%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : NUM275-1 : 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 14:25:04 EDT 2022

% Result   : Timeout 299.99s 300.63s
% Output   : None 
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : NUM275-1 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.04/0.13  % Command  : run_spass %d %s
% 0.14/0.35  % Computer : n007.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 600
% 0.14/0.35  % DateTime : Tue Jul  5 22:37:13 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 299.99/300.63  
% 299.99/300.63  SPASS V 3.9 
% 299.99/300.63  SPASS beiseite: Ran out of time.
% 299.99/300.63  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 299.99/300.63  SPASS derived 187815 clauses, backtracked 25932 clauses, performed 75 splits and kept 76116 clauses.
% 299.99/300.63  SPASS allocated 229547 KBytes.
% 299.99/300.63  SPASS spent	0:05:00.28 on the problem.
% 299.99/300.63  		0:00:00.04 for the input.
% 299.99/300.63  		0:00:00.00 for the FLOTTER CNF translation.
% 299.99/300.63  		0:00:03.25 for inferences.
% 299.99/300.63  		0:0:14.79 for the backtracking.
% 299.99/300.63  		0:4:37.83 for the reduction.
% 299.99/300.63  
% 299.99/300.63  
% 299.99/300.63   The set of clauses at termination is :
% 299.99/300.63  17396[7:Res:13248.1,26.0] ||  -> equal(intersection(intersection(u,v),w),identity_relation) member(regular(intersection(intersection(u,v),w)),v)*.
% 299.99/300.63  239340[7:Obv:239320.0] ||  -> equal(intersection(intersection(u,v),complement(u)),identity_relation)**.
% 299.99/300.63  239452[8:SpR:155147.0,239339.0] ||  -> equal(intersection(intersection(u,subset_relation),inverse(subset_relation)),identity_relation)**.
% 299.99/300.63  239454[8:SpR:147905.0,239339.0] ||  -> equal(intersection(complement(complement(subset_relation)),inverse(subset_relation)),identity_relation)**.
% 299.99/300.63  239339[8:Obv:239319.0] ||  -> equal(intersection(intersection(subset_relation,u),inverse(subset_relation)),identity_relation)**.
% 299.99/300.63  17397[7:Res:13248.1,25.0] ||  -> equal(intersection(intersection(u,v),w),identity_relation) member(regular(intersection(intersection(u,v),w)),u)*.
% 299.99/300.63  237452[16:SpR:195239.0,237181.0] ||  -> equal(intersection(singleton(identity_relation),intersection(u,complement(singleton(identity_relation)))),identity_relation)**.
% 299.99/300.63  237395[7:SpR:33.0,237181.0] ||  -> equal(intersection(complement(u),restrict(u,v,w)),identity_relation)**.
% 299.99/300.63  238388[8:SpR:162584.0,238174.0] ||  -> equal(intersection(symmetrization_of(identity_relation),symmetric_difference(ordinal_numbers,inverse(identity_relation))),identity_relation)**.
% 299.99/300.63  238387[16:SpR:195239.0,238174.0] ||  -> equal(intersection(singleton(identity_relation),symmetric_difference(ordinal_numbers,singleton(identity_relation))),identity_relation)**.
% 299.99/300.63  13572[7:Rew:13036.0,13012.1] || subclass(u,v) -> equal(intersection(w,u),identity_relation) member(regular(intersection(w,u)),v)*.
% 299.99/300.63  238174[8:SpR:155582.0,237830.0] ||  -> equal(intersection(complement(complement(u)),symmetric_difference(ordinal_numbers,u)),identity_relation)**.
% 299.99/300.63  237830[7:Obv:237807.0] ||  -> equal(intersection(complement(u),intersection(u,v)),identity_relation)**.
% 299.99/300.63  237931[8:SpR:147905.0,237831.0] ||  -> equal(intersection(inverse(subset_relation),complement(complement(subset_relation))),identity_relation)**.
% 299.99/300.63  237831[8:Obv:237808.0] ||  -> equal(intersection(inverse(subset_relation),intersection(subset_relation,u)),identity_relation)**.
% 299.99/300.63  13573[7:Rew:13036.0,13015.0] ||  -> equal(intersection(u,intersection(v,w)),identity_relation) member(regular(intersection(u,intersection(v,w))),v)*.
% 299.99/300.63  237269[8:SpR:33.0,237182.0] ||  -> equal(intersection(inverse(subset_relation),restrict(subset_relation,u,v)),identity_relation)**.
% 299.99/300.63  237181[7:Obv:237156.0] ||  -> equal(intersection(complement(u),intersection(v,u)),identity_relation)**.
% 299.99/300.63  237182[8:Obv:237157.0] ||  -> equal(intersection(inverse(subset_relation),intersection(u,subset_relation)),identity_relation)**.
% 299.99/300.63  236994[26:Res:225888.1,194308.0] || equal(symmetric_difference(ordinal_numbers,inverse(identity_relation)),omega)** -> .
% 299.99/300.63  13574[7:Rew:13036.0,13014.0] ||  -> equal(intersection(u,intersection(v,w)),identity_relation) member(regular(intersection(u,intersection(v,w))),w)*.
% 299.99/300.63  236993[26:Res:225888.1,165946.0] || equal(symmetric_difference(ordinal_numbers,singleton(identity_relation)),omega)** -> .
% 299.99/300.63  225888[26:Res:225794.1,143186.0] || equal(symmetric_difference(ordinal_numbers,u),omega) -> member(identity_relation,complement(u))*.
% 299.99/300.63  225887[26:Res:225794.1,143226.0] || equal(symmetric_difference(ordinal_numbers,u),omega)** member(identity_relation,u) -> .
% 299.99/300.63  225639[26:Res:225386.1,217144.1] || equal(power_class(u),omega)** equal(power_class(u),identity_relation) -> .
% 299.99/300.63  17392[7:Res:13248.1,5.0] || subclass(u,v) -> equal(intersection(u,w),identity_relation) member(regular(intersection(u,w)),v)*.
% 299.99/300.63  225452[18:MRR:225441.2,190496.0] || subclass(ordinal_numbers,u) subclass(symmetrization_of(identity_relation),complement(u))* -> .
% 299.99/300.63  225450[16:MRR:225398.2,165227.0] || subclass(singleton(identity_relation),complement(u))* member(identity_relation,u) -> .
% 299.99/300.63  225365[26:Res:165168.1,225263.1] || equal(u,singleton(identity_relation)) equal(complement(u),omega)** -> .
% 299.99/300.63  225364[26:Res:190442.1,225263.1] || equal(u,symmetrization_of(identity_relation))*+ equal(complement(u),omega)** -> .
% 299.99/300.63  66828[0:Res:2503.2,161.0] || subclass(u,omega) -> subclass(u,v) equal(integer_of(not_subclass_element(u,v)),not_subclass_element(u,v))**.
% 299.99/300.63  225363[26:Res:190593.1,225263.1] || equal(u,inverse(identity_relation)) equal(complement(u),omega)** -> .
% 299.99/300.63  225241[26:SpL:72.0,225144.0] || equal(apply(u,v),omega)** subclass(element_relation,identity_relation) -> .
% 299.99/300.63  225140[26:SpL:72.0,224803.0] || subclass(omega,apply(u,v))* subclass(element_relation,identity_relation) -> .
% 299.99/300.63  236590[26:MRR:236586.1,216561.0] || equal(complement(complement(singleton(omega))),singleton(identity_relation))** -> .
% 299.99/300.63  36857[5:Res:10.1,8825.1] || equal(u,complement(v))*+ member(w,ordinal_numbers)* -> member(w,v)* member(w,u)*.
% 299.99/300.63  224802[26:Res:224684.1,165357.1] || subclass(omega,u)* equal(complement(u),singleton(identity_relation)) -> .
% 299.99/300.63  236572[26:MRR:236568.1,216561.0] || equal(complement(complement(singleton(omega))),symmetrization_of(identity_relation))** -> .
% 299.99/300.63  224801[26:Res:224684.1,190532.1] || subclass(omega,u)* equal(complement(u),symmetrization_of(identity_relation)) -> .
% 299.99/300.63  236398[26:MRR:236394.1,216561.0] || equal(complement(complement(singleton(omega))),inverse(identity_relation))** -> .
% 299.99/300.63  19016[0:Res:313.1,28.1] || member(not_subclass_element(intersection(complement(u),v),w),u)* -> subclass(intersection(complement(u),v),w).
% 299.99/300.63  224800[26:Res:224684.1,190641.1] || subclass(omega,u)* equal(complement(u),inverse(identity_relation)) -> .
% 299.99/300.63  224756[26:Res:224684.1,143186.0] || subclass(omega,symmetric_difference(ordinal_numbers,u))* -> member(identity_relation,complement(u)).
% 299.99/300.63  224755[26:Res:224684.1,143226.0] || subclass(omega,symmetric_difference(ordinal_numbers,u))* member(identity_relation,u) -> .
% 299.99/300.63  235179[8:Res:8645.1,234983.0] || subclass(ordinal_numbers,cantor(complement(cross_product(singleton(singleton(u)),ordinal_numbers))))* -> .
% 299.99/300.63  18897[0:Res:303.1,28.1] || member(not_subclass_element(intersection(u,complement(v)),w),v)* -> subclass(intersection(u,complement(v)),w).
% 299.99/300.63  235177[8:Res:143198.1,234983.0] || equal(cantor(complement(cross_product(singleton(singleton(u)),ordinal_numbers))),ordinal_numbers)** -> .
% 299.99/300.63  234639[8:SpL:963.0,234117.0] || subclass(ordinal_numbers,complement(complement(singleton(singleton(singleton(singleton(u)))))))* -> .
% 299.99/300.63  234409[8:Res:210572.1,234119.0] || equal(complement(complement(singleton(singleton(singleton(singleton(u)))))),ordinal_numbers)** -> .
% 299.99/300.63  233751[25:Res:233380.0,165357.1] || equal(complement(complement(singleton(ordered_pair(ordinal_numbers,u)))),singleton(identity_relation))** -> .
% 299.99/300.63  19680[0:Rew:3597.0,19654.0] ||  -> subclass(symmetric_difference(u,inverse(u)),v) member(not_subclass_element(symmetric_difference(u,inverse(u)),v),symmetrization_of(u))*.
% 299.99/300.63  233750[25:Res:233380.0,190532.1] || equal(complement(complement(singleton(ordered_pair(ordinal_numbers,u)))),symmetrization_of(identity_relation))** -> .
% 299.99/300.63  233749[25:Res:233380.0,190641.1] || equal(complement(complement(singleton(ordered_pair(ordinal_numbers,u)))),inverse(identity_relation))** -> .
% 299.99/300.63  236122[8:Res:10.1,236074.1] || equal(flip(subset_relation),rest_relation) equal(inverse(subset_relation),rest_relation)** -> .
% 299.99/300.63  236074[8:Res:10.1,235469.1] || equal(inverse(subset_relation),rest_relation) subclass(rest_relation,flip(subset_relation))* -> .
% 299.99/300.63  19564[0:Rew:3596.0,19536.0] ||  -> subclass(symmetric_difference(u,singleton(u)),v) member(not_subclass_element(symmetric_difference(u,singleton(u)),v),successor(u))*.
% 299.99/300.63  235602[21:Res:28979.1,196905.1] || subclass(rest_relation,rotate(subset_relation))* subclass(domain_relation,inverse(subset_relation)) -> .
% 299.99/300.63  235469[8:Res:28980.1,28976.1] || subclass(rest_relation,flip(subset_relation)) subclass(rest_relation,inverse(subset_relation))* -> .
% 299.99/300.63  235336[18:Res:231883.1,13588.0] || equal(symmetrization_of(identity_relation),ordinal_numbers) -> equal(regular(symmetrization_of(identity_relation)),identity_relation)**.
% 299.99/300.63  235333[18:Res:231883.1,216271.1] inductive(regular(symmetrization_of(identity_relation))) || equal(symmetrization_of(identity_relation),ordinal_numbers)** -> .
% 299.99/300.63  18546[5:Res:8977.2,898.0] || member(u,ordinal_numbers) subclass(ordinal_numbers,restrict(v,w,x))*+ -> member(power_class(u),v)*.
% 299.99/300.63  235201[14:Res:165168.1,234983.0] || equal(cantor(complement(cross_product(singleton(identity_relation),ordinal_numbers))),singleton(identity_relation))** -> .
% 299.99/300.63  235200[18:Res:190442.1,234983.0] || equal(cantor(complement(cross_product(singleton(identity_relation),ordinal_numbers))),symmetrization_of(identity_relation))** -> .
% 299.99/300.63  235199[18:Res:190593.1,234983.0] || equal(cantor(complement(cross_product(singleton(identity_relation),ordinal_numbers))),inverse(identity_relation))** -> .
% 299.99/300.63  235197[8:Res:216591.1,234983.0] || equal(complement(cantor(complement(cross_product(singleton(identity_relation),ordinal_numbers)))),identity_relation)** -> .
% 299.99/300.63  39308[0:SoR:8530.0,76.1] one_to_one(u) || subclass(range_of(inverse(u)),v) -> maps(inverse(u),range_of(u),v)*.
% 299.99/300.63  235162[15:Res:165526.1,234983.0] || subclass(ordinal_numbers,cantor(complement(cross_product(singleton(range_of(identity_relation)),ordinal_numbers))))* -> .
% 299.99/300.63  235160[15:Res:209921.1,234983.0] || equal(cantor(complement(cross_product(singleton(range_of(identity_relation)),ordinal_numbers))),ordinal_numbers)** -> .
% 299.99/300.63  235153[8:Res:216611.1,234983.0] || equal(complement(cantor(complement(cross_product(singleton(omega),ordinal_numbers)))),identity_relation)** -> .
% 299.99/300.63  235012[25:SpR:234956.0,208885.0] ||  -> equal(apply(complement(cross_product(identity_relation,ordinal_numbers)),ordinal_numbers),sum_class(range_of(identity_relation)))**.
% 299.99/300.63  69478[7:Res:13125.2,3617.0] || subclass(omega,symmetric_difference(u,v)) -> equal(integer_of(w),identity_relation) member(w,union(u,v))*.
% 299.99/300.63  234288[22:Res:216691.1,233893.0] || equal(complement(complement(complement(singleton(singleton(singleton(identity_relation)))))),identity_relation)** -> .
% 299.99/300.63  235856[8:Res:10.1,235561.0] || equal(rotate(u),rest_relation)** equal(identity_relation,u) -> .
% 299.99/300.63  235840[8:Res:10.1,235560.0] || equal(rotate(u),rest_relation) subclass(u,identity_relation)* -> .
% 299.99/300.63  235561[8:Res:28979.1,217144.1] || subclass(rest_relation,rotate(u))* equal(identity_relation,u) -> .
% 299.99/300.63  13339[7:Rew:13036.0,10911.2] || subclass(omega,u)*+ subclass(u,v)* -> equal(integer_of(w),identity_relation) member(w,v)*.
% 299.99/300.63  235560[8:Res:28979.1,219073.1] || subclass(rest_relation,rotate(u))* subclass(u,identity_relation) -> .
% 299.99/300.63  235484[8:Res:10.1,235433.0] || equal(flip(u),rest_relation)** equal(identity_relation,u) -> .
% 299.99/300.63  235481[8:Res:10.1,235432.0] || equal(flip(u),rest_relation) subclass(u,identity_relation)* -> .
% 299.99/300.63  235729[21:Res:10.1,235605.0] || equal(rotate(domain_relation),rest_relation)**+ -> equal(identity_relation,u)*.
% 299.99/300.63  19113[5:Res:2503.2,8788.0] || subclass(u,recursion_equation_functions(v))*+ -> subclass(u,w) subclass(not_subclass_element(u,w),cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.63  235756[25:Res:235617.1,208963.0] || equal(rotate(subset_relation),rest_relation)** -> .
% 299.99/300.63  235605[21:Rew:196550.0,235599.1] || subclass(rest_relation,rotate(domain_relation))*+ -> equal(identity_relation,u)*.
% 299.99/300.63  235603[25:Res:28979.1,214614.1] operation(u) || subclass(rest_relation,rotate(subset_relation))* -> .
% 299.99/300.63  36719[0:Res:926.1,4392.1] operation(u) || member(v,cantor(u))*+ -> equal(ordered_pair(first(v),second(v)),v)**.
% 299.99/300.63  235601[25:Res:28979.1,214618.1] operation(u) || subclass(rest_relation,rotate(rest_relation))* -> .
% 299.99/300.63  235573[5:Res:28979.1,18842.0] || subclass(rest_relation,rotate(subset_relation))*+ -> member(u,ordinal_numbers)*.
% 299.99/300.63  235614[8:Res:10.1,235554.0] || equal(rotate(identity_relation),rest_relation)** -> .
% 299.99/300.63  235554[8:Res:28979.1,14676.0] || subclass(rest_relation,rotate(identity_relation))* -> .
% 299.99/300.63  28979[5:MRR:28972.0,8667.0] || subclass(rest_relation,rotate(u)) -> member(ordered_pair(ordered_pair(v,rest_of(ordered_pair(w,v))),w),u)*.
% 299.99/300.63  235433[8:Res:28980.1,217144.1] || subclass(rest_relation,flip(u))* equal(identity_relation,u) -> .
% 299.99/300.63  235432[8:Res:28980.1,219073.1] || subclass(rest_relation,flip(u))* subclass(u,identity_relation) -> .
% 299.99/300.63  235478[8:Res:10.1,235426.0] || equal(flip(identity_relation),rest_relation)** -> .
% 299.99/300.63  235426[8:Res:28980.1,14676.0] || subclass(rest_relation,flip(identity_relation))* -> .
% 299.99/300.63  28980[5:MRR:28971.0,8667.0] || subclass(rest_relation,flip(u)) -> member(ordered_pair(ordered_pair(v,w),rest_of(ordered_pair(w,v))),u)*.
% 299.99/300.63  230445[8:MRR:230408.0,41096.1] || member(u,v) -> member(u,union(v,identity_relation))*.
% 299.99/300.63  235202[8:Res:13049.1,234983.0] || subclass(ordinal_numbers,cantor(complement(cross_product(singleton(identity_relation),ordinal_numbers))))* -> .
% 299.99/300.63  235198[8:Res:192149.1,234983.0] || equal(cantor(complement(cross_product(singleton(identity_relation),ordinal_numbers))),ordinal_numbers)** -> .
% 299.99/300.63  18582[5:Res:8978.2,898.0] || member(u,ordinal_numbers) subclass(ordinal_numbers,restrict(v,w,x))*+ -> member(sum_class(u),v)*.
% 299.99/300.63  235196[26:Res:224684.1,234983.0] || subclass(omega,cantor(complement(cross_product(singleton(identity_relation),ordinal_numbers))))* -> .
% 299.99/300.63  235195[26:Res:225794.1,234983.0] || equal(cantor(complement(cross_product(singleton(identity_relation),ordinal_numbers))),omega)** -> .
% 299.99/300.63  235155[8:Res:8646.1,234983.0] || subclass(ordinal_numbers,cantor(complement(cross_product(singleton(omega),ordinal_numbers))))* -> .
% 299.99/300.63  235154[8:Res:143200.1,234983.0] || equal(cantor(complement(cross_product(singleton(omega),ordinal_numbers))),ordinal_numbers)** -> .
% 299.99/300.63  18655[5:SpR:8647.0,3767.1] operation(flip(cross_product(u,ordinal_numbers))) ||  -> equal(intersection(inverse(u),v),intersection(v,inverse(u)))*.
% 299.99/300.63  235203[8:Res:13056.1,234983.0] inductive(cantor(complement(cross_product(singleton(identity_relation),ordinal_numbers)))) ||  -> .
% 299.99/300.63  235146[25:SpL:208820.0,234983.0] || member(ordinal_numbers,cantor(complement(cross_product(identity_relation,ordinal_numbers))))* -> .
% 299.99/300.63  234983[8:Obv:234972.1] || member(u,cantor(complement(cross_product(singleton(u),ordinal_numbers))))* -> .
% 299.99/300.63  234979[25:Rew:160429.0,234957.0] ||  -> equal(segment(complement(cross_product(u,identity_relation)),u,ordinal_numbers),identity_relation)**.
% 299.99/300.63  41368[5:MRR:29095.0,41183.1] ||  -> member(not_subclass_element(u,image(element_relation,complement(v))),power_class(v))* subclass(u,image(element_relation,complement(v))).
% 299.99/300.63  234956[7:SpR:229238.0,8649.0] ||  -> equal(image(complement(cross_product(u,ordinal_numbers)),u),range_of(identity_relation))**.
% 299.99/300.63  229238[7:SpR:229162.0,32.0] ||  -> equal(restrict(complement(cross_product(u,v)),u,v),identity_relation)**.
% 299.99/300.63  234766[8:Res:10.1,233124.0] || equal(regular(unordered_pair(ordered_pair(u,v),w)),ordinal_numbers)** -> .
% 299.99/300.63  234736[8:Res:10.1,232824.0] || equal(regular(unordered_pair(u,ordered_pair(v,w))),ordinal_numbers)** -> .
% 299.99/300.63  193440[8:SpR:161076.2,72.0] || member(u,ordinal_numbers) -> member(u,cantor(v))* equal(apply(v,u),sum_class(range_of(identity_relation))).
% 299.99/300.63  233133[8:Res:10.1,230695.0] || equal(regular(unordered_pair(unordered_pair(u,v),w)),ordinal_numbers)** -> .
% 299.99/300.63  233124[8:SpL:17.0,230695.0] || subclass(ordinal_numbers,regular(unordered_pair(ordered_pair(u,v),w)))* -> .
% 299.99/300.63  232837[8:Res:10.1,230694.0] || equal(regular(unordered_pair(u,unordered_pair(v,w))),ordinal_numbers)** -> .
% 299.99/300.63  232824[8:SpL:17.0,230694.0] || subclass(ordinal_numbers,regular(unordered_pair(u,ordered_pair(v,w))))* -> .
% 299.99/300.63  196432[21:Rew:196372.1,161160.2] || member(u,ordinal_numbers) subclass(domain_relation,intersection(v,w))*+ -> member(ordered_pair(u,identity_relation),w)*.
% 299.99/300.63  234117[8:Res:233383.0,8843.1] || subclass(ordinal_numbers,complement(complement(singleton(ordered_pair(u,v)))))* -> .
% 299.99/300.63  234115[8:Res:233383.0,210517.1] || equal(complement(complement(singleton(ordered_pair(u,v)))),ordinal_numbers)** -> .
% 299.99/300.63  234591[8:MRR:234589.1,13040.0] || equal(omega,ordinal_numbers)** -> .
% 299.99/300.63  234588[8:MRR:234512.0,216561.0] ||  -> equal(integer_of(omega),identity_relation)**.
% 299.99/300.63  234592[8:MRR:234590.1,13040.0] || subclass(ordinal_numbers,omega)* -> .
% 299.99/300.63  233381[8:MRR:233365.1,216561.0] || member(u,singleton(omega))* -> equal(integer_of(u),identity_relation).
% 299.99/300.63  234420[21:Res:10.1,234195.0] || equal(singleton(ordered_pair(singleton(singleton(identity_relation)),u)),domain_relation)** -> .
% 299.99/300.63  234196[22:Res:205574.1,234106.0] || equal(singleton(ordered_pair(identity_relation,u)),singleton(singleton(identity_relation)))** -> .
% 299.99/300.63  234428[21:Res:10.1,234414.0] || equal(singleton(singleton(singleton(singleton(singleton(identity_relation))))),domain_relation)** -> .
% 299.99/300.63  196423[21:Rew:196372.1,161163.2] || member(u,ordinal_numbers) subclass(domain_relation,intersection(v,w))*+ -> member(ordered_pair(u,identity_relation),v)*.
% 299.99/300.63  234414[21:SpL:963.0,234195.0] || subclass(domain_relation,singleton(singleton(singleton(singleton(singleton(identity_relation))))))* -> .
% 299.99/300.63  234195[21:Res:196904.1,234106.0] || subclass(domain_relation,singleton(ordered_pair(singleton(singleton(identity_relation)),u)))* -> .
% 299.99/300.63  234119[8:SpL:963.0,234113.0] || subclass(complement(singleton(singleton(singleton(singleton(u))))),identity_relation)* -> .
% 299.99/300.63  233748[26:Res:233380.0,225263.1] || equal(complement(complement(singleton(ordered_pair(ordinal_numbers,u)))),omega)** -> .
% 299.99/300.63  18696[7:Res:13237.2,28.1] || well_ordering(u,ordinal_numbers) member(least(u,complement(v)),v)* -> equal(complement(v),identity_relation).
% 299.99/300.63  233387[8:MRR:233354.1,215781.0] || well_ordering(ordinal_numbers,complement(singleton(singleton(singleton(singleton(u))))))* -> .
% 299.99/300.63  234270[25:Res:10.1,233554.1] || equal(complement(rest_relation),domain_relation) subclass(rest_relation,domain_relation)* -> .
% 299.99/300.63  234200[8:Res:10.1,233352.0] || equal(singleton(domain_relation),domain_relation)** -> equal(singleton(domain_relation),identity_relation).
% 299.99/300.63  234035[22:Res:205574.1,233883.0] || equal(singleton(singleton(singleton(identity_relation))),singleton(singleton(identity_relation)))** -> .
% 299.99/300.63  3995[0:SpL:963.0,100.0] || member(ordered_pair(u,singleton(singleton(singleton(v)))),composition_function)* -> equal(compose(u,singleton(v)),v).
% 299.99/300.63  233893[22:Res:233384.0,8843.1] || subclass(ordinal_numbers,complement(complement(singleton(singleton(singleton(identity_relation))))))* -> .
% 299.99/300.63  233892[22:Res:233384.0,210517.1] || equal(complement(complement(singleton(singleton(singleton(identity_relation))))),ordinal_numbers)** -> .
% 299.99/300.63  233554[25:MRR:233542.1,13126.0] || subclass(rest_relation,domain_relation) subclass(domain_relation,complement(rest_relation))* -> .
% 299.99/300.63  233460[14:Res:233378.0,165357.1] || equal(complement(complement(singleton(singleton(identity_relation)))),singleton(identity_relation))** -> .
% 299.99/300.63  161224[8:Rew:140613.0,66159.0] || member(not_subclass_element(union(u,identity_relation),v),symmetric_difference(ordinal_numbers,u))* -> subclass(union(u,identity_relation),v).
% 299.99/300.63  233459[18:Res:233378.0,190532.1] || equal(complement(complement(singleton(singleton(identity_relation)))),symmetrization_of(identity_relation))** -> .
% 299.99/300.63  233458[18:Res:233378.0,190641.1] || equal(complement(complement(singleton(singleton(identity_relation)))),inverse(identity_relation))** -> .
% 299.99/300.63  233352[8:Res:231881.0,81322.1] || subclass(domain_relation,singleton(domain_relation))* -> equal(singleton(domain_relation),identity_relation).
% 299.99/300.63  234106[8:Res:233383.0,28.1] || member(singleton(u),singleton(ordered_pair(u,v)))* -> .
% 299.99/300.63  13560[7:Rew:13036.0,12947.1] || subclass(omega,u) -> equal(integer_of(not_subclass_element(complement(u),v)),identity_relation)** subclass(complement(u),v).
% 299.99/300.63  234113[8:Res:233383.0,219073.1] || subclass(complement(singleton(ordered_pair(u,v))),identity_relation)* -> .
% 299.99/300.63  233383[8:MRR:233316.0,216013.0] ||  -> member(singleton(u),complement(singleton(ordered_pair(u,v))))*.
% 299.99/300.63  233382[8:MRR:233315.1,216013.0] || well_ordering(ordinal_numbers,complement(singleton(ordered_pair(u,v))))* -> .
% 299.99/300.63  233762[25:Res:165168.1,233738.0] || equal(singleton(ordered_pair(ordinal_numbers,u)),singleton(identity_relation))** -> .
% 299.99/300.63  161050[8:Rew:116078.0,13424.2] || subclass(omega,rest_of(u))+ -> equal(integer_of(ordered_pair(v,w)),identity_relation)** member(v,cantor(u))*.
% 299.99/300.63  233761[25:Res:190442.1,233738.0] || equal(singleton(ordered_pair(ordinal_numbers,u)),symmetrization_of(identity_relation))** -> .
% 299.99/300.63  233760[25:Res:190593.1,233738.0] || equal(singleton(ordered_pair(ordinal_numbers,u)),inverse(identity_relation))** -> .
% 299.99/300.63  233890[22:Res:233384.0,219073.1] || subclass(complement(singleton(singleton(singleton(identity_relation)))),identity_relation)* -> .
% 299.99/300.63  18654[5:SpR:8648.0,3767.1] operation(restrict(element_relation,ordinal_numbers,u)) ||  -> equal(intersection(sum_class(u),v),intersection(v,sum_class(u)))*.
% 299.99/300.63  233883[22:Res:233384.0,28.1] || member(singleton(identity_relation),singleton(singleton(singleton(identity_relation))))* -> .
% 299.99/300.63  233457[26:Res:233378.0,225263.1] || equal(complement(complement(singleton(singleton(identity_relation)))),omega)** -> .
% 299.99/300.63  233456[14:Res:233378.0,210517.1] || equal(complement(complement(singleton(singleton(identity_relation)))),ordinal_numbers)** -> .
% 299.99/300.63  233385[22:MRR:233356.1,215781.0] || well_ordering(ordinal_numbers,complement(singleton(singleton(singleton(identity_relation)))))* -> .
% 299.99/300.63  161200[8:Rew:140613.0,67590.1] || member(u,image(element_relation,union(v,identity_relation)))* member(u,power_class(symmetric_difference(ordinal_numbers,v))) -> .
% 299.99/300.63  233384[22:MRR:233355.0,215781.0] ||  -> member(singleton(identity_relation),complement(singleton(singleton(singleton(identity_relation)))))*.
% 299.99/300.63  233757[26:Res:224684.1,233738.0] || subclass(omega,singleton(ordered_pair(ordinal_numbers,u)))* -> .
% 299.99/300.63  233756[26:Res:225794.1,233738.0] || equal(singleton(ordered_pair(ordinal_numbers,u)),omega)** -> .
% 299.99/300.63  233764[25:Res:13056.1,233738.0] inductive(singleton(ordered_pair(ordinal_numbers,u))) ||  -> .
% 299.99/300.63  941[0:SpL:189.0,28.1] || member(u,image(element_relation,power_class(v))) member(u,power_class(image(element_relation,complement(v))))* -> .
% 299.99/300.63  233738[25:Res:233380.0,28.1] || member(identity_relation,singleton(ordered_pair(ordinal_numbers,u)))* -> .
% 299.99/300.63  233380[25:MRR:233323.0,216013.0] ||  -> member(identity_relation,complement(singleton(ordered_pair(ordinal_numbers,u))))*.
% 299.99/300.63  233490[14:Res:165168.1,233447.0] || equal(singleton(singleton(identity_relation)),singleton(identity_relation))** -> .
% 299.99/300.63  233489[18:Res:190442.1,233447.0] || equal(singleton(singleton(identity_relation)),symmetrization_of(identity_relation))** -> .
% 299.99/300.63  13409[7:Rew:13036.0,10939.1] || subclass(omega,union_of_range_map) -> equal(integer_of(ordered_pair(u,v)),identity_relation)** equal(sum_class(range_of(u)),v).
% 299.99/300.63  233488[18:Res:190593.1,233447.0] || equal(singleton(singleton(identity_relation)),inverse(identity_relation))** -> .
% 299.99/300.63  233454[14:Res:233378.0,219073.1] || subclass(complement(singleton(singleton(identity_relation))),identity_relation)* -> .
% 299.99/300.63  233684[21:Res:10.1,233661.0] || equal(rest_of(u),domain_relation)** -> .
% 299.99/300.63  233661[21:MRR:204681.1,233659.1] || subclass(domain_relation,rest_of(u))* -> .
% 299.99/300.63  233379[14:MRR:233357.1,215781.0] || well_ordering(ordinal_numbers,complement(singleton(singleton(identity_relation))))* -> .
% 299.99/300.63  233377[8:MRR:233304.1,216561.0] || equal(complement(complement(singleton(omega))),omega)** -> .
% 299.99/300.63  233376[8:MRR:233303.1,216561.0] || equal(complement(complement(singleton(omega))),ordinal_numbers)** -> .
% 299.99/300.63  233485[26:Res:224684.1,233447.0] || subclass(omega,singleton(singleton(identity_relation)))* -> .
% 299.99/300.63  196424[21:Rew:196372.1,161162.2] || member(u,ordinal_numbers) subclass(domain_relation,complement(v)) member(ordered_pair(u,identity_relation),v)* -> .
% 299.99/300.63  233484[26:Res:225794.1,233447.0] || equal(singleton(singleton(identity_relation)),omega)** -> .
% 299.99/300.63  233492[14:Res:13056.1,233447.0] inductive(singleton(singleton(identity_relation))) ||  -> .
% 299.99/300.63  233447[14:Res:233378.0,28.1] || member(identity_relation,singleton(singleton(identity_relation)))* -> .
% 299.99/300.63  233402[26:Res:165168.1,233373.0] || equal(singleton(omega),singleton(identity_relation))** -> .
% 299.99/300.63  161057[8:Rew:116078.0,18699.2] || well_ordering(u,ordinal_numbers) -> equal(recursion_equation_functions(v),identity_relation) member(cantor(least(u,recursion_equation_functions(v))),ordinal_numbers)*.
% 299.99/300.63  233401[26:Res:190442.1,233373.0] || equal(symmetrization_of(identity_relation),singleton(omega))** -> .
% 299.99/300.63  233400[26:Res:190593.1,233373.0] || equal(inverse(identity_relation),singleton(omega))** -> .
% 299.99/300.63  233378[14:MRR:233358.0,215781.0] ||  -> member(identity_relation,complement(singleton(singleton(identity_relation))))*.
% 299.99/300.63  233375[8:MRR:233369.1,216561.0] || subclass(omega,singleton(omega))* -> .
% 299.99/300.63  13566[7:Rew:13036.0,13008.0] ||  -> equal(intersection(u,recursion_equation_functions(v)),identity_relation) subclass(regular(intersection(u,recursion_equation_functions(v))),cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.63  233374[8:MRR:233368.1,216561.0] || equal(singleton(omega),omega)** -> .
% 299.99/300.63  233404[26:Res:13056.1,233373.0] inductive(singleton(omega)) ||  -> .
% 299.99/300.63  233373[26:MRR:233364.1,216561.0] || member(identity_relation,singleton(omega))* -> .
% 299.99/300.63  231881[8:Obv:231868.0] ||  -> subclass(u,complement(singleton(u)))* equal(singleton(u),identity_relation).
% 299.99/300.63  17388[7:Res:13248.1,8788.0] ||  -> equal(intersection(recursion_equation_functions(u),v),identity_relation) subclass(regular(intersection(recursion_equation_functions(u),v)),cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.63  233149[8:Res:216691.1,233123.0] || equal(complement(regular(unordered_pair(singleton(u),v))),identity_relation)** -> .
% 299.99/300.63  233148[8:Res:10.1,233123.0] || equal(regular(unordered_pair(singleton(u),v)),ordinal_numbers)** -> .
% 299.99/300.63  233159[25:Res:216691.1,233139.0] || equal(complement(regular(unordered_pair(identity_relation,u))),identity_relation)** -> .
% 299.99/300.63  233158[25:Res:10.1,233139.0] || equal(regular(unordered_pair(identity_relation,u)),ordinal_numbers)** -> .
% 299.99/300.63  18447[7:Res:13072.1,288.0] || member(regular(image(element_relation,complement(u))),power_class(u))* -> equal(image(element_relation,complement(u)),identity_relation).
% 299.99/300.63  233139[25:SpL:208820.0,233123.0] || subclass(ordinal_numbers,regular(unordered_pair(identity_relation,u)))* -> .
% 299.99/300.63  233123[8:SpL:16.0,230695.0] || subclass(ordinal_numbers,regular(unordered_pair(singleton(u),v)))* -> .
% 299.99/300.63  230695[8:MRR:230651.0,230651.2,8666.0,217161.0] || subclass(ordinal_numbers,regular(unordered_pair(unordered_pair(u,v),w)))* -> .
% 299.99/300.63  233014[8:Res:216691.1,232981.0] || equal(complement(regular(singleton(ordered_pair(u,v)))),identity_relation)** -> .
% 299.99/300.63  196525[21:Rew:196372.1,196451.1] || member(u,ordinal_numbers) equal(sum_class(range_of(u)),identity_relation) -> member(ordered_pair(u,identity_relation),union_of_range_map)*.
% 299.99/300.63  232990[8:Res:216691.1,232828.0] || equal(complement(regular(singleton(unordered_pair(u,v)))),identity_relation)** -> .
% 299.99/300.63  232851[8:Res:216691.1,232823.0] || equal(complement(regular(unordered_pair(u,singleton(v)))),identity_relation)** -> .
% 299.99/300.63  233013[8:Res:10.1,232981.0] || equal(regular(singleton(ordered_pair(u,v))),ordinal_numbers)** -> .
% 299.99/300.63  232989[8:Res:10.1,232828.0] || equal(regular(singleton(unordered_pair(u,v))),ordinal_numbers)** -> .
% 299.99/300.63  69182[8:Res:13227.2,66086.1] || subclass(u,complement(compose(element_relation,ordinal_numbers)))* member(regular(u),element_relation) -> equal(u,identity_relation).
% 299.99/300.63  232981[8:SpL:17.0,232828.0] || subclass(ordinal_numbers,regular(singleton(ordered_pair(u,v))))* -> .
% 299.99/300.63  232850[8:Res:10.1,232823.0] || equal(regular(unordered_pair(u,singleton(v))),ordinal_numbers)** -> .
% 299.99/300.63  232828[8:SpL:16.0,230694.0] || subclass(ordinal_numbers,regular(singleton(unordered_pair(u,v))))* -> .
% 299.99/300.63  232903[8:Res:216691.1,232845.0] || equal(complement(regular(singleton(singleton(u)))),identity_relation)** -> .
% 299.99/300.63  66822[7:Res:13248.1,161.0] ||  -> equal(intersection(omega,u),identity_relation) equal(integer_of(regular(intersection(omega,u))),regular(intersection(omega,u)))**.
% 299.99/300.63  232859[25:Res:216691.1,232843.0] || equal(complement(regular(unordered_pair(u,identity_relation))),identity_relation)** -> .
% 299.99/300.63  232902[8:Res:10.1,232845.0] || equal(regular(singleton(singleton(u))),ordinal_numbers)** -> .
% 299.99/300.63  232858[25:Res:10.1,232843.0] || equal(regular(unordered_pair(u,identity_relation)),ordinal_numbers)** -> .
% 299.99/300.63  232845[8:SpL:16.0,232823.0] || subclass(ordinal_numbers,regular(singleton(singleton(u))))* -> .
% 299.99/300.63  13575[7:Rew:13036.0,13019.0] ||  -> equal(intersection(u,omega),identity_relation) equal(integer_of(regular(intersection(u,omega))),regular(intersection(u,omega)))**.
% 299.99/300.63  232843[25:SpL:208820.0,232823.0] || subclass(ordinal_numbers,regular(unordered_pair(u,identity_relation)))* -> .
% 299.99/300.63  232823[8:SpL:16.0,230694.0] || subclass(ordinal_numbers,regular(unordered_pair(u,singleton(v))))* -> .
% 299.99/300.63  230694[8:MRR:230652.0,230652.2,8666.0,217156.0] || subclass(ordinal_numbers,regular(unordered_pair(u,unordered_pair(v,w))))* -> .
% 299.99/300.63  232792[16:MRR:232791.1,230705.0] || subclass(complement(singleton(identity_relation)),singleton(identity_relation))* -> .
% 299.99/300.63  18711[8:Res:13237.2,14679.1] || well_ordering(u,ordinal_numbers) member(least(u,inverse(subset_relation)),subset_relation)* -> equal(inverse(subset_relation),identity_relation).
% 299.99/300.63  229468[8:SpR:229359.0,155157.1] || subclass(u,complement(u))*+ -> subclass(ordinal_numbers,complement(u))*.
% 299.99/300.63  231114[8:Res:6.1,230780.0] || equal(not_subclass_element(subset_relation,u),ordinal_numbers)** -> subclass(subset_relation,u).
% 299.99/300.63  231036[8:Res:6.1,230762.0] || subclass(ordinal_numbers,not_subclass_element(subset_relation,u))* -> subclass(subset_relation,u).
% 299.99/300.63  232728[7:SSi:232650.0,54.0] ||  -> equal(segment(element_relation,omega,least(element_relation,omega)),identity_relation)**.
% 299.99/300.63  232563[8:Res:13072.1,230939.0] || equal(regular(regular(subset_relation)),ordinal_numbers)** -> equal(subset_relation,identity_relation).
% 299.99/300.63  230939[8:SpL:18840.1,230797.0] || member(u,subset_relation)* equal(regular(u),ordinal_numbers) -> .
% 299.99/300.63  230867[8:SpL:18840.1,230771.0] || member(u,subset_relation)* equal(complement(u),identity_relation) -> .
% 299.99/300.63  230789[8:SpL:18840.1,230675.0] || member(u,subset_relation) subclass(ordinal_numbers,regular(u))* -> .
% 299.99/300.63  69457[8:Res:13125.2,66086.1] || subclass(omega,complement(compose(element_relation,ordinal_numbers)))*+ member(u,element_relation)* -> equal(integer_of(u),identity_relation).
% 299.99/300.63  230084[8:SpR:59.0,229733.0] ||  -> equal(symmetric_difference(image(element_relation,complement(u)),power_class(u)),ordinal_numbers)**.
% 299.99/300.63  230080[8:SpR:160491.0,229733.0] ||  -> equal(symmetric_difference(symmetric_difference(ordinal_numbers,u),union(u,identity_relation)),ordinal_numbers)**.
% 299.99/300.63  229909[7:SpR:59.0,229590.0] ||  -> equal(intersection(image(element_relation,complement(u)),power_class(u)),identity_relation)**.
% 299.99/300.63  229905[8:SpR:160491.0,229590.0] ||  -> equal(intersection(symmetric_difference(ordinal_numbers,u),union(u,identity_relation)),identity_relation)**.
% 299.99/300.63  17323[7:Res:13227.2,898.0] || subclass(u,restrict(v,w,x))* -> equal(u,identity_relation) member(regular(u),v).
% 299.99/300.63  229723[8:Rew:66036.0,229630.0] ||  -> equal(union(symmetric_difference(ordinal_numbers,u),union(u,identity_relation)),ordinal_numbers)**.
% 299.99/300.63  229481[8:SpR:59.0,229359.0] ||  -> equal(symmetric_difference(power_class(u),image(element_relation,complement(u))),ordinal_numbers)**.
% 299.99/300.63  231880[16:MRR:231853.1,230722.0] ||  -> subclass(regular(complement(singleton(identity_relation))),singleton(identity_relation))*.
% 299.99/300.63  231812[8:Obv:231805.0] ||  -> subclass(regular(u),complement(u))* equal(u,identity_relation).
% 299.99/300.63  18747[8:Res:6.1,14681.0] || member(not_subclass_element(regular(u),v),u)* -> subclass(regular(u),v) equal(u,identity_relation).
% 299.99/300.63  229477[8:SpR:160491.0,229359.0] ||  -> equal(symmetric_difference(union(u,identity_relation),symmetric_difference(ordinal_numbers,u)),ordinal_numbers)**.
% 299.99/300.63  229355[8:Rew:66036.0,229249.0] ||  -> equal(union(union(u,identity_relation),symmetric_difference(ordinal_numbers,u)),ordinal_numbers)**.
% 299.99/300.63  229281[7:SpR:59.0,229162.0] ||  -> equal(intersection(power_class(u),image(element_relation,complement(u))),identity_relation)**.
% 299.99/300.63  229277[8:SpR:160491.0,229162.0] ||  -> equal(intersection(union(u,identity_relation),symmetric_difference(ordinal_numbers,u)),identity_relation)**.
% 299.99/300.63  17447[7:Rew:163.0,17371.0] ||  -> equal(symmetric_difference(u,v),identity_relation) member(regular(symmetric_difference(u,v)),complement(intersection(u,v)))*.
% 299.99/300.63  231109[8:Res:216691.1,231042.0] || equal(complement(regular(subset_relation)),identity_relation)** -> equal(subset_relation,identity_relation).
% 299.99/300.63  230185[8:SpR:162584.0,229638.0] ||  -> equal(symmetric_difference(complement(inverse(identity_relation)),complement(symmetrization_of(identity_relation))),identity_relation)**.
% 299.99/300.63  230798[8:Res:216691.1,230675.0] || equal(complement(regular(ordered_pair(u,v))),identity_relation)** -> .
% 299.99/300.63  13418[7:Rew:13036.0,10915.1] || subclass(omega,restrict(u,v,w))*+ -> equal(integer_of(x),identity_relation) member(x,u)*.
% 299.99/300.63  230780[8:SpL:18840.1,230770.0] || member(u,subset_relation)* equal(u,ordinal_numbers) -> .
% 299.99/300.63  231108[8:Res:10.1,231042.0] || equal(regular(subset_relation),ordinal_numbers)** -> equal(subset_relation,identity_relation).
% 299.99/300.63  231042[8:Res:13072.1,230762.0] || subclass(ordinal_numbers,regular(subset_relation))* -> equal(subset_relation,identity_relation).
% 299.99/300.63  230762[8:SpL:18840.1,230706.0] || member(u,subset_relation)* subclass(ordinal_numbers,u) -> .
% 299.99/300.63  18545[5:Res:8977.2,25.0] || member(u,ordinal_numbers) subclass(ordinal_numbers,intersection(v,w))*+ -> member(power_class(u),v)*.
% 299.99/300.63  230797[8:Res:10.1,230675.0] || equal(regular(ordered_pair(u,v)),ordinal_numbers)** -> .
% 299.99/300.63  18544[5:Res:8977.2,26.0] || member(u,ordinal_numbers) subclass(ordinal_numbers,intersection(v,w))*+ -> member(power_class(u),w)*.
% 299.99/300.63  230771[8:Res:216691.1,230706.0] || equal(complement(ordered_pair(u,v)),identity_relation)** -> .
% 299.99/300.63  230713[8:Res:216691.1,230686.0] || equal(complement(unordered_pair(u,v)),identity_relation)** -> .
% 299.99/300.63  1042[0:Rew:59.0,1028.1] || member(not_subclass_element(power_class(u),v),image(element_relation,complement(u)))* -> subclass(power_class(u),v).
% 299.99/300.63  230675[8:MRR:230668.1,162891.0] || subclass(ordinal_numbers,regular(ordered_pair(u,v)))* -> .
% 299.99/300.63  230770[8:Res:10.1,230706.0] || equal(ordered_pair(u,v),ordinal_numbers)** -> .
% 299.99/300.63  230712[8:Res:10.1,230686.0] || equal(unordered_pair(u,v),ordinal_numbers)** -> .
% 299.99/300.63  230706[8:SpL:17.0,230686.0] || subclass(ordinal_numbers,ordered_pair(u,v))* -> .
% 299.99/300.63  18708[7:Res:13237.2,3700.0] || well_ordering(u,ordinal_numbers) -> equal(singleton(v),identity_relation) equal(least(u,singleton(v)),v)**.
% 299.99/300.63  230722[8:Res:216691.1,230705.0] || equal(complement(singleton(u)),identity_relation)** -> .
% 299.99/300.63  230721[8:Res:10.1,230705.0] || equal(singleton(u),ordinal_numbers)** -> .
% 299.99/300.63  230705[8:SpL:16.0,230686.0] || subclass(ordinal_numbers,singleton(u))* -> .
% 299.99/300.63  230686[8:MRR:230685.0,230685.2,8666.0,216024.0] || subclass(ordinal_numbers,unordered_pair(u,v))* -> .
% 299.99/300.63  18754[8:Res:8643.1,14681.0] || subclass(ordinal_numbers,regular(u)) member(unordered_pair(v,w),u)* -> equal(u,identity_relation).
% 299.99/300.63  230079[8:SpR:162584.0,229733.0] ||  -> equal(symmetric_difference(complement(inverse(identity_relation)),symmetrization_of(identity_relation)),ordinal_numbers)**.
% 299.99/300.63  230028[8:SpR:162584.0,229711.0] ||  -> equal(union(complement(inverse(identity_relation)),symmetrization_of(identity_relation)),ordinal_numbers)**.
% 299.99/300.63  229634[8:Rew:229591.0,213743.0] ||  -> equal(intersection(complement(inverse(identity_relation)),symmetrization_of(identity_relation)),identity_relation)**.
% 299.99/300.63  229476[8:SpR:162584.0,229359.0] ||  -> equal(symmetric_difference(symmetrization_of(identity_relation),complement(inverse(identity_relation))),ordinal_numbers)**.
% 299.99/300.63  161066[8:Rew:140613.0,66155.1] || member(u,ordinal_numbers) -> member(u,symmetric_difference(ordinal_numbers,v))* member(u,union(v,identity_relation)).
% 299.99/300.63  229417[8:SpR:162584.0,229346.0] ||  -> equal(union(symmetrization_of(identity_relation),complement(inverse(identity_relation))),ordinal_numbers)**.
% 299.99/300.63  229276[8:SpR:162584.0,229162.0] ||  -> equal(intersection(symmetrization_of(identity_relation),complement(inverse(identity_relation))),identity_relation)**.
% 299.99/300.63  230199[8:SpR:162584.0,229638.0] ||  -> equal(symmetric_difference(inverse(identity_relation),symmetrization_of(identity_relation)),identity_relation)**.
% 299.99/300.63  229638[7:Rew:229591.0,161315.0] ||  -> equal(symmetric_difference(u,complement(complement(u))),identity_relation)**.
% 299.99/300.63  19679[7:Rew:3597.0,19652.0] ||  -> equal(symmetric_difference(u,inverse(u)),identity_relation) member(regular(symmetric_difference(u,inverse(u))),symmetrization_of(u))*.
% 299.99/300.63  229733[8:Rew:66036.0,229732.0] ||  -> equal(symmetric_difference(u,complement(u)),ordinal_numbers)**.
% 299.99/300.63  229711[8:Rew:66036.0,229608.0] ||  -> equal(union(u,complement(u)),ordinal_numbers)**.
% 299.99/300.63  229590[7:Obv:229583.0] ||  -> equal(intersection(u,complement(u)),identity_relation)**.
% 299.99/300.63  229591[7:Rew:229590.0,143474.0] ||  -> equal(symmetric_difference(u,u),identity_relation)**.
% 299.99/300.63  13571[7:Rew:13036.0,13007.1] || member(regular(intersection(u,complement(v))),v)* -> equal(intersection(u,complement(v)),identity_relation).
% 299.99/300.63  229359[8:Rew:229346.0,229358.0] ||  -> equal(symmetric_difference(complement(u),u),ordinal_numbers)**.
% 299.99/300.63  229346[8:Rew:66036.0,229246.0] ||  -> equal(union(complement(u),u),ordinal_numbers)**.
% 299.99/300.63  229162[7:Obv:229157.0] ||  -> equal(intersection(complement(u),u),identity_relation)**.
% 299.99/300.63  17387[7:Res:13248.1,28.1] || member(regular(intersection(complement(u),v)),u)* -> equal(intersection(complement(u),v),identity_relation).
% 299.99/300.63  222904[8:MRR:222903.2,216107.1] || subclass(singleton(u),inverse(subset_relation))* member(u,subset_relation) -> .
% 299.99/300.63  222310[8:SpL:72.0,222300.0] || subclass(ordinal_numbers,apply(u,v))* subclass(element_relation,identity_relation) -> .
% 299.99/300.63  222305[8:SpL:72.0,222296.0] || equal(apply(u,v),ordinal_numbers)** subclass(element_relation,identity_relation) -> .
% 299.99/300.63  229018[8:Res:13056.1,222292.0] inductive(apply(u,v)) || subclass(element_relation,identity_relation)* -> .
% 299.99/300.63  19563[7:Rew:3596.0,19534.0] ||  -> equal(symmetric_difference(u,singleton(u)),identity_relation) member(regular(symmetric_difference(u,singleton(u))),successor(u))*.
% 299.99/300.63  222292[8:SpL:72.0,222208.0] || member(identity_relation,apply(u,v))* subclass(element_relation,identity_relation) -> .
% 299.99/300.63  228946[8:Res:222115.1,215660.0] || subclass(complement(u),identity_relation) -> member(identity_relation,symmetrization_of(u))*.
% 299.99/300.63  228945[8:Res:222115.1,215661.0] || subclass(complement(u),identity_relation) -> member(omega,symmetrization_of(u))*.
% 299.99/300.63  61018[8:MRR:18751.0,60996.1] || member(apply(choice,regular(u)),u)* -> equal(regular(u),identity_relation) equal(u,identity_relation).
% 299.99/300.63  228807[8:Res:222114.1,215660.0] || subclass(complement(u),identity_relation) -> member(identity_relation,successor(u))*.
% 299.99/300.63  228806[8:Res:222114.1,215661.0] || subclass(complement(u),identity_relation) -> member(omega,successor(u))*.
% 299.99/300.63  222095[8:SpR:219120.1,155582.0] || subclass(complement(u),identity_relation)* -> equal(symmetric_difference(ordinal_numbers,u),identity_relation).
% 299.99/300.63  18535[5:Res:8977.2,28.1] || member(u,ordinal_numbers) subclass(ordinal_numbers,complement(v)) member(power_class(u),v)* -> .
% 299.99/300.63  228647[8:Res:221680.1,215660.0] || equal(complement(u),identity_relation) -> member(identity_relation,symmetrization_of(u))*.
% 299.99/300.63  228646[8:Res:221680.1,215661.0] || equal(complement(u),identity_relation) -> member(omega,symmetrization_of(u))*.
% 299.99/300.63  228547[8:Res:221679.1,215660.0] || equal(complement(u),identity_relation) -> member(identity_relation,successor(u))*.
% 299.99/300.63  18451[5:Res:8643.1,288.0] || subclass(ordinal_numbers,image(element_relation,complement(u))) member(unordered_pair(v,w),power_class(u))* -> .
% 299.99/300.63  228546[8:Res:221679.1,215661.0] || equal(complement(u),identity_relation) -> member(omega,successor(u))*.
% 299.99/300.63  221660[8:SpR:218159.1,155582.0] || equal(complement(u),identity_relation) -> equal(symmetric_difference(ordinal_numbers,u),identity_relation)**.
% 299.99/300.63  221177[21:Res:210572.1,221080.1] || equal(complement(u),ordinal_numbers)** equal(rotate(u),domain_relation) -> .
% 299.99/300.63  196457[21:Rew:196372.1,161028.2] || member(u,ordinal_numbers) subclass(domain_relation,compose_class(v))*+ -> equal(compose(v,u),identity_relation)**.
% 299.99/300.63  221086[21:Res:210572.1,221041.1] || equal(complement(u),ordinal_numbers)** equal(flip(u),domain_relation) -> .
% 299.99/300.63  220841[8:SpL:116239.0,219206.0] || member(inverse(u),range_of(u))* subclass(element_relation,identity_relation) -> .
% 299.99/300.63  220569[21:Res:196657.1,8841.1] || subclass(domain_relation,rotate(u))* subclass(ordinal_numbers,complement(u)) -> .
% 299.99/300.63  228359[21:Res:10.1,228311.0] || equal(rotate(element_relation),domain_relation)** -> .
% 299.99/300.63  196427[21:Rew:196372.1,161029.2] || member(u,ordinal_numbers) subclass(domain_relation,singleton(v))*+ -> equal(ordered_pair(u,identity_relation),v)*.
% 299.99/300.63  228311[21:Res:220551.1,14676.0] || subclass(domain_relation,rotate(element_relation))* -> .
% 299.99/300.63  220543[21:Res:196657.1,210517.1] || subclass(domain_relation,rotate(u))* equal(complement(u),ordinal_numbers) -> .
% 299.99/300.63  220463[21:Res:196656.1,8841.1] || subclass(domain_relation,flip(u))* subclass(ordinal_numbers,complement(u)) -> .
% 299.99/300.63  17313[7:Res:13227.2,8788.0] || subclass(u,recursion_equation_functions(v))*+ -> equal(u,identity_relation) subclass(regular(u),cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.63  220441[21:Res:196656.1,210517.1] || subclass(domain_relation,flip(u))* equal(complement(u),ordinal_numbers) -> .
% 299.99/300.63  220189[8:MRR:220188.2,13040.0] || member(singleton(u),subset_relation)* equal(complement(u),identity_relation) -> .
% 299.99/300.63  220152[8:SpL:116239.0,217492.1] operation(inverse(u)) || equal(complement(range_of(u)),identity_relation)** -> .
% 299.99/300.63  219937[8:Res:8956.1,217200.1] || member(u,ordinal_numbers) equal(singleton(power_class(u)),identity_relation)** -> .
% 299.99/300.63  13412[7:Rew:13036.0,10936.1] || subclass(omega,successor_relation) -> equal(integer_of(ordered_pair(u,v)),identity_relation)** equal(successor(u),v).
% 299.99/300.63  219931[8:Res:148963.1,217200.1] || member(u,ordinal_numbers) equal(singleton(rest_of(u)),identity_relation)** -> .
% 299.99/300.63  219928[8:Res:50064.1,217200.1] || member(u,subset_relation) equal(singleton(second(u)),identity_relation)** -> .
% 299.99/300.63  219927[8:Res:50063.1,217200.1] || member(u,subset_relation) equal(singleton(first(u)),identity_relation)** -> .
% 299.99/300.63  219925[8:Res:8955.1,217200.1] || member(u,ordinal_numbers) equal(singleton(sum_class(u)),identity_relation)** -> .
% 299.99/300.63  160930[8:Rew:116078.0,13411.2] || subclass(omega,domain_relation) -> equal(integer_of(ordered_pair(u,v)),identity_relation)** equal(cantor(u),v).
% 299.99/300.63  219882[15:Res:217197.1,165527.1] || equal(complement(u),identity_relation) subclass(ordinal_numbers,complement(u))* -> .
% 299.99/300.63  219332[15:Res:215659.1,3700.0] || subclass(complement(singleton(u)),identity_relation)* -> equal(range_of(identity_relation),u).
% 299.99/300.63  219196[22:Res:205574.1,219073.1] || equal(u,singleton(singleton(identity_relation)))*+ subclass(u,identity_relation)* -> .
% 299.99/300.63  218561[21:Res:8667.0,196455.0] || subclass(rest_relation,domain_relation) -> equal(rest_of(ordered_pair(u,v)),identity_relation)**.
% 299.99/300.63  13410[7:Rew:13036.0,10938.1] || subclass(omega,rest_relation) -> equal(integer_of(ordered_pair(u,v)),identity_relation)** equal(rest_of(u),v).
% 299.99/300.63  218559[21:Res:8666.0,196455.0] || subclass(rest_relation,domain_relation) -> equal(rest_of(unordered_pair(u,v)),identity_relation)**.
% 299.99/300.63  218385[21:Res:8667.0,196454.0] || subclass(domain_relation,rest_relation) -> equal(rest_of(ordered_pair(u,v)),identity_relation)**.
% 299.99/300.63  218383[21:Res:8666.0,196454.0] || subclass(domain_relation,rest_relation) -> equal(rest_of(unordered_pair(u,v)),identity_relation)**.
% 299.99/300.63  28934[5:Res:8827.2,152.0] || member(u,ordinal_numbers) subclass(rest_relation,recursion_equation_functions(v))*+ -> function(ordered_pair(u,rest_of(u)))*.
% 299.99/300.63  218235[22:Res:205574.1,217144.1] || equal(u,singleton(singleton(identity_relation)))* equal(identity_relation,u) -> .
% 299.99/300.63  217727[8:Res:216691.1,94699.0] || equal(complement(complement(complement(element_relation))),identity_relation)**+ -> member(u,v)*.
% 299.99/300.63  217700[8:Res:216691.1,50032.1] || equal(complement(complement(u)),identity_relation)** member(u,subset_relation) -> .
% 299.99/300.63  19790[5:Res:8665.1,8836.1] function(unordered_pair(u,v)) || member(u,ordinal_numbers) -> member(u,cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.63  217699[8:Res:216691.1,63019.1] || equal(complement(complement(u)),identity_relation)** subclass(domain_relation,u) -> .
% 299.99/300.63  217698[8:Res:216691.1,127130.1] || equal(complement(complement(u)),identity_relation)** subclass(omega,u) -> .
% 299.99/300.63  217697[8:Res:216691.1,147314.1] || equal(complement(complement(u)),identity_relation)** equal(u,omega) -> .
% 299.99/300.63  217696[8:Res:216691.1,9488.1] || equal(complement(complement(u)),identity_relation)** subclass(ordinal_numbers,u) -> .
% 299.99/300.63  19832[5:Res:8665.1,8837.1] function(unordered_pair(u,v)) || member(v,ordinal_numbers) -> member(v,cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.63  217695[8:Res:216691.1,147100.1] || equal(complement(complement(u)),identity_relation)** equal(u,ordinal_numbers) -> .
% 299.99/300.63  217689[8:Res:216691.1,81409.1] || equal(complement(u),identity_relation) equal(complement(u),domain_relation)** -> .
% 299.99/300.63  217687[8:Res:216691.1,167298.1] || equal(complement(u),identity_relation) equal(complement(u),omega)** -> .
% 299.99/300.63  217665[8:Rew:59.0,217654.0] || equal(power_class(u),identity_relation) member(omega,power_class(u))* -> .
% 299.99/300.63  217663[8:Rew:160491.0,217628.0] || equal(union(u,identity_relation),identity_relation) -> member(omega,complement(u))*.
% 299.99/300.63  217611[8:Res:216611.1,151988.0] || equal(complement(complement(complement(u))),identity_relation)** -> member(omega,u).
% 299.99/300.63  217608[8:Res:216611.1,28.1] || equal(complement(complement(u)),identity_relation)** member(omega,u) -> .
% 299.99/300.63  192979[7:SpR:13621.1,8649.0] ||  -> equal(cross_product(u,ordinal_numbers),identity_relation) equal(image(regular(cross_product(u,ordinal_numbers)),u),range_of(identity_relation))**.
% 299.99/300.63  217453[8:Rew:59.0,217432.0] || equal(power_class(u),identity_relation) member(identity_relation,power_class(u))* -> .
% 299.99/300.63  227303[24:SpL:207565.1,227228.0] operation(inverse(identity_relation)) || equal(successor(inverse(identity_relation)),identity_relation)** -> .
% 299.99/300.63  227228[20:Res:217451.1,194308.0] || equal(union(inverse(identity_relation),identity_relation),identity_relation)** -> .
% 299.99/300.63  227227[16:Res:217451.1,165946.0] || equal(union(singleton(identity_relation),identity_relation),identity_relation)** -> .
% 299.99/300.63  61728[5:Res:8827.2,157.0] || member(u,ordinal_numbers) subclass(rest_relation,union_of_range_map) -> equal(sum_class(range_of(u)),rest_of(u))**.
% 299.99/300.63  217451[8:Rew:160491.0,217406.0] || equal(union(u,identity_relation),identity_relation) -> member(identity_relation,complement(u))*.
% 299.99/300.63  217389[8:Res:216591.1,151988.0] || equal(complement(complement(complement(u))),identity_relation)** -> member(identity_relation,u).
% 299.99/300.63  217386[8:Res:216591.1,28.1] || equal(complement(complement(u)),identity_relation)** member(identity_relation,u) -> .
% 299.99/300.63  196520[21:Rew:196372.1,196428.1] || member(u,ordinal_numbers) equal(successor(u),identity_relation) -> member(ordered_pair(u,identity_relation),successor_relation)*.
% 299.99/300.63  217185[8:MRR:216786.2,13108.0] || equal(power_class(u),identity_relation)** equal(power_class(u),ordinal_numbers) -> .
% 299.99/300.63  217177[8:MRR:216695.2,13108.0] || equal(complement(u),identity_relation)** equal(complement(u),ordinal_numbers) -> .
% 299.99/300.63  216692[8:SpR:216188.1,147905.0] || equal(complement(u),identity_relation) -> equal(intersection(u,ordinal_numbers),ordinal_numbers)**.
% 299.99/300.63  226809[21:SpL:18840.1,226662.0] || member(u,subset_relation) subclass(rest_relation,rest_of(u))* -> .
% 299.99/300.63  161100[8:Rew:140613.0,66167.0] || member(regular(union(u,identity_relation)),symmetric_difference(ordinal_numbers,u))* -> equal(union(u,identity_relation),identity_relation).
% 299.99/300.63  226665[21:MRR:226633.1,13039.0] || subclass(rest_relation,rest_of(regular(u)))* -> equal(u,identity_relation).
% 299.99/300.63  226664[21:MRR:226623.1,13039.0] || subclass(rest_relation,rest_of(u))* -> equal(singleton(u),identity_relation).
% 299.99/300.63  226666[21:MRR:226634.1,13039.0] || subclass(rest_relation,rest_of(regular(complement(complement(symmetrization_of(identity_relation))))))* -> .
% 299.99/300.63  226662[21:MRR:226640.1,13039.0] || subclass(rest_relation,rest_of(ordered_pair(u,v)))* -> .
% 299.99/300.63  13622[7:Rew:13036.0,13314.1] || subclass(omega,u) -> equal(integer_of(regular(complement(u))),identity_relation)** equal(complement(u),identity_relation).
% 299.99/300.63  226661[21:MRR:226639.1,13039.0] || subclass(rest_relation,rest_of(unordered_pair(u,v)))* -> .
% 299.99/300.63  226660[21:MRR:226635.1,13039.0] || subclass(rest_relation,rest_of(least(element_relation,omega)))* -> .
% 299.99/300.63  226659[21:MRR:226632.1,13039.0] || subclass(rest_relation,rest_of(regular(symmetrization_of(identity_relation))))* -> .
% 299.99/300.63  226658[21:MRR:226629.1,13039.0] || subclass(rest_relation,rest_of(sum_class(range_of(identity_relation))))* -> .
% 299.99/300.63  13238[7:Rew:13036.0,10907.1] || subclass(omega,recursion_equation_functions(u))*+ -> equal(integer_of(v),identity_relation) subclass(v,cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.63  226656[21:MRR:226631.1,13039.0] || subclass(rest_relation,rest_of(singleton(u)))* -> .
% 299.99/300.63  226657[21:MRR:226646.1,13039.0] || subclass(rest_relation,rest_of(range_of(identity_relation)))* -> .
% 299.99/300.63  226655[21:MRR:226630.1,13039.0] || subclass(rest_relation,rest_of(omega))* -> .
% 299.99/300.63  226654[8:MRR:226622.1,13039.0] || subclass(rest_relation,rest_of(identity_relation))* -> .
% 299.99/300.63  17402[8:Res:13248.1,14679.1] || member(regular(intersection(inverse(subset_relation),u)),subset_relation)* -> equal(intersection(inverse(subset_relation),u),identity_relation).
% 299.99/300.63  216284[8:MRR:216250.0,13126.0] || subclass(rest_relation,rest_of(u)) subclass(cantor(u),identity_relation)* -> .
% 299.99/300.63  17273[8:Res:13210.1,14679.1] || member(regular(intersection(u,inverse(subset_relation))),subset_relation)* -> equal(intersection(u,inverse(subset_relation)),identity_relation).
% 299.99/300.63  222299[14:Res:165168.1,222208.0] || equal(sum_class(u),singleton(identity_relation))**+ subclass(element_relation,identity_relation)* -> .
% 299.99/300.63  222298[18:Res:190442.1,222208.0] || equal(sum_class(u),symmetrization_of(identity_relation))*+ subclass(element_relation,identity_relation)* -> .
% 299.99/300.63  222297[18:Res:190593.1,222208.0] || equal(sum_class(u),inverse(identity_relation))**+ subclass(element_relation,identity_relation)* -> .
% 299.99/300.63  222295[8:Res:216591.1,222208.0] || equal(complement(sum_class(u)),identity_relation)** subclass(element_relation,identity_relation) -> .
% 299.99/300.63  69170[8:Res:13072.1,66086.1] || member(regular(complement(compose(element_relation,ordinal_numbers))),element_relation)* -> equal(complement(compose(element_relation,ordinal_numbers)),identity_relation).
% 299.99/300.63  220375[8:Res:133837.1,219117.0] || well_ordering(ordinal_numbers,complement(subset_relation))*+ subclass(singleton(u),identity_relation)* -> .
% 299.99/300.63  220260[8:Res:133837.1,218156.0] || well_ordering(ordinal_numbers,complement(subset_relation))*+ equal(singleton(u),identity_relation)** -> .
% 299.99/300.63  219101[8:Res:18819.1,219073.1] || member(u,subset_relation)* subclass(cross_product(ordinal_numbers,ordinal_numbers),identity_relation)*+ -> .
% 299.99/300.63  219100[8:Res:69184.1,219073.1] || member(u,element_relation)* subclass(compose(element_relation,ordinal_numbers),identity_relation)*+ -> .
% 299.99/300.63  13258[7:Rew:13036.0,4669.0] ||  -> equal(restrict(u,v,w),identity_relation) member(regular(restrict(u,v,w)),u)*.
% 299.99/300.63  226369[21:Res:226329.1,133836.0] || subclass(rest_relation,domain_relation) well_ordering(ordinal_numbers,rest_relation)* -> .
% 299.99/300.63  226329[21:SpR:963.0,218966.1] || subclass(rest_relation,domain_relation) -> member(singleton(singleton(singleton(identity_relation))),rest_relation)*.
% 299.99/300.63  226327[25:SpR:208820.0,218966.1] || subclass(rest_relation,domain_relation) -> member(ordered_pair(identity_relation,identity_relation),rest_relation)*.
% 299.99/300.63  218966[21:MRR:218912.1,8655.0] || subclass(rest_relation,domain_relation) -> member(ordered_pair(singleton(u),identity_relation),rest_relation)*.
% 299.99/300.63  19860[5:SpR:916.0,8649.0] ||  -> equal(range_of(restrict(cross_product(u,ordinal_numbers),v,w)),image(cross_product(v,w),u))**.
% 299.99/300.63  217800[8:Res:216691.1,94701.0] || equal(complement(complement(complement(subset_relation))),identity_relation)**+ -> member(u,ordinal_numbers)*.
% 299.99/300.63  217771[8:Res:216691.1,50065.0] || equal(complement(inverse(subset_relation)),identity_relation)**+ member(u,subset_relation)* -> .
% 299.99/300.63  217720[8:Res:216691.1,39269.1] || equal(complement(complement(rest_relation)),identity_relation)**+ member(u,ordinal_numbers)* -> .
% 299.99/300.63  217718[8:Res:216691.1,127140.0] || equal(complement(complement(unordered_pair(least(element_relation,omega),u))),identity_relation)** -> .
% 299.99/300.63  17322[7:Res:13227.2,25.0] || subclass(u,intersection(v,w))* -> equal(u,identity_relation) member(regular(u),v).
% 299.99/300.64  217714[8:Res:216691.1,127141.0] || equal(complement(complement(unordered_pair(u,least(element_relation,omega)))),identity_relation)** -> .
% 299.99/300.64  226089[25:Res:9632.1,224596.1] || equal(complement(complement(union_of_range_map)),ordinal_numbers)** subclass(element_relation,identity_relation) -> .
% 299.99/300.64  225905[26:Res:225794.1,56411.0] || equal(rest_of(identity_relation),omega) subclass(ordinal_numbers,complement(element_relation))* -> .
% 299.99/300.64  224773[26:Res:224684.1,56411.0] || subclass(omega,rest_of(identity_relation))* subclass(ordinal_numbers,complement(element_relation)) -> .
% 299.99/300.64  17321[7:Res:13227.2,26.0] || subclass(u,intersection(v,w))* -> equal(u,identity_relation) member(regular(u),w).
% 299.99/300.64  224651[21:Res:10.1,223663.1] || equal(flip(subset_relation),domain_relation) equal(inverse(subset_relation),domain_relation)** -> .
% 299.99/300.64  226091[25:Res:133837.1,224596.1] || well_ordering(ordinal_numbers,complement(union_of_range_map))* subclass(element_relation,identity_relation) -> .
% 299.99/300.64  226087[25:Res:215662.1,224596.1] || subclass(complement(union_of_range_map),identity_relation)* subclass(element_relation,identity_relation) -> .
% 299.99/300.64  224596[25:MRR:224595.2,162904.0] || subclass(element_relation,identity_relation) member(singleton(singleton(identity_relation)),union_of_range_map)* -> .
% 299.99/300.64  13578[7:Rew:13036.0,13033.0] ||  -> equal(symmetric_difference(u,v),identity_relation) member(regular(symmetric_difference(u,v)),union(u,v))*.
% 299.99/300.64  224558[10:MRR:224535.1,13039.0] || subclass(element_relation,identity_relation) member(cross_product(ordinal_numbers,ordinal_numbers),subset_relation)* -> .
% 299.99/300.64  224360[21:MRR:224350.1,13039.0] || subclass(domain_relation,union_of_range_map) -> section(element_relation,range_of(singleton(identity_relation)),ordinal_numbers)*.
% 299.99/300.64  225765[26:Res:10.1,224747.0] || equal(intersection(u,v),omega)** -> member(identity_relation,u).
