238779.1] || equal(rotate(u),universal_class)** -> member(ordinal_numbers,cross_product(cross_product(universal_class,universal_class),universal_class))*. % 300.04/300.41 239725[19:Res:238770.1,167739.0] || equal(singleton(u),universal_class)** -> equal(v,ordinal_numbers) equal(regular(v),u)*. % 300.04/300.41 239740[19:Res:238770.1,169099.2] || equal(u,universal_class) member(u,universal_class) well_ordering(element_relation,u)* -> . % 300.04/300.41 239743[19:Res:238770.1,124906.1] || equal(u,universal_class) subclass(u,v) -> section(w,u,v)*. % 300.04/300.41 239915[19:Res:238770.1,5426.1] function(u) || equal(u,universal_class) -> equal(cross_product(universal_class,universal_class),u)*. % 300.04/300.41 239937[19:Res:238770.1,167961.0] || equal(singleton(u),universal_class)** -> equal(integer_of(v),ordinal_numbers)** equal(v,u)*. % 300.04/300.41 240510[19:Res:239914.1,2.0] || equal(u,universal_class) subclass(u,v)* -> member(regular(element_relation),v)*. % 300.04/300.41 240518[19:Res:239914.1,4127.0] || equal(symmetric_difference(u,v),universal_class) -> member(regular(element_relation),union(u,v))*. % 300.04/300.41 240519[19:Res:239914.1,16910.0] || equal(symmetric_difference(u,inverse(u)),universal_class)** -> member(regular(element_relation),symmetrization_of(u))*. % 300.04/300.41 240601[19:Res:239132.1,25.1] || member(u,successor(v)) member(u,intersection(v,singleton(v)))* -> . % 300.04/300.41 241016[19:Res:240703.0,169221.1] || equal(complement(complement(intersection(singleton(ordinal_numbers),singleton(singleton(ordinal_numbers))))),singleton(ordinal_numbers))** -> . % 300.04/300.41 241693[19:Obv:241620.0] || -> equal(intersection(singleton(u),restrict(v,w,x)),ordinal_numbers)** member(u,v). % 300.04/300.41 241840[19:Obv:241765.0] || -> equal(intersection(restrict(u,v,w),singleton(x)),ordinal_numbers)** member(x,u). % 300.04/300.41 243752[19:Res:167355.1,239702.0] || equal(sum_class(symmetrization_of(ordinal_numbers)),ordinal_numbers) equal(sum_class(symmetrization_of(ordinal_numbers)),universal_class)** -> . % 300.04/300.41 245362[19:SpL:234713.0,215211.0] || subclass(kind_1_ordinals,symmetric_difference(u,v)) -> member(ordinal_numbers,complement(intersection(u,v)))*. % 300.04/300.41 245363[19:SpL:237603.0,215211.0] || subclass(kind_1_ordinals,successor(u)) -> member(ordinal_numbers,complement(intersection(u,singleton(u))))*. % 300.04/300.41 245404[19:SpR:204449.1,217960.0] || equal(complement(symmetric_difference(u,inverse(u))),ordinal_numbers)** -> subclass(universal_class,symmetrization_of(u)). % 300.04/300.41 245407[19:Res:217960.0,167311.1] inductive(complement(complement(symmetric_difference(u,inverse(u))))) || -> member(ordinal_numbers,symmetrization_of(u))*. % 300.04/300.41 246037[19:Res:2526.2,229738.1] || subclass(u,v)* equal(successor(v),ordinal_numbers) -> subclass(u,w)*. % 300.04/300.41 246046[19:Res:167131.2,229738.1] || subclass(u,v)* equal(successor(v),ordinal_numbers) -> equal(u,ordinal_numbers). % 300.04/300.41 246064[19:Res:16913.1,229738.1] || equal(successor(symmetrization_of(u)),ordinal_numbers) -> subclass(symmetric_difference(u,inverse(u)),v)*. % 300.04/300.41 246107[19:Res:168354.1,229738.1] || equal(successor(union(u,v)),ordinal_numbers)** -> equal(symmetric_difference(u,v),ordinal_numbers). % 300.04/300.41 246323[25:SpR:234134.1,204449.1] function(u) || equal(complement(u),ordinal_numbers)** -> equal(successor(u),universal_class). % 300.04/300.41 246332[25:SpR:234134.1,219698.0] function(u) || -> subclass(restrict(complement(successor(u)),v,w),complement(u))*. % 300.04/300.41 246339[25:SpR:234134.1,206400.0] function(u) || -> equal(image(element_relation,successor(u)),complement(power_class(complement(u))))**. % 300.04/300.41 246353[25:SpR:234134.1,197499.0] function(u) || -> equal(intersection(successor(u),intersection(complement(u),v)),ordinal_numbers)**. % 300.04/300.41 246354[25:SpR:234134.1,197702.0] function(u) || -> equal(intersection(successor(u),intersection(v,complement(u))),ordinal_numbers)**. % 300.04/300.41 246375[25:SpR:234134.1,95593.1] function(u) || -> member(v,complement(u)) subclass(singleton(v),successor(u))*. % 300.04/300.41 246398[25:SpR:234134.1,224158.0] function(symmetrization_of(ordinal_numbers)) || -> subclass(complement(complement(successor(symmetrization_of(ordinal_numbers)))),inverse(ordinal_numbers))*. % 300.04/300.41 246402[25:SpR:234134.1,224123.0] function(symmetrization_of(ordinal_numbers)) || -> subclass(intersection(successor(symmetrization_of(ordinal_numbers)),u),inverse(ordinal_numbers))*. % 300.04/300.41 246403[25:SpR:234134.1,224137.0] function(symmetrization_of(ordinal_numbers)) || -> subclass(intersection(u,successor(symmetrization_of(ordinal_numbers))),inverse(ordinal_numbers))*. % 300.04/300.41 246450[25:SpL:234134.1,188653.0] function(u) || equal(successor(u),universal_class) -> equal(complement(u),ordinal_numbers)**. % 300.04/300.41 246456[25:SpL:234134.1,85097.1] function(u) inductive(complement(u)) || equal(successor(u),universal_class)** -> . % 300.04/300.41 246493[25:SpL:234134.1,167091.0] function(u) || well_ordering(universal_class,successor(u))* -> member(ordinal_numbers,complement(u)). % 300.04/300.41 246501[25:SpL:234134.1,178292.1] function(u) inductive(complement(u)) || equal(successor(u),omega)** -> . % 300.04/300.41 246511[25:SpL:234134.1,203423.0] function(u) || subclass(successor(u),ordinal_numbers) -> member(omega,complement(u))*. % 300.04/300.41 246512[25:SpL:234134.1,203422.0] function(u) || subclass(successor(u),ordinal_numbers) -> member(ordinal_numbers,complement(u))*. % 300.04/300.41 246516[25:SpL:234134.1,223787.1] function(u) inductive(complement(u)) || equal(successor(u),kind_1_ordinals)** -> . % 300.04/300.41 246541[25:SpL:234134.1,9734.0] function(u) || subclass(universal_class,successor(u)) -> member(singleton(v),u)*. % 300.04/300.41 246543[25:SpL:234134.1,182427.0] function(u) || equal(successor(u),universal_class) well_ordering(universal_class,u)* -> . % 300.04/300.41 246548[25:SpL:234134.1,169222.0] function(u) || equal(successor(u),singleton(ordinal_numbers)) -> member(ordinal_numbers,u)*. % 300.04/300.41 246577[25:SpL:234134.1,224358.0] function(symmetrization_of(ordinal_numbers)) || equal(complement(complement(successor(symmetrization_of(ordinal_numbers)))),universal_class)** -> . % 300.04/300.41 246579[25:SpL:234134.1,229720.0] function(symmetrization_of(ordinal_numbers)) || equal(successor(complement(successor(symmetrization_of(ordinal_numbers)))),ordinal_numbers)** -> . % 300.04/300.41 246581[25:SpL:234134.1,223015.0] function(symmetrization_of(ordinal_numbers)) || equal(singleton(regular(successor(symmetrization_of(ordinal_numbers)))),ordinal_numbers)** -> . % 300.04/300.41 246582[25:SpL:234134.1,223021.0] function(symmetrization_of(ordinal_numbers)) || equal(rest_of(regular(successor(symmetrization_of(ordinal_numbers)))),rest_relation)** -> . % 300.04/300.41 246583[25:SpL:234134.1,228027.0] function(symmetrization_of(ordinal_numbers)) || subclass(composition_function,rest_of(regular(successor(symmetrization_of(ordinal_numbers)))))* -> . % 300.04/300.41 246584[25:SpL:234134.1,228209.0] function(symmetrization_of(ordinal_numbers)) || equal(rest_of(regular(successor(symmetrization_of(ordinal_numbers)))),composition_function)** -> . % 300.04/300.41 246585[25:SpL:234134.1,223003.0] function(symmetrization_of(ordinal_numbers)) || subclass(successor(symmetrization_of(ordinal_numbers)),complement(inverse(ordinal_numbers)))* -> . % 300.04/300.41 246586[25:SpL:234134.1,223392.0] function(symmetrization_of(ordinal_numbers)) || equal(complement(inverse(ordinal_numbers)),successor(symmetrization_of(ordinal_numbers)))** -> . % 300.04/300.41 246587[25:SpL:234134.1,239294.0] function(symmetrization_of(ordinal_numbers)) || equal(intersection(successor(symmetrization_of(ordinal_numbers)),u),universal_class)** -> . % 300.04/300.41 246588[25:SpL:234134.1,239282.0] function(symmetrization_of(ordinal_numbers)) || equal(intersection(u,successor(symmetrization_of(ordinal_numbers))),universal_class)** -> . % 300.04/300.41 246597[25:SpL:234134.1,167256.0] function(rest_relation) || equal(successor(rest_relation),domain_relation) -> equal(rest_of(ordinal_numbers),ordinal_numbers)**. % 300.04/300.41 246598[25:SpL:234134.1,167257.0] function(rest_relation) || subclass(domain_relation,successor(rest_relation))* -> equal(rest_of(ordinal_numbers),ordinal_numbers). % 300.04/300.41 246615[25:SpL:234134.1,223389.0] function(complement(symmetrization_of(ordinal_numbers))) || equal(successor(complement(symmetrization_of(ordinal_numbers))),universal_class)** -> . % 300.04/300.41 246636[25:Rew:234134.1,246383.2] function(u) || -> member(regular(successor(u)),u)* equal(successor(u),ordinal_numbers). % 300.04/300.41 246659[25:MRR:246658.3,192574.0] function(u) single_valued_class(complement(u)) || equal(successor(u),universal_class)** -> . % 300.04/300.41 246701[25:Res:246381.1,8.0] function(u) || subclass(u,successor(u))* -> equal(successor(u),u). % 300.04/300.41 246977[19:Rew:144658.0,246963.1,144694.0,246963.0] || member(regular(complement(u)),complement(complement(u)))* -> equal(complement(u),ordinal_numbers). % 300.04/300.41 247077[19:SpL:234713.0,238771.0] || equal(symmetric_difference(u,v),universal_class) -> subclass(universal_class,complement(intersection(u,v)))*. % 300.04/300.41 247078[19:SpL:237603.0,238771.0] || equal(successor(u),universal_class) -> subclass(universal_class,complement(intersection(u,singleton(u))))*. % 300.04/300.41 247476[19:Rew:142500.0,247354.1] || equal(u,universal_class) -> equal(complement(intersection(u,v)),symmetric_difference(u,v))**. % 300.04/300.41 247668[19:Rew:142500.0,247528.1] || equal(u,universal_class) -> equal(complement(intersection(v,u)),symmetric_difference(v,u))**. % 300.04/300.41 248150[19:SpL:30.0,245337.0] || equal(restrict(u,v,w),kind_1_ordinals)** -> member(ordinal_numbers,cross_product(v,w))*. % 300.04/300.41 248301[19:Res:248149.1,11848.0] || equal(u,kind_1_ordinals) subclass(u,v)* well_ordering(universal_class,v)* -> . % 300.04/300.41 248306[19:Res:248149.1,16105.1] || equal(intersection(u,v),kind_1_ordinals) member(ordinal_numbers,symmetric_difference(u,v))* -> . % 300.04/300.41 248321[19:Res:248149.1,9.0] || equal(unordered_pair(u,v),kind_1_ordinals)** -> equal(ordinal_numbers,v) equal(ordinal_numbers,u). % 300.04/300.41 248395[19:SpL:234713.0,245391.0] || equal(symmetric_difference(u,v),kind_1_ordinals) -> member(ordinal_numbers,complement(intersection(u,v)))*. % 300.04/300.41 248396[19:SpL:237603.0,245391.0] || equal(successor(u),kind_1_ordinals) -> member(ordinal_numbers,complement(intersection(u,singleton(u))))*. % 300.04/300.41 248481[25:SpR:204449.1,246387.1] function(u) || equal(complement(successor(u)),ordinal_numbers)** -> subclass(universal_class,u). % 300.04/300.41 248482[25:SpR:234134.1,246387.1] function(successor(u)) function(u) || -> subclass(successor(successor(u)),u)*. % 300.04/300.41 248485[25:Res:246387.1,167311.1] function(u) inductive(complement(complement(successor(u)))) || -> member(ordinal_numbers,u)*. % 300.04/300.41 248596[19:Res:217784.0,167311.1] inductive(intersection(symmetric_difference(u,inverse(u)),v)) || -> member(ordinal_numbers,symmetrization_of(u))*. % 300.04/300.41 248654[19:SpR:204449.1,217958.0] || equal(complement(symmetric_difference(u,v)),ordinal_numbers) -> subclass(universal_class,union(u,v))*. % 300.04/300.41 248658[19:Res:217958.0,167311.1] inductive(complement(complement(symmetric_difference(u,v)))) || -> member(ordinal_numbers,union(u,v))*. % 300.04/300.41 248729[19:Res:218724.0,167311.1] inductive(intersection(u,symmetric_difference(v,inverse(v)))) || -> member(ordinal_numbers,symmetrization_of(v))*. % 300.04/300.41 248809[0:Res:49.1,219712.0] inductive(complement(complement(u))) || -> subclass(image(successor_relation,complement(complement(u))),u)*. % 300.04/300.41 248864[0:Res:248818.0,1073.1] inductive(complement(successor(complement(omega)))) || -> equal(complement(successor(complement(omega))),omega)**. % 300.04/300.41 248881[0:Res:248818.0,2497.1] || member(u,universal_class) -> member(u,successor(complement(v)))* member(u,v). % 300.04/300.41 248981[0:Res:248819.0,1073.1] inductive(complement(symmetrization_of(complement(omega)))) || -> equal(complement(symmetrization_of(complement(omega))),omega)**. % 300.04/300.41 248998[0:Res:248819.0,2497.1] || member(u,universal_class) -> member(u,symmetrization_of(complement(v)))* member(u,v). % 300.04/300.41 249046[0:SpR:27.0,248816.0] || -> subclass(complement(union(u,union(v,w))),intersection(complement(v),complement(w)))*. % 300.04/300.41 249060[0:SpR:206408.0,248816.0] || -> subclass(complement(union(u,power_class(complement(power_class(v))))),image(element_relation,power_class(v)))*. % 300.04/300.41 249211[0:SpR:27.0,248817.0] || -> subclass(complement(union(union(u,v),w)),intersection(complement(u),complement(v)))*. % 300.04/300.41 249225[0:SpR:206408.0,248817.0] || -> subclass(complement(union(power_class(complement(power_class(u))),v)),image(element_relation,power_class(u)))*. % 300.04/300.41 249677[25:SpR:234134.1,248882.0] function(u) || -> subclass(complement(successor(complement(complement(successor(u))))),complement(u))*. % 300.04/300.41 249703[19:SpR:225013.1,248882.0] || equal(successor(successor(complement(complement(complement(u))))),ordinal_numbers)** -> subclass(universal_class,u). % 300.04/300.41 249794[25:SpR:234134.1,248999.0] function(u) || -> subclass(complement(symmetrization_of(complement(complement(successor(u))))),complement(u))*. % 300.04/300.41 249820[19:SpR:225013.1,248999.0] || equal(successor(symmetrization_of(complement(complement(complement(u))))),ordinal_numbers)** -> subclass(universal_class,u). % 300.04/300.41 250056[25:SpR:234134.1,248806.0] function(u) || -> member(v,successor(u)) subclass(singleton(v),complement(u))*. % 300.04/300.41 250082[0:Res:248806.0,2.0] || subclass(complement(u),v)* -> subclass(singleton(w),u)* member(w,v)*. % 300.04/300.41 250087[0:Res:248806.0,6432.1] || subclass(universal_class,complement(complement(u))) -> subclass(singleton(unordered_pair(v,w)),u)*. % 300.04/300.41 250088[19:Res:248806.0,167334.0] || -> subclass(singleton(regular(complement(complement(u)))),u)* equal(complement(complement(u)),ordinal_numbers). % 300.04/300.41 250093[0:Res:248806.0,6476.1] || subclass(universal_class,complement(complement(u))) -> subclass(singleton(ordered_pair(v,w)),u)*. % 300.04/300.41 250114[0:Res:248806.0,206414.0] || -> subclass(singleton(not_subclass_element(power_class(u),v)),power_class(u))* subclass(power_class(u),v). % 300.04/300.41 250327[20:Rew:234692.0,250316.0] || equal(successor(complement(intersection(complement(symmetrization_of(ordinal_numbers)),union(u,v)))),ordinal_numbers)** -> . % 300.04/300.41 250477[19:SpL:480.0,250367.0] || equal(complement(intersection(union(u,v),complement(complement(symmetrization_of(ordinal_numbers))))),ordinal_numbers)** -> . % 300.04/300.41 250491[19:SpL:481.0,250475.0] || equal(complement(intersection(complement(complement(symmetrization_of(ordinal_numbers))),union(u,v))),ordinal_numbers)** -> . % 300.04/300.41 250891[25:SpR:234134.1,248811.0] function(complement(u)) || -> subclass(complement(complement(complement(successor(complement(u))))),u)*. % 300.04/300.41 250902[19:SpR:204449.1,248811.0] || equal(complement(complement(complement(complement(complement(u))))),ordinal_numbers)** -> subclass(universal_class,u). % 300.04/300.41 250906[19:Res:248811.0,167311.1] inductive(complement(complement(complement(complement(complement(complement(u))))))) || -> member(ordinal_numbers,u)*. % 300.04/300.41 251497[25:SpR:234134.1,248783.0] function(complement(u)) || -> subclass(intersection(complement(successor(complement(u))),v),u)*. % 300.04/300.41 251526[19:Res:248783.0,167311.1] inductive(intersection(complement(complement(complement(complement(u)))),v)) || -> member(ordinal_numbers,u)*. % 300.04/300.41 251707[0:Rew:144658.0,251674.1,144694.0,251674.0] || -> member(not_subclass_element(u,complement(v)),complement(complement(v)))* subclass(u,complement(v)). % 300.04/300.41 251827[25:SpR:234134.1,248798.0] function(complement(u)) || -> subclass(intersection(v,complement(successor(complement(u)))),u)*. % 300.04/300.41 251850[19:Res:248798.0,167311.1] inductive(intersection(u,complement(complement(complement(complement(v)))))) || -> member(ordinal_numbers,v)*. % 300.04/300.41 251982[19:SpR:204449.1,248810.0] || equal(complement(intersection(u,complement(complement(v)))),ordinal_numbers)** -> subclass(universal_class,v). % 300.04/300.41 251986[19:Res:248810.0,167311.1] inductive(complement(complement(intersection(u,complement(complement(v)))))) || -> member(ordinal_numbers,v)*. % 300.04/300.41 252297[19:SpR:204449.1,248812.0] || equal(complement(intersection(complement(complement(u)),v)),ordinal_numbers)** -> subclass(universal_class,u). % 300.04/300.41 252301[19:Res:248812.0,167311.1] inductive(complement(complement(intersection(complement(complement(u)),v)))) || -> member(ordinal_numbers,u)*. % 300.04/300.41 252431[25:SpR:234134.1,249106.0] function(complement(u)) || -> subclass(complement(union(v,successor(complement(u)))),u)*. % 300.04/300.41 252443[19:SpR:204449.1,249106.0] || equal(union(u,complement(complement(complement(v)))),ordinal_numbers)** -> subclass(universal_class,v). % 300.04/300.41 252446[19:Res:249106.0,167311.1] inductive(complement(union(u,complement(complement(complement(v)))))) || -> member(ordinal_numbers,v)*. % 300.04/300.41 252677[25:SpR:234134.1,249272.0] function(complement(u)) || -> subclass(complement(union(successor(complement(u)),v)),u)*. % 300.04/300.41 252691[19:SpR:204449.1,249272.0] || equal(union(complement(complement(complement(u))),v),ordinal_numbers)** -> subclass(universal_class,u). % 300.04/300.41 252694[19:Res:249272.0,167311.1] inductive(complement(union(complement(complement(complement(u))),v))) || -> member(ordinal_numbers,u)*. % 300.04/300.41 252795[19:Res:250112.0,167311.1] inductive(singleton(not_subclass_element(u,ordinal_numbers))) || -> subclass(u,ordinal_numbers) member(ordinal_numbers,u)*. % 300.04/300.41 252838[22:MRR:252801.1,177216.0] inductive(singleton(not_subclass_element(omega,ordinal_numbers))) || -> equal(singleton(not_subclass_element(omega,ordinal_numbers)),omega)**. % 300.04/300.41 252891[19:SpR:204449.1,220180.1] || equal(complement(u),ordinal_numbers) subclass(u,v)* -> subclass(universal_class,v)*. % 300.04/300.41 252898[19:Res:220180.1,167311.1] inductive(complement(complement(u))) || subclass(u,v)* -> member(ordinal_numbers,v)*. % 300.04/300.41 252905[19:Res:220180.1,186989.0] || subclass(u,complement(complement(complement(u))))* -> equal(complement(complement(u)),ordinal_numbers). % 300.04/300.41 253078[18:SpL:125772.0,227961.1] || member(restrict(element_relation,universal_class,u),v)* member(v,sum_class(u)) -> . % 300.04/300.41 253081[18:SpL:125707.0,227961.1] || member(flip(cross_product(u,universal_class)),v)* member(v,inverse(u)) -> . % 300.04/300.41 253106[18:Res:12015.1,227961.1] || equal(complement(complement(cantor(u))),universal_class)** member(u,singleton(v))* -> . % 300.04/300.41 253121[19:Res:176345.1,227961.1] || subclass(domain_relation,cantor(u)) member(u,singleton(singleton(singleton(ordinal_numbers))))* -> . % 300.04/300.41 253123[19:Res:182463.1,227961.1] || equal(cantor(u),singleton(singleton(ordinal_numbers))) member(u,singleton(ordinal_numbers))* -> . % 300.04/300.41 253172[20:Res:181635.1,227961.1] || subclass(symmetrization_of(ordinal_numbers),cantor(u)) member(u,regular(symmetrization_of(ordinal_numbers)))* -> . % 300.04/300.41 253173[20:Res:175570.1,227961.1] || subclass(inverse(ordinal_numbers),cantor(u)) member(u,regular(symmetrization_of(ordinal_numbers)))* -> . % 300.04/300.41 12437[0:SpL:160.0,5472.0] || subclass(universal_class,symmetric_difference(u,v)) -> member(singleton(w),complement(intersection(u,v)))*. % 300.04/300.41 15958[0:SpL:160.0,12446.0] || equal(symmetric_difference(u,v),universal_class) -> member(singleton(w),complement(intersection(u,v)))*. % 300.04/300.41 16137[0:Res:16133.1,8.0] || member(u,v) subclass(v,singleton(u))* -> equal(v,singleton(u)). % 300.04/300.41 85190[8:SpL:27.0,85097.1] inductive(intersection(complement(u),complement(v))) || equal(union(u,v),universal_class)** -> . % 300.04/300.41 85702[0:SpL:4125.0,6300.0] || equal(symmetric_difference(complement(u),complement(v)),universal_class)** -> member(omega,union(u,v)). % 300.04/300.41 85730[0:SpL:4125.0,2539.0] || subclass(universal_class,symmetric_difference(complement(u),complement(v)))* -> member(omega,union(u,v)). % 300.04/300.41 48513[0:Rew:40.0,48486.0] || member(inverse(u),range_of(u)) -> member(ordered_pair(inverse(u),range_of(u)),element_relation)*. % 300.04/300.41 48877[0:Res:2481.1,16910.0] || subclass(universal_class,symmetric_difference(u,inverse(u)))* -> member(ordered_pair(v,w),symmetrization_of(u))*. % 300.04/300.41 12808[0:Res:2481.1,4127.0] || subclass(universal_class,symmetric_difference(u,v)) -> member(ordered_pair(w,x),union(u,v))*. % 300.04/300.41 6479[0:Res:2481.1,2.0] || subclass(universal_class,u)* subclass(u,v)* -> member(ordered_pair(w,x),v)*. % 300.04/300.41 48725[0:SpL:4105.0,6438.0] || subclass(universal_class,symmetric_difference(u,inverse(u)))* -> member(unordered_pair(v,w),symmetrization_of(u))*. % 300.04/300.41 12043[0:Res:12015.1,897.0] || equal(complement(complement(restrict(u,v,w))),universal_class)** -> member(singleton(x),u)*. % 300.04/300.41 80267[7:Res:80236.0,126.0] || subclass(domain_relation,u) well_ordering(v,u)* -> member(least(v,domain_relation),domain_relation)*. % 300.04/300.41 16450[0:Res:16280.0,8.0] || subclass(u,restrict(u,v,w))* -> equal(restrict(u,v,w),u). % 300.04/300.41 12443[0:SpL:30.0,5472.0] || subclass(universal_class,restrict(u,v,w))* -> member(singleton(x),cross_product(v,w))*. % 300.04/300.41 95570[0:Res:51413.0,25.1] || member(not_subclass_element(u,complement(complement(v))),v)* -> subclass(u,complement(complement(v))). % 300.04/300.41 95602[0:SpR:27.0,95593.1] || -> member(u,intersection(complement(v),complement(w)))* subclass(singleton(u),union(v,w)). % 300.04/300.41 105057[12:SpL:43.0,105054.0] || member(image(u,v),universal_class) member(restrict(u,v,universal_class),universal_class)* -> . % 300.04/300.41 110870[0:Res:36585.2,6476.1] || member(u,universal_class)* member(v,u)* subclass(universal_class,complement(element_relation))* -> . % 300.04/300.41 110883[0:Res:2523.2,6476.1] || member(u,universal_class)* subclass(rest_relation,v) subclass(universal_class,complement(v))* -> . % 300.04/300.41 110986[0:SpL:54.0,110864.0] || member(restrict(element_relation,universal_class,u),sum_class(u))* subclass(universal_class,complement(element_relation)) -> . % 300.04/300.41 110989[0:SpL:39.0,110864.0] || member(flip(cross_product(u,universal_class)),inverse(u))* subclass(universal_class,complement(element_relation)) -> . % 300.04/300.41 135286[0:Res:135236.0,8596.1] single_valued_class(complement(complement(cross_product(universal_class,universal_class)))) || -> function(complement(complement(cross_product(universal_class,universal_class))))*. % 300.04/300.41 135461[0:Res:36588.1,11848.0] || member(u,rest_of(u))* subclass(element_relation,v) well_ordering(universal_class,v)* -> . % 300.04/300.41 135462[8:Res:125926.1,11848.0] || member(u,cantor(u))* subclass(element_relation,v) well_ordering(universal_class,v)* -> . % 300.04/300.41 135884[0:Res:2479.1,16105.1] || subclass(universal_class,intersection(u,v)) member(singleton(w),symmetric_difference(u,v))* -> . % 300.04/300.41 135956[0:Res:2525.1,4178.0] || subclass(ordered_pair(u,v),singleton(w))* -> equal(unordered_pair(u,singleton(v)),w). % 300.04/300.41 137184[0:SpL:5132.1,137177.0] || well_ordering(universal_class,not_subclass_element(cross_product(u,v),w))* -> subclass(cross_product(u,v),w). % 300.04/300.41 137554[0:Res:7.1,15113.1] || equal(singleton(u),universal_class)** member(v,universal_class)* -> equal(sum_class(v),u)*. % 300.04/300.41 137587[0:Res:7.1,15079.1] || equal(singleton(u),universal_class)** member(v,universal_class)* -> equal(power_class(v),u)*. % 300.04/300.41 137605[0:Res:7.1,35668.0] || equal(u,rest_relation) well_ordering(v,u)* -> member(least(v,rest_relation),rest_relation)*. % 300.04/300.41 138787[0:Res:7.1,27170.1] || equal(cross_product(u,v),rest_relation)** member(w,universal_class)* -> member(w,u)*. % 300.04/300.41 138868[0:Res:7.1,26887.1] || equal(cross_product(u,v),domain_relation)** member(w,universal_class)* -> member(w,u)*. % 300.04/300.41 140564[0:Res:12807.1,6432.1] || subclass(universal_class,symmetric_difference(u,v)) subclass(universal_class,complement(union(u,v)))* -> . % 300.04/300.41 140632[0:Res:7.1,6435.0] || equal(u,universal_class) subclass(u,v)* -> member(unordered_pair(w,x),v)*. % 300.04/300.41 140707[0:SpR:44.0,35125.1] || member(u,universal_class) -> member(u,successor(v)) member(u,complement(singleton(v)))*. % 300.04/300.41 140708[0:SpR:114.0,35125.1] || member(u,universal_class) -> member(u,symmetrization_of(v)) member(u,complement(inverse(v)))*. % 300.04/300.41 140755[0:MRR:140729.0,12.0] || subclass(universal_class,complement(union(u,v)))* -> member(unordered_pair(w,x),complement(v))*. % 300.04/300.41 140757[0:MRR:140737.0,940.0] || subclass(universal_class,complement(union(u,v)))* -> member(ordered_pair(w,x),complement(v))*. % 300.04/300.41 140760[0:MRR:140739.0,36682.1] || -> member(not_subclass_element(u,union(v,w)),complement(w))* subclass(u,union(v,w)). % 300.04/300.41 140847[0:MRR:140824.0,12.0] || subclass(universal_class,complement(union(u,v)))* -> member(unordered_pair(w,x),complement(u))*. % 300.04/300.41 140849[0:MRR:140832.0,940.0] || subclass(universal_class,complement(union(u,v)))* -> member(ordered_pair(w,x),complement(u))*. % 300.04/300.41 140852[0:MRR:140834.0,36682.1] || -> member(not_subclass_element(u,union(v,w)),complement(v))* subclass(u,union(v,w)). % 300.04/300.41 146334[12:SpL:146278.0,104245.0] || member(sum_class(image(universal_class,u)),universal_class)* member(cross_product(u,universal_class),universal_class) -> . % 300.04/300.41 146477[0:Res:7.1,16469.0] || equal(singleton(u),v)* -> subclass(v,w) equal(not_subclass_element(v,w),u)*. % 300.04/300.41 148013[8:Res:147404.1,2.0] || member(u,element_relation)* subclass(compose(element_relation,universal_class),v)* -> member(u,v)*. % 300.04/300.41 148017[8:Res:147404.1,6432.1] || member(unordered_pair(u,v),element_relation)* subclass(universal_class,complement(compose(element_relation,universal_class)))* -> . % 300.04/300.41 148027[8:Res:147404.1,6476.1] || member(ordered_pair(u,v),element_relation)* subclass(universal_class,complement(compose(element_relation,universal_class)))* -> . % 300.04/300.41 148029[8:Res:147404.1,4.0] || member(not_subclass_element(u,compose(element_relation,universal_class)),element_relation)* -> subclass(u,compose(element_relation,universal_class)). % 300.04/300.41 148563[0:Res:12015.1,3975.0] || equal(complement(complement(compose_class(u))),universal_class) -> equal(compose(u,singleton(v)),v)**. % 300.04/300.41 149440[0:SpR:149012.1,27.0] || subclass(complement(u),complement(v))* -> equal(union(v,u),complement(complement(u))). % 300.04/300.41 152480[0:Res:52.1,16466.0] inductive(intersection(u,v)) || -> subclass(omega,w) member(not_subclass_element(omega,w),v)*. % 300.04/300.41 152765[0:Res:52.1,16465.0] inductive(intersection(u,v)) || -> subclass(omega,w) member(not_subclass_element(omega,w),u)*. % 300.04/300.41 152779[0:Res:137025.0,16465.0] || -> subclass(complement(successor(u)),v) member(not_subclass_element(complement(successor(u)),v),complement(u))*. % 300.04/300.41 152780[0:Res:137026.0,16465.0] || -> subclass(complement(symmetrization_of(u)),v) member(not_subclass_element(complement(symmetrization_of(u)),v),complement(u))*. % 300.04/300.41 134805[3:Res:134636.1,2500.1] || subclass(unordered_pair(u,v),ordinal_numbers)* member(u,universal_class) -> member(u,kind_1_ordinals). % 300.04/300.41 134807[3:Res:134636.1,2501.1] || subclass(unordered_pair(u,v),ordinal_numbers)* member(v,universal_class) -> member(v,kind_1_ordinals). % 300.04/300.41 160102[8:SpR:80471.0,35125.1] || member(u,universal_class) -> member(u,kind_1_ordinals) member(u,complement(image(successor_relation,ordinal_numbers)))*. % 300.04/300.41 110863[0:Res:98.1,6476.1] || member(ordered_pair(u,v),cross_product(universal_class,universal_class))* subclass(universal_class,complement(composition_function)) -> . % 300.04/300.41 135366[0:Res:280.1,11848.0] || member(u,universal_class) subclass(singleton(u),v)* well_ordering(universal_class,v) -> . % 300.04/300.41 137892[0:Res:7.1,9833.0] || equal(u,universal_class) well_ordering(v,u)* -> member(least(v,universal_class),universal_class)*. % 300.04/300.41 137614[0:Res:137603.1,2.0] || well_ordering(u,universal_class) subclass(rest_relation,v) -> member(least(u,rest_relation),v)*. % 300.04/300.41 137628[0:Res:137613.1,2.0] || well_ordering(u,universal_class) subclass(universal_class,v) -> member(least(u,rest_relation),v)*. % 300.04/300.41 137901[0:Res:137890.1,2.0] || well_ordering(u,universal_class) subclass(universal_class,v) -> member(least(u,universal_class),v)*. % 300.04/300.41 137621[0:Res:137606.1,2.0] || well_ordering(u,rest_relation) subclass(rest_relation,v) -> member(least(u,rest_relation),v)*. % 300.04/300.41 137642[0:Res:137620.1,2.0] || well_ordering(u,rest_relation) subclass(universal_class,v) -> member(least(u,rest_relation),v)*. % 300.04/300.41 166623[8:Res:166605.0,2.0] || subclass(inverse(singleton(u)),v)* -> asymmetric(singleton(u),w)* member(u,v). % 300.04/300.41 166624[8:Res:166605.0,5467.1] || subclass(universal_class,complement(inverse(singleton(singleton(u)))))* -> asymmetric(singleton(singleton(u)),v)*. % 300.04/300.41 167392[19:Rew:166997.0,98567.1] || subclass(domain_relation,complement(complement(intersection(u,v))))* -> member(ordered_pair(ordinal_numbers,ordinal_numbers),u). % 300.04/300.41 167393[19:Rew:166997.0,98562.1] || subclass(domain_relation,complement(complement(complement(u))))* member(ordered_pair(ordinal_numbers,ordinal_numbers),u) -> . % 300.04/300.41 167394[19:Rew:166997.0,84329.2] || equal(rest_relation,domain_relation) subclass(rest_relation,u) -> member(ordered_pair(ordinal_numbers,ordinal_numbers),u)*. % 300.04/300.41 167408[19:Rew:166997.0,98568.1] || subclass(domain_relation,complement(complement(intersection(u,v))))* -> member(ordered_pair(ordinal_numbers,ordinal_numbers),v). % 300.04/300.41 167409[19:Rew:166997.0,84226.2] || subclass(domain_relation,u)* subclass(u,v)* -> member(ordered_pair(ordinal_numbers,ordinal_numbers),v)*. % 300.04/300.41 167426[19:Rew:166997.0,84237.1] || subclass(domain_relation,symmetric_difference(u,v)) -> member(ordered_pair(ordinal_numbers,ordinal_numbers),union(u,v))*. % 300.04/300.41 167427[19:Rew:166997.0,84238.1] || subclass(domain_relation,symmetric_difference(u,inverse(u)))* -> member(ordered_pair(ordinal_numbers,ordinal_numbers),symmetrization_of(u))*. % 300.04/300.41 169328[19:Rew:166997.0,167540.1] || equal(intersection(u,v),singleton(ordinal_numbers)) member(ordinal_numbers,symmetric_difference(u,v))* -> . % 300.04/300.41 169329[19:Rew:166997.0,167543.1] || equal(restrict(u,v,w),singleton(ordinal_numbers))** -> member(ordinal_numbers,cross_product(v,w))*. % 300.04/300.41 167549[19:Rew:166997.0,162721.0] || equal(u,singleton(ordinal_numbers)) subclass(u,v)* well_ordering(universal_class,v)* -> . % 300.04/300.41 169330[19:Rew:166997.0,167554.2,166997.0,167554.1] || equal(unordered_pair(u,v),singleton(ordinal_numbers))** -> equal(ordinal_numbers,v) equal(ordinal_numbers,u). % 300.04/300.41 169334[19:Rew:166997.0,167654.1] inductive(complement(compose(element_relation,universal_class))) || member(ordinal_numbers,element_relation)* -> member(ordinal_numbers,u)*. % 300.04/300.41 169335[19:Rew:166997.0,167666.0] || member(not_subclass_element(u,ordinal_numbers),singleton(v))* -> member(v,u) subclass(u,ordinal_numbers). % 300.04/300.41 167689[19:Rew:166997.0,163743.1] || subclass(u,complement(complement(v)))* -> equal(u,ordinal_numbers) member(regular(u),v). % 300.04/300.41 167779[19:Rew:166997.0,83656.1] || subclass(omega,singleton(u))* -> equal(integer_of(u),ordinal_numbers) equal(singleton(u),omega). % 300.04/300.41 167949[19:Rew:166997.0,163357.1] || subclass(omega,complement(complement(u)))* -> equal(integer_of(v),ordinal_numbers) member(v,u)*. % 300.04/300.41 167980[19:Rew:166997.0,93849.1] || equal(symmetric_difference(complement(u),complement(v)),universal_class)** -> member(ordinal_numbers,union(u,v)). % 300.04/300.41 167981[19:Rew:166997.0,93622.1] || subclass(universal_class,symmetric_difference(complement(u),complement(v)))* -> member(ordinal_numbers,union(u,v)). % 300.04/300.41 168217[19:Rew:166997.0,98594.1] || subclass(domain_relation,complement(complement(rest_of(u))))* -> equal(restrict(u,ordinal_numbers,universal_class),ordinal_numbers). % 300.04/300.41 168328[19:Rew:166997.0,99179.0] || -> equal(complement(complement(singleton(u))),ordinal_numbers) equal(regular(complement(complement(singleton(u)))),u)**. % 300.04/300.41 168333[19:Rew:166997.0,158131.1] inductive(symmetric_difference(universal_class,union(identity_relation,u))) || -> member(ordinal_numbers,complement(complement(complement(u))))*. % 300.04/300.41 169358[19:Rew:166997.0,168357.2,166997.0,168357.1] || connected(ordinal_numbers,u) member(v,not_well_ordering(ordinal_numbers,u))* -> well_ordering(ordinal_numbers,u). % 300.04/300.41 168427[19:Rew:166997.0,164863.1] || well_ordering(universal_class,union(u,v)) -> member(ordinal_numbers,intersection(complement(u),complement(v)))*. % 300.04/300.41 168429[19:Rew:166997.0,163244.1] inductive(complement(union(u,v))) || -> member(ordinal_numbers,intersection(complement(u),complement(v)))*. % 300.04/300.41 168468[19:Rew:166997.0,163648.2] || subclass(u,v)* well_ordering(universal_class,v)* -> equal(intersection(w,u),ordinal_numbers)**. % 300.04/300.41 168473[19:Rew:166997.0,163530.2] || subclass(u,v)* well_ordering(universal_class,v)* -> equal(intersection(u,w),ordinal_numbers)**. % 300.04/300.41 168736[19:Rew:166997.0,159733.0] || -> equal(integer_of(not_subclass_element(u,intersection(omega,u))),ordinal_numbers)** subclass(u,intersection(omega,u)). % 300.04/300.41 168747[19:Rew:166997.0,160279.0] || subclass(not_subclass_element(cross_product(u,v),w),ordinal_numbers)* -> subclass(cross_product(u,v),w). % 300.04/300.41 168748[19:Rew:166997.0,160295.0] || equal(not_subclass_element(cross_product(u,v),w),ordinal_numbers)** -> subclass(cross_product(u,v),w). % 300.04/300.41 168909[19:Rew:166997.0,163245.1] inductive(complement(successor(u))) || -> member(ordinal_numbers,intersection(complement(u),complement(singleton(u))))*. % 300.04/300.41 168910[19:Rew:166997.0,163246.1] inductive(complement(symmetrization_of(u))) || -> member(ordinal_numbers,intersection(complement(u),complement(inverse(u))))*. % 300.04/300.41 168961[19:Rew:166997.0,164602.1] || member(restrict(u,v,universal_class),universal_class)* -> equal(singleton(image(u,v)),ordinal_numbers). % 300.04/300.41 168975[19:Rew:166997.0,164706.1] || member(restrict(u,v,universal_class),universal_class)* -> equal(integer_of(image(u,v)),ordinal_numbers). % 300.04/300.41 168978[19:Rew:166997.0,165124.1] || asymmetric(universal_class,singleton(u)) -> equal(segment(inverse(universal_class),singleton(u),u),ordinal_numbers)**. % 300.04/300.41 169490[19:MRR:167911.3,167057.0] || equal(sum_class(u),ordinal_numbers) member(u,universal_class) well_ordering(element_relation,u)* -> . % 300.04/300.41 169653[19:MRR:168405.1,168405.3,167011.0,167057.0] || equal(apply(u,v),ordinal_numbers) well_ordering(element_relation,image(u,singleton(v)))* -> . % 300.04/300.41 168148[19:Rew:166997.0,160508.0] || -> subclass(symmetric_difference(symmetrization_of(ordinal_numbers),complement(inverse(complement(inverse(ordinal_numbers))))),symmetrization_of(complement(inverse(ordinal_numbers))))*. % 300.04/300.41 168147[19:Rew:166997.0,160503.0] || -> subclass(symmetric_difference(symmetrization_of(ordinal_numbers),complement(singleton(complement(inverse(ordinal_numbers))))),successor(complement(inverse(ordinal_numbers))))*. % 300.04/300.41 169336[19:Rew:166997.0,167679.2,166997.0,167679.0] || subclass(u,symmetrization_of(ordinal_numbers)) -> equal(u,ordinal_numbers) member(regular(u),inverse(ordinal_numbers))*. % 300.04/300.41 169355[19:Rew:166997.0,168150.1] || member(not_subclass_element(symmetrization_of(ordinal_numbers),u),complement(inverse(ordinal_numbers)))* -> subclass(symmetrization_of(ordinal_numbers),u). % 300.04/300.41 169350[19:Rew:166997.0,168026.0] || -> member(u,image(element_relation,symmetrization_of(ordinal_numbers))) subclass(singleton(u),power_class(complement(inverse(ordinal_numbers))))*. % 300.04/300.41 169351[19:Rew:166997.0,168030.1] || well_ordering(universal_class,power_class(complement(inverse(ordinal_numbers))))* -> member(ordinal_numbers,image(element_relation,symmetrization_of(ordinal_numbers))). % 300.04/300.41 174583[19:Res:168102.0,167311.1] inductive(complement(power_class(complement(inverse(ordinal_numbers))))) || -> member(ordinal_numbers,image(element_relation,symmetrization_of(ordinal_numbers)))*. % 300.04/300.41 169353[19:Rew:166997.0,168101.1] || -> subclass(u,complement(symmetrization_of(ordinal_numbers))) member(not_subclass_element(u,complement(symmetrization_of(ordinal_numbers))),inverse(ordinal_numbers))*. % 300.04/300.41 168029[19:Rew:166997.0,166925.1] inductive(image(element_relation,symmetrization_of(identity_relation))) || equal(power_class(complement(inverse(ordinal_numbers))),universal_class)** -> . % 300.04/300.41 174434[19:SpL:167200.0,85097.1] inductive(image(element_relation,symmetrization_of(ordinal_numbers))) || equal(power_class(complement(inverse(ordinal_numbers))),universal_class)** -> . % 300.04/300.41 175803[21:Res:7.1,175799.0] || equal(u,omega) well_ordering(v,u)* -> member(least(v,omega),omega)*. % 300.04/300.41 176107[20:Res:175613.1,2.0] || subclass(universal_class,u)* subclass(u,v)* -> member(regular(symmetrization_of(ordinal_numbers)),v)*. % 300.04/300.41 176113[20:Res:175613.1,4127.0] || subclass(universal_class,symmetric_difference(u,v)) -> member(regular(symmetrization_of(ordinal_numbers)),union(u,v))*. % 300.04/300.41 176115[20:Res:175613.1,16910.0] || subclass(universal_class,symmetric_difference(u,inverse(u)))* -> member(regular(symmetrization_of(ordinal_numbers)),symmetrization_of(u))*. % 300.04/300.41 176156[21:Res:175802.1,2.0] || well_ordering(u,universal_class) subclass(omega,v) -> member(least(u,omega),v)*. % 300.04/300.41 176163[21:Res:175804.1,2.0] || well_ordering(u,omega) subclass(omega,v) -> member(least(u,omega),v)*. % 300.04/300.41 176183[21:Res:176155.1,2.0] || well_ordering(u,universal_class) subclass(universal_class,v) -> member(least(u,omega),v)*. % 300.04/300.41 176189[21:Res:176162.1,2.0] || well_ordering(u,omega) subclass(universal_class,v) -> member(least(u,omega),v)*. % 300.04/300.41 176370[19:Res:66.2,176206.0] function(u) || member(v,universal_class) -> equal(cantor(image(u,v)),ordinal_numbers)**. % 300.04/300.41 176445[19:MRR:176393.1,5.0] || member(u,universal_class) -> equal(u,ordinal_numbers) equal(cantor(apply(choice,u)),ordinal_numbers)**. % 300.04/300.41 177075[19:MRR:177044.3,167057.0] || member(u,universal_class)* subclass(rest_relation,rest_of(v))* -> equal(singleton(v),ordinal_numbers). % 300.04/300.41 177150[19:MRR:177122.3,167057.0] || member(u,universal_class)* subclass(rest_relation,rest_of(regular(v)))* -> equal(v,ordinal_numbers). % 300.04/300.41 177197[22:Res:177171.1,16102.0] || subclass(omega,symmetric_difference(complement(u),complement(v)))* -> member(ordinal_numbers,union(u,v)). % 300.04/300.41 177597[19:SpR:69.0,176366.1] || member(image(u,singleton(v)),universal_class)* -> equal(cantor(apply(u,v)),ordinal_numbers). % 300.04/300.41 177969[19:MRR:177965.0,99.0] || subclass(composition_function,u) well_ordering(v,u)* -> member(least(v,composition_function),composition_function)*. % 300.04/300.41 178378[22:SpL:27.0,178292.1] inductive(intersection(complement(u),complement(v))) || equal(union(u,v),omega)** -> . % 300.04/300.41 178423[19:SpL:168412.1,9769.0] || equal(complement(regular(cross_product(u,v))),universal_class)** -> equal(cross_product(u,v),ordinal_numbers). % 300.04/300.41 178424[19:SpL:168412.1,9712.0] || subclass(universal_class,complement(regular(cross_product(u,v))))* -> equal(cross_product(u,v),ordinal_numbers). % 300.04/300.41 178891[22:SpL:4125.0,178812.0] || equal(symmetric_difference(complement(u),complement(v)),omega)** -> member(ordinal_numbers,union(u,v)). % 300.04/300.41 179119[19:SpL:168799.0,85097.1] inductive(image(element_relation,successor(ordinal_numbers))) || equal(power_class(complement(singleton(ordinal_numbers))),universal_class)** -> . % 300.04/300.41 179152[22:SpL:168799.0,178292.1] inductive(image(element_relation,successor(ordinal_numbers))) || equal(power_class(complement(singleton(ordinal_numbers))),omega)** -> . % 300.04/300.41 179382[22:SpL:167200.0,178292.1] inductive(image(element_relation,symmetrization_of(ordinal_numbers))) || equal(power_class(complement(inverse(ordinal_numbers))),omega)** -> . % 300.04/300.41 180169[19:Rew:180089.0,179109.0] || -> member(u,image(element_relation,singleton(ordinal_numbers))) subclass(singleton(u),power_class(complement(singleton(ordinal_numbers))))*. % 300.04/300.41 180204[19:Rew:180089.0,179146.1] || well_ordering(universal_class,power_class(complement(singleton(ordinal_numbers))))* -> member(ordinal_numbers,image(element_relation,singleton(ordinal_numbers))). % 300.04/300.41 180206[19:Rew:180089.0,179069.1] inductive(complement(power_class(complement(singleton(ordinal_numbers))))) || -> member(ordinal_numbers,image(element_relation,singleton(ordinal_numbers)))*. % 300.04/300.41 180298[19:Rew:180089.0,168815.0] || -> subclass(symmetric_difference(singleton(ordinal_numbers),complement(inverse(complement(singleton(ordinal_numbers))))),symmetrization_of(complement(singleton(ordinal_numbers))))*. % 300.04/300.41 180299[19:Rew:180089.0,168816.0] || -> subclass(symmetric_difference(singleton(ordinal_numbers),complement(singleton(complement(singleton(ordinal_numbers))))),successor(complement(singleton(ordinal_numbers))))*. % 300.04/300.41 180757[19:SpL:180125.0,85097.1] inductive(image(element_relation,singleton(ordinal_numbers))) || equal(power_class(complement(singleton(ordinal_numbers))),universal_class)** -> . % 300.04/300.41 180791[22:SpL:180125.0,178292.1] inductive(image(element_relation,singleton(ordinal_numbers))) || equal(power_class(complement(singleton(ordinal_numbers))),omega)** -> . % 300.04/300.41 181316[19:SpR:146278.0,168752.1] || member(cross_product(u,universal_class),universal_class) -> equal(singleton(sum_class(image(universal_class,u))),ordinal_numbers)**. % 300.04/300.41 181434[19:SpR:146278.0,168753.1] || member(cross_product(u,universal_class),universal_class) -> equal(integer_of(sum_class(image(universal_class,u))),ordinal_numbers)**. % 300.04/300.41 181532[20:MRR:181531.2,175557.0] || member(symmetrization_of(ordinal_numbers),universal_class) -> subclass(singleton(apply(choice,symmetrization_of(ordinal_numbers))),symmetrization_of(ordinal_numbers))*. % 300.04/300.41 181726[20:Res:175570.1,11848.0] || subclass(inverse(ordinal_numbers),u)* subclass(u,v)* well_ordering(universal_class,v)* -> . % 300.04/300.41 181748[20:Res:175570.1,897.0] || subclass(inverse(ordinal_numbers),restrict(u,v,w))* -> member(regular(symmetrization_of(ordinal_numbers)),u). % 300.04/300.41 181752[20:Res:175570.1,110865.0] || subclass(inverse(ordinal_numbers),rest_of(regular(symmetrization_of(ordinal_numbers))))* subclass(universal_class,complement(element_relation)) -> . % 300.04/300.41 181753[20:Res:175570.1,158.0] || subclass(inverse(ordinal_numbers),omega) -> equal(integer_of(regular(symmetrization_of(ordinal_numbers))),regular(symmetrization_of(ordinal_numbers)))**. % 300.04/300.41 181779[19:SpL:146278.0,176272.1] || member(cross_product(u,universal_class),universal_class)* equal(sum_class(image(universal_class,u)),ordinal_numbers) -> . % 300.04/300.41 181809[19:Res:176345.1,897.0] || subclass(domain_relation,restrict(u,v,w))* -> member(singleton(singleton(singleton(ordinal_numbers))),u)*. % 300.04/300.41 182487[19:Res:182467.1,11848.0] || subclass(complement(u),v)* well_ordering(universal_class,v) -> member(singleton(ordinal_numbers),u)*. % 300.04/300.41 182491[19:Res:182467.1,2.0] || subclass(complement(u),v)* -> member(singleton(ordinal_numbers),u)* member(singleton(ordinal_numbers),v)*. % 300.04/300.41 182878[19:Res:182871.1,2.0] || member(u,inverse(ordinal_numbers))* subclass(symmetrization_of(ordinal_numbers),v)* -> member(u,v)*. % 300.04/300.41 182883[19:Res:182871.1,6432.1] || member(unordered_pair(u,v),inverse(ordinal_numbers))* subclass(universal_class,complement(symmetrization_of(ordinal_numbers))) -> . % 300.04/300.41 182889[19:Res:182871.1,6476.1] || member(ordered_pair(u,v),inverse(ordinal_numbers))* subclass(universal_class,complement(symmetrization_of(ordinal_numbers))) -> . % 300.04/300.41 182907[20:Res:181635.1,11848.0] || subclass(symmetrization_of(ordinal_numbers),u)* subclass(u,v)* well_ordering(universal_class,v)* -> . % 300.04/300.41 182929[20:Res:181635.1,897.0] || subclass(symmetrization_of(ordinal_numbers),restrict(u,v,w))* -> member(regular(symmetrization_of(ordinal_numbers)),u). % 300.04/300.41 182933[20:Res:181635.1,110865.0] || subclass(symmetrization_of(ordinal_numbers),rest_of(regular(symmetrization_of(ordinal_numbers))))* subclass(universal_class,complement(element_relation)) -> . % 300.04/300.41 182934[20:Res:181635.1,158.0] || subclass(symmetrization_of(ordinal_numbers),omega) -> equal(integer_of(regular(symmetrization_of(ordinal_numbers))),regular(symmetrization_of(ordinal_numbers)))**. % 300.04/300.41 183035[19:SpL:176364.1,182439.1] || subclass(rest_relation,rest_of(u))* well_ordering(universal_class,ordinal_numbers) -> equal(singleton(u),ordinal_numbers). % 300.04/300.41 183037[19:SpL:125772.0,182439.1] || subclass(rest_relation,rest_of(restrict(element_relation,universal_class,u)))* well_ordering(universal_class,sum_class(u)) -> . % 300.04/300.41 183039[19:SpL:125707.0,182439.1] || subclass(rest_relation,rest_of(flip(cross_product(u,universal_class))))* well_ordering(universal_class,inverse(u)) -> . % 300.04/300.41 183045[19:SpL:176380.1,182439.1] || subclass(rest_relation,rest_of(regular(u)))* well_ordering(universal_class,ordinal_numbers) -> equal(u,ordinal_numbers). % 300.04/300.41 183109[19:Res:182463.1,897.0] || equal(restrict(u,v,w),singleton(singleton(ordinal_numbers)))** -> member(singleton(ordinal_numbers),u). % 300.04/300.41 183113[19:Res:182463.1,110865.0] || equal(rest_of(singleton(ordinal_numbers)),singleton(singleton(ordinal_numbers))) subclass(universal_class,complement(element_relation))* -> . % 300.04/300.41 183363[8:SpR:125772.0,131984.1] || equal(complement(rest_of(restrict(element_relation,universal_class,u))),universal_class)** -> subclass(sum_class(u),v)*. % 300.04/300.41 183365[8:SpR:125707.0,131984.1] || equal(complement(rest_of(flip(cross_product(u,universal_class)))),universal_class)** -> subclass(inverse(u),v)*. % 300.04/300.41 183473[19:Res:148590.0,167311.1] inductive(symmetric_difference(u,complement(complement(u)))) || -> member(ordinal_numbers,complement(complement(complement(u))))*. % 300.04/300.41 183571[19:Res:168184.0,11848.0] || subclass(u,v)* well_ordering(universal_class,v)* -> equal(complement(complement(u)),ordinal_numbers)**. % 300.04/300.41 183711[19:SpL:160.0,169224.0] || equal(symmetric_difference(u,v),singleton(ordinal_numbers)) -> member(ordinal_numbers,complement(intersection(u,v)))*. % 300.04/300.41 183977[23:Rew:183885.0,181302.1] || member(u,universal_class) -> equal(apply(v,sum_class(range_of(u))),apply(v,universal_class))**. % 300.04/300.41 183988[23:Rew:183883.0,181300.1] || member(u,universal_class) -> equal(ordered_pair(v,sum_class(range_of(u))),ordered_pair(v,universal_class))**. % 300.04/300.41 184034[23:Rew:183840.0,183889.0] || asymmetric(u,ordinal_numbers) -> equal(segment(intersection(u,inverse(u)),ordinal_numbers,universal_class),ordinal_numbers)**. % 300.04/300.41 184170[23:SpL:183857.0,97.0] || member(ordered_pair(u,singleton(singleton(ordinal_numbers))),composition_function)* -> equal(compose(u,ordinal_numbers),universal_class). % 300.04/300.41 184177[23:MRR:184176.0,167011.0] || member(singleton(singleton(ordinal_numbers)),cross_product(universal_class,universal_class))* -> member(singleton(singleton(ordinal_numbers)),element_relation). % 300.04/300.41 184268[23:SpL:183885.0,178138.1] || member(image(u,ordinal_numbers),universal_class)* equal(rest_of(apply(u,universal_class)),rest_relation) -> . % 300.04/300.41 184269[23:Rew:183885.0,184251.0] || equal(apply(u,universal_class),ordinal_numbers) -> subclass(apply(u,universal_class),image(u,ordinal_numbers))*. % 300.04/300.41 184393[19:Res:55.1,176273.0] || member(u,universal_class) subclass(domain_relation,rest_relation) -> equal(rest_of(sum_class(u)),ordinal_numbers)**. % 300.04/300.41 184394[19:Res:57.1,176273.0] || member(u,universal_class) subclass(domain_relation,rest_relation) -> equal(rest_of(power_class(u)),ordinal_numbers)**. % 300.04/300.41 184395[19:Res:15058.1,176273.0] function(u) || subclass(domain_relation,rest_relation) -> equal(rest_of(apply(u,v)),ordinal_numbers)**. % 300.04/300.41 184396[19:Res:36682.1,176273.0] || subclass(domain_relation,rest_relation) -> subclass(u,v) equal(rest_of(not_subclass_element(u,v)),ordinal_numbers)**. % 300.04/300.41 184498[19:MRR:184453.1,53.0] || equal(rest_relation,domain_relation) subclass(rest_relation,u) -> member(ordered_pair(omega,ordinal_numbers),u)*. % 300.04/300.41 184525[19:Res:55.1,176274.0] || member(u,universal_class) subclass(rest_relation,domain_relation) -> equal(rest_of(sum_class(u)),ordinal_numbers)**. % 300.04/300.41 184526[19:Res:57.1,176274.0] || member(u,universal_class) subclass(rest_relation,domain_relation) -> equal(rest_of(power_class(u)),ordinal_numbers)**. % 300.04/300.41 184527[19:Res:15058.1,176274.0] function(u) || subclass(rest_relation,domain_relation) -> equal(rest_of(apply(u,v)),ordinal_numbers)**. % 300.04/300.41 184528[19:Res:36682.1,176274.0] || subclass(rest_relation,domain_relation) -> subclass(u,v) equal(rest_of(not_subclass_element(u,v)),ordinal_numbers)**. % 300.04/300.41 184823[19:SpR:946.0,176419.1] || subclass(domain_relation,flip(u)) -> member(ordered_pair(singleton(singleton(singleton(v))),ordinal_numbers),u)*. % 300.04/300.41 184834[19:Res:176419.1,11848.0] || subclass(domain_relation,flip(u))* subclass(u,v)* well_ordering(universal_class,v)* -> . % 300.04/300.41 184843[19:Res:176419.1,4178.0] || subclass(domain_relation,flip(singleton(u)))* -> equal(ordered_pair(ordered_pair(v,w),ordinal_numbers),u)*. % 300.04/300.41 184881[19:Res:176419.1,94.0] || subclass(domain_relation,flip(compose_class(u))) -> equal(compose(u,ordered_pair(v,w)),ordinal_numbers)**. % 300.04/300.41 184887[19:Res:176419.1,34.0] || subclass(domain_relation,flip(rotate(u))) -> member(ordered_pair(ordered_pair(v,ordinal_numbers),w),u)*. % 300.04/300.41 184888[19:Res:176419.1,37.0] || subclass(domain_relation,flip(flip(u))) -> member(ordered_pair(ordered_pair(v,w),ordinal_numbers),u)*. % 300.04/300.41 184905[19:SpR:946.0,176420.1] || subclass(domain_relation,rotate(u)) -> member(ordered_pair(singleton(singleton(singleton(ordinal_numbers))),v),u)*. % 300.04/300.41 184912[19:Res:176420.1,11848.0] || subclass(domain_relation,rotate(u))* subclass(u,v)* well_ordering(universal_class,v)* -> . % 300.04/300.41 184921[19:Res:176420.1,4178.0] || subclass(domain_relation,rotate(singleton(u)))* -> equal(ordered_pair(ordered_pair(v,ordinal_numbers),w),u)*. % 300.04/300.41 184959[19:Res:176420.1,94.0] || subclass(domain_relation,rotate(compose_class(u))) -> equal(compose(u,ordered_pair(v,ordinal_numbers)),w)*. % 300.04/300.41 184969[19:Res:176420.1,34.0] || subclass(domain_relation,rotate(rotate(u))) -> member(ordered_pair(ordered_pair(ordinal_numbers,v),w),u)*. % 300.04/300.41 184970[19:Res:176420.1,37.0] || subclass(domain_relation,rotate(flip(u))) -> member(ordered_pair(ordered_pair(ordinal_numbers,v),w),u)*. % 300.04/300.41 185298[23:Res:185235.1,2.0] || subclass(rest_relation,domain_relation) subclass(rest_relation,u) -> member(ordered_pair(ordinal_numbers,ordinal_numbers),u)*. % 300.04/300.41 185809[0:Res:12.0,30589.0] || subclass(rest_relation,successor_relation) -> equal(rest_of(unordered_pair(u,v)),successor(unordered_pair(u,v)))**. % 300.04/300.41 185810[0:Res:940.0,30589.0] || subclass(rest_relation,successor_relation) -> equal(rest_of(ordered_pair(u,v)),successor(ordered_pair(u,v)))**. % 300.04/300.41 185811[19:Res:167224.0,30589.0] || subclass(rest_relation,successor_relation)* -> equal(singleton(u),ordinal_numbers) equal(rest_of(u),successor(u))**. % 300.04/300.41 185812[19:Res:167115.1,30589.0] || subclass(rest_relation,successor_relation)* -> equal(integer_of(u),ordinal_numbers)** equal(rest_of(u),successor(u)). % 300.04/300.41 185828[20:Res:175569.0,30589.0] || subclass(rest_relation,successor_relation) -> equal(rest_of(regular(symmetrization_of(ordinal_numbers))),successor(regular(symmetrization_of(ordinal_numbers))))**. % 300.04/300.41 186301[19:Obv:186296.1] || subclass(singleton(u),omega)* -> equal(singleton(u),ordinal_numbers) equal(integer_of(u),u). % 300.04/300.41 186402[19:Res:7.1,167960.0] || equal(complement(u),omega) member(v,u)* -> equal(integer_of(v),ordinal_numbers). % 300.04/300.41 186407[19:SpR:146278.0,168950.1] || member(cross_product(u,universal_class),universal_class) -> member(ordinal_numbers,ordered_pair(image(universal_class,u),v))*. % 300.04/300.41 186416[19:Res:168950.1,169221.1] || member(u,universal_class) equal(complement(ordered_pair(range_of(u),v)),singleton(ordinal_numbers))** -> . % 300.04/300.41 186970[19:Res:167116.0,167734.1] || subclass(u,complement(omega))* -> equal(integer_of(regular(u)),ordinal_numbers) equal(u,ordinal_numbers). % 300.04/300.41 187245[19:Res:7.1,168376.0] || equal(intersection(u,v),omega)** -> equal(integer_of(w),ordinal_numbers) member(w,v)*. % 300.04/300.41 187332[19:Res:7.1,168377.0] || equal(intersection(u,v),omega)** -> equal(integer_of(w),ordinal_numbers) member(w,u)*. % 300.04/300.41 187565[19:Res:7.1,167736.0] || equal(intersection(u,v),w)* -> equal(w,ordinal_numbers) member(regular(w),u)*. % 300.04/300.41 187647[19:Res:7.1,167737.0] || equal(intersection(u,v),w)* -> equal(w,ordinal_numbers) member(regular(w),v)*. % 300.04/300.41 187663[19:Res:137025.0,167737.0] || -> equal(complement(successor(u)),ordinal_numbers) member(regular(complement(successor(u))),complement(singleton(u)))*. % 300.04/300.41 187664[19:Res:137026.0,167737.0] || -> equal(complement(symmetrization_of(u)),ordinal_numbers) member(regular(complement(symmetrization_of(u))),complement(inverse(u)))*. % 300.04/300.41 187698[19:Res:177822.1,169221.1] || equal(complement(ordered_pair(inverse(u),v)),singleton(ordinal_numbers))** -> equal(range_of(u),ordinal_numbers). % 300.04/300.41 187785[19:SpL:167004.0,178140.1] function(recursion(u,successor_relation,ordinal_numbers)) || equal(rest_of(ordinal_add(u,v)),rest_relation)** -> . % 300.04/300.41 187960[19:Res:182559.1,167311.1] inductive(symmetric_difference(u,universal_class)) || -> equal(singleton(u),ordinal_numbers) member(ordinal_numbers,complement(u))*. % 300.04/300.41 188621[2:Res:26.2,188593.1] || member(u,universal_class)* equal(complement(complement(v)),universal_class)** -> member(u,v)*. % 300.04/300.41 188749[2:Res:2523.2,188593.1] || member(u,universal_class)* subclass(rest_relation,v)* equal(complement(v),universal_class) -> . % 300.04/300.41 188839[19:SpL:27.0,188653.0] || equal(union(u,v),universal_class) -> equal(intersection(complement(u),complement(v)),ordinal_numbers)**. % 300.04/300.41 188846[19:SpL:167200.0,188653.0] || equal(power_class(complement(inverse(ordinal_numbers))),universal_class) -> equal(image(element_relation,symmetrization_of(ordinal_numbers)),ordinal_numbers)**. % 300.04/300.41 188847[19:SpL:180125.0,188653.0] || equal(power_class(complement(singleton(ordinal_numbers))),universal_class) -> equal(image(element_relation,singleton(ordinal_numbers)),ordinal_numbers)**. % 300.04/300.41 188915[19:Res:188649.1,169097.1] || equal(complement(sum_class(u)),universal_class)** well_ordering(element_relation,u) -> equal(u,ordinal_numbers). % 300.04/300.41 189116[19:Res:188649.1,167105.1] || equal(complement(image(successor_relation,u)),universal_class)** member(ordinal_numbers,u) -> inductive(u). % 300.04/300.41 190307[19:Obv:190215.1] || subclass(intersection(u,complement(v)),v)* -> equal(intersection(u,complement(v)),ordinal_numbers). % 300.04/300.41 190691[19:Obv:190659.1] || subclass(intersection(complement(u),v),u)* -> equal(intersection(complement(u),v),ordinal_numbers). % 300.04/300.41 191006[19:MRR:190982.2,167057.0] inductive(symmetric_difference(inverse(identity_relation),symmetrization_of(identity_relation))) || well_ordering(u,complement(symmetrization_of(ordinal_numbers)))* -> . % 300.04/300.41 191007[19:MRR:190983.2,167057.0] inductive(symmetric_difference(inverse(ordinal_numbers),symmetrization_of(ordinal_numbers))) || well_ordering(u,complement(symmetrization_of(ordinal_numbers)))* -> . % 300.04/300.41 191087[19:Res:168353.1,188593.1] || equal(complement(complement(intersection(u,v))),universal_class)** -> equal(symmetric_difference(u,v),ordinal_numbers). % 300.04/300.41 191263[19:Res:52.1,168435.0] inductive(restrict(u,v,w)) || -> equal(integer_of(x),ordinal_numbers) member(x,u)*. % 300.04/300.41 192188[19:SpR:190384.0,167261.0] || -> equal(range__dfg(complement(cross_product(singleton(u),v)),u,v),second(not_subclass_element(ordinal_numbers,ordinal_numbers)))**. % 300.04/300.41 192308[19:SpL:167362.1,192214.0] || member(u,universal_class) member(range_of(u),cantor(complement(cross_product(ordinal_numbers,universal_class))))* -> . % 300.04/300.41 192309[19:SpL:177036.0,192214.0] || member(inverse(u),cantor(complement(cross_product(ordinal_numbers,universal_class))))* -> equal(range_of(u),ordinal_numbers). % 300.04/300.41 192315[19:Res:125124.2,192214.0] || member(u,universal_class) subclass(rest_relation,rest_of(complement(cross_product(singleton(u),universal_class))))* -> . % 300.04/300.41 192336[19:Res:167131.2,192214.0] || subclass(u,cantor(complement(cross_product(singleton(regular(u)),universal_class))))* -> equal(u,ordinal_numbers). % 300.04/300.41 192338[19:Res:167339.2,192214.0] || subclass(omega,cantor(complement(cross_product(singleton(u),universal_class))))* -> equal(integer_of(u),ordinal_numbers). % 300.04/300.41 192454[23:SpL:192241.0,178140.1] function(complement(cross_product(ordinal_numbers,universal_class))) || equal(rest_of(sum_class(range_of(ordinal_numbers))),rest_relation)** -> . % 300.04/300.41 193169[25:SpR:192881.1,124905.0] function(restrict(u,v,singleton(w))) || -> equal(segment(u,v,w),universal_class)**. % 300.04/300.41 193260[25:SoR:193220.0,12322.2] single_valued_class(regular(symmetrization_of(ordinal_numbers))) || equal(cross_product(universal_class,universal_class),regular(symmetrization_of(ordinal_numbers)))** -> . % 300.04/300.41 193263[25:SoR:193221.0,12322.2] single_valued_class(unordered_pair(u,v)) || equal(cross_product(universal_class,universal_class),unordered_pair(u,v))* -> . % 300.04/300.41 193270[25:SoR:193222.0,12322.2] single_valued_class(ordered_pair(u,v)) || equal(cross_product(universal_class,universal_class),ordered_pair(u,v))* -> . % 300.04/300.41 193304[25:SpR:193223.1,14.0] function(u) || -> equal(unordered_pair(ordinal_numbers,unordered_pair(u,singleton(v))),ordered_pair(u,v))**. % 300.04/300.41 193631[25:Rew:184023.1,193630.2] function(u) || member(singleton(singleton(ordinal_numbers)),compose_class(v))* -> equal(universal_class,u)*. % 300.04/300.41 193835[25:SoR:193167.0,167213.2] single_valued_class(inverse(u)) || equal(inverse(u),ordinal_numbers) -> equal(range_of(u),universal_class)**. % 300.04/300.41 193868[25:SpL:193832.1,99364.1] one_to_one(u) || member(u,universal_class)* equal(rest_of(u),sum_class(universal_class)) -> . % 300.04/300.41 193872[25:SpL:193832.1,110985.0] one_to_one(u) || member(inverse(u),universal_class)* subclass(universal_class,complement(element_relation)) -> . % 300.04/300.41 193886[25:SoR:193233.0,167213.2] single_valued_class(sum_class(u)) || member(u,universal_class)* equal(sum_class(u),ordinal_numbers) -> . % 300.04/300.41 193920[25:SoR:193234.0,167213.2] single_valued_class(power_class(u)) || member(u,universal_class)* equal(power_class(u),ordinal_numbers) -> . % 300.04/300.41 193923[25:SoR:193235.0,167213.2] single_valued_class(rest_of(u)) || member(u,universal_class)* equal(rest_of(u),ordinal_numbers) -> . % 300.04/300.41 194022[19:MRR:193973.0,940.0] || member(u,universal_class) subclass(domain_relation,complement(unordered_pair(ordered_pair(u,ordinal_numbers),v)))* -> . % 300.04/300.41 194023[19:MRR:193974.0,940.0] || member(u,universal_class) subclass(domain_relation,complement(unordered_pair(v,ordered_pair(u,ordinal_numbers))))* -> . % 300.04/300.41 194315[20:MRR:194314.2,175557.0] || well_ordering(u,universal_class) member(least(u,symmetrization_of(ordinal_numbers)),complement(inverse(ordinal_numbers)))* -> . % 300.04/300.41 194432[20:MRR:194380.1,167057.0] || member(u,universal_class) -> equal(apply(regular(symmetrization_of(ordinal_numbers)),u),sum_class(range_of(ordinal_numbers)))**. % 300.04/300.41 194433[19:MRR:194382.1,167057.0] || member(u,universal_class) -> equal(apply(unordered_pair(v,w),u),sum_class(range_of(ordinal_numbers)))**. % 300.04/300.41 194434[19:MRR:194383.1,167057.0] || member(u,universal_class) -> equal(apply(ordered_pair(v,w),u),sum_class(range_of(ordinal_numbers)))**. % 300.04/300.41 194435[22:MRR:194426.0,167011.0] || equal(complement(cantor(u)),omega) -> equal(apply(u,ordinal_numbers),sum_class(range_of(ordinal_numbers)))**. % 300.04/300.41 194438[19:MRR:194410.0,170.0] || well_ordering(universal_class,cantor(u)) -> equal(apply(u,singleton(ordinal_numbers)),sum_class(range_of(ordinal_numbers)))**. % 300.04/300.41 195242[0:Res:27190.1,11848.0] || subclass(rest_relation,flip(u))* subclass(u,v)* well_ordering(universal_class,v)* -> . % 300.04/300.41 195285[0:Res:27190.1,20.0] || subclass(rest_relation,flip(element_relation)) -> member(ordered_pair(u,v),rest_of(ordered_pair(v,u)))*. % 300.04/300.41 195290[0:Res:27190.1,16.0] || subclass(rest_relation,flip(cross_product(u,v)))* -> member(rest_of(ordered_pair(w,x)),v)*. % 300.04/300.41 195339[0:Res:27189.1,11848.0] || subclass(rest_relation,rotate(u))* subclass(u,v)* well_ordering(universal_class,v)* -> . % 300.04/300.41 195382[0:Res:27189.1,20.0] || subclass(rest_relation,rotate(element_relation)) -> member(ordered_pair(u,rest_of(ordered_pair(v,u))),v)*. % 300.04/300.41 196145[19:SpR:188655.1,30.0] || equal(complement(cross_product(u,v)),universal_class) -> equal(restrict(w,u,v),ordinal_numbers)**. % 300.04/300.41 196260[19:Rew:167017.0,196154.1] || equal(complement(complement(u)),universal_class) -> equal(complement(image(element_relation,successor(u))),ordinal_numbers)**. % 300.04/300.41 196261[19:Rew:167017.0,196156.1] || equal(complement(complement(u)),universal_class) -> equal(complement(image(element_relation,symmetrization_of(u))),ordinal_numbers)**. % 300.04/300.41 196535[25:MRR:196534.2,192574.0] single_valued_class(image(element_relation,symmetrization_of(ordinal_numbers))) || equal(power_class(complement(inverse(ordinal_numbers))),universal_class)** -> . % 300.04/300.41 196537[25:MRR:196536.2,192574.0] single_valued_class(image(element_relation,singleton(ordinal_numbers))) || equal(power_class(complement(singleton(ordinal_numbers))),universal_class)** -> . % 300.04/300.41 196539[25:MRR:196538.2,192574.0] single_valued_class(intersection(complement(u),complement(v))) || equal(union(u,v),universal_class)** -> . % 300.04/300.41 196848[19:Res:196731.1,16105.1] || subclass(universal_class,intersection(u,v)) member(regular(element_relation),symmetric_difference(u,v))* -> . % 300.04/300.41 196868[19:Res:196731.1,896.0] || subclass(universal_class,restrict(u,v,w))* -> member(regular(element_relation),cross_product(v,w))*. % 300.04/300.41 197076[19:Res:26.2,197071.0] || member(not_subclass_element(element_relation,ordinal_numbers),universal_class) -> member(not_subclass_element(element_relation,ordinal_numbers),compose(element_relation,universal_class))*. % 300.04/300.41 197078[19:Res:167339.2,197071.0] || subclass(omega,complement(compose(element_relation,universal_class)))* -> equal(integer_of(not_subclass_element(element_relation,ordinal_numbers)),ordinal_numbers). % 300.04/300.41 197150[19:SpL:196827.0,146.0] || member(regular(element_relation),rest_relation) -> equal(rest_of(first(regular(element_relation))),second(regular(element_relation)))**. % 300.04/300.41 197162[19:SpL:196827.0,124911.0] || member(regular(element_relation),domain_relation) -> equal(cantor(first(regular(element_relation))),second(regular(element_relation)))**. % 300.04/300.41 197164[19:SpL:196827.0,46.0] || member(regular(element_relation),successor_relation) -> equal(successor(first(regular(element_relation))),second(regular(element_relation)))**. % 300.04/300.41 197191[19:MRR:197190.1,196720.0] || equal(successor(first(regular(element_relation))),second(regular(element_relation)))** -> member(regular(element_relation),successor_relation). % 300.04/300.41 197336[19:Obv:197251.1] || subclass(u,v)* -> equal(intersection(singleton(w),u),ordinal_numbers)** member(w,v)*. % 300.04/300.41 197555[19:MRR:197552.1,167005.0] || member(singleton(first(regular(element_relation))),element_relation)* -> member(singleton(first(regular(element_relation))),u)*. % 300.04/300.41 197898[19:Obv:197814.1] || subclass(u,v)* -> equal(intersection(u,singleton(w)),ordinal_numbers)** member(w,v)*. % 300.04/300.41 198288[19:SpR:27.0,197499.0] || -> equal(intersection(union(u,v),intersection(intersection(complement(u),complement(v)),w)),ordinal_numbers)**. % 300.04/300.41 198296[19:SpR:167200.0,197499.0] || -> equal(intersection(power_class(complement(inverse(ordinal_numbers))),intersection(image(element_relation,symmetrization_of(ordinal_numbers)),u)),ordinal_numbers)**. % 300.04/300.41 198297[19:SpR:180125.0,197499.0] || -> equal(intersection(power_class(complement(singleton(ordinal_numbers))),intersection(image(element_relation,singleton(ordinal_numbers)),u)),ordinal_numbers)**. % 300.04/300.41 198352[19:Rew:142500.0,198208.0,167055.0,198208.0] || -> equal(symmetric_difference(complement(u),intersection(u,v)),union(complement(u),intersection(u,v)))**. % 300.04/300.41 198935[19:SpR:27.0,197702.0] || -> equal(intersection(union(u,v),intersection(w,intersection(complement(u),complement(v)))),ordinal_numbers)**. % 300.04/300.41 198943[19:SpR:167200.0,197702.0] || -> equal(intersection(power_class(complement(inverse(ordinal_numbers))),intersection(u,image(element_relation,symmetrization_of(ordinal_numbers)))),ordinal_numbers)**. % 300.04/300.41 198944[19:SpR:180125.0,197702.0] || -> equal(intersection(power_class(complement(singleton(ordinal_numbers))),intersection(u,image(element_relation,singleton(ordinal_numbers)))),ordinal_numbers)**. % 300.04/300.41 199009[19:Rew:142500.0,198849.0,167055.0,198849.0] || -> equal(symmetric_difference(complement(u),intersection(v,u)),union(complement(u),intersection(v,u)))**. % 300.04/300.41 199380[19:Rew:198500.0,199366.1] || member(not_subclass_element(complement(u),ordinal_numbers),intersection(u,v))* -> subclass(complement(u),ordinal_numbers). % 300.04/300.41 199558[19:Rew:199166.0,199534.1] || member(not_subclass_element(complement(u),ordinal_numbers),intersection(v,u))* -> subclass(complement(u),ordinal_numbers). % 300.04/300.41 199572[19:Res:125124.2,197186.0] || member(second(regular(element_relation)),universal_class) subclass(rest_relation,rest_of(first(regular(element_relation))))* -> . % 300.04/300.41 199573[19:Res:167339.2,197186.0] || subclass(omega,cantor(first(regular(element_relation))))* -> equal(integer_of(second(regular(element_relation))),ordinal_numbers). % 300.04/300.41 199600[19:Obv:199579.1] || equal(u,v) -> equal(unordered_pair(v,u),ordinal_numbers)** equal(cantor(v),ordinal_numbers). % 300.04/300.41 202721[19:Rew:167017.0,202606.1] || subclass(complement(singleton(u)),ordinal_numbers) -> equal(complement(image(element_relation,successor(u))),ordinal_numbers)**. % 300.04/300.41 202722[19:Rew:167017.0,202608.1] || subclass(complement(inverse(u)),ordinal_numbers) -> equal(complement(image(element_relation,symmetrization_of(u))),ordinal_numbers)**. % 300.04/300.41 202723[19:Rew:167017.0,202609.1] || subclass(complement(image(successor_relation,ordinal_numbers)),ordinal_numbers)* -> equal(complement(image(element_relation,kind_1_ordinals)),ordinal_numbers). % 300.04/300.41 202761[19:Con:202760.2] || subclass(u,ordinal_numbers) member(not_subclass_element(v,ordinal_numbers),u)* -> subclass(v,ordinal_numbers). % 300.04/300.41 202850[19:SpR:197859.1,4125.0] || subclass(union(u,v),ordinal_numbers) -> equal(symmetric_difference(complement(u),complement(v)),ordinal_numbers)**. % 300.04/300.41 203379[19:SpR:27.0,203242.1] || subclass(intersection(complement(u),complement(v)),ordinal_numbers)* -> subclass(universal_class,union(u,v)). % 300.04/300.41 203388[19:SpR:167200.0,203242.1] || subclass(image(element_relation,symmetrization_of(ordinal_numbers)),ordinal_numbers)* -> subclass(universal_class,power_class(complement(inverse(ordinal_numbers)))). % 300.04/300.41 203389[19:SpR:180125.0,203242.1] || subclass(image(element_relation,singleton(ordinal_numbers)),ordinal_numbers)* -> subclass(universal_class,power_class(complement(singleton(ordinal_numbers)))). % 300.04/300.41 203597[26:MRR:203531.0,36583.1] || member(u,cross_product(universal_class,universal_class)) -> member(u,compose(complement(element_relation),inverse(element_relation)))*. % 300.04/300.41 204016[19:SpL:168412.1,203426.0] || subclass(singleton(regular(cross_product(u,v))),ordinal_numbers)* -> equal(cross_product(u,v),ordinal_numbers). % 300.04/300.41 204026[19:MRR:188265.2,204022.0] || member(u,universal_class) subclass(rest_relation,complement(singleton(ordered_pair(u,rest_of(u)))))* -> . % 300.04/300.41 204487[19:SpL:479.0,204472.0] || equal(power_class(intersection(complement(u),complement(v))),image(element_relation,union(u,v)))** -> . % 300.04/300.41 204561[19:MRR:204511.0,167011.0] || subclass(intersection(complement(u),complement(v)),ordinal_numbers)* -> member(ordinal_numbers,union(u,v)). % 300.04/300.41 204682[19:MRR:204643.0,53.0] || subclass(intersection(complement(u),complement(v)),ordinal_numbers)* -> member(omega,union(u,v)). % 300.04/300.41 205373[19:SpL:27.0,203422.0] || subclass(union(u,v),ordinal_numbers) -> member(ordinal_numbers,intersection(complement(u),complement(v)))*. % 300.04/300.41 205385[19:SpL:167200.0,203422.0] || subclass(power_class(complement(inverse(ordinal_numbers))),ordinal_numbers) -> member(ordinal_numbers,image(element_relation,symmetrization_of(ordinal_numbers)))*. % 300.04/300.41 205386[19:SpL:180125.0,203422.0] || subclass(power_class(complement(singleton(ordinal_numbers))),ordinal_numbers) -> member(ordinal_numbers,image(element_relation,singleton(ordinal_numbers)))*. % 300.04/300.41 205396[19:SpL:27.0,203423.0] || subclass(union(u,v),ordinal_numbers) -> member(omega,intersection(complement(u),complement(v)))*. % 300.04/300.41 205408[19:SpL:167200.0,203423.0] || subclass(power_class(complement(inverse(ordinal_numbers))),ordinal_numbers) -> member(omega,image(element_relation,symmetrization_of(ordinal_numbers)))*. % 300.04/300.41 205409[19:SpL:180125.0,203423.0] || subclass(power_class(complement(singleton(ordinal_numbers))),ordinal_numbers) -> member(omega,image(element_relation,singleton(ordinal_numbers)))*. % 300.04/300.41 205494[19:SpR:204449.1,27.0] || equal(intersection(complement(u),complement(v)),ordinal_numbers)** -> equal(union(u,v),universal_class). % 300.04/300.41 205527[19:SpR:204449.1,186353.1] || equal(complement(singleton(u)),ordinal_numbers)** -> equal(integer_of(u),ordinal_numbers) subclass(universal_class,omega). % 300.04/300.41 205538[19:SpR:204449.1,167200.0] || equal(image(element_relation,symmetrization_of(ordinal_numbers)),ordinal_numbers)** -> equal(power_class(complement(inverse(ordinal_numbers))),universal_class). % 300.04/300.41 205539[19:SpR:204449.1,180125.0] || equal(image(element_relation,singleton(ordinal_numbers)),ordinal_numbers)** -> equal(power_class(complement(singleton(ordinal_numbers))),universal_class). % 300.04/300.41 205569[23:SpR:204449.1,192241.0] || equal(cross_product(ordinal_numbers,universal_class),ordinal_numbers) -> equal(apply(universal_class,universal_class),sum_class(range_of(ordinal_numbers)))**. % 300.04/300.41 205819[19:SpL:204449.1,192344.0] || equal(cross_product(singleton(ordinal_numbers),universal_class),ordinal_numbers)** equal(cantor(universal_class),singleton(ordinal_numbers)) -> . % 300.04/300.41 205822[19:SpL:204449.1,192316.0] || equal(cross_product(singleton(singleton(u)),universal_class),ordinal_numbers)** equal(cantor(universal_class),universal_class) -> . % 300.04/300.41 205823[19:SpL:204449.1,192318.0] || equal(cross_product(singleton(singleton(u)),universal_class),ordinal_numbers)** subclass(universal_class,cantor(universal_class)) -> . % 300.04/300.41 205935[19:MRR:167910.3,205934.1] || equal(sum_class(u),ordinal_numbers) well_ordering(v,u)* -> subclass(sum_class(u),w)*. % 300.04/300.41 206005[19:Rew:142500.0,205496.1] || equal(intersection(u,v),ordinal_numbers)** -> equal(symmetric_difference(u,v),union(u,v)). % 300.04/300.41 206006[19:Rew:204449.1,205519.2] || equal(complement(u),ordinal_numbers) -> member(not_subclass_element(universal_class,v),u)* subclass(universal_class,v). % 300.04/300.41 206217[19:SpR:27838.0,197859.1] || subclass(successor(u),ordinal_numbers) -> equal(symmetric_difference(complement(u),complement(singleton(u))),ordinal_numbers)**. % 300.04/300.41 206267[19:SpL:27838.0,167086.0] || subclass(universal_class,symmetric_difference(complement(u),complement(singleton(u))))* -> member(ordinal_numbers,successor(u)). % 300.04/300.41 206270[0:SpL:27838.0,2539.0] || subclass(universal_class,symmetric_difference(complement(u),complement(singleton(u))))* -> member(omega,successor(u)). % 300.04/300.41 206275[19:SpL:27838.0,167084.0] || equal(symmetric_difference(complement(u),complement(singleton(u))),universal_class)** -> member(ordinal_numbers,successor(u)). % 300.04/300.41 206276[0:SpL:27838.0,6300.0] || equal(symmetric_difference(complement(u),complement(singleton(u))),universal_class)** -> member(omega,successor(u)). % 300.04/300.41 206283[22:SpL:27838.0,177190.0] || subclass(omega,symmetric_difference(complement(u),complement(singleton(u))))* -> member(ordinal_numbers,successor(u)). % 300.04/300.41 206285[22:SpL:27838.0,178812.0] || equal(symmetric_difference(complement(u),complement(singleton(u))),omega)** -> member(ordinal_numbers,successor(u)). % 300.04/300.41 206289[0:SpL:27838.0,22.0] || member(u,symmetric_difference(complement(v),complement(singleton(v))))* -> member(u,successor(v)). % 300.04/300.41 206621[0:Rew:206400.0,96529.1] || -> member(u,image(element_relation,power_class(v))) subclass(singleton(u),power_class(complement(power_class(v))))*. % 300.04/300.41 206713[19:Rew:206400.0,205536.1] || equal(image(element_relation,power_class(u)),ordinal_numbers)** -> equal(power_class(complement(power_class(u))),universal_class). % 300.04/300.41 206714[25:Rew:206400.0,196541.1] single_valued_class(image(element_relation,power_class(u))) || equal(power_class(complement(power_class(u))),universal_class)** -> . % 300.04/300.41 206715[19:Rew:206400.0,188844.0] || equal(power_class(complement(power_class(u))),universal_class) -> equal(image(element_relation,power_class(u)),ordinal_numbers)**. % 300.04/300.41 206716[8:Rew:206400.0,85195.1] inductive(image(element_relation,power_class(u))) || equal(power_class(complement(power_class(u))),universal_class)** -> . % 300.04/300.41 206717[19:Rew:206400.0,203386.1] || subclass(image(element_relation,power_class(u)),ordinal_numbers)* -> subclass(universal_class,power_class(complement(power_class(u)))). % 300.04/300.41 206917[19:Rew:206400.0,168485.0] || well_ordering(universal_class,power_class(complement(power_class(u))))* -> member(ordinal_numbers,image(element_relation,power_class(u))). % 300.04/300.41 206932[22:Rew:206400.0,178383.1] inductive(image(element_relation,power_class(u))) || equal(power_class(complement(power_class(u))),omega)** -> . % 300.04/300.41 206960[19:Rew:206400.0,198294.0] || -> equal(intersection(power_class(complement(power_class(u))),intersection(image(element_relation,power_class(u)),v)),ordinal_numbers)**. % 300.04/300.41 206961[19:Rew:206400.0,198941.0] || -> equal(intersection(power_class(complement(power_class(u))),intersection(v,image(element_relation,power_class(u)))),ordinal_numbers)**. % 300.04/300.41 206964[19:Rew:206400.0,205406.0] || subclass(power_class(complement(power_class(u))),ordinal_numbers) -> member(omega,image(element_relation,power_class(u)))*. % 300.04/300.41 206965[19:Rew:206400.0,205383.0] || subclass(power_class(complement(power_class(u))),ordinal_numbers) -> member(ordinal_numbers,image(element_relation,power_class(u)))*. % 300.04/300.41 207097[0:Rew:206400.0,17152.0] || -> subclass(symmetric_difference(power_class(u),complement(singleton(complement(power_class(u))))),successor(complement(power_class(u))))*. % 300.04/300.41 207206[0:Rew:206400.0,17134.0] || -> subclass(symmetric_difference(power_class(u),complement(inverse(complement(power_class(u))))),symmetrization_of(complement(power_class(u))))*. % 300.04/300.41 207767[0:SpR:16826.0,206407.0] || -> equal(complement(complement(complement(image(element_relation,successor(u))))),complement(image(element_relation,successor(u))))**. % 300.04/300.41 207768[0:SpR:16825.0,206407.0] || -> equal(complement(complement(complement(image(element_relation,symmetrization_of(u))))),complement(image(element_relation,symmetrization_of(u))))**. % 300.04/300.41 207928[19:Res:205391.1,11848.0] || equal(complement(u),ordinal_numbers) subclass(u,v)* well_ordering(universal_class,v)* -> . % 300.04/300.41 207947[19:Res:205391.1,9.0] || equal(complement(unordered_pair(u,v)),ordinal_numbers)** -> equal(ordinal_numbers,v) equal(ordinal_numbers,u). % 300.04/300.41 207953[19:Res:205391.1,896.0] || equal(complement(restrict(u,v,w)),ordinal_numbers)** -> member(ordinal_numbers,cross_product(v,w)). % 300.04/300.41 207978[19:MRR:194304.2,207974.0] || member(least(u,complement(symmetrization_of(ordinal_numbers))),inverse(ordinal_numbers))* well_ordering(u,universal_class) -> . % 300.04/300.41 208176[0:Rew:206407.0,208175.0] || -> equal(power_class(complement(complement(image(element_relation,successor(u))))),power_class(image(element_relation,successor(u))))**. % 300.04/300.41 208178[0:Rew:206407.0,208177.0] || -> equal(power_class(complement(complement(image(element_relation,symmetrization_of(u))))),power_class(image(element_relation,symmetrization_of(u))))**. % 300.04/300.41 208245[19:SpR:206403.0,190665.0] || -> equal(intersection(union(u,complement(power_class(v))),intersection(complement(u),power_class(v))),ordinal_numbers)**. % 300.04/300.41 208246[19:SpR:206403.0,190801.0] || -> equal(union(union(u,complement(power_class(v))),intersection(complement(u),power_class(v))),universal_class)**. % 300.04/300.41 208247[19:SpR:206403.0,190813.0] || -> equal(symmetric_difference(union(u,complement(power_class(v))),intersection(complement(u),power_class(v))),universal_class)**. % 300.04/300.41 208406[19:Rew:27.0,208276.0] || -> equal(union(u,complement(complement(image(element_relation,kind_1_ordinals)))),union(u,image(element_relation,kind_1_ordinals)))**. % 300.04/300.41 208478[19:Res:205414.1,9.0] || equal(complement(unordered_pair(u,v)),ordinal_numbers)** -> equal(omega,v) equal(omega,u). % 300.04/300.41 208484[19:Res:205414.1,896.0] || equal(complement(restrict(u,v,w)),ordinal_numbers)** -> member(omega,cross_product(v,w)). % 300.04/300.41 208507[19:MRR:208506.2,167008.0] || equal(complement(ordered_pair(u,v)),ordinal_numbers) -> equal(unordered_pair(u,singleton(v)),omega)**. % 300.04/300.41 208552[19:SpR:206410.0,190665.0] || -> equal(intersection(union(complement(power_class(u)),v),intersection(power_class(u),complement(v))),ordinal_numbers)**. % 300.04/300.41 208553[19:SpR:206410.0,190801.0] || -> equal(union(union(complement(power_class(u)),v),intersection(power_class(u),complement(v))),universal_class)**. % 300.04/300.41 208554[19:SpR:206410.0,190813.0] || -> equal(symmetric_difference(union(complement(power_class(u)),v),intersection(power_class(u),complement(v))),universal_class)**. % 300.04/300.41 208714[19:Rew:27.0,208599.0] || -> equal(union(complement(complement(image(element_relation,kind_1_ordinals))),u),union(image(element_relation,kind_1_ordinals),u))**. % 300.04/300.41 208839[19:Res:205520.1,6439.0] || equal(complement(restrict(u,v,w)),ordinal_numbers)** -> member(unordered_pair(x,y),u)*. % 300.04/300.41 209158[19:Res:167106.1,206404.0] inductive(image(element_relation,power_class(u))) || member(ordinal_numbers,power_class(complement(power_class(u))))* -> . % 300.04/300.41 209193[0:SpR:27.0,206400.0] || -> equal(complement(power_class(intersection(complement(u),complement(v)))),image(element_relation,union(u,v)))**. % 300.04/300.41 209202[19:SpR:167200.0,206400.0] || -> equal(image(element_relation,power_class(complement(inverse(ordinal_numbers)))),complement(power_class(image(element_relation,symmetrization_of(ordinal_numbers)))))**. % 300.04/300.41 209203[19:SpR:180125.0,206400.0] || -> equal(image(element_relation,power_class(complement(singleton(ordinal_numbers)))),complement(power_class(image(element_relation,singleton(ordinal_numbers)))))**. % 300.04/300.41 209204[0:SpR:206408.0,206400.0] || -> equal(image(element_relation,power_class(complement(power_class(u)))),complement(power_class(image(element_relation,power_class(u)))))**. % 300.04/300.41 209492[19:SpL:27.0,208786.0] || equal(union(u,v),ordinal_numbers) -> equal(intersection(complement(u),complement(v)),universal_class)**. % 300.04/300.41 209501[19:SpL:167200.0,208786.0] || equal(power_class(complement(inverse(ordinal_numbers))),ordinal_numbers) -> equal(image(element_relation,symmetrization_of(ordinal_numbers)),universal_class)**. % 300.04/300.41 209502[19:SpL:180125.0,208786.0] || equal(power_class(complement(singleton(ordinal_numbers))),ordinal_numbers) -> equal(image(element_relation,singleton(ordinal_numbers)),universal_class)**. % 300.04/300.41 209503[19:SpL:206408.0,208786.0] || equal(power_class(complement(power_class(u))),ordinal_numbers) -> equal(image(element_relation,power_class(u)),universal_class)**. % 300.04/300.41 209823[0:Obv:209812.0] || subclass(rest_relation,u) member(v,universal_class)* subclass(rest_relation,complement(u))* -> . % 300.04/300.41 210045[19:Res:168474.2,205934.1] || subclass(u,v)* equal(ordinal_numbers,v) -> equal(intersection(u,w),ordinal_numbers)**. % 300.04/300.41 210046[19:Res:168469.2,205934.1] || subclass(u,v)* equal(ordinal_numbers,v) -> equal(intersection(w,u),ordinal_numbers)**. % 300.04/300.41 210136[0:SpR:27168.2,16280.0] || member(u,universal_class) subclass(rest_relation,rest_of(v)) -> subclass(rest_of(u),v)*. % 300.04/300.41 210224[19:SpR:27837.0,197859.1] || subclass(symmetrization_of(u),ordinal_numbers) -> equal(symmetric_difference(complement(u),complement(inverse(u))),ordinal_numbers)**. % 300.04/300.41 210266[19:SpL:27837.0,167086.0] || subclass(universal_class,symmetric_difference(complement(u),complement(inverse(u))))* -> member(ordinal_numbers,symmetrization_of(u)). % 300.04/300.41 210269[0:SpL:27837.0,2539.0] || subclass(universal_class,symmetric_difference(complement(u),complement(inverse(u))))* -> member(omega,symmetrization_of(u)). % 300.04/300.41 210274[19:SpL:27837.0,167084.0] || equal(symmetric_difference(complement(u),complement(inverse(u))),universal_class)** -> member(ordinal_numbers,symmetrization_of(u)). % 300.04/300.41 210275[0:SpL:27837.0,6300.0] || equal(symmetric_difference(complement(u),complement(inverse(u))),universal_class)** -> member(omega,symmetrization_of(u)). % 300.04/300.41 210282[22:SpL:27837.0,177190.0] || subclass(omega,symmetric_difference(complement(u),complement(inverse(u))))* -> member(ordinal_numbers,symmetrization_of(u)). % 300.04/300.41 210284[22:SpL:27837.0,178812.0] || equal(symmetric_difference(complement(u),complement(inverse(u))),omega)** -> member(ordinal_numbers,symmetrization_of(u)). % 300.04/300.41 210288[0:SpL:27837.0,22.0] || member(u,symmetric_difference(complement(v),complement(inverse(v))))* -> member(u,symmetrization_of(v)). % 300.04/300.41 211108[19:MRR:211076.0,53.0] || subclass(image(element_relation,power_class(u)),ordinal_numbers) -> member(omega,power_class(complement(power_class(u))))*. % 300.04/300.41 211110[19:MRR:211101.0,167011.0] || subclass(image(element_relation,power_class(u)),ordinal_numbers) -> member(ordinal_numbers,power_class(complement(power_class(u))))*. % 300.04/300.41 211275[0:Res:170.0,15107.0] || subclass(universal_class,u)* subclass(u,v)* -> member(sum_class(singleton(w)),v)*. % 300.04/300.41 211336[19:Res:196718.0,15107.0] || subclass(universal_class,u)* subclass(u,v)* -> member(sum_class(regular(element_relation)),v)*. % 300.04/300.41 211449[19:Res:167219.1,9806.0] || equal(apply(u,v),ordinal_numbers) -> section(element_relation,image(u,singleton(v)),universal_class)*. % 300.04/300.41 211617[19:Res:203424.1,11848.0] || subclass(complement(u),ordinal_numbers)* subclass(u,v)* well_ordering(universal_class,v)* -> . % 300.04/300.41 211621[19:Res:203424.1,2.0] || subclass(complement(u),ordinal_numbers)* subclass(u,v)* -> member(singleton(w),v)*. % 300.04/300.41 211627[19:Res:203424.1,4127.0] || subclass(complement(symmetric_difference(u,v)),ordinal_numbers) -> member(singleton(w),union(u,v))*. % 300.04/300.41 211629[19:Res:203424.1,16910.0] || subclass(complement(symmetric_difference(u,inverse(u))),ordinal_numbers)* -> member(singleton(v),symmetrization_of(u))*. % 300.04/300.41 211685[19:Rew:27.0,211625.0] || subclass(union(u,v),ordinal_numbers) member(singleton(w),union(u,v))* -> . % 300.04/300.41 211997[19:SpR:205896.1,4125.0] || equal(union(u,v),ordinal_numbers) -> equal(symmetric_difference(complement(u),complement(v)),ordinal_numbers)**. % 300.04/300.41 212375[19:Rew:167017.0,212239.1] || equal(complement(singleton(u)),ordinal_numbers) -> equal(complement(image(element_relation,successor(u))),ordinal_numbers)**. % 300.04/300.41 212376[19:Rew:167017.0,212241.1] || equal(complement(inverse(u)),ordinal_numbers) -> equal(complement(image(element_relation,symmetrization_of(u))),ordinal_numbers)**. % 300.04/300.41 212377[19:Rew:167017.0,212242.1] || equal(complement(image(successor_relation,ordinal_numbers)),ordinal_numbers) -> equal(complement(image(element_relation,kind_1_ordinals)),ordinal_numbers)**. % 300.04/300.41 212433[19:Res:205991.1,2.0] || equal(complement(u),ordinal_numbers) subclass(u,v)* -> member(singleton(w),v)*. % 300.04/300.41 212439[19:Res:205991.1,4127.0] || equal(complement(symmetric_difference(u,v)),ordinal_numbers) -> member(singleton(w),union(u,v))*. % 300.04/300.41 212441[19:Res:205991.1,16910.0] || equal(complement(symmetric_difference(u,inverse(u))),ordinal_numbers)** -> member(singleton(v),symmetrization_of(u))*. % 300.04/300.41 212495[19:Rew:27.0,212437.0] || equal(union(u,v),ordinal_numbers) member(singleton(w),union(u,v))* -> . % 300.04/300.41 212599[19:Rew:167458.0,212554.0] || equal(complement(image(element_relation,kind_1_ordinals)),ordinal_numbers) -> subclass(complement(image(element_relation,kind_1_ordinals)),u)*. % 300.04/300.41 212613[19:Rew:167458.0,212606.0] || equal(complement(image(element_relation,kind_1_ordinals)),ordinal_numbers) -> asymmetric(complement(image(element_relation,kind_1_ordinals)),u)*. % 300.04/300.41 212766[0:Res:170.0,15073.0] || subclass(universal_class,u)* subclass(u,v)* -> member(power_class(singleton(w)),v)*. % 300.04/300.41 212827[19:Res:196718.0,15073.0] || subclass(universal_class,u)* subclass(u,v)* -> member(power_class(regular(element_relation)),v)*. % 300.04/300.41 212971[19:SpL:204449.1,196865.0] || equal(cross_product(singleton(regular(element_relation)),universal_class),ordinal_numbers)** subclass(universal_class,cantor(universal_class)) -> . % 300.04/300.41 213001[19:Obv:212984.1] || -> equal(integer_of(u),ordinal_numbers) subclass(unordered_pair(u,v),omega)* equal(cantor(v),ordinal_numbers). % 300.04/300.41 213002[19:Obv:212987.1] || -> equal(integer_of(u),ordinal_numbers) equal(integer_of(v),ordinal_numbers) subclass(unordered_pair(u,v),omega)*. % 300.04/300.41 213003[19:Obv:212997.2] || member(u,omega) -> equal(integer_of(v),ordinal_numbers) subclass(unordered_pair(v,u),omega)*. % 300.04/300.41 213056[19:Obv:213038.1] || -> equal(integer_of(u),ordinal_numbers) subclass(unordered_pair(v,u),omega)* equal(cantor(v),ordinal_numbers). % 300.04/300.41 213058[19:Obv:213052.2] || member(u,omega) -> equal(integer_of(v),ordinal_numbers) subclass(unordered_pair(u,v),omega)*. % 300.04/300.41 213075[20:Res:167339.2,213033.0] || subclass(omega,complement(inverse(ordinal_numbers))) -> equal(integer_of(not_subclass_element(symmetrization_of(ordinal_numbers),ordinal_numbers)),ordinal_numbers)**. % 300.04/300.41 213236[19:SpL:204449.1,207951.0] || equal(cross_product(singleton(ordinal_numbers),universal_class),ordinal_numbers)** equal(complement(cantor(universal_class)),ordinal_numbers) -> . % 300.04/300.41 213241[19:SpL:204449.1,208482.0] || equal(cross_product(singleton(omega),universal_class),ordinal_numbers)** equal(complement(cantor(universal_class)),ordinal_numbers) -> . % 300.04/300.41 213291[19:SpR:209197.0,206400.0] || -> equal(image(element_relation,image(element_relation,singleton(ordinal_numbers))),complement(power_class(power_class(complement(singleton(ordinal_numbers))))))**. % 300.04/300.41 213320[19:SpR:209197.0,197499.0] || -> equal(intersection(image(element_relation,singleton(ordinal_numbers)),intersection(power_class(complement(singleton(ordinal_numbers))),u)),ordinal_numbers)**. % 300.04/300.41 213321[19:SpR:209197.0,197702.0] || -> equal(intersection(image(element_relation,singleton(ordinal_numbers)),intersection(u,power_class(complement(singleton(ordinal_numbers))))),ordinal_numbers)**. % 300.04/300.41 213337[19:SpR:209197.0,95593.1] || -> member(u,power_class(complement(singleton(ordinal_numbers)))) subclass(singleton(u),image(element_relation,singleton(ordinal_numbers)))*. % 300.04/300.41 213357[19:SpL:209197.0,188653.0] || equal(image(element_relation,singleton(ordinal_numbers)),universal_class)** -> equal(power_class(complement(singleton(ordinal_numbers))),ordinal_numbers). % 300.04/300.41 213363[19:SpL:209197.0,85097.1] inductive(power_class(complement(singleton(ordinal_numbers)))) || equal(image(element_relation,singleton(ordinal_numbers)),universal_class)** -> . % 300.04/300.41 213400[19:SpL:209197.0,167091.0] || well_ordering(universal_class,image(element_relation,singleton(ordinal_numbers)))* -> member(ordinal_numbers,power_class(complement(singleton(ordinal_numbers)))). % 300.04/300.41 213408[22:SpL:209197.0,178292.1] inductive(power_class(complement(singleton(ordinal_numbers)))) || equal(image(element_relation,singleton(ordinal_numbers)),omega)** -> . % 300.04/300.41 213426[19:SpL:209197.0,203423.0] || subclass(image(element_relation,singleton(ordinal_numbers)),ordinal_numbers) -> member(omega,power_class(complement(singleton(ordinal_numbers))))*. % 300.04/300.41 213427[19:SpL:209197.0,203422.0] || subclass(image(element_relation,singleton(ordinal_numbers)),ordinal_numbers) -> member(ordinal_numbers,power_class(complement(singleton(ordinal_numbers))))*. % 300.04/300.41 213503[25:MRR:213502.2,192574.0] single_valued_class(power_class(complement(singleton(ordinal_numbers)))) || equal(image(element_relation,singleton(ordinal_numbers)),universal_class)** -> . % 300.04/300.41 213533[19:SpR:209198.0,206400.0] || -> equal(image(element_relation,image(element_relation,symmetrization_of(ordinal_numbers))),complement(power_class(power_class(complement(inverse(ordinal_numbers))))))**. % 300.04/300.41 213562[19:SpR:209198.0,197499.0] || -> equal(intersection(image(element_relation,symmetrization_of(ordinal_numbers)),intersection(power_class(complement(inverse(ordinal_numbers))),u)),ordinal_numbers)**. % 300.04/300.41 213563[19:SpR:209198.0,197702.0] || -> equal(intersection(image(element_relation,symmetrization_of(ordinal_numbers)),intersection(u,power_class(complement(inverse(ordinal_numbers))))),ordinal_numbers)**. % 300.04/300.41 213579[19:SpR:209198.0,95593.1] || -> member(u,power_class(complement(inverse(ordinal_numbers)))) subclass(singleton(u),image(element_relation,symmetrization_of(ordinal_numbers)))*. % 300.04/300.41 213598[19:SpL:209198.0,188653.0] || equal(image(element_relation,symmetrization_of(ordinal_numbers)),universal_class)** -> equal(power_class(complement(inverse(ordinal_numbers))),ordinal_numbers). % 300.04/300.41 213604[19:SpL:209198.0,85097.1] inductive(power_class(complement(inverse(ordinal_numbers)))) || equal(image(element_relation,symmetrization_of(ordinal_numbers)),universal_class)** -> . % 300.04/300.41 213641[19:SpL:209198.0,167091.0] || well_ordering(universal_class,image(element_relation,symmetrization_of(ordinal_numbers)))* -> member(ordinal_numbers,power_class(complement(inverse(ordinal_numbers)))). % 300.04/300.41 213649[22:SpL:209198.0,178292.1] inductive(power_class(complement(inverse(ordinal_numbers)))) || equal(image(element_relation,symmetrization_of(ordinal_numbers)),omega)** -> . % 300.04/300.41 213667[19:SpL:209198.0,203423.0] || subclass(image(element_relation,symmetrization_of(ordinal_numbers)),ordinal_numbers) -> member(omega,power_class(complement(inverse(ordinal_numbers))))*. % 300.04/300.41 213668[19:SpL:209198.0,203422.0] || subclass(image(element_relation,symmetrization_of(ordinal_numbers)),ordinal_numbers) -> member(ordinal_numbers,power_class(complement(inverse(ordinal_numbers))))*. % 300.04/300.41 213744[25:MRR:213743.2,192574.0] single_valued_class(power_class(complement(inverse(ordinal_numbers)))) || equal(image(element_relation,symmetrization_of(ordinal_numbers)),universal_class)** -> . % 300.04/300.41 213784[19:SpL:204449.1,212976.0] || equal(cross_product(singleton(regular(element_relation)),universal_class),ordinal_numbers)** equal(cantor(universal_class),universal_class) -> . % 300.04/300.41 213922[19:MRR:213834.2,167057.0] || member(u,intersection(complement(singleton(ordinal_numbers)),v))* member(u,singleton(ordinal_numbers)) -> . % 300.04/300.41 214049[19:MRR:213967.2,167057.0] || member(u,intersection(complement(inverse(ordinal_numbers)),v))* member(u,symmetrization_of(ordinal_numbers)) -> . % 300.04/300.41 214177[19:MRR:214094.2,167057.0] || member(u,intersection(v,complement(singleton(ordinal_numbers))))* member(u,singleton(ordinal_numbers)) -> . % 300.04/300.41 214299[19:MRR:214222.2,167057.0] || member(u,intersection(v,complement(inverse(ordinal_numbers))))* member(u,symmetrization_of(ordinal_numbers)) -> . % 300.04/300.41 214526[19:Res:214509.0,126.0] || subclass(kind_1_ordinals,u) well_ordering(v,u)* -> member(least(v,kind_1_ordinals),kind_1_ordinals)*. % 300.04/300.41 214947[25:MRR:214946.1,36583.1] function(u) || member(v,complement(u))* member(v,successor(u)) -> . % 300.04/300.41 214967[8:SpR:160282.0,12.0] || -> equal(regular(ordered_pair(u,v)),singleton(u)) member(regular(ordered_pair(u,v)),universal_class)*. % 300.04/300.41 215153[19:MRR:215147.1,5.0] || well_ordering(u,universal_class) -> equal(v,ordinal_numbers) equal(cantor(least(u,v)),ordinal_numbers)**. % 300.04/300.41 215220[19:Res:214528.1,16102.0] || subclass(kind_1_ordinals,symmetric_difference(complement(u),complement(v)))* -> member(ordinal_numbers,union(u,v)). % 300.04/300.41 216075[19:Rew:167055.0,216042.1,167231.0,216042.0] || member(u,complement(complement(v)))* subclass(universal_class,w) -> member(u,w)*. % 300.04/300.41 216659[19:SpL:481.0,214519.0] || equal(complement(complement(intersection(complement(singleton(ordinal_numbers)),union(u,v)))),singleton(ordinal_numbers))** -> . % 300.04/300.41 216963[19:Obv:216938.1] || member(u,v) -> subclass(unordered_pair(u,w),v)* equal(cantor(w),ordinal_numbers). % 300.04/300.41 216965[0:Obv:216955.2] || member(u,v) member(w,v) -> subclass(unordered_pair(u,w),v)*. % 300.04/300.41 217066[19:Obv:217040.1] || equal(u,v) -> equal(integer_of(v),ordinal_numbers) subclass(unordered_pair(v,u),omega)*. % 300.04/300.41 217067[0:Obv:217054.2] || equal(u,v) member(v,w) -> subclass(unordered_pair(v,u),w)*. % 300.04/300.41 217070[0:Obv:217038.1] || equal(u,v) -> member(v,w) subclass(unordered_pair(v,u),complement(w))*. % 300.04/300.41 217204[19:Obv:217177.1] || member(u,v) -> subclass(unordered_pair(w,u),v)* equal(cantor(w),ordinal_numbers). % 300.04/300.41 217464[0:Obv:217384.1] || subclass(u,v) -> subclass(intersection(u,w),intersection(v,intersection(u,w)))*. % 300.04/300.41 217769[0:Obv:217668.0] || -> subclass(intersection(intersection(u,v),w),intersection(v,intersection(intersection(u,v),w)))*. % 300.04/300.41 218046[0:Res:217853.0,2497.1] || member(u,universal_class) -> member(u,complement(intersection(v,w)))* member(u,w). % 300.04/300.41 218363[0:Obv:218265.0] || -> subclass(intersection(intersection(u,v),w),intersection(u,intersection(intersection(u,v),w)))*. % 300.04/300.41 218700[0:Obv:218621.1] || subclass(u,v) -> subclass(intersection(w,u),intersection(v,intersection(w,u)))*. % 300.04/300.41 218905[0:SpR:4121.0,218280.0] || -> subclass(intersection(symmetric_difference(cross_product(u,v),w),x),complement(restrict(w,u,v)))*. % 300.04/300.41 218906[0:SpR:4119.0,218280.0] || -> subclass(intersection(symmetric_difference(u,cross_product(v,w)),x),complement(restrict(u,v,w)))*. % 300.04/300.41 219355[0:Obv:219252.0] || -> subclass(intersection(u,intersection(v,w)),intersection(w,intersection(u,intersection(v,w))))*. % 300.04/300.41 219375[19:Res:219080.0,2497.1] || member(u,universal_class) -> member(u,complement(symmetrization_of(ordinal_numbers)))* member(u,inverse(ordinal_numbers)). % 300.04/300.41 219655[0:Obv:219555.0] || -> subclass(intersection(u,intersection(v,w)),intersection(v,intersection(u,intersection(v,w))))*. % 300.04/300.41 219914[0:Obv:219895.1] || subclass(u,symmetric_difference(v,w)) -> subclass(u,intersection(union(v,w),u))*. % 300.04/300.41 219983[0:Res:219703.0,2497.1] || member(u,universal_class) -> member(u,complement(complement(complement(v))))* member(u,v). % 300.04/300.41 220135[0:SpR:4121.0,218971.0] || -> subclass(complement(complement(symmetric_difference(cross_product(u,v),w))),complement(restrict(w,u,v)))*. % 300.04/300.41 220136[0:SpR:4119.0,218971.0] || -> subclass(complement(complement(symmetric_difference(u,cross_product(v,w)))),complement(restrict(u,v,w)))*. % 300.04/300.41 220219[0:Res:218971.0,2497.1] || member(u,universal_class) -> member(u,complement(intersection(v,w)))* member(u,v). % 300.04/300.41 220484[19:Res:220439.0,8.0] || subclass(complement(singleton(ordinal_numbers)),complement(kind_1_ordinals))* -> equal(complement(singleton(ordinal_numbers)),complement(kind_1_ordinals)). % 300.04/300.41 220492[0:SpR:206403.0,220426.0] || -> subclass(complement(successor(intersection(complement(u),power_class(v)))),union(u,complement(power_class(v))))*. % 300.04/300.41 220493[0:SpR:206410.0,220426.0] || -> subclass(complement(successor(intersection(power_class(u),complement(v)))),union(complement(power_class(u)),v))*. % 300.04/300.41 220518[0:Res:220426.0,8.0] || subclass(complement(u),complement(successor(u)))* -> equal(complement(successor(u)),complement(u)). % 300.04/300.41 220527[0:SpR:206403.0,220427.0] || -> subclass(complement(symmetrization_of(intersection(complement(u),power_class(v)))),union(u,complement(power_class(v))))*. % 300.04/300.41 220528[0:SpR:206410.0,220427.0] || -> subclass(complement(symmetrization_of(intersection(power_class(u),complement(v)))),union(complement(power_class(u)),v))*. % 300.04/300.41 220552[0:Res:220427.0,8.0] || subclass(complement(u),complement(symmetrization_of(u)))* -> equal(complement(symmetrization_of(u)),complement(u)). % 300.04/300.41 220566[0:SpR:4121.0,218968.0] || -> subclass(intersection(u,symmetric_difference(cross_product(v,w),x)),complement(restrict(x,v,w)))*. % 300.04/300.41 220567[0:SpR:4119.0,218968.0] || -> subclass(intersection(u,symmetric_difference(v,cross_product(w,x))),complement(restrict(v,w,x)))*. % 300.04/300.41 221370[27:Res:221347.0,11848.0] || subclass(intersection(singleton(ordinal_numbers),image(successor_relation,ordinal_numbers)),u)* well_ordering(universal_class,u) -> . % 300.04/300.41 221572[19:Res:219766.1,167739.0] || equal(complement(singleton(u)),ordinal_numbers)** -> equal(v,ordinal_numbers) equal(regular(v),u)*. % 300.04/300.41 221584[19:Res:219766.1,169099.2] || equal(complement(u),ordinal_numbers) member(u,universal_class) well_ordering(element_relation,u)* -> . % 300.04/300.41 221587[19:Res:219766.1,124906.1] || equal(complement(u),ordinal_numbers) subclass(u,v) -> section(w,u,v)*. % 300.04/300.41 221768[19:Res:219766.1,5426.1] function(u) || equal(complement(u),ordinal_numbers)** -> equal(cross_product(universal_class,universal_class),u)*. % 300.04/300.41 221789[19:Res:219766.1,167961.0] || equal(complement(singleton(u)),ordinal_numbers)** -> equal(integer_of(v),ordinal_numbers)** equal(v,u)*. % 300.04/300.41 221996[19:Rew:221566.1,215011.1] || equal(complement(complement(regular(ordered_pair(u,v)))),ordinal_numbers)** -> equal(singleton(u),ordinal_numbers). % 300.04/300.41 222040[19:Res:5.0,177427.0] || well_ordering(omega,universal_class) -> equal(integer_of(ordered_pair(singleton(u),least(omega,universal_class))),ordinal_numbers)**. % 300.04/300.41 222315[0:SpR:27.0,219698.0] || -> subclass(restrict(complement(union(u,v)),w,x),intersection(complement(u),complement(v)))*. % 300.04/300.41 223125[20:SpL:223022.0,182439.1] || subclass(rest_relation,rest_of(regular(complement(complement(symmetrization_of(ordinal_numbers))))))* well_ordering(universal_class,ordinal_numbers) -> . % 300.04/300.41 223129[20:MRR:223118.2,167057.0] || member(u,universal_class)* subclass(rest_relation,rest_of(regular(complement(complement(symmetrization_of(ordinal_numbers))))))* -> . % 300.04/300.41 223202[0:Res:53.0,79384.0] || -> equal(ordered_pair(first(ordered_pair(omega,omega)),second(ordered_pair(omega,omega))),ordered_pair(omega,omega))**. % 300.04/300.41 223235[19:Res:167011.0,79384.0] || -> equal(ordered_pair(first(ordered_pair(ordinal_numbers,omega)),second(ordered_pair(ordinal_numbers,omega))),ordered_pair(ordinal_numbers,omega))**. % 300.04/300.41 223480[19:MRR:213096.1,223479.0] || member(regular(union(u,complement(inverse(ordinal_numbers)))),intersection(complement(u),symmetrization_of(ordinal_numbers)))* -> . % 300.04/300.41 223553[8:Con:223543.0] || member(u,universal_class) subclass(composition_function,rest_of(v)) -> member(u,cantor(v))*. % 300.04/300.41 223619[19:MRR:213111.1,223618.0] || member(regular(union(complement(singleton(ordinal_numbers)),u)),intersection(singleton(ordinal_numbers),complement(u)))* -> . % 300.04/300.41 223671[19:MRR:213112.1,223670.0] || member(regular(union(complement(inverse(ordinal_numbers)),u)),intersection(symmetrization_of(ordinal_numbers),complement(u)))* -> . % 300.04/300.41 223814[19:MRR:223761.0,167011.0] || equal(complement(cantor(u)),kind_1_ordinals) -> equal(apply(u,ordinal_numbers),sum_class(range_of(ordinal_numbers)))**. % 300.04/300.41 224051[19:SpL:27.0,223787.1] inductive(intersection(complement(u),complement(v))) || equal(union(u,v),kind_1_ordinals)** -> . % 300.04/300.41 224060[19:SpL:167200.0,223787.1] inductive(image(element_relation,symmetrization_of(ordinal_numbers))) || equal(power_class(complement(inverse(ordinal_numbers))),kind_1_ordinals)** -> . % 300.04/300.41 224061[19:SpL:180125.0,223787.1] inductive(image(element_relation,singleton(ordinal_numbers))) || equal(power_class(complement(singleton(ordinal_numbers))),kind_1_ordinals)** -> . % 300.04/300.41 224062[19:SpL:206408.0,223787.1] inductive(image(element_relation,power_class(u))) || equal(power_class(complement(power_class(u))),kind_1_ordinals)** -> . % 300.04/300.41 224064[19:SpL:209197.0,223787.1] inductive(power_class(complement(singleton(ordinal_numbers)))) || equal(image(element_relation,singleton(ordinal_numbers)),kind_1_ordinals)** -> . % 300.04/300.41 224065[19:SpL:209198.0,223787.1] inductive(power_class(complement(inverse(ordinal_numbers)))) || equal(image(element_relation,symmetrization_of(ordinal_numbers)),kind_1_ordinals)** -> . % 300.04/300.41 224131[19:Res:9820.1,219089.0] || equal(sum_class(symmetrization_of(ordinal_numbers)),symmetrization_of(ordinal_numbers)) -> subclass(sum_class(symmetrization_of(ordinal_numbers)),inverse(ordinal_numbers))*. % 300.04/300.41 224471[0:Con:224461.0] || member(u,universal_class)* subclass(composition_function,cross_product(v,w))* -> member(u,v)*. % 300.04/300.41 224606[19:Res:203424.1,4728.0] || subclass(complement(composition_function),ordinal_numbers) -> equal(compose(singleton(ordered_pair(u,v)),u),v)**. % 300.04/300.41 225261[19:SpL:168412.1,225030.0] || equal(successor(regular(cross_product(u,v))),ordinal_numbers)** -> equal(cross_product(u,v),ordinal_numbers). % 300.04/300.41 225354[19:Res:53.0,176248.0] || subclass(domain_relation,u)* subclass(u,v)* -> member(ordered_pair(omega,ordinal_numbers),v)*. % 300.04/300.41 226111[0:SpR:207712.0,218971.0] || -> subclass(complement(complement(symmetric_difference(power_class(u),complement(v)))),union(complement(power_class(u)),v))*. % 300.04/300.41 226130[0:SpR:207712.0,218280.0] || -> subclass(intersection(symmetric_difference(power_class(u),complement(v)),w),union(complement(power_class(u)),v))*. % 300.04/300.41 226142[0:SpR:207712.0,218968.0] || -> subclass(intersection(u,symmetric_difference(power_class(v),complement(w))),union(complement(power_class(v)),w))*. % 300.04/300.41 226343[19:SpL:168412.1,225698.0] || equal(symmetrization_of(regular(cross_product(u,v))),ordinal_numbers)** -> equal(cross_product(u,v),ordinal_numbers). % 300.04/300.41 227077[0:SpR:207752.0,218971.0] || -> subclass(complement(complement(symmetric_difference(complement(u),power_class(v)))),union(u,complement(power_class(v))))*. % 300.04/300.41 227096[0:SpR:207752.0,218280.0] || -> subclass(intersection(symmetric_difference(complement(u),power_class(v)),w),union(u,complement(power_class(v))))*. % 300.04/300.41 227108[0:SpR:207752.0,218968.0] || -> subclass(intersection(u,symmetric_difference(complement(v),power_class(w))),union(v,complement(power_class(w))))*. % 300.04/300.41 227803[19:Res:221767.1,2.0] || equal(complement(u),ordinal_numbers) subclass(u,v)* -> member(regular(element_relation),v)*. % 300.04/300.41 227811[19:Res:221767.1,4127.0] || equal(complement(symmetric_difference(u,v)),ordinal_numbers) -> member(regular(element_relation),union(u,v))*. % 300.04/300.41 227813[19:Res:221767.1,16910.0] || equal(complement(symmetric_difference(u,inverse(u))),ordinal_numbers)** -> member(regular(element_relation),symmetrization_of(u)). % 300.04/300.41 227856[19:Rew:27.0,227807.0] || equal(union(u,v),ordinal_numbers) member(regular(element_relation),union(u,v))* -> . % 300.04/300.41 228008[19:Res:223552.1,2.0] || subclass(composition_function,rest_of(u)) subclass(cantor(u),v)* -> member(ordinal_numbers,v). % 300.04/300.41 228322[0:MRR:228300.0,170.0] || well_ordering(u,universal_class) -> member(least(u,ordered_pair(v,w)),ordered_pair(v,w))*. % 300.04/300.41 229061[19:SpR:225013.1,192178.0] || equal(successor(cross_product(u,universal_class)),ordinal_numbers)** -> equal(image(universal_class,u),range_of(ordinal_numbers)). % 300.04/300.41 229342[19:SpL:225013.1,148647.0] || equal(successor(complement(u)),ordinal_numbers)** member(v,universal_class)* -> member(v,u)*. % 300.04/300.41 229506[19:SpL:225013.1,192214.0] || equal(successor(cross_product(singleton(u),universal_class)),ordinal_numbers)** member(u,cantor(universal_class)) -> . % 300.04/300.41 229507[22:SpL:225013.1,192342.0] || equal(successor(cross_product(singleton(ordinal_numbers),universal_class)),ordinal_numbers)** equal(cantor(universal_class),omega) -> . % 300.04/300.41 229508[22:SpL:225013.1,192343.0] || equal(successor(cross_product(singleton(ordinal_numbers),universal_class)),ordinal_numbers)** subclass(omega,cantor(universal_class)) -> . % 300.04/300.41 229509[19:SpL:225013.1,192345.0] || equal(successor(cross_product(singleton(ordinal_numbers),universal_class)),ordinal_numbers)** subclass(universal_class,cantor(universal_class)) -> . % 300.04/300.41 229510[19:SpL:225013.1,192346.0] || equal(successor(cross_product(singleton(ordinal_numbers),universal_class)),ordinal_numbers)** equal(cantor(universal_class),universal_class) -> . % 300.04/300.41 229513[19:SpL:225013.1,215230.0] || equal(successor(cross_product(singleton(ordinal_numbers),universal_class)),ordinal_numbers)** subclass(kind_1_ordinals,cantor(universal_class)) -> . % 300.04/300.41 229514[19:SpL:225013.1,216495.0] || equal(successor(cross_product(singleton(ordinal_numbers),universal_class)),ordinal_numbers)** equal(cantor(universal_class),kind_1_ordinals) -> . % 300.04/300.41 229515[19:SpL:225013.1,228011.0] || equal(successor(cross_product(singleton(ordinal_numbers),universal_class)),ordinal_numbers)** subclass(composition_function,rest_of(universal_class)) -> . % 300.04/300.41 229516[19:SpL:225013.1,228187.0] || equal(successor(cross_product(singleton(ordinal_numbers),universal_class)),ordinal_numbers)** equal(rest_of(universal_class),composition_function) -> . % 300.04/300.41 229517[19:SpL:225013.1,192319.0] || equal(successor(cross_product(singleton(omega),universal_class)),ordinal_numbers)** equal(cantor(universal_class),universal_class) -> . % 300.04/300.41 229518[19:SpL:225013.1,192320.0] || equal(successor(cross_product(singleton(omega),universal_class)),ordinal_numbers)** subclass(universal_class,cantor(universal_class)) -> . % 300.04/300.41 230361[0:Obv:230311.1] || member(u,symmetric_difference(v,w)) -> subclass(singleton(u),complement(intersection(v,w)))*. % 300.04/300.41 230845[19:Res:229698.1,169097.1] || equal(successor(sum_class(u)),ordinal_numbers)** well_ordering(element_relation,u) -> equal(u,ordinal_numbers). % 300.04/300.41 231068[19:Res:229698.1,167105.1] || equal(successor(image(successor_relation,u)),ordinal_numbers)** member(ordinal_numbers,u) -> inductive(u). % 300.04/300.41 231517[19:Obv:231477.0] || -> equal(intersection(symmetric_difference(u,v),singleton(w)),ordinal_numbers)** member(w,union(u,v)). % 300.04/300.41 231753[19:Obv:231712.0] || -> equal(intersection(singleton(u),symmetric_difference(v,w)),ordinal_numbers)** member(u,union(v,w)). % 300.04/300.41 231887[19:SSi:231845.0,70.0] || -> equal(unordered_pair(u,v),ordinal_numbers) member(u,unordered_pair(u,v))* member(v,universal_class). % 300.04/300.41 232026[19:SSi:231984.0,70.0] || -> equal(unordered_pair(u,v),ordinal_numbers) member(v,unordered_pair(u,v))* member(u,universal_class). % 300.04/300.41 232104[19:MRR:232054.0,167011.0] || equal(symmetrization_of(cantor(u)),ordinal_numbers) -> equal(apply(u,ordinal_numbers),sum_class(range_of(ordinal_numbers)))**. % 300.04/300.41 232334[0:Obv:232303.2] || subclass(u,v) subclass(u,w) -> subclass(u,intersection(v,w))*. % 300.04/300.41 232340[0:Obv:232304.1] || subclass(intersection(u,v),w) -> subclass(intersection(u,v),intersection(v,w))*. % 300.04/300.41 232341[0:Obv:232299.1] || subclass(intersection(u,v),w) -> subclass(intersection(u,v),intersection(u,w))*. % 300.04/300.41 232342[0:Obv:232298.1] || subclass(complement(complement(u)),v) -> subclass(complement(complement(u)),intersection(u,v))*. % 300.04/300.41 232676[0:Obv:232614.1] || subclass(intersection(u,v),w) -> subclass(intersection(u,v),intersection(w,v))*. % 300.04/300.41 232709[0:Obv:232591.1] || member(u,v) -> subclass(intersection(w,singleton(u)),intersection(v,singleton(u)))*. % 300.04/300.41 232732[8:MRR:232603.0,36682.1] || subclass(rest_relation,rest_of(u)) -> subclass(intersection(v,w),intersection(cantor(u),w))*. % 300.04/300.41 232821[19:Res:6303.1,225690.1] || subclass(universal_class,symmetric_difference(u,v))* equal(symmetrization_of(union(u,v)),ordinal_numbers) -> . % 300.04/300.41 232822[19:Res:6403.1,225690.1] || equal(symmetric_difference(u,v),universal_class) equal(symmetrization_of(union(u,v)),ordinal_numbers)** -> . % 300.04/300.41 232838[19:MRR:232810.0,53.0] || equal(symmetrization_of(cantor(u)),ordinal_numbers) -> equal(apply(u,omega),sum_class(range_of(ordinal_numbers)))**. % 300.04/300.41 233067[0:Obv:233006.1] || subclass(intersection(u,v),w) -> subclass(intersection(u,v),intersection(w,u))*. % 300.04/300.41 233096[0:Obv:232982.1] || member(u,v) -> subclass(intersection(singleton(u),w),intersection(v,singleton(u)))*. % 300.04/300.41 233124[8:MRR:232995.0,36682.1] || subclass(rest_relation,rest_of(u)) -> subclass(intersection(v,w),intersection(cantor(u),v))*. % 300.04/300.41 234627[19:Rew:233390.0,233887.1] || subclass(complement(u),v)* -> member(ordinal_numbers,complement(complement(u)))* member(ordinal_numbers,v). % 300.04/300.41 234156[19:Rew:233390.0,168337.1] inductive(symmetric_difference(domain_of(u),universal_class)) || equal(complement(complement(cantor(u))),universal_class)** -> . % 300.04/300.41 234158[19:Rew:233390.0,168400.1] inductive(symmetric_difference(cantor(inverse(u)),identity_relation)) || -> member(ordinal_numbers,complement(complement(range_of(u))))*. % 300.04/300.41 234166[19:Rew:233390.0,168401.1] inductive(symmetric_difference(union(identity_relation,u),universal_class)) || -> member(ordinal_numbers,complement(complement(complement(u))))*. % 300.04/300.41 234223[19:Rew:233390.0,188008.1] inductive(symmetric_difference(complement(u),symmetric_difference(universal_class,u))) || -> member(ordinal_numbers,complement(complement(u)))*. % 300.04/300.41 234227[19:Rew:233390.0,168208.1] inductive(symmetric_difference(complement(intersection(universal_class,u)),universal_class)) || -> member(ordinal_numbers,complement(complement(u)))*. % 300.04/300.41 234264[19:Rew:233390.0,188616.1] || member(ordinal_numbers,u) subclass(complement(complement(u)),v)* -> member(ordinal_numbers,v). % 300.04/300.41 234380[19:Rew:234363.0,168402.1] inductive(symmetric_difference(union(u,identity_relation),universal_class)) || -> member(ordinal_numbers,complement(complement(complement(u))))*. % 300.04/300.41 234847[19:Rew:234692.0,223438.0] || member(regular(union(u,complement(singleton(ordinal_numbers)))),intersection(singleton(ordinal_numbers),complement(u)))* -> . % 300.04/300.41 234903[0:Rew:234713.0,209540.0] || -> equal(symmetric_difference(complement(power_class(u)),complement(power_class(v))),symmetric_difference(power_class(u),power_class(v)))**. % 300.04/300.41 235579[19:Rew:235542.0,168329.1] inductive(symmetric_difference(complement(intersection(u,universal_class)),universal_class)) || -> member(ordinal_numbers,complement(complement(u)))*. % 300.04/300.41 235978[19:SpR:234709.0,149012.1] || subclass(complement(compose(element_relation,universal_class)),element_relation)* -> equal(complement(compose(element_relation,universal_class)),ordinal_numbers). % 300.04/300.41 236284[19:SpR:234692.0,168351.1] || -> equal(intersection(u,singleton(v)),ordinal_numbers) equal(regular(intersection(singleton(v),u)),v)**. % 300.04/300.41 236327[19:SpR:234692.0,168356.1] || -> equal(intersection(singleton(u),v),ordinal_numbers) equal(regular(intersection(v,singleton(u))),u)**. % 300.04/300.41 236578[0:SpL:234692.0,42071.0] || member(not_subclass_element(u,intersection(u,v)),v)* -> subclass(u,intersection(v,u)). % 300.04/300.41 236762[19:Rew:208285.0,236688.0] || -> equal(complement(intersection(symmetrization_of(ordinal_numbers),power_class(u))),complement(intersection(power_class(u),symmetrization_of(ordinal_numbers))))*. % 300.04/300.41 236788[0:SpR:234713.0,16276.0] || -> subclass(symmetric_difference(union(u,v),complement(intersection(u,v))),complement(symmetric_difference(u,v)))*. % 300.04/300.41 237481[0:Rew:479.0,237221.0] || -> equal(power_class(intersection(complement(u),complement(v))),power_class(intersection(complement(v),complement(u))))*. % 300.04/300.41 237227[0:SpR:236669.0,12807.1] || subclass(universal_class,symmetric_difference(u,v)) -> member(unordered_pair(w,x),union(v,u))*. % 300.04/300.41 237229[19:SpR:236669.0,168354.1] || -> equal(symmetric_difference(u,v),ordinal_numbers) member(regular(symmetric_difference(u,v)),union(v,u))*. % 300.04/300.41 237483[0:Rew:208286.0,237254.0] || -> equal(complement(intersection(power_class(u),power_class(v))),complement(intersection(power_class(v),power_class(u))))*. % 300.04/300.41 237707[19:Rew:237493.0,237682.0] || -> equal(successor(u),ordinal_numbers) member(regular(successor(u)),complement(intersection(u,singleton(u))))*. % 300.04/300.41 237771[19:SpR:237384.0,168354.1] || -> equal(symmetric_difference(u,v),ordinal_numbers) member(regular(symmetric_difference(v,u)),union(u,v))*. % 300.04/300.41 237806[0:SpL:237384.0,16102.0] || member(u,symmetric_difference(complement(v),complement(w)))* -> member(u,union(w,v)). % 300.04/300.41 238060[19:SpR:237974.1,27.0] || equal(intersection(complement(u),complement(v)),universal_class)** -> equal(union(u,v),ordinal_numbers). % 300.04/300.41 238134[19:SpR:237974.1,206408.0] || equal(image(element_relation,power_class(u)),universal_class)** -> equal(power_class(complement(power_class(u))),ordinal_numbers). % 300.04/300.41 239081[19:SpR:237603.0,188752.1] || equal(complement(complement(intersection(u,singleton(u)))),universal_class)** -> equal(successor(u),ordinal_numbers). % 300.04/300.41 239112[19:SpL:237603.0,5473.0] || subclass(universal_class,successor(u)) -> member(singleton(v),complement(intersection(u,singleton(u))))*. % 300.04/300.41 239118[19:SpL:237603.0,15276.0] || equal(successor(u),universal_class) -> member(singleton(v),complement(intersection(u,singleton(u))))*. % 300.04/300.41 239127[19:SpL:237603.0,169223.0] || equal(successor(u),singleton(ordinal_numbers)) -> member(ordinal_numbers,complement(intersection(u,singleton(u))))*. % 300.04/300.41 239183[19:Rew:237603.0,239155.1] || member(regular(successor(u)),intersection(u,singleton(u)))* -> equal(successor(u),ordinal_numbers). % 300.04/300.41 239239[19:EmS:167895.0,167895.1,73.1,238779.1] one_to_one(u) || equal(inverse(u),universal_class)** -> member(ordinal_numbers,cross_product(universal_class,universal_class))*. % 300.04/300.41 239720[19:Res:238770.1,167737.0] || equal(intersection(u,v),universal_class)** -> equal(w,ordinal_numbers) member(regular(w),v)*. % 300.04/300.41 239721[19:Res:238770.1,167736.0] || equal(intersection(u,v),universal_class)** -> equal(w,ordinal_numbers) member(regular(w),u)*. % 300.04/300.41 239726[19:Res:238770.1,16469.0] || equal(singleton(u),universal_class)** -> subclass(v,w) equal(not_subclass_element(v,w),u)*. % 300.04/300.41 239739[21:Res:238770.1,175799.0] || equal(u,universal_class) well_ordering(v,u)* -> member(least(v,omega),omega)*. % 300.04/300.41 239916[19:Res:238770.1,5331.0] || equal(compose(u,v),universal_class)** -> equal(compose(u,v),cross_product(universal_class,universal_class)). % 300.04/300.41 239919[19:Res:238770.1,1067.0] || equal(rotate(u),universal_class) -> equal(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(u))*. % 300.04/300.41 239920[19:Res:238770.1,1066.0] || equal(flip(u),universal_class) -> equal(cross_product(cross_product(universal_class,universal_class),universal_class),flip(u))*. % 300.04/300.41 239952[19:Res:238770.1,35668.0] || equal(u,universal_class) well_ordering(v,u)* -> member(least(v,rest_relation),rest_relation)*. % 300.04/300.41 240102[19:Res:238770.1,168377.0] || equal(intersection(u,v),universal_class)** -> equal(integer_of(w),ordinal_numbers) member(w,u)*. % 300.04/300.41 240103[19:Res:238770.1,168376.0] || equal(intersection(u,v),universal_class)** -> equal(integer_of(w),ordinal_numbers) member(w,v)*. % 300.04/300.41 240670[19:Rew:218039.1,240615.0] || member(u,successor(u)) -> equal(complement(complement(intersection(u,singleton(u)))),ordinal_numbers)**. % 300.04/300.41 240681[19:SpR:30.0,237678.0] || -> subclass(successor(cross_product(u,v)),complement(restrict(singleton(cross_product(u,v)),u,v)))*. % 300.04/300.41 240997[19:SpR:149012.1,240703.0] || subclass(singleton(singleton(ordinal_numbers)),singleton(ordinal_numbers)) -> member(ordinal_numbers,complement(singleton(singleton(ordinal_numbers))))*. % 300.04/300.41 241010[19:Res:240703.0,2.0] || subclass(complement(intersection(singleton(ordinal_numbers),singleton(singleton(ordinal_numbers)))),u)* -> member(ordinal_numbers,u). % 300.04/300.41 241100[0:SpR:234704.0,207752.0] || -> equal(symmetric_difference(complement(power_class(u)),power_class(v)),symmetric_difference(power_class(u),complement(power_class(v))))**. % 300.04/300.41 241245[19:Rew:4125.0,241146.0,236669.0,241146.0,236669.0,241146.0,237384.0,241146.0] || -> equal(symmetric_difference(complement(singleton(ordinal_numbers)),complement(power_class(u))),symmetric_difference(singleton(ordinal_numbers),power_class(u)))**. % 300.04/300.41 242250[19:Rew:242249.1,228166.1] || equal(rest_of(regular(ordered_pair(u,v))),composition_function)** -> equal(regular(ordinal_numbers),singleton(u)). % 300.04/300.41 243753[19:Res:9820.1,239702.0] || equal(sum_class(symmetrization_of(ordinal_numbers)),symmetrization_of(ordinal_numbers))** equal(sum_class(symmetrization_of(ordinal_numbers)),universal_class) -> . % 300.04/300.41 245313[19:SpL:27838.0,215210.0] || subclass(kind_1_ordinals,symmetric_difference(complement(u),complement(singleton(u))))* -> member(ordinal_numbers,successor(u)). % 300.04/300.41 245314[19:SpL:27837.0,215210.0] || subclass(kind_1_ordinals,symmetric_difference(complement(u),complement(inverse(u))))* -> member(ordinal_numbers,symmetrization_of(u)). % 300.04/300.41 245403[19:SpR:225013.1,217960.0] || equal(successor(complement(symmetric_difference(u,inverse(u)))),ordinal_numbers)** -> subclass(universal_class,symmetrization_of(u)). % 300.04/300.41 245604[19:Rew:209198.0,245589.0] || equal(image(element_relation,symmetrization_of(ordinal_numbers)),ordinal_numbers) -> subclass(image(element_relation,symmetrization_of(ordinal_numbers)),u)*. % 300.04/300.41 245605[19:Rew:209197.0,245590.0] || equal(image(element_relation,singleton(ordinal_numbers)),ordinal_numbers) -> subclass(image(element_relation,singleton(ordinal_numbers)),u)*. % 300.04/300.41 245606[19:Rew:209199.0,245591.0] || equal(image(element_relation,power_class(u)),ordinal_numbers) -> subclass(image(element_relation,power_class(u)),v)*. % 300.04/300.41 246044[19:Res:2523.2,229738.1] || member(u,universal_class)* subclass(rest_relation,v)* equal(successor(v),ordinal_numbers) -> . % 300.04/300.41 246108[19:Res:168353.1,229738.1] || equal(successor(complement(intersection(u,v))),ordinal_numbers)** -> equal(symmetric_difference(u,v),ordinal_numbers). % 300.04/300.41 246125[19:Res:168349.1,229738.1] || equal(successor(cross_product(u,v)),ordinal_numbers) -> equal(restrict(w,u,v),ordinal_numbers)**. % 300.04/300.41 246322[25:SpR:234134.1,225013.1] function(u) || equal(successor(complement(u)),ordinal_numbers)** -> equal(successor(u),universal_class). % 300.04/300.41 246326[25:SpR:234134.1,148172.0] function(u) || -> equal(intersection(complement(u),complement(successor(u))),complement(successor(u)))**. % 300.04/300.41 246328[25:SpR:234134.1,234130.1] function(u) || member(ordinal_numbers,complement(u)) -> member(ordinal_numbers,complement(successor(u)))*. % 300.04/300.41 246335[25:SpR:234134.1,16762.0] function(u) || -> subclass(symmetric_difference(successor(u),complement(v)),union(complement(u),v))*. % 300.04/300.41 246349[25:SpR:234134.1,182467.1] function(u) || -> member(singleton(ordinal_numbers),complement(u))* member(singleton(ordinal_numbers),successor(u)). % 300.04/300.41 246358[25:SpR:234134.1,198248.0] function(u) || -> equal(intersection(successor(u),restrict(complement(u),v,w)),ordinal_numbers)**. % 300.04/300.41 246369[25:SpR:234134.1,16762.0] function(u) || -> subclass(symmetric_difference(complement(v),successor(u)),union(v,complement(u)))*. % 300.04/300.41 246408[25:SpR:234134.1,219943.0] function(complement(symmetrization_of(ordinal_numbers))) || -> subclass(successor(complement(symmetrization_of(ordinal_numbers))),complement(inverse(ordinal_numbers)))*. % 300.04/300.41 246414[25:SpR:234134.1,217976.0] function(restrict(u,v,w)) || -> subclass(successor(restrict(u,v,w)),u)*. % 300.04/300.41 246430[25:SpR:180103.0,234134.1] function(complement(singleton(ordinal_numbers))) || -> equal(successor(complement(singleton(ordinal_numbers))),complement(singleton(ordinal_numbers)))**. % 300.04/300.41 246431[25:SpR:167191.0,234134.1] function(complement(inverse(ordinal_numbers))) || -> equal(successor(complement(inverse(ordinal_numbers))),complement(symmetrization_of(ordinal_numbers)))**. % 300.04/300.41 246432[25:SpR:206407.0,234134.1] function(complement(power_class(u))) || -> equal(successor(complement(power_class(u))),complement(power_class(u)))**. % 300.04/300.41 246461[25:SpL:234134.1,167096.0] function(u) || subclass(universal_class,successor(u)) member(ordinal_numbers,complement(u))* -> . % 300.04/300.41 246462[25:SpL:234134.1,164453.1] function(u) || subclass(domain_relation,complement(u))* subclass(universal_class,successor(u)) -> . % 300.04/300.41 246463[25:SpL:234134.1,2532.0] function(u) || subclass(universal_class,successor(u)) member(omega,complement(u))* -> . % 300.04/300.41 246464[25:SpL:234134.1,167093.0] function(u) || subclass(universal_class,complement(successor(u)))* -> member(ordinal_numbers,complement(u)). % 300.04/300.41 246465[25:SpL:234134.1,148626.0] function(u) || subclass(universal_class,complement(successor(u)))* -> member(omega,complement(u)). % 300.04/300.41 246470[25:SpL:234134.1,6422.0] function(u) || equal(complement(successor(u)),universal_class) -> member(omega,complement(u))*. % 300.04/300.41 246471[25:SpL:234134.1,177183.0] function(u) || subclass(omega,complement(successor(u)))* -> member(ordinal_numbers,complement(u)). % 300.04/300.41 246472[25:SpL:234134.1,178014.0] function(u) || equal(complement(successor(u)),omega) -> member(ordinal_numbers,complement(u))*. % 300.04/300.41 246475[25:SpL:234134.1,221566.0] function(u) || equal(complement(successor(u)),ordinal_numbers)** -> equal(complement(u),ordinal_numbers). % 300.04/300.41 246476[25:SpL:234134.1,215201.0] function(u) || subclass(kind_1_ordinals,complement(successor(u)))* -> member(ordinal_numbers,complement(u)). % 300.04/300.41 246477[25:SpL:234134.1,217156.0] function(u) || equal(complement(successor(u)),kind_1_ordinals) -> member(ordinal_numbers,complement(u))*. % 300.04/300.41 246482[25:SpL:234134.1,97509.1] function(u) || subclass(domain_relation,complement(u))* subclass(domain_relation,successor(u)) -> . % 300.04/300.41 246486[25:SpL:234134.1,97574.1] function(u) || equal(complement(u),domain_relation)** equal(successor(u),domain_relation) -> . % 300.04/300.41 246487[25:SpL:234134.1,186989.0] function(u) || subclass(complement(u),successor(u))* -> equal(complement(u),ordinal_numbers). % 300.04/300.41 246492[25:SpL:234134.1,182395.0] function(u) || well_ordering(universal_class,successor(u)) -> member(singleton(ordinal_numbers),complement(u))*. % 300.04/300.41 246497[25:SpL:234134.1,177179.0] function(u) || subclass(omega,successor(u)) member(ordinal_numbers,complement(u))* -> . % 300.04/300.41 246498[25:SpL:234134.1,217231.1] function(u) || equal(complement(u),kind_1_ordinals)** equal(successor(u),omega) -> . % 300.04/300.41 246500[25:SpL:234134.1,178652.1] function(u) || equal(complement(u),omega)** equal(successor(u),omega) -> . % 300.04/300.41 246503[25:SpL:234134.1,180886.1] function(u) inductive(complement(u)) || equal(successor(u),singleton(ordinal_numbers))** -> . % 300.04/300.41 246510[25:SpL:234134.1,211666.0] function(u) || subclass(successor(u),ordinal_numbers) well_ordering(universal_class,complement(u))* -> . % 300.04/300.41 246513[25:SpL:234134.1,215196.0] function(u) || subclass(kind_1_ordinals,successor(u)) member(ordinal_numbers,complement(u))* -> . % 300.04/300.41 246514[25:SpL:234134.1,228219.1] function(u) || equal(complement(u),kind_1_ordinals)** equal(successor(u),kind_1_ordinals) -> . % 300.04/300.41 246515[25:SpL:234134.1,223782.1] function(u) || equal(complement(u),omega)** equal(successor(u),kind_1_ordinals) -> . % 300.04/300.41 246518[25:SpL:234134.1,235552.0] function(u) || equal(successor(successor(u)),ordinal_numbers)** -> equal(complement(u),universal_class). % 300.04/300.41 246521[25:SpL:234134.1,225693.0] function(u) || equal(symmetrization_of(successor(u)),ordinal_numbers) -> member(omega,complement(u))*. % 300.04/300.41 246522[25:SpL:234134.1,225692.0] function(u) || equal(symmetrization_of(successor(u)),ordinal_numbers) -> member(ordinal_numbers,complement(u))*. % 300.04/300.41 246533[25:SpL:234134.1,148647.0] function(u) || member(v,complement(successor(u)))* -> member(v,complement(u)). % 300.04/300.41 246572[25:SpL:234134.1,189434.0] function(symmetrization_of(u)) || equal(successor(symmetrization_of(u)),universal_class)** -> connected(u,v)*. % 300.04/300.41 246648[25:Rew:234134.1,246380.2] function(u) || -> member(not_subclass_element(successor(u),v),u)* subclass(successor(u),v). % 300.04/300.41 246655[25:Rew:234134.1,246495.2] function(u) || subclass(successor(u),complement(u))* -> equal(successor(u),ordinal_numbers). % 300.04/300.41 246656[25:Rew:234134.1,246505.1] function(u) || equal(successor(u),universal_class) well_ordering(element_relation,successor(u))* -> . % 300.04/300.41 247317[19:SpL:4125.0,238772.0] || equal(symmetric_difference(complement(u),complement(v)),universal_class)** -> subclass(universal_class,union(u,v)). % 300.04/300.41 247318[19:SpL:27838.0,238772.0] || equal(symmetric_difference(complement(u),complement(singleton(u))),universal_class)** -> subclass(universal_class,successor(u)). % 300.04/300.41 247319[19:SpL:27837.0,238772.0] || equal(symmetric_difference(complement(u),complement(inverse(u))),universal_class)** -> subclass(universal_class,symmetrization_of(u)). % 300.04/300.41 248160[19:SpL:4125.0,245337.0] || equal(symmetric_difference(complement(u),complement(v)),kind_1_ordinals)** -> member(ordinal_numbers,union(u,v)). % 300.04/300.41 248161[19:SpL:27838.0,245337.0] || equal(symmetric_difference(complement(u),complement(singleton(u))),kind_1_ordinals)** -> member(ordinal_numbers,successor(u)). % 300.04/300.41 248162[19:SpL:27837.0,245337.0] || equal(symmetric_difference(complement(u),complement(inverse(u))),kind_1_ordinals)** -> member(ordinal_numbers,symmetrization_of(u)). % 300.04/300.41 248480[25:SpR:225013.1,246387.1] function(u) || equal(successor(complement(successor(u))),ordinal_numbers)** -> subclass(universal_class,u). % 300.04/300.41 248533[25:SpL:225013.1,246509.1] function(u) || equal(successor(u),ordinal_numbers) equal(successor(u),universal_class)** -> . % 300.04/300.41 248653[19:SpR:225013.1,217958.0] || equal(successor(complement(symmetric_difference(u,v))),ordinal_numbers)** -> subclass(universal_class,union(u,v)). % 300.04/300.41 248655[25:SpR:234134.1,217958.0] function(symmetric_difference(u,v)) || -> subclass(successor(symmetric_difference(u,v)),union(u,v))*. % 300.04/300.41 248756[25:SpL:234134.1,219712.0] function(u) || subclass(v,complement(successor(u)))* -> subclass(v,complement(u)). % 300.04/300.41 248790[19:Res:167355.1,219712.0] || equal(sum_class(complement(complement(u))),ordinal_numbers) -> subclass(sum_class(complement(complement(u))),u)*. % 300.04/300.41 248814[25:Res:246387.1,219712.0] function(complement(complement(u))) || -> subclass(complement(complement(successor(complement(complement(u))))),u)*. % 300.04/300.41 248835[0:SpR:206403.0,248818.0] || -> subclass(complement(successor(union(u,complement(power_class(v))))),intersection(complement(u),power_class(v)))*. % 300.04/300.41 248838[0:SpR:206410.0,248818.0] || -> subclass(complement(successor(union(complement(power_class(u)),v))),intersection(power_class(u),complement(v)))*. % 300.04/300.41 248863[0:Res:248818.0,8.0] || subclass(u,complement(successor(complement(u))))* -> equal(complement(successor(complement(u))),u). % 300.04/300.41 248952[0:SpR:206403.0,248819.0] || -> subclass(complement(symmetrization_of(union(u,complement(power_class(v))))),intersection(complement(u),power_class(v)))*. % 300.04/300.41 248955[0:SpR:206410.0,248819.0] || -> subclass(complement(symmetrization_of(union(complement(power_class(u)),v))),intersection(power_class(u),complement(v)))*. % 300.04/300.41 248980[0:Res:248819.0,8.0] || subclass(u,complement(symmetrization_of(complement(u))))* -> equal(complement(symmetrization_of(complement(u))),u). % 300.04/300.41 249105[0:Res:248816.0,2497.1] || member(u,universal_class) -> member(u,union(v,complement(w)))* member(u,w). % 300.04/300.41 249271[0:Res:248817.0,2497.1] || member(u,universal_class) -> member(u,union(complement(v),w))* member(u,v). % 300.04/300.41 249670[0:SpR:27.0,248882.0] || -> subclass(complement(successor(complement(complement(union(u,v))))),intersection(complement(u),complement(v)))*. % 300.04/300.41 249787[0:SpR:27.0,248999.0] || -> subclass(complement(symmetrization_of(complement(complement(union(u,v))))),intersection(complement(u),complement(v)))*. % 300.04/300.41 250049[0:SpR:27.0,248806.0] || -> member(u,union(v,w)) subclass(singleton(u),intersection(complement(v),complement(w)))*. % 300.04/300.41 250063[0:SpR:206408.0,248806.0] || -> member(u,power_class(complement(power_class(v)))) subclass(singleton(u),image(element_relation,power_class(v)))*. % 300.04/300.41 250070[27:Res:248806.0,221036.1] || member(u,kind_1_ordinals) -> subclass(singleton(u),intersection(singleton(ordinal_numbers),image(successor_relation,ordinal_numbers)))*. % 300.04/300.41 250072[8:Res:248806.0,82995.1] || member(u,element_relation) -> subclass(singleton(u),compose(element_relation,universal_class))* member(u,v)*. % 300.04/300.41 250078[0:Res:248806.0,11848.0] || subclass(complement(u),v)* well_ordering(universal_class,v) -> subclass(singleton(w),u)*. % 300.04/300.41 250086[0:Res:248806.0,284.0] || -> subclass(singleton(not_subclass_element(complement(complement(u)),v)),u)* subclass(complement(complement(u)),v). % 300.04/300.41 250825[19:SpL:480.0,250368.0] || equal(successor(complement(intersection(union(u,v),complement(complement(symmetrization_of(ordinal_numbers)))))),ordinal_numbers)** -> . % 300.04/300.41 250844[19:SpL:481.0,250609.0] || equal(successor(complement(intersection(complement(complement(symmetrization_of(ordinal_numbers))),union(u,v)))),ordinal_numbers)** -> . % 300.04/300.41 250869[25:SpR:234134.1,248811.0] function(u) || -> subclass(complement(complement(complement(complement(complement(successor(u)))))),complement(u))*. % 300.04/300.41 250901[19:SpR:225013.1,248811.0] || equal(successor(complement(complement(complement(complement(complement(u)))))),ordinal_numbers)** -> subclass(universal_class,u). % 300.04/300.41 251169[25:SpL:234134.1,248972.0] function(u) || equal(symmetrization_of(successor(u)),ordinal_numbers) -> subclass(universal_class,complement(u))*. % 300.04/300.41 251198[25:SpL:234134.1,250085.0] function(u) || subclass(successor(u),ordinal_numbers) -> subclass(singleton(omega),complement(u))*. % 300.04/300.41 251384[25:SpL:234134.1,250124.0] function(u) || subclass(successor(u),ordinal_numbers) -> subclass(singleton(ordinal_numbers),complement(u))*. % 300.04/300.41 251438[25:SpL:234134.1,248778.0] function(u) || equal(complement(successor(u)),universal_class) -> subclass(v,complement(u))*. % 300.04/300.41 251475[25:SpR:234134.1,248783.0] function(u) || -> subclass(intersection(complement(complement(complement(successor(u)))),v),complement(u))*. % 300.04/300.41 251501[25:SpR:234134.1,248783.0] function(complement(complement(u))) || -> subclass(intersection(successor(complement(complement(u))),v),u)*. % 300.04/300.41 251805[25:SpR:234134.1,248798.0] function(u) || -> subclass(intersection(v,complement(complement(complement(successor(u))))),complement(u))*. % 300.04/300.41 251831[25:SpR:234134.1,248798.0] function(complement(complement(u))) || -> subclass(intersection(v,successor(complement(complement(u)))),u)*. % 300.04/300.41 251938[25:SpR:234134.1,248810.0] function(u) || -> subclass(complement(complement(intersection(v,complement(successor(u))))),complement(u))*. % 300.04/300.41 251981[19:SpR:225013.1,248810.0] || equal(successor(complement(intersection(u,complement(complement(v))))),ordinal_numbers)** -> subclass(universal_class,v). % 300.04/300.41 252247[25:SpR:234134.1,248812.0] function(u) || -> subclass(complement(complement(intersection(complement(successor(u)),v))),complement(u))*. % 300.04/300.41 252296[19:SpR:225013.1,248812.0] || equal(successor(complement(intersection(complement(complement(u)),v))),ordinal_numbers)** -> subclass(universal_class,u). % 300.04/300.41 252409[25:SpR:234134.1,249106.0] function(u) || -> subclass(complement(union(v,complement(complement(successor(u))))),complement(u))*. % 300.04/300.41 252442[19:SpR:225013.1,249106.0] || equal(successor(union(u,complement(complement(complement(v))))),ordinal_numbers)** -> subclass(universal_class,v). % 300.04/300.41 252635[18:MRR:252615.1,141.0] || member(u,cantor(v)) member(restrict(v,u,universal_class),cantor(u))* -> . % 300.04/300.41 252655[25:SpR:234134.1,249272.0] function(u) || -> subclass(complement(union(complement(complement(successor(u))),v)),complement(u))*. % 300.04/300.41 252690[19:SpR:225013.1,249272.0] || equal(successor(union(complement(complement(complement(u))),v)),ordinal_numbers)** -> subclass(universal_class,u). % 300.04/300.41 252839[19:Obv:252785.0] || -> subclass(singleton(u),intersection(singleton(u),v))* subclass(intersection(singleton(u),v),ordinal_numbers). % 300.04/300.41 252840[19:Obv:252786.0] || -> subclass(singleton(u),intersection(v,singleton(u)))* subclass(intersection(v,singleton(u)),ordinal_numbers). % 300.04/300.41 252842[25:MRR:252820.2,192606.0] single_valued_class(singleton(not_subclass_element(cross_product(universal_class,universal_class),ordinal_numbers))) || -> subclass(cross_product(universal_class,universal_class),ordinal_numbers)*. % 300.04/300.41 252877[25:SpR:234134.1,220180.1] function(u) || subclass(complement(u),v) -> subclass(complement(successor(u)),v)*. % 300.04/300.41 252890[19:SpR:225013.1,220180.1] || equal(successor(complement(u)),ordinal_numbers)** subclass(u,v)* -> subclass(universal_class,v)*. % 300.04/300.41 252996[25:MRR:252995.2,166995.0] function(least(u,v)) || well_ordering(u,universal_class) -> section(u,ordinal_numbers,v)*. % 300.04/300.41 253102[18:Res:125124.2,227961.1] || member(u,universal_class)* subclass(rest_relation,rest_of(v))* member(v,u)* -> . % 300.04/300.41 253133[18:Res:51413.0,227961.1] || member(u,not_subclass_element(v,complement(cantor(u))))* -> subclass(v,complement(cantor(u))). % 300.04/300.41 253143[19:Res:167131.2,227961.1] || subclass(u,cantor(v)) member(v,regular(u))* -> equal(u,ordinal_numbers). % 300.04/300.41 253147[19:Res:167339.2,227961.1] || subclass(omega,cantor(u))* member(u,v)* -> equal(integer_of(v),ordinal_numbers). % 300.04/300.41 9799[0:SpL:27.0,9715.1] || subclass(universal_class,intersection(complement(u),complement(v)))* subclass(universal_class,union(u,v)) -> . % 300.04/300.41 27851[0:SpL:4125.0,5472.0] || subclass(universal_class,symmetric_difference(complement(u),complement(v)))* -> member(singleton(w),union(u,v))*. % 300.04/300.41 27857[0:SpL:4125.0,12446.0] || equal(symmetric_difference(complement(u),complement(v)),universal_class) -> member(singleton(w),union(u,v))*. % 300.04/300.41 42080[0:Rew:4577.1,42079.1] || member(u,v) member(u,w) -> subclass(singleton(u),intersection(w,v))*. % 300.04/300.41 6425[0:SpL:27.0,6422.0] || equal(complement(union(u,v)),universal_class) -> member(omega,intersection(complement(u),complement(v)))*. % 300.04/300.41 6205[0:SpL:27.0,2532.0] || subclass(universal_class,union(u,v)) member(omega,intersection(complement(u),complement(v)))* -> . % 300.04/300.41 16151[0:Res:2481.1,896.0] || subclass(universal_class,restrict(u,v,w))* -> member(ordered_pair(x,y),cross_product(v,w))*. % 300.04/300.41 5476[0:Res:2479.1,9.0] || subclass(universal_class,unordered_pair(u,v))* -> equal(singleton(w),v)* equal(singleton(w),u)*. % 300.04/300.41 48668[0:SpL:160.0,6437.0] || subclass(universal_class,symmetric_difference(u,v)) -> member(unordered_pair(w,x),complement(intersection(u,v)))*. % 300.04/300.41 43753[0:SpL:5132.1,9769.0] || equal(complement(not_subclass_element(cross_product(u,v),w)),universal_class)** -> subclass(cross_product(u,v),w). % 300.04/300.41 43752[0:SpL:5132.1,9712.0] || subclass(universal_class,complement(not_subclass_element(cross_product(u,v),w)))* -> subclass(cross_product(u,v),w). % 300.04/300.41 12039[0:Res:12015.1,2.0] || equal(complement(complement(u)),universal_class)** subclass(u,v)* -> member(singleton(w),v)*. % 300.04/300.41 12803[0:Res:12015.1,4127.0] || equal(complement(complement(symmetric_difference(u,v))),universal_class) -> member(singleton(w),union(u,v))*. % 300.04/300.41 48869[0:Res:12015.1,16910.0] || equal(complement(complement(symmetric_difference(u,inverse(u)))),universal_class)** -> member(singleton(v),symmetrization_of(u))*. % 300.04/300.41 43029[0:Res:2481.1,8694.0] || subclass(universal_class,compose(u,v)) -> subclass(w,image(u,image(v,singleton(x))))*. % 300.04/300.41 95573[0:Res:51413.0,2.0] || subclass(u,v) -> subclass(w,complement(u)) member(not_subclass_element(w,complement(u)),v)*. % 300.04/300.41 95574[0:Res:51413.0,22.0] || -> subclass(u,complement(intersection(v,w))) member(not_subclass_element(u,complement(intersection(v,w))),v)*. % 300.04/300.41 95575[0:Res:51413.0,23.0] || -> subclass(u,complement(intersection(v,w))) member(not_subclass_element(u,complement(intersection(v,w))),w)*. % 300.04/300.41 95614[0:Res:95593.1,8.0] || subclass(complement(u),singleton(v))* -> member(v,u) equal(complement(u),singleton(v)). % 300.04/300.41 97552[8:SpL:27.0,97509.1] || subclass(domain_relation,intersection(complement(u),complement(v)))* subclass(domain_relation,union(u,v)) -> . % 300.04/300.41 97562[8:SpL:27.0,97513.1] || subclass(universal_class,intersection(complement(u),complement(v)))* subclass(domain_relation,union(u,v)) -> . % 300.04/300.41 97586[8:SpL:27.0,97574.1] || equal(intersection(complement(u),complement(v)),domain_relation)** equal(union(u,v),domain_relation) -> . % 300.04/300.41 105051[12:SpL:43.0,104245.0] || member(sum_class(image(u,v)),universal_class) member(restrict(u,v,universal_class),universal_class)* -> . % 300.04/300.41 95580[0:Res:51413.0,158.0] || -> subclass(u,complement(omega)) equal(integer_of(not_subclass_element(u,complement(omega))),not_subclass_element(u,complement(omega)))**. % 300.04/300.41 131963[8:SpL:125772.0,131613.1] || equal(complement(rest_of(restrict(element_relation,universal_class,u))),universal_class)** member(v,sum_class(u))* -> . % 300.04/300.41 131966[8:SpL:125707.0,131613.1] || equal(complement(rest_of(flip(cross_product(u,universal_class)))),universal_class)** member(v,inverse(u))* -> . % 300.04/300.41 135052[8:SpL:124905.0,83043.0] || member(u,segment(v,w,x))* subclass(universal_class,y) -> member(u,y)*. % 300.04/300.41 135197[0:Res:36865.0,4178.0] || -> subclass(complement(complement(singleton(u))),v) equal(not_subclass_element(complement(complement(singleton(u))),v),u)**. % 300.04/300.41 135536[8:AED:135467.1] || member(u,cantor(v))* subclass(rest_of(v),w)* well_ordering(universal_class,w) -> . % 300.04/300.41 135881[0:Res:24.2,16105.1] || member(u,v) member(u,w) member(u,symmetric_difference(w,v))* -> . % 300.04/300.41 135890[0:Res:2480.1,16105.1] || subclass(universal_class,intersection(u,v)) member(unordered_pair(w,x),symmetric_difference(u,v))* -> . % 300.04/300.41 135905[0:Res:2481.1,16105.1] || subclass(universal_class,intersection(u,v)) member(ordered_pair(w,x),symmetric_difference(u,v))* -> . % 300.04/300.41 135943[0:Res:2525.1,25.1] || subclass(ordered_pair(u,v),complement(w)) member(unordered_pair(u,singleton(v)),w)* -> . % 300.04/300.41 135946[0:Res:2525.1,11848.0] || subclass(ordered_pair(u,v),w)* subclass(w,x)* well_ordering(universal_class,x)* -> . % 300.04/300.41 135953[0:Res:2525.1,22.0] || subclass(ordered_pair(u,v),intersection(w,x))* -> member(unordered_pair(u,singleton(v)),w). % 300.04/300.41 135954[0:Res:2525.1,23.0] || subclass(ordered_pair(u,v),intersection(w,x))* -> member(unordered_pair(u,singleton(v)),x). % 300.04/300.41 138279[8:SpR:124908.0,125124.2] || member(u,universal_class) subclass(rest_relation,rest_of(inverse(v)))* -> member(u,range_of(v))*. % 300.04/300.41 139572[8:SpR:43.0,138596.1] || equal(rest_of(inverse(restrict(u,v,universal_class))),rest_relation)** -> subclass(w,image(u,v))*. % 300.04/300.41 142371[0:MRR:142304.0,36682.1] || -> member(not_subclass_element(u,intersection(complement(v),u)),v)* subclass(u,intersection(complement(v),u)). % 300.04/300.41 146208[0:Res:144532.1,9.0] || equal(unordered_pair(u,v),universal_class)** -> equal(singleton(w),v)* equal(singleton(w),u)*. % 300.04/300.41 146343[0:SpL:146278.0,110985.0] || member(inverse(cross_product(u,universal_class)),image(universal_class,u))* subclass(universal_class,complement(element_relation)) -> . % 300.04/300.41 147350[8:Res:2478.1,82995.1] || subclass(universal_class,complement(compose(element_relation,universal_class)))* member(omega,element_relation) -> member(omega,u)*. % 300.04/300.41 147468[0:MRR:147437.0,55.1] || member(u,universal_class) subclass(universal_class,complement(complement(v)))* -> member(sum_class(u),v)*. % 300.04/300.41 147599[0:MRR:147568.0,57.1] || member(u,universal_class) subclass(universal_class,complement(complement(v)))* -> member(power_class(u),v)*. % 300.04/300.41 148008[8:Res:147404.1,11848.0] || member(u,element_relation)* subclass(compose(element_relation,universal_class),v)* well_ordering(universal_class,v) -> . % 300.04/300.41 148130[0:Res:7.1,15111.1] || equal(intersection(u,v),universal_class)** member(w,universal_class) -> member(sum_class(w),v)*. % 300.04/300.41 148322[0:Res:7.1,15110.1] || equal(intersection(u,v),universal_class)** member(w,universal_class) -> member(sum_class(w),u)*. % 300.04/300.41 148601[0:SpR:148172.0,30.0] || -> equal(restrict(complement(complement(cross_product(u,v))),u,v),complement(complement(cross_product(u,v))))**. % 300.04/300.41 148746[0:Res:7.1,15077.1] || equal(intersection(u,v),universal_class)** member(w,universal_class) -> member(power_class(w),v)*. % 300.04/300.41 148750[0:SpL:27.0,148626.0] || subclass(universal_class,complement(union(u,v))) -> member(omega,intersection(complement(u),complement(v)))*. % 300.04/300.41 148822[0:Res:7.1,15076.1] || equal(intersection(u,v),universal_class)** member(w,universal_class) -> member(power_class(w),u)*. % 300.04/300.41 148824[0:SpL:27.0,148647.0] || member(u,complement(union(v,w))) -> member(u,intersection(complement(v),complement(w)))*. % 300.04/300.41 148873[0:Res:51413.0,148647.0] || -> subclass(u,complement(complement(complement(v)))) member(not_subclass_element(u,complement(complement(complement(v)))),v)*. % 300.04/300.41 148874[0:Res:2526.2,148647.0] || subclass(u,complement(complement(v))) -> subclass(u,w) member(not_subclass_element(u,w),v)*. % 300.04/300.41 148892[0:Res:2525.1,148647.0] || subclass(ordered_pair(u,v),complement(complement(w)))* -> member(unordered_pair(u,singleton(v)),w). % 300.04/300.41 149451[0:SpR:149012.1,160.0] || subclass(u,v) -> equal(intersection(complement(u),union(v,u)),symmetric_difference(v,u))**. % 300.04/300.41 149465[0:SpR:149012.1,29.0] || subclass(cross_product(u,v),w)* -> equal(restrict(w,u,v),cross_product(u,v)). % 300.04/300.41 149466[2:SpR:149012.1,80099.1] || subclass(inverse(u),u)* asymmetric(u,v) -> section(inverse(u),v,v)*. % 300.04/300.41 149476[0:SpR:149012.1,4126.1] || subclass(u,v) member(w,symmetric_difference(v,u))* -> member(w,complement(u)). % 300.04/300.41 149543[0:SpL:149012.1,16105.1] || subclass(u,v) member(w,symmetric_difference(v,u))* member(w,u) -> . % 300.04/300.41 149602[0:Res:7.1,27171.1] || equal(cross_product(u,v),rest_relation)** member(w,universal_class) -> member(rest_of(w),v)*. % 300.04/300.41 152477[0:Res:7.1,16466.0] || equal(intersection(u,v),w)* -> subclass(w,x) member(not_subclass_element(w,x),v)*. % 300.04/300.41 152494[0:Res:137025.0,16466.0] || -> subclass(complement(successor(u)),v) member(not_subclass_element(complement(successor(u)),v),complement(singleton(u)))*. % 300.04/300.41 152495[0:Res:137026.0,16466.0] || -> subclass(complement(symmetrization_of(u)),v) member(not_subclass_element(complement(symmetrization_of(u)),v),complement(inverse(u)))*. % 300.04/300.41 152762[0:Res:7.1,16465.0] || equal(intersection(u,v),w)* -> subclass(w,x) member(not_subclass_element(w,x),u)*. % 300.04/300.41 153094[0:SpR:149179.0,4126.1] || member(u,symmetric_difference(v,intersection(v,w)))* -> member(u,complement(intersection(v,w))). % 300.04/300.41 153175[0:SpL:149179.0,16105.1] || member(u,symmetric_difference(v,intersection(v,w)))* member(u,intersection(v,w)) -> . % 300.04/300.41 153364[0:SpR:149318.0,4126.1] || member(u,symmetric_difference(v,intersection(w,v)))* -> member(u,complement(intersection(w,v))). % 300.04/300.41 153447[0:SpL:149318.0,16105.1] || member(u,symmetric_difference(v,intersection(w,v)))* member(u,intersection(w,v)) -> . % 300.04/300.41 154750[0:Res:144532.1,36025.1] || equal(u,universal_class) member(u,universal_class) -> member(singleton(singleton(singleton(u))),element_relation)*. % 300.04/300.41 154752[0:Res:2479.1,36025.1] || subclass(universal_class,u) member(u,universal_class) -> member(singleton(singleton(singleton(u))),element_relation)*. % 300.04/300.41 165003[8:SpL:27.0,164453.1] || subclass(domain_relation,intersection(complement(u),complement(v)))* subclass(universal_class,union(u,v)) -> . % 300.04/300.41 135373[0:Res:10.1,11848.0] || member(u,universal_class) subclass(unordered_pair(u,v),w)* well_ordering(universal_class,w) -> . % 300.04/300.41 135374[0:Res:11.1,11848.0] || member(u,universal_class) subclass(unordered_pair(v,u),w)* well_ordering(universal_class,w) -> . % 300.04/300.41 135705[2:Res:35220.2,4178.0] inductive(singleton(u)) || well_ordering(v,universal_class) -> equal(least(v,singleton(u)),u)**. % 300.04/300.41 166619[8:Res:166605.0,11848.0] || subclass(inverse(singleton(u)),v)* well_ordering(universal_class,v) -> asymmetric(singleton(u),w)*. % 300.04/300.41 167391[19:Rew:166997.0,98586.1] || subclass(domain_relation,complement(complement(restrict(u,v,w))))* -> member(ordered_pair(ordinal_numbers,ordinal_numbers),u). % 300.04/300.41 167418[19:Rew:166997.0,98573.1] || subclass(domain_relation,complement(complement(omega)))* -> equal(integer_of(ordered_pair(ordinal_numbers,ordinal_numbers)),ordered_pair(ordinal_numbers,ordinal_numbers)). % 300.04/300.41 167432[19:Rew:166997.0,99069.1] || subclass(domain_relation,symmetric_difference(u,v)) -> member(ordered_pair(ordinal_numbers,ordinal_numbers),complement(intersection(u,v)))*. % 300.04/300.41 167434[19:Rew:166997.0,84230.1] || subclass(domain_relation,restrict(u,v,w))* -> member(ordered_pair(ordinal_numbers,ordinal_numbers),cross_product(v,w))*. % 300.04/300.41 167436[19:Rew:166997.0,164413.1] || subclass(domain_relation,intersection(u,v)) member(ordered_pair(ordinal_numbers,ordinal_numbers),symmetric_difference(u,v))* -> . % 300.04/300.41 169368[19:Rew:166997.0,167514.2] || member(u,universal_class) member(singleton(singleton(ordinal_numbers)),element_relation)* -> member(ordinal_numbers,range_of(u))*. % 300.04/300.41 169370[19:Rew:166997.0,167556.1] || equal(symmetric_difference(complement(u),complement(v)),singleton(ordinal_numbers))** -> member(ordinal_numbers,union(u,v)). % 300.04/300.41 169375[19:Rew:166997.0,167652.1] || subclass(universal_class,complement(compose(element_relation,universal_class)))* member(ordinal_numbers,element_relation) -> member(ordinal_numbers,u)*. % 300.04/300.41 167686[19:Rew:166997.0,163772.2] || subclass(u,rest_of(regular(u)))* subclass(universal_class,complement(element_relation)) -> equal(u,ordinal_numbers). % 300.04/300.41 169376[19:Rew:166997.0,167694.2,166997.0,167694.0] || member(not_subclass_element(regular(u),ordinal_numbers),u)* -> equal(u,ordinal_numbers) subclass(regular(u),ordinal_numbers). % 300.04/300.41 167773[19:Rew:166997.0,163386.2] || subclass(omega,rest_of(u))* subclass(universal_class,complement(element_relation)) -> equal(integer_of(u),ordinal_numbers). % 300.04/300.41 167915[19:Rew:166997.0,93563.0] || equal(sum_class(u),ordinal_numbers) subclass(u,sum_class(u))* -> equal(sum_class(u),u). % 300.04/300.41 167979[19:Rew:166997.0,82388.1] || subclass(universal_class,intersection(complement(u),complement(v)))* member(ordinal_numbers,union(u,v)) -> . % 300.04/300.41 168220[19:Rew:166997.0,159804.1] || member(regular(intersection(u,v)),symmetric_difference(u,v))* -> equal(intersection(u,v),ordinal_numbers). % 300.04/300.41 168332[19:Rew:166997.0,158287.1] inductive(symmetric_difference(identity_relation,intersection(universal_class,complement(u)))) || -> member(ordinal_numbers,complement(complement(complement(u))))*. % 300.04/300.41 168395[19:Rew:166997.0,99171.1] || member(regular(complement(complement(complement(u)))),u)* -> equal(complement(complement(complement(u))),ordinal_numbers). % 300.04/300.41 168404[19:Rew:166997.0,93609.2] single_valued_class(inverse(u)) function(u) || equal(inverse(u),ordinal_numbers)** -> one_to_one(u). % 300.04/300.41 168408[19:Rew:166997.0,93567.0] || equal(apply(u,v),ordinal_numbers) -> subclass(apply(u,v),image(u,singleton(v)))*. % 300.04/300.41 168417[19:Rew:166997.0,80779.0] || -> equal(symmetric_difference(u,inverse(u)),ordinal_numbers) member(regular(symmetric_difference(u,inverse(u))),symmetrization_of(u))*. % 300.04/300.41 168428[19:Rew:166997.0,164710.1] || subclass(universal_class,complement(union(u,v))) -> member(ordinal_numbers,intersection(complement(u),complement(v)))*. % 300.04/300.41 168430[19:Rew:166997.0,85557.1] || equal(complement(union(u,v)),universal_class) -> member(ordinal_numbers,intersection(complement(u),complement(v)))*. % 300.04/300.41 168431[19:Rew:166997.0,84375.1] || subclass(universal_class,union(u,v)) member(ordinal_numbers,intersection(complement(u),complement(v)))* -> . % 300.04/300.41 168436[19:Rew:166997.0,84896.2] || subclass(omega,u) subclass(universal_class,complement(u))* -> equal(integer_of(singleton(v)),ordinal_numbers)**. % 300.04/300.41 168454[19:Rew:166997.0,161614.2] || member(u,universal_class) -> member(u,cantor(universal_class)) equal(cross_product(singleton(u),universal_class),ordinal_numbers)**. % 300.04/300.41 168490[19:Rew:166997.0,159701.1] inductive(power_class(image(element_relation,complement(u)))) || member(ordinal_numbers,image(element_relation,power_class(u)))* -> . % 300.04/300.41 168548[19:Rew:166997.0,163132.1] || -> member(regular(complement(union(u,v))),complement(u))* equal(complement(union(u,v)),ordinal_numbers). % 300.04/300.41 168549[19:Rew:166997.0,163131.1] || -> member(regular(complement(union(u,v))),complement(v))* equal(complement(union(u,v)),ordinal_numbers). % 300.04/300.41 168735[19:Rew:166997.0,159674.1] inductive(complement(compose(element_relation,universal_class))) || member(ordinal_numbers,element_relation) well_ordering(u,v)* -> . % 300.04/300.41 168738[19:Rew:166997.0,159732.1] || subclass(u,complement(omega)) -> equal(integer_of(not_subclass_element(u,v)),ordinal_numbers)** subclass(u,v). % 300.04/300.41 168739[19:Rew:166997.0,159735.2] || member(u,universal_class) subclass(universal_class,complement(omega))* -> equal(integer_of(sum_class(u)),ordinal_numbers)**. % 300.04/300.41 168740[19:Rew:166997.0,159736.2] || member(u,universal_class) subclass(universal_class,complement(omega))* -> equal(integer_of(power_class(u)),ordinal_numbers)**. % 300.04/300.41 168744[19:Rew:166997.0,163113.1] || member(regular(complement(compose(element_relation,universal_class))),element_relation)* -> equal(complement(compose(element_relation,universal_class)),ordinal_numbers). % 300.04/300.41 169602[19:MRR:169170.3,167057.0] || subclass(unordered_pair(u,v),ordinal_numbers)* member(u,universal_class) well_ordering(w,kind_1_ordinals)* -> . % 300.04/300.41 169603[19:MRR:169171.3,167057.0] || subclass(unordered_pair(u,v),ordinal_numbers)* member(v,universal_class) well_ordering(w,kind_1_ordinals)* -> . % 300.04/300.41 173933[19:SpR:142500.0,167926.2] || asymmetric(universal_class,u) subclass(compose(ordinal_numbers,ordinal_numbers),ordinal_numbers)* -> transitive(inverse(universal_class),u)*. % 300.04/300.41 174546[19:SpR:142500.0,167762.1] || asymmetric(universal_class,singleton(u)) -> equal(domain__dfg(inverse(universal_class),singleton(u),u),single_valued3(ordinal_numbers))**. % 300.04/300.41 169404[19:Rew:166997.0,168174.0] || -> equal(intersection(u,symmetrization_of(ordinal_numbers)),ordinal_numbers) member(regular(intersection(u,symmetrization_of(ordinal_numbers))),inverse(ordinal_numbers))*. % 300.04/300.41 169403[19:Rew:166997.0,168172.0] || -> equal(intersection(symmetrization_of(ordinal_numbers),u),ordinal_numbers) member(regular(intersection(symmetrization_of(ordinal_numbers),u)),inverse(ordinal_numbers))*. % 300.04/300.41 168153[19:Rew:166997.0,160511.0] || -> subclass(complement(symmetrization_of(complement(inverse(ordinal_numbers)))),intersection(symmetrization_of(ordinal_numbers),complement(inverse(complement(inverse(ordinal_numbers))))))*. % 300.04/300.41 168151[19:Rew:166997.0,160509.0] || -> subclass(complement(successor(complement(inverse(ordinal_numbers)))),intersection(symmetrization_of(ordinal_numbers),complement(singleton(complement(inverse(ordinal_numbers))))))*. % 300.04/300.41 169402[19:Rew:166997.0,168086.0] || subclass(ordered_pair(u,v),symmetrization_of(ordinal_numbers)) -> member(unordered_pair(u,singleton(v)),inverse(ordinal_numbers))*. % 300.04/300.41 169401[19:Rew:166997.0,168081.0] || subclass(u,symmetrization_of(ordinal_numbers)) -> subclass(u,v) member(not_subclass_element(u,v),inverse(ordinal_numbers))*. % 300.04/300.41 168109[19:Rew:166997.0,166911.0] || -> subclass(symmetric_difference(complement(u),power_class(complement(inverse(ordinal_numbers)))),union(u,image(element_relation,symmetrization_of(ordinal_numbers))))*. % 300.04/300.41 168104[19:Rew:166997.0,166891.0] || -> subclass(symmetric_difference(power_class(complement(inverse(ordinal_numbers))),complement(u)),union(image(element_relation,symmetrization_of(ordinal_numbers)),u))*. % 300.04/300.41 169395[19:Rew:166997.0,168035.0] || subclass(domain_relation,image(element_relation,symmetrization_of(ordinal_numbers)))* subclass(universal_class,power_class(complement(inverse(ordinal_numbers)))) -> . % 300.04/300.41 169397[19:Rew:166997.0,168037.0] || subclass(domain_relation,image(element_relation,symmetrization_of(ordinal_numbers)))* subclass(domain_relation,power_class(complement(inverse(ordinal_numbers)))) -> . % 300.04/300.41 169399[19:Rew:166997.0,168039.0] || equal(image(element_relation,symmetrization_of(ordinal_numbers)),domain_relation)** equal(power_class(complement(inverse(ordinal_numbers))),domain_relation) -> . % 300.04/300.41 169387[19:Rew:166997.0,168015.0] || subclass(universal_class,image(element_relation,symmetrization_of(ordinal_numbers))) member(omega,power_class(complement(inverse(ordinal_numbers))))* -> . % 300.04/300.41 169391[19:Rew:166997.0,168031.0] || subclass(universal_class,image(element_relation,symmetrization_of(ordinal_numbers)))* subclass(universal_class,power_class(complement(inverse(ordinal_numbers)))) -> . % 300.04/300.41 169398[19:Rew:166997.0,168038.0] || subclass(universal_class,image(element_relation,symmetrization_of(ordinal_numbers))) subclass(domain_relation,power_class(complement(inverse(ordinal_numbers))))* -> . % 300.04/300.41 169392[19:Rew:166997.0,168032.1] || subclass(universal_class,power_class(complement(inverse(ordinal_numbers)))) member(omega,image(element_relation,symmetrization_of(ordinal_numbers)))* -> . % 300.04/300.41 169388[19:Rew:166997.0,168017.0] || member(u,image(element_relation,symmetrization_of(ordinal_numbers)))* member(u,power_class(complement(inverse(ordinal_numbers)))) -> . % 300.04/300.41 169394[19:Rew:166997.0,168034.1] || subclass(universal_class,power_class(complement(inverse(ordinal_numbers)))) member(ordinal_numbers,image(element_relation,symmetrization_of(ordinal_numbers)))* -> . % 300.04/300.41 169373[19:Rew:166997.0,167598.0] || member(ordered_pair(u,v),compose(w,ordinal_numbers))* -> member(v,image(w,range_of(ordinal_numbers))). % 300.04/300.41 169377[19:Rew:166997.0,167782.2,166997.0,167782.0] || equal(sum_class(ordinal_numbers),ordinal_numbers) subclass(u,sum_class(ordinal_numbers))* -> equal(u,sum_class(ordinal_numbers)). % 300.04/300.41 175565[20:MRR:173565.2,175557.0] || member(symmetrization_of(ordinal_numbers),universal_class) member(apply(choice,symmetrization_of(ordinal_numbers)),complement(inverse(ordinal_numbers)))* -> . % 300.04/300.41 175985[19:Obv:175970.0] || -> equal(regular(unordered_pair(u,v)),u)** equal(unordered_pair(u,v),ordinal_numbers) member(v,universal_class). % 300.04/300.41 175986[19:Obv:175978.0] || -> equal(regular(unordered_pair(u,v)),v)** equal(unordered_pair(u,v),ordinal_numbers) member(u,universal_class). % 300.04/300.41 176108[20:Res:175613.1,16105.1] || subclass(universal_class,intersection(u,v)) member(regular(symmetrization_of(ordinal_numbers)),symmetric_difference(u,v))* -> . % 300.04/300.41 176125[20:Res:175613.1,896.0] || subclass(universal_class,restrict(u,v,w))* -> member(regular(symmetrization_of(ordinal_numbers)),cross_product(v,w))*. % 300.04/300.41 176237[19:Rew:176206.1,158696.1] || member(restrict(u,v,universal_class),universal_class)* equal(sum_class(image(u,v)),ordinal_numbers) -> . % 300.04/300.41 177038[19:SpR:176364.1,124905.0] || -> equal(singleton(restrict(u,v,singleton(w))),ordinal_numbers)** equal(segment(u,v,w),ordinal_numbers). % 300.04/300.41 177182[22:Res:177171.1,82995.1] || subclass(omega,complement(compose(element_relation,universal_class)))* member(ordinal_numbers,element_relation) -> member(ordinal_numbers,u)*. % 300.04/300.41 177192[22:Res:177171.1,488.0] || subclass(omega,intersection(complement(u),complement(v)))* member(ordinal_numbers,union(u,v)) -> . % 300.04/300.41 177618[19:MRR:177595.3,167057.0] || member(u,universal_class) member(v,universal_class)* subclass(rest_relation,rest_of(sum_class(u)))* -> . % 300.04/300.41 177664[19:MRR:177638.3,167057.0] || member(u,universal_class) member(v,universal_class)* subclass(rest_relation,rest_of(power_class(u)))* -> . % 300.04/300.41 177707[19:MRR:177684.3,167057.0] || member(u,universal_class) member(v,universal_class)* subclass(rest_relation,rest_of(rest_of(u)))* -> . % 300.04/300.41 177926[19:Rew:177036.0,177861.2] || member(singleton(singleton(ordinal_numbers)),element_relation)* -> equal(range_of(u),ordinal_numbers) member(ordinal_numbers,inverse(u))*. % 300.04/300.41 177987[22:SpL:27.0,177179.0] || subclass(omega,union(u,v)) member(ordinal_numbers,intersection(complement(u),complement(v)))* -> . % 300.04/300.41 178001[22:SpL:27.0,177183.0] || subclass(omega,complement(union(u,v))) -> member(ordinal_numbers,intersection(complement(u),complement(v)))*. % 300.04/300.41 178142[18:Res:66.2,177583.1] function(u) || member(v,universal_class) equal(rest_of(image(u,v)),rest_relation)** -> . % 300.04/300.41 178184[19:MRR:178166.1,5.0] || member(u,universal_class) equal(rest_of(apply(choice,u)),rest_relation)** -> equal(u,ordinal_numbers). % 300.04/300.41 178261[22:Res:4126.1,177998.1] || member(ordinal_numbers,symmetric_difference(u,v)) equal(complement(complement(intersection(u,v))),omega)** -> . % 300.04/300.41 178387[22:SpL:27.0,178014.0] || equal(complement(union(u,v)),omega) -> member(ordinal_numbers,intersection(complement(u),complement(v)))*. % 300.04/300.41 178426[19:SpL:168412.1,48410.0] || subclass(universal_class,complement(singleton(regular(cross_product(u,v)))))* -> equal(cross_product(u,v),ordinal_numbers). % 300.04/300.41 178701[22:SpL:27.0,178652.1] || equal(intersection(complement(u),complement(v)),omega)** equal(union(u,v),omega) -> . % 300.04/300.41 178747[19:MRR:178722.3,167057.0] function(u) || member(v,universal_class)* subclass(rest_relation,rest_of(apply(u,w)))* -> . % 300.04/300.41 178927[22:Res:178902.1,488.0] || equal(intersection(complement(u),complement(v)),omega)** member(ordinal_numbers,union(u,v)) -> . % 300.04/300.41 179049[19:MRR:179017.3,167057.0] || member(u,universal_class)* subclass(rest_relation,rest_of(not_subclass_element(v,w)))* -> subclass(v,w). % 300.04/300.41 179379[22:SpL:167200.0,177179.0] || subclass(omega,power_class(complement(inverse(ordinal_numbers)))) member(ordinal_numbers,image(element_relation,symmetrization_of(ordinal_numbers)))* -> . % 300.04/300.41 179380[22:SpL:167200.0,178652.1] || equal(image(element_relation,symmetrization_of(ordinal_numbers)),omega)** equal(power_class(complement(inverse(ordinal_numbers))),omega) -> . % 300.04/300.41 180171[19:Rew:180089.0,169366.0] || member(u,image(element_relation,singleton(ordinal_numbers)))* member(u,power_class(complement(singleton(ordinal_numbers)))) -> . % 300.04/300.41 180172[19:Rew:180089.0,179137.0] || subclass(universal_class,image(element_relation,singleton(ordinal_numbers))) subclass(domain_relation,power_class(complement(singleton(ordinal_numbers))))* -> . % 300.04/300.41 180173[19:Rew:180089.0,179126.0] || subclass(universal_class,image(element_relation,singleton(ordinal_numbers)))* subclass(universal_class,power_class(complement(singleton(ordinal_numbers)))) -> . % 300.04/300.41 180174[19:Rew:180089.0,169367.0] || subclass(universal_class,image(element_relation,singleton(ordinal_numbers))) member(omega,power_class(complement(singleton(ordinal_numbers))))* -> . % 300.04/300.41 180176[19:Rew:180089.0,179104.0] || -> subclass(symmetric_difference(complement(u),power_class(complement(singleton(ordinal_numbers)))),union(u,image(element_relation,singleton(ordinal_numbers))))*. % 300.04/300.41 180182[19:Rew:180089.0,179084.0] || -> subclass(symmetric_difference(power_class(complement(singleton(ordinal_numbers))),complement(u)),union(image(element_relation,singleton(ordinal_numbers)),u))*. % 300.04/300.41 180198[22:Rew:180089.0,179149.1] || subclass(omega,power_class(complement(singleton(ordinal_numbers)))) member(ordinal_numbers,image(element_relation,singleton(ordinal_numbers)))* -> . % 300.04/300.41 180203[19:Rew:180089.0,179121.1] || subclass(universal_class,power_class(complement(singleton(ordinal_numbers)))) member(ordinal_numbers,image(element_relation,singleton(ordinal_numbers)))* -> . % 300.04/300.41 180218[22:Rew:180089.0,179150.0] || equal(image(element_relation,singleton(ordinal_numbers)),omega)** equal(power_class(complement(singleton(ordinal_numbers))),omega) -> . % 300.04/300.41 180220[19:Rew:180089.0,179140.0] || equal(image(element_relation,singleton(ordinal_numbers)),domain_relation)** equal(power_class(complement(singleton(ordinal_numbers))),domain_relation) -> . % 300.04/300.41 180227[19:Rew:180089.0,179138.0] || subclass(domain_relation,image(element_relation,singleton(ordinal_numbers)))* subclass(domain_relation,power_class(complement(singleton(ordinal_numbers)))) -> . % 300.04/300.41 180228[19:Rew:180089.0,179123.0] || subclass(domain_relation,image(element_relation,singleton(ordinal_numbers)))* subclass(universal_class,power_class(complement(singleton(ordinal_numbers)))) -> . % 300.04/300.41 180231[19:Rew:180089.0,179125.1] || subclass(universal_class,power_class(complement(singleton(ordinal_numbers)))) member(omega,image(element_relation,singleton(ordinal_numbers)))* -> . % 300.04/300.41 180303[19:Rew:180089.0,168817.0] || -> subclass(complement(symmetrization_of(complement(singleton(ordinal_numbers)))),intersection(singleton(ordinal_numbers),complement(inverse(complement(singleton(ordinal_numbers))))))*. % 300.04/300.41 180305[19:Rew:180089.0,168819.0] || -> subclass(complement(successor(complement(singleton(ordinal_numbers)))),intersection(singleton(ordinal_numbers),complement(singleton(complement(singleton(ordinal_numbers))))))*. % 300.04/300.41 180845[19:Res:180693.1,11848.0] || well_ordering(element_relation,range_of(ordinal_numbers))* subclass(cantor(choice),u)* well_ordering(universal_class,u) -> . % 300.04/300.41 180849[19:Res:180693.1,2.0] || well_ordering(element_relation,range_of(ordinal_numbers))* subclass(cantor(choice),u) -> member(singleton(ordinal_numbers),u)*. % 300.04/300.41 180962[19:SpL:27.0,180886.1] inductive(intersection(complement(u),complement(v))) || equal(union(u,v),singleton(ordinal_numbers))** -> . % 300.04/300.41 180969[19:SpL:167200.0,180886.1] inductive(image(element_relation,symmetrization_of(ordinal_numbers))) || equal(power_class(complement(inverse(ordinal_numbers))),singleton(ordinal_numbers))** -> . % 300.04/300.41 180970[19:SpL:180125.0,180886.1] inductive(image(element_relation,singleton(ordinal_numbers))) || equal(power_class(complement(singleton(ordinal_numbers))),singleton(ordinal_numbers))** -> . % 300.04/300.41 181314[19:SpR:43.0,168752.1] || member(restrict(u,v,universal_class),universal_class)* -> equal(singleton(sum_class(image(u,v))),ordinal_numbers). % 300.04/300.41 181432[19:SpR:43.0,168753.1] || member(restrict(u,v,universal_class),universal_class)* -> equal(integer_of(sum_class(image(u,v))),ordinal_numbers). % 300.04/300.41 181495[19:Res:169234.0,2.0] || subclass(complement(inverse(ordinal_numbers)),u)* -> subclass(singleton(v),symmetrization_of(ordinal_numbers))* member(v,u)*. % 300.04/300.41 181505[19:Res:169234.0,4.0] || -> subclass(singleton(not_subclass_element(u,complement(inverse(ordinal_numbers)))),symmetrization_of(ordinal_numbers))* subclass(u,complement(inverse(ordinal_numbers))). % 300.04/300.41 181730[20:Res:175570.1,2.0] || subclass(inverse(ordinal_numbers),u)* subclass(u,v)* -> member(regular(symmetrization_of(ordinal_numbers)),v)*. % 300.04/300.41 181736[20:Res:175570.1,4127.0] || subclass(inverse(ordinal_numbers),symmetric_difference(u,v)) -> member(regular(symmetrization_of(ordinal_numbers)),union(u,v))*. % 300.04/300.41 181738[20:Res:175570.1,16910.0] || subclass(inverse(ordinal_numbers),symmetric_difference(u,inverse(u)))* -> member(regular(symmetrization_of(ordinal_numbers)),symmetrization_of(u)). % 300.04/300.41 181791[19:Res:176345.1,2.0] || subclass(domain_relation,u)* subclass(u,v)* -> member(singleton(singleton(singleton(ordinal_numbers))),v)*. % 300.04/300.41 181797[19:Res:176345.1,4127.0] || subclass(domain_relation,symmetric_difference(u,v)) -> member(singleton(singleton(singleton(ordinal_numbers))),union(u,v))*. % 300.04/300.41 181799[19:Res:176345.1,16910.0] || subclass(domain_relation,symmetric_difference(u,inverse(u)))* -> member(singleton(singleton(singleton(ordinal_numbers))),symmetrization_of(u))*. % 300.04/300.41 181814[19:Res:176345.1,158.0] || subclass(domain_relation,omega) -> equal(integer_of(singleton(singleton(singleton(ordinal_numbers)))),singleton(singleton(singleton(ordinal_numbers))))**. % 300.04/300.41 181834[19:MRR:181820.1,170.0] || subclass(domain_relation,singleton(singleton(ordinal_numbers))) -> member(singleton(singleton(singleton(singleton(singleton(ordinal_numbers))))),element_relation)*. % 300.04/300.41 182180[19:Res:167339.2,176410.0] || subclass(omega,domain_relation) -> equal(integer_of(singleton(singleton(singleton(u)))),ordinal_numbers)** equal(ordinal_numbers,u). % 300.04/300.41 182313[18:SpL:69.0,178138.1] || member(image(u,singleton(v)),universal_class)* equal(rest_of(apply(u,v)),rest_relation) -> . % 300.04/300.41 182408[19:Res:4126.1,182393.0] || member(singleton(ordinal_numbers),symmetric_difference(u,v)) well_ordering(universal_class,complement(intersection(u,v)))* -> . % 300.04/300.41 182443[19:MRR:182412.0,170.0] || well_ordering(universal_class,intersection(complement(u),complement(v)))* -> member(singleton(ordinal_numbers),union(u,v)). % 300.04/300.41 182448[19:SpL:27.0,182395.0] || well_ordering(universal_class,union(u,v)) -> member(singleton(ordinal_numbers),intersection(complement(u),complement(v)))*. % 300.04/300.41 182455[19:SpL:167200.0,182395.0] || well_ordering(universal_class,power_class(complement(inverse(ordinal_numbers)))) -> member(singleton(ordinal_numbers),image(element_relation,symmetrization_of(ordinal_numbers)))*. % 300.04/300.41 182456[19:SpL:180125.0,182395.0] || well_ordering(universal_class,power_class(complement(singleton(ordinal_numbers)))) -> member(singleton(ordinal_numbers),image(element_relation,singleton(ordinal_numbers)))*. % 300.04/300.41 182470[19:SpR:27.0,182467.1] || -> member(singleton(ordinal_numbers),intersection(complement(u),complement(v)))* member(singleton(ordinal_numbers),union(u,v)). % 300.04/300.41 182477[19:SpR:167200.0,182467.1] || -> member(singleton(ordinal_numbers),image(element_relation,symmetrization_of(ordinal_numbers)))* member(singleton(ordinal_numbers),power_class(complement(inverse(ordinal_numbers)))). % 300.04/300.41 182478[19:SpR:180125.0,182467.1] || -> member(singleton(ordinal_numbers),image(element_relation,singleton(ordinal_numbers)))* member(singleton(ordinal_numbers),power_class(complement(singleton(ordinal_numbers)))). % 300.04/300.41 182882[19:Res:182871.1,284.0] || member(not_subclass_element(complement(symmetrization_of(ordinal_numbers)),u),inverse(ordinal_numbers))* -> subclass(complement(symmetrization_of(ordinal_numbers)),u). % 300.04/300.41 182911[20:Res:181635.1,2.0] || subclass(symmetrization_of(ordinal_numbers),u)* subclass(u,v)* -> member(regular(symmetrization_of(ordinal_numbers)),v)*. % 300.04/300.41 182917[20:Res:181635.1,4127.0] || subclass(symmetrization_of(ordinal_numbers),symmetric_difference(u,v)) -> member(regular(symmetrization_of(ordinal_numbers)),union(u,v))*. % 300.04/300.41 182919[20:Res:181635.1,16910.0] || subclass(symmetrization_of(ordinal_numbers),symmetric_difference(u,inverse(u)))* -> member(regular(symmetrization_of(ordinal_numbers)),symmetrization_of(u)). % 300.04/300.41 183040[19:SpL:176366.1,182439.1] || member(u,universal_class) subclass(rest_relation,rest_of(sum_class(u)))* well_ordering(universal_class,ordinal_numbers) -> . % 300.04/300.41 183048[19:SpL:176367.1,182439.1] || member(u,universal_class) subclass(rest_relation,rest_of(power_class(u)))* well_ordering(universal_class,ordinal_numbers) -> . % 300.04/300.41 183049[19:SpL:176376.1,182439.1] || member(u,universal_class) subclass(rest_relation,rest_of(rest_of(u)))* well_ordering(universal_class,ordinal_numbers) -> . % 300.04/300.41 183052[19:SpL:176368.1,182439.1] function(u) || subclass(rest_relation,rest_of(apply(u,v)))* well_ordering(universal_class,ordinal_numbers) -> . % 300.04/300.41 183054[19:SpL:176369.1,182439.1] || subclass(rest_relation,rest_of(not_subclass_element(u,v)))* well_ordering(universal_class,ordinal_numbers) -> subclass(u,v). % 300.04/300.41 183087[19:Res:182463.1,11848.0] || equal(u,singleton(singleton(ordinal_numbers)))* subclass(u,v)* well_ordering(universal_class,v)* -> . % 300.04/300.41 183091[19:Res:182463.1,2.0] || equal(u,singleton(singleton(ordinal_numbers)))* subclass(u,v)* -> member(singleton(ordinal_numbers),v)*. % 300.04/300.41 183097[19:Res:182463.1,4127.0] || equal(symmetric_difference(u,v),singleton(singleton(ordinal_numbers))) -> member(singleton(ordinal_numbers),union(u,v))*. % 300.04/300.41 183099[19:Res:182463.1,16910.0] || equal(symmetric_difference(u,inverse(u)),singleton(singleton(ordinal_numbers)))** -> member(singleton(ordinal_numbers),symmetrization_of(u))*. % 300.04/300.41 183832[19:Rew:169229.1,183819.2] || member(not_subclass_element(u,ordinal_numbers),singleton(u))* -> equal(singleton(u),ordinal_numbers) subclass(u,ordinal_numbers). % 300.04/300.41 183973[23:Rew:183885.0,169663.1] || well_ordering(element_relation,image(u,ordinal_numbers)) subclass(apply(u,universal_class),image(u,ordinal_numbers))* -> . % 300.04/300.41 183989[23:Rew:183893.0,168962.1] || member(u,universal_class) -> equal(segment(v,w,range_of(u)),segment(v,w,universal_class))**. % 300.04/300.41 183990[23:Rew:183893.0,177856.1] || -> equal(range_of(u),ordinal_numbers) equal(segment(v,w,inverse(u)),segment(v,w,universal_class))**. % 300.04/300.41 184006[23:Rew:183888.0,168964.1] || member(u,universal_class) -> equal(range__dfg(v,range_of(u),w),range__dfg(v,universal_class,w))**. % 300.04/300.41 184007[23:Rew:183888.0,177851.1] || -> equal(range_of(u),ordinal_numbers) equal(range__dfg(v,inverse(u),w),range__dfg(v,universal_class,w))**. % 300.04/300.41 184009[23:Rew:183894.0,168965.1] || member(u,universal_class) -> equal(domain__dfg(v,w,range_of(u)),domain__dfg(v,w,universal_class))**. % 300.04/300.41 184010[23:Rew:183894.0,177857.1] || -> equal(range_of(u),ordinal_numbers) equal(domain__dfg(v,w,inverse(u)),domain__dfg(v,w,universal_class))**. % 300.04/300.41 184044[23:Rew:183840.0,183890.0] || asymmetric(u,ordinal_numbers) -> equal(domain__dfg(intersection(u,inverse(u)),ordinal_numbers,universal_class),single_valued3(ordinal_numbers))**. % 300.04/300.41 184149[23:SpL:183857.0,99365.1] || equal(sum_class(range_of(ordinal_numbers)),universal_class) member(singleton(singleton(ordinal_numbers)),cross_product(universal_class,universal_class))* -> . % 300.04/300.41 184264[23:SpL:183885.0,9780.0] || subclass(apply(u,universal_class),image(u,ordinal_numbers))* -> section(element_relation,image(u,ordinal_numbers),universal_class). % 300.04/300.41 184398[19:Res:137890.1,176273.0] || well_ordering(u,universal_class) subclass(domain_relation,rest_relation) -> equal(rest_of(least(u,universal_class)),ordinal_numbers)**. % 300.04/300.41 184399[19:Res:137613.1,176273.0] || well_ordering(u,universal_class) subclass(domain_relation,rest_relation) -> equal(rest_of(least(u,rest_relation)),ordinal_numbers)**. % 300.04/300.41 184400[19:Res:137620.1,176273.0] || well_ordering(u,rest_relation) subclass(domain_relation,rest_relation) -> equal(rest_of(least(u,rest_relation)),ordinal_numbers)**. % 300.04/300.41 184401[21:Res:176162.1,176273.0] || well_ordering(u,omega) subclass(domain_relation,rest_relation) -> equal(rest_of(least(u,omega)),ordinal_numbers)**. % 300.04/300.41 184402[21:Res:176155.1,176273.0] || well_ordering(u,universal_class) subclass(domain_relation,rest_relation) -> equal(rest_of(least(u,omega)),ordinal_numbers)**. % 300.04/300.41 184530[19:Res:137890.1,176274.0] || well_ordering(u,universal_class) subclass(rest_relation,domain_relation) -> equal(rest_of(least(u,universal_class)),ordinal_numbers)**. % 300.04/300.41 184531[19:Res:137613.1,176274.0] || well_ordering(u,universal_class) subclass(rest_relation,domain_relation) -> equal(rest_of(least(u,rest_relation)),ordinal_numbers)**. % 300.04/300.41 184532[19:Res:137620.1,176274.0] || well_ordering(u,rest_relation) subclass(rest_relation,domain_relation) -> equal(rest_of(least(u,rest_relation)),ordinal_numbers)**. % 300.04/300.41 184533[21:Res:176162.1,176274.0] || well_ordering(u,omega) subclass(rest_relation,domain_relation) -> equal(rest_of(least(u,omega)),ordinal_numbers)**. % 300.04/300.41 184534[21:Res:176155.1,176274.0] || well_ordering(u,universal_class) subclass(rest_relation,domain_relation) -> equal(rest_of(least(u,omega)),ordinal_numbers)**. % 300.04/300.41 184708[19:MRR:184656.1,170.0] || subclass(rest_relation,domain_relation) subclass(rest_relation,u) -> member(ordered_pair(singleton(v),ordinal_numbers),u)*. % 300.04/300.41 184828[19:Res:176419.1,25.1] || subclass(domain_relation,flip(complement(u))) member(ordered_pair(ordered_pair(v,w),ordinal_numbers),u)* -> . % 300.04/300.41 184832[19:Res:176419.1,148647.0] || subclass(domain_relation,flip(complement(complement(u)))) -> member(ordered_pair(ordered_pair(v,w),ordinal_numbers),u)*. % 300.04/300.41 184840[19:Res:176419.1,22.0] || subclass(domain_relation,flip(intersection(u,v)))* -> member(ordered_pair(ordered_pair(w,x),ordinal_numbers),u)*. % 300.04/300.41 184841[19:Res:176419.1,23.0] || subclass(domain_relation,flip(intersection(u,v)))* -> member(ordered_pair(ordered_pair(w,x),ordinal_numbers),v)*. % 300.04/300.41 184859[19:Res:176419.1,169207.0] || subclass(domain_relation,flip(symmetrization_of(ordinal_numbers))) -> member(ordered_pair(ordered_pair(u,v),ordinal_numbers),inverse(ordinal_numbers))*. % 300.04/300.41 184875[19:Res:176419.1,143.0] || subclass(domain_relation,flip(rest_of(u))) -> equal(restrict(u,ordered_pair(v,w),universal_class),ordinal_numbers)**. % 300.04/300.41 184906[19:Res:176420.1,25.1] || subclass(domain_relation,rotate(complement(u))) member(ordered_pair(ordered_pair(v,ordinal_numbers),w),u)* -> . % 300.04/300.41 184910[19:Res:176420.1,148647.0] || subclass(domain_relation,rotate(complement(complement(u)))) -> member(ordered_pair(ordered_pair(v,ordinal_numbers),w),u)*. % 300.04/300.41 184918[19:Res:176420.1,22.0] || subclass(domain_relation,rotate(intersection(u,v)))* -> member(ordered_pair(ordered_pair(w,ordinal_numbers),x),u)*. % 300.04/300.41 184919[19:Res:176420.1,23.0] || subclass(domain_relation,rotate(intersection(u,v)))* -> member(ordered_pair(ordered_pair(w,ordinal_numbers),x),v)*. % 300.04/300.41 184937[19:Res:176420.1,169207.0] || subclass(domain_relation,rotate(symmetrization_of(ordinal_numbers))) -> member(ordered_pair(ordered_pair(u,ordinal_numbers),v),inverse(ordinal_numbers))*. % 300.04/300.41 184953[19:Res:176420.1,143.0] || subclass(domain_relation,rotate(rest_of(u))) -> equal(restrict(u,ordered_pair(v,ordinal_numbers),universal_class),w)*. % 300.04/300.41 185310[19:Res:185236.1,2.0] || subclass(rest_relation,domain_relation) subclass(rest_relation,u) -> member(singleton(singleton(singleton(ordinal_numbers))),u)*. % 300.04/300.41 185429[23:SpL:185358.0,9.0] || member(u,ordered_pair(universal_class,universal_class))* -> equal(u,unordered_pair(universal_class,ordinal_numbers)) equal(u,ordinal_numbers). % 300.04/300.41 185827[19:Res:167137.1,30589.0] || subclass(rest_relation,successor_relation) -> equal(u,ordinal_numbers) equal(rest_of(regular(u)),successor(regular(u)))**. % 300.04/300.41 186405[19:SpR:43.0,168950.1] || member(restrict(u,v,universal_class),universal_class) -> member(ordinal_numbers,ordered_pair(image(u,v),w))*. % 300.04/300.41 186414[19:Res:168950.1,2.0] || member(u,universal_class) subclass(ordered_pair(range_of(u),v),w)* -> member(ordinal_numbers,w). % 300.04/300.41 187000[19:Rew:167191.0,186953.0] || subclass(u,symmetrization_of(ordinal_numbers)) -> subclass(singleton(regular(u)),symmetrization_of(ordinal_numbers))* equal(u,ordinal_numbers). % 300.04/300.41 187001[19:Rew:180103.0,186954.0] || subclass(u,singleton(ordinal_numbers)) -> subclass(singleton(regular(u)),singleton(ordinal_numbers))* equal(u,ordinal_numbers). % 300.04/300.41 187009[19:Obv:186945.2] || subclass(singleton(u),complement(v))* member(u,v) -> equal(singleton(u),ordinal_numbers). % 300.04/300.41 187509[19:Obv:187505.1] || subclass(omega,u) -> equal(integer_of(v),ordinal_numbers) subclass(intersection(w,singleton(v)),u)*. % 300.04/300.41 187510[19:Obv:187504.1] || subclass(omega,u) -> equal(integer_of(v),ordinal_numbers) subclass(intersection(singleton(v),w),u)*. % 300.04/300.41 187696[19:Res:177822.1,2.0] || subclass(ordered_pair(inverse(u),v),w)* -> equal(range_of(u),ordinal_numbers) member(ordinal_numbers,w). % 300.04/300.41 187772[19:Obv:187750.1] || subclass(symmetric_difference(u,v),complement(union(u,v)))* -> equal(symmetric_difference(u,v),ordinal_numbers). % 300.04/300.41 187812[19:Res:168350.1,11848.0] || subclass(u,v)* well_ordering(universal_class,v)* -> equal(restrict(u,w,x),ordinal_numbers)**. % 300.04/300.41 187858[19:Obv:187851.1] || subclass(restrict(u,v,w),complement(u))* -> equal(restrict(u,v,w),ordinal_numbers). % 300.04/300.41 188269[19:Res:167339.2,187114.0] || subclass(omega,complement(singleton(u)))* -> equal(integer_of(u),ordinal_numbers) equal(singleton(u),ordinal_numbers). % 300.04/300.41 188369[19:Res:176321.2,6476.1] || member(u,universal_class)* equal(successor(u),ordinal_numbers) subclass(universal_class,complement(successor_relation))* -> . % 300.04/300.41 188736[19:Res:176321.2,188593.1] || member(u,universal_class)* equal(successor(u),ordinal_numbers) equal(complement(successor_relation),universal_class) -> . % 300.04/300.41 188914[19:Res:188649.1,169099.2] || equal(complement(sum_class(u)),universal_class)** member(u,universal_class) well_ordering(element_relation,u) -> . % 300.04/300.41 189112[19:Res:188649.1,169641.1] || equal(complement(apply(u,v)),universal_class) well_ordering(element_relation,image(u,singleton(v)))* -> . % 300.04/300.41 189672[19:Res:7.1,176246.1] || equal(singleton(u),domain_relation)** member(v,universal_class) -> equal(ordered_pair(v,ordinal_numbers),u)*. % 300.04/300.41 189708[19:Res:7.1,176276.1] || equal(compose_class(u),domain_relation) member(v,universal_class) -> equal(compose(u,v),ordinal_numbers)**. % 300.04/300.41 190209[19:Res:167116.0,168418.0] || -> equal(integer_of(regular(intersection(u,complement(omega)))),ordinal_numbers)** equal(intersection(u,complement(omega)),ordinal_numbers). % 300.04/300.41 190308[19:MRR:190266.2,167057.0] inductive(symmetric_difference(complement(singleton(ordinal_numbers)),complement(singleton(ordinal_numbers)))) || well_ordering(u,singleton(ordinal_numbers))* -> . % 300.04/300.41 190309[19:MRR:190278.2,167057.0] inductive(symmetric_difference(u,complement(complement(u)))) || well_ordering(v,complement(complement(complement(u))))* -> . % 300.04/300.41 190405[19:SpR:479.0,190219.0] || -> equal(intersection(image(element_relation,union(u,v)),power_class(intersection(complement(u),complement(v)))),ordinal_numbers)**. % 300.04/300.41 190505[19:SpR:479.0,190453.0] || -> equal(union(image(element_relation,union(u,v)),power_class(intersection(complement(u),complement(v)))),universal_class)**. % 300.04/300.41 190550[19:SpR:479.0,190464.0] || -> equal(symmetric_difference(image(element_relation,union(u,v)),power_class(intersection(complement(u),complement(v)))),universal_class)**. % 300.04/300.41 190654[19:Res:167116.0,168419.0] || -> equal(integer_of(regular(intersection(complement(omega),u))),ordinal_numbers)** equal(intersection(complement(omega),u),ordinal_numbers). % 300.04/300.41 190684[19:Rew:160.0,190614.1] || member(regular(symmetric_difference(u,v)),intersection(u,v))* -> equal(symmetric_difference(u,v),ordinal_numbers). % 300.04/300.41 191005[19:MRR:190976.2,167057.0] || member(u,union(inverse(ordinal_numbers),symmetrization_of(ordinal_numbers)))* member(u,complement(symmetrization_of(ordinal_numbers))) -> . % 300.04/300.41 191262[19:Res:7.1,168435.0] || equal(restrict(u,v,w),omega)** -> equal(integer_of(x),ordinal_numbers) member(x,u)*. % 300.04/300.41 191397[19:Res:7.1,167733.0] || equal(restrict(u,v,w),x)* -> equal(x,ordinal_numbers) member(regular(x),u)*. % 300.04/300.41 192238[19:SpR:192178.0,66.2] function(complement(cross_product(u,universal_class))) || member(u,universal_class)* -> member(range_of(ordinal_numbers),universal_class)*. % 300.04/300.41 192311[19:SpL:168752.1,192214.0] || member(u,universal_class) member(sum_class(range_of(u)),cantor(complement(cross_product(ordinal_numbers,universal_class))))* -> . % 300.04/300.41 192326[19:Res:176420.1,192214.0] || subclass(domain_relation,rotate(cantor(complement(cross_product(singleton(ordered_pair(ordered_pair(u,ordinal_numbers),v)),universal_class)))))* -> . % 300.04/300.41 192329[19:Res:176419.1,192214.0] || subclass(domain_relation,flip(cantor(complement(cross_product(singleton(ordered_pair(ordered_pair(u,v),ordinal_numbers)),universal_class)))))* -> . % 300.04/300.41 192331[19:Res:2526.2,192214.0] || subclass(u,cantor(complement(cross_product(singleton(not_subclass_element(u,v)),universal_class))))* -> subclass(u,v). % 300.04/300.41 192332[19:Res:2482.2,192214.0] || member(u,universal_class) subclass(universal_class,cantor(complement(cross_product(singleton(sum_class(u)),universal_class))))* -> . % 300.04/300.41 192333[19:Res:2483.2,192214.0] || member(u,universal_class) subclass(universal_class,cantor(complement(cross_product(singleton(power_class(u)),universal_class))))* -> . % 300.04/300.41 192341[19:Res:2525.1,192214.0] || subclass(ordered_pair(u,v),cantor(complement(cross_product(singleton(unordered_pair(u,singleton(v))),universal_class))))* -> . % 300.04/300.41 193082[25:Rew:192881.1,192870.2] function(restrict(u,v,w)) || section(u,w,v)* -> equal(universal_class,w). % 300.04/300.41 193170[25:SpR:192881.1,124899.1] function(restrict(u,v,w)) || section(u,w,v)* -> subclass(universal_class,w). % 300.04/300.41 193353[25:SpR:193223.1,2525.1] function(u) || subclass(ordered_pair(v,u),w)* -> member(unordered_pair(v,ordinal_numbers),w)*. % 300.04/300.41 193405[25:SpL:193223.1,2557.0] function(u) || member(singleton(singleton(ordinal_numbers)),cross_product(v,w))* -> member(u,w)*. % 300.04/300.41 193513[25:SpL:193223.1,277.0] function(u) || member(image(v,ordinal_numbers),universal_class) -> member(apply(v,u),universal_class)*. % 300.04/300.41 193622[25:Rew:193223.1,193355.1] function(u) || section(v,ordinal_numbers,w) -> subclass(segment(v,w,u),ordinal_numbers)*. % 300.04/300.41 193638[25:MRR:193637.1,166995.0] function(u) || subclass(segment(v,w,u),ordinal_numbers)* -> section(v,ordinal_numbers,w). % 300.04/300.41 193648[25:SoR:193232.0,12322.2] single_valued_class(regular(u)) || equal(cross_product(universal_class,universal_class),regular(u))* -> equal(u,ordinal_numbers). % 300.04/300.41 193936[25:SoR:193238.0,167213.2] function(u) single_valued_class(apply(u,v)) || equal(apply(u,v),ordinal_numbers)** -> . % 300.04/300.41 193958[25:SoR:193239.0,167213.2] single_valued_class(not_subclass_element(u,v)) || equal(not_subclass_element(u,v),ordinal_numbers)** -> subclass(u,v). % 300.04/300.41 194021[19:Obv:194004.0] || equal(successor(u),ordinal_numbers) member(u,universal_class)* subclass(domain_relation,complement(successor_relation))* -> . % 300.04/300.41 194152[25:Rew:184170.1,194151.2] function(u) || member(ordered_pair(v,singleton(singleton(ordinal_numbers))),composition_function)* -> equal(universal_class,u)*. % 300.04/300.41 194185[19:Res:52.1,168499.0] inductive(rest_of(u)) || -> equal(integer_of(ordered_pair(v,w)),ordinal_numbers)** member(v,cantor(u))*. % 300.04/300.41 194439[19:MRR:194425.0,167011.0] || equal(complement(cantor(u)),singleton(ordinal_numbers)) -> equal(apply(u,ordinal_numbers),sum_class(range_of(ordinal_numbers)))**. % 300.04/300.41 194447[19:MRR:194404.0,170.0] || subclass(universal_class,complement(cantor(u)))* -> equal(apply(u,singleton(v)),sum_class(range_of(ordinal_numbers)))**. % 300.04/300.41 194453[19:MRR:194413.0,36682.1] || -> equal(apply(u,not_subclass_element(v,cantor(u))),sum_class(range_of(ordinal_numbers)))** subclass(v,cantor(u)). % 300.04/300.41 195098[25:SpR:193305.1,36588.1] function(rest_of(ordinal_numbers)) || member(ordinal_numbers,rest_of(ordinal_numbers)) -> member(singleton(singleton(ordinal_numbers)),element_relation)*. % 300.04/300.41 195286[0:Res:27190.1,146.0] || subclass(rest_relation,flip(rest_relation)) -> equal(rest_of(ordered_pair(u,v)),rest_of(ordered_pair(v,u)))*. % 300.04/300.41 195296[0:Res:27190.1,46.0] || subclass(rest_relation,flip(successor_relation)) -> equal(rest_of(ordered_pair(u,v)),successor(ordered_pair(v,u)))**. % 300.04/300.41 195383[0:Res:27189.1,146.0] || subclass(rest_relation,rotate(rest_relation)) -> equal(rest_of(ordered_pair(u,rest_of(ordered_pair(v,u)))),v)**. % 300.04/300.41 195393[0:Res:27189.1,46.0] || subclass(rest_relation,rotate(successor_relation)) -> equal(successor(ordered_pair(u,rest_of(ordered_pair(v,u)))),v)**. % 300.04/300.41 195622[19:Res:52.1,168375.0] inductive(u) || subclass(u,v)* -> equal(integer_of(w),ordinal_numbers) member(w,v)*. % 300.04/300.41 196161[19:SpR:188655.1,4125.0] || equal(complement(union(u,v)),universal_class) -> equal(symmetric_difference(complement(u),complement(v)),ordinal_numbers)**. % 300.04/300.41 196487[19:Rew:167017.0,196366.1] || equal(complement(complement(singleton(u))),universal_class) -> equal(complement(image(element_relation,successor(u))),ordinal_numbers)**. % 300.04/300.41 196488[19:Rew:167017.0,196368.1] || equal(complement(complement(inverse(u))),universal_class) -> equal(complement(image(element_relation,symmetrization_of(u))),ordinal_numbers)**. % 300.04/300.41 196489[19:Rew:167017.0,196369.1] || equal(complement(complement(image(successor_relation,ordinal_numbers))),universal_class)** -> equal(complement(image(element_relation,kind_1_ordinals)),ordinal_numbers). % 300.04/300.41 196600[19:Res:167339.2,190819.0] || subclass(omega,complement(u)) -> equal(integer_of(not_subclass_element(u,ordinal_numbers)),ordinal_numbers)** subclass(u,ordinal_numbers). % 300.04/300.41 196606[19:Obv:196591.1] || member(u,complement(intersection(v,singleton(u))))* -> subclass(intersection(v,singleton(u)),ordinal_numbers). % 300.04/300.41 196607[19:Obv:196590.1] || member(u,complement(intersection(singleton(u),v)))* -> subclass(intersection(singleton(u),v),ordinal_numbers). % 300.04/300.41 196617[20:Res:196602.0,2499.1] || member(not_subclass_element(inverse(ordinal_numbers),ordinal_numbers),universal_class) -> member(not_subclass_element(inverse(ordinal_numbers),ordinal_numbers),symmetrization_of(ordinal_numbers))*. % 300.04/300.41 196856[19:Res:196731.1,16102.0] || subclass(universal_class,symmetric_difference(complement(u),complement(v)))* -> member(regular(element_relation),union(u,v)). % 300.04/300.41 196860[19:Res:196731.1,9.0] || subclass(universal_class,unordered_pair(u,v))* -> equal(regular(element_relation),v) equal(regular(element_relation),u). % 300.04/300.41 196928[19:MRR:196893.1,196718.0] || subclass(rest_relation,domain_relation) subclass(rest_relation,u) -> member(ordered_pair(regular(element_relation),ordinal_numbers),u)*. % 300.04/300.41 196988[19:Res:167106.1,168251.0] inductive(regular(u)) || member(ordinal_numbers,u)* -> equal(u,ordinal_numbers) member(ordinal_numbers,v)*. % 300.04/300.41 197051[19:SpL:27.0,196890.1] || subclass(universal_class,intersection(complement(u),complement(v)))* subclass(element_relation,union(u,v)) -> . % 300.04/300.41 197059[19:SpL:167200.0,196890.1] || subclass(universal_class,image(element_relation,symmetrization_of(ordinal_numbers))) subclass(element_relation,power_class(complement(inverse(ordinal_numbers))))* -> . % 300.04/300.41 197060[19:SpL:180125.0,196890.1] || subclass(universal_class,image(element_relation,singleton(ordinal_numbers))) subclass(element_relation,power_class(complement(singleton(ordinal_numbers))))* -> . % 300.04/300.41 197304[19:Res:168469.2,188593.1] || subclass(u,v)* equal(complement(v),universal_class) -> equal(intersection(w,u),ordinal_numbers)**. % 300.04/300.41 197868[19:Res:168474.2,188593.1] || subclass(u,v)* equal(complement(v),universal_class) -> equal(intersection(u,w),ordinal_numbers)**. % 300.04/300.41 198356[19:Rew:197499.0,198343.1] || member(not_subclass_element(intersection(u,v),ordinal_numbers),complement(u))* -> subclass(intersection(u,v),ordinal_numbers). % 300.04/300.41 199014[19:Rew:197702.0,198990.1] || member(not_subclass_element(intersection(u,v),ordinal_numbers),complement(v))* -> subclass(intersection(u,v),ordinal_numbers). % 300.04/300.41 199274[19:SpR:4121.0,198500.0] || -> equal(intersection(symmetric_difference(cross_product(u,v),w),complement(complement(restrict(w,u,v)))),ordinal_numbers)**. % 300.04/300.41 199275[19:SpR:4119.0,198500.0] || -> equal(intersection(symmetric_difference(u,cross_product(v,w)),complement(complement(restrict(u,v,w)))),ordinal_numbers)**. % 300.04/300.41 199601[19:Obv:199574.1] || equal(u,v) -> equal(unordered_pair(v,u),ordinal_numbers) member(v,unordered_pair(v,u))*. % 300.04/300.41 199604[19:Obv:199591.2] || equal(u,v) equal(rest_of(v),rest_relation) -> equal(unordered_pair(v,u),ordinal_numbers)**. % 300.04/300.41 199612[23:MRR:199611.1,167176.0] || equal(unordered_pair(u,ordinal_numbers),singleton(u)) -> equal(regular(ordered_pair(u,universal_class)),singleton(u))**. % 300.04/300.41 200388[19:Res:167106.1,16086.0] inductive(symmetric_difference(cross_product(u,v),w)) || -> member(ordinal_numbers,complement(restrict(w,u,v)))*. % 300.04/300.41 200702[19:Res:167106.1,16083.0] inductive(symmetric_difference(u,cross_product(v,w))) || -> member(ordinal_numbers,complement(restrict(u,v,w)))*. % 300.04/300.41 200767[23:SpR:183840.0,125331.0] || -> equal(cantor(restrict(cross_product(u,ordinal_numbers),v,w)),segment(cross_product(v,w),u,universal_class))**. % 300.04/300.41 201699[26:Rew:200916.0,168993.2] || subclass(unordered_pair(u,v),ordinal_numbers)* member(u,universal_class) well_ordering(w,ordinal_numbers)* -> . % 300.04/300.41 201700[26:Rew:200916.0,168992.2] || subclass(unordered_pair(u,v),ordinal_numbers)* member(v,universal_class) well_ordering(w,ordinal_numbers)* -> . % 300.04/300.41 203107[19:SpR:27.0,202844.1] || subclass(intersection(complement(u),complement(v)),ordinal_numbers)* -> equal(complement(union(u,v)),ordinal_numbers). % 300.04/300.41 203231[19:SpL:202844.1,158050.0] || subclass(symmetrization_of(u),ordinal_numbers)* subclass(cross_product(v,v),ordinal_numbers)* -> connected(u,v)*. % 300.04/300.41 203373[19:MRR:203372.2,166995.0] || subclass(symmetrization_of(u),ordinal_numbers)* connected(u,v)* -> equal(cross_product(v,v),ordinal_numbers)**. % 300.04/300.41 203584[26:Res:167106.1,202277.1] inductive(complement(compose(complement(element_relation),inverse(element_relation)))) || member(ordinal_numbers,cross_product(universal_class,universal_class))* -> . % 300.04/300.41 203631[0:Res:52.1,16468.0] inductive(restrict(u,v,w)) || -> subclass(omega,x) member(not_subclass_element(omega,x),u)*. % 300.04/300.41 204015[19:SpL:5132.1,203426.0] || subclass(singleton(not_subclass_element(cross_product(u,v),w)),ordinal_numbers)* -> subclass(cross_product(u,v),w). % 300.04/300.41 204029[19:MRR:195337.1,204022.0] || subclass(rest_relation,rotate(complement(singleton(ordered_pair(ordered_pair(u,rest_of(ordered_pair(v,u))),v)))))* -> . % 300.04/300.41 204031[19:MRR:195240.1,204022.0] || subclass(rest_relation,flip(complement(singleton(ordered_pair(ordered_pair(u,v),rest_of(ordered_pair(v,u)))))))* -> . % 300.04/300.41 204395[19:Rew:204393.1,204380.1] || equal(ordered_pair(u,v),universal_class)** -> equal(singleton(w),omega)** equal(singleton(w),ordinal_numbers). % 300.04/300.41 204396[19:Rew:204394.1,204386.1] || subclass(universal_class,ordered_pair(u,v))* -> equal(singleton(w),omega)** equal(singleton(w),ordinal_numbers). % 300.04/300.41 204510[19:Res:24.2,203417.1] || member(ordinal_numbers,u) member(ordinal_numbers,v) subclass(intersection(v,u),ordinal_numbers)* -> . % 300.04/300.41 204642[19:Res:24.2,203420.1] || member(omega,u) member(omega,v) subclass(intersection(v,u),ordinal_numbers)* -> . % 300.04/300.41 206013[19:Rew:167049.0,205853.1] || equal(symmetrization_of(u),ordinal_numbers) subclass(cross_product(v,v),ordinal_numbers)* -> connected(u,v)*. % 300.04/300.41 206017[19:Rew:142500.0,205449.1] || equal(ordinal_numbers,u) -> equal(complement(image(element_relation,successor(u))),power_class(complement(singleton(u))))**. % 300.04/300.41 206018[19:Rew:142500.0,205451.1] || equal(ordinal_numbers,u) -> equal(complement(image(element_relation,symmetrization_of(u))),power_class(complement(inverse(u))))**. % 300.04/300.41 206080[19:MRR:206079.2,166995.0] || equal(symmetrization_of(u),ordinal_numbers) connected(u,v)* -> equal(cross_product(v,v),ordinal_numbers)**. % 300.04/300.41 206218[19:SpR:27838.0,188655.1] || equal(complement(successor(u)),universal_class) -> equal(symmetric_difference(complement(u),complement(singleton(u))),ordinal_numbers)**. % 300.04/300.41 206273[0:SpL:27838.0,5472.0] || subclass(universal_class,symmetric_difference(complement(u),complement(singleton(u))))* -> member(singleton(v),successor(u))*. % 300.04/300.41 206279[0:SpL:27838.0,12446.0] || equal(symmetric_difference(complement(u),complement(singleton(u))),universal_class)** -> member(singleton(v),successor(u))*. % 300.04/300.41 206286[19:SpL:27838.0,169224.0] || equal(symmetric_difference(complement(u),complement(singleton(u))),singleton(ordinal_numbers))** -> member(ordinal_numbers,successor(u)). % 300.04/300.41 206489[0:Rew:206400.0,17091.0] || -> subclass(symmetric_difference(complement(u),power_class(complement(power_class(v)))),union(u,image(element_relation,power_class(v))))*. % 300.04/300.41 206725[19:Rew:206400.0,168492.0] || subclass(universal_class,power_class(complement(power_class(u)))) member(ordinal_numbers,image(element_relation,power_class(u)))* -> . % 300.04/300.41 206726[8:Rew:206400.0,165008.1] || subclass(domain_relation,image(element_relation,power_class(u)))* subclass(universal_class,power_class(complement(power_class(u)))) -> . % 300.04/300.41 206731[0:Rew:206400.0,9797.1] || subclass(universal_class,image(element_relation,power_class(u)))* subclass(universal_class,power_class(complement(power_class(u)))) -> . % 300.04/300.41 206732[0:Rew:206400.0,6204.0] || subclass(universal_class,power_class(complement(power_class(u)))) member(omega,image(element_relation,power_class(u)))* -> . % 300.04/300.41 206757[0:Rew:206400.0,17102.0] || -> subclass(symmetric_difference(power_class(complement(power_class(u))),complement(v)),union(image(element_relation,power_class(u)),v))*. % 300.04/300.41 206888[8:Rew:206400.0,97569.1] || subclass(universal_class,image(element_relation,power_class(u))) subclass(domain_relation,power_class(complement(power_class(u))))* -> . % 300.04/300.41 206889[8:Rew:206400.0,97559.1] || subclass(domain_relation,image(element_relation,power_class(u)))* subclass(domain_relation,power_class(complement(power_class(u)))) -> . % 300.04/300.41 206894[8:Rew:206400.0,97593.1] || equal(image(element_relation,power_class(u)),domain_relation)** equal(power_class(complement(power_class(u))),domain_relation) -> . % 300.04/300.41 206896[0:Rew:206400.0,132964.1] || subclass(universal_class,image(element_relation,power_class(u))) member(omega,power_class(complement(power_class(u))))* -> . % 300.04/300.41 206916[19:Rew:206400.0,182453.0] || well_ordering(universal_class,power_class(complement(power_class(u)))) -> member(singleton(ordinal_numbers),image(element_relation,power_class(u)))*. % 300.04/300.41 206920[19:Rew:206400.0,180967.1] inductive(image(element_relation,power_class(u))) || equal(power_class(complement(power_class(u))),singleton(ordinal_numbers))** -> . % 300.04/300.41 206926[22:Rew:206400.0,177208.0] || subclass(omega,power_class(complement(power_class(u)))) member(ordinal_numbers,image(element_relation,power_class(u)))* -> . % 300.04/300.41 206929[22:Rew:206400.0,178706.1] || equal(image(element_relation,power_class(u)),omega)** equal(power_class(complement(power_class(u))),omega) -> . % 300.04/300.41 206930[22:Rew:206400.0,178694.0] || equal(power_class(complement(power_class(u))),omega) member(ordinal_numbers,image(element_relation,power_class(u)))* -> . % 300.04/300.41 206934[19:Rew:206400.0,182475.1] || -> member(singleton(ordinal_numbers),image(element_relation,power_class(u)))* member(singleton(ordinal_numbers),power_class(complement(power_class(u)))). % 300.04/300.41 206958[19:Rew:206400.0,197057.1] || subclass(universal_class,image(element_relation,power_class(u))) subclass(element_relation,power_class(complement(power_class(u))))* -> . % 300.04/300.41 207100[0:Rew:206400.0,137115.0] || -> subclass(complement(successor(complement(power_class(u)))),intersection(power_class(u),complement(singleton(complement(power_class(u))))))*. % 300.04/300.41 207122[19:Rew:206400.0,204479.0] || equal(intersection(power_class(u),complement(singleton(complement(power_class(u))))),successor(complement(power_class(u))))** -> . % 300.04/300.41 207209[0:Rew:206400.0,137147.0] || -> subclass(complement(symmetrization_of(complement(power_class(u)))),intersection(power_class(u),complement(inverse(complement(power_class(u))))))*. % 300.04/300.41 207231[19:Rew:206400.0,204480.0] || equal(intersection(power_class(u),complement(inverse(complement(power_class(u))))),symmetrization_of(complement(power_class(u))))** -> . % 300.04/300.41 207378[19:Rew:206400.0,207037.1] || equal(successor(complement(power_class(u))),universal_class) well_ordering(element_relation,successor(complement(power_class(u))))* -> . % 300.04/300.41 207379[19:Rew:206400.0,207043.0] || subclass(complement(singleton(complement(power_class(u)))),ordinal_numbers)* -> equal(successor(complement(power_class(u))),universal_class). % 300.04/300.41 207383[19:Rew:206400.0,207145.1] || equal(symmetrization_of(complement(power_class(u))),universal_class) well_ordering(element_relation,symmetrization_of(complement(power_class(u))))* -> . % 300.04/300.41 207384[19:Rew:206400.0,207151.0] || subclass(complement(inverse(complement(power_class(u)))),ordinal_numbers)* -> equal(symmetrization_of(complement(power_class(u))),universal_class). % 300.04/300.41 207942[19:Res:205391.1,16102.0] || equal(complement(symmetric_difference(complement(u),complement(v))),ordinal_numbers)** -> member(ordinal_numbers,union(u,v)). % 300.04/300.41 208215[19:SpR:206403.0,190268.0] || -> equal(symmetric_difference(intersection(complement(u),power_class(v)),complement(union(u,complement(power_class(v))))),ordinal_numbers)**. % 300.04/300.41 208231[19:SpR:206403.0,169158.1] || -> member(ordinal_numbers,intersection(complement(u),power_class(v)))* member(ordinal_numbers,union(u,complement(power_class(v)))). % 300.04/300.41 208284[19:SpR:180103.0,206403.0] || -> equal(union(complement(singleton(ordinal_numbers)),complement(power_class(u))),complement(intersection(singleton(ordinal_numbers),power_class(u))))**. % 300.04/300.41 208285[19:SpR:167191.0,206403.0] || -> equal(union(complement(inverse(ordinal_numbers)),complement(power_class(u))),complement(intersection(symmetrization_of(ordinal_numbers),power_class(u))))**. % 300.04/300.41 208473[19:Res:205414.1,16102.0] || equal(complement(symmetric_difference(complement(u),complement(v))),ordinal_numbers)** -> member(omega,union(u,v)). % 300.04/300.41 208522[19:SpR:206410.0,190268.0] || -> equal(symmetric_difference(intersection(power_class(u),complement(v)),complement(union(complement(power_class(u)),v))),ordinal_numbers)**. % 300.04/300.41 208538[19:SpR:206410.0,169158.1] || -> member(ordinal_numbers,intersection(power_class(u),complement(v)))* member(ordinal_numbers,union(complement(power_class(u)),v)). % 300.04/300.41 208779[19:Res:205520.1,9833.0] || equal(complement(u),ordinal_numbers) well_ordering(v,u)* -> member(least(v,universal_class),universal_class)*. % 300.04/300.41 208782[19:Res:205520.1,6435.0] || equal(complement(u),ordinal_numbers) subclass(u,v)* -> member(unordered_pair(w,x),v)*. % 300.04/300.41 208822[19:Res:205520.1,15079.1] || equal(complement(singleton(u)),ordinal_numbers)** member(v,universal_class)* -> equal(power_class(v),u)*. % 300.04/300.41 208823[19:Res:205520.1,15113.1] || equal(complement(singleton(u)),ordinal_numbers)** member(v,universal_class)* -> equal(sum_class(v),u)*. % 300.04/300.41 209153[22:Res:178902.1,206404.0] || equal(image(element_relation,power_class(u)),omega) member(ordinal_numbers,power_class(complement(power_class(u))))* -> . % 300.04/300.41 209154[22:Res:177171.1,206404.0] || subclass(omega,image(element_relation,power_class(u))) member(ordinal_numbers,power_class(complement(power_class(u))))* -> . % 300.04/300.41 209156[19:Res:167104.1,206404.0] || subclass(universal_class,image(element_relation,power_class(u))) member(ordinal_numbers,power_class(complement(power_class(u))))* -> . % 300.04/300.41 209172[19:Rew:206408.0,209112.0] || equal(power_class(complement(power_class(u))),ordinal_numbers) member(omega,power_class(complement(power_class(u))))* -> . % 300.04/300.41 209173[19:Rew:206408.0,209152.0] || equal(power_class(complement(power_class(u))),ordinal_numbers) member(ordinal_numbers,power_class(complement(power_class(u))))* -> . % 300.04/300.41 209516[19:SpL:168412.1,208803.0] || equal(complement(complement(regular(cross_product(u,v)))),ordinal_numbers)** -> equal(cross_product(u,v),ordinal_numbers). % 300.04/300.41 209743[19:SpL:168412.1,203430.0] || subclass(unordered_pair(u,regular(cross_product(v,w))),ordinal_numbers)* -> equal(cross_product(v,w),ordinal_numbers). % 300.04/300.41 209830[0:MRR:209789.0,940.0] || member(u,universal_class) subclass(rest_relation,complement(unordered_pair(v,ordered_pair(u,rest_of(u)))))* -> . % 300.04/300.41 209831[0:MRR:209788.0,940.0] || member(u,universal_class) subclass(rest_relation,complement(unordered_pair(ordered_pair(u,rest_of(u)),v)))* -> . % 300.04/300.41 209857[19:SpL:168412.1,203433.0] || subclass(unordered_pair(regular(cross_product(u,v)),w),ordinal_numbers)* -> equal(cross_product(u,v),ordinal_numbers). % 300.04/300.41 209878[19:Res:24.2,205934.1] || member(u,v)* member(u,w)* equal(intersection(w,v),ordinal_numbers)** -> . % 300.04/300.41 209883[19:Res:35124.1,205934.1] || member(u,universal_class) equal(union(v,w),ordinal_numbers)** -> member(u,complement(v))*. % 300.04/300.41 209884[19:Res:35125.1,205934.1] || member(u,universal_class) equal(union(v,w),ordinal_numbers)** -> member(u,complement(w))*. % 300.04/300.41 209889[19:Res:125124.2,205934.1] || member(u,universal_class)* subclass(rest_relation,rest_of(v))* equal(cantor(v),ordinal_numbers) -> . % 300.04/300.41 209965[19:Res:17.2,205934.1] || member(u,v)* member(w,x)* equal(cross_product(x,v),ordinal_numbers)** -> . % 300.04/300.41 210101[19:SpL:168412.1,205945.0] || equal(unordered_pair(u,regular(cross_product(v,w))),ordinal_numbers)** -> equal(cross_product(v,w),ordinal_numbers). % 300.04/300.41 210119[19:SpL:168412.1,205947.0] || equal(unordered_pair(regular(cross_product(u,v)),w),ordinal_numbers)** -> equal(cross_product(u,v),ordinal_numbers). % 300.04/300.41 210225[19:SpR:27837.0,188655.1] || equal(complement(symmetrization_of(u)),universal_class) -> equal(symmetric_difference(complement(u),complement(inverse(u))),ordinal_numbers)**. % 300.04/300.41 210272[0:SpL:27837.0,5472.0] || subclass(universal_class,symmetric_difference(complement(u),complement(inverse(u))))* -> member(singleton(v),symmetrization_of(u))*. % 300.04/300.41 210278[0:SpL:27837.0,12446.0] || equal(symmetric_difference(complement(u),complement(inverse(u))),universal_class)** -> member(singleton(v),symmetrization_of(u))*. % 300.04/300.41 210285[19:SpL:27837.0,169224.0] || equal(symmetric_difference(complement(u),complement(inverse(u))),singleton(ordinal_numbers))** -> member(ordinal_numbers,symmetrization_of(u)). % 300.04/300.41 210563[19:SpR:142500.0,167923.2] || asymmetric(universal_class,u) equal(compose(ordinal_numbers,ordinal_numbers),ordinal_numbers) -> transitive(inverse(universal_class),u)*. % 300.04/300.41 210833[19:SpL:142500.0,167924.1] || asymmetric(universal_class,u) transitive(inverse(universal_class),u)* -> equal(compose(ordinal_numbers,ordinal_numbers),ordinal_numbers). % 300.04/300.41 210855[19:MRR:210842.0,170.0] || equal(compose(u,singleton(ordinal_numbers)),ordinal_numbers) -> member(singleton(singleton(singleton(ordinal_numbers))),compose_class(u))*. % 300.04/300.41 210987[19:Res:66.2,205988.1] function(u) || member(v,universal_class) equal(singleton(image(u,v)),ordinal_numbers)** -> . % 300.04/300.41 211047[19:MRR:211014.1,5.0] || member(u,universal_class) equal(singleton(apply(choice,u)),ordinal_numbers)** -> equal(u,ordinal_numbers). % 300.04/300.41 211114[19:MRR:211082.0,170.0] || well_ordering(universal_class,image(element_relation,power_class(u))) -> member(singleton(ordinal_numbers),power_class(complement(power_class(u))))*. % 300.04/300.41 211227[19:Obv:211219.2] || equal(u,v) equal(singleton(v),ordinal_numbers) -> equal(unordered_pair(v,u),ordinal_numbers)**. % 300.04/300.41 211276[0:Res:12.0,15107.0] || subclass(universal_class,u)* subclass(u,v)* -> member(sum_class(unordered_pair(w,x)),v)*. % 300.04/300.41 211277[0:Res:940.0,15107.0] || subclass(universal_class,u)* subclass(u,v)* -> member(sum_class(ordered_pair(w,x)),v)*. % 300.04/300.41 211293[20:Res:175569.0,15107.0] || subclass(universal_class,u)* subclass(u,v)* -> member(sum_class(regular(symmetrization_of(ordinal_numbers))),v)*. % 300.04/300.41 211448[2:Res:188649.1,9806.0] || equal(complement(apply(u,v)),universal_class) -> section(element_relation,image(u,singleton(v)),universal_class)*. % 300.04/300.41 211643[19:Res:203424.1,896.0] || subclass(complement(restrict(u,v,w)),ordinal_numbers)* -> member(singleton(x),cross_product(v,w))*. % 300.04/300.41 211657[19:Res:203424.1,99368.1] || subclass(complement(cross_product(universal_class,universal_class)),ordinal_numbers)* equal(sum_class(range_of(singleton(u))),u)** -> . % 300.04/300.41 211870[0:Res:12807.1,27264.1] || subclass(universal_class,symmetric_difference(u,v)) subclass(universal_class,intersection(complement(u),complement(v)))* -> . % 300.04/300.41 211891[19:SpL:27.0,211666.0] || subclass(union(u,v),ordinal_numbers) well_ordering(universal_class,intersection(complement(u),complement(v)))* -> . % 300.04/300.41 211900[19:SpL:167200.0,211666.0] || subclass(power_class(complement(inverse(ordinal_numbers))),ordinal_numbers) well_ordering(universal_class,image(element_relation,symmetrization_of(ordinal_numbers)))* -> . % 300.04/300.41 211901[19:SpL:180125.0,211666.0] || subclass(power_class(complement(singleton(ordinal_numbers))),ordinal_numbers) well_ordering(universal_class,image(element_relation,singleton(ordinal_numbers)))* -> . % 300.04/300.41 211902[19:SpL:206408.0,211666.0] || subclass(power_class(complement(power_class(u))),ordinal_numbers) well_ordering(universal_class,image(element_relation,power_class(u)))* -> . % 300.04/300.41 212455[19:Res:205991.1,896.0] || equal(complement(restrict(u,v,w)),ordinal_numbers)** -> member(singleton(x),cross_product(v,w))*. % 300.04/300.41 212565[19:Res:209033.1,8.0] || equal(power_class(u),ordinal_numbers) subclass(v,power_class(u))* -> equal(v,power_class(u)). % 300.04/300.41 212661[19:SpR:27.0,198248.0] || -> equal(intersection(union(u,v),restrict(intersection(complement(u),complement(v)),w,x)),ordinal_numbers)**. % 300.04/300.41 212670[19:SpR:167200.0,198248.0] || -> equal(intersection(power_class(complement(inverse(ordinal_numbers))),restrict(image(element_relation,symmetrization_of(ordinal_numbers)),u,v)),ordinal_numbers)**. % 300.04/300.41 212671[19:SpR:180125.0,198248.0] || -> equal(intersection(power_class(complement(singleton(ordinal_numbers))),restrict(image(element_relation,singleton(ordinal_numbers)),u,v)),ordinal_numbers)**. % 300.04/300.41 212672[19:SpR:206408.0,198248.0] || -> equal(intersection(power_class(complement(power_class(u))),restrict(image(element_relation,power_class(u)),v,w)),ordinal_numbers)**. % 300.04/300.41 212767[0:Res:12.0,15073.0] || subclass(universal_class,u)* subclass(u,v)* -> member(power_class(unordered_pair(w,x)),v)*. % 300.04/300.41 212768[0:Res:940.0,15073.0] || subclass(universal_class,u)* subclass(u,v)* -> member(power_class(ordered_pair(w,x)),v)*. % 300.04/300.41 212784[20:Res:175569.0,15073.0] || subclass(universal_class,u)* subclass(u,v)* -> member(power_class(regular(symmetrization_of(ordinal_numbers))),v)*. % 300.04/300.41 212959[19:Rew:199281.0,212947.1] || member(not_subclass_element(complement(u),ordinal_numbers),restrict(u,v,w))* -> subclass(complement(u),ordinal_numbers). % 300.04/300.41 213004[19:Obv:212982.1] || -> equal(integer_of(u),ordinal_numbers) subclass(unordered_pair(u,v),omega) member(v,unordered_pair(u,v))*. % 300.04/300.41 213059[19:Obv:213036.1] || -> equal(integer_of(u),ordinal_numbers) subclass(unordered_pair(v,u),omega) member(v,unordered_pair(v,u))*. % 300.04/300.41 213072[20:Res:26.2,213033.0] || member(not_subclass_element(symmetrization_of(ordinal_numbers),ordinal_numbers),universal_class) -> member(not_subclass_element(symmetrization_of(ordinal_numbers),ordinal_numbers),inverse(ordinal_numbers))*. % 300.04/300.41 213084[20:Res:213073.0,2499.1] || member(not_subclass_element(symmetrization_of(ordinal_numbers),ordinal_numbers),universal_class) -> member(not_subclass_element(symmetrization_of(ordinal_numbers),ordinal_numbers),symmetrization_of(ordinal_numbers))*. % 300.04/300.41 213227[23:Rew:183840.0,213224.0] || -> equal(cross_product(u,ordinal_numbers),ordinal_numbers) equal(segment(regular(cross_product(u,ordinal_numbers)),u,universal_class),ordinal_numbers)**. % 300.04/300.41 213263[23:Rew:183840.0,213257.0] || equal(apply(u,universal_class),image(u,ordinal_numbers)) well_ordering(element_relation,image(u,ordinal_numbers))* -> . % 300.04/300.41 213288[19:SpR:209197.0,16762.0] || -> subclass(symmetric_difference(image(element_relation,singleton(ordinal_numbers)),complement(u)),union(power_class(complement(singleton(ordinal_numbers))),u))*. % 300.04/300.41 213326[19:SpR:209197.0,198248.0] || -> equal(intersection(image(element_relation,singleton(ordinal_numbers)),restrict(power_class(complement(singleton(ordinal_numbers))),u,v)),ordinal_numbers)**. % 300.04/300.41 213332[19:SpR:209197.0,16762.0] || -> subclass(symmetric_difference(complement(u),image(element_relation,singleton(ordinal_numbers))),union(u,power_class(complement(singleton(ordinal_numbers)))))*. % 300.04/300.41 213370[19:SpL:209197.0,167096.0] || subclass(universal_class,image(element_relation,singleton(ordinal_numbers))) member(ordinal_numbers,power_class(complement(singleton(ordinal_numbers))))* -> . % 300.04/300.41 213399[19:SpL:209197.0,182395.0] || well_ordering(universal_class,image(element_relation,singleton(ordinal_numbers))) -> member(singleton(ordinal_numbers),power_class(complement(singleton(ordinal_numbers))))*. % 300.04/300.41 213404[22:SpL:209197.0,177179.0] || subclass(omega,image(element_relation,singleton(ordinal_numbers))) member(ordinal_numbers,power_class(complement(singleton(ordinal_numbers))))* -> . % 300.04/300.41 213411[19:SpL:209197.0,180886.1] inductive(power_class(complement(singleton(ordinal_numbers)))) || equal(image(element_relation,singleton(ordinal_numbers)),singleton(ordinal_numbers))** -> . % 300.04/300.41 213422[19:SpL:209197.0,196890.1] || subclass(universal_class,power_class(complement(singleton(ordinal_numbers)))) subclass(element_relation,image(element_relation,singleton(ordinal_numbers)))* -> . % 300.04/300.41 213425[19:SpL:209197.0,211666.0] || subclass(image(element_relation,singleton(ordinal_numbers)),ordinal_numbers) well_ordering(universal_class,power_class(complement(singleton(ordinal_numbers))))* -> . % 300.04/300.41 213530[19:SpR:209198.0,16762.0] || -> subclass(symmetric_difference(image(element_relation,symmetrization_of(ordinal_numbers)),complement(u)),union(power_class(complement(inverse(ordinal_numbers))),u))*. % 300.04/300.41 213568[19:SpR:209198.0,198248.0] || -> equal(intersection(image(element_relation,symmetrization_of(ordinal_numbers)),restrict(power_class(complement(inverse(ordinal_numbers))),u,v)),ordinal_numbers)**. % 300.04/300.41 213574[19:SpR:209198.0,16762.0] || -> subclass(symmetric_difference(complement(u),image(element_relation,symmetrization_of(ordinal_numbers))),union(u,power_class(complement(inverse(ordinal_numbers)))))*. % 300.04/300.41 213611[19:SpL:209198.0,167096.0] || subclass(universal_class,image(element_relation,symmetrization_of(ordinal_numbers))) member(ordinal_numbers,power_class(complement(inverse(ordinal_numbers))))* -> . % 300.04/300.41 213640[19:SpL:209198.0,182395.0] || well_ordering(universal_class,image(element_relation,symmetrization_of(ordinal_numbers))) -> member(singleton(ordinal_numbers),power_class(complement(inverse(ordinal_numbers))))*. % 300.04/300.41 213645[22:SpL:209198.0,177179.0] || subclass(omega,image(element_relation,symmetrization_of(ordinal_numbers))) member(ordinal_numbers,power_class(complement(inverse(ordinal_numbers))))* -> . % 300.04/300.41 213652[19:SpL:209198.0,180886.1] inductive(power_class(complement(inverse(ordinal_numbers)))) || equal(image(element_relation,symmetrization_of(ordinal_numbers)),singleton(ordinal_numbers))** -> . % 300.04/300.41 213663[19:SpL:209198.0,196890.1] || subclass(universal_class,power_class(complement(inverse(ordinal_numbers)))) subclass(element_relation,image(element_relation,symmetrization_of(ordinal_numbers)))* -> . % 300.04/300.41 213666[19:SpL:209198.0,211666.0] || subclass(image(element_relation,symmetrization_of(ordinal_numbers)),ordinal_numbers) well_ordering(universal_class,power_class(complement(inverse(ordinal_numbers))))* -> . % 300.04/300.41 213734[19:Rew:209198.0,213659.0] || equal(image(element_relation,symmetrization_of(ordinal_numbers)),universal_class) well_ordering(element_relation,image(element_relation,symmetrization_of(ordinal_numbers)))* -> . % 300.04/300.41 214974[19:SpR:160282.0,176362.0] || -> equal(regular(ordered_pair(u,v)),singleton(u)) equal(cantor(regular(ordered_pair(u,v))),ordinal_numbers)**. % 300.04/300.41 215012[19:SpL:160282.0,203429.0] || subclass(regular(ordered_pair(u,v)),ordinal_numbers)* -> equal(regular(ordered_pair(u,v)),singleton(u)). % 300.04/300.41 215013[19:SpL:160282.0,204370.0] || equal(regular(ordered_pair(u,v)),ordinal_numbers)** -> equal(regular(ordered_pair(u,v)),singleton(u)). % 300.04/300.41 215014[19:SpL:160282.0,182438.0] || well_ordering(universal_class,regular(ordered_pair(u,ordinal_numbers)))* -> equal(regular(ordered_pair(u,ordinal_numbers)),singleton(u)). % 300.04/300.41 215064[8:MRR:214986.0,170.0] || -> equal(regular(ordered_pair(u,v)),singleton(u)) member(singleton(v),regular(ordered_pair(u,v)))*. % 300.04/300.41 215154[19:MRR:215140.1,5.0] || well_ordering(u,universal_class) equal(singleton(least(u,v)),ordinal_numbers)** -> equal(v,ordinal_numbers). % 300.04/300.41 215155[19:MRR:215146.1,5.0] || well_ordering(u,universal_class) equal(rest_of(least(u,v)),rest_relation)** -> equal(v,ordinal_numbers). % 300.04/300.41 215199[19:Res:214528.1,82995.1] || subclass(kind_1_ordinals,complement(compose(element_relation,universal_class)))* member(ordinal_numbers,element_relation) -> member(ordinal_numbers,u)*. % 300.04/300.41 215212[19:Res:214528.1,488.0] || subclass(kind_1_ordinals,intersection(complement(u),complement(v)))* member(ordinal_numbers,union(u,v)) -> . % 300.04/300.41 215232[19:Res:214528.1,206404.0] || subclass(kind_1_ordinals,image(element_relation,power_class(u))) member(ordinal_numbers,power_class(complement(power_class(u))))* -> . % 300.04/300.41 216781[0:Res:38094.1,22.0] || member(u,union(v,w)) -> member(u,symmetric_difference(v,w))* member(u,v). % 300.04/300.41 216782[0:Res:38094.1,23.0] || member(u,union(v,w)) -> member(u,symmetric_difference(v,w))* member(u,w). % 300.04/300.41 216966[0:Obv:216936.1] || member(u,v) -> subclass(unordered_pair(u,w),v)* member(w,unordered_pair(u,w))*. % 300.04/300.41 216968[0:Obv:216940.1] || member(u,complement(v)) -> member(w,v) subclass(unordered_pair(u,w),complement(v))*. % 300.04/300.41 217110[19:SpL:27.0,215196.0] || subclass(kind_1_ordinals,union(u,v)) member(ordinal_numbers,intersection(complement(u),complement(v)))* -> . % 300.04/300.41 217119[19:SpL:167200.0,215196.0] || subclass(kind_1_ordinals,power_class(complement(inverse(ordinal_numbers)))) member(ordinal_numbers,image(element_relation,symmetrization_of(ordinal_numbers)))* -> . % 300.04/300.41 217120[19:SpL:180125.0,215196.0] || subclass(kind_1_ordinals,power_class(complement(singleton(ordinal_numbers)))) member(ordinal_numbers,image(element_relation,singleton(ordinal_numbers)))* -> . % 300.04/300.41 217121[19:SpL:206408.0,215196.0] || subclass(kind_1_ordinals,power_class(complement(power_class(u)))) member(ordinal_numbers,image(element_relation,power_class(u)))* -> . % 300.04/300.41 217123[19:SpL:209197.0,215196.0] || subclass(kind_1_ordinals,image(element_relation,singleton(ordinal_numbers))) member(ordinal_numbers,power_class(complement(singleton(ordinal_numbers))))* -> . % 300.04/300.41 217124[19:SpL:209198.0,215196.0] || subclass(kind_1_ordinals,image(element_relation,symmetrization_of(ordinal_numbers))) member(ordinal_numbers,power_class(complement(inverse(ordinal_numbers))))* -> . % 300.04/300.41 217132[19:SpL:27.0,215201.0] || subclass(kind_1_ordinals,complement(union(u,v))) -> member(ordinal_numbers,intersection(complement(u),complement(v)))*. % 300.04/300.41 217207[0:Obv:217175.1] || member(u,v) -> subclass(unordered_pair(w,u),v)* member(w,unordered_pair(w,u))*. % 300.04/300.41 217209[0:Obv:217179.1] || member(u,complement(v)) -> member(w,v) subclass(unordered_pair(w,u),complement(v))*. % 300.04/300.41 217872[0:Res:217683.0,1073.1] inductive(intersection(intersection(u,omega),v)) || -> equal(intersection(intersection(u,omega),v),omega)**. % 300.04/300.41 218034[0:Res:217853.0,1073.1] inductive(complement(complement(intersection(u,omega)))) || -> equal(complement(complement(intersection(u,omega))),omega)**. % 300.04/300.41 218377[0:SpR:206403.0,218022.0] || -> subclass(complement(union(u,intersection(complement(v),power_class(w)))),union(v,complement(power_class(w))))*. % 300.04/300.41 218378[0:SpR:206410.0,218022.0] || -> subclass(complement(union(u,intersection(power_class(v),complement(w)))),union(complement(power_class(v)),w))*. % 300.04/300.41 218814[0:Res:217850.0,1073.1] inductive(intersection(u,intersection(v,omega))) || -> equal(intersection(u,intersection(v,omega)),omega)**. % 300.04/300.41 218990[0:Res:218280.0,1073.1] inductive(intersection(intersection(omega,u),v)) || -> equal(intersection(intersection(omega,u),v),omega)**. % 300.04/300.41 219669[0:SpR:206403.0,218920.0] || -> subclass(intersection(complement(union(u,complement(power_class(v)))),w),intersection(complement(u),power_class(v)))*. % 300.04/300.41 219670[0:SpR:206410.0,218920.0] || -> subclass(intersection(complement(union(complement(power_class(u)),v)),w),intersection(power_class(u),complement(v)))*. % 300.04/300.41 219721[0:Res:218920.0,1073.1] inductive(intersection(complement(complement(omega)),u)) || -> equal(intersection(complement(complement(omega)),u),omega)**. % 300.04/300.41 219939[0:SpR:206403.0,219703.0] || -> subclass(complement(complement(complement(union(u,complement(power_class(v)))))),intersection(complement(u),power_class(v)))*. % 300.04/300.41 219940[0:SpR:206410.0,219703.0] || -> subclass(complement(complement(complement(union(complement(power_class(u)),v)))),intersection(power_class(u),complement(v)))*. % 300.04/300.41 219971[0:Res:219703.0,1073.1] inductive(complement(complement(complement(complement(omega))))) || -> equal(complement(complement(complement(complement(omega)))),omega)**. % 300.04/300.41 220070[0:Res:19.0,16462.0] || subclass(cross_product(universal_class,universal_class),u) -> subclass(element_relation,v) member(not_subclass_element(element_relation,v),u)*. % 300.04/300.41 220071[0:Res:145.0,16462.0] || subclass(cross_product(universal_class,universal_class),u) -> subclass(rest_relation,v) member(not_subclass_element(rest_relation,v),u)*. % 300.04/300.41 220072[0:Res:99.0,16462.0] || subclass(cross_product(universal_class,universal_class),u) -> subclass(domain_relation,v) member(not_subclass_element(domain_relation,v),u)*. % 300.04/300.41 220077[0:Res:45.0,16462.0] || subclass(cross_product(universal_class,universal_class),u) -> subclass(successor_relation,v) member(not_subclass_element(successor_relation,v),u)*. % 300.04/300.41 220207[0:Res:218971.0,1073.1] inductive(complement(complement(intersection(omega,u)))) || -> equal(complement(complement(intersection(omega,u))),omega)**. % 300.04/300.41 220300[0:SpR:206403.0,219700.0] || -> subclass(intersection(u,complement(union(v,complement(power_class(w))))),intersection(complement(v),power_class(w)))*. % 300.04/300.41 220301[0:SpR:206410.0,219700.0] || -> subclass(intersection(u,complement(union(complement(power_class(v)),w))),intersection(power_class(v),complement(w)))*. % 300.04/300.41 220349[0:Res:219700.0,1073.1] inductive(intersection(u,complement(complement(omega)))) || -> equal(intersection(u,complement(complement(omega))),omega)**. % 300.04/300.41 220408[0:SpR:206403.0,220194.0] || -> subclass(complement(union(intersection(complement(u),power_class(v)),w)),union(u,complement(power_class(v))))*. % 300.04/300.41 220409[0:SpR:206410.0,220194.0] || -> subclass(complement(union(intersection(power_class(u),complement(v)),w)),union(complement(power_class(u)),v))*. % 300.04/300.41 220499[0:SpR:479.0,220426.0] || -> subclass(complement(successor(image(element_relation,union(u,v)))),power_class(intersection(complement(u),complement(v))))*. % 300.04/300.41 220534[0:SpR:479.0,220427.0] || -> subclass(complement(symmetrization_of(image(element_relation,union(u,v)))),power_class(intersection(complement(u),complement(v))))*. % 300.04/300.41 220654[0:Res:218968.0,1073.1] inductive(intersection(u,intersection(omega,v))) || -> equal(intersection(u,intersection(omega,v)),omega)**. % 300.04/300.41 220841[19:Res:220496.0,2497.1] || member(u,universal_class) -> member(u,successor(complement(inverse(ordinal_numbers))))* member(u,symmetrization_of(ordinal_numbers)). % 300.04/300.41 220925[19:Res:220531.0,2497.1] || member(u,universal_class) -> member(u,symmetrization_of(complement(inverse(ordinal_numbers))))* member(u,symmetrization_of(ordinal_numbers)). % 300.04/300.41 221568[19:Res:219766.1,167737.0] || equal(complement(intersection(u,v)),ordinal_numbers)** -> equal(w,ordinal_numbers) member(regular(w),v)*. % 300.04/300.41 221569[19:Res:219766.1,167736.0] || equal(complement(intersection(u,v)),ordinal_numbers)** -> equal(w,ordinal_numbers) member(regular(w),u)*. % 300.04/300.41 221573[19:Res:219766.1,16469.0] || equal(complement(singleton(u)),ordinal_numbers)** -> subclass(v,w) equal(not_subclass_element(v,w),u)*. % 300.04/300.41 221583[21:Res:219766.1,175799.0] || equal(complement(u),ordinal_numbers) well_ordering(v,u)* -> member(least(v,omega),omega)*. % 300.04/300.41 221769[19:Res:219766.1,5331.0] || equal(complement(compose(u,v)),ordinal_numbers)** -> equal(compose(u,v),cross_product(universal_class,universal_class)). % 300.04/300.41 221772[19:Res:219766.1,1067.0] || equal(complement(rotate(u)),ordinal_numbers)** -> equal(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(u))*. % 300.04/300.41 221773[19:Res:219766.1,1066.0] || equal(complement(flip(u)),ordinal_numbers)** -> equal(cross_product(cross_product(universal_class,universal_class),universal_class),flip(u))*. % 300.04/300.41 221802[19:Res:219766.1,35668.0] || equal(complement(u),ordinal_numbers) well_ordering(v,u)* -> member(least(v,rest_relation),rest_relation)*. % 300.04/300.41 221946[19:Res:219766.1,167960.0] || equal(complement(complement(u)),ordinal_numbers)** member(v,u)* -> equal(integer_of(v),ordinal_numbers). % 300.04/300.41 221949[19:Res:219766.1,168377.0] || equal(complement(intersection(u,v)),ordinal_numbers)** -> equal(integer_of(w),ordinal_numbers) member(w,u)*. % 300.04/300.41 221950[19:Res:219766.1,168376.0] || equal(complement(intersection(u,v)),ordinal_numbers)** -> equal(integer_of(w),ordinal_numbers) member(w,v)*. % 300.04/300.41 222268[0:Res:217976.0,2497.1] || member(u,universal_class) -> member(u,complement(restrict(v,w,x)))* member(u,v). % 300.04/300.41 222736[0:SpR:4121.0,218966.0] || -> subclass(restrict(symmetric_difference(cross_product(u,v),w),x,y),complement(restrict(w,u,v)))*. % 300.04/300.41 222737[0:SpR:4119.0,218966.0] || -> subclass(restrict(symmetric_difference(u,cross_product(v,w)),x,y),complement(restrict(u,v,w)))*. % 300.04/300.41 223746[19:Res:4126.1,217129.1] || member(ordinal_numbers,symmetric_difference(u,v)) equal(complement(complement(intersection(u,v))),kind_1_ordinals)** -> . % 300.04/300.41 224069[19:SpL:27.0,217156.0] || equal(complement(union(u,v)),kind_1_ordinals) -> member(ordinal_numbers,intersection(complement(u),complement(v)))*. % 300.04/300.41 224100[22:SpL:27.0,217231.1] || equal(intersection(complement(u),complement(v)),kind_1_ordinals)** equal(union(u,v),omega) -> . % 300.04/300.41 224109[22:SpL:167200.0,217231.1] || equal(image(element_relation,symmetrization_of(ordinal_numbers)),kind_1_ordinals)** equal(power_class(complement(inverse(ordinal_numbers))),omega) -> . % 300.04/300.41 224110[22:SpL:180125.0,217231.1] || equal(image(element_relation,singleton(ordinal_numbers)),kind_1_ordinals)** equal(power_class(complement(singleton(ordinal_numbers))),omega) -> . % 300.04/300.41 224111[22:SpL:206408.0,217231.1] || equal(image(element_relation,power_class(u)),kind_1_ordinals)** equal(power_class(complement(power_class(u))),omega) -> . % 300.04/300.41 224113[22:SpL:209197.0,217231.1] || equal(power_class(complement(singleton(ordinal_numbers))),kind_1_ordinals) equal(image(element_relation,singleton(ordinal_numbers)),omega)** -> . % 300.04/300.41 224114[22:SpL:209198.0,217231.1] || equal(power_class(complement(inverse(ordinal_numbers))),kind_1_ordinals) equal(image(element_relation,symmetrization_of(ordinal_numbers)),omega)** -> . % 300.04/300.41 224238[20:Res:224150.0,2499.1] || member(not_subclass_element(inverse(ordinal_numbers),ordinal_numbers),universal_class) -> member(not_subclass_element(inverse(ordinal_numbers),ordinal_numbers),inverse(ordinal_numbers))*. % 300.04/300.41 224348[19:MRR:222891.1,224347.0] || subclass(complement(inverse(ordinal_numbers)),u) -> member(regular(complement(complement(complement(symmetrization_of(ordinal_numbers))))),u)*. % 300.04/300.41 224608[0:Res:12015.1,4728.0] || equal(complement(complement(composition_function)),universal_class) -> equal(compose(singleton(ordered_pair(u,v)),u),v)**. % 300.04/300.41 225260[19:SpL:5132.1,225030.0] || equal(successor(not_subclass_element(cross_product(u,v),w)),ordinal_numbers)** -> subclass(cross_product(u,v),w). % 300.04/300.41 225357[19:Res:170.0,176248.0] || subclass(domain_relation,u)* subclass(u,v)* -> member(ordered_pair(singleton(w),ordinal_numbers),v)*. % 300.04/300.41 225428[19:Res:196718.0,176248.0] || subclass(domain_relation,u)* subclass(u,v)* -> member(ordered_pair(regular(element_relation),ordinal_numbers),v)*. % 300.04/300.41 225642[19:SpR:27.0,220544.1] || equal(symmetrization_of(intersection(complement(u),complement(v))),ordinal_numbers)** -> subclass(universal_class,union(u,v)). % 300.04/300.41 225651[19:SpR:167200.0,220544.1] || equal(symmetrization_of(image(element_relation,symmetrization_of(ordinal_numbers))),ordinal_numbers) -> subclass(universal_class,power_class(complement(inverse(ordinal_numbers))))*. % 300.04/300.41 225652[19:SpR:180125.0,220544.1] || equal(symmetrization_of(image(element_relation,singleton(ordinal_numbers))),ordinal_numbers) -> subclass(universal_class,power_class(complement(singleton(ordinal_numbers))))*. % 300.04/300.41 225653[19:SpR:206408.0,220544.1] || equal(symmetrization_of(image(element_relation,power_class(u))),ordinal_numbers) -> subclass(universal_class,power_class(complement(power_class(u))))*. % 300.04/300.41 225655[19:SpR:209197.0,220544.1] || equal(symmetrization_of(power_class(complement(singleton(ordinal_numbers)))),ordinal_numbers) -> subclass(universal_class,image(element_relation,singleton(ordinal_numbers)))*. % 300.04/300.41 