% 299.99/300.64  225794[26:SpL:140603.0,225707.0] || equal(u,omega) -> member(identity_relation,u)*.
% 299.99/300.64  19020[0:Res:313.1,152.0] ||  -> subclass(intersection(recursion_equation_functions(u),v),w) function(not_subclass_element(intersection(recursion_equation_functions(u),v),w))*.
% 299.99/300.64  225707[26:Res:10.1,224746.0] || equal(intersection(u,v),omega)** -> member(identity_relation,v).
% 299.99/300.64  224747[26:Res:224684.1,25.0] || subclass(omega,intersection(u,v))* -> member(identity_relation,u).
% 299.99/300.64  224746[26:Res:224684.1,26.0] || subclass(omega,intersection(u,v))* -> member(identity_relation,v).
% 299.99/300.64  18901[0:Res:303.1,152.0] ||  -> subclass(intersection(u,recursion_equation_functions(v)),w) function(not_subclass_element(intersection(u,recursion_equation_functions(v)),w))*.
% 299.99/300.64  225289[26:Res:10.1,224737.0] || equal(complement(complement(u)),omega)** -> member(identity_relation,u).
% 299.99/300.64  225548[20:Res:10.1,225457.0] || equal(complement(complement(symmetrization_of(identity_relation))),complement(inverse(identity_relation)))** -> .
% 299.99/300.64  225546[20:Res:210572.1,225457.0] || equal(complement(complement(complement(symmetrization_of(identity_relation)))),ordinal_numbers)** -> .
% 299.99/300.64  225457[20:MRR:225443.1,217807.0] || subclass(complement(complement(symmetrization_of(identity_relation))),complement(inverse(identity_relation)))* -> .
% 299.99/300.64  18651[0:SpR:43.0,3767.1] operation(inverse(u)) ||  -> equal(intersection(range_of(u),v),intersection(v,range_of(u)))*.
% 299.99/300.64  225445[7:Obv:225427.1] || subclass(u,complement(u))* -> equal(u,identity_relation).
% 299.99/300.64  225382[26:MRR:225339.0,13126.0] || equal(complement(unordered_pair(u,identity_relation)),omega)** -> .
% 299.99/300.64  225381[26:MRR:225338.0,13126.0] || equal(complement(unordered_pair(identity_relation,u)),omega)** -> .
% 299.99/300.64  225377[26:Res:208830.0,225263.1] || equal(complement(ordered_pair(ordinal_numbers,u)),omega)** -> .
% 299.99/300.64  17312[7:Res:13227.2,28.1] || subclass(u,complement(v)) member(regular(u),v)* -> equal(u,identity_relation).
% 299.99/300.64  225263[26:Res:10.1,224734.0] || equal(complement(u),omega) member(identity_relation,u)* -> .
% 299.99/300.64  225038[26:SpL:116239.0,224910.1] operation(inverse(u)) || equal(range_of(u),omega)** -> .
% 299.99/300.64  225006[26:SpL:116239.0,224842.1] operation(inverse(u)) || subclass(omega,range_of(u))* -> .
% 299.99/300.64  225299[26:Res:10.1,225293.0] || equal(complement(symmetrization_of(identity_relation)),omega)** -> .
% 299.99/300.64  13414[7:Rew:13036.0,10956.1] || subclass(omega,u) -> equal(integer_of(not_subclass_element(v,u)),identity_relation)** subclass(v,u).
% 299.99/300.64  225293[26:MRR:225272.1,194308.0] || subclass(omega,complement(symmetrization_of(identity_relation)))* -> .
% 299.99/300.64  224737[26:Res:224684.1,151988.0] || subclass(omega,complement(complement(u)))* -> member(identity_relation,u).
% 299.99/300.64  224734[26:Res:224684.1,28.1] || subclass(omega,complement(u))* member(identity_relation,u) -> .
% 299.99/300.64  225144[26:Res:10.1,224803.0] || equal(sum_class(u),omega)**+ subclass(element_relation,identity_relation)* -> .
% 299.99/300.64  17399[7:Res:13248.1,3700.0] ||  -> equal(intersection(singleton(u),v),identity_relation) equal(regular(intersection(singleton(u),v)),u)**.
% 299.99/300.64  224803[26:Res:224684.1,222208.0] || subclass(omega,sum_class(u))* subclass(element_relation,identity_relation) -> .
% 299.99/300.64  225130[26:Res:10.1,224772.0] || equal(rest_of(identity_relation),omega) subclass(element_relation,identity_relation)* -> .
% 299.99/300.64  224772[26:Res:224684.1,219203.0] || subclass(omega,rest_of(identity_relation))* subclass(element_relation,identity_relation) -> .
% 299.99/300.64  224978[26:Res:10.1,224766.0] || equal(singleton(u),omega)** -> equal(identity_relation,u).
% 299.99/300.64  13570[7:Rew:13036.0,13017.0] ||  -> equal(intersection(u,singleton(v)),identity_relation) equal(regular(intersection(u,singleton(v))),v)**.
% 299.99/300.64  224910[26:SpL:117380.1,224845.0] operation(u) || equal(cantor(u),omega)** -> .
% 299.99/300.64  225014[26:Res:55.1,224842.1] inductive(cantor(u)) operation(u) ||  -> .
% 299.99/300.64  224842[26:SpL:117380.1,224808.0] operation(u) || subclass(omega,cantor(u))* -> .
% 299.99/300.64  224766[26:Res:224684.1,3700.0] || subclass(omega,singleton(u))* -> equal(identity_relation,u).
% 299.99/300.64  13341[7:Rew:13036.0,10913.1] || subclass(omega,intersection(u,v))*+ -> equal(integer_of(w),identity_relation) member(w,v)*.
% 299.99/300.64  224682[26:MRR:195424.1,224681.0] inductive(successor(identity_relation)) ||  -> equal(singleton(identity_relation),omega)**.
% 299.99/300.64  224845[26:Res:10.1,224808.0] || equal(cross_product(u,v),omega)** -> .
% 299.99/300.64  224906[26:SoR:224847.0,75.1] one_to_one(omega) ||  -> .
% 299.99/300.64  224847[26:Res:8665.1,224808.0] function(omega) ||  -> .
% 299.99/300.64  13340[7:Rew:13036.0,10914.1] || subclass(omega,intersection(u,v))*+ -> equal(integer_of(w),identity_relation) member(w,u)*.
% 299.99/300.64  224808[26:MRR:224768.1,162891.0] || subclass(omega,cross_product(u,v))* -> .
% 299.99/300.64  224836[26:Res:10.1,224799.0] || equal(complement(inverse(identity_relation)),omega)** -> .
% 299.99/300.64  224821[26:Res:10.1,224798.0] || equal(complement(singleton(identity_relation)),omega)** -> .
% 299.99/300.64  224799[26:Res:224684.1,194308.0] || subclass(omega,complement(inverse(identity_relation)))* -> .
% 299.99/300.64  224798[26:Res:224684.1,165946.0] || subclass(omega,complement(singleton(identity_relation)))* -> .
% 299.99/300.64  224815[26:Res:10.1,224797.0] || equal(subset_relation,omega)** -> .
% 299.99/300.64  224797[26:Res:224684.1,60934.0] || subclass(omega,subset_relation)* -> .
% 299.99/300.64  224684[26:MRR:224668.1,13040.0] || subclass(omega,u) -> member(identity_relation,u)*.
% 299.99/300.64  194371[21:MRR:194363.2,14676.0] || member(ordered_pair(u,v),cross_product(ordinal_numbers,ordinal_numbers))* member(v,cantor(u)) -> .
% 299.99/300.64  224699[26:Res:224681.0,165357.1] || equal(complement(omega),singleton(identity_relation))** -> .
% 299.99/300.64  224698[26:Res:224681.0,190532.1] || equal(symmetrization_of(identity_relation),complement(omega))** -> .
% 299.99/300.64  224697[26:Res:224681.0,190641.1] || equal(complement(omega),inverse(identity_relation))** -> .
% 299.99/300.64  224681[26:MRR:224665.0,13040.0] ||  -> member(identity_relation,omega)*.
% 299.99/300.64  18700[7:Res:13237.2,152.0] || well_ordering(u,ordinal_numbers) -> equal(recursion_equation_functions(v),identity_relation) function(least(u,recursion_equation_functions(v)))*.
% 299.99/300.64  224659[26:Spt:224308.1] ||  -> equal(regular(omega),identity_relation)**.
% 299.99/300.64  223946[18:SoR:220967.0,82.1] operation(inverse(identity_relation)) || subclass(cross_product(ordinal_numbers,ordinal_numbers),identity_relation)* -> .
% 299.99/300.64  223944[18:SoR:220967.0,75.1] one_to_one(inverse(identity_relation)) || subclass(cross_product(ordinal_numbers,ordinal_numbers),identity_relation)* -> .
% 299.99/300.64  223698[18:SoR:220956.0,82.1] operation(symmetrization_of(identity_relation)) || subclass(cross_product(ordinal_numbers,ordinal_numbers),identity_relation)* -> .
% 299.99/300.64  19526[5:Res:10.1,9649.0] || equal(u,ordinal_numbers)+ well_ordering(v,u)* -> member(least(v,ordinal_numbers),ordinal_numbers)*.
% 299.99/300.64  223696[18:SoR:220956.0,75.1] one_to_one(symmetrization_of(identity_relation)) || subclass(cross_product(ordinal_numbers,ordinal_numbers),identity_relation)* -> .
% 299.99/300.64  223669[21:Res:10.1,220583.1] || equal(inverse(subset_relation),domain_relation) subclass(domain_relation,rotate(subset_relation))* -> .
% 299.99/300.64  223666[21:Res:10.1,220582.1] || equal(inverse(subset_relation),rest_relation) subclass(domain_relation,rotate(subset_relation))* -> .
% 299.99/300.64  223663[21:Res:10.1,220475.1] || equal(inverse(subset_relation),domain_relation) subclass(domain_relation,flip(subset_relation))* -> .
% 299.99/300.64  66832[7:Res:13227.2,161.0] || subclass(u,omega) -> equal(u,identity_relation) equal(integer_of(regular(u)),regular(u))**.
% 299.99/300.64  223660[10:Res:18517.1,219169.0] || subclass(element_relation,identity_relation) -> equal(singleton(cross_product(ordinal_numbers,ordinal_numbers)),identity_relation)**.
% 299.99/300.64  223659[10:Res:66492.1,219169.0] || subclass(element_relation,identity_relation) -> equal(integer_of(cross_product(ordinal_numbers,ordinal_numbers)),identity_relation)**.
% 299.99/300.64  223576[21:Res:216691.1,223568.1] || equal(complement(complement(rest_relation)),identity_relation)** subclass(rest_relation,domain_relation) -> .
% 299.99/300.64  223013[21:Res:196904.1,974.0] || subclass(domain_relation,union_of_range_map) -> equal(sum_class(range_of(singleton(identity_relation))),identity_relation)**.
% 299.99/300.64  18750[8:Res:13072.1,14681.0] || member(regular(regular(u)),u)* -> equal(regular(u),identity_relation) equal(u,identity_relation).
% 299.99/300.64  224276[16:MRR:224269.1,162891.0] || equal(rest_relation,successor_relation)** -> .
% 299.99/300.64  160992[8:Rew:140613.0,66166.0] ||  -> equal(complement(intersection(union(u,identity_relation),complement(v))),union(symmetric_difference(ordinal_numbers,u),v))**.
% 299.99/300.64  60870[7:Res:13056.1,490.0] inductive(intersection(complement(u),complement(v))) || member(identity_relation,union(u,v))* -> .
% 299.99/300.64  13242[7:Rew:13036.0,10906.2] || subclass(omega,complement(u))*+ member(v,u)* -> equal(integer_of(v),identity_relation).
% 299.99/300.64  223943[18:SoR:220967.0,76.1] one_to_one(identity_relation) || subclass(cross_product(ordinal_numbers,ordinal_numbers),identity_relation)* -> .
% 299.99/300.64  220967[18:Res:8665.1,219270.0] function(inverse(identity_relation)) || subclass(cross_product(ordinal_numbers,ordinal_numbers),identity_relation)* -> .
% 299.99/300.64  160927[8:Rew:140613.0,66157.0] ||  -> equal(complement(intersection(complement(u),union(v,identity_relation))),union(u,symmetric_difference(ordinal_numbers,v)))**.
% 299.99/300.64  220956[18:Res:8665.1,219269.0] function(symmetrization_of(identity_relation)) || subclass(cross_product(ordinal_numbers,ordinal_numbers),identity_relation)* -> .
% 299.99/300.64  220750[14:Res:165168.1,219203.0] || equal(rest_of(identity_relation),singleton(identity_relation)) subclass(element_relation,identity_relation)* -> .
% 299.99/300.64  220749[18:Res:190442.1,219203.0] || equal(rest_of(identity_relation),symmetrization_of(identity_relation)) subclass(element_relation,identity_relation)* -> .
% 299.99/300.64  220748[18:Res:190593.1,219203.0] || equal(rest_of(identity_relation),inverse(identity_relation)) subclass(element_relation,identity_relation)* -> .
% 299.99/300.64  13413[7:Rew:13036.0,10935.1] || subclass(omega,element_relation) -> equal(integer_of(ordered_pair(u,v)),identity_relation)** member(u,v).
% 299.99/300.64  220583[21:Res:196657.1,116738.1] || subclass(domain_relation,rotate(subset_relation)) subclass(domain_relation,inverse(subset_relation))* -> .
% 299.99/300.64  220582[21:Res:196657.1,28976.1] || subclass(domain_relation,rotate(subset_relation)) subclass(rest_relation,inverse(subset_relation))* -> .
% 299.99/300.64  220475[21:Res:196656.1,196905.1] || subclass(domain_relation,flip(subset_relation)) subclass(domain_relation,inverse(subset_relation))* -> .
% 299.99/300.64  219169[10:Res:76912.1,219073.1] || member(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers)* subclass(element_relation,identity_relation) -> .
% 299.99/300.64  223568[21:Res:218825.1,8841.1] || subclass(rest_relation,domain_relation) subclass(ordinal_numbers,complement(rest_relation))* -> .
% 299.99/300.64  223570[21:MRR:223559.0,130876.2] || subclass(rest_relation,u) well_ordering(ordinal_numbers,u)* -> .
% 299.99/300.64  218825[21:MRR:218777.1,165460.0] || subclass(rest_relation,domain_relation) -> member(ordered_pair(range_of(identity_relation),identity_relation),rest_relation)*.
% 299.99/300.64  218592[21:Res:125724.0,196455.0] || subclass(rest_relation,domain_relation) -> equal(rest_of(least(element_relation,omega)),identity_relation)**.
% 299.99/300.64  19485[0:SpR:47.0,481.0] ||  -> equal(power_class(intersection(complement(u),complement(singleton(u)))),complement(image(element_relation,successor(u))))**.
% 299.99/300.64  218571[21:Res:190509.0,196455.0] || subclass(rest_relation,domain_relation) -> equal(rest_of(regular(symmetrization_of(identity_relation))),identity_relation)**.
% 299.99/300.64  218563[21:Res:165431.0,196455.0] || subclass(rest_relation,domain_relation) -> equal(rest_of(sum_class(range_of(identity_relation))),identity_relation)**.
% 299.99/300.64  218416[21:Res:125724.0,196454.0] || subclass(domain_relation,rest_relation) -> equal(rest_of(least(element_relation,omega)),identity_relation)**.
% 299.99/300.64  218395[21:Res:190509.0,196454.0] || subclass(domain_relation,rest_relation) -> equal(rest_of(regular(symmetrization_of(identity_relation))),identity_relation)**.
% 299.99/300.64  19486[0:SpR:117.0,481.0] ||  -> equal(power_class(intersection(complement(u),complement(inverse(u)))),complement(image(element_relation,symmetrization_of(u))))**.
% 299.99/300.64  13306[7:Rew:13036.0,8606.1] || member(regular(power_class(u)),image(element_relation,complement(u)))* -> equal(power_class(u),identity_relation).
% 299.99/300.64  974[0:SpL:963.0,157.0] || member(singleton(singleton(singleton(u))),union_of_range_map)* -> equal(sum_class(range_of(singleton(u))),u).
% 299.99/300.64  196425[21:Rew:196372.1,160882.2] || member(u,ordinal_numbers) subclass(domain_relation,recursion_equation_functions(v))*+ -> function(ordered_pair(u,identity_relation))*.
% 299.99/300.64  17327[8:Res:13227.2,14679.1] || subclass(u,inverse(subset_relation)) member(regular(u),subset_relation)* -> equal(u,identity_relation).
% 299.99/300.64  222760[16:Rew:195224.0,222696.1] || subclass(rest_relation,successor_relation)* -> equal(rest_of(identity_relation),singleton(identity_relation)).
% 299.99/300.64  222685[5:Res:8652.0,31610.0] || subclass(rest_relation,successor_relation)* -> equal(rest_of(omega),successor(omega)).
% 299.99/300.64  31610[5:Res:8827.2,49.0] || member(u,ordinal_numbers)* subclass(rest_relation,successor_relation) -> equal(rest_of(u),successor(u)).
% 299.99/300.64  218387[21:Res:165431.0,196454.0] || subclass(domain_relation,rest_relation) -> equal(rest_of(sum_class(range_of(identity_relation))),identity_relation)**.
% 299.99/300.64  217824[8:MRR:83289.0,217734.0] ||  -> equal(integer_of(regular(complement(complement(omega)))),regular(complement(complement(omega))))**.
% 299.99/300.64  217770[8:Res:216691.1,148908.0] || equal(complement(inverse(subset_relation)),identity_relation)** -> equal(complement(subset_relation),ordinal_numbers).
% 299.99/300.64  217769[8:Res:216691.1,148916.0] || equal(complement(inverse(subset_relation)),identity_relation)** subclass(domain_relation,subset_relation) -> .
% 299.99/300.64  196460[21:Rew:196372.1,192726.2] || member(u,ordinal_numbers) subclass(domain_relation,union_of_range_map) -> equal(sum_class(range_of(u)),identity_relation)**.
% 299.99/300.64  217765[8:Res:216691.1,67737.1] || equal(complement(first(subset_relation)),identity_relation)** member(subset_relation,subset_relation) -> .
% 299.99/300.64  217719[8:Res:216691.1,62611.1] || equal(complement(complement(rest_relation)),identity_relation)** equal(rest_relation,domain_relation) -> .
% 299.99/300.64  69474[8:Res:13125.2,14679.1] || subclass(omega,inverse(subset_relation))*+ member(u,subset_relation)* -> equal(integer_of(u),identity_relation).
% 299.99/300.64  217645[8:Res:216611.1,163154.0] || equal(complement(symmetrization_of(identity_relation)),identity_relation) -> member(omega,inverse(identity_relation))*.
% 299.99/300.64  216703[8:SpR:216188.1,162584.0] || equal(complement(inverse(identity_relation)),identity_relation)** -> equal(symmetrization_of(identity_relation),ordinal_numbers).
% 299.99/300.64  216229[16:SpL:195257.0,216213.0] || equal(image(element_relation,singleton(identity_relation)),power_class(complement(singleton(identity_relation))))** -> .
% 299.99/300.64  216228[8:SpL:162038.0,216213.0] || equal(image(element_relation,symmetrization_of(identity_relation)),power_class(complement(inverse(identity_relation))))** -> .
% 299.99/300.64  167533[8:SoR:162898.0,75.1] one_to_one(image(successor_relation,cross_product(universal_class,universal_class))) || member(identity_relation,cross_product(ordinal_numbers,ordinal_numbers))* -> .
% 299.99/300.64  215603[8:SpR:162584.0,215487.1] || subclass(complement(inverse(identity_relation)),identity_relation)* -> subclass(ordinal_numbers,symmetrization_of(identity_relation)).
% 299.99/300.64  222493[8:Obv:222492.1] || subclass(inverse(u),identity_relation)*+ -> asymmetric(u,v)*.
% 299.99/300.64  219152[8:Res:13210.1,219073.1] || subclass(u,identity_relation) -> equal(intersection(v,u),identity_relation)**.
% 299.99/300.64  222300[8:Res:13049.1,222208.0] || subclass(ordinal_numbers,sum_class(u))* subclass(element_relation,identity_relation) -> .
% 299.99/300.64  167535[8:SoR:162898.0,82.1] operation(image(successor_relation,cross_product(universal_class,universal_class))) || member(identity_relation,cross_product(ordinal_numbers,ordinal_numbers))* -> .
% 299.99/300.64  222296[8:Res:192149.1,222208.0] || equal(sum_class(u),ordinal_numbers)**+ subclass(element_relation,identity_relation)* -> .
% 299.99/300.64  222301[8:Res:13056.1,222208.0] inductive(sum_class(u)) || subclass(element_relation,identity_relation)* -> .
% 299.99/300.64  222208[8:Rew:222073.1,220820.0] || member(identity_relation,sum_class(u))* subclass(element_relation,identity_relation) -> .
% 299.99/300.64  222237[8:Obv:222236.1] || subclass(u,identity_relation)*+ -> asymmetric(u,v)*.
% 299.99/300.64  167601[8:SoR:162899.0,75.1] one_to_one(image(successor_relation,cross_product(ordinal_numbers,ordinal_numbers))) || member(identity_relation,cross_product(ordinal_numbers,ordinal_numbers))* -> .
% 299.99/300.64  219120[8:Res:13248.1,219073.1] || subclass(u,identity_relation) -> equal(intersection(u,v),identity_relation)**.
% 299.99/300.64  218191[8:Res:13210.1,217144.1] || equal(identity_relation,u) -> equal(intersection(v,u),identity_relation)**.
% 299.99/300.64  221824[8:Obv:221823.1] || equal(identity_relation,u) -> asymmetric(u,v)*.
% 299.99/300.64  218159[8:Res:13248.1,217144.1] || equal(identity_relation,u) -> equal(intersection(u,v),identity_relation)**.
% 299.99/300.64  167603[8:SoR:162899.0,82.1] operation(image(successor_relation,cross_product(ordinal_numbers,ordinal_numbers))) || member(identity_relation,cross_product(ordinal_numbers,ordinal_numbers))* -> .
% 299.99/300.64  217199[8:Obv:216894.1] || equal(complement(symmetrization_of(u)),identity_relation)**+ -> connected(u,v)*.
% 299.99/300.64  217198[8:MRR:216862.1,295.0] || equal(complement(u),identity_relation) -> member(singleton(v),u)*.
% 299.99/300.64  221330[8:Res:215662.1,133836.0] || subclass(complement(u),identity_relation)* well_ordering(ordinal_numbers,u) -> .
% 299.99/300.64  39609[2:Res:295.0,9665.1] inductive(u) || well_ordering(v,u) -> member(least(v,u),u)*.
% 299.99/300.64  221347[8:Res:215662.1,60940.0] || subclass(complement(subset_relation),identity_relation)* -> .
% 299.99/300.64  221342[25:Res:215662.1,209339.0] || subclass(complement(successor_relation),identity_relation)* -> .
% 299.99/300.64  221341[25:Res:215662.1,208996.0] || subclass(complement(rest_relation),identity_relation)* -> .
% 299.99/300.64  221340[25:Res:215662.1,208980.0] || subclass(complement(domain_relation),identity_relation)* -> .
% 299.99/300.64  39815[5:Res:8638.0,9661.0] || well_ordering(u,ordinal_numbers)+ -> subclass(v,w)* member(least(u,v),v)*.
% 299.99/300.64  215662[8:Res:215487.1,9496.0] || subclass(complement(u),identity_relation) -> member(singleton(v),u)*.
% 299.99/300.64  221083[21:Res:10.1,220542.0] || equal(rotate(u),domain_relation)** equal(identity_relation,u) -> .
% 299.99/300.64  221080[21:Res:10.1,220541.0] || equal(rotate(u),domain_relation) subclass(u,identity_relation)* -> .
% 299.99/300.64  13236[7:Rew:13036.0,9536.1] || well_ordering(u,v) -> equal(v,identity_relation) member(least(u,v),v)*.
% 299.99/300.64  221044[21:Res:10.1,220440.0] || equal(flip(u),domain_relation)** equal(identity_relation,u) -> .
% 299.99/300.64  221041[21:Res:10.1,220439.0] || equal(flip(u),domain_relation) subclass(u,identity_relation)* -> .
% 299.99/300.64  220542[21:Res:196657.1,217144.1] || subclass(domain_relation,rotate(u))* equal(identity_relation,u) -> .
% 299.99/300.64  220541[21:Res:196657.1,219073.1] || subclass(domain_relation,rotate(u))* subclass(u,identity_relation) -> .
% 299.99/300.64  13319[7:Rew:13036.0,9502.1] || well_ordering(u,v) -> equal(segment(u,v,least(u,v)),identity_relation)**.
% 299.99/300.64  220440[21:Res:196656.1,217144.1] || subclass(domain_relation,flip(u))* equal(identity_relation,u) -> .
% 299.99/300.64  220439[21:Res:196656.1,219073.1] || subclass(domain_relation,flip(u))* subclass(u,identity_relation) -> .
% 299.99/300.64  219933[8:Res:60996.1,217200.1] || equal(singleton(regular(u)),identity_relation)** -> equal(u,identity_relation).
% 299.99/300.64  219919[8:Res:66492.1,217200.1] || equal(singleton(u),identity_relation) -> equal(integer_of(u),identity_relation)**.
% 299.99/300.64  19115[0:Res:2503.2,152.0] || subclass(u,recursion_equation_functions(v))*+ -> subclass(u,w) function(not_subclass_element(u,w))*.
% 299.99/300.64  219270[18:Res:190510.1,219073.1] || subclass(inverse(identity_relation),u)* subclass(u,identity_relation) -> .
% 299.99/300.64  219269[18:Res:194549.1,219073.1] || subclass(symmetrization_of(identity_relation),u)* subclass(u,identity_relation) -> .
% 299.99/300.64  219206[8:Res:117318.1,219073.1] || member(u,cantor(u))* subclass(element_relation,identity_relation) -> .
% 299.99/300.64  220752[8:Res:13056.1,219203.0] inductive(rest_of(identity_relation)) || subclass(element_relation,identity_relation)* -> .
% 299.99/300.64  39607[5:Res:8638.0,9665.1] inductive(u) || well_ordering(v,ordinal_numbers) -> member(least(v,u),u)*.
% 299.99/300.64  219203[8:Res:41112.1,219073.1] || member(u,rest_of(u))* subclass(element_relation,identity_relation) -> .
% 299.99/300.64  220374[8:Res:49995.1,219117.0] || member(subset_relation,subset_relation) subclass(first(subset_relation),identity_relation)* -> .
% 299.99/300.64  220617[21:Res:10.1,220587.0] || equal(rotate(domain_relation),domain_relation)**+ -> equal(identity_relation,u)*.
% 299.99/300.64  17324[7:Res:13227.2,3700.0] || subclass(u,singleton(v))* -> equal(u,identity_relation) equal(regular(u),v).
% 299.99/300.64  220641[25:Res:220596.1,208963.0] || equal(rotate(subset_relation),domain_relation)** -> .
% 299.99/300.64  220587[21:Rew:196550.0,220579.1] || subclass(domain_relation,rotate(domain_relation))*+ -> equal(identity_relation,u)*.
% 299.99/300.64  220585[25:Res:196657.1,214614.1] operation(u) || subclass(domain_relation,rotate(subset_relation))* -> .
% 299.99/300.64  220581[25:Res:196657.1,214618.1] operation(u) || subclass(domain_relation,rotate(rest_relation))* -> .
% 299.99/300.64  220554[21:Res:196657.1,18842.0] || subclass(domain_relation,rotate(subset_relation))*+ -> member(u,ordinal_numbers)*.
% 299.99/300.64  220593[21:Res:10.1,220537.0] || equal(rotate(identity_relation),domain_relation)** -> .
% 299.99/300.64  220537[21:Res:196657.1,14676.0] || subclass(domain_relation,rotate(identity_relation))* -> .
% 299.99/300.64  196657[21:Rew:196550.0,161030.1] || subclass(domain_relation,rotate(u)) -> member(ordered_pair(ordered_pair(v,identity_relation),w),u)*.
% 299.99/300.64  220485[21:Res:10.1,220477.0] || equal(flip(element_relation),domain_relation)** -> .
% 299.99/300.64  220482[21:Res:10.1,220435.0] || equal(flip(identity_relation),domain_relation)** -> .
% 299.99/300.64  220477[21:MRR:220449.1,14676.0] || subclass(domain_relation,flip(element_relation))* -> .
% 299.99/300.64  220435[21:Res:196656.1,14676.0] || subclass(domain_relation,flip(identity_relation))* -> .
% 299.99/300.64  196656[21:Rew:196550.0,161031.1] || subclass(domain_relation,flip(u)) -> member(ordered_pair(ordered_pair(v,w),identity_relation),u)*.
% 299.99/300.64  219117[8:Res:51313.1,219073.1] || member(singleton(u),subset_relation)* subclass(u,identity_relation) -> .
% 299.99/300.64  219097[8:Res:8705.1,219073.1] || member(u,ordinal_numbers) subclass(singleton(u),identity_relation)* -> .
% 299.99/300.64  219058[8:Rew:17351.0,219009.1] || subclass(u,identity_relation) -> equal(union(u,identity_relation),identity_relation)**.
% 299.99/300.64  218308[18:Res:190510.1,217144.1] || subclass(inverse(identity_relation),u)* equal(identity_relation,u) -> .
% 299.99/300.64  13243[7:Rew:13036.0,10916.1] || subclass(omega,singleton(u))*+ -> equal(integer_of(v),identity_relation)** equal(v,u)*.
% 299.99/300.64  218307[18:Res:194549.1,217144.1] || subclass(symmetrization_of(identity_relation),u)* equal(identity_relation,u) -> .
% 299.99/300.64  218292[18:Res:190442.1,217144.1] || equal(u,symmetrization_of(identity_relation))* equal(identity_relation,u) -> .
% 299.99/300.64  218156[8:Res:51313.1,217144.1] || member(singleton(u),subset_relation)* equal(identity_relation,u) -> .
% 299.99/300.64  217710[8:Res:216691.1,9494.0] || equal(complement(complement(unordered_pair(u,singleton(v)))),identity_relation)** -> .
% 299.99/300.64  13568[7:Rew:13036.0,13010.0] ||  -> equal(intersection(u,recursion_equation_functions(v)),identity_relation) function(regular(intersection(u,recursion_equation_functions(v))))*.
% 299.99/300.64  217709[8:Res:216691.1,9495.0] || equal(complement(complement(unordered_pair(singleton(u),v))),identity_relation)** -> .
% 299.99/300.64  217705[8:Res:216691.1,40071.0] || equal(complement(complement(singleton(unordered_pair(u,v)))),identity_relation)** -> .
% 299.99/300.64  217704[8:Res:216691.1,39295.0] || equal(complement(complement(singleton(ordered_pair(u,v)))),identity_relation)** -> .
% 299.99/300.64  17390[7:Res:13248.1,152.0] ||  -> equal(intersection(recursion_equation_functions(u),v),identity_relation) function(regular(intersection(recursion_equation_functions(u),v)))*.
% 299.99/300.64  217492[8:SpL:117380.1,217454.0] operation(u) || equal(complement(cantor(u)),identity_relation)** -> .
% 299.99/300.64  217207[8:Obv:217045.1] || equal(rest_of(u),identity_relation)** -> equal(cantor(u),identity_relation).
% 299.99/300.64  219935[20:Res:217871.0,217200.1] || equal(singleton(regular(complement(complement(symmetrization_of(identity_relation))))),identity_relation)** -> .
% 299.99/300.64  160772[8:Rew:140613.0,66156.0] || member(u,symmetric_difference(ordinal_numbers,v))* member(u,union(v,identity_relation)) -> .
% 299.99/300.64  219934[18:Res:190509.0,217200.1] || equal(singleton(regular(symmetrization_of(identity_relation))),identity_relation)** -> .
% 299.99/300.64  219926[15:Res:165431.0,217200.1] || equal(singleton(sum_class(range_of(identity_relation))),identity_relation)** -> .
% 299.99/300.64  217200[8:Obv:216935.2] || equal(singleton(u),identity_relation) member(u,ordinal_numbers)* -> .
% 299.99/300.64  217197[15:MRR:216859.1,295.0] || equal(complement(u),identity_relation) -> member(range_of(identity_relation),u)*.
% 299.99/300.64  67614[8:MRR:67613.0,41096.1] || member(u,union(v,identity_relation)) -> member(u,symmetric_difference(complement(v),ordinal_numbers))*.
% 299.99/300.64  217196[8:Obv:216857.1] || equal(complement(u),identity_relation) well_ordering(ordinal_numbers,u)* -> .
% 299.99/300.64  217188[14:Obv:216793.2] || equal(identity_relation,u) equal(u,singleton(identity_relation))* -> .
% 299.99/300.64  217187[18:Obv:216792.2] || equal(identity_relation,u) equal(u,inverse(identity_relation))* -> .
% 299.99/300.64  67561[8:SpR:66160.0,3618.1] || member(u,symmetric_difference(complement(v),ordinal_numbers))* -> member(u,union(v,identity_relation)).
% 299.99/300.64  216269[14:Res:165168.1,215631.1] || equal(u,singleton(identity_relation)) subclass(u,identity_relation)* -> .
% 299.99/300.64  216268[18:Res:190442.1,215631.1] || equal(u,symmetrization_of(identity_relation)) subclass(u,identity_relation)* -> .
% 299.99/300.64  216267[18:Res:190593.1,215631.1] || equal(u,inverse(identity_relation)) subclass(u,identity_relation)* -> .
% 299.99/300.64  9461[5:Res:6.1,8788.0] ||  -> subclass(recursion_equation_functions(u),v) subclass(not_subclass_element(recursion_equation_functions(u),v),cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.64  216107[8:SpL:18840.1,216013.0] || member(u,subset_relation)* equal(singleton(u),identity_relation) -> .
% 299.99/300.64  66834[7:MRR:66830.1,13040.0] || well_ordering(u,ordinal_numbers) -> equal(integer_of(least(u,omega)),least(u,omega))**.
% 299.99/300.64  215659[15:Res:215487.1,165530.0] || subclass(complement(u),identity_relation) -> member(range_of(identity_relation),u)*.
% 299.99/300.64  215644[8:Res:215487.1,50044.1] || subclass(singleton(u),identity_relation)* member(u,subset_relation) -> .
% 299.99/300.64  219073[8:MRR:219048.1,41096.1] || subclass(u,identity_relation) member(v,u)* -> .
% 299.99/300.64  66653[8:Res:8646.1,14681.0] || subclass(ordinal_numbers,regular(u))* member(omega,u) -> equal(u,identity_relation).
% 299.99/300.64  215273[8:MRR:215263.2,13055.1] inductive(complement(complement(u))) || subclass(u,identity_relation)* -> .
% 299.99/300.64  218560[21:Res:8655.0,196455.0] || subclass(rest_relation,domain_relation) -> equal(rest_of(singleton(u)),identity_relation)**.
% 299.99/300.64  218384[21:Res:8655.0,196454.0] || subclass(domain_relation,rest_relation) -> equal(rest_of(singleton(u)),identity_relation)**.
% 299.99/300.64  217810[15:Res:216691.1,194978.0] || equal(complement(complement(unordered_pair(range_of(identity_relation),u))),identity_relation)** -> .
% 299.99/300.64  160679[8:Rew:116078.0,13355.2,116078.0,13355.2] operation(u) inductive(range_of(u)) ||  -> member(identity_relation,cantor(cantor(u)))*.
% 299.99/300.64  217808[15:Res:216691.1,194979.0] || equal(complement(complement(unordered_pair(u,range_of(identity_relation)))),identity_relation)** -> .
% 299.99/300.64  218573[21:Res:165460.0,196455.0] || subclass(rest_relation,domain_relation) -> equal(rest_of(range_of(identity_relation)),identity_relation)**.
% 299.99/300.64  218509[21:MRR:218462.1,8652.0] || equal(rest_relation,domain_relation) -> member(ordered_pair(omega,identity_relation),rest_relation)*.
% 299.99/300.64  218397[21:Res:165460.0,196454.0] || subclass(domain_relation,rest_relation) -> equal(rest_of(range_of(identity_relation)),identity_relation)**.
% 299.99/300.64  973[0:SpL:963.0,49.0] || member(singleton(singleton(singleton(u))),successor_relation)* -> equal(successor(singleton(u)),u).
% 299.99/300.64  217888[21:Res:217871.0,197870.1] || equal(rest_of(regular(complement(complement(symmetrization_of(identity_relation))))),rest_relation)** -> .
% 299.99/300.64  217707[8:Res:216691.1,127139.0] || equal(complement(complement(singleton(least(element_relation,omega)))),identity_relation)** -> .
% 299.99/300.64  66645[5:Res:8646.1,288.0] || subclass(ordinal_numbers,image(element_relation,complement(u)))* member(omega,power_class(u)) -> .
% 299.99/300.64  217208[8:Obv:217082.2] || equal(first(subset_relation),identity_relation) member(subset_relation,subset_relation)* -> .
% 299.99/300.64  217162[8:Obv:217035.1] || equal(inverse(u),identity_relation) -> asymmetric(u,v)*.
% 299.99/300.64  218569[21:Res:13126.0,196455.0] || subclass(rest_relation,domain_relation)* -> equal(rest_of(identity_relation),identity_relation).
% 299.99/300.64  218558[21:Res:8652.0,196455.0] || subclass(rest_relation,domain_relation)* -> equal(rest_of(omega),identity_relation).
% 299.99/300.64  196455[21:Rew:196372.1,160728.2] || member(u,ordinal_numbers)* subclass(rest_relation,domain_relation) -> equal(rest_of(u),identity_relation).
% 299.99/300.64  217161[8:Obv:217017.1] || equal(unordered_pair(unordered_pair(u,v),w),identity_relation)** -> .
% 299.99/300.64  217160[8:Obv:217015.1] || equal(unordered_pair(ordered_pair(u,v),w),identity_relation)** -> .
% 299.99/300.64  218460[21:Res:10.1,218382.0] || equal(rest_relation,domain_relation) -> equal(rest_of(omega),identity_relation)**.
% 299.99/300.64  218382[21:Res:8652.0,196454.0] || subclass(domain_relation,rest_relation)* -> equal(rest_of(omega),identity_relation).
% 299.99/300.64  196454[21:Rew:196372.1,160729.2] || member(u,ordinal_numbers)* subclass(domain_relation,rest_relation) -> equal(rest_of(u),identity_relation).
% 299.99/300.64  217156[8:Obv:216982.1] || equal(unordered_pair(u,unordered_pair(v,w)),identity_relation)** -> .
% 299.99/300.64  217155[8:Obv:216978.1] || equal(unordered_pair(u,ordered_pair(v,w)),identity_relation)** -> .
% 299.99/300.64  217144[8:MRR:216847.2,41096.1] || equal(identity_relation,u) member(v,u)* -> .
% 299.99/300.64  215654[8:Res:215487.1,40073.0] || subclass(unordered_pair(unordered_pair(u,v),w),identity_relation)* -> .
% 299.99/300.64  208010[24:MRR:40041.2,207937.1] operation(sum_class(cross_product(ordinal_numbers,ordinal_numbers))) || well_ordering(element_relation,cross_product(ordinal_numbers,ordinal_numbers))* -> .
% 299.99/300.64  215653[8:Res:215487.1,39297.0] || subclass(unordered_pair(ordered_pair(u,v),w),identity_relation)* -> .
% 299.99/300.64  215650[8:Res:215487.1,40072.0] || subclass(unordered_pair(u,unordered_pair(v,w)),identity_relation)* -> .
% 299.99/300.64  215649[8:Res:215487.1,39296.0] || subclass(unordered_pair(u,ordered_pair(v,w)),identity_relation)* -> .
% 299.99/300.64  217708[8:Res:216691.1,9486.0] || equal(complement(complement(ordered_pair(u,v))),identity_relation)** -> .
% 299.99/300.64  194662[9:MRR:194655.2,65891.0] || member(complement(omega),ordinal_numbers) -> equal(integer_of(apply(choice,complement(omega))),identity_relation)**.
% 299.99/300.64  217692[8:Res:216691.1,8954.0] || equal(complement(u),identity_relation)** -> equal(ordinal_numbers,u).
% 299.99/300.64  217139[8:Obv:216796.2] || equal(identity_relation,u) equal(u,domain_relation)* -> .
% 299.99/300.64  217117[11:Rew:17351.0,216652.1,80563.0,216652.1] || equal(identity_relation,u) -> equal(power_class(u),identity_relation)**.
% 299.99/300.64  217811[25:Res:216691.1,208928.0] || equal(complement(complement(unordered_pair(identity_relation,u))),identity_relation)** -> .
% 299.99/300.64  18824[7:Res:13056.1,897.0] inductive(restrict(u,v,w)) ||  -> member(identity_relation,cross_product(v,w))*.
% 299.99/300.64  217809[25:Res:216691.1,208948.0] || equal(complement(complement(unordered_pair(u,identity_relation))),identity_relation)** -> .
% 299.99/300.64  217802[23:Res:216691.1,205620.0] || equal(complement(complement(complement(recursion_equation_functions(u)))),identity_relation)** -> .
% 299.99/300.64  217703[8:Res:216691.1,9493.0] || equal(complement(complement(singleton(singleton(u)))),identity_relation)** -> .
% 299.99/300.64  17315[7:Res:13227.2,152.0] || subclass(u,recursion_equation_functions(v))* -> equal(u,identity_relation) function(regular(u)).
% 299.99/300.64  217890[21:Res:217871.0,196372.0] ||  -> equal(cantor(regular(complement(complement(symmetrization_of(identity_relation))))),identity_relation)**.
% 299.99/300.64  217887[24:Res:217871.0,207853.1] operation(regular(complement(complement(symmetrization_of(identity_relation))))) ||  -> .
% 299.99/300.64  217871[20:Res:217827.0,41096.0] ||  -> member(regular(complement(complement(symmetrization_of(identity_relation)))),ordinal_numbers)*.
% 299.99/300.64  217827[20:MRR:217547.0,217807.0] ||  -> member(regular(complement(complement(symmetrization_of(identity_relation)))),inverse(identity_relation))*.
% 299.99/300.64  18749[8:Res:13056.1,14681.0] inductive(regular(u)) || member(identity_relation,u)* -> equal(u,identity_relation).
% 299.99/300.64  217804[15:Res:216691.1,194976.0] || equal(complement(complement(singleton(range_of(identity_relation)))),identity_relation)** -> .
% 299.99/300.64  217807[20:Res:216691.1,194311.0] || equal(complement(complement(symmetrization_of(identity_relation))),identity_relation)** -> .
% 299.99/300.64  217750[8:Res:216691.1,60039.0] || equal(complement(rest_of(u)),identity_relation)** -> .
% 299.99/300.64  217734[8:Res:216691.1,127127.0] || equal(complement(complement(omega)),identity_relation)** -> .
% 299.99/300.64  13278[7:Rew:13036.0,9783.2] inductive(sum_class(u)) || member(u,ordinal_numbers)* -> member(identity_relation,u)*.
% 299.99/300.64  217702[8:Res:216691.1,60961.0] || equal(complement(complement(domain_relation)),identity_relation)** -> .
% 299.99/300.64  217791[8:Res:216691.1,8752.0] || equal(complement(union_of_range_map),identity_relation)** -> .
% 299.99/300.64  216691[8:SpR:216188.1,130678.0] || equal(complement(u),identity_relation) -> subclass(ordinal_numbers,u)*.
% 299.99/300.64  216611[8:Res:19172.1,215661.0] || equal(complement(u),identity_relation) -> member(omega,u)*.
% 299.99/300.64  13240[7:Rew:13036.0,10908.1] || subclass(omega,recursion_equation_functions(u))*+ -> equal(integer_of(v),identity_relation)** function(v).
% 299.99/300.64  217594[8:Res:210572.1,217592.0] || equal(complement(complement(cross_product(ordinal_numbers,ordinal_numbers))),ordinal_numbers)** -> .
% 299.99/300.64  217596[8:Res:10.1,217592.0] || equal(complement(cross_product(ordinal_numbers,ordinal_numbers)),subset_relation)** -> .
% 299.99/300.64  217592[8:MRR:217591.1,217454.0] || subclass(complement(cross_product(ordinal_numbers,ordinal_numbers)),subset_relation)* -> .
% 299.99/300.64  217456[8:MRR:18852.1,217454.0] || member(regular(complement(cross_product(ordinal_numbers,ordinal_numbers))),subset_relation)* -> .
% 299.99/300.64  61019[7:MRR:13503.0,60996.1] ||  -> member(regular(complement(complement(u))),u)* equal(complement(complement(u)),identity_relation).
% 299.99/300.64  217454[8:MRR:217417.1,162891.0] || equal(complement(cross_product(u,v)),identity_relation)** -> .
% 299.99/300.64  217490[8:SoR:217455.0,82.1] operation(complement(cross_product(ordinal_numbers,ordinal_numbers))) ||  -> .
% 299.99/300.64  217488[8:SoR:217455.0,75.1] one_to_one(complement(cross_product(ordinal_numbers,ordinal_numbers))) ||  -> .
% 299.99/300.64  217455[8:MRR:17353.1,217454.0] function(complement(cross_product(ordinal_numbers,ordinal_numbers))) ||  -> .
% 299.99/300.64  13166[7:Rew:13036.0,9803.2] function(u) inductive(u) ||  -> member(identity_relation,cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.64  216591[8:Res:19172.1,215660.0] || equal(complement(u),identity_relation) -> member(identity_relation,u)*.
% 299.99/300.64  216489[8:Res:19172.1,215637.0] || equal(identity_relation,u) subclass(domain_relation,u)* -> .
% 299.99/300.64  216458[8:Res:19172.1,215636.0] || equal(identity_relation,u) subclass(omega,u)* -> .
% 299.99/300.64  216426[8:Res:19172.1,215635.0] || equal(identity_relation,u) equal(u,omega)* -> .
% 299.99/300.64  18446[7:Res:13056.1,288.0] inductive(image(element_relation,complement(u))) || member(identity_relation,power_class(u))* -> .
% 299.99/300.64  216395[8:Res:19172.1,215634.0] || equal(identity_relation,u) subclass(ordinal_numbers,u)* -> .
% 299.99/300.64  216364[8:Res:19172.1,215633.0] || equal(identity_relation,u)* equal(u,ordinal_numbers) -> .
% 299.99/300.64  216227[8:SpL:59.0,216213.0] || equal(image(element_relation,complement(u)),power_class(u))** -> .
% 299.99/300.64  216223[8:SpL:160491.0,216213.0] || equal(symmetric_difference(ordinal_numbers,u),union(u,identity_relation))** -> .
% 299.99/300.64  13152[7:Rew:13036.0,9463.0] ||  -> equal(recursion_equation_functions(u),identity_relation) subclass(regular(recursion_equation_functions(u)),cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.64  217111[10:MRR:217028.1,8638.0] || equal(compose(element_relation,ordinal_numbers),identity_relation)** -> .
% 299.99/300.64  217095[8:Obv:216901.1] || equal(complement(composition_function),identity_relation)** -> .
% 299.99/300.64  217093[16:MRR:216895.1,8638.0] || equal(complement(successor_relation),identity_relation)** -> .
% 299.99/300.64  217092[25:Obv:216882.1] || equal(complement(domain_relation),identity_relation)** -> .
% 299.99/300.64  13558[7:Rew:13036.0,12941.0] ||  -> equal(integer_of(not_subclass_element(complement(omega),u)),identity_relation)** subclass(complement(omega),u).
% 299.99/300.64  217091[25:Obv:216880.1] || equal(complement(rest_relation),identity_relation)** -> .
% 299.99/300.64  217089[8:Obv:216866.1] || equal(complement(element_relation),identity_relation)** -> .
% 299.99/300.64  216188[8:Res:19172.1,215630.0] || equal(identity_relation,u) -> equal(complement(u),ordinal_numbers)**.
% 299.99/300.64  215665[8:Res:215487.1,94699.0] || subclass(complement(element_relation),identity_relation)*+ -> member(u,v)*.
% 299.99/300.64  196905[21:MRR:196865.0,18843.1] || subclass(domain_relation,inverse(subset_relation)) member(ordered_pair(u,identity_relation),subset_relation)* -> .
% 299.99/300.64  215661[8:Res:215487.1,151970.0] || subclass(complement(u),identity_relation)* -> member(omega,u).
% 299.99/300.64  215660[8:Res:215487.1,163545.0] || subclass(complement(u),identity_relation)* -> member(identity_relation,u).
% 299.99/300.64  216572[8:Res:19172.1,216554.0] || equal(unordered_pair(u,omega),identity_relation)** -> .
% 299.99/300.64  216568[8:Res:19172.1,216553.0] || equal(unordered_pair(omega,u),identity_relation)** -> .
% 299.99/300.64  194370[21:MRR:194348.2,14676.0] inductive(application_function) || well_ordering(u,cross_product(ordinal_numbers,cross_product(ordinal_numbers,ordinal_numbers)))* -> .
% 299.99/300.64  216554[8:MRR:216532.0,8652.0] || subclass(unordered_pair(u,omega),identity_relation)* -> .
% 299.99/300.64  216553[8:MRR:216531.0,8652.0] || subclass(unordered_pair(omega,u),identity_relation)* -> .
% 299.99/300.64  216561[8:Res:19172.1,216552.0] || equal(singleton(omega),identity_relation)** -> .
% 299.99/300.64  216552[8:MRR:216530.0,8652.0] || subclass(singleton(omega),identity_relation)* -> .
% 299.99/300.64  13196[7:Rew:13036.0,9806.1] inductive(flip(u)) ||  -> member(identity_relation,cross_product(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers))*.
% 299.99/300.64  215637[8:Res:215487.1,63019.1] || subclass(u,identity_relation)*+ subclass(domain_relation,u)* -> .
% 299.99/300.64  215636[8:Res:215487.1,127130.1] || subclass(u,identity_relation)*+ subclass(omega,u)* -> .
% 299.99/300.64  215635[8:Res:215487.1,147314.1] || subclass(u,identity_relation)* equal(u,omega) -> .
% 299.99/300.64  13195[7:Rew:13036.0,9807.1] inductive(rotate(u)) ||  -> member(identity_relation,cross_product(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers))*.
% 299.99/300.64  215634[8:Res:215487.1,9488.1] || subclass(u,identity_relation)*+ subclass(ordinal_numbers,u)* -> .
% 299.99/300.64  215633[8:Res:215487.1,147100.1] || subclass(u,identity_relation)* equal(u,ordinal_numbers) -> .
% 299.99/300.64  216287[8:Res:19172.1,216271.1] inductive(u) || equal(identity_relation,u)* -> .
% 299.99/300.64  216292[8:Res:18949.0,216271.1] inductive(restrict(identity_relation,u,v)) ||  -> .
% 299.99/300.64  80250[11:Rew:80200.0,66233.0] ||  -> equal(power_class(intersection(complement(singleton(identity_relation)),complement(image(successor_relation,ordinal_numbers)))),identity_relation)**.
% 299.99/300.64  216299[8:Res:18926.0,216271.1] inductive(intersection(u,identity_relation)) ||  -> .
% 299.99/300.64  216290[8:Res:19045.0,216271.1] inductive(intersection(identity_relation,u)) ||  -> .
% 299.99/300.64  216296[8:Res:130678.0,216271.1] inductive(complement(complement(identity_relation))) ||  -> .
% 299.99/300.64  216306[8:MRR:216295.1,13126.0] inductive(sum_class(identity_relation)) ||  -> .
% 299.99/300.64  18728[7:SpR:13320.1,8650.0] || well_ordering(element_relation,ordinal_numbers) -> equal(sum_class(singleton(least(element_relation,ordinal_numbers))),identity_relation)**.
% 299.99/300.64  216271[8:Res:13056.1,215631.1] inductive(u) || subclass(u,identity_relation)* -> .
% 299.99/300.64  216213[8:MRR:216212.1,13108.0] || equal(complement(u),u)** -> .
% 299.99/300.64  215630[8:Res:215487.1,8954.0] || subclass(u,identity_relation)* -> equal(complement(u),ordinal_numbers).
% 299.99/300.64  216064[8:MRR:60884.1,216061.0] inductive(ordered_pair(u,v)) ||  -> equal(singleton(u),identity_relation)**.
% 299.99/300.64  216168[25:Res:216145.1,208963.0] || equal(complement(subset_relation),identity_relation)** -> .
% 299.99/300.64  216141[8:Res:19172.1,215656.0] || equal(unordered_pair(least(element_relation,omega),u),identity_relation)** -> .
% 299.99/300.64  216136[8:Res:19172.1,215652.0] || equal(unordered_pair(u,least(element_relation,omega)),identity_relation)** -> .
% 299.99/300.64  10142[0:SpL:159.0,95.2] operation(recursion(u,successor_relation,union_of_range_map)) operation(v) || equal(ordinal_add(u,ordered_pair(apply(w,not_homomorphism1(w,v,recursion(u,successor_relation,union_of_range_map))),apply(w,not_homomorphism2(w,v,recursion(u,successor_relation,union_of_range_map))))),apply(w,apply(v,ordered_pair(not_homomorphism1(w,v,recursion(u,successor_relation,union_of_range_map)),not_homomorphism2(w,v,recursion(u,successor_relation,union_of_range_map))))))* compatible(w,v,recursion(u,successor_relation,union_of_range_map)) -> homomorphism(w,v,recursion(u,successor_relation,union_of_range_map)).
% 299.99/300.64  215656[8:Res:215487.1,127140.0] || subclass(unordered_pair(least(element_relation,omega),u),identity_relation)* -> .
% 299.99/300.64  215652[8:Res:215487.1,127141.0] || subclass(unordered_pair(u,least(element_relation,omega)),identity_relation)* -> .
% 299.99/300.64  216061[8:Res:19172.1,215648.0] || equal(unordered_pair(u,singleton(v)),identity_relation)** -> .
% 299.99/300.64  10143[0:SpL:159.0,95.2] operation(u) operation(recursion(v,successor_relation,union_of_range_map)) || equal(apply(u,ordered_pair(apply(w,not_homomorphism1(w,recursion(v,successor_relation,union_of_range_map),u)),apply(w,not_homomorphism2(w,recursion(v,successor_relation,union_of_range_map),u)))),apply(w,ordinal_add(v,ordered_pair(not_homomorphism1(w,recursion(v,successor_relation,union_of_range_map),u),not_homomorphism2(w,recursion(v,successor_relation,union_of_range_map),u)))))* compatible(w,recursion(v,successor_relation,union_of_range_map),u) -> homomorphism(w,recursion(v,successor_relation,union_of_range_map),u).
% 299.99/300.64  216036[8:Res:19172.1,215647.0] || equal(unordered_pair(singleton(u),v),identity_relation)** -> .
% 299.99/300.64  216024[8:Res:19172.1,215643.0] || equal(singleton(unordered_pair(u,v)),identity_relation)** -> .
% 299.99/300.64  216013[8:Res:19172.1,215642.0] || equal(singleton(ordered_pair(u,v)),identity_relation)** -> .
% 299.99/300.64  215648[8:Res:215487.1,9494.0] || subclass(unordered_pair(u,singleton(v)),identity_relation)* -> .
% 299.99/300.64  10145[0:Rew:159.0,10144.2,159.0,10144.2] operation(u) operation(v) || equal(apply(u,ordered_pair(ordinal_add(w,not_homomorphism1(recursion(w,successor_relation,union_of_range_map),v,u)),ordinal_add(w,not_homomorphism2(recursion(w,successor_relation,union_of_range_map),v,u)))),ordinal_add(w,apply(v,ordered_pair(not_homomorphism1(recursion(w,successor_relation,union_of_range_map),v,u),not_homomorphism2(recursion(w,successor_relation,union_of_range_map),v,u)))))* compatible(recursion(w,successor_relation,union_of_range_map),v,u) -> homomorphism(recursion(w,successor_relation,union_of_range_map),v,u).
% 299.99/300.64  215647[8:Res:215487.1,9495.0] || subclass(unordered_pair(singleton(u),v),identity_relation)* -> .
% 299.99/300.64  215643[8:Res:215487.1,40071.0] || subclass(singleton(unordered_pair(u,v)),identity_relation)* -> .
% 299.99/300.64  215642[8:Res:215487.1,39295.0] || subclass(singleton(ordered_pair(u,v)),identity_relation)* -> .
% 299.99/300.64  215997[15:Res:19172.1,215683.0] || equal(unordered_pair(range_of(identity_relation),u),identity_relation)** -> .
% 299.99/300.64  10054[0:SpR:126.0,94.3] operation(u) operation(restrict(v,w,singleton(x))) || compatible(y,restrict(v,w,singleton(x)),u) -> member(ordered_pair(not_homomorphism1(y,restrict(v,w,singleton(x)),u),not_homomorphism2(y,restrict(v,w,singleton(x)),u)),segment(v,w,x))* homomorphism(y,restrict(v,w,singleton(x)),u).
% 299.99/300.64  215992[15:Res:19172.1,215681.0] || equal(unordered_pair(u,range_of(identity_relation)),identity_relation)** -> .
% 299.99/300.64  215683[15:Res:215487.1,194978.0] || subclass(unordered_pair(range_of(identity_relation),u),identity_relation)* -> .
% 299.99/300.64  215681[15:Res:215487.1,194979.0] || subclass(unordered_pair(u,range_of(identity_relation)),identity_relation)* -> .
% 299.99/300.64  215925[8:Res:19172.1,215645.0] || equal(singleton(least(element_relation,omega)),identity_relation)** -> .
% 299.99/300.64  10130[0:MRR:10125.1,90.1] operation(u) || compatible(v,w,u) homomorphism(x,w,y) -> homomorphism(v,w,u) equal(apply(y,ordered_pair(apply(x,not_homomorphism1(v,w,u)),apply(x,not_homomorphism2(v,w,u)))),apply(x,apply(w,ordered_pair(not_homomorphism1(v,w,u),not_homomorphism2(v,w,u)))))*.
% 299.99/300.64  215645[8:Res:215487.1,127139.0] || subclass(singleton(least(element_relation,omega)),identity_relation)* -> .
% 299.99/300.64  215873[25:Res:19172.1,215684.0] || equal(unordered_pair(identity_relation,u),identity_relation)** -> .
% 299.99/300.64  215866[25:Res:19172.1,215682.0] || equal(unordered_pair(u,identity_relation),identity_relation)** -> .
% 299.99/300.64  215860[23:Res:19172.1,215675.0] || equal(complement(recursion_equation_functions(u)),identity_relation)** -> .
% 299.99/300.64  13530[7:Rew:13036.0,10002.2] || member(image(u,image(v,singleton(w))),ordinal_numbers) member(ordered_pair(w,apply(choice,image(u,image(v,singleton(w))))),cross_product(ordinal_numbers,ordinal_numbers)) -> equal(image(u,image(v,singleton(w))),identity_relation) member(ordered_pair(w,apply(choice,image(u,image(v,singleton(w))))),compose(u,v))*.
% 299.99/300.64  215781[8:Res:19172.1,215641.0] || equal(singleton(singleton(u)),identity_relation)** -> .
% 299.99/300.64  215684[25:Res:215487.1,208928.0] || subclass(unordered_pair(identity_relation,u),identity_relation)* -> .
% 299.99/300.64  215682[25:Res:215487.1,208948.0] || subclass(unordered_pair(u,identity_relation),identity_relation)* -> .
% 299.99/300.64  215675[23:Res:215487.1,205620.0] || subclass(complement(recursion_equation_functions(u)),identity_relation)* -> .
% 299.99/300.64  13361[7:Rew:13036.0,9820.2] || transitive(u,v) well_ordering(w,restrict(u,v,v)) -> equal(compose(restrict(u,v,v),restrict(u,v,v)),identity_relation) member(least(w,compose(restrict(u,v,v),restrict(u,v,v))),compose(restrict(u,v,v),restrict(u,v,v)))*.
% 299.99/300.64  215641[8:Res:215487.1,9493.0] || subclass(singleton(singleton(u)),identity_relation)* -> .
% 299.99/300.64  215757[15:Res:19172.1,215677.0] || equal(singleton(range_of(identity_relation)),identity_relation)** -> .
% 299.99/300.64  215718[16:MRR:215602.1,195236.0] || subclass(complement(singleton(identity_relation)),identity_relation)* -> .
% 299.99/300.64  117822[8:Rew:116078.0,116092.2] function(restrict(u,v,singleton(w))) || subclass(range_of(restrict(u,v,singleton(w))),cantor(segment(u,v,w)))* equal(cross_product(cantor(segment(u,v,w)),cantor(segment(u,v,w))),segment(u,v,w)) -> operation(restrict(u,v,singleton(w))).
% 299.99/300.64  215677[15:Res:215487.1,194976.0] || subclass(singleton(range_of(identity_relation)),identity_relation)* -> .
% 299.99/300.64  215676[16:Res:215487.1,165955.0] || subclass(singleton(identity_relation),identity_relation)* -> .
% 299.99/300.64  10056[5:SpR:8647.0,94.3] operation(u) operation(flip(cross_product(v,ordinal_numbers))) || compatible(w,flip(cross_product(v,ordinal_numbers)),u) -> member(ordered_pair(not_homomorphism1(w,flip(cross_product(v,ordinal_numbers)),u),not_homomorphism2(w,flip(cross_product(v,ordinal_numbers)),u)),inverse(v))* homomorphism(w,flip(cross_product(v,ordinal_numbers)),u).
% 299.99/300.64  155157[0:SpR:154737.1,19069.0] || subclass(u,v) -> subclass(symmetric_difference(v,u),complement(u))*.
% 299.99/300.64  215108[5:SpR:147905.0,151862.1] ||  -> member(u,v) subclass(complement(complement(singleton(u))),complement(v))*.
% 299.99/300.64  151862[5:Obv:151792.0] ||  -> member(u,v) subclass(intersection(singleton(u),w),complement(v))*.
% 299.99/300.64  10055[5:SpR:8648.0,94.3] operation(u) operation(restrict(element_relation,ordinal_numbers,v)) || compatible(w,restrict(element_relation,ordinal_numbers,v),u) -> member(ordered_pair(not_homomorphism1(w,restrict(element_relation,ordinal_numbers,v),u),not_homomorphism2(w,restrict(element_relation,ordinal_numbers,v),u)),sum_class(v))* homomorphism(w,restrict(element_relation,ordinal_numbers,v),u).
% 299.99/300.64  215011[5:SpR:147905.0,151861.1] || member(u,v) -> subclass(complement(complement(singleton(u))),v)*.
% 299.99/300.64  151861[0:Obv:151827.1] || member(u,v) -> subclass(intersection(singleton(u),w),v)*.
% 299.99/300.64  151502[5:Obv:151440.0] ||  -> member(u,v) subclass(intersection(w,singleton(u)),complement(v))*.
% 299.99/300.64  151501[0:Obv:151469.1] || member(u,v) -> subclass(intersection(w,singleton(u)),v)*.
% 299.99/300.64  10120[0:SpL:126.0,93.0] || member(ordered_pair(u,v),segment(w,x,y))+ homomorphism(z,restrict(w,x,singleton(y)),x1)* -> equal(apply(x1,ordered_pair(apply(z,u),apply(z,v))),apply(z,apply(restrict(w,x,singleton(y)),ordered_pair(u,v))))*.
% 299.99/300.64  214376[25:Rew:159.0,214338.1] operation(u) ||  -> equal(ordinal_add(v,u),ordinal_add(v,ordinal_numbers))*.
% 299.99/300.64  214833[8:Rew:117.0,214820.0] || equal(symmetrization_of(u),ordinal_numbers) -> inductive(symmetrization_of(u))*.
% 299.99/300.64  214832[8:Rew:47.0,214819.0] || equal(successor(u),ordinal_numbers) -> inductive(successor(u))*.
% 299.99/300.64  211494[8:Rew:30.0,211475.0] || equal(union(u,v),ordinal_numbers) -> inductive(union(u,v))*.
% 299.99/300.64  9997[5:Res:6.1,8803.0] || member(ordered_pair(u,not_subclass_element(image(v,image(w,singleton(u))),x)),cross_product(ordinal_numbers,ordinal_numbers)) -> 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))*.
% 299.99/300.64  211064[8:Res:210572.1,160667.0] || equal(complement(cross_product(u,u)),ordinal_numbers)**+ -> connected(v,u)*.
% 299.99/300.64  214780[25:Obv:214761.0] operation(u) || member(ordered_pair(v,ordinal_numbers),rest_relation)* -> .
% 299.99/300.64  214773[25:Res:39298.1,214618.1] operation(u) || subclass(ordinal_numbers,complement(complement(rest_relation)))* -> .
% 299.99/300.64  214618[25:MRR:214487.2,61224.0] operation(u) || member(ordered_pair(v,u),rest_relation)* -> .
% 299.99/300.64  9664[0:Res:62.1,129.0] || 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))))*.
% 299.99/300.64  214730[25:Rew:207558.1,214713.1] operation(u) || member(singleton(singleton(identity_relation)),subset_relation)* -> .
% 299.99/300.64  214725[25:Res:39298.1,214614.1] operation(u) || subclass(ordinal_numbers,complement(complement(subset_relation)))* -> .
% 299.99/300.64  214614[25:MRR:214491.2,208963.0] operation(u) || member(ordered_pair(v,u),subset_relation)* -> .
% 299.99/300.64  214615[25:MRR:214546.2,207853.1] operation(u) || member(ordered_pair(v,ordinal_numbers),subset_relation)* -> .
% 299.99/300.64  13360[7:Rew:13036.0,9821.2] || 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)))),identity_relation)**.
% 299.99/300.64  208985[25:Rew:208873.0,207616.1] operation(u) ||  -> equal(ordered_pair(v,ordinal_numbers),ordered_pair(v,u))*.
% 299.99/300.64  214339[25:SpR:208972.1,209425.0] operation(u) ||  -> equal(apply(element_relation,u),sum_class(ordinal_numbers))**.
% 299.99/300.64  208972[25:Rew:208885.0,207628.1] operation(u) ||  -> equal(apply(v,ordinal_numbers),apply(v,u))*.
% 299.99/300.64  208887[25:SpR:208820.0,116154.0] ||  -> equal(cantor(restrict(u,v,identity_relation)),segment(u,v,ordinal_numbers))**.
% 299.99/300.64  10122[5:SpL:8647.0,93.0] || member(ordered_pair(u,v),inverse(w)) homomorphism(x,flip(cross_product(w,ordinal_numbers)),y)*+ -> equal(apply(y,ordered_pair(apply(x,u),apply(x,v))),apply(x,apply(flip(cross_product(w,ordinal_numbers)),ordered_pair(u,v))))*.
% 299.99/300.64  207615[24:SpR:207558.1,964.0] operation(u) ||  -> member(unordered_pair(v,identity_relation),ordered_pair(v,u))*.
% 299.99/300.64  198465[21:Res:41183.1,197870.1] || equal(rest_of(not_subclass_element(u,v)),rest_relation)** -> subclass(u,v).
% 299.99/300.64  10121[5:SpL:8648.0,93.0] || member(ordered_pair(u,v),sum_class(w)) homomorphism(x,restrict(element_relation,ordinal_numbers,w),y)*+ -> equal(apply(y,ordered_pair(apply(x,u),apply(x,v))),apply(x,apply(restrict(element_relation,ordinal_numbers,w),ordered_pair(u,v))))*.
% 299.99/300.64  13044[7:Rew:13036.0,9849.1] || subclass(ordinal_numbers,restrict(u,v,w))* -> member(identity_relation,u).
% 299.99/300.64  13050[7:Rew:13036.0,10018.1] || equal(restrict(u,v,w),ordinal_numbers)** -> member(identity_relation,u).
% 299.99/300.64  13080[7:Rew:13036.0,9779.2] inductive(u) || equal(v,u)*+ -> member(identity_relation,v)*.
% 299.99/300.64  18033[8:SpR:15272.1,15528.0] single_valued_class(u) ||  -> equal(single_valued2(u),range__dfg(identity_relation,v,w))*.
% 299.99/300.64  13529[7:Rew:13036.0,10001.1] || member(ordered_pair(u,regular(image(v,image(w,singleton(u))))),cross_product(ordinal_numbers,ordinal_numbers)) -> equal(image(v,image(w,singleton(u))),identity_relation) member(ordered_pair(u,regular(image(v,image(w,singleton(u))))),compose(v,w))*.
% 299.99/300.64  17976[8:SpR:15265.1,15528.0] function(u) ||  -> equal(single_valued2(u),range__dfg(identity_relation,v,w))*.
% 299.99/300.64  18206[7:Res:13056.1,3617.0] inductive(symmetric_difference(u,v)) ||  -> member(identity_relation,union(u,v))*.
% 299.99/300.64  214039[5:Res:8646.1,152274.0] || subclass(ordinal_numbers,complement(singleton(omega)))*+ -> subclass(singleton(omega),u)*.
% 299.99/300.64  9880[0:Res:62.1,131.3] || 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)* -> .
% 299.99/300.64  10052[0:SpR:43.0,94.3] operation(u) operation(inverse(v)) || compatible(w,inverse(v),u) -> member(ordered_pair(not_homomorphism1(w,inverse(v),u),not_homomorphism2(w,inverse(v),u)),range_of(v))* homomorphism(w,inverse(v),u).
% 299.99/300.64  151512[5:Obv:151441.0] ||  -> subclass(intersection(u,singleton(v)),complement(recursion_equation_functions(w)))* function(v).
% 299.99/300.64  117776[8:Rew:116078.0,116099.2] function(restrict(element_relation,ordinal_numbers,u)) || subclass(range_of(restrict(element_relation,ordinal_numbers,u)),cantor(sum_class(u)))* equal(cross_product(cantor(sum_class(u)),cantor(sum_class(u))),sum_class(u)) -> operation(restrict(element_relation,ordinal_numbers,u)).
% 299.99/300.64  213622[5:SpR:147905.0,151877.0] ||  -> subclass(complement(complement(singleton(u))),complement(recursion_equation_functions(v)))* function(u).
% 299.99/300.64  151877[5:Obv:151793.0] ||  -> subclass(intersection(singleton(u),v),complement(recursion_equation_functions(w)))* function(u).
% 299.99/300.64  213477[25:SpR:208820.0,145761.0] ||  -> equal(segment(ordinal_numbers,u,ordinal_numbers),cantor(cross_product(u,identity_relation)))**.
% 299.99/300.64  116127[8:Rew:116078.0,10058.3] operation(u) operation(v) || compatible(w,v,u) subclass(cantor(v),x) -> homomorphism(w,v,u) member(ordered_pair(not_homomorphism1(w,v,u),not_homomorphism2(w,v,u)),x)*.
% 299.99/300.64  145761[8:SpR:143170.0,116154.0] ||  -> equal(cantor(cross_product(u,singleton(v))),segment(ordinal_numbers,u,v))**.
% 299.99/300.64  211409[8:Res:210606.1,160667.0] || equal(complement(complement(symmetrization_of(u))),ordinal_numbers)**+ -> connected(u,v)*.
% 299.99/300.64  211138[8:Res:210572.1,65.0] || equal(complement(compose(u,inverse(u))),ordinal_numbers)** -> single_valued_class(u).
% 299.99/300.64  211021[8:Res:210572.1,8787.1] single_valued_class(u) || equal(complement(u),ordinal_numbers)** -> function(u).
% 299.99/300.64  10118[0:SpL:43.0,93.0] || member(ordered_pair(u,v),range_of(w))+ homomorphism(x,inverse(w),y)* -> equal(apply(y,ordered_pair(apply(x,u),apply(x,v))),apply(x,apply(inverse(w),ordered_pair(u,v))))*.
% 299.99/300.64  213390[8:Obv:213389.1] || equal(complement(inverse(u)),ordinal_numbers)**+ -> asymmetric(u,v)*.
% 299.99/300.64  210610[8:Res:13210.1,210517.1] || equal(complement(u),ordinal_numbers) -> equal(intersection(v,u),identity_relation)**.
% 299.99/300.64  213203[8:Obv:213202.1] || equal(complement(u),ordinal_numbers) -> asymmetric(u,v)*.
% 299.99/300.64  210579[8:Res:13248.1,210517.1] || equal(complement(u),ordinal_numbers) -> equal(intersection(u,v),identity_relation)**.
% 299.99/300.64  117763[8:Rew:116078.0,116128.6] operation(u) operation(v) || compatible(w,v,u)+ subclass(cantor(v),x)* well_ordering(y,x)* -> homomorphism(w,v,u)* member(least(y,cantor(v)),cantor(v))*.
% 299.99/300.64  212894[12:Rew:17351.0,212787.1,80980.0,212787.1] || equal(power_class(u),ordinal_numbers) -> equal(power_class(power_class(u)),identity_relation)**.
% 299.99/300.64  212662[12:Rew:17351.0,212492.1,80980.0,212492.1] || equal(complement(u),ordinal_numbers) -> equal(power_class(complement(u)),identity_relation)**.
% 299.99/300.64  211670[8:Res:211441.1,17333.0] || equal(power_class(u),ordinal_numbers) -> equal(complement(power_class(u)),identity_relation)**.
% 299.99/300.64  211629[8:Res:211441.1,9586.0] || equal(power_class(u),ordinal_numbers) -> section(element_relation,power_class(u),ordinal_numbers)*.