225656[19:SpR:209198.0,220544.1] || equal(symmetrization_of(power_class(complement(inverse(ordinal_numbers)))),ordinal_numbers) -> subclass(universal_class,image(element_relation,symmetrization_of(ordinal_numbers)))*. % 300.04/300.41 226131[19:SpR:207712.0,198500.0] || -> equal(intersection(symmetric_difference(power_class(u),complement(v)),complement(union(complement(power_class(u)),v))),ordinal_numbers)**. % 300.04/300.41 226134[0:SpR:207712.0,218966.0] || -> subclass(restrict(symmetric_difference(power_class(u),complement(v)),w,x),union(complement(power_class(u)),v))*. % 300.04/300.41 226342[19:SpL:5132.1,225698.0] || equal(symmetrization_of(not_subclass_element(cross_product(u,v),w)),ordinal_numbers)** -> subclass(cross_product(u,v),w). % 300.04/300.41 226692[19:SpL:168412.1,225696.0] || equal(symmetrization_of(singleton(regular(cross_product(u,v)))),ordinal_numbers)** -> equal(cross_product(u,v),ordinal_numbers). % 300.04/300.41 227097[19:SpR:207752.0,198500.0] || -> equal(intersection(symmetric_difference(complement(u),power_class(v)),complement(union(u,complement(power_class(v))))),ordinal_numbers)**. % 300.04/300.41 227100[0:SpR:207752.0,218966.0] || -> subclass(restrict(symmetric_difference(complement(u),power_class(v)),w,x),union(u,complement(power_class(v))))*. % 300.04/300.41 227753[19:SpL:27.0,221566.0] || equal(complement(union(u,v)),ordinal_numbers) -> equal(intersection(complement(u),complement(v)),ordinal_numbers)**. % 300.04/300.41 227827[19:Res:221767.1,896.0] || equal(complement(restrict(u,v,w)),ordinal_numbers)** -> member(regular(element_relation),cross_product(v,w))*. % 300.04/300.41 227962[12:MRR:227940.2,19.0] || member(u,universal_class)* member(v,u)* equal(sum_class(range_of(v)),u)* -> . % 300.04/300.41 227965[0:MRR:227956.0,227956.3,149603.1,36583.1] || member(u,rest_of(u))* subclass(element_relation,v) subclass(rest_relation,complement(v))* -> . % 300.04/300.41 228004[19:Res:223552.1,11848.0] || subclass(composition_function,rest_of(u)) subclass(cantor(u),v)* well_ordering(universal_class,v) -> . % 300.04/300.41 228175[19:SpL:5132.1,228164.0] || equal(rest_of(not_subclass_element(cross_product(u,v),w)),composition_function)** -> subclass(cross_product(u,v),w). % 300.04/300.41 228226[22:SpL:27.0,223782.1] || equal(intersection(complement(u),complement(v)),omega)** equal(union(u,v),kind_1_ordinals) -> . % 300.04/300.41 228241[22:SpL:206408.0,223782.1] || equal(image(element_relation,power_class(u)),omega)** equal(power_class(complement(power_class(u))),kind_1_ordinals) -> . % 300.04/300.41 228360[19:Res:224120.1,8.0] || equal(symmetrization_of(ordinal_numbers),u) subclass(inverse(ordinal_numbers),u)* -> equal(inverse(ordinal_numbers),u). % 300.04/300.41 228389[19:Res:224120.1,2499.1] || equal(symmetrization_of(ordinal_numbers),singleton(u)) member(u,universal_class) -> member(u,inverse(ordinal_numbers))*. % 300.04/300.41 228930[19:SpR:225013.1,27.0] || equal(successor(intersection(complement(u),complement(v))),ordinal_numbers)** -> equal(union(u,v),universal_class). % 300.04/300.41 228981[19:SpR:225013.1,186353.1] || equal(successor(complement(singleton(u))),ordinal_numbers)** -> equal(integer_of(u),ordinal_numbers) subclass(universal_class,omega). % 300.04/300.41 229012[19:SpR:225013.1,167200.0] || equal(successor(image(element_relation,symmetrization_of(ordinal_numbers))),ordinal_numbers)** -> equal(power_class(complement(inverse(ordinal_numbers))),universal_class). % 300.04/300.41 229013[19:SpR:225013.1,180125.0] || equal(successor(image(element_relation,singleton(ordinal_numbers))),ordinal_numbers)** -> equal(power_class(complement(singleton(ordinal_numbers))),universal_class). % 300.04/300.41 229014[19:SpR:225013.1,206408.0] || equal(successor(image(element_relation,power_class(u))),ordinal_numbers)** -> equal(power_class(complement(power_class(u))),universal_class). % 300.04/300.41 229059[23:SpR:225013.1,192241.0] || equal(successor(cross_product(ordinal_numbers,universal_class)),ordinal_numbers)** -> equal(apply(universal_class,universal_class),sum_class(range_of(ordinal_numbers))). % 300.04/300.41 229081[19:SpR:225013.1,209197.0] || equal(successor(power_class(complement(singleton(ordinal_numbers)))),ordinal_numbers)** -> equal(image(element_relation,singleton(ordinal_numbers)),universal_class). % 300.04/300.41 229082[19:SpR:225013.1,209198.0] || equal(successor(power_class(complement(inverse(ordinal_numbers)))),ordinal_numbers)** -> equal(image(element_relation,symmetrization_of(ordinal_numbers)),universal_class). % 300.04/300.41 229095[19:SpR:225013.1,137025.0] || equal(successor(successor(u)),ordinal_numbers) -> subclass(universal_class,intersection(complement(u),complement(singleton(u))))*. % 300.04/300.41 229103[19:SpR:225013.1,137026.0] || equal(successor(symmetrization_of(u)),ordinal_numbers) -> subclass(universal_class,intersection(complement(u),complement(inverse(u))))*. % 300.04/300.41 229511[19:SpL:225013.1,192344.0] || equal(successor(cross_product(singleton(ordinal_numbers),universal_class)),ordinal_numbers)** equal(cantor(universal_class),singleton(ordinal_numbers)) -> . % 300.04/300.41 229512[19:SpL:225013.1,207951.0] || equal(successor(cross_product(singleton(ordinal_numbers),universal_class)),ordinal_numbers)** equal(complement(cantor(universal_class)),ordinal_numbers) -> . % 300.04/300.41 229519[19:SpL:225013.1,208482.0] || equal(successor(cross_product(singleton(omega),universal_class)),ordinal_numbers)** equal(complement(cantor(universal_class)),ordinal_numbers) -> . % 300.04/300.41 229520[19:SpL:225013.1,192316.0] || equal(successor(cross_product(singleton(singleton(u)),universal_class)),ordinal_numbers)** equal(cantor(universal_class),universal_class) -> . % 300.04/300.41 229521[19:SpL:225013.1,192318.0] || equal(successor(cross_product(singleton(singleton(u)),universal_class)),ordinal_numbers)** subclass(universal_class,cantor(universal_class)) -> . % 300.04/300.41 229522[19:SpL:225013.1,196865.0] || equal(successor(cross_product(singleton(regular(element_relation)),universal_class)),ordinal_numbers)** subclass(universal_class,cantor(universal_class)) -> . % 300.04/300.41 229523[19:SpL:225013.1,212976.0] || equal(successor(cross_product(singleton(regular(element_relation)),universal_class)),ordinal_numbers)** equal(cantor(universal_class),universal_class) -> . % 300.04/300.41 229792[19:Rew:229791.1,225288.1] || equal(successor(singleton(regular(ordered_pair(u,v)))),ordinal_numbers)** -> equal(regular(ordinal_numbers),singleton(u)). % 300.04/300.41 229813[19:Rew:142500.0,228934.1] || equal(successor(intersection(u,v)),ordinal_numbers)** -> equal(symmetric_difference(u,v),union(u,v)). % 300.04/300.41 229815[19:Rew:225013.1,228970.2] || equal(successor(complement(u)),ordinal_numbers) -> member(not_subclass_element(universal_class,v),u)* subclass(universal_class,v). % 300.04/300.41 230395[0:Obv:230330.1] || subclass(u,symmetric_difference(v,w)) -> subclass(intersection(x,u),complement(intersection(v,w)))*. % 300.04/300.41 230396[0:Obv:230327.1] || subclass(u,symmetric_difference(v,w)) -> subclass(intersection(u,x),complement(intersection(v,w)))*. % 300.04/300.41 230844[19:Res:229698.1,169099.2] || equal(successor(sum_class(u)),ordinal_numbers)** member(u,universal_class) well_ordering(element_relation,u) -> . % 300.04/300.41 231063[19:Res:229698.1,9806.0] || equal(successor(apply(u,v)),ordinal_numbers) -> section(element_relation,image(u,singleton(v)),universal_class)*. % 300.04/300.41 231064[19:Res:229698.1,169641.1] || equal(successor(apply(u,v)),ordinal_numbers) well_ordering(element_relation,image(u,singleton(v)))* -> . % 300.04/300.41 231890[19:SSi:231847.0,70.0] || -> equal(unordered_pair(u,v),ordinal_numbers) member(u,unordered_pair(u,v))* equal(cantor(v),ordinal_numbers). % 300.04/300.41 232029[19:SSi:231986.0,70.0] || -> equal(unordered_pair(u,v),ordinal_numbers) member(v,unordered_pair(u,v))* equal(cantor(u),ordinal_numbers). % 300.04/300.41 232039[19:Res:4126.1,225687.1] || member(ordinal_numbers,symmetric_difference(u,v)) equal(symmetrization_of(complement(intersection(u,v))),ordinal_numbers)** -> . % 300.04/300.41 232105[19:MRR:232044.0,167011.0] || equal(symmetrization_of(intersection(complement(u),complement(v))),ordinal_numbers)** -> member(ordinal_numbers,union(u,v)). % 300.04/300.41 232106[19:MRR:232056.0,167011.0] || equal(symmetrization_of(image(element_relation,power_class(u))),ordinal_numbers) -> member(ordinal_numbers,power_class(complement(power_class(u))))*. % 300.04/300.41 232327[19:Rew:190665.0,232255.2] || subclass(u,v) member(not_subclass_element(u,ordinal_numbers),complement(v))* -> subclass(u,ordinal_numbers). % 300.04/300.41 232795[19:Res:4126.1,225690.1] || member(omega,symmetric_difference(u,v)) equal(symmetrization_of(complement(intersection(u,v))),ordinal_numbers)** -> . % 300.04/300.41 232839[19:MRR:232800.0,53.0] || equal(symmetrization_of(intersection(complement(u),complement(v))),ordinal_numbers)** -> member(omega,union(u,v)). % 300.04/300.41 232840[19:MRR:232812.0,53.0] || equal(symmetrization_of(image(element_relation,power_class(u))),ordinal_numbers) -> member(omega,power_class(complement(power_class(u))))*. % 300.04/300.41 233755[19:Rew:233350.0,226281.1] || equal(power_class(u),universal_class) -> equal(symmetric_difference(power_class(u),complement(v)),complement(complement(v)))**. % 300.04/300.41 233760[2:Rew:233350.0,219815.1] single_valued_class(symmetric_difference(universal_class,complement(cross_product(universal_class,universal_class)))) || -> function(complement(complement(cross_product(universal_class,universal_class))))*. % 300.04/300.41 234675[19:Rew:233390.0,233886.2] || subclass(complement(u),v)* well_ordering(universal_class,v) -> member(ordinal_numbers,complement(complement(u)))*. % 300.04/300.41 233911[19:Rew:233350.0,206026.1] || equal(singleton(u),ordinal_numbers) -> equal(complement(image(element_relation,successor(u))),power_class(complement(u)))**. % 300.04/300.41 233914[19:Rew:233350.0,206027.1] || equal(inverse(u),ordinal_numbers) -> equal(complement(image(element_relation,symmetrization_of(u))),power_class(complement(u)))**. % 300.04/300.41 234105[25:Rew:233350.0,213172.1] function(u) || member(regular(successor(u)),complement(u))* -> equal(successor(u),ordinal_numbers). % 300.04/300.41 234154[19:Rew:233390.0,181275.1] || member(u,universal_class) -> equal(complement(complement(sum_class(range_of(u)))),successor(sum_class(range_of(u))))**. % 300.04/300.41 234213[19:Rew:233390.0,168331.1] inductive(symmetric_difference(identity_relation,intersection(complement(u),universal_class))) || -> member(ordinal_numbers,complement(complement(complement(u))))*. % 300.04/300.41 234263[19:Rew:233390.0,188612.1] || member(ordinal_numbers,u) subclass(complement(complement(u)),v)* well_ordering(universal_class,v) -> . % 300.04/300.41 234379[19:Rew:234363.0,227243.1] || equal(power_class(u),universal_class) -> equal(symmetric_difference(complement(v),power_class(u)),complement(complement(v)))**. % 300.04/300.41 234815[19:Rew:234692.0,187192.1] || -> equal(intersection(singleton(u),v),ordinal_numbers) equal(intersection(u,intersection(singleton(u),v)),ordinal_numbers)**. % 300.04/300.41 234866[19:Rew:234692.0,187073.1] || -> equal(intersection(u,singleton(v)),ordinal_numbers) equal(intersection(v,intersection(u,singleton(v))),ordinal_numbers)**. % 300.04/300.41 235317[19:MRR:235316.2,167057.0] inductive(symmetric_difference(complement(u),symmetric_difference(universal_class,u))) || well_ordering(v,complement(complement(u)))* -> . % 300.04/300.41 235562[19:Rew:235542.0,234312.1] || member(ordinal_numbers,intersection(complement(u),complement(v)))* -> member(ordinal_numbers,complement(union(u,v))). % 300.04/300.41 235578[25:Rew:235542.0,234318.1] function(image(element_relation,complement(u))) || -> equal(successor(complement(power_class(u))),complement(power_class(u)))**. % 300.04/300.41 236256[19:SpR:234692.0,168353.1] || -> equal(symmetric_difference(u,v),ordinal_numbers) member(regular(symmetric_difference(u,v)),complement(intersection(v,u)))*. % 300.04/300.41 236283[0:SpR:234692.0,16365.1] || -> subclass(intersection(u,singleton(v)),w) equal(not_subclass_element(intersection(singleton(v),u),w),v)**. % 300.04/300.41 236324[0:SpR:234692.0,16238.1] || -> subclass(intersection(singleton(u),v),w) equal(not_subclass_element(intersection(v,singleton(u)),w),u)**. % 300.04/300.41 236490[0:SpL:234692.0,82316.0] || subclass(universal_class,intersection(complement(u),complement(v)))* member(omega,union(v,u)) -> . % 300.04/300.41 236547[19:SpL:234692.0,168419.0] || member(regular(intersection(u,complement(v))),v)* -> equal(intersection(complement(v),u),ordinal_numbers). % 300.04/300.41 236549[0:SpL:234692.0,488.0] || member(u,intersection(complement(v),complement(w)))* member(u,union(w,v)) -> . % 300.04/300.41 236552[19:SpL:234692.0,168418.0] || member(regular(intersection(complement(u),v)),u)* -> equal(intersection(v,complement(u)),ordinal_numbers). % 300.04/300.41 237228[0:SpR:236669.0,12798.1] || -> subclass(symmetric_difference(u,v),w) member(not_subclass_element(symmetric_difference(u,v),w),union(v,u))*. % 300.04/300.41 237461[0:Rew:237384.0,16885.0] || -> subclass(symmetric_difference(symmetrization_of(u),complement(intersection(u,inverse(u)))),complement(symmetric_difference(u,inverse(u))))*. % 300.04/300.41 237604[19:Rew:237493.0,234891.1] || subclass(singleton(u),u) -> equal(intersection(successor(u),complement(singleton(u))),successor(u))**. % 300.04/300.41 237708[19:Rew:237493.0,237680.0] || -> subclass(successor(u),v) member(not_subclass_element(successor(u),v),complement(intersection(u,singleton(u))))*. % 300.04/300.41 237769[0:SpR:237384.0,12798.1] || -> subclass(symmetric_difference(u,v),w) member(not_subclass_element(symmetric_difference(v,u),w),union(u,v))*. % 300.04/300.41 237772[19:SpR:237384.0,168353.1] || -> equal(symmetric_difference(u,v),ordinal_numbers) member(regular(symmetric_difference(v,u)),complement(intersection(u,v)))*. % 300.04/300.41 239109[19:SpL:237603.0,6438.0] || subclass(universal_class,successor(u)) -> member(unordered_pair(v,w),complement(intersection(u,singleton(u))))*. % 300.04/300.41 239184[19:Rew:237603.0,239156.1] || member(not_subclass_element(successor(u),v),intersection(u,singleton(u)))* -> subclass(successor(u),v). % 300.04/300.41 239722[19:Res:238770.1,16465.0] || equal(intersection(u,v),universal_class)** -> subclass(w,x) member(not_subclass_element(w,x),u)*. % 300.04/300.41 239723[19:Res:238770.1,16466.0] || equal(intersection(u,v),universal_class)** -> subclass(w,x) member(not_subclass_element(w,x),v)*. % 300.04/300.41 239943[19:Res:238770.1,1070.1] inductive(u) || equal(image(successor_relation,u),universal_class)** -> equal(image(successor_relation,u),u). % 300.04/300.41 239945[19:Res:238770.1,169641.1] || equal(image(u,singleton(v)),universal_class) well_ordering(element_relation,image(u,singleton(v)))* -> . % 300.04/300.41 240521[19:Res:239914.1,16102.0] || equal(symmetric_difference(complement(u),complement(v)),universal_class) -> member(regular(element_relation),union(u,v))*. % 300.04/300.41 240524[19:Res:239914.1,9.0] || equal(unordered_pair(u,v),universal_class)** -> equal(regular(element_relation),v) equal(regular(element_relation),u). % 300.04/300.41 240611[19:Res:239132.1,225690.1] || member(omega,successor(u)) equal(symmetrization_of(complement(intersection(u,singleton(u)))),ordinal_numbers)** -> . % 300.04/300.41 240618[19:Res:239132.1,182393.0] || member(singleton(ordinal_numbers),successor(u)) well_ordering(universal_class,complement(intersection(u,singleton(u))))* -> . % 300.04/300.41 240641[19:Res:239132.1,225687.1] || member(ordinal_numbers,successor(u)) equal(symmetrization_of(complement(intersection(u,singleton(u)))),ordinal_numbers)** -> . % 300.04/300.41 240642[19:Res:239132.1,217129.1] || member(ordinal_numbers,successor(u)) equal(complement(complement(intersection(u,singleton(u)))),kind_1_ordinals)** -> . % 300.04/300.41 240645[22:Res:239132.1,177998.1] || member(ordinal_numbers,successor(u)) equal(complement(complement(intersection(u,singleton(u)))),omega)** -> . % 300.04/300.41 241006[19:Res:240703.0,11848.0] || subclass(complement(intersection(singleton(ordinal_numbers),singleton(singleton(ordinal_numbers)))),u)* well_ordering(universal_class,u) -> . % 300.04/300.41 241976[0:Obv:241917.0] || -> member(u,unordered_pair(u,v))* member(v,w) subclass(unordered_pair(u,v),complement(w))*. % 300.04/300.41 242070[19:SpL:27.0,225692.0] || equal(symmetrization_of(union(u,v)),ordinal_numbers) -> member(ordinal_numbers,intersection(complement(u),complement(v)))*. % 300.04/300.41 242081[19:SpL:167200.0,225692.0] || equal(symmetrization_of(power_class(complement(inverse(ordinal_numbers)))),ordinal_numbers) -> member(ordinal_numbers,image(element_relation,symmetrization_of(ordinal_numbers)))*. % 300.04/300.41 242082[19:SpL:180125.0,225692.0] || equal(symmetrization_of(power_class(complement(singleton(ordinal_numbers)))),ordinal_numbers) -> member(ordinal_numbers,image(element_relation,singleton(ordinal_numbers)))*. % 300.04/300.41 242083[19:SpL:206408.0,225692.0] || equal(symmetrization_of(power_class(complement(power_class(u)))),ordinal_numbers) -> member(ordinal_numbers,image(element_relation,power_class(u)))*. % 300.04/300.41 242084[19:SpL:209197.0,225692.0] || equal(symmetrization_of(image(element_relation,singleton(ordinal_numbers))),ordinal_numbers) -> member(ordinal_numbers,power_class(complement(singleton(ordinal_numbers))))*. % 300.04/300.41 242085[19:SpL:209198.0,225692.0] || equal(symmetrization_of(image(element_relation,symmetrization_of(ordinal_numbers))),ordinal_numbers) -> member(ordinal_numbers,power_class(complement(inverse(ordinal_numbers))))*. % 300.04/300.41 242154[19:Rew:241966.1,242148.1] || equal(unordered_pair(u,v),ordinal_numbers) -> equal(v,u) subclass(unordered_pair(u,v),w)*. % 300.04/300.41 242159[0:Obv:242096.0] || -> member(u,unordered_pair(v,u))* member(v,w) subclass(unordered_pair(v,u),complement(w))*. % 300.04/300.41 242188[19:SpL:27.0,225693.0] || equal(symmetrization_of(union(u,v)),ordinal_numbers) -> member(omega,intersection(complement(u),complement(v)))*. % 300.04/300.41 242199[19:SpL:167200.0,225693.0] || equal(symmetrization_of(power_class(complement(inverse(ordinal_numbers)))),ordinal_numbers) -> member(omega,image(element_relation,symmetrization_of(ordinal_numbers)))*. % 300.04/300.41 242200[19:SpL:180125.0,225693.0] || equal(symmetrization_of(power_class(complement(singleton(ordinal_numbers)))),ordinal_numbers) -> member(omega,image(element_relation,singleton(ordinal_numbers)))*. % 300.04/300.41 242201[19:SpL:206408.0,225693.0] || equal(symmetrization_of(power_class(complement(power_class(u)))),ordinal_numbers) -> member(omega,image(element_relation,power_class(u)))*. % 300.04/300.41 242202[19:SpL:209197.0,225693.0] || equal(symmetrization_of(image(element_relation,singleton(ordinal_numbers))),ordinal_numbers) -> member(omega,power_class(complement(singleton(ordinal_numbers))))*. % 300.04/300.41 242203[19:SpL:209198.0,225693.0] || equal(symmetrization_of(image(element_relation,symmetrization_of(ordinal_numbers))),ordinal_numbers) -> member(omega,power_class(complement(inverse(ordinal_numbers))))*. % 300.04/300.41 242256[19:Obv:242238.2] || equal(u,v) subclass(composition_function,rest_of(v))* -> equal(unordered_pair(v,u),ordinal_numbers)**. % 300.04/300.41 242312[19:SpL:27.0,228219.1] || equal(intersection(complement(u),complement(v)),kind_1_ordinals)** equal(union(u,v),kind_1_ordinals) -> . % 300.04/300.41 242323[19:SpL:167200.0,228219.1] || equal(image(element_relation,symmetrization_of(ordinal_numbers)),kind_1_ordinals)** equal(power_class(complement(inverse(ordinal_numbers))),kind_1_ordinals) -> . % 300.04/300.41 242324[19:SpL:180125.0,228219.1] || equal(image(element_relation,singleton(ordinal_numbers)),kind_1_ordinals)** equal(power_class(complement(singleton(ordinal_numbers))),kind_1_ordinals) -> . % 300.04/300.41 242325[19:SpL:206408.0,228219.1] || equal(image(element_relation,power_class(u)),kind_1_ordinals)** equal(power_class(complement(power_class(u))),kind_1_ordinals) -> . % 300.04/300.41 242533[19:SpL:27.0,235552.0] || equal(successor(union(u,v)),ordinal_numbers) -> equal(intersection(complement(u),complement(v)),universal_class)**. % 300.04/300.41 242546[19:SpL:206408.0,235552.0] || equal(successor(power_class(complement(power_class(u)))),ordinal_numbers)** -> equal(image(element_relation,power_class(u)),universal_class). % 300.04/300.41 242849[19:Res:5.0,177428.0] || well_ordering(omega,universal_class) -> equal(integer_of(ordered_pair(unordered_pair(u,v),least(omega,universal_class))),ordinal_numbers)**. % 300.04/300.41 243456[19:Res:5.0,177429.0] || well_ordering(omega,universal_class) -> equal(integer_of(ordered_pair(ordered_pair(u,v),least(omega,universal_class))),ordinal_numbers)**. % 300.04/300.41 243834[19:Obv:243823.2] || equal(u,v) equal(rest_of(v),composition_function) -> equal(unordered_pair(v,u),ordinal_numbers)**. % 300.04/300.41 245255[19:MRR:245254.2,167057.0] || subclass(universal_class,complement(symmetrization_of(ordinal_numbers))) member(omega,union(inverse(ordinal_numbers),symmetrization_of(ordinal_numbers)))* -> . % 300.04/300.41 245909[19:Res:239132.1,229738.1] || member(u,successor(v))* equal(successor(complement(intersection(v,singleton(v)))),ordinal_numbers)** -> . % 300.04/300.41 246030[19:Res:176321.2,229738.1] || member(u,universal_class)* equal(successor(u),ordinal_numbers) equal(successor(successor_relation),ordinal_numbers) -> . % 300.04/300.41 246109[19:Res:168557.1,229738.1] || equal(successor(union(u,v)),ordinal_numbers) -> equal(symmetric_difference(complement(u),complement(v)),ordinal_numbers)**. % 300.04/300.41 246115[19:Res:168474.2,229738.1] || subclass(u,v)* equal(successor(v),ordinal_numbers) -> equal(intersection(u,w),ordinal_numbers)**. % 300.04/300.41 246117[19:Res:168469.2,229738.1] || subclass(u,v)* equal(successor(v),ordinal_numbers) -> equal(intersection(w,u),ordinal_numbers)**. % 300.04/300.41 246319[25:SpR:234134.1,27.0] function(u) || -> equal(complement(intersection(successor(u),complement(v))),union(complement(u),v))**. % 300.04/300.41 246321[25:SpR:234134.1,135266.0] function(u) || -> subclass(complement(union(complement(u),v)),intersection(successor(u),complement(v)))*. % 300.04/300.41 246334[25:SpR:234134.1,234134.1] function(u) function(complement(u)) || -> equal(complement(successor(u)),successor(complement(u)))**. % 300.04/300.41 246337[25:SpR:234134.1,17083.0] function(u) || -> subclass(symmetric_difference(successor(u),complement(singleton(complement(u)))),successor(complement(u)))*. % 300.04/300.41 246340[25:SpR:234134.1,17082.0] function(u) || -> subclass(symmetric_difference(successor(u),complement(inverse(complement(u)))),symmetrization_of(complement(u)))*. % 300.04/300.41 246366[25:SpR:234134.1,27.0] function(u) || -> equal(complement(intersection(complement(v),successor(u))),union(v,complement(u)))**. % 300.04/300.41 246368[25:SpR:234134.1,135266.0] function(u) || -> subclass(complement(union(v,complement(u))),intersection(complement(v),successor(u)))*. % 300.04/300.41 246407[25:SpR:234134.1,224158.0] function(complement(complement(symmetrization_of(ordinal_numbers)))) || -> subclass(successor(complement(complement(symmetrization_of(ordinal_numbers)))),inverse(ordinal_numbers))*. % 300.04/300.41 246412[25:SpR:234134.1,224157.0] function(intersection(u,symmetrization_of(ordinal_numbers))) || -> subclass(successor(intersection(u,symmetrization_of(ordinal_numbers))),inverse(ordinal_numbers))*. % 300.04/300.41 246413[25:SpR:234134.1,224159.0] function(intersection(symmetrization_of(ordinal_numbers),u)) || -> subclass(successor(intersection(symmetrization_of(ordinal_numbers),u)),inverse(ordinal_numbers))*. % 300.04/300.41 246415[25:SpR:234134.1,217960.0] function(symmetric_difference(u,inverse(u))) || -> subclass(successor(symmetric_difference(u,inverse(u))),symmetrization_of(u))*. % 300.04/300.41 246457[25:SpL:234134.1,195669.1] function(u) || equal(rotate(complement(u)),rest_relation) subclass(universal_class,successor(u))* -> . % 300.04/300.41 246458[25:SpL:234134.1,195635.1] function(u) || equal(flip(complement(u)),rest_relation) subclass(universal_class,successor(u))* -> . % 300.04/300.41 246459[25:SpL:234134.1,185733.1] function(u) || equal(rotate(complement(u)),domain_relation) subclass(universal_class,successor(u))* -> . % 300.04/300.41 246460[25:SpL:234134.1,185656.1] function(u) || equal(flip(complement(u)),domain_relation) subclass(universal_class,successor(u))* -> . % 300.04/300.41 246466[25:SpL:234134.1,9734.0] function(u) || subclass(universal_class,complement(successor(u))) -> member(singleton(v),complement(u))*. % 300.04/300.41 246468[25:SpL:234134.1,182427.0] function(u) || equal(complement(successor(u)),universal_class) well_ordering(universal_class,complement(u))* -> . % 300.04/300.41 246473[25:SpL:234134.1,169222.0] function(u) || equal(complement(successor(u)),singleton(ordinal_numbers)) -> member(ordinal_numbers,complement(u))*. % 300.04/300.41 246479[25:SpL:234134.1,195678.1] function(u) || equal(rotate(complement(u)),rest_relation) subclass(domain_relation,successor(u))* -> . % 300.04/300.41 246480[25:SpL:234134.1,194014.1] function(u) || subclass(domain_relation,flip(complement(u)))* subclass(domain_relation,successor(u)) -> . % 300.04/300.41 246481[25:SpL:234134.1,194013.1] function(u) || subclass(domain_relation,rotate(complement(u)))* subclass(domain_relation,successor(u)) -> . % 300.04/300.41 246483[25:SpL:234134.1,196068.0] function(u) || equal(successor(u),domain_relation) equal(rotate(complement(u)),rest_relation)** -> . % 300.04/300.41 246484[25:SpL:234134.1,195719.1] function(u) || equal(flip(complement(u)),domain_relation)** equal(successor(u),domain_relation) -> . % 300.04/300.41 246485[25:SpL:234134.1,195630.1] function(u) || equal(rotate(complement(u)),domain_relation)** equal(successor(u),domain_relation) -> . % 300.04/300.41 246499[25:SpL:234134.1,178289.1] function(u) || equal(complement(u),singleton(ordinal_numbers))** equal(successor(u),omega) -> . % 300.04/300.41 246502[25:SpL:234134.1,180881.1] function(u) || equal(complement(u),omega)** equal(successor(u),singleton(ordinal_numbers)) -> . % 300.04/300.41 246504[25:SpL:234134.1,186994.0] function(u) || subclass(singleton(ordinal_numbers),successor(u))* member(ordinal_numbers,complement(u)) -> . % 300.04/300.41 246611[25:SpL:234134.1,203614.0] function(complement(singleton(singleton(u)))) || equal(successor(complement(singleton(singleton(u)))),universal_class)** -> . % 300.04/300.41 246612[25:SpL:234134.1,224358.0] function(complement(complement(symmetrization_of(ordinal_numbers)))) || equal(successor(complement(complement(symmetrization_of(ordinal_numbers)))),universal_class)** -> . % 300.04/300.41 246621[25:SpL:234134.1,224619.0] function(intersection(u,symmetrization_of(ordinal_numbers))) || equal(successor(intersection(u,symmetrization_of(ordinal_numbers))),universal_class)** -> . % 300.04/300.41 246622[25:SpL:234134.1,224697.0] function(intersection(symmetrization_of(ordinal_numbers),u)) || equal(successor(intersection(symmetrization_of(ordinal_numbers),u)),universal_class)** -> . % 300.04/300.41 246657[25:Rew:234134.1,246374.2] function(u) || -> member(not_subclass_element(v,successor(u)),complement(u))* subclass(v,successor(u)). % 300.04/300.41 246736[25:SoR:246593.0,12322.2] single_valued_class(successor_relation) || subclass(domain_relation,successor(successor_relation))* equal(cross_product(universal_class,universal_class),successor_relation) -> . % 300.04/300.41 246739[25:SoR:246594.0,12322.2] single_valued_class(successor_relation) || equal(successor(successor_relation),domain_relation) equal(cross_product(universal_class,universal_class),successor_relation)** -> . % 300.04/300.41 246888[25:SoR:246595.0,12322.2] single_valued_class(successor_relation) || equal(successor(successor_relation),universal_class) equal(cross_product(universal_class,universal_class),successor_relation)** -> . % 300.04/300.41 246891[25:SoR:246599.0,12322.2] single_valued_class(rest_relation) || equal(successor(rest_relation),universal_class) equal(cross_product(universal_class,universal_class),rest_relation)** -> . % 300.04/300.41 246894[25:SoR:246601.0,12322.2] single_valued_class(domain_relation) || equal(successor(domain_relation),universal_class) equal(cross_product(universal_class,universal_class),domain_relation)** -> . % 300.04/300.41 246987[19:Obv:246976.1] || subclass(complement(u),union(v,u))* -> equal(intersection(complement(v),complement(u)),ordinal_numbers). % 300.04/300.41 246988[19:Obv:246975.1] || subclass(complement(u),union(u,v))* -> equal(intersection(complement(u),complement(v)),ordinal_numbers). % 300.04/300.41 247477[19:Rew:247476.1,209583.1] || equal(power_class(u),universal_class) -> equal(symmetric_difference(power_class(u),power_class(v)),complement(power_class(v)))**. % 300.04/300.41 247482[19:Rew:142500.0,247378.1,234692.0,247378.1] || equal(complement(u),universal_class) -> equal(symmetric_difference(complement(u),complement(v)),union(u,v))**. % 300.04/300.41 247669[19:Rew:247668.1,235569.1] || equal(power_class(u),universal_class) -> equal(symmetric_difference(power_class(v),power_class(u)),complement(power_class(v)))**. % 300.04/300.41 247672[19:Rew:142500.0,247552.1,234692.0,247552.1] || equal(complement(u),universal_class) -> equal(symmetric_difference(complement(v),complement(u)),union(v,u))**. % 300.04/300.41 248203[0:Res:53.0,27142.0] || subclass(rest_relation,u)* subclass(u,v)* -> member(ordered_pair(omega,rest_of(omega)),v)*. % 300.04/300.41 248222[19:Res:167011.0,27142.0] || subclass(rest_relation,u)* subclass(u,v)* -> member(ordered_pair(ordinal_numbers,rest_of(ordinal_numbers)),v)*. % 300.04/300.41 248309[19:Res:248149.1,488.0] || equal(intersection(complement(u),complement(v)),kind_1_ordinals)** member(ordinal_numbers,union(u,v)) -> . % 300.04/300.41 248327[19:Res:248149.1,206404.0] || equal(image(element_relation,power_class(u)),kind_1_ordinals) member(ordinal_numbers,power_class(complement(power_class(u))))* -> . % 300.04/300.41 248542[25:SpL:234134.1,246509.1] function(u) function(complement(u)) || equal(successor(complement(u)),successor(u))** -> . % 300.04/300.41 248749[0:SpL:27.0,219712.0] || subclass(u,complement(union(v,w))) -> subclass(u,intersection(complement(v),complement(w)))*. % 300.04/300.41 248843[0:SpR:479.0,248818.0] || -> subclass(complement(successor(power_class(intersection(complement(u),complement(v))))),image(element_relation,union(u,v)))*. % 300.04/300.41 248960[0:SpR:479.0,248819.0] || -> subclass(complement(symmetrization_of(power_class(intersection(complement(u),complement(v))))),image(element_relation,union(u,v)))*. % 300.04/300.41 249049[0:SpR:206403.0,248816.0] || -> subclass(complement(union(u,union(v,complement(power_class(w))))),intersection(complement(v),power_class(w)))*. % 300.04/300.41 249052[0:SpR:206410.0,248816.0] || -> subclass(complement(union(u,union(complement(power_class(v)),w))),intersection(power_class(v),complement(w)))*. % 300.04/300.41 249088[0:Res:248816.0,1073.1] inductive(complement(union(u,complement(omega)))) || -> equal(complement(union(u,complement(omega))),omega)**. % 300.04/300.41 249214[0:SpR:206403.0,248817.0] || -> subclass(complement(union(union(u,complement(power_class(v))),w)),intersection(complement(u),power_class(v)))*. % 300.04/300.41 249217[0:SpR:206410.0,248817.0] || -> subclass(complement(union(union(complement(power_class(u)),v),w)),intersection(power_class(u),complement(v)))*. % 300.04/300.41 249254[0:Res:248817.0,1073.1] inductive(complement(union(complement(omega),u))) || -> equal(complement(union(complement(omega),u)),omega)**. % 300.04/300.41 249338[19:Res:248841.0,2497.1] || member(u,universal_class) -> member(u,successor(symmetrization_of(ordinal_numbers))) member(u,complement(inverse(ordinal_numbers)))*. % 300.04/300.41 249434[19:Res:248877.0,2497.1] || member(u,universal_class) -> member(u,successor(complement(symmetrization_of(ordinal_numbers))))* member(u,inverse(ordinal_numbers)). % 300.04/300.41 249458[19:Res:248958.0,2497.1] || member(u,universal_class) -> member(u,symmetrization_of(symmetrization_of(ordinal_numbers)))* member(u,complement(inverse(ordinal_numbers))). % 300.04/300.41 249508[19:Res:248994.0,2497.1] || member(u,universal_class) -> member(u,symmetrization_of(complement(symmetrization_of(ordinal_numbers))))* member(u,inverse(ordinal_numbers)). % 300.04/300.41 249529[23:Rew:167760.0,249524.1,183857.0,249524.1,13.0,249524.0,183840.0,249524.0] || -> equal(apply(choice,singleton(singleton(ordinal_numbers))),singleton(ordinal_numbers))** equal(apply(choice,ordinal_numbers),singleton(ordinal_numbers)). % 300.04/300.41 249578[0:Res:53.0,42928.0] || well_ordering(u,universal_class) -> member(omega,v) member(least(u,complement(v)),complement(v))*. % 300.04/300.41 249597[19:Res:167011.0,42928.0] || well_ordering(u,universal_class) -> member(ordinal_numbers,v) member(least(u,complement(v)),complement(v))*. % 300.04/300.41 249730[0:Res:248882.0,2497.1] || member(u,universal_class) -> member(u,successor(complement(complement(complement(v)))))* member(u,v). % 300.04/300.41 249847[0:Res:248999.0,2497.1] || member(u,universal_class) -> member(u,symmetrization_of(complement(complement(complement(v)))))* member(u,v). % 300.04/300.41 250071[8:Res:248806.0,82994.1] || member(u,element_relation) well_ordering(v,w)* -> subclass(singleton(u),compose(element_relation,universal_class))*. % 300.04/300.41 250073[26:Res:248806.0,202277.1] || member(u,cross_product(universal_class,universal_class)) -> subclass(singleton(u),compose(complement(element_relation),inverse(element_relation)))*. % 300.04/300.41 250103[19:Res:248806.0,167734.1] || subclass(u,complement(complement(v))) -> subclass(singleton(regular(u)),v)* equal(u,ordinal_numbers). % 300.04/300.41 250862[0:SpR:27.0,248811.0] || -> subclass(complement(complement(complement(complement(complement(union(u,v)))))),intersection(complement(u),complement(v)))*. % 300.04/300.41 251162[19:SpL:27.0,248972.0] || equal(symmetrization_of(union(u,v)),ordinal_numbers) -> subclass(universal_class,intersection(complement(u),complement(v)))*. % 300.04/300.41 251176[19:SpL:206408.0,248972.0] || equal(symmetrization_of(power_class(complement(power_class(u)))),ordinal_numbers) -> subclass(universal_class,image(element_relation,power_class(u)))*. % 300.04/300.41 251191[19:SpL:27.0,250085.0] || subclass(union(u,v),ordinal_numbers) -> subclass(singleton(omega),intersection(complement(u),complement(v)))*. % 300.04/300.41 251203[19:SpL:167200.0,250085.0] || subclass(power_class(complement(inverse(ordinal_numbers))),ordinal_numbers) -> subclass(singleton(omega),image(element_relation,symmetrization_of(ordinal_numbers)))*. % 300.04/300.41 251204[19:SpL:180125.0,250085.0] || subclass(power_class(complement(singleton(ordinal_numbers))),ordinal_numbers) -> subclass(singleton(omega),image(element_relation,singleton(ordinal_numbers)))*. % 300.04/300.41 251205[19:SpL:206408.0,250085.0] || subclass(power_class(complement(power_class(u))),ordinal_numbers) -> subclass(singleton(omega),image(element_relation,power_class(u)))*. % 300.04/300.41 251206[19:SpL:209197.0,250085.0] || subclass(image(element_relation,singleton(ordinal_numbers)),ordinal_numbers) -> subclass(singleton(omega),power_class(complement(singleton(ordinal_numbers))))*. % 300.04/300.41 251207[19:SpL:209198.0,250085.0] || subclass(image(element_relation,symmetrization_of(ordinal_numbers)),ordinal_numbers) -> subclass(singleton(omega),power_class(complement(inverse(ordinal_numbers))))*. % 300.04/300.41 251377[19:SpL:27.0,250124.0] || subclass(union(u,v),ordinal_numbers) -> subclass(singleton(ordinal_numbers),intersection(complement(u),complement(v)))*. % 300.04/300.41 251389[19:SpL:167200.0,250124.0] || subclass(power_class(complement(inverse(ordinal_numbers))),ordinal_numbers) -> subclass(singleton(ordinal_numbers),image(element_relation,symmetrization_of(ordinal_numbers)))*. % 300.04/300.41 251390[19:SpL:180125.0,250124.0] || subclass(power_class(complement(singleton(ordinal_numbers))),ordinal_numbers) -> subclass(singleton(ordinal_numbers),image(element_relation,singleton(ordinal_numbers)))*. % 300.04/300.41 251391[19:SpL:206408.0,250124.0] || subclass(power_class(complement(power_class(u))),ordinal_numbers) -> subclass(singleton(ordinal_numbers),image(element_relation,power_class(u)))*. % 300.04/300.41 251392[19:SpL:209197.0,250124.0] || subclass(image(element_relation,singleton(ordinal_numbers)),ordinal_numbers) -> subclass(singleton(ordinal_numbers),power_class(complement(singleton(ordinal_numbers))))*. % 300.04/300.41 251393[19:SpL:209198.0,250124.0] || subclass(image(element_relation,symmetrization_of(ordinal_numbers)),ordinal_numbers) -> subclass(singleton(ordinal_numbers),power_class(complement(inverse(ordinal_numbers))))*. % 300.04/300.41 251431[19:SpL:27.0,248778.0] || equal(complement(union(u,v)),universal_class) -> subclass(w,intersection(complement(u),complement(v)))*. % 300.04/300.41 251468[0:SpR:27.0,248783.0] || -> subclass(intersection(complement(complement(complement(union(u,v)))),w),intersection(complement(u),complement(v)))*. % 300.04/300.41 251798[0:SpR:27.0,248798.0] || -> subclass(intersection(u,complement(complement(complement(union(v,w))))),intersection(complement(v),complement(w)))*. % 300.04/300.41 251931[0:SpR:27.0,248810.0] || -> subclass(complement(complement(intersection(u,complement(union(v,w))))),intersection(complement(v),complement(w)))*. % 300.04/300.41 252240[0:SpR:27.0,248812.0] || -> subclass(complement(complement(intersection(complement(union(u,v)),w))),intersection(complement(u),complement(v)))*. % 300.04/300.41 252402[0:SpR:27.0,249106.0] || -> subclass(complement(union(u,complement(complement(union(v,w))))),intersection(complement(v),complement(w)))*. % 300.04/300.41 252631[19:Res:125121.2,205934.1] || member(u,cantor(v))* subclass(rest_of(v),w)* equal(ordinal_numbers,w) -> . % 300.04/300.41 252636[12:MRR:252618.1,141.0] || member(u,cantor(v)) equal(restrict(v,u,universal_class),sum_class(range_of(u)))** -> . % 300.04/300.41 252637[8:MRR:252614.1,141.0] || member(u,cantor(v))* subclass(composition_function,rest_of(w)) -> member(u,cantor(w))*. % 300.04/300.41 252638[8:MRR:252613.1,141.0] || member(u,cantor(v))* subclass(composition_function,cross_product(w,x))* -> member(u,w)*. % 300.04/300.41 252648[0:SpR:27.0,249272.0] || -> subclass(complement(union(complement(complement(union(u,v))),w)),intersection(complement(u),complement(v)))*. % 300.04/300.41 252870[0:SpR:27.0,220180.1] || subclass(intersection(complement(u),complement(v)),w)* -> subclass(complement(union(u,v)),w). % 300.04/300.41 252904[0:Res:220180.1,1073.1] inductive(complement(complement(u))) || subclass(u,omega) -> equal(complement(complement(u)),omega)**. % 300.04/300.41 252933[19:Res:220180.1,186996.0] || subclass(u,complement(singleton(regular(complement(complement(u))))))* -> equal(complement(complement(u)),ordinal_numbers). % 300.04/300.41 252999[19:MRR:252998.1,289.0] || well_ordering(u,universal_class) -> equal(singleton(v),ordinal_numbers) section(u,singleton(v),singleton(v))*. % 300.04/300.41 253009[19:Res:252894.1,8.0] || subclass(inverse(ordinal_numbers),u)* subclass(u,symmetrization_of(ordinal_numbers))* -> equal(u,symmetrization_of(ordinal_numbers)). % 300.04/300.41 253035[19:Res:252894.1,8596.1] single_valued_class(symmetrization_of(ordinal_numbers)) || subclass(inverse(ordinal_numbers),cross_product(universal_class,universal_class))* -> function(symmetrization_of(ordinal_numbers)). % 300.04/300.41 253116[19:Res:168184.0,227961.1] || member(u,regular(complement(complement(cantor(u)))))* -> equal(complement(complement(cantor(u))),ordinal_numbers). % 300.04/300.41 253117[19:Res:167341.1,227961.1] || member(u,regular(intersection(cantor(u),v)))* -> equal(intersection(cantor(u),v),ordinal_numbers). % 300.04/300.41 253128[19:Res:176420.1,227961.1] || subclass(domain_relation,rotate(cantor(u))) member(u,ordered_pair(ordered_pair(v,ordinal_numbers),w))* -> . % 300.04/300.41 253132[19:Res:176419.1,227961.1] || subclass(domain_relation,flip(cantor(u))) member(u,ordered_pair(ordered_pair(v,w),ordinal_numbers))* -> . % 300.04/300.41 253134[18:Res:2526.2,227961.1] || subclass(u,cantor(v)) member(v,not_subclass_element(u,w))* -> subclass(u,w). % 300.04/300.41 253139[18:Res:2482.2,227961.1] || member(u,universal_class) subclass(universal_class,cantor(v)) member(v,sum_class(u))* -> . % 300.04/300.41 253140[18:Res:2483.2,227961.1] || member(u,universal_class) subclass(universal_class,cantor(v)) member(v,power_class(u))* -> . % 300.04/300.41 253144[19:Res:167340.1,227961.1] || member(u,regular(intersection(v,cantor(u))))* -> equal(intersection(v,cantor(u)),ordinal_numbers). % 300.04/300.41 253152[18:Res:2525.1,227961.1] || subclass(ordered_pair(u,v),cantor(w)) member(w,unordered_pair(u,singleton(v)))* -> . % 300.04/300.41 12009[0:SpL:27.0,9734.0] || subclass(universal_class,complement(union(u,v))) -> member(singleton(w),intersection(complement(u),complement(v)))*. % 300.04/300.41 16111[0:Res:4126.1,5467.1] || member(singleton(u),symmetric_difference(v,w))* subclass(universal_class,complement(complement(intersection(v,w))))* -> . % 300.04/300.41 16661[0:Res:16403.0,8.0] || subclass(union(u,v),symmetric_difference(u,v))* -> equal(symmetric_difference(u,v),union(u,v)). % 300.04/300.41 27261[0:Res:2479.1,488.0] || subclass(universal_class,intersection(complement(u),complement(v)))* member(singleton(w),union(u,v))* -> . % 300.04/300.41 27696[0:SpR:481.0,16403.0] || -> subclass(symmetric_difference(u,intersection(complement(v),complement(w))),complement(intersection(complement(u),union(v,w))))*. % 300.04/300.41 27753[0:SpR:480.0,16403.0] || -> subclass(symmetric_difference(intersection(complement(u),complement(v)),w),complement(intersection(union(u,v),complement(w))))*. % 300.04/300.41 48563[0:Res:36588.1,2.0] || member(u,rest_of(u)) subclass(element_relation,v) -> member(ordered_pair(u,rest_of(u)),v)*. % 300.04/300.41 40482[0:Obv:40470.0] || -> equal(not_subclass_element(unordered_pair(u,v),w),v)** subclass(unordered_pair(u,v),w) member(u,universal_class). % 300.04/300.41 40483[0:Obv:40462.0] || -> equal(not_subclass_element(unordered_pair(u,v),w),u)** subclass(unordered_pair(u,v),w) member(v,universal_class). % 300.04/300.41 48684[0:SpL:4125.0,6437.0] || subclass(universal_class,symmetric_difference(complement(u),complement(v))) -> member(unordered_pair(w,x),union(u,v))*. % 300.04/300.41 48438[0:SpL:5132.1,48430.0] || equal(complement(singleton(not_subclass_element(cross_product(u,v),w))),universal_class)** -> subclass(cross_product(u,v),w). % 300.04/300.41 48426[0:SpL:5132.1,48410.0] || subclass(universal_class,complement(singleton(not_subclass_element(cross_product(u,v),w))))* -> subclass(cross_product(u,v),w). % 300.04/300.41 16147[0:Res:12015.1,896.0] || equal(complement(complement(restrict(u,v,w))),universal_class)** -> member(singleton(x),cross_product(v,w))*. % 300.04/300.41 16452[0:Res:16280.0,8596.1] single_valued_class(restrict(cross_product(universal_class,universal_class),u,v)) || -> function(restrict(cross_product(universal_class,universal_class),u,v))*. % 300.04/300.41 85693[0:SpL:4119.0,6300.0] || equal(symmetric_difference(u,cross_product(v,w)),universal_class) -> member(omega,complement(restrict(u,v,w)))*. % 300.04/300.41 85721[0:SpL:4119.0,2539.0] || subclass(universal_class,symmetric_difference(u,cross_product(v,w))) -> member(omega,complement(restrict(u,v,w)))*. % 300.04/300.41 85694[0:SpL:4121.0,6300.0] || equal(symmetric_difference(cross_product(u,v),w),universal_class) -> member(omega,complement(restrict(w,u,v)))*. % 300.04/300.41 85722[0:SpL:4121.0,2539.0] || subclass(universal_class,symmetric_difference(cross_product(u,v),w)) -> member(omega,complement(restrict(w,u,v)))*. % 300.04/300.41 16681[0:Res:16650.0,8.0] || subclass(symmetrization_of(u),symmetric_difference(u,inverse(u)))* -> equal(symmetric_difference(u,inverse(u)),symmetrization_of(u)). % 300.04/300.41 109243[0:Res:6403.1,2.0] || equal(symmetric_difference(u,v),universal_class) subclass(union(u,v),w)* -> member(omega,w). % 300.04/300.41 109263[0:Res:6303.1,2.0] || subclass(universal_class,symmetric_difference(u,v)) subclass(union(u,v),w)* -> member(omega,w). % 300.04/300.41 110869[0:Res:17.2,6476.1] || member(u,v)* member(w,x)* subclass(universal_class,complement(cross_product(x,v)))* -> . % 300.04/300.41 117713[0:Res:2526.2,110865.0] || subclass(u,rest_of(not_subclass_element(u,v)))* subclass(universal_class,complement(element_relation)) -> subclass(u,v). % 300.04/300.41 126025[8:Rew:124836.0,125458.0] || member(u,cantor(u)) subclass(element_relation,v) -> member(ordered_pair(u,cantor(u)),v)*. % 300.04/300.41 130533[0:SpL:43.0,110985.0] || member(inverse(restrict(u,v,universal_class)),image(u,v))* subclass(universal_class,complement(element_relation)) -> . % 300.04/300.41 135186[0:Res:36865.0,25.1] || member(not_subclass_element(complement(complement(complement(u))),v),u)* -> subclass(complement(complement(complement(u))),v). % 300.04/300.41 135496[0:Res:2526.2,11848.0] || subclass(u,v)* subclass(v,w)* well_ordering(universal_class,w)* -> subclass(u,x)*. % 300.04/300.41 135843[0:SpL:29.0,16105.1] || member(u,symmetric_difference(v,cross_product(w,x)))* member(u,restrict(v,w,x)) -> . % 300.04/300.41 135846[0:SpL:30.0,16105.1] || member(u,symmetric_difference(cross_product(v,w),x))* member(u,restrict(x,v,w)) -> . % 300.04/300.41 135887[0:Res:3.1,16105.1] || member(not_subclass_element(intersection(u,v),w),symmetric_difference(u,v))* -> subclass(intersection(u,v),w). % 300.04/300.41 135979[0:Res:2525.1,897.0] || subclass(ordered_pair(u,v),restrict(w,x,y))* -> member(unordered_pair(u,singleton(v)),w). % 300.04/300.41 135982[0:Res:2525.1,110865.0] || subclass(ordered_pair(u,v),rest_of(unordered_pair(u,singleton(v))))* subclass(universal_class,complement(element_relation)) -> . % 300.04/300.41 138598[8:SpR:124905.0,138594.1] || equal(rest_of(restrict(u,v,singleton(w))),rest_relation)** -> subclass(x,segment(u,v,w))*. % 300.04/300.41 139927[0:Res:2481.1,16102.0] || subclass(universal_class,symmetric_difference(complement(u),complement(v))) -> member(ordered_pair(w,x),union(u,v))*. % 300.04/300.41 140763[0:MRR:140728.0,36682.1] || -> member(not_subclass_element(complement(union(u,v)),w),complement(v))* subclass(complement(union(u,v)),w). % 300.04/300.41 140855[0:MRR:140823.0,36682.1] || -> member(not_subclass_element(complement(union(u,v)),w),complement(u))* subclass(complement(union(u,v)),w). % 300.04/300.41 146284[0:SpR:144504.0,119.1] || transitive(universal_class,u) -> subclass(compose(cross_product(u,u),cross_product(u,u)),cross_product(u,u))*. % 300.04/300.41 146302[8:SpL:144504.0,124903.0] || equal(cantor(cross_product(u,v)),v)** subclass(v,u) -> section(universal_class,v,u). % 300.04/300.41 146303[0:SpL:144504.0,120.0] || subclass(compose(cross_product(u,u),cross_product(u,u)),cross_product(u,u))* -> transitive(universal_class,u). % 300.04/300.41 146304[0:SpL:144504.0,11772.0] || equal(compose(cross_product(u,u),cross_product(u,u)),cross_product(u,u))** -> transitive(universal_class,u). % 300.04/300.41 146312[8:SpL:144504.0,124906.1] || subclass(u,v) subclass(cantor(cross_product(v,u)),u)* -> section(universal_class,u,v). % 300.04/300.41 148016[8:Res:147404.1,284.0] || member(not_subclass_element(complement(compose(element_relation,universal_class)),u),element_relation)* -> subclass(complement(compose(element_relation,universal_class)),u). % 300.04/300.41 151021[0:Obv:150972.1] || member(u,v) -> subclass(intersection(singleton(u),w),intersection(v,intersection(singleton(u),w)))*. % 300.04/300.41 151407[0:Obv:151360.1] || member(u,v) -> subclass(intersection(w,singleton(u)),intersection(v,intersection(w,singleton(u))))*. % 300.04/300.41 153123[0:SpR:4125.0,149179.0] || -> equal(intersection(union(u,v),symmetric_difference(complement(u),complement(v))),symmetric_difference(complement(u),complement(v)))**. % 300.04/300.41 154658[8:Res:2478.1,82994.1] || subclass(universal_class,complement(compose(element_relation,universal_class)))* member(omega,element_relation) well_ordering(u,v)* -> . % 300.04/300.41 157129[0:Res:7.1,27150.1] || equal(singleton(u),rest_relation)** member(v,universal_class) -> equal(ordered_pair(v,rest_of(v)),u)*. % 300.04/300.41 157305[0:Res:7.1,27175.1] || equal(compose_class(u),rest_relation) member(v,universal_class) -> equal(compose(u,v),rest_of(v))**. % 300.04/300.41 134809[3:Res:134636.1,2497.1] || subclass(complement(u),ordinal_numbers)* member(v,universal_class) -> member(v,u)* member(v,kind_1_ordinals)*. % 300.04/300.41 135693[2:Res:35220.2,25.1] inductive(complement(u)) || well_ordering(v,universal_class) member(least(v,complement(u)),u)* -> . % 300.04/300.41 136349[2:Res:35222.2,4178.0] inductive(singleton(u)) || well_ordering(v,singleton(u)) -> equal(least(v,singleton(u)),u)**. % 300.04/300.41 166469[0:Res:150982.0,7972.2] || member(u,v)* member(u,singleton(w))* -> member(w,v)* member(u,x)*. % 300.04/300.41 166626[8:Res:166605.0,6432.1] || subclass(universal_class,complement(inverse(singleton(unordered_pair(u,v)))))* -> asymmetric(singleton(unordered_pair(u,v)),w)*. % 300.04/300.41 166628[8:Res:166605.0,6476.1] || subclass(universal_class,complement(inverse(singleton(ordered_pair(u,v)))))* -> asymmetric(singleton(ordered_pair(u,v)),w)*. % 300.04/300.41 167407[19:Rew:166997.0,98566.2] || subclass(domain_relation,complement(complement(u)))* subclass(u,v)* -> member(ordered_pair(ordinal_numbers,ordinal_numbers),v)*. % 300.04/300.41 167424[19:Rew:166997.0,99080.1] || subclass(domain_relation,symmetric_difference(complement(u),complement(v))) -> member(ordered_pair(ordinal_numbers,ordinal_numbers),union(u,v))*. % 300.04/300.41 167425[19:Rew:166997.0,98571.1] || subclass(domain_relation,complement(complement(symmetric_difference(u,v)))) -> member(ordered_pair(ordinal_numbers,ordinal_numbers),union(u,v))*. % 300.04/300.41 169429[19:Rew:166997.0,167559.1] || equal(intersection(complement(u),complement(v)),singleton(ordinal_numbers))** member(ordinal_numbers,union(u,v)) -> . % 300.04/300.41 167685[19:Rew:166997.0,163744.3] || subclass(u,v)* subclass(v,w)* well_ordering(universal_class,w)* -> equal(u,ordinal_numbers). % 300.04/300.41 167730[19:Rew:166997.0,80620.1] || subclass(u,symmetric_difference(v,inverse(v)))* -> equal(u,ordinal_numbers) member(regular(u),symmetrization_of(v)). % 300.04/300.41 167957[19:Rew:166997.0,84850.1] || subclass(omega,symmetric_difference(u,inverse(u)))* -> equal(integer_of(v),ordinal_numbers) member(v,symmetrization_of(u))*. % 300.04/300.41 168183[19:Rew:166997.0,99175.1] || subclass(u,v) -> equal(complement(complement(u)),ordinal_numbers) member(regular(complement(complement(u))),v)*. % 300.04/300.41 168214[19:Rew:166997.0,97519.2] || subclass(omega,u) subclass(domain_relation,complement(u))* -> equal(integer_of(ordered_pair(ordinal_numbers,ordinal_numbers)),ordinal_numbers)**. % 300.04/300.41 168445[19:Rew:166997.0,99296.1] || subclass(omega,element_relation) -> equal(integer_of(singleton(singleton(singleton(u)))),ordinal_numbers)** member(singleton(u),u)*. % 300.04/300.41 168447[19:Rew:166997.0,99182.0] || -> equal(complement(complement(omega)),ordinal_numbers) equal(integer_of(regular(complement(complement(omega)))),regular(complement(complement(omega))))**. % 300.04/300.41 168452[19:Rew:166997.0,99177.0] || -> equal(complement(complement(intersection(u,v))),ordinal_numbers) member(regular(complement(complement(intersection(u,v)))),v)*. % 300.04/300.41 168453[19:Rew:166997.0,99176.0] || -> equal(complement(complement(intersection(u,v))),ordinal_numbers) member(regular(complement(complement(intersection(u,v)))),u)*. % 300.04/300.41 168462[19:Rew:166997.0,80800.1] || subclass(union(u,v),intersection(complement(u),complement(v)))* -> equal(union(u,v),ordinal_numbers). % 300.04/300.41 169450[19:Rew:166997.0,168464.1] || -> equal(singleton(cross_product(u,v)),ordinal_numbers) equal(restrict(singleton(cross_product(u,v)),u,v),ordinal_numbers)**. % 300.04/300.41 168483[19:Rew:166997.0,82519.0] || equal(compose(restrict(u,v,v),restrict(u,v,v)),ordinal_numbers)** -> transitive(u,v). % 300.04/300.41 168494[19:Rew:166997.0,163425.2] || subclass(omega,u) subclass(universal_class,complement(u))* -> equal(integer_of(ordered_pair(v,w)),ordinal_numbers)**. % 300.04/300.41 168504[19:Rew:166997.0,84897.2] || subclass(omega,u) subclass(universal_class,complement(u))* -> equal(integer_of(unordered_pair(v,w)),ordinal_numbers)**. % 300.04/300.41 169453[19:Rew:166997.0,168577.1] || -> member(ordinal_numbers,image(element_relation,union(u,v))) member(ordinal_numbers,power_class(intersection(complement(u),complement(v))))*. % 300.04/300.41 168734[19:Rew:166997.0,160950.1] || subclass(universal_class,complement(compose(element_relation,universal_class)))* member(ordinal_numbers,element_relation) well_ordering(u,v)* -> . % 300.04/300.41 168930[19:Rew:166997.0,163529.0] || -> equal(intersection(complement(complement(u)),v),ordinal_numbers) member(regular(intersection(complement(complement(u)),v)),u)*. % 300.04/300.41 168938[19:Rew:166997.0,163647.0] || -> equal(intersection(u,complement(complement(v))),ordinal_numbers) member(regular(intersection(u,complement(complement(v)))),v)*. % 300.04/300.41 169058[19:Rew:166997.0,166237.1] || equal(symmetric_difference(cross_product(u,v),w),universal_class) -> member(ordinal_numbers,complement(restrict(w,u,v)))*. % 300.04/300.41 169059[19:Rew:166997.0,166184.1] || subclass(universal_class,symmetric_difference(cross_product(u,v),w)) -> member(ordinal_numbers,complement(restrict(w,u,v)))*. % 300.04/300.41 169060[19:Rew:166997.0,166238.1] || equal(symmetric_difference(u,cross_product(v,w)),universal_class) -> member(ordinal_numbers,complement(restrict(u,v,w)))*. % 300.04/300.41 169061[19:Rew:166997.0,166185.1] || subclass(universal_class,symmetric_difference(u,cross_product(v,w))) -> member(ordinal_numbers,complement(restrict(u,v,w)))*. % 300.04/300.41 169444[19:Rew:166997.0,168080.1] || well_ordering(u,inverse(ordinal_numbers)) -> equal(segment(u,symmetrization_of(ordinal_numbers),least(u,symmetrization_of(ordinal_numbers))),ordinal_numbers)**. % 300.04/300.41 169443[19:Rew:166997.0,168075.0] || member(u,symmetric_difference(complement(v),symmetrization_of(ordinal_numbers)))* -> member(u,union(v,complement(inverse(ordinal_numbers)))). % 300.04/300.41 169442[19:Rew:166997.0,168072.0] || member(u,symmetric_difference(symmetrization_of(ordinal_numbers),complement(v)))* -> member(u,union(complement(inverse(ordinal_numbers)),v)). % 300.04/300.41 169449[19:Rew:166997.0,168175.1] || -> subclass(intersection(u,symmetrization_of(ordinal_numbers)),v) member(not_subclass_element(intersection(u,symmetrization_of(ordinal_numbers)),v),inverse(ordinal_numbers))*. % 300.04/300.41 169448[19:Rew:166997.0,168173.1] || -> subclass(intersection(symmetrization_of(ordinal_numbers),u),v) member(not_subclass_element(intersection(symmetrization_of(ordinal_numbers),u),v),inverse(ordinal_numbers))*. % 300.04/300.41 168110[19:Rew:166997.0,166910.0] || -> subclass(complement(union(u,image(element_relation,symmetrization_of(ordinal_numbers)))),intersection(complement(u),power_class(complement(inverse(ordinal_numbers)))))*. % 300.04/300.41 168105[19:Rew:166997.0,166886.0] || -> subclass(complement(union(image(element_relation,symmetrization_of(ordinal_numbers)),u)),intersection(power_class(complement(inverse(ordinal_numbers))),complement(u)))*. % 300.04/300.41 169446[19:Rew:166997.0,168100.1] || -> subclass(complement(complement(symmetrization_of(ordinal_numbers))),u) member(not_subclass_element(complement(complement(symmetrization_of(ordinal_numbers))),u),inverse(ordinal_numbers))*. % 300.04/300.41 169430[19:Rew:166997.0,167610.0] || member(ordered_pair(u,not_subclass_element(v,range_of(ordinal_numbers))),compose(ordinal_numbers,w))* -> subclass(v,range_of(ordinal_numbers)). % 300.04/300.41 176116[20:Res:175613.1,16102.0] || subclass(universal_class,symmetric_difference(complement(u),complement(v))) -> member(regular(symmetrization_of(ordinal_numbers)),union(u,v))*. % 300.04/300.41 176193[18:SpL:124905.0,175681.1] || member(restrict(u,v,singleton(w)),universal_class)* member(x,segment(u,v,w))* -> . % 300.04/300.41 176241[19:Rew:176206.1,164740.2] || member(u,universal_class) subclass(domain_relation,complement(complement(v))) -> member(ordered_pair(u,ordinal_numbers),v)*. % 300.04/300.41 176269[19:Rew:176206.1,169501.2] || member(u,universal_class) subclass(domain_relation,symmetrization_of(ordinal_numbers)) -> member(ordered_pair(u,ordinal_numbers),inverse(ordinal_numbers))*. % 300.04/300.41 177082[19:MRR:177061.1,166995.0] || subclass(u,v) -> equal(singleton(restrict(w,v,u)),ordinal_numbers)** section(w,u,v). % 300.04/300.41 177154[19:Obv:177129.0] || -> equal(regular(unordered_pair(u,v)),u)** equal(unordered_pair(u,v),ordinal_numbers) equal(cantor(v),ordinal_numbers). % 300.04/300.41 177155[19:Obv:177128.0] || -> equal(regular(unordered_pair(u,v)),v)** equal(unordered_pair(u,v),ordinal_numbers) equal(cantor(u),ordinal_numbers). % 300.04/300.41 177181[22:Res:177171.1,82994.1] || subclass(omega,complement(compose(element_relation,universal_class)))* member(ordinal_numbers,element_relation) well_ordering(u,v)* -> . % 300.04/300.41 177299[19:SSi:177282.0,70.0] || -> equal(unordered_pair(u,v),ordinal_numbers) equal(apply(choice,unordered_pair(u,v)),u)** member(v,universal_class). % 300.04/300.41 177300[19:SSi:177289.0,70.0] || -> equal(unordered_pair(u,v),ordinal_numbers) equal(apply(choice,unordered_pair(u,v)),v)** member(u,universal_class). % 300.04/300.41 178263[22:Res:24.2,177998.1] || member(ordinal_numbers,u) member(ordinal_numbers,v) equal(complement(intersection(v,u)),omega)** -> . % 300.04/300.41 178431[19:SpL:168412.1,48663.0] || equal(complement(unordered_pair(regular(cross_product(u,v)),w)),universal_class)** -> equal(cross_product(u,v),ordinal_numbers). % 300.04/300.41 178432[19:SpL:168412.1,48618.0] || subclass(universal_class,complement(unordered_pair(regular(cross_product(u,v)),w)))* -> equal(cross_product(u,v),ordinal_numbers). % 300.04/300.41 178456[19:SpL:168412.1,48630.0] || equal(complement(unordered_pair(u,regular(cross_product(v,w)))),universal_class)** -> equal(cross_product(v,w),ordinal_numbers). % 300.04/300.41 178457[19:SpL:168412.1,48587.0] || subclass(universal_class,complement(unordered_pair(u,regular(cross_product(v,w)))))* -> equal(cross_product(v,w),ordinal_numbers). % 300.04/300.41 178776[22:SpL:4121.0,177190.0] || subclass(omega,symmetric_difference(cross_product(u,v),w)) -> member(ordinal_numbers,complement(restrict(w,u,v)))*. % 300.04/300.41 178777[22:SpL:4119.0,177190.0] || subclass(omega,symmetric_difference(u,cross_product(v,w))) -> member(ordinal_numbers,complement(restrict(u,v,w)))*. % 300.04/300.41 178877[22:SpL:4121.0,178812.0] || equal(symmetric_difference(cross_product(u,v),w),omega) -> member(ordinal_numbers,complement(restrict(w,u,v)))*. % 300.04/300.41 178878[22:SpL:4119.0,178812.0] || equal(symmetric_difference(u,cross_product(v,w)),omega) -> member(ordinal_numbers,complement(restrict(u,v,w)))*. % 300.04/300.41 180177[19:Rew:180089.0,179103.0] || -> subclass(complement(union(u,image(element_relation,singleton(ordinal_numbers)))),intersection(complement(u),power_class(complement(singleton(ordinal_numbers)))))*. % 300.04/300.41 180183[19:Rew:180089.0,179079.0] || -> subclass(complement(union(image(element_relation,singleton(ordinal_numbers)),u)),intersection(power_class(complement(singleton(ordinal_numbers))),complement(u)))*. % 300.04/300.41 180314[19:Rew:180089.0,169423.0] || member(u,symmetric_difference(singleton(ordinal_numbers),complement(v)))* -> member(u,union(complement(singleton(ordinal_numbers)),v)). % 300.04/300.41 180392[19:Rew:180089.0,180079.1,180103.0,180079.0] || subclass(u,singleton(ordinal_numbers)) -> subclass(singleton(not_subclass_element(u,v)),singleton(ordinal_numbers))* subclass(u,v). % 300.04/300.41 180855[19:Res:4126.1,169221.1] || member(ordinal_numbers,symmetric_difference(u,v)) equal(complement(complement(intersection(u,v))),singleton(ordinal_numbers))** -> . % 300.04/300.41 180978[19:SpL:27.0,169222.0] || equal(complement(union(u,v)),singleton(ordinal_numbers)) -> member(ordinal_numbers,intersection(complement(u),complement(v)))*. % 300.04/300.41 181388[19:Rew:168752.1,181320.2] || member(u,universal_class) member(singleton(singleton(ordinal_numbers)),element_relation)* -> member(ordinal_numbers,sum_class(range_of(u)))*. % 300.04/300.41 181527[19:Rew:167191.0,181506.0] || subclass(u,symmetrization_of(ordinal_numbers)) -> subclass(singleton(not_subclass_element(u,v)),symmetrization_of(ordinal_numbers))* subclass(u,v). % 300.04/300.41 181626[20:Res:181516.0,8.0] || subclass(symmetrization_of(ordinal_numbers),singleton(regular(symmetrization_of(ordinal_numbers))))* -> equal(singleton(regular(symmetrization_of(ordinal_numbers))),symmetrization_of(ordinal_numbers)). % 300.04/300.41 181731[20:Res:175570.1,16105.1] || subclass(inverse(ordinal_numbers),intersection(u,v)) member(regular(symmetrization_of(ordinal_numbers)),symmetric_difference(u,v))* -> . % 300.04/300.41 181747[20:Res:175570.1,896.0] || subclass(inverse(ordinal_numbers),restrict(u,v,w))* -> member(regular(symmetrization_of(ordinal_numbers)),cross_product(v,w))*. % 300.04/300.41 181792[19:Res:176345.1,16105.1] || subclass(domain_relation,intersection(u,v)) member(singleton(singleton(singleton(ordinal_numbers))),symmetric_difference(u,v))* -> . % 300.04/300.41 181808[19:Res:176345.1,896.0] || subclass(domain_relation,restrict(u,v,w))* -> member(singleton(singleton(singleton(ordinal_numbers))),cross_product(v,w))*. % 300.04/300.41 181915[19:MRR:181895.3,167057.0] || well_ordering(u,universal_class) member(v,universal_class)* subclass(rest_relation,rest_of(least(u,universal_class)))* -> . % 300.04/300.41 181958[19:MRR:181938.3,167057.0] || well_ordering(u,universal_class) member(v,universal_class)* subclass(rest_relation,rest_of(least(u,rest_relation)))* -> . % 300.04/300.41 182073[19:MRR:182052.3,167057.0] || well_ordering(u,rest_relation) member(v,universal_class)* subclass(rest_relation,rest_of(least(u,rest_relation)))* -> . % 300.04/300.41 182116[21:MRR:182096.3,167057.0] || well_ordering(u,omega) member(v,universal_class)* subclass(rest_relation,rest_of(least(u,omega)))* -> . % 300.04/300.41 182160[21:MRR:182139.3,167057.0] || well_ordering(u,universal_class) member(v,universal_class)* subclass(rest_relation,rest_of(least(u,omega)))* -> . % 300.04/300.41 182329[22:SpL:27.0,178289.1] || equal(intersection(complement(u),complement(v)),singleton(ordinal_numbers))** equal(union(u,v),omega) -> . % 300.04/300.41 182336[22:SpL:167200.0,178289.1] || equal(image(element_relation,symmetrization_of(ordinal_numbers)),singleton(ordinal_numbers))** equal(power_class(complement(inverse(ordinal_numbers))),omega) -> . % 300.04/300.41 182337[22:SpL:180125.0,178289.1] || equal(image(element_relation,singleton(ordinal_numbers)),singleton(ordinal_numbers))** equal(power_class(complement(singleton(ordinal_numbers))),omega) -> . % 300.04/300.41 182769[22:SpL:27.0,180881.1] || equal(intersection(complement(u),complement(v)),omega)** equal(union(u,v),singleton(ordinal_numbers)) -> . % 300.04/300.41 182776[22:SpL:167200.0,180881.1] || equal(image(element_relation,symmetrization_of(ordinal_numbers)),omega)** equal(power_class(complement(inverse(ordinal_numbers))),singleton(ordinal_numbers)) -> . % 300.04/300.41 182777[22:SpL:180125.0,180881.1] || equal(image(element_relation,singleton(ordinal_numbers)),omega)** equal(power_class(complement(singleton(ordinal_numbers))),singleton(ordinal_numbers)) -> . % 300.04/300.41 182912[20:Res:181635.1,16105.1] || subclass(symmetrization_of(ordinal_numbers),intersection(u,v)) member(regular(symmetrization_of(ordinal_numbers)),symmetric_difference(u,v))* -> . % 300.04/300.41 182928[20:Res:181635.1,896.0] || subclass(symmetrization_of(ordinal_numbers),restrict(u,v,w))* -> member(regular(symmetrization_of(ordinal_numbers)),cross_product(v,w))*. % 300.04/300.41 183021[19:SpL:27.0,182427.0] || equal(complement(union(u,v)),universal_class) well_ordering(universal_class,intersection(complement(u),complement(v)))* -> . % 300.04/300.41 183055[19:SpL:176371.1,182439.1] || well_ordering(u,universal_class) subclass(rest_relation,rest_of(least(u,universal_class)))* well_ordering(universal_class,ordinal_numbers) -> . % 300.04/300.41 183056[19:SpL:176373.1,182439.1] || well_ordering(u,rest_relation) subclass(rest_relation,rest_of(least(u,rest_relation)))* well_ordering(universal_class,ordinal_numbers) -> . % 300.04/300.41 183057[19:SpL:176372.1,182439.1] || well_ordering(u,universal_class) subclass(rest_relation,rest_of(least(u,rest_relation)))* well_ordering(universal_class,ordinal_numbers) -> . % 300.04/300.41 183058[21:SpL:176375.1,182439.1] || well_ordering(u,universal_class) subclass(rest_relation,rest_of(least(u,omega)))* well_ordering(universal_class,ordinal_numbers) -> . % 300.04/300.41 183059[21:SpL:176374.1,182439.1] || well_ordering(u,omega) subclass(rest_relation,rest_of(least(u,omega)))* well_ordering(universal_class,ordinal_numbers) -> . % 300.04/300.41 183092[19:Res:182463.1,16105.1] || equal(intersection(u,v),singleton(singleton(ordinal_numbers))) member(singleton(ordinal_numbers),symmetric_difference(u,v))* -> . % 300.04/300.41 183108[19:Res:182463.1,896.0] || equal(restrict(u,v,w),singleton(singleton(ordinal_numbers)))** -> member(singleton(ordinal_numbers),cross_product(v,w))*. % 300.04/300.41 183569[19:Res:168184.0,148647.0] || -> equal(complement(complement(complement(complement(u)))),ordinal_numbers) member(regular(complement(complement(complement(complement(u))))),u)*. % 300.04/300.41 183858[23:SpR:183840.0,59.1] || member(ordered_pair(universal_class,u),compose(v,w))* -> member(u,image(v,image(w,ordinal_numbers))). % 300.04/300.41 183991[23:Rew:183893.0,181310.1] || member(u,universal_class) -> equal(segment(v,w,sum_class(range_of(u))),segment(v,w,universal_class))**. % 300.04/300.41 184008[23:Rew:183888.0,181305.1] || member(u,universal_class) -> equal(range__dfg(v,sum_class(range_of(u)),w),range__dfg(v,universal_class,w))**. % 300.04/300.41 184011[23:Rew:183894.0,181311.1] || member(u,universal_class) -> equal(domain__dfg(v,w,sum_class(range_of(u))),domain__dfg(v,w,universal_class))**. % 300.04/300.41 184024[23:Rew:184023.1,169525.2] || member(u,universal_class)* member(singleton(singleton(ordinal_numbers)),compose_class(v))* -> equal(range_of(u),universal_class). % 300.04/300.41 184026[23:Rew:184023.1,177943.2] || member(singleton(singleton(ordinal_numbers)),compose_class(u))* -> equal(range_of(v),ordinal_numbers)** equal(inverse(v),universal_class). % 300.04/300.41 184050[23:Rew:184024.2,184025.2] || member(u,universal_class)* member(singleton(singleton(ordinal_numbers)),compose_class(v))* -> equal(sum_class(universal_class),universal_class). % 300.04/300.41 184117[23:SpR:183857.0,17.2] || member(universal_class,u) member(ordinal_numbers,v) -> member(singleton(singleton(ordinal_numbers)),cross_product(v,u))*. % 300.04/300.41 184253[23:SpR:183885.0,2482.2] || member(image(u,ordinal_numbers),universal_class) subclass(universal_class,v) -> member(apply(u,universal_class),v)*. % 300.04/300.41 184270[23:Rew:183885.0,184252.0] || equal(apply(u,universal_class),image(u,ordinal_numbers)) -> subclass(apply(u,universal_class),image(u,ordinal_numbers))*. % 300.04/300.41 184857[19:Res:176419.1,897.0] || subclass(domain_relation,flip(restrict(u,v,w)))* -> member(ordered_pair(ordered_pair(x,y),ordinal_numbers),u)*. % 300.04/300.41 184861[19:Res:176419.1,110865.0] || subclass(domain_relation,flip(rest_of(ordered_pair(ordered_pair(u,v),ordinal_numbers))))* subclass(universal_class,complement(element_relation)) -> . % 300.04/300.41 184880[19:Res:176419.1,99365.1] || subclass(domain_relation,flip(cross_product(universal_class,universal_class)))* equal(sum_class(range_of(ordered_pair(u,v))),ordinal_numbers)** -> . % 300.04/300.41 184935[19:Res:176420.1,897.0] || subclass(domain_relation,rotate(restrict(u,v,w)))* -> member(ordered_pair(ordered_pair(x,ordinal_numbers),y),u)*. % 300.04/300.41 184939[19:Res:176420.1,110865.0] || subclass(domain_relation,rotate(rest_of(ordered_pair(ordered_pair(u,ordinal_numbers),v))))* subclass(universal_class,complement(element_relation)) -> . % 300.04/300.41 185093[19:Res:16280.0,167739.0] || -> equal(restrict(singleton(u),v,w),ordinal_numbers) equal(regular(restrict(singleton(u),v,w)),u)**. % 300.04/300.41 185162[20:MRR:185114.1,175569.0] || subclass(rest_relation,domain_relation) subclass(rest_relation,u) -> member(ordered_pair(regular(symmetrization_of(ordinal_numbers)),ordinal_numbers),u)*. % 300.04/300.41 185262[19:Res:168252.2,4178.0] || well_ordering(u,singleton(v)) -> equal(singleton(v),ordinal_numbers) equal(least(u,singleton(v)),v)**. % 300.04/300.41 185380[23:SpL:183856.0,9.0] || member(u,ordered_pair(universal_class,v))* -> equal(u,unordered_pair(universal_class,singleton(v))) equal(u,ordinal_numbers). % 300.04/300.41 185596[19:MRR:185547.1,12.0] || subclass(rest_relation,domain_relation) subclass(rest_relation,u) -> member(ordered_pair(unordered_pair(v,w),ordinal_numbers),u)*. % 300.04/300.41 185651[19:MRR:185601.1,940.0] || subclass(rest_relation,domain_relation) subclass(rest_relation,u) -> member(ordered_pair(ordered_pair(v,w),ordinal_numbers),u)*. % 300.04/300.41 185738[19:SpL:27.0,185656.1] || equal(flip(intersection(complement(u),complement(v))),domain_relation)** subclass(universal_class,union(u,v)) -> . % 300.04/300.41 185745[19:SpL:167200.0,185656.1] || equal(flip(image(element_relation,symmetrization_of(ordinal_numbers))),domain_relation) subclass(universal_class,power_class(complement(inverse(ordinal_numbers))))* -> . % 300.04/300.41 185746[19:SpL:180125.0,185656.1] || equal(flip(image(element_relation,singleton(ordinal_numbers))),domain_relation) subclass(universal_class,power_class(complement(singleton(ordinal_numbers))))* -> . % 300.04/300.41 185759[19:SpL:27.0,185733.1] || equal(rotate(intersection(complement(u),complement(v))),domain_relation)** subclass(universal_class,union(u,v)) -> . % 300.04/300.41 185766[19:SpL:167200.0,185733.1] || equal(rotate(image(element_relation,symmetrization_of(ordinal_numbers))),domain_relation) subclass(universal_class,power_class(complement(inverse(ordinal_numbers))))* -> . % 300.04/300.41 185767[19:SpL:180125.0,185733.1] || equal(rotate(image(element_relation,singleton(ordinal_numbers))),domain_relation) subclass(universal_class,power_class(complement(singleton(ordinal_numbers))))* -> . % 300.04/300.41 185813[0:Res:55.1,30589.0] || member(u,universal_class) subclass(rest_relation,successor_relation) -> equal(rest_of(sum_class(u)),successor(sum_class(u)))**. % 300.04/300.41 185814[0:Res:57.1,30589.0] || member(u,universal_class) subclass(rest_relation,successor_relation) -> equal(rest_of(power_class(u)),successor(power_class(u)))**. % 300.04/300.41 185871[0:Rew:30589.2,185823.2] || member(u,universal_class) subclass(rest_relation,successor_relation) -> equal(rest_of(successor(u)),successor(successor(u)))**. % 300.04/300.41 186390[19:SpL:180103.0,167960.0] || subclass(omega,singleton(ordinal_numbers)) member(u,complement(singleton(ordinal_numbers)))* -> equal(integer_of(u),ordinal_numbers). % 300.04/300.41 186969[19:Res:182871.1,167734.1] || member(regular(u),inverse(ordinal_numbers))* subclass(u,complement(symmetrization_of(ordinal_numbers))) -> equal(u,ordinal_numbers). % 300.04/300.41 186971[19:Res:147404.1,167734.1] || member(regular(u),element_relation) subclass(u,complement(compose(element_relation,universal_class)))* -> equal(u,ordinal_numbers). % 300.04/300.41 187013[19:MRR:186960.0,167137.1] || subclass(u,complement(union(v,w)))* -> member(regular(u),complement(w)) equal(u,ordinal_numbers). % 300.04/300.41 187014[19:MRR:186959.0,167137.1] || subclass(u,complement(union(v,w)))* -> member(regular(u),complement(v)) equal(u,ordinal_numbers). % 300.04/300.41 187456[19:SpL:27.0,186994.0] || subclass(singleton(ordinal_numbers),union(u,v)) member(ordinal_numbers,intersection(complement(u),complement(v)))* -> . % 300.04/300.41 187463[19:SpL:167200.0,186994.0] || subclass(singleton(ordinal_numbers),power_class(complement(inverse(ordinal_numbers))))* member(ordinal_numbers,image(element_relation,symmetrization_of(ordinal_numbers))) -> . % 300.04/300.41 187464[19:SpL:180125.0,186994.0] || subclass(singleton(ordinal_numbers),power_class(complement(singleton(ordinal_numbers))))* member(ordinal_numbers,image(element_relation,singleton(ordinal_numbers))) -> . % 300.04/300.41 187588[20:SpL:27.0,186995.1] || subclass(universal_class,intersection(complement(u),complement(v)))* subclass(symmetrization_of(ordinal_numbers),union(u,v)) -> . % 300.04/300.41 187595[20:SpL:167200.0,186995.1] || subclass(universal_class,image(element_relation,symmetrization_of(ordinal_numbers))) subclass(symmetrization_of(ordinal_numbers),power_class(complement(inverse(ordinal_numbers))))* -> . % 300.04/300.41 187596[20:SpL:180125.0,186995.1] || subclass(universal_class,image(element_relation,singleton(ordinal_numbers))) subclass(symmetrization_of(ordinal_numbers),power_class(complement(singleton(ordinal_numbers))))* -> . % 300.04/300.41 187745[19:Res:168354.1,11848.0] || subclass(union(u,v),w)* well_ordering(universal_class,w) -> equal(symmetric_difference(u,v),ordinal_numbers). % 300.04/300.41 187904[19:Rew:167022.0,187888.1,27.0,187888.1,167022.0,187888.0,27.0,187888.0] || -> 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)). % 300.04/300.41 188062[23:SpR:167362.1,183883.0] || member(u,universal_class) -> equal(unordered_pair(ordinal_numbers,unordered_pair(range_of(u),ordinal_numbers)),ordered_pair(range_of(u),universal_class))**. % 300.04/300.41 188063[23:SpR:177036.0,183883.0] || -> equal(range_of(u),ordinal_numbers) equal(unordered_pair(ordinal_numbers,unordered_pair(inverse(u),ordinal_numbers)),ordered_pair(inverse(u),universal_class))**. % 300.04/300.41 188087[23:SpL:183883.0,9.0] || member(u,ordered_pair(v,universal_class))* -> equal(u,unordered_pair(v,ordinal_numbers)) equal(u,singleton(v)). % 300.04/300.41 188094[23:MRR:188093.0,167176.0] || -> equal(regular(ordered_pair(u,universal_class)),unordered_pair(u,ordinal_numbers))** equal(regular(ordered_pair(u,universal_class)),singleton(u)). % 300.04/300.41 188301[23:SpR:169372.1,183885.0] || -> equal(cross_product(ordinal_numbers,universal_class),ordinal_numbers) equal(apply(regular(cross_product(ordinal_numbers,universal_class)),universal_class),sum_class(range_of(ordinal_numbers)))**. % 300.04/300.41 188356[19:Obv:188348.1] || equal(intersection(singleton(u),v),complement(singleton(u)))** -> equal(intersection(singleton(u),v),ordinal_numbers). % 300.04/300.41 188357[19:Obv:188347.1] || equal(intersection(u,singleton(v)),complement(singleton(v)))** -> equal(intersection(u,singleton(v)),ordinal_numbers). % 300.04/300.41 188626[2:Res:24.2,188593.1] || member(u,v)* member(u,w)* equal(complement(intersection(w,v)),universal_class)** -> . % 300.04/300.41 188631[2:Res:35124.1,188593.1] || member(u,universal_class) equal(complement(union(v,w)),universal_class)** -> member(u,complement(v))*. % 300.04/300.41 188632[2:Res:35125.1,188593.1] || member(u,universal_class) equal(complement(union(v,w)),universal_class)** -> member(u,complement(w))*. % 300.04/300.41 188718[2:Res:17.2,188593.1] || member(u,v)* member(w,x)* equal(complement(cross_product(x,v)),universal_class)** -> . % 300.04/300.41 189883[19:SpL:188654.1,158050.0] || equal(complement(symmetrization_of(u)),universal_class)** subclass(cross_product(v,v),ordinal_numbers)* -> connected(u,v)*. % 300.04/300.41 189997[19:MRR:189996.2,166995.0] || equal(complement(symmetrization_of(u)),universal_class)** connected(u,v)* -> equal(cross_product(v,v),ordinal_numbers)**. % 300.04/300.41 190102[19:Obv:190086.0] || well_ordering(u,universal_class) -> equal(singleton(v),ordinal_numbers) equal(segment(u,singleton(v),v),ordinal_numbers)**. % 300.04/300.41 190303[19:Rew:167191.0,190196.1,167191.0,190196.0] || -> subclass(singleton(regular(intersection(u,symmetrization_of(ordinal_numbers)))),symmetrization_of(ordinal_numbers))* equal(intersection(u,symmetrization_of(ordinal_numbers)),ordinal_numbers). % 300.04/300.41 190687[19:Rew:167191.0,190641.1,167191.0,190641.0] || -> subclass(singleton(regular(intersection(symmetrization_of(ordinal_numbers),u))),symmetrization_of(ordinal_numbers))* equal(intersection(symmetrization_of(ordinal_numbers),u),ordinal_numbers). % 300.04/300.41 191124[19:Obv:191086.1] || subclass(symmetric_difference(u,v),complement(complement(intersection(u,v))))* -> equal(symmetric_difference(u,v),ordinal_numbers). % 300.04/300.41 192072[19:Rew:167022.0,192039.1,27.0,192039.1,167022.0,192039.0,27.0,192039.0] || member(regular(image(element_relation,kind_1_ordinals)),complement(image(element_relation,kind_1_ordinals)))* -> equal(image(element_relation,kind_1_ordinals),ordinal_numbers). % 300.04/300.41 192335[19:Res:176235.2,192214.0] || member(u,universal_class) subclass(domain_relation,cantor(complement(cross_product(singleton(ordered_pair(u,ordinal_numbers)),universal_class))))* -> . % 300.04/300.41 193367[25:SpR:193223.1,104.0] function(single_valued1(u)) || -> equal(domain__dfg(u,image(inverse(u),ordinal_numbers),single_valued2(u)),single_valued3(u))**. % 300.04/300.41 193447[25:SpL:193223.1,167253.1] function(u) || member(u,cantor(v))* equal(restrict(v,ordinal_numbers,universal_class),ordinal_numbers)** -> . % 300.04/300.41 193834[25:SoR:193167.0,12322.2] single_valued_class(inverse(u)) || equal(cross_product(universal_class,universal_class),inverse(u))* -> equal(range_of(u),universal_class)**. % 300.04/300.41 193864[25:SpR:193832.1,17187.0] one_to_one(restrict(cross_product(u,universal_class),v,w)) || -> equal(image(cross_product(v,w),u),universal_class)**. % 300.04/300.41 193885[25:SoR:193233.0,12322.2] single_valued_class(sum_class(u)) || member(u,universal_class)* equal(cross_product(universal_class,universal_class),sum_class(u))* -> . % 300.04/300.41 193919[25:SoR:193234.0,12322.2] single_valued_class(power_class(u)) || member(u,universal_class)* equal(cross_product(universal_class,universal_class),power_class(u))* -> . % 300.04/300.41 193922[25:SoR:193235.0,12322.2] single_valued_class(rest_of(u)) || member(u,universal_class)* equal(cross_product(universal_class,universal_class),rest_of(u))* -> . % 300.04/300.41 193982[19:Res:167116.0,176244.2] || member(u,universal_class) subclass(domain_relation,complement(omega)) -> equal(integer_of(ordered_pair(u,ordinal_numbers)),ordinal_numbers)**. % 300.04/300.41 194024[19:MRR:193990.2,36583.1] || member(ordinal_numbers,u) member(v,w)* subclass(domain_relation,complement(cross_product(w,u)))* -> . % 300.04/300.41 194138[25:SoR:193242.0,167213.2] single_valued_class(least(u,universal_class)) || well_ordering(u,universal_class) equal(least(u,universal_class),ordinal_numbers)** -> . % 300.04/300.41 194161[25:SoR:193243.0,167213.2] single_valued_class(least(u,rest_relation)) || well_ordering(u,rest_relation) equal(least(u,rest_relation),ordinal_numbers)** -> . % 300.04/300.41 194164[25:SoR:193244.0,167213.2] single_valued_class(least(u,rest_relation)) || well_ordering(u,universal_class) equal(least(u,rest_relation),ordinal_numbers)** -> . % 300.04/300.41 194167[25:SoR:193245.0,167213.2] single_valued_class(least(u,omega)) || well_ordering(u,universal_class) equal(least(u,omega),ordinal_numbers)** -> . % 300.04/300.41 194170[25:SoR:193246.0,167213.2] single_valued_class(least(u,omega)) || well_ordering(u,omega) equal(least(u,omega),ordinal_numbers)** -> . % 300.04/300.41 194184[19:Res:7.1,168499.0] || equal(rest_of(u),omega) -> equal(integer_of(ordered_pair(v,w)),ordinal_numbers)** member(v,cantor(u))*. % 300.04/300.41 194436[19:MRR:194370.2,167057.0] || member(u,universal_class) -> equal(singleton(v),ordinal_numbers) equal(apply(v,u),sum_class(range_of(ordinal_numbers)))**. % 300.04/300.41 194437[19:MRR:194381.2,167057.0] || member(u,universal_class) -> equal(v,ordinal_numbers) equal(apply(regular(v),u),sum_class(range_of(ordinal_numbers)))**. % 300.04/300.41 194454[19:MRR:194412.0,940.0] || subclass(universal_class,complement(cantor(u))) -> equal(apply(u,ordered_pair(v,w)),sum_class(range_of(ordinal_numbers)))**. % 300.04/300.41 194455[19:MRR:194406.0,12.0] || subclass(universal_class,complement(cantor(u))) -> equal(apply(u,unordered_pair(v,w)),sum_class(range_of(ordinal_numbers)))**. % 300.04/300.41 194457[19:MRR:194407.0,167137.1] || -> equal(apply(u,regular(complement(cantor(u)))),sum_class(range_of(ordinal_numbers)))** equal(complement(cantor(u)),ordinal_numbers). % 300.04/300.41 194814[19:Res:7.1,176243.1] || equal(intersection(u,v),domain_relation)** member(w,universal_class) -> member(ordered_pair(w,ordinal_numbers),u)*. % 300.04/300.41 195000[19:Res:7.1,176249.1] || equal(intersection(u,v),domain_relation)** member(w,universal_class) -> member(ordered_pair(w,ordinal_numbers),v)*. % 300.04/300.41 195202[19:SpL:27.0,194013.1] || subclass(domain_relation,rotate(intersection(complement(u),complement(v))))* subclass(domain_relation,union(u,v)) -> . % 300.04/300.41 195210[19:SpL:167200.0,194013.1] || subclass(domain_relation,rotate(image(element_relation,symmetrization_of(ordinal_numbers))))* subclass(domain_relation,power_class(complement(inverse(ordinal_numbers)))) -> . % 300.04/300.41 195211[19:SpL:180125.0,194013.1] || subclass(domain_relation,rotate(image(element_relation,singleton(ordinal_numbers))))* subclass(domain_relation,power_class(complement(singleton(ordinal_numbers)))) -> . % 300.04/300.41 195226[23:SpR:183857.0,27190.1] || subclass(rest_relation,flip(u)) -> member(ordered_pair(ordered_pair(universal_class,ordinal_numbers),rest_of(singleton(singleton(ordinal_numbers)))),u)*. % 300.04/300.41 195234[23:SpR:183857.0,27190.1] || subclass(rest_relation,flip(u)) -> member(ordered_pair(singleton(singleton(ordinal_numbers)),rest_of(ordered_pair(universal_class,ordinal_numbers))),u)*. % 300.04/300.41 195328[23:SpR:183857.0,27189.1] || subclass(rest_relation,rotate(u)) -> member(ordered_pair(ordered_pair(universal_class,rest_of(singleton(singleton(ordinal_numbers)))),ordinal_numbers),u)*. % 300.04/300.41 195384[8:Res:27189.1,124881.0] || subclass(rest_relation,rotate(rest_of(u))) -> member(ordered_pair(v,rest_of(ordered_pair(w,v))),cantor(u))*. % 300.04/300.41 195386[0:Res:27189.1,15.0] || subclass(rest_relation,rotate(cross_product(u,v)))* -> member(ordered_pair(w,rest_of(ordered_pair(x,w))),u)*. % 300.04/300.41 195547[19:SpL:27.0,194014.1] || subclass(domain_relation,flip(intersection(complement(u),complement(v))))* subclass(domain_relation,union(u,v)) -> . % 300.04/300.41 195555[19:SpL:167200.0,194014.1] || subclass(domain_relation,flip(image(element_relation,symmetrization_of(ordinal_numbers))))* subclass(domain_relation,power_class(complement(inverse(ordinal_numbers)))) -> . % 300.04/300.41 195556[19:SpL:180125.0,194014.1] || subclass(domain_relation,flip(image(element_relation,singleton(ordinal_numbers))))* subclass(domain_relation,power_class(complement(singleton(ordinal_numbers)))) -> . % 300.04/300.41 195620[19:Res:7.1,168375.0] || equal(u,omega) subclass(u,v)* -> equal(integer_of(w),ordinal_numbers) member(w,v)*. % 300.04/300.41 195641[0:Res:16913.1,11848.0] || subclass(symmetrization_of(u),v)* well_ordering(universal_class,v) -> subclass(symmetric_difference(u,inverse(u)),w)*. % 300.04/300.41 195657[0:Obv:195648.1] || subclass(symmetric_difference(u,inverse(u)),complement(symmetrization_of(u)))* -> subclass(symmetric_difference(u,inverse(u)),v)*. % 300.04/300.41 195721[19:SpL:27.0,195630.1] || equal(rotate(intersection(complement(u),complement(v))),domain_relation)** equal(union(u,v),domain_relation) -> . % 300.04/300.41 195729[19:SpL:167200.0,195630.1] || equal(rotate(image(element_relation,symmetrization_of(ordinal_numbers))),domain_relation)** equal(power_class(complement(inverse(ordinal_numbers))),domain_relation) -> . % 300.04/300.41 195730[19:SpL:180125.0,195630.1] || equal(rotate(image(element_relation,singleton(ordinal_numbers))),domain_relation)** equal(power_class(complement(singleton(ordinal_numbers))),domain_relation) -> . % 300.04/300.41 195734[0:SpL:27.0,195635.1] || equal(flip(intersection(complement(u),complement(v))),rest_relation)** subclass(universal_class,union(u,v)) -> . % 300.04/300.41 195742[19:SpL:167200.0,195635.1] || equal(flip(image(element_relation,symmetrization_of(ordinal_numbers))),rest_relation) subclass(universal_class,power_class(complement(inverse(ordinal_numbers))))* -> . % 300.04/300.41 195743[19:SpL:180125.0,195635.1] || equal(flip(image(element_relation,singleton(ordinal_numbers))),rest_relation) subclass(universal_class,power_class(complement(singleton(ordinal_numbers))))* -> . % 300.04/300.41 195810[19:Res:167116.0,16224.0] || -> equal(integer_of(not_subclass_element(intersection(complement(omega),u),v)),ordinal_numbers)** subclass(intersection(complement(omega),u),v). % 300.04/300.41 195861[0:Rew:160.0,195769.1] || member(not_subclass_element(symmetric_difference(u,v),w),intersection(u,v))* -> subclass(symmetric_difference(u,v),w). % 300.04/300.41 195911[0:SpL:27.0,195669.1] || equal(rotate(intersection(complement(u),complement(v))),rest_relation)** subclass(universal_class,union(u,v)) -> . % 300.04/300.41 195919[19:SpL:167200.0,195669.1] || equal(rotate(image(element_relation,symmetrization_of(ordinal_numbers))),rest_relation) subclass(universal_class,power_class(complement(inverse(ordinal_numbers))))* -> . % 300.04/300.41 195920[19:SpL:180125.0,195669.1] || equal(rotate(image(element_relation,singleton(ordinal_numbers))),rest_relation) subclass(universal_class,power_class(complement(singleton(ordinal_numbers))))* -> . % 300.04/300.41 195994[19:Res:167116.0,16351.0] || -> equal(integer_of(not_subclass_element(intersection(u,complement(omega)),v)),ordinal_numbers)** subclass(intersection(u,complement(omega)),v). % 300.04/300.41 196052[19:SpL:27.0,195678.1] || equal(rotate(intersection(complement(u),complement(v))),rest_relation)** subclass(domain_relation,union(u,v)) -> . % 300.04/300.41 196060[19:SpL:167200.0,195678.1] || equal(rotate(image(element_relation,symmetrization_of(ordinal_numbers))),rest_relation) subclass(domain_relation,power_class(complement(inverse(ordinal_numbers))))* -> . % 300.04/300.41 196061[19:SpL:180125.0,195678.1] || equal(rotate(image(element_relation,singleton(ordinal_numbers))),rest_relation) subclass(domain_relation,power_class(complement(singleton(ordinal_numbers))))* -> . % 300.04/300.41 196071[19:SpL:27.0,195719.1] || equal(flip(intersection(complement(u),complement(v))),domain_relation)** equal(union(u,v),domain_relation) -> . % 300.04/300.41 196079[19:SpL:167200.0,195719.1] || equal(flip(image(element_relation,symmetrization_of(ordinal_numbers))),domain_relation)** equal(power_class(complement(inverse(ordinal_numbers))),domain_relation) -> . % 300.04/300.41 196080[19:SpL:180125.0,195719.1] || equal(flip(image(element_relation,singleton(ordinal_numbers))),domain_relation)** equal(power_class(complement(singleton(ordinal_numbers))),domain_relation) -> . % 300.04/300.41 196084[19:SpL:27.0,196068.0] || equal(union(u,v),domain_relation) equal(rotate(intersection(complement(u),complement(v))),rest_relation)** -> . % 300.04/300.41 196092[19:SpL:167200.0,196068.0] || equal(power_class(complement(inverse(ordinal_numbers))),domain_relation) equal(rotate(image(element_relation,symmetrization_of(ordinal_numbers))),rest_relation)** -> . % 300.04/300.41 196093[19:SpL:180125.0,196068.0] || equal(power_class(complement(singleton(ordinal_numbers))),domain_relation) equal(rotate(image(element_relation,singleton(ordinal_numbers))),rest_relation)** -> . % 300.04/300.41 196624[19:Res:7.1,167728.0] || equal(u,v)* subclass(u,w)* -> equal(v,ordinal_numbers) member(regular(v),w)*. % 300.04/300.41 196655[19:Res:141.0,167728.0] || subclass(cross_product(universal_class,universal_class),u) -> equal(rest_of(v),ordinal_numbers) member(regular(rest_of(v)),u)*. % 300.04/300.41 196656[19:Res:93.0,167728.0] || subclass(cross_product(universal_class,universal_class),u) -> equal(compose_class(v),ordinal_numbers) member(regular(compose_class(v)),u)*. % 300.04/300.41 196705[19:Rew:167222.1,196664.3] || subclass(complement(u),v)* -> member(w,u)* equal(singleton(w),ordinal_numbers) member(w,v)*. % 300.04/300.41 196794[19:Obv:196779.1] || subclass(complement(union(u,v)),symmetric_difference(u,v))* -> equal(complement(union(u,v)),ordinal_numbers). % 300.04/300.41 196851[19:Res:196731.1,488.0] || subclass(universal_class,intersection(complement(u),complement(v)))* member(regular(element_relation),union(u,v)) -> . % 300.04/300.41 196942[19:Res:144531.1,168251.0] || equal(regular(u),universal_class) member(omega,u)* -> equal(u,ordinal_numbers) member(omega,v)*. % 300.04/300.41 196943[19:Res:2478.1,168251.0] || subclass(universal_class,regular(u))* member(omega,u) -> equal(u,ordinal_numbers) member(omega,v)*. % 300.04/300.41 196983[22:Res:178902.1,168251.0] || equal(regular(u),omega) member(ordinal_numbers,u)* -> equal(u,ordinal_numbers) member(ordinal_numbers,v)*. % 300.04/300.41 196984[22:Res:177171.1,168251.0] || subclass(omega,regular(u))* member(ordinal_numbers,u) -> equal(u,ordinal_numbers) member(ordinal_numbers,v)*. % 300.04/300.41 196986[19:Res:167104.1,168251.0] || subclass(universal_class,regular(u))* member(ordinal_numbers,u) -> equal(u,ordinal_numbers) member(ordinal_numbers,v)*. % 300.04/300.41 196987[19:Res:167087.1,168251.0] || equal(regular(u),universal_class) member(ordinal_numbers,u)* -> equal(u,ordinal_numbers) member(ordinal_numbers,v)*. % 300.04/300.41 197157[19:SpL:196827.0,94.0] || member(regular(element_relation),compose_class(u)) -> equal(compose(u,first(regular(element_relation))),second(regular(element_relation)))**. % 300.04/300.41 197193[19:MRR:197192.1,196720.0] || equal(compose(u,first(regular(element_relation))),second(regular(element_relation)))** -> member(regular(element_relation),compose_class(u)). % 300.04/300.41 199567[25:SoR:197131.0,167213.2] single_valued_class(first(regular(element_relation))) || equal(first(regular(element_relation)),ordinal_numbers) -> member(ordinal_numbers,regular(element_relation))*. % 300.04/300.41 199605[19:Obv:199595.2] || equal(u,v) equal(complement(singleton(v)),universal_class) -> equal(unordered_pair(v,u),ordinal_numbers)**. % 300.04/300.41 200756[8:SpR:125331.0,124905.0] || -> equal(segment(cross_product(u,singleton(v)),w,x),segment(cross_product(w,singleton(x)),u,v))*. % 300.04/300.41 202109[26:Rew:167055.0,202108.1] inductive(inverse(subset_relation)) || well_ordering(u,universal_class) -> member(least(u,inverse(ordinal_numbers)),inverse(ordinal_numbers))*. % 300.04/300.41 202780[19:SpR:197859.1,4121.0] || subclass(complement(restrict(u,v,w)),ordinal_numbers)* -> equal(symmetric_difference(cross_product(v,w),u),ordinal_numbers). % 300.04/300.41 202781[19:SpR:197859.1,4119.0] || subclass(complement(restrict(u,v,w)),ordinal_numbers)* -> equal(symmetric_difference(u,cross_product(v,w)),ordinal_numbers). % 300.04/300.41 203579[26:Res:178902.1,202277.1] || equal(complement(compose(complement(element_relation),inverse(element_relation))),omega)** member(ordinal_numbers,cross_product(universal_class,universal_class)) -> . % 300.04/300.41 203580[26:Res:177171.1,202277.1] || subclass(omega,complement(compose(complement(element_relation),inverse(element_relation))))* member(ordinal_numbers,cross_product(universal_class,universal_class)) -> . % 300.04/300.41 203628[0:Res:7.1,16468.0] || equal(restrict(u,v,w),x)* -> subclass(x,y) member(not_subclass_element(x,y),u)*. % 300.04/300.41 204497[19:SpL:196827.0,204394.0] || subclass(universal_class,regular(element_relation)) -> equal(unordered_pair(first(regular(element_relation)),singleton(second(regular(element_relation)))),omega)**. % 300.04/300.41 204603[12:Res:12015.1,99368.1] || equal(complement(complement(cross_product(universal_class,universal_class))),universal_class)** equal(sum_class(range_of(singleton(u))),u)** -> . % 300.04/300.41 206100[0:Res:37525.2,5467.1] || member(u,universal_class) equal(successor(singleton(u)),u)** subclass(universal_class,complement(successor_relation))* -> . % 300.04/300.41 206102[2:Res:37525.2,188593.1] || member(u,universal_class) equal(successor(singleton(u)),u)** equal(complement(successor_relation),universal_class) -> . % 300.04/300.41 206127[19:Res:52.1,167954.0] inductive(image(element_relation,complement(u))) || member(v,power_class(u))* -> equal(integer_of(v),ordinal_numbers). % 300.04/300.41 206268[0:SpL:27838.0,6437.0] || subclass(universal_class,symmetric_difference(complement(u),complement(singleton(u))))* -> member(unordered_pair(v,w),successor(u))*. % 300.04/300.41 206494[0:Rew:206400.0,137007.0] || -> subclass(complement(union(u,image(element_relation,power_class(v)))),intersection(complement(u),power_class(complement(power_class(v)))))*. % 300.04/300.41 206500[19:Rew:206400.0,205254.0] || equal(intersection(complement(u),power_class(complement(power_class(v)))),union(u,image(element_relation,power_class(v))))** -> . % 300.04/300.41 206718[19:Rew:206400.0,196870.0] || subclass(universal_class,power_class(complement(power_class(u)))) member(regular(element_relation),image(element_relation,power_class(u)))* -> . % 300.04/300.41 206719[0:Rew:206400.0,195917.1] || equal(rotate(image(element_relation,power_class(u))),rest_relation) subclass(universal_class,power_class(complement(power_class(u))))* -> . % 300.04/300.41 206720[0:Rew:206400.0,195740.1] || equal(flip(image(element_relation,power_class(u))),rest_relation) subclass(universal_class,power_class(complement(power_class(u))))* -> . % 300.04/300.41 206721[19:Rew:206400.0,185764.1] || equal(rotate(image(element_relation,power_class(u))),domain_relation) subclass(universal_class,power_class(complement(power_class(u))))* -> . % 300.04/300.41 206722[19:Rew:206400.0,185743.1] || equal(flip(image(element_relation,power_class(u))),domain_relation) subclass(universal_class,power_class(complement(power_class(u))))* -> . % 300.04/300.41 206729[0:Rew:206400.0,154816.0] || subclass(universal_class,power_class(complement(power_class(u)))) member(singleton(v),image(element_relation,power_class(u)))* -> . % 300.04/300.41 206761[0:Rew:206400.0,137019.0] || -> subclass(complement(union(image(element_relation,power_class(u)),v)),intersection(power_class(complement(power_class(u))),complement(v)))*. % 300.04/300.41 206767[19:Rew:206400.0,204915.0] || equal(intersection(power_class(complement(power_class(u))),complement(v)),union(image(element_relation,power_class(u)),v))** -> . % 300.04/300.41 206883[19:Rew:206400.0,196058.1] || equal(rotate(image(element_relation,power_class(u))),rest_relation) subclass(domain_relation,power_class(complement(power_class(u))))* -> . % 300.04/300.41 206884[19:Rew:206400.0,195553.1] || subclass(domain_relation,flip(image(element_relation,power_class(u))))* subclass(domain_relation,power_class(complement(power_class(u)))) -> . % 300.04/300.41 206885[19:Rew:206400.0,195208.1] || subclass(domain_relation,rotate(image(element_relation,power_class(u))))* subclass(domain_relation,power_class(complement(power_class(u)))) -> . % 300.04/300.41 206890[19:Rew:206400.0,196090.0] || equal(power_class(complement(power_class(u))),domain_relation) equal(rotate(image(element_relation,power_class(u))),rest_relation)** -> . % 300.04/300.41 206891[19:Rew:206400.0,196077.1] || equal(flip(image(element_relation,power_class(u))),domain_relation)** equal(power_class(complement(power_class(u))),domain_relation) -> . % 300.04/300.41 206892[19:Rew:206400.0,195727.1] || equal(rotate(image(element_relation,power_class(u))),domain_relation)** equal(power_class(complement(power_class(u))),domain_relation) -> . % 300.04/300.41 206919[22:Rew:206400.0,182774.1] || equal(image(element_relation,power_class(u)),omega)** equal(power_class(complement(power_class(u))),singleton(ordinal_numbers)) -> . % 300.04/300.41 206921[19:Rew:206400.0,169476.0] || equal(power_class(complement(power_class(u))),singleton(ordinal_numbers)) member(ordinal_numbers,image(element_relation,power_class(u)))* -> . % 300.04/300.41 206928[22:Rew:206400.0,182334.1] || equal(image(element_relation,power_class(u)),singleton(ordinal_numbers))** equal(power_class(complement(power_class(u))),omega) -> . % 300.04/300.41 206938[20:Rew:206400.0,187593.1] || subclass(universal_class,image(element_relation,power_class(u))) subclass(symmetrization_of(ordinal_numbers),power_class(complement(power_class(u))))* -> . % 300.04/300.41 206947[19:Rew:206400.0,187461.0] || subclass(singleton(ordinal_numbers),power_class(complement(power_class(u))))* member(ordinal_numbers,image(element_relation,power_class(u))) -> . % 300.04/300.41 206966[19:Rew:206400.0,205283.0] || subclass(power_class(complement(power_class(u))),ordinal_numbers) -> equal(union(v,image(element_relation,power_class(u))),universal_class)**. % 300.04/300.41 206967[19:Rew:206400.0,204944.0] || subclass(power_class(complement(power_class(u))),ordinal_numbers) -> equal(union(image(element_relation,power_class(u)),v),universal_class)**. % 300.04/300.41 207104[19:Rew:206400.0,203744.0] || -> equal(intersection(successor(complement(power_class(u))),intersection(power_class(u),complement(singleton(complement(power_class(u)))))),ordinal_numbers)**. % 300.04/300.41 207105[19:Rew:206400.0,203746.0] || -> equal(symmetric_difference(successor(complement(power_class(u))),intersection(power_class(u),complement(singleton(complement(power_class(u)))))),universal_class)**. % 300.04/300.41 207213[19:Rew:206400.0,204093.0] || -> equal(intersection(symmetrization_of(complement(power_class(u))),intersection(power_class(u),complement(inverse(complement(power_class(u)))))),ordinal_numbers)**. % 300.04/300.41 207214[19:Rew:206400.0,204095.0] || -> equal(symmetric_difference(symmetrization_of(complement(power_class(u))),intersection(power_class(u),complement(inverse(complement(power_class(u)))))),universal_class)**. % 300.04/300.41 207315[19:Rew:206400.0,186393.1] || subclass(omega,power_class(u)) member(v,complement(power_class(u)))* -> equal(integer_of(v),ordinal_numbers). % 300.04/300.41 207389[19:Rew:206400.0,207042.0] || equal(complement(complement(singleton(complement(power_class(u))))),universal_class)** -> equal(successor(complement(power_class(u))),universal_class). % 300.04/300.41 207390[19:Rew:206400.0,207150.0] || equal(complement(complement(inverse(complement(power_class(u))))),universal_class)** -> equal(symmetrization_of(complement(power_class(u))),universal_class). % 300.04/300.41 207855[0:SpL:206407.0,16102.0] || member(u,symmetric_difference(power_class(v),complement(w)))* -> member(u,union(complement(power_class(v)),w)). % 300.04/300.41 207872[0:SpL:206407.0,16102.0] || member(u,symmetric_difference(complement(v),power_class(w)))* -> member(u,union(v,complement(power_class(w)))). % 300.04/300.41 207975[19:MRR:169614.1,207974.0] || well_ordering(u,complement(inverse(ordinal_numbers))) -> member(least(u,complement(symmetrization_of(ordinal_numbers))),complement(symmetrization_of(ordinal_numbers)))*. % 300.04/300.41 207977[19:MRR:182885.2,207974.0] || member(apply(choice,complement(symmetrization_of(ordinal_numbers))),inverse(ordinal_numbers))* member(complement(symmetrization_of(ordinal_numbers)),universal_class) -> . % 300.04/300.41 208209[19:SpR:206403.0,204449.1] || equal(intersection(complement(u),power_class(v)),ordinal_numbers)** -> equal(union(u,complement(power_class(v))),universal_class). % 300.04/300.41 208249[19:SpR:206403.0,197499.0] || -> equal(intersection(union(u,complement(power_class(v))),intersection(intersection(complement(u),power_class(v)),w)),ordinal_numbers)**. % 300.04/300.41 208250[19:SpR:206403.0,197702.0] || -> equal(intersection(union(u,complement(power_class(v))),intersection(w,intersection(complement(u),power_class(v)))),ordinal_numbers)**. % 300.04/300.41 208263[0:SpR:206403.0,95593.1] || -> member(u,intersection(complement(v),power_class(w))) subclass(singleton(u),union(v,complement(power_class(w))))*. % 300.04/300.41 208300[0:SpR:149012.1,206403.0] || subclass(power_class(u),complement(v)) -> equal(union(v,complement(power_class(u))),complement(power_class(u)))**. % 300.04/300.41 208306[19:SpL:206403.0,188653.0] || equal(union(u,complement(power_class(v))),universal_class) -> equal(intersection(complement(u),power_class(v)),ordinal_numbers)**. % 300.04/300.41 208312[8:SpL:206403.0,85097.1] inductive(intersection(complement(u),power_class(v))) || equal(union(u,complement(power_class(v))),universal_class)** -> . % 300.04/300.41 208348[19:SpL:206403.0,167091.0] || well_ordering(universal_class,union(u,complement(power_class(v))))* -> member(ordinal_numbers,intersection(complement(u),power_class(v))). % 300.04/300.41 208356[22:SpL:206403.0,178292.1] inductive(intersection(complement(u),power_class(v))) || equal(union(u,complement(power_class(v))),omega)** -> . % 300.04/300.41 208373[19:SpL:206403.0,203423.0] || subclass(union(u,complement(power_class(v))),ordinal_numbers) -> member(omega,intersection(complement(u),power_class(v)))*. % 300.04/300.41 208374[19:SpL:206403.0,203422.0] || subclass(union(u,complement(power_class(v))),ordinal_numbers) -> member(ordinal_numbers,intersection(complement(u),power_class(v)))*. % 300.04/300.41 208423[0:Rew:27.0,208274.0] || -> equal(union(u,complement(complement(image(element_relation,successor(v))))),union(u,image(element_relation,successor(v))))**. % 300.04/300.41 208424[0:Rew:27.0,208275.0] || -> equal(union(u,complement(complement(image(element_relation,symmetrization_of(v))))),union(u,image(element_relation,symmetrization_of(v))))**. % 300.04/300.41 208430[25:MRR:208429.2,192574.0] single_valued_class(intersection(complement(u),power_class(v))) || equal(union(u,complement(power_class(v))),universal_class)** -> . % 300.04/300.41 208516[19:SpR:206410.0,204449.1] || equal(intersection(power_class(u),complement(v)),ordinal_numbers)** -> equal(union(complement(power_class(u)),v),universal_class). % 300.04/300.41 208556[19:SpR:206410.0,197499.0] || -> equal(intersection(union(complement(power_class(u)),v),intersection(intersection(power_class(u),complement(v)),w)),ordinal_numbers)**. % 300.04/300.41 208557[19:SpR:206410.0,197702.0] || -> equal(intersection(union(complement(power_class(u)),v),intersection(w,intersection(power_class(u),complement(v)))),ordinal_numbers)**. % 300.04/300.41 208570[0:SpR:206410.0,95593.1] || -> member(u,intersection(power_class(v),complement(w))) subclass(singleton(u),union(complement(power_class(v)),w))*. % 300.04/300.41 208610[0:SpR:149012.1,206410.0] || subclass(complement(u),power_class(v)) -> equal(union(complement(power_class(v)),u),complement(complement(u)))**. % 300.04/300.41 208616[19:SpL:206410.0,188653.0] || equal(union(complement(power_class(u)),v),universal_class) -> equal(intersection(power_class(u),complement(v)),ordinal_numbers)**. % 300.04/300.41 208622[8:SpL:206410.0,85097.1] inductive(intersection(power_class(u),complement(v))) || equal(union(complement(power_class(u)),v),universal_class)** -> . % 300.04/300.41 208658[19:SpL:206410.0,167091.0] || well_ordering(universal_class,union(complement(power_class(u)),v))* -> member(ordinal_numbers,intersection(power_class(u),complement(v))). % 300.04/300.41 208666[22:SpL:206410.0,178292.1] inductive(intersection(power_class(u),complement(v))) || equal(union(complement(power_class(u)),v),omega)** -> . % 300.04/300.41 208683[19:SpL:206410.0,203423.0] || subclass(union(complement(power_class(u)),v),ordinal_numbers) -> member(omega,intersection(power_class(u),complement(v)))*. % 300.04/300.41 208684[19:SpL:206410.0,203422.0] || subclass(union(complement(power_class(u)),v),ordinal_numbers) -> member(ordinal_numbers,intersection(power_class(u),complement(v)))*. % 300.04/300.41 208731[0:Rew:27.0,208597.0] || -> equal(union(complement(complement(image(element_relation,successor(u)))),v),union(image(element_relation,successor(u)),v))**. % 300.04/300.41 208732[0:Rew:27.0,208598.0] || -> equal(union(complement(complement(image(element_relation,symmetrization_of(u)))),v),union(image(element_relation,symmetrization_of(u)),v))**. % 300.04/300.41 208738[25:MRR:208737.2,192574.0] single_valued_class(intersection(power_class(u),complement(v))) || equal(union(complement(power_class(u)),v),universal_class)** -> . % 300.04/300.41 208833[19:Res:205520.1,15076.1] || equal(complement(intersection(u,v)),ordinal_numbers)** member(w,universal_class) -> member(power_class(w),u)*. % 300.04/300.41 208834[19:Res:205520.1,15077.1] || equal(complement(intersection(u,v)),ordinal_numbers)** member(w,universal_class) -> member(power_class(w),v)*. % 300.04/300.41 208835[19:Res:205520.1,15110.1] || equal(complement(intersection(u,v)),ordinal_numbers)** member(w,universal_class) -> member(sum_class(w),u)*. % 300.04/300.41 208836[19:Res:205520.1,15111.1] || equal(complement(intersection(u,v)),ordinal_numbers)** member(w,universal_class) -> member(sum_class(w),v)*. % 300.04/300.41 208838[19:Res:205520.1,16150.0] || equal(complement(restrict(u,v,w)),ordinal_numbers)** -> member(unordered_pair(x,y),cross_product(v,w))*. % 300.04/300.41 209111[0:Res:2479.1,206404.0] || subclass(universal_class,image(element_relation,power_class(u))) member(singleton(v),power_class(complement(power_class(u))))* -> . % 300.04/300.41 209155[19:Res:169181.1,206404.0] || equal(image(element_relation,power_class(u)),singleton(ordinal_numbers)) member(ordinal_numbers,power_class(complement(power_class(u))))* -> . % 300.04/300.41 209163[19:Res:196731.1,206404.0] || subclass(universal_class,image(element_relation,power_class(u))) member(regular(element_relation),power_class(complement(power_class(u))))* -> . % 300.04/300.41 209194[0:SpR:206403.0,206400.0] || -> equal(image(element_relation,union(u,complement(power_class(v)))),complement(power_class(intersection(complement(u),power_class(v)))))**. % 300.04/300.41 209195[0:SpR:206410.0,206400.0] || -> equal(image(element_relation,union(complement(power_class(u)),v)),complement(power_class(intersection(power_class(u),complement(v)))))**. % 300.04/300.41 209493[19:SpL:206403.0,208786.0] || equal(union(u,complement(power_class(v))),ordinal_numbers) -> equal(intersection(complement(u),power_class(v)),universal_class)**. % 300.04/300.41 209494[19:SpL:206410.0,208786.0] || equal(union(complement(power_class(u)),v),ordinal_numbers) -> equal(intersection(power_class(u),complement(v)),universal_class)**. % 300.04/300.41 209515[19:SpL:5132.1,208803.0] || equal(complement(complement(not_subclass_element(cross_product(u,v),w))),ordinal_numbers)** -> subclass(cross_product(u,v),w). % 300.04/300.41 209742[19:SpL:5132.1,203430.0] || subclass(unordered_pair(u,not_subclass_element(cross_product(v,w),x)),ordinal_numbers)* -> subclass(cross_product(v,w),x). % 300.04/300.41 209824[19:MRR:209766.1,167011.0] || equal(rest_relation,domain_relation) subclass(rest_relation,complement(u)) member(ordered_pair(ordinal_numbers,ordinal_numbers),u)* -> . % 300.04/300.41 209825[19:MRR:209767.1,53.0] || equal(rest_relation,domain_relation) subclass(rest_relation,complement(u)) member(ordered_pair(omega,ordinal_numbers),u)* -> . % 300.04/300.41 209845[0:MRR:209844.0,149603.1] || equal(rest_of(u),successor(u)) member(u,universal_class)* subclass(rest_relation,complement(successor_relation))* -> . % 300.04/300.41 209856[19:SpL:5132.1,203433.0] || subclass(unordered_pair(not_subclass_element(cross_product(u,v),w),x),ordinal_numbers)* -> subclass(cross_product(u,v),w). % 300.04/300.41 210100[19:SpL:5132.1,205945.0] || equal(unordered_pair(u,not_subclass_element(cross_product(v,w),x)),ordinal_numbers)** -> subclass(cross_product(v,w),x). % 300.04/300.41 210118[19:SpL:5132.1,205947.0] || equal(unordered_pair(not_subclass_element(cross_product(u,v),w),x),ordinal_numbers)** -> subclass(cross_product(u,v),w). % 300.04/300.41 210132[0:SpR:27168.2,144504.0] || member(u,universal_class) subclass(rest_relation,rest_of(universal_class))* -> equal(cross_product(u,universal_class),rest_of(u))**. % 300.04/300.41 210137[0:SpR:27168.2,16283.0] || member(u,universal_class) subclass(rest_relation,rest_of(v))* -> subclass(rest_of(u),cross_product(u,universal_class))*. % 300.04/300.41 210267[0:SpL:27837.0,6437.0] || subclass(universal_class,symmetric_difference(complement(u),complement(inverse(u))))* -> member(unordered_pair(v,w),symmetrization_of(u))*. % 300.04/300.41 210382[0:Res:31137.2,6476.1] || member(u,universal_class)* equal(rest_of(u),successor(u)) subclass(universal_class,complement(successor_relation))* -> . % 300.04/300.41 210385[2:Res:31137.2,188593.1] || member(u,universal_class)* equal(rest_of(u),successor(u)) equal(complement(successor_relation),universal_class) -> . % 300.04/300.41 210853[19:Res:176326.2,205934.1] || member(u,universal_class) equal(compose(v,u),ordinal_numbers)** equal(compose_class(v),ordinal_numbers) -> . % 300.04/300.41 210891[19:Res:170.0,177022.0] || -> member(singleton(u),image(universal_class,singleton(singleton(u))))* asymmetric(cross_product(singleton(singleton(u)),universal_class),v)*. % 300.04/300.41 210952[19:Res:196718.0,177022.0] || -> member(regular(element_relation),image(universal_class,singleton(regular(element_relation))))* asymmetric(cross_product(singleton(regular(element_relation)),universal_class),u)*. % 300.04/300.41 211631[19:Res:203424.1,16102.0] || subclass(complement(symmetric_difference(complement(u),complement(v))),ordinal_numbers)* -> member(singleton(w),union(u,v))*. % 300.04/300.41 211636[19:Res:203424.1,9.0] || subclass(complement(unordered_pair(u,v)),ordinal_numbers)* -> equal(singleton(w),v)* equal(singleton(w),u)*. % 300.04/300.41 211652[19:Res:203424.1,36025.1] || subclass(complement(u),ordinal_numbers) member(u,universal_class) -> member(singleton(singleton(singleton(u))),element_relation)*. % 300.04/300.41 211686[19:Rew:206408.0,211642.0] || subclass(power_class(complement(power_class(u))),ordinal_numbers) member(singleton(v),power_class(complement(power_class(u))))* -> . % 300.04/300.41 211924[19:SpR:205896.1,4121.0] || equal(complement(restrict(u,v,w)),ordinal_numbers) -> equal(symmetric_difference(cross_product(v,w),u),ordinal_numbers)**. % 300.04/300.41 211925[19:SpR:205896.1,4119.0] || equal(complement(restrict(u,v,w)),ordinal_numbers) -> equal(symmetric_difference(u,cross_product(v,w)),ordinal_numbers)**. % 300.04/300.41 212443[19:Res:205991.1,16102.0] || equal(complement(symmetric_difference(complement(u),complement(v))),ordinal_numbers)** -> member(singleton(w),union(u,v))*. % 300.04/300.41 212448[19:Res:205991.1,9.0] || equal(complement(unordered_pair(u,v)),ordinal_numbers)** -> equal(singleton(w),v)* equal(singleton(w),u)*. % 300.04/300.41 212464[19:Res:205991.1,36025.1] || equal(complement(u),ordinal_numbers) member(u,universal_class) -> member(singleton(singleton(singleton(u))),element_relation)*. % 300.04/300.41 212496[19:Rew:206408.0,212454.0] || equal(power_class(complement(power_class(u))),ordinal_numbers) member(singleton(v),power_class(complement(power_class(u))))* -> . % 300.04/300.41 212497[19:Rew:207991.1,212458.2,208507.1,212458.1] || equal(complement(ordered_pair(u,v)),ordinal_numbers)** -> equal(singleton(w),omega)** equal(singleton(w),ordinal_numbers). % 300.04/300.41 212597[19:Rew:16826.0,212552.0] || equal(complement(image(element_relation,successor(u))),ordinal_numbers) -> subclass(complement(image(element_relation,successor(u))),v)*. % 300.04/300.41 212598[19:Rew:16825.0,212553.0] || equal(complement(image(element_relation,symmetrization_of(u))),ordinal_numbers) -> subclass(complement(image(element_relation,symmetrization_of(u))),v)*. % 300.04/300.41 212611[19:Rew:16826.0,212604.0] || equal(complement(image(element_relation,successor(u))),ordinal_numbers) -> asymmetric(complement(image(element_relation,successor(u))),v)*. % 300.04/300.41 212612[19:Rew:16825.0,212605.0] || equal(complement(image(element_relation,symmetrization_of(u))),ordinal_numbers) -> asymmetric(complement(image(element_relation,symmetrization_of(u))),v)*. % 300.04/300.41 212730[19:Rew:142500.0,212615.0,167055.0,212615.0] || -> equal(symmetric_difference(complement(u),restrict(u,v,w)),union(complement(u),restrict(u,v,w)))**. % 300.04/300.41 213169[19:Rew:44.0,213135.1] || member(regular(successor(u)),intersection(complement(u),complement(singleton(u))))* -> equal(successor(u),ordinal_numbers). % 300.04/300.41 213170[19:Rew:114.0,213136.1] || member(regular(symmetrization_of(u)),intersection(complement(u),complement(inverse(u))))* -> equal(symmetrization_of(u),ordinal_numbers). % 300.04/300.41 213206[19:Res:52.1,168498.0] inductive(compose_class(u)) || -> equal(integer_of(ordered_pair(v,w)),ordinal_numbers)** equal(compose(u,v),w)*. % 300.04/300.41 213276[19:SpR:209197.0,27.0] || -> equal(complement(intersection(image(element_relation,singleton(ordinal_numbers)),complement(u))),union(power_class(complement(singleton(ordinal_numbers))),u))**. % 300.04/300.41 213278[19:SpR:209197.0,135266.0] || -> subclass(complement(union(power_class(complement(singleton(ordinal_numbers))),u)),intersection(image(element_relation,singleton(ordinal_numbers)),complement(u)))*. % 300.04/300.41 213329[19:SpR:209197.0,27.0] || -> equal(complement(intersection(complement(u),image(element_relation,singleton(ordinal_numbers)))),union(u,power_class(complement(singleton(ordinal_numbers)))))**. % 300.04/300.41 213331[19:SpR:209197.0,135266.0] || -> subclass(complement(union(u,power_class(complement(singleton(ordinal_numbers))))),intersection(complement(u),image(element_relation,singleton(ordinal_numbers))))*. % 300.04/300.41 213365[19:SpL:209197.0,195669.1] || equal(rotate(power_class(complement(singleton(ordinal_numbers)))),rest_relation) subclass(universal_class,image(element_relation,singleton(ordinal_numbers)))* -> . % 300.04/300.41 213366[19:SpL:209197.0,195635.1] || equal(flip(power_class(complement(singleton(ordinal_numbers)))),rest_relation) subclass(universal_class,image(element_relation,singleton(ordinal_numbers)))* -> . % 300.04/300.41 213367[19:SpL:209197.0,185733.1] || equal(rotate(power_class(complement(singleton(ordinal_numbers)))),domain_relation) subclass(universal_class,image(element_relation,singleton(ordinal_numbers)))* -> . % 300.04/300.41 213368[19:SpL:209197.0,185656.1] || equal(flip(power_class(complement(singleton(ordinal_numbers)))),domain_relation) subclass(universal_class,image(element_relation,singleton(ordinal_numbers)))* -> . % 300.04/300.41 213385[19:SpL:209197.0,195678.1] || equal(rotate(power_class(complement(singleton(ordinal_numbers)))),rest_relation) subclass(domain_relation,image(element_relation,singleton(ordinal_numbers)))* -> . % 300.04/300.41 213386[19:SpL:209197.0,194014.1] || subclass(domain_relation,flip(power_class(complement(singleton(ordinal_numbers)))))* subclass(domain_relation,image(element_relation,singleton(ordinal_numbers))) -> . % 300.04/300.41 213387[19:SpL:209197.0,194013.1] || subclass(domain_relation,rotate(power_class(complement(singleton(ordinal_numbers)))))* subclass(domain_relation,image(element_relation,singleton(ordinal_numbers))) -> . % 300.04/300.41 213390[19:SpL:209197.0,196068.0] || equal(image(element_relation,singleton(ordinal_numbers)),domain_relation) equal(rotate(power_class(complement(singleton(ordinal_numbers)))),rest_relation)** -> . % 300.04/300.41 213391[19:SpL:209197.0,195719.1] || equal(flip(power_class(complement(singleton(ordinal_numbers)))),domain_relation)** equal(image(element_relation,singleton(ordinal_numbers)),domain_relation) -> . % 300.04/300.41 213392[19:SpL:209197.0,195630.1] || equal(rotate(power_class(complement(singleton(ordinal_numbers)))),domain_relation)** equal(image(element_relation,singleton(ordinal_numbers)),domain_relation) -> . % 300.04/300.41 213415[19:SpL:209197.0,186994.0] || subclass(singleton(ordinal_numbers),image(element_relation,singleton(ordinal_numbers)))* member(ordinal_numbers,power_class(complement(singleton(ordinal_numbers)))) -> . % 300.04/300.41 213416[20:SpL:209197.0,186995.1] || subclass(universal_class,power_class(complement(singleton(ordinal_numbers)))) subclass(symmetrization_of(ordinal_numbers),image(element_relation,singleton(ordinal_numbers)))* -> . % 300.04/300.41 213518[19:SpR:209198.0,27.0] || -> equal(complement(intersection(image(element_relation,symmetrization_of(ordinal_numbers)),complement(u))),union(power_class(complement(inverse(ordinal_numbers))),u))**. % 300.04/300.41 213520[19:SpR:209198.0,135266.0] || -> subclass(complement(union(power_class(complement(inverse(ordinal_numbers))),u)),intersection(image(element_relation,symmetrization_of(ordinal_numbers)),complement(u)))*. % 300.04/300.41 213571[19:SpR:209198.0,27.0] || -> equal(complement(intersection(complement(u),image(element_relation,symmetrization_of(ordinal_numbers)))),union(u,power_class(complement(inverse(ordinal_numbers)))))**. % 300.04/300.41 213573[19:SpR:209198.0,135266.0] || -> subclass(complement(union(u,power_class(complement(inverse(ordinal_numbers))))),intersection(complement(u),image(element_relation,symmetrization_of(ordinal_numbers))))*. % 300.04/300.41 213606[19:SpL:209198.0,195669.1] || equal(rotate(power_class(complement(inverse(ordinal_numbers)))),rest_relation) subclass(universal_class,image(element_relation,symmetrization_of(ordinal_numbers)))* -> . % 300.04/300.41 