% 299.99/300.64  117762[8:Rew:116078.0,116080.2,116078.0,116080.2,116078.0,116080.1,116078.0,116080.1] function(restrict(u,v,ordinal_numbers)) || subclass(image(u,v),cantor(cantor(w))) equal(cantor(cantor(x)),cantor(restrict(u,v,ordinal_numbers))) -> compatible(restrict(u,v,ordinal_numbers),x,w)*.
% 299.99/300.64  211432[8:Res:210606.1,17333.0] || equal(complement(u),ordinal_numbers) -> equal(complement(complement(u)),identity_relation)**.
% 299.99/300.64  211311[8:Res:210606.1,9586.0] || equal(complement(u),ordinal_numbers) -> section(element_relation,complement(u),ordinal_numbers)*.
% 299.99/300.64  210853[8:Res:210572.1,9586.0] || equal(complement(sum_class(u)),ordinal_numbers) -> section(element_relation,u,ordinal_numbers)*.
% 299.99/300.64  210719[18:Res:190510.1,210517.1] || subclass(inverse(identity_relation),u)* equal(complement(u),ordinal_numbers) -> .
% 299.99/300.64  13259[7:Rew:13036.0,8939.1] || member(cross_product(u,v),ordinal_numbers) -> equal(cross_product(u,v),identity_relation) equal(ordered_pair(first(apply(choice,cross_product(u,v))),second(apply(choice,cross_product(u,v)))),apply(choice,cross_product(u,v)))**.
% 299.99/300.64  210718[18:Res:194549.1,210517.1] || subclass(symmetrization_of(identity_relation),u)* equal(complement(u),ordinal_numbers) -> .
% 299.99/300.64  212333[8:Res:49995.1,210577.0] || member(subset_relation,subset_relation) equal(complement(first(subset_relation)),ordinal_numbers)** -> .
% 299.99/300.64  210577[8:Res:51313.1,210517.1] || member(singleton(u),subset_relation)* equal(complement(u),ordinal_numbers) -> .
% 299.99/300.64  210558[8:Res:8705.1,210517.1] || member(u,ordinal_numbers) equal(complement(singleton(u)),ordinal_numbers)** -> .
% 299.99/300.64  161774[8:Rew:116078.0,13336.3,116078.0,13336.2] || section(u,v,w) well_ordering(x,v) -> equal(cantor(restrict(u,w,v)),identity_relation) member(least(x,cantor(restrict(u,w,v))),cantor(restrict(u,w,v)))*.
% 299.99/300.64  210511[7:Res:13049.1,143226.0] || subclass(ordinal_numbers,symmetric_difference(ordinal_numbers,u))* member(identity_relation,u) -> .
% 299.99/300.64  210460[5:Res:8646.1,143226.0] || subclass(ordinal_numbers,symmetric_difference(ordinal_numbers,u))* member(omega,u) -> .
% 299.99/300.64  211139[8:Res:210572.1,14761.0] || equal(complement(compose(identity_relation,identity_relation)),ordinal_numbers)**+ -> transitive(identity_relation,u)*.
% 299.99/300.64  212131[12:Rew:17351.0,212017.1,80980.0,212017.1] || equal(symmetrization_of(identity_relation),ordinal_numbers) -> equal(power_class(symmetrization_of(identity_relation)),identity_relation)**.
% 299.99/300.64  9962[5:Rew:43.0,9953.2,43.0,9953.1,8647.0,9953.1] function(flip(cross_product(u,ordinal_numbers))) || subclass(range_of(flip(cross_product(u,ordinal_numbers))),range_of(u))* equal(cross_product(range_of(u),range_of(u)),inverse(u)) -> operation(flip(cross_product(u,ordinal_numbers))).
% 299.99/300.64  212161[8:MRR:212160.1,8638.0] || equal(symmetrization_of(identity_relation),ordinal_numbers) -> connected(identity_relation,u)*.
% 299.99/300.64  211586[8:Res:211438.1,17333.0] || equal(symmetrization_of(identity_relation),ordinal_numbers) -> equal(complement(symmetrization_of(identity_relation)),identity_relation)**.
% 299.99/300.64  211545[8:Res:211438.1,9586.0] || equal(symmetrization_of(identity_relation),ordinal_numbers) -> section(element_relation,symmetrization_of(identity_relation),ordinal_numbers)*.
% 299.99/300.64  211034[8:Res:210572.1,155658.0] || equal(complement(compose(subset_relation,subset_relation)),ordinal_numbers)** -> transitive(subset_relation,ordinal_numbers).
% 299.99/300.64  10061[5:Res:20.2,8820.1] || member(u,ordinal_numbers) member(ordered_pair(v,w),cross_product(ordinal_numbers,ordinal_numbers)) member(ordered_pair(ordered_pair(w,v),u),x) -> member(ordered_pair(ordered_pair(v,w),u),flip(x))*.
% 299.99/300.64  211812[8:Rew:117064.0,211682.1,66036.0,211682.1] || equal(symmetrization_of(identity_relation),ordinal_numbers)** -> equal(inverse(identity_relation),ordinal_numbers).
% 299.99/300.64  211441[8:Rew:59.0,211296.0] || equal(power_class(u),ordinal_numbers) -> subclass(v,power_class(u))*.
% 299.99/300.64  211594[18:SoR:211589.0,82.1] operation(symmetrization_of(identity_relation)) || equal(symmetrization_of(identity_relation),ordinal_numbers)** -> .
% 299.99/300.64  10093[5:Res:20.2,8821.1] || member(u,ordinal_numbers) member(ordered_pair(v,w),cross_product(ordinal_numbers,ordinal_numbers)) member(ordered_pair(ordered_pair(w,u),v),x) -> member(ordered_pair(ordered_pair(v,w),u),rotate(x))*.
% 299.99/300.64  211592[18:SoR:211589.0,75.1] one_to_one(symmetrization_of(identity_relation)) || equal(symmetrization_of(identity_relation),ordinal_numbers)** -> .
% 299.99/300.64  211589[18:MRR:211581.2,190576.0] function(symmetrization_of(identity_relation)) || equal(symmetrization_of(identity_relation),ordinal_numbers)** -> .
% 299.99/300.64  211438[8:Rew:162584.0,211292.0] || equal(symmetrization_of(identity_relation),ordinal_numbers) -> subclass(u,symmetrization_of(identity_relation))*.
% 299.99/300.64  211493[8:Rew:59.0,211481.0] || equal(power_class(u),ordinal_numbers) -> inductive(power_class(u))*.
% 299.99/300.64  8632[0:SpL:72.0,141.1] || well_ordering(element_relation,image(u,singleton(v))) subclass(apply(u,v),image(u,singleton(v)))* -> equal(image(u,singleton(v)),ordinal_numbers) member(image(u,singleton(v)),ordinal_numbers).
% 299.99/300.64  211442[8:MRR:211317.1,192149.1] || equal(complement(u),ordinal_numbers) -> inductive(complement(u))*.
% 299.99/300.64  211408[10:Res:210606.1,162776.0] || equal(complement(compose(element_relation,ordinal_numbers)),ordinal_numbers)** -> .
% 299.99/300.64  210606[8:Res:60219.0,210517.1] || equal(complement(u),ordinal_numbers) -> subclass(v,complement(u))*.
% 299.99/300.64  8534[0:SpR:126.0,116.2] function(restrict(u,v,singleton(w))) || subclass(range_of(restrict(u,v,singleton(w))),x) -> maps(restrict(u,v,singleton(w)),segment(u,v,w),x)*.
% 299.99/300.64  211136[8:Res:210572.1,15309.0] || equal(complement(ordinals_with_null_class_as_identity),ordinal_numbers)** -> .
% 299.99/300.64  211063[10:Res:210572.1,162776.0] || equal(complement(element_relation),ordinal_numbers)** -> .
% 299.99/300.64  210572[8:Res:6.1,210517.1] || equal(complement(u),ordinal_numbers) -> subclass(u,v)*.
% 299.99/300.64  210578[8:Res:13072.1,210517.1] || equal(complement(u),ordinal_numbers)** -> equal(u,identity_relation).
% 299.99/300.64  117728[8:Rew:116078.0,116081.2,116078.0,116081.2,116078.0,116081.1] function(u) || subclass(range_of(u),cantor(segment(v,w,x))) equal(cantor(cantor(y)),cantor(u)) -> compatible(u,y,restrict(v,w,singleton(x)))*.
% 299.99/300.64  210517[8:MRR:210449.1,41096.1] || equal(complement(u),ordinal_numbers) member(v,u)* -> .
% 299.99/300.64  210512[7:Res:13056.1,143226.0] inductive(symmetric_difference(ordinal_numbers,u)) || member(identity_relation,u)* -> .
% 299.99/300.64  143226[5:SpL:140603.0,18794.1] || member(u,symmetric_difference(ordinal_numbers,v))* member(u,v) -> .
% 299.99/300.64  117719[8:Rew:116078.0,116107.2] function(inverse(u)) || subclass(range_of(inverse(u)),cantor(range_of(u))) equal(cross_product(cantor(range_of(u)),cantor(range_of(u))),range_of(u))** -> operation(inverse(u)).
% 299.99/300.64  210404[14:Res:165177.0,143186.0] ||  -> member(identity_relation,union(u,identity_relation))* member(identity_relation,complement(u)).
% 299.99/300.64  143186[5:SpR:140603.0,3618.1] || member(u,symmetric_difference(ordinal_numbers,v))* -> member(u,complement(v)).
% 299.99/300.64  140864[8:Rew:140603.0,68967.0] || member(u,complement(v)) -> member(u,symmetric_difference(ordinal_numbers,v))*.
% 299.99/300.64  209772[23:Res:10.1,205619.0] || equal(u,complement(recursion_equation_functions(v)))*+ -> member(singleton(identity_relation),u)*.
% 299.99/300.64  161701[8:Rew:116078.0,13331.2] || section(u,v,w) well_ordering(x,v) -> equal(segment(x,cantor(restrict(u,w,v)),least(x,cantor(restrict(u,w,v)))),identity_relation)**.
% 299.99/300.64  209761[23:Res:10.1,205615.0] || equal(u,complement(recursion_equation_functions(v)))*+ well_ordering(ordinal_numbers,u)* -> .
% 299.99/300.64  209753[21:Res:10.1,204678.0] || equal(cross_product(u,v),domain_relation)**+ -> member(singleton(identity_relation),u)*.
% 299.99/300.64  208873[25:SpR:208820.0,17.0] ||  -> equal(unordered_pair(singleton(u),unordered_pair(u,identity_relation)),ordered_pair(u,ordinal_numbers))**.
% 299.99/300.64  208722[8:SpR:208708.1,19069.0] ||  -> equal(singleton(u),identity_relation) subclass(symmetric_difference(u,ordinal_numbers),complement(u))*.
% 299.99/300.64  161699[8:Rew:160496.0,13334.1] || connected(u,v)* well_ordering(w,complement(complement(symmetrization_of(u))))*+ -> equal(cross_product(v,v),identity_relation) member(least(w,cross_product(v,v)),cross_product(v,v))*.
% 299.99/300.64  208593[15:Res:10.1,165538.0] || equal(intersection(u,v),ordinal_numbers)**+ -> member(range_of(identity_relation),u)*.
% 299.99/300.64  117657[8:Rew:116078.0,116098.2,116078.0,116098.2,116078.0,116098.2] function(u) || subclass(range_of(u),cantor(sum_class(v))) equal(cantor(cantor(w)),cantor(u)) -> compatible(u,w,restrict(element_relation,ordinal_numbers,v))*.
% 299.99/300.64  209921[15:SpL:140603.0,208474.0] || equal(u,ordinal_numbers) -> member(range_of(identity_relation),u)*.
% 299.99/300.64  208474[15:Res:10.1,165537.0] || equal(intersection(u,v),ordinal_numbers)**+ -> member(range_of(identity_relation),v)*.
% 299.99/300.64  207866[24:Rew:140613.0,207571.1,66036.0,207571.1] operation(u) ||  -> subclass(complement(successor(u)),symmetric_difference(ordinal_numbers,u))*.
% 299.99/300.64  207863[24:Rew:66036.0,207569.1] operation(u) ||  -> subclass(symmetric_difference(complement(u),ordinal_numbers),successor(u))*.
% 299.99/300.64  13330[7:Rew:13036.0,9508.3] || 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))),identity_relation)**.
% 299.99/300.64  206259[8:Rew:160491.0,206187.0] ||  -> subclass(symmetric_difference(complement(u),symmetric_difference(ordinal_numbers,u)),union(u,identity_relation))*.
% 299.99/300.64  205619[23:Res:205609.0,5.0] || subclass(complement(recursion_equation_functions(u)),v)* -> member(singleton(identity_relation),v).
% 299.99/300.64  116094[8:Rew:116078.0,3761.1] operation(restrict(u,v,singleton(w))) ||  -> equal(cross_product(cantor(segment(u,v,w)),cantor(segment(u,v,w))),segment(u,v,w))**.
% 299.99/300.64  205615[23:Res:205609.0,9876.0] || subclass(complement(recursion_equation_functions(u)),v)* well_ordering(ordinal_numbers,v) -> .
% 299.99/300.64  204678[21:Res:196904.1,2200.0] || subclass(domain_relation,cross_product(u,v))* -> member(singleton(identity_relation),u).
% 299.99/300.64  209659[25:SpR:208820.0,208841.0] ||  -> equal(unordered_pair(identity_relation,unordered_pair(ordinal_numbers,identity_relation)),ordered_pair(ordinal_numbers,ordinal_numbers))**.
% 299.99/300.64  208841[25:SpR:208820.0,17.0] ||  -> equal(unordered_pair(identity_relation,unordered_pair(ordinal_numbers,singleton(u))),ordered_pair(ordinal_numbers,u))**.
% 299.99/300.64  9471[0:Res:62.1,7.0] || 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)))).
% 299.99/300.64  209607[25:SoR:209455.0,75.1] one_to_one(ordered_pair(ordinal_numbers,u)) ||  -> member(identity_relation,cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.64  209455[25:Res:8665.1,209226.0] function(ordered_pair(ordinal_numbers,u)) ||  -> member(identity_relation,cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.64  9639[5:Res:8704.1,129.0] || member(u,ordinal_numbers) subclass(unordered_pair(v,u),w)*+ well_ordering(x,w)* -> member(least(x,unordered_pair(v,u)),unordered_pair(v,u))*.
% 299.99/300.64  9640[5:Res:8703.1,129.0] || member(u,ordinal_numbers) subclass(unordered_pair(u,v),w)*+ well_ordering(x,w)* -> member(least(x,unordered_pair(u,v)),unordered_pair(u,v))*.
% 299.99/300.64  209352[25:Res:13125.2,209339.0] || subclass(omega,successor_relation) -> equal(integer_of(singleton(singleton(identity_relation))),identity_relation)**.
% 299.99/300.64  9633[5:Res:8700.2,129.0] || member(u,ordinal_numbers)* subclass(complement(v),w)*+ well_ordering(x,w)* -> member(u,v)* member(least(x,complement(v)),complement(v))*.
% 299.99/300.64  209261[25:Res:13125.2,208996.0] || subclass(omega,rest_relation) -> equal(integer_of(singleton(singleton(identity_relation))),identity_relation)**.
% 299.99/300.64  161646[8:Rew:160496.0,13329.1] || connected(u,v)* well_ordering(w,complement(complement(symmetrization_of(u))))*+ -> equal(segment(w,cross_product(v,v),least(w,cross_product(v,v))),identity_relation)**.
% 299.99/300.64  117630[8:Rew:116078.0,116131.2,116078.0,116131.2] function(u) || subclass(range_of(u),range_of(v)) equal(cantor(cantor(w)),cantor(u)) -> compatible(u,w,flip(cross_product(v,ordinal_numbers)))*.
% 299.99/300.64  209246[25:Res:13125.2,208980.0] || subclass(omega,domain_relation) -> equal(integer_of(singleton(singleton(identity_relation))),identity_relation)**.
% 299.99/300.64  209453[25:Res:10.1,209226.0] || equal(u,ordered_pair(ordinal_numbers,v))*+ -> member(identity_relation,u)*.
% 299.99/300.64  13664[7:Rew:13036.0,13522.2] inductive(image(u,image(v,singleton(w)))) || member(ordered_pair(w,identity_relation),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(w,identity_relation),compose(u,v))*.
% 299.99/300.64  209226[25:Res:208830.0,5.0] || subclass(ordered_pair(ordinal_numbers,u),v)* -> member(identity_relation,v).
% 299.99/300.64  209425[25:SpR:80980.0,208885.0] ||  -> equal(apply(element_relation,ordinal_numbers),sum_class(ordinal_numbers))**.
% 299.99/300.64  208885[25:SpR:208820.0,72.0] ||  -> equal(sum_class(image(u,identity_relation)),apply(u,ordinal_numbers))**.
% 299.99/300.64  117617[8:Rew:116078.0,116106.2,116078.0,116106.2,116078.0,116106.2] function(u) || subclass(range_of(u),cantor(range_of(v)))*+ equal(cantor(cantor(w)),cantor(u)) -> compatible(u,w,inverse(v))*.
% 299.99/300.64  209230[25:Res:208830.0,165357.1] || equal(complement(ordered_pair(ordinal_numbers,u)),singleton(identity_relation))** -> .
% 299.99/300.64  209229[25:Res:208830.0,190532.1] || equal(complement(ordered_pair(ordinal_numbers,u)),symmetrization_of(identity_relation))** -> .
% 299.99/300.64  209228[25:Res:208830.0,190641.1] || equal(complement(ordered_pair(ordinal_numbers,u)),inverse(identity_relation))** -> .
% 299.99/300.64  208872[25:SpR:208820.0,964.0] ||  -> member(unordered_pair(u,identity_relation),ordered_pair(u,ordinal_numbers))*.
% 299.99/300.64  9617[5:SpR:154.1,8801.1] || member(u,recursion_equation_functions(v)) member(ordered_pair(v,rest_of(u)),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(v,ordered_pair(rest_of(u),u)),composition_function)*.
% 299.99/300.64  208948[25:SpL:208820.0,9494.0] || subclass(ordinal_numbers,complement(unordered_pair(u,identity_relation)))* -> .
% 299.99/300.64  208928[25:SpL:208820.0,9495.0] || subclass(ordinal_numbers,complement(unordered_pair(identity_relation,u)))* -> .
% 299.99/300.64  209354[25:Res:9632.1,209339.0] || equal(complement(complement(successor_relation)),ordinal_numbers)** -> .
% 299.99/300.64  209356[25:Res:133837.1,209339.0] || well_ordering(ordinal_numbers,complement(successor_relation))* -> .
% 299.99/300.64  9101[5:SpR:8648.0,116.2] function(restrict(element_relation,ordinal_numbers,u)) || subclass(range_of(restrict(element_relation,ordinal_numbers,u)),v) -> maps(restrict(element_relation,ordinal_numbers,u),sum_class(u),v)*.
% 299.99/300.64  209355[25:Res:8645.1,209339.0] || subclass(ordinal_numbers,successor_relation)* -> .
% 299.99/300.64  209339[25:MRR:209338.1,195237.0] || member(singleton(singleton(identity_relation)),successor_relation)* -> .
% 299.99/300.64  208840[25:SpR:208820.0,963.0] ||  -> equal(ordered_pair(identity_relation,ordinal_numbers),singleton(singleton(identity_relation)))**.
% 299.99/300.64  209263[25:Res:9632.1,208996.0] || equal(complement(complement(rest_relation)),ordinal_numbers)** -> .
% 299.99/300.64  9014[5:Rew:8637.0,8777.2] function(restrict(element_relation,universal_class,u)) || subclass(range_of(restrict(element_relation,ordinal_numbers,u)),v) -> maps(restrict(element_relation,ordinal_numbers,u),sum_class(u),v)*.
% 299.99/300.64  209248[25:Res:9632.1,208980.0] || equal(complement(complement(domain_relation)),ordinal_numbers)** -> .
% 299.99/300.64  209265[25:Res:133837.1,208996.0] || well_ordering(ordinal_numbers,complement(rest_relation))* -> .
% 299.99/300.64  209264[25:Res:8645.1,208996.0] || subclass(ordinal_numbers,rest_relation)* -> .
% 299.99/300.64  208996[25:MRR:208995.1,61224.0] || member(singleton(singleton(identity_relation)),rest_relation)* -> .
% 299.99/300.64  9087[5:SpR:8647.0,116.2] function(flip(cross_product(u,ordinal_numbers))) || subclass(range_of(flip(cross_product(u,ordinal_numbers))),v) -> maps(flip(cross_product(u,ordinal_numbers)),inverse(u),v)*.
% 299.99/300.64  209250[25:Res:133837.1,208980.0] || well_ordering(ordinal_numbers,complement(domain_relation))* -> .
% 299.99/300.64  209249[25:Res:8645.1,208980.0] || subclass(ordinal_numbers,domain_relation)* -> .
% 299.99/300.64  208980[25:MRR:208906.1,13108.0] || member(singleton(singleton(identity_relation)),domain_relation)* -> .
% 299.99/300.64  9013[5:Rew:8637.0,8773.2] function(flip(cross_product(u,universal_class))) || subclass(range_of(flip(cross_product(u,ordinal_numbers))),v) -> maps(flip(cross_product(u,ordinal_numbers)),inverse(u),v)*.
% 299.99/300.64  208830[25:SpR:208820.0,962.0] ||  -> member(identity_relation,ordered_pair(ordinal_numbers,u))*.
% 299.99/300.64  209035[25:Res:66492.1,208963.0] ||  -> equal(integer_of(ordinal_numbers),identity_relation)**.
% 299.99/300.64  208982[25:Obv:208981.1] || member(ordinal_numbers,subset_relation)* -> .
% 299.99/300.64  208963[25:MRR:208835.1,14676.0] || member(ordinal_numbers,ordinal_numbers)* -> .
% 299.99/300.64  208968[25:MRR:10872.1,208966.0] single_valued_class(element_relation) ||  -> .
% 299.99/300.64  208966[25:MRR:81031.1,208963.0] function(element_relation) ||  -> .
% 299.99/300.64  208965[25:MRR:81037.1,208963.0] one_to_one(element_relation) ||  -> .
% 299.99/300.64  117603[8:Rew:116078.0,116113.2,116078.0,116113.2,116078.0,116113.2,116078.0,116113.1] function(u) || equal(cantor(cantor(v)),range_of(u)) equal(cantor(cantor(w)),cantor(u)) -> compatible(u,w,v)*.
% 299.99/300.64  208964[25:MRR:81038.1,208963.0] operation(element_relation) ||  -> .
% 299.99/300.64  208820[25:Spt:208807.1] ||  -> equal(singleton(ordinal_numbers),identity_relation)**.
% 299.99/300.64  208708[8:SpR:13096.1,118070.0] ||  -> equal(singleton(u),identity_relation) equal(intersection(u,ordinal_numbers),u)**.
% 299.99/300.64  13096[7:Rew:13036.0,6983.0] ||  -> equal(singleton(u),identity_relation) equal(apply(choice,singleton(u)),u)**.
% 299.99/300.64  9618[5:Res:8801.1,5.0] || member(ordered_pair(u,v),cross_product(ordinal_numbers,ordinal_numbers)) subclass(composition_function,w) -> member(ordered_pair(u,ordered_pair(v,compose(u,v))),w)*.
% 299.99/300.64  198470[21:Res:18510.1,197870.1] function(u) || equal(rest_of(apply(u,v)),rest_relation)** -> .
% 299.99/300.64  165538[15:Res:165526.1,25.0] || subclass(ordinal_numbers,intersection(u,v))* -> member(range_of(identity_relation),u).
% 299.99/300.64  13260[7:Rew:13036.0,8543.0] ||  -> equal(cross_product(u,v),identity_relation) equal(ordered_pair(first(regular(cross_product(u,v))),second(regular(cross_product(u,v)))),regular(cross_product(u,v)))**.
% 299.99/300.64  165537[15:Res:165526.1,26.0] || subclass(ordinal_numbers,intersection(u,v))* -> member(range_of(identity_relation),v).
% 299.99/300.64  198162[21:SpR:197474.0,962.0] ||  -> equal(range_of(u),identity_relation) member(identity_relation,ordered_pair(inverse(u),v))*.
% 299.99/300.64  117604[8:Rew:116078.0,116138.3,116078.0,116138.2,116078.0,116138.2,116078.0,116138.1] operation(u) || member(v,cantor(cantor(u))) member(w,cantor(cantor(u))) -> member(ordered_pair(w,v),cantor(u))*.
% 299.99/300.64  207572[24:SpR:207558.1,963.0] operation(u) ||  -> equal(ordered_pair(identity_relation,u),singleton(singleton(identity_relation)))**.
% 299.99/300.64  208173[24:SpR:207931.1,6984.0] operation(apply(choice,omega)) ||  -> equal(apply(choice,omega),identity_relation)**.
% 299.99/300.64  207565[24:SpR:207558.1,47.0] operation(u) ||  -> equal(union(u,identity_relation),successor(u))**.
% 299.99/300.64  207965[24:Res:133495.1,207853.1] operation(least(u,rest_relation)) || well_ordering(u,ordinal_numbers)* -> .
% 299.99/300.64  161591[8:Rew:160496.0,3262.2,160496.0,3262.1] || connected(u,v) subclass(complement(complement(symmetrization_of(u))),cross_product(v,v))* -> equal(complement(complement(symmetrization_of(u))),cross_product(v,v)).
% 299.99/300.64  207964[24:Res:133502.1,207853.1] operation(least(u,rest_relation)) || well_ordering(u,rest_relation)* -> .
% 299.99/300.64  207963[24:Res:19525.1,207853.1] operation(least(u,ordinal_numbers)) || well_ordering(u,ordinal_numbers)* -> .
% 299.99/300.64  13333[7:Rew:13036.0,9535.2] inductive(u) || well_ordering(v,u) -> equal(image(successor_relation,u),identity_relation) member(least(v,image(successor_relation,u)),image(successor_relation,u))*.
% 299.99/300.64  207942[24:Res:41183.1,207853.1] operation(not_subclass_element(u,v)) ||  -> subclass(u,v)*.
% 299.99/300.64  207951[24:Res:18510.1,207853.1] function(u) operation(apply(u,v)) ||  -> .
% 299.99/300.64  207562[24:SpR:207558.1,962.0] operation(u) ||  -> member(identity_relation,ordered_pair(u,v))*.
% 299.99/300.64  207950[24:Res:8956.1,207853.1] operation(power_class(u)) || member(u,ordinal_numbers)* -> .
% 299.99/300.64  207944[24:Res:148963.1,207853.1] operation(rest_of(u)) || member(u,ordinal_numbers)* -> .
% 299.99/300.64  207941[24:Res:50064.1,207853.1] operation(second(u)) || member(u,subset_relation)* -> .
% 299.99/300.64  207940[24:Res:50063.1,207853.1] operation(first(u)) || member(u,subset_relation)* -> .
% 299.99/300.64  9563[2:MRR:9542.3,4574.1] || connected(u,v) well_ordering(w,v) -> well_ordering(u,v) member(least(w,not_well_ordering(u,v)),not_well_ordering(u,v))*.
% 299.99/300.64  207937[24:Res:8955.1,207853.1] operation(sum_class(u)) || member(u,ordinal_numbers)* -> .
% 299.99/300.64  207947[24:Res:60996.1,207853.1] operation(regular(u)) ||  -> equal(u,identity_relation)*.
% 299.99/300.64  207931[24:Res:66492.1,207853.1] operation(u) ||  -> equal(integer_of(u),identity_relation)**.
% 299.99/300.64  9470[0:Res:62.1,5.0] || member(ordered_pair(u,v),compose(w,x))* subclass(image(w,image(x,singleton(u))),y)*+ -> member(v,y)*.
% 299.99/300.64  207872[24:Obv:207871.2] operation(u) || member(u,subset_relation)* -> .
% 299.99/300.64  207948[24:Res:190509.0,207853.1] operation(regular(symmetrization_of(identity_relation))) ||  -> .
% 299.99/300.64  207938[24:Res:165431.0,207853.1] operation(sum_class(range_of(identity_relation))) ||  -> .
% 299.99/300.64  208002[24:MRR:207924.1,13108.0] operation(regular(ordinal_numbers)) ||  -> .
% 299.99/300.64  8865[5:Rew:8637.0,2146.0] || member(restrict(u,v,singleton(w)),ordinal_numbers) -> member(ordered_pair(restrict(u,v,singleton(w)),segment(u,v,w)),domain_relation)*.
% 299.99/300.64  207853[24:MRR:207567.2,14676.0] operation(u) || member(u,ordinal_numbers)* -> .
% 299.99/300.64  207858[24:Obv:207857.1] operation(unordered_pair(u,v)) ||  -> .
% 299.99/300.64  207855[24:Obv:207854.1] operation(ordered_pair(u,v)) ||  -> .
% 299.99/300.64  207861[24:MRR:207860.1,8638.0] operation(least(element_relation,omega)) ||  -> .
% 299.99/300.64  161565[8:Rew:116078.0,13332.1,116078.0,13332.1] operation(u) || well_ordering(v,cantor(cantor(u))) -> equal(range_of(u),identity_relation) member(least(v,range_of(u)),range_of(u))*.
% 299.99/300.64  207847[24:Obv:207846.1] operation(singleton(u)) ||  -> .
% 299.99/300.64  207851[24:Obv:207850.1] operation(range_of(identity_relation)) ||  -> .
% 299.99/300.64  207842[24:Obv:207841.1] operation(omega) ||  -> .
% 299.99/300.64  207837[24:MRR:207638.1,14676.0] operation(identity_relation) ||  -> .
% 299.99/300.64  116093[8:Rew:116078.0,2144.1] operation(restrict(u,v,singleton(w))) ||  -> subclass(range_of(restrict(u,v,singleton(w))),cantor(segment(u,v,w)))*.
% 299.99/300.64  207558[24:Spt:197517.0,197517.1] operation(u) ||  -> equal(singleton(u),identity_relation)**.
% 299.99/300.64  192400[8:SpR:188530.1,19069.0] || member(u,ordinals_with_null_class_as_identity) -> subclass(symmetric_difference(u,ordinal_numbers),complement(u))*.
% 299.99/300.64  190652[18:Res:190593.1,25.0] || equal(intersection(u,v),inverse(identity_relation))** -> member(identity_relation,u).
% 299.99/300.64  190651[18:Res:190593.1,26.0] || equal(intersection(u,v),inverse(identity_relation))** -> member(identity_relation,v).
% 299.99/300.64  13262[7:Rew:13036.0,6985.0] ||  -> equal(unordered_pair(u,v),identity_relation) equal(apply(choice,unordered_pair(u,v)),v)** equal(apply(choice,unordered_pair(u,v)),u)**.
% 299.99/300.64  190543[18:Res:190442.1,25.0] || equal(intersection(u,v),symmetrization_of(identity_relation))** -> member(identity_relation,u).
% 299.99/300.64  190542[18:Res:190442.1,26.0] || equal(intersection(u,v),symmetrization_of(identity_relation))** -> member(identity_relation,v).
% 299.99/300.64  165368[14:Res:165168.1,25.0] || equal(intersection(u,v),singleton(identity_relation))** -> member(identity_relation,u).
% 299.99/300.64  165367[14:Res:165168.1,26.0] || equal(intersection(u,v),singleton(identity_relation))** -> member(identity_relation,v).
% 299.99/300.64  13326[7:Rew:13036.0,9501.2] inductive(u) || well_ordering(v,u) -> equal(segment(v,image(successor_relation,u),least(v,image(successor_relation,u))),identity_relation)**.
% 299.99/300.64  161460[8:Rew:116078.0,13327.1,116078.0,13327.1] operation(u) || well_ordering(v,cantor(cantor(u))) -> equal(segment(v,range_of(u),least(v,range_of(u))),identity_relation)**.
% 299.99/300.64  9837[5:Res:20.2,8798.1] || member(u,ordinal_numbers) member(v,ordinal_numbers) equal(sum_class(range_of(v)),u) -> member(ordered_pair(v,u),union_of_range_map)*.
% 299.99/300.64  13246[7:Rew:13036.0,8912.1] || member(intersection(u,v),ordinal_numbers) -> equal(intersection(u,v),identity_relation) member(apply(choice,intersection(u,v)),u)*.
% 299.99/300.64  13247[7:Rew:13036.0,8913.1] || member(intersection(u,v),ordinal_numbers) -> equal(intersection(u,v),identity_relation) member(apply(choice,intersection(u,v)),v)*.
% 299.99/300.64  13600[7:Rew:13036.0,13097.1] ||  -> equal(singleton(u),identity_relation) equal(intersection(singleton(u),u),identity_relation)**.
% 299.99/300.64  13225[7:Rew:13036.0,8824.2] || member(u,ordinal_numbers) subclass(u,v) -> equal(u,identity_relation) member(apply(choice,u),v)*.
% 299.99/300.64  206540[7:SpR:147905.0,165795.1] ||  -> equal(integer_of(u),identity_relation) subclass(complement(complement(singleton(u))),omega)*.
% 299.99/300.64  165795[7:Obv:165789.0] ||  -> equal(integer_of(u),identity_relation) subclass(intersection(singleton(u),v),omega)*.
% 299.99/300.64  165794[7:Obv:165788.0] ||  -> equal(integer_of(u),identity_relation) subclass(intersection(v,singleton(u)),omega)*.
% 299.99/300.64  117507[8:Rew:116078.0,116134.1] operation(restrict(u,v,universal_class)) ||  -> subclass(image(u,v),cantor(cantor(restrict(u,v,ordinal_numbers))))*.
% 299.99/300.64  82835[7:Res:55.1,13240.0] inductive(recursion_equation_functions(u)) ||  -> equal(integer_of(v),identity_relation)** function(v).
% 299.99/300.64  19338[7:Res:19314.0,13082.1] inductive(symmetric_difference(u,singleton(u))) ||  -> member(identity_relation,successor(u))*.
% 299.99/300.64  19349[7:Res:19315.0,13082.1] inductive(symmetric_difference(u,inverse(u))) ||  -> member(identity_relation,symmetrization_of(u))*.
% 299.99/300.64  166250[7:Res:144251.0,13082.1] inductive(symmetric_difference(u,u)) ||  -> member(identity_relation,complement(complement(u)))*.
% 299.99/300.64  117506[8:Rew:116078.0,116133.1] operation(restrict(u,v,ordinal_numbers)) ||  -> subclass(image(u,v),cantor(cantor(restrict(u,v,ordinal_numbers))))*.
% 299.99/300.64  9006[5:Rew:8637.0,8916.2] function(u) || member(v,ordinal_numbers) subclass(ordinal_numbers,w) -> member(image(u,v),w)*.
% 299.99/300.64  155582[8:SpR:140613.0,154945.0] ||  -> equal(intersection(complement(u),symmetric_difference(ordinal_numbers,u)),symmetric_difference(ordinal_numbers,u))**.
% 299.99/300.64  13167[7:Rew:13036.0,9802.1] inductive(compose(u,v)) ||  -> member(identity_relation,cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.64  206175[23:Res:205574.1,205613.0] || equal(recursion_equation_functions(u),singleton(singleton(identity_relation)))* -> .
% 299.99/300.64  8530[0:SpR:43.0,116.2] function(inverse(u)) || subclass(range_of(inverse(u)),v) -> maps(inverse(u),range_of(u),v)*.
% 299.99/300.64  206176[22:Res:205574.1,60940.0] || equal(singleton(singleton(identity_relation)),subset_relation)** -> .
% 299.99/300.64  205574[22:Res:10.1,202352.0] || equal(u,singleton(singleton(identity_relation))) -> member(singleton(identity_relation),u)*.
% 299.99/300.64  205498[22:Res:10.1,202348.0] || equal(u,singleton(singleton(identity_relation)))*+ well_ordering(ordinal_numbers,u)* -> .
% 299.99/300.64  117508[8:Rew:116078.0,116141.2,116078.0,116141.2,116078.0,116141.1] operation(u) || subclass(cantor(cantor(u)),range_of(u))* -> equal(cantor(cantor(u)),range_of(u)).
% 299.99/300.64  206008[20:MRR:205995.1,194308.0] || equal(symmetric_difference(ordinal_numbers,symmetrization_of(identity_relation)),ordinal_numbers)** -> .
% 299.99/300.64  204042[8:Res:192333.1,151988.0] || equal(symmetric_difference(ordinal_numbers,complement(u)),ordinal_numbers)** -> member(identity_relation,u).
% 299.99/300.64  204039[8:Res:192333.1,28.1] || equal(symmetric_difference(ordinal_numbers,u),ordinal_numbers)** member(identity_relation,u) -> .
% 299.99/300.64  205932[23:Res:10.1,205630.0] || equal(recursion_equation_functions(u),omega)**+ -> equal(integer_of(singleton(identity_relation)),identity_relation)**.
% 299.99/300.64  13313[7:Rew:13036.0,8911.2] || member(complement(u),ordinal_numbers) member(apply(choice,complement(u)),u)* -> equal(complement(u),identity_relation).
% 299.99/300.64  205933[23:Res:55.1,205630.0] inductive(recursion_equation_functions(u)) ||  -> equal(integer_of(singleton(identity_relation)),identity_relation)**.
% 299.99/300.64  205630[23:Res:13125.2,205613.0] || subclass(omega,recursion_equation_functions(u))* -> equal(integer_of(singleton(identity_relation)),identity_relation).
% 299.99/300.64  9005[5:Rew:8637.0,8779.0] || member(restrict(element_relation,ordinal_numbers,u),ordinal_numbers) -> member(ordered_pair(restrict(element_relation,ordinal_numbers,u),sum_class(u)),domain_relation)*.
% 299.99/300.64  205859[23:SoR:205856.0,82.1] operation(successor(identity_relation)) ||  -> .
% 299.99/300.64  205857[23:SoR:205856.0,75.1] one_to_one(successor(identity_relation)) ||  -> .
% 299.99/300.64  205856[23:MRR:205855.1,165984.1] function(successor(identity_relation)) ||  -> .
% 299.99/300.64  205611[23:MRR:195528.2,205608.0] single_valued_class(successor(identity_relation)) || member(identity_relation,cross_product(ordinal_numbers,ordinal_numbers))* -> .
% 299.99/300.64  284[0:SpR:72.0,139.1] || member(image(u,singleton(v)),ordinal_numbers) -> subclass(apply(u,v),image(u,singleton(v)))*.
% 299.99/300.64  193953[18:SoR:191931.0,82.1] operation(inverse(identity_relation)) || well_ordering(ordinal_numbers,cross_product(ordinal_numbers,ordinal_numbers))* -> .
% 299.99/300.64  193951[18:SoR:191931.0,75.1] one_to_one(inverse(identity_relation)) || well_ordering(ordinal_numbers,cross_product(ordinal_numbers,ordinal_numbers))* -> .
% 299.99/300.64  193948[18:SoR:191914.0,82.1] operation(symmetrization_of(identity_relation)) || well_ordering(ordinal_numbers,cross_product(ordinal_numbers,ordinal_numbers))* -> .
% 299.99/300.64  193946[18:SoR:191914.0,75.1] one_to_one(symmetrization_of(identity_relation)) || well_ordering(ordinal_numbers,cross_product(ordinal_numbers,ordinal_numbers))* -> .
% 299.99/300.64  161076[8:Rew:116078.0,13312.1] || member(u,ordinal_numbers) -> member(u,cantor(v)) equal(image(v,singleton(u)),range_of(identity_relation))**.
% 299.99/300.64  191931[18:Res:8665.1,190447.0] function(inverse(identity_relation)) || well_ordering(ordinal_numbers,cross_product(ordinal_numbers,ordinal_numbers))* -> .
% 299.99/300.64  191914[18:Res:8665.1,190433.0] function(symmetrization_of(identity_relation)) || well_ordering(ordinal_numbers,cross_product(ordinal_numbers,ordinal_numbers))* -> .
% 299.99/300.64  116101[8:Rew:116078.0,8776.1] operation(restrict(element_relation,universal_class,u)) ||  -> subclass(range_of(restrict(element_relation,ordinal_numbers,u)),cantor(sum_class(u)))*.
% 299.99/300.64  167595[14:Res:8665.1,164499.0] function(singleton(identity_relation)) || well_ordering(ordinal_numbers,cross_product(ordinal_numbers,ordinal_numbers))* -> .
% 299.99/300.64  205578[22:Res:79560.1,202352.0] ||  -> member(singleton(identity_relation),u) member(singleton(identity_relation),complement(u))*.
% 299.99/300.64  13169[7:Rew:13036.0,9800.1] inductive(rest_of(u)) ||  -> member(identity_relation,cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.64  116100[8:Rew:116078.0,9098.1] operation(restrict(element_relation,ordinal_numbers,u)) ||  -> subclass(range_of(restrict(element_relation,ordinal_numbers,u)),cantor(sum_class(u)))*.
% 299.99/300.64  13168[7:Rew:13036.0,9801.1] inductive(compose_class(u)) ||  -> member(identity_relation,cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.64  193950[18:SoR:191931.0,76.1] one_to_one(identity_relation) || well_ordering(ordinal_numbers,cross_product(ordinal_numbers,ordinal_numbers))* -> .
% 299.99/300.64  191036[18:SoR:190595.0,82.1] operation(inverse(identity_relation)) ||  -> member(identity_relation,cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.64  191034[18:SoR:190595.0,75.1] one_to_one(inverse(identity_relation)) ||  -> member(identity_relation,cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.64  161207[8:Rew:140613.0,15186.0] ||  -> equal(symmetric_difference(ordinal_numbers,intersection(singleton(identity_relation),image(successor_relation,ordinal_numbers))),symmetric_difference(singleton(identity_relation),image(successor_relation,ordinal_numbers)))**.
% 299.99/300.64  191032[18:SoR:190444.0,82.1] operation(symmetrization_of(identity_relation)) ||  -> member(identity_relation,cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.64  191030[18:SoR:190444.0,75.1] one_to_one(symmetrization_of(identity_relation)) ||  -> member(identity_relation,cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.64  190595[18:Res:8665.1,190451.0] function(inverse(identity_relation)) ||  -> member(identity_relation,cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.64  190444[18:Res:8665.1,190437.0] function(symmetrization_of(identity_relation)) ||  -> member(identity_relation,cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.64  8835[5:Rew:8637.0,988.0] || member(u,ordinal_numbers) -> member(u,image(element_relation,complement(v)))* member(u,power_class(v)).
% 299.99/300.64  165170[14:Res:8665.1,164503.0] function(singleton(identity_relation)) ||  -> member(identity_relation,cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.64  1300[0:Res:52.1,11.0] inductive(u) || subclass(u,image(successor_relation,u))* -> equal(image(successor_relation,u),u).
% 299.99/300.64  191033[18:SoR:190595.0,76.1] one_to_one(identity_relation) ||  -> member(identity_relation,cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.64  13174[7:Rew:13036.0,9795.1] inductive(union_of_range_map) ||  -> member(identity_relation,cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.64  13170[7:Rew:13036.0,9799.1] inductive(element_relation) ||  -> member(identity_relation,cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.64  13173[7:Rew:13036.0,9796.1] inductive(rest_relation) ||  -> member(identity_relation,cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.64  9091[5:Rew:43.0,9086.1] operation(flip(cross_product(u,ordinal_numbers))) ||  -> equal(cross_product(range_of(u),range_of(u)),inverse(u))**.
% 299.99/300.64  13172[7:Rew:13036.0,9797.1] inductive(domain_relation) ||  -> member(identity_relation,cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.64  13171[7:Rew:13036.0,9798.1] inductive(successor_relation) ||  -> member(identity_relation,cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.64  162898[8:MRR:13453.2,162894.0] function(image(successor_relation,cross_product(universal_class,universal_class))) || member(identity_relation,cross_product(ordinal_numbers,ordinal_numbers))* -> .
% 299.99/300.64  205632[23:Res:9632.1,205613.0] || equal(complement(complement(recursion_equation_functions(u))),ordinal_numbers)** -> .
% 299.99/300.64  205620[23:Res:205609.0,8843.1] || subclass(ordinal_numbers,complement(complement(recursion_equation_functions(u))))* -> .
% 299.99/300.64  205633[23:Res:8645.1,205613.0] || subclass(ordinal_numbers,recursion_equation_functions(u))* -> .
% 299.99/300.64  205631[23:Res:143198.1,205613.0] || equal(recursion_equation_functions(u),ordinal_numbers)** -> .
% 299.99/300.64  162899[8:MRR:13454.2,162894.0] function(image(successor_relation,cross_product(ordinal_numbers,ordinal_numbers))) || member(identity_relation,cross_product(ordinal_numbers,ordinal_numbers))* -> .
% 299.99/300.64  205613[23:Res:205609.0,28.1] || member(singleton(identity_relation),recursion_equation_functions(u))* -> .
% 299.99/300.64  205610[23:MRR:205505.1,205608.0] || well_ordering(ordinal_numbers,complement(recursion_equation_functions(u)))* -> .
% 299.99/300.64  205626[23:Res:75.1,205608.0] one_to_one(singleton(identity_relation)) ||  -> .
% 299.99/300.64  205608[23:Spt:205607.0,205581.0,205582.0] || function(singleton(identity_relation))* -> .
% 299.99/300.64  205609[23:Spt:205607.0,205581.1] ||  -> member(singleton(identity_relation),complement(recursion_equation_functions(u)))*.
% 299.99/300.64  202352[22:Res:202344.0,5.0] || subclass(singleton(singleton(identity_relation)),u)* -> member(singleton(identity_relation),u).
% 299.99/300.64  3768[0:Rew:43.0,3752.1] operation(flip(cross_product(u,universal_class))) ||  -> equal(cross_product(range_of(u),range_of(u)),inverse(u))**.
% 299.99/300.64  205502[22:Res:79560.1,202348.0] || well_ordering(ordinal_numbers,complement(u))* -> member(singleton(identity_relation),u).
% 299.99/300.64  205552[22:MRR:205530.0,8655.0] || well_ordering(ordinal_numbers,unordered_pair(u,singleton(identity_relation)))* -> .
% 299.99/300.64  205551[22:MRR:205529.0,8655.0] || well_ordering(ordinal_numbers,unordered_pair(singleton(identity_relation),u))* -> .
% 299.99/300.64  205501[22:Res:10714.1,202348.0] || member(singleton(identity_relation),u)* well_ordering(ordinal_numbers,u) -> .
% 299.99/300.64  116109[8:Rew:116078.0,3750.1] operation(inverse(u)) ||  -> equal(cross_product(cantor(range_of(u)),cantor(range_of(u))),range_of(u))**.
% 299.99/300.64  205503[22:Res:13059.1,202348.0] || well_ordering(ordinal_numbers,omega) -> equal(integer_of(singleton(identity_relation)),identity_relation)**.
% 299.99/300.64  205499[22:Res:295.0,202348.0] || well_ordering(ordinal_numbers,singleton(singleton(identity_relation)))* -> .
% 299.99/300.64  202348[22:Res:202344.0,9876.0] || subclass(singleton(singleton(identity_relation)),u)* well_ordering(ordinal_numbers,u) -> .
% 299.99/300.64  13438[7:Rew:13036.0,8910.1] || member(recursion_equation_functions(u),ordinal_numbers) -> equal(recursion_equation_functions(u),identity_relation) function(apply(choice,recursion_equation_functions(u)))*.
% 299.99/300.64  202345[21:Con:198094.1] || member(u,ordinal_numbers) subclass(rest_relation,rest_of(power_class(u)))* -> .
% 299.99/300.64  177049[8:SoR:162921.0,82.1] operation(range_of(u)) || equal(rest_of(inverse(u)),rest_relation)** -> .
% 299.99/300.64  177047[8:SoR:162921.0,75.1] one_to_one(range_of(u)) || equal(rest_of(inverse(u)),rest_relation)** -> .
% 299.99/300.64  162921[8:MRR:136423.2,162904.0] function(range_of(u)) || equal(rest_of(inverse(u)),rest_relation)** -> .
% 299.99/300.64  9090[5:Rew:43.0,9084.1] operation(flip(cross_product(u,ordinal_numbers))) ||  -> subclass(range_of(flip(cross_product(u,ordinal_numbers))),range_of(u))*.
% 299.99/300.64  8772[5:Rew:8637.0,275.1] operation(flip(cross_product(u,universal_class))) ||  -> subclass(range_of(flip(cross_product(u,ordinal_numbers))),range_of(u))*.
% 299.99/300.64  196624[21:Rew:196549.0,160662.1] || member(singleton(singleton(singleton(u))),domain_relation)* -> equal(identity_relation,u).
% 299.99/300.64  481[0:SpR:30.0,59.0] ||  -> equal(complement(image(element_relation,union(u,v))),power_class(intersection(complement(u),complement(v))))**.
% 299.99/300.64  198469[21:Res:8956.1,197870.1] || member(u,ordinal_numbers) equal(rest_of(power_class(u)),rest_relation)** -> .
% 299.99/300.64  485[0:SpR:59.0,30.0] ||  -> equal(union(u,image(element_relation,complement(v))),complement(intersection(complement(u),power_class(v))))**.
% 299.99/300.64  165178[14:SpR:59.0,165172.1] ||  -> member(identity_relation,image(element_relation,complement(u)))* member(identity_relation,power_class(u)).
% 299.99/300.64  195033[15:Res:10.1,165530.0] || equal(complement(complement(u)),ordinal_numbers) -> member(range_of(identity_relation),u)*.
% 299.99/300.64  487[0:SpR:59.0,30.0] ||  -> equal(union(image(element_relation,complement(u)),v),complement(intersection(power_class(u),complement(v))))**.
% 299.99/300.64  165530[15:Res:165526.1,151988.0] || subclass(ordinal_numbers,complement(complement(u)))* -> member(range_of(identity_relation),u).
% 299.99/300.64  165527[15:Res:165526.1,28.1] || subclass(ordinal_numbers,complement(u)) member(range_of(identity_relation),u)* -> .
% 299.99/300.64  13311[7:Rew:13036.0,8989.1] || asymmetric(u,ordinal_numbers) -> equal(image(intersection(u,inverse(u)),ordinal_numbers),range_of(identity_relation))**.
% 299.99/300.64  136362[8:Res:135061.1,8954.0] || equal(rest_of(inverse(u)),rest_relation)** -> equal(range_of(u),ordinal_numbers).
% 299.99/300.64  167629[14:SpL:116239.0,165401.1] operation(inverse(u)) || equal(range_of(u),singleton(identity_relation))** -> .
% 299.99/300.64  192008[18:SpL:116239.0,190588.1] operation(inverse(u)) || equal(range_of(u),symmetrization_of(identity_relation))** -> .
% 299.99/300.64  8977[5:Rew:8637.0,8838.1] || member(u,ordinal_numbers) subclass(ordinal_numbers,v) -> member(power_class(u),v)*.
% 299.99/300.64  192014[18:SpL:116239.0,190699.1] operation(inverse(u)) || equal(range_of(u),inverse(identity_relation))** -> .
% 299.99/300.64  198467[21:Res:148963.1,197870.1] || member(u,ordinal_numbers) equal(rest_of(rest_of(u)),rest_relation)** -> .
% 299.99/300.64  198464[21:Res:50064.1,197870.1] || member(u,subset_relation) equal(rest_of(second(u)),rest_relation)** -> .
% 299.99/300.64  198463[21:Res:50063.1,197870.1] || member(u,subset_relation) equal(rest_of(first(u)),rest_relation)** -> .
% 299.99/300.64  8979[5:Rew:8637.0,8858.1] || member(image(u,singleton(v)),ordinal_numbers)* -> member(apply(u,v),ordinal_numbers).
% 299.99/300.64  198460[21:Res:8955.1,197870.1] || member(u,ordinal_numbers) equal(rest_of(sum_class(u)),rest_relation)** -> .
% 299.99/300.64  288[0:SpL:59.0,28.1] || member(u,image(element_relation,complement(v)))* member(u,power_class(v)) -> .
% 299.99/300.64  13280[7:Rew:13036.0,6999.1] || equal(image(successor_relation,u),u)** member(identity_relation,u) -> inductive(u).
% 299.99/300.64  116108[8:Rew:116078.0,272.1] operation(inverse(u)) ||  -> subclass(range_of(inverse(u)),cantor(range_of(u)))*.
% 299.99/300.64  204853[21:Res:10.1,204666.0] || equal(recursion_equation_functions(u),domain_relation)**+ -> function(singleton(singleton(singleton(identity_relation))))*.
% 299.99/300.64  204666[21:Res:196904.1,152.0] || subclass(domain_relation,recursion_equation_functions(u))*+ -> function(singleton(singleton(singleton(identity_relation))))*.
% 299.99/300.64  189[0:SpR:59.0,59.0] ||  -> equal(complement(image(element_relation,power_class(u))),power_class(image(element_relation,complement(u))))**.
% 299.99/300.64  196904[21:MRR:196839.0,8655.0] || subclass(domain_relation,u) -> member(singleton(singleton(singleton(identity_relation))),u)*.
% 299.99/300.64  196581[21:Res:133495.1,196372.0] || well_ordering(u,ordinal_numbers) -> equal(cantor(least(u,rest_relation)),identity_relation)**.
% 299.99/300.64  155824[5:SpR:155653.0,8649.0] ||  -> equal(image(complement(compose(complement(element_relation),inverse(element_relation))),ordinal_numbers),range_of(subset_relation))**.
% 299.99/300.64  196580[21:Res:133502.1,196372.0] || well_ordering(u,rest_relation) -> equal(cantor(least(u,rest_relation)),identity_relation)**.
% 299.99/300.64  196579[21:Res:19525.1,196372.0] || well_ordering(u,ordinal_numbers) -> equal(cantor(least(u,ordinal_numbers)),identity_relation)**.
% 299.99/300.64  196255[18:Res:13049.1,190641.1] || subclass(ordinal_numbers,u)* equal(complement(u),inverse(identity_relation)) -> .
% 299.99/300.64  95[0:Inp] operation(u) operation(v) || equal(apply(u,ordered_pair(apply(w,not_homomorphism1(w,v,u)),apply(w,not_homomorphism2(w,v,u)))),apply(w,apply(v,ordered_pair(not_homomorphism1(w,v,u),not_homomorphism2(w,v,u)))))* compatible(w,v,u) -> homomorphism(w,v,u).
% 299.99/300.64  196251[18:Res:192149.1,190641.1] || equal(u,ordinal_numbers) equal(complement(u),inverse(identity_relation))** -> .
% 299.99/300.64  196165[18:Res:13049.1,190532.1] || subclass(ordinal_numbers,u)* equal(complement(u),symmetrization_of(identity_relation)) -> .
% 299.99/300.64  196161[18:Res:192149.1,190532.1] || equal(u,ordinal_numbers) equal(complement(u),symmetrization_of(identity_relation))* -> .
% 299.99/300.64  195271[16:Rew:195224.0,163199.1] ||  -> member(u,complement(singleton(identity_relation)))* subclass(singleton(u),singleton(identity_relation)).
% 299.99/300.64  8803[5:Rew:8637.0,63.1] || member(u,image(v,image(w,singleton(x))))* member(ordered_pair(x,u),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(x,u),compose(v,w)).
% 299.99/300.64  195114[14:Res:13049.1,165357.1] || subclass(ordinal_numbers,u)* equal(complement(u),singleton(identity_relation)) -> .
% 299.99/300.64  195109[14:Res:192149.1,165357.1] || equal(u,ordinal_numbers) equal(complement(u),singleton(identity_relation))** -> .
% 299.99/300.64  204324[18:Res:10.1,204204.0] || equal(recursion_equation_functions(u),symmetrization_of(identity_relation))**+ -> function(regular(symmetrization_of(identity_relation)))*.
% 299.99/300.64  204204[18:Res:194549.1,152.0] || subclass(symmetrization_of(identity_relation),recursion_equation_functions(u))* -> function(regular(symmetrization_of(identity_relation))).
% 299.99/300.64  117631[8:Rew:116078.0,116135.2,116078.0,116135.2,116078.0,116135.1] function(u) || subclass(range_of(u),cantor(cantor(u))) equal(cross_product(cantor(cantor(u)),cantor(cantor(u))),cantor(u))** -> operation(u).
% 299.99/300.64  204205[18:Res:194549.1,14676.0] || subclass(symmetrization_of(identity_relation),identity_relation)* -> .
% 299.99/300.64  194549[18:Res:194543.0,5.0] || subclass(symmetrization_of(identity_relation),u) -> member(regular(symmetrization_of(identity_relation)),u)*.
% 299.99/300.64  204134[8:MRR:204130.1,41096.1] || member(u,inverse(identity_relation)) -> member(u,symmetrization_of(identity_relation))*.
% 299.99/300.64  194487[8:Res:163112.0,28.1] || member(u,inverse(identity_relation)) -> subclass(singleton(u),symmetrization_of(identity_relation))*.
% 299.99/300.64  117602[8:Rew:116078.0,116112.2,116078.0,116112.2,116078.0,116112.2,116078.0,116112.1] function(u) || subclass(range_of(u),cantor(cantor(v)))*+ equal(cantor(cantor(w)),cantor(u)) -> compatible(u,w,v)*.
% 299.99/300.64  204050[20:Res:192333.1,194308.0] || equal(symmetric_difference(ordinal_numbers,inverse(identity_relation)),ordinal_numbers)** -> .
% 299.99/300.64  204049[16:Res:192333.1,165946.0] || equal(symmetric_difference(ordinal_numbers,singleton(identity_relation)),ordinal_numbers)** -> .
% 299.99/300.64  192333[8:SpL:140613.0,13051.0] || equal(symmetric_difference(ordinal_numbers,u),ordinal_numbers) -> member(identity_relation,complement(u))*.
% 299.99/300.64  8798[5:Rew:8637.0,158.1] || equal(sum_class(range_of(u)),v) member(ordered_pair(u,v),cross_product(ordinal_numbers,ordinal_numbers))* -> member(ordered_pair(u,v),union_of_range_map).
% 299.99/300.64  192293[8:SpL:140613.0,13045.0] || subclass(ordinal_numbers,symmetric_difference(ordinal_numbers,u))* -> member(identity_relation,complement(u)).
% 299.99/300.64  62[0:Inp] || member(ordered_pair(u,v),compose(w,x)) -> member(v,image(w,image(x,singleton(u))))*.
% 299.99/300.64  116203[8:Rew:116078.0,116.2] function(u) || subclass(range_of(u),v) -> maps(u,cantor(u),v)*.
% 299.99/300.64  195257[16:Rew:195224.0,162037.0] ||  -> equal(complement(image(element_relation,singleton(identity_relation))),power_class(complement(singleton(identity_relation))))**.
% 299.99/300.64  107[0:Inp] ||  -> equal(domain__dfg(u,image(inverse(u),singleton(single_valued1(u))),single_valued2(u)),single_valued3(u))**.
% 299.99/300.64  195258[16:Rew:195224.0,163180.0] ||  -> subclass(complement(power_class(complement(singleton(identity_relation)))),image(element_relation,singleton(identity_relation)))*.
% 299.99/300.64  163093[8:SpR:162584.0,130710.0] ||  -> subclass(complement(power_class(complement(inverse(identity_relation)))),image(element_relation,symmetrization_of(identity_relation)))*.
% 299.99/300.64  162038[8:Rew:140603.0,161954.0] ||  -> equal(complement(image(element_relation,symmetrization_of(identity_relation))),power_class(complement(inverse(identity_relation))))**.
% 299.99/300.64  1977[0:SSi:1972.0,54.0] inductive(image(successor_relation,omega)) ||  -> equal(image(successor_relation,omega),omega)**.
% 299.99/300.64  13084[7:Rew:13036.0,4560.1] || member(u,ordinal_numbers) equal(ordinal_add(identity_relation,u),u)** -> member(u,ordinals_with_null_class_as_identity).
% 299.99/300.64  167474[15:Res:165526.1,163154.0] || subclass(ordinal_numbers,symmetrization_of(identity_relation)) -> member(range_of(identity_relation),inverse(identity_relation))*.
% 299.99/300.64  163366[8:SpR:159.0,118070.0] ||  -> equal(intersection(ordinal_add(u,v),ordinal_numbers),ordinal_add(u,v))**.
% 299.99/300.64  13069[7:Rew:13036.0,8699.1] || member(u,ordinal_numbers) -> equal(u,identity_relation) member(apply(choice,u),u)*.
% 299.99/300.64  118070[8:SpR:72.0,117140.0] ||  -> equal(intersection(apply(u,v),ordinal_numbers),apply(u,v))**.
% 299.99/300.64  117335[8:Rew:8649.0,116952.0] ||  -> equal(intersection(image(u,v),ordinal_numbers),image(u,v))**.
% 299.99/300.64  196564[21:Res:18510.1,196372.0] function(u) ||  -> equal(cantor(apply(u,v)),identity_relation)**.
% 299.99/300.64  165378[14:Res:165168.1,3700.0] || equal(singleton(u),singleton(identity_relation))* -> equal(identity_relation,u).
% 299.99/300.64  8976[5:Rew:8637.0,8745.2] function(u) || member(v,ordinal_numbers) -> member(image(u,v),ordinal_numbers)*.
% 299.99/300.64  190554[18:Res:190442.1,3700.0] || equal(singleton(u),symmetrization_of(identity_relation))* -> equal(identity_relation,u).
% 299.99/300.64  190663[18:Res:190593.1,3700.0] || equal(singleton(u),inverse(identity_relation))* -> equal(identity_relation,u).
% 299.99/300.64  196563[21:Res:8956.1,196372.0] || member(u,ordinal_numbers) -> equal(cantor(power_class(u)),identity_relation)**.
% 299.99/300.64  165442[15:Res:165431.0,5.0] || subclass(ordinal_numbers,u) -> member(sum_class(range_of(identity_relation)),u)*.
% 299.99/300.64  13052[7:Rew:13036.0,4541.0] || member(identity_relation,u) subclass(image(successor_relation,u),u)* -> inductive(u).
% 299.99/300.64  165433[15:MRR:15635.0,165430.0] || subclass(range_of(identity_relation),u) -> maps(identity_relation,identity_relation,u)*.
% 299.99/300.64  165075[8:SpL:116239.0,164087.1] operation(inverse(u)) || subclass(ordinal_numbers,range_of(u))* -> .
% 299.99/300.64  117261[8:Rew:116078.0,116130.1] || compatible(u,v,w)*+ -> subclass(range_of(u),cantor(cantor(w)))*.
% 299.99/300.64  141389[8:Rew:140613.0,117941.0] ||  -> equal(symmetric_difference(range_of(u),ordinal_numbers),symmetric_difference(ordinal_numbers,range_of(u)))**.
% 299.99/300.64  165084[8:SpL:116239.0,164088.1] operation(inverse(u)) || equal(range_of(u),ordinal_numbers)** -> .
% 299.99/300.64  13088[7:Rew:13036.0,4580.1] inductive(cantor(inverse(u))) ||  -> member(identity_relation,range_of(u))*.
% 299.99/300.64  198568[21:Res:66492.1,198282.0] ||  -> equal(integer_of(inverse(u)),identity_relation)** equal(range_of(u),identity_relation).
% 299.99/300.64  157[0:Inp] || member(ordered_pair(u,v),union_of_range_map)* -> equal(sum_class(range_of(u)),v).
% 299.99/300.64  198289[21:Obv:198288.1] || member(inverse(u),subset_relation)* -> equal(range_of(u),identity_relation).
% 299.99/300.64  198282[21:MRR:198167.2,14676.0] || member(inverse(u),ordinal_numbers)* -> equal(range_of(u),identity_relation).
% 299.99/300.64  197474[21:SpR:196546.1,116239.0] ||  -> equal(singleton(inverse(u)),identity_relation)** equal(range_of(u),identity_relation).
% 299.99/300.64  159[0:Inp] ||  -> equal(apply(recursion(u,successor_relation,union_of_range_map),v),ordinal_add(u,v))**.
% 299.99/300.64  13099[7:Rew:13036.0,4567.0] ||  -> equal(recursion(identity_relation,apply(add_relation,u),union_of_range_map),ordinal_multiply(u,v))*.
% 299.99/300.64  15583[8:Res:15426.1,157.0] || subclass(domain_relation,union_of_range_map) -> equal(sum_class(range_of(identity_relation)),identity_relation)**.
% 299.99/300.64  15643[8:MRR:15642.1,13039.0] || subclass(domain_relation,union_of_range_map) -> section(element_relation,range_of(identity_relation),ordinal_numbers)*.
% 299.99/300.64  115[0:Inp] || maps(u,v,w)* -> subclass(range_of(u),w).
% 299.99/300.64  18510[5:MRR:18508.1,8655.0] function(u) ||  -> member(apply(u,v),ordinal_numbers)*.
% 299.99/300.64  130710[5:SpR:59.0,130678.0] ||  -> subclass(complement(power_class(u)),image(element_relation,complement(u)))*.
% 299.99/300.64  72[0:Inp] ||  -> equal(sum_class(image(u,singleton(v))),apply(u,v))**.
% 299.99/300.64  165526[15:Res:165460.0,5.0] || subclass(ordinal_numbers,u) -> member(range_of(identity_relation),u)*.
% 299.99/300.64  145758[5:SpR:143170.0,8649.0] ||  -> equal(range_of(cross_product(u,ordinal_numbers)),image(ordinal_numbers,u))**.
% 299.99/300.64  8649[5:Rew:8637.0,46.0] ||  -> equal(range_of(restrict(u,v,ordinal_numbers)),image(u,v))**.
% 299.99/300.64  194978[15:MRR:194957.0,165460.0] || subclass(ordinal_numbers,complement(unordered_pair(range_of(identity_relation),u)))* -> .
% 299.99/300.64  195001[15:Res:10.1,194978.0] || equal(complement(unordered_pair(range_of(identity_relation),u)),ordinal_numbers)** -> .
% 299.99/300.64  194979[15:MRR:194958.0,165460.0] || subclass(ordinal_numbers,complement(unordered_pair(u,range_of(identity_relation))))* -> .
% 299.99/300.64  195007[15:Res:10.1,194979.0] || equal(complement(unordered_pair(u,range_of(identity_relation))),ordinal_numbers)** -> .
% 299.99/300.64  13085[7:Rew:13036.0,4561.1] || member(u,ordinals_with_null_class_as_identity) -> equal(ordinal_add(identity_relation,u),u)**.
% 299.99/300.64  6984[4:MRR:6981.0,6981.1,56.0,6407.0] ||  -> equal(integer_of(apply(choice,omega)),apply(choice,omega))**.
% 299.99/300.64  116935[8:Rew:116239.0,66084.0] ||  -> equal(intersection(range_of(u),ordinal_numbers),range_of(u))**.
% 299.99/300.64  117217[8:Rew:116078.0,116136.1] operation(u) ||  -> subclass(range_of(u),cantor(cantor(u)))*.
% 299.99/300.64  14769[8:SpR:14756.0,72.0] ||  -> equal(apply(identity_relation,u),sum_class(range_of(identity_relation)))**.
% 299.99/300.64  198461[21:Res:165431.0,197870.1] || equal(rest_of(sum_class(range_of(identity_relation))),rest_relation)** -> .
% 299.99/300.64  52[0:Inp] inductive(u) ||  -> subclass(image(successor_relation,u),u)*.
% 299.99/300.64  194976[15:MRR:194956.0,165460.0] || subclass(ordinal_numbers,complement(singleton(range_of(identity_relation))))* -> .
% 299.99/300.64  194988[15:Res:10.1,194976.0] || equal(complement(singleton(range_of(identity_relation))),ordinal_numbers)** -> .
% 299.99/300.64  8956[5:Rew:8637.0,8707.1] || member(u,ordinal_numbers) -> member(power_class(u),ordinal_numbers)*.
% 299.99/300.64  14756[8:SpR:14650.0,8649.0] ||  -> equal(image(identity_relation,u),range_of(identity_relation))**.
% 299.99/300.64  195851[16:Res:195573.0,3700.0] ||  -> equal(apply(choice,singleton(identity_relation)),identity_relation)**.
% 299.99/300.64  196552[21:Res:165431.0,196372.0] ||  -> equal(cantor(sum_class(range_of(identity_relation))),identity_relation)**.
% 299.99/300.64  59[0:Inp] ||  -> equal(complement(image(element_relation,complement(u))),power_class(u))**.
% 299.99/300.64  198473[21:Res:165460.0,197870.1] || equal(rest_of(range_of(identity_relation)),rest_relation)** -> .
% 299.99/300.64  155656[5:Rew:155653.0,8945.0] ||  -> equal(image(subset_relation,ordinal_numbers),range_of(subset_relation))**.
% 299.99/300.64  80980[12:Res:80967.0,8954.0] ||  -> equal(image(element_relation,identity_relation),ordinal_numbers)**.
% 299.99/300.64  15179[8:Rew:15174.0,13140.0] ||  -> equal(union(singleton(identity_relation),image(successor_relation,ordinal_numbers)),ordinal_numbers)**.
% 299.99/300.64  80563[11:Res:80550.0,8954.0] ||  -> equal(image(element_relation,ordinal_numbers),ordinal_numbers)**.
% 299.99/300.64  165431[15:MRR:18512.0,165430.0] ||  -> member(sum_class(range_of(identity_relation)),ordinal_numbers)*.
% 299.99/300.64  196567[21:Res:165460.0,196372.0] ||  -> equal(cantor(range_of(identity_relation)),identity_relation)**.
% 299.99/300.64  80615[12:Spt:79617.1] ||  -> equal(power_class(ordinal_numbers),identity_relation)**.
% 299.99/300.64  116239[8:Rew:116078.0,43.0] ||  -> equal(cantor(inverse(u)),range_of(u))**.
% 299.99/300.64  80200[11:Spt:79601.1] ||  -> equal(power_class(identity_relation),identity_relation)**.
% 299.99/300.64  165460[15:Res:8652.0,165432.0] ||  -> member(range_of(identity_relation),ordinal_numbers)*.
% 299.99/300.64  202344[22:Spt:201031.0,198163.1] ||  -> member(singleton(identity_relation),singleton(singleton(identity_relation)))*.
% 299.99/300.64  13515[7:Rew:13036.0,9556.1] || well_ordering(u,cross_product(ordinal_numbers,ordinal_numbers)) -> equal(compose(v,w),identity_relation) member(least(u,compose(v,w)),compose(v,w))*.
% 299.99/300.64  13362[7:Rew:13036.0,9875.3] || member(u,v)+ subclass(v,w)* well_ordering(omega,w)* -> equal(integer_of(ordered_pair(u,least(omega,v))),identity_relation)**.
% 299.99/300.64  196556[21:Res:41183.1,196372.0] ||  -> subclass(u,v) equal(cantor(not_subclass_element(u,v)),identity_relation)**.
% 299.99/300.64  198565[21:SpL:18840.1,198459.0] || member(u,subset_relation)* equal(rest_of(u),rest_relation) -> .
% 299.99/300.64  198474[21:Res:60996.1,197870.1] || equal(rest_of(regular(u)),rest_relation)** -> equal(u,identity_relation).
% 299.99/300.64  198455[21:Res:18517.1,197870.1] || equal(rest_of(u),rest_relation)** -> equal(singleton(u),identity_relation).
% 299.99/300.64  198454[21:Res:66492.1,197870.1] || equal(rest_of(u),rest_relation) -> equal(integer_of(u),identity_relation)**.
% 299.99/300.64  198459[21:Res:8667.0,197870.1] || equal(rest_of(ordered_pair(u,v)),rest_relation)** -> .
% 299.99/300.64  198457[21:Res:8666.0,197870.1] || equal(rest_of(unordered_pair(u,v)),rest_relation)** -> .
% 299.99/300.64  13511[7:Rew:13036.0,9537.2] || member(u,ordinal_numbers) well_ordering(v,u) -> equal(sum_class(u),identity_relation) member(least(v,sum_class(u)),sum_class(u))*.
% 299.99/300.64  198491[21:Res:125724.0,197870.1] || equal(rest_of(least(element_relation,omega)),rest_relation)** -> .
% 299.99/300.64  198475[21:Res:190509.0,197870.1] || equal(rest_of(regular(symmetrization_of(identity_relation))),rest_relation)** -> .
% 299.99/300.64  198458[21:Res:8655.0,197870.1] || equal(rest_of(singleton(u)),rest_relation)** -> .
% 299.99/300.64  197870[21:Res:10.1,196510.0] || equal(rest_of(u),rest_relation) member(u,ordinal_numbers)* -> .
% 299.99/300.64  13512[7:Rew:13036.0,9560.1] || well_ordering(u,cross_product(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers))*+ -> equal(flip(v),identity_relation) member(least(u,flip(v)),flip(v))*.
% 299.99/300.64  196558[21:Res:148963.1,196372.0] || member(u,ordinal_numbers) -> equal(cantor(rest_of(u)),identity_relation)**.
% 299.99/300.64  13513[7:Rew:13036.0,9561.1] || well_ordering(u,cross_product(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers))*+ -> equal(rotate(v),identity_relation) member(least(u,rotate(v)),rotate(v))*.
% 299.99/300.64  196555[21:Res:50064.1,196372.0] || member(u,subset_relation) -> equal(cantor(second(u)),identity_relation)**.
% 299.99/300.64  196554[21:Res:50063.1,196372.0] || member(u,subset_relation) -> equal(cantor(first(u)),identity_relation)**.
% 299.99/300.64  196551[21:Res:8955.1,196372.0] || member(u,ordinal_numbers) -> equal(cantor(sum_class(u)),identity_relation)**.
% 299.99/300.64  196510[21:Con:196362.0] || subclass(rest_relation,rest_of(u))* member(u,ordinal_numbers) -> .
% 299.99/300.64  13302[7:Rew:13036.0,8507.1] || asymmetric(cross_product(u,v),w) -> equal(restrict(restrict(inverse(cross_product(u,v)),u,v),w,w),identity_relation)**.
% 299.99/300.64  13301[7:Rew:13036.0,8523.0] || equal(restrict(restrict(inverse(cross_product(u,v)),u,v),w,w),identity_relation)** -> asymmetric(cross_product(u,v),w).
% 299.99/300.64  197806[21:MRR:197805.0,66422.0] || equal(rest_of(omega),rest_relation)** -> .
% 299.99/300.64  13504[7:Rew:13036.0,9503.2] || member(u,ordinal_numbers) well_ordering(v,u) -> equal(segment(v,sum_class(u),least(v,sum_class(u))),identity_relation)**.
% 299.99/300.64  197211[21:SpR:18840.1,196550.0] || member(u,subset_relation)* -> equal(cantor(u),identity_relation).
% 299.99/300.64  196568[21:Res:60996.1,196372.0] ||  -> equal(u,identity_relation) equal(cantor(regular(u)),identity_relation)**.
% 299.99/300.64  196546[21:Res:18517.1,196372.0] ||  -> equal(singleton(u),identity_relation) equal(cantor(u),identity_relation)**.
% 299.99/300.64  196545[21:Res:66492.1,196372.0] ||  -> equal(integer_of(u),identity_relation)** equal(cantor(u),identity_relation).
% 299.99/300.64  196410[21:Res:13056.1,196356.1] inductive(cantor(u)) || member(u,ordinal_numbers)* -> .
% 299.99/300.64  13505[7:Rew:13036.0,9522.1] || well_ordering(u,cross_product(ordinal_numbers,ordinal_numbers)) -> equal(segment(u,compose(v,w),least(u,compose(v,w))),identity_relation)**.
% 299.99/300.64  13299[7:Rew:13036.0,8505.1] || asymmetric(u,singleton(v)) -> equal(range__dfg(intersection(u,inverse(u)),v,singleton(v)),second(not_subclass_element(identity_relation,identity_relation)))**.
% 299.99/300.64  13506[7:Rew:13036.0,9526.1] || well_ordering(u,cross_product(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers)) -> equal(segment(u,flip(v),least(u,flip(v))),identity_relation)**.
% 299.99/300.64  13507[7:Rew:13036.0,9527.1] || well_ordering(u,cross_product(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers)) -> equal(segment(u,rotate(v),least(u,rotate(v))),identity_relation)**.
% 299.99/300.64  196550[21:Res:8667.0,196372.0] ||  -> equal(cantor(ordered_pair(u,v)),identity_relation)**.
% 299.99/300.64  13263[7:Rew:13036.0,4671.0] ||  -> equal(unordered_pair(u,v),identity_relation) equal(regular(unordered_pair(u,v)),v)** equal(regular(unordered_pair(u,v)),u)**.
% 299.99/300.64  196548[21:Res:8666.0,196372.0] ||  -> equal(cantor(unordered_pair(u,v)),identity_relation)**.
% 299.99/300.64  13224[7:Rew:13036.0,9557.2] function(u) || well_ordering(v,cross_product(ordinal_numbers,ordinal_numbers))*+ -> equal(u,identity_relation) member(least(v,u),u)*.
% 299.99/300.64  197104[21:Res:196792.0,133836.0] || well_ordering(ordinal_numbers,domain_relation)* -> .
% 299.99/300.64  196792[21:MRR:196784.0,8655.0] ||  -> member(singleton(singleton(singleton(identity_relation))),domain_relation)*.
% 299.99/300.64  13499[7:Rew:13036.0,9523.2] function(u) || well_ordering(v,cross_product(ordinal_numbers,ordinal_numbers)) -> equal(segment(v,u,least(v,u)),identity_relation)**.
% 299.99/300.64  196584[21:Res:125724.0,196372.0] ||  -> equal(cantor(least(element_relation,omega)),identity_relation)**.
% 299.99/300.64  196569[21:Res:190509.0,196372.0] ||  -> equal(cantor(regular(symmetrization_of(identity_relation))),identity_relation)**.
% 299.99/300.64  196549[21:Res:8655.0,196372.0] ||  -> equal(cantor(singleton(u)),identity_relation)**.
% 299.99/300.64  196416[21:Rew:196372.1,160880.2] || member(u,ordinal_numbers) subclass(domain_relation,v) -> member(ordered_pair(u,identity_relation),v)*.
% 299.99/300.64  196783[21:Res:10.1,196681.0] || equal(rest_relation,element_relation)** -> .
% 299.99/300.64  196415[21:Rew:196372.1,160534.1] || member(u,ordinal_numbers) -> member(ordered_pair(u,identity_relation),domain_relation)*.
% 299.99/300.64  196681[21:MRR:196659.1,14676.0] || subclass(rest_relation,element_relation)* -> .
% 299.99/300.64  196547[21:Res:8652.0,196372.0] ||  -> equal(cantor(omega),identity_relation)**.
% 299.99/300.64  196372[21:Res:13072.1,196356.1] || member(u,ordinal_numbers)* -> equal(cantor(u),identity_relation).
% 299.99/300.64  161356[8:Rew:116078.0,13300.1] || member(u,ordinal_numbers) -> member(u,cantor(v)) equal(second(not_subclass_element(identity_relation,identity_relation)),range__dfg(v,u,ordinal_numbers))*.
% 299.99/300.64  191768[18:Res:190442.1,13047.1] || equal(u,symmetrization_of(identity_relation))*+ equal(complement(u),ordinal_numbers)** -> .
% 299.99/300.64  191767[18:Res:190593.1,13047.1] || equal(u,inverse(identity_relation)) equal(complement(u),ordinal_numbers)** -> .
% 299.99/300.64  190644[18:Res:190593.1,151988.0] || equal(complement(complement(u)),inverse(identity_relation))** -> member(identity_relation,u).
% 299.99/300.64  196256[18:Res:13056.1,190641.1] inductive(u) || equal(complement(u),inverse(identity_relation))** -> .
% 299.99/300.64  13500[7:Rew:13036.0,9554.1] || well_ordering(u,cross_product(ordinal_numbers,ordinal_numbers)) -> equal(rest_of(v),identity_relation) member(least(u,rest_of(v)),rest_of(v))*.
% 299.99/300.64  196265[18:MRR:196233.0,13126.0] || equal(complement(unordered_pair(u,identity_relation)),inverse(identity_relation))** -> .
% 299.99/300.64  196264[18:MRR:196232.0,13126.0] || equal(complement(unordered_pair(identity_relation,u)),inverse(identity_relation))** -> .
% 299.99/300.64  196258[18:Res:190432.0,190641.1] || equal(complement(symmetrization_of(identity_relation)),inverse(identity_relation))** -> .
% 299.99/300.64  190641[18:Res:190593.1,28.1] || equal(complement(u),inverse(identity_relation)) member(identity_relation,u)* -> .
% 299.99/300.64  13501[7:Rew:13036.0,9555.1] || well_ordering(u,cross_product(ordinal_numbers,ordinal_numbers)) -> equal(compose_class(v),identity_relation) member(least(u,compose_class(v)),compose_class(v))*.
% 299.99/300.64  190535[18:Res:190442.1,151988.0] || equal(complement(complement(u)),symmetrization_of(identity_relation))** -> member(identity_relation,u).
% 299.99/300.64  196166[18:Res:13056.1,190532.1] inductive(u) || equal(complement(u),symmetrization_of(identity_relation))* -> .
% 299.99/300.64  196175[18:MRR:196143.0,13126.0] || equal(complement(unordered_pair(u,identity_relation)),symmetrization_of(identity_relation))** -> .
% 299.99/300.64  196174[18:MRR:196142.0,13126.0] || equal(complement(unordered_pair(identity_relation,u)),symmetrization_of(identity_relation))** -> .
% 299.99/300.64  9016[5:MRR:9015.2,8764.0] function(sum_class(cross_product(universal_class,universal_class))) || well_ordering(element_relation,cross_product(ordinal_numbers,ordinal_numbers))* -> member(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers).
% 299.99/300.64  190532[18:Res:190442.1,28.1] || equal(complement(u),symmetrization_of(identity_relation)) member(identity_relation,u)* -> .
% 299.99/300.64  196128[18:Res:10.1,196109.0] || equal(recursion_equation_functions(u),inverse(identity_relation))**+ -> function(regular(symmetrization_of(identity_relation)))*.
% 299.99/300.64  196109[18:Res:190510.1,152.0] || subclass(inverse(identity_relation),recursion_equation_functions(u))* -> function(regular(symmetrization_of(identity_relation))).
% 299.99/300.64  196114[18:Res:190510.1,190500.0] || subclass(inverse(identity_relation),complement(inverse(identity_relation)))* -> .
% 299.99/300.64  9113[5:MRR:9111.2,8764.0] function(sum_class(cross_product(ordinal_numbers,ordinal_numbers))) || well_ordering(element_relation,cross_product(ordinal_numbers,ordinal_numbers))* -> member(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers).
% 299.99/300.64  196112[18:Res:190510.1,14676.0] || subclass(inverse(identity_relation),identity_relation)* -> .
% 299.99/300.64  190510[18:Res:190499.0,5.0] || subclass(inverse(identity_relation),u) -> member(regular(symmetrization_of(identity_relation)),u)*.
% 299.99/300.64  189823[8:Rew:17351.0,189772.1] || equal(complement(u),ordinal_numbers) -> equal(union(u,identity_relation),identity_relation)**.
% 299.99/300.64  15574[8:Res:15426.1,3700.0] || subclass(domain_relation,singleton(u))* -> equal(ordered_pair(identity_relation,identity_relation),u).
% 299.99/300.64  13235[7:Rew:13036.0,9534.2] || equal(u,v)*+ well_ordering(w,u)* -> equal(v,identity_relation) member(least(w,v),v)*.
% 299.99/300.64  18039[8:Res:10.1,15574.0] || equal(singleton(u),domain_relation)**+ -> equal(ordered_pair(identity_relation,identity_relation),u)*.
% 299.99/300.64  13325[7:Rew:13036.0,9500.2] || equal(u,v)*+ well_ordering(w,u)* -> equal(segment(w,v,least(w,v)),identity_relation)**.
% 299.99/300.64  195256[16:Rew:195224.0,68756.0] ||  -> equal(symmetric_difference(ordinal_numbers,complement(singleton(identity_relation))),intersection(singleton(identity_relation),ordinal_numbers))**.
% 299.99/300.64  15666[8:Rew:15663.0,13298.1] || asymmetric(u,singleton(v)) -> equal(domain__dfg(intersection(u,inverse(u)),singleton(v),v),single_valued3(identity_relation))**.
% 299.99/300.64  195571[16:MRR:195277.1,165946.0] inductive(symmetric_difference(singleton(identity_relation),successor(identity_relation))) ||  -> .
% 299.99/300.64  195254[16:Rew:195224.0,192046.0] || subclass(singleton(identity_relation),complement(singleton(identity_relation)))* -> .
% 299.99/300.64  195239[16:Rew:195224.0,162607.0] ||  -> equal(complement(complement(singleton(identity_relation))),singleton(identity_relation))**.
% 299.99/300.64  195231[16:Rew:195224.0,166563.0] ||  -> equal(regular(singleton(identity_relation)),identity_relation)**.
% 299.99/300.64  195224[16:MRR:163258.0,195220.0] ||  -> equal(successor(identity_relation),singleton(identity_relation))**.
% 299.99/300.64  195115[14:Res:13056.1,165357.1] inductive(u) || equal(complement(u),singleton(identity_relation))** -> .
% 299.99/300.64  195124[14:MRR:195089.0,13126.0] || equal(complement(unordered_pair(u,identity_relation)),singleton(identity_relation))** -> .
% 299.99/300.64  195123[14:MRR:195088.0,13126.0] || equal(complement(unordered_pair(identity_relation,u)),singleton(identity_relation))** -> .
% 299.99/300.64  165357[14:Res:165168.1,28.1] || equal(complement(u),singleton(identity_relation)) member(identity_relation,u)* -> .
% 299.99/300.64  195077[20:MRR:195064.1,194308.0] || equal(complement(symmetrization_of(identity_relation)),singleton(identity_relation))** -> .
% 299.99/300.64  165360[14:Res:165168.1,151988.0] || equal(complement(complement(u)),singleton(identity_relation))** -> member(identity_relation,u).
% 299.99/300.64  166987[14:Res:165168.1,13047.1] || equal(u,singleton(identity_relation)) equal(complement(u),ordinal_numbers)** -> .
% 299.99/300.64  13344[7:Rew:13036.0,9771.1] || asymmetric(u,v) subclass(compose(identity_relation,identity_relation),identity_relation) -> transitive(intersection(u,inverse(u)),v)*.
% 299.99/300.64  13493[7:Rew:13036.0,9520.1] || well_ordering(u,cross_product(ordinal_numbers,ordinal_numbers)) -> equal(segment(u,rest_of(v),least(u,rest_of(v))),identity_relation)**.
% 299.99/300.64  13494[7:Rew:13036.0,9521.1] || well_ordering(u,cross_product(ordinal_numbers,ordinal_numbers)) -> equal(segment(u,compose_class(v),least(u,compose_class(v))),identity_relation)**.
% 299.99/300.64  15272[7:SpR:13585.1,106.0] single_valued_class(u) ||  -> equal(second(not_subclass_element(identity_relation,identity_relation)),single_valued2(u))*.
% 299.99/300.64  15265[7:SpR:13584.1,106.0] function(u) ||  -> equal(second(not_subclass_element(identity_relation,identity_relation)),single_valued2(u))*.
% 299.99/300.64  66293[8:Rew:66141.0,66201.0] ||  -> equal(intersection(union(u,identity_relation),ordinal_numbers),symmetric_difference(complement(u),ordinal_numbers))**.
% 299.99/300.64  83444[7:Res:13072.1,39963.0] || equal(complement(rest_of(u)),ordinal_numbers)** -> equal(cantor(u),identity_relation).
% 299.99/300.64  15588[8:Res:15426.1,97.0] || subclass(domain_relation,compose_class(u))* -> equal(compose(u,identity_relation),identity_relation).
% 299.99/300.64  18040[8:Res:10.1,15588.0] || equal(compose_class(u),domain_relation) -> equal(compose(u,identity_relation),identity_relation)**.
% 299.99/300.64  69395[8:SpR:66423.0,66160.0] ||  -> equal(union(intersection(u,ordinal_numbers),identity_relation),complement(symmetric_difference(u,ordinal_numbers)))**.
% 299.99/300.64  13496[7:Rew:13036.0,9525.1] || well_ordering(u,cross_product(ordinal_numbers,cross_product(ordinal_numbers,ordinal_numbers)))*+ -> equal(segment(u,composition_function,least(u,composition_function)),identity_relation)**.
% 299.99/300.64  194543[18:MRR:194542.0,190509.0] ||  -> member(regular(symmetrization_of(identity_relation)),symmetrization_of(identity_relation))*.
% 299.99/300.64  194513[18:Res:163112.0,190500.0] ||  -> subclass(singleton(regular(symmetrization_of(identity_relation))),symmetrization_of(identity_relation))*.
% 299.99/300.64  194511[20:Res:163112.0,194308.0] ||  -> subclass(singleton(identity_relation),symmetrization_of(identity_relation))*.
% 299.99/300.64  163112[8:SpR:162584.0,79560.1] ||  -> member(u,complement(inverse(identity_relation)))* subclass(singleton(u),symmetrization_of(identity_relation)).
% 299.99/300.64  165177[14:SpR:160491.0,165172.1] ||  -> member(identity_relation,symmetric_difference(ordinal_numbers,u))* member(identity_relation,union(u,identity_relation)).
% 299.99/300.64  163153[8:SpL:162584.0,9496.0] || subclass(ordinal_numbers,symmetrization_of(identity_relation)) -> member(singleton(u),inverse(identity_relation))*.
% 299.99/300.64  163152[8:SpL:162584.0,151970.0] || subclass(ordinal_numbers,symmetrization_of(identity_relation)) -> member(omega,inverse(identity_relation))*.
% 299.99/300.64  194368[21:MRR:194360.1,193815.0] || equal(cross_product(ordinal_numbers,cross_product(ordinal_numbers,ordinal_numbers)),identity_relation)** -> .
% 299.99/300.64  194373[21:MRR:194337.2,14676.0] || member(u,cantor(v)) member(ordered_pair(v,ordered_pair(u,w)),cross_product(ordinal_numbers,cross_product(ordinal_numbers,ordinal_numbers)))* -> .
% 299.99/300.64  194328[20:Res:165168.1,194308.0] || equal(complement(inverse(identity_relation)),singleton(identity_relation))** -> .
% 299.99/300.64  194311[20:MRR:167514.1,194308.0] || subclass(ordinal_numbers,complement(symmetrization_of(identity_relation)))* -> .
% 299.99/300.64  194331[21:Spt:13497.1] ||  -> equal(application_function,identity_relation)**.
% 299.99/300.64  194330[20:Res:13056.1,194308.0] inductive(complement(inverse(identity_relation))) ||  -> .
% 299.99/300.64  194308[20:Spt:194306.0,194275.0,194297.0] || member(identity_relation,complement(inverse(identity_relation)))* -> .
% 299.99/300.64  194310[20:MRR:166266.1,194308.0] inductive(complement(symmetrization_of(identity_relation))) ||  -> .
% 299.99/300.64  13324[7:Rew:13036.0,9505.2] inductive(u) || well_ordering(v,u)*+ -> equal(segment(v,omega,least(v,omega)),identity_relation)**.
% 299.99/300.64  8634[0:Res:10.1,141.1] || equal(sum_class(u),u) well_ordering(element_relation,u)* -> equal(u,ordinal_numbers) member(u,ordinal_numbers).
% 299.99/300.64  166169[8:MRR:166154.0,60996.1] || subclass(rest_relation,rest_of(u))* -> equal(complement(cantor(u)),identity_relation).
% 299.99/300.64  8998[5:Rew:8637.0,8810.1] || subclass(cross_product(ordinal_numbers,cross_product(ordinal_numbers,ordinal_numbers)),composition_function)* -> equal(cross_product(ordinal_numbers,cross_product(ordinal_numbers,ordinal_numbers)),composition_function).
% 299.99/300.64  9649[5:Res:8652.0,129.0] || subclass(ordinal_numbers,u)+ well_ordering(v,u)* -> member(least(v,ordinal_numbers),ordinal_numbers)*.
% 299.99/300.64  13320[7:Rew:13036.0,9499.1] || well_ordering(u,ordinal_numbers) -> equal(segment(u,v,least(u,v)),identity_relation)**.
% 299.99/300.64  13237[7:Rew:13036.0,9533.1] || well_ordering(u,ordinal_numbers) -> equal(v,identity_relation) member(least(u,v),v)*.
% 299.99/300.64  9562[4:MRR:9539.2,6407.0] inductive(u) || well_ordering(v,u)*+ -> member(least(v,omega),omega)*.
% 299.99/300.64  162411[7:Res:13061.0,133836.0] || well_ordering(ordinal_numbers,omega) -> equal(integer_of(singleton(singleton(u))),identity_relation)**.
% 299.99/300.64  166246[8:Res:157013.0,13082.1] inductive(intersection(inverse(subset_relation),u)) ||  -> member(identity_relation,complement(subset_relation))*.
% 299.99/300.64  166245[8:Res:156893.0,13082.1] inductive(intersection(u,inverse(subset_relation))) ||  -> member(identity_relation,complement(subset_relation))*.
% 299.99/300.64  8802[5:Rew:8637.0,98.1] || equal(compose(u,v),w) member(ordered_pair(v,w),cross_product(ordinal_numbers,ordinal_numbers))*+ -> member(ordered_pair(v,w),compose_class(u))*.
% 299.99/300.64  193927[18:Res:10.1,190592.0] || equal(inverse(subset_relation),inverse(identity_relation)) -> member(identity_relation,complement(subset_relation))*.
% 299.99/300.64  193924[18:Res:10.1,190441.0] || equal(symmetrization_of(identity_relation),inverse(subset_relation)) -> member(identity_relation,complement(subset_relation))*.
% 299.99/300.64  193906[14:Res:10.1,165167.0] || equal(inverse(subset_relation),singleton(identity_relation)) -> member(identity_relation,complement(subset_relation))*.
% 299.99/300.64  8799[5:Rew:8637.0,50.1] || equal(successor(u),v) member(ordered_pair(u,v),cross_product(ordinal_numbers,ordinal_numbers))* -> member(ordered_pair(u,v),successor_relation).
% 299.99/300.64  190592[18:Res:148858.1,190451.0] || subclass(inverse(identity_relation),inverse(subset_relation))* -> member(identity_relation,complement(subset_relation)).
% 299.99/300.64  190441[18:Res:148858.1,190437.0] || subclass(symmetrization_of(identity_relation),inverse(subset_relation))* -> member(identity_relation,complement(subset_relation)).
% 299.99/300.64  8800[5:Rew:8637.0,24.1] || member(u,v) member(ordered_pair(u,v),cross_product(ordinal_numbers,ordinal_numbers))* -> member(ordered_pair(u,v),element_relation).
% 299.99/300.64  165167[14:Res:148858.1,164503.0] || subclass(singleton(identity_relation),inverse(subset_relation))* -> member(identity_relation,complement(subset_relation)).
% 299.99/300.64  61580[8:SpR:15663.0,50063.1] || member(not_subclass_element(identity_relation,identity_relation),subset_relation)* -> member(single_valued3(identity_relation),ordinal_numbers).
% 299.99/300.64  82401[8:Res:10.1,82297.0] || equal(complement(complement(rest_relation)),domain_relation)** -> equal(rest_of(identity_relation),identity_relation).
% 299.99/300.64  8801[5:Rew:8637.0,101.0] || member(ordered_pair(u,v),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(u,ordered_pair(v,compose(u,v))),composition_function)*.
% 299.99/300.64  133486[5:Res:8638.0,40321.0] || well_ordering(u,ordinal_numbers) -> member(least(u,rest_relation),rest_relation)*.
% 299.99/300.64  133488[5:Res:295.0,40321.0] || well_ordering(u,rest_relation) -> member(least(u,rest_relation),rest_relation)*.
% 299.99/300.64  133502[5:Res:133488.1,41096.0] || well_ordering(u,rest_relation) -> member(least(u,rest_relation),ordinal_numbers)*.
% 299.99/300.64  133495[5:Res:133486.1,41096.0] || well_ordering(u,ordinal_numbers) -> member(least(u,rest_relation),ordinal_numbers)*.
% 299.99/300.64  141[0:Inp] || well_ordering(element_relation,u) subclass(sum_class(u),u)* -> equal(u,ordinal_numbers) member(u,ordinal_numbers).
% 299.99/300.64  19525[5:Res:8638.0,9649.0] || well_ordering(u,ordinal_numbers) -> member(least(u,ordinal_numbers),ordinal_numbers)*.
% 299.99/300.64  165667[5:Res:143198.1,133836.0] || equal(u,ordinal_numbers) well_ordering(ordinal_numbers,u)* -> .
% 299.99/300.64  130893[5:Res:8652.0,9876.0] || subclass(ordinal_numbers,u) well_ordering(ordinal_numbers,u)* -> .
% 299.99/300.64  132444[5:SpL:18840.1,132439.0] || member(u,subset_relation) well_ordering(ordinal_numbers,u)* -> .
% 299.99/300.64  100[0:Inp] || member(ordered_pair(u,ordered_pair(v,w)),composition_function)* -> equal(compose(u,v),w).
% 299.99/300.64  166450[7:Res:133837.1,18858.0] || well_ordering(ordinal_numbers,complement(subset_relation))*+ -> member(u,ordinal_numbers)*.
% 299.99/300.64  138[0:Inp] || member(u,ordinal_numbers) -> well_ordering(element_relation,u)*.
% 299.99/300.64  160714[5:MRR:95454.1,96209.1] || equal(complement(complement(composition_function)),ordinal_numbers)** -> .
% 299.99/300.64  8669[5:Rew:8637.0,99.0] ||  -> subclass(composition_function,cross_product(ordinal_numbers,cross_product(ordinal_numbers,ordinal_numbers)))*.
% 299.99/300.64  193815[19:Spt:193797.0,13498.1,193636.0] || equal(composition_function,identity_relation)** -> .
% 299.99/300.64  132437[5:Res:8638.0,130942.0] || well_ordering(ordinal_numbers,ordinal_numbers)* -> .
% 299.99/300.64  8754[5:Rew:8637.0,8441.0] || subclass(ordinal_numbers,composition_function)* -> .
% 299.99/300.64  8755[5:Rew:8637.0,8447.0] || equal(composition_function,ordinal_numbers)** -> .
% 299.99/300.64  193816[19:Spt:193797.0,13498.0,13498.2] || well_ordering(u,cross_product(ordinal_numbers,cross_product(ordinal_numbers,ordinal_numbers)))* -> member(least(u,composition_function),composition_function).
% 299.99/300.64  82297[8:Res:81336.1,149.0] || subclass(domain_relation,complement(complement(rest_relation)))* -> equal(rest_of(identity_relation),identity_relation).
% 299.99/300.64  15135[8:Res:13072.1,14679.1] || member(regular(inverse(subset_relation)),subset_relation)* -> equal(inverse(subset_relation),identity_relation).
% 299.99/300.64  15320[8:Rew:15300.0,13281.1] || asymmetric(u,singleton(v)) -> equal(segment(intersection(u,inverse(u)),singleton(v),v),identity_relation)**.
% 299.99/300.64  13189[7:Rew:13036.0,9805.1] inductive(composition_function) ||  -> member(identity_relation,cross_product(ordinal_numbers,cross_product(ordinal_numbers,ordinal_numbers)))*.
% 299.99/300.64  13190[7:Rew:13036.0,9804.1] inductive(application_function) ||  -> member(identity_relation,cross_product(ordinal_numbers,cross_product(ordinal_numbers,ordinal_numbers)))*.
% 299.99/300.64  69169[8:Res:13056.1,66086.1] inductive(complement(compose(element_relation,ordinal_numbers))) || member(identity_relation,element_relation)* -> .
% 299.99/300.64  68757[8:SpR:117.0,66292.0] ||  -> equal(symmetric_difference(ordinal_numbers,complement(inverse(identity_relation))),intersection(symmetrization_of(identity_relation),ordinal_numbers))**.
% 299.99/300.64  162318[0:Rew:79.0,162310.1] || member(not_subclass_element(subset_relation,identity_relation),inverse(subset_relation))* -> subclass(subset_relation,identity_relation).
% 299.99/300.64  166265[8:Res:157036.0,13082.1] inductive(complement(complement(inverse(subset_relation)))) ||  -> member(identity_relation,complement(subset_relation))*.
% 299.99/300.64  8786[5:Rew:8637.0,8587.1] || equal(compose(u,inverse(u)),identity_relation)**+ subclass(u,cross_product(ordinal_numbers,ordinal_numbers))* -> function(u).
% 299.99/300.64  164991[8:Res:49995.1,162888.0] || member(subset_relation,subset_relation) subclass(singleton(first(subset_relation)),identity_relation)* -> .
% 299.99/300.64  166264[8:Res:153473.0,13082.1] inductive(complement(compose(element_relation,ordinal_numbers))) ||  -> member(identity_relation,complement(element_relation))*.
% 299.99/300.64  193179[8:Obv:193178.0] ||  -> member(u,inverse(singleton(u)))* asymmetric(singleton(u),v)*.
% 299.99/300.64  193055[7:MRR:193048.2,13040.0] inductive(intersection(singleton(u),v)) ||  -> member(u,v)*.
% 299.99/300.64  193044[7:Res:151847.0,13588.0] ||  -> member(u,v) equal(intersection(singleton(u),v),identity_relation)**.
% 299.99/300.64  192846[7:MRR:192843.2,13040.0] inductive(intersection(u,singleton(v))) ||  -> member(v,u)*.
% 299.99/300.64  13621[7:Rew:13036.0,13261.1] ||  -> equal(cross_product(u,v),identity_relation) equal(restrict(regular(cross_product(u,v)),u,v),identity_relation)**.
% 299.99/300.64  192834[7:Res:151488.0,13588.0] ||  -> member(u,v) equal(intersection(v,singleton(u)),identity_relation)**.
% 299.99/300.64  192649[7:MRR:192642.2,13040.0] inductive(intersection(singleton(u),recursion_equation_functions(v))) ||  -> function(u)*.
% 299.99/300.64  192639[7:Res:151856.0,13588.0] ||  -> function(u) equal(intersection(singleton(u),recursion_equation_functions(v)),identity_relation)**.
% 299.99/300.64  192525[7:MRR:192521.2,13040.0] inductive(intersection(recursion_equation_functions(u),singleton(v))) ||  -> function(v)*.
% 299.99/300.64  192514[7:Res:151497.0,13588.0] ||  -> function(u) equal(intersection(recursion_equation_functions(v),singleton(u)),identity_relation)**.
% 299.99/300.64  13053[7:Rew:13036.0,4540.1] inductive(restrict(u,v,w)) ||  -> member(identity_relation,u)*.
% 299.99/300.64  19204[8:Res:19172.1,121.0] || equal(cross_product(u,u),identity_relation)**+ -> connected(v,u)*.
% 299.99/300.64  15691[8:SpR:15528.0,15528.0] ||  -> equal(range__dfg(identity_relation,u,v),range__dfg(identity_relation,w,x))*.
% 299.99/300.64  188530[8:SpR:13085.1,163366.0] || member(u,ordinals_with_null_class_as_identity) -> equal(intersection(u,ordinal_numbers),u)**.
% 299.99/300.64  15587[8:Res:15426.1,18.0] || subclass(domain_relation,cross_product(u,v))* -> member(identity_relation,u).
% 299.99/300.64  15889[8:Res:10.1,15587.0] || equal(cross_product(u,v),domain_relation)** -> member(identity_relation,u).
% 299.99/300.64  13051[7:Rew:13036.0,9990.1] || equal(intersection(u,v),ordinal_numbers)** -> member(identity_relation,u).
% 299.99/300.64  13045[7:Rew:13036.0,9848.1] || subclass(ordinal_numbers,intersection(u,v))* -> member(identity_relation,u).
% 299.99/300.64  13098[7:Rew:13036.0,4670.0] ||  -> equal(singleton(u),identity_relation) equal(regular(singleton(u)),u)**.
% 299.99/300.64  19277[8:Res:19172.1,8787.1] single_valued_class(u) || equal(identity_relation,u) -> function(u)*.
% 299.99/300.64  15586[8:Res:15426.1,19.0] || subclass(domain_relation,cross_product(u,v))* -> member(identity_relation,v).
% 299.99/300.64  15885[8:Res:10.1,15586.0] || equal(cross_product(u,v),domain_relation)** -> member(identity_relation,v).
% 299.99/300.64  192149[7:SpL:140603.0,13081.0] || equal(u,ordinal_numbers) -> member(identity_relation,u)*.
% 299.99/300.64  13081[7:Rew:13036.0,9977.1] || equal(intersection(u,v),ordinal_numbers)** -> member(identity_relation,v).
% 299.99/300.64  13079[7:Rew:13036.0,9847.1] || subclass(ordinal_numbers,intersection(u,v))* -> member(identity_relation,v).
% 299.99/300.64  19531[8:Res:19201.1,8729.0] || equal(sum_class(u),identity_relation) -> subclass(sum_class(u),u)*.
% 299.99/300.64  17333[7:Obv:17330.1] || subclass(complement(u),u)* -> equal(complement(u),identity_relation).
% 299.99/300.64  166249[7:Res:143389.0,13082.1] inductive(symmetric_difference(u,u)) ||  -> member(identity_relation,complement(u))*.
% 299.99/300.64  191929[18:Res:10.1,190447.0] || equal(u,inverse(identity_relation)) well_ordering(ordinal_numbers,u)* -> .
% 299.99/300.64  191912[18:Res:10.1,190433.0] || equal(u,symmetrization_of(identity_relation)) well_ordering(ordinal_numbers,u)* -> .
% 299.99/300.64  13475[7:Rew:13036.0,9515.1] || well_ordering(u,cross_product(ordinal_numbers,ordinal_numbers)) -> equal(segment(u,union_of_range_map,least(u,union_of_range_map)),identity_relation)**.
% 299.99/300.64  190699[18:SpL:117380.1,190685.0] operation(u) || equal(cantor(u),inverse(identity_relation))** -> .
% 299.99/300.64  190588[18:SpL:117380.1,190576.0] operation(u) || equal(cantor(u),symmetrization_of(identity_relation))* -> .
% 299.99/300.64  13476[7:Rew:13036.0,9516.1] || well_ordering(u,cross_product(ordinal_numbers,ordinal_numbers)) -> equal(segment(u,rest_relation,least(u,rest_relation)),identity_relation)**.
% 299.99/300.64  191973[18:Res:190515.1,190500.0] || subclass(ordinal_numbers,complement(inverse(identity_relation)))* -> .
% 299.99/300.64  13477[7:Rew:13036.0,9517.1] || well_ordering(u,cross_product(ordinal_numbers,ordinal_numbers)) -> equal(segment(u,domain_relation,least(u,domain_relation)),identity_relation)**.
% 299.99/300.64  190515[18:Res:190509.0,5.0] || subclass(ordinal_numbers,u) -> member(regular(symmetrization_of(identity_relation)),u)*.
% 299.99/300.64  190447[18:Res:190445.0,9876.0] || subclass(inverse(identity_relation),u)* well_ordering(ordinal_numbers,u) -> .
% 299.99/300.64  191915[18:Res:163118.0,190433.0] || well_ordering(ordinal_numbers,inverse(identity_relation))* -> .
% 299.99/300.64  191913[18:Res:295.0,190433.0] || well_ordering(ordinal_numbers,symmetrization_of(identity_relation))* -> .
% 299.99/300.64  13478[7:Rew:13036.0,9518.1] || well_ordering(u,cross_product(ordinal_numbers,ordinal_numbers)) -> equal(segment(u,successor_relation,least(u,successor_relation)),identity_relation)**.
% 299.99/300.64  190433[18:Res:190432.0,9876.0] || subclass(symmetrization_of(identity_relation),u)* well_ordering(ordinal_numbers,u) -> .
% 299.99/300.64  167593[14:Res:10.1,164499.0] || equal(u,singleton(identity_relation)) well_ordering(ordinal_numbers,u)* -> .
% 299.99/300.64  13479[7:Rew:13036.0,9519.1] || well_ordering(u,cross_product(ordinal_numbers,ordinal_numbers)) -> equal(segment(u,element_relation,least(u,element_relation)),identity_relation)**.
% 299.99/300.64  166216[7:Res:143160.0,13082.1] inductive(symmetric_difference(ordinal_numbers,u)) ||  -> member(identity_relation,complement(u))*.
% 299.99/300.64  163545[7:Res:13049.1,151988.0] || subclass(ordinal_numbers,complement(complement(u)))* -> member(identity_relation,u).
% 299.99/300.64  13046[7:Rew:13036.0,9928.1] || equal(complement(complement(u)),ordinal_numbers)** -> member(identity_relation,u).
% 299.99/300.64  191776[18:Res:190445.0,13047.1] || equal(complement(inverse(identity_relation)),ordinal_numbers)** -> .
% 299.99/300.64  13048[7:Rew:13036.0,9840.1] || subclass(ordinal_numbers,complement(u))* member(identity_relation,u) -> .
% 299.99/300.64  15426[8:Res:15380.0,5.0] || subclass(domain_relation,u) -> member(ordered_pair(identity_relation,identity_relation),u)*.
% 299.99/300.64  164499[14:Res:164498.0,9876.0] || subclass(singleton(identity_relation),u)* well_ordering(ordinal_numbers,u) -> .
% 299.99/300.64  160963[8:Rew:140603.0,66122.1] ||  -> equal(u,identity_relation) equal(symmetric_difference(u,regular(u)),union(u,regular(u)))**.
% 299.99/300.64  165401[14:SpL:117380.1,165399.0] operation(u) || equal(cantor(u),singleton(identity_relation))** -> .
% 299.99/300.64  163154[8:SpL:162584.0,151988.0] || member(u,symmetrization_of(identity_relation))* -> member(u,inverse(identity_relation)).
% 299.99/300.64  19201[8:Res:19172.1,9586.0] || equal(sum_class(u),identity_relation) -> section(element_relation,u,ordinal_numbers)*.
% 299.99/300.64  15528[8:SpR:14650.0,13101.0] ||  -> equal(second(not_subclass_element(identity_relation,identity_relation)),range__dfg(identity_relation,u,v))*.
% 299.99/300.64  160659[8:Rew:67835.0,155231.1] || subclass(ordinal_numbers,u) -> equal(symmetric_difference(u,ordinal_numbers),identity_relation)**.
% 299.99/300.64  14681[8:MRR:13630.3,14676.0] || member(u,regular(v))* member(u,v) -> equal(v,identity_relation).
% 299.99/300.64  164966[8:Res:6.1,162888.0] || subclass(not_subclass_element(subset_relation,u),identity_relation)* -> subclass(subset_relation,u).
% 299.99/300.64  165038[8:Res:6.1,162901.0] || equal(not_subclass_element(subset_relation,u),identity_relation)** -> subclass(subset_relation,u).
% 299.99/300.64  81353[8:Res:10.1,81335.0] || equal(complement(unordered_pair(u,ordered_pair(identity_relation,identity_relation))),domain_relation)** -> .
% 299.99/300.64  81335[8:MRR:81311.0,8667.0] || subclass(domain_relation,complement(unordered_pair(u,ordered_pair(identity_relation,identity_relation))))* -> .
% 299.99/300.64  81350[8:Res:10.1,81334.0] || equal(complement(unordered_pair(ordered_pair(identity_relation,identity_relation),u)),domain_relation)** -> .
% 299.99/300.64  81334[8:MRR:81310.0,8667.0] || subclass(domain_relation,complement(unordered_pair(ordered_pair(identity_relation,identity_relation),u)))* -> .
% 299.99/300.64  15649[8:Res:10.1,15567.0] || equal(recursion_equation_functions(u),domain_relation)**+ -> function(ordered_pair(identity_relation,identity_relation))*.
% 299.99/300.64  191304[18:Res:10.1,191300.0] || equal(complement(inverse(identity_relation)),symmetrization_of(identity_relation))** -> .
% 299.99/300.64  191300[18:MRR:191299.1,190496.0] || subclass(symmetrization_of(identity_relation),complement(inverse(identity_relation)))* -> .
% 299.99/300.64  13227[7:Rew:13036.0,4665.1] || subclass(u,v) -> equal(u,identity_relation) member(regular(u),v)*.
% 299.99/300.64  15567[8:Res:15426.1,152.0] || subclass(domain_relation,recursion_equation_functions(u))*+ -> function(ordered_pair(identity_relation,identity_relation))*.
% 299.99/300.64  18858[7:Rew:18517.0,18854.0] || member(singleton(singleton(identity_relation)),subset_relation)*+ -> member(u,ordinal_numbers)*.
% 299.99/300.64  13210[7:Rew:13036.0,4568.0] ||  -> equal(intersection(u,v),identity_relation) member(regular(intersection(u,v)),v)*.
% 299.99/300.64  14761[8:SpL:14650.0,123.0] || subclass(compose(identity_relation,identity_relation),identity_relation)*+ -> transitive(identity_relation,u)*.
% 299.99/300.64  61517[8:MRR:61516.1,13039.0] || transitive(identity_relation,u)*+ -> equal(compose(identity_relation,identity_relation),identity_relation)**.
% 299.99/300.64  15007[8:Res:10.1,14761.0] || equal(compose(identity_relation,identity_relation),identity_relation)**+ -> transitive(identity_relation,u)*.
% 299.99/300.64  13248[7:Rew:13036.0,4569.0] ||  -> equal(intersection(u,v),identity_relation) member(regular(intersection(u,v)),u)*.
% 299.99/300.64  13604[7:Rew:13036.0,13063.1] inductive(unordered_pair(u,v)) ||  -> equal(identity_relation,v)* equal(identity_relation,u)*.
% 299.99/300.64  13125[7:Rew:13036.0,4625.1] || subclass(omega,u) -> equal(integer_of(v),identity_relation) member(v,u)*.
% 299.99/300.64  15628[8:MRR:15618.1,13126.0] || equal(rest_relation,domain_relation) -> member(ordered_pair(identity_relation,identity_relation),rest_relation)*.
% 299.99/300.64  8973[5:Rew:8637.0,8793.1] || subclass(cross_product(ordinal_numbers,ordinal_numbers),union_of_range_map)* -> equal(cross_product(ordinal_numbers,ordinal_numbers),union_of_range_map).
% 299.99/300.64  13082[7:Rew:13036.0,4553.2] inductive(u) || subclass(u,v)*+ -> member(identity_relation,v)*.
% 299.99/300.64  13105[7:Rew:13036.0,4563.1] || member(regular(complement(u)),u)* -> equal(complement(u),identity_relation).
% 299.99/300.64  61006[7:Res:13072.1,50033.0] || equal(complement(regular(subset_relation)),ordinal_numbers)** -> equal(subset_relation,identity_relation).
% 299.99/300.64  17337[8:Obv:17332.1] || subclass(inverse(subset_relation),subset_relation)* -> equal(inverse(subset_relation),identity_relation).
% 299.99/300.64  163859[8:Res:19172.1,155658.0] || equal(compose(subset_relation,subset_relation),identity_relation)** -> transitive(subset_relation,ordinal_numbers).
% 299.99/300.64  190685[18:MRR:190665.1,162891.0] || equal(cross_product(u,v),inverse(identity_relation))** -> .
% 299.99/300.64  13585[7:MRR:4726.1,13039.0] single_valued_class(u) ||  -> equal(compose(u,inverse(u)),identity_relation)**.
% 299.99/300.64  190680[18:Res:190593.1,165946.0] || equal(complement(singleton(identity_relation)),inverse(identity_relation))** -> .
% 299.99/300.64  190679[18:Res:190593.1,60934.0] || equal(inverse(identity_relation),subset_relation)** -> .
% 299.99/300.64  190593[18:Res:10.1,190451.0] || equal(u,inverse(identity_relation)) -> member(identity_relation,u)*.
% 299.99/300.64  190636[18:MRR:164112.1,190633.0] || equal(inverse(subset_relation),subset_relation)** -> .
% 299.99/300.64  4746[0:Res:10.1,65.0] || equal(compose(u,inverse(u)),identity_relation)** -> single_valued_class(u).
% 299.99/300.64  190633[18:Res:190589.1,14676.0] || equal(inverse(identity_relation),identity_relation)** -> .
% 299.99/300.64  190451[18:Res:190445.0,5.0] || subclass(inverse(identity_relation),u)* -> member(identity_relation,u).
% 299.99/300.64  190576[18:MRR:190556.1,162891.0] || equal(cross_product(u,v),symmetrization_of(identity_relation))** -> .
% 299.99/300.64  13584[7:MRR:4712.1,13039.0] function(u) ||  -> equal(compose(u,inverse(u)),identity_relation)**.
% 299.99/300.64  190571[18:Res:190442.1,165946.0] || equal(complement(singleton(identity_relation)),symmetrization_of(identity_relation))** -> .
% 299.99/300.64  190570[18:Res:190442.1,60934.0] || equal(symmetrization_of(identity_relation),subset_relation)** -> .
% 299.99/300.64  190442[18:Res:10.1,190437.0] || equal(u,symmetrization_of(identity_relation)) -> member(identity_relation,u)*.
% 299.99/300.64  190500[18:MRR:166166.1,190496.0] || member(regular(symmetrization_of(identity_relation)),complement(inverse(identity_relation)))* -> .
% 299.99/300.64  13089[7:Rew:13036.0,4559.0] ||  -> equal(integer_of(not_subclass_element(u,omega)),identity_relation)** subclass(u,omega).
% 299.99/300.64  190509[18:Res:190499.0,41096.0] ||  -> member(regular(symmetrization_of(identity_relation)),ordinal_numbers)*.
% 299.99/300.64  190499[18:MRR:166539.0,190496.0] ||  -> member(regular(symmetrization_of(identity_relation)),inverse(identity_relation))*.
% 299.99/300.64  190496[18:Res:190438.1,14676.0] || equal(symmetrization_of(identity_relation),identity_relation)** -> .
% 299.99/300.64  190446[18:MRR:167000.0,190445.0] || equal(complement(symmetrization_of(identity_relation)),ordinal_numbers)** -> .
% 299.99/300.64  190445[18:Res:163118.0,190437.0] ||  -> member(identity_relation,inverse(identity_relation))*.
% 299.99/300.64  190437[18:Res:190432.0,5.0] || subclass(symmetrization_of(identity_relation),u)* -> member(identity_relation,u).
% 299.99/300.64  190432[18:Spt:165176.1] ||  -> member(identity_relation,symmetrization_of(identity_relation))*.
% 299.99/300.64  13122[7:Rew:13036.0,4578.2] || connected(u,v) member(w,not_well_ordering(u,v)) equal(segment(u,not_well_ordering(u,v),w),identity_relation)** -> well_ordering(u,v).
% 299.99/300.64  15307[8:MRR:14764.1,15296.0] || subclass(u,v) -> section(identity_relation,u,v)*.
% 299.99/300.64  13054[7:Rew:13036.0,4542.1] inductive(intersection(u,v)) ||  -> member(identity_relation,u)*.
% 299.99/300.64  13060[7:Rew:13036.0,4550.0] ||  -> equal(integer_of(u),identity_relation)** equal(integer_of(u),u)**.
% 299.99/300.64  13094[7:Rew:13036.0,6776.0] ||  -> equal(singleton(u),identity_relation) member(u,singleton(u))*.
% 299.99/300.64  13066[7:Rew:13036.0,4558.0] || equal(identity_relation,u) -> equal(integer_of(u),u)**.
% 299.99/300.64  13083[7:Rew:13036.0,4554.1] inductive(intersection(u,v)) ||  -> member(identity_relation,v)*.
% 299.99/300.64  13070[7:Rew:13036.0,4546.2] || subclass(u,v)*+ well_ordering(w,v)* -> equal(u,identity_relation) member(least(w,u),u)*.
% 299.99/300.64  167597[14:Res:79560.1,164499.0] || well_ordering(ordinal_numbers,complement(u))* -> member(identity_relation,u).
% 299.99/300.64  167596[14:Res:10714.1,164499.0] || member(identity_relation,u) well_ordering(ordinal_numbers,u)* -> .
% 299.99/300.64  13113[7:Rew:13036.0,4577.2] || subclass(u,v)*+ well_ordering(w,v)* -> equal(segment(w,u,least(w,u)),identity_relation)**.
% 299.99/300.64  165168[14:Res:10.1,164503.0] || equal(u,singleton(identity_relation)) -> member(identity_relation,u)*.
% 299.99/300.64  164503[14:Res:164498.0,5.0] || subclass(singleton(identity_relation),u)* -> member(identity_relation,u).
% 299.99/300.64  162332[7:Res:13056.1,151988.0] inductive(complement(complement(u))) ||  -> member(identity_relation,u)*.
% 299.99/300.64  13055[7:Rew:13036.0,4543.1] inductive(complement(u)) || member(identity_relation,u)* -> .
% 299.99/300.64  161038[8:Rew:116078.0,13110.1] || member(u,ordinal_numbers) -> member(u,cantor(v)) equal(restrict(v,singleton(u),ordinal_numbers),identity_relation)**.
% 299.99/300.64  13059[7:Rew:13036.0,10713.0] ||  -> equal(integer_of(u),identity_relation) subclass(singleton(u),omega)*.
% 299.99/300.64  162901[8:SpL:18840.1,162891.0] || member(u,subset_relation)* equal(u,identity_relation) -> .
% 299.99/300.64  13154[7:Rew:13036.0,4544.0] ||  -> equal(recursion_equation_functions(u),identity_relation) function(regular(recursion_equation_functions(u)))*.
% 299.99/300.64  8664[5:Rew:8637.0,68.0] || subclass(u,cross_product(ordinal_numbers,ordinal_numbers)) subclass(compose(u,inverse(u)),identity_relation)* -> function(u).
% 299.99/300.64  15667[8:Rew:15663.0,15273.1] single_valued_class(u) ||  -> equal(single_valued3(identity_relation),single_valued1(u))*.
% 299.99/300.64  15668[8:Rew:15663.0,15266.1] function(u) ||  -> equal(single_valued3(identity_relation),single_valued1(u))*.
% 299.99/300.64  13104[7:Rew:13036.0,4570.1] || asymmetric(u,v) -> equal(restrict(intersection(u,inverse(u)),v,v),identity_relation)**.
% 299.99/300.64  162888[8:SpL:18840.1,162248.0] || member(u,subset_relation)* subclass(u,identity_relation) -> .
% 299.99/300.64  66340[8:SpR:66036.0,19421.0] ||  -> subclass(symmetric_difference(complement(u),ordinal_numbers),union(u,identity_relation))*.
% 299.99/300.64  160491[8:Rew:140613.0,66160.0] ||  -> equal(complement(symmetric_difference(ordinal_numbers,u)),union(u,identity_relation))**.
% 299.99/300.64  162025[8:Rew:140613.0,161960.0] ||  -> subclass(complement(union(u,identity_relation)),symmetric_difference(ordinal_numbers,u))*.
% 299.99/300.64  13103[7:Rew:13036.0,4571.0] || equal(restrict(intersection(u,inverse(u)),v,v),identity_relation)** -> asymmetric(u,v).
% 299.99/300.64  68388[8:Res:13056.1,66290.0] inductive(domain_of(u)) ||  -> member(identity_relation,cantor(u))*.
% 299.99/300.64  18262[8:MRR:18260.1,13039.0] || equal(compose_class(identity_relation),domain_relation) -> transitive(identity_relation,u)*.
% 299.99/300.64  13102[7:Rew:13036.0,4574.1] || connected(u,v) equal(not_well_ordering(u,v),identity_relation)** -> well_ordering(u,v).
% 299.99/300.64  81340[8:Res:10.1,81333.0] || equal(complement(singleton(ordered_pair(identity_relation,identity_relation))),domain_relation)** -> .
% 299.99/300.64  81333[8:MRR:81308.0,8667.0] || subclass(domain_relation,complement(singleton(ordered_pair(identity_relation,identity_relation))))* -> .
% 299.99/300.64  13100[7:Rew:13036.0,4576.0] ||  -> equal(first(not_subclass_element(restrict(u,v,singleton(w)),identity_relation)),domain__dfg(u,v,w))**.
% 299.99/300.64  163119[8:SpR:162584.0,147905.0] ||  -> equal(intersection(inverse(identity_relation),symmetrization_of(identity_relation)),symmetrization_of(identity_relation))**.
% 299.99/300.64  81698[8:Res:81695.0,13082.1] inductive(inverse(subset_relation)) ||  -> member(identity_relation,complement(subset_relation))*.
% 299.99/300.64  13101[7:Rew:13036.0,4575.0] ||  -> equal(second(not_subclass_element(restrict(u,singleton(v),w),identity_relation)),range__dfg(u,v,w))**.
% 299.99/300.64  15582[8:Res:15426.1,149.0] || subclass(domain_relation,rest_relation)* -> equal(rest_of(identity_relation),identity_relation).
% 299.99/300.64  15614[8:Res:10.1,15582.0] || equal(rest_relation,domain_relation) -> equal(rest_of(identity_relation),identity_relation)**.
% 299.99/300.64  165000[8:Res:19172.1,164974.0] || equal(regular(subset_relation),identity_relation)** -> equal(subset_relation,identity_relation).
% 299.99/300.64  164974[8:Res:13072.1,162888.0] || subclass(regular(subset_relation),identity_relation)* -> equal(subset_relation,identity_relation).
% 299.99/300.64  160735[8:Rew:116078.0,13111.0] || member(u,cantor(v)) equal(restrict(v,singleton(u),ordinal_numbers),identity_relation)** -> .
% 299.99/300.64  162274[0:SpR:79.0,154737.1] || subclass(subset_relation,inverse(subset_relation))* -> equal(subset_relation,identity_relation).
% 299.99/300.64  62277[8:Res:50256.1,13588.0] || equal(inverse(subset_relation),ordinal_numbers)** -> equal(subset_relation,identity_relation).
% 299.99/300.64  19172[8:Res:10.1,19126.0] || equal(identity_relation,u) -> subclass(u,v)*.
% 299.99/300.64  19126[8:Res:2503.2,14676.0] || subclass(u,identity_relation)*+ -> subclass(u,v)*.
% 299.99/300.64  165172[14:Res:79560.1,164503.0] ||  -> member(identity_relation,u) member(identity_relation,complement(u))*.
% 299.99/300.64  13049[7:Rew:13036.0,9825.1] || subclass(ordinal_numbers,u) -> member(identity_relation,u)*.
% 299.99/300.64  165399[14:MRR:165380.1,162891.0] || equal(cross_product(u,v),singleton(identity_relation))** -> .
% 299.99/300.64  66492[7:Res:13061.0,41096.0] ||  -> equal(integer_of(u),identity_relation) member(u,ordinal_numbers)*.
% 299.99/300.64  60996[7:Res:13072.1,41096.0] ||  -> equal(u,identity_relation) member(regular(u),ordinal_numbers)*.
% 299.99/300.64  13588[7:Rew:13036.0,13073.0] || subclass(u,identity_relation)* -> equal(u,identity_relation).
% 299.99/300.64  13587[7:Rew:13036.0,13067.1] || equal(identity_relation,u)* -> equal(u,identity_relation).
% 299.99/300.64  15665[8:Rew:15663.0,15486.0] ||  -> equal(domain__dfg(identity_relation,u,v),single_valued3(identity_relation))**.
% 299.99/300.64  13586[7:Rew:13036.0,13062.1] || connected(u,identity_relation) -> well_ordering(u,identity_relation)*.
% 299.99/300.64  18517[7:SSi:18513.0,73.0] ||  -> equal(singleton(u),identity_relation) member(u,ordinal_numbers)*.
% 299.99/300.64  13068[7:Rew:13036.0,4557.1] inductive(singleton(u)) ||  -> equal(identity_relation,u)*.
% 299.99/300.64  160480[8:Rew:140603.0,66087.0] ||  -> equal(symmetric_difference(u,identity_relation),union(u,identity_relation))**.
% 299.99/300.64  160496[8:Rew:140603.0,66216.0] ||  -> equal(union(identity_relation,u),complement(complement(u)))**.
% 299.99/300.64  105[0:Inp] ||  -> equal(first(not_subclass_element(compose(u,inverse(u)),identity_relation)),single_valued1(u))**.
% 299.99/300.64  160498[8:Rew:160496.0,160492.0] ||  -> equal(symmetric_difference(identity_relation,u),complement(complement(u)))**.
% 299.99/300.64  13163[7:Rew:13036.0,9926.0] || equal(complement(unordered_pair(identity_relation,u)),ordinal_numbers)** -> .
% 299.99/300.64  13162[7:Rew:13036.0,9925.0] || equal(complement(unordered_pair(u,identity_relation)),ordinal_numbers)** -> .
% 299.99/300.64  106[0:Inp] ||  -> equal(second(not_subclass_element(compose(u,inverse(u)),identity_relation)),single_valued2(u))**.
% 299.99/300.64  15663[8:SpR:15486.0,107.0] ||  -> equal(first(not_subclass_element(identity_relation,identity_relation)),single_valued3(identity_relation))**.
% 299.99/300.64  162023[8:Rew:140603.0,161953.0] ||  -> subclass(complement(symmetrization_of(identity_relation)),complement(inverse(identity_relation)))*.
% 299.99/300.64  162584[8:Rew:160498.0,162583.0] ||  -> equal(complement(complement(inverse(identity_relation))),symmetrization_of(identity_relation))**.
% 299.99/300.64  15314[8:Rew:15300.0,14753.0] ||  -> equal(segment(identity_relation,u,v),identity_relation)**.
% 299.99/300.64  13596[7:Rew:13036.0,13071.1] ||  -> equal(u,identity_relation) equal(intersection(u,regular(u)),identity_relation)**.
% 299.99/300.64  14650[8:SpR:14565.0,33.0] ||  -> equal(restrict(identity_relation,u,v),identity_relation)**.
% 299.99/300.64  13155[7:Rew:13036.0,4538.0] ||  -> equal(recursion_equation_functions(u),identity_relation)** function(u).
% 299.99/300.64  162248[8:Res:2504.1,14676.0] || subclass(ordered_pair(u,v),identity_relation)* -> .
% 299.99/300.64  162891[8:Res:10.1,162248.0] || equal(ordered_pair(u,v),identity_relation)** -> .
% 299.99/300.64  65[0:Inp] || subclass(compose(u,inverse(u)),identity_relation)* -> single_valued_class(u).
% 299.99/300.64  13139[7:Rew:13036.0,9924.0] || equal(complement(singleton(identity_relation)),ordinal_numbers)** -> .
% 299.99/300.64  165955[16:Res:13049.1,165946.0] || subclass(ordinal_numbers,complement(singleton(identity_relation)))* -> .
% 299.99/300.64  65892[9:Spt:65866.0,13601.0] ||  -> equal(integer_of(regular(complement(omega))),identity_relation)**.
% 299.99/300.64  160479[13:MRR:81877.1,160427.0] || equal(cross_product(ordinal_numbers,ordinal_numbers),identity_relation)** -> .
% 299.99/300.64  163373[8:Res:156888.0,13588.0] ||  -> equal(intersection(subset_relation,inverse(subset_relation)),identity_relation)**.
% 299.99/300.64  14565[8:Spt:14563.0,13565.0] ||  -> equal(intersection(u,identity_relation),identity_relation)**.
% 299.99/300.64  15313[8:Rew:15300.0,14570.0] || section(u,ordinals_with_null_class_as_identity,identity_relation)* -> .
% 299.99/300.64  17401[8:Res:13248.1,14676.0] ||  -> equal(intersection(identity_relation,u),identity_relation)**.
% 299.99/300.64  66085[8:Rew:66036.0,13078.0] ||  -> equal(intersection(complement(compose(element_relation,ordinal_numbers)),element_relation),identity_relation)**.
% 299.99/300.64  10868[5:Res:8656.0,8787.1] single_valued_class(union_of_range_map) ||  -> function(union_of_range_map)*.
% 299.99/300.64  166593[8:Res:8652.0,166458.1] || equal(rest_of(identity_relation),rest_relation)** -> .
% 299.99/300.64  13072[7:Rew:13036.0,4549.0] ||  -> equal(u,identity_relation) member(regular(u),u)*.
% 299.99/300.64  15380[8:MRR:15374.0,13126.0] ||  -> member(ordered_pair(identity_relation,identity_relation),domain_relation)*.
% 299.99/300.64  60940[8:Res:51313.1,14676.0] || member(singleton(identity_relation),subset_relation)* -> .
% 299.99/300.64  165394[14:Res:165168.1,60934.0] || equal(singleton(identity_relation),subset_relation)** -> .
% 299.99/300.64  13061[7:Rew:13036.0,4551.1] ||  -> member(u,omega)* equal(integer_of(u),identity_relation).
% 299.99/300.64  167594[14:Res:295.0,164499.0] || well_ordering(ordinal_numbers,singleton(identity_relation))* -> .
% 299.99/300.64  163118[8:SpR:162584.0,130678.0] ||  -> subclass(symmetrization_of(identity_relation),inverse(identity_relation))*.
% 299.99/300.64  13056[7:Rew:13036.0,4537.1] inductive(u) ||  -> member(identity_relation,u)*.
% 299.99/300.64  165227[14:Res:165164.1,14676.0] || equal(singleton(identity_relation),identity_relation)** -> .
% 299.99/300.64  79[0:Inp] ||  -> equal(intersection(inverse(subset_relation),subset_relation),identity_relation)**.
% 299.99/300.64  18232[8:MRR:18230.0,17473.0] ||  -> section(identity_relation,u,u)*.
% 299.99/300.64  14676[8:MRR:13147.1,14657.1] || member(u,identity_relation)* -> .
% 299.99/300.64  165946[16:Spt:165945.0,165175.0,165928.0] || member(identity_relation,complement(singleton(identity_relation)))* -> .
% 299.99/300.64  160429[8:Rew:116078.0,15300.0] ||  -> equal(cantor(identity_relation),identity_relation)**.
% 299.99/300.64  15592[8:Res:10.1,15577.0] || equal(domain_relation,identity_relation)** -> .
% 299.99/300.64  15577[8:Res:15426.1,14676.0] || subclass(domain_relation,identity_relation)* -> .
% 299.99/300.64  62299[8:Res:8655.0,60946.0] || subclass(rest_relation,identity_relation)* -> .
% 299.99/300.64  8656[5:Rew:8637.0,156.0] ||  -> subclass(union_of_range_map,cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.64  62337[8:Res:19172.1,62299.0] || equal(rest_relation,identity_relation)** -> .
% 299.99/300.64  60934[8:Res:49995.1,14676.0] || member(identity_relation,subset_relation)* -> .
% 299.99/300.64  13118[7:Rew:13036.0,9809.0] ||  -> equal(sum_class(identity_relation),identity_relation)**.
% 299.99/300.64  13127[7:Rew:13036.0,9832.0] ||  -> section(element_relation,identity_relation,ordinal_numbers)*.
% 299.99/300.64  65891[9:Spt:65866.0,13601.1,15996.0] || equal(complement(omega),identity_relation)** -> .
% 299.99/300.64  69279[8:Res:13072.1,69257.0] ||  -> equal(regular(ordinal_numbers),identity_relation)**.
% 299.99/300.64  66036[8:Res:65911.0,8954.0] ||  -> equal(complement(identity_relation),ordinal_numbers)**.
% 299.99/300.64  17351[7:Res:8638.0,17333.0] ||  -> equal(complement(ordinal_numbers),identity_relation)**.
% 299.99/300.64  13041[7:Rew:13036.0,4532.0] ||  -> equal(integer_of(identity_relation),identity_relation)**.
% 299.99/300.64  187541[17:Spt:187539.0,62802.1,167633.0] || equal(identity_relation,union_of_range_map)** -> .
% 299.99/300.64  13108[7:Rew:13036.0,8653.0] || equal(identity_relation,ordinal_numbers)** -> .
% 299.99/300.64  13109[7:Rew:13036.0,8654.0] || subclass(ordinal_numbers,identity_relation)* -> .
% 299.99/300.64  15310[8:Rew:15300.0,14569.0] || equal(identity_relation,ordinals_with_null_class_as_identity)** -> .
% 299.99/300.64  160434[7:Rew:17351.0,126663.0] || subclass(omega,identity_relation)* -> .
% 299.99/300.64  76791[10:Spt:76678.0,13484.1,70053.0] || equal(element_relation,identity_relation)** -> .
% 299.99/300.64  164498[14:Spt:164434.0,163260.0] ||  -> member(identity_relation,singleton(identity_relation))*.
% 299.99/300.64  13040[7:Rew:13036.0,6407.0] || equal(omega,identity_relation)** -> .
% 299.99/300.64  17473[8:Obv:17472.0] ||  -> asymmetric(identity_relation,u)*.
% 299.99/300.64  13039[7:Rew:13036.0,4531.0] ||  -> subclass(identity_relation,u)*.
% 299.99/300.64  13036[7:Spt:13030.0] ||  -> equal(singleton_relation,identity_relation)**.
% 299.99/300.64  15309[8:Rew:15300.0,14568.0] || subclass(ordinals_with_null_class_as_identity,identity_relation)* -> .
% 299.99/300.64  13037[7:Rew:13036.0,4608.0] ||  -> equal(limit_ordinals,identity_relation)**.
% 299.99/300.64  13038[7:Rew:13036.0,4530.0] ||  -> equal(null_class,identity_relation)**.
% 299.99/300.64  13126[7:Rew:13036.0,9808.0] ||  -> member(identity_relation,ordinal_numbers)*.
% 299.99/300.64  165430[15:Spt:165425.0] ||  -> function(identity_relation)*.
% 299.99/300.64  160427[13:Spt:160421.0,13483.1,83953.0] || equal(identity_relation,successor_relation)** -> .
% 299.99/300.64  187542[17:Spt:187539.0,62802.0,62802.2] || well_ordering(u,cross_product(ordinal_numbers,ordinal_numbers))* -> member(least(u,union_of_range_map),union_of_range_map).
% 299.99/300.64  176788[8:Res:144409.1,151988.0] || equal(symmetric_difference(ordinal_numbers,complement(u)),ordinal_numbers)** -> member(omega,u).
% 299.99/300.64  176785[8:Res:144409.1,28.1] || equal(symmetric_difference(ordinal_numbers,u),ordinal_numbers)** member(omega,u) -> .
% 299.99/300.64  9706[5:Res:20.2,8799.1] || member(u,ordinal_numbers) member(v,ordinal_numbers) equal(successor(v),u) -> member(ordered_pair(v,u),successor_relation)*.
% 299.99/300.64  117511[8:Rew:116078.0,116144.1] operation(u) ||  -> equal(restrict(v,cantor(cantor(u)),cantor(cantor(u))),intersection(cantor(u),v))**.
% 299.99/300.64  163499[5:Res:39298.1,49.0] || subclass(ordinal_numbers,complement(complement(successor_relation)))*+ -> equal(successor(u),v)*.
% 299.99/300.64  161304[8:MRR:134737.0,8655.0] || subclass(rest_relation,rest_of(u)) well_ordering(ordinal_numbers,cantor(u))* -> .
% 299.99/300.64  161196[8:Rew:160496.0,161195.2] operation(u) || connected(v,cantor(cantor(u))) -> subclass(cantor(u),complement(complement(symmetrization_of(v))))*.
% 299.99/300.64  134026[5:Res:9632.1,133836.0] || equal(complement(complement(u)),ordinal_numbers)** well_ordering(ordinal_numbers,u) -> .
% 299.99/300.64  161194[8:Rew:160496.0,161193.1] operation(u) || subclass(cantor(u),complement(complement(symmetrization_of(v))))* -> connected(v,cantor(cantor(u))).
% 299.99/300.64  50843[5:Res:49995.1,152.0] || member(recursion_equation_functions(u),subset_relation) -> function(singleton(first(recursion_equation_functions(u))))*.
% 299.99/300.64  176864[8:Res:148858.1,155244.0] || subclass(ordinal_numbers,inverse(subset_relation))* -> equal(symmetric_difference(ordinal_numbers,subset_relation),ordinal_numbers).
% 299.99/300.64  155244[8:SpR:154737.1,140613.0] || subclass(ordinal_numbers,complement(u))* -> equal(symmetric_difference(ordinal_numbers,u),ordinal_numbers).
% 299.99/300.64  144460[8:Rew:140613.0,144376.0,66141.0,144376.0] ||  -> equal(symmetric_difference(ordinal_numbers,symmetric_difference(ordinal_numbers,u)),symmetric_difference(complement(u),ordinal_numbers))**.
% 299.99/300.64  144419[8:SpL:140613.0,8732.0] || subclass(ordinal_numbers,symmetric_difference(ordinal_numbers,u))* -> member(omega,complement(u)).
% 299.99/300.64  144409[8:SpL:140613.0,8735.0] || equal(symmetric_difference(ordinal_numbers,u),ordinal_numbers) -> member(omega,complement(u))*.
% 299.99/300.64  116103[8:Rew:116078.0,3754.1] operation(restrict(element_relation,universal_class,u)) ||  -> equal(cross_product(cantor(sum_class(u)),cantor(sum_class(u))),sum_class(u))**.
% 299.99/300.64  116102[8:Rew:116078.0,9100.1] operation(restrict(element_relation,ordinal_numbers,u)) ||  -> equal(cross_product(cantor(sum_class(u)),cantor(sum_class(u))),sum_class(u))**.
% 299.99/300.64  128178[5:Res:55.1,127981.0] inductive(complement(complement(recursion_equation_functions(u)))) ||  -> function(least(element_relation,omega))*.
% 299.99/300.64  9004[5:Rew:8637.0,8775.0] || member(flip(cross_product(u,ordinal_numbers)),ordinal_numbers) -> member(ordered_pair(flip(cross_product(u,ordinal_numbers)),inverse(u)),domain_relation)*.
% 299.99/300.64  117450[8:Rew:116078.0,116140.2,116078.0,116140.1] operation(u) || member(ordered_pair(v,w),cantor(u))* -> member(w,cantor(cantor(u))).
% 299.99/300.64  128096[8:Res:55.1,128043.1] inductive(inverse(subset_relation)) || equal(complement(complement(subset_relation)),omega)** -> .
% 299.99/300.64  117449[8:Rew:116078.0,116139.2,116078.0,116139.1] operation(u) || member(ordered_pair(v,w),cantor(u))* -> member(v,cantor(cantor(u))).
% 299.99/300.64  117418[8:Rew:116078.0,116110.1,116078.0,116110.1] operation(u) || equal(cantor(cantor(v)),cantor(u)) -> compatible(u,v,u)*.
% 299.99/300.64  167438[8:SoR:162919.0,82.1] operation(cantor(u)) || equal(rest_of(u),rest_relation)** -> .
% 299.99/300.64  167436[8:SoR:162919.0,75.1] one_to_one(cantor(u)) || equal(rest_of(u),rest_relation)** -> .
% 299.99/300.64  167369[5:Res:10.1,147101.1] || equal(complement(u),omega)** equal(u,ordinal_numbers) -> .
% 299.99/300.64  167298[5:Res:10.1,126664.1] || equal(complement(u),omega) subclass(ordinal_numbers,u)* -> .
% 299.99/300.64  162919[8:MRR:135177.2,162904.0] function(cantor(u)) || equal(rest_of(u),rest_relation)** -> .
% 299.99/300.64  160668[8:Rew:160496.0,2711.0] || equal(complement(complement(symmetrization_of(u))),cross_product(v,v))*+ -> connected(u,v)*.
% 299.99/300.64  167370[5:Res:55.1,147101.1] inductive(complement(u)) || equal(u,ordinal_numbers)* -> .
% 299.99/300.64  147101[5:Res:143193.1,125896.1] || equal(u,ordinal_numbers) subclass(omega,complement(u))* -> .
% 299.99/300.64  147100[5:Res:143193.1,125973.1] || equal(u,ordinal_numbers) subclass(ordinal_numbers,complement(u))* -> .
% 299.99/300.64  167299[5:Res:55.1,126664.1] inductive(complement(u)) || subclass(ordinal_numbers,u)* -> .
% 299.99/300.64  126664[5:Res:125731.1,125896.1] || subclass(ordinal_numbers,u) subclass(omega,complement(u))* -> .
% 299.99/300.64  8958[5:Rew:8637.0,8639.1] || equal(u,ordinal_numbers) equal(complement(u),ordinal_numbers)** -> .
% 299.99/300.64  81488[8:Res:10.1,81409.1] || equal(u,ordinal_numbers) equal(complement(u),domain_relation)** -> .
% 299.99/300.64  8959[5:Rew:8637.0,8644.1] || subclass(ordinal_numbers,u)* equal(complement(u),ordinal_numbers) -> .
% 299.99/300.64  9488[5:Res:8645.1,8843.1] || subclass(ordinal_numbers,u) subclass(ordinal_numbers,complement(u))* -> .
% 299.99/300.64  81326[8:Res:8642.1,15565.1] || subclass(ordinal_numbers,u) subclass(domain_relation,complement(u))* -> .
% 299.99/300.64  81409[8:Res:10.1,81326.1] || equal(complement(u),domain_relation) subclass(ordinal_numbers,u)* -> .
% 299.99/300.64  116209[8:Rew:116078.0,3767.1] operation(u) ||  -> equal(intersection(cantor(u),v),intersection(v,cantor(u)))*.
% 299.99/300.64  147805[5:Res:10.1,147315.1] || equal(complement(u),omega)** equal(u,omega) -> .
% 299.99/300.64  147750[5:Res:10.1,147314.1] || equal(complement(u),ordinal_numbers)** equal(u,omega) -> .
% 299.99/300.64  127430[5:Res:10.1,127130.1] || equal(complement(u),ordinal_numbers) subclass(omega,u)* -> .
% 299.99/300.64  166753[5:Res:55.1,127031.1] inductive(u) || equal(complement(u),omega)** -> .
% 299.99/300.64  127031[5:Res:10.1,126665.1] || equal(complement(u),omega) subclass(omega,u)* -> .
% 299.99/300.64  94701[5:Res:39298.1,18843.0] || subclass(ordinal_numbers,complement(complement(subset_relation)))*+ -> member(u,ordinal_numbers)*.
% 299.99/300.64  125901[5:Res:125725.1,152.0] || subclass(omega,recursion_equation_functions(u))*+ -> function(least(element_relation,omega))*.
% 299.99/300.64  8970[5:Rew:8637.0,8790.1] || subclass(cross_product(ordinal_numbers,ordinal_numbers),successor_relation)* -> equal(cross_product(ordinal_numbers,ordinal_numbers),successor_relation).
% 299.99/300.64  125950[5:Res:10.1,125901.0] || equal(recursion_equation_functions(u),omega)**+ -> function(least(element_relation,omega))*.