213607[19:SpL:209198.0,195635.1] || equal(flip(power_class(complement(inverse(ordinal_numbers)))),rest_relation) subclass(universal_class,image(element_relation,symmetrization_of(ordinal_numbers)))* -> . % 300.04/300.41 213608[19:SpL:209198.0,185733.1] || equal(rotate(power_class(complement(inverse(ordinal_numbers)))),domain_relation) subclass(universal_class,image(element_relation,symmetrization_of(ordinal_numbers)))* -> . % 300.04/300.41 213609[19:SpL:209198.0,185656.1] || equal(flip(power_class(complement(inverse(ordinal_numbers)))),domain_relation) subclass(universal_class,image(element_relation,symmetrization_of(ordinal_numbers)))* -> . % 300.04/300.41 213626[19:SpL:209198.0,195678.1] || equal(rotate(power_class(complement(inverse(ordinal_numbers)))),rest_relation) subclass(domain_relation,image(element_relation,symmetrization_of(ordinal_numbers)))* -> . % 300.04/300.41 213627[19:SpL:209198.0,194014.1] || subclass(domain_relation,flip(power_class(complement(inverse(ordinal_numbers)))))* subclass(domain_relation,image(element_relation,symmetrization_of(ordinal_numbers))) -> . % 300.04/300.41 213628[19:SpL:209198.0,194013.1] || subclass(domain_relation,rotate(power_class(complement(inverse(ordinal_numbers)))))* subclass(domain_relation,image(element_relation,symmetrization_of(ordinal_numbers))) -> . % 300.04/300.41 213631[19:SpL:209198.0,196068.0] || equal(image(element_relation,symmetrization_of(ordinal_numbers)),domain_relation) equal(rotate(power_class(complement(inverse(ordinal_numbers)))),rest_relation)** -> . % 300.04/300.41 213632[19:SpL:209198.0,195719.1] || equal(flip(power_class(complement(inverse(ordinal_numbers)))),domain_relation)** equal(image(element_relation,symmetrization_of(ordinal_numbers)),domain_relation) -> . % 300.04/300.41 213633[19:SpL:209198.0,195630.1] || equal(rotate(power_class(complement(inverse(ordinal_numbers)))),domain_relation)** equal(image(element_relation,symmetrization_of(ordinal_numbers)),domain_relation) -> . % 300.04/300.41 213656[19:SpL:209198.0,186994.0] || subclass(singleton(ordinal_numbers),image(element_relation,symmetrization_of(ordinal_numbers)))* member(ordinal_numbers,power_class(complement(inverse(ordinal_numbers)))) -> . % 300.04/300.41 213657[20:SpL:209198.0,186995.1] || subclass(universal_class,power_class(complement(inverse(ordinal_numbers)))) subclass(symmetrization_of(ordinal_numbers),image(element_relation,symmetrization_of(ordinal_numbers)))* -> . % 300.04/300.41 214319[19:SpL:196827.0,204401.0] || subclass(universal_class,regular(element_relation))* -> equal(unordered_pair(u,v),omega)** equal(unordered_pair(u,v),ordinal_numbers). % 300.04/300.41 214623[19:Res:167106.1,207852.0] inductive(intersection(power_class(u),complement(v))) || member(ordinal_numbers,union(complement(power_class(u)),v))* -> . % 300.04/300.41 214786[19:Res:167106.1,207871.0] inductive(intersection(complement(u),power_class(v))) || member(ordinal_numbers,union(u,complement(power_class(v))))* -> . % 300.04/300.41 214921[19:Res:167106.1,27258.2] inductive(union(u,v)) || member(ordinal_numbers,complement(v))* member(ordinal_numbers,complement(u))* -> . % 300.04/300.41 214982[8:SpR:160282.0,947.0] || -> equal(regular(ordered_pair(u,v)),singleton(u)) member(regular(ordered_pair(u,v)),ordered_pair(u,v))*. % 300.04/300.41 214999[19:SpL:160282.0,203427.0] || subclass(singleton(regular(ordered_pair(u,v))),ordinal_numbers)* -> equal(regular(ordered_pair(u,v)),singleton(u)). % 300.04/300.41 215000[19:SpL:160282.0,204039.0] || equal(singleton(regular(ordered_pair(u,v))),ordinal_numbers)** -> equal(regular(ordered_pair(u,v)),singleton(u)). % 300.04/300.41 215008[18:SpL:160282.0,178134.0] || equal(rest_of(regular(ordered_pair(u,v))),rest_relation)** -> equal(regular(ordered_pair(u,v)),singleton(u)). % 300.04/300.41 215009[8:SpL:160282.0,9784.0] || equal(complement(regular(ordered_pair(u,v))),universal_class)** -> equal(regular(ordered_pair(u,v)),singleton(u)). % 300.04/300.41 215010[8:SpL:160282.0,9732.0] || subclass(universal_class,complement(regular(ordered_pair(u,v))))* -> equal(regular(ordered_pair(u,v)),singleton(u)). % 300.04/300.41 215160[19:MRR:215099.3,215154.1] || well_ordering(u,universal_class) subclass(v,complement(singleton(least(u,v))))* -> equal(v,ordinal_numbers). % 300.04/300.41 215198[19:Res:214528.1,82994.1] || subclass(kind_1_ordinals,complement(compose(element_relation,universal_class)))* member(ordinal_numbers,element_relation) well_ordering(u,v)* -> . % 300.04/300.41 215200[26:Res:214528.1,202277.1] || subclass(kind_1_ordinals,complement(compose(complement(element_relation),inverse(element_relation))))* member(ordinal_numbers,cross_product(universal_class,universal_class)) -> . % 300.04/300.41 215219[19:Res:214528.1,16083.0] || subclass(kind_1_ordinals,symmetric_difference(u,cross_product(v,w))) -> member(ordinal_numbers,complement(restrict(u,v,w)))*. % 300.04/300.41 215224[19:Res:214528.1,16086.0] || subclass(kind_1_ordinals,symmetric_difference(cross_product(u,v),w)) -> member(ordinal_numbers,complement(restrict(w,u,v)))*. % 300.04/300.41 215240[19:Res:214528.1,168251.0] || subclass(kind_1_ordinals,regular(u))* member(ordinal_numbers,u) -> equal(u,ordinal_numbers) member(ordinal_numbers,v)*. % 300.04/300.41 215333[19:Res:167106.1,168249.0] inductive(regular(u)) || member(ordinal_numbers,u)* well_ordering(v,w)* -> equal(u,ordinal_numbers). % 300.04/300.41 215379[19:Res:52.1,168373.0] inductive(unordered_pair(u,v)) || -> equal(integer_of(w),ordinal_numbers)** equal(w,v)* equal(w,u)*. % 300.04/300.41 215408[19:Res:52.1,168434.0] inductive(restrict(u,v,w)) || -> equal(integer_of(x),ordinal_numbers) member(x,cross_product(v,w))*. % 300.04/300.41 215950[23:MRR:215949.1,167176.0] || equal(unordered_pair(u,ordinal_numbers),singleton(u)) -> equal(apply(choice,ordered_pair(u,universal_class)),singleton(u))**. % 300.04/300.41 216815[19:Res:38094.1,214449.0] || member(ordinal_numbers,union(complement(singleton(ordinal_numbers)),u)) -> member(ordinal_numbers,symmetric_difference(complement(singleton(ordinal_numbers)),u))*. % 300.04/300.41 216816[19:Res:38094.1,214471.0] || member(ordinal_numbers,union(u,complement(singleton(ordinal_numbers)))) -> member(ordinal_numbers,symmetric_difference(u,complement(singleton(ordinal_numbers))))*. % 300.04/300.41 217426[19:Rew:167193.0,217313.1] || subclass(inverse(ordinal_numbers),u) -> subclass(symmetrization_of(ordinal_numbers),v) member(not_subclass_element(symmetrization_of(ordinal_numbers),v),u)*. % 300.04/300.41 217466[19:MRR:217332.2,210986.0] || subclass(u,complement(singleton(not_subclass_element(intersection(u,v),w))))* -> subclass(intersection(u,v),w). % 300.04/300.41 217871[0:Res:217683.0,8.0] || subclass(u,intersection(intersection(v,u),w))* -> equal(intersection(intersection(v,u),w),u). % 300.04/300.41 218033[0:Res:217853.0,8.0] || subclass(u,complement(complement(intersection(v,u))))* -> equal(complement(complement(intersection(v,u))),u). % 300.04/300.41 218384[0:SpR:479.0,218022.0] || -> subclass(complement(union(u,image(element_relation,union(v,w)))),power_class(intersection(complement(v),complement(w))))*. % 300.04/300.41 218421[0:Res:218022.0,8.0] || subclass(complement(u),complement(union(v,u)))* -> equal(complement(union(v,u)),complement(u)). % 300.04/300.41 218451[19:Res:218408.0,8.0] || subclass(complement(image(successor_relation,ordinal_numbers)),complement(kind_1_ordinals))* -> equal(complement(image(successor_relation,ordinal_numbers)),complement(kind_1_ordinals)). % 300.04/300.41 218470[0:Res:218395.0,8.0] || subclass(complement(singleton(u)),complement(successor(u)))* -> equal(complement(successor(u)),complement(singleton(u))). % 300.04/300.41 218489[0:Res:218396.0,8.0] || subclass(complement(inverse(u)),complement(symmetrization_of(u)))* -> equal(complement(symmetrization_of(u)),complement(inverse(u))). % 300.04/300.41 218702[19:MRR:218569.2,210986.0] || subclass(u,complement(singleton(not_subclass_element(intersection(v,u),w))))* -> subclass(intersection(v,u),w). % 300.04/300.41 218813[0:Res:217850.0,8.0] || subclass(u,intersection(v,intersection(w,u)))* -> equal(intersection(v,intersection(w,u)),u). % 300.04/300.41 218989[0:Res:218280.0,8.0] || subclass(u,intersection(intersection(u,v),w))* -> equal(intersection(intersection(u,v),w),u). % 300.04/300.41 219100[19:Res:218952.0,8.0] || subclass(inverse(ordinal_numbers),intersection(symmetrization_of(ordinal_numbers),u))* -> equal(intersection(symmetrization_of(ordinal_numbers),u),inverse(ordinal_numbers)). % 300.04/300.41 219373[19:Res:219080.0,8.0] || subclass(inverse(ordinal_numbers),complement(complement(symmetrization_of(ordinal_numbers))))* -> equal(complement(complement(symmetrization_of(ordinal_numbers))),inverse(ordinal_numbers)). % 300.04/300.41 219403[19:Res:219077.0,8.0] || subclass(inverse(ordinal_numbers),intersection(u,symmetrization_of(ordinal_numbers)))* -> equal(intersection(u,symmetrization_of(ordinal_numbers)),inverse(ordinal_numbers)). % 300.04/300.41 219720[0:Res:218920.0,8.0] || subclass(u,intersection(complement(complement(u)),v))* -> equal(intersection(complement(complement(u)),v),u). % 300.04/300.41 219970[0:Res:219703.0,8.0] || subclass(u,complement(complement(complement(complement(u)))))* -> equal(complement(complement(complement(complement(u)))),u). % 300.04/300.41 220043[0:Res:52.1,16462.0] inductive(u) || subclass(u,v)* -> subclass(omega,w) member(not_subclass_element(omega,w),v)*. % 300.04/300.41 220206[0:Res:218971.0,8.0] || subclass(u,complement(complement(intersection(u,v))))* -> equal(complement(complement(intersection(u,v))),u). % 300.04/300.41 220348[0:Res:219700.0,8.0] || subclass(u,intersection(v,complement(complement(u))))* -> equal(intersection(v,complement(complement(u))),u). % 300.04/300.41 220415[0:SpR:479.0,220194.0] || -> subclass(complement(union(image(element_relation,union(u,v)),w)),power_class(intersection(complement(u),complement(v))))*. % 300.04/300.41 220453[0:Res:220194.0,8.0] || subclass(complement(u),complement(union(u,v)))* -> equal(complement(union(u,v)),complement(u)). % 300.04/300.41 220478[19:Res:220439.0,167728.0] || subclass(complement(singleton(ordinal_numbers)),u) -> equal(complement(kind_1_ordinals),ordinal_numbers) member(regular(complement(kind_1_ordinals)),u)*. % 300.04/300.41 220653[0:Res:218968.0,8.0] || subclass(u,intersection(v,intersection(u,w)))* -> equal(intersection(v,intersection(u,w)),u). % 300.04/300.41 221244[19:SpR:27168.2,219075.0] || member(u,universal_class) subclass(rest_relation,rest_of(symmetrization_of(ordinal_numbers))) -> subclass(rest_of(u),inverse(ordinal_numbers))*. % 300.04/300.41 221570[19:Res:219766.1,16465.0] || equal(complement(intersection(u,v)),ordinal_numbers)** -> subclass(w,x) member(not_subclass_element(w,x),u)*. % 300.04/300.41 221571[19:Res:219766.1,16466.0] || equal(complement(intersection(u,v)),ordinal_numbers)** -> subclass(w,x) member(not_subclass_element(w,x),v)*. % 300.04/300.41 221576[19:Res:219766.1,167733.0] || equal(complement(restrict(u,v,w)),ordinal_numbers)** -> equal(x,ordinal_numbers) member(regular(x),u)*. % 300.04/300.41 221794[19:Res:219766.1,1070.1] inductive(u) || equal(complement(image(successor_relation,u)),ordinal_numbers)** -> equal(image(successor_relation,u),u). % 300.04/300.41 221796[19:Res:219766.1,169641.1] || equal(complement(image(u,singleton(v))),ordinal_numbers) well_ordering(element_relation,image(u,singleton(v)))* -> . % 300.04/300.41 221968[19:Res:219766.1,168435.0] || equal(complement(restrict(u,v,w)),ordinal_numbers)** -> equal(integer_of(x),ordinal_numbers) member(x,u)*. % 300.04/300.41 222017[19:Rew:221866.1,214998.1] || equal(complement(complement(singleton(regular(ordered_pair(u,v))))),ordinal_numbers)** -> equal(regular(ordinal_numbers),singleton(u)). % 300.04/300.41 222241[0:SpR:27168.2,217976.0] || member(u,universal_class) subclass(rest_relation,rest_of(v)) -> subclass(complement(complement(rest_of(u))),v)*. % 300.04/300.41 222316[0:SpR:206403.0,219698.0] || -> subclass(restrict(complement(union(u,complement(power_class(v)))),w,x),intersection(complement(u),power_class(v)))*. % 300.04/300.41 222317[0:SpR:206410.0,219698.0] || -> subclass(restrict(complement(union(complement(power_class(u)),v)),w,x),intersection(power_class(u),complement(v)))*. % 300.04/300.41 222338[0:SpR:27168.2,219698.0] || member(u,universal_class) subclass(rest_relation,rest_of(complement(complement(v))))* -> subclass(rest_of(u),v)*. % 300.04/300.41 222404[0:SpR:27168.2,217800.0] || member(u,universal_class) subclass(rest_relation,rest_of(v)) -> subclass(intersection(rest_of(u),w),v)*. % 300.04/300.41 222553[0:SpR:27168.2,217848.0] || member(u,universal_class) subclass(rest_relation,rest_of(intersection(v,w)))* -> subclass(rest_of(u),w)*. % 300.04/300.41 222649[0:SpR:27168.2,218740.0] || member(u,universal_class) subclass(rest_relation,rest_of(v)) -> subclass(intersection(w,rest_of(u)),v)*. % 300.04/300.41 222795[0:SpR:27168.2,218966.0] || member(u,universal_class) subclass(rest_relation,rest_of(intersection(v,w)))* -> subclass(rest_of(u),v)*. % 300.04/300.41 222899[19:Res:219943.0,2497.1] || member(u,universal_class) -> member(u,complement(complement(symmetrization_of(ordinal_numbers))))* member(u,complement(inverse(ordinal_numbers))). % 300.04/300.41 223029[25:SoR:223017.0,167213.2] single_valued_class(regular(complement(complement(symmetrization_of(ordinal_numbers))))) || equal(regular(complement(complement(symmetrization_of(ordinal_numbers)))),ordinal_numbers)** -> . % 300.04/300.41 223130[20:MRR:223117.1,167057.0] || member(u,universal_class) -> equal(apply(regular(complement(complement(symmetrization_of(ordinal_numbers)))),u),sum_class(range_of(ordinal_numbers)))**. % 300.04/300.41 223472[19:Res:218381.0,2497.1] || member(u,universal_class) -> member(u,union(v,complement(inverse(ordinal_numbers))))* member(u,symmetrization_of(ordinal_numbers)). % 300.04/300.41 223663[19:Res:220412.0,2497.1] || member(u,universal_class) -> member(u,union(complement(inverse(ordinal_numbers)),v))* member(u,symmetrization_of(ordinal_numbers)). % 300.04/300.41 223750[19:Res:24.2,217129.1] || member(ordinal_numbers,u) member(ordinal_numbers,v) equal(complement(intersection(v,u)),kind_1_ordinals)** -> . % 300.04/300.41 224052[19:SpL:206403.0,223787.1] inductive(intersection(complement(u),power_class(v))) || equal(union(u,complement(power_class(v))),kind_1_ordinals)** -> . % 300.04/300.41 224053[19:SpL:206410.0,223787.1] inductive(intersection(power_class(u),complement(v))) || equal(union(complement(power_class(u)),v),kind_1_ordinals)** -> . % 300.04/300.41 224142[19:Res:124899.1,219089.0] || section(u,symmetrization_of(ordinal_numbers),v) -> subclass(cantor(restrict(u,v,symmetrization_of(ordinal_numbers))),inverse(ordinal_numbers))*. % 300.04/300.41 224173[20:Res:224149.0,8.0] || subclass(inverse(ordinal_numbers),singleton(regular(symmetrization_of(ordinal_numbers))))* -> equal(singleton(regular(symmetrization_of(ordinal_numbers))),inverse(ordinal_numbers)). % 300.04/300.41 224346[19:Res:224158.0,2497.1] || member(u,universal_class) -> member(u,complement(complement(complement(symmetrization_of(ordinal_numbers)))))* member(u,inverse(ordinal_numbers)). % 300.04/300.41 224558[19:Res:224157.0,2497.1] || member(u,universal_class) -> member(u,complement(intersection(v,symmetrization_of(ordinal_numbers))))* member(u,inverse(ordinal_numbers)). % 300.04/300.41 224613[25:Rew:224611.1,224612.2] function(u) || member(singleton(singleton(singleton(singleton(singleton(ordinal_numbers))))),composition_function)* -> equal(universal_class,u)*. % 300.04/300.41 224654[19:Res:224159.0,2497.1] || member(u,universal_class) -> member(u,complement(intersection(symmetrization_of(ordinal_numbers),v)))* member(u,inverse(ordinal_numbers)). % 300.04/300.41 224881[23:Rew:183840.0,224880.0] || -> equal(cross_product(u,ordinal_numbers),ordinal_numbers) equal(domain__dfg(regular(cross_product(u,ordinal_numbers)),u,universal_class),single_valued3(ordinal_numbers))**. % 300.04/300.41 225281[19:SpL:5132.1,225028.0] || equal(successor(singleton(not_subclass_element(cross_product(u,v),w))),ordinal_numbers)** -> subclass(cross_product(u,v),w). % 300.04/300.41 225358[19:Res:12.0,176248.0] || subclass(domain_relation,u)* subclass(u,v)* -> member(ordered_pair(unordered_pair(w,x),ordinal_numbers),v)*. % 300.04/300.41 225359[19:Res:940.0,176248.0] || subclass(domain_relation,u)* subclass(u,v)* -> member(ordered_pair(ordered_pair(w,x),ordinal_numbers),v)*. % 300.04/300.41 225375[20:Res:175569.0,176248.0] || subclass(domain_relation,u)* subclass(u,v)* -> member(ordered_pair(regular(symmetrization_of(ordinal_numbers)),ordinal_numbers),v)*. % 300.04/300.41 226117[19:SpR:207712.0,205896.1] || equal(union(complement(power_class(u)),v),ordinal_numbers) -> equal(symmetric_difference(power_class(u),complement(v)),ordinal_numbers)**. % 300.04/300.41 226118[19:SpR:207712.0,197859.1] || subclass(union(complement(power_class(u)),v),ordinal_numbers)* -> equal(symmetric_difference(power_class(u),complement(v)),ordinal_numbers). % 300.04/300.41 226210[19:SpL:207712.0,167086.0] || subclass(universal_class,symmetric_difference(power_class(u),complement(v))) -> member(ordinal_numbers,union(complement(power_class(u)),v))*. % 300.04/300.41 226213[0:SpL:207712.0,2539.0] || subclass(universal_class,symmetric_difference(power_class(u),complement(v))) -> member(omega,union(complement(power_class(u)),v))*. % 300.04/300.41 226218[19:SpL:207712.0,167084.0] || equal(symmetric_difference(power_class(u),complement(v)),universal_class) -> member(ordinal_numbers,union(complement(power_class(u)),v))*. % 300.04/300.41 226219[0:SpL:207712.0,6300.0] || equal(symmetric_difference(power_class(u),complement(v)),universal_class) -> member(omega,union(complement(power_class(u)),v))*. % 300.04/300.41 226226[22:SpL:207712.0,177190.0] || subclass(omega,symmetric_difference(power_class(u),complement(v))) -> member(ordinal_numbers,union(complement(power_class(u)),v))*. % 300.04/300.41 226228[22:SpL:207712.0,178812.0] || equal(symmetric_difference(power_class(u),complement(v)),omega) -> member(ordinal_numbers,union(complement(power_class(u)),v))*. % 300.04/300.41 226691[19:SpL:5132.1,225696.0] || equal(symmetrization_of(singleton(not_subclass_element(cross_product(u,v),w))),ordinal_numbers)** -> subclass(cross_product(u,v),w). % 300.04/300.41 227057[19:SpL:160282.0,225699.0] || equal(symmetrization_of(regular(ordered_pair(u,v))),ordinal_numbers)** -> equal(regular(ordered_pair(u,v)),singleton(u)). % 300.04/300.41 227083[19:SpR:207752.0,205896.1] || equal(union(u,complement(power_class(v))),ordinal_numbers) -> equal(symmetric_difference(complement(u),power_class(v)),ordinal_numbers)**. % 300.04/300.41 227084[19:SpR:207752.0,197859.1] || subclass(union(u,complement(power_class(v))),ordinal_numbers)* -> equal(symmetric_difference(complement(u),power_class(v)),ordinal_numbers). % 300.04/300.41 227174[19:SpL:207752.0,167086.0] || subclass(universal_class,symmetric_difference(complement(u),power_class(v))) -> member(ordinal_numbers,union(u,complement(power_class(v))))*. % 300.04/300.41 227177[0:SpL:207752.0,2539.0] || subclass(universal_class,symmetric_difference(complement(u),power_class(v))) -> member(omega,union(u,complement(power_class(v))))*. % 300.04/300.41 227182[19:SpL:207752.0,167084.0] || equal(symmetric_difference(complement(u),power_class(v)),universal_class) -> member(ordinal_numbers,union(u,complement(power_class(v))))*. % 300.04/300.41 227183[0:SpL:207752.0,6300.0] || equal(symmetric_difference(complement(u),power_class(v)),universal_class) -> member(omega,union(u,complement(power_class(v))))*. % 300.04/300.41 227190[22:SpL:207752.0,177190.0] || subclass(omega,symmetric_difference(complement(u),power_class(v))) -> member(ordinal_numbers,union(u,complement(power_class(v))))*. % 300.04/300.41 227192[22:SpL:207752.0,178812.0] || equal(symmetric_difference(complement(u),power_class(v)),omega) -> member(ordinal_numbers,union(u,complement(power_class(v))))*. % 300.04/300.41 227815[19:Res:221767.1,16102.0] || equal(complement(symmetric_difference(complement(u),complement(v))),ordinal_numbers)** -> member(regular(element_relation),union(u,v)). % 300.04/300.41 227820[19:Res:221767.1,9.0] || equal(complement(unordered_pair(u,v)),ordinal_numbers)** -> equal(regular(element_relation),v) equal(regular(element_relation),u). % 300.04/300.41 227857[19:Rew:206408.0,227826.0] || equal(power_class(complement(power_class(u))),ordinal_numbers) member(regular(element_relation),power_class(complement(power_class(u))))* -> . % 300.04/300.41 227963[0:MRR:227945.0,940.0] || member(u,ordered_pair(v,w))* subclass(element_relation,composition_function) -> equal(compose(u,v),w). % 300.04/300.41 227980[19:SpR:124905.0,223552.1] || subclass(composition_function,rest_of(restrict(u,v,singleton(w))))* -> member(ordinal_numbers,segment(u,v,w)). % 300.04/300.41 228115[19:SpL:160282.0,228023.0] || subclass(composition_function,rest_of(regular(ordered_pair(u,v))))* -> equal(regular(ordered_pair(u,v)),singleton(u)). % 300.04/300.41 228298[0:SpR:13.0,43050.2] || member(u,universal_class) well_ordering(v,universal_class) -> member(least(v,singleton(u)),singleton(u))*. % 300.04/300.41 228315[0:Res:43050.2,36583.0] || member(u,universal_class) well_ordering(v,universal_class) -> member(least(v,unordered_pair(u,w)),universal_class)*. % 300.04/300.41 228419[19:Res:224120.1,2500.1] || equal(unordered_pair(u,v),symmetrization_of(ordinal_numbers))** member(u,universal_class) -> member(u,inverse(ordinal_numbers))*. % 300.04/300.41 228421[19:Res:224120.1,2501.1] || equal(unordered_pair(u,v),symmetrization_of(ordinal_numbers))** member(v,universal_class) -> member(v,inverse(ordinal_numbers))*. % 300.04/300.41 228431[19:Res:224120.1,35668.0] || equal(symmetrization_of(ordinal_numbers),rest_relation) well_ordering(u,inverse(ordinal_numbers)) -> member(least(u,rest_relation),rest_relation)*. % 300.04/300.41 228466[0:Res:43071.2,36583.0] || member(u,universal_class) well_ordering(v,universal_class) -> member(least(v,unordered_pair(w,u)),universal_class)*. % 300.04/300.41 229818[19:Rew:167049.0,229580.1] || equal(successor(symmetrization_of(u)),ordinal_numbers)** subclass(cross_product(v,v),ordinal_numbers)* -> connected(u,v)*. % 300.04/300.41 229819[19:Rew:142500.0,228872.1] || equal(successor(u),ordinal_numbers) -> equal(complement(image(element_relation,successor(u))),power_class(complement(singleton(u))))**. % 300.04/300.41 229820[19:Rew:142500.0,228874.1] || equal(successor(u),ordinal_numbers) -> equal(complement(image(element_relation,symmetrization_of(u))),power_class(complement(inverse(u))))**. % 300.04/300.41 229912[19:MRR:229911.2,166995.0] || equal(successor(symmetrization_of(u)),ordinal_numbers)** connected(u,v)* -> equal(cross_product(v,v),ordinal_numbers)**. % 300.04/300.41 230424[0:Obv:230315.1] || member(u,symmetric_difference(v,w)) -> subclass(intersection(x,singleton(u)),complement(intersection(v,w)))*. % 300.04/300.41 230425[0:Obv:230314.1] || member(u,symmetric_difference(v,w)) -> subclass(intersection(singleton(u),x),complement(intersection(v,w)))*. % 300.04/300.41 230599[2:SpL:142500.0,79427.2] || asymmetric(universal_class,u) member(v,cross_product(u,u))* member(v,inverse(universal_class)) -> . % 300.04/300.41 230751[19:SpR:168558.0,167260.0] || -> equal(domain__dfg(cross_product(u,singleton(v)),w,x),domain__dfg(cross_product(w,singleton(x)),u,v))*. % 300.04/300.41 230798[19:SpR:168559.0,167261.0] || -> equal(range__dfg(cross_product(singleton(u),v),w,x),range__dfg(cross_product(singleton(w),x),u,v))*. % 300.04/300.41 231891[19:SSi:231866.0,70.0] || equal(rest_of(u),rest_relation) -> equal(unordered_pair(v,u),ordinal_numbers) member(v,unordered_pair(v,u))*. % 300.04/300.41 231897[19:MRR:231896.0,12.0] || -> member(u,unordered_pair(u,v))* equal(unordered_pair(u,v),ordinal_numbers) member(v,unordered_pair(u,v))*. % 300.04/300.41 232030[19:SSi:232005.0,70.0] || equal(rest_of(u),rest_relation) -> equal(unordered_pair(u,v),ordinal_numbers) member(v,unordered_pair(u,v))*. % 300.04/300.41 232043[19:Res:24.2,225687.1] || member(ordinal_numbers,u) member(ordinal_numbers,v) equal(symmetrization_of(intersection(v,u)),ordinal_numbers)** -> . % 300.04/300.41 232347[0:Obv:232272.2] || subclass(singleton(u),v) member(u,w) -> subclass(singleton(u),intersection(w,v))*. % 300.04/300.41 232366[0:Obv:232312.1] || subclass(restrict(u,v,w),x) -> subclass(restrict(u,v,w),intersection(u,x))*. % 300.04/300.41 232381[0:Obv:232308.1] || subclass(symmetric_difference(u,v),w) -> subclass(symmetric_difference(u,v),intersection(union(u,v),w))*. % 300.04/300.41 232382[8:MRR:232291.0,36682.1] || subclass(rest_relation,rest_of(u)) subclass(v,w) -> subclass(v,intersection(cantor(u),w))*. % 300.04/300.41 232799[19:Res:24.2,225690.1] || member(omega,u) member(omega,v) equal(symmetrization_of(intersection(v,u)),ordinal_numbers)** -> . % 300.04/300.41 233816[19:Rew:233350.0,177938.1] || -> equal(range_of(u),ordinal_numbers) equal(complement(image(element_relation,successor(inverse(u)))),power_class(complement(inverse(u))))**. % 300.04/300.41 233827[12:Rew:233350.0,164679.1] || member(u,universal_class) -> equal(complement(image(element_relation,successor(range_of(u)))),power_class(complement(range_of(u))))**. % 300.04/300.41 233860[25:Rew:233350.0,211883.1] function(u) || subclass(universal_class,complement(u)) member(unordered_pair(v,w),successor(u))* -> . % 300.04/300.41 233910[19:Rew:233350.0,229825.1] || equal(successor(singleton(u)),ordinal_numbers) -> equal(complement(image(element_relation,successor(u))),power_class(complement(u)))**. % 300.04/300.41 233913[19:Rew:233350.0,229827.1] || equal(successor(inverse(u)),ordinal_numbers) -> equal(complement(image(element_relation,symmetrization_of(u))),power_class(complement(u)))**. % 300.04/300.41 234120[25:Rew:233350.0,230561.1] function(u) || member(not_subclass_element(successor(u),v),complement(u))* -> subclass(successor(u),v). % 300.04/300.41 234876[0:Rew:234692.0,148610.0] || -> equal(intersection(complement(union(u,v)),intersection(complement(u),complement(v))),complement(union(u,v)))**. % 300.04/300.41 234889[27:Rew:234692.0,220976.1] || subclass(image(successor_relation,ordinal_numbers),singleton(ordinal_numbers)) -> equal(intersection(kind_1_ordinals,complement(image(successor_relation,ordinal_numbers))),ordinal_numbers)**. % 300.04/300.41 235037[19:Rew:234687.1,234317.1] || equal(singleton(complement(power_class(u))),ordinal_numbers) -> equal(successor(complement(power_class(u))),complement(power_class(u)))**. % 300.04/300.41 235038[19:Rew:234687.1,234319.1] || equal(inverse(complement(power_class(u))),ordinal_numbers) -> equal(symmetrization_of(complement(power_class(u))),complement(power_class(u)))**. % 300.04/300.41 236763[0:Rew:480.0,236251.0] || -> equal(complement(intersection(union(u,v),complement(w))),complement(intersection(union(v,u),complement(w))))*. % 300.04/300.41 236257[0:SpR:234692.0,16274.1] || -> subclass(symmetric_difference(u,v),w) member(not_subclass_element(symmetric_difference(u,v),w),complement(intersection(v,u)))*. % 300.04/300.41 236273[19:SpR:234692.0,168476.1] || -> equal(intersection(intersection(u,v),w),ordinal_numbers) member(regular(intersection(intersection(v,u),w)),u)*. % 300.04/300.41 236274[19:SpR:234692.0,168477.1] || -> equal(intersection(intersection(u,v),w),ordinal_numbers) member(regular(intersection(intersection(v,u),w)),v)*. % 300.04/300.41 236286[19:SpR:234692.0,168479.1] || -> equal(intersection(u,omega),ordinal_numbers) equal(integer_of(regular(intersection(omega,u))),regular(intersection(omega,u)))**. % 300.04/300.41 236289[19:SpR:234692.0,168471.1] || -> equal(intersection(u,intersection(v,w)),ordinal_numbers) member(regular(intersection(intersection(v,w),u)),v)*. % 300.04/300.41 236290[19:SpR:234692.0,168472.1] || -> equal(intersection(u,intersection(v,w)),ordinal_numbers) member(regular(intersection(intersection(v,w),u)),w)*. % 300.04/300.41 236305[19:SpR:234692.0,168471.1] || -> equal(intersection(u,intersection(v,w)),ordinal_numbers) member(regular(intersection(u,intersection(w,v))),v)*. % 300.04/300.41 236306[19:SpR:234692.0,168472.1] || -> equal(intersection(u,intersection(v,w)),ordinal_numbers) member(regular(intersection(u,intersection(w,v))),w)*. % 300.04/300.41 236314[19:SpR:234692.0,168474.2] || subclass(u,v) -> equal(intersection(u,w),ordinal_numbers) member(regular(intersection(w,u)),v)*. % 300.04/300.41 236316[19:SpR:234692.0,168476.1] || -> equal(intersection(intersection(u,v),w),ordinal_numbers) member(regular(intersection(w,intersection(u,v))),u)*. % 300.04/300.41 236317[19:SpR:234692.0,168477.1] || -> equal(intersection(intersection(u,v),w),ordinal_numbers) member(regular(intersection(w,intersection(u,v))),v)*. % 300.04/300.41 236764[0:Rew:481.0,236333.0] || -> equal(complement(intersection(complement(u),union(v,w))),complement(intersection(complement(u),union(w,v))))*. % 300.04/300.41 236344[19:SpR:234692.0,168478.1] || -> equal(intersection(omega,u),ordinal_numbers) equal(integer_of(regular(intersection(u,omega))),regular(intersection(u,omega)))**. % 300.04/300.41 236353[19:SpR:234692.0,168469.2] || subclass(u,v) -> equal(intersection(w,u),ordinal_numbers) member(regular(intersection(u,w)),v)*. % 300.04/300.41 236548[0:SpL:234692.0,16224.0] || member(not_subclass_element(intersection(u,complement(v)),w),v)* -> subclass(intersection(complement(v),u),w). % 300.04/300.41 236553[0:SpL:234692.0,16351.0] || member(not_subclass_element(intersection(complement(u),v),w),u)* -> subclass(intersection(v,complement(u)),w). % 300.04/300.41 237060[0:Rew:237023.0,220565.0] || -> subclass(intersection(u,symmetric_difference(union(v,w),complement(intersection(v,w)))),complement(symmetric_difference(v,w)))*. % 300.04/300.41 237086[0:Rew:237023.0,220134.0] || -> subclass(complement(complement(symmetric_difference(union(u,v),complement(intersection(u,v))))),complement(symmetric_difference(u,v)))*. % 300.04/300.41 237120[0:Rew:237023.0,218904.0] || -> subclass(intersection(symmetric_difference(union(u,v),complement(intersection(u,v))),w),complement(symmetric_difference(u,v)))*. % 300.04/300.41 237220[0:SpR:236669.0,4125.0] || -> equal(intersection(union(u,v),union(complement(v),complement(u))),symmetric_difference(complement(v),complement(u)))**. % 300.04/300.41 237230[19:SpR:236669.0,168374.2] || subclass(omega,symmetric_difference(u,v)) -> equal(integer_of(w),ordinal_numbers) member(w,union(v,u))*. % 300.04/300.41 237486[0:Rew:480.0,237235.0] || -> equal(complement(intersection(union(u,v),complement(w))),complement(intersection(complement(w),union(u,v))))*. % 300.04/300.41 237244[19:SpR:236669.0,167729.2] || subclass(u,symmetric_difference(v,w)) -> equal(u,ordinal_numbers) member(regular(u),union(w,v))*. % 300.04/300.41 237448[19:Rew:237384.0,180313.0] || member(u,symmetric_difference(singleton(ordinal_numbers),complement(v)))* -> member(u,union(v,complement(singleton(ordinal_numbers)))). % 300.04/300.41 237616[0:Rew:207699.0,237239.0] || -> equal(union(intersection(power_class(u),complement(v)),w),union(intersection(complement(v),power_class(u)),w))*. % 300.04/300.41 237619[0:Rew:207766.0,237256.0] || -> equal(union(u,intersection(complement(v),power_class(w))),union(u,intersection(power_class(w),complement(v))))*. % 300.04/300.41 237712[0:SpR:481.0,237218.0] || -> subclass(symmetric_difference(intersection(complement(u),complement(v)),w),complement(intersection(complement(w),union(u,v))))*. % 300.04/300.41 237718[0:SpR:480.0,237218.0] || -> subclass(symmetric_difference(u,intersection(complement(v),complement(w))),complement(intersection(union(v,w),complement(u))))*. % 300.04/300.41 237748[0:Res:237218.0,8.0] || subclass(union(u,v),symmetric_difference(v,u))* -> equal(symmetric_difference(v,u),union(u,v)). % 300.04/300.41 237770[0:SpR:237384.0,16274.1] || -> subclass(symmetric_difference(u,v),w) member(not_subclass_element(symmetric_difference(v,u),w),complement(intersection(u,v)))*. % 300.04/300.41 238063[19:SpR:237974.1,206403.0] || equal(intersection(complement(u),power_class(v)),universal_class)** -> equal(union(u,complement(power_class(v))),ordinal_numbers). % 300.04/300.41 238074[19:SpR:237974.1,206410.0] || equal(intersection(power_class(u),complement(v)),universal_class)** -> equal(union(complement(power_class(u)),v),ordinal_numbers). % 300.04/300.41 239710[19:Res:238770.1,167728.0] || equal(u,universal_class) subclass(u,v)* -> equal(w,ordinal_numbers) member(regular(w),v)*. % 300.04/300.41 239735[19:Res:238770.1,168375.0] || equal(u,universal_class) subclass(u,v)* -> equal(integer_of(w),ordinal_numbers) member(w,v)*. % 300.04/300.41 239890[19:Res:238770.1,176249.1] || equal(intersection(u,v),universal_class)** member(w,universal_class) -> member(ordered_pair(w,ordinal_numbers),v)*. % 300.04/300.41 239891[19:Res:238770.1,176243.1] || equal(intersection(u,v),universal_class)** member(w,universal_class) -> member(ordered_pair(w,ordinal_numbers),u)*. % 300.04/300.41 239947[19:Res:238770.1,8693.1] || equal(u,universal_class) member(ordered_pair(v,w),compose(x,y))* -> member(w,u)*. % 300.04/300.41 240596[19:SpR:149012.1,239132.1] || subclass(singleton(u),u)* member(v,successor(u)) -> member(v,complement(singleton(u)))*. % 300.04/300.41 240610[19:Res:239132.1,5467.1] || member(singleton(u),successor(v))* subclass(universal_class,complement(complement(intersection(v,singleton(v)))))* -> . % 300.04/300.41 240644[19:Res:239132.1,169221.1] || member(ordinal_numbers,successor(u)) equal(complement(complement(intersection(u,singleton(u)))),singleton(ordinal_numbers))** -> . % 300.04/300.41 240951[19:Res:167106.1,237637.0] inductive(symmetric_difference(successor(u),complement(intersection(u,singleton(u))))) || -> member(ordinal_numbers,complement(successor(u)))*. % 300.04/300.41 242485[19:Rew:4577.1,242484.0] || member(u,element_relation) member(u,complement(compose(element_relation,universal_class)))* -> subclass(singleton(u),ordinal_numbers). % 300.04/300.41 242671[19:MRR:242670.2,207974.0] || member(complement(symmetrization_of(ordinal_numbers)),universal_class) -> member(apply(choice,complement(symmetrization_of(ordinal_numbers))),complement(inverse(ordinal_numbers)))*. % 300.04/300.41 243764[19:Res:124899.1,239702.0] || section(u,symmetrization_of(ordinal_numbers),v) equal(cantor(restrict(u,v,symmetrization_of(ordinal_numbers))),universal_class)** -> . % 300.04/300.41 245316[19:SpL:207752.0,215210.0] || subclass(kind_1_ordinals,symmetric_difference(complement(u),power_class(v))) -> member(ordinal_numbers,union(u,complement(power_class(v))))*. % 300.04/300.41 245371[19:SpL:234704.0,215211.0] || subclass(kind_1_ordinals,symmetric_difference(power_class(u),complement(v))) -> member(ordinal_numbers,union(complement(power_class(u)),v))*. % 300.04/300.41 245416[0:Res:217960.0,2497.1] || member(u,universal_class) -> member(u,complement(symmetric_difference(v,inverse(v))))* member(u,symmetrization_of(v)). % 300.04/300.41 245611[19:Rew:209193.0,245588.0] || equal(image(element_relation,union(u,v)),ordinal_numbers) -> subclass(image(element_relation,union(u,v)),w)*. % 300.04/300.41 245627[19:SpL:168412.1,225032.0] || equal(successor(unordered_pair(u,regular(cross_product(v,w)))),ordinal_numbers)** -> equal(cross_product(v,w),ordinal_numbers). % 300.04/300.41 245681[0:MRR:245651.1,66.2] function(u) || member(v,universal_class) subclass(universal_class,complement(singleton(image(u,v))))* -> . % 300.04/300.41 245711[19:SpL:168412.1,225035.0] || equal(successor(unordered_pair(regular(cross_product(u,v)),w)),ordinal_numbers)** -> equal(cross_product(u,v),ordinal_numbers). % 300.04/300.41 245732[19:SpL:168412.1,225700.0] || equal(symmetrization_of(unordered_pair(u,regular(cross_product(v,w)))),ordinal_numbers)** -> equal(cross_product(v,w),ordinal_numbers). % 300.04/300.41 245775[19:SpL:168412.1,225703.0] || equal(symmetrization_of(unordered_pair(regular(cross_product(u,v)),w)),ordinal_numbers)** -> equal(cross_product(u,v),ordinal_numbers). % 300.04/300.41 245880[19:MRR:245846.0,167740.2] || member(u,universal_class) subclass(u,complement(singleton(apply(choice,u))))* -> equal(u,ordinal_numbers). % 300.04/300.41 245913[19:Res:24.2,229738.1] || member(u,v)* member(u,w)* equal(successor(intersection(w,v)),ordinal_numbers)** -> . % 300.04/300.41 245917[19:Res:35124.1,229738.1] || member(u,universal_class) equal(successor(union(v,w)),ordinal_numbers)** -> member(u,complement(v))*. % 300.04/300.41 245918[19:Res:35125.1,229738.1] || member(u,universal_class) equal(successor(union(v,w)),ordinal_numbers)** -> member(u,complement(w))*. % 300.04/300.41 245926[19:Res:125124.2,229738.1] || member(u,universal_class)* subclass(rest_relation,rest_of(v))* equal(successor(cantor(v)),ordinal_numbers) -> . % 300.04/300.41 245953[19:Res:37525.2,229738.1] || member(u,universal_class) equal(successor(singleton(u)),u)** equal(successor(successor_relation),ordinal_numbers) -> . % 300.04/300.41 246001[19:Res:31137.2,229738.1] || member(u,universal_class)* equal(rest_of(u),successor(u)) equal(successor(successor_relation),ordinal_numbers) -> . % 300.04/300.41 246010[19:Res:17.2,229738.1] || member(u,v)* member(w,x)* equal(successor(cross_product(x,v)),ordinal_numbers)** -> . % 300.04/300.41 246297[19:Rew:144694.0,246284.1] || subclass(omega,complement(u)) member(v,complement(complement(u)))* -> equal(integer_of(v),ordinal_numbers). % 300.04/300.41 246342[25:SpR:234134.1,137025.0] function(u) || -> subclass(complement(successor(complement(u))),intersection(successor(u),complement(singleton(complement(u)))))*. % 300.04/300.41 246344[25:SpR:234134.1,137026.0] function(u) || -> subclass(complement(symmetrization_of(complement(u))),intersection(successor(u),complement(inverse(complement(u)))))*. % 300.04/300.41 246395[25:SpR:234134.1,158049.1] function(symmetrization_of(u)) || connected(u,v) -> subclass(cross_product(v,v),successor(symmetrization_of(u)))*. % 300.04/300.41 246508[25:SpL:234134.1,190819.0] function(u) || member(not_subclass_element(complement(u),ordinal_numbers),successor(u))* -> subclass(complement(u),ordinal_numbers). % 300.04/300.41 246568[25:SpL:234134.1,158048.0] function(symmetrization_of(u)) || equal(successor(symmetrization_of(u)),cross_product(v,v))* -> connected(u,v)*. % 300.04/300.41 246573[25:SpL:234134.1,158050.0] function(symmetrization_of(u)) || subclass(cross_product(v,v),successor(symmetrization_of(u)))* -> connected(u,v). % 300.04/300.41 247002[19:Rew:168356.1,247001.0] || member(ordinal_numbers,union(complement(singleton(ordinal_numbers)),u))* -> equal(intersection(singleton(ordinal_numbers),complement(u)),ordinal_numbers). % 300.04/300.41 247008[19:Rew:168356.1,247007.0] || member(ordinal_numbers,union(u,complement(singleton(ordinal_numbers))))* -> equal(intersection(singleton(ordinal_numbers),complement(u)),ordinal_numbers). % 300.04/300.41 247054[25:SoR:246596.0,12322.2] single_valued_class(successor_relation) || equal(complement(successor(successor_relation)),ordinal_numbers) equal(cross_product(universal_class,universal_class),successor_relation)** -> . % 300.04/300.41 247086[19:SpL:234704.0,238771.0] || equal(symmetric_difference(power_class(u),complement(v)),universal_class) -> subclass(universal_class,union(complement(power_class(u)),v))*. % 300.04/300.41 247105[25:MRR:195117.3,247104.0] function(u) || member(ordinal_numbers,cantor(v)) equal(restrict(v,ordinal_numbers,universal_class),u)* -> . % 300.04/300.41 247295[19:SpL:4121.0,238772.0] || equal(symmetric_difference(cross_product(u,v),w),universal_class) -> subclass(universal_class,complement(restrict(w,u,v)))*. % 300.04/300.42 247296[19:SpL:4119.0,238772.0] || equal(symmetric_difference(u,cross_product(v,w)),universal_class) -> subclass(universal_class,complement(restrict(u,v,w)))*. % 300.04/300.42 247321[19:SpL:207752.0,238772.0] || equal(symmetric_difference(complement(u),power_class(v)),universal_class) -> subclass(universal_class,union(u,complement(power_class(v))))*. % 300.04/300.42 247489[19:Rew:142500.0,247363.1,234692.0,247363.1] || equal(u,universal_class) -> equal(symmetric_difference(u,cross_product(v,w)),complement(restrict(u,v,w)))**. % 300.04/300.42 247686[19:Rew:142500.0,247563.1,234692.0,247563.1] || equal(u,universal_class) -> equal(symmetric_difference(cross_product(v,w),u),complement(restrict(u,v,w)))**. % 300.04/300.42 248138[19:SpL:4121.0,245337.0] || equal(symmetric_difference(cross_product(u,v),w),kind_1_ordinals) -> member(ordinal_numbers,complement(restrict(w,u,v)))*. % 300.04/300.42 248139[19:SpL:4119.0,245337.0] || equal(symmetric_difference(u,cross_product(v,w)),kind_1_ordinals) -> member(ordinal_numbers,complement(restrict(u,v,w)))*. % 300.04/300.42 248164[19:SpL:207752.0,245337.0] || equal(symmetric_difference(complement(u),power_class(v)),kind_1_ordinals) -> member(ordinal_numbers,union(u,complement(power_class(v))))*. % 300.04/300.42 248296[26:Res:248149.1,202277.1] || equal(complement(compose(complement(element_relation),inverse(element_relation))),kind_1_ordinals)** member(ordinal_numbers,cross_product(universal_class,universal_class)) -> . % 300.04/300.42 248336[19:Res:248149.1,168251.0] || equal(regular(u),kind_1_ordinals) member(ordinal_numbers,u)* -> equal(u,ordinal_numbers) member(ordinal_numbers,v)*. % 300.04/300.42 248404[19:SpL:234704.0,245391.0] || equal(symmetric_difference(power_class(u),complement(v)),kind_1_ordinals) -> member(ordinal_numbers,union(complement(power_class(u)),v))*. % 300.04/300.42 248508[25:Res:246387.1,2497.1] function(u) || member(v,universal_class) -> member(v,complement(successor(u)))* member(v,u). % 300.04/300.42 248665[0:Res:217958.0,2497.1] || member(u,universal_class) -> member(u,complement(symmetric_difference(v,w)))* member(u,union(v,w)). % 300.04/300.42 248791[0:Res:9820.1,219712.0] || equal(sum_class(complement(complement(u))),complement(complement(u))) -> subclass(sum_class(complement(complement(u))),u)*. % 300.04/300.42 248870[19:Res:248818.0,167739.0] || -> equal(complement(successor(complement(singleton(u)))),ordinal_numbers) equal(regular(complement(successor(complement(singleton(u))))),u)**. % 300.04/300.42 248879[0:Res:248818.0,8596.1] single_valued_class(complement(successor(complement(cross_product(universal_class,universal_class))))) || -> function(complement(successor(complement(cross_product(universal_class,universal_class)))))*. % 300.04/300.42 248987[19:Res:248819.0,167739.0] || -> equal(complement(symmetrization_of(complement(singleton(u)))),ordinal_numbers) equal(regular(complement(symmetrization_of(complement(singleton(u))))),u)**. % 300.04/300.42 248996[0:Res:248819.0,8596.1] single_valued_class(complement(symmetrization_of(complement(cross_product(universal_class,universal_class))))) || -> function(complement(symmetrization_of(complement(cross_product(universal_class,universal_class)))))*. % 300.04/300.42 249057[0:SpR:479.0,248816.0] || -> subclass(complement(union(u,power_class(intersection(complement(v),complement(w))))),image(element_relation,union(v,w)))*. % 300.04/300.42 249087[0:Res:248816.0,8.0] || subclass(u,complement(union(v,complement(u))))* -> equal(complement(union(v,complement(u))),u). % 300.04/300.42 249222[0:SpR:479.0,248817.0] || -> subclass(complement(union(power_class(intersection(complement(u),complement(v))),w)),image(element_relation,union(u,v)))*. % 300.04/300.42 249253[0:Res:248817.0,8.0] || subclass(u,complement(union(complement(u),v)))* -> equal(complement(union(complement(u),v)),u). % 300.04/300.42 249581[0:Res:170.0,42928.0] || well_ordering(u,universal_class) -> member(singleton(v),w)* member(least(u,complement(w)),complement(w))*. % 300.04/300.42 249658[19:Res:196718.0,42928.0] || well_ordering(u,universal_class) -> member(regular(element_relation),v) member(least(u,complement(v)),complement(v))*. % 300.04/300.42 249673[0:SpR:206403.0,248882.0] || -> subclass(complement(successor(complement(complement(union(u,complement(power_class(v))))))),intersection(complement(u),power_class(v)))*. % 300.04/300.42 249676[0:SpR:206410.0,248882.0] || -> subclass(complement(successor(complement(complement(union(complement(power_class(u)),v))))),intersection(power_class(u),complement(v)))*. % 300.04/300.42 249790[0:SpR:206403.0,248999.0] || -> subclass(complement(symmetrization_of(complement(complement(union(u,complement(power_class(v))))))),intersection(complement(u),power_class(v)))*. % 300.04/300.42 249793[0:SpR:206410.0,248999.0] || -> subclass(complement(symmetrization_of(complement(complement(union(complement(power_class(u)),v))))),intersection(power_class(u),complement(v)))*. % 300.04/300.42 250006[19:Rew:144694.0,249951.1] || subclass(u,complement(v)) member(regular(u),complement(complement(v)))* -> equal(u,ordinal_numbers). % 300.04/300.42 250052[0:SpR:206403.0,248806.0] || -> member(u,union(v,complement(power_class(w)))) subclass(singleton(u),intersection(complement(v),power_class(w)))*. % 300.04/300.42 250055[0:SpR:206410.0,248806.0] || -> member(u,union(complement(power_class(v)),w)) subclass(singleton(u),intersection(power_class(v),complement(w)))*. % 300.04/300.42 250095[0:Res:248806.0,16455.1] || subclass(u,complement(complement(v))) -> subclass(singleton(not_subclass_element(u,w)),v)* subclass(u,w). % 300.04/300.42 250096[0:Res:248806.0,42071.0] || -> subclass(singleton(not_subclass_element(u,intersection(complement(v),u))),v)* subclass(u,intersection(complement(v),u)). % 300.04/300.42 250099[0:Res:248806.0,15100.2] || member(u,universal_class) subclass(universal_class,complement(complement(v))) -> subclass(singleton(sum_class(u)),v)*. % 300.04/300.42 250100[0:Res:248806.0,15066.2] || member(u,universal_class) subclass(universal_class,complement(complement(v))) -> subclass(singleton(power_class(u)),v)*. % 300.04/300.42 250177[19:Res:249055.0,2497.1] || member(u,universal_class) -> member(u,union(v,symmetrization_of(ordinal_numbers)))* member(u,complement(inverse(ordinal_numbers))). % 300.04/300.42 250527[19:Res:249101.0,2497.1] || member(u,universal_class) -> member(u,union(v,complement(symmetrization_of(ordinal_numbers))))* member(u,inverse(ordinal_numbers)). % 300.04/300.42 250581[19:Res:249220.0,2497.1] || member(u,universal_class) -> member(u,union(symmetrization_of(ordinal_numbers),v))* member(u,complement(inverse(ordinal_numbers))). % 300.04/300.42 250638[19:Res:249267.0,2497.1] || member(u,universal_class) -> member(u,union(complement(symmetrization_of(ordinal_numbers)),v))* member(u,inverse(ordinal_numbers)). % 300.04/300.42 250747[19:MRR:250699.0,53.0] || subclass(intersection(power_class(u),complement(v)),ordinal_numbers) -> member(omega,union(complement(power_class(u)),v))*. % 300.04/300.42 250749[19:MRR:250732.0,167011.0] || subclass(intersection(power_class(u),complement(v)),ordinal_numbers) -> member(ordinal_numbers,union(complement(power_class(u)),v))*. % 300.04/300.42 250903[25:SpR:234134.1,248811.0] function(complement(complement(complement(complement(u))))) || -> subclass(successor(complement(complement(complement(complement(u))))),u)*. % 300.04/300.42 250932[0:Res:248811.0,2497.1] || member(u,universal_class) -> member(u,complement(complement(complement(complement(complement(v))))))* member(u,v). % 300.04/300.42 251090[19:MRR:251043.0,53.0] || subclass(intersection(complement(u),power_class(v)),ordinal_numbers) -> member(omega,union(u,complement(power_class(v))))*. % 300.04/300.42 251092[19:MRR:251076.0,167011.0] || subclass(intersection(complement(u),power_class(v)),ordinal_numbers) -> member(ordinal_numbers,union(u,complement(power_class(v))))*. % 300.04/300.42 251755[0:Obv:251684.0] || -> member(u,union(v,w)) subclass(intersection(x,singleton(u)),intersection(complement(v),complement(w)))*. % 300.04/300.42 251756[0:Obv:251683.0] || -> member(u,union(v,w)) subclass(intersection(singleton(u),x),intersection(complement(v),complement(w)))*. % 300.04/300.42 251983[25:SpR:234134.1,248810.0] function(intersection(u,complement(complement(v)))) || -> subclass(successor(intersection(u,complement(complement(v)))),v)*. % 300.04/300.42 252012[0:Res:248810.0,2497.1] || member(u,universal_class) -> member(u,complement(intersection(v,complement(complement(w)))))* member(u,w). % 300.04/300.42 252298[25:SpR:234134.1,248812.0] function(intersection(complement(complement(u)),v)) || -> subclass(successor(intersection(complement(complement(u)),v)),u)*. % 300.04/300.42 252327[0:Res:248812.0,2497.1] || member(u,universal_class) -> member(u,complement(intersection(complement(complement(v)),w)))* member(u,v). % 300.04/300.42 252472[0:Res:249106.0,2497.1] || member(u,universal_class) -> member(u,union(v,complement(complement(complement(w)))))* member(u,w). % 300.04/300.42 252609[8:Res:125121.2,124881.0] || member(u,cantor(v))* subclass(rest_of(v),rest_of(w))* -> member(u,cantor(w))*. % 300.04/300.42 252611[8:Res:125121.2,15.0] || member(u,cantor(v))* subclass(rest_of(v),cross_product(w,x))* -> member(u,w)*. % 300.04/300.42 252621[8:Res:125121.2,6476.1] || member(u,cantor(v))* subclass(rest_of(v),w)* subclass(universal_class,complement(w)) -> . % 300.04/300.42 252630[19:Res:125121.2,229738.1] || member(u,cantor(v))* subclass(rest_of(v),w)* equal(successor(w),ordinal_numbers) -> . % 300.04/300.42 252632[8:Res:125121.2,188593.1] || member(u,cantor(v))* subclass(rest_of(v),w)* equal(complement(w),universal_class) -> . % 300.04/300.42 252720[0:Res:249272.0,2497.1] || member(u,universal_class) -> member(u,union(complement(complement(complement(v))),w))* member(u,v). % 300.04/300.42 252845[19:Obv:252791.1] || equal(u,v) -> subclass(singleton(v),unordered_pair(v,u))* subclass(unordered_pair(v,u),ordinal_numbers). % 300.04/300.42 252903[0:Res:220180.1,8.0] || subclass(u,v) subclass(v,complement(complement(u)))* -> equal(v,complement(complement(u))). % 300.04/300.42 252926[0:Res:220180.1,8596.1] single_valued_class(complement(complement(u))) || subclass(u,cross_product(universal_class,universal_class))* -> function(complement(complement(u))). % 300.04/300.42 252928[0:Res:220180.1,2497.1] || subclass(u,v)* member(w,universal_class) -> member(w,complement(u))* member(w,v)*. % 300.04/300.42 253079[18:SpL:124905.0,227961.1] || member(restrict(u,v,singleton(w)),x)* member(x,segment(u,v,w)) -> . % 300.04/300.42 253101[19:Res:167580.1,227961.1] || member(u,universal_class) member(v,u) -> equal(apply(v,u),sum_class(range_of(ordinal_numbers)))**. % 300.04/300.42 253112[18:Res:36865.0,227961.1] || member(u,not_subclass_element(complement(complement(cantor(u))),v))* -> subclass(complement(complement(cantor(u))),v). % 300.04/300.42 253113[18:Res:315.1,227961.1] || member(u,not_subclass_element(intersection(cantor(u),v),w))* -> subclass(intersection(cantor(u),v),w). % 300.04/300.42 253125[18:Res:35220.2,227961.1] inductive(cantor(u)) || well_ordering(v,universal_class) member(u,least(v,cantor(u)))* -> . % 300.04/300.42 253135[18:Res:297.1,227961.1] || member(u,not_subclass_element(intersection(v,cantor(u)),w))* -> subclass(intersection(v,cantor(u)),w). % 300.04/300.42 253137[19:Res:167372.2,227961.1] || well_ordering(u,universal_class) member(v,least(u,cantor(v)))* -> equal(cantor(v),ordinal_numbers). % 300.04/300.42 253142[19:Res:176235.2,227961.1] || member(u,universal_class) subclass(domain_relation,cantor(v)) member(v,ordered_pair(u,ordinal_numbers))* -> . % 300.04/300.42 27805[0:SpR:4125.0,16276.0] || -> subclass(symmetric_difference(union(u,v),union(complement(u),complement(v))),complement(symmetric_difference(complement(u),complement(v))))*. % 300.04/300.42 48891[0:Res:2482.2,16910.0] || member(u,universal_class) subclass(universal_class,symmetric_difference(v,inverse(v)))* -> member(sum_class(u),symmetrization_of(v))*. % 300.04/300.42 85196[8:SpL:479.0,85097.1] inductive(image(element_relation,union(u,v))) || equal(power_class(intersection(complement(u),complement(v))),universal_class)** -> . % 300.04/300.42 27265[0:Res:2481.1,488.0] || subclass(universal_class,intersection(complement(u),complement(v))) member(ordered_pair(w,x),union(u,v))* -> . % 300.04/300.42 6485[0:Res:2481.1,9.0] || subclass(universal_class,unordered_pair(u,v))* -> equal(ordered_pair(w,x),v)* equal(ordered_pair(w,x),u)*. % 300.04/300.42 48372[0:Res:4126.1,6432.1] || member(unordered_pair(u,v),symmetric_difference(w,x))* subclass(universal_class,complement(complement(intersection(w,x)))) -> . % 300.04/300.42 12045[0:Res:12015.1,9.0] || equal(complement(complement(unordered_pair(u,v))),universal_class)** -> equal(singleton(w),v)* equal(singleton(w),u)*. % 300.04/300.42 48712[0:SpL:5132.1,48630.0] || equal(complement(unordered_pair(u,not_subclass_element(cross_product(v,w),x))),universal_class)** -> subclass(cross_product(v,w),x). % 300.04/300.42 48626[0:SpL:5132.1,48587.0] || subclass(universal_class,complement(unordered_pair(u,not_subclass_element(cross_product(v,w),x))))* -> subclass(cross_product(v,w),x). % 300.04/300.42 48718[0:SpL:5132.1,48663.0] || equal(complement(unordered_pair(not_subclass_element(cross_product(u,v),w),x)),universal_class)** -> subclass(cross_product(u,v),w). % 300.04/300.42 48659[0:SpL:5132.1,48618.0] || subclass(universal_class,complement(unordered_pair(not_subclass_element(cross_product(u,v),w),x)))* -> subclass(cross_product(u,v),w). % 300.04/300.42 48892[0:Res:2483.2,16910.0] || member(u,universal_class) subclass(universal_class,symmetric_difference(v,inverse(v)))* -> member(power_class(u),symmetrization_of(v))*. % 300.04/300.42 48889[0:Res:2526.2,16910.0] || subclass(u,symmetric_difference(v,inverse(v)))* -> subclass(u,w) member(not_subclass_element(u,w),symmetrization_of(v))*. % 300.04/300.42 36374[0:SpL:4119.0,5472.0] || subclass(universal_class,symmetric_difference(u,cross_product(v,w))) -> member(singleton(x),complement(restrict(u,v,w)))*. % 300.04/300.42 36380[0:SpL:4119.0,12446.0] || equal(symmetric_difference(u,cross_product(v,w)),universal_class) -> member(singleton(x),complement(restrict(u,v,w)))*. % 300.04/300.42 36514[0:SpL:4121.0,5472.0] || subclass(universal_class,symmetric_difference(cross_product(u,v),w)) -> member(singleton(x),complement(restrict(w,u,v)))*. % 300.04/300.42 36520[0:SpL:4121.0,12446.0] || equal(symmetric_difference(cross_product(u,v),w),universal_class) -> member(singleton(x),complement(restrict(w,u,v)))*. % 300.04/300.42 11906[0:Res:2481.1,128.3] || subclass(universal_class,u) member(v,w)* subclass(w,x)* well_ordering(u,x)* -> . % 300.04/300.42 95578[0:Res:51413.0,4127.0] || -> subclass(u,complement(symmetric_difference(v,w))) member(not_subclass_element(u,complement(symmetric_difference(v,w))),union(v,w))*. % 300.04/300.42 95600[0:Rew:27.0,95560.1] || -> member(not_subclass_element(u,union(v,w)),intersection(complement(v),complement(w)))* subclass(u,union(v,w)). % 300.04/300.42 95767[0:Res:51413.0,897.0] || -> subclass(u,complement(restrict(v,w,x))) member(not_subclass_element(u,complement(restrict(v,w,x))),v)*. % 300.04/300.42 98716[0:SpR:479.0,95593.1] || -> member(u,image(element_relation,union(v,w))) subclass(singleton(u),power_class(intersection(complement(v),complement(w))))*. % 300.04/300.42 110842[0:Res:4126.1,6476.1] || member(ordered_pair(u,v),symmetric_difference(w,x))* subclass(universal_class,complement(complement(intersection(w,x)))) -> . % 300.04/300.42 110987[0:SpL:123.0,110864.0] || member(restrict(u,v,singleton(w)),segment(u,v,w))* subclass(universal_class,complement(element_relation)) -> . % 300.04/300.42 135193[0:Res:36865.0,2.0] || subclass(u,v) -> subclass(complement(complement(u)),w) member(not_subclass_element(complement(complement(u)),w),v)*. % 300.04/300.42 135194[0:Res:36865.0,22.0] || -> subclass(complement(complement(intersection(u,v))),w) member(not_subclass_element(complement(complement(intersection(u,v))),w),u)*. % 300.04/300.42 135195[0:Res:36865.0,23.0] || -> subclass(complement(complement(intersection(u,v))),w) member(not_subclass_element(complement(complement(intersection(u,v))),w),v)*. % 300.04/300.42 135951[0:Res:2525.1,2.0] || subclass(ordered_pair(u,v),w)* subclass(w,x)* -> member(unordered_pair(u,singleton(v)),x)*. % 300.04/300.42 135957[0:Res:2525.1,4127.0] || subclass(ordered_pair(u,v),symmetric_difference(w,x)) -> member(unordered_pair(u,singleton(v)),union(w,x))*. % 300.04/300.42 135959[0:Res:2525.1,16910.0] || subclass(ordered_pair(u,v),symmetric_difference(w,inverse(w)))* -> member(unordered_pair(u,singleton(v)),symmetrization_of(w)). % 300.04/300.42 135983[0:Res:2525.1,158.0] || subclass(ordered_pair(u,v),omega) -> equal(integer_of(unordered_pair(u,singleton(v))),unordered_pair(u,singleton(v)))**. % 300.04/300.42 137128[0:Res:137025.0,2497.1] || member(u,universal_class) -> member(u,successor(v)) member(u,intersection(complement(v),complement(singleton(v))))*. % 300.04/300.42 137160[0:Res:137026.0,2497.1] || member(u,universal_class) -> member(u,symmetrization_of(v)) member(u,intersection(complement(v),complement(inverse(v))))*. % 300.04/300.42 137223[0:SpR:16826.0,57.1] || member(intersection(complement(u),complement(singleton(u))),universal_class)* -> member(complement(image(element_relation,successor(u))),universal_class). % 300.04/300.42 137294[0:SpR:16825.0,57.1] || member(intersection(complement(u),complement(inverse(u))),universal_class)* -> member(complement(image(element_relation,symmetrization_of(u))),universal_class). % 300.04/300.42 138280[8:SpR:125772.0,125124.2] || member(u,universal_class) subclass(rest_relation,rest_of(restrict(element_relation,universal_class,v)))* -> member(u,sum_class(v))*. % 300.04/300.42 138283[8:SpR:125707.0,125124.2] || member(u,universal_class) subclass(rest_relation,rest_of(flip(cross_product(v,universal_class))))* -> member(u,inverse(v))*. % 300.04/300.42 138718[8:Rew:138645.1,138636.2] || equal(rest_of(restrict(u,v,w)),rest_relation)** section(u,w,v) -> equal(universal_class,w). % 300.04/300.42 139903[0:Res:12015.1,16102.0] || equal(complement(complement(symmetric_difference(complement(u),complement(v)))),universal_class)** -> member(singleton(w),union(u,v))*. % 300.04/300.42 146335[12:SpL:146278.0,99364.1] || member(cross_product(u,universal_class),universal_class)* equal(rest_of(cross_product(u,universal_class)),sum_class(image(universal_class,u))) -> . % 300.04/300.42 146481[0:Res:16280.0,16469.0] || -> subclass(restrict(singleton(u),v,w),x) equal(not_subclass_element(restrict(singleton(u),v,w),x),u)**. % 300.04/300.42 147471[0:MRR:147444.0,55.1] || member(u,universal_class) subclass(universal_class,complement(union(v,w)))* -> member(sum_class(u),complement(w))*. % 300.04/300.42 147472[0:MRR:147443.0,55.1] || member(u,universal_class) subclass(universal_class,complement(union(v,w)))* -> member(sum_class(u),complement(v))*. % 300.04/300.42 147602[0:MRR:147575.0,57.1] || member(u,universal_class) subclass(universal_class,complement(union(v,w)))* -> member(power_class(u),complement(w))*. % 300.04/300.42 147603[0:MRR:147574.0,57.1] || member(u,universal_class) subclass(universal_class,complement(union(v,w)))* -> member(power_class(u),complement(v))*. % 300.04/300.42 148032[8:Res:147404.1,15100.2] || member(sum_class(u),element_relation)* member(u,universal_class) subclass(universal_class,complement(compose(element_relation,universal_class)))* -> . % 300.04/300.42 148033[8:Res:147404.1,15066.2] || member(power_class(u),element_relation)* member(u,universal_class) subclass(universal_class,complement(compose(element_relation,universal_class)))* -> . % 300.04/300.42 148842[0:Res:36865.0,148647.0] || -> subclass(complement(complement(complement(complement(u)))),v) member(not_subclass_element(complement(complement(complement(complement(u)))),v),u)*. % 300.04/300.42 148843[0:Res:315.1,148647.0] || -> subclass(intersection(complement(complement(u)),v),w) member(not_subclass_element(intersection(complement(complement(u)),v),w),u)*. % 300.04/300.42 148875[0:Res:297.1,148647.0] || -> subclass(intersection(u,complement(complement(v))),w) member(not_subclass_element(intersection(u,complement(complement(v))),w),v)*. % 300.04/300.42 148882[0:Res:2523.2,148647.0] || member(u,universal_class) subclass(rest_relation,complement(complement(v))) -> member(ordered_pair(u,rest_of(u)),v)*. % 300.04/300.42 149443[0:SpR:149012.1,160.0] || subclass(union(u,v),complement(intersection(u,v)))* -> equal(symmetric_difference(u,v),union(u,v)). % 300.04/300.42 149445[0:SpR:149012.1,4105.0] || subclass(symmetrization_of(u),complement(intersection(u,inverse(u))))* -> equal(symmetric_difference(u,inverse(u)),symmetrization_of(u)). % 300.04/300.42 151024[0:Rew:16238.1,151023.1] || member(u,v) member(u,w) -> subclass(intersection(singleton(u),x),intersection(w,v))*. % 300.04/300.42 151410[0:Rew:16365.1,151409.1] || member(u,v) member(u,w) -> subclass(intersection(x,singleton(u)),intersection(w,v))*. % 300.04/300.42 151711[8:Res:147404.1,16455.1] || member(not_subclass_element(u,v),element_relation)* subclass(u,complement(compose(element_relation,universal_class)))* -> subclass(u,v). % 300.04/300.42 151742[0:MRR:151701.0,36682.1] || subclass(u,complement(union(v,w)))* -> member(not_subclass_element(u,x),complement(w))* subclass(u,x). % 300.04/300.42 151743[0:MRR:151700.0,36682.1] || subclass(u,complement(union(v,w)))* -> member(not_subclass_element(u,x),complement(v))* subclass(u,x). % 300.04/300.42 153080[0:SpR:149179.0,160.0] || -> equal(intersection(complement(intersection(u,v)),union(u,intersection(u,v))),symmetric_difference(u,intersection(u,v)))**. % 300.04/300.42 153349[0:SpR:149318.0,160.0] || -> equal(intersection(complement(intersection(u,v)),union(v,intersection(u,v))),symmetric_difference(v,intersection(u,v)))**. % 300.04/300.42 154751[0:Res:12015.1,36025.1] || equal(complement(complement(u)),universal_class) member(u,universal_class) -> member(singleton(singleton(singleton(u))),element_relation)*. % 300.04/300.42 134787[8:Res:134636.1,124906.1] || subclass(cantor(restrict(u,v,kind_1_ordinals)),ordinal_numbers)* subclass(kind_1_ordinals,v) -> section(u,kind_1_ordinals,v). % 300.04/300.42 135459[0:Res:98.1,11848.0] || member(ordered_pair(u,v),cross_product(universal_class,universal_class))* subclass(composition_function,w) well_ordering(universal_class,w)* -> . % 300.04/300.42 135361[0:Res:26.2,11848.0] || member(u,universal_class)* subclass(complement(v),w)* well_ordering(universal_class,w) -> member(u,v)*. % 300.04/300.42 135471[0:Res:36585.2,11848.0] || member(u,universal_class)* member(v,u)* subclass(element_relation,w) well_ordering(universal_class,w)* -> . % 300.04/300.42 135503[0:Res:2523.2,11848.0] || member(u,universal_class)* subclass(rest_relation,v)* subclass(v,w)* well_ordering(universal_class,w)* -> . % 300.04/300.42 135701[2:Res:35220.2,2.0] inductive(u) || well_ordering(v,universal_class) subclass(u,w) -> member(least(v,u),w)*. % 300.04/300.42 148864[2:Res:35220.2,148647.0] inductive(complement(complement(u))) || well_ordering(v,universal_class) -> member(least(v,complement(complement(u))),u)*. % 300.04/300.42 135702[2:Res:35220.2,22.0] inductive(intersection(u,v)) || well_ordering(w,universal_class) -> member(least(w,intersection(u,v)),u)*. % 300.04/300.42 135703[2:Res:35220.2,23.0] inductive(intersection(u,v)) || well_ordering(w,universal_class) -> member(least(w,intersection(u,v)),v)*. % 300.04/300.42 136344[2:Res:35222.2,2.0] inductive(u) || well_ordering(v,u) subclass(u,w) -> member(least(v,u),w)*. % 300.04/300.42 136336[2:Res:35222.2,25.1] inductive(complement(u)) || well_ordering(v,complement(u)) member(least(v,complement(u)),u)* -> . % 300.04/300.42 166494[8:MRR:166493.4,80465.0] || member(u,v)* member(u,singleton(w))* well_ordering(x,y)* -> member(w,v)*. % 300.04/300.42 169468[19:Rew:166997.0,167403.1] || subclass(domain_relation,unordered_pair(u,v))* -> equal(ordered_pair(ordinal_numbers,ordinal_numbers),v) equal(ordered_pair(ordinal_numbers,ordinal_numbers),u). % 300.04/300.42 167423[19:Rew:166997.0,84229.1] || subclass(domain_relation,intersection(complement(u),complement(v))) member(ordered_pair(ordinal_numbers,ordinal_numbers),union(u,v))* -> . % 300.04/300.42 167433[19:Rew:166997.0,98585.1] || subclass(domain_relation,complement(complement(restrict(u,v,w))))* -> member(ordered_pair(ordinal_numbers,ordinal_numbers),cross_product(v,w)). % 300.04/300.42 167437[19:Rew:166997.0,97493.0] || member(ordered_pair(ordinal_numbers,ordinal_numbers),symmetric_difference(u,v))* subclass(domain_relation,complement(complement(intersection(u,v)))) -> . % 300.04/300.42 167516[19:Rew:166997.0,164611.1] || member(u,universal_class) member(singleton(singleton(ordinal_numbers)),cross_product(v,w))* -> member(range_of(u),w)*. % 300.04/300.42 169474[19:Rew:166997.0,167529.2] || subclass(singleton(ordinal_numbers),u)* well_ordering(v,u)* -> member(least(v,singleton(ordinal_numbers)),singleton(ordinal_numbers))*. % 300.04/300.42 167684[19:Rew:166997.0,163749.2] || subclass(u,intersection(v,w)) member(regular(u),symmetric_difference(v,w))* -> equal(u,ordinal_numbers). % 300.04/300.42 167745[19:Rew:166997.0,161135.0] || equal(ordinal_numbers,u) section(v,u,w) -> equal(cantor(restrict(v,w,u)),u)**. % 300.04/300.42 169486[19:Rew:166997.0,167746.2] || equal(ordinal_numbers,u) well_ordering(v,w)* -> equal(segment(v,u,least(v,u)),ordinal_numbers)**. % 300.04/300.42 167747[19:Rew:166997.0,82469.0] || equal(ordinal_numbers,u) connected(v,u) -> well_ordering(v,u) equal(not_well_ordering(v,u),u)**. % 300.04/300.42 167763[19:Rew:166997.0,84178.1] single_valued_class(u) || -> equal(domain__dfg(u,image(inverse(u),singleton(single_valued3(ordinal_numbers))),single_valued2(u)),single_valued3(u))**. % 300.04/300.42 167764[19:Rew:166997.0,84174.1] function(u) || -> equal(domain__dfg(u,image(inverse(u),singleton(single_valued3(ordinal_numbers))),single_valued2(u)),single_valued3(u))**. % 300.04/300.42 168242[19:Rew:166997.0,80690.2] || member(u,v) member(u,singleton(v))* -> equal(singleton(v),ordinal_numbers) member(u,w)*. % 300.04/300.42 168365[19:Rew:166997.0,163363.2] || subclass(omega,intersection(u,v)) member(w,symmetric_difference(u,v))* -> equal(integer_of(w),ordinal_numbers). % 300.04/300.42 168444[19:Rew:166997.0,163399.1] || subclass(omega,rest_relation) -> equal(integer_of(singleton(singleton(singleton(u)))),ordinal_numbers)** equal(rest_of(singleton(u)),u). % 300.04/300.42 168523[19:Rew:166997.0,80825.1] || well_ordering(u,v) -> equal(segment(u,intersection(w,v),least(u,intersection(w,v))),ordinal_numbers)**. % 300.04/300.42 168524[19:Rew:166997.0,80826.1] || well_ordering(u,v) -> equal(segment(u,intersection(v,w),least(u,intersection(v,w))),ordinal_numbers)**. % 300.04/300.42 168528[19:Rew:166997.0,158542.0] || equal(cantor(restrict(u,v,w)),ordinal_numbers)** subclass(w,v) -> section(u,w,v). % 300.04/300.42 168529[19:Rew:166997.0,82483.0] || equal(cross_product(cross_product(universal_class,universal_class),universal_class),ordinal_numbers) -> equal(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(u))*. % 300.04/300.42 168530[19:Rew:166997.0,82482.0] || equal(cross_product(cross_product(universal_class,universal_class),universal_class),ordinal_numbers) -> equal(cross_product(cross_product(universal_class,universal_class),universal_class),flip(u))*. % 300.04/300.42 168538[19:Rew:166997.0,161771.2] || subclass(u,ordinal_numbers) well_ordering(v,kind_1_ordinals) -> equal(segment(v,u,least(v,u)),ordinal_numbers)**. % 300.04/300.42 168575[19:Rew:166997.0,164869.1] || well_ordering(universal_class,power_class(intersection(complement(u),complement(v))))* -> member(ordinal_numbers,image(element_relation,union(u,v))). % 300.04/300.42 168759[19:Rew:166997.0,161571.2] || subclass(inverse(u),u)* asymmetric(u,v) -> equal(restrict(inverse(u),v,v),ordinal_numbers)**. % 300.04/300.42 168760[19:Rew:166997.0,161505.1] || subclass(inverse(u),u)* equal(restrict(inverse(u),v,v),ordinal_numbers)** -> asymmetric(u,v). % 300.04/300.42 168766[19:Rew:166997.0,161708.1] || well_ordering(u,v) -> equal(segment(u,complement(complement(v)),least(u,complement(complement(v)))),ordinal_numbers)**. % 300.04/300.42 168863[19:Rew:166997.0,163937.1] || well_ordering(u,universal_class) -> equal(complement(complement(v)),ordinal_numbers) member(least(u,complement(complement(v))),v)*. % 300.04/300.42 168963[19:Rew:166997.0,164574.1] || member(u,universal_class) -> equal(unordered_pair(ordinal_numbers,unordered_pair(range_of(u),singleton(v))),ordered_pair(range_of(u),v))**. % 300.04/300.42 169629[19:MRR:169175.4,167057.0] || subclass(complement(u),ordinal_numbers)* member(v,universal_class)* well_ordering(w,kind_1_ordinals)* -> member(v,u)*. % 300.04/300.42 169500[19:Rew:166997.0,168087.1] || member(u,universal_class) subclass(rest_relation,symmetrization_of(ordinal_numbers)) -> member(ordered_pair(u,rest_of(u)),inverse(ordinal_numbers))*. % 300.04/300.42 169497[19:Rew:166997.0,168074.0] || member(u,intersection(complement(v),symmetrization_of(ordinal_numbers)))* member(u,union(v,complement(inverse(ordinal_numbers)))) -> . % 300.04/300.42 169496[19:Rew:166997.0,168071.0] || member(u,intersection(symmetrization_of(ordinal_numbers),complement(v)))* member(u,union(complement(inverse(ordinal_numbers)),v)) -> . % 300.04/300.42 169495[19:Rew:166997.0,168059.0] || subclass(universal_class,intersection(complement(u),symmetrization_of(ordinal_numbers))) member(omega,union(u,complement(inverse(ordinal_numbers))))* -> . % 300.04/300.42 169494[19:Rew:166997.0,168058.0] || subclass(universal_class,intersection(symmetrization_of(ordinal_numbers),complement(u))) member(omega,union(complement(inverse(ordinal_numbers)),u))* -> . % 300.04/300.42 169505[19:Rew:166997.0,168133.1] || subclass(power_class(complement(inverse(ordinal_numbers))),image(element_relation,symmetrization_of(ordinal_numbers)))* -> equal(power_class(complement(inverse(ordinal_numbers))),ordinal_numbers). % 300.04/300.42 169493[19:Rew:166997.0,168016.1] || member(u,universal_class) -> member(u,image(element_relation,symmetrization_of(ordinal_numbers)))* member(u,power_class(complement(inverse(ordinal_numbers)))). % 300.04/300.42 167623[19:Rew:166997.0,164141.2] || subclass(inverse(u),u)* asymmetric(u,universal_class) -> equal(image(inverse(u),universal_class),range_of(ordinal_numbers))**. % 300.04/300.42 169479[19:Rew:166997.0,167612.0] || member(ordered_pair(u,v),compose(ordinal_numbers,w))* subclass(range_of(ordinal_numbers),x)* -> member(v,x)*. % 300.04/300.42 175568[20:Res:175558.0,126.0] || subclass(inverse(ordinal_numbers),u)* well_ordering(v,u)* -> member(least(v,inverse(ordinal_numbers)),inverse(ordinal_numbers))*. % 300.04/300.42 175883[19:Res:168563.2,36583.0] || well_ordering(u,cross_product(universal_class,universal_class)) -> equal(compose_class(v),ordinal_numbers) member(least(u,compose_class(v)),universal_class)*. % 300.04/300.42 175902[19:Res:168564.2,36583.0] || well_ordering(u,cross_product(universal_class,universal_class)) -> equal(rest_of(v),ordinal_numbers) member(least(u,rest_of(v)),universal_class)*. % 300.04/300.42 176111[20:Res:175613.1,488.0] || subclass(universal_class,intersection(complement(u),complement(v))) member(regular(symmetrization_of(ordinal_numbers)),union(u,v))* -> . % 300.04/300.42 176118[20:Res:175613.1,9.0] || subclass(universal_class,unordered_pair(u,v))* -> equal(regular(symmetrization_of(ordinal_numbers)),v) equal(regular(symmetrization_of(ordinal_numbers)),u). % 300.04/300.42 176170[19:SpR:142500.0,167788.1] || asymmetric(universal_class,singleton(u)) -> equal(range__dfg(inverse(universal_class),u,singleton(u)),second(not_subclass_element(ordinal_numbers,ordinal_numbers)))**. % 300.04/300.42 177445[19:Res:167011.0,168644.0] || subclass(universal_class,u) well_ordering(omega,u)* -> equal(integer_of(ordered_pair(ordinal_numbers,least(omega,universal_class))),ordinal_numbers)**. % 300.04/300.42 177498[22:Res:177170.0,168644.0] || subclass(omega,u) well_ordering(omega,u)* -> equal(integer_of(ordered_pair(ordinal_numbers,least(omega,omega))),ordinal_numbers)**. % 300.04/300.42 177826[19:SpR:177036.0,14.0] || -> equal(range_of(u),ordinal_numbers) equal(unordered_pair(ordinal_numbers,unordered_pair(inverse(u),singleton(v))),ordered_pair(inverse(u),v))**. % 300.04/300.42 177864[19:SpL:177036.0,2557.0] || member(singleton(singleton(ordinal_numbers)),cross_product(u,v))* -> equal(range_of(w),ordinal_numbers) member(inverse(w),v)*. % 300.04/300.42 178384[22:SpL:479.0,178292.1] inductive(image(element_relation,union(u,v))) || equal(power_class(intersection(complement(u),complement(v))),omega)** -> . % 300.04/300.42 178438[19:SpL:168412.1,135397.0] || subclass(regular(cross_product(u,v)),w)* well_ordering(universal_class,w) -> equal(cross_product(u,v),ordinal_numbers). % 300.04/300.42 178459[19:SpL:168412.1,137176.0] || equal(u,regular(cross_product(v,w)))* well_ordering(universal_class,u)* -> equal(cross_product(v,w),ordinal_numbers). % 300.04/300.42 178519[19:Obv:178516.1] || equal(rest_of(u),rest_relation) -> equal(regular(unordered_pair(v,u)),v)** equal(unordered_pair(v,u),ordinal_numbers). % 300.04/300.42 178520[19:Obv:178515.1] || equal(rest_of(u),rest_relation) -> equal(regular(unordered_pair(u,v)),v)** equal(unordered_pair(u,v),ordinal_numbers). % 300.04/300.42 178750[19:SSi:178725.0,70.0] || -> equal(unordered_pair(u,v),ordinal_numbers) equal(apply(choice,unordered_pair(u,v)),v)** equal(cantor(u),ordinal_numbers). % 300.04/300.42 178751[19:SSi:178726.0,70.0] || -> equal(unordered_pair(u,v),ordinal_numbers) equal(apply(choice,unordered_pair(u,v)),u)** equal(cantor(v),ordinal_numbers). % 300.04/300.42 179052[19:Obv:179023.0] || -> equal(not_subclass_element(unordered_pair(u,v),w),u)** subclass(unordered_pair(u,v),w) equal(cantor(v),ordinal_numbers). % 300.04/300.42 179053[19:Obv:179022.0] || -> equal(not_subclass_element(unordered_pair(u,v),w),v)** subclass(unordered_pair(u,v),w) equal(cantor(u),ordinal_numbers). % 300.04/300.42 180170[19:Rew:180089.0,169469.1] || member(u,universal_class) -> member(u,image(element_relation,singleton(ordinal_numbers)))* member(u,power_class(complement(singleton(ordinal_numbers)))). % 300.04/300.42 180244[19:Rew:180089.0,179166.0] || subclass(power_class(complement(singleton(ordinal_numbers))),image(element_relation,singleton(ordinal_numbers)))* -> equal(power_class(complement(singleton(ordinal_numbers))),ordinal_numbers). % 300.04/300.42 180288[19:Rew:180089.0,169471.0] || subclass(universal_class,intersection(singleton(ordinal_numbers),complement(u))) member(omega,union(complement(singleton(ordinal_numbers)),u))* -> . % 300.04/300.42 180326[19:Rew:180089.0,169473.0] || member(u,intersection(singleton(ordinal_numbers),complement(v)))* member(u,union(complement(singleton(ordinal_numbers)),v)) -> . % 300.04/300.42 180857[19:Res:24.2,169221.1] || member(ordinal_numbers,u) member(ordinal_numbers,v) equal(complement(intersection(v,u)),singleton(ordinal_numbers))** -> . % 300.04/300.42 181633[20:Res:181628.0,126.0] || subclass(symmetrization_of(ordinal_numbers),u)* well_ordering(v,u)* -> member(least(v,symmetrization_of(ordinal_numbers)),symmetrization_of(ordinal_numbers))*. % 300.04/300.42 181739[20:Res:175570.1,16102.0] || subclass(inverse(ordinal_numbers),symmetric_difference(complement(u),complement(v)))* -> member(regular(symmetrization_of(ordinal_numbers)),union(u,v)). % 300.04/300.42 181800[19:Res:176345.1,16102.0] || subclass(domain_relation,symmetric_difference(complement(u),complement(v))) -> member(singleton(singleton(singleton(ordinal_numbers))),union(u,v))*. % 300.04/300.42 182411[19:Res:24.2,182393.0] || member(singleton(ordinal_numbers),u) member(singleton(ordinal_numbers),v) well_ordering(universal_class,intersection(v,u))* -> . % 300.04/300.42 182865[19:Res:181489.1,8.0] || member(u,inverse(ordinal_numbers)) subclass(symmetrization_of(ordinal_numbers),singleton(u))* -> equal(symmetrization_of(ordinal_numbers),singleton(u)). % 300.04/300.42 182891[19:Res:182871.1,16455.1] || member(not_subclass_element(u,v),inverse(ordinal_numbers))* subclass(u,complement(symmetrization_of(ordinal_numbers))) -> subclass(u,v). % 300.04/300.42 182892[19:Res:182871.1,42071.0] || member(not_subclass_element(u,intersection(symmetrization_of(ordinal_numbers),u)),inverse(ordinal_numbers))* -> subclass(u,intersection(symmetrization_of(ordinal_numbers),u)). % 300.04/300.42 182894[19:Res:182871.1,15100.2] || member(sum_class(u),inverse(ordinal_numbers))* member(u,universal_class) subclass(universal_class,complement(symmetrization_of(ordinal_numbers))) -> . % 300.04/300.42 182895[19:Res:182871.1,15066.2] || member(power_class(u),inverse(ordinal_numbers))* member(u,universal_class) subclass(universal_class,complement(symmetrization_of(ordinal_numbers))) -> . % 300.04/300.42 182920[20:Res:181635.1,16102.0] || subclass(symmetrization_of(ordinal_numbers),symmetric_difference(complement(u),complement(v)))* -> member(regular(symmetrization_of(ordinal_numbers)),union(u,v)). % 300.04/300.42 183038[19:SpL:124905.0,182439.1] || subclass(rest_relation,rest_of(restrict(u,v,singleton(w))))* well_ordering(universal_class,segment(u,v,w)) -> . % 300.04/300.42 183100[19:Res:182463.1,16102.0] || equal(symmetric_difference(complement(u),complement(v)),singleton(singleton(ordinal_numbers))) -> member(singleton(ordinal_numbers),union(u,v))*. % 300.04/300.42 183101[19:Res:182463.1,9.0] || equal(unordered_pair(u,v),singleton(singleton(ordinal_numbers)))** -> equal(singleton(ordinal_numbers),v) equal(singleton(ordinal_numbers),u). % 300.04/300.42 183364[8:SpR:124905.0,131984.1] || equal(complement(rest_of(restrict(u,v,singleton(w)))),universal_class)** -> subclass(segment(u,v,w),x)*. % 300.04/300.42 183716[19:SpL:4121.0,169224.0] || equal(symmetric_difference(cross_product(u,v),w),singleton(ordinal_numbers)) -> member(ordinal_numbers,complement(restrict(w,u,v)))*. % 300.04/300.42 183717[19:SpL:4119.0,169224.0] || equal(symmetric_difference(u,cross_product(v,w)),singleton(ordinal_numbers)) -> member(ordinal_numbers,complement(restrict(u,v,w)))*. % 300.04/300.42 184052[23:Rew:183840.0,183891.0] || asymmetric(u,ordinal_numbers) -> equal(range__dfg(intersection(u,inverse(u)),universal_class,ordinal_numbers),second(not_subclass_element(ordinal_numbers,ordinal_numbers)))**. % 300.04/300.42 184140[23:SpL:183857.0,34.0] || member(ordered_pair(singleton(singleton(ordinal_numbers)),u),rotate(v))* -> member(ordered_pair(ordered_pair(universal_class,u),ordinal_numbers),v). % 300.04/300.42 184141[23:SpL:183857.0,37.0] || member(ordered_pair(singleton(singleton(ordinal_numbers)),u),flip(v))* -> member(ordered_pair(ordered_pair(universal_class,ordinal_numbers),u),v). % 300.04/300.42 184653[19:Res:167339.2,956.0] || subclass(omega,successor_relation) -> equal(integer_of(singleton(singleton(singleton(u)))),ordinal_numbers)** equal(successor(singleton(u)),u). % 300.04/300.42 184838[19:Res:176419.1,2.0] || subclass(domain_relation,flip(u))* subclass(u,v)* -> member(ordered_pair(ordered_pair(w,x),ordinal_numbers),v)*. % 300.04/300.42 184844[19:Res:176419.1,4127.0] || subclass(domain_relation,flip(symmetric_difference(u,v))) -> member(ordered_pair(ordered_pair(w,x),ordinal_numbers),union(u,v))*. % 300.04/300.42 184846[19:Res:176419.1,16910.0] || subclass(domain_relation,flip(symmetric_difference(u,inverse(u))))* -> member(ordered_pair(ordered_pair(v,w),ordinal_numbers),symmetrization_of(u))*. % 300.04/300.42 184916[19:Res:176420.1,2.0] || subclass(domain_relation,rotate(u))* subclass(u,v)* -> member(ordered_pair(ordered_pair(w,ordinal_numbers),x),v)*. % 300.04/300.42 184922[19:Res:176420.1,4127.0] || subclass(domain_relation,rotate(symmetric_difference(u,v))) -> member(ordered_pair(ordered_pair(w,ordinal_numbers),x),union(u,v))*. % 300.04/300.42 184924[19:Res:176420.1,16910.0] || subclass(domain_relation,rotate(symmetric_difference(u,inverse(u))))* -> member(ordered_pair(ordered_pair(v,ordinal_numbers),w),symmetrization_of(u))*. % 300.04/300.42 185110[19:MRR:185101.2,167262.1] || connected(u,singleton(v)) -> well_ordering(u,singleton(v)) equal(regular(not_well_ordering(u,singleton(v))),v)**. % 300.04/300.42 185247[19:Res:168252.2,25.1] || well_ordering(u,complement(v)) member(least(u,complement(v)),v)* -> equal(complement(v),ordinal_numbers). % 300.04/300.42 185257[19:Res:168252.2,2.0] || well_ordering(u,v) subclass(v,w) -> equal(v,ordinal_numbers) member(least(u,v),w)*. % 300.04/300.42 185438[23:MRR:185437.0,167176.0] || -> equal(apply(choice,ordered_pair(universal_class,universal_class)),unordered_pair(universal_class,ordinal_numbers))** equal(apply(choice,ordered_pair(universal_class,universal_class)),ordinal_numbers). % 300.04/300.42 185815[0:Res:15058.1,30589.0] function(u) || subclass(rest_relation,successor_relation) -> equal(rest_of(apply(u,v)),successor(apply(u,v)))**. % 300.04/300.42 185816[0:Res:36682.1,30589.0] || subclass(rest_relation,successor_relation) -> subclass(u,v) equal(rest_of(not_subclass_element(u,v)),successor(not_subclass_element(u,v)))**. % 300.04/300.42 186336[19:Res:167776.1,1073.1] inductive(intersection(u,singleton(v))) || -> equal(integer_of(v),ordinal_numbers) equal(intersection(u,singleton(v)),omega)**. % 300.04/300.42 186366[19:Res:167777.1,1073.1] inductive(intersection(singleton(u),v)) || -> equal(integer_of(u),ordinal_numbers) equal(intersection(singleton(u),v),omega)**. % 300.04/300.42 186384[19:Res:186353.1,1073.1] inductive(complement(complement(singleton(u)))) || -> equal(integer_of(u),ordinal_numbers) equal(complement(complement(singleton(u))),omega)**. % 300.04/300.42 186386[19:Res:186353.1,2497.1] || member(u,universal_class) -> equal(integer_of(v),ordinal_numbers) member(u,complement(singleton(v)))* member(u,omega). % 300.04/300.42 186964[19:Res:166605.0,167734.1] || subclass(u,complement(inverse(singleton(regular(u)))))* -> asymmetric(singleton(regular(u)),v)* equal(u,ordinal_numbers). % 300.04/300.42 187074[19:Obv:187022.1] || subclass(intersection(u,singleton(v)),w)* -> equal(intersection(u,singleton(v)),ordinal_numbers) member(v,w). % 300.04/300.42 187104[19:SpL:167200.0,186989.0] || subclass(image(element_relation,symmetrization_of(ordinal_numbers)),power_class(complement(inverse(ordinal_numbers))))* -> equal(image(element_relation,symmetrization_of(ordinal_numbers)),ordinal_numbers). % 300.04/300.42 187105[19:SpL:180125.0,186989.0] || subclass(image(element_relation,singleton(ordinal_numbers)),power_class(complement(singleton(ordinal_numbers))))* -> equal(image(element_relation,singleton(ordinal_numbers)),ordinal_numbers). % 300.04/300.42 187193[19:Obv:187131.1] || subclass(intersection(singleton(u),v),w)* -> equal(intersection(singleton(u),v),ordinal_numbers) member(u,w). % 300.04/300.42 187289[19:SpL:160.0,168377.0] || subclass(omega,symmetric_difference(u,v)) -> equal(integer_of(w),ordinal_numbers) member(w,complement(intersection(u,v)))*. % 300.04/300.42 187522[19:SpL:160.0,167736.0] || subclass(u,symmetric_difference(v,w)) -> equal(u,ordinal_numbers) member(regular(u),complement(intersection(v,w)))*. % 300.04/300.42 187806[19:Res:168350.1,25.1] || member(regular(restrict(complement(u),v,w)),u)* -> equal(restrict(complement(u),v,w),ordinal_numbers). % 300.04/300.42 187836[19:Res:168350.1,169207.0] || -> equal(restrict(symmetrization_of(ordinal_numbers),u,v),ordinal_numbers) member(regular(restrict(symmetrization_of(ordinal_numbers),u,v)),inverse(ordinal_numbers))*. % 300.04/300.42 188845[19:SpL:479.0,188653.0] || equal(power_class(intersection(complement(u),complement(v))),universal_class)** -> equal(image(element_relation,union(u,v)),ordinal_numbers). % 300.04/300.42 189086[2:Res:188649.1,1065.0] || equal(complement(cross_product(universal_class,cross_product(universal_class,universal_class))),universal_class)** -> equal(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function). % 300.04/300.42 189099[2:Res:188649.1,120.0] || equal(complement(compose(restrict(u,v,v),restrict(u,v,v))),universal_class)** -> transitive(u,v). % 300.04/300.42 189172[19:Res:188649.1,167173.1] || equal(complement(compose(u,inverse(u))),universal_class)** subclass(u,cross_product(universal_class,universal_class)) -> function(u). % 300.04/300.42 190300[19:Rew:167191.0,190174.1] || member(regular(intersection(u,symmetrization_of(ordinal_numbers))),complement(inverse(ordinal_numbers)))* -> equal(intersection(u,symmetrization_of(ordinal_numbers)),ordinal_numbers). % 300.04/300.42 190681[19:Rew:167191.0,190604.1] || member(regular(intersection(symmetrization_of(ordinal_numbers),u)),complement(inverse(ordinal_numbers)))* -> equal(intersection(symmetrization_of(ordinal_numbers),u),ordinal_numbers). % 300.04/300.42 191050[19:SpR:149012.1,168353.1] || subclass(u,v) -> equal(symmetric_difference(v,u),ordinal_numbers) member(regular(symmetric_difference(v,u)),complement(u))*. % 300.04/300.42 191081[19:Res:168353.1,11848.0] || subclass(complement(intersection(u,v)),w)* well_ordering(universal_class,w) -> equal(symmetric_difference(u,v),ordinal_numbers). % 300.04/300.42 192334[19:Res:2523.2,192214.0] || member(u,universal_class) subclass(rest_relation,cantor(complement(cross_product(singleton(ordered_pair(u,rest_of(u))),universal_class))))* -> . % 300.04/300.42 193632[25:Rew:193223.1,193359.1] function(u) || asymmetric(v,ordinal_numbers) -> equal(segment(intersection(v,inverse(v)),ordinal_numbers,u),ordinal_numbers)**. % 300.04/300.42 193876[25:SpL:193832.1,99366.2] one_to_one(u) || member(v,universal_class)* member(u,universal_class)* equal(sum_class(universal_class),v) -> . % 300.04/300.42 193935[25:SoR:193238.0,12322.2] function(u) single_valued_class(apply(u,v)) || equal(apply(u,v),cross_product(universal_class,universal_class))** -> . % 300.04/300.42 193957[25:SoR:193239.0,12322.2] single_valued_class(not_subclass_element(u,v)) || equal(cross_product(universal_class,universal_class),not_subclass_element(u,v))* -> subclass(u,v). % 300.04/300.42 194017[19:Rew:167191.0,193964.1] || member(u,universal_class) subclass(domain_relation,symmetrization_of(ordinal_numbers)) -> subclass(singleton(ordered_pair(u,ordinal_numbers)),symmetrization_of(ordinal_numbers))*. % 300.04/300.42 194018[19:Rew:180103.0,193965.1] || member(u,universal_class) subclass(domain_relation,singleton(ordinal_numbers)) -> subclass(singleton(ordered_pair(u,ordinal_numbers)),singleton(ordinal_numbers))*. % 300.04/300.42 194032[19:MRR:194031.0,167011.0] || equal(compose(u,v),ordinal_numbers)** member(v,universal_class) subclass(domain_relation,complement(compose_class(u)))* -> . % 300.04/300.42 194154[23:Rew:184170.1,194153.2] || member(ordered_pair(u,singleton(singleton(ordinal_numbers))),composition_function)* -> equal(range_of(v),ordinal_numbers)** equal(inverse(v),universal_class). % 300.04/300.42 194156[23:Rew:184170.1,194155.2] || member(u,universal_class)* member(ordered_pair(v,singleton(singleton(ordinal_numbers))),composition_function)* -> equal(range_of(u),universal_class). % 300.04/300.42 194158[23:Rew:184170.1,194157.2,194156.2,194157.2] || member(u,universal_class)* member(ordered_pair(v,singleton(singleton(ordinal_numbers))),composition_function)* -> equal(sum_class(universal_class),universal_class). % 300.04/300.42 194372[19:SpR:124908.0,167580.1] || member(u,universal_class) -> member(u,range_of(v)) equal(apply(inverse(v),u),sum_class(range_of(ordinal_numbers)))**. % 300.04/300.42 194401[19:Res:167580.1,110991.0] || member(u,universal_class) subclass(universal_class,complement(element_relation))* -> equal(apply(u,u),sum_class(range_of(ordinal_numbers)))**. % 300.04/300.42 194440[19:MRR:194376.2,167057.0] || member(u,universal_class) member(v,universal_class) -> equal(apply(sum_class(u),v),sum_class(range_of(ordinal_numbers)))**. % 300.04/300.42 194441[19:MRR:194384.2,167057.0] || member(u,universal_class) member(v,universal_class) -> equal(apply(power_class(u),v),sum_class(range_of(ordinal_numbers)))**. % 300.04/300.42 194442[19:MRR:194385.2,167057.0] || member(u,universal_class) member(v,universal_class) -> equal(apply(rest_of(u),v),sum_class(range_of(ordinal_numbers)))**. % 300.04/300.42 194445[19:MRR:194388.2,167057.0] function(u) || member(v,universal_class) -> equal(apply(apply(u,w),v),sum_class(range_of(ordinal_numbers)))**. % 300.04/300.42 194446[19:MRR:194389.2,167057.0] || member(u,universal_class) -> subclass(v,w) equal(apply(not_subclass_element(v,w),u),sum_class(range_of(ordinal_numbers)))**. % 300.04/300.42 194461[19:MRR:194405.0,36682.1] || -> equal(apply(u,not_subclass_element(complement(cantor(u)),v)),sum_class(range_of(ordinal_numbers)))** subclass(complement(cantor(u)),v). % 300.04/300.42 195094[25:SpR:193305.1,168194.1] function(u) || subclass(omega,element_relation) -> equal(integer_of(singleton(singleton(ordinal_numbers))),ordinal_numbers)** member(ordinal_numbers,u)*. % 300.04/300.42 195195[25:MRR:195194.3,184175.0] function(u) || equal(singleton(ordinal_numbers),u)* member(singleton(singleton(ordinal_numbers)),cross_product(universal_class,universal_class))* -> . % 300.04/300.42 195227[19:SpR:184522.1,27190.1] || subclass(rest_relation,domain_relation) subclass(rest_relation,flip(u)) -> member(ordered_pair(ordered_pair(v,w),ordinal_numbers),u)*. % 300.04/300.42 195228[19:SpR:184390.1,27190.1] || subclass(domain_relation,rest_relation) subclass(rest_relation,flip(u)) -> member(ordered_pair(ordered_pair(v,w),ordinal_numbers),u)*. % 300.04/300.42 195251[0:Res:27190.1,4178.0] || subclass(rest_relation,flip(singleton(u)))* -> equal(ordered_pair(ordered_pair(v,w),rest_of(ordered_pair(w,v))),u)*. % 300.04/300.42 195295[0:Res:27190.1,94.0] || subclass(rest_relation,flip(compose_class(u))) -> equal(compose(u,ordered_pair(v,w)),rest_of(ordered_pair(w,v)))**. % 300.04/300.42 195299[0:Res:27190.1,34.0] || subclass(rest_relation,flip(rotate(u))) -> member(ordered_pair(ordered_pair(v,rest_of(ordered_pair(v,w))),w),u)*. % 300.04/300.42 195300[0:Res:27190.1,37.0] || subclass(rest_relation,flip(flip(u))) -> member(ordered_pair(ordered_pair(v,w),rest_of(ordered_pair(v,w))),u)*. % 300.04/300.42 195329[19:SpR:184522.1,27189.1] || subclass(rest_relation,domain_relation) subclass(rest_relation,rotate(u)) -> member(ordered_pair(ordered_pair(v,ordinal_numbers),w),u)*. % 300.04/300.42 195330[19:SpR:184390.1,27189.1] || subclass(domain_relation,rest_relation) subclass(rest_relation,rotate(u)) -> member(ordered_pair(ordered_pair(v,ordinal_numbers),w),u)*. % 300.04/300.42 195348[0:Res:27189.1,4178.0] || subclass(rest_relation,rotate(singleton(u)))* -> equal(ordered_pair(ordered_pair(v,rest_of(ordered_pair(w,v))),w),u)*. % 300.04/300.42 195392[0:Res:27189.1,94.0] || subclass(rest_relation,rotate(compose_class(u))) -> equal(compose(u,ordered_pair(v,rest_of(ordered_pair(w,v)))),w)**. % 300.04/300.42 195399[0:Res:27189.1,34.0] || subclass(rest_relation,rotate(rotate(u))) -> member(ordered_pair(ordered_pair(rest_of(ordered_pair(v,w)),v),w),u)*. % 300.04/300.42 195400[0:Res:27189.1,37.0] || subclass(rest_relation,rotate(flip(u))) -> member(ordered_pair(ordered_pair(rest_of(ordered_pair(v,w)),w),v),u)*. % 300.04/300.42 195858[19:Rew:167191.0,195797.1,167191.0,195797.0] || -> subclass(singleton(not_subclass_element(intersection(symmetrization_of(ordinal_numbers),u),v)),symmetrization_of(ordinal_numbers))* subclass(intersection(symmetrization_of(ordinal_numbers),u),v). % 300.04/300.42 196036[19:Rew:167191.0,195981.1,167191.0,195981.0] || -> subclass(singleton(not_subclass_element(intersection(u,symmetrization_of(ordinal_numbers)),v)),symmetrization_of(ordinal_numbers))* subclass(intersection(u,symmetrization_of(ordinal_numbers)),v). % 300.04/300.42 196106[19:SpR:188655.1,4121.0] || equal(complement(complement(restrict(u,v,w))),universal_class)** -> equal(symmetric_difference(cross_product(v,w),u),ordinal_numbers). % 300.04/300.42 196107[19:SpR:188655.1,4119.0] || equal(complement(complement(restrict(u,v,w))),universal_class)** -> equal(symmetric_difference(u,cross_product(v,w)),ordinal_numbers). % 300.04/300.42 196543[25:MRR:196542.2,192574.0] single_valued_class(image(element_relation,union(u,v))) || equal(power_class(intersection(complement(u),complement(v))),universal_class)** -> . % 300.04/300.42 196564[19:Obv:196551.2] || subclass(u,omega) subclass(omega,v) -> equal(not_subclass_element(u,v),ordinal_numbers)** subclass(u,v). % 300.04/300.42 196658[19:Res:63.1,167728.0] function(u) || subclass(cross_product(universal_class,universal_class),v)* -> equal(u,ordinal_numbers) member(regular(u),v)*. % 300.04/300.42 196792[19:Obv:196780.2] || subclass(u,symmetric_difference(v,w)) subclass(u,complement(union(v,w)))* -> equal(u,ordinal_numbers). % 300.04/300.42 196793[19:Obv:196768.1] || subclass(singleton(u),symmetric_difference(v,w))* -> equal(singleton(u),ordinal_numbers) member(u,union(v,w)). % 300.04/300.42 196838[19:Res:196731.1,82994.1] || subclass(universal_class,complement(compose(element_relation,universal_class)))* member(regular(element_relation),element_relation) well_ordering(u,v)* -> . % 300.04/300.42 196839[19:Res:196731.1,82995.1] || subclass(universal_class,complement(compose(element_relation,universal_class)))* member(regular(element_relation),element_relation) -> member(regular(element_relation),u)*. % 300.04/300.42 196985[19:Res:169181.1,168251.0] || equal(regular(u),singleton(ordinal_numbers)) member(ordinal_numbers,u)* -> equal(u,ordinal_numbers) member(ordinal_numbers,v)*. % 300.04/300.42 197130[19:SpR:196827.0,168194.1] || subclass(omega,element_relation) -> equal(integer_of(regular(element_relation)),ordinal_numbers) member(first(regular(element_relation)),second(regular(element_relation)))*. % 300.04/300.42 197152[19:SpL:196827.0,143.0] || member(regular(element_relation),rest_of(u)) -> equal(restrict(u,first(regular(element_relation)),universal_class),second(regular(element_relation)))**. % 300.04/300.42 197183[19:SpL:196827.0,97.0] || member(ordered_pair(u,regular(element_relation)),composition_function)* -> equal(compose(u,first(regular(element_relation))),second(regular(element_relation))). % 300.04/300.42 197268[19:Res:168469.2,4178.0] || subclass(u,singleton(v))* -> equal(intersection(w,u),ordinal_numbers) equal(regular(intersection(w,u)),v)*. % 300.04/300.42 197342[19:Obv:197303.2] || subclass(u,v) subclass(intersection(w,u),complement(v))* -> equal(intersection(w,u),ordinal_numbers). % 300.04/300.42 197533[19:Obv:197474.1] || subclass(intersection(u,intersection(v,w)),complement(v))* -> equal(intersection(u,intersection(v,w)),ordinal_numbers). % 300.04/300.42 197549[19:Res:197122.0,126.0] || subclass(regular(element_relation),u)* well_ordering(v,u)* -> member(least(v,regular(element_relation)),regular(element_relation))*. % 300.04/300.42 197737[19:Obv:197675.1] || subclass(intersection(u,intersection(v,w)),complement(w))* -> equal(intersection(u,intersection(v,w)),ordinal_numbers). % 300.04/300.42 197832[19:Res:168474.2,4178.0] || subclass(u,singleton(v))* -> equal(intersection(u,w),ordinal_numbers) equal(regular(intersection(u,w)),v)*. % 300.04/300.42 197904[19:Obv:197867.2] || subclass(u,v) subclass(intersection(u,w),complement(v))* -> equal(intersection(u,w),ordinal_numbers). % 300.04/300.42 198295[19:SpR:479.0,197499.0] || -> equal(intersection(power_class(intersection(complement(u),complement(v))),intersection(image(element_relation,union(u,v)),w)),ordinal_numbers)**. % 300.04/300.42 198542[19:Obv:198478.1] || subclass(intersection(intersection(u,v),w),complement(u))* -> equal(intersection(intersection(u,v),w),ordinal_numbers). % 300.04/300.42 198942[19:SpR:479.0,197702.0] || -> equal(intersection(power_class(intersection(complement(u),complement(v))),intersection(w,image(element_relation,union(u,v)))),ordinal_numbers)**. % 300.04/300.42 199213[19:Obv:199142.1] || subclass(intersection(intersection(u,v),w),complement(v))* -> equal(intersection(intersection(u,v),w),ordinal_numbers). % 300.04/300.42 200393[19:Res:196731.1,16086.0] || subclass(universal_class,symmetric_difference(cross_product(u,v),w)) -> member(regular(element_relation),complement(restrict(w,u,v)))*. % 300.04/300.42 200708[19:Res:196731.1,16083.0] || subclass(universal_class,symmetric_difference(u,cross_product(v,w))) -> member(regular(element_relation),complement(restrict(u,v,w)))*. % 300.04/300.42 200757[8:SpR:125331.0,124899.1] || section(cross_product(u,singleton(v)),w,x) -> subclass(segment(cross_product(x,w),u,v),w)*. % 300.04/300.42 200898[19:Res:168349.1,11848.0] || subclass(cross_product(u,v),w)* well_ordering(universal_class,w) -> equal(restrict(x,u,v),ordinal_numbers)**. % 300.04/300.42 200908[19:Obv:200904.1] || subclass(restrict(u,v,w),complement(cross_product(v,w)))* -> equal(restrict(u,v,w),ordinal_numbers). % 300.04/300.42 201698[26:Rew:200916.0,169004.2] || subclass(complement(u),ordinal_numbers)* member(v,universal_class)* well_ordering(w,ordinal_numbers)* -> member(v,u)*. % 300.04/300.42 203387[19:SpR:479.0,203242.1] || subclass(image(element_relation,union(u,v)),ordinal_numbers) -> subclass(universal_class,power_class(intersection(complement(u),complement(v))))*. % 300.04/300.42 203581[26:Res:169181.1,202277.1] || equal(complement(compose(complement(element_relation),inverse(element_relation))),singleton(ordinal_numbers))** member(ordinal_numbers,cross_product(universal_class,universal_class)) -> . % 300.04/300.42 203672[19:Res:7.1,177417.0] || equal(u,universal_class) well_ordering(omega,u)* -> equal(integer_of(ordered_pair(omega,least(omega,universal_class))),ordinal_numbers)**. % 300.04/300.42 204402[20:Rew:204394.1,204389.1] || subclass(universal_class,ordered_pair(u,v))* -> equal(regular(symmetrization_of(ordinal_numbers)),omega) equal(regular(symmetrization_of(ordinal_numbers)),ordinal_numbers). % 300.04/300.42 204703[19:MRR:204696.3,167176.0] || member(u,universal_class)* subclass(domain_relation,omega) subclass(omega,successor_relation) -> equal(successor(u),ordinal_numbers). % 300.04/300.42 204704[19:MRR:204695.3,167176.0] || member(u,universal_class)* subclass(domain_relation,omega) subclass(omega,rest_relation) -> equal(rest_of(u),ordinal_numbers). % 300.04/300.42 205384[19:SpL:479.0,203422.0] || subclass(power_class(intersection(complement(u),complement(v))),ordinal_numbers)* -> member(ordinal_numbers,image(element_relation,union(u,v))). % 300.04/300.42 205407[19:SpL:479.0,203423.0] || subclass(power_class(intersection(complement(u),complement(v))),ordinal_numbers)* -> member(omega,image(element_relation,union(u,v))). % 300.04/300.42 205537[19:SpR:204449.1,479.0] || equal(image(element_relation,union(u,v)),ordinal_numbers) -> equal(power_class(intersection(complement(u),complement(v))),universal_class)**. % 300.04/300.42 206216[0:SpR:27838.0,149179.0] || -> equal(intersection(successor(u),symmetric_difference(complement(u),complement(singleton(u)))),symmetric_difference(complement(u),complement(singleton(u))))**. % 300.04/300.42 206503[19:Rew:206400.0,205108.0] || -> equal(intersection(union(u,image(element_relation,power_class(v))),intersection(complement(u),power_class(complement(power_class(v))))),ordinal_numbers)**. % 300.04/300.42 206504[19:Rew:206400.0,205110.0] || -> equal(symmetric_difference(union(u,image(element_relation,power_class(v))),intersection(complement(u),power_class(complement(power_class(v))))),universal_class)**. % 300.04/300.42 206674[19:Rew:206400.0,190310.0] || member(regular(intersection(u,power_class(v))),complement(power_class(v)))* -> equal(intersection(u,power_class(v)),ordinal_numbers). % 300.04/300.42 206724[20:Rew:206400.0,176127.0] || subclass(universal_class,power_class(complement(power_class(u)))) member(regular(symmetrization_of(ordinal_numbers)),image(element_relation,power_class(u)))* -> . % 300.04/300.42 206727[0:Rew:206400.0,154843.0] || subclass(universal_class,power_class(complement(power_class(u)))) member(ordered_pair(v,w),image(element_relation,power_class(u)))* -> . % 300.04/300.42 206728[0:Rew:206400.0,154822.0] || subclass(universal_class,power_class(complement(power_class(u)))) member(unordered_pair(v,w),image(element_relation,power_class(u)))* -> . % 300.04/300.42 206770[19:Rew:206400.0,204770.0] || -> equal(intersection(union(image(element_relation,power_class(u)),v),intersection(power_class(complement(power_class(u))),complement(v))),ordinal_numbers)**. % 300.04/300.42 206771[19:Rew:206400.0,204772.0] || -> equal(symmetric_difference(union(image(element_relation,power_class(u)),v),intersection(power_class(complement(power_class(u))),complement(v))),universal_class)**. % 300.04/300.42 206887[19:Rew:206400.0,167447.0] || subclass(domain_relation,power_class(complement(power_class(u)))) member(ordered_pair(ordinal_numbers,ordinal_numbers),image(element_relation,power_class(u)))* -> . % 300.04/300.42 206946[19:Rew:206400.0,187102.0] || subclass(image(element_relation,power_class(u)),power_class(complement(power_class(u))))* -> equal(image(element_relation,power_class(u)),ordinal_numbers). % 300.04/300.42 207286[19:Rew:206400.0,186070.0] || subclass(omega,complement(power_class(u)))* -> equal(integer_of(regular(power_class(u))),ordinal_numbers) equal(power_class(u),ordinal_numbers). % 300.04/300.42 207317[19:Rew:206400.0,190692.0] || member(regular(intersection(power_class(u),v)),complement(power_class(u)))* -> equal(intersection(power_class(u),v),ordinal_numbers). % 300.04/300.42 207344[0:Rew:206403.0,147300.1] || subclass(universal_class,intersection(complement(u),power_class(v))) member(omega,union(u,complement(power_class(v))))* -> . % 300.04/300.42 207360[0:Rew:206410.0,147301.1] || subclass(universal_class,intersection(power_class(u),complement(v))) member(omega,union(complement(power_class(u)),v))* -> . % 300.04/300.42 207392[19:Rew:206400.0,206922.1] || subclass(power_class(complement(power_class(u))),image(element_relation,power_class(u)))* -> equal(power_class(complement(power_class(u))),ordinal_numbers). % 300.04/300.42 207393[19:Rew:206400.0,207046.0] || -> member(ordinal_numbers,intersection(power_class(u),complement(singleton(complement(power_class(u))))))* member(ordinal_numbers,successor(complement(power_class(u)))). % 300.04/300.42 207394[19:Rew:206400.0,207154.0] || -> member(ordinal_numbers,intersection(power_class(u),complement(inverse(complement(power_class(u))))))* member(ordinal_numbers,symmetrization_of(complement(power_class(u)))). % 300.04/300.42 207680[19:Rew:167022.0,206370.1,27.0,206370.1,167022.0,206370.0,27.0,206370.0] || member(not_subclass_element(image(element_relation,kind_1_ordinals),u),complement(image(element_relation,kind_1_ordinals)))* -> subclass(image(element_relation,kind_1_ordinals),u). % 300.04/300.42 207941[19:Res:205391.1,16083.0] || equal(complement(symmetric_difference(u,cross_product(v,w))),ordinal_numbers) -> member(ordinal_numbers,complement(restrict(u,v,w)))*. % 300.04/300.42 207946[19:Res:205391.1,16086.0] || equal(complement(symmetric_difference(cross_product(u,v),w)),ordinal_numbers) -> member(ordinal_numbers,complement(restrict(w,u,v)))*. % 300.04/300.42 207960[19:Res:205391.1,168251.0] || equal(complement(regular(u)),ordinal_numbers)** member(ordinal_numbers,u) -> equal(u,ordinal_numbers) member(ordinal_numbers,v)*. % 300.04/300.42 208218[0:SpR:206403.0,16762.0] || -> subclass(symmetric_difference(union(u,complement(power_class(v))),complement(w)),union(intersection(complement(u),power_class(v)),w))*. % 300.04/300.42 208236[19:SpR:206403.0,182467.1] || -> member(singleton(ordinal_numbers),intersection(complement(u),power_class(v)))* member(singleton(ordinal_numbers),union(u,complement(power_class(v)))). % 300.04/300.42 208258[0:SpR:206403.0,16762.0] || -> subclass(symmetric_difference(complement(u),union(v,complement(power_class(w)))),union(u,intersection(complement(v),power_class(w))))*. % 300.04/300.42 208319[19:SpL:206403.0,167096.0] || subclass(universal_class,union(u,complement(power_class(v)))) member(ordinal_numbers,intersection(complement(u),power_class(v)))* -> . % 300.04/300.42 208320[8:SpL:206403.0,164453.1] || subclass(domain_relation,intersection(complement(u),power_class(v)))* subclass(universal_class,union(u,complement(power_class(v)))) -> . % 300.04/300.42 208322[0:SpL:206403.0,2532.0] || subclass(universal_class,union(u,complement(power_class(v)))) member(omega,intersection(complement(u),power_class(v)))* -> . % 300.04/300.42 208323[0:SpL:206403.0,9715.1] || subclass(universal_class,intersection(complement(u),power_class(v)))* subclass(universal_class,union(u,complement(power_class(v)))) -> . % 300.04/300.42 208324[19:SpL:206403.0,167093.0] || subclass(universal_class,complement(union(u,complement(power_class(v)))))* -> member(ordinal_numbers,intersection(complement(u),power_class(v))). % 300.04/300.42 208325[0:SpL:206403.0,148626.0] || subclass(universal_class,complement(union(u,complement(power_class(v)))))* -> member(omega,intersection(complement(u),power_class(v))). % 300.04/300.42 208328[19:SpL:206403.0,167094.0] || equal(complement(union(u,complement(power_class(v)))),universal_class) -> member(ordinal_numbers,intersection(complement(u),power_class(v)))*. % 300.04/300.42 208329[0:SpL:206403.0,6422.0] || equal(complement(union(u,complement(power_class(v)))),universal_class) -> member(omega,intersection(complement(u),power_class(v)))*. % 300.04/300.42 208330[22:SpL:206403.0,177183.0] || subclass(omega,complement(union(u,complement(power_class(v)))))* -> member(ordinal_numbers,intersection(complement(u),power_class(v))). % 300.04/300.42 208331[22:SpL:206403.0,178014.0] || equal(complement(union(u,complement(power_class(v)))),omega) -> member(ordinal_numbers,intersection(complement(u),power_class(v)))*. % 300.04/300.42 208337[8:SpL:206403.0,97513.1] || subclass(universal_class,intersection(complement(u),power_class(v))) subclass(domain_relation,union(u,complement(power_class(v))))* -> . % 300.04/300.42 208338[8:SpL:206403.0,97509.1] || subclass(domain_relation,intersection(complement(u),power_class(v)))* subclass(domain_relation,union(u,complement(power_class(v)))) -> . % 300.04/300.42 208343[8:SpL:206403.0,97574.1] || equal(intersection(complement(u),power_class(v)),domain_relation)** equal(union(u,complement(power_class(v))),domain_relation) -> . % 300.04/300.42 208347[19:SpL:206403.0,182395.0] || well_ordering(universal_class,union(u,complement(power_class(v)))) -> member(singleton(ordinal_numbers),intersection(complement(u),power_class(v)))*. % 300.04/300.42 208352[22:SpL:206403.0,177179.0] || subclass(omega,union(u,complement(power_class(v)))) member(ordinal_numbers,intersection(complement(u),power_class(v)))* -> . % 300.04/300.42 208354[22:SpL:206403.0,178652.1] || equal(intersection(complement(u),power_class(v)),omega)** equal(union(u,complement(power_class(v))),omega) -> . % 300.04/300.42 208359[19:SpL:206403.0,180886.1] inductive(intersection(complement(u),power_class(v))) || equal(union(u,complement(power_class(v))),singleton(ordinal_numbers))** -> . % 300.04/300.42 208370[19:SpL:206403.0,196890.1] || subclass(universal_class,intersection(complement(u),power_class(v))) subclass(element_relation,union(u,complement(power_class(v))))* -> . % 300.04/300.42 208381[0:SpL:206403.0,148647.0] || member(u,complement(union(v,complement(power_class(w)))))* -> member(u,intersection(complement(v),power_class(w))). % 300.04/300.42 208472[19:Res:205414.1,16083.0] || equal(complement(symmetric_difference(u,cross_product(v,w))),ordinal_numbers) -> member(omega,complement(restrict(u,v,w)))*. % 300.04/300.42 208477[19:Res:205414.1,16086.0] || equal(complement(symmetric_difference(cross_product(u,v),w)),ordinal_numbers) -> member(omega,complement(restrict(w,u,v)))*. % 300.04/300.42 208491[19:Res:205414.1,168251.0] || equal(complement(regular(u)),ordinal_numbers)** member(omega,u) -> equal(u,ordinal_numbers) member(omega,v)*. % 300.04/300.42 208525[0:SpR:206410.0,16762.0] || -> subclass(symmetric_difference(union(complement(power_class(u)),v),complement(w)),union(intersection(power_class(u),complement(v)),w))*. % 300.04/300.42 208543[19:SpR:206410.0,182467.1] || -> member(singleton(ordinal_numbers),intersection(power_class(u),complement(v)))* member(singleton(ordinal_numbers),union(complement(power_class(u)),v)). % 300.04/300.42 208565[0:SpR:206410.0,16762.0] || -> subclass(symmetric_difference(complement(u),union(complement(power_class(v)),w)),union(u,intersection(power_class(v),complement(w))))*. % 300.04/300.42 208629[19:SpL:206410.0,167096.0] || subclass(universal_class,union(complement(power_class(u)),v)) member(ordinal_numbers,intersection(power_class(u),complement(v)))* -> . % 300.04/300.42 208630[8:SpL:206410.0,164453.1] || subclass(domain_relation,intersection(power_class(u),complement(v)))* subclass(universal_class,union(complement(power_class(u)),v)) -> . % 300.04/300.42 208632[0:SpL:206410.0,2532.0] || subclass(universal_class,union(complement(power_class(u)),v)) member(omega,intersection(power_class(u),complement(v)))* -> . % 300.04/300.42 208633[0:SpL:206410.0,9715.1] || subclass(universal_class,intersection(power_class(u),complement(v)))* subclass(universal_class,union(complement(power_class(u)),v)) -> . % 300.04/300.42 208634[19:SpL:206410.0,167093.0] || subclass(universal_class,complement(union(complement(power_class(u)),v)))* -> member(ordinal_numbers,intersection(power_class(u),complement(v))). % 300.04/300.42 208635[0:SpL:206410.0,148626.0] || subclass(universal_class,complement(union(complement(power_class(u)),v)))* -> member(omega,intersection(power_class(u),complement(v))). % 300.04/300.42 208638[19:SpL:206410.0,167094.0] || equal(complement(union(complement(power_class(u)),v)),universal_class) -> member(ordinal_numbers,intersection(power_class(u),complement(v)))*. % 300.04/300.42 208639[0:SpL:206410.0,6422.0] || equal(complement(union(complement(power_class(u)),v)),universal_class) -> member(omega,intersection(power_class(u),complement(v)))*. % 300.04/300.42 208640[22:SpL:206410.0,177183.0] || subclass(omega,complement(union(complement(power_class(u)),v)))* -> member(ordinal_numbers,intersection(power_class(u),complement(v))). % 300.04/300.42 208641[22:SpL:206410.0,178014.0] || equal(complement(union(complement(power_class(u)),v)),omega) -> member(ordinal_numbers,intersection(power_class(u),complement(v)))*. % 300.04/300.42 208647[8:SpL:206410.0,97513.1] || subclass(universal_class,intersection(power_class(u),complement(v))) subclass(domain_relation,union(complement(power_class(u)),v))* -> . % 300.04/300.42 208648[8:SpL:206410.0,97509.1] || subclass(domain_relation,intersection(power_class(u),complement(v)))* subclass(domain_relation,union(complement(power_class(u)),v)) -> . % 300.04/300.42 208653[8:SpL:206410.0,97574.1] || equal(intersection(power_class(u),complement(v)),domain_relation)** equal(union(complement(power_class(u)),v),domain_relation) -> . % 300.04/300.42 208657[19:SpL:206410.0,182395.0] || well_ordering(universal_class,union(complement(power_class(u)),v)) -> member(singleton(ordinal_numbers),intersection(power_class(u),complement(v)))*. % 300.04/300.42 208662[22:SpL:206410.0,177179.0] || subclass(omega,union(complement(power_class(u)),v)) member(ordinal_numbers,intersection(power_class(u),complement(v)))* -> . % 300.04/300.42 208664[22:SpL:206410.0,178652.1] || equal(intersection(power_class(u),complement(v)),omega)** equal(union(complement(power_class(u)),v),omega) -> . % 300.04/300.42 208669[19:SpL:206410.0,180886.1] inductive(intersection(power_class(u),complement(v))) || equal(union(complement(power_class(u)),v),singleton(ordinal_numbers))** -> . % 300.04/300.42 208680[19:SpL:206410.0,196890.1] || subclass(universal_class,intersection(power_class(u),complement(v))) subclass(element_relation,union(complement(power_class(u)),v))* -> . % 300.04/300.42 208691[0:SpL:206410.0,148647.0] || member(u,complement(union(complement(power_class(v)),w)))* -> member(u,intersection(power_class(v),complement(w))). % 300.04/300.42 208841[19:Res:205520.1,15078.1] || equal(complement(restrict(u,v,w)),ordinal_numbers)** member(x,universal_class) -> member(power_class(x),u)*. % 300.04/300.42 208842[19:Res:205520.1,15112.1] || equal(complement(restrict(u,v,w)),ordinal_numbers)** member(x,universal_class) -> member(sum_class(x),u)*. % 300.04/300.42 208927[19:Rew:167049.0,208903.2] || equal(complement(complement(symmetrization_of(u))),ordinal_numbers)** connected(u,v)* -> equal(cross_product(v,v),ordinal_numbers)**. % 300.04/300.42 209071[19:SpR:205892.1,16826.0] || equal(intersection(complement(u),complement(singleton(u))),ordinal_numbers)** -> equal(complement(image(element_relation,successor(u))),ordinal_numbers). % 300.04/300.42 209072[19:SpR:205892.1,16825.0] || equal(intersection(complement(u),complement(inverse(u))),ordinal_numbers)** -> equal(complement(image(element_relation,symmetrization_of(u))),ordinal_numbers). % 300.04/300.42 209118[0:Res:2480.1,206404.0] || subclass(universal_class,image(element_relation,power_class(u))) member(unordered_pair(v,w),power_class(complement(power_class(u))))* -> . % 300.04/300.42 209128[0:Res:2481.1,206404.0] || subclass(universal_class,image(element_relation,power_class(u))) member(ordered_pair(v,w),power_class(complement(power_class(u))))* -> . % 300.04/300.42 209132[19:Res:167127.1,206404.0] || subclass(domain_relation,image(element_relation,power_class(u))) member(ordered_pair(ordinal_numbers,ordinal_numbers),power_class(complement(power_class(u))))* -> . % 300.04/300.42 209161[20:Res:175613.1,206404.0] || subclass(universal_class,image(element_relation,power_class(u))) member(regular(symmetrization_of(ordinal_numbers)),power_class(complement(power_class(u))))* -> . % 300.04/300.42 209201[0:SpR:479.0,206400.0] || -> equal(image(element_relation,power_class(intersection(complement(u),complement(v)))),complement(power_class(image(element_relation,union(u,v)))))**. % 300.04/300.42 209500[19:SpL:479.0,208786.0] || equal(power_class(intersection(complement(u),complement(v))),ordinal_numbers)** -> equal(image(element_relation,union(u,v)),universal_class). % 300.04/300.42 209795[19:Res:167116.0,27138.2] || member(u,universal_class) subclass(rest_relation,complement(omega)) -> equal(integer_of(ordered_pair(u,rest_of(u))),ordinal_numbers)**. % 300.04/300.42 209829[0:MRR:209805.2,36583.1] || member(rest_of(u),v)* member(u,w)* subclass(rest_relation,complement(cross_product(w,v)))* -> . % 300.04/300.42 209832[19:MRR:209771.1,196718.0] || subclass(rest_relation,domain_relation) subclass(rest_relation,complement(u)) member(ordered_pair(regular(element_relation),ordinal_numbers),u)* -> . % 300.04/300.42 209833[19:MRR:209770.1,196718.0] || subclass(domain_relation,rest_relation) subclass(rest_relation,complement(u)) member(ordered_pair(regular(element_relation),ordinal_numbers),u)* -> . % 300.04/300.42 209834[19:MRR:209765.1,170.0] || subclass(domain_relation,rest_relation) subclass(rest_relation,complement(u)) member(ordered_pair(singleton(v),ordinal_numbers),u)* -> . % 300.04/300.42 209835[19:MRR:209764.1,170.0] || subclass(rest_relation,domain_relation) subclass(rest_relation,complement(u)) member(ordered_pair(singleton(v),ordinal_numbers),u)* -> . % 300.04/300.42 209888[19:Res:167580.1,205934.1] || member(u,universal_class) equal(cantor(v),ordinal_numbers) -> equal(apply(v,u),sum_class(range_of(ordinal_numbers)))**. % 300.04/300.42 210006[19:Res:9790.2,205934.1] || member(ordered_pair(u,v),cross_product(universal_class,universal_class))* subclass(composition_function,w)* equal(ordinal_numbers,w) -> . % 300.04/300.42 210095[0:SoR:28088.0,72.1] one_to_one(complement(u)) || member(v,universal_class) -> member(v,u)* member(v,cross_product(universal_class,universal_class))*. % 300.04/300.42 210135[19:SpR:27168.2,190384.0] || member(u,universal_class) subclass(rest_relation,rest_of(complement(cross_product(u,universal_class))))* -> equal(rest_of(u),ordinal_numbers). % 300.04/300.42 210143[0:SpR:27168.2,43.0] || member(u,universal_class) subclass(rest_relation,rest_of(v))* -> equal(range_of(rest_of(u)),image(v,u))*. % 300.04/300.42 210187[19:MRR:210174.0,170.0] || subclass(rest_relation,rest_of(u)) member(v,cantor(u))* equal(rest_of(singleton(v)),ordinal_numbers) -> . % 300.04/300.42 210188[19:MRR:210150.0,170.0] || subclass(rest_relation,rest_of(u)) -> equal(second(not_subclass_element(rest_of(singleton(v)),ordinal_numbers)),range__dfg(u,v,universal_class))*. % 300.04/300.42 210223[0:SpR:27837.0,149179.0] || -> equal(intersection(symmetrization_of(u),symmetric_difference(complement(u),complement(inverse(u)))),symmetric_difference(complement(u),complement(inverse(u))))**. % 300.04/300.42 210851[19:Res:176326.2,6476.1] || member(u,universal_class) equal(compose(v,u),ordinal_numbers)** subclass(universal_class,complement(compose_class(v)))* -> . % 300.04/300.42 210854[19:Res:176326.2,188593.1] || member(u,universal_class) equal(compose(v,u),ordinal_numbers)** equal(complement(compose_class(v)),universal_class) -> . % 300.04/300.42 210894[19:Res:167224.0,177022.0] || -> equal(singleton(u),ordinal_numbers) member(u,image(universal_class,singleton(u)))* asymmetric(cross_product(singleton(u),universal_class),v)*. % 300.04/300.42 210895[19:Res:167115.1,177022.0] || -> equal(integer_of(u),ordinal_numbers) member(u,image(universal_class,singleton(u)))* asymmetric(cross_product(singleton(u),universal_class),v)*. % 300.04/300.42 211040[20:MRR:181623.1,210996.0] || well_ordering(u,symmetrization_of(ordinal_numbers)) -> member(least(u,singleton(regular(symmetrization_of(ordinal_numbers)))),singleton(regular(symmetrization_of(ordinal_numbers))))*. % 300.04/300.42 211228[19:Obv:211218.1] || equal(singleton(u),ordinal_numbers) -> equal(regular(unordered_pair(v,u)),v)** equal(unordered_pair(v,u),ordinal_numbers). % 300.04/300.42 211229[19:Obv:211217.1] || equal(singleton(u),ordinal_numbers) -> equal(regular(unordered_pair(u,v)),v)** equal(unordered_pair(u,v),ordinal_numbers). % 300.04/300.42 211278[19:Res:167224.0,15107.0] || subclass(universal_class,u)* subclass(u,v)* -> equal(singleton(w),ordinal_numbers) member(sum_class(w),v)*. % 300.04/300.42 