% 299.99/300.64  166270[8:MRR:166240.2,60934.0] inductive(compose(subset_relation,subset_relation)) || transitive(subset_relation,ordinal_numbers)* -> .
% 299.99/300.64  166269[16:MRR:166267.1,165946.0] inductive(complement(successor(identity_relation))) ||  -> .
% 299.99/300.64  8788[5:Rew:8637.0,4606.1] || member(u,recursion_equation_functions(v))*+ -> subclass(u,cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.64  166027[16:MRR:82399.1,166020.0] || equal(complement(complement(successor_relation)),domain_relation)** -> .
% 299.99/300.64  166026[16:MRR:82296.1,166020.0] || subclass(domain_relation,complement(complement(successor_relation)))* -> .
% 299.99/300.64  166025[16:MRR:15580.1,166020.0] || subclass(domain_relation,successor_relation)* -> .
% 299.99/300.64  213[0:Res:6.1,152.0] ||  -> subclass(recursion_equation_functions(u),v) function(not_subclass_element(recursion_equation_functions(u),v))*.
% 299.99/300.64  165956[16:Res:13056.1,165946.0] inductive(complement(singleton(identity_relation))) ||  -> .
% 299.99/300.64  165922[8:MRR:165915.1,13139.0] || equal(domain_relation,successor_relation)** -> .
% 299.99/300.64  81321[8:Res:15628.1,15565.1] || equal(rest_relation,domain_relation) subclass(domain_relation,complement(rest_relation))* -> .
% 299.99/300.64  62611[8:Res:15628.1,8841.1] || equal(rest_relation,domain_relation) subclass(ordinal_numbers,complement(rest_relation))* -> .
% 299.99/300.64  4719[0:Res:82.1,77.1] operation(inverse(u)) function(u) ||  -> one_to_one(u)*.
% 299.99/300.64  143198[5:SpL:140603.0,10114.0] || equal(u,ordinal_numbers) -> member(singleton(v),u)*.
% 299.99/300.64  116165[8:Rew:116078.0,155.2] function(u) function(v) || member(cantor(u),ordinal_numbers) equal(compose(v,rest_of(u)),u)** -> member(u,recursion_equation_functions(v)).
% 299.99/300.64  96837[5:Obv:96834.0] ||  -> subclass(singleton(u),complement(recursion_equation_functions(v)))* function(u).
% 299.99/300.64  165231[14:MRR:66277.1,165227.0] inductive(domain_of(singleton_relation)) ||  -> .
% 299.99/300.64  164088[8:SpL:117380.1,162904.0] operation(u) || equal(cantor(u),ordinal_numbers)** -> .
% 299.99/300.64  164087[8:SpL:117380.1,162895.0] operation(u) || subclass(ordinal_numbers,cantor(u))* -> .
% 299.99/300.64  162365[8:Res:15380.0,9876.0] || subclass(domain_relation,u) well_ordering(ordinal_numbers,u)* -> .
% 299.99/300.64  164619[8:Obv:164618.0] ||  -> asymmetric(subset_relation,u)*.
% 299.99/300.64  125951[5:Res:55.1,125901.0] inductive(recursion_equation_functions(u)) ||  -> function(least(element_relation,omega))*.
% 299.99/300.64  117380[8:Rew:116078.0,116137.1] operation(u) ||  -> equal(cross_product(cantor(cantor(u)),cantor(cantor(u))),cantor(u))**.
% 299.99/300.64  160669[8:Rew:160496.0,120.1] || connected(u,v) -> subclass(cross_product(v,v),complement(complement(symmetrization_of(u))))*.
% 299.99/300.64  160667[8:Rew:160496.0,121.0] || subclass(cross_product(u,u),complement(complement(symmetrization_of(v))))* -> connected(v,u).
% 299.99/300.64  154[0:Inp] || member(u,recursion_equation_functions(v)) -> equal(compose(v,rest_of(u)),u)**.
% 299.99/300.64  143200[5:SpL:140603.0,8736.0] || equal(u,ordinal_numbers) -> member(omega,u)*.
% 299.99/300.64  49[0:Inp] || member(ordered_pair(u,v),successor_relation)* -> equal(successor(u),v).
% 299.99/300.64  163466[8:Rew:140603.0,163424.0,66036.0,163424.0] ||  -> equal(symmetric_difference(subset_relation,inverse(subset_relation)),symmetrization_of(subset_relation))**.
% 299.99/300.64  163405[8:MRR:163388.1,13040.0] inductive(intersection(subset_relation,inverse(subset_relation))) ||  -> .
% 299.99/300.64  163263[10:Res:10.1,162776.0] || equal(complement(compose(element_relation,ordinal_numbers)),element_relation)** -> .
% 299.99/300.64  162776[10:MRR:162740.1,76791.0] || subclass(element_relation,complement(compose(element_relation,ordinal_numbers)))* -> .
% 299.99/300.64  92[0:Inp] || homomorphism(u,v,w)* -> compatible(u,v,w).
% 299.99/300.64  162904[8:Res:10.1,162895.0] || equal(cross_product(u,v),ordinal_numbers)** -> .
% 299.99/300.64  162917[8:MRR:68075.1,162904.0] function(symmetric_difference(ordinal_numbers,identity_relation)) ||  -> .
% 299.99/300.64  162916[8:MRR:68530.1,162904.0] one_to_one(symmetric_difference(ordinal_numbers,identity_relation)) ||  -> .
% 299.99/300.64  162915[8:MRR:68531.1,162904.0] operation(symmetric_difference(ordinal_numbers,identity_relation)) ||  -> .
% 299.99/300.64  162914[8:MRR:66241.1,162904.0] function(complement(identity_relation)) ||  -> .
% 299.99/300.64  162913[8:MRR:67121.1,162904.0] one_to_one(complement(identity_relation)) ||  -> .
% 299.99/300.64  162912[8:MRR:67122.1,162904.0] operation(complement(identity_relation)) ||  -> .
% 299.99/300.64  162911[8:MRR:9116.1,162904.0] operation(ordinal_numbers) ||  -> .
% 299.99/300.64  162910[8:MRR:8692.1,162904.0] operation(universal_class) ||  -> .
% 299.99/300.64  116166[8:Rew:116078.0,153.1] || member(u,recursion_equation_functions(v))*+ -> member(cantor(u),ordinal_numbers)*.
% 299.99/300.64  162909[8:MRR:9115.1,162904.0] one_to_one(ordinal_numbers) ||  -> .
% 299.99/300.64  162908[8:MRR:8693.1,162904.0] one_to_one(universal_class) ||  -> .
% 299.99/300.64  162907[8:MRR:8694.1,162904.0] function(universal_class) ||  -> .
% 299.99/300.64  162905[8:Res:8665.1,162895.0] function(ordinal_numbers) ||  -> .
% 299.99/300.64  162895[8:MRR:13473.1,162891.0] || subclass(ordinal_numbers,cross_product(u,v))* -> .
% 299.99/300.64  162894[8:MRR:13474.1,162891.0] inductive(cross_product(u,v)) ||  -> .
% 299.99/300.64  178[0:Res:51.1,151.0] inductive(recursion_equation_functions(u)) ||  -> function(u)*.
% 299.99/300.64  91[0:Inp] || homomorphism(u,v,w)* -> operation(w).
% 299.99/300.64  90[0:Inp] || homomorphism(u,v,w)* -> operation(v).
% 299.99/300.64  152[0:Inp] || member(u,recursion_equation_functions(v))* -> function(u).
% 299.99/300.64  127152[5:Res:10.1,127127.0] || equal(complement(omega),ordinal_numbers)** -> .
% 299.99/300.64  10871[5:Res:8659.0,8787.1] single_valued_class(successor_relation) ||  -> function(successor_relation)*.
% 299.99/300.64  82[0:Inp] operation(u) ||  -> function(u)*.
% 299.99/300.64  8659[5:Rew:8637.0,48.0] ||  -> subclass(successor_relation,cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.64  8752[5:Rew:8637.0,8160.0] || subclass(ordinal_numbers,union_of_range_map)* -> .
% 299.99/300.64  8753[5:Rew:8637.0,8166.0] || equal(union_of_range_map,ordinal_numbers)** -> .
% 299.99/300.64  160428[13:Spt:160421.0,13483.0,13483.2] || well_ordering(u,cross_product(ordinal_numbers,ordinal_numbers))* -> member(least(u,successor_relation),successor_relation).
% 299.99/300.64  28963[5:Res:8827.2,97.0] || member(u,ordinal_numbers) subclass(rest_relation,compose_class(v))*+ -> equal(compose(v,u),rest_of(u))**.
% 299.99/300.64  8785[5:Rew:8637.0,3910.1] || member(singleton(singleton(singleton(u))),rest_of(v))* -> equal(restrict(v,singleton(u),ordinal_numbers),u).
% 299.99/300.64  28944[5:Res:8827.2,3700.0] || member(u,ordinal_numbers) subclass(rest_relation,singleton(v))*+ -> equal(ordered_pair(u,rest_of(u)),v)*.
% 299.99/300.64  157036[8:SpR:147905.0,157013.0] ||  -> subclass(complement(complement(inverse(subset_relation))),complement(subset_relation))*.
% 299.99/300.64  157013[8:Obv:157003.0] ||  -> subclass(intersection(inverse(subset_relation),u),complement(subset_relation))*.
% 299.99/300.64  19032[8:Res:313.1,14679.1] || member(not_subclass_element(intersection(inverse(subset_relation),u),v),subset_relation)* -> subclass(intersection(inverse(subset_relation),u),v).
% 299.99/300.64  156922[8:Con:156921.1] || member(u,inverse(subset_relation)) -> member(u,complement(subset_relation))*.
% 299.99/300.64  156904[8:SpR:33.0,156893.0] ||  -> subclass(restrict(inverse(subset_relation),u,v),complement(subset_relation))*.
% 299.99/300.64  156893[8:Obv:156884.0] ||  -> subclass(intersection(u,inverse(subset_relation)),complement(subset_relation))*.
% 299.99/300.64  18913[8:Res:303.1,14679.1] || member(not_subclass_element(intersection(u,inverse(subset_relation)),v),subset_relation)* -> subclass(intersection(u,inverse(subset_relation)),v).
% 299.99/300.64  40594[5:MRR:40586.1,8655.0] || member(u,ordinal_numbers) member(singleton(u),u)*+ -> member(singleton(singleton(singleton(u))),element_relation)*.
% 299.99/300.64  155663[5:Rew:155653.0,51958.0] || transitive(subset_relation,ordinal_numbers) subclass(subset_relation,compose(subset_relation,subset_relation))* -> equal(compose(subset_relation,subset_relation),subset_relation).
% 299.99/300.64  155846[5:SpL:155653.0,9777.0] || equal(compose(subset_relation,subset_relation),subset_relation) -> transitive(complement(compose(complement(element_relation),inverse(element_relation))),ordinal_numbers)*.
% 299.99/300.64  156513[5:SpR:155666.0,19045.0] ||  -> subclass(symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation),complement(subset_relation))*.
% 299.99/300.64  155666[5:Rew:155653.0,41019.0] ||  -> equal(intersection(complement(subset_relation),union(cross_product(ordinal_numbers,ordinal_numbers),subset_relation)),symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation))**.
% 299.99/300.64  156404[5:SpR:155665.0,19045.0] ||  -> subclass(symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers)),complement(subset_relation))*.
% 299.99/300.64  155665[5:Rew:155653.0,40900.0] ||  -> equal(intersection(complement(subset_relation),union(subset_relation,cross_product(ordinal_numbers,ordinal_numbers))),symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers)))**.
% 299.99/300.64  155845[5:SpL:155653.0,123.0] || subclass(compose(subset_relation,subset_relation),subset_relation) -> transitive(complement(compose(complement(element_relation),inverse(element_relation))),ordinal_numbers)*.
% 299.99/300.64  155147[0:MRR:155094.0,18926.0] ||  -> equal(intersection(u,intersection(v,u)),intersection(v,u))**.
% 299.99/300.64  155827[5:SpR:155653.0,122.1] || transitive(complement(compose(complement(element_relation),inverse(element_relation))),ordinal_numbers)* -> subclass(compose(subset_relation,subset_relation),subset_relation).
% 299.99/300.64  155664[5:Rew:155653.0,44876.1] || equal(compose(subset_relation,subset_relation),subset_relation)** -> transitive(subset_relation,ordinal_numbers).
% 299.99/300.64  155658[5:Rew:155653.0,9772.1] || subclass(compose(subset_relation,subset_relation),subset_relation)* -> transitive(subset_relation,ordinal_numbers).
% 299.99/300.64  155657[5:Rew:155653.0,9814.0] || transitive(subset_relation,ordinal_numbers) -> subclass(compose(subset_relation,subset_relation),subset_relation)*.
% 299.99/300.64  155818[5:SpR:155653.0,18949.0] ||  -> subclass(subset_relation,complement(compose(complement(element_relation),inverse(element_relation))))*.
% 299.99/300.64  155653[5:Rew:155652.0,8770.0] ||  -> equal(restrict(complement(compose(complement(element_relation),inverse(element_relation))),ordinal_numbers,ordinal_numbers),subset_relation)**.
% 299.99/300.64  154945[0:MRR:154902.0,18926.0] ||  -> equal(intersection(u,intersection(u,v)),intersection(u,v))**.
% 299.99/300.64  154737[0:MRR:154645.1,18926.0] || subclass(u,v) -> equal(intersection(v,u),u)**.
% 299.99/300.64  151988[5:SpL:147905.0,25.0] || member(u,complement(complement(v)))* -> member(u,v).
% 299.99/300.64  153473[8:Obv:153471.0] ||  -> subclass(complement(compose(element_relation,ordinal_numbers)),complement(element_relation))*.
% 299.99/300.64  69161[8:Res:6.1,66086.1] || member(not_subclass_element(complement(compose(element_relation,ordinal_numbers)),u),element_relation)* -> subclass(complement(compose(element_relation,ordinal_numbers)),u).
% 299.99/300.64  919[0:Res:6.1,898.0] ||  -> subclass(restrict(u,v,w),x) member(not_subclass_element(restrict(u,v,w),x),u)*.
% 299.99/300.64  18204[0:Res:6.1,3617.0] ||  -> subclass(symmetric_difference(u,v),w) member(not_subclass_element(symmetric_difference(u,v),w),union(u,v))*.
% 299.99/300.64  19120[0:Res:2503.2,26.0] || subclass(u,intersection(v,w))*+ -> subclass(u,x) member(not_subclass_element(u,x),w)*.
% 299.99/300.64  151970[5:SpL:147905.0,8732.0] || subclass(ordinal_numbers,complement(complement(u)))* -> member(omega,u).
% 299.99/300.64  19121[0:Res:2503.2,25.0] || subclass(u,intersection(v,w))*+ -> subclass(u,x) member(not_subclass_element(u,x),v)*.
% 299.99/300.64  152223[0:Obv:152213.1] || subclass(u,complement(u))*+ -> subclass(u,v)*.
% 299.99/300.64  19111[0:Res:2503.2,28.1] || subclass(u,complement(v)) member(not_subclass_element(u,w),v)* -> subclass(u,w).
% 299.99/300.64  18829[5:Res:8643.1,897.0] || subclass(ordinal_numbers,restrict(u,v,w))*+ -> member(unordered_pair(x,y),cross_product(v,w))*.
% 299.99/300.64  147905[5:MRR:147894.0,18926.0] ||  -> equal(intersection(u,complement(complement(u))),complement(complement(u)))**.
% 299.99/300.64  19029[0:Res:313.1,3700.0] ||  -> subclass(intersection(singleton(u),v),w) equal(not_subclass_element(intersection(singleton(u),v),w),u)**.
% 299.99/300.64  18910[0:Res:303.1,3700.0] ||  -> subclass(intersection(u,singleton(v)),w) equal(not_subclass_element(intersection(u,singleton(v)),w),v)**.
% 299.99/300.64  148963[5:Res:8657.0,28958.1] || member(u,ordinal_numbers) -> member(rest_of(u),ordinal_numbers)*.
% 299.99/300.64  28958[5:Res:8827.2,19.0] || member(u,ordinal_numbers) subclass(rest_relation,cross_product(v,w))*+ -> member(rest_of(u),w)*.
% 299.99/300.64  148916[8:Res:148858.1,63019.1] || subclass(ordinal_numbers,inverse(subset_relation))* subclass(domain_relation,subset_relation) -> .
% 299.99/300.64  148908[8:Res:148858.1,8954.0] || subclass(ordinal_numbers,inverse(subset_relation))* -> equal(complement(subset_relation),ordinal_numbers).
% 299.99/300.64  148858[8:Obv:148853.1] || subclass(u,inverse(subset_relation)) -> subclass(u,complement(subset_relation))*.
% 299.99/300.64  19127[8:Res:2503.2,14679.1] || subclass(u,inverse(subset_relation)) member(not_subclass_element(u,v),subset_relation)* -> subclass(u,v).
% 299.99/300.64  143171[8:SpR:140603.0,15308.1] || asymmetric(ordinal_numbers,u) -> section(inverse(ordinal_numbers),u,u)*.
% 299.99/300.64  3572[0:SpL:963.0,97.0] || member(singleton(singleton(singleton(u))),compose_class(v))* -> equal(compose(v,singleton(u)),u).
% 299.99/300.64  18581[5:Res:8978.2,25.0] || member(u,ordinal_numbers) subclass(ordinal_numbers,intersection(v,w))*+ -> member(sum_class(u),v)*.
% 299.99/300.64  18580[5:Res:8978.2,26.0] || member(u,ordinal_numbers) subclass(ordinal_numbers,intersection(v,w))*+ -> member(sum_class(u),w)*.
% 299.99/300.64  147806[5:Res:55.1,147315.1] inductive(complement(u)) || equal(u,omega)* -> .
% 299.99/300.64  147315[5:Res:143222.1,125896.1] || equal(u,omega) subclass(omega,complement(u))* -> .
% 299.99/300.64  147314[5:Res:143222.1,125973.1] || equal(u,omega) subclass(ordinal_numbers,complement(u))* -> .
% 299.99/300.64  46149[5:Rew:8648.0,46142.2] || section(element_relation,u,ordinal_numbers)*+ subclass(u,sum_class(u))* -> equal(sum_class(u),u).
% 299.99/300.64  143222[5:SpL:140603.0,130481.0] || equal(u,omega) -> member(least(element_relation,omega),u)*.
% 299.99/300.64  143193[5:SpL:140603.0,130610.0] || equal(u,ordinal_numbers) -> member(least(element_relation,omega),u)*.
% 299.99/300.64  141394[8:Rew:140613.0,66423.0] ||  -> equal(symmetric_difference(ordinal_numbers,intersection(u,ordinal_numbers)),symmetric_difference(u,ordinal_numbers))**.
% 299.99/300.64  141388[8:Rew:140613.0,118001.0] ||  -> equal(symmetric_difference(inverse(u),ordinal_numbers),symmetric_difference(ordinal_numbers,inverse(u)))**.
% 299.99/300.64  141387[8:Rew:140613.0,118064.0] ||  -> equal(symmetric_difference(sum_class(u),ordinal_numbers),symmetric_difference(ordinal_numbers,sum_class(u)))**.
% 299.99/300.64  18571[5:Res:8978.2,28.1] || member(u,ordinal_numbers) subclass(ordinal_numbers,complement(v)) member(sum_class(u),v)* -> .
% 299.99/300.64  66637[5:Res:8646.1,490.0] || subclass(ordinal_numbers,intersection(complement(u),complement(v)))* member(omega,union(u,v)) -> .
% 299.99/300.64  28462[5:Res:10.1,8990.1] function(u) || equal(u,cross_product(ordinal_numbers,ordinal_numbers))* -> equal(cross_product(ordinal_numbers,ordinal_numbers),u).
% 299.99/300.64  143170[5:SpR:140603.0,32.0] ||  -> equal(restrict(ordinal_numbers,u,v),cross_product(u,v))**.
% 299.99/300.64  141399[8:Rew:140613.0,119461.0] ||  -> equal(symmetric_difference(segment(u,v,w),ordinal_numbers),symmetric_difference(ordinal_numbers,segment(u,v,w)))**.
% 299.99/300.64  140613[8:Rew:140603.0,66380.0] ||  -> equal(intersection(complement(u),ordinal_numbers),symmetric_difference(ordinal_numbers,u))**.
% 299.99/300.64  140618[8:Rew:140603.0,66130.0] ||  -> equal(symmetric_difference(complement(compose(element_relation,ordinal_numbers)),element_relation),union(complement(compose(element_relation,ordinal_numbers)),element_relation))**.
% 299.99/300.64  143407[0:SpR:143349.0,30.0] ||  -> equal(union(u,u),complement(complement(u)))**.
% 299.99/300.64  141390[8:Rew:140613.0,116163.0] ||  -> equal(symmetric_difference(cantor(u),ordinal_numbers),symmetric_difference(ordinal_numbers,cantor(u)))**.
% 299.99/300.64  140622[8:Rew:140603.0,66106.0] ||  -> equal(symmetric_difference(inverse(subset_relation),subset_relation),union(inverse(subset_relation),subset_relation))**.
% 299.99/300.64  143160[5:SpR:140603.0,19069.0] ||  -> subclass(symmetric_difference(ordinal_numbers,u),complement(u))*.
% 299.99/300.64  143349[0:MRR:143286.0,18926.0] ||  -> equal(intersection(u,u),u)**.
% 299.99/300.64  140603[5:MRR:140499.0,18926.0] ||  -> equal(intersection(ordinal_numbers,u),u)**.
% 299.99/300.64  47534[0:Obv:47525.1] || member(not_subclass_element(u,intersection(v,u)),v)* -> subclass(u,intersection(v,u)).
% 299.99/300.64  19124[0:Res:2503.2,3700.0] || subclass(u,singleton(v))*+ -> subclass(u,w) equal(not_subclass_element(u,w),v)*.
% 299.99/300.64  39530[5:Res:8832.1,25.0] || member(u,ordinal_numbers) -> member(u,union(v,w))* member(u,complement(v)).
% 299.99/300.64  39529[5:Res:8832.1,26.0] || member(u,ordinal_numbers) -> member(u,union(v,w))* member(u,complement(w)).
% 299.99/300.64  8813[5:Rew:8637.0,6904.0] || subclass(ordinal_numbers,u)*+ subclass(u,v)* -> member(unordered_pair(w,x),v)*.
% 299.99/300.64  1971[0:Res:10.1,1303.1] inductive(u) || equal(omega,u)* -> equal(u,omega).
% 299.99/300.64  8716[5:Rew:8637.0,6739.0] || equal(complement(singleton(omega)),ordinal_numbers)** -> .
% 299.99/300.64  18211[5:Res:8643.1,3617.0] || subclass(ordinal_numbers,symmetric_difference(u,v)) -> member(unordered_pair(w,x),union(u,v))*.
% 299.99/300.64  19830[5:Res:10.1,8837.1] || equal(u,unordered_pair(v,w))*+ member(w,ordinal_numbers) -> member(w,u)*.
% 299.99/300.64  19788[5:Res:10.1,8836.1] || equal(u,unordered_pair(v,w))*+ member(v,ordinal_numbers) -> member(v,u)*.
% 299.99/300.64  18791[0:SpR:30.0,3618.1] || member(u,symmetric_difference(complement(v),complement(w)))* -> member(u,union(v,w)).
% 299.99/300.64  28680[5:Res:8826.2,18.0] || member(u,ordinal_numbers)* subclass(domain_relation,cross_product(v,w))*+ -> member(u,v)*.
% 299.99/300.64  28959[5:Res:8827.2,18.0] || member(u,ordinal_numbers)* subclass(rest_relation,cross_product(v,w))*+ -> member(u,v)*.
% 299.99/300.64  135117[8:Res:135059.1,8954.0] || equal(rest_of(u),rest_relation)** -> equal(cantor(u),ordinal_numbers).
% 299.99/300.64  2200[0:SpL:963.0,18.0] || member(singleton(singleton(singleton(u))),cross_product(v,w))* -> member(singleton(u),v).
% 299.99/300.64  134760[8:MRR:134733.0,41183.1] || subclass(rest_relation,rest_of(u))*+ -> subclass(v,cantor(u))*.
% 299.99/300.64  116453[8:Rew:116078.0,1027.1] || member(singleton(singleton(singleton(u))),rest_of(v))* -> member(singleton(u),cantor(v)).
% 299.99/300.64  116403[8:Rew:116078.0,28957.2] || member(u,ordinal_numbers) subclass(rest_relation,rest_of(v)) -> member(u,cantor(v))*.
% 299.99/300.64  132824[5:Res:10.1,125985.0] || equal(intersection(u,v),ordinal_numbers)**+ -> member(least(element_relation,omega),u)*.
% 299.99/300.64  132463[5:SpL:963.0,132438.0] || equal(u,singleton(singleton(singleton(v))))*+ well_ordering(ordinal_numbers,u)* -> .
% 299.99/300.64  134134[5:Res:133837.1,2557.0] || well_ordering(ordinal_numbers,complement(cross_product(u,v)))*+ -> member(w,v)*.
% 299.99/300.64  134131[5:Res:133837.1,970.0] || well_ordering(ordinal_numbers,complement(element_relation))*+ -> member(singleton(u),u)*.
% 299.99/300.64  134130[5:Res:133837.1,133836.0] || well_ordering(ordinal_numbers,complement(u))* well_ordering(ordinal_numbers,u) -> .
% 299.99/300.64  133837[5:Res:79560.1,130944.0] || well_ordering(ordinal_numbers,complement(u)) -> member(singleton(singleton(v)),u)*.
% 299.99/300.64  134031[5:MRR:134007.0,8655.0] || well_ordering(ordinal_numbers,unordered_pair(u,singleton(singleton(v))))* -> .
% 299.99/300.64  134030[5:MRR:134006.0,8655.0] || well_ordering(ordinal_numbers,unordered_pair(singleton(singleton(u)),v))* -> .
% 299.99/300.64  133836[5:Res:10714.1,130944.0] || member(singleton(singleton(u)),v)* well_ordering(ordinal_numbers,v) -> .
% 299.99/300.64  130944[5:Res:967.0,9876.0] || subclass(singleton(singleton(singleton(u))),v)* well_ordering(ordinal_numbers,v) -> .
% 299.99/300.64  40321[5:Res:8655.0,9659.0] || subclass(rest_relation,u)+ well_ordering(v,u)* -> member(least(v,rest_relation),rest_relation)*.
% 299.99/300.64  130610[5:Res:10.1,125984.0] || equal(intersection(u,v),ordinal_numbers)**+ -> member(least(element_relation,omega),v)*.
% 299.99/300.64  133075[8:Res:55.1,133068.0] inductive(complement(complement(subset_relation))) || equal(inverse(subset_relation),omega)** -> .
% 299.99/300.64  133068[8:Res:126679.1,133059.1] || subclass(omega,complement(complement(subset_relation)))* equal(inverse(subset_relation),omega) -> .
% 299.99/300.64  133059[8:Res:132899.1,14679.1] || equal(inverse(subset_relation),omega) member(least(element_relation,omega),subset_relation)* -> .
% 299.99/300.64  130556[5:Res:10.1,125908.0] || equal(intersection(u,v),omega)**+ -> member(least(element_relation,omega),u)*.
% 299.99/300.64  130481[5:Res:10.1,125907.0] || equal(intersection(u,v),omega)**+ -> member(least(element_relation,omega),v)*.
% 299.99/300.64  125985[5:Res:125731.1,25.0] || subclass(ordinal_numbers,intersection(u,v))*+ -> member(least(element_relation,omega),u)*.
% 299.99/300.64  19167[5:Res:10.1,8986.0] || equal(compose_class(u),cross_product(ordinal_numbers,ordinal_numbers))* -> equal(cross_product(ordinal_numbers,ordinal_numbers),compose_class(u)).
% 299.99/300.64  19311[5:Res:10.1,8987.0] || equal(rest_of(u),cross_product(ordinal_numbers,ordinal_numbers))* -> equal(cross_product(ordinal_numbers,ordinal_numbers),rest_of(u)).
% 299.99/300.64  69166[8:Res:8643.1,66086.1] || subclass(ordinal_numbers,complement(compose(element_relation,ordinal_numbers)))*+ member(unordered_pair(u,v),element_relation)* -> .
% 299.99/300.64  132438[5:Res:10.1,130942.0] || equal(u,ordered_pair(v,w))*+ well_ordering(ordinal_numbers,u)* -> .
% 299.99/300.64  132441[5:SpL:963.0,132439.0] || well_ordering(ordinal_numbers,singleton(singleton(singleton(u))))* -> .
% 299.99/300.64  132439[5:Res:295.0,130942.0] || well_ordering(ordinal_numbers,ordered_pair(u,v))* -> .
% 299.99/300.64  130942[5:Res:962.0,9876.0] || subclass(ordered_pair(u,v),w)* well_ordering(ordinal_numbers,w) -> .
% 299.99/300.64  132294[5:SpR:117.0,130703.0] ||  -> subclass(complement(symmetrization_of(u)),intersection(complement(u),complement(inverse(u))))*.
% 299.99/300.64  39817[0:Res:295.0,9661.0] || well_ordering(u,v)+ -> subclass(v,w)* member(least(u,v),v)*.
% 299.99/300.64  132293[5:SpR:47.0,130703.0] ||  -> subclass(complement(successor(u)),intersection(complement(u),complement(singleton(u))))*.
% 299.99/300.64  130703[5:SpR:30.0,130678.0] ||  -> subclass(complement(union(u,v)),intersection(complement(u),complement(v)))*.
% 299.99/300.64  8854[5:Rew:8637.0,6908.0] || subclass(ordinal_numbers,restrict(u,v,w))*+ -> member(unordered_pair(x,y),u)*.
% 299.99/300.64  2504[0:Res:964.0,5.0] || subclass(ordered_pair(u,v),w) -> member(unordered_pair(u,singleton(v)),w)*.
% 299.99/300.64  18794[0:Res:3618.1,28.1] || member(u,symmetric_difference(v,w)) member(u,intersection(v,w))* -> .
% 299.99/300.64  130722[5:Res:130678.0,1303.1] inductive(complement(complement(omega))) ||  -> equal(complement(complement(omega)),omega)**.
% 299.99/300.64  130931[5:Res:125717.0,9876.0] || subclass(omega,u) well_ordering(ordinal_numbers,u)* -> .
% 299.99/300.64  9876[5:Res:8667.0,131.3] || member(u,v)*+ subclass(v,w)* well_ordering(ordinal_numbers,w)* -> .
% 299.99/300.64  130678[5:Obv:130675.0] ||  -> subclass(complement(complement(u)),u)*.
% 299.99/300.64  41371[5:MRR:8866.0,41183.1] ||  -> member(not_subclass_element(complement(complement(u)),v),u)* subclass(complement(complement(u)),v).
% 299.99/300.64  125984[5:Res:125731.1,26.0] || subclass(ordinal_numbers,intersection(u,v))*+ -> member(least(element_relation,omega),v)*.
% 299.99/300.64  130557[5:Res:55.1,125908.0] inductive(intersection(u,v)) ||  -> member(least(element_relation,omega),u)*.
% 299.99/300.64  125908[5:Res:125725.1,25.0] || subclass(omega,intersection(u,v))*+ -> member(least(element_relation,omega),u)*.
% 299.99/300.64  130482[5:Res:55.1,125907.0] inductive(intersection(u,v)) ||  -> member(least(element_relation,omega),v)*.
% 299.99/300.64  2557[0:SpL:963.0,19.0] || member(singleton(singleton(singleton(u))),cross_product(v,w))* -> member(u,w).
% 299.99/300.64  125907[5:Res:125725.1,26.0] || subclass(omega,intersection(u,v))*+ -> member(least(element_relation,omega),v)*.
% 299.99/300.64  8840[5:Rew:8637.0,4727.0] || member(u,ordinal_numbers) subclass(singleton(u),v)* -> member(u,v).
% 299.99/300.64  127147[5:MRR:127097.0,125724.0] || subclass(ordinal_numbers,complement(complement(u))) -> member(least(element_relation,omega),u)*.
% 299.99/300.64  128044[8:Res:55.1,128029.0] inductive(complement(complement(subset_relation))) || subclass(omega,inverse(subset_relation))* -> .
% 299.99/300.64  128029[8:Res:126679.1,125923.1] || subclass(omega,complement(complement(subset_relation)))* subclass(omega,inverse(subset_relation)) -> .
% 299.99/300.64  126679[5:MRR:126634.0,125724.0] || subclass(omega,complement(complement(u))) -> member(least(element_relation,omega),u)*.
% 299.99/300.64  127130[5:Res:125725.1,125973.1] || subclass(omega,u) subclass(ordinal_numbers,complement(u))* -> .
% 299.99/300.64  127185[5:Res:10.1,127141.0] || equal(complement(unordered_pair(u,least(element_relation,omega))),ordinal_numbers)** -> .
% 299.99/300.64  127179[5:Res:10.1,127140.0] || equal(complement(unordered_pair(least(element_relation,omega),u)),ordinal_numbers)** -> .
% 299.99/300.64  127141[5:MRR:127110.0,125724.0] || subclass(ordinal_numbers,complement(unordered_pair(u,least(element_relation,omega))))* -> .
% 299.99/300.64  127140[5:MRR:127109.0,125724.0] || subclass(ordinal_numbers,complement(unordered_pair(least(element_relation,omega),u)))* -> .
% 299.99/300.64  127169[5:Res:10.1,127139.0] || equal(complement(singleton(least(element_relation,omega))),ordinal_numbers)** -> .
% 299.99/300.64  127139[5:MRR:127108.0,125724.0] || subclass(ordinal_numbers,complement(singleton(least(element_relation,omega))))* -> .
% 299.99/300.64  127127[5:Res:125717.0,125973.1] || subclass(ordinal_numbers,complement(omega))* -> .
% 299.99/300.64  125973[5:Res:125731.1,28.1] || subclass(ordinal_numbers,complement(u)) member(least(element_relation,omega),u)* -> .
% 299.99/300.64  127032[5:Res:55.1,126665.1] inductive(complement(u)) || subclass(omega,u)* -> .
% 299.99/300.64  126665[5:Res:125725.1,125896.1] || subclass(omega,u) subclass(omega,complement(u))* -> .
% 299.99/300.64  126925[5:Res:10.1,126675.0] || equal(complement(unordered_pair(u,least(element_relation,omega))),omega)** -> .
% 299.99/300.64  126860[5:Res:10.1,126674.0] || equal(complement(unordered_pair(least(element_relation,omega),u)),omega)** -> .
% 299.99/300.64  126926[5:Res:55.1,126675.0] inductive(complement(unordered_pair(u,least(element_relation,omega)))) ||  -> .
% 299.99/300.64  126675[5:MRR:126645.0,125724.0] || subclass(omega,complement(unordered_pair(u,least(element_relation,omega))))* -> .
% 299.99/300.64  126861[5:Res:55.1,126674.0] inductive(complement(unordered_pair(least(element_relation,omega),u))) ||  -> .
% 299.99/300.64  126674[5:MRR:126644.0,125724.0] || subclass(omega,complement(unordered_pair(least(element_relation,omega),u)))* -> .
% 299.99/300.64  126751[5:Res:10.1,126673.0] || equal(complement(singleton(least(element_relation,omega))),omega)** -> .
% 299.99/300.64  126752[5:Res:55.1,126673.0] inductive(complement(singleton(least(element_relation,omega)))) ||  -> .
% 299.99/300.64  126673[5:MRR:126643.0,125724.0] || subclass(omega,complement(singleton(least(element_relation,omega))))* -> .
% 299.99/300.64  126739[5:Res:55.1,126662.0] inductive(complement(omega)) ||  -> .
% 299.99/300.64  126662[5:Res:125717.0,125896.1] || subclass(omega,complement(omega))* -> .
% 299.99/300.64  125896[5:Res:125725.1,28.1] || subclass(omega,complement(u)) member(least(element_relation,omega),u)* -> .
% 299.99/300.64  125923[8:Res:125725.1,14679.1] || subclass(omega,inverse(subset_relation)) member(least(element_relation,omega),subset_relation)* -> .
% 299.99/300.64  126428[5:Res:10.1,125920.0] || equal(singleton(u),omega)**+ -> equal(least(element_relation,omega),u)*.
% 299.99/300.64  126429[5:Res:55.1,125920.0] inductive(singleton(u)) ||  -> equal(least(element_relation,omega),u)*.
% 299.99/300.64  125920[5:Res:125725.1,3700.0] || subclass(omega,singleton(u))* -> equal(least(element_relation,omega),u).
% 299.99/300.64  125731[5:Res:125724.0,5.0] || subclass(ordinal_numbers,u) -> member(least(element_relation,omega),u)*.
% 299.99/300.64  125725[5:Res:125717.0,5.0] || subclass(omega,u) -> member(least(element_relation,omega),u)*.
% 299.99/300.64  971[0:SpL:963.0,149.0] || member(singleton(singleton(singleton(u))),rest_relation)* -> equal(rest_of(singleton(u)),u).
% 299.99/300.64  125726[5:Res:125717.0,161.0] ||  -> equal(integer_of(least(element_relation,omega)),least(element_relation,omega))**.
% 299.99/300.64  116738[8:Rew:116078.0,28697.1] || subclass(domain_relation,inverse(subset_relation)) member(ordered_pair(u,cantor(u)),subset_relation)* -> .
% 299.99/300.64  125724[5:Res:125717.0,41096.0] ||  -> member(least(element_relation,omega),ordinal_numbers)*.
% 299.99/300.64  125717[5:SSi:125669.0,54.0] ||  -> member(least(element_relation,omega),omega)*.
% 299.99/300.64  28976[8:MRR:28946.0,18843.1] || subclass(rest_relation,inverse(subset_relation)) member(ordered_pair(u,rest_of(u)),subset_relation)* -> .
% 299.99/300.64  94706[5:Res:39298.1,18.0] || subclass(ordinal_numbers,complement(complement(cross_product(u,v))))*+ -> member(w,u)*.
% 299.99/300.64  94705[5:Res:39298.1,19.0] || subclass(ordinal_numbers,complement(complement(cross_product(u,v))))*+ -> member(w,v)*.
% 299.99/300.64  9594[5:Res:8665.1,9586.0] function(sum_class(cross_product(ordinal_numbers,ordinal_numbers))) ||  -> section(element_relation,cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers)*.
% 299.99/300.64  19676[0:SpL:3597.0,26.0] || member(u,symmetric_difference(v,inverse(v)))* -> member(u,symmetrization_of(v)).
% 299.99/300.64  117318[8:Rew:116078.0,116167.0] || member(u,cantor(u)) -> member(ordered_pair(u,cantor(u)),element_relation)*.
% 299.99/300.64  116180[8:Rew:116078.0,94704.1] || subclass(ordinal_numbers,complement(complement(rest_of(u))))*+ -> member(v,cantor(u))*.
% 299.99/300.64  116179[8:Rew:116078.0,94798.1] || equal(complement(complement(rest_of(u))),ordinal_numbers)**+ -> member(v,cantor(u))*.
% 299.99/300.64  116122[8:Rew:116078.0,39299.0] || member(u,cantor(v))* subclass(ordinal_numbers,complement(rest_of(v)))*+ -> .
% 299.99/300.64  116116[8:Rew:116078.0,9877.0] || member(u,cantor(v)) equal(restrict(v,u,ordinal_numbers),least(rest_of(v),w))*+ member(u,w)* subclass(w,x)* well_ordering(rest_of(v),x)* -> .
% 299.99/300.64  116117[8:Rew:116078.0,9744.0] || member(u,cantor(v)) equal(restrict(v,u,ordinal_numbers),w)*+ subclass(rest_of(v),x)* -> member(ordered_pair(u,w),x)*.
% 299.99/300.64  119376[8:Res:8665.1,116155.1] function(cantor(restrict(u,v,cross_product(ordinal_numbers,ordinal_numbers)))) || subclass(cross_product(ordinal_numbers,ordinal_numbers),v) -> section(u,cross_product(ordinal_numbers,ordinal_numbers),v)*.
% 299.99/300.64  117594[8:Rew:116078.0,116149.2] || section(u,v,w) subclass(v,cantor(restrict(u,w,v)))* -> equal(cantor(restrict(u,w,v)),v).
% 299.99/300.64  116152[8:Rew:116078.0,9583.0] || equal(cantor(restrict(u,v,w)),w)** subclass(w,v) -> section(u,w,v).
% 299.99/300.64  117262[8:Rew:116154.0,66117.0] ||  -> equal(intersection(segment(u,v,w),ordinal_numbers),segment(u,v,w))**.
% 299.99/300.64  116123[8:Rew:116078.0,8784.0] || member(u,cantor(v)) equal(restrict(v,u,ordinal_numbers),w) -> member(ordered_pair(u,w),rest_of(v))*.
% 299.99/300.64  116159[8:Rew:116078.0,94712.1] || subclass(ordinal_numbers,complement(complement(domain_relation)))*+ -> equal(cantor(u),v)*.
% 299.99/300.64  116155[8:Rew:116078.0,137.1] || subclass(u,v) subclass(cantor(restrict(w,v,u)),u)* -> section(w,u,v).
% 299.99/300.64  116148[8:Rew:116078.0,136.1] || section(u,v,w) -> subclass(cantor(restrict(u,w,v)),v)*.
% 299.99/300.64  116154[8:Rew:116078.0,126.0] ||  -> equal(cantor(restrict(u,v,singleton(w))),segment(u,v,w))**.
% 299.99/300.64  116129[8:Rew:116078.0,145.1] || member(ordered_pair(u,v),rest_of(w))* -> member(u,cantor(w)).
% 299.99/300.64  117260[8:Rew:116078.0,116111.1,116078.0,116111.1] || compatible(u,v,w)* -> equal(cantor(cantor(v)),cantor(u)).
% 299.99/300.64  116160[8:Rew:116078.0,103.1] || member(ordered_pair(u,v),domain_relation)* -> equal(cantor(u),v).
% 299.99/300.64  116161[8:Rew:116078.0,114.1] || maps(u,v,w)* -> equal(cantor(u),v).
% 299.99/300.64  117142[8:Rew:117140.0,66095.0] ||  -> equal(cantor(restrict(element_relation,ordinal_numbers,u)),sum_class(u))**.
% 299.99/300.64  117066[8:Rew:117064.0,66096.0] ||  -> equal(cantor(flip(cross_product(u,ordinal_numbers))),inverse(u))**.
% 299.99/300.64  117140[8:Rew:66095.0,116156.0] ||  -> equal(intersection(sum_class(u),ordinal_numbers),sum_class(u))**.
% 299.99/300.64  117064[8:Rew:66096.0,116147.0] ||  -> equal(intersection(inverse(u),ordinal_numbers),inverse(u))**.
% 299.99/300.64  116158[8:Rew:116078.0,66077.0] ||  -> equal(intersection(cantor(u),ordinal_numbers),cantor(u))**.
% 299.99/300.64  116078[8:MRR:66612.0,116077.0] ||  -> equal(domain_of(u),cantor(u))**.
% 299.99/300.64  8847[5:Rew:8637.0,6906.0] || subclass(ordinal_numbers,intersection(u,v))*+ -> member(unordered_pair(w,x),v)*.
% 299.99/300.64  8846[5:Rew:8637.0,6907.0] || subclass(ordinal_numbers,intersection(u,v))*+ -> member(unordered_pair(w,x),u)*.
% 299.99/300.64  19559[0:SpL:3596.0,26.0] || member(u,symmetric_difference(v,singleton(v)))* -> member(u,successor(v)).
% 299.99/300.64  212[0:Res:6.1,161.0] ||  -> subclass(omega,u) equal(integer_of(not_subclass_element(omega,u)),not_subclass_element(omega,u))**.
% 299.99/300.64  161[0:Inp] || member(u,omega)* -> equal(integer_of(u),u).
% 299.99/300.64  9872[0:Res:27.2,131.3] || 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)* -> .
% 299.99/300.64  9822[0:Res:122.1,11.0] || 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)).
% 299.99/300.64  9660[0:Res:20.2,129.0] || 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))*.
% 299.99/300.64  9636[0:Res:27.2,129.0] || member(u,v)* member(u,w)* subclass(intersection(w,v),x)*+ well_ordering(y,x)* -> member(least(y,intersection(w,v)),intersection(w,v))*.
% 299.99/300.64  9878[0:Res:20.2,131.3] || member(least(cross_product(u,v),w),v)*+ member(x,u)* member(x,w)* subclass(w,y)* well_ordering(cross_product(u,v),y)* -> .
% 299.99/300.64  6355[0:Res:6.1,21.0] ||  -> 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))**.
% 299.99/300.64  8562[0:Res:27.2,7.0] || member(not_subclass_element(u,intersection(v,w)),w)*+ member(not_subclass_element(u,intersection(v,w)),v)* -> subclass(u,intersection(v,w)).
% 299.99/300.64  9882[5:MRR:9869.0,8667.0] || member(u,v) subclass(v,w)* well_ordering(complement(x),w)*+ -> member(ordered_pair(u,least(complement(x),v)),x)*.
% 299.99/300.64  9421[0:Res:20.2,21.0] || member(u,v)*+ member(w,x)* -> equal(ordered_pair(first(ordered_pair(w,u)),second(ordered_pair(w,u))),ordered_pair(w,u))**.
% 299.99/300.64  9585[5:Res:8665.1,137.1] function(domain_of(restrict(u,v,cross_product(ordinal_numbers,ordinal_numbers)))) || subclass(cross_product(ordinal_numbers,ordinal_numbers),v) -> section(u,cross_product(ordinal_numbers,ordinal_numbers),v)*.
% 299.99/300.64  9865[5:Res:20.2,8802.1] || member(u,ordinal_numbers) member(v,ordinal_numbers) equal(compose(w,v),u) -> member(ordered_pair(v,u),compose_class(w))*.
% 299.99/300.64  3695[0:Res:6.1,12.0] ||  -> 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)**.
% 299.99/300.64  9420[0:Res:20.2,5.0] || member(u,v)* member(w,x)* subclass(cross_product(x,v),y)*+ -> member(ordered_pair(w,u),y)*.
% 299.99/300.64  9777[0:Res:10.1,123.0] || equal(compose(restrict(u,v,v),restrict(u,v,v)),restrict(u,v,v))** -> transitive(u,v).
% 299.99/300.64  3729[0:Res:133.2,11.0] || connected(u,v) subclass(v,not_well_ordering(u,v))* -> well_ordering(u,v) equal(not_well_ordering(u,v),v).
% 299.99/300.64  9580[0:SpL:126.0,137.1] || subclass(singleton(u),v) subclass(segment(w,v,u),singleton(u))* -> section(w,singleton(u),v).
% 299.99/300.64  3603[0:SpR:32.0,163.0] ||  -> equal(intersection(complement(restrict(u,v,w)),union(u,cross_product(v,w))),symmetric_difference(u,cross_product(v,w)))**.
% 299.99/300.64  3606[0:SpR:33.0,163.0] ||  -> equal(intersection(complement(restrict(u,v,w)),union(cross_product(v,w),u)),symmetric_difference(cross_product(v,w),u))**.
% 299.99/300.64  9009[5:Rew:8637.0,8818.1] || subclass(cross_product(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers),flip(u))* -> equal(cross_product(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers),flip(u)).
% 299.99/300.64  9010[5:Rew:8637.0,8819.1] || subclass(cross_product(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers),rotate(u))* -> equal(cross_product(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers),rotate(u)).
% 299.99/300.64  9661[0:Res:6.1,129.0] || subclass(u,v)*+ well_ordering(w,v)* -> subclass(u,x)* member(least(w,u),u)*.
% 299.99/300.64  8551[0:SpR:32.0,27.2] || member(u,cross_product(v,w)) member(u,x) -> member(u,restrict(x,v,w))*.
% 299.99/300.64  83844[5:Res:10.1,8815.0] || equal(u,ordinal_numbers)+ subclass(u,v)* -> member(omega,v)*.
% 299.99/300.64  9665[2:Res:4537.1,129.0] inductive(u) || subclass(u,v)*+ well_ordering(w,v)* -> member(least(w,u),u)*.
% 299.99/300.64  3689[0:SpL:17.0,12.0] || member(u,ordered_pair(v,w))* -> equal(u,unordered_pair(v,singleton(w))) equal(u,singleton(v)).
% 299.99/300.64  66438[8:Rew:66388.0,66431.0] ||  -> equal(symmetric_difference(cross_product(u,v),ordinal_numbers),symmetric_difference(ordinal_numbers,cross_product(u,v)))**.
% 299.99/300.64  18034[7:SpR:15272.1,15272.1] single_valued_class(u) single_valued_class(v) ||  -> equal(single_valued2(u),single_valued2(v))*.
% 299.99/300.64  15687[8:SpR:15668.1,15667.1] function(u) single_valued_class(v) ||  -> equal(single_valued1(u),single_valued1(v))*.
% 299.99/300.64  8832[5:Rew:8637.0,992.0] || member(u,ordinal_numbers) -> member(u,intersection(complement(v),complement(w)))* member(u,union(v,w)).
% 299.99/300.64  15683[8:SpR:15667.1,15667.1] single_valued_class(u) single_valued_class(v) ||  -> equal(single_valued1(u),single_valued1(v))*.
% 299.99/300.64  18035[7:SpR:15272.1,15265.1] single_valued_class(u) function(v) ||  -> equal(single_valued2(u),single_valued2(v))*.
% 299.99/300.64  50007[5:SpR:18840.1,8642.1] || member(u,subset_relation)*+ subclass(ordinal_numbers,v) -> member(u,v)*.
% 299.99/300.64  40074[5:MRR:40047.0,8666.0] || subclass(ordinal_numbers,complement(complement(u))) -> member(unordered_pair(v,w),u)*.
% 299.99/300.64  8842[5:Rew:8637.0,6901.0] || subclass(ordinal_numbers,complement(u)) member(unordered_pair(v,w),u)* -> .
% 299.99/300.64  94700[5:Res:39298.1,149.0] || subclass(ordinal_numbers,complement(complement(rest_relation)))*+ -> equal(rest_of(u),v)*.
% 299.99/300.64  94699[5:Res:39298.1,23.0] || subclass(ordinal_numbers,complement(complement(element_relation)))*+ -> member(u,v)*.
% 299.99/300.64  39298[5:MRR:39254.0,8667.0] || subclass(ordinal_numbers,complement(complement(u))) -> member(ordered_pair(v,w),u)*.
% 299.99/300.64  18840[5:Res:18819.1,21.0] || member(u,subset_relation) -> equal(ordered_pair(first(u),second(u)),u)**.
% 299.99/300.64  8841[5:Rew:8637.0,6938.0] || subclass(ordinal_numbers,complement(u)) member(ordered_pair(v,w),u)* -> .
% 299.99/300.64  41112[5:MRR:28981.0,41096.1] || member(u,rest_of(u)) -> member(ordered_pair(u,rest_of(u)),element_relation)*.
% 299.99/300.64  8825[5:Rew:8637.0,6923.0] || member(u,ordinal_numbers)* subclass(complement(v),w)*+ -> member(u,v)* member(u,w)*.
% 299.99/300.64  8995[5:Rew:8637.0,8797.1] || subclass(cross_product(ordinal_numbers,ordinal_numbers),compose(u,v))* -> equal(compose(u,v),cross_product(ordinal_numbers,ordinal_numbers)).
% 299.99/300.64  8827[5:Rew:8637.0,6831.0] || member(u,ordinal_numbers) subclass(rest_relation,v) -> member(ordered_pair(u,rest_of(u)),v)*.
% 299.99/300.64  8990[5:Rew:8637.0,8796.2] function(u) || subclass(cross_product(ordinal_numbers,ordinal_numbers),u)* -> equal(cross_product(ordinal_numbers,ordinal_numbers),u).
% 299.99/300.64  8815[5:Rew:8637.0,4630.0] || subclass(ordinal_numbers,u)*+ subclass(u,v)* -> member(omega,v)*.
% 299.99/300.64  8892[5:Rew:8637.0,6872.0] || equal(symmetric_difference(u,v),ordinal_numbers) -> member(omega,union(u,v))*.
% 299.99/300.64  8881[5:Rew:8637.0,6837.0] || subclass(ordinal_numbers,symmetric_difference(u,v)) -> member(omega,union(u,v))*.
% 299.99/300.64  916[0:SpR:32.0,33.0] ||  -> equal(restrict(cross_product(u,v),w,x),restrict(cross_product(w,x),u,v))*.
% 299.99/300.64  3652[0:SpR:126.0,136.1] || section(u,singleton(v),w) -> subclass(segment(u,w,v),singleton(v))*.
% 299.99/300.64  8837[5:Rew:8637.0,4823.0] || member(u,ordinal_numbers) subclass(unordered_pair(v,u),w)* -> member(u,w).
% 299.99/300.64  8836[5:Rew:8637.0,4803.0] || member(u,ordinal_numbers) subclass(unordered_pair(u,v),w)* -> member(u,w).
% 299.99/300.64  83442[7:Res:13056.1,39963.0] inductive(cantor(u)) || equal(complement(rest_of(u)),ordinal_numbers)** -> .
% 299.99/300.64  3597[0:SpR:117.0,163.0] ||  -> equal(intersection(complement(intersection(u,inverse(u))),symmetrization_of(u)),symmetric_difference(u,inverse(u)))**.
% 299.99/300.64  68245[5:SpL:3597.0,8736.0] || equal(symmetric_difference(u,inverse(u)),ordinal_numbers)** -> member(omega,symmetrization_of(u)).
% 299.99/300.64  66649[5:Res:8646.1,19676.0] || subclass(ordinal_numbers,symmetric_difference(u,inverse(u)))* -> member(omega,symmetrization_of(u)).
% 299.99/300.64  3596[0:SpR:47.0,163.0] ||  -> equal(intersection(complement(intersection(u,singleton(u))),successor(u)),symmetric_difference(u,singleton(u)))**.
% 299.99/300.64  10858[5:Res:10.1,8787.1] single_valued_class(u) || equal(cross_product(ordinal_numbers,ordinal_numbers),u)*+ -> function(u)*.
% 299.99/300.64  1301[0:Res:139.1,11.0] || member(u,ordinal_numbers) subclass(u,sum_class(u))* -> equal(sum_class(u),u).
% 299.99/300.64  50058[5:SpL:18840.1,39296.0] || member(u,subset_relation) subclass(ordinal_numbers,complement(unordered_pair(v,u)))* -> .
% 299.99/300.64  50059[5:SpL:18840.1,39499.0] || member(u,subset_relation) equal(complement(unordered_pair(v,u)),ordinal_numbers)** -> .
% 299.99/300.64  41098[5:MRR:9600.1,41096.1] || member(u,ordinal_numbers) member(v,u) -> member(ordered_pair(v,u),element_relation)*.
% 299.99/300.64  50046[5:SpL:18840.1,39297.0] || member(u,subset_relation) subclass(ordinal_numbers,complement(unordered_pair(u,v)))* -> .
% 299.99/300.64  50047[5:SpL:18840.1,39562.0] || member(u,subset_relation) equal(complement(unordered_pair(u,v)),ordinal_numbers)** -> .
% 299.99/300.64  68244[5:SpL:3596.0,8736.0] || equal(symmetric_difference(u,singleton(u)),ordinal_numbers)** -> member(omega,successor(u)).
% 299.99/300.64  66648[5:Res:8646.1,19559.0] || subclass(ordinal_numbers,symmetric_difference(u,singleton(u)))* -> member(omega,successor(u)).
% 299.99/300.64  50855[5:Res:49995.1,3700.0] || member(singleton(u),subset_relation) -> equal(singleton(first(singleton(u))),u)**.
% 299.99/300.64  51204[5:SpR:50855.1,967.0] || member(singleton(u),subset_relation) -> member(singleton(u),singleton(singleton(u)))*.
% 299.99/300.64  9688[5:Res:9632.1,3700.0] || equal(complement(complement(singleton(u))),ordinal_numbers)**+ -> equal(singleton(v),u)*.
% 299.99/300.64  8986[5:Rew:8637.0,8794.1] || subclass(cross_product(ordinal_numbers,ordinal_numbers),compose_class(u))* -> equal(cross_product(ordinal_numbers,ordinal_numbers),compose_class(u)).
% 299.99/300.64  970[0:SpL:963.0,23.0] || member(singleton(singleton(singleton(u))),element_relation)*+ -> member(singleton(u),u)*.
% 299.99/300.64  8987[5:Rew:8637.0,8795.1] || subclass(cross_product(ordinal_numbers,ordinal_numbers),rest_of(u))* -> equal(cross_product(ordinal_numbers,ordinal_numbers),rest_of(u)).
% 299.99/300.64  897[0:SpL:33.0,25.0] || member(u,restrict(v,w,x))* -> member(u,cross_product(w,x)).
% 299.99/300.64  2503[0:Res:6.1,5.0] || subclass(u,v) -> subclass(u,w) member(not_subclass_element(u,w),v)*.
% 299.99/300.64  303[0:Res:6.1,26.0] ||  -> subclass(intersection(u,v),w) member(not_subclass_element(intersection(u,v),w),v)*.
% 299.99/300.64  82516[8:Res:10.1,82431.1] || equal(inverse(subset_relation),domain_relation) equal(complement(complement(subset_relation)),domain_relation)** -> .
% 299.99/300.64  82431[8:Res:10.1,82312.0] || equal(complement(complement(subset_relation)),domain_relation) subclass(domain_relation,inverse(subset_relation))* -> .
% 299.99/300.64  313[0:Res:6.1,25.0] ||  -> subclass(intersection(u,v),w) member(not_subclass_element(intersection(u,v),w),u)*.
% 299.99/300.64  82312[8:Res:81336.1,15578.1] || subclass(domain_relation,complement(complement(subset_relation)))* subclass(domain_relation,inverse(subset_relation)) -> .
% 299.99/300.64  82318[8:Res:10.1,82314.0] || equal(complement(complement(element_relation)),domain_relation)** -> .
% 299.99/300.64  82314[8:MRR:82295.1,14676.0] || subclass(domain_relation,complement(complement(element_relation)))* -> .
% 299.99/300.64  19447[5:Res:18946.0,8787.1] single_valued_class(restrict(u,ordinal_numbers,ordinal_numbers)) ||  -> function(restrict(u,ordinal_numbers,ordinal_numbers))*.
% 299.99/300.64  8978[5:Rew:8637.0,8839.1] || member(u,ordinal_numbers) subclass(ordinal_numbers,v) -> member(sum_class(u),v)*.
% 299.99/300.64  81699[8:Res:81695.0,11.0] || subclass(complement(subset_relation),inverse(subset_relation))* -> equal(complement(subset_relation),inverse(subset_relation)).
% 299.99/300.64  81695[8:Obv:81694.0] ||  -> subclass(inverse(subset_relation),complement(subset_relation))*.
% 299.99/300.64  15132[8:Res:6.1,14679.1] || member(not_subclass_element(inverse(subset_relation),u),subset_relation)* -> subclass(inverse(subset_relation),u).
% 299.99/300.64  15308[8:MRR:13282.1,15296.0] || asymmetric(u,v) -> section(intersection(u,inverse(u)),v,v)*.
% 299.99/300.64  290[0:Res:6.1,28.1] || member(not_subclass_element(complement(u),v),u)* -> subclass(complement(u),v).
% 299.99/300.64  81412[8:Res:10.1,81399.1] || equal(u,domain_relation) equal(complement(u),domain_relation)** -> .
% 299.99/300.64  81414[8:Res:8658.0,81399.1] || equal(complement(cross_product(ordinal_numbers,ordinal_numbers)),domain_relation)** -> .
% 299.99/300.64  81399[8:Res:10.1,81322.1] || equal(complement(u),domain_relation) subclass(domain_relation,u)* -> .
% 299.99/300.64  81322[8:Res:15426.1,15565.1] || subclass(domain_relation,u) subclass(domain_relation,complement(u))* -> .
% 299.99/300.64  81320[8:Res:15380.0,15565.1] || subclass(domain_relation,complement(domain_relation))* -> .
% 299.99/300.64  8787[5:Rew:8637.0,8588.1] single_valued_class(u) || subclass(u,cross_product(ordinal_numbers,ordinal_numbers))* -> function(u).
% 299.99/300.64  62339[8:MRR:13481.1,62337.0] || well_ordering(u,cross_product(ordinal_numbers,ordinal_numbers))* -> member(least(u,rest_relation),rest_relation).
% 299.99/300.64  15593[8:MRR:13482.1,15592.0] || well_ordering(u,cross_product(ordinal_numbers,ordinal_numbers))* -> member(least(u,domain_relation),domain_relation).
% 299.99/300.64  66086[8:Rew:66036.0,14680.1] || member(u,element_relation) member(u,complement(compose(element_relation,ordinal_numbers)))* -> .
% 299.99/300.64  80198[10:Res:76912.1,41096.0] || member(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers) -> member(least(element_relation,element_relation),ordinal_numbers)*.
% 299.99/300.64  80082[8:Res:64007.1,41096.0] || member(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers) -> member(least(element_relation,rest_relation),ordinal_numbers)*.
% 299.99/300.64  8820[5:Rew:8637.0,41.1] || member(ordered_pair(ordered_pair(u,v),w),x) member(ordered_pair(ordered_pair(v,u),w),cross_product(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers))*+ -> member(ordered_pair(ordered_pair(v,u),w),flip(x))*.
% 299.99/300.64  8821[5:Rew:8637.0,38.1] || member(ordered_pair(ordered_pair(u,v),w),x) member(ordered_pair(ordered_pair(w,u),v),cross_product(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers))*+ -> member(ordered_pair(ordered_pair(w,u),v),rotate(x))*.
% 299.99/300.64  76912[10:Res:138.1,76792.0] || member(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers) -> member(least(element_relation,element_relation),element_relation)*.
% 299.99/300.64  131[0:Inp] || member(u,v) subclass(v,w)* well_ordering(x,w)* member(ordered_pair(u,least(x,v)),x)*+ -> .
% 299.99/300.64  8971[5:Rew:8637.0,8791.1] || subclass(cross_product(ordinal_numbers,ordinal_numbers),domain_relation)* -> equal(cross_product(ordinal_numbers,ordinal_numbers),domain_relation).
% 299.99/300.64  8972[5:Rew:8637.0,8792.1] || subclass(cross_product(ordinal_numbers,ordinal_numbers),rest_relation)* -> equal(cross_product(ordinal_numbers,ordinal_numbers),rest_relation).
% 299.99/300.64  19452[5:Res:19442.0,11.0] || subclass(cross_product(ordinal_numbers,ordinal_numbers),subset_relation)* -> equal(cross_product(ordinal_numbers,ordinal_numbers),subset_relation).
% 299.99/300.64  50858[5:Res:49995.1,50033.0] || member(subset_relation,subset_relation) equal(complement(singleton(first(subset_relation))),ordinal_numbers)** -> .
% 299.99/300.64  122[0:Inp] || transitive(u,v) -> subclass(compose(restrict(u,v,v),restrict(u,v,v)),restrict(u,v,v))*.
% 299.99/300.64  64007[8:Res:138.1,62339.0] || member(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers) -> member(least(element_relation,rest_relation),rest_relation)*.
% 299.99/300.64  123[0:Inp] || subclass(compose(restrict(u,v,v),restrict(u,v,v)),restrict(u,v,v))* -> transitive(u,v).
% 299.99/300.64  129[0:Inp] || member(u,v)*+ subclass(v,w)* well_ordering(x,w)* -> member(least(x,v),v)*.
% 299.99/300.64  69174[8:Res:8646.1,66086.1] || subclass(ordinal_numbers,complement(compose(element_relation,ordinal_numbers)))* member(omega,element_relation) -> .
% 299.99/300.64  8969[5:Rew:8637.0,8789.1] || subclass(cross_product(ordinal_numbers,ordinal_numbers),element_relation)* -> equal(cross_product(ordinal_numbers,ordinal_numbers),element_relation).
% 299.99/300.64  17124[8:Res:138.1,15593.0] || member(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers) -> member(least(element_relation,domain_relation),domain_relation)*.
% 299.99/300.64  40[0:Inp] || member(ordered_pair(ordered_pair(u,v),w),flip(x))* -> member(ordered_pair(ordered_pair(v,u),w),x).
% 299.99/300.64  41203[8:Res:17124.1,41096.0] || member(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers) -> member(least(element_relation,domain_relation),ordinal_numbers)*.
% 299.99/300.64  898[0:SpL:33.0,26.0] || member(u,restrict(v,w,x))* -> member(u,v).
% 299.99/300.64  37[0:Inp] || member(ordered_pair(ordered_pair(u,v),w),rotate(x))* -> member(ordered_pair(ordered_pair(v,w),u),x).
% 299.99/300.64  79560[5:Obv:79536.0] ||  -> member(u,v) subclass(singleton(u),complement(v))*.
% 299.99/300.64  60219[5:MRR:40691.0,8638.0] ||  -> member(not_subclass_element(u,complement(v)),v)* subclass(u,complement(v)).
% 299.99/300.64  10702[0:Res:10.1,2486.0] || equal(u,ordered_pair(v,w))*+ -> member(singleton(v),u)*.
% 299.99/300.64  2486[0:Res:962.0,5.0] || subclass(ordered_pair(u,v),w)* -> member(singleton(u),w).
% 299.99/300.64  20[0:Inp] || member(u,v) member(w,x) -> member(ordered_pair(w,u),cross_product(x,v))*.
% 299.99/300.64  3705[0:Res:6.1,3700.0] ||  -> subclass(singleton(u),v) equal(not_subclass_element(singleton(u),v),u)**.
% 299.99/300.64  8857[5:Rew:8637.0,4634.0] || subclass(ordinal_numbers,restrict(u,v,w))* -> member(omega,u).
% 299.99/300.64  8890[5:Rew:8637.0,6871.0] || equal(restrict(u,v,w),ordinal_numbers)** -> member(omega,u).
% 299.99/300.64  8908[5:Rew:8637.0,6966.0] || subclass(ordinal_numbers,compose_class(u))*+ -> equal(compose(u,v),w)*.
% 299.99/300.64  8848[5:Rew:8637.0,4736.0] || subclass(ordinal_numbers,intersection(u,v))*+ -> member(singleton(w),u)*.
% 299.99/300.64  10088[5:Res:10.1,8848.0] || equal(intersection(u,v),ordinal_numbers)**+ -> member(singleton(w),u)*.
% 299.99/300.64  8849[5:Rew:8637.0,4735.0] || subclass(ordinal_numbers,intersection(u,v))*+ -> member(singleton(w),v)*.
% 299.99/300.64  10114[5:Res:10.1,8849.0] || equal(intersection(u,v),ordinal_numbers)**+ -> member(singleton(w),v)*.
% 299.99/300.64  9632[5:Res:10.1,9496.0] || equal(complement(complement(u)),ordinal_numbers) -> member(singleton(v),u)*.
% 299.99/300.64  9496[5:MRR:9475.0,8655.0] || subclass(ordinal_numbers,complement(complement(u)))*+ -> member(singleton(v),u)*.
% 299.99/300.64  8843[5:Rew:8637.0,4730.0] || subclass(ordinal_numbers,complement(u)) member(singleton(v),u)* -> .
% 299.99/300.64  51313[5:MRR:51213.1,50063.1] || member(singleton(u),subset_relation) -> member(first(singleton(u)),u)*.
% 299.99/300.64  21[0:Inp] || member(u,cross_product(v,w))*+ -> equal(ordered_pair(first(u),second(u)),u)**.
% 299.99/300.64  70033[7:MRR:70032.2,13040.0] inductive(domain_of(u)) || equal(complement(rest_of(u)),ordinal_numbers)** -> .
% 299.99/300.64  8651[5:Rew:8637.0,146.1] || member(ordered_pair(u,v),rest_of(w))* -> equal(restrict(w,u,ordinal_numbers),v).
% 299.99/300.64  50429[5:Res:6.1,50033.0] || equal(complement(not_subclass_element(subset_relation,u)),ordinal_numbers)** -> subclass(subset_relation,u).
% 299.99/300.64  50044[5:SpL:18840.1,39295.0] || member(u,subset_relation) subclass(ordinal_numbers,complement(singleton(u)))* -> .
% 299.99/300.64  50045[5:SpL:18840.1,39306.0] || member(u,subset_relation) equal(complement(singleton(u)),ordinal_numbers)** -> .
% 299.99/300.64  56525[5:Res:926.1,56480.0] || member(u,cantor(u))* subclass(ordinal_numbers,complement(element_relation)) -> .
% 299.99/300.64  56411[5:Res:41112.1,8841.1] || member(u,rest_of(u))* subclass(ordinal_numbers,complement(element_relation)) -> .
% 299.99/300.64  133[0:Inp] || connected(u,v) -> well_ordering(u,v) subclass(not_well_ordering(u,v),v)*.
% 299.99/300.64  12[0:Inp] || member(u,unordered_pair(v,w))* -> equal(u,w) equal(u,v).
% 299.99/300.64  97[0:Inp] || member(ordered_pair(u,v),compose_class(w))* -> equal(compose(w,u),v).
% 299.99/300.64  10875[5:Res:8663.0,8787.1] single_valued_class(compose(u,v)) ||  -> function(compose(u,v))*.
% 299.99/300.64  19[0:Inp] || member(ordered_pair(u,v),cross_product(w,x))* -> member(v,x).
% 299.99/300.64  8643[5:Rew:8637.0,4503.0] || subclass(ordinal_numbers,u) -> member(unordered_pair(v,w),u)*.
% 299.99/300.64  8642[5:Rew:8637.0,4505.0] || subclass(ordinal_numbers,u) -> member(ordered_pair(v,w),u)*.
% 299.99/300.64  9604[5:Res:9592.1,8729.0] || equal(sum_class(u),u) -> subclass(sum_class(u),u)*.
% 299.99/300.64  18[0:Inp] || member(ordered_pair(u,v),cross_product(w,x))* -> member(u,w).
% 299.99/300.64  19734[0:SpR:117.0,19421.0] ||  -> subclass(symmetric_difference(complement(u),complement(inverse(u))),symmetrization_of(u))*.
% 299.99/300.64  14684[8:MRR:13463.2,14676.0] single_valued_class(u) inductive(compose(u,inverse(u))) ||  -> .
% 299.99/300.64  8700[5:Rew:8637.0,29.0] || member(u,ordinal_numbers) -> member(u,v) member(u,complement(v))*.
% 299.99/300.64  40073[5:MRR:40056.0,8666.0] || subclass(ordinal_numbers,complement(unordered_pair(unordered_pair(u,v),w)))* -> .
% 299.99/300.64  40101[5:Res:10.1,40073.0] || equal(complement(unordered_pair(unordered_pair(u,v),w)),ordinal_numbers)** -> .
% 299.99/300.64  40072[5:MRR:40055.0,8666.0] || subclass(ordinal_numbers,complement(unordered_pair(u,unordered_pair(v,w))))* -> .
% 299.99/300.64  40095[5:Res:10.1,40072.0] || equal(complement(unordered_pair(u,unordered_pair(v,w))),ordinal_numbers)** -> .
% 299.99/300.64  39296[5:MRR:39260.0,8667.0] || subclass(ordinal_numbers,complement(unordered_pair(u,ordered_pair(v,w))))* -> .
% 299.99/300.64  39499[5:Res:10.1,39296.0] || equal(complement(unordered_pair(u,ordered_pair(v,w))),ordinal_numbers)** -> .
% 299.99/300.64  18843[5:Res:18819.1,18.0] || member(ordered_pair(u,v),subset_relation)* -> member(u,ordinal_numbers).
% 299.99/300.64  18842[5:Res:18819.1,19.0] || member(ordered_pair(u,v),subset_relation)* -> member(v,ordinal_numbers).
% 299.99/300.64  39297[5:MRR:39261.0,8667.0] || subclass(ordinal_numbers,complement(unordered_pair(ordered_pair(u,v),w)))* -> .
% 299.99/300.64  39562[5:Res:10.1,39297.0] || equal(complement(unordered_pair(ordered_pair(u,v),w)),ordinal_numbers)** -> .
% 299.99/300.64  17[0:Inp] ||  -> equal(unordered_pair(singleton(u),unordered_pair(u,singleton(v))),ordered_pair(u,v))**.
% 299.99/300.64  49995[5:SpR:18840.1,962.0] || member(u,subset_relation) -> member(singleton(first(u)),u)*.
% 299.99/300.64  963[0:Rew:16.0,961.0] ||  -> equal(ordered_pair(singleton(u),u),singleton(singleton(singleton(u))))**.
% 299.99/300.64  19733[0:SpR:47.0,19421.0] ||  -> subclass(symmetric_difference(complement(u),complement(singleton(u))),successor(u))*.
% 299.99/300.64  8729[5:Rew:8637.0,3651.0] || section(element_relation,u,ordinal_numbers)*+ -> subclass(sum_class(u),u)*.
% 299.99/300.64  33[0:Inp] ||  -> equal(intersection(cross_product(u,v),w),restrict(w,u,v))**.
% 299.99/300.64  9592[5:Res:10.1,9586.0] || equal(sum_class(u),u) -> section(element_relation,u,ordinal_numbers)*.