211279[19:Res:167115.1,15107.0] || subclass(universal_class,u)* subclass(u,v)* -> equal(integer_of(w),ordinal_numbers) member(sum_class(w),v)*. % 300.04/300.42 211292[19:Res:167137.1,15107.0] || subclass(universal_class,u)* subclass(u,v)* -> equal(w,ordinal_numbers) member(sum_class(regular(w)),v)*. % 300.04/300.42 211356[19:SpL:5132.1,208801.0] || equal(complement(complement(singleton(not_subclass_element(cross_product(u,v),w)))),ordinal_numbers)** -> subclass(cross_product(u,v),w). % 300.04/300.42 211385[19:Res:167224.0,15098.0] || subclass(universal_class,u) -> equal(singleton(image(v,singleton(w))),ordinal_numbers)** member(apply(v,w),u)*. % 300.04/300.42 211386[19:Res:167115.1,15098.0] || subclass(universal_class,u) -> equal(integer_of(image(v,singleton(w))),ordinal_numbers)** member(apply(v,w),u)*. % 300.04/300.42 211450[0:Res:7.1,9806.0] || equal(image(u,singleton(v)),apply(u,v)) -> section(element_relation,image(u,singleton(v)),universal_class)*. % 300.04/300.42 211600[0:Res:7.1,27147.1] || equal(intersection(u,v),rest_relation)** member(w,universal_class) -> member(ordered_pair(w,rest_of(w)),v)*. % 300.04/300.42 211755[0:Res:7.1,27146.1] || equal(intersection(u,v),rest_relation)** member(w,universal_class) -> member(ordered_pair(w,rest_of(w)),u)*. % 300.04/300.42 211843[0:SpL:44.0,27264.1] || subclass(universal_class,intersection(complement(u),complement(singleton(u))))* member(unordered_pair(v,w),successor(u))* -> . % 300.04/300.42 211844[0:SpL:114.0,27264.1] || subclass(universal_class,intersection(complement(u),complement(inverse(u))))* member(unordered_pair(v,w),symmetrization_of(u))* -> . % 300.04/300.42 211873[0:Res:2525.1,27264.1] || subclass(ordered_pair(u,v),union(w,x))* subclass(universal_class,intersection(complement(w),complement(x))) -> . % 300.04/300.42 211892[19:SpL:206403.0,211666.0] || subclass(union(u,complement(power_class(v))),ordinal_numbers) well_ordering(universal_class,intersection(complement(u),power_class(v)))* -> . % 300.04/300.42 211893[19:SpL:206410.0,211666.0] || subclass(union(complement(power_class(u)),v),ordinal_numbers) well_ordering(universal_class,intersection(power_class(u),complement(v)))* -> . % 300.04/300.42 212656[19:SpR:27168.2,198248.0] || member(u,universal_class) subclass(rest_relation,rest_of(v)) -> equal(intersection(complement(v),rest_of(u)),ordinal_numbers)**. % 300.04/300.42 212662[19:SpR:206403.0,198248.0] || -> equal(intersection(union(u,complement(power_class(v))),restrict(intersection(complement(u),power_class(v)),w,x)),ordinal_numbers)**. % 300.04/300.42 212663[19:SpR:206410.0,198248.0] || -> equal(intersection(union(complement(power_class(u)),v),restrict(intersection(power_class(u),complement(v)),w,x)),ordinal_numbers)**. % 300.04/300.42 212737[19:Rew:198248.0,212720.1] || member(not_subclass_element(restrict(u,v,w),ordinal_numbers),complement(u))* -> subclass(restrict(u,v,w),ordinal_numbers). % 300.04/300.42 212769[19:Res:167224.0,15073.0] || subclass(universal_class,u)* subclass(u,v)* -> equal(singleton(w),ordinal_numbers) member(power_class(w),v)*. % 300.04/300.42 212770[19:Res:167115.1,15073.0] || subclass(universal_class,u)* subclass(u,v)* -> equal(integer_of(w),ordinal_numbers) member(power_class(w),v)*. % 300.04/300.42 212783[19:Res:167137.1,15073.0] || subclass(universal_class,u)* subclass(u,v)* -> equal(w,ordinal_numbers) member(power_class(regular(w)),v)*. % 300.04/300.42 212899[19:SpR:27168.2,199281.0] || member(u,universal_class) subclass(rest_relation,rest_of(v)) -> equal(intersection(rest_of(u),complement(v)),ordinal_numbers)**. % 300.04/300.42 213205[19:Res:7.1,168498.0] || equal(compose_class(u),omega) -> equal(integer_of(ordered_pair(v,w)),ordinal_numbers)** equal(compose(u,v),w)*. % 300.04/300.42 213778[19:Res:7.1,176242.1] || equal(restrict(u,v,w),domain_relation)** member(x,universal_class) -> member(ordered_pair(x,ordinal_numbers),u)*. % 300.04/300.42 213969[19:SpR:198291.0,149012.1] || subclass(intersection(complement(inverse(ordinal_numbers)),u),symmetrization_of(ordinal_numbers))* -> equal(intersection(complement(inverse(ordinal_numbers)),u),ordinal_numbers). % 300.04/300.42 214224[19:SpR:198938.0,149012.1] || subclass(intersection(u,complement(inverse(ordinal_numbers))),symmetrization_of(ordinal_numbers))* -> equal(intersection(u,complement(inverse(ordinal_numbers))),ordinal_numbers). % 300.04/300.42 214324[19:Res:7.1,204401.0] || equal(ordered_pair(u,v),universal_class)** -> equal(unordered_pair(w,x),omega)** equal(unordered_pair(w,x),ordinal_numbers). % 300.04/300.42 214523[19:Res:214509.0,168644.0] || subclass(kind_1_ordinals,u) well_ordering(omega,u)* -> equal(integer_of(ordered_pair(ordinal_numbers,least(omega,kind_1_ordinals))),ordinal_numbers)**. % 300.04/300.42 214618[22:Res:178902.1,207852.0] || equal(intersection(power_class(u),complement(v)),omega) member(ordinal_numbers,union(complement(power_class(u)),v))* -> . % 300.04/300.42 214619[22:Res:177171.1,207852.0] || subclass(omega,intersection(power_class(u),complement(v))) member(ordinal_numbers,union(complement(power_class(u)),v))* -> . % 300.04/300.42 214621[19:Res:167104.1,207852.0] || subclass(universal_class,intersection(power_class(u),complement(v))) member(ordinal_numbers,union(complement(power_class(u)),v))* -> . % 300.04/300.42 214781[22:Res:178902.1,207871.0] || equal(intersection(complement(u),power_class(v)),omega) member(ordinal_numbers,union(u,complement(power_class(v))))* -> . % 300.04/300.42 214782[22:Res:177171.1,207871.0] || subclass(omega,intersection(complement(u),power_class(v))) member(ordinal_numbers,union(u,complement(power_class(v))))* -> . % 300.04/300.42 214784[19:Res:167104.1,207871.0] || subclass(universal_class,intersection(complement(u),power_class(v))) member(ordinal_numbers,union(u,complement(power_class(v))))* -> . % 300.04/300.42 214844[0:SpL:44.0,27258.2] || member(u,complement(singleton(v)))* member(u,complement(v)) member(u,successor(v)) -> . % 300.04/300.42 214845[0:SpL:114.0,27258.2] || member(u,complement(inverse(v)))* member(u,complement(v)) member(u,symmetrization_of(v)) -> . % 300.04/300.42 214871[0:Res:144531.1,27258.2] || equal(union(u,v),universal_class)** member(omega,complement(v))* member(omega,complement(u))* -> . % 300.04/300.42 214872[0:Res:2478.1,27258.2] || subclass(universal_class,union(u,v))* member(omega,complement(v)) member(omega,complement(u)) -> . % 300.04/300.42 214884[0:Res:6303.1,27258.2] || subclass(universal_class,symmetric_difference(u,v))* member(omega,complement(v)) member(omega,complement(u)) -> . % 300.04/300.42 214885[0:Res:6403.1,27258.2] || equal(symmetric_difference(u,v),universal_class)** member(omega,complement(v))* member(omega,complement(u))* -> . % 300.04/300.42 214916[22:Res:178902.1,27258.2] || equal(union(u,v),omega)** member(ordinal_numbers,complement(v))* member(ordinal_numbers,complement(u))* -> . % 300.04/300.42 214917[22:Res:177171.1,27258.2] || subclass(omega,union(u,v))* member(ordinal_numbers,complement(v)) member(ordinal_numbers,complement(u)) -> . % 300.04/300.42 214919[19:Res:167104.1,27258.2] || subclass(universal_class,union(u,v))* member(ordinal_numbers,complement(v)) member(ordinal_numbers,complement(u)) -> . % 300.04/300.42 214920[19:Res:167087.1,27258.2] || equal(union(u,v),universal_class)** member(ordinal_numbers,complement(v))* member(ordinal_numbers,complement(u))* -> . % 300.04/300.42 214996[8:SpL:160282.0,48413.0] || equal(complement(singleton(regular(ordered_pair(u,v)))),universal_class)** -> equal(regular(ordered_pair(u,v)),singleton(u)). % 300.04/300.42 214997[8:SpL:160282.0,48400.0] || subclass(universal_class,complement(singleton(regular(ordered_pair(u,v)))))* -> equal(regular(ordered_pair(u,v)),singleton(u)). % 300.04/300.42 215003[19:SpL:160282.0,203434.0] || subclass(unordered_pair(regular(ordered_pair(u,v)),w),ordinal_numbers)* -> equal(regular(ordered_pair(u,v)),singleton(u)). % 300.04/300.42 215004[19:SpL:160282.0,205948.0] || equal(unordered_pair(regular(ordered_pair(u,v)),w),ordinal_numbers)** -> equal(regular(ordered_pair(u,v)),singleton(u)). % 300.04/300.42 215046[19:SpL:160282.0,203431.0] || subclass(unordered_pair(u,regular(ordered_pair(v,w))),ordinal_numbers)* -> equal(regular(ordered_pair(v,w)),singleton(v)). % 300.04/300.42 215047[19:SpL:160282.0,205946.0] || equal(unordered_pair(u,regular(ordered_pair(v,w))),ordinal_numbers)** -> equal(regular(ordered_pair(v,w)),singleton(v)). % 300.04/300.42 215060[23:Rew:183840.0,214989.0] || -> equal(regular(ordered_pair(universal_class,u)),ordinal_numbers) equal(unordered_pair(ordinal_numbers,regular(ordered_pair(universal_class,u))),ordered_pair(universal_class,u))**. % 300.04/300.42 215213[19:Res:214528.1,207852.0] || subclass(kind_1_ordinals,intersection(power_class(u),complement(v))) member(ordinal_numbers,union(complement(power_class(u)),v))* -> . % 300.04/300.42 215214[19:Res:214528.1,207871.0] || subclass(kind_1_ordinals,intersection(complement(u),power_class(v))) member(ordinal_numbers,union(u,complement(power_class(v))))* -> . % 300.04/300.42 215225[19:Res:214528.1,27258.2] || subclass(kind_1_ordinals,union(u,v))* member(ordinal_numbers,complement(v)) member(ordinal_numbers,complement(u)) -> . % 300.04/300.42 215284[19:Res:144531.1,168249.0] || equal(regular(u),universal_class) member(omega,u)* well_ordering(v,w)* -> equal(u,ordinal_numbers). % 300.04/300.42 215285[19:Res:2478.1,168249.0] || subclass(universal_class,regular(u))* member(omega,u) well_ordering(v,w)* -> equal(u,ordinal_numbers). % 300.04/300.42 215326[19:Res:214528.1,168249.0] || subclass(kind_1_ordinals,regular(u))* member(ordinal_numbers,u) well_ordering(v,w)* -> equal(u,ordinal_numbers). % 300.04/300.42 215328[22:Res:178902.1,168249.0] || equal(regular(u),omega) member(ordinal_numbers,u)* well_ordering(v,w)* -> equal(u,ordinal_numbers). % 300.04/300.42 215329[22:Res:177171.1,168249.0] || subclass(omega,regular(u))* member(ordinal_numbers,u) well_ordering(v,w)* -> equal(u,ordinal_numbers). % 300.04/300.42 215331[19:Res:167104.1,168249.0] || subclass(universal_class,regular(u))* member(ordinal_numbers,u) well_ordering(v,w)* -> equal(u,ordinal_numbers). % 300.04/300.42 215332[19:Res:167087.1,168249.0] || equal(regular(u),universal_class) member(ordinal_numbers,u)* well_ordering(v,w)* -> equal(u,ordinal_numbers). % 300.04/300.42 215378[19:Res:7.1,168373.0] || equal(unordered_pair(u,v),omega)** -> equal(integer_of(w),ordinal_numbers)** equal(w,v)* equal(w,u)*. % 300.04/300.42 215407[19:Res:7.1,168434.0] || equal(restrict(u,v,w),omega)** -> equal(integer_of(x),ordinal_numbers) member(x,cross_product(v,w))*. % 300.04/300.42 215953[19:MRR:215952.1,167176.0] || equal(unordered_pair(u,singleton(v)),singleton(u)) -> equal(apply(choice,ordered_pair(u,v)),singleton(u))**. % 300.04/300.42 216068[0:Res:7.1,16107.1] || equal(u,complement(intersection(v,w)))* member(x,symmetric_difference(v,w))* -> member(x,u)*. % 300.04/300.42 216084[19:Rew:198352.0,216083.0] || member(u,union(complement(v),intersection(v,w)))* subclass(universal_class,x) -> member(u,x)*. % 300.04/300.42 216086[19:Rew:199009.0,216085.0] || member(u,union(complement(v),intersection(w,v)))* subclass(universal_class,x) -> member(u,x)*. % 300.04/300.42 216239[0:Res:7.1,6441.0] || equal(unordered_pair(u,v),universal_class)** -> equal(unordered_pair(w,x),v)* equal(unordered_pair(w,x),u)*. % 300.04/300.42 216409[19:Res:7.1,167724.0] || equal(restrict(u,v,w),x)* -> equal(x,ordinal_numbers) member(regular(x),cross_product(v,w))*. % 300.04/300.42 216925[19:SpL:27168.2,214469.0] || member(u,universal_class) subclass(rest_relation,rest_of(complement(singleton(ordinal_numbers))))* member(ordinal_numbers,rest_of(u))* -> . % 300.04/300.42 217071[19:Obv:217059.2] || equal(u,v) member(v,complement(unordered_pair(v,u)))* -> subclass(unordered_pair(v,u),ordinal_numbers). % 300.04/300.42 217111[19:SpL:206403.0,215196.0] || subclass(kind_1_ordinals,union(u,complement(power_class(v)))) member(ordinal_numbers,intersection(complement(u),power_class(v)))* -> . % 300.04/300.42 217112[19:SpL:206410.0,215196.0] || subclass(kind_1_ordinals,union(complement(power_class(u)),v)) member(ordinal_numbers,intersection(power_class(u),complement(v)))* -> . % 300.04/300.42 217133[19:SpL:206403.0,215201.0] || subclass(kind_1_ordinals,complement(union(u,complement(power_class(v)))))* -> member(ordinal_numbers,intersection(complement(u),power_class(v))). % 300.04/300.42 217134[19:SpL:206410.0,215201.0] || subclass(kind_1_ordinals,complement(union(complement(power_class(u)),v)))* -> member(ordinal_numbers,intersection(power_class(u),complement(v))). % 300.04/300.42 217240[22:SpL:27168.2,215821.0] || member(u,universal_class)* subclass(rest_relation,rest_of(complement(singleton(ordinal_numbers))))* equal(rest_of(u),omega) -> . % 300.04/300.42 217244[22:SpL:27168.2,215848.0] || member(u,universal_class) subclass(rest_relation,rest_of(complement(singleton(ordinal_numbers))))* subclass(omega,rest_of(u))* -> . % 300.04/300.42 217487[19:SpL:27168.2,216163.0] || member(u,universal_class) subclass(rest_relation,rest_of(complement(singleton(ordinal_numbers))))* subclass(kind_1_ordinals,rest_of(u))* -> . % 300.04/300.42 217494[19:SpL:27168.2,216356.0] || member(u,universal_class)* subclass(rest_relation,rest_of(complement(singleton(ordinal_numbers))))* equal(rest_of(u),kind_1_ordinals) -> . % 300.04/300.42 217952[0:Rew:29.0,217884.1] single_valued_class(intersection(intersection(u,cross_product(universal_class,universal_class)),v)) || -> function(intersection(restrict(u,universal_class,universal_class),v))*. % 300.04/300.42 218119[0:Rew:29.0,218044.1] single_valued_class(complement(complement(intersection(u,cross_product(universal_class,universal_class))))) || -> function(complement(complement(restrict(u,universal_class,universal_class))))*. % 300.04/300.42 218445[19:Res:218408.0,167728.0] || subclass(complement(image(successor_relation,ordinal_numbers)),u)* -> equal(complement(kind_1_ordinals),ordinal_numbers) member(regular(complement(kind_1_ordinals)),u). % 300.04/300.42 218894[0:Rew:29.0,218826.1] single_valued_class(intersection(u,intersection(v,cross_product(universal_class,universal_class)))) || -> function(intersection(u,restrict(v,universal_class,universal_class)))*. % 300.04/300.42 219070[0:Rew:30.0,219002.1] single_valued_class(intersection(intersection(cross_product(universal_class,universal_class),u),v)) || -> function(intersection(restrict(u,universal_class,universal_class),v))*. % 300.04/300.42 219913[0:Obv:219894.2] || subclass(u,symmetric_difference(v,w)) subclass(u,complement(union(v,w)))* -> subclass(u,x)*. % 300.04/300.42 220038[0:Res:7.1,16462.0] || equal(u,v)* subclass(u,w)* -> subclass(v,x) member(not_subclass_element(v,x),w)*. % 300.04/300.42 220073[0:Res:141.0,16462.0] || subclass(cross_product(universal_class,universal_class),u) -> subclass(rest_of(v),w) member(not_subclass_element(rest_of(v),w),u)*. % 300.04/300.42 220074[0:Res:93.0,16462.0] || subclass(cross_product(universal_class,universal_class),u) -> subclass(compose_class(v),w) member(not_subclass_element(compose_class(v),w),u)*. % 300.04/300.42 220078[0:Res:96.0,16462.0] || subclass(cross_product(universal_class,cross_product(universal_class,universal_class)),u)* -> subclass(composition_function,v) member(not_subclass_element(composition_function,v),u)*. % 300.04/300.42 220294[0:Rew:30.0,220217.1] single_valued_class(complement(complement(intersection(cross_product(universal_class,universal_class),u)))) || -> function(complement(complement(restrict(u,universal_class,universal_class))))*. % 300.04/300.42 220477[19:Res:220439.0,16462.0] || subclass(complement(singleton(ordinal_numbers)),u) -> subclass(complement(kind_1_ordinals),v) member(not_subclass_element(complement(kind_1_ordinals),v),u)*. % 300.04/300.42 220480[19:Res:220439.0,167276.0] || well_ordering(u,complement(singleton(ordinal_numbers))) -> equal(segment(u,complement(kind_1_ordinals),least(u,complement(kind_1_ordinals))),ordinal_numbers)**. % 300.04/300.42 220512[19:Res:220426.0,167728.0] || subclass(complement(u),v) -> equal(complement(successor(u)),ordinal_numbers) member(regular(complement(successor(u))),v)*. % 300.04/300.42 220546[19:Res:220427.0,167728.0] || subclass(complement(u),v) -> equal(complement(symmetrization_of(u)),ordinal_numbers) member(regular(complement(symmetrization_of(u))),v)*. % 300.04/300.42 220734[0:Rew:30.0,220666.1] single_valued_class(intersection(u,intersection(cross_product(universal_class,universal_class),v))) || -> function(intersection(u,restrict(v,universal_class,universal_class)))*. % 300.04/300.42 220787[19:Res:125327.1,167211.1] inductive(cantor(restrict(cross_product(u,ordinal_numbers),v,w))) || section(cross_product(v,w),ordinal_numbers,u)* -> . % 300.04/300.42 221268[27:Res:203424.1,221036.1] || subclass(complement(complement(intersection(singleton(ordinal_numbers),image(successor_relation,ordinal_numbers)))),ordinal_numbers)* member(singleton(u),kind_1_ordinals)* -> . % 300.04/300.42 221294[27:Res:167127.1,221036.1] || subclass(domain_relation,complement(intersection(singleton(ordinal_numbers),image(successor_relation,ordinal_numbers))))* member(ordered_pair(ordinal_numbers,ordinal_numbers),kind_1_ordinals) -> . % 300.04/300.42 221558[19:Res:219766.1,167728.0] || equal(complement(u),ordinal_numbers) subclass(u,v)* -> equal(w,ordinal_numbers) member(regular(w),v)*. % 300.04/300.42 221575[19:Res:219766.1,16468.0] || equal(complement(restrict(u,v,w)),ordinal_numbers)** -> subclass(x,y) member(not_subclass_element(x,y),u)*. % 300.04/300.42 221579[19:Res:219766.1,168375.0] || equal(complement(u),ordinal_numbers) subclass(u,v)* -> equal(integer_of(w),ordinal_numbers) member(w,v)*. % 300.04/300.42 221742[19:Res:219766.1,176249.1] || equal(complement(intersection(u,v)),ordinal_numbers)** member(w,universal_class) -> member(ordered_pair(w,ordinal_numbers),v)*. % 300.04/300.42 221743[19:Res:219766.1,176243.1] || equal(complement(intersection(u,v)),ordinal_numbers)** member(w,universal_class) -> member(ordered_pair(w,ordinal_numbers),u)*. % 300.04/300.42 221798[19:Res:219766.1,8693.1] || equal(complement(u),ordinal_numbers) member(ordered_pair(v,w),compose(x,y))* -> member(w,u)*. % 300.04/300.42 222256[0:Res:217976.0,1073.1] inductive(complement(complement(restrict(omega,u,v)))) || -> equal(complement(complement(restrict(omega,u,v))),omega)**. % 300.04/300.42 222347[0:Res:219698.0,1073.1] inductive(restrict(complement(complement(omega)),u,v)) || -> equal(restrict(complement(complement(omega)),u,v),omega)**. % 300.04/300.42 222434[0:Res:217800.0,1073.1] inductive(intersection(restrict(omega,u,v),w)) || -> equal(intersection(restrict(omega,u,v),w),omega)**. % 300.04/300.42 222563[0:Res:217848.0,1073.1] inductive(restrict(intersection(u,omega),v,w)) || -> equal(restrict(intersection(u,omega),v,w),omega)**. % 300.04/300.42 222676[0:Res:218740.0,1073.1] inductive(intersection(u,restrict(omega,v,w))) || -> equal(intersection(u,restrict(omega,v,w)),omega)**. % 300.04/300.42 222805[0:Res:218966.0,1073.1] inductive(restrict(intersection(omega,u),v,w)) || -> equal(restrict(intersection(omega,u),v,w),omega)**. % 300.04/300.42 222903[20:MRR:219370.1,222900.0] || well_ordering(u,inverse(ordinal_numbers)) -> member(least(u,complement(complement(symmetrization_of(ordinal_numbers)))),complement(complement(symmetrization_of(ordinal_numbers))))*. % 300.04/300.42 223013[20:Res:222998.0,15073.0] || subclass(universal_class,u)* subclass(u,v)* -> member(power_class(regular(complement(complement(symmetrization_of(ordinal_numbers))))),v)*. % 300.04/300.42 223014[20:Res:222998.0,15107.0] || subclass(universal_class,u)* subclass(u,v)* -> member(sum_class(regular(complement(complement(symmetrization_of(ordinal_numbers))))),v)*. % 300.04/300.42 223190[0:Res:945.0,79384.0] || -> equal(ordered_pair(first(ordered_pair(singleton(u),omega)),second(ordered_pair(singleton(u),omega))),ordered_pair(singleton(u),omega))**. % 300.04/300.42 223353[19:Res:196718.0,79384.0] || -> equal(ordered_pair(first(ordered_pair(regular(element_relation),omega)),second(ordered_pair(regular(element_relation),omega))),ordered_pair(regular(element_relation),omega))**. % 300.04/300.42 223943[19:Res:167106.1,14972.1] inductive(power_class(intersection(complement(u),complement(v)))) || member(ordinal_numbers,image(element_relation,union(u,v)))* -> . % 300.04/300.42 223975[19:Rew:209193.0,223887.0] || equal(image(element_relation,union(u,v)),ordinal_numbers) member(omega,image(element_relation,union(u,v)))* -> . % 300.04/300.42 223976[19:Rew:209193.0,223937.0] || equal(image(element_relation,union(u,v)),ordinal_numbers) member(ordinal_numbers,image(element_relation,union(u,v)))* -> . % 300.04/300.42 224059[19:SpL:479.0,223787.1] inductive(image(element_relation,union(u,v))) || equal(power_class(intersection(complement(u),complement(v))),kind_1_ordinals)** -> . % 300.04/300.42 224070[19:SpL:206403.0,217156.0] || equal(complement(union(u,complement(power_class(v)))),kind_1_ordinals) -> member(ordinal_numbers,intersection(complement(u),power_class(v)))*. % 300.04/300.42 224071[19:SpL:206410.0,217156.0] || equal(complement(union(complement(power_class(u)),v)),kind_1_ordinals) -> member(ordinal_numbers,intersection(power_class(u),complement(v)))*. % 300.04/300.42 224101[22:SpL:206403.0,217231.1] || equal(intersection(complement(u),power_class(v)),kind_1_ordinals)** equal(union(u,complement(power_class(v))),omega) -> . % 300.04/300.42 224102[22:SpL:206410.0,217231.1] || equal(intersection(power_class(u),complement(v)),kind_1_ordinals)** equal(union(complement(power_class(u)),v),omega) -> . % 300.04/300.42 224141[19:Res:130.2,219089.0] || connected(u,symmetrization_of(ordinal_numbers)) -> well_ordering(u,symmetrization_of(ordinal_numbers)) subclass(not_well_ordering(u,symmetrization_of(ordinal_numbers)),inverse(ordinal_numbers))*. % 300.04/300.42 224177[20:MRR:224170.1,210996.0] || well_ordering(u,inverse(ordinal_numbers)) -> member(least(u,singleton(regular(symmetrization_of(ordinal_numbers)))),singleton(regular(symmetrization_of(ordinal_numbers))))*. % 300.04/300.42 225111[19:Res:52.1,168497.0] inductive(rest_of(u)) || -> equal(integer_of(ordered_pair(v,w)),ordinal_numbers)** equal(restrict(u,v,universal_class),w)*. % 300.04/300.42 225270[23:SpL:183840.0,168561.1] || member(universal_class,cantor(cross_product(u,v))) equal(restrict(cross_product(ordinal_numbers,universal_class),u,v),ordinal_numbers)** -> . % 300.04/300.42 225643[19:SpR:206403.0,220544.1] || equal(symmetrization_of(intersection(complement(u),power_class(v))),ordinal_numbers) -> subclass(universal_class,union(u,complement(power_class(v))))*. % 300.04/300.42 225644[19:SpR:206410.0,220544.1] || equal(symmetrization_of(intersection(power_class(u),complement(v))),ordinal_numbers) -> subclass(universal_class,union(complement(power_class(u)),v))*. % 300.04/300.42 226119[19:SpR:207712.0,188655.1] || equal(complement(union(complement(power_class(u)),v)),universal_class)** -> equal(symmetric_difference(power_class(u),complement(v)),ordinal_numbers). % 300.04/300.42 226216[0:SpL:207712.0,5472.0] || subclass(universal_class,symmetric_difference(power_class(u),complement(v))) -> member(singleton(w),union(complement(power_class(u)),v))*. % 300.04/300.42 226222[0:SpL:207712.0,12446.0] || equal(symmetric_difference(power_class(u),complement(v)),universal_class) -> member(singleton(w),union(complement(power_class(u)),v))*. % 300.04/300.42 226229[19:SpL:207712.0,169224.0] || equal(symmetric_difference(power_class(u),complement(v)),singleton(ordinal_numbers)) -> member(ordinal_numbers,union(complement(power_class(u)),v))*. % 300.04/300.42 226698[19:SpL:160282.0,225697.0] || equal(symmetrization_of(singleton(regular(ordered_pair(u,v)))),ordinal_numbers)** -> equal(regular(ordered_pair(u,v)),singleton(u)). % 300.04/300.42 227085[19:SpR:207752.0,188655.1] || equal(complement(union(u,complement(power_class(v)))),universal_class)** -> equal(symmetric_difference(complement(u),power_class(v)),ordinal_numbers). % 300.04/300.42 227180[0:SpL:207752.0,5472.0] || subclass(universal_class,symmetric_difference(complement(u),power_class(v))) -> member(singleton(w),union(u,complement(power_class(v))))*. % 300.04/300.42 227186[0:SpL:207752.0,12446.0] || equal(symmetric_difference(complement(u),power_class(v)),universal_class) -> member(singleton(w),union(u,complement(power_class(v))))*. % 300.04/300.42 227193[19:SpL:207752.0,169224.0] || equal(symmetric_difference(complement(u),power_class(v)),singleton(ordinal_numbers)) -> member(ordinal_numbers,union(u,complement(power_class(v))))*. % 300.04/300.42 227756[19:SpL:206403.0,221566.0] || equal(complement(union(u,complement(power_class(v)))),ordinal_numbers)** -> equal(intersection(complement(u),power_class(v)),ordinal_numbers). % 300.04/300.42 227759[19:SpL:206410.0,221566.0] || equal(complement(union(complement(power_class(u)),v)),ordinal_numbers)** -> equal(intersection(power_class(u),complement(v)),ordinal_numbers). % 300.04/300.42 227930[0:Res:36606.3,146.0] || member(u,universal_class)* member(v,u)* subclass(element_relation,rest_relation) -> equal(rest_of(v),u). % 300.04/300.42 227942[0:Res:36606.3,46.0] || member(u,universal_class)* member(v,u)* subclass(element_relation,successor_relation) -> equal(successor(v),u). % 300.04/300.42 227954[8:Res:36606.3,124911.0] || member(u,universal_class)* member(v,u)* subclass(element_relation,domain_relation) -> equal(cantor(v),u). % 300.04/300.42 227958[19:Res:36606.3,205934.1] || member(u,universal_class)* member(v,u)* subclass(element_relation,w)* equal(ordinal_numbers,w) -> . % 300.04/300.42 227964[19:MRR:227877.3,204022.0] || member(u,universal_class) member(v,u) subclass(element_relation,complement(singleton(ordered_pair(v,u))))* -> . % 300.04/300.42 228229[22:SpL:206403.0,223782.1] || equal(intersection(complement(u),power_class(v)),omega)** equal(union(u,complement(power_class(v))),kind_1_ordinals) -> . % 300.04/300.42 228232[22:SpL:206410.0,223782.1] || equal(intersection(power_class(u),complement(v)),omega)** equal(union(complement(power_class(u)),v),kind_1_ordinals) -> . % 300.04/300.42 228933[19:SpR:225013.1,206403.0] || equal(successor(intersection(complement(u),power_class(v))),ordinal_numbers)** -> equal(union(u,complement(power_class(v))),universal_class). % 300.04/300.42 228947[19:SpR:225013.1,206410.0] || equal(successor(intersection(power_class(u),complement(v))),ordinal_numbers)** -> equal(union(complement(power_class(u)),v),universal_class). % 300.04/300.42 229890[19:Rew:229756.1,229889.1] || equal(successor(power_class(u)),ordinal_numbers) -> equal(symmetric_difference(power_class(u),complement(v)),complement(complement(complement(v))))**. % 300.04/300.42 230081[19:Res:167106.1,16079.0] inductive(symmetric_difference(complement(intersection(u,v)),union(u,v))) || -> member(ordinal_numbers,complement(symmetric_difference(u,v)))*. % 300.04/300.42 230558[0:Rew:44.0,230520.1] || member(not_subclass_element(successor(u),v),intersection(complement(u),complement(singleton(u))))* -> subclass(successor(u),v). % 300.04/300.42 230559[0:Rew:114.0,230521.1] || member(not_subclass_element(symmetrization_of(u),v),intersection(complement(u),complement(inverse(u))))* -> subclass(symmetrization_of(u),v). % 300.04/300.42 230574[19:Rew:167022.0,230534.1] || member(not_subclass_element(kind_1_ordinals,u),intersection(complement(singleton(ordinal_numbers)),complement(image(successor_relation,ordinal_numbers))))* -> subclass(kind_1_ordinals,u). % 300.04/300.42 230669[19:Res:167106.1,79427.2] inductive(intersection(u,inverse(u))) || asymmetric(u,v)* member(ordinal_numbers,cross_product(v,v))* -> . % 300.04/300.42 230757[23:SpR:183840.0,168558.0] || -> equal(first(not_subclass_element(restrict(cross_product(u,ordinal_numbers),v,w),ordinal_numbers)),domain__dfg(cross_product(v,w),u,universal_class))**. % 300.04/300.42 230804[23:SpR:183840.0,168559.0] || -> equal(second(not_subclass_element(restrict(cross_product(ordinal_numbers,u),v,w),ordinal_numbers)),range__dfg(cross_product(v,w),universal_class,u))**. % 300.04/300.42 231037[19:Res:229698.1,1065.0] || equal(successor(cross_product(universal_class,cross_product(universal_class,universal_class))),ordinal_numbers)** -> equal(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function). % 300.04/300.42 231051[19:Res:229698.1,120.0] || equal(successor(compose(restrict(u,v,v),restrict(u,v,v))),ordinal_numbers)** -> transitive(u,v). % 300.04/300.42 231153[19:Res:229698.1,167173.1] || equal(successor(compose(u,inverse(u))),ordinal_numbers)** subclass(u,cross_product(universal_class,universal_class)) -> function(u). % 300.04/300.42 232352[19:Rew:199166.0,232231.2] || subclass(u,complement(v)) member(not_subclass_element(u,ordinal_numbers),intersection(w,v))* -> subclass(u,ordinal_numbers). % 300.04/300.42 232353[19:Rew:198500.0,232230.2] || subclass(u,complement(v)) member(not_subclass_element(u,ordinal_numbers),intersection(v,w))* -> subclass(u,ordinal_numbers). % 300.04/300.42 232354[19:Rew:190748.0,232229.2] || subclass(u,complement(inverse(ordinal_numbers))) member(not_subclass_element(u,ordinal_numbers),symmetrization_of(ordinal_numbers))* -> subclass(u,ordinal_numbers). % 300.04/300.42 232358[19:Rew:190401.0,232215.2] || subclass(u,symmetrization_of(ordinal_numbers)) member(not_subclass_element(u,ordinal_numbers),complement(inverse(ordinal_numbers)))* -> subclass(u,ordinal_numbers). % 300.04/300.42 232359[19:Rew:167159.0,232214.2] || subclass(u,element_relation) member(not_subclass_element(u,ordinal_numbers),complement(compose(element_relation,universal_class)))* -> subclass(u,ordinal_numbers). % 300.04/300.42 232360[19:Rew:197702.0,232205.2] || subclass(u,intersection(v,w))* member(not_subclass_element(u,ordinal_numbers),complement(w))* -> subclass(u,ordinal_numbers). % 300.04/300.42 232361[19:Rew:197499.0,232204.2] || subclass(u,intersection(v,w))* member(not_subclass_element(u,ordinal_numbers),complement(v))* -> subclass(u,ordinal_numbers). % 300.04/300.42 232385[0:Obv:232310.1] || subclass(symmetric_difference(u,inverse(u)),v) -> subclass(symmetric_difference(u,inverse(u)),intersection(symmetrization_of(u),v))*. % 300.04/300.42 232395[0:Obv:232309.1] || subclass(symmetric_difference(u,v),w) -> subclass(symmetric_difference(u,v),intersection(complement(intersection(u,v)),w))*. % 300.04/300.42 232397[0:Rew:30.0,232396.1] || subclass(restrict(u,v,w),x) -> subclass(restrict(u,v,w),restrict(x,v,w))*. % 300.04/300.42 232704[19:Rew:167159.0,232463.1] || member(not_subclass_element(intersection(u,element_relation),ordinal_numbers),complement(compose(element_relation,universal_class)))* -> subclass(intersection(u,element_relation),ordinal_numbers). % 300.04/300.42 233091[19:Rew:167159.0,232855.1] || member(not_subclass_element(intersection(element_relation,u),ordinal_numbers),complement(compose(element_relation,universal_class)))* -> subclass(intersection(element_relation,u),ordinal_numbers). % 300.04/300.42 233877[2:Rew:233350.0,188466.2] inductive(symmetric_difference(universal_class,u)) || well_ordering(v,universal_class) -> member(least(v,complement(u)),complement(u))*. % 300.04/300.42 233879[2:Rew:233350.0,188558.2] inductive(symmetric_difference(universal_class,u)) || well_ordering(v,universal_class) member(least(v,complement(u)),u)* -> . % 300.04/300.42 234159[19:Rew:233390.0,229884.1] || equal(successor(power_class(u)),ordinal_numbers) -> equal(symmetric_difference(complement(v),power_class(u)),complement(complement(complement(v))))**. % 300.04/300.42 234840[19:Rew:234692.0,180323.0] || member(u,intersection(singleton(ordinal_numbers),complement(v)))* member(u,union(v,complement(singleton(ordinal_numbers)))) -> . % 300.04/300.42 234845[19:Rew:234692.0,180284.0] || subclass(universal_class,intersection(singleton(ordinal_numbers),complement(u))) member(omega,union(u,complement(singleton(ordinal_numbers))))* -> . % 300.04/300.42 234867[19:Rew:234692.0,199608.2] || equal(u,v) -> equal(unordered_pair(v,u),ordinal_numbers) equal(intersection(v,unordered_pair(v,u)),ordinal_numbers)**. % 300.04/300.42 234890[0:Rew:234692.0,149467.1] || subclass(inverse(u),u) -> equal(intersection(symmetrization_of(u),complement(inverse(u))),symmetric_difference(u,inverse(u)))**. % 300.04/300.42 236275[0:SpR:234692.0,16235.1] || -> subclass(intersection(intersection(u,v),w),x) member(not_subclass_element(intersection(intersection(v,u),w),x),v)*. % 300.04/300.42 236276[0:SpR:234692.0,16234.1] || -> subclass(intersection(intersection(u,v),w),x) member(not_subclass_element(intersection(intersection(v,u),w),x),u)*. % 300.04/300.42 236292[0:SpR:234692.0,16362.1] || -> subclass(intersection(u,intersection(v,w)),x) member(not_subclass_element(intersection(intersection(v,w),u),x),w)*. % 300.04/300.42 236293[0:SpR:234692.0,16361.1] || -> subclass(intersection(u,intersection(v,w)),x) member(not_subclass_element(intersection(intersection(v,w),u),x),v)*. % 300.04/300.42 236303[0:SpR:234692.0,38094.1] || member(u,union(v,w)) -> member(u,intersection(w,v))* member(u,symmetric_difference(v,w)). % 300.04/300.42 236308[0:SpR:234692.0,16362.1] || -> subclass(intersection(u,intersection(v,w)),x) member(not_subclass_element(intersection(u,intersection(w,v)),x),w)*. % 300.04/300.42 236309[0:SpR:234692.0,16361.1] || -> subclass(intersection(u,intersection(v,w)),x) member(not_subclass_element(intersection(u,intersection(w,v)),x),v)*. % 300.04/300.42 236311[19:SpR:234692.0,168520.2] || well_ordering(u,universal_class) -> equal(intersection(v,w),ordinal_numbers) member(least(u,intersection(w,v)),v)*. % 300.04/300.42 236312[19:SpR:234692.0,168521.2] || well_ordering(u,universal_class) -> equal(intersection(v,w),ordinal_numbers) member(least(u,intersection(w,v)),w)*. % 300.04/300.42 236315[0:SpR:234692.0,16231.2] || subclass(u,v) -> subclass(intersection(u,w),x) member(not_subclass_element(intersection(w,u),x),v)*. % 300.04/300.42 236318[0:SpR:234692.0,16235.1] || -> subclass(intersection(intersection(u,v),w),x) member(not_subclass_element(intersection(w,intersection(u,v)),x),v)*. % 300.04/300.42 236319[0:SpR:234692.0,16234.1] || -> subclass(intersection(intersection(u,v),w),x) member(not_subclass_element(intersection(w,intersection(u,v)),x),u)*. % 300.04/300.42 236332[0:SpR:234692.0,978.1] || member(u,universal_class) -> member(u,intersection(complement(v),complement(w)))* member(u,union(w,v)). % 300.04/300.42 236354[0:SpR:234692.0,16358.2] || subclass(u,v) -> subclass(intersection(w,u),x) member(not_subclass_element(intersection(u,w),x),v)*. % 300.04/300.42 236491[19:SpL:234692.0,168461.0] || member(regular(union(u,v)),intersection(complement(v),complement(u)))* -> equal(union(u,v),ordinal_numbers). % 300.04/300.42 236493[0:SpL:234692.0,207871.0] || member(u,intersection(power_class(v),complement(w)))* member(u,union(w,complement(power_class(v)))) -> . % 300.04/300.42 236525[0:SpL:234692.0,16107.1] || member(u,symmetric_difference(v,w))* subclass(complement(intersection(w,v)),x)* -> member(u,x)*. % 300.04/300.42 236551[0:SpL:234692.0,207852.0] || member(u,intersection(complement(v),power_class(w)))* member(u,union(complement(power_class(w)),v)) -> . % 300.04/300.42 236709[19:Rew:236669.0,216087.0] || member(u,union(element_relation,complement(compose(element_relation,universal_class))))* subclass(universal_class,v) -> member(u,v)*. % 300.04/300.42 236775[19:Rew:44.0,236755.0] || member(u,successor(v))* subclass(universal_class,w) -> equal(singleton(v),ordinal_numbers) member(u,w)*. % 300.04/300.42 237116[19:Rew:237023.0,198240.0] || -> equal(intersection(complement(complement(symmetric_difference(u,v))),symmetric_difference(union(u,v),complement(intersection(u,v)))),ordinal_numbers)**. % 300.04/300.42 237124[0:Rew:237023.0,222735.0] || -> subclass(restrict(symmetric_difference(union(u,v),complement(intersection(u,v))),w,x),complement(symmetric_difference(u,v)))*. % 300.04/300.42 237245[0:SpR:236669.0,15119.2] || member(u,universal_class) subclass(universal_class,symmetric_difference(v,w)) -> member(sum_class(u),union(w,v))*. % 300.04/300.42 237246[0:SpR:236669.0,15085.2] || member(u,universal_class) subclass(universal_class,symmetric_difference(v,w)) -> member(power_class(u),union(w,v))*. % 300.04/300.42 237247[0:SpR:236669.0,16475.2] || subclass(u,symmetric_difference(v,w)) -> subclass(u,x) member(not_subclass_element(u,x),union(w,v))*. % 300.04/300.42 237324[0:SpL:236669.0,27264.1] || subclass(universal_class,intersection(complement(u),complement(v))) member(unordered_pair(w,x),union(v,u))* -> . % 300.04/300.42 237325[19:SpL:236669.0,168461.0] || member(regular(union(u,v)),intersection(complement(v),complement(u)))* -> equal(union(v,u),ordinal_numbers). % 300.04/300.42 237401[19:Rew:237384.0,207215.0] || -> equal(symmetric_difference(complement(symmetrization_of(complement(power_class(u)))),intersection(power_class(u),complement(inverse(complement(power_class(u)))))),ordinal_numbers)**. % 300.04/300.42 237403[19:Rew:237384.0,207106.0] || -> equal(symmetric_difference(complement(successor(complement(power_class(u)))),intersection(power_class(u),complement(singleton(complement(power_class(u)))))),ordinal_numbers)**. % 300.04/300.42 237636[19:Rew:237493.0,237469.1] || member(u,symmetric_difference(successor(v),complement(intersection(v,singleton(v)))))* member(u,successor(v)) -> . % 300.04/300.42 238131[19:SpR:237974.1,479.0] || equal(image(element_relation,union(u,v)),universal_class) -> equal(power_class(intersection(complement(u),complement(v))),ordinal_numbers)**. % 300.04/300.42 239121[19:SpL:237603.0,168376.0] || subclass(omega,successor(u)) -> equal(integer_of(v),ordinal_numbers) member(v,complement(intersection(u,singleton(u))))*. % 300.04/300.42 239137[19:SpL:237603.0,167737.0] || subclass(u,successor(v)) -> equal(u,ordinal_numbers) member(regular(u),complement(intersection(v,singleton(v))))*. % 300.04/300.42 239472[19:Rew:124836.0,239252.1] || section(u,v,w) equal(cantor(restrict(u,w,v)),universal_class)** -> member(ordinal_numbers,v). % 300.04/300.42 239393[19:SoR:167812.0,238779.1] || connected(u,v) equal(not_well_ordering(u,v),universal_class)** -> well_ordering(u,v) member(ordinal_numbers,v). % 300.04/300.42 239709[19:Res:238770.1,16462.0] || equal(u,universal_class) subclass(u,v)* -> subclass(w,x) member(not_subclass_element(w,x),v)*. % 300.04/300.42 239712[19:Res:238770.1,167276.0] || equal(u,universal_class) well_ordering(v,u)* -> equal(segment(v,w,least(v,w)),ordinal_numbers)**. % 300.04/300.42 239713[19:Res:238770.1,167133.0] || equal(u,universal_class) well_ordering(v,u)* -> equal(w,ordinal_numbers) member(least(v,w),w)*. % 300.04/300.42 239714[19:Res:238770.1,9856.0] || equal(u,universal_class) well_ordering(v,u)* -> subclass(w,x)* member(least(v,w),w)*. % 300.04/300.42 239715[19:Res:238770.1,9859.1] inductive(u) || equal(v,universal_class) well_ordering(w,v)* -> member(least(w,u),u)*. % 300.04/300.42 239985[19:Res:238770.1,27146.1] || equal(intersection(u,v),universal_class)** member(w,universal_class) -> member(ordered_pair(w,rest_of(w)),u)*. % 300.04/300.42 239986[19:Res:238770.1,27147.1] || equal(intersection(u,v),universal_class)** member(w,universal_class) -> member(ordered_pair(w,rest_of(w)),v)*. % 300.04/300.42 240118[19:Res:238770.1,168373.0] || equal(unordered_pair(u,v),universal_class)** -> equal(integer_of(w),ordinal_numbers)** equal(w,v)* equal(w,u)*. % 300.04/300.42 240400[19:Rew:167140.0,240296.1] || equal(symmetric_difference(u,v),universal_class) -> equal(symmetric_difference(union(u,v),complement(intersection(u,v))),ordinal_numbers)**. % 300.04/300.42 240520[19:Res:239914.1,16083.0] || equal(symmetric_difference(u,cross_product(v,w)),universal_class) -> member(regular(element_relation),complement(restrict(u,v,w)))*. % 300.04/300.42 240522[19:Res:239914.1,16086.0] || equal(symmetric_difference(cross_product(u,v),w),universal_class) -> member(regular(element_relation),complement(restrict(w,u,v)))*. % 300.04/300.42 240609[19:Res:239132.1,2.0] || member(u,successor(v))* subclass(complement(intersection(v,singleton(v))),w)* -> member(u,w)*. % 300.04/300.42 240614[19:Res:239132.1,6432.1] || member(unordered_pair(u,v),successor(w))* subclass(universal_class,complement(complement(intersection(w,singleton(w)))))* -> . % 300.04/300.42 240620[19:Res:239132.1,6476.1] || member(ordered_pair(u,v),successor(w))* subclass(universal_class,complement(complement(intersection(w,singleton(w)))))* -> . % 300.04/300.42 240772[0:SpR:207751.0,236254.0] || -> subclass(symmetric_difference(union(complement(power_class(u)),v),complement(w)),union(w,intersection(power_class(u),complement(v))))*. % 300.04/300.42 240773[0:SpR:207766.0,236254.0] || -> subclass(symmetric_difference(union(u,complement(power_class(v))),complement(w)),union(w,intersection(complement(u),power_class(v))))*. % 300.04/300.42 240775[0:SpR:207699.0,236254.0] || -> subclass(symmetric_difference(complement(u),union(complement(power_class(v)),w)),union(intersection(power_class(v),complement(w)),u))*. % 300.04/300.42 240776[0:SpR:207747.0,236254.0] || -> subclass(symmetric_difference(complement(u),union(v,complement(power_class(w)))),union(intersection(complement(v),power_class(w)),u))*. % 300.04/300.42 240895[19:Res:144531.1,237637.0] || equal(symmetric_difference(successor(u),complement(intersection(u,singleton(u)))),universal_class)** -> member(omega,complement(successor(u))). % 300.04/300.42 240896[19:Res:2478.1,237637.0] || subclass(universal_class,symmetric_difference(successor(u),complement(intersection(u,singleton(u)))))* -> member(omega,complement(successor(u))). % 300.04/300.42 240944[19:Res:214528.1,237637.0] || subclass(kind_1_ordinals,symmetric_difference(successor(u),complement(intersection(u,singleton(u)))))* -> member(ordinal_numbers,complement(successor(u))). % 300.04/300.42 240946[22:Res:178902.1,237637.0] || equal(symmetric_difference(successor(u),complement(intersection(u,singleton(u)))),omega)** -> member(ordinal_numbers,complement(successor(u))). % 300.04/300.42 240947[22:Res:177171.1,237637.0] || subclass(omega,symmetric_difference(successor(u),complement(intersection(u,singleton(u)))))* -> member(ordinal_numbers,complement(successor(u))). % 300.04/300.42 240949[19:Res:167104.1,237637.0] || subclass(universal_class,symmetric_difference(successor(u),complement(intersection(u,singleton(u)))))* -> member(ordinal_numbers,complement(successor(u))). % 300.04/300.42 240950[19:Res:167087.1,237637.0] || equal(symmetric_difference(successor(u),complement(intersection(u,singleton(u)))),universal_class)** -> member(ordinal_numbers,complement(successor(u))). % 300.04/300.42 241478[19:Res:167106.1,236817.0] inductive(symmetric_difference(union(u,v),complement(intersection(u,v)))) || -> member(ordinal_numbers,complement(symmetric_difference(u,v)))*. % 300.04/300.42 242073[19:SpL:206403.0,225692.0] || equal(symmetrization_of(union(u,complement(power_class(v)))),ordinal_numbers) -> member(ordinal_numbers,intersection(complement(u),power_class(v)))*. % 300.04/300.42 242076[19:SpL:206410.0,225692.0] || equal(symmetrization_of(union(complement(power_class(u)),v)),ordinal_numbers) -> member(ordinal_numbers,intersection(power_class(u),complement(v)))*. % 300.04/300.42 242191[19:SpL:206403.0,225693.0] || equal(symmetrization_of(union(u,complement(power_class(v)))),ordinal_numbers) -> member(omega,intersection(complement(u),power_class(v)))*. % 300.04/300.42 242194[19:SpL:206410.0,225693.0] || equal(symmetrization_of(union(complement(power_class(u)),v)),ordinal_numbers) -> member(omega,intersection(power_class(u),complement(v)))*. % 300.04/300.42 242257[19:Obv:242237.1] || subclass(composition_function,rest_of(u)) -> equal(regular(unordered_pair(v,u)),v)** equal(unordered_pair(v,u),ordinal_numbers). % 300.04/300.42 242258[19:Obv:242236.1] || subclass(composition_function,rest_of(u)) -> equal(regular(unordered_pair(u,v)),v)** equal(unordered_pair(u,v),ordinal_numbers). % 300.04/300.42 242281[0:Res:52.1,16467.0] inductive(restrict(u,v,w)) || -> subclass(omega,x) member(not_subclass_element(omega,x),cross_product(v,w))*. % 300.04/300.42 242315[19:SpL:206403.0,228219.1] || equal(intersection(complement(u),power_class(v)),kind_1_ordinals)** equal(union(u,complement(power_class(v))),kind_1_ordinals) -> . % 300.04/300.42 242318[19:SpL:206410.0,228219.1] || equal(intersection(power_class(u),complement(v)),kind_1_ordinals)** equal(union(complement(power_class(u)),v),kind_1_ordinals) -> . % 300.04/300.42 242379[19:SpR:206403.0,234130.1] || member(ordinal_numbers,intersection(complement(u),power_class(v))) -> member(ordinal_numbers,complement(union(u,complement(power_class(v)))))*. % 300.04/300.42 242382[19:SpR:206410.0,234130.1] || member(ordinal_numbers,intersection(power_class(u),complement(v))) -> member(ordinal_numbers,complement(union(complement(power_class(u)),v)))*. % 300.04/300.42 242536[19:SpL:206403.0,235552.0] || equal(successor(union(u,complement(power_class(v)))),ordinal_numbers)** -> equal(intersection(complement(u),power_class(v)),universal_class). % 300.04/300.42 242539[19:SpL:206410.0,235552.0] || equal(successor(union(complement(power_class(u)),v)),ordinal_numbers)** -> equal(intersection(power_class(u),complement(v)),universal_class). % 300.04/300.42 242666[20:MRR:242635.1,222900.0] || member(complement(complement(symmetrization_of(ordinal_numbers))),universal_class) -> member(apply(choice,complement(complement(symmetrization_of(ordinal_numbers)))),inverse(ordinal_numbers))*. % 300.04/300.42 243378[19:SpR:243093.1,16826.0] || equal(intersection(complement(u),complement(singleton(u))),universal_class)** -> equal(complement(image(element_relation,successor(u))),ordinal_numbers). % 300.04/300.42 243379[19:SpR:243093.1,16825.0] || equal(intersection(complement(u),complement(inverse(u))),universal_class)** -> equal(complement(image(element_relation,symmetrization_of(u))),ordinal_numbers). % 300.04/300.42 243721[19:MRR:243711.1,53.0] || equal(rest_relation,domain_relation) subclass(rest_relation,omega) -> equal(integer_of(ordered_pair(omega,ordinal_numbers)),ordered_pair(omega,ordinal_numbers))**. % 300.04/300.42 243722[19:MRR:243710.1,167011.0] || equal(rest_relation,domain_relation) subclass(rest_relation,omega) -> equal(integer_of(ordered_pair(ordinal_numbers,ordinal_numbers)),ordered_pair(ordinal_numbers,ordinal_numbers))**. % 300.04/300.42 243723[19:MRR:243706.3,167176.0] || member(u,universal_class) subclass(rest_relation,omega) subclass(omega,element_relation) -> member(u,rest_of(u))*. % 300.04/300.42 243729[19:MRR:243728.3,167176.0] || member(u,universal_class)* subclass(rest_relation,omega) subclass(omega,domain_relation) -> equal(rest_of(u),ordinal_numbers). % 300.04/300.42 243763[19:Res:130.2,239702.0] || connected(u,symmetrization_of(ordinal_numbers)) equal(not_well_ordering(u,symmetrization_of(ordinal_numbers)),universal_class)** -> well_ordering(u,symmetrization_of(ordinal_numbers)). % 300.04/300.42 243835[19:Obv:243822.1] || equal(rest_of(u),composition_function) -> equal(regular(unordered_pair(v,u)),v)** equal(unordered_pair(v,u),ordinal_numbers). % 300.04/300.42 243836[19:Obv:243821.1] || equal(rest_of(u),composition_function) -> equal(regular(unordered_pair(u,v)),v)** equal(unordered_pair(u,v),ordinal_numbers). % 300.04/300.42 245506[19:Res:40606.2,205934.1] || member(u,universal_class) equal(compose(v,singleton(u)),u)** equal(compose_class(v),ordinal_numbers) -> . % 300.04/300.42 245626[19:SpL:5132.1,225032.0] || equal(successor(unordered_pair(u,not_subclass_element(cross_product(v,w),x))),ordinal_numbers)** -> subclass(cross_product(v,w),x). % 300.04/300.42 245684[0:MRR:245658.1,66.2] function(u) || member(v,universal_class) subclass(universal_class,complement(unordered_pair(w,image(u,v))))* -> . % 300.04/300.42 245685[0:MRR:245657.1,66.2] function(u) || member(v,universal_class) subclass(universal_class,complement(unordered_pair(image(u,v),w)))* -> . % 300.04/300.42 245710[19:SpL:5132.1,225035.0] || equal(successor(unordered_pair(not_subclass_element(cross_product(u,v),w),x)),ordinal_numbers)** -> subclass(cross_product(u,v),w). % 300.04/300.42 245731[19:SpL:5132.1,225700.0] || equal(symmetrization_of(unordered_pair(u,not_subclass_element(cross_product(v,w),x))),ordinal_numbers)** -> subclass(cross_product(v,w),x). % 300.04/300.42 245774[19:SpL:5132.1,225703.0] || equal(symmetrization_of(unordered_pair(not_subclass_element(cross_product(u,v),w),x)),ordinal_numbers)** -> subclass(cross_product(u,v),w). % 300.04/300.42 245883[19:MRR:245853.0,167740.2] || member(u,universal_class) subclass(u,complement(unordered_pair(v,apply(choice,u))))* -> equal(u,ordinal_numbers). % 300.04/300.42 245884[19:MRR:245852.0,167740.2] || member(u,universal_class) subclass(u,complement(unordered_pair(apply(choice,u),v)))* -> equal(u,ordinal_numbers). % 300.04/300.42 246031[19:Res:176326.2,229738.1] || member(u,universal_class) equal(compose(v,u),ordinal_numbers)** equal(successor(compose_class(v)),ordinal_numbers) -> . % 300.04/300.42 246304[19:Rew:27.0,246294.0] || equal(union(u,v),ordinal_numbers) member(w,union(u,v))* -> equal(integer_of(w),ordinal_numbers). % 300.04/300.42 246356[25:SpR:234134.1,206403.0] function(u) || -> equal(union(complement(u),complement(power_class(v))),complement(intersection(successor(u),power_class(v))))**. % 300.04/300.42 246377[25:SpR:234134.1,206410.0] function(u) || -> equal(union(complement(power_class(v)),complement(u)),complement(intersection(power_class(v),successor(u))))**. % 300.04/300.42 246664[25:Rew:209198.0,246434.1] function(image(element_relation,symmetrization_of(ordinal_numbers))) || -> equal(successor(image(element_relation,symmetrization_of(ordinal_numbers))),image(element_relation,symmetrization_of(ordinal_numbers)))**. % 300.04/300.42 246665[25:Rew:209197.0,246435.1] function(image(element_relation,singleton(ordinal_numbers))) || -> equal(successor(image(element_relation,singleton(ordinal_numbers))),image(element_relation,singleton(ordinal_numbers)))**. % 300.04/300.42 246666[25:Rew:209199.0,246436.1] function(image(element_relation,power_class(u))) || -> equal(successor(image(element_relation,power_class(u))),image(element_relation,power_class(u)))**. % 300.04/300.42 246695[25:Res:246381.1,167728.0] function(u) || subclass(u,v) -> equal(successor(u),ordinal_numbers) member(regular(successor(u)),v)*. % 300.04/300.42 246718[25:Res:246381.1,8596.1] function(cross_product(universal_class,universal_class)) single_valued_class(successor(cross_product(universal_class,universal_class))) || -> function(successor(cross_product(universal_class,universal_class)))*. % 300.04/300.42 247277[19:Res:27192.2,205934.1] || member(u,universal_class) equal(compose(v,u),rest_of(u))** equal(compose_class(v),ordinal_numbers) -> . % 300.04/300.42 247497[19:Rew:142500.0,247381.1,234692.0,247381.1] || equal(complement(u),universal_class) -> equal(symmetric_difference(complement(u),power_class(v)),union(u,complement(power_class(v))))**. % 300.04/300.42 247688[19:Rew:142500.0,247581.1] || equal(complement(u),universal_class) -> equal(symmetric_difference(power_class(v),complement(u)),union(complement(power_class(v)),u))**. % 300.04/300.42 248206[0:Res:170.0,27142.0] || subclass(rest_relation,u)* subclass(u,v)* -> member(ordered_pair(singleton(w),rest_of(singleton(w))),v)*. % 300.04/300.42 248282[19:Res:196718.0,27142.0] || subclass(rest_relation,u)* subclass(u,v)* -> member(ordered_pair(regular(element_relation),rest_of(regular(element_relation))),v)*. % 300.04/300.42 248310[19:Res:248149.1,207852.0] || equal(intersection(power_class(u),complement(v)),kind_1_ordinals) member(ordinal_numbers,union(complement(power_class(u)),v))* -> . % 300.04/300.42 248311[19:Res:248149.1,207871.0] || equal(intersection(complement(u),power_class(v)),kind_1_ordinals) member(ordinal_numbers,union(u,complement(power_class(v))))* -> . % 300.04/300.42 248317[19:Res:248149.1,237637.0] || equal(symmetric_difference(successor(u),complement(intersection(u,singleton(u)))),kind_1_ordinals)** -> member(ordinal_numbers,complement(successor(u))). % 300.04/300.42 248320[19:Res:248149.1,27258.2] || equal(union(u,v),kind_1_ordinals)** member(ordinal_numbers,complement(v))* member(ordinal_numbers,complement(u))* -> . % 300.04/300.42 248335[19:Res:248149.1,168249.0] || equal(regular(u),kind_1_ordinals) member(ordinal_numbers,u)* well_ordering(v,w)* -> equal(u,ordinal_numbers). % 300.04/300.42 248490[25:Res:246387.1,8.0] function(u) || subclass(u,complement(complement(successor(u))))* -> equal(complement(complement(successor(u))),u). % 300.04/300.42 248752[0:SpL:206403.0,219712.0] || subclass(u,complement(union(v,complement(power_class(w)))))* -> subclass(u,intersection(complement(v),power_class(w))). % 300.04/300.42 248755[0:SpL:206410.0,219712.0] || subclass(u,complement(union(complement(power_class(v)),w)))* -> subclass(u,intersection(power_class(v),complement(w))). % 300.04/300.42 248803[8:Res:124899.1,219712.0] || section(u,complement(complement(v)),w) -> subclass(cantor(restrict(u,w,complement(complement(v)))),v)*. % 300.04/300.42 248871[0:Res:248818.0,16469.0] || -> subclass(complement(successor(complement(singleton(u)))),v) equal(not_subclass_element(complement(successor(complement(singleton(u)))),v),u)**. % 300.04/300.42 248988[0:Res:248819.0,16469.0] || -> subclass(complement(symmetrization_of(complement(singleton(u)))),v) equal(not_subclass_element(complement(symmetrization_of(complement(singleton(u)))),v),u)**. % 300.04/300.42 249582[0:Res:12.0,42928.0] || well_ordering(u,universal_class) -> member(unordered_pair(v,w),x)* member(least(u,complement(x)),complement(x))*. % 300.04/300.42 249583[0:Res:940.0,42928.0] || well_ordering(u,universal_class) -> member(ordered_pair(v,w),x)* member(least(u,complement(x)),complement(x))*. % 300.04/300.42 249599[20:Res:175569.0,42928.0] || well_ordering(u,universal_class) -> member(regular(symmetrization_of(ordinal_numbers)),v) member(least(u,complement(v)),complement(v))*. % 300.04/300.42 249713[0:Res:248882.0,1073.1] inductive(complement(successor(complement(complement(complement(omega)))))) || -> equal(complement(successor(complement(complement(complement(omega))))),omega)**. % 300.04/300.42 249830[0:Res:248999.0,1073.1] inductive(complement(symmetrization_of(complement(complement(complement(omega)))))) || -> equal(complement(symmetrization_of(complement(complement(complement(omega))))),omega)**. % 300.04/300.42 250016[19:Rew:27.0,249961.0] || equal(union(u,v),ordinal_numbers) member(regular(w),union(u,v))* -> equal(w,ordinal_numbers). % 300.04/300.42 250060[0:SpR:479.0,248806.0] || -> member(u,power_class(intersection(complement(v),complement(w))))* subclass(singleton(u),image(element_relation,union(v,w))). % 300.04/300.42 250102[19:Res:248806.0,176244.2] || member(u,universal_class) subclass(domain_relation,complement(complement(v))) -> subclass(singleton(ordered_pair(u,ordinal_numbers)),v)*. % 300.04/300.42 250128[19:Res:248806.0,168418.0] || -> subclass(singleton(regular(intersection(u,complement(complement(v))))),v)* equal(intersection(u,complement(complement(v))),ordinal_numbers). % 300.04/300.42 250129[19:Res:248806.0,168419.0] || -> subclass(singleton(regular(intersection(complement(complement(u)),v))),u)* equal(intersection(complement(complement(u)),v),ordinal_numbers). % 300.04/300.42 250752[19:MRR:250730.0,167011.0] || equal(symmetrization_of(intersection(power_class(u),complement(v))),ordinal_numbers) -> member(ordinal_numbers,union(complement(power_class(u)),v))*. % 300.04/300.42 250755[19:MRR:250698.0,53.0] || equal(symmetrization_of(intersection(power_class(u),complement(v))),ordinal_numbers) -> member(omega,union(complement(power_class(u)),v))*. % 300.04/300.42 250764[19:MRR:250705.0,170.0] || well_ordering(universal_class,intersection(power_class(u),complement(v))) -> member(singleton(ordinal_numbers),union(complement(power_class(u)),v))*. % 300.04/300.42 250865[0:SpR:206403.0,248811.0] || -> subclass(complement(complement(complement(complement(complement(union(u,complement(power_class(v)))))))),intersection(complement(u),power_class(v)))*. % 300.04/300.42 250868[0:SpR:206410.0,248811.0] || -> subclass(complement(complement(complement(complement(complement(union(complement(power_class(u)),v)))))),intersection(power_class(u),complement(v)))*. % 300.04/300.42 251095[19:MRR:251074.0,167011.0] || equal(symmetrization_of(intersection(complement(u),power_class(v))),ordinal_numbers) -> member(ordinal_numbers,union(u,complement(power_class(v))))*. % 300.04/300.42 251098[19:MRR:251042.0,53.0] || equal(symmetrization_of(intersection(complement(u),power_class(v))),ordinal_numbers) -> member(omega,union(u,complement(power_class(v))))*. % 300.04/300.42 251105[19:MRR:251049.0,170.0] || well_ordering(universal_class,intersection(complement(u),power_class(v))) -> member(singleton(ordinal_numbers),union(u,complement(power_class(v))))*. % 300.04/300.42 251165[19:SpL:206403.0,248972.0] || equal(symmetrization_of(union(u,complement(power_class(v)))),ordinal_numbers) -> subclass(universal_class,intersection(complement(u),power_class(v)))*. % 300.04/300.42 251168[19:SpL:206410.0,248972.0] || equal(symmetrization_of(union(complement(power_class(u)),v)),ordinal_numbers) -> subclass(universal_class,intersection(power_class(u),complement(v)))*. % 300.04/300.42 251194[19:SpL:206403.0,250085.0] || subclass(union(u,complement(power_class(v))),ordinal_numbers) -> subclass(singleton(omega),intersection(complement(u),power_class(v)))*. % 300.04/300.42 251197[19:SpL:206410.0,250085.0] || subclass(union(complement(power_class(u)),v),ordinal_numbers) -> subclass(singleton(omega),intersection(power_class(u),complement(v)))*. % 300.04/300.42 251380[19:SpL:206403.0,250124.0] || subclass(union(u,complement(power_class(v))),ordinal_numbers) -> subclass(singleton(ordinal_numbers),intersection(complement(u),power_class(v)))*. % 300.04/300.42 251383[19:SpL:206410.0,250124.0] || subclass(union(complement(power_class(u)),v),ordinal_numbers) -> subclass(singleton(ordinal_numbers),intersection(power_class(u),complement(v)))*. % 300.04/300.42 251434[19:SpL:206403.0,248778.0] || equal(complement(union(u,complement(power_class(v)))),universal_class) -> subclass(w,intersection(complement(u),power_class(v)))*. % 300.04/300.42 251437[19:SpL:206410.0,248778.0] || equal(complement(union(complement(power_class(u)),v)),universal_class) -> subclass(w,intersection(power_class(u),complement(v)))*. % 300.04/300.42 251471[0:SpR:206403.0,248783.0] || -> subclass(intersection(complement(complement(complement(union(u,complement(power_class(v)))))),w),intersection(complement(u),power_class(v)))*. % 300.04/300.42 251474[0:SpR:206410.0,248783.0] || -> subclass(intersection(complement(complement(complement(union(complement(power_class(u)),v)))),w),intersection(power_class(u),complement(v)))*. % 300.04/300.42 251801[0:SpR:206403.0,248798.0] || -> subclass(intersection(u,complement(complement(complement(union(v,complement(power_class(w))))))),intersection(complement(v),power_class(w)))*. % 300.04/300.42 251804[0:SpR:206410.0,248798.0] || -> subclass(intersection(u,complement(complement(complement(union(complement(power_class(v)),w))))),intersection(power_class(v),complement(w)))*. % 300.04/300.42 251934[0:SpR:206403.0,248810.0] || -> subclass(complement(complement(intersection(u,complement(union(v,complement(power_class(w))))))),intersection(complement(v),power_class(w)))*. % 300.04/300.42 251937[0:SpR:206410.0,248810.0] || -> subclass(complement(complement(intersection(u,complement(union(complement(power_class(v)),w))))),intersection(power_class(v),complement(w)))*. % 300.04/300.42 252243[0:SpR:206403.0,248812.0] || -> subclass(complement(complement(intersection(complement(union(u,complement(power_class(v)))),w))),intersection(complement(u),power_class(v)))*. % 300.04/300.42 252246[0:SpR:206410.0,248812.0] || -> subclass(complement(complement(intersection(complement(union(complement(power_class(u)),v)),w))),intersection(power_class(u),complement(v)))*. % 300.04/300.42 252405[0:SpR:206403.0,249106.0] || -> subclass(complement(union(u,complement(complement(union(v,complement(power_class(w))))))),intersection(complement(v),power_class(w)))*. % 300.04/300.42 252408[0:SpR:206410.0,249106.0] || -> subclass(complement(union(u,complement(complement(union(complement(power_class(v)),w))))),intersection(power_class(v),complement(w)))*. % 300.04/300.42 252607[8:Res:125121.2,20.0] || member(u,cantor(v)) subclass(rest_of(v),element_relation) -> member(u,restrict(v,u,universal_class))*. % 300.04/300.42 252651[0:SpR:206403.0,249272.0] || -> subclass(complement(union(complement(complement(union(u,complement(power_class(v))))),w)),intersection(complement(u),power_class(v)))*. % 300.04/300.42 252654[0:SpR:206410.0,249272.0] || -> subclass(complement(union(complement(complement(union(complement(power_class(u)),v))),w)),intersection(power_class(u),complement(v)))*. % 300.04/300.42 252800[19:Res:250112.0,8.0] || subclass(u,singleton(not_subclass_element(u,ordinal_numbers)))* -> subclass(u,ordinal_numbers) equal(singleton(not_subclass_element(u,ordinal_numbers)),u). % 300.04/300.42 252849[19:Obv:252789.0] || -> member(u,unordered_pair(u,v))* subclass(singleton(v),unordered_pair(u,v))* subclass(unordered_pair(u,v),ordinal_numbers). % 300.04/300.42 252850[19:Obv:252787.0] || -> member(u,unordered_pair(v,u))* subclass(singleton(v),unordered_pair(v,u))* subclass(unordered_pair(v,u),ordinal_numbers). % 300.04/300.42 252873[0:SpR:206403.0,220180.1] || subclass(intersection(complement(u),power_class(v)),w) -> subclass(complement(union(u,complement(power_class(v)))),w)*. % 300.04/300.42 252876[0:SpR:206410.0,220180.1] || subclass(intersection(power_class(u),complement(v)),w) -> subclass(complement(union(complement(power_class(u)),v)),w)*. % 300.04/300.42 252915[19:Res:220180.1,167739.0] || subclass(u,singleton(v))* -> equal(complement(complement(u)),ordinal_numbers) equal(regular(complement(complement(u))),v)*. % 300.04/300.42 253022[19:Res:252894.1,16469.0] || subclass(inverse(ordinal_numbers),singleton(u))* -> subclass(symmetrization_of(ordinal_numbers),v) equal(not_subclass_element(symmetrization_of(ordinal_numbers),v),u)*. % 300.04/300.42 253058[20:MRR:253006.2,175557.0] || subclass(inverse(ordinal_numbers),u)* well_ordering(v,u)* -> member(least(v,symmetrization_of(ordinal_numbers)),symmetrization_of(ordinal_numbers))*. % 300.04/300.42 253118[19:Res:167135.2,227961.1] || member(cantor(u),universal_class) member(u,apply(choice,cantor(u)))* -> equal(cantor(u),ordinal_numbers). % 300.04/300.42 253124[18:Res:35222.2,227961.1] inductive(cantor(u)) || well_ordering(v,cantor(u)) member(u,least(v,cantor(u)))* -> . % 300.04/300.42 253136[19:Res:168252.2,227961.1] || well_ordering(u,cantor(v)) member(v,least(u,cantor(v)))* -> equal(cantor(v),ordinal_numbers). % 300.04/300.42 253141[18:Res:2523.2,227961.1] || member(u,universal_class) subclass(rest_relation,cantor(v)) member(v,ordered_pair(u,rest_of(u)))* -> . % 300.04/300.42 253175[19:Res:168350.1,227961.1] || member(u,regular(restrict(cantor(u),v,w)))* -> equal(restrict(cantor(u),v,w),ordinal_numbers). % 300.04/300.42 9719[0:Res:24.2,5467.1] || member(singleton(u),v)* member(singleton(u),w)* subclass(universal_class,complement(intersection(w,v)))* -> . % 300.04/300.42 16770[0:Res:16276.0,8.0] || subclass(complement(intersection(u,v)),symmetric_difference(u,v))* -> equal(complement(intersection(u,v)),symmetric_difference(u,v)). % 300.04/300.42 48526[0:Rew:39.0,48491.0] || member(flip(cross_product(u,universal_class)),inverse(u)) -> member(ordered_pair(flip(cross_product(u,universal_class)),inverse(u)),element_relation)*. % 300.04/300.42 48527[0:Rew:54.0,48488.0] || member(restrict(element_relation,universal_class,u),sum_class(u)) -> member(ordered_pair(restrict(element_relation,universal_class,u),sum_class(u)),element_relation)*. % 300.04/300.42 84059[0:SpL:479.0,2532.0] || subclass(universal_class,power_class(intersection(complement(u),complement(v))))* member(omega,image(element_relation,union(u,v))) -> . % 300.04/300.42 16838[0:SpL:479.0,9715.1] || subclass(universal_class,image(element_relation,union(u,v))) subclass(universal_class,power_class(intersection(complement(u),complement(v))))* -> . % 300.04/300.42 17105[0:SpR:479.0,16762.0] || -> subclass(symmetric_difference(power_class(intersection(complement(u),complement(v))),complement(w)),union(image(element_relation,union(u,v)),w))*. % 300.04/300.42 17094[0:SpR:479.0,16762.0] || -> subclass(symmetric_difference(complement(u),power_class(intersection(complement(v),complement(w)))),union(u,image(element_relation,union(v,w))))*. % 300.04/300.42 43034[0:Obv:43024.1] || member(ordered_pair(u,v),compose(w,x)) -> subclass(singleton(v),image(w,image(x,singleton(u))))*. % 300.04/300.42 48676[0:SpL:4121.0,6437.0] || subclass(universal_class,symmetric_difference(cross_product(u,v),w)) -> member(unordered_pair(x,y),complement(restrict(w,u,v)))*. % 300.04/300.42 48675[0:SpL:4119.0,6437.0] || subclass(universal_class,symmetric_difference(u,cross_product(v,w))) -> member(unordered_pair(x,y),complement(restrict(u,v,w)))*. % 300.04/300.42 16807[0:Res:16283.0,8.0] || subclass(cross_product(u,v),restrict(w,u,v))* -> equal(restrict(w,u,v),cross_product(u,v)). % 300.04/300.42 84225[8:Res:81104.1,126.0] || subclass(domain_relation,u) subclass(u,v)* well_ordering(w,v)* -> member(least(w,u),u)*. % 300.04/300.42 9835[0:Res:2479.1,126.0] || subclass(universal_class,u) subclass(u,v)* well_ordering(w,v)* -> member(least(w,u),u)*. % 300.04/300.42 95701[0:Res:51413.0,126.0] || subclass(u,v)* well_ordering(w,v)* -> subclass(x,complement(u))* member(least(w,u),u)*. % 300.04/300.42 98747[8:SpL:479.0,97513.1] || subclass(universal_class,image(element_relation,union(u,v))) subclass(domain_relation,power_class(intersection(complement(u),complement(v))))* -> . % 300.04/300.42 98748[8:SpL:479.0,97509.1] || subclass(domain_relation,image(element_relation,union(u,v))) subclass(domain_relation,power_class(intersection(complement(u),complement(v))))* -> . % 300.04/300.42 98750[8:SpL:479.0,97574.1] || equal(image(element_relation,union(u,v)),domain_relation) equal(power_class(intersection(complement(u),complement(v))),domain_relation)** -> . % 300.04/300.42 113778[0:Obv:113764.0] || -> equal(not_subclass_element(unordered_pair(u,v),complement(w)),v)** member(u,w) subclass(unordered_pair(u,v),complement(w)). % 300.04/300.42 113779[0:Obv:113753.0] || -> equal(not_subclass_element(unordered_pair(u,v),complement(w)),u)** member(v,w) subclass(unordered_pair(u,v),complement(w)). % 300.04/300.42 125686[8:Rew:124908.0,52655.2] inductive(cantor(inverse(u))) || well_ordering(v,range_of(u)) -> member(least(v,range_of(u)),range_of(u))*. % 300.04/300.42 131964[8:SpL:124905.0,131613.1] || equal(complement(rest_of(restrict(u,v,singleton(w)))),universal_class)** member(x,segment(u,v,w))* -> . % 300.04/300.42 132558[0:Res:51413.0,16910.0] || -> subclass(u,complement(symmetric_difference(v,inverse(v)))) member(not_subclass_element(u,complement(symmetric_difference(v,inverse(v)))),symmetrization_of(v))*. % 300.04/300.42 132957[0:SpL:27.0,82322.0] || subclass(universal_class,image(element_relation,union(u,v))) member(omega,power_class(intersection(complement(u),complement(v))))* -> . % 300.04/300.42 135222[0:Res:36865.0,158.0] || -> subclass(complement(complement(omega)),u) equal(integer_of(not_subclass_element(complement(complement(omega)),u)),not_subclass_element(complement(complement(omega)),u))**. % 300.04/300.42 135255[0:Obv:135233.1] || member(not_subclass_element(complement(complement(u)),intersection(v,u)),v)* -> subclass(complement(complement(u)),intersection(v,u)). % 300.04/300.42 135912[0:Res:2526.2,16105.1] || subclass(u,intersection(v,w)) member(not_subclass_element(u,x),symmetric_difference(v,w))* -> subclass(u,x). % 300.04/300.42 135915[0:Res:2482.2,16105.1] || member(u,universal_class) subclass(universal_class,intersection(v,w)) member(sum_class(u),symmetric_difference(v,w))* -> . % 300.04/300.42 135916[0:Res:2483.2,16105.1] || member(u,universal_class) subclass(universal_class,intersection(v,w)) member(power_class(u),symmetric_difference(v,w))* -> . % 300.04/300.42 135952[0:Res:2525.1,16105.1] || subclass(ordered_pair(u,v),intersection(w,x)) member(unordered_pair(u,singleton(v)),symmetric_difference(w,x))* -> . % 300.04/300.42 135978[0:Res:2525.1,896.0] || subclass(ordered_pair(u,v),restrict(w,x,y))* -> member(unordered_pair(u,singleton(v)),cross_product(x,y))*. % 300.04/300.42 137169[0:SpL:5132.1,135397.0] || subclass(not_subclass_element(cross_product(u,v),w),x)* well_ordering(universal_class,x) -> subclass(cross_product(u,v),w). % 300.04/300.42 137279[0:SpL:5132.1,137176.0] || equal(u,not_subclass_element(cross_product(v,w),x))* well_ordering(universal_class,u)* -> subclass(cross_product(v,w),x). % 300.04/300.42 138307[8:Res:125124.2,2.0] || member(u,universal_class)* subclass(rest_relation,rest_of(v)) subclass(cantor(v),w)* -> member(u,w)*. % 300.04/300.42 140563[0:Res:12807.1,2.0] || subclass(universal_class,symmetric_difference(u,v)) subclass(union(u,v),w)* -> member(unordered_pair(x,y),w)*. % 300.04/300.42 140725[0:Res:35125.1,2.0] || member(u,universal_class) subclass(union(v,w),x)* -> member(u,complement(w))* member(u,x)*. % 300.04/300.42 140820[0:Res:35124.1,2.0] || member(u,universal_class) subclass(union(v,w),x)* -> member(u,complement(v))* member(u,x)*. % 300.04/300.42 140901[12:SpL:17187.0,105054.0] || member(image(cross_product(u,v),w),universal_class) member(restrict(cross_product(w,universal_class),u,v),universal_class)* -> . % 300.04/300.42 142352[0:Rew:30.0,142264.1] || member(not_subclass_element(u,restrict(u,v,w)),cross_product(v,w))* -> subclass(u,restrict(u,v,w)). % 300.04/300.42 142376[0:MRR:142316.0,36682.1] || -> member(not_subclass_element(u,intersection(union(v,w),u)),complement(w))* subclass(u,intersection(union(v,w),u)). % 300.04/300.42 142377[0:MRR:142315.0,36682.1] || -> member(not_subclass_element(u,intersection(union(v,w),u)),complement(v))* subclass(u,intersection(union(v,w),u)). % 300.04/300.42 146346[12:SpL:146278.0,99366.2] || member(u,universal_class)* member(cross_product(v,universal_class),universal_class)* equal(sum_class(image(universal_class,v)),u)* -> . % 300.04/300.42 148030[8:Res:147404.1,42071.0] || member(not_subclass_element(u,intersection(compose(element_relation,universal_class),u)),element_relation)* -> subclass(u,intersection(compose(element_relation,universal_class),u)). % 300.04/300.42 148285[0:SpL:160.0,15110.1] || member(u,universal_class) subclass(universal_class,symmetric_difference(v,w)) -> member(sum_class(u),complement(intersection(v,w)))*. % 300.04/300.42 148783[0:SpL:160.0,15076.1] || member(u,universal_class) subclass(universal_class,symmetric_difference(v,w)) -> member(power_class(u),complement(intersection(v,w)))*. % 300.04/300.42 149485[0:SpR:149012.1,16826.0] || subclass(complement(singleton(u)),complement(u))* -> equal(complement(image(element_relation,successor(u))),power_class(complement(singleton(u)))). % 300.04/300.42 149487[0:SpR:149012.1,16825.0] || subclass(complement(inverse(u)),complement(u))* -> equal(complement(image(element_relation,symmetrization_of(u))),power_class(complement(inverse(u)))). % 300.04/300.42 152712[0:SpL:160.0,16465.0] || subclass(u,symmetric_difference(v,w)) -> subclass(u,x) member(not_subclass_element(u,x),complement(intersection(v,w)))*. % 300.04/300.42 152862[0:Res:905.1,25.1] || member(not_subclass_element(restrict(complement(u),v,w),x),u)* -> subclass(restrict(complement(u),v,w),x). % 300.04/300.42 153107[0:SpR:4121.0,149179.0] || -> equal(intersection(complement(restrict(u,v,w)),symmetric_difference(cross_product(v,w),u)),symmetric_difference(cross_product(v,w),u))**. % 300.04/300.42 153108[0:SpR:4119.0,149179.0] || -> equal(intersection(complement(restrict(u,v,w)),symmetric_difference(u,cross_product(v,w))),symmetric_difference(u,cross_product(v,w)))**. % 300.04/300.42 154763[8:MRR:154744.0,170.0] || subclass(rest_relation,rest_of(u)) member(cantor(u),universal_class) -> member(singleton(singleton(singleton(cantor(u)))),element_relation)*. % 300.04/300.42 154764[0:MRR:154737.0,170.0] || member(complement(u),universal_class) -> member(singleton(complement(u)),u)* member(singleton(singleton(singleton(complement(u)))),element_relation)*. % 300.04/300.42 134796[3:Res:134636.1,7972.2] || subclass(intersection(u,v),ordinal_numbers)* member(w,v)* member(w,u)* -> member(w,kind_1_ordinals)*. % 300.04/300.42 145457[0:Res:144531.1,126.0] || equal(u,universal_class) subclass(u,v)* well_ordering(w,v)* -> member(least(w,u),u)*. % 300.04/300.42 163795[0:SpR:146278.0,433.1] || member(inverse(cross_product(u,universal_class)),universal_class) -> member(ordered_pair(inverse(cross_product(u,universal_class)),image(universal_class,u)),domain_relation)*. % 300.04/300.42 165009[8:SpL:479.0,164453.1] || subclass(domain_relation,image(element_relation,union(u,v))) subclass(universal_class,power_class(intersection(complement(u),complement(v))))* -> . % 300.04/300.42 117057[0:Res:9790.2,6476.1] || member(ordered_pair(u,v),cross_product(universal_class,universal_class))* subclass(composition_function,w) subclass(universal_class,complement(w))* -> . % 300.04/300.42 166630[8:Res:166605.0,15100.2] || member(u,universal_class) subclass(universal_class,complement(inverse(singleton(sum_class(u)))))* -> asymmetric(singleton(sum_class(u)),v)*. % 300.04/300.42 166631[8:Res:166605.0,15066.2] || member(u,universal_class) subclass(universal_class,complement(inverse(singleton(power_class(u)))))* -> asymmetric(singleton(power_class(u)),v)*. % 300.04/300.42 167446[19:Rew:166997.0,164405.1] || subclass(domain_relation,complement(compose(element_relation,universal_class)))* member(ordered_pair(ordinal_numbers,ordinal_numbers),element_relation) well_ordering(u,v)* -> . % 300.04/300.42 167683[19:Rew:166997.0,163757.1] || subclass(u,symmetric_difference(complement(v),complement(w)))* -> equal(u,ordinal_numbers) member(regular(u),union(v,w)). % 300.04/300.42 168241[19:Rew:166997.0,80689.3] || member(u,v) member(u,singleton(v))* well_ordering(w,x)* -> equal(singleton(v),ordinal_numbers). % 300.04/300.42 168364[19:Rew:166997.0,163371.1] || subclass(omega,symmetric_difference(complement(u),complement(v)))* -> equal(integer_of(w),ordinal_numbers) member(w,union(u,v))*. % 300.04/300.42 168550[19:Rew:166997.0,99207.1] || -> member(regular(complement(union(u,v))),intersection(complement(u),complement(v)))* equal(complement(union(u,v)),ordinal_numbers). % 300.04/300.42 168552[19:Rew:166997.0,99195.0] || -> equal(complement(complement(restrict(u,v,w))),ordinal_numbers) member(regular(complement(complement(restrict(u,v,w)))),u)*. % 300.04/300.42 168553[19:Rew:166997.0,99180.0] || -> equal(complement(complement(symmetric_difference(u,v))),ordinal_numbers) member(regular(complement(complement(symmetric_difference(u,v)))),union(u,v))*. % 300.04/300.42 168571[19:Rew:166997.0,81083.1] || member(u,v)* -> equal(ordered_pair(first(ordered_pair(u,ordinal_numbers)),second(ordered_pair(u,ordinal_numbers))),ordered_pair(u,ordinal_numbers))**. % 300.04/300.42 168574[19:Rew:166997.0,82526.0] || equal(segment(u,v,w),ordinal_numbers) subclass(singleton(w),v) -> section(u,singleton(w),v)*. % 300.04/300.42 168579[19:Rew:166997.0,84378.1] || subclass(universal_class,power_class(intersection(complement(u),complement(v))))* member(ordinal_numbers,image(element_relation,union(u,v))) -> . % 300.04/300.42 168919[19:Rew:166997.0,163403.1] || subclass(omega,rest_of(u)) -> equal(integer_of(singleton(singleton(singleton(v)))),ordinal_numbers)** member(singleton(v),cantor(u))*. % 300.04/300.42 168920[19:Rew:166997.0,163439.1] || subclass(omega,u) -> equal(integer_of(not_subclass_element(v,intersection(u,v))),ordinal_numbers)** subclass(v,intersection(u,v)). % 300.04/300.42 168966[19:Rew:166997.0,164603.1] || member(restrict(cross_product(u,universal_class),v,w),universal_class)* -> equal(singleton(image(cross_product(v,w),u)),ordinal_numbers). % 300.04/300.42 168967[19:Rew:166997.0,164642.2] || member(u,universal_class) member(range_of(u),cantor(v))* equal(restrict(v,ordinal_numbers,universal_class),ordinal_numbers) -> . % 300.04/300.42 168976[19:Rew:166997.0,164707.1] || member(restrict(cross_product(u,universal_class),v,w),universal_class)* -> equal(integer_of(image(cross_product(v,w),u)),ordinal_numbers). % 300.04/300.42 169545[19:Rew:166997.0,168177.1] || -> subclass(restrict(symmetrization_of(ordinal_numbers),u,v),w) member(not_subclass_element(restrict(symmetrization_of(ordinal_numbers),u,v),w),inverse(ordinal_numbers))*. % 300.04/300.42 168159[19:Rew:166997.0,160523.0] || -> equal(intersection(union(u,complement(inverse(ordinal_numbers))),union(complement(u),symmetrization_of(ordinal_numbers))),symmetric_difference(complement(u),symmetrization_of(ordinal_numbers)))**. % 300.04/300.42 169541[19:Rew:166997.0,168054.1] || member(u,universal_class) subclass(symmetrization_of(ordinal_numbers),v)* -> member(u,complement(inverse(ordinal_numbers)))* member(u,v)*. % 300.04/300.42 168157[19:Rew:166997.0,160534.0] || -> equal(complement(intersection(complement(u),union(v,complement(inverse(ordinal_numbers))))),union(u,intersection(complement(v),symmetrization_of(ordinal_numbers))))**. % 300.04/300.42 168156[19:Rew:166997.0,160522.0] || -> equal(complement(intersection(complement(u),union(complement(inverse(ordinal_numbers)),v))),union(u,intersection(symmetrization_of(ordinal_numbers),complement(v))))**. % 300.04/300.42 168154[19:Rew:166997.0,160512.0] || -> equal(power_class(intersection(symmetrization_of(ordinal_numbers),complement(inverse(complement(inverse(ordinal_numbers)))))),complement(image(element_relation,symmetrization_of(complement(inverse(ordinal_numbers))))))**. % 300.04/300.42 168152[19:Rew:166997.0,160510.0] || -> equal(power_class(intersection(symmetrization_of(ordinal_numbers),complement(singleton(complement(inverse(ordinal_numbers)))))),complement(image(element_relation,successor(complement(inverse(ordinal_numbers))))))**. % 300.04/300.42 168146[19:Rew:166997.0,160518.0] || -> equal(complement(intersection(union(u,complement(inverse(ordinal_numbers))),complement(v))),union(intersection(complement(u),symmetrization_of(ordinal_numbers)),v))**. % 300.04/300.42 168143[19:Rew:166997.0,160497.0] || -> equal(complement(intersection(union(complement(inverse(ordinal_numbers)),u),complement(v))),union(intersection(symmetrization_of(ordinal_numbers),complement(u)),v))**. % 300.04/300.42 169543[19:Rew:166997.0,168134.1] || member(regular(power_class(complement(inverse(ordinal_numbers)))),image(element_relation,symmetrization_of(ordinal_numbers)))* -> equal(power_class(complement(inverse(ordinal_numbers))),ordinal_numbers). % 300.04/300.42 168130[19:Rew:166997.0,166897.0] || -> subclass(symmetric_difference(power_class(complement(inverse(ordinal_numbers))),complement(inverse(image(element_relation,symmetrization_of(ordinal_numbers))))),symmetrization_of(image(element_relation,symmetrization_of(ordinal_numbers))))*. % 300.04/300.42 168127[19:Rew:166997.0,166892.0] || -> subclass(symmetric_difference(power_class(complement(inverse(ordinal_numbers))),complement(singleton(image(element_relation,symmetrization_of(ordinal_numbers))))),successor(image(element_relation,symmetrization_of(ordinal_numbers))))*. % 300.04/300.42 169542[19:Rew:166997.0,168117.1] || -> member(not_subclass_element(u,image(element_relation,symmetrization_of(ordinal_numbers))),power_class(complement(inverse(ordinal_numbers))))* subclass(u,image(element_relation,symmetrization_of(ordinal_numbers))). % 300.04/300.42 169540[19:Rew:166997.0,168041.0] || -> member(not_subclass_element(u,power_class(complement(inverse(ordinal_numbers)))),image(element_relation,symmetrization_of(ordinal_numbers)))* subclass(u,power_class(complement(inverse(ordinal_numbers)))). % 300.04/300.42 175790[19:SpR:167785.2,167354.0] || member(u,universal_class) -> member(u,cantor(v)) equal(range__dfg(v,u,universal_class),range__dfg(ordinal_numbers,w,x))*. % 300.04/300.42 176100[20:Res:175613.1,82994.1] || subclass(universal_class,complement(compose(element_relation,universal_class)))* member(regular(symmetrization_of(ordinal_numbers)),element_relation) well_ordering(u,v)* -> . % 300.04/300.42 176256[19:Rew:176206.1,158693.2] || member(u,universal_class) subclass(domain_relation,symmetric_difference(v,inverse(v)))* -> member(ordered_pair(u,ordinal_numbers),symmetrization_of(v))*. % 300.04/300.42 177186[22:Res:177171.1,126.0] || subclass(omega,u) subclass(u,v)* well_ordering(w,v)* -> member(least(w,u),u)*. % 300.04/300.42 177640[19:SpR:16826.0,176367.1] || member(intersection(complement(u),complement(singleton(u))),universal_class)* -> equal(cantor(complement(image(element_relation,successor(u)))),ordinal_numbers). % 300.04/300.42 177641[19:SpR:16825.0,176367.1] || member(intersection(complement(u),complement(inverse(u))),universal_class)* -> equal(cantor(complement(image(element_relation,symmetrization_of(u)))),ordinal_numbers). % 300.04/300.42 177895[19:SpL:177036.0,167253.1] || member(inverse(u),cantor(v))* equal(restrict(v,ordinal_numbers,universal_class),ordinal_numbers) -> equal(range_of(u),ordinal_numbers). % 300.04/300.42 177993[22:SpL:479.0,177179.0] || subclass(omega,power_class(intersection(complement(u),complement(v))))* member(ordinal_numbers,image(element_relation,union(u,v))) -> . % 300.04/300.42 178458[19:SpL:168412.1,6476.1] || subclass(universal_class,complement(u)) member(regular(cross_product(v,w)),u)* -> equal(cross_product(v,w),ordinal_numbers). % 300.04/300.42 178707[22:SpL:479.0,178652.1] || equal(image(element_relation,union(u,v)),omega) equal(power_class(intersection(complement(u),complement(v))),omega)** -> . % 300.04/300.42 178921[22:Res:178902.1,126.0] || equal(u,omega) subclass(u,v)* well_ordering(w,v)* -> member(least(w,u),u)*. % 300.04/300.42 180395[19:Rew:180089.0,180196.1] || -> member(not_subclass_element(u,image(element_relation,singleton(ordinal_numbers))),power_class(complement(singleton(ordinal_numbers))))* subclass(u,image(element_relation,singleton(ordinal_numbers))). % 300.04/300.42 180238[19:Rew:180089.0,179085.0] || -> subclass(symmetric_difference(power_class(complement(singleton(ordinal_numbers))),complement(singleton(image(element_relation,singleton(ordinal_numbers))))),successor(image(element_relation,singleton(ordinal_numbers))))*. % 300.04/300.42 180241[19:Rew:180089.0,179090.0] || -> subclass(symmetric_difference(power_class(complement(singleton(ordinal_numbers))),complement(inverse(image(element_relation,singleton(ordinal_numbers))))),symmetrization_of(image(element_relation,singleton(ordinal_numbers))))*. % 300.04/300.42 180245[19:Rew:180089.0,179167.0] || -> member(not_subclass_element(u,power_class(complement(singleton(ordinal_numbers)))),image(element_relation,singleton(ordinal_numbers)))* subclass(u,power_class(complement(singleton(ordinal_numbers)))). % 300.04/300.42 180246[19:Rew:180089.0,179168.0] || member(regular(power_class(complement(singleton(ordinal_numbers)))),image(element_relation,singleton(ordinal_numbers)))* -> equal(power_class(complement(singleton(ordinal_numbers))),ordinal_numbers). % 300.04/300.42 180289[19:Rew:180089.0,168814.0] || -> equal(complement(intersection(union(complement(singleton(ordinal_numbers)),u),complement(v))),union(intersection(singleton(ordinal_numbers),complement(u)),v))**. % 300.04/300.42 180304[19:Rew:180089.0,168818.0] || -> equal(power_class(intersection(singleton(ordinal_numbers),complement(inverse(complement(singleton(ordinal_numbers)))))),complement(image(element_relation,symmetrization_of(complement(singleton(ordinal_numbers))))))**. % 300.04/300.42 180306[19:Rew:180089.0,168820.0] || -> equal(power_class(intersection(singleton(ordinal_numbers),complement(singleton(complement(singleton(ordinal_numbers)))))),complement(image(element_relation,successor(complement(singleton(ordinal_numbers))))))**. % 300.04/300.42 180327[19:Rew:180089.0,168826.0] || -> equal(complement(intersection(complement(u),union(complement(singleton(ordinal_numbers)),v))),union(u,intersection(singleton(ordinal_numbers),complement(v))))**. % 300.04/300.42 180968[19:SpL:479.0,180886.1] inductive(image(element_relation,union(u,v))) || equal(power_class(intersection(complement(u),complement(v))),singleton(ordinal_numbers))** -> . % 300.04/300.42 181323[19:SpL:168752.1,2557.0] || member(u,universal_class) member(singleton(singleton(ordinal_numbers)),cross_product(v,w))* -> member(sum_class(range_of(u)),w)*. % 300.04/300.42 181734[20:Res:175570.1,488.0] || subclass(inverse(ordinal_numbers),intersection(complement(u),complement(v)))* member(regular(symmetrization_of(ordinal_numbers)),union(u,v)) -> . % 300.04/300.42 181740[20:Res:175570.1,9.0] || subclass(inverse(ordinal_numbers),unordered_pair(u,v))* -> equal(regular(symmetrization_of(ordinal_numbers)),v) equal(regular(symmetrization_of(ordinal_numbers)),u). % 300.04/300.42 181795[19:Res:176345.1,488.0] || subclass(domain_relation,intersection(complement(u),complement(v))) member(singleton(singleton(singleton(ordinal_numbers))),union(u,v))* -> . % 300.04/300.42 182454[19:SpL:479.0,182395.0] || well_ordering(universal_class,power_class(intersection(complement(u),complement(v))))* -> member(singleton(ordinal_numbers),image(element_relation,union(u,v))). % 300.04/300.42 182476[19:SpR:479.0,182467.1] || -> member(singleton(ordinal_numbers),image(element_relation,union(u,v))) member(singleton(ordinal_numbers),power_class(intersection(complement(u),complement(v))))*. % 300.04/300.42 182915[20:Res:181635.1,488.0] || subclass(symmetrization_of(ordinal_numbers),intersection(complement(u),complement(v)))* member(regular(symmetrization_of(ordinal_numbers)),union(u,v)) -> . % 300.04/300.42 182921[20:Res:181635.1,9.0] || subclass(symmetrization_of(ordinal_numbers),unordered_pair(u,v))* -> equal(regular(symmetrization_of(ordinal_numbers)),v) equal(regular(symmetrization_of(ordinal_numbers)),u). % 300.04/300.42 183095[19:Res:182463.1,488.0] || equal(intersection(complement(u),complement(v)),singleton(singleton(ordinal_numbers))) member(singleton(ordinal_numbers),union(u,v))* -> . % 300.04/300.42 183397[8:Res:131984.1,124906.1] || equal(complement(rest_of(restrict(u,v,w))),universal_class)** subclass(w,v) -> section(u,w,v). % 300.04/300.42 184172[23:SpL:183857.0,166844.1] || member(ordinal_numbers,cantor(u)) member(ordered_pair(u,singleton(singleton(ordinal_numbers))),cross_product(universal_class,cross_product(universal_class,universal_class)))* -> . % 300.04/300.42 184265[23:SpL:183885.0,15100.2] || member(image(u,ordinal_numbers),universal_class) subclass(universal_class,complement(v)) member(apply(u,universal_class),v)* -> . % 300.04/300.42 184397[19:Res:66.2,176273.0] function(u) || member(v,universal_class) subclass(domain_relation,rest_relation) -> equal(rest_of(image(u,v)),ordinal_numbers)**. % 300.04/300.42 184443[19:MRR:184422.1,5.0] || member(u,universal_class) subclass(domain_relation,rest_relation) -> equal(u,ordinal_numbers) equal(rest_of(apply(choice,u)),ordinal_numbers)**. % 300.04/300.42 184529[19:Res:66.2,176274.0] function(u) || member(v,universal_class) subclass(rest_relation,domain_relation) -> equal(rest_of(image(u,v)),ordinal_numbers)**. % 300.04/300.42 184575[19:MRR:184554.1,5.0] || member(u,universal_class) subclass(rest_relation,domain_relation) -> equal(u,ordinal_numbers) equal(rest_of(apply(choice,u)),ordinal_numbers)**. % 300.04/300.42 184839[19:Res:176419.1,16105.1] || subclass(domain_relation,flip(intersection(u,v))) member(ordered_pair(ordered_pair(w,x),ordinal_numbers),symmetric_difference(u,v))* -> . % 300.04/300.42 184856[19:Res:176419.1,896.0] || subclass(domain_relation,flip(restrict(u,v,w)))* -> member(ordered_pair(ordered_pair(x,y),ordinal_numbers),cross_product(v,w))*. % 300.04/300.42 184862[19:Res:176419.1,158.0] || subclass(domain_relation,flip(omega)) -> equal(integer_of(ordered_pair(ordered_pair(u,v),ordinal_numbers)),ordered_pair(ordered_pair(u,v),ordinal_numbers))**. % 300.04/300.42 184917[19:Res:176420.1,16105.1] || subclass(domain_relation,rotate(intersection(u,v))) member(ordered_pair(ordered_pair(w,ordinal_numbers),x),symmetric_difference(u,v))* -> . % 300.04/300.42 184934[19:Res:176420.1,896.0] || subclass(domain_relation,rotate(restrict(u,v,w)))* -> member(ordered_pair(ordered_pair(x,ordinal_numbers),y),cross_product(v,w))*. % 300.04/300.42 184940[19:Res:176420.1,158.0] || subclass(domain_relation,rotate(omega)) -> equal(integer_of(ordered_pair(ordered_pair(u,ordinal_numbers),v)),ordered_pair(ordered_pair(u,ordinal_numbers),v))**. % 300.04/300.42 184964[19:Res:176420.1,8694.0] || subclass(domain_relation,rotate(compose(u,v))) -> subclass(w,image(u,image(v,singleton(ordered_pair(x,ordinal_numbers)))))*. % 300.04/300.42 185106[19:Res:49.1,167739.0] inductive(singleton(u)) || -> equal(image(successor_relation,singleton(u)),ordinal_numbers) equal(regular(image(successor_relation,singleton(u))),u)**. % 300.04/300.42 185818[0:Res:137890.1,30589.0] || well_ordering(u,universal_class) subclass(rest_relation,successor_relation) -> equal(rest_of(least(u,universal_class)),successor(least(u,universal_class)))**. % 300.04/300.42 185819[0:Res:137613.1,30589.0] || well_ordering(u,universal_class) subclass(rest_relation,successor_relation) -> equal(rest_of(least(u,rest_relation)),successor(least(u,rest_relation)))**. % 300.04/300.42 185820[0:Res:137620.1,30589.0] || well_ordering(u,rest_relation) subclass(rest_relation,successor_relation) -> equal(rest_of(least(u,rest_relation)),successor(least(u,rest_relation)))**. % 300.04/300.42 185821[21:Res:176162.1,30589.0] || well_ordering(u,omega) subclass(rest_relation,successor_relation) -> equal(rest_of(least(u,omega)),successor(least(u,omega)))**. % 300.04/300.42 185822[21:Res:176155.1,30589.0] || well_ordering(u,universal_class) subclass(rest_relation,successor_relation) -> equal(rest_of(least(u,omega)),successor(least(u,omega)))**. % 300.04/300.42 186335[19:Res:167776.1,8.0] || subclass(omega,intersection(u,singleton(v)))* -> equal(integer_of(v),ordinal_numbers) equal(intersection(u,singleton(v)),omega). % 300.04/300.42 186365[19:Res:167777.1,8.0] || subclass(omega,intersection(singleton(u),v))* -> equal(integer_of(u),ordinal_numbers) equal(intersection(singleton(u),v),omega). % 300.04/300.42 186383[19:Res:186353.1,8.0] || subclass(omega,complement(complement(singleton(u))))* -> equal(integer_of(u),ordinal_numbers) equal(complement(complement(singleton(u))),omega). % 300.04/300.42 186982[19:Res:167339.2,167734.1] || subclass(omega,u) subclass(v,complement(u))* -> equal(integer_of(regular(v)),ordinal_numbers) equal(v,ordinal_numbers). % 300.04/300.42 187076[19:Obv:187025.1] || subclass(intersection(u,singleton(v)),omega)* -> equal(intersection(u,singleton(v)),ordinal_numbers) equal(integer_of(v),v). % 300.04/300.42 187097[19:SpL:27.0,186989.0] || subclass(intersection(complement(u),complement(v)),union(u,v))* -> equal(intersection(complement(u),complement(v)),ordinal_numbers). % 300.04/300.42 187195[19:Obv:187134.1] || subclass(intersection(singleton(u),v),omega)* -> equal(intersection(singleton(u),v),ordinal_numbers) equal(integer_of(u),u). % 300.04/300.42 187569[19:Res:16280.0,167736.0] || -> equal(restrict(intersection(u,v),w,x),ordinal_numbers) member(regular(restrict(intersection(u,v),w,x)),u)*. % 300.04/300.42 187651[19:Res:16280.0,167737.0] || -> equal(restrict(intersection(u,v),w,x),ordinal_numbers) member(regular(restrict(intersection(u,v),w,x)),v)*. % 300.04/300.42 187749[19:Res:168354.1,2.0] || subclass(union(u,v),w) -> equal(symmetric_difference(u,v),ordinal_numbers) member(regular(symmetric_difference(u,v)),w)*. % 300.04/300.42 187794[19:SSi:187787.0,70.0] || equal(rest_of(u),rest_relation) -> equal(unordered_pair(v,u),ordinal_numbers) equal(apply(choice,unordered_pair(v,u)),v)**. % 300.04/300.42 187795[19:SSi:187786.0,70.0] || equal(rest_of(u),rest_relation) -> equal(unordered_pair(u,v),ordinal_numbers) equal(apply(choice,unordered_pair(u,v)),v)**. % 300.04/300.42 187810[19:Res:168350.1,148647.0] || -> equal(restrict(complement(complement(u)),v,w),ordinal_numbers) member(regular(restrict(complement(complement(u)),v,w)),u)*. % 300.04/300.42 187816[19:Res:168350.1,2.0] || subclass(u,v) -> equal(restrict(u,w,x),ordinal_numbers) member(regular(restrict(u,w,x)),v)*. % 300.04/300.42 187882[19:SpR:167458.0,57.1] || member(intersection(complement(singleton(ordinal_numbers)),complement(image(successor_relation,ordinal_numbers))),universal_class)* -> member(complement(image(element_relation,kind_1_ordinals)),universal_class). % 300.04/300.42 188065[23:SpR:168752.1,183883.0] || member(u,universal_class) -> equal(unordered_pair(ordinal_numbers,unordered_pair(sum_class(range_of(u)),ordinal_numbers)),ordered_pair(sum_class(range_of(u)),universal_class))**. % 300.04/300.42 188297[19:SpR:169372.1,69.0] || -> equal(cross_product(singleton(u),universal_class),ordinal_numbers) equal(apply(regular(cross_product(singleton(u),universal_class)),u),sum_class(range_of(ordinal_numbers)))**. % 300.04/300.42 188363[19:Res:176321.2,11848.0] || member(u,universal_class)* equal(successor(u),ordinal_numbers) subclass(successor_relation,v) well_ordering(universal_class,v)* -> . % 300.04/300.42 188758[2:Res:9790.2,188593.1] || member(ordered_pair(u,v),cross_product(universal_class,universal_class))* subclass(composition_function,w)* equal(complement(w),universal_class) -> . % 300.04/300.42 188896[19:Res:188649.1,167276.0] || equal(complement(u),universal_class) well_ordering(v,w)* -> equal(segment(v,u,least(v,u)),ordinal_numbers)**. % 300.04/300.42 188917[8:Res:188649.1,124906.1] || equal(complement(cantor(restrict(u,v,w))),universal_class)** subclass(w,v) -> section(u,w,v). % 300.04/300.42 188922[2:Res:188649.1,4278.1] || equal(complement(u),universal_class) connected(v,u) -> well_ordering(v,u) equal(not_well_ordering(v,u),u)**. % 300.04/300.42 188923[8:Res:188649.1,126121.1] || equal(complement(u),universal_class) section(v,u,w) -> equal(cantor(restrict(v,w,u)),u)**. % 300.04/300.42 189087[2:Res:188649.1,1067.0] || equal(complement(cross_product(cross_product(universal_class,universal_class),universal_class)),universal_class)** -> equal(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(u))*. % 300.04/300.42 189088[2:Res:188649.1,1066.0] || equal(complement(cross_product(cross_product(universal_class,universal_class),universal_class)),universal_class)** -> equal(cross_product(cross_product(universal_class,universal_class),universal_class),flip(u))*. % 300.04/300.42 190147[19:Obv:190141.1] || equal(complement(singleton(u)),universal_class) -> equal(regular(unordered_pair(v,u)),v)** equal(unordered_pair(v,u),ordinal_numbers). % 300.04/300.42 190148[19:Obv:190140.1] || equal(complement(singleton(u)),universal_class) -> equal(regular(unordered_pair(u,v)),v)** equal(unordered_pair(u,v),ordinal_numbers). % 300.04/300.42 190208[19:Res:182871.1,168418.0] || member(regular(intersection(u,complement(symmetrization_of(ordinal_numbers)))),inverse(ordinal_numbers))* -> equal(intersection(u,complement(symmetrization_of(ordinal_numbers))),ordinal_numbers). % 300.04/300.42 190653[19:Res:182871.1,168419.0] || member(regular(intersection(complement(symmetrization_of(ordinal_numbers)),u)),inverse(ordinal_numbers))* -> equal(intersection(complement(symmetrization_of(ordinal_numbers)),u),ordinal_numbers). % 300.04/300.42 192058[19:Rew:180103.0,192044.1] || member(regular(image(element_relation,singleton(ordinal_numbers))),power_class(complement(singleton(ordinal_numbers))))* -> equal(image(element_relation,singleton(ordinal_numbers)),ordinal_numbers). % 300.04/300.42 192059[19:Rew:167191.0,192045.1] || member(regular(image(element_relation,symmetrization_of(ordinal_numbers))),power_class(complement(inverse(ordinal_numbers))))* -> equal(image(element_relation,symmetrization_of(ordinal_numbers)),ordinal_numbers). % 300.04/300.42 193083[25:Rew:192881.1,192891.2] function(cantor(u)) function(v) || equal(cantor(cantor(w)),universal_class) -> compatible(v,w,u)*. % 300.04/300.42 193101[25:SoR:192883.0,12322.2] single_valued_class(complement(cross_product(singleton(omega),universal_class))) || equal(complement(cross_product(singleton(omega),universal_class)),cross_product(universal_class,universal_class))** -> . % 300.04/300.42 193104[25:SoR:192884.0,12322.2] single_valued_class(complement(cross_product(singleton(ordinal_numbers),universal_class))) || equal(complement(cross_product(singleton(ordinal_numbers),universal_class)),cross_product(universal_class,universal_class))** -> . % 300.04/300.42 193635[25:Rew:193223.1,193360.1] function(u) || asymmetric(v,ordinal_numbers) -> equal(domain__dfg(intersection(v,inverse(v)),ordinal_numbers,u),single_valued3(ordinal_numbers))**. % 300.04/300.42 193636[25:Rew:193223.1,193514.1] function(u) || well_ordering(element_relation,image(v,ordinal_numbers)) subclass(apply(v,u),image(v,ordinal_numbers))* -> . % 300.04/300.42 193981[19:Res:182871.1,176244.2] || member(ordered_pair(u,ordinal_numbers),inverse(ordinal_numbers))* member(u,universal_class) subclass(domain_relation,complement(symmetrization_of(ordinal_numbers))) -> . % 300.04/300.42 193983[19:Res:147404.1,176244.2] || member(ordered_pair(u,ordinal_numbers),element_relation)* member(u,universal_class) subclass(domain_relation,complement(compose(element_relation,universal_class)))* -> . % 300.04/300.42 194029[19:MRR:193972.0,940.0] || member(u,universal_class) subclass(domain_relation,complement(union(v,w)))* -> member(ordered_pair(u,ordinal_numbers),complement(w))*. % 300.04/300.42 194030[19:MRR:193971.0,940.0] || member(u,universal_class) subclass(domain_relation,complement(union(v,w)))* -> member(ordered_pair(u,ordinal_numbers),complement(v))*. % 300.04/300.42 194137[25:SoR:193242.0,12322.2] single_valued_class(least(u,universal_class)) || well_ordering(u,universal_class) equal(least(u,universal_class),cross_product(universal_class,universal_class))** -> . % 300.04/300.42 194160[25:SoR:193243.0,12322.2] single_valued_class(least(u,rest_relation)) || well_ordering(u,rest_relation) equal(least(u,rest_relation),cross_product(universal_class,universal_class))** -> . % 300.04/300.42 194163[25:SoR:193244.0,12322.2] single_valued_class(least(u,rest_relation)) || well_ordering(u,universal_class) equal(least(u,rest_relation),cross_product(universal_class,universal_class))** -> . % 300.04/300.42 194166[25:SoR:193245.0,12322.2] single_valued_class(least(u,omega)) || well_ordering(u,universal_class) equal(least(u,omega),cross_product(universal_class,universal_class))** -> . % 300.04/300.42 194169[25:SoR:193246.0,12322.2] single_valued_class(least(u,omega)) || well_ordering(u,omega) equal(least(u,omega),cross_product(universal_class,universal_class))** -> . % 300.04/300.42 194263[19:Rew:167191.0,194253.2] || subclass(omega,complement(inverse(ordinal_numbers))) -> equal(integer_of(not_subclass_element(symmetrization_of(ordinal_numbers),u)),ordinal_numbers)** subclass(symmetrization_of(ordinal_numbers),u). % 300.04/300.42 194422[19:Res:167580.1,188593.1] || member(u,universal_class) equal(complement(cantor(v)),universal_class) -> equal(apply(v,u),sum_class(range_of(ordinal_numbers)))**. % 300.04/300.42 194448[21:MRR:194394.2,167057.0] || well_ordering(u,omega) member(v,universal_class) -> equal(apply(least(u,omega),v),sum_class(range_of(ordinal_numbers)))**. % 300.04/300.42 194449[21:MRR:194393.2,167057.0] || well_ordering(u,universal_class) member(v,universal_class) -> equal(apply(least(u,omega),v),sum_class(range_of(ordinal_numbers)))**. % 300.04/300.42 194450[19:MRR:194392.2,167057.0] || well_ordering(u,universal_class) member(v,universal_class) -> equal(apply(least(u,rest_relation),v),sum_class(range_of(ordinal_numbers)))**. % 300.04/300.42 194451[19:MRR:194391.2,167057.0] || well_ordering(u,rest_relation) member(v,universal_class) -> equal(apply(least(u,rest_relation),v),sum_class(range_of(ordinal_numbers)))**. % 300.04/300.42 194452[19:MRR:194390.2,167057.0] || well_ordering(u,universal_class) member(v,universal_class) -> equal(apply(least(u,universal_class),v),sum_class(range_of(ordinal_numbers)))**. % 300.04/300.42 194456[19:MRR:194421.0,167137.1] || subclass(u,complement(cantor(v)))* -> equal(apply(v,regular(u)),sum_class(range_of(ordinal_numbers))) equal(u,ordinal_numbers). % 300.04/300.42 195052[25:SoR:193168.0,167213.2] single_valued_class(restrict(element_relation,universal_class,u)) || equal(restrict(element_relation,universal_class,u),ordinal_numbers)** -> equal(sum_class(u),universal_class). % 300.04/300.42 195078[25:SoR:193173.0,167213.2] single_valued_class(flip(cross_product(u,universal_class))) || equal(flip(cross_product(u,universal_class)),ordinal_numbers)** -> equal(inverse(u),universal_class). % 300.04/300.42 195150[25:SpL:193305.1,99365.1] function(u) || equal(sum_class(range_of(ordinal_numbers)),u)* member(singleton(singleton(ordinal_numbers)),cross_product(universal_class,universal_class))* -> . % 300.04/300.42 195221[0:SpR:946.0,27190.1] || subclass(rest_relation,flip(u)) -> member(ordered_pair(ordered_pair(v,singleton(v)),rest_of(singleton(singleton(singleton(v))))),u)*. % 300.04/300.42 195229[0:SpR:946.0,27190.1] || subclass(rest_relation,flip(u)) -> member(ordered_pair(singleton(singleton(singleton(v))),rest_of(ordered_pair(v,singleton(v)))),u)*. % 300.04/300.42 195235[0:Res:27190.1,25.1] || subclass(rest_relation,flip(complement(u))) member(ordered_pair(ordered_pair(v,w),rest_of(ordered_pair(w,v))),u)* -> . % 300.04/300.42 195239[0:Res:27190.1,148647.0] || subclass(rest_relation,flip(complement(complement(u)))) -> member(ordered_pair(ordered_pair(v,w),rest_of(ordered_pair(w,v))),u)*. % 300.04/300.42 195248[0:Res:27190.1,22.0] || subclass(rest_relation,flip(intersection(u,v)))* -> member(ordered_pair(ordered_pair(w,x),rest_of(ordered_pair(x,w))),u)*. % 300.04/300.42 195249[0:Res:27190.1,23.0] || subclass(rest_relation,flip(intersection(u,v)))* -> member(ordered_pair(ordered_pair(w,x),rest_of(ordered_pair(x,w))),v)*. % 300.04/300.42 195264[19:Res:27190.1,192214.0] || subclass(rest_relation,flip(cantor(complement(cross_product(singleton(ordered_pair(ordered_pair(u,v),rest_of(ordered_pair(v,u)))),universal_class)))))* -> . % 300.04/300.42 195270[19:Res:27190.1,169207.0] || subclass(rest_relation,flip(symmetrization_of(ordinal_numbers))) -> member(ordered_pair(ordered_pair(u,v),rest_of(ordered_pair(v,u))),inverse(ordinal_numbers))*. % 300.04/300.42 195288[0:Res:27190.1,143.0] || subclass(rest_relation,flip(rest_of(u))) -> equal(restrict(u,ordered_pair(v,w),universal_class),rest_of(ordered_pair(w,v)))**. % 300.04/300.42 195323[0:SpR:946.0,27189.1] || subclass(rest_relation,rotate(u)) -> member(ordered_pair(ordered_pair(v,rest_of(singleton(singleton(singleton(v))))),singleton(v)),u)*. % 300.04/300.42 195332[0:Res:27189.1,25.1] || subclass(rest_relation,rotate(complement(u))) member(ordered_pair(ordered_pair(v,rest_of(ordered_pair(w,v))),w),u)* -> . % 300.04/300.42 195336[0:Res:27189.1,148647.0] || subclass(rest_relation,rotate(complement(complement(u)))) -> member(ordered_pair(ordered_pair(v,rest_of(ordered_pair(w,v))),w),u)*. % 300.04/300.42 195345[0:Res:27189.1,22.0] || subclass(rest_relation,rotate(intersection(u,v)))* -> member(ordered_pair(ordered_pair(w,rest_of(ordered_pair(x,w))),x),u)*. % 300.04/300.42 195346[0:Res:27189.1,23.0] || subclass(rest_relation,rotate(intersection(u,v)))* -> member(ordered_pair(ordered_pair(w,rest_of(ordered_pair(x,w))),x),v)*. % 300.04/300.42 195361[19:Res:27189.1,192214.0] || subclass(rest_relation,rotate(cantor(complement(cross_product(singleton(ordered_pair(ordered_pair(u,rest_of(ordered_pair(v,u))),v)),universal_class)))))* -> . % 300.04/300.42 195367[19:Res:27189.1,169207.0] || subclass(rest_relation,rotate(symmetrization_of(ordinal_numbers))) -> member(ordered_pair(ordered_pair(u,rest_of(ordered_pair(v,u))),v),inverse(ordinal_numbers))*. % 300.04/300.42 195385[0:Res:27189.1,143.0] || subclass(rest_relation,rotate(rest_of(u))) -> equal(restrict(u,ordered_pair(v,rest_of(ordered_pair(w,v))),universal_class),w)**. % 300.04/300.42 195395[0:Res:27189.1,97.0] || subclass(rest_relation,rotate(composition_function)) -> equal(compose(ordered_pair(u,rest_of(ordered_pair(ordered_pair(v,w),u))),v),w)**. % 300.04/300.42 195516[19:Res:168374.2,182393.0] || subclass(omega,symmetric_difference(u,v)) well_ordering(universal_class,union(u,v))* -> equal(integer_of(singleton(ordinal_numbers)),ordinal_numbers). % 300.04/300.42 195851[19:Rew:167191.0,195758.1] || member(not_subclass_element(intersection(symmetrization_of(ordinal_numbers),u),v),complement(inverse(ordinal_numbers)))* -> subclass(intersection(symmetrization_of(ordinal_numbers),u),v). % 300.04/300.42 196028[19:Rew:167191.0,195956.1] || member(not_subclass_element(intersection(u,symmetrization_of(ordinal_numbers)),v),complement(inverse(ordinal_numbers)))* -> subclass(intersection(u,symmetrization_of(ordinal_numbers)),v). % 300.04/300.42 196297[19:SpL:180103.0,28086.0] || equal(u,singleton(ordinal_numbers)) member(v,universal_class) -> member(v,complement(singleton(ordinal_numbers)))* member(v,u)*. % 300.04/300.42 196298[19:SpL:167191.0,28086.0] || equal(u,symmetrization_of(ordinal_numbers)) member(v,universal_class) -> member(v,complement(inverse(ordinal_numbers)))* member(v,u)*. % 300.04/300.42 196616[20:Res:196602.0,8.0] || subclass(symmetrization_of(ordinal_numbers),singleton(not_subclass_element(inverse(ordinal_numbers),ordinal_numbers)))* -> equal(singleton(not_subclass_element(inverse(ordinal_numbers),ordinal_numbers)),symmetrization_of(ordinal_numbers)). % 300.04/300.42 196657[19:Res:58.0,167728.0] || subclass(cross_product(universal_class,universal_class),u) -> equal(compose(v,w),ordinal_numbers) member(regular(compose(v,w)),u)*. % 300.04/300.42 196661[19:Res:33.0,167728.0] || subclass(cross_product(cross_product(universal_class,universal_class),universal_class),u)* -> equal(rotate(v),ordinal_numbers) member(regular(rotate(v)),u)*. % 300.04/300.42 196662[19:Res:36.0,167728.0] || subclass(cross_product(cross_product(universal_class,universal_class),universal_class),u)* -> equal(flip(v),ordinal_numbers) member(regular(flip(v)),u)*. % 300.04/300.42 196713[19:MRR:196637.3,167262.1] || connected(u,v) subclass(v,w) -> well_ordering(u,v) member(regular(not_well_ordering(u,v)),w)*. % 300.04/300.42 196726[19:Res:196718.0,168644.0] || subclass(universal_class,u) well_ordering(omega,u)* -> equal(integer_of(ordered_pair(regular(element_relation),least(omega,universal_class))),ordinal_numbers)**. % 300.04/300.42 196939[19:Res:144532.1,168251.0] || equal(regular(u),universal_class) member(singleton(v),u)* -> equal(u,ordinal_numbers) member(singleton(v),w)*. % 300.04/300.42 196941[19:Res:2479.1,168251.0] || subclass(universal_class,regular(u)) member(singleton(v),u)* -> equal(u,ordinal_numbers) member(singleton(v),w)*. % 300.04/300.42 196993[19:Res:196731.1,168251.0] || subclass(universal_class,regular(u)) member(regular(element_relation),u)* -> equal(u,ordinal_numbers) member(regular(element_relation),v)*. % 300.04/300.42 197058[19:SpL:479.0,196890.1] || subclass(universal_class,image(element_relation,union(u,v))) subclass(element_relation,power_class(intersection(complement(u),complement(v))))* -> . % 300.04/300.42 197127[19:SpR:196827.0,168191.1] || subclass(omega,rest_relation) -> equal(integer_of(regular(element_relation)),ordinal_numbers) equal(rest_of(first(regular(element_relation))),second(regular(element_relation)))**. % 300.04/300.42 197128[19:SpR:196827.0,168190.1] || subclass(omega,successor_relation) -> equal(integer_of(regular(element_relation)),ordinal_numbers) equal(successor(first(regular(element_relation))),second(regular(element_relation)))**. % 300.04/300.42 197129[19:SpR:196827.0,168189.1] || subclass(omega,domain_relation) -> equal(integer_of(regular(element_relation)),ordinal_numbers) equal(cantor(first(regular(element_relation))),second(regular(element_relation)))**. % 300.04/300.42 197252[19:Res:168469.2,25.1] || subclass(u,complement(v)) member(regular(intersection(w,u)),v)* -> equal(intersection(w,u),ordinal_numbers). % 300.04/300.42 197256[19:Res:168469.2,148647.0] || subclass(u,complement(complement(v))) -> equal(intersection(w,u),ordinal_numbers) member(regular(intersection(w,u)),v)*. % 300.04/300.42 197259[19:Res:168469.2,11848.0] || subclass(u,v)* subclass(v,w)* well_ordering(universal_class,w)* -> equal(intersection(x,u),ordinal_numbers)**. % 300.04/300.42 197265[19:Res:168469.2,22.0] || subclass(u,intersection(v,w))* -> equal(intersection(x,u),ordinal_numbers) member(regular(intersection(x,u)),v)*. % 300.04/300.42 197266[19:Res:168469.2,23.0] || subclass(u,intersection(v,w))* -> equal(intersection(x,u),ordinal_numbers) member(regular(intersection(x,u)),w)*. % 300.04/300.42 197281[19:Res:168469.2,192214.0] || subclass(u,cantor(complement(cross_product(singleton(regular(intersection(v,u))),universal_class))))* -> equal(intersection(v,u),ordinal_numbers). % 300.04/300.42 197287[19:Res:168469.2,169207.0] || subclass(u,symmetrization_of(ordinal_numbers)) -> equal(intersection(v,u),ordinal_numbers) member(regular(intersection(v,u)),inverse(ordinal_numbers))*. % 300.04/300.42 197442[19:Res:168471.1,4178.0] || -> equal(intersection(u,intersection(singleton(v),w)),ordinal_numbers) equal(regular(intersection(u,intersection(singleton(v),w))),v)**. % 300.04/300.42 197643[19:Res:168472.1,4178.0] || -> equal(intersection(u,intersection(v,singleton(w))),ordinal_numbers) equal(regular(intersection(u,intersection(v,singleton(w)))),w)**. % 300.04/300.42 197816[19:Res:168474.2,25.1] || subclass(u,complement(v)) member(regular(intersection(u,w)),v)* -> equal(intersection(u,w),ordinal_numbers). % 300.04/300.42 197820[19:Res:168474.2,148647.0] || subclass(u,complement(complement(v))) -> equal(intersection(u,w),ordinal_numbers) member(regular(intersection(u,w)),v)*. % 300.04/300.42 197823[19:Res:168474.2,11848.0] || subclass(u,v)* subclass(v,w)* well_ordering(universal_class,w)* -> equal(intersection(u,x),ordinal_numbers)**. % 300.04/300.42 197829[19:Res:168474.2,22.0] || subclass(u,intersection(v,w))* -> equal(intersection(u,x),ordinal_numbers) member(regular(intersection(u,x)),v)*. % 300.04/300.42 197830[19:Res:168474.2,23.0] || subclass(u,intersection(v,w))* -> equal(intersection(u,x),ordinal_numbers) member(regular(intersection(u,x)),w)*. % 300.04/300.42 197845[19:Res:168474.2,192214.0] || subclass(u,cantor(complement(cross_product(singleton(regular(intersection(u,v))),universal_class))))* -> equal(intersection(u,v),ordinal_numbers). % 300.04/300.42 197851[19:Res:168474.2,169207.0] || subclass(u,symmetrization_of(ordinal_numbers)) -> equal(intersection(u,v),ordinal_numbers) member(regular(intersection(u,v)),inverse(ordinal_numbers))*. % 300.04/300.42 198446[19:Res:168476.1,4178.0] || -> equal(intersection(intersection(singleton(u),v),w),ordinal_numbers) equal(regular(intersection(intersection(singleton(u),v),w)),u)**. % 300.04/300.42 199110[19:Res:168477.1,4178.0] || -> equal(intersection(intersection(u,singleton(v)),w),ordinal_numbers) equal(regular(intersection(intersection(u,singleton(v)),w)),v)**. % 300.04/300.42 199566[25:SoR:197131.0,12322.2] single_valued_class(first(regular(element_relation))) || equal(cross_product(universal_class,universal_class),first(regular(element_relation))) -> member(ordinal_numbers,regular(element_relation))*. % 300.04/300.42 199571[19:Res:167580.1,197186.0] || member(second(regular(element_relation)),universal_class) -> equal(apply(first(regular(element_relation)),second(regular(element_relation))),sum_class(range_of(ordinal_numbers)))**. % 300.04/300.42 199609[19:Obv:199594.2] || equal(u,v) equal(unordered_pair(v,u),complement(singleton(v)))** -> equal(unordered_pair(v,u),ordinal_numbers). % 300.04/300.42 199610[19:Obv:199593.2] || equal(u,v) subclass(unordered_pair(v,u),complement(singleton(v)))* -> equal(unordered_pair(v,u),ordinal_numbers). % 300.04/300.42 199774[0:SpR:149012.1,16274.1] || subclass(u,v) -> subclass(symmetric_difference(v,u),w) member(not_subclass_element(symmetric_difference(v,u),w),complement(u))*. % 300.04/300.42 200359[0:Res:2481.1,16086.0] || subclass(universal_class,symmetric_difference(cross_product(u,v),w)) -> member(ordered_pair(x,y),complement(restrict(w,u,v)))*. % 300.04/300.42 200363[19:Res:167127.1,16086.0] || subclass(domain_relation,symmetric_difference(cross_product(u,v),w)) -> member(ordered_pair(ordinal_numbers,ordinal_numbers),complement(restrict(w,u,v)))*. % 300.04/300.42 200391[20:Res:175613.1,16086.0] || subclass(universal_class,symmetric_difference(cross_product(u,v),w)) -> member(regular(symmetrization_of(ordinal_numbers)),complement(restrict(w,u,v)))*. % 300.04/300.42 200673[0:Res:2481.1,16083.0] || subclass(universal_class,symmetric_difference(u,cross_product(v,w))) -> member(ordered_pair(x,y),complement(restrict(u,v,w)))*. % 300.04/300.42 200677[19:Res:167127.1,16083.0] || subclass(domain_relation,symmetric_difference(u,cross_product(v,w))) -> member(ordered_pair(ordinal_numbers,ordinal_numbers),complement(restrict(u,v,w)))*. % 300.04/300.42 200706[20:Res:175613.1,16083.0] || subclass(universal_class,symmetric_difference(u,cross_product(v,w))) -> member(regular(symmetrization_of(ordinal_numbers)),complement(restrict(u,v,w)))*. % 300.04/300.42 200751[25:SpR:125331.0,192881.1] function(restrict(cross_product(u,singleton(v)),w,x)) || -> equal(segment(cross_product(w,x),u,v),universal_class)**. % 300.04/300.42 202353[26:Rew:167055.0,202352.1] inductive(complement(complement(inverse(subset_relation)))) || well_ordering(u,universal_class) -> member(least(u,symmetrization_of(ordinal_numbers)),symmetrization_of(ordinal_numbers))*. % 300.04/300.42 203598[26:MRR:203566.0,15.1] || subclass(domain_relation,complement(compose(complement(element_relation),inverse(element_relation))))* member(ordered_pair(u,ordinal_numbers),cross_product(universal_class,universal_class))* -> . % 300.04/300.42 204523[19:Res:7968.2,203417.1] || member(ordinal_numbers,cross_product(u,v)) member(ordinal_numbers,w) subclass(restrict(w,u,v),ordinal_numbers)* -> . % 300.04/300.42 204530[19:Res:59.1,203417.1] || member(ordered_pair(u,ordinal_numbers),compose(v,w)) subclass(image(v,image(w,singleton(u))),ordinal_numbers)* -> . % 300.04/300.42 204655[19:Res:7968.2,203420.1] || member(omega,cross_product(u,v)) member(omega,w) subclass(restrict(w,u,v),ordinal_numbers)* -> . % 300.04/300.42 204667[19:Res:59.1,203420.1] || member(ordered_pair(u,omega),compose(v,w)) subclass(image(v,image(w,singleton(u))),ordinal_numbers)* -> . % 300.04/300.42 206208[0:SpR:27838.0,16276.0] || -> subclass(symmetric_difference(successor(u),union(complement(u),complement(singleton(u)))),complement(symmetric_difference(complement(u),complement(singleton(u)))))*. % 300.04/300.42 206280[19:SpL:27838.0,168377.0] || subclass(omega,symmetric_difference(complement(u),complement(singleton(u))))* -> equal(integer_of(v),ordinal_numbers) member(v,successor(u))*. % 300.04/300.42 206294[19:SpL:27838.0,167736.0] || subclass(u,symmetric_difference(complement(v),complement(singleton(v))))* -> equal(u,ordinal_numbers) member(regular(u),successor(v)). % 300.04/300.42 206518[19:Rew:206400.0,205094.0] || -> member(ordinal_numbers,intersection(complement(u),power_class(complement(power_class(v)))))* member(ordinal_numbers,union(u,image(element_relation,power_class(v)))). % 300.04/300.42 206639[0:Rew:206400.0,157098.0] || -> member(not_subclass_element(u,image(element_relation,power_class(v))),power_class(complement(power_class(v))))* subclass(u,image(element_relation,power_class(v))). % 300.04/300.42 206675[19:Rew:206400.0,194322.1] || well_ordering(u,universal_class) member(least(u,power_class(v)),complement(power_class(v)))* -> equal(power_class(v),ordinal_numbers). % 300.04/300.42 206677[0:Rew:206400.0,196039.0] || member(not_subclass_element(intersection(u,power_class(v)),w),complement(power_class(v)))* -> subclass(intersection(u,power_class(v)),w). % 300.04/300.42 206678[0:Rew:206400.0,196300.2] || equal(u,power_class(v))* member(w,universal_class) -> member(w,complement(power_class(v)))* member(w,u)*. % 300.04/300.42 206785[19:Rew:206400.0,204756.0] || -> member(ordinal_numbers,intersection(power_class(complement(power_class(u))),complement(v)))* member(ordinal_numbers,union(image(element_relation,power_class(u)),v)). % 300.04/300.42 206859[0:Rew:206400.0,17153.0] || -> subclass(symmetric_difference(power_class(complement(power_class(u))),complement(singleton(image(element_relation,power_class(u))))),successor(image(element_relation,power_class(u))))*. % 300.04/300.42 206860[0:Rew:206400.0,17135.0] || -> subclass(symmetric_difference(power_class(complement(power_class(u))),complement(inverse(image(element_relation,power_class(u))))),symmetrization_of(image(element_relation,power_class(u))))*. % 300.04/300.42 206886[19:Rew:206400.0,181810.0] || subclass(domain_relation,power_class(complement(power_class(u)))) member(singleton(singleton(singleton(ordinal_numbers))),image(element_relation,power_class(u)))* -> . % 300.04/300.42 206933[20:Rew:206400.0,181749.0] || subclass(inverse(ordinal_numbers),power_class(complement(power_class(u)))) member(regular(symmetrization_of(ordinal_numbers)),image(element_relation,power_class(u)))* -> . % 300.04/300.42 206939[20:Rew:206400.0,182930.0] || subclass(symmetrization_of(ordinal_numbers),power_class(complement(power_class(u)))) member(regular(symmetrization_of(ordinal_numbers)),image(element_relation,power_class(u)))* -> . % 300.04/300.42 206940[19:Rew:206400.0,183110.0] || equal(power_class(complement(power_class(u))),singleton(singleton(ordinal_numbers))) member(singleton(ordinal_numbers),image(element_relation,power_class(u)))* -> . % 300.04/300.42 206956[19:Rew:206400.0,192062.0] || member(regular(image(element_relation,power_class(u))),power_class(complement(power_class(u))))* -> equal(image(element_relation,power_class(u)),ordinal_numbers). % 300.04/300.42 206974[19:Rew:206400.0,205162.0] || -> equal(union(complement(singleton(ordinal_numbers)),image(element_relation,power_class(u))),complement(intersection(singleton(ordinal_numbers),power_class(complement(power_class(u))))))**. % 300.04/300.42 206975[19:Rew:206400.0,205163.0] || -> equal(union(complement(inverse(ordinal_numbers)),image(element_relation,power_class(u))),complement(intersection(symmetrization_of(ordinal_numbers),power_class(complement(power_class(u))))))**. % 300.04/300.42 207101[0:Rew:206400.0,137249.0] || -> equal(power_class(intersection(power_class(u),complement(singleton(complement(power_class(u)))))),complement(image(element_relation,successor(complement(power_class(u))))))**. % 300.04/300.42 207108[19:Rew:206400.0,203748.0] || -> equal(intersection(successor(complement(power_class(u))),intersection(intersection(power_class(u),complement(singleton(complement(power_class(u))))),v)),ordinal_numbers)**. % 300.04/300.42 207110[19:Rew:206400.0,203749.0] || -> equal(intersection(successor(complement(power_class(u))),intersection(v,intersection(power_class(u),complement(singleton(complement(power_class(u))))))),ordinal_numbers)**. % 300.04/300.42 207210[0:Rew:206400.0,137311.0] || -> equal(power_class(intersection(power_class(u),complement(inverse(complement(power_class(u)))))),complement(image(element_relation,symmetrization_of(complement(power_class(u))))))**. % 300.04/300.42 207217[19:Rew:206400.0,204097.0] || -> equal(intersection(symmetrization_of(complement(power_class(u))),intersection(intersection(power_class(u),complement(inverse(complement(power_class(u))))),v)),ordinal_numbers)**. % 300.04/300.42 207219[19:Rew:206400.0,204098.0] || -> equal(intersection(symmetrization_of(complement(power_class(u))),intersection(v,intersection(power_class(u),complement(inverse(complement(power_class(u))))))),ordinal_numbers)**. % 300.04/300.42 207288[19:Rew:206400.0,168924.0] || subclass(omega,complement(power_class(u))) -> equal(integer_of(not_subclass_element(power_class(u),v)),ordinal_numbers)** subclass(power_class(u),v). % 300.04/300.42 207319[0:Rew:206400.0,195864.0] || member(not_subclass_element(intersection(power_class(u),v),w),complement(power_class(u)))* -> subclass(intersection(power_class(u),v),w). % 300.04/300.42 207398[0:Rew:206400.0,206622.1] || -> member(not_subclass_element(u,power_class(complement(power_class(v)))),image(element_relation,power_class(v)))* subclass(u,power_class(complement(power_class(v)))). % 300.04/300.42 207401[0:Rew:206400.0,206686.1] || -> member(u,intersection(power_class(v),complement(singleton(complement(power_class(v))))))* subclass(singleton(u),successor(complement(power_class(v)))). % 300.04/300.42 207402[0:Rew:206400.0,206689.1] || member(u,symmetric_difference(power_class(v),complement(singleton(complement(power_class(v))))))* -> member(u,successor(complement(power_class(v)))). % 300.04/300.42 207403[0:Rew:206400.0,206702.1] || -> member(u,intersection(power_class(v),complement(inverse(complement(power_class(v))))))* subclass(singleton(u),symmetrization_of(complement(power_class(v)))). % 300.04/300.42 207404[0:Rew:206400.0,206705.1] || member(u,symmetric_difference(power_class(v),complement(inverse(complement(power_class(v))))))* -> member(u,symmetrization_of(complement(power_class(v)))). % 300.04/300.42 207412[19:Rew:206400.0,207033.0] || equal(intersection(power_class(u),complement(singleton(complement(power_class(u))))),ordinal_numbers)** -> equal(successor(complement(power_class(u))),universal_class). % 300.04/300.42 207413[19:Rew:206400.0,207040.1] || equal(successor(complement(power_class(u))),universal_class) -> equal(intersection(power_class(u),complement(singleton(complement(power_class(u))))),ordinal_numbers)**. % 300.04/300.42 207414[19:Rew:206400.0,207048.1] || well_ordering(universal_class,successor(complement(power_class(u)))) -> member(ordinal_numbers,intersection(power_class(u),complement(singleton(complement(power_class(u))))))*. % 300.04/300.42 207415[19:Rew:206400.0,207095.1] || subclass(successor(complement(power_class(u))),ordinal_numbers) -> member(omega,intersection(power_class(u),complement(singleton(complement(power_class(u))))))*. % 300.04/300.42 207416[19:Rew:206400.0,207096.1] || subclass(successor(complement(power_class(u))),ordinal_numbers) -> member(ordinal_numbers,intersection(power_class(u),complement(singleton(complement(power_class(u))))))*. % 300.04/300.42 207417[19:Rew:206400.0,207141.0] || equal(intersection(power_class(u),complement(inverse(complement(power_class(u))))),ordinal_numbers)** -> equal(symmetrization_of(complement(power_class(u))),universal_class). % 300.04/300.42 207418[19:Rew:206400.0,207148.1] || equal(symmetrization_of(complement(power_class(u))),universal_class) -> equal(intersection(power_class(u),complement(inverse(complement(power_class(u))))),ordinal_numbers)**. % 300.04/300.42 207419[19:Rew:206400.0,207156.1] || well_ordering(universal_class,symmetrization_of(complement(power_class(u)))) -> member(ordinal_numbers,intersection(power_class(u),complement(inverse(complement(power_class(u))))))*. % 300.04/300.42 207420[19:Rew:206400.0,207203.1] || subclass(symmetrization_of(complement(power_class(u))),ordinal_numbers) -> member(omega,intersection(power_class(u),complement(inverse(complement(power_class(u))))))*. % 300.04/300.42 207421[19:Rew:206400.0,207204.1] || subclass(symmetrization_of(complement(power_class(u))),ordinal_numbers) -> member(ordinal_numbers,intersection(power_class(u),complement(inverse(complement(power_class(u))))))*. % 300.04/300.42 208208[0:SpR:206403.0,135266.0] || -> subclass(complement(union(intersection(complement(u),power_class(v)),w)),intersection(union(u,complement(power_class(v))),complement(w)))*. % 300.04/300.42 208257[0:SpR:206403.0,135266.0] || -> subclass(complement(union(u,intersection(complement(v),power_class(w)))),intersection(complement(u),union(v,complement(power_class(w)))))*. % 300.04/300.42 208289[19:SpR:167200.0,206403.0] || -> equal(union(image(element_relation,symmetrization_of(ordinal_numbers)),complement(power_class(u))),complement(intersection(power_class(complement(inverse(ordinal_numbers))),power_class(u))))**. % 300.04/300.42 208290[19:SpR:180125.0,206403.0] || -> equal(union(image(element_relation,singleton(ordinal_numbers)),complement(power_class(u))),complement(intersection(power_class(complement(singleton(ordinal_numbers))),power_class(u))))**. % 300.04/300.42 208314[0:SpL:206403.0,195669.1] || equal(rotate(intersection(complement(u),power_class(v))),rest_relation) subclass(universal_class,union(u,complement(power_class(v))))* -> . % 300.04/300.42 208315[0:SpL:206403.0,195635.1] || equal(flip(intersection(complement(u),power_class(v))),rest_relation) subclass(universal_class,union(u,complement(power_class(v))))* -> . % 300.04/300.42 208316[19:SpL:206403.0,185733.1] || equal(rotate(intersection(complement(u),power_class(v))),domain_relation) subclass(universal_class,union(u,complement(power_class(v))))* -> . % 300.04/300.42 208317[19:SpL:206403.0,185656.1] || equal(flip(intersection(complement(u),power_class(v))),domain_relation) subclass(universal_class,union(u,complement(power_class(v))))* -> . % 300.04/300.42 208326[0:SpL:206403.0,9734.0] || subclass(universal_class,complement(union(u,complement(power_class(v))))) -> member(singleton(w),intersection(complement(u),power_class(v)))*. % 300.04/300.42 208327[19:SpL:206403.0,182427.0] || equal(complement(union(u,complement(power_class(v)))),universal_class) well_ordering(universal_class,intersection(complement(u),power_class(v)))* -> . % 300.04/300.42 208332[19:SpL:206403.0,169222.0] || equal(complement(union(u,complement(power_class(v)))),singleton(ordinal_numbers)) -> member(ordinal_numbers,intersection(complement(u),power_class(v)))*. % 300.04/300.42 208334[19:SpL:206403.0,195678.1] || equal(rotate(intersection(complement(u),power_class(v))),rest_relation) subclass(domain_relation,union(u,complement(power_class(v))))* -> . % 300.04/300.42 208335[19:SpL:206403.0,194014.1] || subclass(domain_relation,flip(intersection(complement(u),power_class(v))))* subclass(domain_relation,union(u,complement(power_class(v)))) -> . % 300.04/300.42 208336[19:SpL:206403.0,194013.1] || subclass(domain_relation,rotate(intersection(complement(u),power_class(v))))* subclass(domain_relation,union(u,complement(power_class(v)))) -> . % 300.04/300.42 208339[19:SpL:206403.0,196068.0] || equal(union(u,complement(power_class(v))),domain_relation) equal(rotate(intersection(complement(u),power_class(v))),rest_relation)** -> . % 300.04/300.42 208340[19:SpL:206403.0,195719.1] || equal(flip(intersection(complement(u),power_class(v))),domain_relation)** equal(union(u,complement(power_class(v))),domain_relation) -> . % 300.04/300.42 208341[19:SpL:206403.0,195630.1] || equal(rotate(intersection(complement(u),power_class(v))),domain_relation)** equal(union(u,complement(power_class(v))),domain_relation) -> . % 300.04/300.42 208353[22:SpL:206403.0,178289.1] || equal(intersection(complement(u),power_class(v)),singleton(ordinal_numbers))** equal(union(u,complement(power_class(v))),omega) -> . % 300.04/300.42 208358[22:SpL:206403.0,180881.1] || equal(intersection(complement(u),power_class(v)),omega)** equal(union(u,complement(power_class(v))),singleton(ordinal_numbers)) -> . % 300.04/300.42 208363[19:SpL:206403.0,186994.0] || subclass(singleton(ordinal_numbers),union(u,complement(power_class(v))))* member(ordinal_numbers,intersection(complement(u),power_class(v))) -> . % 300.04/300.42 208364[20:SpL:206403.0,186995.1] || subclass(universal_class,intersection(complement(u),power_class(v))) subclass(symmetrization_of(ordinal_numbers),union(u,complement(power_class(v))))* -> . % 300.04/300.42 208515[0:SpR:206410.0,135266.0] || -> subclass(complement(union(intersection(power_class(u),complement(v)),w)),intersection(union(complement(power_class(u)),v),complement(w)))*. % 300.04/300.42 208564[0:SpR:206410.0,135266.0] || -> subclass(complement(union(u,intersection(power_class(v),complement(w)))),intersection(complement(u),union(complement(power_class(v)),w)))*. % 300.04/300.42 208591[19:SpR:167200.0,206410.0] || -> equal(union(complement(power_class(u)),image(element_relation,symmetrization_of(ordinal_numbers))),complement(intersection(power_class(u),power_class(complement(inverse(ordinal_numbers))))))**. % 300.04/300.42 208592[19:SpR:180125.0,206410.0] || -> equal(union(complement(power_class(u)),image(element_relation,singleton(ordinal_numbers))),complement(intersection(power_class(u),power_class(complement(singleton(ordinal_numbers))))))**. % 300.04/300.42 208624[0:SpL:206410.0,195669.1] || equal(rotate(intersection(power_class(u),complement(v))),rest_relation) subclass(universal_class,union(complement(power_class(u)),v))* -> . % 300.04/300.42 208625[0:SpL:206410.0,195635.1] || equal(flip(intersection(power_class(u),complement(v))),rest_relation) subclass(universal_class,union(complement(power_class(u)),v))* -> . % 300.04/300.42 208626[19:SpL:206410.0,185733.1] || equal(rotate(intersection(power_class(u),complement(v))),domain_relation) subclass(universal_class,union(complement(power_class(u)),v))* -> . % 300.04/300.42 208627[19:SpL:206410.0,185656.1] || equal(flip(intersection(power_class(u),complement(v))),domain_relation) subclass(universal_class,union(complement(power_class(u)),v))* -> . % 300.04/300.42 208636[0:SpL:206410.0,9734.0] || subclass(universal_class,complement(union(complement(power_class(u)),v))) -> member(singleton(w),intersection(power_class(u),complement(v)))*. % 300.04/300.42 208637[19:SpL:206410.0,182427.0] || equal(complement(union(complement(power_class(u)),v)),universal_class) well_ordering(universal_class,intersection(power_class(u),complement(v)))* -> . % 300.04/300.42 208642[19:SpL:206410.0,169222.0] || equal(complement(union(complement(power_class(u)),v)),singleton(ordinal_numbers)) -> member(ordinal_numbers,intersection(power_class(u),complement(v)))*. % 300.04/300.42 208644[19:SpL:206410.0,195678.1] || equal(rotate(intersection(power_class(u),complement(v))),rest_relation) subclass(domain_relation,union(complement(power_class(u)),v))* -> . % 300.04/300.42 208645[19:SpL:206410.0,194014.1] || subclass(domain_relation,flip(intersection(power_class(u),complement(v))))* subclass(domain_relation,union(complement(power_class(u)),v)) -> . % 300.04/300.42 208646[19:SpL:206410.0,194013.1] || subclass(domain_relation,rotate(intersection(power_class(u),complement(v))))* subclass(domain_relation,union(complement(power_class(u)),v)) -> . % 300.04/300.42 208649[19:SpL:206410.0,196068.0] || equal(union(complement(power_class(u)),v),domain_relation) equal(rotate(intersection(power_class(u),complement(v))),rest_relation)** -> . % 300.04/300.42 208650[19:SpL:206410.0,195719.1] || equal(flip(intersection(power_class(u),complement(v))),domain_relation)** equal(union(complement(power_class(u)),v),domain_relation) -> . % 300.04/300.42 208651[19:SpL:206410.0,195630.1] || equal(rotate(intersection(power_class(u),complement(v))),domain_relation)** equal(union(complement(power_class(u)),v),domain_relation) -> . % 300.04/300.42 208663[22:SpL:206410.0,178289.1] || equal(intersection(power_class(u),complement(v)),singleton(ordinal_numbers))** equal(union(complement(power_class(u)),v),omega) -> . % 300.04/300.42 208668[22:SpL:206410.0,180881.1] || equal(intersection(power_class(u),complement(v)),omega)** equal(union(complement(power_class(u)),v),singleton(ordinal_numbers)) -> . % 300.04/300.42 208673[19:SpL:206410.0,186994.0] || subclass(singleton(ordinal_numbers),union(complement(power_class(u)),v))* member(ordinal_numbers,intersection(power_class(u),complement(v))) -> . % 300.04/300.42 208674[20:SpL:206410.0,186995.1] || subclass(universal_class,intersection(power_class(u),complement(v))) subclass(symmetrization_of(ordinal_numbers),union(complement(power_class(u)),v))* -> . % 300.04/300.42 208776[19:Res:205520.1,177417.0] || equal(complement(u),ordinal_numbers) well_ordering(omega,u)* -> equal(integer_of(ordered_pair(omega,least(omega,universal_class))),ordinal_numbers)**. % 300.04/300.42 209073[19:SpR:205892.1,167458.0] || equal(intersection(complement(singleton(ordinal_numbers)),complement(image(successor_relation,ordinal_numbers))),ordinal_numbers)** -> equal(complement(image(element_relation,kind_1_ordinals)),ordinal_numbers). % 300.04/300.42 209124[19:Res:176345.1,206404.0] || subclass(domain_relation,image(element_relation,power_class(u))) member(singleton(singleton(singleton(ordinal_numbers))),power_class(complement(power_class(u))))* -> . % 300.04/300.42 209125[19:Res:182463.1,206404.0] || equal(image(element_relation,power_class(u)),singleton(singleton(ordinal_numbers))) member(singleton(ordinal_numbers),power_class(complement(power_class(u))))* -> . % 300.04/300.42 209159[20:Res:181635.1,206404.0] || subclass(symmetrization_of(ordinal_numbers),image(element_relation,power_class(u))) member(regular(symmetrization_of(ordinal_numbers)),power_class(complement(power_class(u))))* -> . % 300.04/300.42 209160[20:Res:175570.1,206404.0] || subclass(inverse(ordinal_numbers),image(element_relation,power_class(u))) member(regular(symmetrization_of(ordinal_numbers)),power_class(complement(power_class(u))))* -> . % 300.04/300.42 209826[19:Rew:167191.0,209779.1] || member(u,universal_class) subclass(rest_relation,symmetrization_of(ordinal_numbers)) -> subclass(singleton(ordered_pair(u,rest_of(u))),symmetrization_of(ordinal_numbers))*. % 300.04/300.42 209827[19:Rew:180103.0,209780.1] || member(u,universal_class) subclass(rest_relation,singleton(ordinal_numbers)) -> subclass(singleton(ordered_pair(u,rest_of(u))),singleton(ordinal_numbers))*. % 300.04/300.42 209838[19:MRR:209775.1,940.0] || subclass(domain_relation,rest_relation) subclass(rest_relation,complement(u)) member(ordered_pair(ordered_pair(v,w),ordinal_numbers),u)* -> . % 300.04/300.42 209839[19:MRR:209774.1,940.0] || subclass(rest_relation,domain_relation) subclass(rest_relation,complement(u)) member(ordered_pair(ordered_pair(v,w),ordinal_numbers),u)* -> . % 300.04/300.42 209840[19:MRR:209773.1,12.0] || subclass(domain_relation,rest_relation) subclass(rest_relation,complement(u)) member(ordered_pair(unordered_pair(v,w),ordinal_numbers),u)* -> . % 300.04/300.42 209841[19:MRR:209772.1,12.0] || subclass(rest_relation,domain_relation) subclass(rest_relation,complement(u)) member(ordered_pair(unordered_pair(v,w),ordinal_numbers),u)* -> . % 300.04/300.42 209842[20:MRR:209769.1,175569.0] || subclass(domain_relation,rest_relation) subclass(rest_relation,complement(u)) member(ordered_pair(regular(symmetrization_of(ordinal_numbers)),ordinal_numbers),u)* -> . % 300.04/300.42 209843[20:MRR:209768.1,175569.0] || subclass(rest_relation,domain_relation) subclass(rest_relation,complement(u)) member(ordered_pair(regular(symmetrization_of(ordinal_numbers)),ordinal_numbers),u)* -> . % 300.04/300.42 209849[0:MRR:209848.0,149603.1] || equal(compose(u,v),rest_of(v))** member(v,universal_class) subclass(rest_relation,complement(compose_class(u)))* -> . % 300.04/300.42 209890[19:Res:7968.2,205934.1] || member(u,cross_product(v,w))* member(u,x)* equal(restrict(x,v,w),ordinal_numbers)** -> . % 300.04/300.42 210002[19:Res:59.1,205934.1] || member(ordered_pair(u,v),compose(w,x))* equal(image(w,image(x,singleton(u))),ordinal_numbers) -> . % 300.04/300.42 210178[0:SpL:27168.2,897.0] || member(u,universal_class) subclass(rest_relation,rest_of(v))* member(w,rest_of(u))* -> member(w,v)*. % 300.04/300.42 210215[0:SpR:27837.0,16276.0] || -> subclass(symmetric_difference(symmetrization_of(u),union(complement(u),complement(inverse(u)))),complement(symmetric_difference(complement(u),complement(inverse(u)))))*. % 300.04/300.42 210279[19:SpL:27837.0,168377.0] || subclass(omega,symmetric_difference(complement(u),complement(inverse(u))))* -> equal(integer_of(v),ordinal_numbers) member(v,symmetrization_of(u))*. % 300.04/300.42 210293[19:SpL:27837.0,167736.0] || subclass(u,symmetric_difference(complement(v),complement(inverse(v))))* -> equal(u,ordinal_numbers) member(regular(u),symmetrization_of(v)). % 300.04/300.42 211280[0:Res:55.1,15107.0] || member(u,universal_class) subclass(universal_class,v)* subclass(v,w)* -> member(sum_class(sum_class(u)),w)*. % 300.04/300.42 211281[0:Res:57.1,15107.0] || member(u,universal_class) subclass(universal_class,v)* subclass(v,w)* -> member(sum_class(power_class(u)),w)*. % 300.04/300.42 211282[0:Res:15058.1,15107.0] function(u) || subclass(universal_class,v)* subclass(v,w)* -> member(sum_class(apply(u,x)),w)*. % 300.04/300.42 211283[0:Res:36682.1,15107.0] || subclass(universal_class,u)* subclass(u,v)* -> subclass(w,x) member(sum_class(not_subclass_element(w,x)),v)*. % 300.04/300.42 211290[0:Res:149603.1,15107.0] || member(u,universal_class) subclass(universal_class,v)* subclass(v,w)* -> member(sum_class(rest_of(u)),w)*. % 300.04/300.42 211456[25:Rew:193223.1,211431.2] function(u) || subclass(apply(v,u),image(v,ordinal_numbers))* -> section(element_relation,image(v,ordinal_numbers),universal_class). % 300.04/300.42 211611[19:Res:203424.1,82994.1] || subclass(complement(complement(compose(element_relation,universal_class))),ordinal_numbers)* member(singleton(u),element_relation)* well_ordering(v,w)* -> . % 300.04/300.42 211612[19:Res:203424.1,82995.1] || subclass(complement(complement(compose(element_relation,universal_class))),ordinal_numbers)* member(singleton(u),element_relation)* -> member(singleton(u),v)*. % 300.04/300.42 211613[26:Res:203424.1,202277.1] || subclass(complement(complement(compose(complement(element_relation),inverse(element_relation)))),ordinal_numbers)* member(singleton(u),cross_product(universal_class,universal_class))* -> . % 300.04/300.42 211630[19:Res:203424.1,16083.0] || subclass(complement(symmetric_difference(u,cross_product(v,w))),ordinal_numbers) -> member(singleton(x),complement(restrict(u,v,w)))*. % 300.04/300.42 211635[19:Res:203424.1,16086.0] || subclass(complement(symmetric_difference(cross_product(u,v),w)),ordinal_numbers) -> member(singleton(x),complement(restrict(w,u,v)))*. % 300.04/300.42 211637[19:Res:203424.1,18.0] || subclass(complement(cross_product(u,v)),ordinal_numbers)* -> equal(ordered_pair(first(singleton(w)),second(singleton(w))),singleton(w))**. % 300.04/300.42 211899[19:SpL:479.0,211666.0] || subclass(power_class(intersection(complement(u),complement(v))),ordinal_numbers)* well_ordering(universal_class,image(element_relation,union(u,v))) -> . % 300.04/300.42 212442[19:Res:205991.1,16083.0] || equal(complement(symmetric_difference(u,cross_product(v,w))),ordinal_numbers) -> member(singleton(x),complement(restrict(u,v,w)))*. % 300.04/300.42 212447[19:Res:205991.1,16086.0] || equal(complement(symmetric_difference(cross_product(u,v),w)),ordinal_numbers) -> member(singleton(x),complement(restrict(w,u,v)))*. % 300.04/300.42 212669[19:SpR:479.0,198248.0] || -> equal(intersection(power_class(intersection(complement(u),complement(v))),restrict(image(element_relation,union(u,v)),w,x)),ordinal_numbers)**. % 300.04/300.42 212771[0:Res:55.1,15073.0] || member(u,universal_class) subclass(universal_class,v)* subclass(v,w)* -> member(power_class(sum_class(u)),w)*. % 300.04/300.42 212772[0:Res:57.1,15073.0] || member(u,universal_class) subclass(universal_class,v)* subclass(v,w)* -> member(power_class(power_class(u)),w)*. % 300.04/300.42 212773[0:Res:15058.1,15073.0] function(u) || subclass(universal_class,v)* subclass(v,w)* -> member(power_class(apply(u,x)),w)*. % 300.04/300.42 212774[0:Res:36682.1,15073.0] || subclass(universal_class,u)* subclass(u,v)* -> subclass(w,x) member(power_class(not_subclass_element(w,x)),v)*. % 300.04/300.42 212781[0:Res:149603.1,15073.0] || member(u,universal_class) subclass(universal_class,v)* subclass(v,w)* -> member(power_class(rest_of(u)),w)*. % 300.04/300.42 213083[20:Res:213073.0,8.0] || subclass(symmetrization_of(ordinal_numbers),singleton(not_subclass_element(symmetrization_of(ordinal_numbers),ordinal_numbers)))* -> equal(singleton(not_subclass_element(symmetrization_of(ordinal_numbers),ordinal_numbers)),symmetrization_of(ordinal_numbers)). % 300.04/300.42 213228[25:Rew:193223.1,213220.1] function(u) || -> equal(cross_product(v,ordinal_numbers),ordinal_numbers) equal(segment(regular(cross_product(v,ordinal_numbers)),v,u),ordinal_numbers)**. % 300.04/300.42 213264[25:Rew:193223.1,213253.1] function(u) || equal(apply(v,u),image(v,ordinal_numbers))** well_ordering(element_relation,image(v,ordinal_numbers))* -> . % 300.04/300.42 213289[19:SpR:209197.0,17083.0] || -> subclass(symmetric_difference(image(element_relation,singleton(ordinal_numbers)),complement(singleton(power_class(complement(singleton(ordinal_numbers)))))),successor(power_class(complement(singleton(ordinal_numbers)))))*. % 300.04/300.42 213292[19:SpR:209197.0,17082.0] || -> subclass(symmetric_difference(image(element_relation,singleton(ordinal_numbers)),complement(inverse(power_class(complement(singleton(ordinal_numbers)))))),symmetrization_of(power_class(complement(singleton(ordinal_numbers)))))*. % 300.04/300.42 213324[19:SpR:209197.0,206403.0] || -> equal(union(power_class(complement(singleton(ordinal_numbers))),complement(power_class(u))),complement(intersection(image(element_relation,singleton(ordinal_numbers)),power_class(u))))**. % 300.04/300.42 213339[19:SpR:209197.0,206410.0] || -> equal(union(complement(power_class(u)),power_class(complement(singleton(ordinal_numbers)))),complement(intersection(power_class(u),image(element_relation,singleton(ordinal_numbers)))))**. % 300.04/300.42 213531[19:SpR:209198.0,17083.0] || -> subclass(symmetric_difference(image(element_relation,symmetrization_of(ordinal_numbers)),complement(singleton(power_class(complement(inverse(ordinal_numbers)))))),successor(power_class(complement(inverse(ordinal_numbers)))))*. % 300.04/300.42 213534[19:SpR:209198.0,17082.0] || -> subclass(symmetric_difference(image(element_relation,symmetrization_of(ordinal_numbers)),complement(inverse(power_class(complement(inverse(ordinal_numbers)))))),symmetrization_of(power_class(complement(inverse(ordinal_numbers)))))*. % 300.04/300.42 213566[19:SpR:209198.0,206403.0] || -> equal(union(power_class(complement(inverse(ordinal_numbers))),complement(power_class(u))),complement(intersection(image(element_relation,symmetrization_of(ordinal_numbers)),power_class(u))))**. % 300.04/300.42 213581[19:SpR:209198.0,206410.0] || -> equal(union(complement(power_class(u)),power_class(complement(inverse(ordinal_numbers)))),complement(intersection(power_class(u),image(element_relation,symmetrization_of(ordinal_numbers)))))**. % 300.04/300.42 213926[19:Rew:142500.0,213805.0,167055.0,213805.0] || -> equal(symmetric_difference(singleton(ordinal_numbers),intersection(complement(singleton(ordinal_numbers)),u)),union(singleton(ordinal_numbers),intersection(complement(singleton(ordinal_numbers)),u)))**. % 300.04/300.42 214053[19:Rew:142500.0,213938.0,167055.0,213938.0] || -> equal(symmetric_difference(symmetrization_of(ordinal_numbers),intersection(complement(inverse(ordinal_numbers)),u)),union(symmetrization_of(ordinal_numbers),intersection(complement(inverse(ordinal_numbers)),u)))**. % 300.04/300.42 214181[19:Rew:142500.0,214065.0,167055.0,214065.0] || -> equal(symmetric_difference(singleton(ordinal_numbers),intersection(u,complement(singleton(ordinal_numbers)))),union(singleton(ordinal_numbers),intersection(u,complement(singleton(ordinal_numbers)))))**. % 300.04/300.42 214303[19:Rew:142500.0,214193.0,167055.0,214193.0] || -> equal(symmetric_difference(symmetrization_of(ordinal_numbers),intersection(u,complement(inverse(ordinal_numbers)))),union(symmetrization_of(ordinal_numbers),intersection(u,complement(inverse(ordinal_numbers)))))**. % 300.04/300.42 214315[19:SpL:946.0,204401.0] || subclass(universal_class,singleton(singleton(singleton(u))))* -> equal(unordered_pair(v,w),omega)** equal(unordered_pair(v,w),ordinal_numbers). % 300.04/300.42 214325[19:Res:205520.1,204401.0] || equal(complement(ordered_pair(u,v)),ordinal_numbers)** -> equal(unordered_pair(w,x),omega)** equal(unordered_pair(w,x),ordinal_numbers). % 300.04/300.42 214576[0:Res:2479.1,207852.0] || subclass(universal_class,intersection(power_class(u),complement(v))) member(singleton(w),union(complement(power_class(u)),v))* -> . % 300.04/300.42 214620[19:Res:169181.1,207852.0] || equal(intersection(power_class(u),complement(v)),singleton(ordinal_numbers)) member(ordinal_numbers,union(complement(power_class(u)),v))* -> . % 300.04/300.42 214628[19:Res:196731.1,207852.0] || subclass(universal_class,intersection(power_class(u),complement(v))) member(regular(element_relation),union(complement(power_class(u)),v))* -> . % 300.04/300.42 214739[0:Res:2479.1,207871.0] || subclass(universal_class,intersection(complement(u),power_class(v))) member(singleton(w),union(u,complement(power_class(v))))* -> . % 300.04/300.42 214783[19:Res:169181.1,207871.0] || equal(intersection(complement(u),power_class(v)),singleton(ordinal_numbers)) member(ordinal_numbers,union(u,complement(power_class(v))))* -> . % 300.04/300.42 214791[19:Res:196731.1,207871.0] || subclass(universal_class,intersection(complement(u),power_class(v))) member(regular(element_relation),union(u,complement(power_class(v))))* -> . % 300.04/300.42 214857[19:SpL:167022.0,27258.2] || member(u,complement(image(successor_relation,ordinal_numbers)))* member(u,complement(singleton(ordinal_numbers))) member(u,kind_1_ordinals) -> . % 300.04/300.42 214870[19:Res:205414.1,27258.2] || equal(complement(union(u,v)),ordinal_numbers)** member(omega,complement(v)) member(omega,complement(u)) -> . % 300.04/300.42 214915[19:Res:205391.1,27258.2] || equal(complement(union(u,v)),ordinal_numbers)** member(ordinal_numbers,complement(v)) member(ordinal_numbers,complement(u)) -> . % 300.04/300.42 214918[19:Res:169181.1,27258.2] || equal(union(u,v),singleton(ordinal_numbers))** member(ordinal_numbers,complement(v))* member(ordinal_numbers,complement(u))* -> . % 300.04/300.42 214988[8:SpR:160282.0,2480.1] || subclass(universal_class,u) -> equal(regular(ordered_pair(v,w)),singleton(v)) member(regular(ordered_pair(v,w)),u)*. % 300.04/300.42 215001[8:SpL:160282.0,48621.0] || equal(complement(unordered_pair(regular(ordered_pair(u,v)),w)),universal_class)** -> equal(regular(ordered_pair(u,v)),singleton(u)). % 300.04/300.42 215002[8:SpL:160282.0,48402.0] || subclass(universal_class,complement(unordered_pair(regular(ordered_pair(u,v)),w)))* -> equal(regular(ordered_pair(u,v)),singleton(u)). % 300.04/300.42 215044[8:SpL:160282.0,48591.0] || equal(complement(unordered_pair(u,regular(ordered_pair(v,w)))),universal_class)** -> equal(regular(ordered_pair(v,w)),singleton(v)). % 300.04/300.42 215045[8:SpL:160282.0,48401.0] || subclass(universal_class,complement(unordered_pair(u,regular(ordered_pair(v,w)))))* -> equal(regular(ordered_pair(v,w)),singleton(v)). % 300.04/300.42 215112[19:Res:168245.3,4178.0] || well_ordering(u,universal_class) subclass(v,singleton(w))* -> equal(v,ordinal_numbers) equal(least(u,v),w)*. % 300.04/300.42 215158[19:MRR:215145.1,5.0] || well_ordering(u,universal_class) subclass(domain_relation,rest_relation) -> equal(v,ordinal_numbers) equal(rest_of(least(u,v)),ordinal_numbers)**. % 300.04/300.42 215159[19:MRR:215144.1,5.0] || well_ordering(u,universal_class) subclass(rest_relation,domain_relation) -> equal(v,ordinal_numbers) equal(rest_of(least(u,v)),ordinal_numbers)**. % 300.04/300.42 215206[19:Res:214528.1,126.0] || subclass(kind_1_ordinals,u) subclass(u,v)* well_ordering(w,v)* -> member(least(w,u),u)*. % 300.04/300.42 215280[19:Res:144532.1,168249.0] || equal(regular(u),universal_class) member(singleton(v),u)* well_ordering(w,x)* -> equal(u,ordinal_numbers). % 300.04/300.42 215282[19:Res:2479.1,168249.0] || subclass(universal_class,regular(u)) member(singleton(v),u)* well_ordering(w,x)* -> equal(u,ordinal_numbers). % 300.04/300.42 215283[19:Res:205414.1,168249.0] || equal(complement(regular(u)),ordinal_numbers)** member(omega,u) well_ordering(v,w)* -> equal(u,ordinal_numbers). % 300.04/300.42 215290[19:Res:167139.1,168249.0] || member(regular(regular(u)),u)* well_ordering(v,w)* -> equal(regular(u),ordinal_numbers) equal(u,ordinal_numbers). % 300.04/300.42 215327[19:Res:205391.1,168249.0] || equal(complement(regular(u)),ordinal_numbers)** member(ordinal_numbers,u) well_ordering(v,w)* -> equal(u,ordinal_numbers). % 300.04/300.42 215330[19:Res:169181.1,168249.0] || equal(regular(u),singleton(ordinal_numbers)) member(ordinal_numbers,u)* well_ordering(v,w)* -> equal(u,ordinal_numbers). % 300.04/300.42 215338[19:Res:196731.1,168249.0] || subclass(universal_class,regular(u)) member(regular(element_relation),u)* well_ordering(v,w)* -> equal(u,ordinal_numbers). % 300.04/300.42 216062[0:SpL:27.0,16107.1] || member(u,symmetric_difference(complement(v),complement(w)))* subclass(union(v,w),x)* -> member(u,x)*. % 300.04/300.42 216071[0:Res:63.1,16107.1] function(complement(intersection(u,v))) || member(w,symmetric_difference(u,v))* -> member(w,cross_product(universal_class,universal_class)). % 300.04/300.42 216098[19:Rew:212730.0,216097.0] || member(u,union(complement(v),restrict(v,w,x)))* subclass(universal_class,y) -> member(u,y)*. % 300.04/300.42 216104[19:Rew:202956.1,216103.1] || subclass(u,ordinal_numbers) member(v,union(u,w))* subclass(universal_class,x) -> member(v,x)*. % 300.04/300.42 216105[19:Rew:167055.0,216014.1,167130.1,216014.0] || member(u,union(v,regular(v)))* subclass(universal_class,w) -> equal(v,ordinal_numbers) member(u,w)*. % 300.04/300.42 216107[19:Rew:166596.1,216106.0] || member(u,union(singleton(v),w))* subclass(universal_class,x) -> member(v,w) member(u,x)*. % 300.04/300.42 216120[19:Rew:202717.1,216119.1] || subclass(u,ordinal_numbers) member(v,union(w,u))* subclass(universal_class,x) -> member(v,x)*. % 300.04/300.42 216122[19:Rew:166761.1,216121.0] || member(u,union(v,singleton(w)))* subclass(universal_class,x) -> member(w,v) member(u,x)*. % 300.04/300.42 216240[19:Res:205520.1,6441.0] || equal(complement(unordered_pair(u,v)),ordinal_numbers)** -> equal(unordered_pair(w,x),v)* equal(unordered_pair(w,x),u)*. % 300.04/300.42 216787[19:Res:38094.1,203420.1] || member(omega,union(u,v)) subclass(intersection(u,v),ordinal_numbers) -> member(omega,symmetric_difference(u,v))*. % 300.04/300.42 216812[19:Res:38094.1,203417.1] || member(ordinal_numbers,union(u,v)) subclass(intersection(u,v),ordinal_numbers) -> member(ordinal_numbers,symmetric_difference(u,v))*. % 300.04/300.42 216975[19:Obv:216944.2] || member(u,v) subclass(omega,v) -> equal(integer_of(w),ordinal_numbers) subclass(unordered_pair(u,w),v)*. % 300.04/300.42 217074[19:Obv:217042.2] || equal(u,v) subclass(omega,w) -> equal(integer_of(v),ordinal_numbers) subclass(unordered_pair(v,u),w)*. % 300.04/300.42 217084[0:Obv:217057.2] || equal(u,v) member(v,w) -> subclass(unordered_pair(v,u),intersection(w,unordered_pair(v,u)))*. % 300.04/300.42 217118[19:SpL:479.0,215196.0] || subclass(kind_1_ordinals,power_class(intersection(complement(u),complement(v))))* member(ordinal_numbers,image(element_relation,union(u,v))) -> . % 300.04/300.42 217216[19:Obv:217184.2] || member(u,v) subclass(omega,v) -> equal(integer_of(w),ordinal_numbers) subclass(unordered_pair(w,u),v)*. % 300.04/300.42 217345[0:Res:16231.2,4178.0] || subclass(u,singleton(v))* -> subclass(intersection(u,w),x) equal(not_subclass_element(intersection(u,w),x),v)*. % 300.04/300.42 218039[19:Res:217853.0,167739.0] || -> equal(complement(complement(intersection(u,singleton(v)))),ordinal_numbers) equal(regular(complement(complement(intersection(u,singleton(v))))),v)**. % 300.04/300.42 218447[19:Res:218408.0,167276.0] || well_ordering(u,complement(image(successor_relation,ordinal_numbers))) -> equal(segment(u,complement(kind_1_ordinals),least(u,complement(kind_1_ordinals))),ordinal_numbers)**. % 300.04/300.42 218464[19:Res:218395.0,167728.0] || subclass(complement(singleton(u)),v) -> equal(complement(successor(u)),ordinal_numbers) member(regular(complement(successor(u))),v)*. % 300.04/300.42 218483[19:Res:218396.0,167728.0] || subclass(complement(inverse(u)),v) -> equal(complement(symmetrization_of(u)),ordinal_numbers) member(regular(complement(symmetrization_of(u))),v)*. % 300.04/300.42 218582[0:Res:16358.2,4178.0] || subclass(u,singleton(v))* -> subclass(intersection(w,u),x) equal(not_subclass_element(intersection(w,u),x),v)*. % 300.04/300.42 219726[19:Res:218920.0,167739.0] || -> equal(intersection(complement(complement(singleton(u))),v),ordinal_numbers) equal(regular(intersection(complement(complement(singleton(u))),v)),u)**. % 300.04/300.42 219733[0:Res:218920.0,8596.1] single_valued_class(intersection(complement(complement(cross_product(universal_class,universal_class))),u)) || -> function(intersection(complement(complement(cross_product(universal_class,universal_class))),u))*. % 300.04/300.42 219976[19:Res:219703.0,167739.0] || -> equal(complement(complement(complement(complement(singleton(u))))),ordinal_numbers) equal(regular(complement(complement(complement(complement(singleton(u)))))),u)**. % 300.04/300.42 219981[0:Res:219703.0,8596.1] single_valued_class(complement(complement(complement(complement(cross_product(universal_class,universal_class)))))) || -> function(complement(complement(complement(complement(cross_product(universal_class,universal_class))))))*. % 300.04/300.42 220076[0:Res:63.1,16462.0] function(u) || subclass(cross_product(universal_class,universal_class),v) -> subclass(u,w) member(not_subclass_element(u,w),v)*. % 300.04/300.42 220105[19:Res:218408.0,16462.0] || subclass(complement(image(successor_relation,ordinal_numbers)),u) -> subclass(complement(kind_1_ordinals),v) member(not_subclass_element(complement(kind_1_ordinals),v),u)*. % 300.04/300.42 220212[19:Res:218971.0,167739.0] || -> equal(complement(complement(intersection(singleton(u),v))),ordinal_numbers) equal(regular(complement(complement(intersection(singleton(u),v)))),u)**. % 300.04/300.42 220354[19:Res:219700.0,167739.0] || -> equal(intersection(u,complement(complement(singleton(v)))),ordinal_numbers) equal(regular(intersection(u,complement(complement(singleton(v))))),v)**. % 300.04/300.42 220361[0:Res:219700.0,8596.1] single_valued_class(intersection(u,complement(complement(cross_product(universal_class,universal_class))))) || -> function(intersection(u,complement(complement(cross_product(universal_class,universal_class)))))*. % 300.04/300.42 220481[19:Res:220439.0,167133.0] || well_ordering(u,complement(singleton(ordinal_numbers))) -> equal(complement(kind_1_ordinals),ordinal_numbers) member(least(u,complement(kind_1_ordinals)),complement(kind_1_ordinals))*. % 300.04/300.42 220511[0:Res:220426.0,16462.0] || subclass(complement(u),v) -> subclass(complement(successor(u)),w) member(not_subclass_element(complement(successor(u)),w),v)*. % 300.04/300.42 220514[19:Res:220426.0,167276.0] || well_ordering(u,complement(v)) -> equal(segment(u,complement(successor(v)),least(u,complement(successor(v)))),ordinal_numbers)**. % 300.04/300.42 220545[0:Res:220427.0,16462.0] || subclass(complement(u),v) -> subclass(complement(symmetrization_of(u)),w) member(not_subclass_element(complement(symmetrization_of(u)),w),v)*. % 300.04/300.42 220548[19:Res:220427.0,167276.0] || well_ordering(u,complement(v)) -> equal(segment(u,complement(symmetrization_of(v)),least(u,complement(symmetrization_of(v)))),ordinal_numbers)**. % 300.04/300.42 220772[8:Res:125327.1,124906.1] || section(cross_product(u,v),v,w)* subclass(v,u) -> section(cross_product(w,v),v,u)*. % 300.04/300.42 220839[19:Res:220496.0,8.0] || subclass(symmetrization_of(ordinal_numbers),complement(successor(complement(inverse(ordinal_numbers)))))* -> equal(complement(successor(complement(inverse(ordinal_numbers)))),symmetrization_of(ordinal_numbers)). % 300.04/300.42 220923[19:Res:220531.0,8.0] || subclass(symmetrization_of(ordinal_numbers),complement(symmetrization_of(complement(inverse(ordinal_numbers)))))* -> equal(complement(symmetrization_of(complement(inverse(ordinal_numbers)))),symmetrization_of(ordinal_numbers)). % 300.04/300.42 220978[27:Rew:220929.0,185013.2] inductive(symmetric_difference(singleton(ordinal_numbers),image(successor_relation,ordinal_numbers))) || well_ordering(u,universal_class) -> member(least(u,ordinal_numbers),kind_1_ordinals)*. % 300.04/300.42 221057[27:Rew:220929.0,220977.1] inductive(symmetric_difference(singleton(ordinal_numbers),image(successor_relation,ordinal_numbers))) || well_ordering(u,ordinal_numbers) -> member(least(u,ordinal_numbers),kind_1_ordinals)*. % 300.04/300.42 221252[19:Res:219075.0,8.0] || subclass(inverse(ordinal_numbers),restrict(symmetrization_of(ordinal_numbers),u,v))* -> equal(restrict(symmetrization_of(ordinal_numbers),u,v),inverse(ordinal_numbers)). % 300.04/300.42 221270[27:Res:12015.1,221036.1] || equal(complement(complement(complement(intersection(singleton(ordinal_numbers),image(successor_relation,ordinal_numbers))))),universal_class)** member(singleton(u),kind_1_ordinals)* -> . % 300.04/300.42 221284[27:Res:176345.1,221036.1] || subclass(domain_relation,complement(intersection(singleton(ordinal_numbers),image(successor_relation,ordinal_numbers))))* member(singleton(singleton(singleton(ordinal_numbers))),kind_1_ordinals) -> . % 300.04/300.42 221285[27:Res:182463.1,221036.1] || equal(complement(intersection(singleton(ordinal_numbers),image(successor_relation,ordinal_numbers))),singleton(singleton(ordinal_numbers)))** member(singleton(ordinal_numbers),kind_1_ordinals) -> . % 300.04/300.42 221335[27:Res:181635.1,221036.1] || subclass(symmetrization_of(ordinal_numbers),complement(intersection(singleton(ordinal_numbers),image(successor_relation,ordinal_numbers))))* member(regular(symmetrization_of(ordinal_numbers)),kind_1_ordinals) -> . % 300.04/300.42 221336[27:Res:175570.1,221036.1] || subclass(inverse(ordinal_numbers),complement(intersection(singleton(ordinal_numbers),image(successor_relation,ordinal_numbers))))* member(regular(symmetrization_of(ordinal_numbers)),kind_1_ordinals) -> . % 300.04/300.42 221557[19:Res:219766.1,16462.0] || equal(complement(u),ordinal_numbers) subclass(u,v)* -> subclass(w,x) member(not_subclass_element(w,x),v)*. % 300.04/300.42 221560[19:Res:219766.1,167276.0] || equal(complement(u),ordinal_numbers) well_ordering(v,u)* -> equal(segment(v,w,least(v,w)),ordinal_numbers)**. % 300.04/300.42 221561[19:Res:219766.1,167133.0] || equal(complement(u),ordinal_numbers) well_ordering(v,u)* -> equal(w,ordinal_numbers) member(least(v,w),w)*. % 300.04/300.42 221562[19:Res:219766.1,9856.0] || equal(complement(u),ordinal_numbers) well_ordering(v,u)* -> subclass(w,x)* member(least(v,w),w)*. % 300.04/300.42 221563[19:Res:219766.1,9859.1] inductive(u) || equal(complement(v),ordinal_numbers) well_ordering(w,v)* -> member(least(w,u),u)*. % 300.04/300.42 221574[19:Res:219766.1,167724.0] || equal(complement(restrict(u,v,w)),ordinal_numbers)** -> equal(x,ordinal_numbers) member(regular(x),cross_product(v,w))*. % 300.04/300.42 221745[19:Res:219766.1,176242.1] || equal(complement(restrict(u,v,w)),ordinal_numbers)** member(x,universal_class) -> member(ordered_pair(x,ordinal_numbers),u)*. % 300.04/300.42 221835[19:Res:219766.1,27146.1] || equal(complement(intersection(u,v)),ordinal_numbers)** member(w,universal_class) -> member(ordered_pair(w,rest_of(w)),u)*. % 300.04/300.42 221836[19:Res:219766.1,27147.1] || equal(complement(intersection(u,v)),ordinal_numbers)** member(w,universal_class) -> member(ordered_pair(w,rest_of(w)),v)*. % 300.04/300.42 221967[19:Res:219766.1,168434.0] || equal(complement(restrict(u,v,w)),ordinal_numbers)** -> equal(integer_of(x),ordinal_numbers) member(x,cross_product(v,w))*. % 300.04/300.42 221971[19:Res:219766.1,168373.0] || equal(complement(unordered_pair(u,v)),ordinal_numbers)** -> equal(integer_of(w),ordinal_numbers)** equal(w,v)* equal(w,u)*. % 300.04/300.42 222042[19:Res:7.1,177427.0] || equal(u,universal_class) well_ordering(omega,u)* -> equal(integer_of(ordered_pair(singleton(v),least(omega,universal_class))),ordinal_numbers)**. % 300.04/300.42 222255[0:Res:217976.0,8.0] || subclass(u,complement(complement(restrict(u,v,w))))* -> equal(complement(complement(restrict(u,v,w))),u). % 300.04/300.42 222346[0:Res:219698.0,8.0] || subclass(u,restrict(complement(complement(u)),v,w))* -> equal(restrict(complement(complement(u)),v,w),u). % 300.04/300.42 222433[0:Res:217800.0,8.0] || subclass(u,intersection(restrict(u,v,w),x))* -> equal(intersection(restrict(u,v,w),x),u). % 300.04/300.42 222562[0:Res:217848.0,8.0] || subclass(u,restrict(intersection(v,u),w,x))* -> equal(restrict(intersection(v,u),w,x),u). % 300.04/300.42 222675[0:Res:218740.0,8.0] || subclass(u,intersection(v,restrict(u,w,x)))* -> equal(intersection(v,restrict(u,w,x)),u). % 300.04/300.42 222804[0:Res:218966.0,8.0] || subclass(u,restrict(intersection(u,v),w,x))* -> equal(restrict(intersection(u,v),w,x),u). % 300.04/300.42 222906[0:SpR:208291.0,16403.0] || -> subclass(symmetric_difference(image(element_relation,power_class(u)),complement(power_class(v))),complement(intersection(power_class(complement(power_class(u))),power_class(v))))*. % 300.04/300.42 223018[20:Res:222998.0,30589.0] || subclass(rest_relation,successor_relation) -> equal(rest_of(regular(complement(complement(symmetrization_of(ordinal_numbers))))),successor(regular(complement(complement(symmetrization_of(ordinal_numbers))))))**. % 300.04/300.42 223028[25:SoR:223017.0,12322.2] single_valued_class(regular(complement(complement(symmetrization_of(ordinal_numbers))))) || equal(regular(complement(complement(symmetrization_of(ordinal_numbers)))),cross_product(universal_class,universal_class))** -> . % 300.04/300.42 223031[0:SpR:208593.0,16403.0] || -> subclass(symmetric_difference(complement(power_class(u)),image(element_relation,power_class(v))),complement(intersection(power_class(u),power_class(complement(power_class(v))))))*. % 300.04/300.42 223157[19:Res:167223.1,79384.0] || -> equal(singleton(u),ordinal_numbers) equal(ordered_pair(first(ordered_pair(u,omega)),second(ordered_pair(u,omega))),ordered_pair(u,omega))**. % 300.04/300.42 223171[19:Res:167116.0,79384.0] || -> equal(integer_of(u),ordinal_numbers) equal(ordered_pair(first(ordered_pair(u,omega)),second(ordered_pair(u,omega))),ordered_pair(u,omega))**. % 300.04/300.42 223938[22:Res:178902.1,14972.1] || equal(power_class(intersection(complement(u),complement(v))),omega) member(ordinal_numbers,image(element_relation,union(u,v)))* -> . % 300.04/300.42 223981[19:Rew:209193.0,223882.0] || equal(image(element_relation,union(u,v)),ordinal_numbers) member(singleton(w),image(element_relation,union(u,v)))* -> . % 300.04/300.42 223982[19:Rew:209193.0,223883.0] || subclass(image(element_relation,union(u,v)),ordinal_numbers) member(singleton(w),image(element_relation,union(u,v)))* -> . % 300.04/300.42 224044[0:Res:7.1,34759.2] function(u) || equal(singleton(v),universal_class)** member(w,universal_class) -> equal(image(u,w),v)*. % 300.04/300.42 224108[22:SpL:479.0,217231.1] || equal(image(element_relation,union(u,v)),kind_1_ordinals) equal(power_class(intersection(complement(u),complement(v))),omega)** -> . % 300.04/300.42 224237[20:Res:224150.0,8.0] || subclass(inverse(ordinal_numbers),singleton(not_subclass_element(inverse(ordinal_numbers),ordinal_numbers)))* -> equal(singleton(not_subclass_element(inverse(ordinal_numbers),ordinal_numbers)),inverse(ordinal_numbers)). % 300.04/300.42 224251[20:Res:224151.0,8.0] || subclass(inverse(ordinal_numbers),singleton(not_subclass_element(symmetrization_of(ordinal_numbers),ordinal_numbers)))* -> equal(singleton(not_subclass_element(symmetrization_of(ordinal_numbers),ordinal_numbers)),inverse(ordinal_numbers)). % 300.04/300.42 224611[23:Rew:183857.0,224601.1] || member(singleton(singleton(singleton(singleton(singleton(ordinal_numbers))))),composition_function)* -> equal(compose(singleton(singleton(singleton(ordinal_numbers))),ordinal_numbers),universal_class). % 300.04/300.42 224706[19:Res:7.1,167723.1] || equal(singleton(u),v)* member(v,universal_class) -> equal(v,ordinal_numbers) equal(apply(choice,v),u)*. % 300.04/300.42 225110[19:Res:7.1,168497.0] || equal(rest_of(u),omega) -> equal(integer_of(ordered_pair(v,w)),ordinal_numbers)** equal(restrict(u,v,universal_class),w)*. % 300.04/300.42 225187[19:Res:168557.1,11848.0] || subclass(union(u,v),w)* well_ordering(universal_class,w) -> equal(symmetric_difference(complement(u),complement(v)),ordinal_numbers)**. % 300.04/300.42 225311[23:SpR:183857.0,169006.1] || subclass(omega,composition_function) -> equal(integer_of(ordered_pair(u,singleton(singleton(ordinal_numbers)))),ordinal_numbers)** equal(compose(u,ordinal_numbers),universal_class). % 300.04/300.42 225360[19:Res:167224.0,176248.0] || subclass(domain_relation,u)* subclass(u,v)* -> equal(singleton(w),ordinal_numbers) member(ordered_pair(w,ordinal_numbers),v)*. % 300.04/300.42 225361[19:Res:167115.1,176248.0] || subclass(domain_relation,u)* subclass(u,v)* -> equal(integer_of(w),ordinal_numbers) member(ordered_pair(w,ordinal_numbers),v)*. % 300.04/300.42 225374[19:Res:167137.1,176248.0] || subclass(domain_relation,u)* subclass(u,v)* -> equal(w,ordinal_numbers) member(ordered_pair(regular(w),ordinal_numbers),v)*. % 300.04/300.42 225429[20:Res:222998.0,176248.0] || subclass(domain_relation,u)* subclass(u,v)* -> member(ordered_pair(regular(complement(complement(symmetrization_of(ordinal_numbers)))),ordinal_numbers),v)*. % 300.04/300.42 225569[19:Res:176255.2,6476.1] || member(u,universal_class)* subclass(domain_relation,symmetric_difference(v,w)) subclass(universal_class,complement(union(v,w)))* -> . % 300.04/300.42 225585[19:Obv:225570.0] || subclass(domain_relation,symmetric_difference(u,v)) member(w,universal_class)* subclass(domain_relation,complement(union(u,v)))* -> . % 300.04/300.42 225650[19:SpR:479.0,220544.1] || equal(symmetrization_of(image(element_relation,union(u,v))),ordinal_numbers) -> subclass(universal_class,power_class(intersection(complement(u),complement(v))))*. % 300.04/300.42 225977[19:SpL:207699.0,204472.0] || equal(intersection(union(complement(power_class(u)),v),complement(w)),union(intersection(power_class(u),complement(v)),w))** -> . % 300.04/300.42 226018[19:Rew:167055.0,225890.1] || subclass(union(complement(power_class(u)),v),ordinal_numbers) -> equal(union(intersection(power_class(u),complement(v)),w),universal_class)**. % 300.04/300.42 226028[19:Rew:27.0,225874.1,167230.0,225874.1] || equal(power_class(u),universal_class) -> equal(union(intersection(power_class(u),complement(v)),w),union(complement(v),w))**. % 300.04/300.42 226116[0:SpR:207712.0,149179.0] || -> equal(intersection(union(complement(power_class(u)),v),symmetric_difference(power_class(u),complement(v))),symmetric_difference(power_class(u),complement(v)))**. % 300.04/300.42 226211[0:SpL:207712.0,6437.0] || subclass(universal_class,symmetric_difference(power_class(u),complement(v))) -> member(unordered_pair(w,x),union(complement(power_class(u)),v))*. % 300.04/300.42 226567[19:SpL:207747.0,204472.0] || equal(intersection(union(u,complement(power_class(v))),complement(w)),union(intersection(complement(u),power_class(v)),w))** -> . % 300.04/300.42 226609[19:Rew:167055.0,226480.1] || subclass(union(u,complement(power_class(v))),ordinal_numbers) -> equal(union(intersection(complement(u),power_class(v)),w),universal_class)**. % 300.04/300.42 226929[19:SpL:207751.0,204472.0] || equal(intersection(complement(u),union(complement(power_class(v)),w)),union(u,intersection(power_class(v),complement(w))))** -> . % 300.04/300.42 226970[19:Rew:167055.0,226847.1] || subclass(union(complement(power_class(u)),v),ordinal_numbers) -> equal(union(w,intersection(power_class(u),complement(v))),universal_class)**. % 300.04/300.42 226983[19:Rew:27.0,226805.1,167230.0,226805.1] || equal(power_class(u),universal_class) -> equal(union(v,intersection(power_class(u),complement(w))),union(v,complement(w)))**. % 300.04/300.42 227082[0:SpR:207752.0,149179.0] || -> equal(intersection(union(u,complement(power_class(v))),symmetric_difference(complement(u),power_class(v))),symmetric_difference(complement(u),power_class(v)))**. % 300.04/300.42 227175[0:SpL:207752.0,6437.0] || subclass(universal_class,symmetric_difference(complement(u),power_class(v))) -> member(unordered_pair(w,x),union(u,complement(power_class(v))))*. % 300.04/300.42 227621[19:SpL:207766.0,204472.0] || equal(intersection(complement(u),union(v,complement(power_class(w)))),union(u,intersection(complement(v),power_class(w))))** -> . % 300.04/300.42 227663[19:Rew:167055.0,227539.1] || subclass(union(u,complement(power_class(v))),ordinal_numbers) -> equal(union(w,intersection(complement(u),power_class(v))),universal_class)**. % 300.04/300.42 227814[19:Res:221767.1,16083.0] || equal(complement(symmetric_difference(u,cross_product(v,w))),ordinal_numbers) -> member(regular(element_relation),complement(restrict(u,v,w)))*. % 300.04/300.42 227818[19:Res:221767.1,16086.0] || equal(complement(symmetric_difference(cross_product(u,v),w)),ordinal_numbers) -> member(regular(element_relation),complement(restrict(w,u,v)))*. % 300.04/300.42 227862[19:Rew:209193.0,227836.0] || equal(image(element_relation,union(u,v)),ordinal_numbers) member(regular(element_relation),image(element_relation,union(u,v)))* -> . % 300.04/300.42 227931[8:Res:36606.3,124881.0] || member(u,universal_class)* member(v,u)* subclass(element_relation,rest_of(w)) -> member(v,cantor(w))*. % 300.04/300.42 227933[0:Res:36606.3,15.0] || member(u,universal_class)* member(v,u)* subclass(element_relation,cross_product(w,x))* -> member(v,w)*. % 300.04/300.42 227934[0:Res:36606.3,16.0] || member(u,universal_class)* member(v,u)* subclass(element_relation,cross_product(w,x))* -> member(u,x)*. % 300.04/300.42 227948[0:Res:36606.3,6476.1] || member(u,universal_class)* member(v,u)* subclass(element_relation,w) subclass(universal_class,complement(w))* -> . % 300.04/300.42 227959[2:Res:36606.3,188593.1] || member(u,universal_class)* member(v,u)* subclass(element_relation,w)* equal(complement(w),universal_class) -> . % 300.04/300.42 227967[8:MRR:227936.2,19.0] || member(u,universal_class)* member(v,u)* subclass(composition_function,rest_of(w)) -> member(v,cantor(w))*. % 300.04/300.42 227968[0:MRR:227935.2,19.0] || member(u,universal_class)* member(v,u)* subclass(composition_function,cross_product(w,x))* -> member(v,w)*. % 300.04/300.42 227969[0:MRR:227947.0,170.0] || member(u,singleton(singleton(singleton(v))))* subclass(element_relation,composition_function) -> equal(compose(u,singleton(v)),v). % 300.04/300.42 228098[0:Res:7.1,27149.1] || equal(restrict(u,v,w),rest_relation)** member(x,universal_class) -> member(ordered_pair(x,rest_of(x)),u)*. % 300.04/300.42 228238[22:SpL:479.0,223782.1] || equal(image(element_relation,union(u,v)),omega) equal(power_class(intersection(complement(u),complement(v))),kind_1_ordinals)** -> . % 300.04/300.42 228338[19:Res:224090.1,14972.1] || equal(power_class(intersection(complement(u),complement(v))),kind_1_ordinals) member(ordinal_numbers,image(element_relation,union(u,v)))* -> . % 300.04/300.42 228354[19:Res:224120.1,167728.0] || equal(symmetrization_of(ordinal_numbers),u) subclass(inverse(ordinal_numbers),v) -> equal(u,ordinal_numbers) member(regular(u),v)*. % 300.04/300.42 228413[19:Res:224120.1,5426.1] function(inverse(ordinal_numbers)) || equal(cross_product(universal_class,universal_class),symmetrization_of(ordinal_numbers))** -> equal(cross_product(universal_class,universal_class),inverse(ordinal_numbers)). % 300.04/300.42 228423[19:Res:224120.1,2497.1] || equal(symmetrization_of(ordinal_numbers),complement(u)) member(v,universal_class) -> member(v,u)* member(v,inverse(ordinal_numbers))*. % 300.04/300.42 229011[19:SpR:225013.1,479.0] || equal(successor(image(element_relation,union(u,v))),ordinal_numbers) -> equal(power_class(intersection(complement(u),complement(v))),universal_class)**. % 300.04/300.42 230357[0:Rew:149012.1,230289.2] || subclass(u,v) member(not_subclass_element(w,complement(u)),symmetric_difference(v,u))* -> subclass(w,complement(u)). % 300.04/300.42 230362[0:Rew:27.0,230304.1] || member(not_subclass_element(u,union(v,w)),symmetric_difference(complement(v),complement(w)))* -> subclass(u,union(v,w)). % 300.04/300.42 230613[2:Res:144531.1,79427.2] || equal(intersection(u,inverse(u)),universal_class)** asymmetric(u,v)* member(omega,cross_product(v,v))* -> . % 300.04/300.42 230614[2:Res:2478.1,79427.2] || subclass(universal_class,intersection(u,inverse(u)))* asymmetric(u,v)* member(omega,cross_product(v,v))* -> . % 300.04/300.42 230662[19:Res:214528.1,79427.2] || subclass(kind_1_ordinals,intersection(u,inverse(u)))* asymmetric(u,v)* member(ordinal_numbers,cross_product(v,v))* -> . % 300.04/300.42 230664[22:Res:178902.1,79427.2] || equal(intersection(u,inverse(u)),omega)** asymmetric(u,v)* member(ordinal_numbers,cross_product(v,v))* -> . % 300.04/300.42 230665[22:Res:177171.1,79427.2] || subclass(omega,intersection(u,inverse(u)))* asymmetric(u,v)* member(ordinal_numbers,cross_product(v,v))* -> . % 300.04/300.42 230667[19:Res:167104.1,79427.2] || subclass(universal_class,intersection(u,inverse(u)))* asymmetric(u,v)* member(ordinal_numbers,cross_product(v,v))* -> . % 300.04/300.42 230668[19:Res:167087.1,79427.2] || equal(intersection(u,inverse(u)),universal_class)** asymmetric(u,v)* member(ordinal_numbers,cross_product(v,v))* -> . % 300.04/300.42 230700[19:Res:7.1,167722.0] || equal(unordered_pair(u,v),w)* -> equal(w,ordinal_numbers) equal(regular(w),v)* equal(regular(w),u)*. % 300.04/300.42 230816[19:Res:229698.1,167276.0] || equal(successor(u),ordinal_numbers) well_ordering(v,w)* -> equal(segment(v,u,least(v,u)),ordinal_numbers)**. % 300.04/300.42 230847[19:Res:229698.1,124906.1] || equal(successor(cantor(restrict(u,v,w))),ordinal_numbers)** subclass(w,v) -> section(u,w,v). % 300.04/300.42 230864[19:Res:229698.1,4278.1] || equal(successor(u),ordinal_numbers) connected(v,u) -> well_ordering(v,u) equal(not_well_ordering(v,u),u)**. % 300.04/300.42 230865[19:Res:229698.1,126121.1] || equal(successor(u),ordinal_numbers) section(v,u,w) -> equal(cantor(restrict(v,w,u)),u)**. % 300.04/300.42 231038[19:Res:229698.1,1067.0] || equal(successor(cross_product(cross_product(universal_class,universal_class),universal_class)),ordinal_numbers)** -> equal(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(u))*. % 300.04/300.42 231039[19:Res:229698.1,1066.0] || equal(successor(cross_product(cross_product(universal_class,universal_class),universal_class)),ordinal_numbers)** -> equal(cross_product(cross_product(universal_class,universal_class),universal_class),flip(u))*. % 300.04/300.42 232295[19:Res:167116.0,42073.1] || subclass(u,v) -> equal(integer_of(not_subclass_element(u,intersection(omega,v))),ordinal_numbers)** subclass(u,intersection(omega,v)). % 300.04/300.42 232338[19:Rew:197295.1,232257.3] || subclass(u,ordinal_numbers)* subclass(v,u)* member(not_subclass_element(v,ordinal_numbers),w)* -> subclass(v,ordinal_numbers). % 300.04/300.42 232344[19:Rew:167375.1,232260.3] || subclass(u,singleton(v))* member(not_subclass_element(u,ordinal_numbers),w)* -> member(v,w)* subclass(u,ordinal_numbers). % 300.04/300.42 232345[19:Rew:167374.1,232226.3] || subclass(u,v)* member(not_subclass_element(u,ordinal_numbers),singleton(w))* -> member(w,v)* subclass(u,ordinal_numbers). % 300.04/300.42 232346[19:Rew:169201.1,232223.3] || subclass(u,regular(v)) member(not_subclass_element(u,ordinal_numbers),v)* -> equal(v,ordinal_numbers) subclass(u,ordinal_numbers). % 300.04/300.42 232373[19:Rew:199281.0,232233.2] || subclass(u,complement(v)) member(not_subclass_element(u,ordinal_numbers),restrict(v,w,x))* -> subclass(u,ordinal_numbers). % 300.04/300.42 232376[19:Rew:198248.0,232206.2] || subclass(u,restrict(v,w,x))* member(not_subclass_element(u,ordinal_numbers),complement(v))* -> subclass(u,ordinal_numbers). % 300.04/300.42 232378[0:Obv:232320.2] || subclass(u,symmetric_difference(v,w)) subclass(u,x) -> subclass(u,intersection(union(v,w),x))*. % 300.04/300.42 232379[0:Obv:232317.2] || subclass(u,v) subclass(intersection(w,u),x) -> subclass(intersection(w,u),intersection(v,x))*. % 300.04/300.42 232380[0:Obv:232314.2] || subclass(u,v) subclass(intersection(u,w),x) -> subclass(intersection(u,w),intersection(v,x))*. % 300.04/300.42 232391[0:Obv:232319.1] || subclass(intersection(u,intersection(v,w)),x) -> subclass(intersection(u,intersection(v,w)),intersection(v,x))*. % 300.04/300.42 232392[0:Obv:232318.1] || subclass(intersection(u,intersection(v,w)),x) -> subclass(intersection(u,intersection(v,w)),intersection(w,x))*. % 300.04/300.42 232393[0:Obv:232316.1] || subclass(intersection(intersection(u,v),w),x) -> subclass(intersection(intersection(u,v),w),intersection(u,x))*. % 300.04/300.42 232394[0:Obv:232315.1] || subclass(intersection(intersection(u,v),w),x) -> subclass(intersection(intersection(u,v),w),intersection(v,x))*. % 300.04/300.42 232607[19:Res:167116.0,42076.0] || -> equal(integer_of(not_subclass_element(intersection(u,v),intersection(omega,v))),ordinal_numbers)** subclass(intersection(u,v),intersection(omega,v)). % 300.04/300.42 232688[19:Rew:167374.1,232475.2] || member(not_subclass_element(intersection(u,v),ordinal_numbers),singleton(w))* -> member(w,v) subclass(intersection(u,v),ordinal_numbers). % 300.04/300.42 232715[19:Rew:199166.0,232480.1] || member(not_subclass_element(intersection(u,complement(v)),ordinal_numbers),intersection(w,v))* -> subclass(intersection(u,complement(v)),ordinal_numbers). % 300.04/300.42 232716[19:Rew:198500.0,232479.1] || member(not_subclass_element(intersection(u,complement(v)),ordinal_numbers),intersection(v,w))* -> subclass(intersection(u,complement(v)),ordinal_numbers). % 300.04/300.42 232751[0:Obv:232625.1] || subclass(intersection(u,v),symmetric_difference(w,x)) -> subclass(intersection(u,v),intersection(union(w,x),v))*. % 300.04/300.42 232829[19:Res:168374.2,225690.1] || subclass(omega,symmetric_difference(u,v))* equal(symmetrization_of(union(u,v)),ordinal_numbers) -> equal(integer_of(omega),ordinal_numbers). % 300.04/300.42 232999[19:Res:167116.0,42077.0] || -> equal(integer_of(not_subclass_element(intersection(u,v),intersection(omega,u))),ordinal_numbers)** subclass(intersection(u,v),intersection(omega,u)). % 300.04/300.42 233069[19:Rew:167193.0,232971.1] || member(not_subclass_element(symmetrization_of(ordinal_numbers),intersection(u,inverse(ordinal_numbers))),u)* -> subclass(symmetrization_of(ordinal_numbers),intersection(u,inverse(ordinal_numbers))). % 300.04/300.42 233078[19:Rew:167374.1,232867.2] || member(not_subclass_element(intersection(u,v),ordinal_numbers),singleton(w))* -> member(w,u) subclass(intersection(u,v),ordinal_numbers). % 300.04/300.42 233107[19:Rew:199166.0,232872.1] || member(not_subclass_element(intersection(complement(u),v),ordinal_numbers),intersection(w,u))* -> subclass(intersection(complement(u),v),ordinal_numbers). % 300.04/300.42 233108[19:Rew:198500.0,232871.1] || member(not_subclass_element(intersection(complement(u),v),ordinal_numbers),intersection(u,w))* -> subclass(intersection(complement(u),v),ordinal_numbers). % 300.04/300.42 233142[0:Obv:233017.1] || subclass(intersection(u,v),symmetric_difference(w,x)) -> subclass(intersection(u,v),intersection(union(w,x),u))*. % 300.04/300.42 233323[19:Res:233022.0,167728.0] || subclass(intersection(u,v),w) -> equal(intersection(v,u),ordinal_numbers) member(regular(intersection(v,u)),w)*. % 300.04/300.42 233556[19:Rew:233350.0,226617.1] || equal(power_class(u),universal_class) -> equal(union(intersection(complement(v),power_class(u)),w),union(complement(v),w))**. % 300.04/300.42 233669[19:Rew:233350.0,227674.1] || equal(power_class(u),universal_class) -> equal(union(v,intersection(complement(w),power_class(u))),union(v,complement(w)))**. % 300.04/300.42 233818[19:Rew:233350.0,181401.1] || member(u,universal_class) -> equal(complement(image(element_relation,successor(sum_class(range_of(u))))),power_class(complement(sum_class(range_of(u)))))**. % 300.04/300.42 233880[2:Rew:233350.0,144815.2] inductive(symmetric_difference(universal_class,u)) || well_ordering(v,complement(u)) -> member(least(v,complement(u)),complement(u))*. % 300.04/300.42 234841[19:Rew:234692.0,180324.0] || -> equal(complement(intersection(complement(u),union(v,complement(singleton(ordinal_numbers))))),union(u,intersection(singleton(ordinal_numbers),complement(v))))**. % 300.04/300.42 234846[19:Rew:234692.0,180285.0] || -> equal(complement(intersection(union(u,complement(singleton(ordinal_numbers))),complement(v))),union(intersection(singleton(ordinal_numbers),complement(u)),v))**. % 300.04/300.42 234863[19:Rew:234692.0,180340.0] || -> equal(intersection(union(singleton(ordinal_numbers),complement(u)),union(complement(singleton(ordinal_numbers)),u)),symmetric_difference(singleton(ordinal_numbers),complement(u)))**. % 300.04/300.42 234864[19:Rew:234692.0,168158.0] || -> equal(intersection(union(symmetrization_of(ordinal_numbers),complement(u)),union(complement(inverse(ordinal_numbers)),u)),symmetric_difference(symmetrization_of(ordinal_numbers),complement(u)))**. % 300.04/300.42 235121[2:Rew:233350.0,233878.1] inductive(symmetric_difference(universal_class,u)) || well_ordering(v,complement(u)) member(least(v,complement(u)),u)* -> . % 300.04/300.42 235662[19:Rew:167049.0,235622.2] || equal(successor(complement(complement(symmetrization_of(u)))),ordinal_numbers)** connected(u,v)* -> equal(cross_product(v,v),ordinal_numbers)**. % 300.04/300.42 236287[0:SpR:234692.0,79959.1] || -> subclass(intersection(u,omega),v) equal(integer_of(not_subclass_element(intersection(omega,u),v)),not_subclass_element(intersection(omega,u),v))**. % 300.04/300.42 236301[19:SpR:234692.0,168570.1] || -> equal(intersection(u,symmetric_difference(v,w)),ordinal_numbers) member(regular(intersection(symmetric_difference(v,w),u)),union(v,w))*. % 300.04/300.42 236322[19:SpR:234692.0,168569.1] || -> equal(intersection(symmetric_difference(u,v),w),ordinal_numbers) member(regular(intersection(w,symmetric_difference(u,v))),union(u,v))*. % 300.04/300.42 236345[0:SpR:234692.0,79954.1] || -> subclass(intersection(omega,u),v) equal(integer_of(not_subclass_element(intersection(u,omega),v)),not_subclass_element(intersection(u,omega),v))**. % 300.04/300.42 236492[0:SpL:234692.0,1032.0] || member(not_subclass_element(union(u,v),w),intersection(complement(v),complement(u)))* -> subclass(union(u,v),w). % 300.04/300.42 236516[0:SpL:234692.0,42076.0] || member(not_subclass_element(intersection(u,v),intersection(w,u)),w)* -> subclass(intersection(v,u),intersection(w,u)). % 300.04/300.42 236517[0:SpL:234692.0,42077.0] || member(not_subclass_element(intersection(u,v),intersection(w,v)),w)* -> subclass(intersection(v,u),intersection(w,v)). % 300.04/300.42 236527[0:SpL:234692.0,16109.0] || member(not_subclass_element(u,complement(intersection(v,w))),symmetric_difference(w,v))* -> subclass(u,complement(intersection(w,v))). % 300.04/300.42 236545[0:SpL:234692.0,42073.1] || subclass(u,v) member(not_subclass_element(u,intersection(v,w)),w)* -> subclass(u,intersection(w,v)). % 300.04/300.42 236546[0:SpL:234692.0,42076.0] || member(not_subclass_element(intersection(u,v),intersection(v,w)),w)* -> subclass(intersection(u,v),intersection(w,v)). % 300.04/300.42 236550[0:SpL:234692.0,14972.1] || member(u,image(element_relation,union(v,w))) member(u,power_class(intersection(complement(w),complement(v))))* -> . % 300.04/300.42 236574[0:SpL:234692.0,42077.0] || member(not_subclass_element(intersection(u,v),intersection(u,w)),w)* -> subclass(intersection(u,v),intersection(w,u)). % 300.04/300.42 236834[0:SpR:234713.0,149012.1] || subclass(complement(intersection(u,v)),union(u,v))* -> equal(complement(intersection(u,v)),symmetric_difference(u,v)). % 300.04/300.42 236928[0:SpL:234713.0,16105.1] || member(u,symmetric_difference(union(v,w),complement(intersection(v,w))))* member(u,symmetric_difference(v,w)) -> . % 300.04/300.42 237079[19:Rew:237023.0,168555.0] || subclass(universal_class,symmetric_difference(union(u,v),complement(intersection(u,v))))* -> member(ordinal_numbers,complement(symmetric_difference(u,v))). % 300.04/300.42 237081[0:Rew:237023.0,85723.0] || subclass(universal_class,symmetric_difference(union(u,v),complement(intersection(u,v))))* -> member(omega,complement(symmetric_difference(u,v))). % 300.04/300.42 237083[19:Rew:237023.0,168554.0] || equal(symmetric_difference(union(u,v),complement(intersection(u,v))),universal_class)** -> member(ordinal_numbers,complement(symmetric_difference(u,v))). % 300.04/300.42 237084[0:Rew:237023.0,85695.0] || equal(symmetric_difference(union(u,v),complement(intersection(u,v))),universal_class)** -> member(omega,complement(symmetric_difference(u,v))). % 300.04/300.42 237105[19:Rew:237023.0,211923.1] || equal(complement(symmetric_difference(u,v)),ordinal_numbers) -> equal(symmetric_difference(union(u,v),complement(intersection(u,v))),ordinal_numbers)**. % 300.04/300.42 237106[19:Rew:237023.0,202779.1] || subclass(complement(symmetric_difference(u,v)),ordinal_numbers) -> equal(symmetric_difference(union(u,v),complement(intersection(u,v))),ordinal_numbers)**. % 300.04/300.42 237113[22:Rew:237023.0,178775.0] || subclass(omega,symmetric_difference(union(u,v),complement(intersection(u,v))))* -> member(ordinal_numbers,complement(symmetric_difference(u,v))). % 300.04/300.42 237114[22:Rew:237023.0,178876.0] || equal(symmetric_difference(union(u,v),complement(intersection(u,v))),omega)** -> member(ordinal_numbers,complement(symmetric_difference(u,v))). % 300.04/300.42 237127[19:Rew:237023.0,230074.0] || subclass(kind_1_ordinals,symmetric_difference(union(u,v),complement(intersection(u,v))))* -> member(ordinal_numbers,complement(symmetric_difference(u,v))). % 300.04/300.42 237231[19:SpR:236669.0,168557.1] || -> equal(symmetric_difference(complement(u),complement(v)),ordinal_numbers) member(regular(symmetric_difference(complement(u),complement(v))),union(v,u))*. % 300.04/300.42 237232[19:SpR:236669.0,168569.1] || -> equal(intersection(symmetric_difference(u,v),w),ordinal_numbers) member(regular(intersection(symmetric_difference(u,v),w)),union(v,u))*. % 300.04/300.42 237240[0:SpR:236669.0,207752.0] || -> equal(intersection(union(complement(power_class(u)),v),union(complement(v),power_class(u))),symmetric_difference(complement(v),power_class(u)))**. % 300.04/300.42 237248[19:SpR:236669.0,176255.2] || member(u,universal_class) subclass(domain_relation,symmetric_difference(v,w)) -> member(ordered_pair(u,ordinal_numbers),union(w,v))*. % 300.04/300.42 237249[19:SpR:236669.0,168570.1] || -> equal(intersection(u,symmetric_difference(v,w)),ordinal_numbers) member(regular(intersection(u,symmetric_difference(v,w))),union(w,v))*. % 300.04/300.42 237252[0:SpR:236669.0,207752.0] || -> equal(intersection(union(u,complement(power_class(v))),union(power_class(v),complement(u))),symmetric_difference(complement(u),power_class(v)))**. % 300.04/300.42 237326[0:SpL:236669.0,1032.0] || member(not_subclass_element(union(u,v),w),intersection(complement(v),complement(u)))* -> subclass(union(v,u),w). % 300.04/300.42 237433[0:Rew:237384.0,236526.0] || member(u,symmetric_difference(union(v,w),complement(intersection(w,v))))* -> member(u,complement(symmetric_difference(v,w))). % 300.04/300.42 237435[19:Rew:237384.0,206772.0] || -> equal(symmetric_difference(complement(union(image(element_relation,power_class(u)),v)),intersection(power_class(complement(power_class(u))),complement(v))),ordinal_numbers)**. % 300.04/300.42 237436[19:Rew:237384.0,206505.0] || -> equal(symmetric_difference(complement(union(u,image(element_relation,power_class(v)))),intersection(complement(u),power_class(complement(power_class(v))))),ordinal_numbers)**. % 300.04/300.42 237452[19:Rew:237384.0,236713.0] || -> equal(intersection(union(u,complement(singleton(ordinal_numbers))),union(singleton(ordinal_numbers),complement(u))),symmetric_difference(singleton(ordinal_numbers),complement(u)))**. % 300.04/300.42 237568[19:Rew:237493.0,135707.2] inductive(symmetric_difference(u,singleton(u))) || well_ordering(v,universal_class) -> member(least(v,successor(u)),successor(u))*. % 300.04/300.42 237695[19:SpL:237493.0,16086.0] || member(u,successor(cross_product(v,w))) -> member(u,complement(restrict(singleton(cross_product(v,w)),v,w)))*. % 300.04/300.42 237720[0:SpR:208593.0,237218.0] || -> subclass(symmetric_difference(image(element_relation,power_class(u)),complement(power_class(v))),complement(intersection(power_class(v),power_class(complement(power_class(u))))))*. % 300.04/300.42 237727[0:SpR:208291.0,237218.0] || -> subclass(symmetric_difference(complement(power_class(u)),image(element_relation,power_class(v))),complement(intersection(power_class(complement(power_class(v))),power_class(u))))*. % 300.04/300.42 237742[19:Res:237218.0,167728.0] || subclass(union(u,v),w) -> equal(symmetric_difference(v,u),ordinal_numbers) member(regular(symmetric_difference(v,u)),w)*. % 300.04/300.42 237773[19:SpR:237384.0,168569.1] || -> equal(intersection(symmetric_difference(u,v),w),ordinal_numbers) member(regular(intersection(symmetric_difference(v,u),w)),union(u,v))*. % 300.04/300.42 237779[19:SpR:237384.0,168570.1] || -> equal(intersection(u,symmetric_difference(v,w)),ordinal_numbers) member(regular(intersection(u,symmetric_difference(w,v))),union(v,w))*. % 300.04/300.42 237781[19:SpR:237384.0,168557.1] || -> equal(symmetric_difference(complement(u),complement(v)),ordinal_numbers) member(regular(symmetric_difference(complement(v),complement(u))),union(u,v))*. % 300.04/300.42 237804[0:SpL:237384.0,16109.0] || member(not_subclass_element(u,complement(intersection(v,w))),symmetric_difference(w,v))* -> subclass(u,complement(intersection(v,w))). % 300.04/300.42 239077[19:SpR:237603.0,149012.1] || subclass(complement(intersection(u,singleton(u))),successor(u))* -> equal(complement(intersection(u,singleton(u))),successor(u)). % 300.04/300.42 239140[19:SpL:237603.0,16466.0] || subclass(u,successor(v)) -> subclass(u,w) member(not_subclass_element(u,w),complement(intersection(v,singleton(v))))*. % 300.04/300.42 239143[19:SpL:237603.0,15077.1] || member(u,universal_class) subclass(universal_class,successor(v)) -> member(power_class(u),complement(intersection(v,singleton(v))))*. % 300.04/300.42 239145[19:SpL:237603.0,15111.1] || member(u,universal_class) subclass(universal_class,successor(v)) -> member(sum_class(u),complement(intersection(v,singleton(v))))*. % 300.04/300.42 239196[19:Rew:237603.0,239075.1] || subclass(complement(intersection(u,singleton(u))),v)* -> equal(successor(u),ordinal_numbers) member(regular(successor(u)),v). % 300.04/300.42 239197[19:Rew:237603.0,239064.0] || -> equal(intersection(u,successor(v)),ordinal_numbers) member(regular(intersection(u,successor(v))),complement(intersection(v,singleton(v))))*. % 300.04/300.42 239198[19:Rew:237603.0,239053.0] || -> equal(intersection(successor(u),v),ordinal_numbers) member(regular(intersection(successor(u),v)),complement(intersection(u,singleton(u))))*. % 300.04/300.42 239396[19:SoR:168518.0,238779.1] || section(u,singleton(v),w)* equal(segment(u,w,v),universal_class) -> member(ordinal_numbers,singleton(v)). % 300.04/300.42 239724[19:Res:238770.1,167723.1] || equal(singleton(u),universal_class)** member(v,universal_class) -> equal(v,ordinal_numbers) equal(apply(choice,v),u)*. % 300.04/300.42 239731[19:Res:238770.1,167722.0] || equal(unordered_pair(u,v),universal_class)** -> equal(w,ordinal_numbers) equal(regular(w),v)* equal(regular(w),u)*. % 300.04/300.42 239922[19:Res:238770.1,8668.2] || equal(u,universal_class) member(v,w)* member(x,y)* -> member(ordered_pair(x,v),u)*. % 300.04/300.42 240538[19:Res:239914.1,168249.0] || equal(regular(u),universal_class) member(regular(element_relation),u)* well_ordering(v,w)* -> equal(u,ordinal_numbers). % 300.04/300.42 240539[19:Res:239914.1,168251.0] || equal(regular(u),universal_class) member(regular(element_relation),u)* -> equal(u,ordinal_numbers) member(regular(element_relation),v)*. % 300.04/300.42 240605[19:Res:239132.1,11848.0] || member(u,successor(v))* subclass(complement(intersection(v,singleton(v))),w)* well_ordering(universal_class,w) -> . % 300.04/300.42 240801[0:Res:236254.0,8.0] || subclass(complement(intersection(u,v)),symmetric_difference(v,u))* -> equal(complement(intersection(u,v)),symmetric_difference(v,u)). % 300.04/300.42 240891[19:Res:144532.1,237637.0] || equal(symmetric_difference(successor(u),complement(intersection(u,singleton(u)))),universal_class)** -> member(singleton(v),complement(successor(u)))*. % 300.04/300.42 240893[19:Res:2479.1,237637.0] || subclass(universal_class,symmetric_difference(successor(u),complement(intersection(u,singleton(u)))))* -> member(singleton(v),complement(successor(u)))*. % 300.04/300.42 240894[19:Res:205414.1,237637.0] || equal(complement(symmetric_difference(successor(u),complement(intersection(u,singleton(u))))),ordinal_numbers)** -> member(omega,complement(successor(u))). % 300.04/300.42 240945[19:Res:205391.1,237637.0] || equal(complement(symmetric_difference(successor(u),complement(intersection(u,singleton(u))))),ordinal_numbers)** -> member(ordinal_numbers,complement(successor(u))). % 300.04/300.42 240948[19:Res:169181.1,237637.0] || equal(symmetric_difference(successor(u),complement(intersection(u,singleton(u)))),singleton(ordinal_numbers))** -> member(ordinal_numbers,complement(successor(u))). % 300.04/300.42 240956[19:Res:239914.1,237637.0] || equal(symmetric_difference(successor(u),complement(intersection(u,singleton(u)))),universal_class)** -> member(regular(element_relation),complement(successor(u))). % 300.04/300.42 240958[19:Res:196731.1,237637.0] || subclass(universal_class,symmetric_difference(successor(u),complement(intersection(u,singleton(u)))))* -> member(regular(element_relation),complement(successor(u))). % 300.04/300.42 241125[0:SpR:236669.0,234704.0] || -> equal(intersection(union(power_class(u),complement(v)),union(v,complement(power_class(u)))),symmetric_difference(power_class(u),complement(v)))**. % 300.04/300.42 241165[0:SpR:236669.0,234704.0] || -> equal(intersection(union(complement(u),power_class(v)),union(complement(power_class(v)),u)),symmetric_difference(power_class(v),complement(u)))**. % 300.04/300.42 241399[0:SpL:236669.0,236817.0] || member(u,symmetric_difference(union(v,w),complement(intersection(w,v))))* -> member(u,complement(symmetric_difference(w,v))). % 300.04/300.42 241606[19:SpR:234692.0,168566.1] || -> equal(intersection(u,restrict(v,w,x)),ordinal_numbers) member(regular(intersection(restrict(v,w,x),u)),v)*. % 300.04/300.42 241746[19:SpR:234692.0,168568.1] || -> equal(intersection(restrict(u,v,w),x),ordinal_numbers) member(regular(intersection(x,restrict(u,v,w))),u)*. % 300.04/300.42 241979[19:Obv:241947.1] || member(u,complement(unordered_pair(v,u)))* -> member(v,unordered_pair(v,u))* subclass(unordered_pair(v,u),ordinal_numbers). % 300.04/300.42 242080[19:SpL:479.0,225692.0] || equal(symmetrization_of(power_class(intersection(complement(u),complement(v)))),ordinal_numbers)** -> member(ordinal_numbers,image(element_relation,union(u,v))). % 300.04/300.42 242162[19:Obv:242129.1] || member(u,complement(unordered_pair(u,v)))* -> member(v,unordered_pair(u,v))* subclass(unordered_pair(u,v),ordinal_numbers). % 300.04/300.42 242198[19:SpL:479.0,225693.0] || equal(symmetrization_of(power_class(intersection(complement(u),complement(v)))),ordinal_numbers)** -> member(omega,image(element_relation,union(u,v))). % 300.04/300.42 242275[0:Res:7.1,16467.0] || equal(restrict(u,v,w),x)* -> subclass(x,y) member(not_subclass_element(x,y),cross_product(v,w))*. % 300.04/300.42 242322[19:SpL:479.0,228219.1] || equal(image(element_relation,union(u,v)),kind_1_ordinals) equal(power_class(intersection(complement(u),complement(v))),kind_1_ordinals)** -> . % 300.04/300.42 242492[19:Rew:16365.1,242491.0] || member(u,element_relation) member(u,complement(compose(element_relation,universal_class)))* -> subclass(intersection(v,singleton(u)),ordinal_numbers)*. % 300.04/300.42 242494[19:Rew:16238.1,242493.0] || member(u,element_relation) member(u,complement(compose(element_relation,universal_class)))* -> subclass(intersection(singleton(u),v),ordinal_numbers)*. % 300.04/300.42 242543[19:SpL:479.0,235552.0] || equal(successor(power_class(intersection(complement(u),complement(v)))),ordinal_numbers)** -> equal(image(element_relation,union(u,v)),universal_class). % 300.04/300.42 243730[19:MRR:243704.3,167176.0] || member(u,universal_class)* subclass(rest_relation,omega) subclass(omega,successor_relation) -> equal(rest_of(u),successor(u)). % 300.04/300.42 243805[19:SpL:196827.0,204403.1] || member(u,universal_class)* subclass(universal_class,regular(element_relation))* -> equal(power_class(u),omega) equal(power_class(u),ordinal_numbers). % 300.04/300.42 243862[19:SpL:196827.0,204404.1] || member(u,universal_class)* subclass(universal_class,regular(element_relation))* -> equal(sum_class(u),omega) equal(sum_class(u),ordinal_numbers). % 300.04/300.42 245504[0:Res:40606.2,5467.1] || member(u,universal_class) equal(compose(v,singleton(u)),u)** subclass(universal_class,complement(compose_class(v)))* -> . % 300.04/300.42 245507[2:Res:40606.2,188593.1] || member(u,universal_class) equal(compose(v,singleton(u)),u)** equal(complement(compose_class(v)),universal_class) -> . % 300.04/300.42 245697[19:SpL:160282.0,225033.0] || equal(successor(unordered_pair(u,regular(ordered_pair(v,w)))),ordinal_numbers)** -> equal(regular(ordered_pair(v,w)),singleton(v)). % 300.04/300.42 245720[19:SpL:160282.0,225036.0] || equal(successor(unordered_pair(regular(ordered_pair(u,v)),w)),ordinal_numbers)** -> equal(regular(ordered_pair(u,v)),singleton(u)). % 300.04/300.42 245761[19:SpL:160282.0,225701.0] || equal(symmetrization_of(unordered_pair(u,regular(ordered_pair(v,w)))),ordinal_numbers)** -> equal(regular(ordered_pair(v,w)),singleton(v)). % 300.04/300.42 245783[19:SpL:160282.0,225704.0] || equal(symmetrization_of(unordered_pair(regular(ordered_pair(u,v)),w)),ordinal_numbers)** -> equal(regular(ordered_pair(u,v)),singleton(u)). % 300.04/300.42 245925[19:Res:167580.1,229738.1] || member(u,universal_class) equal(successor(cantor(v)),ordinal_numbers) -> equal(apply(v,u),sum_class(range_of(ordinal_numbers)))**. % 300.04/300.42 245952[19:Res:40606.2,229738.1] || member(u,universal_class) equal(compose(v,singleton(u)),u)** equal(successor(compose_class(v)),ordinal_numbers) -> . % 300.04/300.42 246057[19:Res:9790.2,229738.1] || member(ordered_pair(u,v),cross_product(universal_class,universal_class))* subclass(composition_function,w)* equal(successor(w),ordinal_numbers) -> . % 300.04/300.42 246058[19:Res:36606.3,229738.1] || member(u,universal_class)* member(v,u)* subclass(element_relation,w)* equal(successor(w),ordinal_numbers) -> . % 300.04/300.42 246296[19:Res:52.1,168370.0] inductive(intersection(complement(u),complement(v))) || member(w,union(u,v))* -> equal(integer_of(w),ordinal_numbers). % 300.04/300.42 246496[25:SpL:234134.1,167960.0] function(u) || subclass(omega,successor(u)) member(v,complement(u))* -> equal(integer_of(v),ordinal_numbers). % 300.04/300.42 246532[25:SpL:234134.1,16102.0] function(u) || member(v,symmetric_difference(successor(u),complement(w)))* -> member(v,union(complement(u),w)). % 300.04/300.42 246626[25:SpL:234134.1,16102.0] function(u) || member(v,symmetric_difference(complement(w),successor(u)))* -> member(v,union(w,complement(u))). % 300.04/300.42 246694[25:Res:246381.1,16462.0] function(u) || subclass(u,v) -> subclass(successor(u),w) member(not_subclass_element(successor(u),w),v)*. % 300.04/300.42 246697[25:Res:246381.1,167276.0] function(u) || well_ordering(v,u) -> equal(segment(v,successor(u),least(v,successor(u))),ordinal_numbers)**. % 300.04/300.42 246863[19:Obv:246816.1] || subclass(complement(complement(intersection(u,v))),symmetric_difference(u,v))* -> equal(complement(complement(intersection(u,v))),ordinal_numbers). % 300.04/300.42 247014[19:Obv:246974.1] || subclass(intersection(complement(u),complement(v)),symmetric_difference(u,v))* -> equal(intersection(complement(u),complement(v)),ordinal_numbers). % 300.04/300.42 247274[0:Res:27192.2,6476.1] || member(u,universal_class) equal(compose(v,u),rest_of(u))** subclass(universal_class,complement(compose_class(v)))* -> . % 300.04/300.42 247276[19:Res:27192.2,229738.1] || member(u,universal_class) equal(compose(v,u),rest_of(u))** equal(successor(compose_class(v)),ordinal_numbers) -> . % 300.04/300.42 247278[2:Res:27192.2,188593.1] || member(u,universal_class) equal(compose(v,u),rest_of(u))** equal(complement(compose_class(v)),universal_class) -> . % 300.04/300.42 247320[19:SpL:237138.0,238772.0] || equal(symmetric_difference(union(u,v),complement(intersection(u,v))),universal_class)** -> subclass(universal_class,complement(symmetric_difference(u,v))). % 300.04/300.42 247743[0:Res:27157.2,6476.1] || member(u,universal_class)* subclass(rest_relation,symmetric_difference(v,w)) subclass(universal_class,complement(union(v,w)))* -> . % 300.04/300.42 247757[0:Obv:247744.0] || subclass(rest_relation,symmetric_difference(u,v)) member(w,universal_class)* subclass(rest_relation,complement(union(u,v)))* -> . % 300.04/300.42 247758[19:MRR:247725.1,53.0] || equal(rest_relation,domain_relation) subclass(rest_relation,symmetric_difference(u,v)) -> member(ordered_pair(omega,ordinal_numbers),union(u,v))*. % 300.04/300.42 247759[19:MRR:247724.1,167011.0] || equal(rest_relation,domain_relation) subclass(rest_relation,symmetric_difference(u,v)) -> member(ordered_pair(ordinal_numbers,ordinal_numbers),union(u,v))*. % 300.04/300.42 248163[19:SpL:237138.0,245337.0] || equal(symmetric_difference(union(u,v),complement(intersection(u,v))),kind_1_ordinals)** -> member(ordinal_numbers,complement(symmetric_difference(u,v))). % 300.04/300.42 248303[19:Res:248149.1,126.0] || equal(u,kind_1_ordinals) subclass(u,v)* well_ordering(w,v)* -> member(least(w,u),u)*. % 300.04/300.42 248353[19:Res:248149.1,79427.2] || equal(intersection(u,inverse(u)),kind_1_ordinals)** asymmetric(u,v)* member(ordinal_numbers,cross_product(v,v))* -> . % 300.04/300.42 248615[0:SpR:481.0,217958.0] || -> subclass(complement(complement(symmetric_difference(u,intersection(complement(v),complement(w))))),complement(intersection(complement(u),union(v,w))))*. % 300.04/300.42 248621[0:SpR:480.0,217958.0] || -> subclass(complement(complement(symmetric_difference(intersection(complement(u),complement(v)),w))),complement(intersection(union(u,v),complement(w))))*. % 300.04/300.42 248857[19:Res:248818.0,167728.0] || subclass(u,v) -> equal(complement(successor(complement(u))),ordinal_numbers) member(regular(complement(successor(complement(u)))),v)*. % 300.04/300.42 248865[19:Res:248818.0,167737.0] || -> equal(complement(successor(complement(intersection(u,v)))),ordinal_numbers) member(regular(complement(successor(complement(intersection(u,v))))),v)*. % 300.04/300.42 248866[19:Res:248818.0,167736.0] || -> equal(complement(successor(complement(intersection(u,v)))),ordinal_numbers) member(regular(complement(successor(complement(intersection(u,v))))),u)*. % 300.04/300.42 248974[19:Res:248819.0,167728.0] || subclass(u,v) -> equal(complement(symmetrization_of(complement(u))),ordinal_numbers) member(regular(complement(symmetrization_of(complement(u)))),v)*. % 300.04/300.42 248982[19:Res:248819.0,167737.0] || -> equal(complement(symmetrization_of(complement(intersection(u,v)))),ordinal_numbers) member(regular(complement(symmetrization_of(complement(intersection(u,v))))),v)*. % 300.04/300.42 248983[19:Res:248819.0,167736.0] || -> equal(complement(symmetrization_of(complement(intersection(u,v)))),ordinal_numbers) member(regular(complement(symmetrization_of(complement(intersection(u,v))))),u)*. % 300.04/300.42 249094[19:Res:248816.0,167739.0] || -> equal(complement(union(u,complement(singleton(v)))),ordinal_numbers) equal(regular(complement(union(u,complement(singleton(v))))),v)**. % 300.04/300.42 249103[0:Res:248816.0,8596.1] single_valued_class(complement(union(u,complement(cross_product(universal_class,universal_class))))) || -> function(complement(union(u,complement(cross_product(universal_class,universal_class)))))*. % 300.04/300.42 249260[19:Res:248817.0,167739.0] || -> equal(complement(union(complement(singleton(u)),v)),ordinal_numbers) equal(regular(complement(union(complement(singleton(u)),v))),u)**. % 300.04/300.42 249269[0:Res:248817.0,8596.1] single_valued_class(complement(union(complement(cross_product(universal_class,universal_class)),u))) || -> function(complement(union(complement(cross_product(universal_class,universal_class)),u)))*. % 300.04/300.42 249336[19:Res:248841.0,8.0] || subclass(complement(inverse(ordinal_numbers)),complement(successor(symmetrization_of(ordinal_numbers))))* -> equal(complement(successor(symmetrization_of(ordinal_numbers))),complement(inverse(ordinal_numbers))). % 300.04/300.42 249432[19:Res:248877.0,8.0] || subclass(inverse(ordinal_numbers),complement(successor(complement(symmetrization_of(ordinal_numbers)))))* -> equal(complement(successor(complement(symmetrization_of(ordinal_numbers)))),inverse(ordinal_numbers)). % 300.04/300.42 249456[19:Res:248958.0,8.0] || subclass(complement(inverse(ordinal_numbers)),complement(symmetrization_of(symmetrization_of(ordinal_numbers))))* -> equal(complement(symmetrization_of(symmetrization_of(ordinal_numbers))),complement(inverse(ordinal_numbers))). % 300.04/300.42 249506[19:Res:248994.0,8.0] || subclass(inverse(ordinal_numbers),complement(symmetrization_of(complement(symmetrization_of(ordinal_numbers)))))* -> equal(complement(symmetrization_of(complement(symmetrization_of(ordinal_numbers)))),inverse(ordinal_numbers)). % 300.04/300.42 249531[19:Rew:167760.0,249518.1,946.0,249518.1,13.0,249518.0] || -> equal(apply(choice,singleton(singleton(singleton(u)))),singleton(singleton(u)))** equal(apply(choice,ordinal_numbers),singleton(singleton(u))). % 300.04/300.42 249712[0:Res:248882.0,8.0] || subclass(u,complement(successor(complement(complement(complement(u))))))* -> equal(complement(successor(complement(complement(complement(u))))),u). % 300.04/300.42 249829[0:Res:248999.0,8.0] || subclass(u,complement(symmetrization_of(complement(complement(complement(u))))))* -> equal(complement(symmetrization_of(complement(complement(complement(u))))),u). % 300.04/300.42 250069[0:Res:248806.0,7963.1] || member(u,union(v,w)) -> subclass(singleton(u),intersection(v,w))* member(u,symmetric_difference(v,w)). % 300.04/300.42 250098[19:Res:248806.0,169002.1] || well_ordering(u,universal_class) -> subclass(singleton(least(u,complement(complement(v)))),v)* equal(complement(complement(v)),ordinal_numbers). % 300.04/300.42 250101[0:Res:248806.0,27138.2] || member(u,universal_class) subclass(rest_relation,complement(complement(v))) -> subclass(singleton(ordered_pair(u,rest_of(u))),v)*. % 300.04/300.42 250115[0:Res:248806.0,16224.0] || -> subclass(singleton(not_subclass_element(intersection(complement(complement(u)),v),w)),u)* subclass(intersection(complement(complement(u)),v),w). % 300.04/300.42 250116[0:Res:248806.0,16351.0] || -> subclass(singleton(not_subclass_element(intersection(u,complement(complement(v))),w)),v)* subclass(intersection(u,complement(complement(v))),w). % 300.04/300.42 250118[19:Res:248806.0,169567.1] || member(not_subclass_element(u,ordinal_numbers),element_relation) -> subclass(singleton(not_subclass_element(u,ordinal_numbers)),compose(element_relation,universal_class))* subclass(u,ordinal_numbers). % 300.04/300.42 250131[19:Res:248806.0,207289.1] || member(power_class(u),universal_class) -> subclass(singleton(apply(choice,power_class(u))),power_class(u))* equal(power_class(u),ordinal_numbers). % 300.04/300.42 250146[19:Res:250113.0,8.0] || subclass(compose(element_relation,universal_class),singleton(not_subclass_element(element_relation,ordinal_numbers)))* -> equal(singleton(not_subclass_element(element_relation,ordinal_numbers)),compose(element_relation,universal_class)). % 300.04/300.42 250148[19:Rew:167222.1,250140.2] || subclass(compose(element_relation,universal_class),u) -> equal(singleton(not_subclass_element(element_relation,ordinal_numbers)),ordinal_numbers) member(not_subclass_element(element_relation,ordinal_numbers),u)*. % 300.04/300.42 251173[19:SpL:479.0,248972.0] || equal(symmetrization_of(power_class(intersection(complement(u),complement(v)))),ordinal_numbers)** -> subclass(universal_class,image(element_relation,union(u,v))). % 300.04/300.42 251202[19:SpL:479.0,250085.0] || subclass(power_class(intersection(complement(u),complement(v))),ordinal_numbers)* -> subclass(singleton(omega),image(element_relation,union(u,v))). % 300.04/300.42 251323[19:Res:167106.1,237458.0] inductive(symmetric_difference(symmetrization_of(u),complement(intersection(u,inverse(u))))) || -> member(ordinal_numbers,complement(symmetric_difference(u,inverse(u))))*. % 300.04/300.42 251388[19:SpL:479.0,250124.0] || subclass(power_class(intersection(complement(u),complement(v))),ordinal_numbers)* -> subclass(singleton(ordinal_numbers),image(element_relation,union(u,v))). % 300.04/300.42 251692[0:Res:36863.0,11848.0] || subclass(union(u,v),w)* well_ordering(universal_class,w) -> subclass(x,intersection(complement(u),complement(v)))*. % 300.04/300.42 252535[8:SpR:144504.0,125121.2] || member(u,cantor(universal_class)) subclass(rest_of(universal_class),v) -> member(ordered_pair(u,cross_product(u,universal_class)),v)*. % 300.04/300.42 252608[8:Res:125121.2,146.0] || member(u,cantor(v)) subclass(rest_of(v),rest_relation) -> equal(restrict(v,u,universal_class),rest_of(u))**. % 300.04/300.42 252620[8:Res:125121.2,46.0] || member(u,cantor(v)) subclass(rest_of(v),successor_relation) -> equal(restrict(v,u,universal_class),successor(u))**. % 300.04/300.42 252627[8:Res:125121.2,124911.0] || member(u,cantor(v)) subclass(rest_of(v),domain_relation) -> equal(restrict(v,u,universal_class),cantor(u))**. % 300.04/300.42 252640[19:MRR:252553.2,204022.0] || member(u,cantor(v)) subclass(rest_of(v),complement(singleton(ordered_pair(u,restrict(v,u,universal_class)))))* -> . % 300.04/300.42 252909[19:Res:220180.1,167737.0] || subclass(u,intersection(v,w))* -> equal(complement(complement(u)),ordinal_numbers) member(regular(complement(complement(u))),w)*. % 300.04/300.42 252910[19:Res:220180.1,167736.0] || subclass(u,intersection(v,w))* -> equal(complement(complement(u)),ordinal_numbers) member(regular(complement(complement(u))),v)*. % 300.04/300.42 252916[0:Res:220180.1,16469.0] || subclass(u,singleton(v))* -> subclass(complement(complement(u)),w) equal(not_subclass_element(complement(complement(u)),w),v)*. % 300.04/300.42 253017[19:Res:252894.1,16465.0] || subclass(inverse(ordinal_numbers),intersection(u,v))* -> subclass(symmetrization_of(ordinal_numbers),w) member(not_subclass_element(symmetrization_of(ordinal_numbers),w),u)*. % 300.04/300.42 253018[19:Res:252894.1,16466.0] || subclass(inverse(ordinal_numbers),intersection(u,v))* -> subclass(symmetrization_of(ordinal_numbers),w) member(not_subclass_element(symmetrization_of(ordinal_numbers),w),v)*. % 300.04/300.42 253059[20:MRR:253020.2,175557.0] || subclass(inverse(ordinal_numbers),singleton(u))* member(symmetrization_of(ordinal_numbers),universal_class) -> equal(apply(choice,symmetrization_of(ordinal_numbers)),u). % 300.04/300.42 253129[18:Res:27190.1,227961.1] || subclass(rest_relation,flip(cantor(u))) member(u,ordered_pair(ordered_pair(v,w),rest_of(ordered_pair(w,v))))* -> . % 300.04/300.42 253130[18:Res:27189.1,227961.1] || subclass(rest_relation,rotate(cantor(u))) member(u,ordered_pair(ordered_pair(v,rest_of(ordered_pair(w,v))),w))* -> . % 300.04/300.42 253155[18:Res:905.1,227961.1] || member(u,not_subclass_element(restrict(cantor(u),v,w),x))* -> subclass(restrict(cantor(u),v,w),x). % 300.04/300.42 253180[19:Res:168474.2,227961.1] || subclass(u,cantor(v)) member(v,regular(intersection(u,w)))* -> equal(intersection(u,w),ordinal_numbers). % 300.04/300.42 253182[19:Res:168469.2,227961.1] || subclass(u,cantor(v)) member(v,regular(intersection(w,u)))* -> equal(intersection(w,u),ordinal_numbers). % 300.04/300.42 17157[0:SpR:27.0,17083.0] || -> subclass(symmetric_difference(union(u,v),complement(singleton(intersection(complement(u),complement(v))))),successor(intersection(complement(u),complement(v))))*. % 300.04/300.42 48562[0:Res:36588.1,126.0] || member(u,rest_of(u))* subclass(element_relation,v) well_ordering(w,v)* -> member(least(w,element_relation),element_relation)*. % 300.04/300.42 48893[0:Res:2523.2,16910.0] || member(u,universal_class) subclass(rest_relation,symmetric_difference(v,inverse(v)))* -> member(ordered_pair(u,rest_of(u)),symmetrization_of(v))*. % 300.04/300.42 12048[0:Res:12015.1,18.0] || equal(complement(complement(cross_product(u,v))),universal_class)** -> equal(ordered_pair(first(singleton(w)),second(singleton(w))),singleton(w))**. % 300.04/300.42 43726[0:SpR:5132.1,945.0] || -> 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))*. % 300.04/300.42 16244[0:Res:315.1,4127.0] || -> subclass(intersection(symmetric_difference(u,v),w),x) member(not_subclass_element(intersection(symmetric_difference(u,v),w),x),union(u,v))*. % 300.04/300.42 16371[0:Res:297.1,4127.0] || -> subclass(intersection(u,symmetric_difference(v,w)),x) member(not_subclass_element(intersection(u,symmetric_difference(v,w)),x),union(v,w))*. % 300.04/300.42 16237[0:Res:315.1,897.0] || -> subclass(intersection(restrict(u,v,w),x),y) member(not_subclass_element(intersection(restrict(u,v,w),x),y),u)*. % 300.04/300.42 16364[0:Res:297.1,897.0] || -> subclass(intersection(u,restrict(v,w,x)),y) member(not_subclass_element(intersection(u,restrict(v,w,x)),y),v)*. % 300.04/300.42 36487[0:SpR:4121.0,16276.0] || -> subclass(symmetric_difference(complement(restrict(u,v,w)),union(cross_product(v,w),u)),complement(symmetric_difference(cross_product(v,w),u)))*. % 300.04/300.42 36349[0:SpR:4119.0,16276.0] || -> subclass(symmetric_difference(complement(restrict(u,v,w)),union(u,cross_product(v,w))),complement(symmetric_difference(u,cross_product(v,w))))*. % 300.04/300.42 17139[0:SpR:27.0,17082.0] || -> subclass(symmetric_difference(union(u,v),complement(inverse(intersection(complement(u),complement(v))))),symmetrization_of(intersection(complement(u),complement(v))))*. % 300.04/300.42 35417[0:SpL:123.0,9777.0] || equal(segment(u,v,w),singleton(w)) subclass(singleton(w),v) -> section(u,singleton(w),v)*. % 300.04/300.42 35223[2:Res:16254.0,9859.1] inductive(intersection(u,v)) || well_ordering(w,u) -> member(least(w,intersection(u,v)),intersection(u,v))*. % 300.04/300.42 35234[2:Res:16381.0,9859.1] inductive(intersection(u,v)) || well_ordering(w,v) -> member(least(w,intersection(u,v)),intersection(u,v))*. % 300.04/300.42 98319[0:Res:51413.0,896.0] || -> subclass(u,complement(restrict(v,w,x))) member(not_subclass_element(u,complement(restrict(v,w,x))),cross_product(w,x))*. % 300.04/300.42 107103[12:SpL:43.0,99364.1] || member(restrict(u,v,universal_class),universal_class)* equal(rest_of(restrict(u,v,universal_class)),sum_class(image(u,v))) -> . % 300.04/300.42 118530[0:SpL:5132.1,6476.1] || subclass(universal_class,complement(u)) member(not_subclass_element(cross_product(v,w),x),u)* -> subclass(cross_product(v,w),x). % 300.04/300.42 125468[8:Rew:124836.0,48507.0] || member(u,cantor(u))* subclass(element_relation,v) well_ordering(w,v)* -> member(least(w,element_relation),element_relation)*. % 300.04/300.42 135198[0:Res:36865.0,4127.0] || -> subclass(complement(complement(symmetric_difference(u,v))),w) member(not_subclass_element(complement(complement(symmetric_difference(u,v))),w),union(u,v))*. % 300.04/300.42 135219[0:Res:36865.0,897.0] || -> subclass(complement(complement(restrict(u,v,w))),x) member(not_subclass_element(complement(complement(restrict(u,v,w))),x),u)*. % 300.04/300.42 135253[0:Rew:27.0,135174.1] || -> member(not_subclass_element(complement(union(u,v)),w),intersection(complement(u),complement(v)))* subclass(complement(union(u,v)),w). % 300.04/300.42 135279[2:Res:135236.0,9859.1] inductive(complement(complement(u))) || well_ordering(v,u) -> member(least(v,complement(complement(u))),complement(complement(u)))*. % 300.04/300.42 135363[0:Res:24.2,11848.0] || member(u,v)* member(u,w)* subclass(intersection(w,v),x)* well_ordering(universal_class,x) -> . % 300.04/300.42 135468[0:Res:17.2,11848.0] || member(u,v)* member(w,x)* subclass(cross_product(x,v),y)* well_ordering(universal_class,y) -> . % 300.04/300.42 137008[0:SpR:479.0,135266.0] || -> subclass(complement(union(u,image(element_relation,union(v,w)))),intersection(complement(u),power_class(intersection(complement(v),complement(w)))))*. % 300.04/300.42 137020[0:SpR:479.0,135266.0] || -> subclass(complement(union(image(element_relation,union(u,v)),w)),intersection(power_class(intersection(complement(u),complement(v))),complement(w)))*. % 300.04/300.42 138362[8:MRR:138320.0,940.0] || subclass(rest_relation,rest_of(u)) member(v,w)* subclass(w,x)* well_ordering(cantor(u),x)* -> . % 300.04/300.42 139934[0:Res:2526.2,16102.0] || subclass(u,symmetric_difference(complement(v),complement(w))) -> subclass(u,x) member(not_subclass_element(u,x),union(v,w))*. % 300.04/300.42 139938[0:Res:2482.2,16102.0] || member(u,universal_class) subclass(universal_class,symmetric_difference(complement(v),complement(w)))* -> member(sum_class(u),union(v,w))*. % 300.04/300.42 139939[0:Res:2483.2,16102.0] || member(u,universal_class) subclass(universal_class,symmetric_difference(complement(v),complement(w)))* -> member(power_class(u),union(v,w))*. % 300.04/300.42 139949[0:Res:2525.1,16102.0] || subclass(ordered_pair(u,v),symmetric_difference(complement(w),complement(x)))* -> member(unordered_pair(u,singleton(v)),union(w,x)). % 300.04/300.42 140897[12:SpL:17187.0,104245.0] || member(sum_class(image(cross_product(u,v),w)),universal_class) member(restrict(cross_product(w,universal_class),u,v),universal_class)* -> . % 300.04/300.42 146317[0:Rew:144504.0,146280.0] || member(cross_product(u,singleton(v)),universal_class) -> member(ordered_pair(cross_product(u,singleton(v)),segment(universal_class,u,v)),domain_relation)*. % 300.04/300.42 146318[8:Rew:144504.0,146306.2] || section(universal_class,u,v) subclass(u,cantor(cross_product(v,u)))* -> equal(cantor(cross_product(v,u)),u). % 300.04/300.42 147347[8:Res:12015.1,82995.1] || equal(complement(complement(complement(compose(element_relation,universal_class)))),universal_class)** member(singleton(u),element_relation)* -> member(singleton(u),v)*. % 300.04/300.42 147431[0:SpL:69.0,15100.2] || member(image(u,singleton(v)),universal_class)* subclass(universal_class,complement(w)) member(apply(u,v),w)* -> . % 300.04/300.42 148891[0:Res:6521.3,148647.0] function(u) || member(v,universal_class) subclass(universal_class,complement(complement(w))) -> member(image(u,v),w)*. % 300.04/300.42 152314[0:Res:12798.1,2.0] || subclass(union(u,v),w) -> subclass(symmetric_difference(u,v),x) member(not_subclass_element(symmetric_difference(u,v),x),w)*. % 300.04/300.42 152481[0:Res:16280.0,16466.0] || -> subclass(restrict(intersection(u,v),w,x),y) member(not_subclass_element(restrict(intersection(u,v),w,x),y),v)*. % 300.04/300.42 152766[0:Res:16280.0,16465.0] || -> subclass(restrict(intersection(u,v),w,x),y) member(not_subclass_element(restrict(intersection(u,v),w,x),y),u)*. % 300.04/300.42 152865[0:Res:905.1,148647.0] || -> subclass(restrict(complement(complement(u)),v,w),x) member(not_subclass_element(restrict(complement(complement(u)),v,w),x),u)*. % 300.04/300.42 152871[0:Res:905.1,2.0] || subclass(u,v) -> subclass(restrict(u,w,x),y) member(not_subclass_element(restrict(u,w,x),y),v)*. % 300.04/300.42 154655[8:Res:12015.1,82994.1] || equal(complement(complement(complement(compose(element_relation,universal_class)))),universal_class)** member(singleton(u),element_relation)* well_ordering(v,w)* -> . % 300.04/300.42 157108[0:Rew:114.0,157059.1,27.0,157059.1,114.0,157059.0,27.0,157059.0] || -> 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))). % 300.04/300.42 157109[0:Rew:44.0,157058.1,27.0,157058.1,44.0,157058.0,27.0,157058.0] || -> member(not_subclass_element(u,image(element_relation,successor(v))),complement(image(element_relation,successor(v))))* subclass(u,image(element_relation,successor(v))). % 300.04/300.42 33554[0:Res:16133.1,1070.1] inductive(singleton(u)) || member(u,image(successor_relation,singleton(u)))* -> equal(image(successor_relation,singleton(u)),singleton(u)). % 300.04/300.42 160117[0:Res:49.1,16469.0] inductive(singleton(u)) || -> subclass(image(successor_relation,singleton(u)),v) equal(not_subclass_element(image(successor_relation,singleton(u)),v),u)**. % 300.04/300.42 138302[8:Res:125124.2,11848.0] || member(u,universal_class)* subclass(rest_relation,rest_of(v)) subclass(cantor(v),w)* well_ordering(universal_class,w) -> . % 300.04/300.42 140720[0:Res:35125.1,11848.0] || member(u,universal_class) subclass(union(v,w),x)* well_ordering(universal_class,x) -> member(u,complement(w))*. % 300.04/300.42 140815[0:Res:35124.1,11848.0] || member(u,universal_class) subclass(union(v,w),x)* well_ordering(universal_class,x) -> member(u,complement(v))*. % 300.04/300.42 40928[2:Res:9765.3,36583.0] || connected(u,v) well_ordering(w,v) -> well_ordering(u,v) member(least(w,not_well_ordering(u,v)),universal_class)*. % 300.04/300.42 135723[8:Res:35220.2,83043.0] inductive(cantor(u)) || well_ordering(v,universal_class) subclass(universal_class,w) -> member(least(v,cantor(u)),w)*. % 300.04/300.42 158726[8:Rew:157842.0,82966.2] inductive(symmetric_difference(singleton_relation,u)) || well_ordering(v,universal_class) -> member(least(v,complement(complement(u))),complement(complement(u)))*. % 300.04/300.42 135706[2:Res:35220.2,4127.0] inductive(symmetric_difference(u,v)) || well_ordering(w,universal_class) -> member(least(w,symmetric_difference(u,v)),union(u,v))*. % 300.04/300.42 135727[2:Res:35220.2,897.0] inductive(restrict(u,v,w)) || well_ordering(x,universal_class) -> member(least(x,restrict(u,v,w)),u)*. % 300.04/300.42 148863[2:Res:35222.2,148647.0] inductive(complement(complement(u))) || well_ordering(v,complement(complement(u))) -> member(least(v,complement(complement(u))),u)*. % 300.04/300.42 136346[2:Res:35222.2,22.0] inductive(intersection(u,v)) || well_ordering(w,intersection(u,v)) -> member(least(w,intersection(u,v)),u)*. % 300.04/300.42 136347[2:Res:35222.2,23.0] inductive(intersection(u,v)) || well_ordering(w,intersection(u,v)) -> member(least(w,intersection(u,v)),v)*. % 300.04/300.42 166629[8:Res:166605.0,16455.1] || subclass(u,complement(inverse(singleton(not_subclass_element(u,v)))))* -> asymmetric(singleton(not_subclass_element(u,v)),w)* subclass(u,v). % 300.04/300.42 169557[19:Rew:166997.0,167389.1] || subclass(domain_relation,complement(compose(element_relation,universal_class)))* member(ordered_pair(ordinal_numbers,ordinal_numbers),element_relation) -> member(ordered_pair(ordinal_numbers,ordinal_numbers),u)*. % 300.04/300.42 169558[19:Rew:166997.0,167402.1] || subclass(domain_relation,complement(complement(unordered_pair(u,v))))* -> equal(ordered_pair(ordinal_numbers,ordinal_numbers),v) equal(ordered_pair(ordinal_numbers,ordinal_numbers),u). % 300.04/300.42 167548[19:Rew:166997.0,162723.0] || equal(u,singleton(ordinal_numbers)) subclass(u,v)* well_ordering(w,v)* -> member(least(w,u),u)*. % 300.04/300.42 167772[19:Rew:166997.0,163356.2] || subclass(omega,complement(compose(element_relation,universal_class)))* member(u,element_relation)* -> equal(integer_of(u),ordinal_numbers) member(u,v)*. % 300.04/300.42 167786[19:Rew:166997.0,94675.1] function(u) || -> equal(domain__dfg(u,image(inverse(u),singleton(single_valued1(u))),second(not_subclass_element(ordinal_numbers,ordinal_numbers))),single_valued3(u))**. % 300.04/300.42 167787[19:Rew:166997.0,94666.1] single_valued_class(u) || -> equal(domain__dfg(u,image(inverse(u),singleton(single_valued1(u))),second(not_subclass_element(ordinal_numbers,ordinal_numbers))),single_valued3(u))**. % 300.04/300.42 169569[19:Rew:166997.0,167953.2] || well_ordering(u,omega) -> equal(integer_of(v),ordinal_numbers) equal(segment(u,singleton(v),least(u,singleton(v))),ordinal_numbers)**. % 300.04/300.42 167968[19:Rew:166997.0,95522.1] function(u) || -> equal(domain__dfg(u,image(inverse(u),singleton(single_valued1(u))),range__dfg(ordinal_numbers,v,w)),single_valued3(u))**. % 300.04/300.42 167969[19:Rew:166997.0,95506.1] single_valued_class(u) || -> equal(domain__dfg(u,image(inverse(u),singleton(single_valued1(u))),range__dfg(ordinal_numbers,v,w)),single_valued3(u))**. % 300.04/300.42 169571[19:Rew:166997.0,167977.2] || subclass(universal_class,complement(intersection(u,v)))* member(ordinal_numbers,union(u,v)) -> member(ordinal_numbers,symmetric_difference(u,v)). % 300.04/300.42 168181[19:Rew:166997.0,99173.2] || subclass(u,v)* well_ordering(w,v)* -> equal(complement(complement(u)),ordinal_numbers) member(least(w,u),u)*. % 300.04/300.42 168470[19:Rew:166997.0,163653.1] || member(regular(intersection(u,intersection(v,w))),symmetric_difference(v,w))* -> equal(intersection(u,intersection(v,w)),ordinal_numbers). % 300.04/300.42 168475[19:Rew:166997.0,163535.1] || member(regular(intersection(intersection(u,v),w)),symmetric_difference(u,v))* -> equal(intersection(intersection(u,v),w),ordinal_numbers). % 300.04/300.42 168522[19:Rew:166997.0,80822.1] || well_ordering(u,v) -> equal(intersection(v,w),ordinal_numbers) member(least(u,intersection(v,w)),intersection(v,w))*. % 300.04/300.42 168580[19:Rew:166997.0,166140.1] single_valued_class(recursion(u,successor_relation,identity_relation)) || equal(recursion(u,successor_relation,ordinal_numbers),ordinal_numbers) -> member(ordinal_add(u,v),universal_class)*. % 300.04/300.42 168581[19:Rew:166997.0,99328.1] single_valued_class(recursion(u,successor_relation,union_of_range_map)) || equal(recursion(u,successor_relation,ordinal_numbers),ordinal_numbers) -> member(ordinal_add(u,v),universal_class)*. % 300.04/300.42 168583[19:Rew:166997.0,95613.2] || well_ordering(u,complement(v))* -> member(w,v)* equal(segment(u,singleton(w),least(u,singleton(w))),ordinal_numbers)**. % 300.04/300.42 168585[19:Rew:166997.0,80848.0] || -> equal(intersection(symmetric_difference(u,inverse(u)),v),ordinal_numbers) member(regular(intersection(symmetric_difference(u,inverse(u)),v)),symmetrization_of(u))*. % 300.04/300.42 168587[19:Rew:166997.0,80850.0] || -> equal(intersection(u,symmetric_difference(v,inverse(v))),ordinal_numbers) member(regular(intersection(u,symmetric_difference(v,inverse(v)))),symmetrization_of(v))*. % 300.04/300.42 168590[19:Rew:166997.0,80858.1] || well_ordering(u,universal_class) -> equal(restrict(v,w,x),ordinal_numbers) member(least(u,restrict(v,w,x)),v)*. % 300.04/300.42 168595[19:Rew:166997.0,80863.1] || well_ordering(u,v) -> equal(intersection(w,v),ordinal_numbers) member(least(u,intersection(w,v)),intersection(w,v))*. % 300.04/300.42 168597[19:Rew:166997.0,80866.1] || well_ordering(u,union(v,w)) -> equal(segment(u,symmetric_difference(v,w),least(u,symmetric_difference(v,w))),ordinal_numbers)**. % 300.04/300.42 168598[19:Rew:166997.0,80867.2] || member(u,v)* well_ordering(w,v)* -> equal(segment(w,singleton(u),least(w,singleton(u))),ordinal_numbers)**. % 300.04/300.42 168599[19:Rew:166997.0,80868.1] || well_ordering(u,v) -> equal(segment(u,restrict(v,w,x),least(u,restrict(v,w,x))),ordinal_numbers)**. % 300.04/300.42 168613[19:Rew:166997.0,80885.2] || subclass(u,v)* well_ordering(w,v)* -> equal(intersection(x,u),ordinal_numbers)** member(least(w,u),u)*. % 300.04/300.42 168614[19:Rew:166997.0,80886.2] || subclass(u,v)* well_ordering(w,v)* -> equal(intersection(u,x),ordinal_numbers)** member(least(w,u),u)*. % 300.04/300.42 168864[19:Rew:166997.0,162041.1] || well_ordering(u,v) -> equal(complement(complement(v)),ordinal_numbers) member(least(u,complement(complement(v))),complement(complement(v)))*. % 300.04/300.42 168918[19:Rew:166997.0,163404.1] || subclass(omega,compose_class(u)) -> equal(integer_of(singleton(singleton(singleton(v)))),ordinal_numbers)** equal(compose(u,singleton(v)),v)**. % 300.04/300.42 168921[19:Rew:166997.0,163438.2] || subclass(omega,u) subclass(v,complement(u))* -> equal(integer_of(not_subclass_element(v,w)),ordinal_numbers)** subclass(v,w). % 300.04/300.42 168922[19:Rew:166997.0,163441.3] || subclass(omega,u) member(v,universal_class) subclass(universal_class,complement(u))* -> equal(integer_of(sum_class(v)),ordinal_numbers)**. % 300.04/300.42 168923[19:Rew:166997.0,163442.3] || subclass(omega,u) member(v,universal_class) subclass(universal_class,complement(u))* -> equal(integer_of(power_class(v)),ordinal_numbers)**. % 300.04/300.42 168979[19:Rew:166997.0,165126.2] || subclass(inverse(u),u)* asymmetric(u,singleton(v)) -> equal(segment(inverse(u),singleton(v),v),ordinal_numbers)**. % 300.04/300.42 169020[19:Rew:166997.0,163958.2] || well_ordering(u,universal_class) subclass(universal_class,v) -> equal(cantor(w),ordinal_numbers) member(least(u,cantor(w)),v)*. % 300.04/300.42 169055[19:Rew:166997.0,165945.0] || equal(sum_class(singleton(u)),ordinal_numbers) -> subclass(sum_class(singleton(u)),v) equal(not_subclass_element(sum_class(singleton(u)),v),u)**. % 300.04/300.42 169658[19:MRR:169172.4,167057.0] || subclass(cross_product(u,v),ordinal_numbers)* member(w,v)* member(x,u)* well_ordering(y,kind_1_ordinals)* -> . % 300.04/300.42 169659[19:MRR:169174.4,167057.0] || subclass(intersection(u,v),ordinal_numbers)* member(w,v)* member(w,u)* well_ordering(x,kind_1_ordinals)* -> . % 300.04/300.42 174495[19:Res:167727.3,148647.0] || member(u,universal_class) subclass(u,complement(complement(v))) -> equal(u,ordinal_numbers) member(apply(choice,u),v)*. % 300.04/300.42 169577[19:Rew:166997.0,168073.1] || member(u,universal_class) -> member(u,intersection(complement(v),symmetrization_of(ordinal_numbers)))* member(u,union(v,complement(inverse(ordinal_numbers)))). % 300.04/300.42 169576[19:Rew:166997.0,168070.1] || member(u,universal_class) -> member(u,intersection(symmetrization_of(ordinal_numbers),complement(v)))* member(u,union(complement(inverse(ordinal_numbers)),v)). % 300.04/300.42 174521[19:Res:167727.3,169207.0] || member(u,universal_class) subclass(u,symmetrization_of(ordinal_numbers)) -> equal(u,ordinal_numbers) member(apply(choice,u),inverse(ordinal_numbers))*. % 300.04/300.42 169574[19:Rew:166997.0,168043.1] || member(u,symmetric_difference(complement(v),power_class(complement(inverse(ordinal_numbers)))))* -> member(u,union(v,image(element_relation,symmetrization_of(ordinal_numbers)))). % 300.04/300.42 169573[19:Rew:166997.0,168042.1] || member(u,symmetric_difference(power_class(complement(inverse(ordinal_numbers))),complement(v)))* -> member(u,union(image(element_relation,symmetrization_of(ordinal_numbers)),v)). % 300.04/300.42 169572[19:Rew:166997.0,168025.0] || member(not_subclass_element(power_class(complement(inverse(ordinal_numbers))),u),image(element_relation,symmetrization_of(ordinal_numbers)))* -> subclass(power_class(complement(inverse(ordinal_numbers))),u). % 300.04/300.42 168131[19:Rew:166997.0,166900.0] || -> subclass(complement(symmetrization_of(image(element_relation,symmetrization_of(ordinal_numbers)))),intersection(power_class(complement(inverse(ordinal_numbers))),complement(inverse(image(element_relation,symmetrization_of(ordinal_numbers))))))*. % 300.04/300.42 168128[19:Rew:166997.0,166898.0] || -> subclass(complement(successor(image(element_relation,symmetrization_of(ordinal_numbers)))),intersection(power_class(complement(inverse(ordinal_numbers))),complement(singleton(image(element_relation,symmetrization_of(ordinal_numbers))))))*. % 300.04/300.42 169566[19:Rew:166997.0,167600.0] || member(ordered_pair(u,v),compose(w,ordinal_numbers))* subclass(image(w,range_of(ordinal_numbers)),x)* -> member(v,x)*. % 300.04/300.42 176101[20:Res:175613.1,82995.1] || subclass(universal_class,complement(compose(element_relation,universal_class)))* member(regular(symmetrization_of(ordinal_numbers)),element_relation) -> member(regular(symmetrization_of(ordinal_numbers)),u)*. % 300.04/300.42 176146[0:Res:9914.3,6476.1] || member(u,universal_class)* member(v,universal_class)* equal(successor(v),u)* subclass(universal_class,complement(successor_relation))* -> . % 300.04/300.42 176263[19:Rew:176206.1,164746.2] || member(u,universal_class) subclass(domain_relation,intersection(v,w)) member(ordered_pair(u,ordinal_numbers),symmetric_difference(v,w))* -> . % 300.04/300.42 177180[22:Res:177171.1,7963.1] || subclass(omega,complement(intersection(u,v)))* member(ordinal_numbers,union(u,v)) -> member(ordinal_numbers,symmetric_difference(u,v)). % 300.04/300.42 177447[20:Res:175569.0,168644.0] || subclass(universal_class,u) well_ordering(omega,u)* -> equal(integer_of(ordered_pair(regular(symmetrization_of(ordinal_numbers)),least(omega,universal_class))),ordinal_numbers)**. % 300.04/300.42 177462[19:Res:167117.0,168644.0] || subclass(domain_relation,u) well_ordering(omega,u)* -> equal(integer_of(ordered_pair(ordered_pair(ordinal_numbers,ordinal_numbers),least(omega,domain_relation))),ordinal_numbers)**. % 300.04/300.42 177487[19:Res:167277.0,168644.0] || subclass(singleton(ordinal_numbers),u)* well_ordering(omega,u) -> equal(integer_of(ordered_pair(ordinal_numbers,least(omega,singleton(ordinal_numbers)))),ordinal_numbers)**. % 300.04/300.42 177577[19:Res:168642.2,36583.0] || well_ordering(u,cross_product(universal_class,universal_class)) -> equal(compose(v,w),ordinal_numbers) member(least(u,compose(v,w)),universal_class)*. % 300.04/300.42 178275[22:Res:7968.2,177998.1] || member(ordinal_numbers,cross_product(u,v)) member(ordinal_numbers,w) equal(complement(restrict(w,u,v)),omega)** -> . % 300.04/300.42 178281[22:Res:59.1,177998.1] || member(ordered_pair(u,ordinal_numbers),compose(v,w)) equal(complement(image(v,image(w,singleton(u)))),omega)** -> . % 300.04/300.42 178914[22:Res:178902.1,7963.1] || equal(complement(intersection(u,v)),omega) member(ordinal_numbers,union(u,v)) -> member(ordinal_numbers,symmetric_difference(u,v))*. % 300.04/300.42 180197[19:Rew:180089.0,169559.0] || member(not_subclass_element(power_class(complement(singleton(ordinal_numbers))),u),image(element_relation,singleton(ordinal_numbers)))* -> subclass(power_class(complement(singleton(ordinal_numbers))),u). % 300.04/300.42 180239[19:Rew:180089.0,179091.0] || -> subclass(complement(successor(image(element_relation,singleton(ordinal_numbers)))),intersection(power_class(complement(singleton(ordinal_numbers))),complement(singleton(image(element_relation,singleton(ordinal_numbers))))))*. % 300.04/300.42 180242[19:Rew:180089.0,179093.0] || -> subclass(complement(symmetrization_of(image(element_relation,singleton(ordinal_numbers)))),intersection(power_class(complement(singleton(ordinal_numbers))),complement(inverse(image(element_relation,singleton(ordinal_numbers))))))*. % 300.04/300.42 180249[19:Rew:180089.0,179159.1] || member(u,symmetric_difference(power_class(complement(singleton(ordinal_numbers))),complement(v)))* -> member(u,union(image(element_relation,singleton(ordinal_numbers)),v)). % 300.04/300.42 180253[19:Rew:180089.0,179162.1] || member(u,symmetric_difference(complement(v),power_class(complement(singleton(ordinal_numbers)))))* -> member(u,union(v,image(element_relation,singleton(ordinal_numbers)))). % 300.04/300.42 