% 299.99/300.64  9586[5:MRR:9581.0,8638.0] || subclass(sum_class(u),u)*+ -> section(element_relation,u,ordinal_numbers)*.
% 299.99/300.64  32[0:Inp] ||  -> equal(intersection(u,cross_product(v,w)),restrict(u,v,w))**.
% 299.99/300.64  149[0:Inp] || member(ordered_pair(u,v),rest_relation)* -> equal(rest_of(u),v).
% 299.99/300.64  63453[8:Res:10.1,63019.1] || equal(complement(u),ordinal_numbers) subclass(domain_relation,u)* -> .
% 299.99/300.64  63019[8:Res:15426.1,8841.1] || subclass(domain_relation,u) subclass(ordinal_numbers,complement(u))* -> .
% 299.99/300.64  63479[8:Res:10.1,63453.1] || equal(u,domain_relation) equal(complement(u),ordinal_numbers)** -> .
% 299.99/300.64  14679[8:MRR:8557.2,14676.0] || member(u,subset_relation) member(u,inverse(subset_relation))* -> .
% 299.99/300.64  50033[5:SpL:18840.1,9529.0] || member(u,subset_relation)* equal(complement(u),ordinal_numbers) -> .
% 299.99/300.64  50032[5:SpL:18840.1,9486.0] || member(u,subset_relation) subclass(ordinal_numbers,complement(u))* -> .
% 299.99/300.64  18819[5:SpL:8770.0,897.0] || member(u,subset_relation) -> member(u,cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.64  66889[7:MRR:66888.2,13040.0] || member(singleton(u),subset_relation)* subclass(ordinal_numbers,u) -> .
% 299.99/300.64  66856[7:MRR:66855.2,13040.0] || member(singleton(u),subset_relation)* equal(u,ordinal_numbers) -> .
% 299.99/300.64  69184[8:MRR:69157.0,41096.1] || member(u,element_relation) -> member(u,compose(element_relation,ordinal_numbers))*.
% 299.99/300.64  8702[5:Rew:8637.0,150.0] || member(u,ordinal_numbers) -> member(ordered_pair(u,rest_of(u)),rest_relation)*.
% 299.99/300.64  39269[5:Res:8702.1,8841.1] || member(u,ordinal_numbers)* subclass(ordinal_numbers,complement(rest_relation))*+ -> .
% 299.99/300.64  50065[8:Obv:50038.0] || subclass(ordinal_numbers,inverse(subset_relation))*+ member(u,subset_relation)* -> .
% 299.99/300.64  10860[5:Res:295.0,8787.1] single_valued_class(cross_product(ordinal_numbers,ordinal_numbers)) ||  -> function(cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.64  7[0:Inp] || member(not_subclass_element(u,v),v)* -> subclass(u,v).
% 299.99/300.64  18624[8:Res:15426.1,15578.1] || subclass(domain_relation,subset_relation) subclass(domain_relation,inverse(subset_relation))* -> .
% 299.99/300.64  18631[8:Res:10.1,18627.1] || equal(domain_relation,subset_relation) equal(inverse(subset_relation),domain_relation)** -> .
% 299.99/300.64  18627[8:Res:10.1,18624.1] || equal(inverse(subset_relation),domain_relation) subclass(domain_relation,subset_relation)* -> .
% 299.99/300.64  8704[5:Rew:8637.0,14.0] || member(u,ordinal_numbers) -> member(u,unordered_pair(v,u))*.
% 299.99/300.64  67730[7:Res:49995.1,66856.0] || member(subset_relation,subset_relation)* equal(first(subset_relation),ordinal_numbers) -> .
% 299.99/300.64  8703[5:Rew:8637.0,13.0] || member(u,ordinal_numbers) -> member(u,unordered_pair(u,v))*.
% 299.99/300.64  67737[7:Res:49995.1,66889.0] || member(subset_relation,subset_relation) subclass(ordinal_numbers,first(subset_relation))* -> .
% 299.99/300.64  60885[7:Res:13056.1,56411.0] inductive(rest_of(identity_relation)) || subclass(ordinal_numbers,complement(element_relation))* -> .
% 299.99/300.64  23[0:Inp] || member(ordered_pair(u,v),element_relation)* -> member(u,v).
% 299.99/300.64  18946[0:SpR:32.0,18926.0] ||  -> subclass(restrict(u,v,w),cross_product(v,w))*.
% 299.99/300.64  41183[5:Res:6.1,41096.0] ||  -> subclass(u,v) member(not_subclass_element(u,v),ordinal_numbers)*.
% 299.99/300.64  964[0:MRR:959.0,15.0] ||  -> member(unordered_pair(u,singleton(v)),ordered_pair(u,v))*.
% 299.99/300.64  3700[0:Obv:3688.1] || member(u,singleton(v))* -> equal(u,v).
% 299.99/300.64  10714[0:Obv:10709.1] || member(u,v) -> subclass(singleton(u),v)*.
% 299.99/300.64  9582[5:Res:8638.0,137.1] || subclass(ordinal_numbers,u) -> section(v,ordinal_numbers,u)*.
% 299.99/300.64  8645[5:Rew:8637.0,4495.0] || subclass(ordinal_numbers,u) -> member(singleton(v),u)*.
% 299.99/300.64  8705[5:Rew:8637.0,286.0] || member(u,ordinal_numbers) -> member(u,singleton(u))*.
% 299.99/300.64  77[0:Inp] function(u) || function(inverse(u))* -> one_to_one(u).
% 299.99/300.64  50064[5:Obv:50040.0] || member(u,subset_relation) -> member(second(u),ordinal_numbers)*.
% 299.99/300.64  50063[5:Obv:50039.0] || member(u,subset_relation) -> member(first(u),ordinal_numbers)*.
% 299.99/300.64  40071[5:MRR:40054.0,8666.0] || subclass(ordinal_numbers,complement(singleton(unordered_pair(u,v))))* -> .
% 299.99/300.64  40080[5:Res:10.1,40071.0] || equal(complement(singleton(unordered_pair(u,v))),ordinal_numbers)** -> .
% 299.99/300.64  39295[5:MRR:39259.0,8667.0] || subclass(ordinal_numbers,complement(singleton(ordered_pair(u,v))))* -> .
% 299.99/300.64  6[0:Inp] ||  -> subclass(u,v) member(not_subclass_element(u,v),u)*.
% 299.99/300.64  39306[5:Res:10.1,39295.0] || equal(complement(singleton(ordered_pair(u,v))),ordinal_numbers)** -> .
% 299.99/300.64  967[0:SpR:963.0,962.0] ||  -> member(singleton(singleton(u)),singleton(singleton(singleton(u))))*.
% 299.99/300.64  9494[5:MRR:9481.0,8655.0] || subclass(ordinal_numbers,complement(unordered_pair(u,singleton(v))))* -> .
% 299.99/300.64  9532[5:Res:10.1,9494.0] || equal(complement(unordered_pair(u,singleton(v))),ordinal_numbers)** -> .
% 299.99/300.64  139[0:Inp] || member(u,ordinal_numbers) -> subclass(sum_class(u),u)*.
% 299.99/300.64  9495[5:MRR:9482.0,8655.0] || subclass(ordinal_numbers,complement(unordered_pair(singleton(u),v)))* -> .
% 299.99/300.64  9566[5:Res:10.1,9495.0] || equal(complement(unordered_pair(singleton(u),v)),ordinal_numbers)** -> .
% 299.99/300.64  8650[5:Rew:8637.0,2150.0] ||  -> equal(segment(element_relation,ordinal_numbers,u),sum_class(singleton(u)))**.
% 299.99/300.64  9593[5:Res:139.1,9586.0] || member(u,ordinal_numbers) -> section(element_relation,u,ordinal_numbers)*.
% 299.99/300.64  8665[5:Rew:8637.0,66.1] function(u) ||  -> subclass(u,cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.64  8955[5:Rew:8637.0,8706.1] || member(u,ordinal_numbers) -> member(sum_class(u),ordinal_numbers)*.
% 299.99/300.64  8689[5:Rew:8637.0,39.0] ||  -> subclass(flip(u),cross_product(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers))*.
% 299.99/300.64  8951[5:MRR:1976.1,8652.0] inductive(sum_class(omega)) ||  -> equal(sum_class(omega),omega)**.
% 299.99/300.64  8690[5:Rew:8637.0,36.0] ||  -> subclass(rotate(u),cross_product(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers))*.
% 299.99/300.64  19315[0:SpR:117.0,18950.0] ||  -> subclass(symmetric_difference(u,inverse(u)),symmetrization_of(u))*.
% 299.99/300.64  19314[0:SpR:47.0,18950.0] ||  -> subclass(symmetric_difference(u,singleton(u)),successor(u))*.
% 299.99/300.64  66272[8:Obv:66079.1] inductive(domain_of(restrict(identity_relation,u,v))) ||  -> .
% 299.99/300.64  10873[5:Res:8661.0,8787.1] single_valued_class(rest_of(u)) ||  -> function(rest_of(u))*.
% 299.99/300.64  10874[5:Res:8662.0,8787.1] single_valued_class(compose_class(u)) ||  -> function(compose_class(u))*.
% 299.99/300.64  127[0:Inp] || well_ordering(u,v)* -> connected(u,v).
% 299.99/300.64  9486[5:Res:962.0,8843.1] || subclass(ordinal_numbers,complement(ordered_pair(u,v)))* -> .
% 299.99/300.64  9529[5:Res:10.1,9486.0] || equal(complement(ordered_pair(u,v)),ordinal_numbers)** -> .
% 299.99/300.64  186[0:Res:138.1,127.0] || member(u,ordinal_numbers) -> connected(element_relation,u)*.
% 299.99/300.64  117[0:Inp] ||  -> equal(union(u,inverse(u)),symmetrization_of(u))**.
% 299.99/300.64  8725[5:Rew:8637.0,6759.0] || equal(complement(unordered_pair(omega,u)),ordinal_numbers)** -> .
% 299.99/300.64  8720[5:Rew:8637.0,6746.0] || equal(complement(unordered_pair(u,omega)),ordinal_numbers)** -> .
% 299.99/300.64  47[0:Inp] ||  -> equal(union(u,singleton(u)),successor(u))**.
% 299.99/300.64  9493[5:MRR:9479.0,8655.0] || subclass(ordinal_numbers,complement(singleton(singleton(u))))* -> .
% 299.99/300.64  9498[5:Res:10.1,9493.0] || equal(complement(singleton(singleton(u))),ordinal_numbers)** -> .
% 299.99/300.64  63481[8:Res:8658.0,63453.1] || equal(complement(cross_product(ordinal_numbers,ordinal_numbers)),ordinal_numbers)** -> .
% 299.99/300.64  18949[0:SpR:33.0,18926.0] ||  -> subclass(restrict(u,v,w),u)*.
% 299.99/300.64  8663[5:Rew:8637.0,61.0] ||  -> subclass(compose(u,v),cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.64  962[0:MRR:958.0,172.0] ||  -> member(singleton(u),ordered_pair(u,v))*.
% 299.99/300.64  66269[8:Obv:66222.1] inductive(domain_of(intersection(u,identity_relation))) ||  -> .
% 299.99/300.64  61083[8:Res:9632.1,60940.0] || equal(complement(complement(subset_relation)),ordinal_numbers)** -> .
% 299.99/300.64  10850[5:Con:10849.0] || equal(complement(complement(element_relation)),ordinal_numbers)** -> .
% 299.99/300.64  16[0:Inp] ||  -> equal(unordered_pair(u,u),singleton(u))**.
% 299.99/300.64  4748[0:Res:67.1,65.0] function(u) ||  -> single_valued_class(u)*.
% 299.99/300.64  8667[5:Rew:8637.0,957.0] ||  -> member(ordered_pair(u,v),ordinal_numbers)*.
% 299.99/300.64  10686[5:MRR:10345.1,10685.1] || equal(compose_class(u),ordinal_numbers)** -> .
% 299.99/300.64  76[0:Inp] one_to_one(u) ||  -> function(inverse(u))*.
% 299.99/300.64  10870[5:Res:8658.0,8787.1] single_valued_class(domain_relation) ||  -> function(domain_relation)*.
% 299.99/300.64  8661[5:Rew:8637.0,144.0] ||  -> subclass(rest_of(u),cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.64  60961[8:Res:15380.0,8841.1] || subclass(ordinal_numbers,complement(domain_relation))* -> .
% 299.99/300.64  61122[8:Res:10.1,60961.0] || equal(complement(domain_relation),ordinal_numbers)** -> .
% 299.99/300.64  10869[5:Res:8657.0,8787.1] single_valued_class(rest_relation) ||  -> function(rest_relation)*.
% 299.99/300.64  39365[5:Res:8655.0,39363.1] || equal(complement(rest_relation),ordinal_numbers)** -> .
% 299.99/300.64  8662[5:Rew:8637.0,96.0] ||  -> subclass(compose_class(u),cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.64  19442[5:SpR:8770.0,18946.0] ||  -> subclass(subset_relation,cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.64  19453[5:Res:19442.0,8787.1] single_valued_class(subset_relation) ||  -> function(subset_relation)*.
% 299.99/300.64  8655[5:Rew:8637.0,172.0] ||  -> member(singleton(u),ordinal_numbers)*.
% 299.99/300.64  8666[5:Rew:8637.0,15.0] ||  -> member(unordered_pair(u,v),ordinal_numbers)*.
% 299.99/300.64  15299[8:Res:13056.1,15285.0] inductive(domain_of(identity_relation)) ||  -> .
% 299.99/300.64  15431[8:Res:13056.1,15291.0] inductive(cantor(identity_relation)) ||  -> .
% 299.99/300.64  8658[5:Rew:8637.0,102.0] ||  -> subclass(domain_relation,cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.64  8657[5:Rew:8637.0,148.0] ||  -> subclass(rest_relation,cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.64  8750[5:Rew:8637.0,7597.0] || equal(domain_relation,ordinal_numbers)** -> .
% 299.99/300.64  8751[5:Rew:8637.0,7880.0] || equal(rest_relation,ordinal_numbers)** -> .
% 299.99/300.64  61084[8:Res:8645.1,60940.0] || subclass(ordinal_numbers,subset_relation)* -> .
% 299.99/300.64  61085[8:Res:10.1,61084.0] || equal(subset_relation,ordinal_numbers)** -> .
% 299.99/300.64  66378[8:SpR:66140.0,47.0] ||  -> equal(successor(ordinal_numbers),ordinal_numbers)**.
% 299.99/300.64  8660[5:Rew:8637.0,22.0] ||  -> subclass(element_relation,cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.64  8730[5:Rew:8637.0,6830.0] || subclass(ordinal_numbers,element_relation)* -> .
% 299.99/300.64  8731[5:Rew:8637.0,6833.0] || equal(element_relation,ordinal_numbers)** -> .
% 299.99/300.64  9591[5:Res:8638.0,9586.0] ||  -> section(element_relation,ordinal_numbers,ordinal_numbers)*.
% 299.99/300.64  15590[8:MRR:15579.1,14676.0] || subclass(domain_relation,element_relation)* -> .
% 299.99/300.64  15594[8:Res:10.1,15590.0] || equal(domain_relation,element_relation)** -> .
% 299.99/300.64  66422[8:MRR:66421.0,8638.0] ||  -> connected(ordinal_numbers,u)*.
% 299.99/300.64  76792[10:Spt:76678.0,13484.0,13484.2] || well_ordering(u,cross_product(ordinal_numbers,ordinal_numbers))* -> member(least(u,element_relation),element_relation).
% 299.99/300.64  68831[0:Res:18926.0,1303.1] inductive(intersection(u,omega)) ||  -> equal(intersection(u,omega),omega)**.
% 299.99/300.64  68825[0:Res:19045.0,1303.1] inductive(intersection(omega,u)) ||  -> equal(intersection(omega,u),omega)**.
% 299.99/300.64  69278[8:Res:13056.1,69257.0] inductive(regular(ordinal_numbers)) ||  -> .
% 299.99/300.64  69121[8:Obv:69097.1] inductive(intersection(ordinal_numbers,regular(ordinal_numbers))) ||  -> .
% 299.99/300.64  1303[0:Res:55.1,11.0] inductive(u) || subclass(u,omega)* -> equal(u,omega).
% 299.99/300.64  8732[5:Rew:8637.0,4633.0] || subclass(ordinal_numbers,intersection(u,v))* -> member(omega,u).
% 299.99/300.64  8735[5:Rew:8637.0,6859.0] || equal(intersection(u,v),ordinal_numbers)** -> member(omega,u).
% 299.99/300.64  8733[5:Rew:8637.0,4632.0] || subclass(ordinal_numbers,intersection(u,v))* -> member(omega,v).
% 299.99/300.64  8736[5:Rew:8637.0,6842.0] || equal(intersection(u,v),ordinal_numbers)** -> member(omega,v).
% 299.99/300.64  67823[8:MRR:67792.1,14676.0] inductive(symmetric_difference(ordinal_numbers,ordinal_numbers)) ||  -> .
% 299.99/300.64  8738[5:Rew:8637.0,6926.0] || equal(complement(complement(u)),ordinal_numbers)** -> member(omega,u).
% 299.99/300.64  8712[5:Rew:8637.0,4628.0] || subclass(ordinal_numbers,complement(u))* member(omega,u) -> .
% 299.99/300.64  8646[5:Rew:8637.0,4493.0] || subclass(ordinal_numbers,u) -> member(omega,u)*.
% 299.99/300.64  66141[8:Rew:66036.0,65998.0] ||  -> equal(union(u,ordinal_numbers),ordinal_numbers)**.
% 299.99/300.64  66379[8:SpR:66140.0,117.0] ||  -> equal(symmetrization_of(ordinal_numbers),ordinal_numbers)**.
% 299.99/300.64  55[0:Inp] inductive(u) ||  -> subclass(omega,u)*.
% 299.99/300.64  66140[8:Rew:66036.0,65996.0] ||  -> equal(union(ordinal_numbers,u),ordinal_numbers)**.
% 299.99/300.64  66054[8:Rew:66036.0,15311.0] ||  -> equal(diagonalise(u),ordinal_numbers)**.
% 299.99/300.64  66020[8:Res:13056.1,60934.0] inductive(subset_relation) ||  -> .
% 299.99/300.64  65912[8:MRR:119.0,65911.0] ||  -> irreflexive(u,v)*.
% 299.99/300.64  8652[5:Rew:8637.0,56.0] ||  -> member(omega,ordinal_numbers)*.
% 299.99/300.64  54[0:Inp] ||  -> inductive(omega)*.
% 299.99/300.64  9922[5:Res:4537.1,9906.1] inductive(u) || equal(complement(u),ordinal_numbers)** -> .
% 299.99/300.64  61224[5:Res:10.1,60039.0] || equal(rest_of(u),ordinal_numbers)** -> .
% 299.99/300.64  60039[5:MRR:39236.1,39227.1] || subclass(ordinal_numbers,rest_of(u))* -> .
% 299.99/300.64  3594[0:SpR:163.0,163.0] ||  -> equal(intersection(complement(symmetric_difference(u,v)),union(complement(intersection(u,v)),union(u,v))),symmetric_difference(complement(intersection(u,v)),union(u,v)))**.
% 299.99/300.64  8554[0:SpR:163.0,27.2] || member(u,union(v,w)) member(u,complement(intersection(v,w)))* -> member(u,symmetric_difference(v,w)).
% 299.99/300.64  41096[5:Con:41090.1] || member(u,v)*+ -> member(u,ordinal_numbers)*.
% 299.99/300.64  8559[0:Res:27.2,5.0] || member(u,v)* member(u,w)* subclass(intersection(w,v),x)*+ -> member(u,x)*.
% 299.99/300.64  17977[7:SpR:15265.1,15265.1] function(u) function(v) ||  -> equal(single_valued2(u),single_valued2(v))*.
% 299.99/300.64  15686[8:SpR:15668.1,15668.1] function(u) function(v) ||  -> equal(single_valued1(u),single_valued1(v))*.
% 299.99/300.64  3616[0:SpR:30.0,163.0] ||  -> equal(intersection(union(u,v),union(complement(u),complement(v))),symmetric_difference(complement(u),complement(v)))**.
% 299.99/300.64  483[0:SpR:30.0,30.0] ||  -> equal(union(u,intersection(complement(v),complement(w))),complement(intersection(complement(u),union(v,w))))**.
% 299.99/300.64  482[0:SpR:30.0,30.0] ||  -> equal(union(intersection(complement(u),complement(v)),w),complement(intersection(union(u,v),complement(w))))**.
% 299.99/300.64  490[0:SpL:30.0,28.1] || member(u,intersection(complement(v),complement(w)))* member(u,union(v,w)) -> .
% 299.99/300.64  19421[0:SpR:30.0,19069.0] ||  -> subclass(symmetric_difference(complement(u),complement(v)),union(u,v))*.
% 299.99/300.64  19069[0:SpR:163.0,19045.0] ||  -> subclass(symmetric_difference(u,v),complement(intersection(u,v)))*.
% 299.99/300.64  18950[0:SpR:163.0,18926.0] ||  -> subclass(symmetric_difference(u,v),union(u,v))*.
% 299.99/300.64  19045[0:Obv:19040.0] ||  -> subclass(intersection(u,v),u)*.
% 299.99/300.64  18926[0:Obv:18921.0] ||  -> subclass(intersection(u,v),v)*.
% 299.99/300.64  3618[0:SpL:163.0,25.0] || member(u,symmetric_difference(v,w)) -> member(u,complement(intersection(v,w)))*.
% 299.99/300.64  3617[0:SpL:163.0,26.0] || member(u,symmetric_difference(v,w))* -> member(u,union(v,w)).
% 299.99/300.64  14683[8:MRR:13464.2,14676.0] function(u) inductive(compose(u,inverse(u))) ||  -> .
% 299.99/300.64  4720[0:Res:75.1,77.1] one_to_one(inverse(u)) function(u) ||  -> one_to_one(u)*.
% 299.99/300.64  15174[8:Res:15170.0,8954.0] ||  -> equal(kind_1_ordinals,ordinal_numbers)**.
% 299.99/300.64  15125[8:MRR:15122.1,13126.0] inductive(complement(kind_1_ordinals)) ||  -> .
% 299.99/300.64  86[0:Inp] || compatible(u,v,w)* -> function(u).
% 299.99/300.64  113[0:Inp] || maps(u,v,w)* -> function(u).
% 299.99/300.64  75[0:Inp] one_to_one(u) ||  -> function(u)*.
% 299.99/300.64  73[0:Inp] ||  -> function(choice)*.
% 299.99/300.64  13676[7:MRR:13674.1,13040.0] inductive(identity_relation) ||  -> .
% 299.99/300.64  9810[5:MRR:8952.0,9808.0] ||  -> inductive(ordinal_numbers)*.
% 299.99/300.64  8954[5:Rew:8637.0,8641.0] || subclass(ordinal_numbers,u)* -> equal(ordinal_numbers,u).
% 299.99/300.64  8953[5:Rew:8637.0,8640.1] || equal(u,ordinal_numbers)* -> equal(ordinal_numbers,u).
% 299.99/300.64  8749[5:Rew:8637.0,7307.0] || equal(successor_relation,ordinal_numbers)** -> .
% 299.99/300.64  8638[5:Rew:8637.0,8.0] ||  -> subclass(u,ordinal_numbers)*.
% 299.99/300.64  8637[5:Spt:8633.1] ||  -> equal(universal_class,ordinal_numbers)**.
% 299.99/300.64  27[0:Inp] || member(u,v) member(u,w) -> member(u,intersection(w,v))*.
% 299.99/300.64  6784[2:SpR:4567.0,4567.0] ||  -> equal(ordinal_multiply(u,v),ordinal_multiply(u,w))*.
% 299.99/300.64  6410[4:MRR:4586.1,6407.0] inductive(singleton_relation) ||  -> .
% 299.99/300.64  6409[4:MRR:4535.1,6407.0] inductive(null_class) ||  -> .
% 299.99/300.64  163[0:Rew:30.0,31.0] ||  -> equal(intersection(complement(intersection(u,v)),union(u,v)),symmetric_difference(u,v))**.
% 299.99/300.64  5[0:Inp] || member(u,v)*+ subclass(v,w)* -> member(u,w)*.
% 299.99/300.64  30[0:Inp] ||  -> equal(complement(intersection(complement(u),complement(v))),union(u,v))**.
% 299.99/300.64  26[0:Inp] || member(u,intersection(v,w))* -> member(u,w).
% 299.99/300.64  25[0:Inp] || member(u,intersection(v,w))* -> member(u,v).
% 299.99/300.64  28[0:Inp] || member(u,v) member(u,complement(v))* -> .
% 299.99/300.64  11[0:Inp] || subclass(u,v)*+ subclass(v,u)* -> equal(v,u).
% 299.99/300.64  295[0:Obv:293.0] ||  -> subclass(u,u)*.
% 299.99/300.64  135[0:Inp] || section(u,v,w)* -> subclass(v,w).
% 299.99/300.64  10[0:Inp] || equal(u,v) -> subclass(v,u)*.239842[7:SpR:155147.0,239340.0] ||  -> equal(intersection(intersection(u,v),complement(v)),identity_relation)**.
% 299.99/300.64  239450[8:SpR:32.0,239339.0] ||  -> equal(intersection(restrict(subset_relation,u,v),inverse(subset_relation)),identity_relation)**.
% 299.99/300.64  239840[7:SpR:32.0,239340.0] ||  -> equal(intersection(restrict(u,v,w),complement(u)),identity_relation)**.
% 299.99/300.64  239845[8:SpR:155582.0,239340.0] ||  -> equal(intersection(symmetric_difference(ordinal_numbers,u),complement(complement(u))),identity_relation)**.
% 299.99/300.64  143399[0:SpR:143349.0,32.0] ||  -> equal(restrict(cross_product(u,v),u,v),cross_product(u,v))**.
% 299.99/300.64  155518[0:SpR:154945.0,19069.0] ||  -> subclass(symmetric_difference(u,intersection(u,v)),complement(intersection(u,v)))*.
% 299.99/300.64  155937[0:SpR:155147.0,19069.0] ||  -> subclass(symmetric_difference(u,intersection(v,u)),complement(intersection(v,u)))*.
% 299.99/300.64  215651[8:Res:215487.1,50046.1] || subclass(unordered_pair(u,v),identity_relation)* member(u,subset_relation) -> .
% 299.99/300.64  215655[8:Res:215487.1,50058.1] || subclass(unordered_pair(u,v),identity_relation)* member(v,subset_relation) -> .
% 299.99/300.64  215663[8:Res:215487.1,94706.0] || subclass(complement(cross_product(u,v)),identity_relation)* -> member(w,u)*.
% 299.99/300.64  215664[8:Res:215487.1,94705.0] || subclass(complement(cross_product(u,v)),identity_relation)* -> member(w,v)*.
% 299.99/300.64  215668[8:Res:215487.1,116180.0] || subclass(complement(rest_of(u)),identity_relation)* -> member(v,cantor(u))*.
% 299.99/300.64  215671[8:Res:215487.1,116122.1] || subclass(rest_of(u),identity_relation) member(v,cantor(u))* -> .
% 299.99/300.64  216219[8:SpL:30.0,216213.0] || equal(intersection(complement(u),complement(v)),union(u,v))** -> .
% 299.99/300.64  216282[8:MRR:216241.0,13126.0] || subclass(union(u,v),identity_relation)* -> member(identity_relation,complement(u)).
% 299.99/300.64  216283[8:MRR:216242.0,13126.0] || subclass(union(u,v),identity_relation)* -> member(identity_relation,complement(v)).
% 299.99/300.64  216555[8:MRR:216527.0,8652.0] || subclass(union(u,v),identity_relation)* -> member(omega,complement(u)).
% 299.99/300.64  216556[8:MRR:216528.0,8652.0] || subclass(union(u,v),identity_relation)* -> member(omega,complement(v)).
% 299.99/300.64  217223[8:Obv:216984.2] || equal(unordered_pair(u,v),identity_relation)** member(u,subset_relation) -> .
% 299.99/300.64  217224[8:Obv:216998.2] || equal(unordered_pair(u,v),identity_relation)** member(v,subset_relation) -> .
% 299.99/300.64  217398[8:Res:216591.1,26.0] || equal(complement(intersection(u,v)),identity_relation)** -> member(identity_relation,v).
% 299.99/300.64  217399[8:Res:216591.1,25.0] || equal(complement(intersection(u,v)),identity_relation)** -> member(identity_relation,u).
% 299.99/300.64  217620[8:Res:216611.1,26.0] || equal(complement(intersection(u,v)),identity_relation)** -> member(omega,v).
% 299.99/300.64  217621[8:Res:216611.1,25.0] || equal(complement(intersection(u,v)),identity_relation)** -> member(omega,u).
% 299.99/300.64  217711[8:Res:216691.1,39296.0] || equal(complement(complement(unordered_pair(u,ordered_pair(v,w)))),identity_relation)** -> .
% 299.99/300.64  217712[8:Res:216691.1,40072.0] || equal(complement(complement(unordered_pair(u,unordered_pair(v,w)))),identity_relation)** -> .
% 299.99/300.64  217715[8:Res:216691.1,39297.0] || equal(complement(complement(unordered_pair(ordered_pair(u,v),w))),identity_relation)** -> .
% 299.99/300.64  217716[8:Res:216691.1,40073.0] || equal(complement(complement(unordered_pair(unordered_pair(u,v),w))),identity_relation)** -> .
% 299.99/300.64  218137[8:Res:8703.1,217144.1] || member(u,ordinal_numbers) equal(unordered_pair(u,v),identity_relation)** -> .
% 299.99/300.64  218138[8:Res:8704.1,217144.1] || member(u,ordinal_numbers) equal(unordered_pair(v,u),identity_relation)** -> .
% 299.99/300.64  218279[8:Res:2504.1,217144.1] || subclass(ordered_pair(u,v),w)* equal(identity_relation,w) -> .
% 299.99/300.64  219098[8:Res:8703.1,219073.1] || member(u,ordinal_numbers) subclass(unordered_pair(u,v),identity_relation)* -> .
% 299.99/300.64  219099[8:Res:8704.1,219073.1] || member(u,ordinal_numbers) subclass(unordered_pair(v,u),identity_relation)* -> .
% 299.99/300.64  219241[8:Res:2504.1,219073.1] || subclass(ordered_pair(u,v),w)* subclass(w,identity_relation) -> .
% 299.99/300.64  219929[8:Res:41183.1,217200.1] || equal(singleton(not_subclass_element(u,v)),identity_relation)** -> subclass(u,v).
% 299.99/300.64  219938[8:Res:18510.1,217200.1] function(u) || equal(singleton(apply(u,v)),identity_relation)** -> .
% 299.99/300.64  220455[21:Res:196656.1,19.0] || subclass(domain_relation,flip(cross_product(u,v)))* -> member(identity_relation,v).
% 299.99/300.64  220557[21:Res:196657.1,19.0] || subclass(domain_relation,rotate(cross_product(u,v)))* -> member(w,v)*.
% 299.99/300.64  221295[8:Res:215662.1,3700.0] || subclass(complement(singleton(u)),identity_relation)* -> equal(singleton(v),u)*.
% 299.99/300.64  221638[8:SpR:218159.1,32.0] || equal(identity_relation,u) -> equal(restrict(u,v,w),identity_relation)**.
% 299.99/300.64  221780[8:Rew:66036.0,221657.1] || equal(complement(u),identity_relation) -> equal(union(u,v),ordinal_numbers)**.
% 299.99/300.64  221996[8:Rew:66036.0,221878.1] || equal(complement(u),identity_relation) -> equal(union(v,u),ordinal_numbers)**.
% 299.99/300.64  222073[8:SpR:219120.1,32.0] || subclass(u,identity_relation) -> equal(restrict(u,v,w),identity_relation)**.
% 299.99/300.64  222211[8:Rew:66036.0,222092.1] || subclass(complement(u),identity_relation)* -> equal(union(u,v),ordinal_numbers)**.
% 299.99/300.64  222467[8:Rew:66036.0,222351.1] || subclass(complement(u),identity_relation)* -> equal(union(v,u),ordinal_numbers)**.
% 299.99/300.64  224775[26:Res:224684.1,898.0] || subclass(omega,restrict(u,v,w))* -> member(identity_relation,u).
% 299.99/300.64  224810[26:MRR:224777.1,216061.0] || subclass(omega,ordered_pair(u,v))* -> equal(singleton(u),identity_relation).
% 299.99/300.64  225211[7:Obv:225157.0] ||  -> equal(intersection(singleton(u),singleton(v)),identity_relation)** equal(u,v).
% 299.99/300.64  225375[26:Res:207562.1,225263.1] operation(u) || equal(complement(ordered_pair(u,v)),omega)** -> .
% 299.99/300.64  225453[8:MRR:225413.1,219933.0] || subclass(u,complement(singleton(regular(u))))* -> equal(u,identity_relation).
% 299.99/300.64  225517[7:Res:10714.1,225445.0] || member(u,complement(singleton(u)))* -> equal(singleton(u),identity_relation).
% 299.99/300.64  225778[26:SpL:33.0,225707.0] || equal(restrict(u,v,w),omega)** -> member(identity_relation,u).
% 299.99/300.64  225933[26:Res:225794.1,190641.1] || equal(u,omega) equal(complement(u),inverse(identity_relation))** -> .
% 299.99/300.64  225934[26:Res:225794.1,190532.1] || equal(u,omega) equal(complement(u),symmetrization_of(identity_relation))* -> .
% 299.99/300.64  225935[26:Res:225794.1,165357.1] || equal(u,omega) equal(complement(u),singleton(identity_relation))** -> .
% 299.99/300.64  225944[26:MRR:225909.1,216061.0] || equal(ordered_pair(u,v),omega)** -> equal(singleton(u),identity_relation).
% 299.99/300.64  226549[8:Res:215687.1,216271.1] inductive(symmetric_difference(u,ordinal_numbers)) || subclass(complement(u),identity_relation)* -> .
% 299.99/300.64  226552[8:Res:215687.1,13588.0] || subclass(complement(u),identity_relation)* -> equal(symmetric_difference(u,ordinal_numbers),identity_relation).
% 299.99/300.64  226651[8:Res:19172.1,216284.1] || equal(cantor(u),identity_relation) subclass(rest_relation,rest_of(u))* -> .
% 299.99/300.64  226667[21:MRR:226628.2,13039.0] || member(u,ordinal_numbers) subclass(rest_relation,rest_of(sum_class(u)))* -> .
% 299.99/300.64  226668[21:MRR:226641.2,13039.0] || member(u,subset_relation) subclass(rest_relation,rest_of(first(u)))* -> .
% 299.99/300.64  226669[21:MRR:226642.2,13039.0] || member(u,subset_relation) subclass(rest_relation,rest_of(second(u)))* -> .
% 299.99/300.64  226670[21:MRR:226643.2,13039.0] || member(u,ordinal_numbers) subclass(rest_relation,rest_of(rest_of(u)))* -> .
% 299.99/300.64  226671[21:MRR:226644.1,13039.0] || subclass(rest_relation,rest_of(not_subclass_element(u,v)))* -> subclass(u,v).
% 299.99/300.64  226672[21:MRR:226648.2,13039.0] function(u) || subclass(rest_relation,rest_of(apply(u,v)))* -> .
% 299.99/300.64  227028[8:Rew:67835.0,226945.1] || equal(complement(u),identity_relation) -> equal(symmetric_difference(u,ordinal_numbers),identity_relation)**.
% 299.99/300.64  227042[8:Obv:226972.1] || equal(complement(u),identity_relation) -> member(least(element_relation,omega),u)*.
% 299.99/300.64  227044[8:MRR:226985.1,295.0] || equal(complement(u),identity_relation) -> member(unordered_pair(v,w),u)*.
% 299.99/300.64  227217[8:Res:217451.1,151988.0] || equal(union(complement(u),identity_relation),identity_relation)** -> member(identity_relation,u).
% 299.99/300.64  227319[26:Res:224684.1,217453.1] || subclass(omega,power_class(u))* equal(power_class(u),identity_relation) -> .
% 299.99/300.64  227325[8:Res:13049.1,217453.1] || subclass(ordinal_numbers,power_class(u))* equal(power_class(u),identity_relation) -> .
% 299.99/300.64  227456[8:Res:217663.1,151988.0] || equal(union(complement(u),identity_relation),identity_relation)** -> member(omega,u).
% 299.99/300.64  227559[8:Rew:59.0,227550.0] || equal(power_class(u),identity_relation) equal(power_class(u),domain_relation)** -> .
% 299.99/300.64  228256[21:Res:10.1,220463.0] || equal(flip(u),domain_relation) subclass(ordinal_numbers,complement(u))* -> .
% 299.99/300.64  228370[21:Res:10.1,220569.0] || equal(rotate(u),domain_relation) subclass(ordinal_numbers,complement(u))* -> .
% 299.99/300.64  228513[8:MRR:228465.2,14676.0] || equal(complement(u),identity_relation) member(v,complement(u))* -> .
% 299.99/300.64  228541[8:Res:221679.1,216271.1] inductive(complement(successor(u))) || equal(complement(u),identity_relation)** -> .
% 299.99/300.64  228544[8:Res:221679.1,13588.0] || equal(complement(u),identity_relation) -> equal(complement(successor(u)),identity_relation)**.
% 299.99/300.64  228545[8:Res:221679.1,221330.0] || equal(complement(u),identity_relation) well_ordering(ordinal_numbers,successor(u))* -> .
% 299.99/300.64  228563[8:MRR:228521.2,13109.0] || equal(successor(u),identity_relation) equal(complement(u),identity_relation)** -> .
% 299.99/300.64  228575[8:Res:228546.1,219073.1] || equal(complement(u),identity_relation) subclass(successor(u),identity_relation)* -> .
% 299.99/300.64  228641[8:Res:221680.1,216271.1] inductive(complement(symmetrization_of(u))) || equal(complement(u),identity_relation)** -> .
% 299.99/300.64  228644[8:Res:221680.1,13588.0] || equal(complement(u),identity_relation) -> equal(complement(symmetrization_of(u)),identity_relation)**.
% 299.99/300.64  228645[8:Res:221680.1,221330.0] || equal(complement(u),identity_relation) well_ordering(ordinal_numbers,symmetrization_of(u))* -> .
% 299.99/300.64  228663[8:MRR:228620.2,13109.0] || equal(symmetrization_of(u),identity_relation)** equal(complement(u),identity_relation) -> .
% 299.99/300.64  228675[8:Res:228646.1,219073.1] || equal(complement(u),identity_relation) subclass(symmetrization_of(u),identity_relation)* -> .
% 299.99/300.64  228800[8:Res:222114.1,216271.1] inductive(complement(successor(u))) || subclass(complement(u),identity_relation)* -> .
% 299.99/300.64  228803[8:Res:222114.1,13588.0] || subclass(complement(u),identity_relation)* -> equal(complement(successor(u)),identity_relation).
% 299.99/300.64  228805[8:Res:222114.1,221330.0] || subclass(complement(u),identity_relation) well_ordering(ordinal_numbers,successor(u))* -> .
% 299.99/300.64  228822[8:MRR:228780.2,13109.0] || equal(successor(u),identity_relation) subclass(complement(u),identity_relation)* -> .
% 299.99/300.64  228834[8:Res:228806.1,219073.1] || subclass(complement(u),identity_relation)* subclass(successor(u),identity_relation) -> .
% 299.99/300.64  228939[8:Res:222115.1,216271.1] inductive(complement(symmetrization_of(u))) || subclass(complement(u),identity_relation)* -> .
% 299.99/300.64  228942[8:Res:222115.1,13588.0] || subclass(complement(u),identity_relation)* -> equal(complement(symmetrization_of(u)),identity_relation).
% 299.99/300.64  228944[8:Res:222115.1,221330.0] || subclass(complement(u),identity_relation) well_ordering(ordinal_numbers,symmetrization_of(u))* -> .
% 299.99/300.64  228960[8:MRR:228918.2,13109.0] || equal(symmetrization_of(u),identity_relation) subclass(complement(u),identity_relation)* -> .
% 299.99/300.64  228972[8:Res:228945.1,219073.1] || subclass(complement(u),identity_relation) subclass(symmetrization_of(u),identity_relation)* -> .
% 299.99/300.64  229004[8:SpL:159.0,222292.0] || member(identity_relation,ordinal_add(u,v))* subclass(element_relation,identity_relation) -> .
% 299.99/300.64  229055[8:SpL:159.0,222305.0] || equal(ordinal_add(u,v),ordinal_numbers)** subclass(element_relation,identity_relation) -> .
% 299.99/300.64  229067[8:SpL:159.0,222310.0] || subclass(ordinal_numbers,ordinal_add(u,v))* subclass(element_relation,identity_relation) -> .
% 299.99/300.64  229083[8:Res:10.1,222904.0] || equal(inverse(subset_relation),singleton(u)) member(u,subset_relation)* -> .
% 299.99/300.64  229369[7:Rew:229162.0,229344.1] || member(not_subclass_element(u,identity_relation),complement(u))* -> subclass(u,identity_relation).
% 299.99/300.64  229755[8:MRR:229664.2,14676.0] inductive(symmetric_difference(u,u)) || well_ordering(v,complement(u))* -> .
% 299.99/300.64  230186[8:SpR:160491.0,229638.0] ||  -> equal(symmetric_difference(symmetric_difference(ordinal_numbers,u),complement(union(u,identity_relation))),identity_relation)**.
% 299.99/300.64  230190[7:SpR:59.0,229638.0] ||  -> equal(symmetric_difference(image(element_relation,complement(u)),complement(power_class(u))),identity_relation)**.
% 299.99/300.64  231201[8:SpL:18840.1,230798.0] || member(u,subset_relation) equal(complement(regular(u)),identity_relation)** -> .
% 299.99/300.64  231882[8:MRR:231852.2,217177.0] || equal(complement(u),ordinal_numbers) -> subclass(regular(complement(u)),identity_relation)*.
% 299.99/300.64  231884[8:MRR:231864.2,217185.0] || equal(power_class(u),ordinal_numbers) -> subclass(regular(power_class(u)),identity_relation)*.
% 299.99/300.64  232483[8:Res:6.1,230867.0] || equal(complement(not_subclass_element(subset_relation,u)),identity_relation)** -> subclass(subset_relation,u).
% 299.99/300.64  232557[8:Res:6.1,230939.0] || equal(regular(not_subclass_element(subset_relation,u)),ordinal_numbers)** -> subclass(subset_relation,u).
% 299.99/300.64  232838[8:Res:216691.1,230694.0] || equal(complement(regular(unordered_pair(u,unordered_pair(v,w)))),identity_relation)** -> .
% 299.99/300.64  232861[25:MRR:232854.1,215866.0] || subclass(ordinal_numbers,u) -> equal(regular(unordered_pair(u,identity_relation)),identity_relation)**.
% 299.99/300.64  232890[7:Obv:232886.0] ||  -> equal(intersection(singleton(u),omega),identity_relation)** equal(integer_of(u),u).
% 299.99/300.64  232912[25:MRR:232909.1,215866.0] || equal(u,ordinal_numbers) -> equal(regular(unordered_pair(u,identity_relation)),identity_relation)**.
% 299.99/300.64  232964[7:Obv:232959.0] ||  -> equal(intersection(omega,singleton(u)),identity_relation)** equal(integer_of(u),u).
% 299.99/300.64  233003[8:SpL:18840.1,232981.0] || member(u,subset_relation) subclass(ordinal_numbers,regular(singleton(u)))* -> .
% 299.99/300.64  233070[8:SpL:18840.1,233013.0] || member(u,subset_relation) equal(regular(singleton(u)),ordinal_numbers)** -> .
% 299.99/300.64  233134[8:Res:216691.1,230695.0] || equal(complement(regular(unordered_pair(unordered_pair(u,v),w))),identity_relation)** -> .
% 299.99/300.64  233161[25:MRR:233155.1,215873.0] || subclass(ordinal_numbers,u) -> equal(regular(unordered_pair(identity_relation,u)),identity_relation)**.
% 299.99/300.64  233216[25:MRR:233214.1,215873.0] || equal(u,ordinal_numbers) -> equal(regular(unordered_pair(identity_relation,u)),identity_relation)**.
% 299.99/300.64  233386[8:MRR:233353.1,215781.0] || member(u,ordinal_numbers) -> member(u,complement(singleton(singleton(u))))*.
% 299.99/300.64  233453[14:Res:233378.0,5.0] || subclass(complement(singleton(singleton(identity_relation))),u)* -> member(identity_relation,u).
% 299.99/300.64  233557[21:MRR:233530.1,8667.0] || subclass(domain_relation,rotate(u)) subclass(domain_relation,complement(u))* -> .
% 299.99/300.64  233558[21:MRR:233548.1,8667.0] || subclass(domain_relation,flip(u)) subclass(domain_relation,complement(u))* -> .
% 299.99/300.64  234082[8:SpL:18840.1,233382.0] || member(u,subset_relation) well_ordering(ordinal_numbers,complement(singleton(u)))* -> .
% 299.99/300.64  234090[8:SpR:963.0,233383.0] ||  -> member(singleton(singleton(u)),complement(singleton(singleton(singleton(singleton(u))))))*.
% 299.99/300.64  234101[24:SpR:207558.1,233383.0] operation(u) ||  -> member(identity_relation,complement(singleton(ordered_pair(u,v))))*.
% 299.99/300.64  234122[8:SpL:18840.1,234113.0] || member(u,subset_relation) subclass(complement(singleton(u)),identity_relation)* -> .
% 299.99/300.64  234173[8:SpL:963.0,234106.0] || member(singleton(singleton(u)),singleton(singleton(singleton(singleton(u)))))* -> .
% 299.99/300.64  234183[24:SpL:207558.1,234106.0] operation(u) || member(identity_relation,singleton(ordered_pair(u,v)))* -> .
% 299.99/300.64  234655[8:Res:216691.1,234117.0] || equal(complement(complement(complement(singleton(ordered_pair(u,v))))),identity_relation)** -> .
% 299.99/300.64  234737[8:Res:216691.1,232824.0] || equal(complement(regular(unordered_pair(u,ordered_pair(v,w)))),identity_relation)** -> .
% 299.99/300.64  234767[8:Res:216691.1,233124.0] || equal(complement(regular(unordered_pair(ordered_pair(u,v),w))),identity_relation)** -> .
% 299.99/300.64  234980[8:Rew:160429.0,234942.0] ||  -> equal(segment(complement(cross_product(u,singleton(v))),u,v),identity_relation)**.
% 299.99/300.64  235273[8:Res:230445.1,219073.1] || member(u,v)* subclass(union(v,identity_relation),identity_relation)* -> .
% 299.99/300.64  235274[8:Res:230445.1,217144.1] || member(u,v)* equal(union(v,identity_relation),identity_relation)** -> .
% 299.99/300.64  235434[8:Res:28980.1,210517.1] || subclass(rest_relation,flip(u))* equal(complement(u),ordinal_numbers) -> .
% 299.99/300.64  235457[5:Res:28980.1,8841.1] || subclass(rest_relation,flip(u))* subclass(ordinal_numbers,complement(u)) -> .
% 299.99/300.64  235562[8:Res:28979.1,210517.1] || subclass(rest_relation,rotate(u))* equal(complement(u),ordinal_numbers) -> .
% 299.99/300.64  235576[5:Res:28979.1,19.0] || subclass(rest_relation,rotate(cross_product(u,v)))* -> member(w,v)*.
% 299.99/300.64  235589[5:Res:28979.1,8841.1] || subclass(rest_relation,rotate(u))* subclass(ordinal_numbers,complement(u)) -> .
% 299.99/300.64  235610[21:MRR:235587.1,8667.0] || subclass(rest_relation,rotate(u))* subclass(domain_relation,complement(u)) -> .
% 299.99/300.64  235810[8:Res:210572.1,235481.1] || equal(complement(u),ordinal_numbers)** equal(flip(u),rest_relation) -> .
% 299.99/300.64  235859[8:Res:210572.1,235840.1] || equal(complement(u),ordinal_numbers)** equal(rotate(u),rest_relation) -> .
% 299.99/300.64  236309[5:Obv:236276.0] ||  -> subclass(intersection(u,complement(power_class(v))),image(element_relation,complement(v)))*.
% 299.99/300.64  236523[5:Obv:236480.0] ||  -> subclass(intersection(complement(power_class(u)),v),image(element_relation,complement(u)))*.
% 299.99/300.64  236621[26:SpL:159.0,225140.0] || subclass(omega,ordinal_add(u,v))* subclass(element_relation,identity_relation) -> .
% 299.99/300.64  236638[26:SpL:159.0,225241.0] || equal(ordinal_add(u,v),omega)** subclass(element_relation,identity_relation) -> .
% 299.99/300.64  236900[8:Obv:236891.1] || subclass(u,subset_relation) -> equal(intersection(u,inverse(subset_relation)),identity_relation)**.
% 299.99/300.64  236901[7:Obv:236893.1] || subclass(u,v) -> equal(intersection(u,complement(v)),identity_relation)**.
% 299.99/300.64  236983[26:Res:225888.1,151988.0] || equal(symmetric_difference(ordinal_numbers,complement(u)),omega)** -> member(identity_relation,u).
% 299.99/300.64  237397[7:SpR:163.0,237181.0] ||  -> equal(intersection(complement(union(u,v)),symmetric_difference(u,v)),identity_relation)**.
% 299.99/300.64  237398[7:SpR:3596.0,237181.0] ||  -> equal(intersection(complement(successor(u)),symmetric_difference(u,singleton(u))),identity_relation)**.
% 299.99/300.64  237399[7:SpR:3597.0,237181.0] ||  -> equal(intersection(complement(symmetrization_of(u)),symmetric_difference(u,inverse(u))),identity_relation)**.
% 299.99/300.64  237453[8:SpR:162584.0,237181.0] ||  -> equal(intersection(symmetrization_of(identity_relation),intersection(u,complement(inverse(identity_relation)))),identity_relation)**.
% 299.99/300.64  237940[8:SpR:154737.1,237831.0] || subclass(u,subset_relation) -> equal(intersection(inverse(subset_relation),u),identity_relation)**.
% 299.99/300.64  238213[7:SpR:154737.1,237830.0] || subclass(u,v) -> equal(intersection(complement(v),u),identity_relation)**.
% 299.99/300.64  238234[16:SpR:195239.0,237830.0] ||  -> equal(intersection(singleton(identity_relation),intersection(complement(singleton(identity_relation)),u)),identity_relation)**.
% 299.99/300.64  238235[8:SpR:162584.0,237830.0] ||  -> equal(intersection(symmetrization_of(identity_relation),intersection(complement(inverse(identity_relation)),u)),identity_relation)**.
% 299.99/300.64  239824[16:SpR:195239.0,239340.0] ||  -> equal(intersection(intersection(complement(singleton(identity_relation)),u),singleton(identity_relation)),identity_relation)**.
% 299.99/300.64  239825[8:SpR:162584.0,239340.0] ||  -> equal(intersection(intersection(complement(inverse(identity_relation)),u),symmetrization_of(identity_relation)),identity_relation)**.
% 299.99/300.64  18970[0:Res:18926.0,11.0] || subclass(u,intersection(v,u))* -> equal(intersection(v,u),u).
% 299.99/300.64  19089[0:Res:19045.0,11.0] || subclass(u,intersection(u,v))* -> equal(intersection(u,v),u).
% 299.99/300.64  10158[5:SpL:32.0,10088.0] || equal(restrict(u,v,w),ordinal_numbers)** -> member(singleton(x),u)*.
% 299.99/300.64  8856[5:Rew:8637.0,4737.0] || subclass(ordinal_numbers,restrict(u,v,w))* -> member(singleton(x),u)*.
% 299.99/300.64  8844[5:Rew:8637.0,6944.0] || subclass(ordinal_numbers,intersection(u,v))* -> member(ordered_pair(w,x),u)*.
% 299.99/300.64  8845[5:Rew:8637.0,6943.0] || subclass(ordinal_numbers,intersection(u,v))* -> member(ordered_pair(w,x),v)*.
% 299.99/300.64  56849[5:Res:10.1,8846.0] || equal(intersection(u,v),ordinal_numbers)** -> member(unordered_pair(w,x),u)*.
% 299.99/300.64  56805[5:Res:10.1,8847.0] || equal(intersection(u,v),ordinal_numbers)** -> member(unordered_pair(w,x),v)*.
% 299.99/300.64  19403[0:SpR:33.0,19069.0] ||  -> subclass(symmetric_difference(cross_product(u,v),w),complement(restrict(w,u,v)))*.
% 299.99/300.64  19400[0:SpR:32.0,19069.0] ||  -> subclass(symmetric_difference(u,cross_product(v,w)),complement(restrict(u,v,w)))*.
% 299.99/300.64  124891[5:Res:10.1,94705.0] || equal(complement(complement(cross_product(u,v))),ordinal_numbers)** -> member(w,v)*.
% 299.99/300.64  124896[5:Res:10.1,94706.0] || equal(complement(complement(cross_product(u,v))),ordinal_numbers)** -> member(w,u)*.
% 299.99/300.64  130721[5:Res:130678.0,11.0] || subclass(u,complement(complement(u)))* -> equal(complement(complement(u)),u).
% 299.99/300.64  130876[5:Res:6.1,9876.0] || subclass(u,v)* well_ordering(ordinal_numbers,v)* -> subclass(u,w)*.
% 299.99/300.64  131578[5:Res:2504.1,8842.1] || subclass(ordered_pair(u,v),w)* subclass(ordinal_numbers,complement(w)) -> .
% 299.99/300.64  134105[5:Res:133837.1,3700.0] || well_ordering(ordinal_numbers,complement(singleton(u)))* -> equal(singleton(singleton(v)),u)*.
% 299.99/300.64  134913[8:Res:133837.1,116453.0] || well_ordering(ordinal_numbers,complement(rest_of(u)))* -> member(singleton(v),cantor(u))*.
% 299.99/300.64  135242[5:Res:133837.1,2200.0] || well_ordering(ordinal_numbers,complement(cross_product(u,v)))* -> member(singleton(w),u)*.
% 299.99/300.64  139807[5:MRR:139781.0,8652.0] || equal(complement(union(u,v)),ordinal_numbers)** -> member(omega,complement(v)).
% 299.99/300.64  139892[5:MRR:139867.0,8652.0] || equal(complement(union(u,v)),ordinal_numbers)** -> member(omega,complement(u)).
% 299.99/300.64  140452[0:Obv:140379.1] || member(u,v) -> subclass(singleton(u),intersection(v,singleton(u)))*.
% 299.99/300.64  140461[8:MRR:140403.0,41183.1] || subclass(rest_relation,rest_of(u)) -> subclass(v,intersection(cantor(u),v))*.
% 299.99/300.64  144407[8:SpL:140613.0,10088.0] || equal(symmetric_difference(ordinal_numbers,u),ordinal_numbers) -> member(singleton(v),complement(u))*.
% 299.99/300.64  144417[8:SpL:140613.0,8848.0] || subclass(ordinal_numbers,symmetric_difference(ordinal_numbers,u)) -> member(singleton(v),complement(u))*.
% 299.99/300.64  145767[8:SpR:143170.0,116148.1] || section(ordinal_numbers,u,v) -> subclass(cantor(cross_product(v,u)),u)*.
% 299.99/300.64  146778[5:MRR:146753.0,8955.1] || member(u,ordinal_numbers) subclass(ordinal_numbers,complement(singleton(sum_class(u))))* -> .
% 299.99/300.64  147260[5:Res:143222.1,28.1] || equal(complement(u),omega) member(least(element_relation,omega),u)* -> .
% 299.99/300.64  151923[5:SpR:147905.0,30.0] ||  -> equal(union(u,complement(complement(u))),complement(complement(complement(complement(u)))))**.
% 299.99/300.64  151953[5:SpL:147905.0,132824.0] || equal(complement(complement(u)),ordinal_numbers) -> member(least(element_relation,omega),u)*.
% 299.99/300.64  151982[5:SpL:147905.0,130556.0] || equal(complement(complement(u)),omega) -> member(least(element_relation,omega),u)*.
% 299.99/300.64  152229[5:MRR:152197.0,41183.1] || subclass(u,complement(singleton(not_subclass_element(u,v))))* -> subclass(u,v).
% 299.99/300.64  155543[0:SpR:32.0,154945.0] ||  -> equal(intersection(u,restrict(u,v,w)),restrict(u,v,w))**.
% 299.99/300.64  155970[0:SpR:163.0,155147.0] ||  -> equal(intersection(union(u,v),symmetric_difference(u,v)),symmetric_difference(u,v))**.
% 299.99/300.64  156633[5:Res:155846.1,155827.0] || equal(compose(subset_relation,subset_relation),subset_relation) -> subclass(compose(subset_relation,subset_relation),subset_relation)*.
% 299.99/300.64  10704[5:Res:8665.1,2486.0] function(ordered_pair(u,v)) ||  -> member(singleton(u),cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.64  127981[5:Res:126679.1,152.0] || subclass(omega,complement(complement(recursion_equation_functions(u))))* -> function(least(element_relation,omega)).
% 299.99/300.64  79541[5:Res:60219.0,152.0] ||  -> subclass(u,complement(recursion_equation_functions(v))) function(not_subclass_element(u,complement(recursion_equation_functions(v))))*.
% 299.99/300.64  51490[5:Res:51313.1,152.0] || member(singleton(recursion_equation_functions(u)),subset_relation) -> function(first(singleton(recursion_equation_functions(u))))*.
% 299.99/300.64  128507[5:Res:96837.0,8840.1] || member(u,ordinal_numbers) -> function(u) member(u,complement(recursion_equation_functions(v)))*.
% 299.99/300.64  37672[5:SoR:10704.0,75.1] one_to_one(ordered_pair(u,v)) ||  -> member(singleton(u),cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.64  132036[0:Res:55.1,19115.0] inductive(recursion_equation_functions(u)) ||  -> subclass(omega,v) function(not_subclass_element(omega,v))*.
% 299.99/300.64  128177[5:Res:10.1,127981.0] || equal(complement(complement(recursion_equation_functions(u))),omega)** -> function(least(element_relation,omega)).
% 299.99/300.64  128043[8:Res:10.1,128029.0] || equal(complement(complement(subset_relation)),omega) subclass(omega,inverse(subset_relation))* -> .
% 299.99/300.64  128095[8:Res:10.1,128043.1] || equal(inverse(subset_relation),omega) equal(complement(complement(subset_relation)),omega)** -> .
% 299.99/300.64  125214[8:Res:39298.1,28976.1] || subclass(ordinal_numbers,complement(complement(subset_relation)))* subclass(rest_relation,inverse(subset_relation)) -> .
% 299.99/300.64  125812[8:Res:39298.1,116738.1] || subclass(ordinal_numbers,complement(complement(subset_relation)))* subclass(domain_relation,inverse(subset_relation)) -> .
% 299.99/300.64  128364[8:Res:127147.1,125923.1] || subclass(ordinal_numbers,complement(complement(subset_relation)))* subclass(omega,inverse(subset_relation)) -> .
% 299.99/300.64  133067[8:Res:127147.1,133059.1] || subclass(ordinal_numbers,complement(complement(subset_relation)))* equal(inverse(subset_relation),omega) -> .
% 299.99/300.64  160650[5:Rew:143407.0,146655.1] || subclass(ordinal_numbers,complement(u)) member(omega,complement(complement(u)))* -> .
% 299.99/300.64  83705[8:Res:83681.1,15565.1] || equal(cantor(u),domain_relation) subclass(domain_relation,complement(cantor(u)))* -> .
% 299.99/300.64  117125[8:Rew:117064.0,83718.0] || equal(inverse(u),domain_relation) subclass(domain_relation,complement(inverse(u)))* -> .
% 299.99/300.64  117201[8:Rew:117140.0,83717.0] || equal(sum_class(u),domain_relation) subclass(domain_relation,complement(sum_class(u)))* -> .
% 299.99/300.64  161831[13:Res:138.1,160428.0] || member(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers) -> member(least(element_relation,successor_relation),successor_relation)*.
% 299.99/300.64  162333[7:Res:13056.1,9876.0] inductive(u) || subclass(u,v)* well_ordering(ordinal_numbers,v)* -> .
% 299.99/300.64  165076[8:SpL:117066.0,164087.1] operation(flip(cross_product(u,ordinal_numbers))) || subclass(ordinal_numbers,inverse(u))* -> .
% 299.99/300.64  165077[8:SpL:117142.0,164087.1] operation(restrict(element_relation,ordinal_numbers,u)) || subclass(ordinal_numbers,sum_class(u))* -> .
% 299.99/300.64  165085[8:SpL:117066.0,164088.1] operation(flip(cross_product(u,ordinal_numbers))) || equal(inverse(u),ordinal_numbers)** -> .
% 299.99/300.64  165086[8:SpL:117142.0,164088.1] operation(restrict(element_relation,ordinal_numbers,u)) || equal(sum_class(u),ordinal_numbers)** -> .
% 299.99/300.64  175571[0:SpR:154737.1,151847.0] || subclass(u,singleton(v))* -> subclass(u,w)* member(v,u).
% 299.99/300.64  167402[8:SpR:160659.1,141387.0] || subclass(ordinal_numbers,sum_class(u)) -> equal(symmetric_difference(ordinal_numbers,sum_class(u)),identity_relation)**.
% 299.99/300.64  167401[8:SpR:160659.1,141388.0] || subclass(ordinal_numbers,inverse(u)) -> equal(symmetric_difference(ordinal_numbers,inverse(u)),identity_relation)**.
% 299.99/300.64  167399[8:SpR:160659.1,141390.0] || subclass(ordinal_numbers,cantor(u)) -> equal(symmetric_difference(ordinal_numbers,cantor(u)),identity_relation)**.
% 299.99/300.64  166254[7:Res:96837.0,13082.1] inductive(singleton(u)) ||  -> function(u)* member(identity_relation,complement(recursion_equation_functions(v)))*.
% 299.99/300.64  167006[7:MRR:166972.0,13126.0] || equal(complement(union(u,v)),ordinal_numbers)** -> member(identity_relation,complement(u)).
% 299.99/300.64  165048[8:Res:60219.0,162901.0] || equal(not_subclass_element(u,complement(subset_relation)),identity_relation)** -> subclass(u,complement(subset_relation)).
% 299.99/300.64  165043[8:Res:51313.1,162901.0] || member(singleton(subset_relation),subset_relation)* equal(first(singleton(subset_relation)),identity_relation) -> .
% 299.99/300.64  164976[8:Res:60219.0,162888.0] || subclass(not_subclass_element(u,complement(subset_relation)),identity_relation)* -> subclass(u,complement(subset_relation)).
% 299.99/300.64  164971[8:Res:51313.1,162888.0] || member(singleton(subset_relation),subset_relation) subclass(first(singleton(subset_relation)),identity_relation)* -> .
% 299.99/300.64  164614[7:SpL:140603.0,13103.0] || equal(restrict(inverse(ordinal_numbers),u,u),identity_relation)** -> asymmetric(ordinal_numbers,u).
% 299.99/300.64  164708[7:SpR:140603.0,13104.1] || asymmetric(ordinal_numbers,u) -> equal(restrict(inverse(ordinal_numbers),u,u),identity_relation)**.
% 299.99/300.64  166243[7:Res:156404.0,13082.1] inductive(symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers))) ||  -> member(identity_relation,complement(subset_relation))*.
% 299.99/300.64  166244[7:Res:156513.0,13082.1] inductive(symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation)) ||  -> member(identity_relation,complement(subset_relation))*.
% 299.99/300.64  166247[8:Res:156904.0,13082.1] inductive(restrict(inverse(subset_relation),u,v)) ||  -> member(identity_relation,complement(subset_relation))*.
% 299.99/300.64  162418[7:MRR:162413.0,8652.0] ||  -> equal(integer_of(singleton(omega)),identity_relation) member(singleton(singleton(singleton(omega))),element_relation)*.
% 299.99/300.64  162338[7:Res:13056.1,18794.1] inductive(intersection(u,v)) || member(identity_relation,symmetric_difference(u,v))* -> .
% 299.99/300.64  166268[8:Res:162025.0,13082.1] inductive(complement(union(u,identity_relation))) ||  -> member(identity_relation,symmetric_difference(ordinal_numbers,u))*.
% 299.99/300.64  160759[8:Rew:140603.0,69723.0] ||  -> equal(union(symmetric_difference(ordinal_numbers,u),identity_relation),complement(symmetric_difference(complement(u),ordinal_numbers)))**.
% 299.99/300.64  160692[8:Rew:140613.0,79570.0] ||  -> member(u,symmetric_difference(ordinal_numbers,v)) subclass(singleton(u),union(v,identity_relation))*.
% 299.99/300.64  18519[7:Res:18517.1,5.0] || subclass(ordinal_numbers,u) -> equal(singleton(v),identity_relation) member(v,u)*.
% 299.99/300.64  61999[7:Res:60996.1,5.0] || subclass(ordinal_numbers,u) -> equal(v,identity_relation) member(regular(v),u)*.
% 299.99/300.64  79578[7:Res:79560.1,13082.1] inductive(singleton(u)) ||  -> member(u,v)* member(identity_relation,complement(v))*.
% 299.99/300.64  167007[7:MRR:166973.0,13126.0] || equal(complement(union(u,v)),ordinal_numbers)** -> member(identity_relation,complement(v)).
% 299.99/300.64  81307[8:Res:13061.0,15565.1] || subclass(domain_relation,complement(omega)) -> equal(integer_of(ordered_pair(identity_relation,identity_relation)),identity_relation)**.
% 299.99/300.64  66989[8:Res:66340.0,13082.1] inductive(symmetric_difference(complement(u),ordinal_numbers)) ||  -> member(identity_relation,union(u,identity_relation))*.
% 299.99/300.64  67006[8:Res:66560.0,13082.1] inductive(symmetric_difference(domain_of(u),ordinal_numbers)) ||  -> member(identity_relation,complement(cantor(u)))*.
% 299.99/300.64  19426[7:Res:19069.0,13082.1] inductive(symmetric_difference(u,v)) ||  -> member(identity_relation,complement(intersection(u,v)))*.
% 299.99/300.64  19675[7:SpL:3597.0,13079.0] || subclass(ordinal_numbers,symmetric_difference(u,inverse(u)))* -> member(identity_relation,symmetrization_of(u)).
% 299.99/300.64  19666[7:SpL:3597.0,13081.0] || equal(symmetric_difference(u,inverse(u)),ordinal_numbers)** -> member(identity_relation,symmetrization_of(u)).
% 299.99/300.64  19558[7:SpL:3596.0,13079.0] || subclass(ordinal_numbers,symmetric_difference(u,singleton(u)))* -> member(identity_relation,successor(u)).
% 299.99/300.64  19549[7:SpL:3596.0,13081.0] || equal(symmetric_difference(u,singleton(u)),ordinal_numbers)** -> member(identity_relation,successor(u)).
% 299.99/300.64  82834[7:Res:10.1,13240.0] || equal(recursion_equation_functions(u),omega)**+ -> equal(integer_of(v),identity_relation)** function(v).
% 299.99/300.64  66696[7:Res:66492.1,5.0] || subclass(ordinal_numbers,u) -> equal(integer_of(v),identity_relation) member(v,u)*.
% 299.99/300.64  163168[8:Res:163118.0,11.0] || subclass(inverse(identity_relation),symmetrization_of(identity_relation))* -> equal(symmetrization_of(identity_relation),inverse(identity_relation)).
% 299.99/300.64  163159[8:Rew:162584.0,163117.1] ||  -> member(not_subclass_element(symmetrization_of(identity_relation),u),inverse(identity_relation))* subclass(symmetrization_of(identity_relation),u).
% 299.99/300.64  163107[8:SpR:162584.0,19421.0] ||  -> subclass(symmetric_difference(complement(u),symmetrization_of(identity_relation)),union(u,complement(inverse(identity_relation))))*.
% 299.99/300.64  163088[8:SpR:162584.0,19421.0] ||  -> subclass(symmetric_difference(symmetrization_of(identity_relation),complement(u)),union(complement(inverse(identity_relation)),u))*.
% 299.99/300.64  163087[8:SpR:162584.0,147905.0] ||  -> equal(intersection(complement(inverse(identity_relation)),complement(symmetrization_of(identity_relation))),complement(symmetrization_of(identity_relation)))**.
% 299.99/300.64  167500[8:Res:15426.1,163154.0] || subclass(domain_relation,symmetrization_of(identity_relation)) -> member(ordered_pair(identity_relation,identity_relation),inverse(identity_relation))*.
% 299.99/300.64  164140[8:SpL:163119.0,125908.0] || subclass(omega,symmetrization_of(identity_relation)) -> member(least(element_relation,omega),inverse(identity_relation))*.
% 299.99/300.64  164142[8:SpL:163119.0,130556.0] || equal(symmetrization_of(identity_relation),omega) -> member(least(element_relation,omega),inverse(identity_relation))*.
% 299.99/300.64  163135[8:SpL:162584.0,81322.1] || subclass(domain_relation,complement(inverse(identity_relation)))* subclass(domain_relation,symmetrization_of(identity_relation)) -> .
% 299.99/300.64  163136[8:SpL:162584.0,81412.1] || equal(complement(inverse(identity_relation)),domain_relation)** equal(symmetrization_of(identity_relation),domain_relation) -> .
% 299.99/300.64  163142[8:SpL:162584.0,28.1] || member(u,complement(inverse(identity_relation)))* member(u,symmetrization_of(identity_relation)) -> .
% 299.99/300.64  163150[8:SpL:162584.0,151988.0] || member(u,complement(symmetrization_of(identity_relation)))* -> member(u,complement(inverse(identity_relation))).
% 299.99/300.64  69168[8:Res:13049.1,66086.1] || subclass(ordinal_numbers,complement(compose(element_relation,ordinal_numbers)))* member(identity_relation,element_relation) -> .
% 299.99/300.64  13373[7:Rew:13036.0,10019.1] || equal(symmetric_difference(u,v),ordinal_numbers) -> member(identity_relation,union(u,v))*.
% 299.99/300.64  13374[7:Rew:13036.0,9971.1] || subclass(ordinal_numbers,symmetric_difference(u,v)) -> member(identity_relation,union(u,v))*.
% 299.99/300.64  82303[8:Res:81336.1,19.0] || subclass(domain_relation,complement(complement(cross_product(u,v))))* -> member(identity_relation,v).
% 299.99/300.64  83599[8:Res:10.1,82303.0] || equal(complement(complement(cross_product(u,v))),domain_relation)** -> member(identity_relation,v).
% 299.99/300.64  13349[7:Rew:13036.0,9845.2] || subclass(ordinal_numbers,u)*+ subclass(u,v)* -> member(identity_relation,v)*.
% 299.99/300.64  13350[7:Rew:13036.0,10725.2] inductive(singleton(u)) || member(u,v)* -> member(identity_relation,v)*.
% 299.99/300.64  83744[7:Res:10.1,13349.0] || equal(u,ordinal_numbers) subclass(u,v)* -> member(identity_relation,v)*.
% 299.99/300.64  166760[8:SpL:160491.0,166753.1] inductive(symmetric_difference(ordinal_numbers,u)) || equal(union(u,identity_relation),omega)** -> .
% 299.99/300.64  167607[14:SpL:160491.0,167597.0] || well_ordering(ordinal_numbers,union(u,identity_relation))* -> member(identity_relation,symmetric_difference(ordinal_numbers,u)).
% 299.99/300.64  164895[8:SpL:160491.0,9922.1] inductive(symmetric_difference(ordinal_numbers,u)) || equal(union(u,identity_relation),ordinal_numbers)** -> .
% 299.99/300.64  67606[8:Rew:67605.0,67546.0] ||  -> subclass(symmetric_difference(union(u,identity_relation),ordinal_numbers),complement(symmetric_difference(complement(u),ordinal_numbers)))*.
% 299.99/300.64  160606[8:Rew:116078.0,82302.1] || subclass(domain_relation,complement(complement(rest_of(u))))* -> member(identity_relation,cantor(u)).
% 299.99/300.64  160607[8:Rew:116078.0,82702.1] || equal(complement(complement(rest_of(u))),domain_relation)** -> member(identity_relation,cantor(u)).
% 299.99/300.64  162656[7:Res:13072.1,9876.0] || subclass(u,v)* well_ordering(ordinal_numbers,v)* -> equal(u,identity_relation).
% 299.99/300.64  19195[8:Res:19172.1,11.0] || equal(identity_relation,u) subclass(v,u)* -> equal(v,u).
% 299.99/300.64  82304[8:Res:81336.1,18.0] || subclass(domain_relation,complement(complement(cross_product(u,v))))* -> member(identity_relation,u).
% 299.99/300.64  83602[8:Res:10.1,82304.0] || equal(complement(complement(cross_product(u,v))),domain_relation)** -> member(identity_relation,u).
% 299.99/300.64  165191[14:Res:165172.1,5.0] || subclass(complement(u),v)* -> member(identity_relation,u) member(identity_relation,v).
% 299.99/300.64  165385[14:Res:165168.1,898.0] || equal(restrict(u,v,w),singleton(identity_relation))** -> member(identity_relation,u).
% 299.99/300.64  165383[14:Res:165168.1,56411.0] || equal(rest_of(identity_relation),singleton(identity_relation)) subclass(ordinal_numbers,complement(element_relation))* -> .
% 299.99/300.64  62833[8:SoR:10704.0,15567.1] || subclass(domain_relation,recursion_equation_functions(u))*+ -> member(singleton(identity_relation),cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.64  62851[8:SoR:10704.0,15649.1] || equal(recursion_equation_functions(u),domain_relation)**+ -> member(singleton(identity_relation),cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.64  161078[8:Rew:117140.0,83707.1,117140.0,83707.0] || equal(sum_class(u),domain_relation) -> member(ordered_pair(identity_relation,identity_relation),sum_class(u))*.
% 299.99/300.64  161077[8:Rew:117064.0,83708.1,117064.0,83708.0] || equal(inverse(u),domain_relation) -> member(ordered_pair(identity_relation,identity_relation),inverse(u))*.
% 299.99/300.64  15571[8:Res:15426.1,26.0] || subclass(domain_relation,intersection(u,v))*+ -> member(ordered_pair(identity_relation,identity_relation),v)*.
% 299.99/300.64  83166[8:Res:10.1,15571.0] || equal(intersection(u,v),domain_relation)**+ -> member(ordered_pair(identity_relation,identity_relation),v)*.
% 299.99/300.64  160610[8:Rew:116078.0,83661.1] || equal(cantor(u),domain_relation) -> member(ordered_pair(identity_relation,identity_relation),cantor(u))*.
% 299.99/300.64  82270[8:Res:81336.1,152.0] || subclass(domain_relation,complement(complement(recursion_equation_functions(u))))* -> function(ordered_pair(identity_relation,identity_relation)).
% 299.99/300.64  82519[8:Res:10.1,82270.0] || equal(complement(complement(recursion_equation_functions(u))),domain_relation)** -> function(ordered_pair(identity_relation,identity_relation)).
% 299.99/300.64  15565[8:Res:15426.1,28.1] || subclass(domain_relation,complement(u)) member(ordered_pair(identity_relation,identity_relation),u)* -> .
% 299.99/300.64  81336[8:MRR:81303.0,8667.0] || subclass(domain_relation,complement(complement(u))) -> member(ordered_pair(identity_relation,identity_relation),u)*.
% 299.99/300.64  15572[8:Res:15426.1,25.0] || subclass(domain_relation,intersection(u,v))*+ -> member(ordered_pair(identity_relation,identity_relation),u)*.
% 299.99/300.64  83195[8:Res:10.1,15572.0] || equal(intersection(u,v),domain_relation)**+ -> member(ordered_pair(identity_relation,identity_relation),u)*.
% 299.99/300.64  187582[8:Rew:67835.0,186606.1] || equal(complement(u),ordinal_numbers) -> equal(symmetric_difference(complement(u),ordinal_numbers),identity_relation)**.
% 299.99/300.64  187609[17:Res:138.1,187542.0] || member(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers) -> member(least(element_relation,union_of_range_map),union_of_range_map)*.
% 299.99/300.64  190559[18:Res:190442.1,56411.0] || equal(rest_of(identity_relation),symmetrization_of(identity_relation)) subclass(ordinal_numbers,complement(element_relation))* -> .
% 299.99/300.64  190561[18:Res:190442.1,898.0] || equal(restrict(u,v,w),symmetrization_of(identity_relation))** -> member(identity_relation,u).
% 299.99/300.64  190668[18:Res:190593.1,56411.0] || equal(rest_of(identity_relation),inverse(identity_relation)) subclass(ordinal_numbers,complement(element_relation))* -> .
% 299.99/300.64  190670[18:Res:190593.1,898.0] || equal(restrict(u,v,w),inverse(identity_relation))** -> member(identity_relation,u).
% 299.99/300.64  191932[18:Res:190515.1,28.1] || subclass(ordinal_numbers,complement(u)) member(regular(symmetrization_of(identity_relation)),u)* -> .
% 299.99/300.64  191935[18:Res:190515.1,151988.0] || subclass(ordinal_numbers,complement(complement(u))) -> member(regular(symmetrization_of(identity_relation)),u)*.
% 299.99/300.64  191942[18:Res:190515.1,26.0] || subclass(ordinal_numbers,intersection(u,v))* -> member(regular(symmetrization_of(identity_relation)),v)*.
% 299.99/300.64  191943[18:Res:190515.1,25.0] || subclass(ordinal_numbers,intersection(u,v))* -> member(regular(symmetrization_of(identity_relation)),u)*.
% 299.99/300.64  192418[8:SpR:188530.1,141394.0] || member(u,ordinals_with_null_class_as_identity) -> equal(symmetric_difference(ordinal_numbers,u),symmetric_difference(u,ordinal_numbers))*.
% 299.99/300.64  193107[7:SpR:193044.1,154737.1] || subclass(u,singleton(v))* -> member(v,u) equal(identity_relation,u).
% 299.99/300.64  193566[8:SpR:68757.0,160491.0] ||  -> equal(union(complement(inverse(identity_relation)),identity_relation),complement(intersection(symmetrization_of(identity_relation),ordinal_numbers)))**.
% 299.99/300.64  193571[8:SpL:68757.0,176788.0] || equal(intersection(symmetrization_of(identity_relation),ordinal_numbers),ordinal_numbers)** -> member(omega,inverse(identity_relation)).
% 299.99/300.64  94713[5:Res:39298.1,100.0] || subclass(ordinal_numbers,complement(complement(composition_function)))*+ -> equal(compose(u,v),w)*.
% 299.99/300.64  132451[5:SpL:50855.1,132441.0] || member(singleton(u),subset_relation) well_ordering(ordinal_numbers,singleton(singleton(u)))* -> .
% 299.99/300.64  190501[18:MRR:167482.1,190496.0] || well_ordering(u,ordinal_numbers) -> member(least(u,symmetrization_of(identity_relation)),inverse(identity_relation))*.
% 299.99/300.64  80111[7:MRR:80110.1,13039.0] || well_ordering(element_relation,ordinal_numbers) -> section(element_relation,singleton(least(element_relation,ordinal_numbers)),ordinal_numbers)*.
% 299.99/300.64  167592[14:Res:148858.1,164499.0] || subclass(singleton(identity_relation),inverse(subset_relation))* well_ordering(ordinal_numbers,complement(subset_relation)) -> .
% 299.99/300.64  191911[18:Res:148858.1,190433.0] || subclass(symmetrization_of(identity_relation),inverse(subset_relation))* well_ordering(ordinal_numbers,complement(subset_relation)) -> .
% 299.99/300.64  191928[18:Res:148858.1,190447.0] || subclass(inverse(identity_relation),inverse(subset_relation))* well_ordering(ordinal_numbers,complement(subset_relation)) -> .
% 299.99/300.64  167499[8:Res:8642.1,163154.0] || subclass(ordinal_numbers,symmetrization_of(identity_relation)) -> member(ordered_pair(u,v),inverse(identity_relation))*.
% 299.99/300.64  164135[8:SpL:163119.0,8846.0] || subclass(ordinal_numbers,symmetrization_of(identity_relation)) -> member(unordered_pair(u,v),inverse(identity_relation))*.
% 299.99/300.64  164132[8:SpL:163119.0,125985.0] || subclass(ordinal_numbers,symmetrization_of(identity_relation)) -> member(least(element_relation,omega),inverse(identity_relation))*.
% 299.99/300.64  163130[8:SpL:162584.0,8712.0] || subclass(ordinal_numbers,symmetrization_of(identity_relation)) member(omega,complement(inverse(identity_relation)))* -> .
% 299.99/300.64  163129[8:SpL:162584.0,50032.1] || member(complement(inverse(identity_relation)),subset_relation)* subclass(ordinal_numbers,symmetrization_of(identity_relation)) -> .
% 299.99/300.64  163128[8:SpL:162584.0,63019.1] || subclass(domain_relation,complement(inverse(identity_relation)))* subclass(ordinal_numbers,symmetrization_of(identity_relation)) -> .
% 299.99/300.64  193583[8:Rew:162584.0,193563.0] || equal(symmetrization_of(identity_relation),ordinal_numbers) -> equal(intersection(symmetrization_of(identity_relation),ordinal_numbers),ordinal_numbers)**.
% 299.99/300.64  194516[8:Rew:162584.0,194505.0] || subclass(ordinal_numbers,symmetrization_of(identity_relation)) -> subclass(singleton(singleton(u)),symmetrization_of(identity_relation))*.
% 299.99/300.64  194531[20:Res:194511.0,11.0] || subclass(symmetrization_of(identity_relation),singleton(identity_relation))* -> equal(symmetrization_of(identity_relation),singleton(identity_relation)).
% 299.99/300.64  195110[18:Res:190593.1,165357.1] || equal(u,inverse(identity_relation)) equal(complement(u),singleton(identity_relation))** -> .
% 299.99/300.64  195111[18:Res:190442.1,165357.1] || equal(u,symmetrization_of(identity_relation))* equal(complement(u),singleton(identity_relation))** -> .
% 299.99/300.64  195113[14:Res:165168.1,165357.1] || equal(u,singleton(identity_relation)) equal(complement(u),singleton(identity_relation))** -> .
% 299.99/300.64  195307[16:Rew:195224.0,193275.0] ||  -> equal(union(complement(singleton(identity_relation)),identity_relation),complement(intersection(singleton(identity_relation),ordinal_numbers)))**.
% 299.99/300.64  195416[16:Rew:195224.0,167587.1] || well_ordering(u,ordinal_numbers) -> member(least(u,singleton(identity_relation)),singleton(identity_relation))*.
% 299.99/300.64  195417[16:Rew:195224.0,163175.0] ||  -> subclass(symmetric_difference(singleton(identity_relation),complement(u)),union(complement(singleton(identity_relation)),u))*.
% 299.99/300.64  195418[16:Rew:195224.0,163194.0] ||  -> subclass(symmetric_difference(complement(u),singleton(identity_relation)),union(u,complement(singleton(identity_relation))))*.
% 299.99/300.64  196091[18:Res:190510.1,162901.0] || subclass(inverse(identity_relation),subset_relation)* equal(regular(symmetrization_of(identity_relation)),identity_relation) -> .
% 299.99/300.64  196092[18:Res:190510.1,162888.0] || subclass(inverse(identity_relation),subset_relation) subclass(regular(symmetrization_of(identity_relation)),identity_relation)* -> .
% 299.99/300.64  196096[18:Res:190510.1,3700.0] || subclass(inverse(identity_relation),singleton(u))* -> equal(regular(symmetrization_of(identity_relation)),u).
% 299.99/300.64  196162[18:Res:190593.1,190532.1] || equal(u,inverse(identity_relation)) equal(complement(u),symmetrization_of(identity_relation))* -> .
% 299.99/300.64  196163[18:Res:190442.1,190532.1] || equal(u,symmetrization_of(identity_relation)) equal(complement(u),symmetrization_of(identity_relation))* -> .
% 299.99/300.64  196164[18:Res:165168.1,190532.1] || equal(u,singleton(identity_relation)) equal(complement(u),symmetrization_of(identity_relation))* -> .
% 299.99/300.64  196252[18:Res:190593.1,190641.1] || equal(u,inverse(identity_relation)) equal(complement(u),inverse(identity_relation))** -> .
% 299.99/300.64  196253[18:Res:190442.1,190641.1] || equal(u,symmetrization_of(identity_relation))* equal(complement(u),inverse(identity_relation))** -> .
% 299.99/300.64  196254[18:Res:165168.1,190641.1] || equal(u,singleton(identity_relation)) equal(complement(u),inverse(identity_relation))** -> .
% 299.99/300.64  197465[21:SpR:196546.1,117066.0] ||  -> equal(singleton(flip(cross_product(u,ordinal_numbers))),identity_relation)** equal(inverse(u),identity_relation).
% 299.99/300.64  197469[21:SpR:196546.1,117142.0] ||  -> equal(singleton(restrict(element_relation,ordinal_numbers,u)),identity_relation)** equal(sum_class(u),identity_relation).
% 299.99/300.64  197931[21:SpR:15663.0,196554.1] || member(not_subclass_element(identity_relation,identity_relation),subset_relation)* -> equal(cantor(single_valued3(identity_relation)),identity_relation).
% 299.99/300.64  198486[21:Res:19525.1,197870.1] || well_ordering(u,ordinal_numbers) equal(rest_of(least(u,ordinal_numbers)),rest_relation)** -> .
% 299.99/300.64  198487[21:Res:133502.1,197870.1] || well_ordering(u,rest_relation) equal(rest_of(least(u,rest_relation)),rest_relation)** -> .
% 299.99/300.64  198488[21:Res:133495.1,197870.1] || well_ordering(u,ordinal_numbers) equal(rest_of(least(u,rest_relation)),rest_relation)** -> .
% 299.99/300.64  163624[5:Res:39298.1,157.0] || subclass(ordinal_numbers,complement(complement(union_of_range_map)))* -> equal(sum_class(range_of(u)),v)*.
% 299.99/300.64  160680[8:Rew:116239.0,67749.1] inductive(symmetric_difference(range_of(u),ordinal_numbers)) ||  -> member(identity_relation,complement(range_of(u)))*.
% 299.99/300.64  117047[8:Rew:116239.0,83710.0] || equal(range_of(u),domain_relation) subclass(domain_relation,complement(range_of(u)))* -> .
% 299.99/300.64  160699[8:Rew:116239.0,83662.0] || equal(range_of(u),domain_relation) -> member(ordered_pair(identity_relation,identity_relation),range_of(u))*.
% 299.99/300.64  177020[8:SpL:116239.0,161304.1] || subclass(rest_relation,rest_of(inverse(u)))* well_ordering(ordinal_numbers,range_of(u)) -> .
% 299.99/300.64  70004[5:SpR:43.0,39971.1] || equal(complement(rest_of(inverse(u))),ordinal_numbers)**+ -> subclass(range_of(u),v)*.
% 299.99/300.64  56504[5:SpL:43.0,56480.0] || member(inverse(u),range_of(u))* subclass(ordinal_numbers,complement(element_relation)) -> .
% 299.99/300.64  167400[8:SpR:160659.1,141389.0] || subclass(ordinal_numbers,range_of(u)) -> equal(symmetric_difference(ordinal_numbers,range_of(u)),identity_relation)**.
% 299.99/300.64  194977[15:Rew:162584.0,194950.0] || subclass(ordinal_numbers,symmetrization_of(identity_relation)) -> subclass(singleton(range_of(identity_relation)),symmetrization_of(identity_relation))*.
% 299.99/300.64  167622[7:SpR:140603.0,13311.1] || asymmetric(ordinal_numbers,ordinal_numbers) -> equal(image(inverse(ordinal_numbers),ordinal_numbers),range_of(identity_relation))**.
% 299.99/300.64  165555[15:Res:165526.1,898.0] || subclass(ordinal_numbers,restrict(u,v,w))* -> member(range_of(identity_relation),u).
% 299.99/300.64  191878[15:Res:165442.1,163154.0] || subclass(ordinal_numbers,symmetrization_of(identity_relation)) -> member(sum_class(range_of(identity_relation)),inverse(identity_relation))*.
% 299.99/300.64  191858[15:Res:165442.1,26.0] || subclass(ordinal_numbers,intersection(u,v))* -> member(sum_class(range_of(identity_relation)),v)*.
% 299.99/300.64  191848[15:Res:165442.1,28.1] || subclass(ordinal_numbers,complement(u)) member(sum_class(range_of(identity_relation)),u)* -> .
% 299.99/300.64  191851[15:Res:165442.1,151988.0] || subclass(ordinal_numbers,complement(complement(u))) -> member(sum_class(range_of(identity_relation)),u)*.
% 299.99/300.64  191859[15:Res:165442.1,25.0] || subclass(ordinal_numbers,intersection(u,v))* -> member(sum_class(range_of(identity_relation)),u)*.
% 299.99/300.64  81324[8:Res:16042.1,15565.1] || equal(sum_class(range_of(identity_relation)),identity_relation) subclass(domain_relation,complement(union_of_range_map))* -> .
% 299.99/300.64  81586[8:Res:10.1,81324.1] || equal(complement(union_of_range_map),domain_relation) equal(sum_class(range_of(identity_relation)),identity_relation)** -> .
% 299.99/300.64  82298[8:Res:81336.1,157.0] || subclass(domain_relation,complement(complement(union_of_range_map)))* -> equal(sum_class(range_of(identity_relation)),identity_relation).
% 299.99/300.64  82429[8:Res:10.1,82298.0] || equal(complement(complement(union_of_range_map)),domain_relation)** -> equal(sum_class(range_of(identity_relation)),identity_relation).
% 299.99/300.64  16042[8:MRR:16040.0,8658.0] || equal(sum_class(range_of(identity_relation)),identity_relation) -> member(ordered_pair(identity_relation,identity_relation),union_of_range_map)*.
% 299.99/300.64  166259[7:Res:130710.0,13082.1] inductive(complement(power_class(u))) ||  -> member(identity_relation,image(element_relation,complement(u)))*.
% 299.99/300.64  167608[14:SpL:59.0,167597.0] || well_ordering(ordinal_numbers,power_class(u)) -> member(identity_relation,image(element_relation,complement(u)))*.
% 299.99/300.64  144397[8:SpR:59.0,140613.0] ||  -> equal(symmetric_difference(ordinal_numbers,image(element_relation,complement(u))),intersection(power_class(u),ordinal_numbers))**.
% 299.99/300.64  159457[5:Obv:159435.0] ||  -> member(u,power_class(v)) subclass(singleton(u),image(element_relation,complement(v)))*.
% 299.99/300.64  79577[5:SpR:59.0,79560.1] ||  -> member(u,image(element_relation,complement(v)))* subclass(singleton(u),power_class(v)).
% 299.99/300.64  193476[8:SpR:162038.0,143160.0] ||  -> subclass(symmetric_difference(ordinal_numbers,image(element_relation,symmetrization_of(identity_relation))),power_class(complement(inverse(identity_relation))))*.
% 299.99/300.64  130711[5:SpR:189.0,130678.0] ||  -> subclass(complement(power_class(image(element_relation,complement(u)))),image(element_relation,power_class(u)))*.
% 299.99/300.64  164861[8:SpR:160491.0,130710.0] ||  -> subclass(complement(power_class(symmetric_difference(ordinal_numbers,u))),image(element_relation,union(u,identity_relation)))*.
% 299.99/300.64  141402[8:Rew:140613.0,118468.0] ||  -> equal(symmetric_difference(image(u,v),ordinal_numbers),symmetric_difference(ordinal_numbers,image(u,v)))**.
% 299.99/300.64  139658[5:SpR:19860.0,8649.0] ||  -> equal(image(cross_product(u,ordinal_numbers),v),image(cross_product(v,ordinal_numbers),u))*.
% 299.99/300.64  195335[16:Rew:195224.0,193312.0] ||  -> subclass(symmetric_difference(ordinal_numbers,image(element_relation,singleton(identity_relation))),power_class(complement(singleton(identity_relation))))*.
% 299.99/300.64  166175[7:Rew:59.0,166156.1,59.0,166156.0] ||  -> subclass(singleton(regular(power_class(u))),power_class(u))* equal(power_class(u),identity_relation).
% 299.99/300.64  146848[5:MRR:146823.0,8956.1] || member(u,ordinal_numbers) subclass(ordinal_numbers,complement(singleton(power_class(u))))* -> .
% 299.99/300.64  166761[5:SpL:59.0,166753.1] inductive(image(element_relation,complement(u))) || equal(power_class(u),omega)** -> .
% 299.99/300.64  96970[5:Rew:59.0,96961.0] || subclass(ordinal_numbers,power_class(u)) -> subclass(singleton(singleton(v)),power_class(u))*.
% 299.99/300.64  9932[5:SpL:59.0,9922.1] inductive(image(element_relation,complement(u))) || equal(power_class(u),ordinal_numbers)** -> .
% 299.99/300.64  197338[21:SpR:196545.0,6984.0] ||  -> equal(cantor(apply(choice,omega)),identity_relation)** equal(apply(choice,omega),identity_relation).
% 299.99/300.64  141401[8:Rew:140613.0,118534.0] ||  -> equal(symmetric_difference(apply(u,v),ordinal_numbers),symmetric_difference(ordinal_numbers,apply(u,v)))**.
% 299.99/300.64  175228[8:SpR:163366.0,141394.0] ||  -> equal(symmetric_difference(ordinal_add(u,v),ordinal_numbers),symmetric_difference(ordinal_numbers,ordinal_add(u,v)))**.
% 299.99/300.64  18511[5:SpR:159.0,18510.1] function(recursion(u,successor_relation,union_of_range_map)) ||  -> member(ordinal_add(u,v),ordinal_numbers)*.
% 299.99/300.64  37691[5:SoR:18511.0,75.1] one_to_one(recursion(u,successor_relation,union_of_range_map)) ||  -> member(ordinal_add(u,v),ordinal_numbers)*.
% 299.99/300.64  37692[5:SoR:18511.0,82.1] operation(recursion(u,successor_relation,union_of_range_map)) ||  -> member(ordinal_add(u,v),ordinal_numbers)*.
% 299.99/300.64  192424[8:SpR:188530.1,140613.0] || member(complement(u),ordinals_with_null_class_as_identity)* -> equal(symmetric_difference(ordinal_numbers,u),complement(u)).
% 299.99/300.64  41185[5:Res:62.1,41096.0] || member(ordered_pair(u,v),compose(w,x))* -> member(v,ordinal_numbers).
% 299.99/300.64  204186[18:Res:194549.1,162901.0] || subclass(symmetrization_of(identity_relation),subset_relation)* equal(regular(symmetrization_of(identity_relation)),identity_relation) -> .
% 299.99/300.64  204187[18:Res:194549.1,162888.0] || subclass(symmetrization_of(identity_relation),subset_relation) subclass(regular(symmetrization_of(identity_relation)),identity_relation)* -> .
% 299.99/300.64  204191[18:Res:194549.1,3700.0] || subclass(symmetrization_of(identity_relation),singleton(u))* -> equal(regular(symmetrization_of(identity_relation)),u).
% 299.99/300.64  204653[21:Res:196904.1,3700.0] || subclass(domain_relation,singleton(u))* -> equal(singleton(singleton(singleton(identity_relation))),u)*.
% 299.99/300.64  204682[21:Res:196904.1,3572.0] || subclass(domain_relation,compose_class(u)) -> equal(compose(u,singleton(identity_relation)),identity_relation)**.
% 299.99/300.64  205193[15:Res:195033.1,3700.0] || equal(complement(complement(singleton(u))),ordinal_numbers)** -> equal(range_of(identity_relation),u).
% 299.99/300.64  205520[22:Res:156922.1,205501.0] || member(singleton(identity_relation),inverse(subset_relation))* well_ordering(ordinal_numbers,complement(subset_relation)) -> .
% 299.99/300.64  205531[22:Res:69184.1,205501.0] || member(singleton(identity_relation),element_relation) well_ordering(ordinal_numbers,compose(element_relation,ordinal_numbers))* -> .
% 299.99/300.64  205553[22:MRR:205525.0,8655.0] || well_ordering(ordinal_numbers,union(u,v))* -> member(singleton(identity_relation),complement(u)).
% 299.99/300.64  205554[22:MRR:205526.0,8655.0] || well_ordering(ordinal_numbers,union(u,v))* -> member(singleton(identity_relation),complement(v)).
% 299.99/300.64  205576[22:Res:8665.1,202352.0] function(singleton(singleton(identity_relation))) ||  -> member(singleton(identity_relation),cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.64  132440[5:Res:8665.1,130942.0] function(ordered_pair(u,v)) || well_ordering(ordinal_numbers,cross_product(ordinal_numbers,ordinal_numbers))* -> .
% 299.99/300.64  132703[5:SoR:132440.0,75.1] one_to_one(ordered_pair(u,v)) || well_ordering(ordinal_numbers,cross_product(ordinal_numbers,ordinal_numbers))* -> .
% 299.99/300.64  205500[22:Res:8665.1,202348.0] function(singleton(singleton(identity_relation))) || well_ordering(ordinal_numbers,cross_product(ordinal_numbers,ordinal_numbers))* -> .
% 299.99/300.64  205771[22:SpR:162584.0,205578.1] ||  -> member(singleton(identity_relation),complement(inverse(identity_relation)))* member(singleton(identity_relation),symmetrization_of(identity_relation)).
% 299.99/300.64  206149[22:Res:205574.1,3700.0] || equal(singleton(u),singleton(singleton(identity_relation)))* -> equal(singleton(identity_relation),u).
% 299.99/300.64  206172[22:Res:205574.1,8843.1] || equal(u,singleton(singleton(identity_relation))) subclass(ordinal_numbers,complement(u))* -> .
% 299.99/300.64  206492[22:Res:205574.1,165628.1] || equal(u,singleton(singleton(identity_relation)))* equal(complement(u),ordinal_numbers)** -> .
% 299.99/300.64  206511[7:SpR:33.0,165794.1] ||  -> equal(integer_of(u),identity_relation) subclass(restrict(singleton(u),v,w),omega)*.
% 299.99/300.64  207268[14:SpL:155582.0,165368.0] || equal(symmetric_difference(ordinal_numbers,u),singleton(identity_relation)) -> member(identity_relation,complement(u))*.
% 299.99/300.64  207358[18:SpL:155582.0,190543.0] || equal(symmetric_difference(ordinal_numbers,u),symmetrization_of(identity_relation)) -> member(identity_relation,complement(u))*.
% 299.99/300.64  207477[18:SpL:155582.0,190652.0] || equal(symmetric_difference(ordinal_numbers,u),inverse(identity_relation)) -> member(identity_relation,complement(u))*.
% 299.99/300.64  207838[24:MRR:165435.2,207837.0] || subclass(range_of(identity_relation),identity_relation)* equal(cross_product(identity_relation,identity_relation),identity_relation) -> .
% 299.99/300.64  207943[24:Res:41203.1,207853.1] operation(least(element_relation,domain_relation)) || member(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers)* -> .
% 299.99/300.64  207966[24:Res:80082.1,207853.1] operation(least(element_relation,rest_relation)) || member(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers)* -> .
% 299.99/300.64  207967[24:Res:80198.1,207853.1] operation(least(element_relation,element_relation)) || member(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers)* -> .
% 299.99/300.64  208005[24:Rew:207947.1,197799.1] operation(regular(omega)) ||  -> equal(regular(identity_relation),identity_relation) connected(u,identity_relation)*.
% 299.99/300.64  208207[24:Res:207562.1,190641.1] operation(u) || equal(complement(ordered_pair(u,v)),inverse(identity_relation))** -> .
% 299.99/300.64  208208[24:Res:207562.1,190532.1] operation(u) || equal(complement(ordered_pair(u,v)),symmetrization_of(identity_relation))** -> .
% 299.99/300.64  208209[24:Res:207562.1,165357.1] operation(u) || equal(complement(ordered_pair(u,v)),singleton(identity_relation))** -> .
% 299.99/300.64  208554[15:SpL:155582.0,165538.0] || subclass(ordinal_numbers,symmetric_difference(ordinal_numbers,u)) -> member(range_of(identity_relation),complement(u))*.
% 299.99/300.64  208744[8:SpR:208708.1,141394.0] ||  -> equal(singleton(u),identity_relation) equal(symmetric_difference(ordinal_numbers,u),symmetric_difference(u,ordinal_numbers))*.
% 299.99/300.64  208752[8:SpR:208708.1,140613.0] ||  -> equal(singleton(complement(u)),identity_relation) equal(symmetric_difference(ordinal_numbers,u),complement(u))**.
% 299.99/300.64  208874[25:SpR:208820.0,2504.1] || subclass(ordered_pair(u,ordinal_numbers),v) -> member(unordered_pair(u,identity_relation),v)*.
% 299.99/300.64  208898[25:SpL:208820.0,2557.0] || member(singleton(singleton(identity_relation)),cross_product(u,v))* -> member(ordinal_numbers,v).
% 299.99/300.64  208958[25:SpL:208820.0,8979.0] || member(image(u,identity_relation),ordinal_numbers) -> member(apply(u,ordinal_numbers),ordinal_numbers)*.
% 299.99/300.64  208988[25:Rew:208887.0,160689.1] || section(u,identity_relation,v) -> equal(segment(u,v,ordinal_numbers),identity_relation)**.
% 299.99/300.64  209004[25:Rew:208820.0,208897.1] || member(singleton(singleton(identity_relation)),cross_product(u,v))* -> member(identity_relation,u).
% 299.99/300.64  209005[25:Rew:208820.0,208902.1] || member(singleton(singleton(identity_relation)),rest_of(u))* -> member(identity_relation,cantor(u)).
% 299.99/300.64  209024[25:MRR:209023.0,13039.0] || subclass(segment(u,v,ordinal_numbers),identity_relation)* -> section(u,identity_relation,v).
% 299.99/300.64  209323[25:SpL:208840.0,157.0] || member(singleton(singleton(identity_relation)),union_of_range_map)* -> equal(sum_class(range_of(identity_relation)),ordinal_numbers).
% 299.99/300.64  209452[25:Res:148858.1,209226.0] || subclass(ordered_pair(ordinal_numbers,u),inverse(subset_relation))* -> member(identity_relation,complement(subset_relation)).
% 299.99/300.64  209763[23:Res:8665.1,205615.0] function(complement(recursion_equation_functions(u))) || well_ordering(ordinal_numbers,cross_product(ordinal_numbers,ordinal_numbers))* -> .
% 299.99/300.64  209774[23:Res:8665.1,205619.0] function(complement(recursion_equation_functions(u))) ||  -> member(singleton(identity_relation),cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.64  209906[15:SpL:33.0,208474.0] || equal(restrict(u,v,w),ordinal_numbers)** -> member(range_of(identity_relation),u).
% 299.99/300.64  210070[15:SpL:155582.0,208593.0] || equal(symmetric_difference(ordinal_numbers,u),ordinal_numbers) -> member(range_of(identity_relation),complement(u))*.
% 299.99/300.64  210200[25:MRR:210197.1,8666.0] || equal(u,ordered_pair(v,ordinal_numbers)) -> member(unordered_pair(v,identity_relation),u)*.
% 299.99/300.64  210318[8:Rew:162584.0,210269.0] || member(u,symmetrization_of(identity_relation)) -> member(u,intersection(symmetrization_of(identity_relation),ordinal_numbers))*.
% 299.99/300.64  210319[16:Rew:195239.0,210270.0] || member(u,singleton(identity_relation)) -> member(u,intersection(singleton(identity_relation),ordinal_numbers))*.
% 299.99/300.64  210422[24:SpR:207565.1,210404.0] operation(u) ||  -> member(identity_relation,successor(u)) member(identity_relation,complement(u))*.
% 299.99/300.64  210440[14:Rew:59.0,210429.1,66036.0,210429.0] ||  -> member(identity_relation,complement(intersection(power_class(u),ordinal_numbers)))* member(identity_relation,power_class(u)).
% 299.99/300.64  210469[15:Res:209921.1,143226.0] || equal(symmetric_difference(ordinal_numbers,u),ordinal_numbers) member(range_of(identity_relation),u)* -> .
% 299.99/300.64  210471[15:Res:165526.1,143226.0] || subclass(ordinal_numbers,symmetric_difference(ordinal_numbers,u))* member(range_of(identity_relation),u) -> .
% 299.99/300.64  210491[5:Res:143198.1,143226.0] || equal(symmetric_difference(ordinal_numbers,u),ordinal_numbers) member(singleton(v),u)* -> .
% 299.99/300.64  210493[5:Res:8645.1,143226.0] || subclass(ordinal_numbers,symmetric_difference(ordinal_numbers,u))* member(singleton(v),u)* -> .
% 299.99/300.64  210508[18:Res:190593.1,143226.0] || equal(symmetric_difference(ordinal_numbers,u),inverse(identity_relation))** member(identity_relation,u) -> .
% 299.99/300.64  210509[18:Res:190442.1,143226.0] || equal(symmetric_difference(ordinal_numbers,u),symmetrization_of(identity_relation))** member(identity_relation,u) -> .
% 299.99/300.64  210510[14:Res:165168.1,143226.0] || equal(symmetric_difference(ordinal_numbers,u),singleton(identity_relation))** member(identity_relation,u) -> .
% 299.99/300.64  210559[8:Res:8703.1,210517.1] || member(u,ordinal_numbers) equal(complement(unordered_pair(u,v)),ordinal_numbers)** -> .
% 299.99/300.64  210560[8:Res:8704.1,210517.1] || member(u,ordinal_numbers) equal(complement(unordered_pair(v,u)),ordinal_numbers)** -> .
% 299.99/300.64  210691[8:Res:2504.1,210517.1] || subclass(ordered_pair(u,v),w)* equal(complement(w),ordinal_numbers) -> .
% 299.99/300.64  210751[8:Rew:160491.0,210554.1] || member(u,complement(v))* equal(union(v,identity_relation),ordinal_numbers) -> .
% 299.99/300.64  210788[8:SpL:160491.0,210578.0] || equal(union(u,identity_relation),ordinal_numbers) -> equal(symmetric_difference(ordinal_numbers,u),identity_relation)**.
% 299.99/300.64  210791[8:SpL:59.0,210578.0] || equal(power_class(u),ordinal_numbers) -> equal(image(element_relation,complement(u)),identity_relation)**.
% 299.99/300.64  211443[8:Rew:30.0,211290.0] || equal(union(u,v),ordinal_numbers) -> subclass(w,union(u,v))*.
% 299.99/300.64  211465[8:SoR:130722.0,211442.1] || equal(complement(complement(omega)),ordinal_numbers)** -> equal(complement(complement(omega)),omega).
% 299.99/300.64  211468[8:SoR:166265.0,211442.1] || equal(complement(complement(inverse(subset_relation))),ordinal_numbers)** -> member(identity_relation,complement(subset_relation)).
% 299.99/300.64  211845[11:Rew:66036.0,211731.1,80200.0,211731.1] || equal(symmetrization_of(identity_relation),ordinal_numbers) -> subclass(ordinal_numbers,image(element_relation,symmetrization_of(identity_relation)))*.
% 299.99/300.64  212128[8:Rew:17401.0,212010.1] || equal(symmetrization_of(identity_relation),ordinal_numbers) -> equal(symmetric_difference(ordinal_numbers,symmetrization_of(identity_relation)),identity_relation)**.
% 299.99/300.64  212141[8:Rew:66036.0,211994.1,17401.0,211994.1] || equal(symmetrization_of(identity_relation),ordinal_numbers) -> equal(union(symmetrization_of(identity_relation),u),ordinal_numbers)**.
% 299.99/300.64  212150[8:Rew:66036.0,212028.1,14565.0,212028.1] || equal(symmetrization_of(identity_relation),ordinal_numbers) -> equal(union(u,symmetrization_of(identity_relation)),ordinal_numbers)**.
% 299.99/300.64  212162[8:Rew:17401.0,212007.1] || equal(symmetrization_of(identity_relation),ordinal_numbers) -> subclass(complement(successor(symmetrization_of(identity_relation))),identity_relation)*.
% 299.99/300.64  212163[8:Rew:17401.0,212008.1] || equal(symmetrization_of(identity_relation),ordinal_numbers) -> subclass(complement(symmetrization_of(symmetrization_of(identity_relation))),identity_relation)*.
% 299.99/300.64  212334[8:Res:133837.1,210577.0] || well_ordering(ordinal_numbers,complement(subset_relation))* equal(complement(singleton(u)),ordinal_numbers)** -> .
% 299.99/300.64  212659[8:Rew:17401.0,212485.1] || equal(complement(u),ordinal_numbers) -> equal(symmetric_difference(ordinal_numbers,complement(u)),identity_relation)**.
% 299.99/300.64  212675[8:Rew:66036.0,212468.1,17401.0,212468.1] || equal(complement(u),ordinal_numbers) -> equal(union(complement(u),v),ordinal_numbers)**.
% 299.99/300.64  212686[8:Rew:66036.0,212504.1,14565.0,212504.1] || equal(complement(u),ordinal_numbers) -> equal(union(v,complement(u)),ordinal_numbers)**.
% 299.99/300.64  212698[8:Rew:17401.0,212482.1] || equal(complement(u),ordinal_numbers) -> subclass(complement(successor(complement(u))),identity_relation)*.
% 299.99/300.64  212699[8:Rew:17401.0,212483.1] || equal(complement(u),ordinal_numbers) -> subclass(complement(symmetrization_of(complement(u))),identity_relation)*.
% 299.99/300.64  212888[8:Rew:66036.0,212768.1] || equal(power_class(u),ordinal_numbers) -> equal(intersection(power_class(u),ordinal_numbers),ordinal_numbers)**.
% 299.99/300.64  212891[8:Rew:17401.0,212780.1] || equal(power_class(u),ordinal_numbers) -> equal(symmetric_difference(ordinal_numbers,power_class(u)),identity_relation)**.
% 299.99/300.64  212904[8:Rew:66036.0,212763.1,17401.0,212763.1] || equal(power_class(u),ordinal_numbers) -> equal(union(power_class(u),v),ordinal_numbers)**.
% 299.99/300.64  212915[8:Rew:66036.0,212799.1,14565.0,212799.1] || equal(power_class(u),ordinal_numbers) -> equal(union(v,power_class(u)),ordinal_numbers)**.
% 299.99/300.64  212924[8:Rew:17401.0,212777.1] || equal(power_class(u),ordinal_numbers) -> subclass(complement(successor(power_class(u))),identity_relation)*.
% 299.99/300.64  212925[8:Rew:17401.0,212778.1] || equal(power_class(u),ordinal_numbers) -> subclass(complement(symmetrization_of(power_class(u))),identity_relation)*.
% 299.99/300.64  213059[8:SpR:210579.1,32.0] || equal(complement(u),ordinal_numbers) -> equal(restrict(u,v,w),identity_relation)**.
% 299.99/300.64  213079[8:SpR:210579.1,155582.0] || equal(complement(complement(u)),ordinal_numbers) -> equal(symmetric_difference(ordinal_numbers,u),identity_relation)**.
% 299.99/300.64  213096[8:SpR:210579.1,132293.0] || equal(complement(complement(u)),ordinal_numbers) -> subclass(complement(successor(u)),identity_relation)*.
% 299.99/300.64  213097[8:SpR:210579.1,132294.0] || equal(complement(complement(u)),ordinal_numbers) -> subclass(complement(symmetrization_of(u)),identity_relation)*.
% 299.99/300.64  213184[8:Rew:66036.0,213076.1] || equal(complement(complement(u)),ordinal_numbers) -> equal(union(u,v),ordinal_numbers)**.
% 299.99/300.64  213368[8:Rew:66036.0,213252.1] || equal(complement(complement(u)),ordinal_numbers) -> equal(union(v,u),ordinal_numbers)**.
% 299.99/300.64  213617[5:SpR:32.0,151877.0] ||  -> subclass(restrict(singleton(u),v,w),complement(recursion_equation_functions(x)))* function(u).
% 299.99/300.64  214070[8:Res:144409.1,152274.0] || equal(symmetric_difference(ordinal_numbers,singleton(omega)),ordinal_numbers)** -> subclass(singleton(omega),u)*.
% 299.99/300.64  214316[25:MRR:214308.1,13039.0] || equal(segment(u,v,ordinal_numbers),identity_relation)** -> section(u,identity_relation,v).
% 299.99/300.64  214914[0:SpR:33.0,151501.1] || member(u,v) -> subclass(restrict(singleton(u),w,x),v)*.
% 299.99/300.64  214972[5:SpR:33.0,151502.1] ||  -> member(u,v) subclass(restrict(singleton(u),w,x),complement(v))*.
% 299.99/300.64  215361[8:SpR:162584.0,215271.1] || subclass(complement(inverse(identity_relation)),identity_relation)* -> equal(complement(symmetrization_of(identity_relation)),identity_relation).
% 299.99/300.64  215604[8:SpR:160491.0,215487.1] || subclass(symmetric_difference(ordinal_numbers,u),identity_relation)* -> subclass(ordinal_numbers,union(u,identity_relation)).
% 299.99/300.64  215608[8:SpR:59.0,215487.1] || subclass(image(element_relation,complement(u)),identity_relation)* -> subclass(ordinal_numbers,power_class(u)).
% 299.99/300.64  216029[8:SpL:50855.1,215647.0] || member(singleton(u),subset_relation) subclass(unordered_pair(u,v),identity_relation)* -> .
% 299.99/300.64  216056[8:SpL:50855.1,215648.0] || member(singleton(u),subset_relation) subclass(unordered_pair(v,u),identity_relation)* -> .
% 299.99/300.64  216067[14:MRR:165389.1,216061.0] || equal(ordered_pair(u,v),singleton(identity_relation))** -> equal(singleton(u),identity_relation).
% 299.99/300.64  216068[18:MRR:190562.1,216061.0] || equal(ordered_pair(u,v),symmetrization_of(identity_relation))** -> equal(singleton(u),identity_relation).
% 299.99/300.64  216069[18:MRR:190671.1,216061.0] || equal(ordered_pair(u,v),inverse(identity_relation))** -> equal(singleton(u),identity_relation).
% 299.99/300.64  216123[8:SpL:50855.1,216036.0] || member(singleton(u),subset_relation)* equal(unordered_pair(u,v),identity_relation)** -> .
% 299.99/300.64  216130[8:SpL:50855.1,216061.0] || member(singleton(u),subset_relation)* equal(unordered_pair(v,u),identity_relation)** -> .
% 299.99/300.64  216230[8:SpL:189.0,216213.0] || equal(power_class(image(element_relation,complement(u))),image(element_relation,power_class(u)))** -> .
% 299.99/300.64  216275[14:Res:165177.0,215631.1] || subclass(symmetric_difference(ordinal_numbers,u),identity_relation) -> member(identity_relation,union(u,identity_relation))*.
% 299.99/300.64  216278[14:Res:165178.0,215631.1] || subclass(image(element_relation,complement(u)),identity_relation)* -> member(identity_relation,power_class(u)).
% 299.99/300.64  216557[8:MRR:216540.0,8652.0] || subclass(image(element_relation,complement(u)),identity_relation)* -> member(omega,power_class(u)).
% 299.99/300.64  216580[8:SpL:160491.0,215660.0] || subclass(union(u,identity_relation),identity_relation) -> member(identity_relation,symmetric_difference(ordinal_numbers,u))*.
% 299.99/300.64  216584[8:SpL:59.0,215660.0] || subclass(power_class(u),identity_relation) -> member(identity_relation,image(element_relation,complement(u)))*.
% 299.99/300.64  216600[8:SpL:160491.0,215661.0] || subclass(union(u,identity_relation),identity_relation) -> member(omega,symmetric_difference(ordinal_numbers,u))*.
% 299.99/300.64  216604[8:SpL:59.0,215661.0] || subclass(power_class(u),identity_relation) -> member(omega,image(element_relation,complement(u)))*.
% 299.99/300.64  216711[8:SpR:216188.1,160491.0] || equal(symmetric_difference(ordinal_numbers,u),identity_relation)** -> equal(union(u,identity_relation),ordinal_numbers).
% 299.99/300.64  216779[8:SpR:216188.1,59.0] || equal(image(element_relation,complement(u)),identity_relation)** -> equal(power_class(u),ordinal_numbers).
% 299.99/300.64  217164[8:Rew:140603.0,216627.1] || equal(identity_relation,u) -> equal(union(u,v),complement(complement(v)))**.
% 299.99/300.64  217169[8:Rew:140603.0,216642.1] || equal(identity_relation,u) -> subclass(complement(successor(u)),complement(singleton(u)))*.
% 299.99/300.64  217170[8:Rew:140603.0,216643.1] || equal(identity_relation,u) -> subclass(complement(symmetrization_of(u)),complement(inverse(u)))*.
% 299.99/300.64  217174[8:Rew:160491.0,216669.1,140613.0,216669.1] || equal(identity_relation,u) -> equal(union(v,identity_relation),union(v,u))*.
% 299.99/300.64  217328[8:SpL:160491.0,216227.0] || equal(image(element_relation,union(u,identity_relation)),power_class(symmetric_difference(ordinal_numbers,u)))** -> .
% 299.99/300.64  217422[8:Res:216591.1,898.0] || equal(complement(restrict(u,v,w)),identity_relation)** -> member(identity_relation,u).
% 299.99/300.64  217442[18:Res:216591.1,190641.1] || equal(complement(u),identity_relation) equal(complement(u),inverse(identity_relation))** -> .
% 299.99/300.64  217444[14:Res:216591.1,165357.1] || equal(complement(u),identity_relation) equal(complement(u),singleton(identity_relation))** -> .
% 299.99/300.64  217612[8:Res:216611.1,152274.0] || equal(complement(complement(singleton(omega))),identity_relation)** -> subclass(singleton(omega),u)*.
% 299.99/300.64  217644[8:Res:216611.1,898.0] || equal(complement(restrict(u,v,w)),identity_relation)** -> member(omega,u).
% 299.99/300.64  217694[8:Res:216691.1,155244.0] || equal(complement(complement(u)),identity_relation) -> equal(symmetric_difference(ordinal_numbers,u),ordinal_numbers)**.
% 299.99/300.64  217706[8:Res:216691.1,50044.1] || equal(complement(complement(singleton(u))),identity_relation)** member(u,subset_relation) -> .
% 299.99/300.64  217721[15:Res:216691.1,165530.0] || equal(complement(complement(complement(u))),identity_relation)** -> member(range_of(identity_relation),u).
% 299.99/300.64  217724[8:Res:216691.1,9496.0] || equal(complement(complement(complement(u))),identity_relation)** -> member(singleton(v),u)*.
% 299.99/300.64  217728[8:Res:216691.1,94700.0] || equal(complement(complement(complement(rest_relation))),identity_relation)** -> equal(rest_of(u),v)*.
% 299.99/300.64  217729[8:Res:216691.1,116159.0] || equal(complement(complement(complement(domain_relation))),identity_relation)** -> equal(cantor(u),v)*.
% 299.99/300.64  217735[15:Res:216691.1,165538.0] || equal(complement(intersection(u,v)),identity_relation)** -> member(range_of(identity_relation),u).
% 299.99/300.64  217736[15:Res:216691.1,165537.0] || equal(complement(intersection(u,v)),identity_relation)** -> member(range_of(identity_relation),v).
% 299.99/300.64  217743[8:Res:216691.1,8848.0] || equal(complement(intersection(u,v)),identity_relation)** -> member(singleton(w),u)*.
% 299.99/300.64  217744[8:Res:216691.1,8849.0] || equal(complement(intersection(u,v)),identity_relation)** -> member(singleton(w),v)*.
% 299.99/300.64  217766[8:Res:216691.1,176864.0] || equal(complement(inverse(subset_relation)),identity_relation) -> equal(symmetric_difference(ordinal_numbers,subset_relation),ordinal_numbers)**.
% 299.99/300.64  217776[8:Res:216691.1,8908.0] || equal(complement(compose_class(u)),identity_relation) -> equal(compose(u,v),w)*.
% 299.99/300.64  217801[8:Res:216691.1,163499.0] || equal(complement(complement(complement(successor_relation))),identity_relation)** -> equal(successor(u),v)*.
% 299.99/300.64  217885[20:Res:217871.0,5.0] || subclass(ordinal_numbers,u) -> member(regular(complement(complement(symmetrization_of(identity_relation)))),u)*.
% 299.99/300.64  217940[7:Res:10.1,17315.0] || equal(recursion_equation_functions(u),v)* -> equal(v,identity_relation) function(regular(v))*.
% 299.99/300.64  218040[8:SpL:160491.0,217692.0] || equal(union(u,identity_relation),identity_relation) -> equal(symmetric_difference(ordinal_numbers,u),ordinal_numbers)**.
% 299.99/300.64  218044[8:SpL:59.0,217692.0] || equal(power_class(u),identity_relation) -> equal(image(element_relation,complement(u)),ordinal_numbers)**.
% 299.99/300.64  218132[8:Res:140864.1,217144.1] || member(u,complement(v))* equal(symmetric_difference(ordinal_numbers,v),identity_relation) -> .
% 299.99/300.64  218188[8:Res:2503.2,217144.1] || subclass(u,v)* equal(identity_relation,v) -> subclass(u,w)*.
% 299.99/300.64  218192[8:Res:13227.2,217144.1] || subclass(u,v)* equal(identity_relation,v) -> equal(u,identity_relation).
% 299.99/300.64  219014[8:SpR:215491.1,141394.0] || subclass(intersection(u,ordinal_numbers),identity_relation)* -> equal(symmetric_difference(u,ordinal_numbers),ordinal_numbers).
% 299.99/300.64  219089[8:Res:163112.0,219073.1] || subclass(complement(inverse(identity_relation)),identity_relation)* -> subclass(singleton(u),symmetrization_of(identity_relation))*.
% 299.99/300.64  219093[8:Res:140864.1,219073.1] || member(u,complement(v))* subclass(symmetric_difference(ordinal_numbers,v),identity_relation)* -> .
% 299.99/300.64  219149[8:Res:2503.2,219073.1] || subclass(u,v)* subclass(v,identity_relation)* -> subclass(u,w)*.
% 299.99/300.64  219153[8:Res:13227.2,219073.1] || subclass(u,v)* subclass(v,identity_relation)* -> equal(u,identity_relation).
% 299.99/300.64  219303[15:Res:215659.1,28.1] || subclass(complement(complement(u)),identity_relation)* member(range_of(identity_relation),u) -> .
% 299.99/300.64  219306[15:Res:215659.1,151988.0] || subclass(complement(complement(complement(u))),identity_relation)* -> member(range_of(identity_relation),u).
% 299.99/300.64  219315[15:Res:215659.1,26.0] || subclass(complement(intersection(u,v)),identity_relation)* -> member(range_of(identity_relation),v).
% 299.99/300.64  219316[15:Res:215659.1,25.0] || subclass(complement(intersection(u,v)),identity_relation)* -> member(range_of(identity_relation),u).
% 299.99/300.64  219335[15:Res:215659.1,14679.1] || subclass(complement(inverse(subset_relation)),identity_relation)* member(range_of(identity_relation),subset_relation) -> .
% 299.99/300.64  219340[15:Res:215659.1,163154.0] || subclass(complement(symmetrization_of(identity_relation)),identity_relation) -> member(range_of(identity_relation),inverse(identity_relation))*.
% 299.99/300.64  219342[15:Res:215659.1,161.0] || subclass(complement(omega),identity_relation)* -> equal(integer_of(range_of(identity_relation)),range_of(identity_relation)).
% 299.99/300.64  219365[15:Rew:160491.0,219323.0] || subclass(union(u,identity_relation),identity_relation) -> member(range_of(identity_relation),complement(u))*.
% 299.99/300.64  219821[8:MRR:219781.2,14676.0] || subclass(ordinal_numbers,complement(u)) member(v,union(u,identity_relation))* -> .
% 299.99/300.64  219830[15:Res:217197.1,28.1] || equal(complement(complement(u)),identity_relation) member(range_of(identity_relation),u)* -> .
% 299.99/300.64  219869[15:Res:217197.1,163154.0] || equal(complement(symmetrization_of(identity_relation)),identity_relation) -> member(range_of(identity_relation),inverse(identity_relation))*.
% 299.99/300.64  219893[15:Rew:160491.0,219851.0] || equal(union(u,identity_relation),identity_relation) -> member(range_of(identity_relation),complement(u))*.
% 299.99/300.64  219895[15:Rew:59.0,219878.0] || equal(power_class(u),identity_relation) member(range_of(identity_relation),power_class(u))* -> .
% 299.99/300.64  219950[8:Res:19525.1,217200.1] || well_ordering(u,ordinal_numbers) equal(singleton(least(u,ordinal_numbers)),identity_relation)** -> .
% 299.99/300.64  219951[8:Res:133502.1,217200.1] || well_ordering(u,rest_relation) equal(singleton(least(u,rest_relation)),identity_relation)** -> .
% 299.99/300.64  219952[8:Res:133495.1,217200.1] || well_ordering(u,ordinal_numbers) equal(singleton(least(u,rest_relation)),identity_relation)** -> .
% 299.99/300.64  220013[8:Res:140864.1,160772.0] || member(u,complement(v)) member(u,union(v,identity_relation))* -> .
% 299.99/300.64  220074[8:Res:13056.1,160772.0] inductive(symmetric_difference(ordinal_numbers,u)) || member(identity_relation,union(u,identity_relation))* -> .
% 299.99/300.64  220289[7:Res:55.1,13243.0] inductive(singleton(u)) ||  -> equal(integer_of(v),identity_relation)** equal(v,u)*.
% 299.99/300.64  220321[24:SpR:219058.1,207565.1] operation(u) || subclass(u,identity_relation)* -> equal(successor(u),identity_relation).
% 299.99/300.64  220450[21:Res:196656.1,149.0] || subclass(domain_relation,flip(rest_relation)) -> equal(rest_of(ordered_pair(u,v)),identity_relation)**.
% 299.99/300.64  220461[21:Res:196656.1,49.0] || subclass(domain_relation,flip(successor_relation)) -> equal(successor(ordered_pair(u,v)),identity_relation)**.
% 299.99/300.64  220552[21:Res:196657.1,149.0] || subclass(domain_relation,rotate(rest_relation)) -> equal(rest_of(ordered_pair(u,identity_relation)),v)*.
% 299.99/300.64  220563[21:Res:196657.1,49.0] || subclass(domain_relation,rotate(successor_relation)) -> equal(successor(ordered_pair(u,identity_relation)),v)*.
% 299.99/300.64  220690[7:MRR:220673.0,8655.0] ||  -> equal(sum_class(singleton(u)),identity_relation) equal(regular(sum_class(singleton(u))),u)**.
% 299.99/300.64  220712[15:Res:215659.1,219203.0] || subclass(complement(rest_of(range_of(identity_relation))),identity_relation)* subclass(element_relation,identity_relation) -> .
% 299.99/300.64  220722[8:Res:143222.1,219203.0] || equal(rest_of(least(element_relation,omega)),omega)** subclass(element_relation,identity_relation) -> .
% 299.99/300.64  220727[8:Res:125725.1,219203.0] || subclass(omega,rest_of(least(element_relation,omega)))* subclass(element_relation,identity_relation) -> .
% 299.99/300.64  221263[8:Res:215662.1,28.1] || subclass(complement(complement(u)),identity_relation)* member(singleton(v),u)* -> .
% 299.99/300.64  221266[8:Res:215662.1,151988.0] || subclass(complement(complement(complement(u))),identity_relation)* -> member(singleton(v),u)*.
% 299.99/300.64  221275[8:Res:215662.1,26.0] || subclass(complement(intersection(u,v)),identity_relation)* -> member(singleton(w),v)*.
% 299.99/300.64  221276[8:Res:215662.1,25.0] || subclass(complement(intersection(u,v)),identity_relation)* -> member(singleton(w),u)*.
% 299.99/300.64  221298[8:Res:215662.1,14679.1] || subclass(complement(inverse(subset_relation)),identity_relation)* member(singleton(u),subset_relation)* -> .
% 299.99/300.64  221301[8:Res:215662.1,219203.0] || subclass(complement(rest_of(singleton(u))),identity_relation)* subclass(element_relation,identity_relation) -> .
% 299.99/300.64  221305[8:Res:215662.1,163154.0] || subclass(complement(symmetrization_of(identity_relation)),identity_relation) -> member(singleton(u),inverse(identity_relation))*.
% 299.99/300.64  221307[8:Res:215662.1,161.0] || subclass(complement(omega),identity_relation)* -> equal(integer_of(singleton(u)),singleton(u))**.
% 299.99/300.64  221358[8:Rew:160491.0,221285.0] || subclass(union(u,identity_relation),identity_relation) -> member(singleton(v),complement(u))*.
% 299.99/300.64  221520[8:Res:217198.1,28.1] || equal(complement(complement(u)),identity_relation) member(singleton(v),u)* -> .
% 299.99/300.64  221562[8:Res:217198.1,163154.0] || equal(complement(symmetrization_of(identity_relation)),identity_relation) -> member(singleton(u),inverse(identity_relation))*.
% 299.99/300.64  221613[8:Rew:160491.0,221542.0] || equal(union(u,identity_relation),identity_relation) -> member(singleton(v),complement(u))*.
% 299.99/300.64  221616[8:Rew:59.0,221571.0] || equal(power_class(u),identity_relation) member(singleton(v),power_class(u))* -> .
% 299.99/300.64  221808[8:Rew:217164.1,221807.1] || equal(identity_relation,u) -> equal(symmetric_difference(u,v),complement(complement(v)))**.
% 299.99/300.64  221817[8:Rew:221808.1,221816.1] || equal(identity_relation,u) -> equal(complement(complement(inverse(u))),symmetrization_of(u))**.
% 299.99/300.64  221819[8:Rew:221808.1,221818.1] || equal(identity_relation,u) -> equal(complement(complement(singleton(u))),successor(u))**.
% 299.99/300.64  221882[8:SpR:218191.1,163.0] || equal(union(u,v),identity_relation) -> equal(symmetric_difference(u,v),identity_relation)**.
% 299.99/300.64  221883[8:SpR:218191.1,3596.0] || equal(successor(u),identity_relation) -> equal(symmetric_difference(u,singleton(u)),identity_relation)**.
% 299.99/300.64  221884[8:SpR:218191.1,3597.0] || equal(symmetrization_of(u),identity_relation) -> equal(symmetric_difference(u,inverse(u)),identity_relation)**.
% 299.99/300.64  221901[8:SpR:218191.1,132294.0] || equal(complement(inverse(u)),identity_relation) -> subclass(complement(symmetrization_of(u)),identity_relation)*.
% 299.99/300.64  222023[8:Rew:140603.0,221844.1,66036.0,221844.1] || equal(identity_relation,u) -> equal(symmetric_difference(v,u),union(v,u))**.
% 299.99/300.64  222032[8:Rew:217174.1,222031.1,222023.1,222031.1] || equal(inverse(u),identity_relation) -> equal(union(u,identity_relation),symmetrization_of(u))**.
% 299.99/300.64  222034[8:Rew:217174.1,222033.1,222023.1,222033.1] || equal(singleton(u),identity_relation) -> equal(union(u,identity_relation),successor(u))**.
% 299.99/300.64  222225[8:Rew:140603.0,222057.1,66036.0,222057.1] || subclass(u,identity_relation) -> equal(symmetric_difference(u,v),union(u,v))**.
% 299.99/300.64  222355[8:SpR:219152.1,163.0] || subclass(union(u,v),identity_relation)* -> equal(symmetric_difference(u,v),identity_relation).
% 299.99/300.64  222356[8:SpR:219152.1,3596.0] || subclass(successor(u),identity_relation) -> equal(symmetric_difference(u,singleton(u)),identity_relation)**.
% 299.99/300.64  222357[8:SpR:219152.1,3597.0] || subclass(symmetrization_of(u),identity_relation) -> equal(symmetric_difference(u,inverse(u)),identity_relation)**.
% 299.99/300.64  222373[8:SpR:219152.1,132293.0] || subclass(complement(singleton(u)),identity_relation) -> subclass(complement(successor(u)),identity_relation)*.
% 299.99/300.64  222374[8:SpR:219152.1,132294.0] || subclass(complement(inverse(u)),identity_relation) -> subclass(complement(symmetrization_of(u)),identity_relation)*.
% 299.99/300.64  222481[8:Rew:140603.0,222316.1,66036.0,222316.1] || subclass(u,identity_relation) -> equal(symmetric_difference(v,u),union(v,u))**.
% 299.99/300.64  222687[5:Res:8655.0,31610.0] || subclass(rest_relation,successor_relation) -> equal(rest_of(singleton(u)),successor(singleton(u)))**.
% 299.99/300.64  222700[15:Res:165460.0,31610.0] || subclass(rest_relation,successor_relation) -> equal(rest_of(range_of(identity_relation)),successor(range_of(identity_relation)))**.
% 299.99/300.64  222897[18:MRR:222893.2,190496.0] || subclass(inverse(identity_relation),subset_relation) subclass(symmetrization_of(identity_relation),inverse(subset_relation))* -> .
% 299.99/300.64  223008[8:Res:215662.1,974.0] || subclass(complement(union_of_range_map),identity_relation) -> equal(sum_class(range_of(singleton(u))),u)**.
% 299.99/300.65  223012[5:Res:133837.1,974.0] || well_ordering(ordinal_numbers,complement(union_of_range_map)) -> equal(sum_class(range_of(singleton(u))),u)**.
% 299.99/300.65  223351[21:MRR:223293.1,165431.0] || subclass(rest_relation,domain_relation) -> member(ordered_pair(sum_class(range_of(identity_relation)),identity_relation),rest_relation)*.
% 299.99/300.65  223417[21:MRR:223361.1,190509.0] || subclass(rest_relation,domain_relation) -> member(ordered_pair(regular(symmetrization_of(identity_relation)),identity_relation),rest_relation)*.
% 299.99/300.65  223548[21:MRR:223495.1,125724.0] || subclass(rest_relation,domain_relation) -> member(ordered_pair(least(element_relation,omega),identity_relation),rest_relation)*.
% 299.99/300.65  224377[10:SpR:223660.1,962.0] || subclass(element_relation,identity_relation) -> member(identity_relation,ordered_pair(cross_product(ordinal_numbers,ordinal_numbers),u))*.
% 299.99/300.65  224602[25:MRR:224601.2,162904.0] || subclass(element_relation,identity_relation) member(singleton(singleton(identity_relation)),compose_class(u))* -> .
% 299.99/300.65  224608[25:MRR:224607.2,162904.0] || subclass(element_relation,identity_relation) member(singleton(singleton(identity_relation)),rest_of(u))* -> .
% 299.99/300.65  224711[21:Res:18819.1,194371.0] || member(ordered_pair(u,v),subset_relation)* member(v,cantor(u)) -> .
% 299.99/300.65  224736[26:Res:224684.1,66086.1] || subclass(omega,complement(compose(element_relation,ordinal_numbers)))* member(identity_relation,element_relation) -> .
% 299.99/300.65  224744[26:Res:224684.1,5.0] || subclass(omega,u)* subclass(u,v)* -> member(identity_relation,v)*.
% 299.99/300.65  224749[26:Res:224684.1,3617.0] || subclass(omega,symmetric_difference(u,v)) -> member(identity_relation,union(u,v))*.
% 299.99/300.65  224750[26:Res:224684.1,19559.0] || subclass(omega,symmetric_difference(u,singleton(u)))* -> member(identity_relation,successor(u)).
% 299.99/300.65  224751[26:Res:224684.1,19676.0] || subclass(omega,symmetric_difference(u,inverse(u)))* -> member(identity_relation,symmetrization_of(u)).
% 299.99/300.65  224985[26:SpL:117066.0,224842.1] operation(flip(cross_product(u,ordinal_numbers))) || subclass(omega,inverse(u))* -> .
% 299.99/300.65  224986[26:SpL:117142.0,224842.1] operation(restrict(element_relation,ordinal_numbers,u)) || subclass(omega,sum_class(u))* -> .
% 299.99/300.65  225017[26:SpL:117066.0,224910.1] operation(flip(cross_product(u,ordinal_numbers))) || equal(inverse(u),omega)** -> .
% 299.99/300.65  225018[26:SpL:117142.0,224910.1] operation(restrict(element_relation,ordinal_numbers,u)) || equal(sum_class(u),omega)** -> .
% 299.99/300.65  225327[26:Res:156922.1,225263.1] || member(identity_relation,inverse(subset_relation))* equal(complement(complement(subset_relation)),omega) -> .
% 299.99/300.65  225340[26:Res:69184.1,225263.1] || member(identity_relation,element_relation) equal(complement(compose(element_relation,ordinal_numbers)),omega)** -> .
% 299.99/300.65  225342[26:Res:193179.0,225263.1] || equal(complement(inverse(singleton(identity_relation))),omega)** -> asymmetric(singleton(identity_relation),u)*.
% 299.99/300.65  225372[26:Res:210513.1,225263.1] || member(identity_relation,u) equal(complement(union(u,identity_relation)),omega)** -> .
% 299.99/300.65  225384[26:Rew:160491.0,225333.1] || member(identity_relation,complement(u))* equal(union(u,identity_relation),omega) -> .
% 299.99/300.65  225387[26:MRR:225334.0,13126.0] || equal(complement(union(u,v)),omega)** -> member(identity_relation,complement(u)).
% 299.99/300.65  225388[26:MRR:225335.0,13126.0] || equal(complement(union(u,v)),omega)** -> member(identity_relation,complement(v)).
% 299.99/300.65  225456[18:MRR:225440.2,190496.0] || subclass(inverse(identity_relation),u) subclass(symmetrization_of(identity_relation),complement(u))* -> .
% 299.99/300.65  225461[7:MRR:225415.0,60996.1] || subclass(u,complement(unordered_pair(regular(u),v)))* -> equal(u,identity_relation).
% 299.99/300.65  225462[7:MRR:225416.0,60996.1] || subclass(u,complement(unordered_pair(v,regular(u))))* -> equal(u,identity_relation).
% 299.99/300.65  225780[26:SpL:163.0,225707.0] || equal(symmetric_difference(u,v),omega) -> member(identity_relation,union(u,v))*.
% 299.99/300.65  225781[26:SpL:3596.0,225707.0] || equal(symmetric_difference(u,singleton(u)),omega)** -> member(identity_relation,successor(u)).
% 299.99/300.65  225782[26:SpL:3597.0,225707.0] || equal(symmetric_difference(u,inverse(u)),omega)** -> member(identity_relation,symmetrization_of(u)).
% 299.99/300.65  225876[26:Res:225794.1,5.0] || equal(u,omega) subclass(u,v)* -> member(identity_relation,v)*.
% 299.99/300.65  226191[26:Res:216691.1,225905.1] || equal(complement(complement(element_relation)),identity_relation)** equal(rest_of(identity_relation),omega) -> .
% 299.99/300.65  226470[8:SpL:72.0,222295.0] || equal(complement(apply(u,v)),identity_relation)** subclass(element_relation,identity_relation) -> .
% 299.99/300.65  226478[18:SpL:72.0,222297.0] || equal(apply(u,v),inverse(identity_relation))** subclass(element_relation,identity_relation) -> .
% 299.99/300.65  226484[18:SpL:72.0,222298.0] || equal(apply(u,v),symmetrization_of(identity_relation))** subclass(element_relation,identity_relation) -> .
% 299.99/300.65  226491[14:SpL:72.0,222299.0] || equal(apply(u,v),singleton(identity_relation))** subclass(element_relation,identity_relation) -> .
% 299.99/300.65  226518[8:Obv:226508.1] || member(u,subset_relation) -> equal(intersection(singleton(u),inverse(subset_relation)),identity_relation)**.
% 299.99/300.65  226645[8:SpL:116239.0,216284.1] || subclass(rest_relation,rest_of(inverse(u)))* subclass(range_of(u),identity_relation) -> .
% 299.99/300.65  226673[21:MRR:226636.2,13039.0] || well_ordering(u,ordinal_numbers) subclass(rest_relation,rest_of(least(u,ordinal_numbers)))* -> .
% 299.99/300.65  226674[21:MRR:226637.2,13039.0] || well_ordering(u,ordinal_numbers) subclass(rest_relation,rest_of(least(u,rest_relation)))* -> .
% 299.99/300.65  226675[21:MRR:226638.2,13039.0] || well_ordering(u,rest_relation) subclass(rest_relation,rest_of(least(u,rest_relation)))* -> .
% 299.99/300.65  226710[8:Obv:226695.1] || member(u,subset_relation) -> equal(intersection(inverse(subset_relation),singleton(u)),identity_relation)**.
% 299.99/300.65  227322[18:Res:190593.1,217453.1] || equal(power_class(u),inverse(identity_relation))** equal(power_class(u),identity_relation) -> .
% 299.99/300.65  227324[14:Res:165168.1,217453.1] || equal(power_class(u),singleton(identity_relation))** equal(power_class(u),identity_relation) -> .
% 299.99/300.65  227955[21:MRR:227893.1,8666.0] || subclass(rest_relation,domain_relation) -> member(ordered_pair(unordered_pair(u,v),identity_relation),rest_relation)*.
% 299.99/300.65  228049[21:MRR:227983.1,8667.0] || subclass(rest_relation,domain_relation) -> member(ordered_pair(ordered_pair(u,v),identity_relation),rest_relation)*.
% 299.99/300.65  228804[8:Res:222114.1,222095.0] || subclass(complement(u),identity_relation) -> equal(symmetric_difference(ordinal_numbers,successor(u)),identity_relation)**.
% 299.99/300.65  228943[8:Res:222115.1,222095.0] || subclass(complement(u),identity_relation) -> equal(symmetric_difference(ordinal_numbers,symmetrization_of(u)),identity_relation)**.
% 299.99/300.65  229184[14:MRR:229183.1,165227.0] || member(regular(complement(u)),u)* -> equal(symmetric_difference(ordinal_numbers,u),identity_relation).
% 299.99/300.65  229190[7:Obv:229133.1] || member(u,v) -> equal(intersection(complement(v),singleton(u)),identity_relation)**.
% 299.99/300.65  229271[7:SpR:30.0,229162.0] ||  -> equal(intersection(union(u,v),intersection(complement(u),complement(v))),identity_relation)**.
% 299.99/300.65  229282[8:SpR:162038.0,229162.0] ||  -> equal(intersection(power_class(complement(inverse(identity_relation))),image(element_relation,symmetrization_of(identity_relation))),identity_relation)**.
% 299.99/300.65  229283[16:SpR:195257.0,229162.0] ||  -> equal(intersection(power_class(complement(singleton(identity_relation))),image(element_relation,singleton(identity_relation))),identity_relation)**.
% 299.99/300.65  229423[8:SpR:162038.0,229346.0] ||  -> equal(union(power_class(complement(inverse(identity_relation))),image(element_relation,symmetrization_of(identity_relation))),ordinal_numbers)**.
% 299.99/300.65  229424[16:SpR:195257.0,229346.0] ||  -> equal(union(power_class(complement(singleton(identity_relation))),image(element_relation,singleton(identity_relation))),ordinal_numbers)**.
% 299.99/300.65  229471[8:SpR:30.0,229359.0] ||  -> equal(symmetric_difference(union(u,v),intersection(complement(u),complement(v))),ordinal_numbers)**.
% 299.99/300.65  229482[8:SpR:162038.0,229359.0] ||  -> equal(symmetric_difference(power_class(complement(inverse(identity_relation))),image(element_relation,symmetrization_of(identity_relation))),ordinal_numbers)**.
% 299.99/300.65  229483[16:SpR:195257.0,229359.0] ||  -> equal(symmetric_difference(power_class(complement(singleton(identity_relation))),image(element_relation,singleton(identity_relation))),ordinal_numbers)**.
% 299.99/300.65  229734[16:Rew:66036.0,229624.0] ||  -> equal(union(image(element_relation,singleton(identity_relation)),power_class(complement(singleton(identity_relation)))),ordinal_numbers)**.
% 299.99/300.65  229735[8:Rew:66036.0,229627.0] ||  -> equal(union(image(element_relation,symmetrization_of(identity_relation)),power_class(complement(inverse(identity_relation)))),ordinal_numbers)**.
% 299.99/300.65  229758[8:MRR:229663.2,14676.0] inductive(symmetric_difference(u,u)) || well_ordering(v,complement(complement(u)))* -> .
% 299.99/300.65  229768[7:Obv:229562.1] || member(u,v) -> equal(intersection(singleton(u),complement(v)),identity_relation)**.
% 299.99/300.65  229899[7:SpR:30.0,229590.0] ||  -> equal(intersection(intersection(complement(u),complement(v)),union(u,v)),identity_relation)**.
% 299.99/300.65  229910[8:SpR:162038.0,229590.0] ||  -> equal(intersection(image(element_relation,symmetrization_of(identity_relation)),power_class(complement(inverse(identity_relation)))),identity_relation)**.
% 299.99/300.65  229911[16:SpR:195257.0,229590.0] ||  -> equal(intersection(image(element_relation,singleton(identity_relation)),power_class(complement(singleton(identity_relation)))),identity_relation)**.
% 299.99/300.65  230074[8:SpR:30.0,229733.0] ||  -> equal(symmetric_difference(intersection(complement(u),complement(v)),union(u,v)),ordinal_numbers)**.
% 299.99/300.65  230085[8:SpR:162038.0,229733.0] ||  -> equal(symmetric_difference(image(element_relation,symmetrization_of(identity_relation)),power_class(complement(inverse(identity_relation)))),ordinal_numbers)**.
% 299.99/300.65  230086[16:SpR:195257.0,229733.0] ||  -> equal(symmetric_difference(image(element_relation,singleton(identity_relation)),power_class(complement(singleton(identity_relation)))),ordinal_numbers)**.
% 299.99/300.65  230222[8:Rew:230199.0,164113.0] ||  -> equal(intersection(complement(symmetrization_of(identity_relation)),union(inverse(identity_relation),symmetrization_of(identity_relation))),identity_relation)**.
% 299.99/300.65  230244[8:Rew:66036.0,230187.1] || equal(symmetrization_of(identity_relation),ordinal_numbers) -> equal(symmetric_difference(symmetrization_of(identity_relation),ordinal_numbers),identity_relation)**.
% 299.99/300.65  230248[8:Rew:66036.0,230195.1] || equal(power_class(u),ordinal_numbers) -> equal(symmetric_difference(power_class(u),ordinal_numbers),identity_relation)**.