180325[19:Rew:180089.0,169561.1] || member(u,universal_class) -> member(u,intersection(singleton(ordinal_numbers),complement(v)))* member(u,union(complement(singleton(ordinal_numbers)),v)). % 300.04/300.42 181008[19:SpR:167783.1,167785.2] function(u) || member(v,universal_class) -> member(v,cantor(w)) equal(single_valued2(u),range__dfg(w,v,universal_class))*. % 300.04/300.42 181015[19:SpR:167784.1,167785.2] single_valued_class(u) || member(v,universal_class) -> member(v,cantor(w)) equal(single_valued2(u),range__dfg(w,v,universal_class))*. % 300.04/300.42 181278[19:SpR:168752.1,14.0] || member(u,universal_class) -> equal(unordered_pair(ordinal_numbers,unordered_pair(sum_class(range_of(u)),singleton(v))),ordered_pair(sum_class(range_of(u)),v))**. % 300.04/300.42 181315[19:SpR:17187.0,168752.1] || member(restrict(cross_product(u,universal_class),v,w),universal_class)* -> equal(singleton(sum_class(image(cross_product(v,w),u))),ordinal_numbers). % 300.04/300.42 181357[19:SpL:168752.1,167253.1] || member(u,universal_class) member(sum_class(range_of(u)),cantor(v))* equal(restrict(v,ordinal_numbers,universal_class),ordinal_numbers) -> . % 300.04/300.42 181433[19:SpR:17187.0,168753.1] || member(restrict(cross_product(u,universal_class),v,w),universal_class)* -> equal(integer_of(sum_class(image(cross_product(v,w),u))),ordinal_numbers). % 300.04/300.42 181507[19:Res:169234.0,42071.0] || -> subclass(singleton(not_subclass_element(u,intersection(complement(inverse(ordinal_numbers)),u))),symmetrization_of(ordinal_numbers))* subclass(u,intersection(complement(inverse(ordinal_numbers)),u)). % 300.04/300.42 181722[20:Res:175570.1,82994.1] || subclass(inverse(ordinal_numbers),complement(compose(element_relation,universal_class)))* member(regular(symmetrization_of(ordinal_numbers)),element_relation) well_ordering(u,v)* -> . % 300.04/300.42 181728[20:Res:175570.1,126.0] || subclass(inverse(ordinal_numbers),u) subclass(u,v)* well_ordering(w,v)* -> member(least(w,u),u)*. % 300.04/300.42 181778[19:SpL:17187.0,176272.1] || member(restrict(cross_product(u,universal_class),v,w),universal_class)* equal(sum_class(image(cross_product(v,w),u)),ordinal_numbers) -> . % 300.04/300.42 181783[19:Res:176345.1,82994.1] || subclass(domain_relation,complement(compose(element_relation,universal_class))) member(singleton(singleton(singleton(ordinal_numbers))),element_relation)* well_ordering(u,v)* -> . % 300.04/300.42 181801[19:Res:176345.1,9.0] || subclass(domain_relation,unordered_pair(u,v))* -> equal(singleton(singleton(singleton(ordinal_numbers))),v) equal(singleton(singleton(singleton(ordinal_numbers))),u). % 300.04/300.42 182314[18:SpL:16826.0,178139.1] || member(intersection(complement(u),complement(singleton(u))),universal_class)* equal(rest_of(complement(image(element_relation,successor(u)))),rest_relation) -> . % 300.04/300.42 182315[18:SpL:16825.0,178139.1] || member(intersection(complement(u),complement(inverse(u))),universal_class)* equal(rest_of(complement(image(element_relation,symmetrization_of(u)))),rest_relation) -> . % 300.04/300.42 182335[22:SpL:479.0,178289.1] || equal(image(element_relation,union(u,v)),singleton(ordinal_numbers)) equal(power_class(intersection(complement(u),complement(v))),omega)** -> . % 300.04/300.42 182435[19:Res:59.1,182393.0] || member(ordered_pair(u,singleton(ordinal_numbers)),compose(v,w)) well_ordering(universal_class,image(v,image(w,singleton(u))))* -> . % 300.04/300.42 182775[22:SpL:479.0,180881.1] || equal(image(element_relation,union(u,v)),omega) equal(power_class(intersection(complement(u),complement(v))),singleton(ordinal_numbers))** -> . % 300.04/300.42 182903[20:Res:181635.1,82994.1] || subclass(symmetrization_of(ordinal_numbers),complement(compose(element_relation,universal_class)))* member(regular(symmetrization_of(ordinal_numbers)),element_relation) well_ordering(u,v)* -> . % 300.04/300.42 182909[20:Res:181635.1,126.0] || subclass(symmetrization_of(ordinal_numbers),u) subclass(u,v)* well_ordering(w,v)* -> member(least(w,u),u)*. % 300.04/300.42 183083[19:Res:182463.1,82994.1] || equal(complement(compose(element_relation,universal_class)),singleton(singleton(ordinal_numbers)))** member(singleton(ordinal_numbers),element_relation) well_ordering(u,v)* -> . % 300.04/300.42 183084[19:Res:182463.1,82995.1] || equal(complement(compose(element_relation,universal_class)),singleton(singleton(ordinal_numbers)))** member(singleton(ordinal_numbers),element_relation) -> member(singleton(ordinal_numbers),u)*. % 300.04/300.42 183102[19:Res:182463.1,18.0] || equal(cross_product(u,v),singleton(singleton(ordinal_numbers)))** -> equal(ordered_pair(first(singleton(ordinal_numbers)),second(singleton(ordinal_numbers))),singleton(ordinal_numbers))**. % 300.04/300.42 183583[19:Res:168184.0,16910.0] || -> equal(complement(complement(symmetric_difference(u,inverse(u)))),ordinal_numbers) member(regular(complement(complement(symmetric_difference(u,inverse(u))))),symmetrization_of(u))*. % 300.04/300.42 184055[23:Rew:183840.0,183892.0] || member(restrict(u,v,ordinal_numbers),universal_class) -> member(ordered_pair(restrict(u,v,ordinal_numbers),segment(u,v,universal_class)),domain_relation)*. % 300.04/300.42 184255[23:SpR:183885.0,79961.2] || member(image(u,ordinal_numbers),universal_class)* subclass(universal_class,omega) -> equal(integer_of(apply(u,universal_class)),apply(u,universal_class)). % 300.04/300.42 184825[19:SpR:168412.1,176419.1] || subclass(domain_relation,flip(u)) -> equal(cross_product(v,w),ordinal_numbers) member(ordered_pair(regular(cross_product(v,w)),ordinal_numbers),u)*. % 300.04/300.42 184836[19:Res:176419.1,126.0] || subclass(domain_relation,flip(u)) subclass(u,v)* well_ordering(w,v)* -> member(least(w,u),u)*. % 300.04/300.42 184847[19:Res:176419.1,16102.0] || subclass(domain_relation,flip(symmetric_difference(complement(u),complement(v)))) -> member(ordered_pair(ordered_pair(w,x),ordinal_numbers),union(u,v))*. % 300.04/300.42 184914[19:Res:176420.1,126.0] || subclass(domain_relation,rotate(u)) subclass(u,v)* well_ordering(w,v)* -> member(least(w,u),u)*. % 300.04/300.42 184925[19:Res:176420.1,16102.0] || subclass(domain_relation,rotate(symmetric_difference(complement(u),complement(v)))) -> member(ordered_pair(ordered_pair(w,ordinal_numbers),x),union(u,v))*. % 300.04/300.42 185095[19:Res:9820.1,167739.0] || equal(sum_class(singleton(u)),singleton(u)) -> equal(sum_class(singleton(u)),ordinal_numbers) equal(regular(sum_class(singleton(u))),u)**. % 300.04/300.42 185251[19:Res:168252.2,148647.0] || well_ordering(u,complement(complement(v))) -> equal(complement(complement(v)),ordinal_numbers) member(least(u,complement(complement(v))),v)*. % 300.04/300.42 185259[19:Res:168252.2,22.0] || well_ordering(u,intersection(v,w)) -> equal(intersection(v,w),ordinal_numbers) member(least(u,intersection(v,w)),v)*. % 300.04/300.42 185260[19:Res:168252.2,23.0] || well_ordering(u,intersection(v,w)) -> equal(intersection(v,w),ordinal_numbers) member(least(u,intersection(v,w)),w)*. % 300.04/300.42 185341[19:MRR:185337.2,166995.0] || well_ordering(u,v) subclass(singleton(least(u,v)),v) -> section(u,singleton(least(u,v)),v)*. % 300.04/300.42 185744[19:SpL:479.0,185656.1] || equal(flip(image(element_relation,union(u,v))),domain_relation) subclass(universal_class,power_class(intersection(complement(u),complement(v))))* -> . % 300.04/300.42 185765[19:SpL:479.0,185733.1] || equal(rotate(image(element_relation,union(u,v))),domain_relation) subclass(universal_class,power_class(intersection(complement(u),complement(v))))* -> . % 300.04/300.42 186389[19:SpL:27.0,167960.0] || subclass(omega,union(u,v)) member(w,intersection(complement(u),complement(v)))* -> equal(integer_of(w),ordinal_numbers). % 300.04/300.42 186396[19:SpL:167200.0,167960.0] || subclass(omega,power_class(complement(inverse(ordinal_numbers)))) member(u,image(element_relation,symmetrization_of(ordinal_numbers)))* -> equal(integer_of(u),ordinal_numbers). % 300.04/300.42 186397[19:SpL:180125.0,167960.0] || subclass(omega,power_class(complement(singleton(ordinal_numbers)))) member(u,image(element_relation,singleton(ordinal_numbers)))* -> equal(integer_of(u),ordinal_numbers). % 300.04/300.42 186406[19:SpR:17187.0,168950.1] || member(restrict(cross_product(u,universal_class),v,w),universal_class) -> member(ordinal_numbers,ordered_pair(image(cross_product(v,w),u),x))*. % 300.04/300.42 186951[19:Res:4126.1,167734.1] || member(regular(u),symmetric_difference(v,w)) subclass(u,complement(complement(intersection(v,w))))* -> equal(u,ordinal_numbers). % 300.04/300.42 186997[20:Rew:186971.2,182904.2] || subclass(symmetrization_of(ordinal_numbers),complement(compose(element_relation,universal_class)))* member(regular(symmetrization_of(ordinal_numbers)),element_relation) -> member(regular(ordinal_numbers),u)*. % 300.04/300.42 187079[19:Obv:187044.2] || subclass(intersection(u,singleton(v)),complement(w))* member(v,w) -> equal(intersection(u,singleton(v)),ordinal_numbers). % 300.04/300.42 187198[19:Obv:187158.2] || subclass(intersection(singleton(u),v),complement(w))* member(u,w) -> equal(intersection(singleton(u),v),ordinal_numbers). % 300.04/300.42 187462[19:SpL:479.0,186994.0] || subclass(singleton(ordinal_numbers),power_class(intersection(complement(u),complement(v))))* member(ordinal_numbers,image(element_relation,union(u,v))) -> . % 300.04/300.42 187594[20:SpL:479.0,186995.1] || subclass(universal_class,image(element_relation,union(u,v))) subclass(symmetrization_of(ordinal_numbers),power_class(intersection(complement(u),complement(v))))* -> . % 300.04/300.42 187838[19:Res:168350.1,158.0] || -> equal(restrict(omega,u,v),ordinal_numbers) equal(integer_of(regular(restrict(omega,u,v))),regular(restrict(omega,u,v)))**. % 300.04/300.42 187887[19:SpR:167458.0,176367.1] || member(intersection(complement(singleton(ordinal_numbers)),complement(image(successor_relation,ordinal_numbers))),universal_class)* -> equal(cantor(complement(image(element_relation,kind_1_ordinals))),ordinal_numbers). % 300.04/300.42 188228[19:Obv:188212.2] || subclass(omega,u) subclass(complement(u),omega)* -> equal(complement(u),ordinal_numbers) equal(regular(complement(u)),ordinal_numbers). % 300.04/300.42 188367[19:Res:176321.2,2.0] || member(u,universal_class) equal(successor(u),ordinal_numbers) subclass(successor_relation,v) -> member(ordered_pair(u,ordinal_numbers),v)*. % 300.04/300.42 188640[2:Res:7968.2,188593.1] || member(u,cross_product(v,w))* member(u,x)* equal(complement(restrict(x,v,w)),universal_class)** -> . % 300.04/300.42 188685[2:Res:9765.3,188593.1] || connected(u,v) well_ordering(w,v)* equal(complement(not_well_ordering(u,v)),universal_class)** -> well_ordering(u,v). % 300.04/300.42 188723[2:Res:9914.3,188593.1] || member(u,universal_class)* member(v,universal_class)* equal(successor(v),u)* equal(complement(successor_relation),universal_class) -> . % 300.04/300.42 188755[2:Res:59.1,188593.1] || member(ordered_pair(u,v),compose(w,x))* equal(complement(image(w,image(x,singleton(u)))),universal_class)** -> . % 300.04/300.42 189105[2:Res:188649.1,9773.1] || equal(complement(segment(u,v,w)),universal_class)** subclass(singleton(w),v) -> section(u,singleton(w),v). % 300.04/300.42 190210[19:Res:147404.1,168418.0] || member(regular(intersection(u,complement(compose(element_relation,universal_class)))),element_relation)* -> equal(intersection(u,complement(compose(element_relation,universal_class))),ordinal_numbers). % 300.04/300.42 190217[19:Res:167339.2,168418.0] || subclass(omega,u) -> equal(integer_of(regular(intersection(v,complement(u)))),ordinal_numbers)** equal(intersection(v,complement(u)),ordinal_numbers). % 300.04/300.42 190320[19:MRR:190202.0,167137.1] || -> member(regular(intersection(u,complement(union(v,w)))),complement(w))* equal(intersection(u,complement(union(v,w))),ordinal_numbers). % 300.04/300.42 190321[19:MRR:190201.0,167137.1] || -> member(regular(intersection(u,complement(union(v,w)))),complement(v))* equal(intersection(u,complement(union(v,w))),ordinal_numbers). % 300.04/300.42 190655[19:Res:147404.1,168419.0] || member(regular(intersection(complement(compose(element_relation,universal_class)),u)),element_relation)* -> equal(intersection(complement(compose(element_relation,universal_class)),u),ordinal_numbers). % 300.04/300.42 190662[19:Res:167339.2,168419.0] || subclass(omega,u) -> equal(integer_of(regular(intersection(complement(u),v))),ordinal_numbers)** equal(intersection(complement(u),v),ordinal_numbers). % 300.04/300.42 190706[19:MRR:190647.0,167137.1] || -> member(regular(intersection(complement(union(u,v)),w)),complement(v))* equal(intersection(complement(union(u,v)),w),ordinal_numbers). % 300.04/300.42 190707[19:MRR:190646.0,167137.1] || -> member(regular(intersection(complement(union(u,v)),w)),complement(u))* equal(intersection(complement(union(u,v)),w),ordinal_numbers). % 300.04/300.42 191024[19:SpR:149179.0,168353.1] || -> equal(symmetric_difference(u,intersection(u,v)),ordinal_numbers) member(regular(symmetric_difference(u,intersection(u,v))),complement(intersection(u,v)))*. % 300.04/300.42 191025[19:SpR:149318.0,168353.1] || -> equal(symmetric_difference(u,intersection(v,u)),ordinal_numbers) member(regular(symmetric_difference(u,intersection(v,u))),complement(intersection(v,u)))*. % 300.04/300.42 191085[19:Res:168353.1,2.0] || subclass(complement(intersection(u,v)),w) -> equal(symmetric_difference(u,v),ordinal_numbers) member(regular(symmetric_difference(u,v)),w)*. % 300.04/300.42 192070[19:Rew:114.0,192038.1,27.0,192038.1,114.0,192038.0,27.0,192038.0] || member(regular(image(element_relation,symmetrization_of(u))),complement(image(element_relation,symmetrization_of(u))))* -> equal(image(element_relation,symmetrization_of(u)),ordinal_numbers). % 300.04/300.42 192071[19:Rew:44.0,192037.1,27.0,192037.1,44.0,192037.0,27.0,192037.0] || member(regular(image(element_relation,successor(u))),complement(image(element_relation,successor(u))))* -> equal(image(element_relation,successor(u)),ordinal_numbers). % 300.04/300.42 192239[19:SpR:192178.0,6521.3] function(complement(cross_product(u,universal_class))) || member(u,universal_class)* subclass(universal_class,v) -> member(range_of(ordinal_numbers),v)*. % 300.04/300.42 192242[19:SpR:192178.0,59.1] || member(ordered_pair(u,v),compose(w,complement(cross_product(singleton(u),universal_class))))* -> member(v,image(w,range_of(ordinal_numbers))). % 300.04/300.42 192247[19:SpR:192178.0,59.1] || member(ordered_pair(u,v),compose(complement(cross_product(image(w,singleton(u)),universal_class)),w))* -> member(v,range_of(ordinal_numbers)). % 300.04/300.42 192337[19:Res:167727.3,192214.0] || member(u,universal_class) subclass(u,cantor(complement(cross_product(singleton(apply(choice,u)),universal_class))))* -> equal(u,ordinal_numbers). % 300.04/300.42 192339[19:Res:6521.3,192214.0] function(u) || member(v,universal_class) subclass(universal_class,cantor(complement(cross_product(singleton(image(u,v)),universal_class))))* -> . % 300.04/300.42 192968[25:Rew:192881.1,176487.2] function(u) || subclass(range_of(u),ordinal_numbers) equal(cantor(cantor(v)),universal_class) -> compatible(u,v,omega)*. % 300.04/300.42 192969[25:Rew:192881.1,168640.2] function(u) || equal(range_of(u),ordinal_numbers) equal(cantor(cantor(v)),universal_class) -> compatible(u,v,w)*. % 300.04/300.42 192970[25:Rew:192881.1,169599.2] function(u) || subclass(range_of(u),ordinal_numbers) equal(cantor(cantor(v)),universal_class) -> compatible(u,v,ordinal_numbers)*. % 300.04/300.42 193084[25:Rew:192881.1,192892.2] function(range_of(u)) function(v) || equal(cantor(cantor(w)),universal_class) -> compatible(v,w,inverse(u))*. % 300.04/300.42 193200[25:SpL:192881.1,124906.1] function(restrict(u,v,w)) || subclass(w,v) subclass(universal_class,w) -> section(u,w,v)*. % 300.04/300.42 193306[25:SpR:193223.1,59.1] function(u) || member(ordered_pair(u,v),compose(w,x))* -> member(v,image(w,image(x,ordinal_numbers))). % 300.04/300.42 193939[25:SpR:168412.1,193300.1] function(first(regular(cross_product(u,v)))) || -> equal(cross_product(u,v),ordinal_numbers) member(ordinal_numbers,regular(cross_product(u,v)))*. % 300.04/300.42 194028[19:MRR:193989.2,36583.1] || member(u,cantor(v)) equal(restrict(v,u,universal_class),ordinal_numbers)** subclass(domain_relation,complement(rest_of(v)))* -> . % 300.04/300.42 194333[25:SoR:193813.0,12322.2] single_valued_class(apply(choice,omega)) || equal(apply(choice,omega),cross_product(universal_class,universal_class))** -> equal(apply(choice,omega),ordinal_numbers). % 300.04/300.42 194373[19:SpR:125772.0,167580.1] || member(u,universal_class) -> member(u,sum_class(v)) equal(apply(restrict(element_relation,universal_class,v),u),sum_class(range_of(ordinal_numbers)))**. % 300.04/300.42 194375[19:SpR:125707.0,167580.1] || member(u,universal_class) -> member(u,inverse(v)) equal(apply(flip(cross_product(v,universal_class)),u),sum_class(range_of(ordinal_numbers)))**. % 300.04/300.42 194458[19:MRR:194419.0,57.1] || member(u,universal_class) subclass(universal_class,complement(cantor(v)))* -> equal(apply(v,power_class(u)),sum_class(range_of(ordinal_numbers)))**. % 300.04/300.42 194459[19:MRR:194418.0,55.1] || member(u,universal_class) subclass(universal_class,complement(cantor(v)))* -> equal(apply(v,sum_class(u)),sum_class(range_of(ordinal_numbers)))**. % 300.04/300.42 194460[19:MRR:194414.0,36682.1] || subclass(u,complement(cantor(v))) -> equal(apply(v,not_subclass_element(u,w)),sum_class(range_of(ordinal_numbers)))** subclass(u,w). % 300.04/300.42 194463[19:MRR:194415.0,36682.1] || -> equal(apply(u,not_subclass_element(v,intersection(cantor(u),v))),sum_class(range_of(ordinal_numbers)))** subclass(v,intersection(cantor(u),v)). % 300.04/300.42 194764[19:SpL:160.0,176243.1] || member(u,universal_class) subclass(domain_relation,symmetric_difference(v,w)) -> member(ordered_pair(u,ordinal_numbers),complement(intersection(v,w)))*. % 300.04/300.42 195108[25:SpR:193305.1,17.2] function(u) || member(u,v)* member(ordinal_numbers,w) -> member(singleton(singleton(ordinal_numbers)),cross_product(w,v))*. % 300.04/300.42 195209[19:SpL:479.0,194013.1] || subclass(domain_relation,rotate(image(element_relation,union(u,v)))) subclass(domain_relation,power_class(intersection(complement(u),complement(v))))* -> . % 300.04/300.42 195222[25:SpR:193305.1,27190.1] function(u) || subclass(rest_relation,flip(v)) -> member(ordered_pair(ordered_pair(u,ordinal_numbers),rest_of(singleton(singleton(ordinal_numbers)))),v)*. % 300.04/300.42 195230[25:SpR:193305.1,27190.1] function(u) || subclass(rest_relation,flip(v)) -> member(ordered_pair(singleton(singleton(ordinal_numbers)),rest_of(ordered_pair(u,ordinal_numbers))),v)*. % 300.04/300.42 195244[0:Res:27190.1,126.0] || subclass(rest_relation,flip(u)) subclass(u,v)* well_ordering(w,v)* -> member(least(w,u),u)*. % 300.04/300.42 195268[0:Res:27190.1,897.0] || subclass(rest_relation,flip(restrict(u,v,w)))* -> member(ordered_pair(ordered_pair(x,y),rest_of(ordered_pair(y,x))),u)*. % 300.04/300.42 195272[0:Res:27190.1,110865.0] || subclass(rest_relation,flip(rest_of(ordered_pair(ordered_pair(u,v),rest_of(ordered_pair(v,u))))))* subclass(universal_class,complement(element_relation)) -> . % 300.04/300.42 195294[12:Res:27190.1,99365.1] || 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)))** -> . % 300.04/300.42 195324[25:SpR:193305.1,27189.1] function(u) || subclass(rest_relation,rotate(v)) -> member(ordered_pair(ordered_pair(u,rest_of(singleton(singleton(ordinal_numbers)))),ordinal_numbers),v)*. % 300.04/300.42 195331[25:SpR:193305.1,27189.1] function(rest_of(ordered_pair(u,ordinal_numbers))) || subclass(rest_relation,rotate(v)) -> member(ordered_pair(singleton(singleton(ordinal_numbers)),u),v)*. % 300.04/300.42 195341[0:Res:27189.1,126.0] || subclass(rest_relation,rotate(u)) subclass(u,v)* well_ordering(w,v)* -> member(least(w,u),u)*. % 300.04/300.42 195365[0:Res:27189.1,897.0] || subclass(rest_relation,rotate(restrict(u,v,w)))* -> member(ordered_pair(ordered_pair(x,rest_of(ordered_pair(y,x))),y),u)*. % 300.04/300.42 195369[0:Res:27189.1,110865.0] || subclass(rest_relation,rotate(rest_of(ordered_pair(ordered_pair(u,rest_of(ordered_pair(v,u))),v))))* subclass(universal_class,complement(element_relation)) -> . % 300.04/300.42 195391[12:Res:27189.1,99365.1] || 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)** -> . % 300.04/300.42 195510[19:Res:168374.2,5467.1] || subclass(omega,symmetric_difference(u,v)) subclass(universal_class,complement(union(u,v)))* -> equal(integer_of(singleton(w)),ordinal_numbers)**. % 300.04/300.42 195554[19:SpL:479.0,194014.1] || subclass(domain_relation,flip(image(element_relation,union(u,v)))) subclass(domain_relation,power_class(intersection(complement(u),complement(v))))* -> . % 300.04/300.42 195728[19:SpL:479.0,195630.1] || equal(rotate(image(element_relation,union(u,v))),domain_relation) equal(power_class(intersection(complement(u),complement(v))),domain_relation)** -> . % 300.04/300.42 195741[0:SpL:479.0,195635.1] || equal(flip(image(element_relation,union(u,v))),rest_relation) subclass(universal_class,power_class(intersection(complement(u),complement(v))))* -> . % 300.04/300.42 195809[19:Res:182871.1,16224.0] || member(not_subclass_element(intersection(complement(symmetrization_of(ordinal_numbers)),u),v),inverse(ordinal_numbers))* -> subclass(intersection(complement(symmetrization_of(ordinal_numbers)),u),v). % 300.04/300.42 195918[0:SpL:479.0,195669.1] || equal(rotate(image(element_relation,union(u,v))),rest_relation) subclass(universal_class,power_class(intersection(complement(u),complement(v))))* -> . % 300.04/300.42 195993[19:Res:182871.1,16351.0] || member(not_subclass_element(intersection(u,complement(symmetrization_of(ordinal_numbers))),v),inverse(ordinal_numbers))* -> subclass(intersection(u,complement(symmetrization_of(ordinal_numbers))),v). % 300.04/300.42 196059[19:SpL:479.0,195678.1] || equal(rotate(image(element_relation,union(u,v))),rest_relation) subclass(domain_relation,power_class(intersection(complement(u),complement(v))))* -> . % 300.04/300.42 196078[19:SpL:479.0,195719.1] || equal(flip(image(element_relation,union(u,v))),domain_relation) equal(power_class(intersection(complement(u),complement(v))),domain_relation)** -> . % 300.04/300.42 196091[19:SpL:479.0,196068.0] || equal(power_class(intersection(complement(u),complement(v))),domain_relation)** equal(rotate(image(element_relation,union(u,v))),rest_relation) -> . % 300.04/300.42 196630[19:Res:9820.1,167728.0] || equal(sum_class(u),u) subclass(u,v) -> equal(sum_class(u),ordinal_numbers) member(regular(sum_class(u)),v)*. % 300.04/300.42 196642[19:Res:16650.0,167728.0] || subclass(symmetrization_of(u),v) -> equal(symmetric_difference(u,inverse(u)),ordinal_numbers) member(regular(symmetric_difference(u,inverse(u))),v)*. % 300.04/300.42 196674[19:Res:49.1,167728.0] inductive(u) || subclass(u,v) -> equal(image(successor_relation,u),ordinal_numbers) member(regular(image(successor_relation,u)),v)*. % 300.04/300.42 196709[20:Rew:167222.1,196668.2] || subclass(symmetrization_of(ordinal_numbers),u) -> equal(singleton(not_subclass_element(inverse(ordinal_numbers),ordinal_numbers)),ordinal_numbers) member(not_subclass_element(inverse(ordinal_numbers),ordinal_numbers),u)*. % 300.04/300.42 196948[19:Res:167139.1,168251.0] || member(regular(regular(u)),u)* -> equal(regular(u),ordinal_numbers) equal(u,ordinal_numbers) member(regular(regular(u)),v)*. % 300.04/300.42 197132[19:SpR:196827.0,17.2] || member(second(regular(element_relation)),u) member(first(regular(element_relation)),v) -> member(regular(element_relation),cross_product(v,u))*. % 300.04/300.42 197140[19:SpR:196827.0,27190.1] || subclass(rest_relation,flip(u)) -> member(ordered_pair(regular(element_relation),rest_of(ordered_pair(second(regular(element_relation)),first(regular(element_relation))))),u)*. % 300.04/300.42 197143[19:SpR:196827.0,27190.1] || subclass(rest_relation,flip(u)) -> member(ordered_pair(ordered_pair(second(regular(element_relation)),first(regular(element_relation))),rest_of(regular(element_relation))),u)*. % 300.04/300.42 197144[19:SpR:196827.0,27189.1] || subclass(rest_relation,rotate(u)) -> member(ordered_pair(ordered_pair(second(regular(element_relation)),rest_of(regular(element_relation))),first(regular(element_relation))),u)*. % 300.04/300.42 197185[19:SpL:196827.0,166844.1] || member(first(regular(element_relation)),cantor(u)) member(ordered_pair(u,regular(element_relation)),cross_product(universal_class,cross_product(universal_class,universal_class)))* -> . % 300.04/300.42 197285[19:Res:168469.2,897.0] || subclass(u,restrict(v,w,x))* -> equal(intersection(y,u),ordinal_numbers) member(regular(intersection(y,u)),v)*. % 300.04/300.42 197289[19:Res:168469.2,110865.0] || subclass(u,rest_of(regular(intersection(v,u))))* subclass(universal_class,complement(element_relation)) -> equal(intersection(v,u),ordinal_numbers). % 300.04/300.42 197427[19:Res:168471.1,25.1] || member(regular(intersection(u,intersection(complement(v),w))),v)* -> equal(intersection(u,intersection(complement(v),w)),ordinal_numbers). % 300.04/300.42 197459[19:Res:168471.1,169207.0] || -> equal(intersection(u,intersection(symmetrization_of(ordinal_numbers),v)),ordinal_numbers) member(regular(intersection(u,intersection(symmetrization_of(ordinal_numbers),v))),inverse(ordinal_numbers))*. % 300.04/300.42 197536[19:Rew:160.0,197365.0] || -> equal(intersection(u,symmetric_difference(v,w)),ordinal_numbers) member(regular(intersection(u,symmetric_difference(v,w))),complement(intersection(v,w)))*. % 300.04/300.42 197628[19:Res:168472.1,25.1] || member(regular(intersection(u,intersection(v,complement(w)))),w)* -> equal(intersection(u,intersection(v,complement(w))),ordinal_numbers). % 300.04/300.42 197660[19:Res:168472.1,169207.0] || -> equal(intersection(u,intersection(v,symmetrization_of(ordinal_numbers))),ordinal_numbers) member(regular(intersection(u,intersection(v,symmetrization_of(ordinal_numbers)))),inverse(ordinal_numbers))*. % 300.04/300.42 197849[19:Res:168474.2,897.0] || subclass(u,restrict(v,w,x))* -> equal(intersection(u,y),ordinal_numbers) member(regular(intersection(u,y)),v)*. % 300.04/300.42 197853[19:Res:168474.2,110865.0] || subclass(u,rest_of(regular(intersection(u,v))))* subclass(universal_class,complement(element_relation)) -> equal(intersection(u,v),ordinal_numbers). % 300.04/300.42 198431[19:Res:168476.1,25.1] || member(regular(intersection(intersection(complement(u),v),w)),u)* -> equal(intersection(intersection(complement(u),v),w),ordinal_numbers). % 300.04/300.42 198463[19:Res:168476.1,169207.0] || -> equal(intersection(intersection(symmetrization_of(ordinal_numbers),u),v),ordinal_numbers) member(regular(intersection(intersection(symmetrization_of(ordinal_numbers),u),v)),inverse(ordinal_numbers))*. % 300.04/300.42 198545[19:Rew:160.0,198365.0] || -> equal(intersection(symmetric_difference(u,v),w),ordinal_numbers) member(regular(intersection(symmetric_difference(u,v),w)),complement(intersection(u,v)))*. % 300.04/300.42 199095[19:Res:168477.1,25.1] || member(regular(intersection(intersection(u,complement(v)),w)),v)* -> equal(intersection(intersection(u,complement(v)),w),ordinal_numbers). % 300.04/300.42 199127[19:Res:168477.1,169207.0] || -> equal(intersection(intersection(u,symmetrization_of(ordinal_numbers)),v),ordinal_numbers) member(regular(intersection(intersection(u,symmetrization_of(ordinal_numbers)),v)),inverse(ordinal_numbers))*. % 300.04/300.42 199614[19:Obv:199577.2] || equal(u,v) subclass(unordered_pair(v,u),w)* -> equal(unordered_pair(v,u),ordinal_numbers) member(v,w). % 300.04/300.42 200340[0:Res:12015.1,16086.0] || equal(complement(complement(symmetric_difference(cross_product(u,v),w))),universal_class) -> member(singleton(x),complement(restrict(w,u,v)))*. % 300.04/300.42 200354[19:Res:176345.1,16086.0] || subclass(domain_relation,symmetric_difference(cross_product(u,v),w)) -> member(singleton(singleton(singleton(ordinal_numbers))),complement(restrict(w,u,v)))*. % 300.04/300.42 200356[19:Res:182463.1,16086.0] || equal(symmetric_difference(cross_product(u,v),w),singleton(singleton(ordinal_numbers))) -> member(singleton(ordinal_numbers),complement(restrict(w,u,v)))*. % 300.04/300.42 200389[20:Res:181635.1,16086.0] || subclass(symmetrization_of(ordinal_numbers),symmetric_difference(cross_product(u,v),w)) -> member(regular(symmetrization_of(ordinal_numbers)),complement(restrict(w,u,v)))*. % 300.04/300.42 200390[20:Res:175570.1,16086.0] || subclass(inverse(ordinal_numbers),symmetric_difference(cross_product(u,v),w)) -> member(regular(symmetrization_of(ordinal_numbers)),complement(restrict(w,u,v)))*. % 300.04/300.42 200654[0:Res:12015.1,16083.0] || equal(complement(complement(symmetric_difference(u,cross_product(v,w)))),universal_class) -> member(singleton(x),complement(restrict(u,v,w)))*. % 300.04/300.42 200668[19:Res:176345.1,16083.0] || subclass(domain_relation,symmetric_difference(u,cross_product(v,w))) -> member(singleton(singleton(singleton(ordinal_numbers))),complement(restrict(u,v,w)))*. % 300.04/300.42 200670[19:Res:182463.1,16083.0] || equal(symmetric_difference(u,cross_product(v,w)),singleton(singleton(ordinal_numbers))) -> member(singleton(ordinal_numbers),complement(restrict(u,v,w)))*. % 300.04/300.42 200704[20:Res:181635.1,16083.0] || subclass(symmetrization_of(ordinal_numbers),symmetric_difference(u,cross_product(v,w))) -> member(regular(symmetrization_of(ordinal_numbers)),complement(restrict(u,v,w)))*. % 300.04/300.42 200705[20:Res:175570.1,16083.0] || subclass(inverse(ordinal_numbers),symmetric_difference(u,cross_product(v,w))) -> member(regular(symmetrization_of(ordinal_numbers)),complement(restrict(u,v,w)))*. % 300.04/300.42 200755[19:SpR:125331.0,176364.1] || -> equal(singleton(restrict(cross_product(u,singleton(v)),w,x)),ordinal_numbers)** equal(segment(cross_product(w,x),u,v),ordinal_numbers). % 300.04/300.42 201715[26:Rew:200916.0,169018.3] || subclass(intersection(u,v),ordinal_numbers)* member(w,v)* member(w,u)* well_ordering(x,ordinal_numbers)* -> . % 300.04/300.42 201717[26:Rew:200916.0,169022.3] || subclass(cross_product(u,v),ordinal_numbers)* member(w,v)* member(x,u)* well_ordering(y,ordinal_numbers)* -> . % 300.04/300.42 203533[26:Res:12015.1,202277.1] || equal(complement(complement(complement(compose(complement(element_relation),inverse(element_relation))))),universal_class)** member(singleton(u),cross_product(universal_class,universal_class))* -> . % 300.04/300.42 203546[26:Res:176345.1,202277.1] || subclass(domain_relation,complement(compose(complement(element_relation),inverse(element_relation)))) member(singleton(singleton(singleton(ordinal_numbers))),cross_product(universal_class,universal_class))* -> . % 300.04/300.42 203547[26:Res:182463.1,202277.1] || equal(complement(compose(complement(element_relation),inverse(element_relation))),singleton(singleton(ordinal_numbers)))** member(singleton(ordinal_numbers),cross_product(universal_class,universal_class)) -> . % 300.04/300.42 203585[26:Res:181635.1,202277.1] || subclass(symmetrization_of(ordinal_numbers),complement(compose(complement(element_relation),inverse(element_relation))))* member(regular(symmetrization_of(ordinal_numbers)),cross_product(universal_class,universal_class)) -> . % 300.04/300.42 203586[26:Res:175570.1,202277.1] || subclass(inverse(ordinal_numbers),complement(compose(complement(element_relation),inverse(element_relation))))* member(regular(symmetrization_of(ordinal_numbers)),cross_product(universal_class,universal_class)) -> . % 300.04/300.42 203599[26:MRR:203565.0,15.1] || subclass(rest_relation,complement(compose(complement(element_relation),inverse(element_relation)))) member(ordered_pair(u,rest_of(u)),cross_product(universal_class,universal_class))* -> . % 300.04/300.42 206074[19:Rew:142500.0,205576.1] || equal(restrict(u,v,w),ordinal_numbers) -> equal(symmetric_difference(u,cross_product(v,w)),union(u,cross_product(v,w)))**. % 300.04/300.42 206075[19:Rew:142500.0,205575.1] || equal(restrict(u,v,w),ordinal_numbers) -> equal(symmetric_difference(cross_product(v,w),u),union(cross_product(v,w),u))**. % 300.04/300.42 206095[0:Res:37525.2,11848.0] || member(u,universal_class) equal(successor(singleton(u)),u)** subclass(successor_relation,v) well_ordering(universal_class,v)* -> . % 300.04/300.42 206113[19:SpL:180103.0,167954.0] || subclass(omega,image(element_relation,singleton(ordinal_numbers))) member(u,power_class(complement(singleton(ordinal_numbers))))* -> equal(integer_of(u),ordinal_numbers). % 300.04/300.42 206114[19:SpL:167191.0,167954.0] || subclass(omega,image(element_relation,symmetrization_of(ordinal_numbers))) member(u,power_class(complement(inverse(ordinal_numbers))))* -> equal(integer_of(u),ordinal_numbers). % 300.04/300.42 206295[0:SpL:27838.0,16465.0] || subclass(u,symmetric_difference(complement(v),complement(singleton(v))))* -> subclass(u,w) member(not_subclass_element(u,w),successor(v))*. % 300.04/300.42 206298[0:SpL:27838.0,15076.1] || member(u,universal_class) subclass(universal_class,symmetric_difference(complement(v),complement(singleton(v))))* -> member(power_class(u),successor(v))*. % 300.04/300.42 206300[0:SpL:27838.0,15110.1] || member(u,universal_class) subclass(universal_class,symmetric_difference(complement(v),complement(singleton(v))))* -> member(sum_class(u),successor(v))*. % 300.04/300.42 206318[19:Rew:27838.0,206220.0] || -> equal(symmetric_difference(complement(u),complement(singleton(u))),ordinal_numbers) member(regular(symmetric_difference(complement(u),complement(singleton(u)))),successor(u))*. % 300.04/300.42 206438[0:Rew:206400.0,205125.0] || -> member(u,intersection(complement(v),power_class(complement(power_class(w)))))* subclass(singleton(u),union(v,image(element_relation,power_class(w)))). % 300.04/300.42 206455[0:Rew:206400.0,139886.0] || member(u,symmetric_difference(complement(v),power_class(complement(power_class(w)))))* -> member(u,union(v,image(element_relation,power_class(w)))). % 300.04/300.42 206506[19:Rew:206400.0,205374.1] || subclass(union(u,image(element_relation,power_class(v))),ordinal_numbers) -> member(ordinal_numbers,intersection(complement(u),power_class(complement(power_class(v)))))*. % 300.04/300.42 206517[19:Rew:206400.0,205230.1] || well_ordering(universal_class,union(u,image(element_relation,power_class(v)))) -> member(ordinal_numbers,intersection(complement(u),power_class(complement(power_class(v)))))*. % 300.04/300.42 206519[0:Rew:206400.0,205075.0] || -> subclass(complement(power_class(intersection(complement(u),power_class(complement(power_class(v)))))),image(element_relation,union(u,image(element_relation,power_class(v)))))*. % 300.04/300.42 206533[19:Rew:206400.0,206159.0] || equal(image(element_relation,union(u,image(element_relation,power_class(v)))),power_class(intersection(complement(u),power_class(complement(power_class(v))))))** -> . % 300.04/300.42 206535[19:Rew:206400.0,205112.0] || -> equal(intersection(union(u,image(element_relation,power_class(v))),intersection(intersection(complement(u),power_class(complement(power_class(v)))),w)),ordinal_numbers)**. % 300.04/300.42 206537[19:Rew:206400.0,205113.0] || -> equal(intersection(union(u,image(element_relation,power_class(v))),intersection(w,intersection(complement(u),power_class(complement(power_class(v)))))),ordinal_numbers)**. % 300.04/300.42 206538[19:Rew:206400.0,205495.0] || equal(intersection(complement(u),power_class(complement(power_class(v)))),ordinal_numbers)** -> equal(union(u,image(element_relation,power_class(v))),universal_class). % 300.04/300.42 206540[19:Rew:206400.0,205184.1] || equal(union(u,image(element_relation,power_class(v))),universal_class) -> equal(intersection(complement(u),power_class(complement(power_class(v)))),ordinal_numbers)**. % 300.04/300.42 206554[19:Rew:206400.0,205397.1] || subclass(union(u,image(element_relation,power_class(v))),ordinal_numbers) -> member(omega,intersection(complement(u),power_class(complement(power_class(v)))))*. % 300.04/300.42 206601[0:Rew:206400.0,204786.0] || -> member(u,intersection(power_class(complement(power_class(v))),complement(w)))* subclass(singleton(u),union(image(element_relation,power_class(v)),w)). % 300.04/300.42 206626[19:Rew:206400.0,167680.0] || subclass(u,power_class(complement(power_class(v)))) member(regular(u),image(element_relation,power_class(v)))* -> equal(u,ordinal_numbers). % 300.04/300.42 206629[0:Rew:206400.0,139899.0] || member(u,symmetric_difference(power_class(complement(power_class(v))),complement(w)))* -> member(u,union(image(element_relation,power_class(v)),w)). % 300.04/300.42 206646[0:Rew:206400.0,204839.0] || subclass(complement(u),power_class(complement(power_class(v))))* -> equal(union(image(element_relation,power_class(v)),u),complement(complement(u))). % 300.04/300.42 206773[19:Rew:206400.0,205377.1] || subclass(union(image(element_relation,power_class(u)),v),ordinal_numbers) -> member(ordinal_numbers,intersection(power_class(complement(power_class(u))),complement(v)))*. % 300.04/300.42 206784[19:Rew:206400.0,204891.1] || well_ordering(universal_class,union(image(element_relation,power_class(u)),v)) -> member(ordinal_numbers,intersection(power_class(complement(power_class(u))),complement(v)))*. % 300.04/300.42 206786[0:Rew:206400.0,204737.0] || -> subclass(complement(power_class(intersection(power_class(complement(power_class(u))),complement(v)))),image(element_relation,union(image(element_relation,power_class(u)),v)))*. % 300.04/300.42 206800[19:Rew:206400.0,206162.0] || equal(image(element_relation,union(image(element_relation,power_class(u)),v)),power_class(intersection(power_class(complement(power_class(u))),complement(v))))** -> . % 300.04/300.42 206802[19:Rew:206400.0,204774.0] || -> equal(intersection(union(image(element_relation,power_class(u)),v),intersection(intersection(power_class(complement(power_class(u))),complement(v)),w)),ordinal_numbers)**. % 300.04/300.42 206804[19:Rew:206400.0,204775.0] || -> equal(intersection(union(image(element_relation,power_class(u)),v),intersection(w,intersection(power_class(complement(power_class(u))),complement(v)))),ordinal_numbers)**. % 300.04/300.42 206805[19:Rew:206400.0,205506.0] || equal(intersection(power_class(complement(power_class(u))),complement(v)),ordinal_numbers)** -> equal(union(image(element_relation,power_class(u)),v),universal_class). % 300.04/300.42 206807[19:Rew:206400.0,204845.1] || equal(union(image(element_relation,power_class(u)),v),universal_class) -> equal(intersection(power_class(complement(power_class(u))),complement(v)),ordinal_numbers)**. % 300.04/300.42 206821[19:Rew:206400.0,205400.1] || subclass(union(image(element_relation,power_class(u)),v),ordinal_numbers) -> member(omega,intersection(power_class(complement(power_class(u))),complement(v)))*. % 300.04/300.42 206897[0:Rew:206400.0,137116.0] || -> subclass(complement(successor(image(element_relation,power_class(u)))),intersection(power_class(complement(power_class(u))),complement(singleton(image(element_relation,power_class(u))))))*. % 300.04/300.42 206899[0:Rew:206400.0,137148.0] || -> subclass(complement(symmetrization_of(image(element_relation,power_class(u)))),intersection(power_class(complement(power_class(u))),complement(inverse(image(element_relation,power_class(u))))))*. % 300.04/300.42 206927[19:Rew:206400.0,167948.0] || subclass(omega,power_class(complement(power_class(u)))) member(v,image(element_relation,power_class(u)))* -> equal(integer_of(v),ordinal_numbers). % 300.04/300.42 206978[19:Rew:206400.0,206116.1] || subclass(omega,image(element_relation,power_class(u))) member(v,power_class(complement(power_class(u))))* -> equal(integer_of(v),ordinal_numbers). % 300.04/300.42 207034[25:Rew:206400.0,203979.1] single_valued_class(intersection(power_class(u),complement(singleton(image(element_relation,complement(u)))))) || equal(successor(complement(power_class(u))),universal_class)** -> . % 300.04/300.42 207039[8:Rew:206400.0,203812.1] inductive(intersection(power_class(u),complement(singleton(image(element_relation,complement(u)))))) || equal(successor(complement(power_class(u))),universal_class)** -> . % 300.04/300.42 207052[22:Rew:206400.0,203863.1] inductive(intersection(power_class(u),complement(singleton(image(element_relation,complement(u)))))) || equal(successor(complement(power_class(u))),omega)** -> . % 300.04/300.42 207142[25:Rew:206400.0,204327.1] single_valued_class(intersection(power_class(u),complement(inverse(image(element_relation,complement(u)))))) || equal(symmetrization_of(complement(power_class(u))),universal_class)** -> . % 300.04/300.42 207147[8:Rew:206400.0,204161.1] inductive(intersection(power_class(u),complement(inverse(image(element_relation,complement(u)))))) || equal(symmetrization_of(complement(power_class(u))),universal_class)** -> . % 300.04/300.42 207160[22:Rew:206400.0,204212.1] inductive(intersection(power_class(u),complement(inverse(image(element_relation,complement(u)))))) || equal(symmetrization_of(complement(power_class(u))),omega)** -> . % 300.04/300.42 207431[0:Rew:206400.0,206684.1] || member(u,intersection(power_class(v),complement(singleton(complement(power_class(v))))))* member(u,successor(complement(power_class(v)))) -> . % 300.04/300.42 207432[0:Rew:206400.0,206685.0] || member(u,complement(successor(complement(power_class(v))))) -> member(u,intersection(power_class(v),complement(singleton(complement(power_class(v))))))*. % 300.04/300.42 207433[0:Rew:206400.0,206700.1] || member(u,intersection(power_class(v),complement(inverse(complement(power_class(v))))))* member(u,symmetrization_of(complement(power_class(v)))) -> . % 300.04/300.42 207434[0:Rew:206400.0,206701.0] || member(u,complement(symmetrization_of(complement(power_class(v))))) -> member(u,intersection(power_class(v),complement(inverse(complement(power_class(v))))))*. % 300.04/300.42 207437[22:Rew:206400.0,207017.1] || equal(complement(successor(complement(power_class(u)))),omega) -> member(ordinal_numbers,intersection(power_class(u),complement(singleton(complement(power_class(u))))))*. % 300.04/300.42 207438[22:Rew:206400.0,207018.1] || subclass(omega,complement(successor(complement(power_class(u))))) -> member(ordinal_numbers,intersection(power_class(u),complement(singleton(complement(power_class(u))))))*. % 300.04/300.42 207439[19:Rew:206400.0,207020.1] || equal(complement(successor(complement(power_class(u)))),universal_class) -> member(ordinal_numbers,intersection(power_class(u),complement(singleton(complement(power_class(u))))))*. % 300.04/300.42 207440[0:Rew:206400.0,207021.1] || equal(complement(successor(complement(power_class(u)))),universal_class) -> member(omega,intersection(power_class(u),complement(singleton(complement(power_class(u))))))*. % 300.04/300.42 207441[19:Rew:206400.0,207023.1] || subclass(universal_class,complement(successor(complement(power_class(u))))) -> member(ordinal_numbers,intersection(power_class(u),complement(singleton(complement(power_class(u))))))*. % 300.04/300.42 207442[0:Rew:206400.0,207024.1] || subclass(universal_class,complement(successor(complement(power_class(u))))) -> member(omega,intersection(power_class(u),complement(singleton(complement(power_class(u))))))*. % 300.04/300.42 207443[19:Rew:206400.0,207047.1] || well_ordering(universal_class,successor(complement(power_class(u)))) -> member(singleton(ordinal_numbers),intersection(power_class(u),complement(singleton(complement(power_class(u))))))*. % 300.04/300.42 207444[22:Rew:206400.0,207050.0] || equal(intersection(power_class(u),complement(singleton(complement(power_class(u))))),omega)** equal(successor(complement(power_class(u))),omega) -> . % 300.04/300.42 207445[22:Rew:206400.0,207051.0] || equal(intersection(power_class(u),complement(singleton(complement(power_class(u))))),universal_class)** equal(successor(complement(power_class(u))),omega) -> . % 300.04/300.42 207446[19:Rew:206400.0,207053.0] || equal(intersection(power_class(u),complement(singleton(complement(power_class(u))))),universal_class)** equal(successor(complement(power_class(u))),element_relation) -> . % 300.04/300.42 207447[19:Rew:206400.0,207054.0] || subclass(universal_class,intersection(power_class(u),complement(singleton(complement(power_class(u))))))* subclass(element_relation,successor(complement(power_class(u)))) -> . % 300.04/300.42 207448[22:Rew:206400.0,207059.1] || subclass(omega,successor(complement(power_class(u)))) member(ordinal_numbers,intersection(power_class(u),complement(singleton(complement(power_class(u))))))* -> . % 300.04/300.42 207449[8:Rew:206400.0,207063.0] || equal(intersection(power_class(u),complement(singleton(complement(power_class(u))))),universal_class)** equal(successor(complement(power_class(u))),domain_relation) -> . % 300.04/300.42 207450[8:Rew:206400.0,207064.0] || equal(intersection(power_class(u),complement(singleton(complement(power_class(u))))),domain_relation)** equal(successor(complement(power_class(u))),domain_relation) -> . % 300.04/300.42 207451[8:Rew:206400.0,207068.0] || subclass(universal_class,intersection(power_class(u),complement(singleton(complement(power_class(u))))))* subclass(domain_relation,successor(complement(power_class(u)))) -> . % 300.04/300.42 207452[8:Rew:206400.0,207069.0] || subclass(domain_relation,intersection(power_class(u),complement(singleton(complement(power_class(u))))))* subclass(domain_relation,successor(complement(power_class(u)))) -> . % 300.04/300.42 207453[19:Rew:206400.0,207074.1] || subclass(universal_class,successor(complement(power_class(u)))) member(ordinal_numbers,intersection(power_class(u),complement(singleton(complement(power_class(u))))))* -> . % 300.04/300.42 207454[8:Rew:206400.0,207075.0] || subclass(domain_relation,intersection(power_class(u),complement(singleton(complement(power_class(u))))))* subclass(universal_class,successor(complement(power_class(u)))) -> . % 300.04/300.42 207455[0:Rew:206400.0,207076.0] || equal(intersection(power_class(u),complement(singleton(complement(power_class(u))))),universal_class)** subclass(universal_class,successor(complement(power_class(u)))) -> . % 300.04/300.42 207456[0:Rew:206400.0,207077.1] || subclass(universal_class,successor(complement(power_class(u)))) member(omega,intersection(power_class(u),complement(singleton(complement(power_class(u))))))* -> . % 300.04/300.42 207457[0:Rew:206400.0,207078.0] || subclass(universal_class,intersection(power_class(u),complement(singleton(complement(power_class(u))))))* subclass(universal_class,successor(complement(power_class(u)))) -> . % 300.04/300.42 207458[19:Rew:206400.0,207079.0] || -> member(singleton(ordinal_numbers),intersection(power_class(u),complement(singleton(complement(power_class(u))))))* member(singleton(ordinal_numbers),successor(complement(power_class(u)))). % 300.04/300.42 207459[22:Rew:206400.0,207127.1] || equal(complement(symmetrization_of(complement(power_class(u)))),omega) -> member(ordinal_numbers,intersection(power_class(u),complement(inverse(complement(power_class(u))))))*. % 300.04/300.42 207460[22:Rew:206400.0,207128.1] || subclass(omega,complement(symmetrization_of(complement(power_class(u))))) -> member(ordinal_numbers,intersection(power_class(u),complement(inverse(complement(power_class(u))))))*. % 300.04/300.42 207461[19:Rew:206400.0,207130.1] || equal(complement(symmetrization_of(complement(power_class(u)))),universal_class) -> member(ordinal_numbers,intersection(power_class(u),complement(inverse(complement(power_class(u))))))*. % 300.04/300.42 207462[0:Rew:206400.0,207131.1] || equal(complement(symmetrization_of(complement(power_class(u)))),universal_class) -> member(omega,intersection(power_class(u),complement(inverse(complement(power_class(u))))))*. % 300.04/300.42 207463[19:Rew:206400.0,207133.1] || subclass(universal_class,complement(symmetrization_of(complement(power_class(u))))) -> member(ordinal_numbers,intersection(power_class(u),complement(inverse(complement(power_class(u))))))*. % 300.04/300.42 207464[0:Rew:206400.0,207134.1] || subclass(universal_class,complement(symmetrization_of(complement(power_class(u))))) -> member(omega,intersection(power_class(u),complement(inverse(complement(power_class(u))))))*. % 300.04/300.42 207465[19:Rew:206400.0,207155.1] || well_ordering(universal_class,symmetrization_of(complement(power_class(u)))) -> member(singleton(ordinal_numbers),intersection(power_class(u),complement(inverse(complement(power_class(u))))))*. % 300.04/300.42 207466[22:Rew:206400.0,207158.0] || equal(intersection(power_class(u),complement(inverse(complement(power_class(u))))),omega)** equal(symmetrization_of(complement(power_class(u))),omega) -> . % 300.04/300.42 207467[22:Rew:206400.0,207159.0] || equal(intersection(power_class(u),complement(inverse(complement(power_class(u))))),universal_class)** equal(symmetrization_of(complement(power_class(u))),omega) -> . % 300.04/300.42 207468[19:Rew:206400.0,207161.0] || equal(intersection(power_class(u),complement(inverse(complement(power_class(u))))),universal_class)** equal(symmetrization_of(complement(power_class(u))),element_relation) -> . % 300.04/300.42 207469[19:Rew:206400.0,207162.0] || subclass(universal_class,intersection(power_class(u),complement(inverse(complement(power_class(u))))))* subclass(element_relation,symmetrization_of(complement(power_class(u)))) -> . % 300.04/300.42 207470[22:Rew:206400.0,207167.1] || subclass(omega,symmetrization_of(complement(power_class(u)))) member(ordinal_numbers,intersection(power_class(u),complement(inverse(complement(power_class(u))))))* -> . % 300.04/300.42 207471[8:Rew:206400.0,207171.0] || equal(intersection(power_class(u),complement(inverse(complement(power_class(u))))),universal_class)** equal(symmetrization_of(complement(power_class(u))),domain_relation) -> . % 300.04/300.42 207472[8:Rew:206400.0,207172.0] || equal(intersection(power_class(u),complement(inverse(complement(power_class(u))))),domain_relation)** equal(symmetrization_of(complement(power_class(u))),domain_relation) -> . % 300.04/300.42 207473[8:Rew:206400.0,207176.0] || subclass(universal_class,intersection(power_class(u),complement(inverse(complement(power_class(u))))))* subclass(domain_relation,symmetrization_of(complement(power_class(u)))) -> . % 300.04/300.42 207474[8:Rew:206400.0,207177.0] || subclass(domain_relation,intersection(power_class(u),complement(inverse(complement(power_class(u))))))* subclass(domain_relation,symmetrization_of(complement(power_class(u)))) -> . % 300.04/300.42 207475[19:Rew:206400.0,207182.1] || subclass(universal_class,symmetrization_of(complement(power_class(u)))) member(ordinal_numbers,intersection(power_class(u),complement(inverse(complement(power_class(u))))))* -> . % 300.04/300.42 207476[8:Rew:206400.0,207183.0] || subclass(domain_relation,intersection(power_class(u),complement(inverse(complement(power_class(u))))))* subclass(universal_class,symmetrization_of(complement(power_class(u)))) -> . % 300.04/300.42 207477[0:Rew:206400.0,207184.0] || equal(intersection(power_class(u),complement(inverse(complement(power_class(u))))),universal_class)** subclass(universal_class,symmetrization_of(complement(power_class(u)))) -> . % 300.04/300.42 207478[0:Rew:206400.0,207185.1] || subclass(universal_class,symmetrization_of(complement(power_class(u)))) member(omega,intersection(power_class(u),complement(inverse(complement(power_class(u))))))* -> . % 300.04/300.42 207479[0:Rew:206400.0,207186.0] || subclass(universal_class,intersection(power_class(u),complement(inverse(complement(power_class(u))))))* subclass(universal_class,symmetrization_of(complement(power_class(u)))) -> . % 300.04/300.42 207480[19:Rew:206400.0,207187.0] || -> member(singleton(ordinal_numbers),intersection(power_class(u),complement(inverse(complement(power_class(u))))))* member(singleton(ordinal_numbers),symmetrization_of(complement(power_class(u)))). % 300.04/300.42 207487[19:Rew:167191.0,206383.1] || member(not_subclass_element(image(element_relation,symmetrization_of(ordinal_numbers)),u),power_class(complement(inverse(ordinal_numbers))))* -> subclass(image(element_relation,symmetrization_of(ordinal_numbers)),u). % 300.04/300.42 207488[19:Rew:180103.0,206382.1] || member(not_subclass_element(image(element_relation,singleton(ordinal_numbers)),u),power_class(complement(singleton(ordinal_numbers))))* -> subclass(image(element_relation,singleton(ordinal_numbers)),u). % 300.04/300.42 207930[19:Res:205391.1,126.0] || equal(complement(u),ordinal_numbers) subclass(u,v)* well_ordering(w,v)* -> member(least(w,u),u)*. % 300.04/300.42 209115[0:Res:3.1,206404.0] || member(not_subclass_element(image(element_relation,power_class(u)),v),power_class(complement(power_class(u))))* -> subclass(image(element_relation,power_class(u)),v). % 300.04/300.42 209143[19:Res:167131.2,206404.0] || subclass(u,image(element_relation,power_class(v))) member(regular(u),power_class(complement(power_class(v))))* -> equal(u,ordinal_numbers). % 300.04/300.42 209794[19:Res:182871.1,27138.2] || member(ordered_pair(u,rest_of(u)),inverse(ordinal_numbers))* member(u,universal_class) subclass(rest_relation,complement(symmetrization_of(ordinal_numbers))) -> . % 300.04/300.42 209796[8:Res:147404.1,27138.2] || member(ordered_pair(u,rest_of(u)),element_relation)* member(u,universal_class) subclass(rest_relation,complement(compose(element_relation,universal_class))) -> . % 300.04/300.42 209846[0:MRR:209787.0,940.0] || member(u,universal_class) subclass(rest_relation,complement(union(v,w)))* -> member(ordered_pair(u,rest_of(u)),complement(w))*. % 300.04/300.42 209847[0:MRR:209786.0,940.0] || member(u,universal_class) subclass(rest_relation,complement(union(v,w)))* -> member(ordered_pair(u,rest_of(u)),complement(v))*. % 300.04/300.42 210186[19:Rew:27168.2,210141.2] || member(u,universal_class) subclass(rest_relation,rest_of(v)) -> equal(rest_of(u),ordinal_numbers) member(regular(rest_of(u)),v)*. % 300.04/300.42 210294[0:SpL:27837.0,16465.0] || subclass(u,symmetric_difference(complement(v),complement(inverse(v))))* -> subclass(u,w) member(not_subclass_element(u,w),symmetrization_of(v))*. % 300.04/300.42 210297[0:SpL:27837.0,15076.1] || member(u,universal_class) subclass(universal_class,symmetric_difference(complement(v),complement(inverse(v))))* -> member(power_class(u),symmetrization_of(v))*. % 300.04/300.42 210299[0:SpL:27837.0,15110.1] || member(u,universal_class) subclass(universal_class,symmetric_difference(complement(v),complement(inverse(v))))* -> member(sum_class(u),symmetrization_of(v))*. % 300.04/300.42 210312[19:Rew:27837.0,210227.0] || -> equal(symmetric_difference(complement(u),complement(inverse(u))),ordinal_numbers) member(regular(symmetric_difference(complement(u),complement(inverse(u)))),symmetrization_of(u))*. % 300.04/300.42 210376[0:Res:31137.2,11848.0] || member(u,universal_class)* equal(rest_of(u),successor(u)) subclass(successor_relation,v) well_ordering(universal_class,v)* -> . % 300.04/300.42 210892[19:Res:12.0,177022.0] || -> member(unordered_pair(u,v),image(universal_class,singleton(unordered_pair(u,v))))* asymmetric(cross_product(singleton(unordered_pair(u,v)),universal_class),w)*. % 300.04/300.42 210893[19:Res:940.0,177022.0] || -> member(ordered_pair(u,v),image(universal_class,singleton(ordered_pair(u,v))))* asymmetric(cross_product(singleton(ordered_pair(u,v)),universal_class),w)*. % 300.04/300.42 210908[19:Res:167137.1,177022.0] || -> equal(u,ordinal_numbers) member(regular(u),image(universal_class,singleton(regular(u))))* asymmetric(cross_product(singleton(regular(u)),universal_class),v)*. % 300.04/300.42 210909[20:Res:175569.0,177022.0] || -> member(regular(symmetrization_of(ordinal_numbers)),image(universal_class,singleton(regular(symmetrization_of(ordinal_numbers)))))* asymmetric(cross_product(singleton(regular(symmetrization_of(ordinal_numbers))),universal_class),u)*. % 300.04/300.42 211285[0:Res:137890.1,15107.0] || well_ordering(u,universal_class) subclass(universal_class,v)* subclass(v,w)* -> member(sum_class(least(u,universal_class)),w)*. % 300.04/300.42 211286[0:Res:137613.1,15107.0] || well_ordering(u,universal_class) subclass(universal_class,v)* subclass(v,w)* -> member(sum_class(least(u,rest_relation)),w)*. % 300.04/300.42 211287[0:Res:137620.1,15107.0] || well_ordering(u,rest_relation) subclass(universal_class,v)* subclass(v,w)* -> member(sum_class(least(u,rest_relation)),w)*. % 300.04/300.42 211288[21:Res:176162.1,15107.0] || well_ordering(u,omega) subclass(universal_class,v)* subclass(v,w)* -> member(sum_class(least(u,omega)),w)*. % 300.04/300.42 211289[21:Res:176155.1,15107.0] || well_ordering(u,universal_class) subclass(universal_class,v)* subclass(v,w)* -> member(sum_class(least(u,omega)),w)*. % 300.04/300.42 211376[25:SpL:193223.1,15098.0] function(u) || member(image(v,ordinal_numbers),universal_class) subclass(universal_class,w) -> member(apply(v,u),w)*. % 300.04/300.42 211619[19:Res:203424.1,126.0] || subclass(complement(u),ordinal_numbers) subclass(u,v)* well_ordering(w,v)* -> member(least(w,u),u)*. % 300.04/300.42 211650[19:Res:203424.1,168251.0] || subclass(complement(regular(u)),ordinal_numbers)* member(singleton(v),u)* -> equal(u,ordinal_numbers) member(singleton(v),w)*. % 300.04/300.42 212462[19:Res:205991.1,168251.0] || equal(complement(regular(u)),ordinal_numbers) member(singleton(v),u)* -> equal(u,ordinal_numbers) member(singleton(v),w)*. % 300.04/300.42 212776[0:Res:137890.1,15073.0] || well_ordering(u,universal_class) subclass(universal_class,v)* subclass(v,w)* -> member(power_class(least(u,universal_class)),w)*. % 300.04/300.42 212777[0:Res:137613.1,15073.0] || well_ordering(u,universal_class) subclass(universal_class,v)* subclass(v,w)* -> member(power_class(least(u,rest_relation)),w)*. % 300.04/300.42 212778[0:Res:137620.1,15073.0] || well_ordering(u,rest_relation) subclass(universal_class,v)* subclass(v,w)* -> member(power_class(least(u,rest_relation)),w)*. % 300.04/300.42 212779[21:Res:176162.1,15073.0] || well_ordering(u,omega) subclass(universal_class,v)* subclass(v,w)* -> member(power_class(least(u,omega)),w)*. % 300.04/300.42 212780[21:Res:176155.1,15073.0] || well_ordering(u,universal_class) subclass(universal_class,v)* subclass(v,w)* -> member(power_class(least(u,omega)),w)*. % 300.04/300.42 213007[19:Obv:212986.2] || subclass(unordered_pair(u,v),w)* -> equal(integer_of(u),ordinal_numbers) subclass(unordered_pair(u,v),omega)* member(v,w). % 300.04/300.42 213066[19:Obv:213040.2] || subclass(unordered_pair(u,v),w)* -> equal(integer_of(v),ordinal_numbers) subclass(unordered_pair(u,v),omega)* member(u,w). % 300.04/300.42 213086[20:Rew:167222.1,213077.2] || subclass(symmetrization_of(ordinal_numbers),u) -> equal(singleton(not_subclass_element(symmetrization_of(ordinal_numbers),ordinal_numbers)),ordinal_numbers) member(not_subclass_element(symmetrization_of(ordinal_numbers),ordinal_numbers),u)*. % 300.04/300.42 213294[19:SpR:209197.0,137025.0] || -> subclass(complement(successor(power_class(complement(singleton(ordinal_numbers))))),intersection(image(element_relation,singleton(ordinal_numbers)),complement(singleton(power_class(complement(singleton(ordinal_numbers)))))))*. % 300.04/300.42 213296[19:SpR:209197.0,137026.0] || -> subclass(complement(symmetrization_of(power_class(complement(singleton(ordinal_numbers))))),intersection(image(element_relation,singleton(ordinal_numbers)),complement(inverse(power_class(complement(singleton(ordinal_numbers)))))))*. % 300.04/300.42 213434[19:SpL:209197.0,16102.0] || member(u,symmetric_difference(image(element_relation,singleton(ordinal_numbers)),complement(v)))* -> member(u,union(power_class(complement(singleton(ordinal_numbers))),v)). % 300.04/300.42 213441[19:SpL:209197.0,16102.0] || member(u,symmetric_difference(complement(v),image(element_relation,singleton(ordinal_numbers))))* -> member(u,union(v,power_class(complement(singleton(ordinal_numbers))))). % 300.04/300.42 213536[19:SpR:209198.0,137025.0] || -> subclass(complement(successor(power_class(complement(inverse(ordinal_numbers))))),intersection(image(element_relation,symmetrization_of(ordinal_numbers)),complement(singleton(power_class(complement(inverse(ordinal_numbers)))))))*. % 300.04/300.42 213538[19:SpR:209198.0,137026.0] || -> subclass(complement(symmetrization_of(power_class(complement(inverse(ordinal_numbers))))),intersection(image(element_relation,symmetrization_of(ordinal_numbers)),complement(inverse(power_class(complement(inverse(ordinal_numbers)))))))*. % 300.04/300.42 213675[19:SpL:209198.0,16102.0] || member(u,symmetric_difference(image(element_relation,symmetrization_of(ordinal_numbers)),complement(v)))* -> member(u,union(power_class(complement(inverse(ordinal_numbers))),v)). % 300.04/300.42 213682[19:SpL:209198.0,16102.0] || member(u,symmetric_difference(complement(v),image(element_relation,symmetrization_of(ordinal_numbers))))* -> member(u,union(v,power_class(complement(inverse(ordinal_numbers))))). % 300.04/300.42 213781[19:Res:211476.1,40806.0] || subclass(range_of(ordinal_numbers),sum_class(range_of(ordinal_numbers)))* -> member(singleton(ordinal_numbers),cantor(choice)) equal(sum_class(range_of(ordinal_numbers)),range_of(ordinal_numbers)). % 300.04/300.42 214058[19:Rew:198291.0,214043.1] || member(not_subclass_element(intersection(complement(inverse(ordinal_numbers)),u),ordinal_numbers),symmetrization_of(ordinal_numbers))* -> subclass(intersection(complement(inverse(ordinal_numbers)),u),ordinal_numbers). % 300.04/300.42 214308[19:Rew:198938.0,214294.1] || member(not_subclass_element(intersection(u,complement(inverse(ordinal_numbers))),ordinal_numbers),symmetrization_of(ordinal_numbers))* -> subclass(intersection(u,complement(inverse(ordinal_numbers))),ordinal_numbers). % 300.04/300.42 214571[0:Res:24.2,207852.0] || member(u,complement(v)) member(u,power_class(w)) member(u,union(complement(power_class(w)),v))* -> . % 300.04/300.42 214583[0:Res:2480.1,207852.0] || subclass(universal_class,intersection(power_class(u),complement(v))) member(unordered_pair(w,x),union(complement(power_class(u)),v))* -> . % 300.04/300.42 214593[0:Res:2481.1,207852.0] || subclass(universal_class,intersection(power_class(u),complement(v))) member(ordered_pair(w,x),union(complement(power_class(u)),v))* -> . % 300.04/300.42 214597[19:Res:167127.1,207852.0] || subclass(domain_relation,intersection(power_class(u),complement(v))) member(ordered_pair(ordinal_numbers,ordinal_numbers),union(complement(power_class(u)),v))* -> . % 300.04/300.42 214626[20:Res:175613.1,207852.0] || subclass(universal_class,intersection(power_class(u),complement(v))) member(regular(symmetrization_of(ordinal_numbers)),union(complement(power_class(u)),v))* -> . % 300.04/300.42 214734[0:Res:24.2,207871.0] || member(u,power_class(v)) member(u,complement(w)) member(u,union(w,complement(power_class(v))))* -> . % 300.04/300.42 214746[0:Res:2480.1,207871.0] || subclass(universal_class,intersection(complement(u),power_class(v))) member(unordered_pair(w,x),union(u,complement(power_class(v))))* -> . % 300.04/300.42 214756[0:Res:2481.1,207871.0] || subclass(universal_class,intersection(complement(u),power_class(v))) member(ordered_pair(w,x),union(u,complement(power_class(v))))* -> . % 300.04/300.42 214760[19:Res:167127.1,207871.0] || subclass(domain_relation,intersection(complement(u),power_class(v))) member(ordered_pair(ordinal_numbers,ordinal_numbers),union(u,complement(power_class(v))))* -> . % 300.04/300.42 214789[20:Res:175613.1,207871.0] || subclass(universal_class,intersection(complement(u),power_class(v))) member(regular(symmetrization_of(ordinal_numbers)),union(u,complement(power_class(v))))* -> . % 300.04/300.42 214867[0:Res:144532.1,27258.2] || equal(union(u,v),universal_class)** member(singleton(w),complement(v))* member(singleton(w),complement(u))* -> . % 300.04/300.42 214869[0:Res:2479.1,27258.2] || subclass(universal_class,union(u,v))* member(singleton(w),complement(v))* member(singleton(w),complement(u))* -> . % 300.04/300.42 214931[19:Res:196731.1,27258.2] || subclass(universal_class,union(u,v))* member(regular(element_relation),complement(v))* member(regular(element_relation),complement(u))* -> . % 300.04/300.42 214975[19:SpR:160282.0,184521.1] || subclass(rest_relation,domain_relation) -> equal(regular(ordered_pair(u,v)),singleton(u)) equal(rest_of(regular(ordered_pair(u,v))),ordinal_numbers)**. % 300.04/300.42 214976[19:SpR:160282.0,184389.1] || subclass(domain_relation,rest_relation) -> equal(regular(ordered_pair(u,v)),singleton(u)) equal(rest_of(regular(ordered_pair(u,v))),ordinal_numbers)**. % 300.04/300.42 214983[8:SpR:160282.0,14.0] || -> equal(regular(ordered_pair(u,v)),singleton(u)) equal(unordered_pair(singleton(u),regular(ordered_pair(u,v))),ordered_pair(u,v))**. % 300.04/300.42 214991[25:SpR:193223.1,160282.0] function(u) || -> equal(regular(ordered_pair(v,u)),unordered_pair(v,ordinal_numbers))** equal(regular(ordered_pair(v,u)),singleton(v)). % 300.04/300.42 215067[8:MRR:215051.1,170.0] || equal(u,regular(ordered_pair(v,w)))* -> equal(regular(ordered_pair(v,w)),singleton(v))** member(singleton(w),u)*. % 300.04/300.42 215068[8:MRR:215019.0,170.0] || subclass(regular(ordered_pair(u,v)),w)* -> equal(regular(ordered_pair(u,v)),singleton(u)) member(singleton(v),w). % 300.04/300.42 215093[19:Res:168245.3,25.1] || well_ordering(u,universal_class) subclass(v,complement(w)) member(least(u,v),w)* -> equal(v,ordinal_numbers). % 300.04/300.42 215098[19:Res:168245.3,148647.0] || well_ordering(u,universal_class) subclass(v,complement(complement(w))) -> equal(v,ordinal_numbers) member(least(u,v),w)*. % 300.04/300.42 215107[19:Res:168245.3,22.0] || well_ordering(u,universal_class) subclass(v,intersection(w,x))* -> equal(v,ordinal_numbers) member(least(u,v),w)*. % 300.04/300.42 215108[19:Res:168245.3,23.0] || well_ordering(u,universal_class) subclass(v,intersection(w,x))* -> equal(v,ordinal_numbers) member(least(u,v),x)*. % 300.04/300.42 215127[19:Res:168245.3,192214.0] || well_ordering(u,universal_class) subclass(v,cantor(complement(cross_product(singleton(least(u,v)),universal_class))))* -> equal(v,ordinal_numbers). % 300.04/300.42 215132[19:Res:168245.3,169207.0] || well_ordering(u,universal_class) subclass(v,symmetrization_of(ordinal_numbers)) -> equal(v,ordinal_numbers) member(least(u,v),inverse(ordinal_numbers))*. % 300.04/300.42 215197[19:Res:214528.1,7963.1] || subclass(kind_1_ordinals,complement(intersection(u,v)))* member(ordinal_numbers,union(u,v)) -> member(ordinal_numbers,symmetric_difference(u,v)). % 300.04/300.42 215278[19:Res:205991.1,168249.0] || equal(complement(regular(u)),ordinal_numbers) member(singleton(v),u)* well_ordering(w,x)* -> equal(u,ordinal_numbers). % 300.04/300.42 215279[19:Res:203424.1,168249.0] || subclass(complement(regular(u)),ordinal_numbers)* member(singleton(v),u)* well_ordering(w,x)* -> equal(u,ordinal_numbers). % 300.04/300.42 215286[19:Res:3.1,168249.0] || member(not_subclass_element(regular(u),v),u)* well_ordering(w,x)* -> subclass(regular(u),v) equal(u,ordinal_numbers). % 300.04/300.42 215289[19:Res:2480.1,168249.0] || subclass(universal_class,regular(u)) member(unordered_pair(v,w),u)* well_ordering(x,y)* -> equal(u,ordinal_numbers). % 300.04/300.42 215301[19:Res:2481.1,168249.0] || subclass(universal_class,regular(u)) member(ordered_pair(v,w),u)* well_ordering(x,y)* -> equal(u,ordinal_numbers). % 300.04/300.42 215305[19:Res:167127.1,168249.0] || subclass(domain_relation,regular(u)) member(ordered_pair(ordinal_numbers,ordinal_numbers),u)* well_ordering(v,w)* -> equal(u,ordinal_numbers). % 300.04/300.42 215336[20:Res:175613.1,168249.0] || subclass(universal_class,regular(u)) member(regular(symmetrization_of(ordinal_numbers)),u)* well_ordering(v,w)* -> equal(u,ordinal_numbers). % 300.04/300.42 215347[19:Con:215311.2] || well_ordering(u,universal_class) member(least(u,regular(v)),v)* -> equal(regular(v),ordinal_numbers) equal(v,ordinal_numbers). % 300.04/300.42 215349[19:Con:215300.3] inductive(regular(u)) || well_ordering(v,universal_class) member(least(v,regular(u)),u)* -> equal(u,ordinal_numbers). % 300.04/300.42 215353[19:MRR:215293.0,167137.1] || member(apply(choice,regular(u)),u)* well_ordering(v,w)* -> equal(regular(u),ordinal_numbers) equal(u,ordinal_numbers). % 300.04/300.42 215383[23:Rew:204377.1,215373.3] || subclass(omega,ordered_pair(u,universal_class))* -> equal(integer_of(v),ordinal_numbers)** equal(v,unordered_pair(u,ordinal_numbers))* equal(v,ordinal_numbers). % 300.04/300.42 215540[19:Res:168520.2,4178.0] || well_ordering(u,universal_class) -> equal(intersection(singleton(v),w),ordinal_numbers) equal(least(u,intersection(singleton(v),w)),v)**. % 300.04/300.42 215741[19:Res:168521.2,4178.0] || well_ordering(u,universal_class) -> equal(intersection(v,singleton(w)),ordinal_numbers) equal(least(u,intersection(v,singleton(w))),w)**. % 300.04/300.42 216012[0:SpL:149179.0,16107.1] || member(u,symmetric_difference(v,intersection(v,w)))* subclass(complement(intersection(v,w)),x)* -> member(u,x)*. % 300.04/300.42 216013[0:SpL:149318.0,16107.1] || member(u,symmetric_difference(v,intersection(w,v)))* subclass(complement(intersection(w,v)),x)* -> member(u,x)*. % 300.04/300.42 216048[0:SpL:149012.1,16107.1] || subclass(u,v) member(w,symmetric_difference(v,u))* subclass(complement(u),x)* -> member(w,x)*. % 300.04/300.42 216134[19:Rew:196263.1,216133.1] || equal(complement(u),universal_class) member(v,union(u,w))* subclass(universal_class,x) -> member(v,x)*. % 300.04/300.42 216138[19:Rew:196482.1,216137.1] || equal(complement(u),universal_class) member(v,union(w,u))* subclass(universal_class,x) -> member(v,x)*. % 300.04/300.42 216140[19:Rew:213926.0,216139.0] || member(u,union(singleton(ordinal_numbers),intersection(complement(singleton(ordinal_numbers)),v)))* subclass(universal_class,w) -> member(u,w)*. % 300.04/300.42 216142[19:Rew:214181.0,216141.0] || member(u,union(singleton(ordinal_numbers),intersection(v,complement(singleton(ordinal_numbers)))))* subclass(universal_class,w) -> member(u,w)*. % 300.04/300.42 216144[19:Rew:214053.0,216143.0] || member(u,union(symmetrization_of(ordinal_numbers),intersection(complement(inverse(ordinal_numbers)),v)))* subclass(universal_class,w) -> member(u,w)*. % 300.04/300.42 216146[19:Rew:214303.0,216145.0] || member(u,union(symmetrization_of(ordinal_numbers),intersection(v,complement(inverse(ordinal_numbers)))))* subclass(universal_class,w) -> member(u,w)*. % 300.04/300.42 216807[2:Res:38094.1,188593.1] || member(u,union(v,w)) equal(complement(intersection(v,w)),universal_class) -> member(u,symmetric_difference(v,w))*. % 300.04/300.42 216976[0:Obv:216941.2] || member(u,v) subclass(unordered_pair(u,w),x)* -> subclass(unordered_pair(u,w),v)* member(w,x). % 300.04/300.42 217217[0:Obv:217180.2] || member(u,v) subclass(unordered_pair(w,u),x)* -> subclass(unordered_pair(w,u),v)* member(w,x). % 300.04/300.42 217326[0:Res:16231.2,25.1] || subclass(u,complement(v)) member(not_subclass_element(intersection(u,w),x),v)* -> subclass(intersection(u,w),x). % 300.04/300.42 217331[0:Res:16231.2,148647.0] || subclass(u,complement(complement(v))) -> subclass(intersection(u,w),x) member(not_subclass_element(intersection(u,w),x),v)*. % 300.04/300.42 217340[0:Res:16231.2,22.0] || subclass(u,intersection(v,w))* -> subclass(intersection(u,x),y) member(not_subclass_element(intersection(u,x),y),v)*. % 300.04/300.42 217341[0:Res:16231.2,23.0] || subclass(u,intersection(v,w))* -> subclass(intersection(u,x),y) member(not_subclass_element(intersection(u,x),y),w)*. % 300.04/300.42 217360[19:Res:16231.2,192214.0] || subclass(u,cantor(complement(cross_product(singleton(not_subclass_element(intersection(u,v),w)),universal_class))))* -> subclass(intersection(u,v),w). % 300.04/300.42 217365[19:Res:16231.2,169207.0] || subclass(u,symmetrization_of(ordinal_numbers)) -> subclass(intersection(u,v),w) member(not_subclass_element(intersection(u,v),w),inverse(ordinal_numbers))*. % 300.04/300.42 217632[0:Res:16235.1,4178.0] || -> subclass(intersection(intersection(u,singleton(v)),w),x) equal(not_subclass_element(intersection(intersection(u,singleton(v)),w),x),v)**. % 300.04/300.42 218040[0:Res:217853.0,16469.0] || -> subclass(complement(complement(intersection(u,singleton(v)))),w) equal(not_subclass_element(complement(complement(intersection(u,singleton(v)))),w),v)**. % 300.04/300.42 218229[0:Res:16234.1,4178.0] || -> subclass(intersection(intersection(singleton(u),v),w),x) equal(not_subclass_element(intersection(intersection(singleton(u),v),w),x),u)**. % 300.04/300.42 218415[19:Res:218022.0,167728.0] || subclass(complement(u),v) -> equal(complement(union(w,u)),ordinal_numbers) member(regular(complement(union(w,u))),v)*. % 300.04/300.42 218448[19:Res:218408.0,167133.0] || well_ordering(u,complement(image(successor_relation,ordinal_numbers))) -> equal(complement(kind_1_ordinals),ordinal_numbers) member(least(u,complement(kind_1_ordinals)),complement(kind_1_ordinals))*. % 300.04/300.42 218466[19:Res:218395.0,167276.0] || well_ordering(u,complement(singleton(v))) -> equal(segment(u,complement(successor(v)),least(u,complement(successor(v)))),ordinal_numbers)**. % 300.04/300.42 218485[19:Res:218396.0,167276.0] || well_ordering(u,complement(inverse(v))) -> equal(segment(u,complement(symmetrization_of(v)),least(u,complement(symmetrization_of(v)))),ordinal_numbers)**. % 300.04/300.42 218563[0:Res:16358.2,25.1] || subclass(u,complement(v)) member(not_subclass_element(intersection(w,u),x),v)* -> subclass(intersection(w,u),x). % 300.04/300.42 218568[0:Res:16358.2,148647.0] || subclass(u,complement(complement(v))) -> subclass(intersection(w,u),x) member(not_subclass_element(intersection(w,u),x),v)*. % 300.04/300.42 218577[0:Res:16358.2,22.0] || subclass(u,intersection(v,w))* -> subclass(intersection(x,u),y) member(not_subclass_element(intersection(x,u),y),v)*. % 300.04/300.42 218578[0:Res:16358.2,23.0] || subclass(u,intersection(v,w))* -> subclass(intersection(x,u),y) member(not_subclass_element(intersection(x,u),y),w)*. % 300.04/300.42 218597[19:Res:16358.2,192214.0] || subclass(u,cantor(complement(cross_product(singleton(not_subclass_element(intersection(v,u),w)),universal_class))))* -> subclass(intersection(v,u),w). % 300.04/300.42 218602[19:Res:16358.2,169207.0] || subclass(u,symmetrization_of(ordinal_numbers)) -> subclass(intersection(v,u),w) member(not_subclass_element(intersection(v,u),w),inverse(ordinal_numbers))*. % 300.04/300.42 218820[0:Res:217850.0,16469.0] || -> subclass(intersection(u,intersection(v,singleton(w))),x) equal(not_subclass_element(intersection(u,intersection(v,singleton(w))),x),w)**. % 300.04/300.42 219094[19:Res:218952.0,167728.0] || subclass(inverse(ordinal_numbers),u) -> equal(intersection(symmetrization_of(ordinal_numbers),v),ordinal_numbers) member(regular(intersection(symmetrization_of(ordinal_numbers),v)),u)*. % 300.04/300.42 219397[19:Res:219077.0,167728.0] || subclass(inverse(ordinal_numbers),u) -> equal(intersection(v,symmetrization_of(ordinal_numbers)),ordinal_numbers) member(regular(intersection(v,symmetrization_of(ordinal_numbers))),u)*. % 300.04/300.42 219519[0:Res:16361.1,4178.0] || -> subclass(intersection(u,intersection(singleton(v),w)),x) equal(not_subclass_element(intersection(u,intersection(singleton(v),w)),x),v)**. % 300.04/300.42 219727[0:Res:218920.0,16469.0] || -> subclass(intersection(complement(complement(singleton(u))),v),w) equal(not_subclass_element(intersection(complement(complement(singleton(u))),v),w),u)**. % 300.04/300.42 219977[0:Res:219703.0,16469.0] || -> subclass(complement(complement(complement(complement(singleton(u))))),v) equal(not_subclass_element(complement(complement(complement(complement(singleton(u))))),v),u)**. % 300.04/300.42 220075[0:Res:58.0,16462.0] || subclass(cross_product(universal_class,universal_class),u) -> subclass(compose(v,w),x) member(not_subclass_element(compose(v,w),x),u)*. % 300.04/300.42 220079[0:Res:33.0,16462.0] || subclass(cross_product(cross_product(universal_class,universal_class),universal_class),u)* -> subclass(rotate(v),w) member(not_subclass_element(rotate(v),w),u)*. % 300.04/300.42 220080[0:Res:36.0,16462.0] || subclass(cross_product(cross_product(universal_class,universal_class),universal_class),u)* -> subclass(flip(v),w) member(not_subclass_element(flip(v),w),u)*. % 300.04/300.42 220106[0:Res:218396.0,16462.0] || subclass(complement(inverse(u)),v) -> subclass(complement(symmetrization_of(u)),w) member(not_subclass_element(complement(symmetrization_of(u)),w),v)*. % 300.04/300.42 220107[0:Res:218395.0,16462.0] || subclass(complement(singleton(u)),v) -> subclass(complement(successor(u)),w) member(not_subclass_element(complement(successor(u)),w),v)*. % 300.04/300.42 220213[0:Res:218971.0,16469.0] || -> subclass(complement(complement(intersection(singleton(u),v))),w) equal(not_subclass_element(complement(complement(intersection(singleton(u),v))),w),u)**. % 300.04/300.42 220355[0:Res:219700.0,16469.0] || -> subclass(intersection(u,complement(complement(singleton(v)))),w) equal(not_subclass_element(intersection(u,complement(complement(singleton(v)))),w),v)**. % 300.04/300.42 220447[19:Res:220194.0,167728.0] || subclass(complement(u),v) -> equal(complement(union(u,w)),ordinal_numbers) member(regular(complement(union(u,w))),v)*. % 300.04/300.42 220751[25:SpR:192881.1,125327.1] function(restrict(cross_product(u,v),w,x)) || section(cross_product(w,x),v,u)* -> subclass(universal_class,v). % 300.04/300.42 221263[27:SpL:149012.1,221036.1] || subclass(image(successor_relation,ordinal_numbers),singleton(ordinal_numbers)) member(u,kind_1_ordinals) member(u,complement(image(successor_relation,ordinal_numbers)))* -> . % 300.04/300.42 221306[27:Res:167131.2,221036.1] || subclass(u,complement(intersection(singleton(ordinal_numbers),image(successor_relation,ordinal_numbers))))* member(regular(u),kind_1_ordinals) -> equal(u,ordinal_numbers). % 300.04/300.42 221775[19:Res:219766.1,8668.2] || equal(complement(u),ordinal_numbers) member(v,w)* member(x,y)* -> member(ordered_pair(x,v),u)*. % 300.04/300.42 222041[19:Res:219766.1,177427.0] || equal(complement(u),ordinal_numbers) well_ordering(omega,u)* -> equal(integer_of(ordered_pair(singleton(v),least(omega,universal_class))),ordinal_numbers)**. % 300.04/300.42 222640[0:Rew:29.0,222573.1] single_valued_class(restrict(intersection(u,cross_product(universal_class,universal_class)),v,w)) || -> function(restrict(restrict(u,universal_class,universal_class),v,w))*. % 300.04/300.42 222882[0:Rew:30.0,222815.1] single_valued_class(restrict(intersection(cross_product(universal_class,universal_class),u),v,w)) || -> function(restrict(restrict(u,universal_class,universal_class),v,w))*. % 300.04/300.42 223544[8:Res:27190.1,125075.0] || subclass(rest_relation,flip(cross_product(universal_class,universal_class))) subclass(composition_function,rest_of(u)) -> member(ordered_pair(v,w),cantor(u))*. % 300.04/300.42 223547[19:Res:176419.1,125075.0] || subclass(domain_relation,flip(cross_product(universal_class,universal_class))) subclass(composition_function,rest_of(u)) -> member(ordered_pair(v,w),cantor(u))*. % 300.04/300.42 223749[19:Res:38094.1,217129.1] || member(ordinal_numbers,union(u,v)) equal(complement(intersection(u,v)),kind_1_ordinals) -> member(ordinal_numbers,symmetric_difference(u,v))*. % 300.04/300.42 223764[19:Res:7968.2,217129.1] || member(ordinal_numbers,cross_product(u,v)) member(ordinal_numbers,w) equal(complement(restrict(w,u,v)),kind_1_ordinals)** -> . % 300.04/300.42 223771[19:Res:59.1,217129.1] || member(ordered_pair(u,ordinal_numbers),compose(v,w)) equal(complement(image(v,image(w,singleton(u)))),kind_1_ordinals)** -> . % 300.04/300.42 223886[0:Res:2479.1,14972.1] || subclass(universal_class,power_class(intersection(complement(u),complement(v)))) member(singleton(w),image(element_relation,union(u,v)))* -> . % 300.04/300.42 223940[19:Res:169181.1,14972.1] || equal(power_class(intersection(complement(u),complement(v))),singleton(ordinal_numbers)) member(ordinal_numbers,image(element_relation,union(u,v)))* -> . % 300.04/300.42 223948[19:Res:196731.1,14972.1] || subclass(universal_class,power_class(intersection(complement(u),complement(v)))) member(regular(element_relation),image(element_relation,union(u,v)))* -> . % 300.04/300.42 224043[19:Res:219766.1,34759.2] function(u) || equal(complement(singleton(v)),ordinal_numbers)** member(w,universal_class) -> equal(image(u,w),v)*. % 300.04/300.42 224239[20:Rew:167222.1,224231.2] || subclass(inverse(ordinal_numbers),u) -> equal(singleton(not_subclass_element(inverse(ordinal_numbers),ordinal_numbers)),ordinal_numbers) member(not_subclass_element(inverse(ordinal_numbers),ordinal_numbers),u)*. % 300.04/300.42 224253[20:Rew:167222.1,224245.2] || subclass(inverse(ordinal_numbers),u) -> equal(singleton(not_subclass_element(symmetrization_of(ordinal_numbers),ordinal_numbers)),ordinal_numbers) member(not_subclass_element(symmetrization_of(ordinal_numbers),ordinal_numbers),u)*. % 300.04/300.42 224462[0:Res:27190.1,41507.0] || subclass(rest_relation,flip(cross_product(universal_class,universal_class)))* subclass(composition_function,cross_product(u,v))* -> member(ordered_pair(w,x),u)*. % 300.04/300.42 224465[19:Res:176419.1,41507.0] || subclass(domain_relation,flip(cross_product(universal_class,universal_class)))* subclass(composition_function,cross_product(u,v))* -> member(ordered_pair(w,x),u)*. % 300.04/300.42 224705[19:Res:219766.1,167723.1] || equal(complement(singleton(u)),ordinal_numbers)** member(v,universal_class) -> equal(v,ordinal_numbers) equal(apply(choice,v),u)*. % 300.04/300.42 224882[25:Rew:193223.1,224876.1] function(u) || -> equal(cross_product(v,ordinal_numbers),ordinal_numbers) equal(domain__dfg(regular(cross_product(v,ordinal_numbers)),v,u),single_valued3(ordinal_numbers))**. % 300.04/300.42 225229[19:Obv:225193.1] || subclass(symmetric_difference(complement(u),complement(v)),complement(union(u,v)))* -> equal(symmetric_difference(complement(u),complement(v)),ordinal_numbers). % 300.04/300.42 225314[25:Rew:225311.2,225306.3] function(u) || subclass(omega,composition_function) -> equal(integer_of(ordered_pair(v,singleton(singleton(ordinal_numbers)))),ordinal_numbers)** equal(universal_class,u)*. % 300.04/300.42 225362[19:Res:55.1,176248.0] || member(u,universal_class) subclass(domain_relation,v)* subclass(v,w)* -> member(ordered_pair(sum_class(u),ordinal_numbers),w)*. % 300.04/300.42 225363[19:Res:57.1,176248.0] || member(u,universal_class) subclass(domain_relation,v)* subclass(v,w)* -> member(ordered_pair(power_class(u),ordinal_numbers),w)*. % 300.04/300.42 225364[19:Res:15058.1,176248.0] function(u) || subclass(domain_relation,v)* subclass(v,w)* -> member(ordered_pair(apply(u,x),ordinal_numbers),w)*. % 300.04/300.42 225365[19:Res:36682.1,176248.0] || subclass(domain_relation,u)* subclass(u,v)* -> subclass(w,x) member(ordered_pair(not_subclass_element(w,x),ordinal_numbers),v)*. % 300.04/300.42 225372[19:Res:149603.1,176248.0] || member(u,universal_class) subclass(domain_relation,v)* subclass(v,w)* -> member(ordered_pair(rest_of(u),ordinal_numbers),w)*. % 300.04/300.42 225803[19:SpR:207699.0,190665.0] || -> equal(intersection(union(intersection(power_class(u),complement(v)),w),intersection(union(complement(power_class(u)),v),complement(w))),ordinal_numbers)**. % 300.04/300.42 225804[19:SpR:207699.0,190801.0] || -> equal(union(union(intersection(power_class(u),complement(v)),w),intersection(union(complement(power_class(u)),v),complement(w))),universal_class)**. % 300.04/300.42 225805[19:SpR:207699.0,190813.0] || -> equal(symmetric_difference(union(intersection(power_class(u),complement(v)),w),intersection(union(complement(power_class(u)),v),complement(w))),universal_class)**. % 300.04/300.42 225816[0:SpR:207699.0,220426.0] || -> subclass(complement(successor(intersection(union(complement(power_class(u)),v),complement(w)))),union(intersection(power_class(u),complement(v)),w))*. % 300.04/300.42 225817[0:SpR:207699.0,220427.0] || -> subclass(complement(symmetrization_of(intersection(union(complement(power_class(u)),v),complement(w)))),union(intersection(power_class(u),complement(v)),w))*. % 300.04/300.42 226023[19:Rew:167055.0,225891.1] || equal(complement(union(complement(power_class(u)),v)),universal_class) -> equal(union(intersection(power_class(u),complement(v)),w),universal_class)**. % 300.04/300.42 226393[19:SpR:207747.0,190665.0] || -> equal(intersection(union(intersection(complement(u),power_class(v)),w),intersection(union(u,complement(power_class(v))),complement(w))),ordinal_numbers)**. % 300.04/300.42 226394[19:SpR:207747.0,190801.0] || -> equal(union(union(intersection(complement(u),power_class(v)),w),intersection(union(u,complement(power_class(v))),complement(w))),universal_class)**. % 300.04/300.42 226395[19:SpR:207747.0,190813.0] || -> equal(symmetric_difference(union(intersection(complement(u),power_class(v)),w),intersection(union(u,complement(power_class(v))),complement(w))),universal_class)**. % 300.04/300.42 226406[0:SpR:207747.0,220426.0] || -> subclass(complement(successor(intersection(union(u,complement(power_class(v))),complement(w)))),union(intersection(complement(u),power_class(v)),w))*. % 300.04/300.42 226407[0:SpR:207747.0,220427.0] || -> subclass(complement(symmetrization_of(intersection(union(u,complement(power_class(v))),complement(w)))),union(intersection(complement(u),power_class(v)),w))*. % 300.04/300.42 226614[19:Rew:167055.0,226481.1] || equal(complement(union(u,complement(power_class(v)))),universal_class) -> equal(union(intersection(complement(u),power_class(v)),w),universal_class)**. % 300.04/300.42 226749[19:SpR:207751.0,190665.0] || -> equal(intersection(union(u,intersection(power_class(v),complement(w))),intersection(complement(u),union(complement(power_class(v)),w))),ordinal_numbers)**. % 300.04/300.42 226750[19:SpR:207751.0,190801.0] || -> equal(union(union(u,intersection(power_class(v),complement(w))),intersection(complement(u),union(complement(power_class(v)),w))),universal_class)**. % 300.04/300.42 226751[19:SpR:207751.0,190813.0] || -> equal(symmetric_difference(union(u,intersection(power_class(v),complement(w))),intersection(complement(u),union(complement(power_class(v)),w))),universal_class)**. % 300.04/300.42 226762[0:SpR:207751.0,220426.0] || -> subclass(complement(successor(intersection(complement(u),union(complement(power_class(v)),w)))),union(u,intersection(power_class(v),complement(w))))*. % 300.04/300.42 226763[0:SpR:207751.0,220427.0] || -> subclass(complement(symmetrization_of(intersection(complement(u),union(complement(power_class(v)),w)))),union(u,intersection(power_class(v),complement(w))))*. % 300.04/300.42 226975[19:Rew:167055.0,226848.1] || equal(complement(union(complement(power_class(u)),v)),universal_class) -> equal(union(w,intersection(power_class(u),complement(v))),universal_class)**. % 300.04/300.42 227072[0:SpR:207752.0,16276.0] || -> subclass(symmetric_difference(union(u,complement(power_class(v))),union(complement(u),power_class(v))),complement(symmetric_difference(complement(u),power_class(v))))*. % 300.04/300.42 227441[19:SpR:207766.0,190665.0] || -> equal(intersection(union(u,intersection(complement(v),power_class(w))),intersection(complement(u),union(v,complement(power_class(w))))),ordinal_numbers)**. % 300.04/300.42 227442[19:SpR:207766.0,190801.0] || -> equal(union(union(u,intersection(complement(v),power_class(w))),intersection(complement(u),union(v,complement(power_class(w))))),universal_class)**. % 300.04/300.42 227443[19:SpR:207766.0,190813.0] || -> equal(symmetric_difference(union(u,intersection(complement(v),power_class(w))),intersection(complement(u),union(v,complement(power_class(w))))),universal_class)**. % 300.04/300.42 227454[0:SpR:207766.0,220426.0] || -> subclass(complement(successor(intersection(complement(u),union(v,complement(power_class(w)))))),union(u,intersection(complement(v),power_class(w))))*. % 300.04/300.42 227455[0:SpR:207766.0,220427.0] || -> subclass(complement(symmetrization_of(intersection(complement(u),union(v,complement(power_class(w)))))),union(u,intersection(complement(v),power_class(w))))*. % 300.04/300.42 227532[0:SpR:160.0,207766.0] || -> equal(union(intersection(u,complement(power_class(v))),intersection(complement(u),power_class(v))),complement(symmetric_difference(u,complement(power_class(v)))))**. % 300.04/300.42 227668[19:Rew:167055.0,227540.1] || equal(complement(union(u,complement(power_class(v)))),universal_class) -> equal(union(w,intersection(complement(u),power_class(v))),universal_class)**. % 300.04/300.42 227834[19:Res:221767.1,168249.0] || equal(complement(regular(u)),ordinal_numbers) member(regular(element_relation),u)* well_ordering(v,w)* -> equal(u,ordinal_numbers). % 300.04/300.42 227835[19:Res:221767.1,168251.0] || equal(complement(regular(u)),ordinal_numbers) member(regular(element_relation),u)* -> equal(u,ordinal_numbers) member(regular(element_relation),v)*. % 300.04/300.42 227891[0:Res:36606.3,4178.0] || member(u,universal_class) member(v,u) subclass(element_relation,singleton(w))* -> equal(ordered_pair(v,u),w)*. % 300.04/300.42 227941[0:Res:36606.3,94.0] || member(u,universal_class)* member(v,u)* subclass(element_relation,compose_class(w))* -> equal(compose(w,v),u)*. % 300.04/300.42 227970[0:MRR:227938.2,19.0] || member(u,universal_class) member(v,u) equal(successor(v),u) -> member(ordered_pair(v,u),successor_relation)*. % 300.04/300.42 228062[19:Res:219766.1,16162.1] || equal(complement(restrict(u,v,w)),ordinal_numbers)** member(x,universal_class) -> member(sum_class(x),cross_product(v,w))*. % 300.04/300.42 228097[19:Res:219766.1,27149.1] || equal(complement(restrict(u,v,w)),ordinal_numbers)** member(x,universal_class) -> member(ordered_pair(x,rest_of(x)),u)*. % 300.04/300.42 228201[19:Res:219766.1,16161.1] || equal(complement(restrict(u,v,w)),ordinal_numbers)** member(x,universal_class) -> member(power_class(x),cross_product(v,w))*. % 300.04/300.42 228353[19:Res:224120.1,16462.0] || equal(symmetrization_of(ordinal_numbers),u) subclass(inverse(ordinal_numbers),v) -> subclass(u,w) member(not_subclass_element(u,w),v)*. % 300.04/300.42 228356[19:Res:224120.1,167276.0] || equal(symmetrization_of(ordinal_numbers),u) well_ordering(v,inverse(ordinal_numbers)) -> equal(segment(v,u,least(v,u)),ordinal_numbers)**. % 300.04/300.42 228357[19:Res:224120.1,167133.0] || equal(symmetrization_of(ordinal_numbers),u) well_ordering(v,inverse(ordinal_numbers)) -> equal(u,ordinal_numbers) member(least(v,u),u)*. % 300.04/300.42 228358[19:Res:224120.1,9856.0] || equal(symmetrization_of(ordinal_numbers),u) well_ordering(v,inverse(ordinal_numbers)) -> subclass(u,w)* member(least(v,u),u)*. % 300.04/300.42 228436[19:Res:224120.1,16107.1] || equal(complement(intersection(u,v)),symmetrization_of(ordinal_numbers)) member(w,symmetric_difference(u,v))* -> member(w,inverse(ordinal_numbers)). % 300.04/300.42 228832[0:Res:63.1,206475.1] function(power_class(u)) || member(v,universal_class) -> member(v,complement(power_class(u)))* member(v,cross_product(universal_class,universal_class))*. % 300.04/300.42 230432[0:Obv:230318.2] || equal(u,v) member(v,symmetric_difference(w,x)) -> subclass(unordered_pair(v,u),complement(intersection(w,x)))*. % 300.04/300.42 230609[2:Res:144532.1,79427.2] || equal(intersection(u,inverse(u)),universal_class)** asymmetric(u,v)* member(singleton(w),cross_product(v,v))* -> . % 300.04/300.42 230611[2:Res:2479.1,79427.2] || subclass(universal_class,intersection(u,inverse(u)))* asymmetric(u,v)* member(singleton(w),cross_product(v,v))* -> . % 300.04/300.42 230612[19:Res:205414.1,79427.2] || equal(complement(intersection(u,inverse(u))),ordinal_numbers)** asymmetric(u,v)* member(omega,cross_product(v,v))* -> . % 300.04/300.42 230663[19:Res:205391.1,79427.2] || equal(complement(intersection(u,inverse(u))),ordinal_numbers)** asymmetric(u,v)* member(ordinal_numbers,cross_product(v,v))* -> . % 300.04/300.42 230666[19:Res:169181.1,79427.2] || equal(intersection(u,inverse(u)),singleton(ordinal_numbers))** asymmetric(u,v)* member(ordinal_numbers,cross_product(v,v))* -> . % 300.04/300.42 230675[19:Res:196731.1,79427.2] || subclass(universal_class,intersection(u,inverse(u)))* asymmetric(u,v)* member(regular(element_relation),cross_product(v,v))* -> . % 300.04/300.42 230699[19:Res:219766.1,167722.0] || equal(complement(unordered_pair(u,v)),ordinal_numbers)** -> equal(w,ordinal_numbers) equal(regular(w),v)* equal(regular(w),u)*. % 300.04/300.42 231055[19:Res:229698.1,9773.1] || equal(successor(segment(u,v,w)),ordinal_numbers)** subclass(singleton(w),v) -> section(u,singleton(w),v). % 300.04/300.42 231535[19:Obv:231486.1] || subclass(intersection(symmetric_difference(u,v),w),complement(union(u,v)))* -> equal(intersection(symmetric_difference(u,v),w),ordinal_numbers). % 300.04/300.42 231768[19:Obv:231721.1] || subclass(intersection(u,symmetric_difference(v,w)),complement(union(v,w)))* -> equal(intersection(u,symmetric_difference(v,w)),ordinal_numbers). % 300.04/300.42 232042[19:Res:38094.1,225687.1] || member(ordinal_numbers,union(u,v)) equal(symmetrization_of(intersection(u,v)),ordinal_numbers) -> member(ordinal_numbers,symmetric_difference(u,v))*. % 300.04/300.42 232057[19:Res:7968.2,225687.1] || member(ordinal_numbers,cross_product(u,v)) member(ordinal_numbers,w) equal(symmetrization_of(restrict(w,u,v)),ordinal_numbers)** -> . % 300.04/300.42 232064[19:Res:59.1,225687.1] || member(ordered_pair(u,ordinal_numbers),compose(v,w)) equal(symmetrization_of(image(v,image(w,singleton(u)))),ordinal_numbers)** -> . % 300.04/300.42 232348[19:Rew:169229.1,232254.3] || subclass(u,v) member(not_subclass_element(u,ordinal_numbers),singleton(v))* -> equal(singleton(v),ordinal_numbers) subclass(u,ordinal_numbers). % 300.04/300.42 232386[19:Rew:199255.0,232271.2] || subclass(u,singleton(ordinal_numbers)) member(not_subclass_element(u,ordinal_numbers),intersection(complement(singleton(ordinal_numbers)),v))* -> subclass(u,ordinal_numbers). % 300.04/300.42 232387[19:Rew:198938.0,232270.2] || subclass(u,intersection(v,complement(inverse(ordinal_numbers))))* member(not_subclass_element(u,ordinal_numbers),symmetrization_of(ordinal_numbers)) -> subclass(u,ordinal_numbers). % 300.04/300.42 232388[19:Rew:198291.0,232269.2] || subclass(u,intersection(complement(inverse(ordinal_numbers)),v))* member(not_subclass_element(u,ordinal_numbers),symmetrization_of(ordinal_numbers)) -> subclass(u,ordinal_numbers). % 300.04/300.42 232389[19:Rew:198937.0,232263.2] || subclass(u,intersection(v,complement(singleton(ordinal_numbers))))* member(not_subclass_element(u,ordinal_numbers),singleton(ordinal_numbers)) -> subclass(u,ordinal_numbers). % 300.04/300.42 232390[19:Rew:198290.0,232262.2] || subclass(u,intersection(complement(singleton(ordinal_numbers)),v))* member(not_subclass_element(u,ordinal_numbers),singleton(ordinal_numbers)) -> subclass(u,ordinal_numbers). % 300.04/300.42 232398[0:MRR:232280.0,36682.1] || subclass(u,v) -> member(not_subclass_element(u,intersection(complement(w),v)),w)* subclass(u,intersection(complement(w),v)). % 300.04/300.42 232699[19:Rew:169229.1,232503.2] || member(not_subclass_element(intersection(u,v),ordinal_numbers),singleton(v))* -> equal(singleton(v),ordinal_numbers) subclass(intersection(u,v),ordinal_numbers). % 300.04/300.42 232703[19:Rew:169201.1,232472.2] || member(not_subclass_element(intersection(u,regular(v)),ordinal_numbers),v)* -> equal(v,ordinal_numbers) subclass(intersection(u,regular(v)),ordinal_numbers). % 300.04/300.42 232730[19:Rew:197702.0,232454.1] || member(not_subclass_element(intersection(u,intersection(v,w)),ordinal_numbers),complement(w))* -> subclass(intersection(u,intersection(v,w)),ordinal_numbers). % 300.04/300.42 232731[19:Rew:197499.0,232453.1] || member(not_subclass_element(intersection(u,intersection(v,w)),ordinal_numbers),complement(v))* -> subclass(intersection(u,intersection(v,w)),ordinal_numbers). % 300.04/300.42 232739[19:Rew:199281.0,232482.1] || member(not_subclass_element(intersection(u,complement(v)),ordinal_numbers),restrict(v,w,x))* -> subclass(intersection(u,complement(v)),ordinal_numbers). % 300.04/300.42 232763[0:MRR:232592.0,36682.1] || -> member(not_subclass_element(intersection(u,v),intersection(complement(w),v)),w)* subclass(intersection(u,v),intersection(complement(w),v)). % 300.04/300.42 232798[19:Res:38094.1,225690.1] || member(omega,union(u,v)) equal(symmetrization_of(intersection(u,v)),ordinal_numbers) -> member(omega,symmetric_difference(u,v))*. % 300.04/300.42 232813[19:Res:7968.2,225690.1] || member(omega,cross_product(u,v)) member(omega,w) equal(symmetrization_of(restrict(w,u,v)),ordinal_numbers)** -> . % 300.04/300.42 232826[19:Res:59.1,225690.1] || member(ordered_pair(u,omega),compose(v,w)) equal(symmetrization_of(image(v,image(w,singleton(u)))),ordinal_numbers)** -> . % 300.04/300.42 233086[19:Rew:169229.1,232895.2] || member(not_subclass_element(intersection(u,v),ordinal_numbers),singleton(u))* -> equal(singleton(u),ordinal_numbers) subclass(intersection(u,v),ordinal_numbers). % 300.04/300.42 233090[19:Rew:169201.1,232864.2] || member(not_subclass_element(intersection(regular(u),v),ordinal_numbers),u)* -> equal(u,ordinal_numbers) subclass(intersection(regular(u),v),ordinal_numbers). % 300.04/300.42 233122[19:Rew:197702.0,232846.1] || member(not_subclass_element(intersection(intersection(u,v),w),ordinal_numbers),complement(v))* -> subclass(intersection(intersection(u,v),w),ordinal_numbers). % 300.04/300.42 233123[19:Rew:197499.0,232845.1] || member(not_subclass_element(intersection(intersection(u,v),w),ordinal_numbers),complement(u))* -> subclass(intersection(intersection(u,v),w),ordinal_numbers). % 300.04/300.42 233132[19:Rew:199281.0,232874.1] || member(not_subclass_element(intersection(complement(u),v),ordinal_numbers),restrict(u,w,x))* -> subclass(intersection(complement(u),v),ordinal_numbers). % 300.04/300.42 233154[0:MRR:232984.0,36682.1] || -> member(not_subclass_element(intersection(u,v),intersection(complement(w),u)),w)* subclass(intersection(u,v),intersection(complement(w),u)). % 300.04/300.42 233322[0:Res:233022.0,16462.0] || subclass(intersection(u,v),w) -> subclass(intersection(v,u),x) member(not_subclass_element(intersection(v,u),x),w)*. % 300.04/300.42 233325[19:Res:233022.0,167276.0] || well_ordering(u,intersection(v,w)) -> equal(segment(u,intersection(w,v),least(u,intersection(w,v))),ordinal_numbers)**. % 300.04/300.42 234272[19:Rew:233390.0,167884.2] inductive(symmetric_difference(u,singleton_relation)) || well_ordering(v,universal_class) -> member(least(v,complement(complement(u))),complement(complement(u)))*. % 300.04/300.42 234813[19:Rew:234692.0,175989.2] || -> equal(regular(unordered_pair(u,v)),v) equal(unordered_pair(u,v),ordinal_numbers) equal(intersection(u,unordered_pair(u,v)),ordinal_numbers)**. % 300.04/300.42 234839[19:Rew:234692.0,180322.1] || member(u,universal_class) -> member(u,intersection(singleton(ordinal_numbers),complement(v)))* member(u,union(v,complement(singleton(ordinal_numbers)))). % 300.04/300.42 234868[19:Rew:234692.0,175990.2] || -> equal(regular(unordered_pair(u,v)),u) equal(unordered_pair(u,v),ordinal_numbers) equal(intersection(v,unordered_pair(u,v)),ordinal_numbers)**. % 300.04/300.42 235566[25:Rew:235542.0,234314.1] function(intersection(complement(u),complement(v))) || -> equal(successor(intersection(complement(u),complement(v))),complement(union(u,v)))**. % 300.04/300.42 236270[19:SpR:234692.0,168222.2] || member(intersection(u,v),universal_class) -> equal(intersection(u,v),ordinal_numbers) member(apply(choice,intersection(v,u)),v)*. % 300.04/300.42 236271[19:SpR:234692.0,168223.2] || member(intersection(u,v),universal_class) -> equal(intersection(u,v),ordinal_numbers) member(apply(choice,intersection(v,u)),u)*. % 300.04/300.42 236524[0:SpL:234692.0,7963.1] || member(u,union(v,w)) member(u,complement(intersection(w,v)))* -> member(u,symmetric_difference(v,w)). % 300.04/300.42 236676[0:Rew:236669.0,226840.0] || -> equal(union(intersection(power_class(u),complement(v)),intersection(complement(power_class(u)),v)),complement(symmetric_difference(complement(power_class(u)),v)))**. % 300.04/300.42 237078[19:Rew:237023.0,230087.0] || subclass(universal_class,symmetric_difference(union(u,v),complement(intersection(u,v))))* -> member(regular(element_relation),complement(symmetric_difference(u,v))). % 300.04/300.42 237082[0:Rew:237023.0,42655.0] || subclass(universal_class,symmetric_difference(union(u,v),complement(intersection(u,v))))* -> member(singleton(w),complement(symmetric_difference(u,v)))*. % 300.04/300.42 237085[0:Rew:237023.0,42661.0] || equal(symmetric_difference(union(u,v),complement(intersection(u,v))),universal_class)** -> member(singleton(w),complement(symmetric_difference(u,v)))*. % 300.04/300.42 237092[19:Rew:237023.0,230075.0] || equal(complement(symmetric_difference(union(u,v),complement(intersection(u,v)))),ordinal_numbers)** -> member(ordinal_numbers,complement(symmetric_difference(u,v))). % 300.04/300.42 237093[19:Rew:237023.0,230024.0] || equal(complement(symmetric_difference(union(u,v),complement(intersection(u,v)))),ordinal_numbers)** -> member(omega,complement(symmetric_difference(u,v))). % 300.04/300.42 237108[19:Rew:237023.0,196105.1] || equal(complement(complement(symmetric_difference(u,v))),universal_class) -> equal(symmetric_difference(union(u,v),complement(intersection(u,v))),ordinal_numbers)**. % 300.04/300.42 237115[19:Rew:237023.0,183715.0] || equal(symmetric_difference(union(u,v),complement(intersection(u,v))),singleton(ordinal_numbers))** -> member(ordinal_numbers,complement(symmetric_difference(u,v))). % 300.04/300.42 237425[0:Rew:237384.0,226106.0] || -> subclass(symmetric_difference(union(power_class(u),complement(v)),union(complement(power_class(u)),v)),complement(symmetric_difference(power_class(u),complement(v))))*. % 300.04/300.42 237457[0:Rew:237384.0,135836.0] || member(u,symmetric_difference(symmetrization_of(v),complement(intersection(v,inverse(v)))))* member(u,symmetric_difference(v,inverse(v))) -> . % 300.04/300.42 237499[19:Rew:237493.0,234893.0] || -> equal(intersection(successor(cross_product(u,v)),complement(restrict(singleton(cross_product(u,v)),u,v))),successor(cross_product(u,v)))**. % 300.04/300.42 237569[19:Rew:237493.0,35258.2] inductive(symmetric_difference(u,singleton(u))) || well_ordering(v,successor(u)) -> member(least(v,successor(u)),successor(u))*. % 300.04/300.42 237694[19:SpL:237493.0,16109.0] || member(not_subclass_element(u,complement(intersection(v,singleton(v)))),successor(v))* -> subclass(u,complement(intersection(v,singleton(v)))). % 300.04/300.42 237741[0:Res:237218.0,16462.0] || subclass(union(u,v),w) -> subclass(symmetric_difference(v,u),x) member(not_subclass_element(symmetric_difference(v,u),x),w)*. % 300.04/300.42 237744[19:Res:237218.0,167276.0] || well_ordering(u,union(v,w)) -> equal(segment(u,symmetric_difference(w,v),least(u,symmetric_difference(w,v))),ordinal_numbers)**. % 300.04/300.42 239146[19:SpL:237603.0,176249.1] || member(u,universal_class) subclass(domain_relation,successor(v)) -> member(ordered_pair(u,ordinal_numbers),complement(intersection(v,singleton(v))))*. % 300.04/300.42 239199[19:Rew:237603.0,239076.1] || subclass(complement(intersection(u,singleton(u))),v)* -> subclass(successor(u),w) member(not_subclass_element(successor(u),w),v)*. % 300.04/300.42 239200[19:Rew:237603.0,239070.1] || well_ordering(u,universal_class) -> equal(successor(v),ordinal_numbers) member(least(u,successor(v)),complement(intersection(v,singleton(v))))*. % 300.04/300.42 239201[19:Rew:237603.0,239066.0] || -> subclass(intersection(u,successor(v)),w) member(not_subclass_element(intersection(u,successor(v)),w),complement(intersection(v,singleton(v))))*. % 300.04/300.42 239202[19:Rew:237603.0,239054.0] || -> subclass(intersection(successor(u),v),w) member(not_subclass_element(intersection(successor(u),v),w),complement(intersection(u,singleton(u))))*. % 300.04/300.42 239241[19:EmS:167895.0,167895.1,12322.2,238779.1] single_valued_class(u) || equal(cross_product(universal_class,universal_class),u)* equal(u,universal_class) -> member(ordinal_numbers,cross_product(universal_class,universal_class))*. % 300.04/300.42 239760[19:Res:238770.1,4278.1] || equal(not_well_ordering(u,v),universal_class)** connected(u,v) -> well_ordering(u,v) equal(not_well_ordering(u,v),v). % 300.04/300.42 240523[19:Res:239914.1,27258.2] || equal(union(u,v),universal_class)** member(regular(element_relation),complement(v))* member(regular(element_relation),complement(u))* -> . % 300.04/300.42 240555[19:Res:239914.1,79427.2] || equal(intersection(u,inverse(u)),universal_class)** asymmetric(u,v)* member(regular(element_relation),cross_product(v,v))* -> . % 300.04/300.42 240630[19:Res:239132.1,167734.1] || member(regular(u),successor(v)) subclass(u,complement(complement(intersection(v,singleton(v)))))* -> equal(u,ordinal_numbers). % 300.04/300.42 240698[19:Res:237678.0,167276.0] || well_ordering(u,complement(intersection(v,singleton(v)))) -> equal(segment(u,successor(v),least(u,successor(v))),ordinal_numbers)**. % 300.04/300.42 240795[19:Res:236254.0,167728.0] || subclass(complement(intersection(u,v)),w) -> equal(symmetric_difference(v,u),ordinal_numbers) member(regular(symmetric_difference(v,u)),w)*. % 300.04/300.42 240889[19:Res:205991.1,237637.0] || equal(complement(symmetric_difference(successor(u),complement(intersection(u,singleton(u))))),ordinal_numbers)** -> member(singleton(v),complement(successor(u)))*. % 300.04/300.42 240890[19:Res:203424.1,237637.0] || subclass(complement(symmetric_difference(successor(u),complement(intersection(u,singleton(u))))),ordinal_numbers)* -> member(singleton(v),complement(successor(u)))*. % 300.04/300.42 240900[19:Res:2480.1,237637.0] || subclass(universal_class,symmetric_difference(successor(u),complement(intersection(u,singleton(u)))))* -> member(unordered_pair(v,w),complement(successor(u)))*. % 300.04/300.42 240910[19:Res:2481.1,237637.0] || subclass(universal_class,symmetric_difference(successor(u),complement(intersection(u,singleton(u)))))* -> member(ordered_pair(v,w),complement(successor(u)))*. % 300.04/300.42 240914[19:Res:167127.1,237637.0] || subclass(domain_relation,symmetric_difference(successor(u),complement(intersection(u,singleton(u)))))* -> member(ordered_pair(ordinal_numbers,ordinal_numbers),complement(successor(u))). % 300.04/300.42 240954[20:Res:175613.1,237637.0] || subclass(universal_class,symmetric_difference(successor(u),complement(intersection(u,singleton(u)))))* -> member(regular(symmetrization_of(ordinal_numbers)),complement(successor(u))). % 300.04/300.42 240957[19:Res:221767.1,237637.0] || equal(complement(symmetric_difference(successor(u),complement(intersection(u,singleton(u))))),ordinal_numbers)** -> member(regular(element_relation),complement(successor(u))). % 300.04/300.42 241483[19:Res:239914.1,236817.0] || equal(symmetric_difference(union(u,v),complement(intersection(u,v))),universal_class)** -> member(regular(element_relation),complement(symmetric_difference(u,v))). % 300.04/300.42 241700[19:Obv:241675.1] || subclass(intersection(u,restrict(v,w,x)),complement(v))* -> equal(intersection(u,restrict(v,w,x)),ordinal_numbers). % 300.04/300.42 241849[19:Obv:241820.1] || subclass(intersection(restrict(u,v,w),x),complement(u))* -> equal(intersection(restrict(u,v,w),x),ordinal_numbers). % 300.04/300.42 241966[19:Res:40490.2,205934.1] || equal(unordered_pair(u,v),ordinal_numbers) -> equal(not_subclass_element(unordered_pair(u,v),w),v)** subclass(unordered_pair(u,v),w). % 300.04/300.42 241983[19:Obv:241923.1] || subclass(omega,u) -> member(v,unordered_pair(v,w))* equal(integer_of(w),ordinal_numbers) subclass(unordered_pair(v,w),u)*. % 300.04/300.42 241991[0:Obv:241944.1] || member(u,v) -> member(w,unordered_pair(w,u)) subclass(unordered_pair(w,u),intersection(v,unordered_pair(w,u)))*. % 300.04/300.42 242168[19:Obv:242102.1] || subclass(omega,u) -> member(v,unordered_pair(w,v))* equal(integer_of(w),ordinal_numbers) subclass(unordered_pair(w,v),u)*. % 300.04/300.42 242176[0:Obv:242126.1] || member(u,v) -> member(w,unordered_pair(u,w)) subclass(unordered_pair(u,w),intersection(v,unordered_pair(u,w)))*. % 300.04/300.42 242274[19:Res:219766.1,16467.0] || equal(complement(restrict(u,v,w)),ordinal_numbers)** -> subclass(x,y) member(not_subclass_element(x,y),cross_product(v,w))*. % 300.04/300.42 242336[8:SoR:158715.0,72.1] one_to_one(union(identity_relation,symmetrization_of(u))) || connected(u,universal_class) -> equal(complement(complement(symmetrization_of(u))),cross_product(universal_class,universal_class))**. % 300.04/300.42 242369[8:SoR:161073.0,72.1] one_to_one(complement(complement(symmetrization_of(u)))) || connected(u,universal_class) -> equal(complement(complement(symmetrization_of(u))),cross_product(universal_class,universal_class))**. % 300.04/300.42 242850[19:Res:238770.1,177428.0] || equal(u,universal_class) well_ordering(omega,u)* -> equal(integer_of(ordered_pair(unordered_pair(v,w),least(omega,universal_class))),ordinal_numbers)**. % 300.04/300.42 243457[19:Res:238770.1,177429.0] || equal(u,universal_class) well_ordering(omega,u)* -> equal(integer_of(ordered_pair(ordered_pair(v,w),least(omega,universal_class))),ordinal_numbers)**. % 300.04/300.42 243724[19:MRR:243715.1,196718.0] || subclass(rest_relation,domain_relation) subclass(rest_relation,omega) -> equal(integer_of(ordered_pair(regular(element_relation),ordinal_numbers)),ordered_pair(regular(element_relation),ordinal_numbers))**. % 300.04/300.42 243725[19:MRR:243714.1,196718.0] || subclass(domain_relation,rest_relation) subclass(rest_relation,omega) -> equal(integer_of(ordered_pair(regular(element_relation),ordinal_numbers)),ordered_pair(regular(element_relation),ordinal_numbers))**. % 300.04/300.42 243726[19:MRR:243709.1,170.0] || subclass(domain_relation,rest_relation) subclass(rest_relation,omega) -> equal(integer_of(ordered_pair(singleton(u),ordinal_numbers)),ordered_pair(singleton(u),ordinal_numbers))**. % 300.04/300.42 243727[19:MRR:243708.1,170.0] || subclass(rest_relation,domain_relation) subclass(rest_relation,omega) -> equal(integer_of(ordered_pair(singleton(u),ordinal_numbers)),ordered_pair(singleton(u),ordinal_numbers))**. % 300.04/300.42 243811[19:Res:238770.1,204403.1] || equal(ordered_pair(u,v),universal_class)** member(w,universal_class)* -> equal(power_class(w),omega) equal(power_class(w),ordinal_numbers). % 300.04/300.42 243868[19:Res:238770.1,204404.1] || equal(ordered_pair(u,v),universal_class)** member(w,universal_class)* -> equal(sum_class(w),omega) equal(sum_class(w),ordinal_numbers). % 300.04/300.42 245182[0:SpL:234692.0,82309.0] || subclass(universal_class,complement(intersection(u,v)))* member(omega,union(v,u)) -> member(omega,symmetric_difference(v,u)). % 300.04/300.42 245665[19:Res:167116.0,34746.3] function(u) || member(v,universal_class) subclass(universal_class,complement(omega)) -> equal(integer_of(image(u,v)),ordinal_numbers)**. % 300.04/300.42 245749[19:Res:167224.0,104246.1] || member(u,universal_class)* equal(sum_class(image(v,w)),u)* -> equal(singleton(restrict(v,w,universal_class)),ordinal_numbers)**. % 300.04/300.42 245750[19:Res:167115.1,104246.1] || member(u,universal_class)* equal(sum_class(image(v,w)),u)* -> equal(integer_of(restrict(v,w,universal_class)),ordinal_numbers)**. % 300.04/300.42 245860[19:Res:167116.0,167717.2] || member(u,universal_class) subclass(u,complement(omega)) -> equal(integer_of(apply(choice,u)),ordinal_numbers)** equal(u,ordinal_numbers). % 300.04/300.42 245928[19:Res:7968.2,229738.1] || member(u,cross_product(v,w))* member(u,x)* equal(successor(restrict(x,v,w)),ordinal_numbers)** -> . % 300.04/300.42 245978[19:Res:9765.3,229738.1] || connected(u,v) well_ordering(w,v)* equal(successor(not_well_ordering(u,v)),ordinal_numbers)** -> well_ordering(u,v). % 300.04/300.42 246015[19:Res:9914.3,229738.1] || member(u,universal_class)* member(v,universal_class)* equal(successor(v),u)* equal(successor(successor_relation),ordinal_numbers) -> . % 300.04/300.42 246050[19:Res:59.1,229738.1] || member(ordered_pair(u,v),compose(w,x))* equal(successor(image(w,image(x,singleton(u)))),ordinal_numbers)** -> . % 300.04/300.42 246278[19:SpL:234692.0,168370.0] || subclass(omega,intersection(complement(u),complement(v)))* member(w,union(v,u))* -> equal(integer_of(w),ordinal_numbers). % 300.04/300.42 246295[19:Res:7.1,168370.0] || equal(intersection(complement(u),complement(v)),omega)** member(w,union(u,v))* -> equal(integer_of(w),ordinal_numbers). % 300.04/300.42 246343[25:SpR:234134.1,16826.0] function(u) || -> equal(power_class(intersection(successor(u),complement(singleton(complement(u))))),complement(image(element_relation,successor(complement(u)))))**. % 300.04/300.42 246345[25:SpR:234134.1,16825.0] function(u) || -> equal(power_class(intersection(successor(u),complement(inverse(complement(u))))),complement(image(element_relation,symmetrization_of(complement(u)))))**. % 300.04/300.42 246441[25:SpL:234134.1,82316.0] function(u) || subclass(universal_class,intersection(successor(u),complement(v)))* member(omega,union(complement(u),v)) -> . % 300.04/300.42 246524[25:SpL:234134.1,82316.0] function(u) || subclass(universal_class,intersection(complement(v),successor(u)))* member(omega,union(v,complement(u))) -> . % 300.04/300.42 246528[25:SpL:234134.1,488.0] function(u) || member(v,intersection(successor(u),complement(w)))* member(v,union(complement(u),w)) -> . % 300.04/300.42 246624[25:SpL:234134.1,488.0] function(u) || member(v,intersection(complement(w),successor(u)))* member(v,union(w,complement(u))) -> . % 300.04/300.42 246669[25:Rew:234134.1,246347.3] function(u) || subclass(omega,complement(u)) -> equal(integer_of(regular(successor(u))),ordinal_numbers)** equal(successor(u),ordinal_numbers). % 300.04/300.42 246670[25:Rew:234134.1,246506.2] function(u) || member(regular(intersection(successor(u),v)),complement(u))* -> equal(intersection(successor(u),v),ordinal_numbers). % 300.04/300.42 246671[25:Rew:234134.1,246534.2] function(u) || member(regular(intersection(v,successor(u))),complement(u))* -> equal(intersection(v,successor(u)),ordinal_numbers). % 300.04/300.42 246678[25:Rew:234134.1,246389.3,234134.1,246389.1] function(u) || member(successor(u),universal_class) -> member(apply(choice,successor(u)),u)* equal(successor(u),ordinal_numbers). % 300.04/300.42 246698[25:Res:246381.1,167133.0] function(u) || well_ordering(v,u) -> equal(successor(u),ordinal_numbers) member(least(v,successor(u)),successor(u))*. % 300.04/300.42 246700[25:Res:246381.1,9859.1] function(u) inductive(successor(u)) || well_ordering(v,u) -> member(least(v,successor(u)),successor(u))*. % 300.04/300.42 246703[25:Res:246381.1,167737.0] function(intersection(u,v)) || -> equal(successor(intersection(u,v)),ordinal_numbers) member(regular(successor(intersection(u,v))),v)*. % 300.04/300.42 246704[25:Res:246381.1,167736.0] function(intersection(u,v)) || -> equal(successor(intersection(u,v)),ordinal_numbers) member(regular(successor(intersection(u,v))),u)*. % 300.04/300.42 246741[19:SpL:237384.0,168451.0] || member(regular(complement(complement(intersection(u,v)))),symmetric_difference(v,u))* -> equal(complement(complement(intersection(u,v))),ordinal_numbers). % 300.04/300.42 246762[19:SpL:234692.0,168451.0] || member(regular(complement(complement(intersection(u,v)))),symmetric_difference(v,u))* -> equal(complement(complement(intersection(v,u))),ordinal_numbers). % 300.04/300.42 246830[19:Rew:149012.1,246795.2] || subclass(u,v) member(regular(complement(complement(u))),symmetric_difference(v,u))* -> equal(complement(complement(u)),ordinal_numbers). % 300.04/300.42 246837[19:Rew:27.0,246805.1] || member(regular(complement(union(u,v))),symmetric_difference(complement(u),complement(v)))* -> equal(complement(union(u,v)),ordinal_numbers). % 300.04/300.42 246896[19:SpL:236669.0,168602.0] || member(regular(intersection(complement(u),complement(v))),union(v,u))* -> equal(intersection(complement(u),complement(v)),ordinal_numbers). % 300.04/300.42 246957[19:SpL:234692.0,168602.0] || member(regular(intersection(complement(u),complement(v))),union(v,u))* -> equal(intersection(complement(v),complement(u)),ordinal_numbers). % 300.04/300.42 247135[19:Res:238770.1,15114.1] || equal(unordered_pair(u,v),universal_class)** member(w,universal_class)* -> equal(sum_class(w),v)* equal(sum_class(w),u)*. % 300.04/300.42 247704[0:SpR:236669.0,27157.2] || member(u,universal_class) subclass(rest_relation,symmetric_difference(v,w)) -> member(ordered_pair(u,rest_of(u)),union(w,v))*. % 300.04/300.42 247760[19:MRR:247729.1,196718.0] || subclass(rest_relation,domain_relation) subclass(rest_relation,symmetric_difference(u,v)) -> member(ordered_pair(regular(element_relation),ordinal_numbers),union(u,v))*. % 300.04/300.42 247761[19:MRR:247728.1,196718.0] || subclass(domain_relation,rest_relation) subclass(rest_relation,symmetric_difference(u,v)) -> member(ordered_pair(regular(element_relation),ordinal_numbers),union(u,v))*. % 300.04/300.42 247762[19:MRR:247723.1,170.0] || subclass(domain_relation,rest_relation) subclass(rest_relation,symmetric_difference(u,v)) -> member(ordered_pair(singleton(w),ordinal_numbers),union(u,v))*. % 300.04/300.42 247763[19:MRR:247722.1,170.0] || subclass(rest_relation,domain_relation) subclass(rest_relation,symmetric_difference(u,v)) -> member(ordered_pair(singleton(w),ordinal_numbers),union(u,v))*. % 300.04/300.42 248207[0:Res:12.0,27142.0] || subclass(rest_relation,u)* subclass(u,v)* -> member(ordered_pair(unordered_pair(w,x),rest_of(unordered_pair(w,x))),v)*. % 300.04/300.42 248208[0:Res:940.0,27142.0] || subclass(rest_relation,u)* subclass(u,v)* -> member(ordered_pair(ordered_pair(w,x),rest_of(ordered_pair(w,x))),v)*. % 300.04/300.42 248209[19:Res:167224.0,27142.0] || subclass(rest_relation,u)* subclass(u,v)* -> equal(singleton(w),ordinal_numbers) member(ordered_pair(w,rest_of(w)),v)*. % 300.04/300.42 248210[19:Res:167115.1,27142.0] || subclass(rest_relation,u)* subclass(u,v)* -> equal(integer_of(w),ordinal_numbers) member(ordered_pair(w,rest_of(w)),v)*. % 300.04/300.42 248224[20:Res:175569.0,27142.0] || subclass(rest_relation,u)* subclass(u,v)* -> member(ordered_pair(regular(symmetrization_of(ordinal_numbers)),rest_of(regular(symmetrization_of(ordinal_numbers)))),v)*. % 300.04/300.42 248802[0:Res:130.2,219712.0] || connected(u,complement(complement(v))) -> well_ordering(u,complement(complement(v))) subclass(not_well_ordering(u,complement(complement(v))),v)*. % 300.04/300.42 248833[0:SpR:207751.0,248818.0] || -> subclass(complement(successor(union(u,intersection(power_class(v),complement(w))))),intersection(complement(u),union(complement(power_class(v)),w)))*. % 300.04/300.42 248834[0:SpR:207766.0,248818.0] || -> subclass(complement(successor(union(u,intersection(complement(v),power_class(w))))),intersection(complement(u),union(v,complement(power_class(w)))))*. % 300.04/300.42 248836[0:SpR:207699.0,248818.0] || -> subclass(complement(successor(union(intersection(power_class(u),complement(v)),w))),intersection(union(complement(power_class(u)),v),complement(w)))*. % 300.04/300.42 248837[0:SpR:207747.0,248818.0] || -> subclass(complement(successor(union(intersection(complement(u),power_class(v)),w))),intersection(union(u,complement(power_class(v))),complement(w)))*. % 300.04/300.42 248856[0:Res:248818.0,16462.0] || subclass(u,v) -> subclass(complement(successor(complement(u))),w) member(not_subclass_element(complement(successor(complement(u))),w),v)*. % 300.04/300.42 248859[19:Res:248818.0,167276.0] || well_ordering(u,v) -> equal(segment(u,complement(successor(complement(v))),least(u,complement(successor(complement(v))))),ordinal_numbers)**. % 300.04/300.42 248867[0:Res:248818.0,16465.0] || -> subclass(complement(successor(complement(intersection(u,v)))),w) member(not_subclass_element(complement(successor(complement(intersection(u,v)))),w),u)*. % 300.04/300.42 248868[0:Res:248818.0,16466.0] || -> subclass(complement(successor(complement(intersection(u,v)))),w) member(not_subclass_element(complement(successor(complement(intersection(u,v)))),w),v)*. % 300.04/300.42 248935[19:Res:238770.1,15080.1] || equal(unordered_pair(u,v),universal_class)** member(w,universal_class)* -> equal(power_class(w),v)* equal(power_class(w),u)*. % 300.04/300.42 248950[0:SpR:207751.0,248819.0] || -> subclass(complement(symmetrization_of(union(u,intersection(power_class(v),complement(w))))),intersection(complement(u),union(complement(power_class(v)),w)))*. % 300.04/300.42 248951[0:SpR:207766.0,248819.0] || -> subclass(complement(symmetrization_of(union(u,intersection(complement(v),power_class(w))))),intersection(complement(u),union(v,complement(power_class(w)))))*. % 300.04/300.42 248953[0:SpR:207699.0,248819.0] || -> subclass(complement(symmetrization_of(union(intersection(power_class(u),complement(v)),w))),intersection(union(complement(power_class(u)),v),complement(w)))*. % 300.04/300.42 248954[0:SpR:207747.0,248819.0] || -> subclass(complement(symmetrization_of(union(intersection(complement(u),power_class(v)),w))),intersection(union(u,complement(power_class(v))),complement(w)))*. % 300.04/300.42 248973[0:Res:248819.0,16462.0] || subclass(u,v) -> subclass(complement(symmetrization_of(complement(u))),w) member(not_subclass_element(complement(symmetrization_of(complement(u))),w),v)*. % 300.04/300.42 248976[19:Res:248819.0,167276.0] || well_ordering(u,v) -> equal(segment(u,complement(symmetrization_of(complement(v))),least(u,complement(symmetrization_of(complement(v))))),ordinal_numbers)**. % 300.04/300.42 248984[0:Res:248819.0,16465.0] || -> subclass(complement(symmetrization_of(complement(intersection(u,v)))),w) member(not_subclass_element(complement(symmetrization_of(complement(intersection(u,v)))),w),u)*. % 300.04/300.42 248985[0:Res:248819.0,16466.0] || -> subclass(complement(symmetrization_of(complement(intersection(u,v)))),w) member(not_subclass_element(complement(symmetrization_of(complement(intersection(u,v)))),w),v)*. % 300.04/300.42 249095[0:Res:248816.0,16469.0] || -> subclass(complement(union(u,complement(singleton(v)))),w) equal(not_subclass_element(complement(union(u,complement(singleton(v)))),w),v)**. % 300.04/300.42 249202[19:Res:238770.1,34755.2] function(u) || equal(intersection(v,w),universal_class)** member(x,universal_class) -> member(image(u,x),w)*. % 300.04/300.42 249261[0:Res:248817.0,16469.0] || -> subclass(complement(union(complement(singleton(u)),v)),w) equal(not_subclass_element(complement(union(complement(singleton(u)),v)),w),u)**. % 300.04/300.42 249397[19:Res:238770.1,34754.2] function(u) || equal(intersection(v,w),universal_class)** member(x,universal_class) -> member(image(u,x),v)*. % 300.04/300.42 249463[0:SoR:36582.0,72.1] one_to_one(intersection(u,v)) || member(w,v)* member(w,u)* -> member(w,cross_product(universal_class,universal_class))*. % 300.04/300.42 249584[19:Res:167224.0,42928.0] || well_ordering(u,universal_class) -> equal(singleton(v),ordinal_numbers) member(v,w)* member(least(u,complement(w)),complement(w))*. % 300.04/300.42 249585[19:Res:167115.1,42928.0] || well_ordering(u,universal_class) -> equal(integer_of(v),ordinal_numbers) member(v,w)* member(least(u,complement(w)),complement(w))*. % 300.04/300.42 249598[19:Res:167137.1,42928.0] || well_ordering(u,universal_class) -> equal(v,ordinal_numbers) member(regular(v),w)* member(least(u,complement(w)),complement(w))*. % 300.04/300.42 249659[20:Res:222998.0,42928.0] || well_ordering(u,universal_class) -> member(regular(complement(complement(symmetrization_of(ordinal_numbers)))),v)* member(least(u,complement(v)),complement(v))*. % 300.04/300.42 249945[19:SpL:234692.0,167716.0] || subclass(u,intersection(complement(v),complement(w)))* member(regular(u),union(w,v)) -> equal(u,ordinal_numbers). % 300.04/300.42 249962[19:Res:7.1,167716.0] || equal(intersection(complement(u),complement(v)),w) member(regular(w),union(u,v))* -> equal(w,ordinal_numbers). % 300.04/300.42 250033[19:Rew:27.0,250002.1,27.0,250002.0] || member(regular(complement(symmetrization_of(union(u,v)))),union(u,v))* -> equal(complement(symmetrization_of(union(u,v))),ordinal_numbers). % 300.04/300.42 250034[19:Rew:27.0,249995.1,27.0,249995.0] || member(regular(complement(successor(union(u,v)))),union(u,v))* -> equal(complement(successor(union(u,v))),ordinal_numbers). % 300.04/300.42 250090[0:Res:248806.0,36025.1] || member(complement(u),universal_class) -> subclass(singleton(singleton(complement(u))),u)* member(singleton(singleton(singleton(complement(u)))),element_relation)*. % 300.04/300.42 250245[19:Res:238770.1,167718.1] || equal(intersection(u,v),universal_class)** member(w,universal_class) -> equal(w,ordinal_numbers) member(apply(choice,w),u)*. % 300.04/300.42 250247[19:Res:7.1,167718.1] || equal(intersection(u,v),w)* member(w,universal_class) -> equal(w,ordinal_numbers) member(apply(choice,w),u)*. % 300.04/300.42 250417[19:Res:238770.1,167719.1] || equal(intersection(u,v),universal_class)** member(w,universal_class) -> equal(w,ordinal_numbers) member(apply(choice,w),v)*. % 300.04/300.42 250419[19:Res:7.1,167719.1] || equal(intersection(u,v),w)* member(w,universal_class) -> equal(w,ordinal_numbers) member(apply(choice,w),v)*. % 300.04/300.42 250551[19:Res:7.1,176259.1] || equal(restrict(u,v,w),domain_relation)** member(x,universal_class) -> member(ordered_pair(x,ordinal_numbers),cross_product(v,w))*. % 300.04/300.42 250675[0:SpR:234692.0,207750.1] || member(u,universal_class) -> member(u,intersection(complement(v),power_class(w)))* member(u,union(complement(power_class(w)),v)). % 300.04/300.42 250912[0:Res:248811.0,1073.1] inductive(complement(complement(complement(complement(complement(complement(omega))))))) || -> equal(complement(complement(complement(complement(complement(complement(omega)))))),omega)**. % 300.04/300.42 251021[0:SpR:234692.0,207765.1] || member(u,universal_class) -> member(u,intersection(power_class(v),complement(w)))* member(u,union(w,complement(power_class(v)))). % 300.04/300.42 251265[0:Res:144531.1,237458.0] || equal(symmetric_difference(symmetrization_of(u),complement(intersection(u,inverse(u)))),universal_class)** -> member(omega,complement(symmetric_difference(u,inverse(u)))). % 300.04/300.42 251266[0:Res:2478.1,237458.0] || subclass(universal_class,symmetric_difference(symmetrization_of(u),complement(intersection(u,inverse(u)))))* -> member(omega,complement(symmetric_difference(u,inverse(u)))). % 300.04/300.42 251315[19:Res:248149.1,237458.0] || equal(symmetric_difference(symmetrization_of(u),complement(intersection(u,inverse(u)))),kind_1_ordinals)** -> member(ordinal_numbers,complement(symmetric_difference(u,inverse(u)))). % 300.04/300.42 251316[19:Res:214528.1,237458.0] || subclass(kind_1_ordinals,symmetric_difference(symmetrization_of(u),complement(intersection(u,inverse(u)))))* -> member(ordinal_numbers,complement(symmetric_difference(u,inverse(u)))). % 300.04/300.42 251318[22:Res:178902.1,237458.0] || equal(symmetric_difference(symmetrization_of(u),complement(intersection(u,inverse(u)))),omega)** -> member(ordinal_numbers,complement(symmetric_difference(u,inverse(u)))). % 300.04/300.42 251319[22:Res:177171.1,237458.0] || subclass(omega,symmetric_difference(symmetrization_of(u),complement(intersection(u,inverse(u)))))* -> member(ordinal_numbers,complement(symmetric_difference(u,inverse(u)))). % 300.04/300.42 251321[19:Res:167104.1,237458.0] || subclass(universal_class,symmetric_difference(symmetrization_of(u),complement(intersection(u,inverse(u)))))* -> member(ordinal_numbers,complement(symmetric_difference(u,inverse(u)))). % 300.04/300.42 251322[19:Res:167087.1,237458.0] || equal(symmetric_difference(symmetrization_of(u),complement(intersection(u,inverse(u)))),universal_class)** -> member(ordinal_numbers,complement(symmetric_difference(u,inverse(u)))). % 300.04/300.42 251532[0:Res:248783.0,1073.1] inductive(intersection(complement(complement(complement(complement(omega)))),u)) || -> equal(intersection(complement(complement(complement(complement(omega)))),u),omega)**. % 300.04/300.42 251606[0:SpR:236669.0,36863.0] || -> member(not_subclass_element(u,intersection(complement(v),complement(w))),union(w,v))* subclass(u,intersection(complement(v),complement(w))). % 300.04/300.42 251668[0:SpR:234692.0,36863.0] || -> member(not_subclass_element(u,intersection(complement(v),complement(w))),union(w,v))* subclass(u,intersection(complement(w),complement(v))). % 300.04/300.42 251767[0:Obv:251689.1] || equal(u,v) -> member(v,union(w,x)) subclass(unordered_pair(v,u),intersection(complement(w),complement(x)))*. % 300.04/300.42 251856[0:Res:248798.0,1073.1] inductive(intersection(u,complement(complement(complement(complement(omega)))))) || -> equal(intersection(u,complement(complement(complement(complement(omega))))),omega)**. % 300.04/300.42 251992[0:Res:248810.0,1073.1] inductive(complement(complement(intersection(u,complement(complement(omega)))))) || -> equal(complement(complement(intersection(u,complement(complement(omega))))),omega)**. % 300.04/300.42 252081[0:SpR:236669.0,27879.1] || -> subclass(symmetric_difference(complement(u),complement(v)),w) member(not_subclass_element(symmetric_difference(complement(u),complement(v)),w),union(v,u))*. % 300.04/300.42 252143[0:SpR:237384.0,27879.1] || -> subclass(symmetric_difference(complement(u),complement(v)),w) member(not_subclass_element(symmetric_difference(complement(v),complement(u)),w),union(u,v))*. % 300.04/300.42 252307[0:Res:248812.0,1073.1] inductive(complement(complement(intersection(complement(complement(omega)),u)))) || -> equal(complement(complement(intersection(complement(complement(omega)),u))),omega)**. % 300.04/300.42 252452[0:Res:249106.0,1073.1] inductive(complement(union(u,complement(complement(complement(omega)))))) || -> equal(complement(union(u,complement(complement(complement(omega))))),omega)**. % 300.04/300.42 252556[8:Res:125121.2,11848.0] || member(u,cantor(v))* subclass(rest_of(v),w)* subclass(w,x)* well_ordering(universal_class,x)* -> . % 300.04/300.42 252612[8:Res:125121.2,16.0] || member(u,cantor(v)) subclass(rest_of(v),cross_product(w,x))* -> member(restrict(v,u,universal_class),x)*. % 300.04/300.42 252700[0:Res:249272.0,1073.1] inductive(complement(union(complement(complement(complement(omega))),u))) || -> equal(complement(union(complement(complement(complement(omega))),u)),omega)**. % 300.04/300.42 252855[19:Obv:252790.0] || -> equal(not_subclass_element(unordered_pair(u,v),ordinal_numbers),u) subclass(singleton(v),unordered_pair(u,v))* subclass(unordered_pair(u,v),ordinal_numbers). % 300.04/300.42 252856[19:Obv:252788.0] || -> equal(not_subclass_element(unordered_pair(u,v),ordinal_numbers),v) subclass(singleton(u),unordered_pair(u,v))* subclass(unordered_pair(u,v),ordinal_numbers). % 300.04/300.42 252857[19:MRR:252797.2,210986.0] || well_ordering(u,v) -> subclass(v,ordinal_numbers) member(least(u,singleton(not_subclass_element(v,ordinal_numbers))),singleton(not_subclass_element(v,ordinal_numbers)))*. % 300.04/300.42 252911[0:Res:220180.1,16465.0] || subclass(u,intersection(v,w))* -> subclass(complement(complement(u)),x) member(not_subclass_element(complement(complement(u)),x),v)*. % 300.04/300.42 252912[0:Res:220180.1,16466.0] || subclass(u,intersection(v,w))* -> subclass(complement(complement(u)),x) member(not_subclass_element(complement(complement(u)),x),w)*. % 300.04/300.42 252920[19:Res:220180.1,167733.0] || subclass(u,restrict(v,w,x))* -> equal(complement(complement(u)),ordinal_numbers) member(regular(complement(complement(u))),v)*. % 300.04/300.42 253025[19:Res:252894.1,16468.0] || subclass(inverse(ordinal_numbers),restrict(u,v,w))* -> subclass(symmetrization_of(ordinal_numbers),x) member(not_subclass_element(symmetrization_of(ordinal_numbers),x),u)*. % 300.04/300.42 253060[20:MRR:253014.2,175557.0] || subclass(inverse(ordinal_numbers),intersection(u,v))* member(symmetrization_of(ordinal_numbers),universal_class) -> member(apply(choice,symmetrization_of(ordinal_numbers)),u)*. % 300.04/300.42 253061[20:MRR:253013.2,175557.0] || subclass(inverse(ordinal_numbers),intersection(u,v))* member(symmetrization_of(ordinal_numbers),universal_class) -> member(apply(choice,symmetrization_of(ordinal_numbers)),v)*. % 300.04/300.42 253145[19:Res:167727.3,227961.1] || member(u,universal_class) subclass(u,cantor(v)) member(v,apply(choice,u))* -> equal(u,ordinal_numbers). % 300.04/300.42 253148[18:Res:6521.3,227961.1] function(u) || member(v,universal_class) subclass(universal_class,cantor(w)) member(w,image(u,v))* -> . % 300.04/300.42 253153[19:Res:168245.3,227961.1] || well_ordering(u,universal_class) subclass(v,cantor(w)) member(w,least(u,v))* -> equal(v,ordinal_numbers). % 300.04/300.42 253156[18:Res:16231.2,227961.1] || subclass(u,cantor(v)) member(v,not_subclass_element(intersection(u,w),x))* -> subclass(intersection(u,w),x). % 300.04/300.42 253159[18:Res:16358.2,227961.1] || subclass(u,cantor(v)) member(v,not_subclass_element(intersection(w,u),x))* -> subclass(intersection(w,u),x). % 300.04/300.42 253179[19:Res:168471.1,227961.1] || member(u,regular(intersection(v,intersection(cantor(u),w))))* -> equal(intersection(v,intersection(cantor(u),w)),ordinal_numbers). % 300.04/300.42 253183[19:Res:168477.1,227961.1] || member(u,regular(intersection(intersection(v,cantor(u)),w)))* -> equal(intersection(intersection(v,cantor(u)),w),ordinal_numbers). % 300.04/300.42 253184[19:Res:168476.1,227961.1] || member(u,regular(intersection(intersection(cantor(u),v),w)))* -> equal(intersection(intersection(cantor(u),v),w),ordinal_numbers). % 300.04/300.42 253186[19:Res:168472.1,227961.1] || member(u,regular(intersection(v,intersection(w,cantor(u)))))* -> equal(intersection(v,intersection(w,cantor(u))),ordinal_numbers). % 300.04/300.42 253188[19:SpR:236669.0,168592.2] || well_ordering(u,universal_class) -> equal(symmetric_difference(v,w),ordinal_numbers) member(least(u,symmetric_difference(v,w)),union(w,v))*. % 300.04/300.42 253206[19:SpR:237384.0,168592.2] || well_ordering(u,universal_class) -> equal(symmetric_difference(v,w),ordinal_numbers) member(least(u,symmetric_difference(w,v)),union(v,w))*. % 300.04/300.42 17115[0:Res:16762.0,8.0] || subclass(union(u,v),symmetric_difference(complement(u),complement(v)))* -> equal(symmetric_difference(complement(u),complement(v)),union(u,v)). % 300.04/300.42 16822[0:SpR:479.0,26.2] || member(u,universal_class) -> member(u,image(element_relation,union(v,w))) member(u,power_class(intersection(complement(v),complement(w))))*. % 300.04/300.42 27276[0:Res:2482.2,488.0] || member(u,universal_class) subclass(universal_class,intersection(complement(v),complement(w)))* member(sum_class(u),union(v,w))* -> . % 300.04/300.42 14962[0:SpR:43.0,433.1] || member(inverse(restrict(u,v,universal_class)),universal_class) -> member(ordered_pair(inverse(restrict(u,v,universal_class)),image(u,v)),domain_relation)*. % 300.04/300.42 9832[0:Res:945.0,126.0] || subclass(ordered_pair(u,v),w)* well_ordering(x,w)* -> member(least(x,ordered_pair(u,v)),ordered_pair(u,v))*. % 300.04/300.42 9728[0:Res:59.1,5467.1] || member(ordered_pair(u,singleton(v)),compose(w,x))* subclass(universal_class,complement(image(w,image(x,singleton(u)))))* -> . % 300.04/300.42 27148[0:Res:2523.2,896.0] || member(u,universal_class) subclass(rest_relation,restrict(v,w,x))* -> member(ordered_pair(u,rest_of(u)),cross_product(w,x))*. % 300.04/300.42 40374[0:Res:7.1,8668.2] || equal(u,cross_product(v,w))* member(x,w)* member(y,v)* -> member(ordered_pair(y,x),u)*. % 300.04/300.42 48376[0:Res:24.2,6432.1] || member(unordered_pair(u,v),w)* member(unordered_pair(u,v),x)* subclass(universal_class,complement(intersection(x,w)))* -> . % 300.04/300.42 16470[0:Res:2526.2,9.0] || subclass(u,unordered_pair(v,w))* -> subclass(u,x) equal(not_subclass_element(u,x),w)* equal(not_subclass_element(u,x),v)*. % 300.04/300.42 27277[0:Res:2483.2,488.0] || member(u,universal_class) subclass(universal_class,intersection(complement(v),complement(w)))* member(power_class(u),union(v,w))* -> . % 300.04/300.42 27259[0:Res:3.1,488.0] || member(not_subclass_element(intersection(complement(u),complement(v)),w),union(u,v))* -> subclass(intersection(complement(u),complement(v)),w). % 300.04/300.42 16110[0:Res:4126.1,284.0] || member(not_subclass_element(complement(complement(intersection(u,v))),w),symmetric_difference(u,v))* -> subclass(complement(complement(intersection(u,v))),w). % 300.04/300.42 27275[0:Res:2526.2,488.0] || subclass(u,intersection(complement(v),complement(w))) member(not_subclass_element(u,x),union(v,w))* -> subclass(u,x). % 300.04/300.42 48880[0:Res:315.1,16910.0] || -> subclass(intersection(symmetric_difference(u,inverse(u)),v),w) member(not_subclass_element(intersection(symmetric_difference(u,inverse(u)),v),w),symmetrization_of(u))*. % 300.04/300.42 48888[0:Res:297.1,16910.0] || -> subclass(intersection(u,symmetric_difference(v,inverse(v))),w) member(not_subclass_element(intersection(u,symmetric_difference(v,inverse(v))),w),symmetrization_of(v))*. % 300.04/300.42 34758[0:Res:6521.3,897.0] function(u) || member(v,universal_class) subclass(universal_class,restrict(w,x,y))* -> member(image(u,v),w)*. % 300.04/300.42 35249[2:Res:36.0,9859.1] inductive(flip(u)) || well_ordering(v,cross_product(cross_product(universal_class,universal_class),universal_class))* -> member(least(v,flip(u)),flip(u))*. % 300.04/300.42 35250[2:Res:33.0,9859.1] inductive(rotate(u)) || well_ordering(v,cross_product(cross_product(universal_class,universal_class),universal_class))* -> member(least(v,rotate(u)),rotate(u))*. % 300.04/300.42 27751[0:SpR:480.0,44.0] || -> equal(complement(intersection(union(u,v),complement(singleton(intersection(complement(u),complement(v)))))),successor(intersection(complement(u),complement(v))))**. % 300.04/300.42 17166[0:Res:17083.0,8.0] || subclass(successor(u),symmetric_difference(complement(u),complement(singleton(u))))* -> equal(symmetric_difference(complement(u),complement(singleton(u))),successor(u)). % 300.04/300.42 17148[0:Res:17082.0,8.0] || subclass(symmetrization_of(u),symmetric_difference(complement(u),complement(inverse(u))))* -> equal(symmetric_difference(complement(u),complement(inverse(u))),symmetrization_of(u)). % 300.04/300.42 16893[0:SpR:4105.0,24.2] || member(u,symmetrization_of(v)) member(u,complement(intersection(v,inverse(v))))* -> member(u,symmetric_difference(v,inverse(v))). % 300.04/300.42 27750[0:SpR:480.0,114.0] || -> equal(complement(intersection(union(u,v),complement(inverse(intersection(complement(u),complement(v)))))),symmetrization_of(intersection(complement(u),complement(v))))**. % 300.04/300.42 109226[0:SpR:481.0,6403.1] || equal(symmetric_difference(u,intersection(complement(v),complement(w))),universal_class) -> member(omega,complement(intersection(complement(u),union(v,w))))*. % 300.04/300.42 109231[0:SpR:480.0,6403.1] || equal(symmetric_difference(intersection(complement(u),complement(v)),w),universal_class) -> member(omega,complement(intersection(union(u,v),complement(w))))*. % 300.04/300.43 109246[0:SpR:481.0,6303.1] || subclass(universal_class,symmetric_difference(u,intersection(complement(v),complement(w)))) -> member(omega,complement(intersection(complement(u),union(v,w))))*. % 300.04/300.43 109251[0:SpR:480.0,6303.1] || subclass(universal_class,symmetric_difference(intersection(complement(u),complement(v)),w)) -> member(omega,complement(intersection(union(u,v),complement(w))))*. % 300.04/300.43 109344[8:SpR:84173.2,104.0] function(u) function(v) || -> equal(domain__dfg(u,image(inverse(u),singleton(single_valued1(v))),single_valued2(u)),single_valued3(u))**. % 300.04/300.43 110843[0:Res:24.2,6476.1] || member(ordered_pair(u,v),w)* member(ordered_pair(u,v),x)* subclass(universal_class,complement(intersection(x,w)))* -> . % 300.04/300.43 79968[0:Res:6521.3,158.0] function(u) || member(v,universal_class) subclass(universal_class,omega) -> equal(integer_of(image(u,v)),image(u,v))**. % 300.04/300.43 125076[8:Rew:124836.0,79426.3] || member(u,universal_class) member(v,cross_product(singleton(u),universal_class))* member(v,w)* -> member(u,cantor(w))*. % 300.04/300.43 125341[8:Rew:124836.0,4237.2] inductive(domain_of(restrict(u,v,omega))) || section(u,omega,v) -> equal(cantor(restrict(u,v,omega)),omega)**. % 300.04/300.43 125728[8:Rew:125705.0,83137.2] inductive(cantor(flip(cross_product(u,universal_class)))) || well_ordering(v,inverse(u)) -> member(least(v,inverse(u)),inverse(u))*. % 300.04/300.43 125793[8:Rew:125770.0,83151.2] inductive(cantor(restrict(element_relation,universal_class,u))) || well_ordering(v,sum_class(u)) -> member(least(v,sum_class(u)),sum_class(u))*. % 300.04/300.43 127336[8:Res:124899.1,1073.1] inductive(cantor(restrict(u,v,omega))) || section(u,omega,v) -> equal(cantor(restrict(u,v,omega)),omega)**. % 300.04/300.43 135200[0:Res:36865.0,16910.0] || -> subclass(complement(complement(symmetric_difference(u,inverse(u)))),v) member(not_subclass_element(complement(complement(symmetric_difference(u,inverse(u)))),v),symmetrization_of(u))*. % 300.04/300.43 135889[0:Res:315.1,16105.1] || member(not_subclass_element(intersection(intersection(u,v),w),x),symmetric_difference(u,v))* -> subclass(intersection(intersection(u,v),w),x). % 300.04/300.43 135913[0:Res:297.1,16105.1] || member(not_subclass_element(intersection(u,intersection(v,w)),x),symmetric_difference(v,w))* -> subclass(intersection(u,intersection(v,w)),x). % 300.04/300.43 135919[0:Res:2523.2,16105.1] || member(u,universal_class) subclass(rest_relation,intersection(v,w)) member(ordered_pair(u,rest_of(u)),symmetric_difference(v,w))* -> . % 300.04/300.43 135949[0:Res:2525.1,126.0] || subclass(ordered_pair(u,v),w)* subclass(w,x)* well_ordering(y,x)* -> member(least(y,w),w)*. % 300.04/300.43 135955[0:Res:2525.1,488.0] || subclass(ordered_pair(u,v),intersection(complement(w),complement(x)))* member(unordered_pair(u,singleton(v)),union(w,x)) -> . % 300.04/300.43 137108[0:SpR:27.0,137025.0] || -> subclass(complement(successor(intersection(complement(u),complement(v)))),intersection(union(u,v),complement(singleton(intersection(complement(u),complement(v))))))*. % 300.04/300.43 137140[0:SpR:27.0,137026.0] || -> subclass(complement(symmetrization_of(intersection(complement(u),complement(v)))),intersection(union(u,v),complement(inverse(intersection(complement(u),complement(v))))))*. % 300.04/300.43 138281[8:SpR:124905.0,125124.2] || member(u,universal_class) subclass(rest_relation,rest_of(restrict(v,w,singleton(x))))* -> member(u,segment(v,w,x))*. % 300.04/300.43 140907[0:SpL:17187.0,110985.0] || member(inverse(restrict(cross_product(u,universal_class),v,w)),image(cross_product(v,w),u))* subclass(universal_class,complement(element_relation)) -> . % 300.04/300.43 142370[0:Rew:29.0,142261.1] || member(not_subclass_element(cross_product(u,v),restrict(w,u,v)),w)* -> subclass(cross_product(u,v),restrict(w,u,v)). % 300.04/300.43 146483[0:Res:9820.1,16469.0] || equal(sum_class(singleton(u)),singleton(u)) -> subclass(sum_class(singleton(u)),v) equal(not_subclass_element(sum_class(singleton(u)),v),u)**. % 300.04/300.43 147101[0:SpR:69.0,79961.2] || member(image(u,singleton(v)),universal_class)* subclass(universal_class,omega) -> equal(integer_of(apply(u,v)),apply(u,v)). % 300.04/300.43 147438[0:Res:4126.1,15100.2] || member(sum_class(u),symmetric_difference(v,w))* member(u,universal_class) subclass(universal_class,complement(complement(intersection(v,w))))* -> . % 300.04/300.43 147569[0:Res:4126.1,15066.2] || member(power_class(u),symmetric_difference(v,w))* member(u,universal_class) subclass(universal_class,complement(complement(intersection(v,w))))* -> . % 300.04/300.43 151022[0:Obv:150973.1] || member(ordered_pair(u,v),compose(w,x)) -> subclass(intersection(singleton(v),y),image(w,image(x,singleton(u))))*. % 300.04/300.43 151408[0:Obv:151361.1] || member(ordered_pair(u,v),compose(w,x)) -> subclass(intersection(y,singleton(v)),image(w,image(x,singleton(u))))*. % 300.04/300.43 151695[0:Res:4126.1,16455.1] || member(not_subclass_element(u,v),symmetric_difference(w,x))* subclass(u,complement(complement(intersection(w,x)))) -> subclass(u,v). % 300.04/300.43 152933[0:Obv:152915.1] || member(not_subclass_element(restrict(u,v,w),intersection(x,u)),x)* -> subclass(restrict(u,v,w),intersection(x,u)). % 300.04/300.43 134802[3:Res:134636.1,8668.2] || subclass(cross_product(u,v),ordinal_numbers)* member(w,v)* member(x,u)* -> member(ordered_pair(x,w),kind_1_ordinals)*. % 300.04/300.43 41510[0:Res:9790.2,20.0] || member(ordered_pair(u,v),cross_product(universal_class,universal_class))* subclass(composition_function,element_relation) -> member(u,ordered_pair(v,compose(u,v)))*. % 300.04/300.43 43053[0:Res:289.0,9843.1] || member(u,universal_class) well_ordering(v,unordered_pair(u,w)) -> member(least(v,unordered_pair(u,w)),unordered_pair(u,w))*. % 300.04/300.43 43074[0:Res:289.0,9842.1] || member(u,universal_class) well_ordering(v,unordered_pair(w,u)) -> member(least(v,unordered_pair(w,u)),unordered_pair(w,u))*. % 300.04/300.43 42931[0:Res:289.0,9836.1] || member(u,universal_class)* well_ordering(v,complement(w)) -> member(u,w)* member(least(v,complement(w)),complement(w))*. % 300.04/300.43 154714[8:Con:154682.3] inductive(complement(compose(element_relation,universal_class))) || well_ordering(u,universal_class) member(least(u,complement(compose(element_relation,universal_class))),element_relation)* -> . % 300.04/300.43 135708[2:Res:35220.2,16910.0] inductive(symmetric_difference(u,inverse(u))) || well_ordering(v,universal_class) -> member(least(v,symmetric_difference(u,inverse(u))),symmetrization_of(u))*. % 300.04/300.43 135903[2:Res:35220.2,16105.1] inductive(intersection(u,v)) || well_ordering(w,universal_class) member(least(w,intersection(u,v)),symmetric_difference(u,v))* -> . % 300.04/300.43 136369[8:Res:35222.2,83043.0] inductive(cantor(u)) || well_ordering(v,cantor(u)) subclass(universal_class,w) -> member(least(v,cantor(u)),w)*. % 300.04/300.43 35233[2:Res:16133.1,9859.1] inductive(singleton(u)) || member(u,v)* well_ordering(w,v)* -> member(least(w,singleton(u)),singleton(u))*. % 300.04/300.43 109047[2:Res:95593.1,9859.1] inductive(singleton(u)) || well_ordering(v,complement(w))* -> member(u,w)* member(least(v,singleton(u)),singleton(u))*. % 300.04/300.43 166847[18:MRR:166836.2,80465.0] || member(singleton(u),cantor(v)) member(ordered_pair(v,singleton(singleton(singleton(u)))),cross_product(universal_class,cross_product(universal_class,universal_class)))* -> . % 300.04/300.43 169582[19:Rew:166997.0,167390.1] || member(ordered_pair(ordinal_numbers,ordinal_numbers),u) member(ordered_pair(ordinal_numbers,ordinal_numbers),v) subclass(domain_relation,complement(intersection(v,u)))* -> . % 300.04/300.43 167441[19:Rew:166997.0,84234.1] || subclass(domain_relation,cross_product(u,v))* -> equal(ordered_pair(first(ordered_pair(ordinal_numbers,ordinal_numbers)),second(ordered_pair(ordinal_numbers,ordinal_numbers))),ordered_pair(ordinal_numbers,ordinal_numbers))**. % 300.04/300.43 167483[19:Rew:166997.0,80539.0] || -> equal(intersection(kind_1_ordinals,union(complement(singleton(ordinal_numbers)),complement(image(successor_relation,ordinal_numbers)))),symmetric_difference(complement(singleton(ordinal_numbers)),complement(image(successor_relation,ordinal_numbers))))**. % 300.04/300.43 169583[19:Rew:166997.0,167562.2,166997.0,167562.1] || equal(complement(intersection(u,v)),singleton(ordinal_numbers)) member(ordinal_numbers,union(u,v)) -> member(ordinal_numbers,symmetric_difference(u,v))*. % 300.04/300.43 167649[19:Rew:166997.0,162683.2] || subclass(complement(u),v)* well_ordering(w,v)* -> member(ordinal_numbers,u) member(least(w,complement(u)),complement(u))*. % 300.04/300.43 169585[19:Rew:166997.0,167665.1,166997.0,167665.0] || member(not_subclass_element(u,ordinal_numbers),v)* member(not_subclass_element(u,ordinal_numbers),singleton(w))* -> member(w,v)* subclass(u,ordinal_numbers). % 300.04/300.43 169586[19:Rew:166997.0,167669.2,166997.0,167669.1,166997.0,167669.0] || member(not_subclass_element(u,ordinal_numbers),regular(v))* member(not_subclass_element(u,ordinal_numbers),v) -> equal(v,ordinal_numbers) subclass(u,ordinal_numbers). % 300.04/300.43 167712[19:Rew:166997.0,80610.1] || subclass(u,cross_product(v,w))* -> equal(u,ordinal_numbers) equal(ordered_pair(first(regular(u)),second(regular(u))),regular(u))**. % 300.04/300.43 167713[19:Rew:166997.0,80598.2] || member(u,universal_class) subclass(u,restrict(v,w,x))* -> equal(u,ordinal_numbers) member(apply(choice,u),v). % 300.04/300.43 167715[19:Rew:166997.0,80578.2] || member(u,universal_class) subclass(u,omega) -> equal(u,ordinal_numbers) equal(integer_of(apply(choice,u)),apply(choice,u))**. % 300.04/300.43 167755[19:Rew:166997.0,80569.2] || member(u,v)* well_ordering(w,v)* -> equal(singleton(u),ordinal_numbers) member(least(w,singleton(u)),singleton(u))*. % 300.04/300.43 167771[19:Rew:166997.0,163355.3] || subclass(omega,complement(compose(element_relation,universal_class)))* member(u,element_relation)* well_ordering(v,w)* -> equal(integer_of(u),ordinal_numbers). % 300.04/300.43 169587[19:Rew:166997.0,167789.0] || -> equal(cross_product(singleton(u),v),ordinal_numbers) equal(range__dfg(regular(cross_product(singleton(u),v)),u,v),second(not_subclass_element(ordinal_numbers,ordinal_numbers)))**. % 300.04/300.43 169588[19:Rew:166997.0,167951.2] || well_ordering(u,omega) -> equal(integer_of(v),ordinal_numbers) equal(singleton(v),ordinal_numbers) member(least(u,singleton(v)),singleton(v))*. % 300.04/300.43 168004[19:Rew:166997.0,163397.2] || subclass(omega,u) member(u,universal_class) -> equal(integer_of(singleton(u)),ordinal_numbers) member(singleton(singleton(singleton(u))),element_relation)*. % 300.04/300.43 168381[19:Rew:166997.0,160832.2] || member(cantor(u),universal_class) subclass(universal_class,v) -> equal(cantor(u),ordinal_numbers) member(apply(choice,cantor(u)),v)*. % 300.04/300.43 168519[19:Rew:166997.0,163943.2] || well_ordering(u,universal_class) member(least(u,intersection(v,w)),symmetric_difference(v,w))* -> equal(intersection(v,w),ordinal_numbers). % 300.04/300.43 168551[19:Rew:166997.0,99194.0] || -> equal(complement(complement(restrict(u,v,w))),ordinal_numbers) member(regular(complement(complement(restrict(u,v,w)))),cross_product(v,w))*. % 300.04/300.43 168560[19:Rew:166997.0,158776.2] || member(u,universal_class) -> member(u,cantor(cross_product(v,w))) equal(restrict(cross_product(singleton(u),universal_class),v,w),ordinal_numbers)**. % 300.04/300.43 168565[19:Rew:166997.0,80841.0] || -> equal(intersection(u,restrict(v,w,x)),ordinal_numbers) member(regular(intersection(u,restrict(v,w,x))),cross_product(w,x))*. % 300.04/300.43 168567[19:Rew:166997.0,80843.0] || -> equal(intersection(restrict(u,v,w),x),ordinal_numbers) member(regular(intersection(restrict(u,v,w),x)),cross_product(v,w))*. % 300.04/300.43 168596[19:Rew:166997.0,80865.1] || well_ordering(u,complement(intersection(v,w))) -> equal(segment(u,symmetric_difference(v,w),least(u,symmetric_difference(v,w))),ordinal_numbers)**. % 300.04/300.43 168623[19:Rew:166997.0,95612.2] || well_ordering(u,complement(v))* -> member(w,v)* equal(singleton(w),ordinal_numbers) member(least(u,singleton(w)),singleton(w))*. % 300.04/300.43 168624[19:Rew:166997.0,80891.0] || -> equal(symmetric_difference(u,cross_product(v,w)),ordinal_numbers) member(regular(symmetric_difference(u,cross_product(v,w))),complement(restrict(u,v,w)))*. % 300.04/300.43 168625[19:Rew:166997.0,80892.0] || -> equal(symmetric_difference(cross_product(u,v),w),ordinal_numbers) member(regular(symmetric_difference(cross_product(u,v),w)),complement(restrict(w,u,v)))*. % 300.04/300.43 168628[19:Rew:166997.0,80895.1] || well_ordering(u,universal_class) -> equal(symmetric_difference(v,inverse(v)),ordinal_numbers) member(least(u,symmetric_difference(v,inverse(v))),symmetrization_of(v))*. % 300.04/300.43 168633[19:Rew:166997.0,80902.1] || well_ordering(u,symmetrization_of(v)) -> equal(segment(u,symmetric_difference(v,inverse(v)),least(u,symmetric_difference(v,inverse(v)))),ordinal_numbers)**. % 300.04/300.43 168743[19:Rew:166997.0,163972.2] || well_ordering(u,universal_class) member(least(u,complement(compose(element_relation,universal_class))),element_relation)* -> equal(complement(compose(element_relation,universal_class)),ordinal_numbers). % 300.04/300.43 168917[19:Rew:166997.0,163402.1] || subclass(omega,rest_of(u)) -> equal(integer_of(singleton(singleton(singleton(v)))),ordinal_numbers) equal(restrict(u,singleton(v),universal_class),v)**. % 300.04/300.43 173902[19:SoR:169556.0,167213.2] single_valued_class(sum_class(cross_product(universal_class,universal_class))) || well_ordering(element_relation,cross_product(universal_class,universal_class))* equal(sum_class(cross_product(universal_class,universal_class)),ordinal_numbers) -> . % 300.04/300.43 173935[19:SpR:149012.1,167926.2] || subclass(inverse(u),u)* asymmetric(u,v) subclass(compose(ordinal_numbers,ordinal_numbers),ordinal_numbers)* -> transitive(inverse(u),v)*. % 300.04/300.43 174523[19:Res:167727.3,110865.0] || member(u,universal_class) subclass(u,rest_of(apply(choice,u)))* subclass(universal_class,complement(element_relation)) -> equal(u,ordinal_numbers). % 300.04/300.43 174548[19:SpR:149012.1,167762.1] || subclass(inverse(u),u)* asymmetric(u,singleton(v)) -> equal(domain__dfg(inverse(u),singleton(v),v),single_valued3(ordinal_numbers))**. % 300.04/300.43 169595[19:Rew:166997.0,168047.1] || member(u,intersection(complement(v),power_class(complement(inverse(ordinal_numbers)))))* member(u,union(v,image(element_relation,symmetrization_of(ordinal_numbers)))) -> . % 300.04/300.43 169594[19:Rew:166997.0,168045.1] || member(u,intersection(power_class(complement(inverse(ordinal_numbers))),complement(v)))* member(u,union(image(element_relation,symmetrization_of(ordinal_numbers)),v)) -> . % 300.04/300.43 169592[19:Rew:166997.0,168019.1] || subclass(universal_class,intersection(complement(u),power_class(complement(inverse(ordinal_numbers)))))* member(omega,union(u,image(element_relation,symmetrization_of(ordinal_numbers)))) -> . % 300.04/300.43 169591[19:Rew:166997.0,168018.1] || subclass(universal_class,intersection(power_class(complement(inverse(ordinal_numbers))),complement(u)))* member(omega,union(image(element_relation,symmetrization_of(ordinal_numbers)),u)) -> . % 300.04/300.43 169596[19:Rew:166997.0,168067.2] || subclass(complement(inverse(ordinal_numbers)),u)* well_ordering(v,u)* -> member(least(v,complement(inverse(ordinal_numbers))),complement(inverse(ordinal_numbers)))*. % 300.04/300.43 169645[19:MRR:169644.1,169313.1] inductive(singleton(u)) || subclass(singleton(u),range_of(ordinal_numbers))* -> member(u,cantor(successor_relation)) equal(range_of(ordinal_numbers),singleton(u)). % 300.04/300.43 167621[19:Rew:166997.0,161628.2] || member(u,universal_class) -> member(u,cantor(cross_product(v,universal_class))) equal(image(cross_product(singleton(u),universal_class),v),range_of(ordinal_numbers))**. % 300.04/300.43 167617[19:Rew:166997.0,80516.2] || member(single_valued1(u),universal_class) -> member(single_valued1(u),range_of(u)) equal(domain__dfg(u,range_of(ordinal_numbers),single_valued2(u)),single_valued3(u))**. % 300.04/300.43 169584[19:Rew:166997.0,167602.0] || member(ordered_pair(u,not_subclass_element(v,image(w,range_of(ordinal_numbers)))),compose(w,ordinal_numbers))* -> subclass(v,image(w,range_of(ordinal_numbers))). % 300.04/300.43 176252[19:Rew:176206.1,164754.2] || member(u,universal_class) subclass(domain_relation,symmetric_difference(complement(v),complement(w))) -> member(ordered_pair(u,ordinal_numbers),union(v,w))*. % 300.04/300.43 177415[19:Res:176340.0,168644.0] || subclass(domain_relation,u) well_ordering(omega,u)* -> equal(integer_of(ordered_pair(singleton(singleton(singleton(ordinal_numbers))),least(omega,domain_relation))),ordinal_numbers)**. % 300.04/300.43 177496[19:Res:167106.1,168644.0] inductive(u) || subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(ordinal_numbers,least(omega,u))),ordinal_numbers)**. % 300.04/300.43 178024[19:Res:168326.3,36583.0] inductive(u) || well_ordering(v,u) -> equal(image(successor_relation,u),ordinal_numbers) member(least(v,image(successor_relation,u)),universal_class)*. % 300.04/300.43 179673[19:SpR:125772.0,168682.2] || section(element_relation,u,universal_class) well_ordering(v,u) -> equal(segment(v,sum_class(u),least(v,sum_class(u))),ordinal_numbers)**. % 300.04/300.43 179769[19:Res:179714.0,126.0] || subclass(singleton(singleton(ordinal_numbers)),u)* well_ordering(v,u)* -> member(least(v,singleton(singleton(ordinal_numbers))),singleton(singleton(ordinal_numbers)))*. % 300.04/300.43 180178[19:Rew:180089.0,179154.1] || subclass(universal_class,intersection(complement(u),power_class(complement(singleton(ordinal_numbers)))))* member(omega,union(u,image(element_relation,singleton(ordinal_numbers)))) -> . % 300.04/300.43 180184[19:Rew:180089.0,179116.1] || subclass(universal_class,intersection(power_class(complement(singleton(ordinal_numbers))),complement(u)))* member(omega,union(image(element_relation,singleton(ordinal_numbers)),u)) -> . % 300.04/300.43 180248[19:Rew:180089.0,179155.1] || member(u,intersection(power_class(complement(singleton(ordinal_numbers))),complement(v)))* member(u,union(image(element_relation,singleton(ordinal_numbers)),v)) -> . % 300.04/300.43 180252[19:Rew:180089.0,179161.1] || member(u,intersection(complement(v),power_class(complement(singleton(ordinal_numbers)))))* member(u,union(v,image(element_relation,singleton(ordinal_numbers)))) -> . % 300.04/300.43 180473[19:SpL:168409.2,137177.0] || member(cross_product(u,v),universal_class) well_ordering(universal_class,apply(choice,cross_product(u,v)))* -> equal(cross_product(u,v),ordinal_numbers). % 300.04/300.43 180481[19:SpL:168409.2,167175.0] || member(cross_product(u,v),universal_class) subclass(apply(choice,cross_product(u,v)),ordinal_numbers)* -> equal(cross_product(u,v),ordinal_numbers). % 300.04/300.43 180482[19:SpL:168409.2,167176.0] || member(cross_product(u,v),universal_class) equal(apply(choice,cross_product(u,v)),ordinal_numbers)** -> equal(cross_product(u,v),ordinal_numbers). % 300.04/300.43 180869[19:Res:7968.2,169221.1] || member(ordinal_numbers,cross_product(u,v)) member(ordinal_numbers,w) equal(complement(restrict(w,u,v)),singleton(ordinal_numbers))** -> . % 300.04/300.43 180875[19:Res:59.1,169221.1] || member(ordered_pair(u,ordinal_numbers),compose(v,w)) equal(complement(image(v,image(w,singleton(u)))),singleton(ordinal_numbers))** -> . % 300.04/300.43 181622[20:Res:181516.0,167276.0] || well_ordering(u,symmetrization_of(ordinal_numbers)) -> equal(segment(u,singleton(regular(symmetrization_of(ordinal_numbers))),least(u,singleton(regular(symmetrization_of(ordinal_numbers))))),ordinal_numbers)**. % 300.04/300.43 181723[20:Res:175570.1,82995.1] || subclass(inverse(ordinal_numbers),complement(compose(element_relation,universal_class)))* member(regular(symmetrization_of(ordinal_numbers)),element_relation) -> member(regular(symmetrization_of(ordinal_numbers)),u)*. % 300.04/300.43 182423[19:Res:7968.2,182393.0] || member(singleton(ordinal_numbers),cross_product(u,v)) member(singleton(ordinal_numbers),w) well_ordering(universal_class,restrict(w,u,v))* -> . % 300.04/300.43 182886[19:Res:182871.1,36025.1] || member(singleton(symmetrization_of(ordinal_numbers)),inverse(ordinal_numbers)) member(symmetrization_of(ordinal_numbers),universal_class) -> member(singleton(singleton(singleton(symmetrization_of(ordinal_numbers)))),element_relation)*. % 300.04/300.43 183089[19:Res:182463.1,126.0] || equal(u,singleton(singleton(ordinal_numbers))) subclass(u,v)* well_ordering(w,v)* -> member(least(w,u),u)*. % 300.04/300.43 183932[23:SpL:183840.0,8693.1] || member(ordered_pair(universal_class,u),compose(v,w))* subclass(image(v,image(w,ordinal_numbers)),x)* -> member(u,x)*. % 300.04/300.43 184824[19:SpR:5132.1,176419.1] || subclass(domain_relation,flip(u)) -> subclass(cross_product(v,w),x) member(ordered_pair(not_subclass_element(cross_product(v,w),x),ordinal_numbers),u)*. % 300.04/300.43 184842[19:Res:176419.1,488.0] || subclass(domain_relation,flip(intersection(complement(u),complement(v)))) member(ordered_pair(ordered_pair(w,x),ordinal_numbers),union(u,v))* -> . % 300.04/300.43 184920[19:Res:176420.1,488.0] || subclass(domain_relation,rotate(intersection(complement(u),complement(v)))) member(ordered_pair(ordered_pair(w,ordinal_numbers),x),union(u,v))* -> . % 300.04/300.43 184961[19:Res:176420.1,128.3] || subclass(domain_relation,rotate(u))* member(ordered_pair(v,ordinal_numbers),w)* subclass(w,x)* well_ordering(u,x)* -> . % 300.04/300.43 185103[19:Res:4233.1,167739.0] || section(u,singleton(v),w) -> equal(segment(u,w,v),ordinal_numbers) equal(regular(segment(u,w,v)),v)**. % 300.04/300.43 185271[19:Res:168252.2,83043.0] || well_ordering(u,cantor(v)) subclass(universal_class,w) -> equal(cantor(v),ordinal_numbers) member(least(u,cantor(v)),w)*. % 300.04/300.43 187294[19:SpL:4121.0,168377.0] || subclass(omega,symmetric_difference(cross_product(u,v),w)) -> equal(integer_of(x),ordinal_numbers) member(x,complement(restrict(w,u,v)))*. % 300.04/300.43 187295[19:SpL:4119.0,168377.0] || subclass(omega,symmetric_difference(u,cross_product(v,w))) -> equal(integer_of(x),ordinal_numbers) member(x,complement(restrict(u,v,w)))*. % 300.04/300.43 187527[19:SpL:4121.0,167736.0] || subclass(u,symmetric_difference(cross_product(v,w),x)) -> equal(u,ordinal_numbers) member(regular(u),complement(restrict(x,v,w)))*. % 300.04/300.43 187528[19:SpL:4119.0,167736.0] || subclass(u,symmetric_difference(v,cross_product(w,x))) -> equal(u,ordinal_numbers) member(regular(u),complement(restrict(v,w,x)))*. % 300.04/300.43 187587[19:MRR:187577.2,167262.1] || connected(u,intersection(v,w)) -> well_ordering(u,intersection(v,w)) member(regular(not_well_ordering(u,intersection(v,w))),v)*. % 300.04/300.43 187669[19:MRR:187659.2,167262.1] || connected(u,intersection(v,w)) -> well_ordering(u,intersection(v,w)) member(regular(not_well_ordering(u,intersection(v,w))),w)*. % 300.04/300.43 187796[19:SpR:902.0,168350.1] || -> equal(restrict(cross_product(u,v),w,x),ordinal_numbers) member(regular(restrict(cross_product(w,x),u,v)),cross_product(u,v))*. % 300.04/300.43 187814[19:Res:168350.1,126.0] || subclass(u,v)* well_ordering(w,v)* -> equal(restrict(u,x,y),ordinal_numbers)** member(least(w,u),u)*. % 300.04/300.43 187822[19:Res:168350.1,4127.0] || -> equal(restrict(symmetric_difference(u,v),w,x),ordinal_numbers) member(regular(restrict(symmetric_difference(u,v),w,x)),union(u,v))*. % 300.04/300.43 187834[19:Res:168350.1,897.0] || -> equal(restrict(restrict(u,v,w),x,y),ordinal_numbers) member(regular(restrict(restrict(u,v,w),x,y)),u)*. % 300.04/300.43 187891[19:SpR:149012.1,167458.0] || subclass(complement(image(successor_relation,ordinal_numbers)),complement(singleton(ordinal_numbers)))* -> equal(power_class(complement(image(successor_relation,ordinal_numbers))),complement(image(element_relation,kind_1_ordinals))). % 300.04/300.43 187897[19:SpL:167458.0,178139.1] || member(intersection(complement(singleton(ordinal_numbers)),complement(image(successor_relation,ordinal_numbers))),universal_class)* equal(rest_of(complement(image(element_relation,kind_1_ordinals))),rest_relation) -> . % 300.04/300.43 188202[19:Obv:188184.1] || subclass(unordered_pair(u,v),complement(singleton(v)))* -> equal(regular(unordered_pair(u,v)),u) equal(unordered_pair(u,v),ordinal_numbers). % 300.04/300.43 188203[19:Obv:188183.1] || subclass(unordered_pair(u,v),complement(singleton(u)))* -> equal(regular(unordered_pair(u,v)),v) equal(unordered_pair(u,v),ordinal_numbers). % 300.04/300.43 188358[19:Obv:188352.1] || equal(unordered_pair(u,v),complement(singleton(v))) -> equal(regular(unordered_pair(u,v)),u)** equal(unordered_pair(u,v),ordinal_numbers). % 300.04/300.43 188359[19:Obv:188351.1] || equal(unordered_pair(u,v),complement(singleton(u))) -> equal(regular(unordered_pair(u,v)),v)** equal(unordered_pair(u,v),ordinal_numbers). % 300.04/300.43 190702[19:Rew:4119.0,190620.1] || member(regular(symmetric_difference(u,cross_product(v,w))),restrict(u,v,w))* -> equal(symmetric_difference(u,cross_product(v,w)),ordinal_numbers). % 300.04/300.43 190703[19:Rew:4121.0,190619.1] || member(regular(symmetric_difference(cross_product(u,v),w)),restrict(w,u,v))* -> equal(symmetric_difference(cross_product(u,v),w),ordinal_numbers). % 300.04/300.43 191008[19:Rew:142500.0,190984.0,167055.0,190984.0] || -> equal(symmetric_difference(complement(symmetrization_of(ordinal_numbers)),union(inverse(ordinal_numbers),symmetrization_of(ordinal_numbers))),union(complement(symmetrization_of(ordinal_numbers)),union(inverse(ordinal_numbers),symmetrization_of(ordinal_numbers))))**. % 300.04/300.43 192957[25:Rew:192881.1,189075.2] function(u) || equal(complement(range_of(u)),universal_class) equal(cantor(cantor(v)),universal_class) -> compatible(u,v,w)*. % 300.04/300.43 192967[25:Rew:192881.1,176597.2] function(u) || subclass(range_of(u),ordinal_numbers) equal(cantor(cantor(v)),universal_class) -> compatible(u,v,singleton(w))*. % 300.04/300.43 192986[25:Rew:192881.1,138651.2] function(u) || equal(rest_of(cantor(v)),rest_relation) equal(cantor(cantor(w)),universal_class) -> compatible(u,w,v)*. % 300.04/300.43 193639[25:Rew:193223.1,193361.1] function(u) || asymmetric(v,ordinal_numbers) -> equal(range__dfg(intersection(v,inverse(v)),u,ordinal_numbers),second(not_subclass_element(ordinal_numbers,ordinal_numbers)))**. % 300.04/300.43 193825[25:SoR:193247.0,12322.2] 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))** -> . % 300.04/300.43 193882[25:SSi:193874.1,72.1] one_to_one(u) || subclass(universal_class,cantor(cantor(v)))* equal(cantor(cantor(w)),universal_class) -> compatible(u,w,v)*. % 300.04/300.43 193976[19:Res:166605.0,176244.2] || member(u,universal_class) subclass(domain_relation,complement(inverse(singleton(ordered_pair(u,ordinal_numbers)))))* -> asymmetric(singleton(ordered_pair(u,ordinal_numbers)),v)*. % 300.04/300.43 194007[19:Res:167339.2,176244.2] || subclass(omega,u) member(v,universal_class) subclass(domain_relation,complement(u))* -> equal(integer_of(ordered_pair(v,ordinal_numbers)),ordinal_numbers)**. % 300.04/300.43 194149[19:Res:167339.2,4727.0] || subclass(omega,composition_function) -> equal(integer_of(ordered_pair(u,singleton(singleton(singleton(v))))),ordinal_numbers)** equal(compose(u,singleton(v)),v). % 300.04/300.43 194310[19:Res:167339.2,169002.1] || subclass(omega,u) well_ordering(v,universal_class) -> equal(integer_of(least(v,complement(u))),ordinal_numbers)** equal(complement(u),ordinal_numbers). % 300.04/300.43 194328[19:MRR:194299.0,168246.2] || well_ordering(u,universal_class) -> member(least(u,complement(union(v,w))),complement(w))* equal(complement(union(v,w)),ordinal_numbers). % 300.04/300.43 194329[19:MRR:194298.0,168246.2] || well_ordering(u,universal_class) -> member(least(u,complement(union(v,w))),complement(v))* equal(complement(union(v,w)),ordinal_numbers). % 300.04/300.43 194400[19:Res:167580.1,2.0] || member(u,universal_class) subclass(cantor(v),w)* -> equal(apply(v,u),sum_class(range_of(ordinal_numbers)))** member(u,w)*. % 300.04/300.43 194462[19:MRR:194420.0,940.0] || member(u,universal_class) subclass(domain_relation,complement(cantor(v))) -> equal(apply(v,ordered_pair(u,ordinal_numbers)),sum_class(range_of(ordinal_numbers)))**. % 300.04/300.43 194465[19:MRR:194428.0,167137.1] || -> equal(apply(u,regular(intersection(complement(cantor(u)),v))),sum_class(range_of(ordinal_numbers)))** equal(intersection(complement(cantor(u)),v),ordinal_numbers). % 300.04/300.43 194466[19:MRR:194427.0,167137.1] || -> equal(apply(u,regular(intersection(v,complement(cantor(u))))),sum_class(range_of(ordinal_numbers)))** equal(intersection(v,complement(cantor(u))),ordinal_numbers). % 300.04/300.43 195051[25:SoR:193168.0,12322.2] single_valued_class(restrict(element_relation,universal_class,u)) || equal(restrict(element_relation,universal_class,u),cross_product(universal_class,universal_class))** -> equal(sum_class(u),universal_class). % 300.04/300.43 195077[25:SoR:193173.0,12322.2] single_valued_class(flip(cross_product(u,universal_class))) || equal(flip(cross_product(u,universal_class)),cross_product(universal_class,universal_class))** -> equal(inverse(u),universal_class). % 300.04/300.43 195140[25:SpL:193305.1,34.0] function(u) || member(ordered_pair(singleton(singleton(ordinal_numbers)),v),rotate(w))* -> member(ordered_pair(ordered_pair(u,v),ordinal_numbers),w)*. % 300.04/300.43 195141[25:SpL:193305.1,37.0] function(u) || member(ordered_pair(singleton(singleton(ordinal_numbers)),v),flip(w))* -> member(ordered_pair(ordered_pair(u,ordinal_numbers),v),w)*. % 300.04/300.43 195246[0:Res:27190.1,2.0] || subclass(rest_relation,flip(u))* subclass(u,v)* -> member(ordered_pair(ordered_pair(w,x),rest_of(ordered_pair(x,w))),v)*. % 300.04/300.43 195252[0:Res:27190.1,4127.0] || subclass(rest_relation,flip(symmetric_difference(u,v))) -> member(ordered_pair(ordered_pair(w,x),rest_of(ordered_pair(x,w))),union(u,v))*. % 300.04/300.43 195254[0:Res:27190.1,16910.0] || 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))*. % 300.04/300.43 195343[0:Res:27189.1,2.0] || subclass(rest_relation,rotate(u))* subclass(u,v)* -> member(ordered_pair(ordered_pair(w,rest_of(ordered_pair(x,w))),x),v)*. % 300.04/300.43 195349[0:Res:27189.1,4127.0] || subclass(rest_relation,rotate(symmetric_difference(u,v))) -> member(ordered_pair(ordered_pair(w,rest_of(ordered_pair(x,w))),x),union(u,v))*. % 300.04/300.43 195351[0:Res:27189.1,16910.0] || 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))*. % 300.04/300.43 195396[0:Res:27189.1,4727.0] || subclass(rest_relation,rotate(composition_function)) -> equal(compose(ordered_pair(u,rest_of(ordered_pair(singleton(singleton(singleton(v))),u))),singleton(v)),v)**. % 300.04/300.43 195509[19:Res:168374.2,2.0] || subclass(omega,symmetric_difference(u,v)) subclass(union(u,v),w)* -> equal(integer_of(x),ordinal_numbers) member(x,w)*. % 300.04/300.43 195512[19:Res:168374.2,6432.1] || subclass(omega,symmetric_difference(u,v)) subclass(universal_class,complement(union(u,v)))* -> equal(integer_of(unordered_pair(w,x)),ordinal_numbers)**. % 300.04/300.43 195518[19:Res:168374.2,6476.1] || subclass(omega,symmetric_difference(u,v)) subclass(universal_class,complement(union(u,v)))* -> equal(integer_of(ordered_pair(w,x)),ordinal_numbers)**. % 300.04/300.43 195519[19:Res:168374.2,4.0] || subclass(omega,symmetric_difference(u,v)) -> equal(integer_of(not_subclass_element(w,union(u,v))),ordinal_numbers)** subclass(w,union(u,v)). % 300.04/300.43 195645[0:Res:16913.1,2.0] || subclass(symmetrization_of(u),v) -> subclass(symmetric_difference(u,inverse(u)),w) member(not_subclass_element(symmetric_difference(u,inverse(u)),w),v)*. % 300.04/300.43 195811[8:Res:147404.1,16224.0] || 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). % 300.04/300.43 195819[19:Res:167339.2,16224.0] || subclass(omega,u) -> equal(integer_of(not_subclass_element(intersection(complement(u),v),w)),ordinal_numbers)** subclass(intersection(complement(u),v),w). % 300.04/300.43 195878[0:MRR:195803.0,36682.1] || -> member(not_subclass_element(intersection(complement(union(u,v)),w),x),complement(v))* subclass(intersection(complement(union(u,v)),w),x). % 300.04/300.43 195879[0:MRR:195802.0,36682.1] || -> member(not_subclass_element(intersection(complement(union(u,v)),w),x),complement(u))* subclass(intersection(complement(union(u,v)),w),x). % 300.04/300.43 195995[8:Res:147404.1,16351.0] || 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). % 300.04/300.43 196003[19:Res:167339.2,16351.0] || subclass(omega,u) -> equal(integer_of(not_subclass_element(intersection(v,complement(u)),w)),ordinal_numbers)** subclass(intersection(v,complement(u)),w). % 300.04/300.43 196048[0:MRR:195987.0,36682.1] || -> member(not_subclass_element(intersection(u,complement(union(v,w))),x),complement(w))* subclass(intersection(u,complement(union(v,w))),x). % 300.04/300.43 196049[0:MRR:195986.0,36682.1] || -> member(not_subclass_element(intersection(u,complement(union(v,w))),x),complement(v))* subclass(intersection(u,complement(union(v,w))),x). % 300.04/300.43 196569[19:Obv:196553.2] || subclass(complement(u),omega) subclass(omega,u) -> equal(not_subclass_element(complement(u),v),ordinal_numbers)** subclass(complement(u),v). % 300.04/300.43 196608[19:Obv:196593.1] || member(u,complement(unordered_pair(v,u)))* -> equal(not_subclass_element(unordered_pair(v,u),ordinal_numbers),v) subclass(unordered_pair(v,u),ordinal_numbers). % 300.04/300.43 196609[19:Obv:196592.1] || member(u,complement(unordered_pair(u,v)))* -> equal(not_subclass_element(unordered_pair(u,v),ordinal_numbers),v) subclass(unordered_pair(u,v),ordinal_numbers). % 300.04/300.43 196663[19:Res:16283.0,167728.0] || subclass(cross_product(u,v),w) -> equal(restrict(x,u,v),ordinal_numbers) member(regular(restrict(x,u,v)),w)*. % 300.04/300.43 196778[19:Res:167729.2,2.0] || subclass(u,symmetric_difference(v,w))* subclass(union(v,w),x)* -> equal(u,ordinal_numbers) member(regular(u),x)*. % 300.04/300.43 196797[19:Obv:196783.1] || subclass(intersection(complement(union(u,v)),w),symmetric_difference(u,v))* -> equal(intersection(complement(union(u,v)),w),ordinal_numbers). % 300.04/300.43 196798[19:Obv:196782.1] || subclass(intersection(u,complement(union(v,w))),symmetric_difference(v,w))* -> equal(intersection(u,complement(union(v,w))),ordinal_numbers). % 300.04/300.43 196820[25:Rew:167050.0,196814.1] function(u) || subclass(range_of(u),ordinal_numbers) equal(cantor(cantor(v)),universal_class) -> compatible(u,v,regular(element_relation))*. % 300.04/300.43 196824[19:Res:196720.0,126.0] || 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))*. % 300.04/300.43 196940[19:Res:12015.1,168251.0] || equal(complement(complement(regular(u))),universal_class)** member(singleton(v),u)* -> equal(u,ordinal_numbers) member(singleton(v),w)*. % 300.04/300.43 196947[19:Res:2480.1,168251.0] || subclass(universal_class,regular(u)) member(unordered_pair(v,w),u)* -> equal(u,ordinal_numbers) member(unordered_pair(v,w),x)*. % 300.04/300.43 196956[19:Res:182463.1,168251.0] || equal(regular(u),singleton(singleton(ordinal_numbers))) member(singleton(ordinal_numbers),u)* -> equal(u,ordinal_numbers) member(singleton(ordinal_numbers),v)*. % 300.04/300.43 196959[19:Res:2481.1,168251.0] || subclass(universal_class,regular(u)) member(ordered_pair(v,w),u)* -> equal(u,ordinal_numbers) member(ordered_pair(v,w),x)*. % 300.04/300.43 196963[19:Res:167127.1,168251.0] || subclass(domain_relation,regular(u)) member(ordered_pair(ordinal_numbers,ordinal_numbers),u)* -> equal(u,ordinal_numbers) member(ordered_pair(ordinal_numbers,ordinal_numbers),v)*. % 300.04/300.43 196978[19:Res:167339.2,168251.0] || subclass(omega,regular(u))* member(v,u)* -> equal(integer_of(v),ordinal_numbers) equal(u,ordinal_numbers) member(v,w)*. % 300.04/300.43 196991[20:Res:175613.1,168251.0] || subclass(universal_class,regular(u)) member(regular(symmetrization_of(ordinal_numbers)),u)* -> equal(u,ordinal_numbers) member(regular(symmetrization_of(ordinal_numbers)),v)*. % 300.04/300.43 197158[19:SpL:196827.0,34.0] || member(ordered_pair(regular(element_relation),u),rotate(v)) -> member(ordered_pair(ordered_pair(second(regular(element_relation)),u),first(regular(element_relation))),v)*. % 300.04/300.43 197159[19:SpL:196827.0,37.0] || member(ordered_pair(regular(element_relation),u),flip(v)) -> member(ordered_pair(ordered_pair(second(regular(element_relation)),first(regular(element_relation))),u),v)*. % 300.04/300.43 197263[19:Res:168469.2,2.0] || subclass(u,v)* subclass(v,w)* -> equal(intersection(x,u),ordinal_numbers) member(regular(intersection(x,u)),w)*. % 300.04/300.43 197269[19:Res:168469.2,4127.0] || subclass(u,symmetric_difference(v,w)) -> equal(intersection(x,u),ordinal_numbers) member(regular(intersection(x,u)),union(v,w))*. % 300.04/300.43 197271[19:Res:168469.2,16910.0] || subclass(u,symmetric_difference(v,inverse(v)))* -> equal(intersection(w,u),ordinal_numbers) member(regular(intersection(w,u)),symmetrization_of(v))*. % 300.04/300.43 197290[19:Res:168469.2,158.0] || subclass(u,omega) -> equal(intersection(v,u),ordinal_numbers) equal(integer_of(regular(intersection(v,u))),regular(intersection(v,u)))**. % 300.04/300.43 197431[19:Res:168471.1,148647.0] || -> equal(intersection(u,intersection(complement(complement(v)),w)),ordinal_numbers) member(regular(intersection(u,intersection(complement(complement(v)),w))),v)*. % 300.04/300.43 197437[19:Res:168471.1,2.0] || subclass(u,v) -> equal(intersection(w,intersection(u,x)),ordinal_numbers) member(regular(intersection(w,intersection(u,x))),v)*. % 300.04/300.43 197439[19:Res:168471.1,22.0] || -> equal(intersection(u,intersection(intersection(v,w),x)),ordinal_numbers) member(regular(intersection(u,intersection(intersection(v,w),x))),v)*. % 300.04/300.43 197440[19:Res:168471.1,23.0] || -> equal(intersection(u,intersection(intersection(v,w),x)),ordinal_numbers) member(regular(intersection(u,intersection(intersection(v,w),x))),w)*. % 300.04/300.43 197632[19:Res:168472.1,148647.0] || -> equal(intersection(u,intersection(v,complement(complement(w)))),ordinal_numbers) member(regular(intersection(u,intersection(v,complement(complement(w))))),w)*. % 300.04/300.43 197638[19:Res:168472.1,2.0] || subclass(u,v) -> equal(intersection(w,intersection(x,u)),ordinal_numbers) member(regular(intersection(w,intersection(x,u))),v)*. % 300.04/300.43 197640[19:Res:168472.1,22.0] || -> equal(intersection(u,intersection(v,intersection(w,x))),ordinal_numbers) member(regular(intersection(u,intersection(v,intersection(w,x)))),w)*. % 300.04/300.43 197641[19:Res:168472.1,23.0] || -> equal(intersection(u,intersection(v,intersection(w,x))),ordinal_numbers) member(regular(intersection(u,intersection(v,intersection(w,x)))),x)*. % 300.04/300.43 197827[19:Res:168474.2,2.0] || subclass(u,v)* subclass(v,w)* -> equal(intersection(u,x),ordinal_numbers) member(regular(intersection(u,x)),w)*. % 300.04/300.43 197833[19:Res:168474.2,4127.0] || subclass(u,symmetric_difference(v,w)) -> equal(intersection(u,x),ordinal_numbers) member(regular(intersection(u,x)),union(v,w))*. % 300.04/300.43 197835[19:Res:168474.2,16910.0] || subclass(u,symmetric_difference(v,inverse(v)))* -> equal(intersection(u,w),ordinal_numbers) member(regular(intersection(u,w)),symmetrization_of(v))*. % 300.04/300.43 197854[19:Res:168474.2,158.0] || subclass(u,omega) -> equal(intersection(u,v),ordinal_numbers) equal(integer_of(regular(intersection(u,v))),regular(intersection(u,v)))**. % 300.04/300.43 198435[19:Res:168476.1,148647.0] || -> equal(intersection(intersection(complement(complement(u)),v),w),ordinal_numbers) member(regular(intersection(intersection(complement(complement(u)),v),w)),u)*. % 300.04/300.43 198441[19:Res:168476.1,2.0] || subclass(u,v) -> equal(intersection(intersection(u,w),x),ordinal_numbers) member(regular(intersection(intersection(u,w),x)),v)*. % 300.04/300.43 198443[19:Res:168476.1,22.0] || -> equal(intersection(intersection(intersection(u,v),w),x),ordinal_numbers) member(regular(intersection(intersection(intersection(u,v),w),x)),u)*. % 300.04/300.43 198444[19:Res:168476.1,23.0] || -> equal(intersection(intersection(intersection(u,v),w),x),ordinal_numbers) member(regular(intersection(intersection(intersection(u,v),w),x)),v)*. % 300.04/300.43 199099[19:Res:168477.1,148647.0] || -> equal(intersection(intersection(u,complement(complement(v))),w),ordinal_numbers) member(regular(intersection(intersection(u,complement(complement(v))),w)),v)*. % 300.04/300.43 199105[19:Res:168477.1,2.0] || subclass(u,v) -> equal(intersection(intersection(w,u),x),ordinal_numbers) member(regular(intersection(intersection(w,u),x)),v)*. % 300.04/300.43 199107[19:Res:168477.1,22.0] || -> equal(intersection(intersection(u,intersection(v,w)),x),ordinal_numbers) member(regular(intersection(intersection(u,intersection(v,w)),x)),v)*. % 300.04/300.43 199108[19:Res:168477.1,23.0] || -> equal(intersection(intersection(u,intersection(v,w)),x),ordinal_numbers) member(regular(intersection(intersection(u,intersection(v,w)),x)),w)*. % 300.04/300.43 199617[19:Obv:199580.2] || equal(u,v) subclass(unordered_pair(v,u),omega)* -> equal(unordered_pair(v,u),ordinal_numbers) equal(integer_of(v),v). % 300.04/300.43 199744[0:SpR:149179.0,16274.1] || -> subclass(symmetric_difference(u,intersection(u,v)),w) member(not_subclass_element(symmetric_difference(u,intersection(u,v)),w),complement(intersection(u,v)))*. % 300.04/300.43 199745[0:SpR:149318.0,16274.1] || -> subclass(symmetric_difference(u,intersection(v,u)),w) member(not_subclass_element(symmetric_difference(u,intersection(v,u)),w),complement(intersection(v,u)))*. % 300.04/300.43 199827[0:Res:16274.1,2.0] || subclass(complement(intersection(u,v)),w) -> subclass(symmetric_difference(u,v),x) member(not_subclass_element(symmetric_difference(u,v),x),w)*. % 300.04/300.43 200784[19:Rew:146281.0,200783.1] || member(u,universal_class) -> member(u,segment(universal_class,v,w)) equal(segment(cross_product(singleton(u),universal_class),v,w),ordinal_numbers)**. % 300.04/300.43 200887[19:SpR:902.0,168349.1] || -> equal(restrict(cross_product(u,v),w,x),ordinal_numbers) member(regular(restrict(cross_product(w,x),u,v)),cross_product(w,x))*. % 300.04/300.43 203567[26:Res:167131.2,202277.1] || subclass(u,complement(compose(complement(element_relation),inverse(element_relation))))* member(regular(u),cross_product(universal_class,universal_class)) -> equal(u,ordinal_numbers). % 300.04/300.43 203571[26:Res:167339.2,202277.1] || subclass(omega,complement(compose(complement(element_relation),inverse(element_relation))))* member(u,cross_product(universal_class,universal_class))* -> equal(integer_of(u),ordinal_numbers). % 300.04/300.43 204391[22:Rew:204377.1,168369.3] || subclass(omega,ordered_pair(u,v))* -> equal(integer_of(w),ordinal_numbers)** equal(w,unordered_pair(u,singleton(v)))* equal(w,ordinal_numbers). % 300.04/300.43 204610[19:Rew:177036.0,204597.0] || equal(sum_class(range_of(ordinal_numbers)),inverse(u))* member(singleton(singleton(ordinal_numbers)),cross_product(universal_class,universal_class))* -> equal(range_of(u),ordinal_numbers)**. % 300.04/300.43 204611[19:Rew:167362.1,204596.1] || member(u,universal_class)* equal(sum_class(range_of(ordinal_numbers)),range_of(u))* member(singleton(singleton(ordinal_numbers)),cross_product(universal_class,universal_class))* -> . % 300.04/300.43 204851[8:SpL:923.0,85097.1] inductive(intersection(power_class(image(element_relation,complement(u))),complement(v))) || equal(union(image(element_relation,power_class(u)),v),universal_class)** -> . % 300.04/300.43 204899[22:SpL:923.0,178292.1] inductive(intersection(power_class(image(element_relation,complement(u))),complement(v))) || equal(union(image(element_relation,power_class(u)),v),omega)** -> . % 300.04/300.43 205007[25:MRR:205006.2,192574.0] single_valued_class(intersection(power_class(image(element_relation,complement(u))),complement(v))) || equal(union(image(element_relation,power_class(u)),v),universal_class)** -> . % 300.04/300.43 205190[8:SpL:925.0,85097.1] inductive(intersection(complement(u),power_class(image(element_relation,complement(v))))) || equal(union(u,image(element_relation,power_class(v))),universal_class)** -> . % 300.04/300.43 205238[22:SpL:925.0,178292.1] inductive(intersection(complement(u),power_class(image(element_relation,complement(v))))) || equal(union(u,image(element_relation,power_class(v))),omega)** -> . % 300.04/300.43 205348[25:MRR:205347.2,192574.0] single_valued_class(intersection(complement(u),power_class(image(element_relation,complement(v))))) || equal(union(u,image(element_relation,power_class(v))),universal_class)** -> . % 300.04/300.43 206303[19:SpL:27838.0,176243.1] || member(u,universal_class) subclass(domain_relation,symmetric_difference(complement(v),complement(singleton(v))))* -> member(ordered_pair(u,ordinal_numbers),successor(v))*. % 300.04/300.43 206321[0:Rew:27838.0,206215.0] || -> subclass(symmetric_difference(complement(u),complement(singleton(u))),v) member(not_subclass_element(symmetric_difference(complement(u),complement(singleton(u))),v),successor(u))*. % 300.04/300.43 206437[0:Rew:206400.0,205263.1] || member(u,complement(union(v,image(element_relation,power_class(w))))) -> member(u,intersection(complement(v),power_class(complement(power_class(w)))))*. % 300.04/300.43 206440[0:Rew:206400.0,27240.0] || member(u,intersection(complement(v),power_class(complement(power_class(w)))))* member(u,union(v,image(element_relation,power_class(w)))) -> . % 300.04/300.43 206456[0:Rew:206400.0,154868.0] || subclass(ordered_pair(u,v),power_class(complement(power_class(w)))) member(unordered_pair(u,singleton(v)),image(element_relation,power_class(w)))* -> . % 300.04/300.43 206496[0:Rew:206400.0,205201.0] || subclass(universal_class,intersection(complement(u),power_class(complement(power_class(v)))))* subclass(universal_class,union(u,image(element_relation,power_class(v)))) -> . % 300.04/300.43 206497[8:Rew:206400.0,205219.0] || subclass(universal_class,intersection(complement(u),power_class(complement(power_class(v)))))* subclass(domain_relation,union(u,image(element_relation,power_class(v)))) -> . % 300.04/300.43 206498[19:Rew:206400.0,205252.0] || subclass(universal_class,intersection(complement(u),power_class(complement(power_class(v)))))* subclass(element_relation,union(u,image(element_relation,power_class(v)))) -> . % 300.04/300.43 206499[0:Rew:206400.0,147279.0] || subclass(universal_class,intersection(complement(u),power_class(complement(power_class(v)))))* member(omega,union(u,image(element_relation,power_class(v)))) -> . % 300.04/300.43 206511[19:Rew:206400.0,205197.1] || subclass(universal_class,union(u,image(element_relation,power_class(v)))) member(ordinal_numbers,intersection(complement(u),power_class(complement(power_class(v)))))* -> . % 300.04/300.43 206512[19:Rew:206400.0,205202.1] || subclass(universal_class,complement(union(u,image(element_relation,power_class(v))))) -> member(ordinal_numbers,intersection(complement(u),power_class(complement(power_class(v)))))*. % 300.04/300.43 206513[19:Rew:206400.0,205206.1] || equal(complement(union(u,image(element_relation,power_class(v)))),universal_class) -> member(ordinal_numbers,intersection(complement(u),power_class(complement(power_class(v)))))*. % 300.04/300.43 206514[22:Rew:206400.0,205208.1] || subclass(omega,complement(union(u,image(element_relation,power_class(v))))) -> member(ordinal_numbers,intersection(complement(u),power_class(complement(power_class(v)))))*. % 300.04/300.43 206515[22:Rew:206400.0,205209.1] || equal(complement(union(u,image(element_relation,power_class(v)))),omega) -> member(ordinal_numbers,intersection(complement(u),power_class(complement(power_class(v)))))*. % 300.04/300.43 206516[22:Rew:206400.0,205234.1] || subclass(omega,union(u,image(element_relation,power_class(v)))) member(ordinal_numbers,intersection(complement(u),power_class(complement(power_class(v)))))* -> . % 300.04/300.43 206521[19:Rew:206400.0,205080.0] || -> equal(symmetric_difference(power_class(intersection(complement(u),power_class(complement(power_class(v))))),image(element_relation,union(u,image(element_relation,power_class(v))))),universal_class)**. % 300.04/300.43 206522[19:Rew:206400.0,205079.0] || -> equal(intersection(power_class(intersection(complement(u),power_class(complement(power_class(v))))),image(element_relation,union(u,image(element_relation,power_class(v))))),ordinal_numbers)**. % 300.04/300.43 206543[0:Rew:206400.0,205199.0] || equal(intersection(complement(u),power_class(complement(power_class(v)))),universal_class) subclass(universal_class,union(u,image(element_relation,power_class(v))))* -> . % 300.04/300.43 206544[8:Rew:206400.0,205224.0] || equal(intersection(complement(u),power_class(complement(power_class(v)))),universal_class)** equal(union(u,image(element_relation,power_class(v))),domain_relation) -> . % 300.04/300.43 206545[22:Rew:206400.0,205237.0] || equal(intersection(complement(u),power_class(complement(power_class(v)))),universal_class)** equal(union(u,image(element_relation,power_class(v))),omega) -> . % 300.04/300.43 206546[19:Rew:206400.0,205253.0] || equal(intersection(complement(u),power_class(complement(power_class(v)))),universal_class)** equal(union(u,image(element_relation,power_class(v))),element_relation) -> . % 300.04/300.43 206548[22:Rew:206400.0,205236.0] || equal(intersection(complement(u),power_class(complement(power_class(v)))),omega)** equal(union(u,image(element_relation,power_class(v))),omega) -> . % 300.04/300.43 206549[19:Rew:206400.0,205099.0] || -> member(singleton(ordinal_numbers),intersection(complement(u),power_class(complement(power_class(v)))))* member(singleton(ordinal_numbers),union(u,image(element_relation,power_class(v)))). % 300.04/300.43 206550[19:Rew:206400.0,205229.1] || well_ordering(universal_class,union(u,image(element_relation,power_class(v)))) -> member(singleton(ordinal_numbers),intersection(complement(u),power_class(complement(power_class(v)))))*. % 300.04/300.43 206551[8:Rew:206400.0,205225.0] || equal(intersection(complement(u),power_class(complement(power_class(v)))),domain_relation)** equal(union(u,image(element_relation,power_class(v))),domain_relation) -> . % 300.04/300.43 206552[8:Rew:206400.0,205198.0] || subclass(domain_relation,intersection(complement(u),power_class(complement(power_class(v)))))* subclass(universal_class,union(u,image(element_relation,power_class(v)))) -> . % 300.04/300.43 206553[8:Rew:206400.0,205220.0] || subclass(domain_relation,intersection(complement(u),power_class(complement(power_class(v)))))* subclass(domain_relation,union(u,image(element_relation,power_class(v)))) -> . % 300.04/300.43 206556[0:Rew:206400.0,205200.1] || subclass(universal_class,union(u,image(element_relation,power_class(v)))) member(omega,intersection(complement(u),power_class(complement(power_class(v)))))* -> . % 300.04/300.43 206557[0:Rew:206400.0,205203.1] || subclass(universal_class,complement(union(u,image(element_relation,power_class(v))))) -> member(omega,intersection(complement(u),power_class(complement(power_class(v)))))*. % 300.04/300.43 206558[0:Rew:206400.0,205207.1] || equal(complement(union(u,image(element_relation,power_class(v)))),universal_class) -> member(omega,intersection(complement(u),power_class(complement(power_class(v)))))*. % 300.04/300.43 206600[0:Rew:206400.0,204924.1] || member(u,complement(union(image(element_relation,power_class(v)),w))) -> member(u,intersection(power_class(complement(power_class(v))),complement(w)))*. % 300.04/300.43 206603[0:Rew:206400.0,27251.0] || member(u,intersection(power_class(complement(power_class(v))),complement(w)))* member(u,union(image(element_relation,power_class(v)),w)) -> . % 300.04/300.43 206627[0:Rew:206400.0,154851.0] || subclass(u,power_class(complement(power_class(v)))) member(not_subclass_element(u,w),image(element_relation,power_class(v)))* -> subclass(u,w). % 300.04/300.43 206636[0:Rew:206400.0,154855.1] || member(u,universal_class) subclass(universal_class,power_class(complement(power_class(v)))) member(sum_class(u),image(element_relation,power_class(v)))* -> . % 300.04/300.43 206637[0:Rew:206400.0,154856.1] || member(u,universal_class) subclass(universal_class,power_class(complement(power_class(v)))) member(power_class(u),image(element_relation,power_class(v)))* -> . % 300.04/300.43 206691[0:Rew:206400.0,203752.0] || -> equal(union(u,intersection(power_class(v),complement(singleton(complement(power_class(v)))))),complement(intersection(complement(u),successor(complement(power_class(v))))))**. % 300.04/300.43 206707[0:Rew:206400.0,204101.0] || -> equal(union(u,intersection(power_class(v),complement(inverse(complement(power_class(v)))))),complement(intersection(complement(u),symmetrization_of(complement(power_class(v))))))**. % 300.04/300.43 206763[0:Rew:206400.0,204862.0] || subclass(universal_class,intersection(power_class(complement(power_class(u))),complement(v)))* subclass(universal_class,union(image(element_relation,power_class(u)),v)) -> . % 300.04/300.43 206764[8:Rew:206400.0,204880.0] || subclass(universal_class,intersection(power_class(complement(power_class(u))),complement(v)))* subclass(domain_relation,union(image(element_relation,power_class(u)),v)) -> . % 300.04/300.43 206765[19:Rew:206400.0,204913.0] || subclass(universal_class,intersection(power_class(complement(power_class(u))),complement(v)))* subclass(element_relation,union(image(element_relation,power_class(u)),v)) -> . % 300.04/300.43 206766[0:Rew:206400.0,147288.0] || subclass(universal_class,intersection(power_class(complement(power_class(u))),complement(v)))* member(omega,union(image(element_relation,power_class(u)),v)) -> . % 300.04/300.43 206778[19:Rew:206400.0,204858.1] || subclass(universal_class,union(image(element_relation,power_class(u)),v)) member(ordinal_numbers,intersection(power_class(complement(power_class(u))),complement(v)))* -> . % 300.04/300.43 206779[19:Rew:206400.0,204863.1] || subclass(universal_class,complement(union(image(element_relation,power_class(u)),v))) -> member(ordinal_numbers,intersection(power_class(complement(power_class(u))),complement(v)))*. % 300.04/300.43 206780[19:Rew:206400.0,204867.1] || equal(complement(union(image(element_relation,power_class(u)),v)),universal_class) -> member(ordinal_numbers,intersection(power_class(complement(power_class(u))),complement(v)))*. % 300.04/300.43 206781[22:Rew:206400.0,204869.1] || subclass(omega,complement(union(image(element_relation,power_class(u)),v))) -> member(ordinal_numbers,intersection(power_class(complement(power_class(u))),complement(v)))*. % 300.04/300.43 206782[22:Rew:206400.0,204870.1] || equal(complement(union(image(element_relation,power_class(u)),v)),omega) -> member(ordinal_numbers,intersection(power_class(complement(power_class(u))),complement(v)))*. % 300.04/300.43 206783[22:Rew:206400.0,204895.1] || subclass(omega,union(image(element_relation,power_class(u)),v)) member(ordinal_numbers,intersection(power_class(complement(power_class(u))),complement(v)))* -> . % 300.04/300.43 206788[19:Rew:206400.0,204742.0] || -> equal(symmetric_difference(power_class(intersection(power_class(complement(power_class(u))),complement(v))),image(element_relation,union(image(element_relation,power_class(u)),v))),universal_class)**. % 300.04/300.43 206789[19:Rew:206400.0,204741.0] || -> equal(intersection(power_class(intersection(power_class(complement(power_class(u))),complement(v))),image(element_relation,union(image(element_relation,power_class(u)),v))),ordinal_numbers)**. % 300.04/300.43 206810[0:Rew:206400.0,204860.0] || equal(intersection(power_class(complement(power_class(u))),complement(v)),universal_class) subclass(universal_class,union(image(element_relation,power_class(u)),v))* -> . % 300.04/300.43 206811[8:Rew:206400.0,204885.0] || equal(intersection(power_class(complement(power_class(u))),complement(v)),universal_class)** equal(union(image(element_relation,power_class(u)),v),domain_relation) -> . % 300.04/300.43 206812[22:Rew:206400.0,204898.0] || equal(intersection(power_class(complement(power_class(u))),complement(v)),universal_class)** equal(union(image(element_relation,power_class(u)),v),omega) -> . % 300.04/300.43 206813[19:Rew:206400.0,204914.0] || equal(intersection(power_class(complement(power_class(u))),complement(v)),universal_class)** equal(union(image(element_relation,power_class(u)),v),element_relation) -> . % 300.04/300.43 206815[22:Rew:206400.0,204897.0] || equal(intersection(power_class(complement(power_class(u))),complement(v)),omega)** equal(union(image(element_relation,power_class(u)),v),omega) -> . % 300.04/300.43 206816[19:Rew:206400.0,204761.0] || -> member(singleton(ordinal_numbers),intersection(power_class(complement(power_class(u))),complement(v)))* member(singleton(ordinal_numbers),union(image(element_relation,power_class(u)),v)). % 300.04/300.43 206817[19:Rew:206400.0,204890.1] || well_ordering(universal_class,union(image(element_relation,power_class(u)),v)) -> member(singleton(ordinal_numbers),intersection(power_class(complement(power_class(u))),complement(v)))*. % 300.04/300.43 206818[8:Rew:206400.0,204886.0] || equal(intersection(power_class(complement(power_class(u))),complement(v)),domain_relation)** equal(union(image(element_relation,power_class(u)),v),domain_relation) -> . % 300.04/300.43 206819[8:Rew:206400.0,204859.0] || subclass(domain_relation,intersection(power_class(complement(power_class(u))),complement(v)))* subclass(universal_class,union(image(element_relation,power_class(u)),v)) -> . % 300.04/300.43 206820[8:Rew:206400.0,204881.0] || subclass(domain_relation,intersection(power_class(complement(power_class(u))),complement(v)))* subclass(domain_relation,union(image(element_relation,power_class(u)),v)) -> . % 300.04/300.43 206823[0:Rew:206400.0,204861.1] || subclass(universal_class,union(image(element_relation,power_class(u)),v)) member(omega,intersection(power_class(complement(power_class(u))),complement(v)))* -> . % 300.04/300.43 206824[0:Rew:206400.0,204864.1] || subclass(universal_class,complement(union(image(element_relation,power_class(u)),v))) -> member(omega,intersection(power_class(complement(power_class(u))),complement(v)))*. % 300.04/300.43 206825[0:Rew:206400.0,204868.1] || equal(complement(union(image(element_relation,power_class(u)),v)),universal_class) -> member(omega,intersection(power_class(complement(power_class(u))),complement(v)))*. % 300.04/300.43 206942[19:Rew:206400.0,184858.0] || subclass(domain_relation,flip(power_class(complement(power_class(u))))) member(ordered_pair(ordered_pair(v,w),ordinal_numbers),image(element_relation,power_class(u)))* -> . % 300.04/300.43 206944[19:Rew:206400.0,184936.0] || subclass(domain_relation,rotate(power_class(complement(power_class(u))))) member(ordered_pair(ordered_pair(v,ordinal_numbers),w),image(element_relation,power_class(u)))* -> . % 300.04/300.43 207057[19:Rew:206400.0,203866.1] inductive(intersection(power_class(u),complement(singleton(image(element_relation,complement(u)))))) || equal(successor(complement(power_class(u))),singleton(ordinal_numbers))** -> . % 300.04/300.43 207112[0:Rew:206400.0,203696.0] || -> equal(union(intersection(power_class(u),complement(singleton(complement(power_class(u))))),v),complement(intersection(successor(complement(power_class(u))),complement(v))))**. % 300.04/300.43 207165[19:Rew:206400.0,204215.1] inductive(intersection(power_class(u),complement(inverse(image(element_relation,complement(u)))))) || equal(symmetrization_of(complement(power_class(u))),singleton(ordinal_numbers))** -> . % 300.04/300.43 207221[0:Rew:206400.0,204044.0] || -> equal(union(intersection(power_class(u),complement(inverse(complement(power_class(u))))),v),complement(intersection(symmetrization_of(complement(power_class(u))),complement(v))))**. % 300.04/300.43 207263[2:Rew:206400.0,135724.2] inductive(image(element_relation,complement(u))) || well_ordering(v,universal_class) member(least(v,complement(power_class(u))),power_class(u))* -> . % 300.04/300.43 207494[19:Rew:206400.0,207019.1] || equal(complement(successor(complement(power_class(u)))),universal_class) well_ordering(universal_class,intersection(power_class(u),complement(singleton(complement(power_class(u))))))* -> . % 300.04/300.43 207495[0:Rew:206400.0,207022.1] || subclass(universal_class,complement(successor(complement(power_class(u))))) -> member(singleton(v),intersection(power_class(u),complement(singleton(complement(power_class(u))))))*. % 300.04/300.43 207496[19:Rew:206400.0,207025.1] || equal(complement(successor(complement(power_class(u)))),singleton(ordinal_numbers)) -> member(ordinal_numbers,intersection(power_class(u),complement(singleton(complement(power_class(u))))))*. % 300.04/300.43 207498[22:Rew:206400.0,207049.0] || equal(intersection(power_class(u),complement(singleton(complement(power_class(u))))),singleton(ordinal_numbers))** equal(successor(complement(power_class(u))),omega) -> . % 300.04/300.43 207499[19:Rew:206400.0,207055.0] || equal(intersection(power_class(u),complement(singleton(complement(power_class(u))))),universal_class)** equal(successor(complement(power_class(u))),singleton(ordinal_numbers)) -> . % 300.04/300.43 207500[22:Rew:206400.0,207056.0] || equal(intersection(power_class(u),complement(singleton(complement(power_class(u))))),omega)** equal(successor(complement(power_class(u))),singleton(ordinal_numbers)) -> . % 300.04/300.43 207501[19:Rew:206400.0,207060.1] || equal(successor(complement(power_class(u))),domain_relation) equal(rotate(intersection(power_class(u),complement(singleton(complement(power_class(u)))))),rest_relation)** -> . % 300.04/300.43 207502[19:Rew:206400.0,207061.0] || equal(flip(intersection(power_class(u),complement(singleton(complement(power_class(u)))))),domain_relation)** equal(successor(complement(power_class(u))),domain_relation) -> . % 300.04/300.43 207503[19:Rew:206400.0,207062.0] || equal(rotate(intersection(power_class(u),complement(singleton(complement(power_class(u)))))),domain_relation)** equal(successor(complement(power_class(u))),domain_relation) -> . % 300.04/300.43 207504[19:Rew:206400.0,207065.0] || equal(rotate(intersection(power_class(u),complement(singleton(complement(power_class(u)))))),rest_relation)** subclass(domain_relation,successor(complement(power_class(u)))) -> . % 300.04/300.43 207505[19:Rew:206400.0,207066.0] || subclass(domain_relation,flip(intersection(power_class(u),complement(singleton(complement(power_class(u)))))))* subclass(domain_relation,successor(complement(power_class(u)))) -> . % 300.04/300.43 207506[19:Rew:206400.0,207067.0] || subclass(domain_relation,rotate(intersection(power_class(u),complement(singleton(complement(power_class(u)))))))* subclass(domain_relation,successor(complement(power_class(u)))) -> . % 300.04/300.43 207507[0:Rew:206400.0,207070.0] || equal(rotate(intersection(power_class(u),complement(singleton(complement(power_class(u)))))),rest_relation)** subclass(universal_class,successor(complement(power_class(u)))) -> . % 300.04/300.43 207508[0:Rew:206400.0,207071.0] || equal(flip(intersection(power_class(u),complement(singleton(complement(power_class(u)))))),rest_relation)** subclass(universal_class,successor(complement(power_class(u)))) -> . % 300.04/300.43 207509[19:Rew:206400.0,207072.0] || equal(rotate(intersection(power_class(u),complement(singleton(complement(power_class(u)))))),domain_relation)** subclass(universal_class,successor(complement(power_class(u)))) -> . % 300.04/300.43 207510[19:Rew:206400.0,207073.0] || equal(flip(intersection(power_class(u),complement(singleton(complement(power_class(u)))))),domain_relation)** subclass(universal_class,successor(complement(power_class(u)))) -> . % 300.04/300.43 207511[20:Rew:206400.0,207080.0] || equal(intersection(power_class(u),complement(singleton(complement(power_class(u))))),universal_class)** equal(successor(complement(power_class(u))),symmetrization_of(ordinal_numbers)) -> . % 300.04/300.43 207512[20:Rew:206400.0,207081.0] || subclass(universal_class,intersection(power_class(u),complement(singleton(complement(power_class(u))))))* subclass(symmetrization_of(ordinal_numbers),successor(complement(power_class(u)))) -> . % 300.04/300.43 207513[19:Rew:206400.0,207082.1] || subclass(singleton(ordinal_numbers),successor(complement(power_class(u)))) member(ordinal_numbers,intersection(power_class(u),complement(singleton(complement(power_class(u))))))* -> . % 300.04/300.43 207517[19:Rew:206400.0,207129.1] || equal(complement(symmetrization_of(complement(power_class(u)))),universal_class) well_ordering(universal_class,intersection(power_class(u),complement(inverse(complement(power_class(u))))))* -> . % 300.04/300.43 207518[0:Rew:206400.0,207132.1] || subclass(universal_class,complement(symmetrization_of(complement(power_class(u))))) -> member(singleton(v),intersection(power_class(u),complement(inverse(complement(power_class(u))))))*. % 300.04/300.43 207519[19:Rew:206400.0,207135.1] || equal(complement(symmetrization_of(complement(power_class(u)))),singleton(ordinal_numbers)) -> member(ordinal_numbers,intersection(power_class(u),complement(inverse(complement(power_class(u))))))*. % 300.04/300.43 207521[22:Rew:206400.0,207157.0] || equal(intersection(power_class(u),complement(inverse(complement(power_class(u))))),singleton(ordinal_numbers))** equal(symmetrization_of(complement(power_class(u))),omega) -> . % 300.04/300.43 207522[19:Rew:206400.0,207163.0] || equal(intersection(power_class(u),complement(inverse(complement(power_class(u))))),universal_class)** equal(symmetrization_of(complement(power_class(u))),singleton(ordinal_numbers)) -> . % 300.04/300.43 207523[22:Rew:206400.0,207164.0] || equal(intersection(power_class(u),complement(inverse(complement(power_class(u))))),omega)** equal(symmetrization_of(complement(power_class(u))),singleton(ordinal_numbers)) -> . % 300.04/300.43 207524[19:Rew:206400.0,207168.1] || equal(symmetrization_of(complement(power_class(u))),domain_relation) equal(rotate(intersection(power_class(u),complement(inverse(complement(power_class(u)))))),rest_relation)** -> . % 300.04/300.43 207525[19:Rew:206400.0,207169.0] || equal(flip(intersection(power_class(u),complement(inverse(complement(power_class(u)))))),domain_relation)** equal(symmetrization_of(complement(power_class(u))),domain_relation) -> . % 300.04/300.43 207526[19:Rew:206400.0,207170.0] || equal(rotate(intersection(power_class(u),complement(inverse(complement(power_class(u)))))),domain_relation)** equal(symmetrization_of(complement(power_class(u))),domain_relation) -> . % 300.04/300.43 207527[19:Rew:206400.0,207173.0] || equal(rotate(intersection(power_class(u),complement(inverse(complement(power_class(u)))))),rest_relation)** subclass(domain_relation,symmetrization_of(complement(power_class(u)))) -> . % 300.04/300.43 207528[19:Rew:206400.0,207174.0] || subclass(domain_relation,flip(intersection(power_class(u),complement(inverse(complement(power_class(u)))))))* subclass(domain_relation,symmetrization_of(complement(power_class(u)))) -> . % 300.04/300.43 207529[19:Rew:206400.0,207175.0] || subclass(domain_relation,rotate(intersection(power_class(u),complement(inverse(complement(power_class(u)))))))* subclass(domain_relation,symmetrization_of(complement(power_class(u)))) -> . % 300.04/300.43 207530[0:Rew:206400.0,207178.0] || equal(rotate(intersection(power_class(u),complement(inverse(complement(power_class(u)))))),rest_relation)** subclass(universal_class,symmetrization_of(complement(power_class(u)))) -> . % 300.04/300.43 207531[0:Rew:206400.0,207179.0] || equal(flip(intersection(power_class(u),complement(inverse(complement(power_class(u)))))),rest_relation)** subclass(universal_class,symmetrization_of(complement(power_class(u)))) -> . % 300.04/300.43 207532[19:Rew:206400.0,207180.0] || equal(rotate(intersection(power_class(u),complement(inverse(complement(power_class(u)))))),domain_relation)** subclass(universal_class,symmetrization_of(complement(power_class(u)))) -> . % 300.04/300.43 207533[19:Rew:206400.0,207181.0] || equal(flip(intersection(power_class(u),complement(inverse(complement(power_class(u)))))),domain_relation)** subclass(universal_class,symmetrization_of(complement(power_class(u)))) -> . % 300.04/300.43 207534[20:Rew:206400.0,207188.0] || equal(intersection(power_class(u),complement(inverse(complement(power_class(u))))),universal_class)** equal(symmetrization_of(complement(power_class(u))),symmetrization_of(ordinal_numbers)) -> . % 300.04/300.43 207535[20:Rew:206400.0,207189.0] || subclass(universal_class,intersection(power_class(u),complement(inverse(complement(power_class(u))))))* subclass(symmetrization_of(ordinal_numbers),symmetrization_of(complement(power_class(u)))) -> . % 300.04/300.43 207536[19:Rew:206400.0,207190.1] || subclass(singleton(ordinal_numbers),symmetrization_of(complement(power_class(u)))) member(ordinal_numbers,intersection(power_class(u),complement(inverse(complement(power_class(u))))))* -> . % 300.04/300.43 207666[0:Rew:114.0,206369.1,27.0,206369.1,114.0,206369.0,27.0,206369.0] || member(not_subclass_element(image(element_relation,symmetrization_of(u)),v),complement(image(element_relation,symmetrization_of(u))))* -> subclass(image(element_relation,symmetrization_of(u)),v). % 300.04/300.43 207667[0:Rew:44.0,206368.1,27.0,206368.1,44.0,206368.0,27.0,206368.0] || member(not_subclass_element(image(element_relation,successor(u)),v),complement(image(element_relation,successor(u))))* -> subclass(image(element_relation,successor(u)),v). % 300.04/300.43 207921[19:Res:205391.1,7963.1] || equal(complement(complement(intersection(u,v))),ordinal_numbers)** member(ordinal_numbers,union(u,v)) -> member(ordinal_numbers,symmetric_difference(u,v)). % 300.04/300.43 208212[0:SpR:206403.0,148172.0] || -> equal(intersection(intersection(complement(u),power_class(v)),complement(union(u,complement(power_class(v))))),complement(union(u,complement(power_class(v)))))**. % 300.04/300.43 208253[0:SpR:206403.0,206403.0] || -> equal(union(intersection(complement(u),power_class(v)),complement(power_class(w))),complement(intersection(union(u,complement(power_class(v))),power_class(w))))**. % 300.04/300.43 208269[19:SpR:206403.0,168353.1] || -> equal(symmetric_difference(complement(u),power_class(v)),ordinal_numbers) member(regular(symmetric_difference(complement(u),power_class(v))),union(u,complement(power_class(v))))*. % 300.04/300.43 208344[19:SpL:206403.0,186989.0] || subclass(intersection(complement(u),power_class(v)),union(u,complement(power_class(v))))* -> equal(intersection(complement(u),power_class(v)),ordinal_numbers). % 300.04/300.43 208426[19:Rew:206403.0,208350.1] || subclass(union(u,complement(power_class(v))),intersection(complement(u),power_class(v)))* -> equal(union(u,complement(power_class(v))),ordinal_numbers). % 300.04/300.43 208452[19:Res:205414.1,7963.1] || equal(complement(complement(intersection(u,v))),ordinal_numbers)** member(omega,union(u,v)) -> member(omega,symmetric_difference(u,v)). % 300.04/300.43 208519[0:SpR:206410.0,148172.0] || -> equal(intersection(intersection(power_class(u),complement(v)),complement(union(complement(power_class(u)),v))),complement(union(complement(power_class(u)),v)))**. % 300.04/300.43 208560[0:SpR:206410.0,206403.0] || -> equal(union(intersection(power_class(u),complement(v)),complement(power_class(w))),complement(intersection(union(complement(power_class(u)),v),power_class(w))))**. % 300.04/300.43 208572[0:SpR:206410.0,206410.0] || -> equal(union(complement(power_class(u)),intersection(power_class(v),complement(w))),complement(intersection(power_class(u),union(complement(power_class(v)),w))))**. % 300.04/300.43 208576[19:SpR:206410.0,168353.1] || -> equal(symmetric_difference(power_class(u),complement(v)),ordinal_numbers) member(regular(symmetric_difference(power_class(u),complement(v))),union(complement(power_class(u)),v))*. % 300.04/300.43 208584[0:SpR:206403.0,206410.0] || -> equal(union(complement(power_class(u)),intersection(complement(v),power_class(w))),complement(intersection(power_class(u),union(v,complement(power_class(w))))))**. % 300.04/300.43 208654[19:SpL:206410.0,186989.0] || subclass(intersection(power_class(u),complement(v)),union(complement(power_class(u)),v))* -> equal(intersection(power_class(u),complement(v)),ordinal_numbers). % 300.04/300.43 208734[19:Rew:206410.0,208660.1] || subclass(union(complement(power_class(u)),v),intersection(power_class(u),complement(v)))* -> equal(union(complement(power_class(u)),v),ordinal_numbers). % 300.04/300.43 209038[19:Rew:167458.0,209017.1] || member(not_subclass_element(complement(image(element_relation,kind_1_ordinals)),u),complement(complement(image(element_relation,kind_1_ordinals))))* -> subclass(complement(image(element_relation,kind_1_ordinals)),u). % 300.04/300.43 209129[19:Res:176420.1,206404.0] || subclass(domain_relation,rotate(image(element_relation,power_class(u)))) member(ordered_pair(ordered_pair(v,ordinal_numbers),w),power_class(complement(power_class(u))))* -> . % 300.04/300.43 209133[19:Res:176419.1,206404.0] || subclass(domain_relation,flip(image(element_relation,power_class(u)))) member(ordered_pair(ordered_pair(v,w),ordinal_numbers),power_class(complement(power_class(u))))* -> . % 300.04/300.43 209135[0:Res:2526.2,206404.0] || subclass(u,image(element_relation,power_class(v))) member(not_subclass_element(u,w),power_class(complement(power_class(v))))* -> subclass(u,w). % 300.04/300.43 209139[0:Res:2482.2,206404.0] || member(u,universal_class) subclass(universal_class,image(element_relation,power_class(v))) member(sum_class(u),power_class(complement(power_class(v))))* -> . % 300.04/300.43 209140[0:Res:2483.2,206404.0] || member(u,universal_class) subclass(universal_class,image(element_relation,power_class(v))) member(power_class(u),power_class(complement(power_class(v))))* -> . % 300.04/300.43 209150[0:Res:2525.1,206404.0] || subclass(ordered_pair(u,v),image(element_relation,power_class(w))) member(unordered_pair(u,singleton(v)),power_class(complement(power_class(w))))* -> . % 300.04/300.43 209300[0:Rew:209199.0,207550.1] || subclass(power_class(complement(power_class(u))),complement(v))* -> equal(union(v,image(element_relation,power_class(u))),image(element_relation,power_class(u))). % 300.04/300.43 209837[8:MRR:209804.2,36583.1] || member(u,cantor(v)) equal(restrict(v,u,universal_class),rest_of(u))** subclass(rest_relation,complement(rest_of(v)))* -> . % 300.04/300.43 209969[19:Res:11810.3,205934.1] || member(u,universal_class)* member(v,universal_class) equal(compose(w,v),u)* equal(compose_class(w),ordinal_numbers) -> . % 300.04/300.43 210177[0:SpL:27168.2,896.0] || member(u,universal_class) subclass(rest_relation,rest_of(v))* member(w,rest_of(u)) -> member(w,cross_product(u,universal_class))*. % 300.04/300.43 210189[0:Rew:27168.2,210140.2] || member(u,universal_class) subclass(rest_relation,rest_of(v)) -> subclass(rest_of(u),w) member(not_subclass_element(rest_of(u),w),v)*. % 300.04/300.43 210302[19:SpL:27837.0,176243.1] || member(u,universal_class) subclass(domain_relation,symmetric_difference(complement(v),complement(inverse(v))))* -> member(ordered_pair(u,ordinal_numbers),symmetrization_of(v))*. % 300.04/300.43 210315[0:Rew:27837.0,210222.0] || -> subclass(symmetric_difference(complement(u),complement(inverse(u))),v) member(not_subclass_element(symmetric_difference(complement(u),complement(inverse(u))),v),symmetrization_of(u))*. % 300.04/300.43 210567[19:SpR:149012.1,167923.2] || subclass(inverse(u),u)* asymmetric(u,v) equal(compose(ordinal_numbers,ordinal_numbers),ordinal_numbers) -> transitive(inverse(u),v)*. % 300.04/300.43 210837[19:SpL:149012.1,167924.1] || subclass(inverse(u),u)* asymmetric(u,v) transitive(inverse(u),v)* -> equal(compose(ordinal_numbers,ordinal_numbers),ordinal_numbers). % 300.04/300.43 210845[19:Res:176326.2,11848.0] || member(u,universal_class) equal(compose(v,u),ordinal_numbers)** subclass(compose_class(v),w)* well_ordering(universal_class,w) -> . % 300.04/300.43 210896[19:Res:55.1,177022.0] || member(u,universal_class) -> member(sum_class(u),image(universal_class,singleton(sum_class(u))))* asymmetric(cross_product(singleton(sum_class(u)),universal_class),v)*. % 300.04/300.43 210897[19:Res:57.1,177022.0] || member(u,universal_class) -> member(power_class(u),image(universal_class,singleton(power_class(u))))* asymmetric(cross_product(singleton(power_class(u)),universal_class),v)*. % 300.04/300.43 210906[19:Res:149603.1,177022.0] || member(u,universal_class) -> member(rest_of(u),image(universal_class,singleton(rest_of(u))))* asymmetric(cross_product(singleton(rest_of(u)),universal_class),v)*. % 300.04/300.43 211187[23:SpR:183885.0,15119.2] || member(image(u,ordinal_numbers),universal_class) subclass(universal_class,symmetric_difference(v,w)) -> member(apply(u,universal_class),union(v,w))*. % 300.04/300.43 211646[19:Res:203424.1,4165.0] || subclass(complement(ordered_pair(u,v)),ordinal_numbers)* -> equal(singleton(w),unordered_pair(u,singleton(v)))* equal(singleton(w),singleton(u)). % 300.04/300.43 211698[0:SpL:160.0,27146.1] || member(u,universal_class) subclass(rest_relation,symmetric_difference(v,w)) -> member(ordered_pair(u,rest_of(u)),complement(intersection(v,w)))*. % 300.04/300.43 212980[25:SoR:212978.0,12322.2] 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))** -> . % 300.04/300.43 213063[23:Rew:183883.0,213049.2] || -> equal(not_subclass_element(ordered_pair(u,universal_class),omega),singleton(u))** equal(integer_of(unordered_pair(u,ordinal_numbers)),ordinal_numbers) subclass(ordered_pair(u,universal_class),omega). % 300.04/300.43 213351[19:SpL:209197.0,82316.0] || subclass(universal_class,intersection(image(element_relation,singleton(ordinal_numbers)),complement(u)))* member(omega,union(power_class(complement(singleton(ordinal_numbers))),u)) -> . % 300.04/300.43 213429[19:SpL:209197.0,82316.0] || subclass(universal_class,intersection(complement(u),image(element_relation,singleton(ordinal_numbers))))* member(omega,union(u,power_class(complement(singleton(ordinal_numbers))))) -> . % 300.04/300.43 213431[19:SpL:209197.0,488.0] || member(u,intersection(image(element_relation,singleton(ordinal_numbers)),complement(v)))* member(u,union(power_class(complement(singleton(ordinal_numbers))),v)) -> . % 300.04/300.43 213440[19:SpL:209197.0,488.0] || member(u,intersection(complement(v),image(element_relation,singleton(ordinal_numbers))))* member(u,union(v,power_class(complement(singleton(ordinal_numbers))))) -> . % 300.04/300.43 213592[19:SpL:209198.0,82316.0] || subclass(universal_class,intersection(image(element_relation,symmetrization_of(ordinal_numbers)),complement(u)))* member(omega,union(power_class(complement(inverse(ordinal_numbers))),u)) -> . % 300.04/300.43 213670[19:SpL:209198.0,82316.0] || subclass(universal_class,intersection(complement(u),image(element_relation,symmetrization_of(ordinal_numbers))))* member(omega,union(u,power_class(complement(inverse(ordinal_numbers))))) -> . % 300.04/300.43 213672[19:SpL:209198.0,488.0] || member(u,intersection(image(element_relation,symmetrization_of(ordinal_numbers)),complement(v)))* member(u,union(power_class(complement(inverse(ordinal_numbers))),v)) -> . % 300.04/300.43 213681[19:SpL:209198.0,488.0] || member(u,intersection(complement(v),image(element_relation,symmetrization_of(ordinal_numbers))))* member(u,union(v,power_class(complement(inverse(ordinal_numbers))))) -> . % 300.04/300.43 214589[19:Res:176345.1,207852.0] || subclass(domain_relation,intersection(power_class(u),complement(v))) member(singleton(singleton(singleton(ordinal_numbers))),union(complement(power_class(u)),v))* -> . % 300.04/300.43 214590[19:Res:182463.1,207852.0] || equal(intersection(power_class(u),complement(v)),singleton(singleton(ordinal_numbers))) member(singleton(ordinal_numbers),union(complement(power_class(u)),v))* -> . % 300.04/300.43 214624[20:Res:181635.1,207852.0] || subclass(symmetrization_of(ordinal_numbers),intersection(power_class(u),complement(v))) member(regular(symmetrization_of(ordinal_numbers)),union(complement(power_class(u)),v))* -> . % 300.04/300.43 214625[20:Res:175570.1,207852.0] || subclass(inverse(ordinal_numbers),intersection(power_class(u),complement(v))) member(regular(symmetrization_of(ordinal_numbers)),union(complement(power_class(u)),v))* -> . % 300.04/300.43 214680[19:Res:214502.0,126.0] || subclass(successor(singleton(ordinal_numbers)),u)* well_ordering(v,u)* -> member(least(v,successor(singleton(ordinal_numbers))),successor(singleton(ordinal_numbers)))*. % 300.04/300.43 214692[19:Res:214503.0,126.0] || subclass(symmetrization_of(singleton(ordinal_numbers)),u)* well_ordering(v,u)* -> member(least(v,symmetrization_of(singleton(ordinal_numbers))),symmetrization_of(singleton(ordinal_numbers)))*. % 300.04/300.43 214752[19:Res:176345.1,207871.0] || subclass(domain_relation,intersection(complement(u),power_class(v))) member(singleton(singleton(singleton(ordinal_numbers))),union(u,complement(power_class(v))))* -> . % 300.04/300.43 214753[19:Res:182463.1,207871.0] || equal(intersection(complement(u),power_class(v)),singleton(singleton(ordinal_numbers))) member(singleton(ordinal_numbers),union(u,complement(power_class(v))))* -> . % 300.04/300.43 214787[20:Res:181635.1,207871.0] || subclass(symmetrization_of(ordinal_numbers),intersection(complement(u),power_class(v))) member(regular(symmetrization_of(ordinal_numbers)),union(u,complement(power_class(v))))* -> . % 300.04/300.43 214788[20:Res:175570.1,207871.0] || subclass(inverse(ordinal_numbers),intersection(complement(u),power_class(v))) member(regular(symmetrization_of(ordinal_numbers)),union(u,complement(power_class(v))))* -> . % 300.04/300.43 214865[19:Res:205991.1,27258.2] || equal(complement(union(u,v)),ordinal_numbers)** member(singleton(w),complement(v))* member(singleton(w),complement(u))* -> . % 300.10/300.43 214866[19:Res:203424.1,27258.2] || subclass(complement(union(u,v)),ordinal_numbers)* member(singleton(w),complement(v))* member(singleton(w),complement(u))* -> . % 300.10/300.43 214952[0:Rew:206407.0,214852.1,206407.0,214852.0] || member(u,power_class(v)) member(u,power_class(w)) member(u,complement(intersection(power_class(w),power_class(v))))* -> . % 300.10/300.43 214984[8:SpR:160282.0,2525.1] || subclass(ordered_pair(u,v),w) -> equal(regular(ordered_pair(u,v)),singleton(u)) member(regular(ordered_pair(u,v)),w)*. % 300.10/300.43 215048[8:SpL:160282.0,6432.1] || subclass(universal_class,complement(u)) member(regular(ordered_pair(v,w)),u)* -> equal(regular(ordered_pair(v,w)),singleton(v)). % 300.10/300.43 215071[19:MRR:215070.2,215013.0] || equal(singleton(u),v) -> equal(regular(ordered_pair(v,u)),singleton(v)) equal(regular(regular(ordered_pair(v,u))),v)**. % 300.10/300.43 215131[19:Res:168245.3,897.0] || well_ordering(u,universal_class) subclass(v,restrict(w,x,y))* -> equal(v,ordinal_numbers) member(least(u,v),w)*. % 300.10/300.43 215134[19:Res:168245.3,110865.0] || well_ordering(u,universal_class) subclass(v,rest_of(least(u,v)))* subclass(universal_class,complement(element_relation)) -> equal(v,ordinal_numbers). % 300.10/300.43 215135[19:Res:168245.3,158.0] || well_ordering(u,universal_class) subclass(v,omega) -> equal(v,ordinal_numbers) equal(integer_of(least(u,v)),least(u,v))**. % 300.10/300.43 215281[19:Res:12015.1,168249.0] || equal(complement(complement(regular(u))),universal_class)** member(singleton(v),u)* well_ordering(w,x)* -> equal(u,ordinal_numbers). % 300.10/300.43 215295[19:Res:176345.1,168249.0] || subclass(domain_relation,regular(u)) member(singleton(singleton(singleton(ordinal_numbers))),u)* well_ordering(v,w)* -> equal(u,ordinal_numbers). % 300.10/300.43 215298[19:Res:182463.1,168249.0] || equal(regular(u),singleton(singleton(ordinal_numbers))) member(singleton(ordinal_numbers),u)* well_ordering(v,w)* -> equal(u,ordinal_numbers). % 300.10/300.43 215334[20:Res:181635.1,168249.0] || subclass(symmetrization_of(ordinal_numbers),regular(u)) member(regular(symmetrization_of(ordinal_numbers)),u)* well_ordering(v,w)* -> equal(u,ordinal_numbers). % 300.10/300.43 215335[20:Res:175570.1,168249.0] || subclass(inverse(ordinal_numbers),regular(u)) member(regular(symmetrization_of(ordinal_numbers)),u)* well_ordering(v,w)* -> equal(u,ordinal_numbers). % 300.10/300.43 215350[19:Con:215310.2] || well_ordering(u,regular(v)) member(least(u,regular(v)),v)* -> equal(regular(v),ordinal_numbers) equal(v,ordinal_numbers). % 300.10/300.43 215352[19:Con:215299.3] inductive(regular(u)) || well_ordering(v,regular(u)) member(least(v,regular(u)),u)* -> equal(u,ordinal_numbers). % 300.10/300.43 215522[19:Res:168520.2,25.1] || well_ordering(u,universal_class) member(least(u,intersection(complement(v),w)),v)* -> equal(intersection(complement(v),w),ordinal_numbers). % 300.10/300.43 215558[19:Res:168520.2,169207.0] || well_ordering(u,universal_class) -> equal(intersection(symmetrization_of(ordinal_numbers),v),ordinal_numbers) member(least(u,intersection(symmetrization_of(ordinal_numbers),v)),inverse(ordinal_numbers))*. % 300.10/300.43 215597[19:Rew:160.0,215459.1] || well_ordering(u,universal_class) -> equal(symmetric_difference(v,w),ordinal_numbers) member(least(u,symmetric_difference(v,w)),complement(intersection(v,w)))*. % 300.10/300.43 215723[19:Res:168521.2,25.1] || well_ordering(u,universal_class) member(least(u,intersection(v,complement(w))),w)* -> equal(intersection(v,complement(w)),ordinal_numbers). % 300.10/300.43 215759[19:Res:168521.2,169207.0] || well_ordering(u,universal_class) -> equal(intersection(v,symmetrization_of(ordinal_numbers)),ordinal_numbers) member(least(u,intersection(v,symmetrization_of(ordinal_numbers))),inverse(ordinal_numbers))*. % 300.10/300.43 216011[0:SpL:29.0,16107.1] || member(u,symmetric_difference(v,cross_product(w,x)))* subclass(complement(restrict(v,w,x)),y)* -> member(u,y)*. % 300.10/300.43 216016[0:SpL:30.0,16107.1] || member(u,symmetric_difference(cross_product(v,w),x))* subclass(complement(restrict(x,v,w)),y)* -> member(u,y)*. % 300.10/300.43 216149[19:Rew:206005.1,216061.1] || equal(intersection(u,v),ordinal_numbers) member(w,union(u,v))* subclass(universal_class,x) -> member(w,x)*. % 300.10/300.43 216063[0:SpL:206403.0,16107.1] || member(u,symmetric_difference(complement(v),power_class(w)))* subclass(union(v,complement(power_class(w))),x)* -> member(u,x)*. % 300.10/300.43 216064[0:SpL:206410.0,16107.1] || member(u,symmetric_difference(power_class(v),complement(w)))* subclass(union(complement(power_class(v)),w),x)* -> member(u,x)*. % 300.10/300.43 216793[19:Res:38094.1,182393.0] || member(singleton(ordinal_numbers),union(u,v)) well_ordering(universal_class,intersection(u,v)) -> member(singleton(ordinal_numbers),symmetric_difference(u,v))*. % 300.10/300.43 216971[23:Rew:183856.0,216953.2] || member(ordinal_numbers,u) -> equal(not_subclass_element(ordered_pair(universal_class,v),u),unordered_pair(universal_class,singleton(v)))** subclass(ordered_pair(universal_class,v),u). % 300.10/300.43 216981[0:Obv:216939.2] || member(u,v) subclass(unordered_pair(u,w),omega)* -> subclass(unordered_pair(u,w),v)* equal(integer_of(w),w). % 300.10/300.43 217088[0:Rew:40458.2,217087.2] || equal(u,v) member(v,w) member(v,x) -> subclass(unordered_pair(v,u),intersection(x,w))*. % 300.10/300.43 217214[23:Rew:183883.0,217193.2] || member(unordered_pair(u,ordinal_numbers),v) -> equal(not_subclass_element(ordered_pair(u,universal_class),v),singleton(u))** subclass(ordered_pair(u,universal_class),v). % 300.10/300.43 217221[0:Obv:217178.2] || member(u,v) subclass(unordered_pair(w,u),omega)* -> subclass(unordered_pair(w,u),v)* equal(integer_of(w),w). % 300.10/300.43 217364[0:Res:16231.2,897.0] || subclass(u,restrict(v,w,x))* -> subclass(intersection(u,y),z) member(not_subclass_element(intersection(u,y),z),v)*. % 300.10/300.43 217367[0:Res:16231.2,110865.0] || subclass(u,rest_of(not_subclass_element(intersection(u,v),w)))* subclass(universal_class,complement(element_relation)) -> subclass(intersection(u,v),w). % 300.10/300.43 217614[0:Res:16235.1,25.1] || member(not_subclass_element(intersection(intersection(u,complement(v)),w),x),v)* -> subclass(intersection(intersection(u,complement(v)),w),x). % 300.10/300.43 217650[19:Res:16235.1,169207.0] || -> subclass(intersection(intersection(u,symmetrization_of(ordinal_numbers)),v),w) member(not_subclass_element(intersection(intersection(u,symmetrization_of(ordinal_numbers)),v),w),inverse(ordinal_numbers))*. % 300.10/300.43 218027[19:Res:217853.0,167728.0] || subclass(u,v) -> equal(complement(complement(intersection(w,u))),ordinal_numbers) member(regular(complement(complement(intersection(w,u)))),v)*. % 300.10/300.43 218035[19:Res:217853.0,167737.0] || -> equal(complement(complement(intersection(u,intersection(v,w)))),ordinal_numbers) member(regular(complement(complement(intersection(u,intersection(v,w))))),w)*. % 300.10/300.43 218036[19:Res:217853.0,167736.0] || -> equal(complement(complement(intersection(u,intersection(v,w)))),ordinal_numbers) member(regular(complement(complement(intersection(u,intersection(v,w))))),v)*. % 300.10/300.43 218211[0:Res:16234.1,25.1] || member(not_subclass_element(intersection(intersection(complement(u),v),w),x),u)* -> subclass(intersection(intersection(complement(u),v),w),x). % 300.10/300.43 218247[19:Res:16234.1,169207.0] || -> subclass(intersection(intersection(symmetrization_of(ordinal_numbers),u),v),w) member(not_subclass_element(intersection(intersection(symmetrization_of(ordinal_numbers),u),v),w),inverse(ordinal_numbers))*. % 300.10/300.43 218362[0:Rew:160.0,218127.0] || -> subclass(intersection(symmetric_difference(u,v),w),x) member(not_subclass_element(intersection(symmetric_difference(u,v),w),x),complement(intersection(u,v)))*. % 300.10/300.43 218417[19:Res:218022.0,167276.0] || well_ordering(u,complement(v)) -> equal(segment(u,complement(union(w,v)),least(u,complement(union(w,v)))),ordinal_numbers)**. % 300.10/300.43 218601[0:Res:16358.2,897.0] || subclass(u,restrict(v,w,x))* -> subclass(intersection(y,u),z) member(not_subclass_element(intersection(y,u),z),v)*. % 300.10/300.43 218604[0:Res:16358.2,110865.0] || subclass(u,rest_of(not_subclass_element(intersection(v,u),w)))* subclass(universal_class,complement(element_relation)) -> subclass(intersection(v,u),w). % 300.10/300.43 219096[19:Res:218952.0,167276.0] || well_ordering(u,inverse(ordinal_numbers)) -> equal(segment(u,intersection(symmetrization_of(ordinal_numbers),v),least(u,intersection(symmetrization_of(ordinal_numbers),v))),ordinal_numbers)**. % 300.10/300.43 219198[0:Res:16362.1,25.1] || member(not_subclass_element(intersection(u,intersection(v,complement(w))),x),w)* -> subclass(intersection(u,intersection(v,complement(w))),x). % 300.10/300.43 219234[19:Res:16362.1,169207.0] || -> subclass(intersection(u,intersection(v,symmetrization_of(ordinal_numbers))),w) member(not_subclass_element(intersection(u,intersection(v,symmetrization_of(ordinal_numbers))),w),inverse(ordinal_numbers))*. % 300.10/300.43 219369[19:Res:219080.0,167276.0] || well_ordering(u,inverse(ordinal_numbers)) -> equal(segment(u,complement(complement(symmetrization_of(ordinal_numbers))),least(u,complement(complement(symmetrization_of(ordinal_numbers))))),ordinal_numbers)**. % 300.10/300.43 219399[19:Res:219077.0,167276.0] || well_ordering(u,inverse(ordinal_numbers)) -> equal(segment(u,intersection(v,symmetrization_of(ordinal_numbers)),least(u,intersection(v,symmetrization_of(ordinal_numbers)))),ordinal_numbers)**. % 300.10/300.43 219501[0:Res:16361.1,25.1] || member(not_subclass_element(intersection(u,intersection(complement(v),w)),x),v)* -> subclass(intersection(u,intersection(complement(v),w)),x). % 300.10/300.43 219537[19:Res:16361.1,169207.0] || -> subclass(intersection(u,intersection(symmetrization_of(ordinal_numbers),v)),w) member(not_subclass_element(intersection(u,intersection(symmetrization_of(ordinal_numbers),v)),w),inverse(ordinal_numbers))*. % 300.10/300.43 219654[0:Rew:160.0,219415.0] || -> subclass(intersection(u,symmetric_difference(v,w)),x) member(not_subclass_element(intersection(u,symmetric_difference(v,w)),x),complement(intersection(v,w)))*. % 300.10/300.43 219714[19:Res:218920.0,167728.0] || subclass(u,v) -> equal(intersection(complement(complement(u)),w),ordinal_numbers) member(regular(intersection(complement(complement(u)),w)),v)*. % 300.10/300.43 219722[19:Res:218920.0,167737.0] || -> equal(intersection(complement(complement(intersection(u,v))),w),ordinal_numbers) member(regular(intersection(complement(complement(intersection(u,v))),w)),v)*. % 300.10/300.43 219723[19:Res:218920.0,167736.0] || -> equal(intersection(complement(complement(intersection(u,v))),w),ordinal_numbers) member(regular(intersection(complement(complement(intersection(u,v))),w)),u)*. % 300.10/300.43 219964[19:Res:219703.0,167728.0] || subclass(u,v) -> equal(complement(complement(complement(complement(u)))),ordinal_numbers) member(regular(complement(complement(complement(complement(u))))),v)*. % 300.10/300.43 219972[19:Res:219703.0,167737.0] || -> equal(complement(complement(complement(complement(intersection(u,v))))),ordinal_numbers) member(regular(complement(complement(complement(complement(intersection(u,v)))))),v)*. % 300.10/300.43 219973[19:Res:219703.0,167736.0] || -> equal(complement(complement(complement(complement(intersection(u,v))))),ordinal_numbers) member(regular(complement(complement(complement(complement(intersection(u,v)))))),u)*. % 300.10/300.43 220045[19:Res:167355.1,16462.0] || equal(sum_class(u),ordinal_numbers) subclass(u,v) -> subclass(sum_class(u),w) member(not_subclass_element(sum_class(u),w),v)*. % 300.10/300.43 220046[0:Res:9820.1,16462.0] || equal(sum_class(u),u) subclass(u,v) -> subclass(sum_class(u),w) member(not_subclass_element(sum_class(u),w),v)*. % 300.10/300.43 220091[19:Res:218952.0,16462.0] || subclass(inverse(ordinal_numbers),u) -> subclass(intersection(symmetrization_of(ordinal_numbers),v),w) member(not_subclass_element(intersection(symmetrization_of(ordinal_numbers),v),w),u)*. % 300.10/300.43 220092[19:Res:219077.0,16462.0] || subclass(inverse(ordinal_numbers),u) -> subclass(intersection(v,symmetrization_of(ordinal_numbers)),w) member(not_subclass_element(intersection(v,symmetrization_of(ordinal_numbers)),w),u)*. % 300.10/300.43 220094[0:Res:49.1,16462.0] inductive(u) || subclass(u,v) -> subclass(image(successor_relation,u),w) member(not_subclass_element(image(successor_relation,u),w),v)*. % 300.10/300.43 220099[19:Res:219080.0,16462.0] || subclass(inverse(ordinal_numbers),u) -> subclass(complement(complement(symmetrization_of(ordinal_numbers))),v) member(not_subclass_element(complement(complement(symmetrization_of(ordinal_numbers))),v),u)*. % 300.10/300.43 220104[0:Res:218022.0,16462.0] || subclass(complement(u),v) -> subclass(complement(union(w,u)),x) member(not_subclass_element(complement(union(w,u)),x),v)*. % 300.10/300.43 220200[19:Res:218971.0,167728.0] || subclass(u,v) -> equal(complement(complement(intersection(u,w))),ordinal_numbers) member(regular(complement(complement(intersection(u,w)))),v)*. % 300.10/300.43 220208[19:Res:218971.0,167737.0] || -> equal(complement(complement(intersection(intersection(u,v),w))),ordinal_numbers) member(regular(complement(complement(intersection(intersection(u,v),w)))),v)*. % 300.10/300.43 220209[19:Res:218971.0,167736.0] || -> equal(complement(complement(intersection(intersection(u,v),w))),ordinal_numbers) member(regular(complement(complement(intersection(intersection(u,v),w)))),u)*. % 300.10/300.43 220342[19:Res:219700.0,167728.0] || subclass(u,v) -> equal(intersection(w,complement(complement(u))),ordinal_numbers) member(regular(intersection(w,complement(complement(u)))),v)*. % 300.10/300.43 220350[19:Res:219700.0,167737.0] || -> equal(intersection(u,complement(complement(intersection(v,w)))),ordinal_numbers) member(regular(intersection(u,complement(complement(intersection(v,w))))),w)*. % 300.10/300.43 220351[19:Res:219700.0,167736.0] || -> equal(intersection(u,complement(complement(intersection(v,w)))),ordinal_numbers) member(regular(intersection(u,complement(complement(intersection(v,w))))),v)*. % 300.10/300.43 220446[0:Res:220194.0,16462.0] || subclaCputime limit exceeded (core dumped) %------------------------------------------------------------------------------