% 299.99/300.65  230499[8:Rew:162584.0,230492.1] || subclass(complement(inverse(identity_relation)),symmetrization_of(identity_relation))* -> subclass(ordinal_numbers,symmetrization_of(identity_relation)).
% 299.99/300.65  230692[8:MRR:230691.2,227044.0] || subclass(ordinal_numbers,regular(complement(u))) -> member(unordered_pair(v,w),u)*.
% 299.99/300.65  231041[8:Res:51313.1,230762.0] || member(singleton(subset_relation),subset_relation) subclass(ordinal_numbers,first(singleton(subset_relation)))* -> .
% 299.99/300.65  231053[8:Res:60219.0,230762.0] || subclass(ordinal_numbers,not_subclass_element(u,complement(subset_relation)))* -> subclass(u,complement(subset_relation)).
% 299.99/300.65  231102[18:Res:194549.1,230762.0] || subclass(symmetrization_of(identity_relation),subset_relation) subclass(ordinal_numbers,regular(symmetrization_of(identity_relation)))* -> .
% 299.99/300.65  231103[18:Res:190510.1,230762.0] || subclass(inverse(identity_relation),subset_relation) subclass(ordinal_numbers,regular(symmetrization_of(identity_relation)))* -> .
% 299.99/300.65  231119[8:Res:51313.1,230780.0] || member(singleton(subset_relation),subset_relation)* equal(first(singleton(subset_relation)),ordinal_numbers) -> .
% 299.99/300.65  231131[8:Res:60219.0,230780.0] || equal(not_subclass_element(u,complement(subset_relation)),ordinal_numbers)** -> subclass(u,complement(subset_relation)).
% 299.99/300.65  231180[18:Res:194549.1,230780.0] || subclass(symmetrization_of(identity_relation),subset_relation)* equal(regular(symmetrization_of(identity_relation)),ordinal_numbers) -> .
% 299.99/300.65  231181[18:Res:190510.1,230780.0] || subclass(inverse(identity_relation),subset_relation)* equal(regular(symmetrization_of(identity_relation)),ordinal_numbers) -> .
% 299.99/300.65  231423[24:SpR:207565.1,229277.0] operation(u) ||  -> equal(intersection(successor(u),symmetric_difference(ordinal_numbers,u)),identity_relation)**.
% 299.99/300.65  231674[24:SpR:207565.1,229355.0] operation(u) ||  -> equal(union(successor(u),symmetric_difference(ordinal_numbers,u)),ordinal_numbers)**.
% 299.99/300.65  231730[24:SpR:207565.1,229477.0] operation(u) ||  -> equal(symmetric_difference(successor(u),symmetric_difference(ordinal_numbers,u)),ordinal_numbers)**.
% 299.99/300.65  231873[8:Res:231812.0,13082.1] inductive(regular(u)) ||  -> equal(u,identity_relation) member(identity_relation,complement(u))*.
% 299.99/300.65  231978[24:SpR:207565.1,229723.0] operation(u) ||  -> equal(union(symmetric_difference(ordinal_numbers,u),successor(u)),ordinal_numbers)**.
% 299.99/300.65  232095[24:SpR:207565.1,229905.0] operation(u) ||  -> equal(intersection(symmetric_difference(ordinal_numbers,u),successor(u)),identity_relation)**.
% 299.99/300.65  232338[24:SpR:207565.1,230080.0] operation(u) ||  -> equal(symmetric_difference(symmetric_difference(ordinal_numbers,u),successor(u)),ordinal_numbers)**.
% 299.99/300.65  232475[8:MRR:232464.2,162901.1] || member(intersection(singleton(u),v),subset_relation)* subclass(ordinal_numbers,u) -> .
% 299.99/300.65  232476[8:MRR:232465.2,162901.1] || member(intersection(u,singleton(v)),subset_relation)* subclass(ordinal_numbers,v) -> .
% 299.99/300.65  232598[8:Res:49995.1,230939.0] || member(subset_relation,subset_relation) equal(regular(singleton(first(subset_relation))),ordinal_numbers)** -> .
% 299.99/300.65  232929[25:MRR:232925.1,215866.0] || equal(complement(u),identity_relation) -> equal(regular(unordered_pair(u,identity_relation)),identity_relation)**.
% 299.99/300.65  233114[8:SpL:18840.1,233014.0] || member(u,subset_relation) equal(complement(regular(singleton(u))),identity_relation)** -> .
% 299.99/300.65  233224[25:MRR:233221.1,215873.0] || equal(complement(u),identity_relation) -> equal(regular(unordered_pair(identity_relation,u)),identity_relation)**.
% 299.99/300.65  233309[18:Res:231881.0,190451.0] ||  -> equal(singleton(inverse(identity_relation)),identity_relation) member(identity_relation,complement(singleton(inverse(identity_relation))))*.
% 299.99/300.65  233314[18:Res:231881.0,190437.0] ||  -> equal(singleton(symmetrization_of(identity_relation)),identity_relation) member(identity_relation,complement(singleton(symmetrization_of(identity_relation))))*.
% 299.99/300.65  233349[8:Res:231881.0,81399.1] || equal(complement(complement(singleton(domain_relation))),domain_relation)** -> equal(singleton(domain_relation),identity_relation).
% 299.99/300.65  233350[8:Res:231881.0,63453.1] || equal(complement(complement(singleton(domain_relation))),ordinal_numbers)** -> equal(singleton(domain_relation),identity_relation).
% 299.99/300.65  233390[8:MRR:233318.1,216024.0] || member(u,ordinal_numbers) -> member(u,complement(singleton(unordered_pair(u,v))))*.
% 299.99/300.65  233391[8:MRR:233320.1,216024.0] || member(u,ordinal_numbers) -> member(u,complement(singleton(unordered_pair(v,u))))*.
% 299.99/300.65  233449[14:Res:233378.0,9876.0] || subclass(complement(singleton(singleton(identity_relation))),u)* well_ordering(ordinal_numbers,u) -> .
% 299.99/300.65  233744[25:Res:233380.0,5.0] || subclass(complement(singleton(ordered_pair(ordinal_numbers,u))),v)* -> member(identity_relation,v).
% 299.99/300.65  234093[8:SpR:18840.1,233383.0] || member(u,subset_relation) -> member(singleton(first(u)),complement(singleton(u)))*.
% 299.99/300.65  234176[8:SpL:18840.1,234106.0] || member(u,subset_relation) member(singleton(first(u)),singleton(u))* -> .
% 299.99/300.65  234369[9:MRR:234363.2,65891.0] || well_ordering(u,ordinal_numbers) -> equal(integer_of(least(u,complement(omega))),identity_relation)**.
% 299.99/300.65  234528[15:Res:215659.1,233381.0] || subclass(complement(singleton(omega)),identity_relation)* -> equal(integer_of(range_of(identity_relation)),identity_relation).
% 299.99/300.65  234555[8:Res:215662.1,233381.0] || subclass(complement(singleton(omega)),identity_relation)* -> equal(integer_of(singleton(u)),identity_relation)**.
% 299.99/300.65  234568[8:Res:15426.1,233381.0] || subclass(domain_relation,singleton(omega)) -> equal(integer_of(ordered_pair(identity_relation,identity_relation)),identity_relation)**.
% 299.99/300.65  234628[8:SpL:18840.1,234115.0] || member(u,subset_relation) equal(complement(complement(singleton(u))),ordinal_numbers)** -> .
% 299.99/300.65  234642[8:SpL:18840.1,234117.0] || member(u,subset_relation) subclass(ordinal_numbers,complement(complement(singleton(u))))* -> .
% 299.99/300.65  234725[8:SpL:18840.1,232824.0] || member(u,subset_relation) subclass(ordinal_numbers,regular(unordered_pair(v,u)))* -> .
% 299.99/300.65  234755[8:SpL:18840.1,233124.0] || member(u,subset_relation) subclass(ordinal_numbers,regular(unordered_pair(u,v)))* -> .
% 299.99/300.65  234853[21:MRR:234786.1,14676.0] || member(u,ordinal_numbers) -> equal(apply(omega,u),sum_class(range_of(identity_relation)))**.
% 299.99/300.65  234912[8:SpL:18840.1,234736.0] || member(u,subset_relation) equal(regular(unordered_pair(v,u)),ordinal_numbers)** -> .
% 299.99/300.65  234925[8:SpL:18840.1,234766.0] || member(u,subset_relation) equal(regular(unordered_pair(u,v)),ordinal_numbers)** -> .
% 299.99/300.65  234982[8:Rew:15663.0,234943.0] ||  -> equal(domain__dfg(complement(cross_product(u,singleton(v))),u,v),single_valued3(identity_relation))**.
% 299.99/300.65  234987[8:MRR:234986.1,19172.1] || equal(identity_relation,u) -> section(complement(cross_product(v,u)),u,v)*.
% 299.99/300.65  234989[8:MRR:234988.1,13039.0] || subclass(u,v) -> section(complement(cross_product(v,u)),u,v)*.
% 299.99/300.65  235010[7:SpR:234956.0,72.0] ||  -> equal(apply(complement(cross_product(singleton(u),ordinal_numbers)),u),sum_class(range_of(identity_relation)))**.
% 299.99/300.65  235090[8:Res:41368.0,219073.1] || subclass(power_class(u),identity_relation) -> subclass(v,image(element_relation,complement(u)))*.
% 299.99/300.65  235143[24:SpL:207558.1,234983.0] operation(u) || member(u,cantor(complement(cross_product(identity_relation,ordinal_numbers))))* -> .
% 299.99/300.65  235157[8:Res:8643.1,234983.0] || subclass(ordinal_numbers,cantor(complement(cross_product(singleton(unordered_pair(u,v)),ordinal_numbers))))* -> .
% 299.99/300.65  235158[15:Res:217197.1,234983.0] || equal(complement(cantor(complement(cross_product(singleton(range_of(identity_relation)),ordinal_numbers)))),identity_relation)** -> .
% 299.99/300.65  235159[15:Res:215659.1,234983.0] || subclass(complement(cantor(complement(cross_product(singleton(range_of(identity_relation)),ordinal_numbers)))),identity_relation)* -> .
% 299.99/300.65  235163[15:Res:165442.1,234983.0] || subclass(ordinal_numbers,cantor(complement(cross_product(singleton(sum_class(range_of(identity_relation))),ordinal_numbers))))* -> .
% 299.99/300.65  235169[8:Res:143222.1,234983.0] || equal(cantor(complement(cross_product(singleton(least(element_relation,omega)),ordinal_numbers))),omega)** -> .
% 299.99/300.65  235170[8:Res:143193.1,234983.0] || equal(cantor(complement(cross_product(singleton(least(element_relation,omega)),ordinal_numbers))),ordinal_numbers)** -> .
% 299.99/300.65  235173[8:Res:125731.1,234983.0] || subclass(ordinal_numbers,cantor(complement(cross_product(singleton(least(element_relation,omega)),ordinal_numbers))))* -> .
% 299.99/300.65  235174[8:Res:125725.1,234983.0] || subclass(omega,cantor(complement(cross_product(singleton(least(element_relation,omega)),ordinal_numbers))))* -> .
% 299.99/300.65  235175[8:Res:217198.1,234983.0] || equal(complement(cantor(complement(cross_product(singleton(singleton(u)),ordinal_numbers)))),identity_relation)** -> .
% 299.99/300.65  235176[8:Res:215662.1,234983.0] || subclass(complement(cantor(complement(cross_product(singleton(singleton(u)),ordinal_numbers)))),identity_relation)* -> .
% 299.99/300.65  235186[8:Res:8642.1,234983.0] || subclass(ordinal_numbers,cantor(complement(cross_product(singleton(ordered_pair(u,v)),ordinal_numbers))))* -> .
% 299.99/300.65  235189[8:Res:15426.1,234983.0] || subclass(domain_relation,cantor(complement(cross_product(singleton(ordered_pair(identity_relation,identity_relation)),ordinal_numbers))))* -> .
% 299.99/300.65  235206[18:Res:190515.1,234983.0] || subclass(ordinal_numbers,cantor(complement(cross_product(singleton(regular(symmetrization_of(identity_relation))),ordinal_numbers))))* -> .
% 299.99/300.65  235207[25:SpL:216188.1,235146.0] || equal(cross_product(identity_relation,ordinal_numbers),identity_relation) member(ordinal_numbers,cantor(ordinal_numbers))* -> .
% 299.99/300.65  235257[24:SpR:207565.1,230445.1] operation(u) || member(v,u) -> member(v,successor(u))*.
% 299.99/300.65  235275[8:Res:230445.1,210517.1] || member(u,v)* equal(complement(union(v,identity_relation)),ordinal_numbers)** -> .
% 299.99/300.65  235296[22:Res:230445.1,205501.0] || member(singleton(identity_relation),u) well_ordering(ordinal_numbers,union(u,identity_relation))* -> .
% 299.99/300.65  235445[5:Res:28980.1,18842.0] || subclass(rest_relation,flip(subset_relation)) -> member(rest_of(ordered_pair(u,v)),ordinal_numbers)*.
% 299.99/300.65  235468[25:Res:28980.1,214618.1] operation(rest_of(ordered_pair(u,v))) || subclass(rest_relation,flip(rest_relation))* -> .
% 299.99/300.65  235470[25:Res:28980.1,214614.1] operation(rest_of(ordered_pair(u,v))) || subclass(rest_relation,flip(subset_relation))* -> .
% 299.99/300.65  235471[21:Rew:196550.0,235467.1] || subclass(rest_relation,flip(domain_relation)) -> equal(rest_of(ordered_pair(u,v)),identity_relation)**.
% 299.99/300.65  236200[8:Res:216691.1,234639.0] || equal(complement(complement(complement(singleton(singleton(singleton(singleton(u))))))),identity_relation)** -> .
% 299.99/300.65  236609[8:MRR:236601.2,14676.0] || equal(u,ordinal_numbers) member(v,ordinal_numbers)* -> member(v,u)*.
% 299.99/300.65  237219[7:Obv:237089.0] ||  -> equal(intersection(singleton(u),intersection(v,w)),identity_relation)** member(u,w).
% 299.99/300.65  237345[8:MRR:237258.2,14676.0] || member(u,intersection(v,subset_relation))* member(u,inverse(subset_relation)) -> .
% 299.99/300.65  237391[7:SpR:32.0,237181.0] ||  -> equal(intersection(complement(cross_product(u,v)),restrict(w,u,v)),identity_relation)**.
% 299.99/300.65  237454[8:SpR:160491.0,237181.0] ||  -> equal(intersection(union(u,identity_relation),intersection(v,symmetric_difference(ordinal_numbers,u))),identity_relation)**.
% 299.99/300.65  237458[7:SpR:59.0,237181.0] ||  -> equal(intersection(power_class(u),intersection(v,image(element_relation,complement(u)))),identity_relation)**.
% 299.99/300.65  237541[8:MRR:237380.2,14676.0] || member(u,intersection(v,w))* member(u,complement(w)) -> .
% 299.99/300.65  237872[7:Obv:237740.0] ||  -> equal(intersection(singleton(u),intersection(v,w)),identity_relation)** member(u,v).
% 299.99/300.65  238006[8:MRR:237913.2,14676.0] || member(u,intersection(subset_relation,v))* member(u,inverse(subset_relation)) -> .
% 299.99/300.65  238117[8:MRR:238040.2,14676.0] || member(u,complement(complement(subset_relation)))* member(u,inverse(subset_relation)) -> .
% 299.99/300.65  238176[7:SpR:163.0,237830.0] ||  -> equal(intersection(complement(complement(intersection(u,v))),symmetric_difference(u,v)),identity_relation)**.
% 299.99/300.65  238182[7:SpR:155665.0,237830.0] ||  -> equal(intersection(complement(complement(subset_relation)),symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers))),identity_relation)**.
% 299.99/300.65  238183[7:SpR:155666.0,237830.0] ||  -> equal(intersection(complement(complement(subset_relation)),symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation)),identity_relation)**.
% 299.99/300.65  238205[8:SpR:66293.0,237830.0] ||  -> equal(intersection(complement(union(u,identity_relation)),symmetric_difference(complement(u),ordinal_numbers)),identity_relation)**.
% 299.99/300.65  238236[8:SpR:160491.0,237830.0] ||  -> equal(intersection(union(u,identity_relation),intersection(symmetric_difference(ordinal_numbers,u),v)),identity_relation)**.
% 299.99/300.65  238240[7:SpR:59.0,237830.0] ||  -> equal(intersection(power_class(u),intersection(image(element_relation,complement(u)),v)),identity_relation)**.
% 299.99/300.65  238313[8:MRR:238158.2,14676.0] || member(u,intersection(v,w))* member(u,complement(v)) -> .
% 299.99/300.65  238926[7:SpR:155653.0,237395.0] ||  -> equal(intersection(complement(complement(compose(complement(element_relation),inverse(element_relation)))),subset_relation),identity_relation)**.
% 299.99/300.65  238937[16:SpR:195239.0,237395.0] ||  -> equal(intersection(singleton(identity_relation),restrict(complement(singleton(identity_relation)),u,v)),identity_relation)**.
% 299.99/300.65  238938[8:SpR:162584.0,237395.0] ||  -> equal(intersection(symmetrization_of(identity_relation),restrict(complement(inverse(identity_relation)),u,v)),identity_relation)**.
% 299.99/300.65  239395[7:Obv:239252.0] ||  -> equal(intersection(intersection(u,v),singleton(w)),identity_relation)** member(w,u).
% 299.99/300.65  239439[8:SpR:239339.0,154737.1] || subclass(inverse(subset_relation),intersection(subset_relation,u))* -> equal(inverse(subset_relation),identity_relation).
% 299.99/300.65  239568[8:SpR:239454.0,154737.1] || subclass(inverse(subset_relation),complement(complement(subset_relation)))* -> equal(inverse(subset_relation),identity_relation).
% 299.99/300.65  239684[8:SpR:239452.0,154737.1] || subclass(inverse(subset_relation),intersection(u,subset_relation))* -> equal(inverse(subset_relation),identity_relation).
% 299.99/300.65  239813[7:SpR:239340.0,154737.1] || subclass(complement(u),intersection(u,v))* -> equal(complement(u),identity_relation).
% 299.99/300.65  239826[8:SpR:160491.0,239340.0] ||  -> equal(intersection(intersection(symmetric_difference(ordinal_numbers,u),v),union(u,identity_relation)),identity_relation)**.
% 299.99/300.65  239830[7:SpR:59.0,239340.0] ||  -> equal(intersection(intersection(image(element_relation,complement(u)),v),power_class(u)),identity_relation)**.
% 299.99/300.65  239844[7:SpR:33.0,239340.0] ||  -> equal(intersection(restrict(u,v,w),complement(cross_product(v,w))),identity_relation)**.
% 299.99/300.65  239849[7:SpR:163.0,239340.0] ||  -> equal(intersection(symmetric_difference(u,v),complement(complement(intersection(u,v)))),identity_relation)**.
% 299.99/300.65  239855[7:SpR:155665.0,239340.0] ||  -> equal(intersection(symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers)),complement(complement(subset_relation))),identity_relation)**.
% 299.99/300.65  239856[7:SpR:155666.0,239340.0] ||  -> equal(intersection(symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation),complement(complement(subset_relation))),identity_relation)**.
% 299.99/300.65  239879[8:SpR:66293.0,239340.0] ||  -> equal(intersection(symmetric_difference(complement(u),ordinal_numbers),complement(union(u,identity_relation))),identity_relation)**.
% 299.99/300.65  240230[7:Obv:240087.0] ||  -> equal(intersection(intersection(u,v),singleton(w)),identity_relation)** member(w,v).
% 299.99/300.65  8880[5:Rew:8637.0,6854.0] || subclass(ordinal_numbers,symmetric_difference(u,v)) -> member(omega,complement(intersection(u,v)))*.
% 299.99/300.65  8891[5:Rew:8637.0,6882.0] || equal(symmetric_difference(u,v),ordinal_numbers) -> member(omega,complement(intersection(u,v)))*.
% 299.99/300.65  69443[8:MRR:69394.0,41096.1] || member(u,complement(intersection(v,ordinal_numbers)))* -> member(u,symmetric_difference(v,ordinal_numbers)).
% 299.99/300.65  69159[8:Res:8645.1,66086.1] || subclass(ordinal_numbers,complement(compose(element_relation,ordinal_numbers)))* member(singleton(u),element_relation)* -> .
% 299.99/300.65  19712[5:MRR:19710.1,8655.0] || member(u,sum_class(singleton(u)))* -> equal(sum_class(singleton(u)),singleton(u)).
% 299.99/300.65  19668[5:SpL:3597.0,10114.0] || equal(symmetric_difference(u,inverse(u)),ordinal_numbers)** -> member(singleton(v),symmetrization_of(u))*.
% 299.99/300.65  19671[5:SpL:3597.0,8849.0] || subclass(ordinal_numbers,symmetric_difference(u,inverse(u)))* -> member(singleton(v),symmetrization_of(u))*.
% 299.99/300.65  9678[5:Res:9632.1,28.1] || equal(complement(complement(complement(u))),ordinal_numbers)** member(singleton(v),u)* -> .
% 299.99/300.65  9686[5:Res:9632.1,25.0] || equal(complement(complement(intersection(u,v))),ordinal_numbers)** -> member(singleton(w),u)*.
% 299.99/300.65  10108[5:SpL:163.0,8849.0] || subclass(ordinal_numbers,symmetric_difference(u,v)) -> member(singleton(w),union(u,v))*.
% 299.99/300.65  10183[5:SpL:163.0,10114.0] || equal(symmetric_difference(u,v),ordinal_numbers) -> member(singleton(w),union(u,v))*.
% 299.99/300.65  8814[5:Rew:8637.0,4733.0] || subclass(ordinal_numbers,u)* subclass(u,v)* -> member(singleton(w),v)*.
% 299.99/300.65  9685[5:Res:9632.1,26.0] || equal(complement(complement(intersection(u,v))),ordinal_numbers)** -> member(singleton(w),v)*.
% 299.99/300.65  10730[0:Res:10714.1,1303.1] inductive(singleton(u)) || member(u,omega)* -> equal(singleton(u),omega).
% 299.99/300.65  18358[8:Res:9632.1,14679.1] || equal(complement(complement(inverse(subset_relation))),ordinal_numbers)** member(singleton(u),subset_relation)* -> .
% 299.99/300.65  18841[5:Res:18819.1,8843.1] || member(singleton(u),subset_relation)* subclass(ordinal_numbers,complement(cross_product(ordinal_numbers,ordinal_numbers)))* -> .
% 299.99/300.65  51206[5:SpR:50855.1,962.0] || member(singleton(u),subset_relation) -> member(u,ordered_pair(first(singleton(u)),v))*.
% 299.99/300.65  51273[5:SpL:50855.1,9495.0] || member(singleton(u),subset_relation) subclass(ordinal_numbers,complement(unordered_pair(u,v)))* -> .
% 299.99/300.65  51274[5:SpL:50855.1,9566.0] || member(singleton(u),subset_relation) equal(complement(unordered_pair(u,v)),ordinal_numbers)** -> .
% 299.99/300.65  51291[5:SpL:50855.1,9494.0] || member(singleton(u),subset_relation) subclass(ordinal_numbers,complement(unordered_pair(v,u)))* -> .
% 299.99/300.65  51292[5:SpL:50855.1,9532.0] || member(singleton(u),subset_relation) equal(complement(unordered_pair(v,u)),ordinal_numbers)** -> .
% 299.99/300.65  19554[5:SpL:3596.0,8849.0] || subclass(ordinal_numbers,symmetric_difference(u,singleton(u)))* -> member(singleton(v),successor(u))*.
% 299.99/300.65  19551[5:SpL:3596.0,10114.0] || equal(symmetric_difference(u,singleton(u)),ordinal_numbers)** -> member(singleton(v),successor(u))*.
% 299.99/300.65  51502[5:Res:51313.1,3700.0] || member(singleton(singleton(u)),subset_relation)* -> equal(first(singleton(singleton(u))),u).
% 299.99/300.65  4701[0:Res:967.0,5.0] || subclass(singleton(singleton(singleton(u))),v)* -> member(singleton(singleton(u)),v).
% 299.99/300.65  10744[0:SpL:963.0,10702.0] || equal(u,singleton(singleton(singleton(v)))) -> member(singleton(singleton(v)),u)*.
% 299.99/300.65  50838[5:Res:49995.1,28.1] || member(complement(u),subset_relation) member(singleton(first(complement(u))),u)* -> .
% 299.99/300.65  50862[8:Res:49995.1,14679.1] || member(inverse(subset_relation),subset_relation) member(singleton(first(inverse(subset_relation))),subset_relation)* -> .
% 299.99/300.65  49996[5:SpR:18840.1,964.0] || member(u,subset_relation) -> member(unordered_pair(first(u),singleton(second(u))),u)*.
% 299.99/300.65  51506[5:Res:51313.1,50033.0] || member(singleton(subset_relation),subset_relation) equal(complement(first(singleton(subset_relation))),ordinal_numbers)** -> .
% 299.99/300.65  9435[5:Res:8642.1,40.0] || subclass(ordinal_numbers,flip(u)) -> member(ordered_pair(ordered_pair(v,w),x),u)*.
% 299.99/300.65  9444[5:Res:8642.1,37.0] || subclass(ordinal_numbers,rotate(u)) -> member(ordered_pair(ordered_pair(v,w),x),u)*.
% 299.99/300.65  8853[5:Rew:8637.0,6945.0] || subclass(ordinal_numbers,restrict(u,v,w))* -> member(ordered_pair(x,y),u)*.
% 299.99/300.65  42249[5:Res:41183.1,5.0] || subclass(ordinal_numbers,u) -> subclass(v,w) member(not_subclass_element(v,w),u)*.
% 299.99/300.65  50158[5:Res:50063.1,5.0] || member(u,subset_relation) subclass(ordinal_numbers,v) -> member(first(u),v)*.
% 299.99/300.65  50199[5:Res:50064.1,5.0] || member(u,subset_relation) subclass(ordinal_numbers,v) -> member(second(u),v)*.
% 299.99/300.65  18973[5:Rew:32.0,18972.1] single_valued_class(intersection(u,cross_product(ordinal_numbers,ordinal_numbers))) ||  -> function(restrict(u,ordinal_numbers,ordinal_numbers))*.
% 299.99/300.65  19092[5:Rew:33.0,19091.1] single_valued_class(intersection(cross_product(ordinal_numbers,ordinal_numbers),u)) ||  -> function(restrict(u,ordinal_numbers,ordinal_numbers))*.
% 299.99/300.65  68824[0:Res:18949.0,1303.1] inductive(restrict(omega,u,v)) ||  -> equal(restrict(omega,u,v),omega)**.
% 299.99/300.65  8889[5:Rew:8637.0,6869.0] || equal(restrict(u,v,w),ordinal_numbers)** -> member(omega,cross_product(v,w))*.
% 299.99/300.65  8855[5:Rew:8637.0,6834.0] || subclass(ordinal_numbers,restrict(u,v,w))* -> member(omega,cross_product(v,w)).
% 299.99/300.65  79550[5:Res:60219.0,50033.0] || equal(complement(not_subclass_element(u,complement(subset_relation))),ordinal_numbers)** -> subclass(u,complement(subset_relation)).
% 299.99/300.65  79551[5:Res:60219.0,3700.0] ||  -> subclass(u,complement(singleton(v))) equal(not_subclass_element(u,complement(singleton(v))),v)**.
% 299.99/300.65  94682[5:Res:39298.1,3700.0] || subclass(ordinal_numbers,complement(complement(singleton(u))))* -> equal(ordered_pair(v,w),u)*.
% 299.99/300.65  94710[5:Res:39298.1,97.0] || subclass(ordinal_numbers,complement(complement(compose_class(u))))* -> equal(compose(u,v),w)*.
% 299.99/300.65  96370[5:Res:40074.1,3700.0] || subclass(ordinal_numbers,complement(complement(singleton(u))))* -> equal(unordered_pair(v,w),u)*.
% 299.99/300.65  9694[5:Res:9632.1,161.0] || equal(complement(complement(omega)),ordinal_numbers) -> equal(integer_of(singleton(u)),singleton(u))**.
% 299.99/300.65  124777[5:SoR:9594.0,75.1] one_to_one(sum_class(cross_product(ordinal_numbers,ordinal_numbers))) ||  -> section(element_relation,cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers)*.
% 299.99/300.65  125925[5:Res:125725.1,56411.0] || subclass(omega,rest_of(least(element_relation,omega)))* subclass(ordinal_numbers,complement(element_relation)) -> .
% 299.99/300.65  125927[5:Res:125725.1,898.0] || subclass(omega,restrict(u,v,w))* -> member(least(element_relation,omega),u).
% 299.99/300.65  126004[5:Res:125731.1,898.0] || subclass(ordinal_numbers,restrict(u,v,w))* -> member(least(element_relation,omega),u).
% 299.99/300.65  128005[5:Res:126679.1,3700.0] || subclass(omega,complement(complement(singleton(u))))* -> equal(least(element_relation,omega),u).
% 299.99/300.65  128340[5:Res:127147.1,3700.0] || subclass(ordinal_numbers,complement(complement(singleton(u))))* -> equal(least(element_relation,omega),u).
% 299.99/300.65  128502[5:Res:10.1,8840.1] || equal(u,singleton(v)) member(v,ordinal_numbers)* -> member(v,u)*.
% 299.99/300.65  130875[5:Res:8646.1,9876.0] || subclass(ordinal_numbers,u)* subclass(u,v)* well_ordering(ordinal_numbers,v)* -> .
% 299.99/300.65  130908[5:Res:60219.0,9876.0] || subclass(u,v)* well_ordering(ordinal_numbers,v)* -> subclass(w,complement(u))*.
% 299.99/300.65  131441[5:Res:8646.1,18794.1] || subclass(ordinal_numbers,intersection(u,v)) member(omega,symmetric_difference(u,v))* -> .
% 299.99/300.65  131971[5:Res:10.1,8854.0] || equal(restrict(u,v,w),ordinal_numbers)** -> member(unordered_pair(x,y),u)*.
% 299.99/300.65  132393[0:Res:138.1,39817.0] || member(u,ordinal_numbers) -> subclass(u,v)* member(least(element_relation,u),u)*.
% 299.99/300.65  132828[5:SpL:33.0,130481.0] || equal(restrict(u,v,w),omega)** -> member(least(element_relation,omega),u)*.
% 299.99/300.65  133397[5:SpL:33.0,130610.0] || equal(restrict(u,v,w),ordinal_numbers)** -> member(least(element_relation,omega),u)*.
% 299.99/300.65  134008[8:Res:69184.1,133836.0] || member(singleton(singleton(u)),element_relation)* well_ordering(ordinal_numbers,compose(element_relation,ordinal_numbers))* -> .
% 299.99/300.65  134069[5:Res:133837.1,28.1] || well_ordering(ordinal_numbers,complement(complement(u)))* member(singleton(singleton(v)),u)* -> .
% 299.99/300.65  134082[5:Res:133837.1,26.0] || well_ordering(ordinal_numbers,complement(intersection(u,v)))* -> member(singleton(singleton(w)),v)*.
% 299.99/300.65  134083[5:Res:133837.1,25.0] || well_ordering(ordinal_numbers,complement(intersection(u,v)))* -> member(singleton(singleton(w)),u)*.
% 299.99/300.65  135080[8:SpR:117066.0,135059.1] || equal(rest_of(flip(cross_product(u,ordinal_numbers))),rest_relation)** -> subclass(v,inverse(u))*.
% 299.99/300.65  135081[8:SpR:117142.0,135059.1] || equal(rest_of(restrict(element_relation,ordinal_numbers,u)),rest_relation)** -> subclass(v,sum_class(u))*.
% 299.99/300.65  136856[5:MRR:136849.1,8666.0] || equal(u,ordered_pair(v,w)) -> member(unordered_pair(v,singleton(w)),u)*.
% 299.99/300.65  66813[5:Res:49995.1,161.0] || member(omega,subset_relation) -> equal(integer_of(singleton(first(omega))),singleton(first(omega)))**.
% 299.99/300.65  139814[5:MRR:139796.0,8655.0] || subclass(ordinal_numbers,complement(union(u,v)))* -> member(singleton(w),complement(v))*.
% 299.99/300.65  139815[5:MRR:139794.0,8655.0] || well_ordering(ordinal_numbers,union(u,v))* -> member(singleton(singleton(w)),complement(v))*.
% 299.99/300.65  139846[5:SpR:47.0,39530.1] || member(u,ordinal_numbers) -> member(u,successor(v)) member(u,complement(v))*.
% 299.99/300.65  139847[5:SpR:117.0,39530.1] || member(u,ordinal_numbers) -> member(u,symmetrization_of(v))* member(u,complement(v)).
% 299.99/300.65  139897[5:MRR:139882.0,8655.0] || subclass(ordinal_numbers,complement(union(u,v)))* -> member(singleton(w),complement(u))*.
% 299.99/300.65  139898[5:MRR:139880.0,8655.0] || well_ordering(ordinal_numbers,union(u,v))* -> member(singleton(singleton(w)),complement(u))*.
% 299.99/300.65  140282[0:Res:55.1,19124.0] inductive(singleton(u)) ||  -> subclass(omega,v) equal(not_subclass_element(omega,v),u)*.
% 299.99/300.65  140296[5:MRR:140286.0,8655.0] ||  -> subclass(sum_class(singleton(u)),v) equal(not_subclass_element(sum_class(singleton(u)),v),u)**.
% 299.99/300.65  141565[8:Rew:140613.0,66439.0] ||  -> equal(symmetric_difference(complement(intersection(u,ordinal_numbers)),ordinal_numbers),symmetric_difference(ordinal_numbers,symmetric_difference(u,ordinal_numbers)))**.
% 299.99/300.65  144402[8:SpL:140613.0,132824.0] || equal(symmetric_difference(ordinal_numbers,u),ordinal_numbers) -> member(least(element_relation,omega),complement(u))*.
% 299.99/300.65  144411[8:SpL:140613.0,125985.0] || subclass(ordinal_numbers,symmetric_difference(ordinal_numbers,u)) -> member(least(element_relation,omega),complement(u))*.
% 299.99/300.65  144414[8:SpL:140613.0,8846.0] || subclass(ordinal_numbers,symmetric_difference(ordinal_numbers,u)) -> member(unordered_pair(v,w),complement(u))*.
% 299.99/300.65  144427[8:SpL:140613.0,125908.0] || subclass(omega,symmetric_difference(ordinal_numbers,u)) -> member(least(element_relation,omega),complement(u))*.
% 299.99/300.65  144431[8:SpL:140613.0,130556.0] || equal(symmetric_difference(ordinal_numbers,u),omega) -> member(least(element_relation,omega),complement(u))*.
% 299.99/300.65  146779[5:MRR:146754.0,8955.1] || member(u,ordinal_numbers) subclass(ordinal_numbers,complement(unordered_pair(sum_class(u),v)))* -> .
% 299.99/300.65  146780[5:MRR:146755.0,8955.1] || member(u,ordinal_numbers) subclass(ordinal_numbers,complement(unordered_pair(v,sum_class(u))))* -> .
% 299.99/300.65  147297[5:Res:143222.1,56411.0] || equal(rest_of(least(element_relation,omega)),omega)** subclass(ordinal_numbers,complement(element_relation)) -> .
% 299.99/300.65  148170[5:Res:133837.1,3572.0] || well_ordering(ordinal_numbers,complement(compose_class(u)))* -> equal(compose(u,singleton(v)),v)**.
% 299.99/300.65  148859[8:Obv:148854.2] || subclass(u,subset_relation) subclass(u,inverse(subset_relation))* -> subclass(u,v)*.
% 299.99/300.65  148883[8:Res:148858.1,9586.0] || subclass(sum_class(complement(subset_relation)),inverse(subset_relation))* -> section(element_relation,complement(subset_relation),ordinal_numbers).
% 299.99/300.65  148893[8:Res:148858.1,2486.0] || subclass(ordered_pair(u,v),inverse(subset_relation))* -> member(singleton(u),complement(subset_relation)).
% 299.99/300.65  148982[5:Res:148963.1,5.0] || member(u,ordinal_numbers) subclass(ordinal_numbers,v) -> member(rest_of(u),v)*.
% 299.99/300.65  152228[0:Obv:152220.2] || subclass(u,v) subclass(u,complement(v))* -> subclass(u,w)*.
% 299.99/300.65  152238[5:MRR:152198.0,41183.1] || subclass(u,complement(unordered_pair(not_subclass_element(u,v),w)))* -> subclass(u,v).
% 299.99/300.65  152239[5:MRR:152199.0,41183.1] || subclass(u,complement(unordered_pair(v,not_subclass_element(u,w))))* -> subclass(u,w).
% 299.99/300.65  153516[5:Res:8944.1,898.0] || member(u,subset_relation) -> member(u,complement(compose(complement(element_relation),inverse(element_relation))))*.
% 299.99/300.65  154327[5:Res:9632.1,151988.0] || equal(complement(complement(complement(complement(u)))),ordinal_numbers)** -> member(singleton(v),u)*.
% 299.99/300.65  154331[5:Res:133837.1,151988.0] || well_ordering(ordinal_numbers,complement(complement(complement(u))))* -> member(singleton(singleton(v)),u)*.
% 299.99/300.65  155187[0:SpR:154737.1,33.0] || subclass(u,cross_product(v,w))* -> equal(restrict(u,v,w),u).
% 299.99/300.65  155548[0:SpR:163.0,154945.0] ||  -> equal(intersection(complement(intersection(u,v)),symmetric_difference(u,v)),symmetric_difference(u,v))**.
% 299.99/300.65  155652[0:Rew:33.0,155547.0] ||  -> equal(restrict(restrict(u,v,w),v,w),restrict(u,v,w))**.
% 299.99/300.65  155971[0:SpR:3596.0,155147.0] ||  -> equal(intersection(successor(u),symmetric_difference(u,singleton(u))),symmetric_difference(u,singleton(u)))**.
% 299.99/300.65  155972[0:SpR:3597.0,155147.0] ||  -> equal(intersection(symmetrization_of(u),symmetric_difference(u,inverse(u))),symmetric_difference(u,inverse(u)))**.
% 299.99/300.65  156427[5:SpL:155665.0,8735.0] || equal(symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers)),ordinal_numbers)** -> member(omega,complement(subset_relation)).
% 299.99/300.65  156437[5:SpL:155665.0,8732.0] || subclass(ordinal_numbers,symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers)))* -> member(omega,complement(subset_relation)).
% 299.99/300.65  156455[5:SpL:155665.0,25.0] || member(u,symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers)))* -> member(u,complement(subset_relation)).
% 299.99/300.65  156536[5:SpL:155666.0,8735.0] || equal(symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation),ordinal_numbers)** -> member(omega,complement(subset_relation)).
% 299.99/300.65  156546[5:SpL:155666.0,8732.0] || subclass(ordinal_numbers,symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation))* -> member(omega,complement(subset_relation)).
% 299.99/300.65  156564[5:SpL:155666.0,25.0] || member(u,symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation))* -> member(u,complement(subset_relation)).
% 299.99/300.65  156954[8:Res:156922.1,7.0] || member(not_subclass_element(u,complement(subset_relation)),inverse(subset_relation))* -> subclass(u,complement(subset_relation)).
% 299.99/300.65  124778[5:SoR:9594.0,82.1] operation(sum_class(cross_product(ordinal_numbers,ordinal_numbers))) ||  -> section(element_relation,cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers)*.
% 299.99/300.65  131536[0:Res:2504.1,152.0] || subclass(ordered_pair(u,v),recursion_equation_functions(w))* -> function(unordered_pair(u,singleton(v))).
% 299.99/300.65  132033[0:Res:10.1,19115.0] || equal(recursion_equation_functions(u),v)* -> subclass(v,w) function(not_subclass_element(v,w))*.
% 299.99/300.65  125900[5:Res:125725.1,8788.0] || subclass(omega,recursion_equation_functions(u))* -> subclass(least(element_relation,omega),cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.65  147265[5:Res:143222.1,8788.0] || equal(recursion_equation_functions(u),omega)** -> subclass(least(element_relation,omega),cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.65  130936[5:Res:125725.1,9876.0] || subclass(omega,u)* subclass(u,v)* well_ordering(ordinal_numbers,v)* -> .
% 299.99/300.65  147267[5:Res:143222.1,9876.0] || equal(u,omega) subclass(u,v)* well_ordering(ordinal_numbers,v)* -> .
% 299.99/300.65  160707[8:Rew:160496.0,67680.1] inductive(intersection(ordinal_numbers,complement(u))) || equal(complement(complement(u)),ordinal_numbers)** -> .
% 299.99/300.65  147053[5:Res:143193.1,9876.0] || equal(u,ordinal_numbers) subclass(u,v)* well_ordering(ordinal_numbers,v)* -> .
% 299.99/300.65  155263[5:SpL:154737.1,10088.0] || subclass(u,v)* equal(u,ordinal_numbers) -> member(singleton(w),v)*.
% 299.99/300.65  156965[8:Res:156922.1,8843.1] || member(singleton(u),inverse(subset_relation))* subclass(ordinal_numbers,complement(complement(subset_relation))) -> .
% 299.99/300.65  161026[2:SSi:132245.0,54.0] || well_ordering(u,omega) -> equal(integer_of(least(u,omega)),least(u,omega))**.
% 299.99/300.65  161318[8:MRR:156957.1,94701.1] || member(sum_class(u),inverse(subset_relation))* subclass(ordinal_numbers,complement(complement(subset_relation))) -> .
% 299.99/300.65  163589[5:Res:143200.1,18794.1] || equal(intersection(u,v),ordinal_numbers) member(omega,symmetric_difference(u,v))* -> .
% 299.99/300.65  165627[5:SpR:50855.1,143198.1] || member(singleton(u),subset_relation)* equal(v,ordinal_numbers) -> member(u,v)*.
% 299.99/300.65  166897[8:Res:15426.1,9876.0] || subclass(domain_relation,u)* subclass(u,v)* well_ordering(ordinal_numbers,v)* -> .
% 299.99/300.65  176787[8:Res:144409.1,66086.1] || equal(symmetric_difference(ordinal_numbers,compose(element_relation,ordinal_numbers)),ordinal_numbers)** member(omega,element_relation) -> .
% 299.99/300.65  186571[8:SpL:141394.0,176785.0] || equal(symmetric_difference(u,ordinal_numbers),ordinal_numbers) member(omega,intersection(u,ordinal_numbers))* -> .
% 299.99/300.65  186608[8:SpR:176865.1,141394.0] || equal(complement(intersection(u,ordinal_numbers)),ordinal_numbers)** -> equal(symmetric_difference(u,ordinal_numbers),ordinal_numbers).
% 299.99/300.65  166251[8:Res:164114.0,13082.1] inductive(symmetric_difference(inverse(identity_relation),symmetrization_of(identity_relation))) ||  -> member(identity_relation,complement(symmetrization_of(identity_relation)))*.
% 299.99/300.65  166537[8:Rew:140613.0,166486.0] ||  -> equal(symmetric_difference(ordinal_numbers,u),identity_relation) member(regular(symmetric_difference(ordinal_numbers,u)),complement(u))*.
% 299.99/300.65  165055[8:Res:127147.1,162901.0] || subclass(ordinal_numbers,complement(complement(subset_relation)))* equal(least(element_relation,omega),identity_relation) -> .
% 299.99/300.65  165056[8:Res:126679.1,162901.0] || subclass(omega,complement(complement(subset_relation)))* equal(least(element_relation,omega),identity_relation) -> .
% 299.99/300.65  164969[8:Res:40074.1,162888.0] || subclass(ordinal_numbers,complement(complement(subset_relation))) subclass(unordered_pair(u,v),identity_relation)* -> .
% 299.99/300.65  164983[8:Res:127147.1,162888.0] || subclass(ordinal_numbers,complement(complement(subset_relation))) subclass(least(element_relation,omega),identity_relation)* -> .
% 299.99/300.65  164984[8:Res:126679.1,162888.0] || subclass(omega,complement(complement(subset_relation))) subclass(least(element_relation,omega),identity_relation)* -> .
% 299.99/300.65  164838[7:SpR:143170.0,13101.0] ||  -> equal(second(not_subclass_element(cross_product(singleton(u),v),identity_relation)),range__dfg(ordinal_numbers,u,v))**.
% 299.99/300.65  164813[7:SpR:143170.0,13100.0] ||  -> equal(first(not_subclass_element(cross_product(u,singleton(v)),identity_relation)),domain__dfg(ordinal_numbers,u,v))**.
% 299.99/300.65  164168[8:SpL:143170.0,160735.1] || member(u,cantor(ordinal_numbers)) equal(cross_product(singleton(u),ordinal_numbers),identity_relation)** -> .
% 299.99/300.65  166194[8:Res:148858.1,13082.1] inductive(u) || subclass(u,inverse(subset_relation))* -> member(identity_relation,complement(subset_relation))*.
% 299.99/300.65  162781[8:Rew:66085.0,162774.1] || member(not_subclass_element(element_relation,identity_relation),complement(compose(element_relation,ordinal_numbers)))* -> subclass(element_relation,identity_relation).
% 299.99/300.65  163551[7:Res:13049.1,18794.1] || subclass(ordinal_numbers,intersection(u,v)) member(identity_relation,symmetric_difference(u,v))* -> .
% 299.99/300.65  165041[8:Res:40074.1,162901.0] || subclass(ordinal_numbers,complement(complement(subset_relation)))* equal(unordered_pair(u,v),identity_relation)** -> .
% 299.99/300.65  166699[8:Res:13210.1,162901.0] || equal(regular(intersection(u,subset_relation)),identity_relation)** -> equal(intersection(u,subset_relation),identity_relation).
% 299.99/300.65  166700[8:Res:13210.1,162888.0] || subclass(regular(intersection(u,subset_relation)),identity_relation)* -> equal(intersection(u,subset_relation),identity_relation).
% 299.99/300.65  166509[8:Res:13248.1,162901.0] || equal(regular(intersection(subset_relation,u)),identity_relation)** -> equal(intersection(subset_relation,u),identity_relation).
% 299.99/300.65  166510[8:Res:13248.1,162888.0] || subclass(regular(intersection(subset_relation,u)),identity_relation)* -> equal(intersection(subset_relation,u),identity_relation).
% 299.99/300.65  164920[8:SpL:160491.0,151988.0] || member(u,complement(union(v,identity_relation)))* -> member(u,symmetric_difference(ordinal_numbers,v)).
% 299.99/300.65  160771[8:Rew:140613.0,67551.0] ||  -> subclass(symmetric_difference(complement(u),union(v,identity_relation)),union(u,symmetric_difference(ordinal_numbers,v)))*.
% 299.99/300.65  13321[7:Rew:13036.0,9504.1] || well_ordering(u,v)* -> equal(segment(u,identity_relation,least(u,identity_relation)),identity_relation)**.
% 299.99/300.65  83280[7:Res:61019.0,152.0] ||  -> equal(complement(complement(recursion_equation_functions(u))),identity_relation) function(regular(complement(complement(recursion_equation_functions(u)))))*.
% 299.99/300.65  13375[7:Rew:13036.0,10016.1] || equal(restrict(u,v,w),ordinal_numbers)** -> member(identity_relation,cross_product(v,w))*.
% 299.99/300.65  13376[7:Rew:13036.0,9968.1] || subclass(ordinal_numbers,restrict(u,v,w))* -> member(identity_relation,cross_product(v,w)).
% 299.99/300.65  68875[8:SpL:66293.0,13051.0] || equal(symmetric_difference(complement(u),ordinal_numbers),ordinal_numbers) -> member(identity_relation,union(u,identity_relation))*.
% 299.99/300.65  68881[8:SpL:66293.0,13045.0] || subclass(ordinal_numbers,symmetric_difference(complement(u),ordinal_numbers))* -> member(identity_relation,union(u,identity_relation)).
% 299.99/300.65  160751[8:Rew:160491.0,69752.1] inductive(symmetric_difference(intersection(ordinal_numbers,u),identity_relation)) ||  -> member(identity_relation,union(u,identity_relation))*.
% 299.99/300.65  13379[7:Rew:13036.0,10031.1] || equal(symmetric_difference(u,v),ordinal_numbers) -> member(identity_relation,complement(intersection(u,v)))*.
% 299.99/300.65  13380[7:Rew:13036.0,9984.1] || subclass(ordinal_numbers,symmetric_difference(u,v)) -> member(identity_relation,complement(intersection(u,v)))*.
% 299.99/300.65  19820[7:Res:19734.0,13082.1] inductive(symmetric_difference(complement(u),complement(inverse(u)))) ||  -> member(identity_relation,symmetrization_of(u))*.
% 299.99/300.65  19803[7:Res:19733.0,13082.1] inductive(symmetric_difference(complement(u),complement(singleton(u)))) ||  -> member(identity_relation,successor(u))*.
% 299.99/300.65  167494[8:Res:49995.1,163154.0] || member(symmetrization_of(identity_relation),subset_relation) -> member(singleton(first(symmetrization_of(identity_relation))),inverse(identity_relation))*.
% 299.99/300.65  163160[8:Rew:162584.0,163111.1] ||  -> member(not_subclass_element(u,symmetrization_of(identity_relation)),complement(inverse(identity_relation)))* subclass(u,symmetrization_of(identity_relation)).
% 299.99/300.65  163106[8:SpR:162584.0,130703.0] ||  -> subclass(complement(union(u,complement(inverse(identity_relation)))),intersection(complement(u),symmetrization_of(identity_relation)))*.
% 299.99/300.65  163104[8:SpR:162584.0,30.0] ||  -> equal(complement(intersection(complement(u),symmetrization_of(identity_relation))),union(u,complement(inverse(identity_relation))))**.
% 299.99/300.65  163084[8:SpR:162584.0,130703.0] ||  -> subclass(complement(union(complement(inverse(identity_relation)),u)),intersection(symmetrization_of(identity_relation),complement(u)))*.
% 299.99/300.65  163082[8:SpR:162584.0,30.0] ||  -> equal(complement(intersection(symmetrization_of(identity_relation),complement(u))),union(complement(inverse(identity_relation)),u))**.
% 299.99/300.65  167495[8:Res:133837.1,163154.0] || well_ordering(ordinal_numbers,complement(symmetrization_of(identity_relation))) -> member(singleton(singleton(u)),inverse(identity_relation))*.
% 299.99/300.65  167492[8:Res:9632.1,163154.0] || equal(complement(complement(symmetrization_of(identity_relation))),ordinal_numbers) -> member(singleton(u),inverse(identity_relation))*.
% 299.99/300.65  82308[8:Res:81336.1,97.0] || subclass(domain_relation,complement(complement(compose_class(u))))* -> equal(compose(u,identity_relation),identity_relation).
% 299.99/300.65  19763[7:Res:19421.0,13082.1] inductive(symmetric_difference(complement(u),complement(v))) ||  -> member(identity_relation,union(u,v))*.
% 299.99/300.65  165174[14:SpR:30.0,165172.1] ||  -> member(identity_relation,intersection(complement(u),complement(v)))* member(identity_relation,union(u,v)).
% 299.99/300.65  62127[8:Con:62097.3] || equal(complement(u),identity_relation) member(v,ordinal_numbers)* -> member(v,u)*.
% 299.99/300.65  166830[8:SpL:160491.0,147805.0] || equal(union(u,identity_relation),omega) equal(symmetric_difference(ordinal_numbers,u),omega)** -> .
% 299.99/300.65  164910[8:SpL:160491.0,134130.0] || well_ordering(ordinal_numbers,union(u,identity_relation)) well_ordering(ordinal_numbers,symmetric_difference(ordinal_numbers,u))* -> .
% 299.99/300.65  164908[8:SpL:160491.0,147315.1] || equal(symmetric_difference(ordinal_numbers,u),omega) subclass(omega,union(u,identity_relation))* -> .
% 299.99/300.65  164909[8:SpL:160491.0,126665.1] || subclass(omega,symmetric_difference(ordinal_numbers,u))* subclass(omega,union(u,identity_relation)) -> .
% 299.99/300.65  167289[8:SpL:160491.0,126664.1] || subclass(ordinal_numbers,symmetric_difference(ordinal_numbers,u)) subclass(omega,union(u,identity_relation))* -> .
% 299.99/300.65  167360[8:SpL:160491.0,147101.1] || equal(symmetric_difference(ordinal_numbers,u),ordinal_numbers) subclass(omega,union(u,identity_relation))* -> .
% 299.99/300.65  160843[8:Rew:140613.0,67541.0] ||  -> subclass(symmetric_difference(union(u,identity_relation),complement(v)),union(symmetric_difference(ordinal_numbers,u),v))*.
% 299.99/300.65  160838[8:Rew:140613.0,66162.1] || subclass(ordinal_numbers,union(u,identity_relation)) member(identity_relation,symmetric_difference(ordinal_numbers,u))* -> .
% 299.99/300.65  160839[8:Rew:140613.0,66163.0] || subclass(ordinal_numbers,symmetric_difference(ordinal_numbers,u))* subclass(ordinal_numbers,union(u,identity_relation)) -> .
% 299.99/300.65  160840[8:Rew:140613.0,67577.1] || subclass(ordinal_numbers,union(u,identity_relation)) member(omega,symmetric_difference(ordinal_numbers,u))* -> .
% 299.99/300.65  160841[8:Rew:140613.0,67578.0] || subclass(domain_relation,symmetric_difference(ordinal_numbers,u))* subclass(ordinal_numbers,union(u,identity_relation)) -> .
% 299.99/300.65  160842[8:Rew:140613.0,67580.0] || member(symmetric_difference(ordinal_numbers,u),subset_relation)* subclass(ordinal_numbers,union(u,identity_relation)) -> .
% 299.99/300.65  164896[8:SpL:160491.0,147314.1] || equal(symmetric_difference(ordinal_numbers,u),omega) subclass(ordinal_numbers,union(u,identity_relation))* -> .
% 299.99/300.65  164897[8:SpL:160491.0,127130.1] || subclass(omega,symmetric_difference(ordinal_numbers,u))* subclass(ordinal_numbers,union(u,identity_relation)) -> .
% 299.99/300.65  167303[8:SpL:160491.0,147100.1] || equal(symmetric_difference(ordinal_numbers,u),ordinal_numbers) subclass(ordinal_numbers,union(u,identity_relation))* -> .
% 299.99/300.65  160834[8:Rew:140613.0,81391.0] || subclass(domain_relation,symmetric_difference(ordinal_numbers,u))* subclass(domain_relation,union(u,identity_relation)) -> .
% 299.99/300.65  160835[8:Rew:140613.0,81401.0] || subclass(ordinal_numbers,symmetric_difference(ordinal_numbers,u)) subclass(domain_relation,union(u,identity_relation))* -> .
% 299.99/300.65  160832[8:Rew:140613.0,81494.0] || equal(symmetric_difference(ordinal_numbers,u),domain_relation)** equal(union(u,identity_relation),domain_relation) -> .
% 299.99/300.65  160833[8:Rew:140613.0,81502.0] || equal(symmetric_difference(ordinal_numbers,u),ordinal_numbers)** equal(union(u,identity_relation),domain_relation) -> .
% 299.99/300.65  164902[8:SpL:160491.0,151970.0] || subclass(ordinal_numbers,complement(union(u,identity_relation)))* -> member(omega,symmetric_difference(ordinal_numbers,u)).
% 299.99/300.65  167515[8:SpL:160491.0,163545.0] || subclass(ordinal_numbers,complement(union(u,identity_relation)))* -> member(identity_relation,symmetric_difference(ordinal_numbers,u)).
% 299.99/300.65  160836[8:Rew:140613.0,66161.1] || equal(complement(union(u,identity_relation)),ordinal_numbers) -> member(identity_relation,symmetric_difference(ordinal_numbers,u))*.
% 299.99/300.65  160837[8:Rew:140613.0,67582.1] || equal(complement(union(u,identity_relation)),ordinal_numbers) -> member(omega,symmetric_difference(ordinal_numbers,u))*.
% 299.99/300.65  68873[8:SpL:66293.0,8735.0] || equal(symmetric_difference(complement(u),ordinal_numbers),ordinal_numbers) -> member(omega,union(u,identity_relation))*.
% 299.99/300.65  68879[8:SpL:66293.0,8732.0] || subclass(ordinal_numbers,symmetric_difference(complement(u),ordinal_numbers))* -> member(omega,union(u,identity_relation)).
% 299.99/300.65  162049[8:Rew:140613.0,161994.0] || subclass(ordinal_numbers,symmetric_difference(ordinal_numbers,u)) member(omega,union(u,identity_relation))* -> .
% 299.99/300.65  67576[8:SpL:66160.0,9922.1] inductive(intersection(complement(u),ordinal_numbers)) || equal(union(u,identity_relation),ordinal_numbers)** -> .
% 299.99/300.65  160868[8:Rew:160491.0,144478.0] ||  -> equal(symmetric_difference(ordinal_numbers,symmetric_difference(complement(u),ordinal_numbers)),symmetric_difference(union(u,identity_relation),ordinal_numbers))**.
% 299.99/300.65  13391[7:Rew:13036.0,10720.1] inductive(singleton(u)) ||  -> equal(integer_of(u),identity_relation)** equal(singleton(u),omega).
% 299.99/300.65  163021[7:SpR:13596.1,154737.1] || subclass(regular(u),u)* -> equal(u,identity_relation) equal(regular(u),identity_relation).
% 299.99/300.65  166804[8:Res:13227.2,162901.0] || subclass(u,subset_relation)* equal(regular(u),identity_relation) -> equal(u,identity_relation).
% 299.99/300.65  166805[8:Res:13227.2,162888.0] || subclass(u,subset_relation) subclass(regular(u),identity_relation)* -> equal(u,identity_relation).
% 299.99/300.65  167231[8:Res:143200.1,14681.0] || equal(regular(u),ordinal_numbers) member(omega,u)* -> equal(u,identity_relation).
% 299.99/300.65  62966[8:SpR:15528.0,50064.1] || member(not_subclass_element(identity_relation,identity_relation),subset_relation) -> member(range__dfg(identity_relation,u,v),ordinal_numbers)*.
% 299.99/300.65  19707[8:Res:19172.1,1301.1] || equal(identity_relation,u) member(u,ordinal_numbers)* -> equal(sum_class(u),u).
% 299.99/300.65  13265[7:Rew:13036.0,6780.1] || subclass(singleton(u),v)* -> equal(singleton(u),identity_relation) member(u,v).
% 299.99/300.65  165187[14:Res:165172.1,9876.0] || subclass(complement(u),v)* well_ordering(ordinal_numbers,v) -> member(identity_relation,u).
% 299.99/300.65  167631[14:SpL:117142.0,165401.1] operation(restrict(element_relation,ordinal_numbers,u)) || equal(sum_class(u),singleton(identity_relation))** -> .
% 299.99/300.65  167630[14:SpL:117066.0,165401.1] operation(flip(cross_product(u,ordinal_numbers))) || equal(inverse(u),singleton(identity_relation))** -> .
% 299.99/300.65  165372[14:Res:165168.1,19676.0] || equal(symmetric_difference(u,inverse(u)),singleton(identity_relation))** -> member(identity_relation,symmetrization_of(u)).
% 299.99/300.65  165371[14:Res:165168.1,19559.0] || equal(symmetric_difference(u,singleton(u)),singleton(identity_relation))** -> member(identity_relation,successor(u)).
% 299.99/300.65  165370[14:Res:165168.1,3617.0] || equal(symmetric_difference(u,v),singleton(identity_relation)) -> member(identity_relation,union(u,v))*.
% 299.99/300.65  165365[14:Res:165168.1,5.0] || equal(u,singleton(identity_relation)) subclass(u,v)* -> member(identity_relation,v)*.
% 299.99/300.65  165359[14:Res:165168.1,66086.1] || equal(complement(compose(element_relation,ordinal_numbers)),singleton(identity_relation))** member(identity_relation,element_relation) -> .
% 299.99/300.65  15576[8:Res:15426.1,161.0] || subclass(domain_relation,omega) -> equal(integer_of(ordered_pair(identity_relation,identity_relation)),ordered_pair(identity_relation,identity_relation))**.
% 299.99/300.65  16120[8:MRR:16118.0,8658.0] || equal(compose(u,identity_relation),identity_relation) -> member(ordered_pair(identity_relation,identity_relation),compose_class(u))*.
% 299.99/300.65  16719[8:Res:15426.1,8788.0] || subclass(domain_relation,recursion_equation_functions(u))* -> subclass(ordered_pair(identity_relation,identity_relation),cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.65  82281[8:Res:81336.1,3700.0] || subclass(domain_relation,complement(complement(singleton(u))))* -> equal(ordered_pair(identity_relation,identity_relation),u).
% 299.99/300.65  15573[8:Res:15426.1,898.0] || subclass(domain_relation,restrict(u,v,w))* -> member(ordered_pair(identity_relation,identity_relation),u).
% 299.99/300.65  83616[8:SpL:33.0,83166.0] || equal(restrict(u,v,w),domain_relation)** -> member(ordered_pair(identity_relation,identity_relation),u)*.
% 299.99/300.65  187583[8:Rew:160491.0,186611.0] || equal(union(u,identity_relation),ordinal_numbers) -> equal(symmetric_difference(complement(u),ordinal_numbers),ordinal_numbers)**.
% 299.99/300.65  189804[8:SpL:160491.0,167369.0] || equal(union(u,identity_relation),omega) equal(symmetric_difference(ordinal_numbers,u),ordinal_numbers)** -> .
% 299.99/300.65  189825[8:Rew:144460.0,189781.1] || subclass(ordinal_numbers,union(u,identity_relation))* -> equal(symmetric_difference(complement(u),ordinal_numbers),ordinal_numbers).
% 299.99/300.65  190503[18:MRR:165296.1,190496.0] || well_ordering(u,inverse(identity_relation)) -> member(least(u,symmetrization_of(identity_relation)),symmetrization_of(identity_relation))*.
% 299.99/300.65  190534[18:Res:190442.1,66086.1] || equal(complement(compose(element_relation,ordinal_numbers)),symmetrization_of(identity_relation))** member(identity_relation,element_relation) -> .
% 299.99/300.65  190540[18:Res:190442.1,5.0] || equal(u,symmetrization_of(identity_relation)) subclass(u,v)* -> member(identity_relation,v)*.
% 299.99/300.65  190545[18:Res:190442.1,3617.0] || equal(symmetric_difference(u,v),symmetrization_of(identity_relation)) -> member(identity_relation,union(u,v))*.
% 299.99/300.65  190546[18:Res:190442.1,19559.0] || equal(symmetric_difference(u,singleton(u)),symmetrization_of(identity_relation))** -> member(identity_relation,successor(u)).
% 299.99/300.65  190547[18:Res:190442.1,19676.0] || equal(symmetric_difference(u,inverse(u)),symmetrization_of(identity_relation))** -> member(identity_relation,symmetrization_of(u)).
% 299.99/300.65  190643[18:Res:190593.1,66086.1] || equal(complement(compose(element_relation,ordinal_numbers)),inverse(identity_relation))** member(identity_relation,element_relation) -> .
% 299.99/300.65  190649[18:Res:190593.1,5.0] || equal(u,inverse(identity_relation)) subclass(u,v)* -> member(identity_relation,v)*.
% 299.99/300.65  190654[18:Res:190593.1,3617.0] || equal(symmetric_difference(u,v),inverse(identity_relation)) -> member(identity_relation,union(u,v))*.
% 299.99/300.65  190655[18:Res:190593.1,19559.0] || equal(symmetric_difference(u,singleton(u)),inverse(identity_relation))** -> member(identity_relation,successor(u)).
% 299.99/300.65  190656[18:Res:190593.1,19676.0] || equal(symmetric_difference(u,inverse(u)),inverse(identity_relation))** -> member(identity_relation,symmetrization_of(u)).
% 299.99/300.65  191961[18:Res:190515.1,898.0] || subclass(ordinal_numbers,restrict(u,v,w))* -> member(regular(symmetrization_of(identity_relation)),u).
% 299.99/300.65  192005[18:SpL:117066.0,190588.1] operation(flip(cross_product(u,ordinal_numbers))) || equal(inverse(u),symmetrization_of(identity_relation))* -> .
% 299.99/300.65  192006[18:SpL:117142.0,190588.1] operation(restrict(element_relation,ordinal_numbers,u)) || equal(sum_class(u),symmetrization_of(identity_relation))* -> .
% 299.99/300.65  192011[18:SpL:117066.0,190699.1] operation(flip(cross_product(u,ordinal_numbers))) || equal(inverse(u),inverse(identity_relation))* -> .
% 299.99/300.65  192012[18:SpL:117142.0,190699.1] operation(restrict(element_relation,ordinal_numbers,u)) || equal(sum_class(u),inverse(identity_relation))** -> .
% 299.99/300.65  192041[8:Res:148858.1,17333.0] || subclass(complement(complement(subset_relation)),inverse(subset_relation))* -> equal(complement(complement(subset_relation)),identity_relation).
% 299.99/300.65  192176[7:Res:192149.1,18794.1] || equal(intersection(u,v),ordinal_numbers) member(identity_relation,symmetric_difference(u,v))* -> .
% 299.99/300.65  192280[7:SpL:155665.0,13045.0] || subclass(ordinal_numbers,symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers)))* -> member(identity_relation,complement(subset_relation)).
% 299.99/300.65  192281[7:SpL:155666.0,13045.0] || subclass(ordinal_numbers,symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation))* -> member(identity_relation,complement(subset_relation)).
% 299.99/300.65  192320[7:SpL:155665.0,13051.0] || equal(symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers)),ordinal_numbers)** -> member(identity_relation,complement(subset_relation)).
% 299.99/300.65  192321[7:SpL:155666.0,13051.0] || equal(symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation),ordinal_numbers)** -> member(identity_relation,complement(subset_relation)).
% 299.99/300.65  192558[7:SpR:192514.1,154737.1] || subclass(singleton(u),recursion_equation_functions(v))* -> function(u) equal(singleton(u),identity_relation).
% 299.99/300.65  192751[7:SpR:192639.1,154737.1] || subclass(recursion_equation_functions(u),singleton(v))* -> function(v) equal(recursion_equation_functions(u),identity_relation).
% 299.99/300.65  192881[7:SpR:192834.1,33.0] ||  -> member(u,cross_product(v,w)) equal(restrict(singleton(u),v,w),identity_relation)**.
% 299.99/300.65  192949[8:Rew:140603.0,192868.1,66036.0,192868.1] ||  -> member(u,v) equal(symmetric_difference(v,singleton(u)),union(v,singleton(u)))**.
% 299.99/300.65  193096[7:SpR:193044.1,154945.0] ||  -> member(u,intersection(singleton(u),v))* equal(intersection(singleton(u),v),identity_relation).
% 299.99/300.65  193097[7:SpR:193044.1,155147.0] ||  -> member(u,intersection(v,singleton(u)))* equal(intersection(v,singleton(u)),identity_relation).
% 299.99/300.65  193103[7:SpR:193044.1,147905.0] ||  -> member(u,complement(complement(singleton(u))))* equal(complement(complement(singleton(u))),identity_relation).
% 299.99/300.65  193172[8:Rew:140603.0,193077.1,66036.0,193077.1] ||  -> member(u,v) equal(symmetric_difference(singleton(u),v),union(singleton(u),v))**.
% 299.99/300.65  60932[8:Res:9618.2,14676.0] || member(ordered_pair(u,v),cross_product(ordinal_numbers,ordinal_numbers))* subclass(composition_function,identity_relation) -> .
% 299.99/300.65  130950[5:Res:49995.1,9876.0] || member(u,subset_relation)* subclass(u,v)* well_ordering(ordinal_numbers,v)* -> .
% 299.99/300.65  132466[5:SpL:18840.1,132438.0] || member(u,subset_relation)* equal(v,u)* well_ordering(ordinal_numbers,v)* -> .
% 299.99/300.65  134035[5:SpL:50855.1,134030.0] || member(singleton(u),subset_relation) well_ordering(ordinal_numbers,unordered_pair(singleton(u),v))* -> .
% 299.99/300.65  134049[5:SpL:50855.1,134031.0] || member(singleton(u),subset_relation) well_ordering(ordinal_numbers,unordered_pair(v,singleton(u)))* -> .
% 299.99/300.65  134108[8:Res:133837.1,14679.1] || well_ordering(ordinal_numbers,complement(inverse(subset_relation)))* member(singleton(singleton(u)),subset_relation)* -> .
% 299.99/300.65  65402[7:Res:13237.2,41096.0] || well_ordering(u,ordinal_numbers) -> equal(v,identity_relation) member(least(u,v),ordinal_numbers)*.
% 299.99/300.65  131183[5:Res:39607.2,41096.0] inductive(u) || well_ordering(v,ordinal_numbers) -> member(least(v,u),ordinal_numbers)*.
% 299.99/300.65  132209[5:Res:39609.2,41096.0] inductive(u) || well_ordering(v,u) -> member(least(v,u),ordinal_numbers)*.
% 299.99/300.65  148892[8:Res:148858.1,130942.0] || subclass(ordered_pair(u,v),inverse(subset_relation))* well_ordering(ordinal_numbers,complement(subset_relation)) -> .
% 299.99/300.65  156963[8:Res:156922.1,133836.0] || member(singleton(singleton(u)),inverse(subset_relation))* well_ordering(ordinal_numbers,complement(subset_relation)) -> .
% 299.99/300.65  194517[8:Rew:162584.0,194495.0] || subclass(ordinal_numbers,symmetrization_of(identity_relation)) -> subclass(singleton(unordered_pair(u,v)),symmetrization_of(identity_relation))*.
% 299.99/300.65  194518[8:Rew:162584.0,194501.0] || subclass(ordinal_numbers,symmetrization_of(identity_relation)) -> subclass(singleton(least(element_relation,omega)),symmetrization_of(identity_relation))*.
% 299.99/300.65  194519[8:Rew:162584.0,194502.0] || subclass(omega,symmetrization_of(identity_relation)) -> subclass(singleton(least(element_relation,omega)),symmetrization_of(identity_relation))*.
% 299.99/300.65  194520[8:Rew:162584.0,194508.0] || subclass(ordinal_numbers,symmetrization_of(identity_relation)) -> subclass(singleton(ordered_pair(u,v)),symmetrization_of(identity_relation))*.
% 299.99/300.65  194522[8:Rew:162584.0,194494.1,162584.0,194494.0] ||  -> subclass(singleton(not_subclass_element(symmetrization_of(identity_relation),u)),symmetrization_of(identity_relation))* subclass(symmetrization_of(identity_relation),u).
% 299.99/300.65  194535[20:MRR:194527.1,165227.0] || well_ordering(u,symmetrization_of(identity_relation)) -> member(least(u,singleton(identity_relation)),singleton(identity_relation))*.
% 299.99/300.65  194582[8:SpR:188530.1,69395.0] || member(u,ordinals_with_null_class_as_identity) -> equal(complement(symmetric_difference(u,ordinal_numbers)),union(u,identity_relation))**.
% 299.99/300.65  195080[14:Res:156922.1,165357.1] || member(identity_relation,inverse(subset_relation))* equal(complement(complement(subset_relation)),singleton(identity_relation)) -> .
% 299.99/300.65  195092[14:Res:193179.0,165357.1] || equal(complement(inverse(singleton(identity_relation))),singleton(identity_relation))** -> asymmetric(singleton(identity_relation),u)*.
% 299.99/300.65  195127[14:MRR:195084.0,13126.0] || equal(complement(union(u,v)),singleton(identity_relation))** -> member(identity_relation,complement(u)).
% 299.99/300.65  195128[14:MRR:195085.0,13126.0] || equal(complement(union(u,v)),singleton(identity_relation))** -> member(identity_relation,complement(v)).
% 299.99/300.65  195137[14:SpL:160491.0,195115.1] inductive(symmetric_difference(ordinal_numbers,u)) || equal(union(u,identity_relation),singleton(identity_relation))** -> .
% 299.99/300.65  195436[16:Rew:195224.0,163169.0] ||  -> equal(complement(intersection(singleton(identity_relation),complement(u))),union(complement(singleton(identity_relation)),u))**.
% 299.99/300.65  195437[16:Rew:195224.0,163171.0] ||  -> subclass(complement(union(complement(singleton(identity_relation)),u)),intersection(singleton(identity_relation),complement(u)))*.
% 299.99/300.65  195440[16:Rew:195224.0,163191.0] ||  -> equal(complement(intersection(complement(u),singleton(identity_relation))),union(u,complement(singleton(identity_relation))))**.
% 299.99/300.65  195441[16:Rew:195224.0,163193.0] ||  -> subclass(complement(union(u,complement(singleton(identity_relation)))),intersection(complement(u),singleton(identity_relation)))*.
% 299.99/300.65  195574[16:Rew:195224.0,195444.1] ||  -> member(not_subclass_element(u,singleton(identity_relation)),complement(singleton(identity_relation)))* subclass(u,singleton(identity_relation)).
% 299.99/300.65  195453[16:Rew:195224.0,166028.1] || well_ordering(u,singleton(identity_relation)) -> member(least(u,singleton(identity_relation)),singleton(identity_relation))*.
% 299.99/300.65  195594[16:Rew:195224.0,195211.1,195239.0,195211.0] || subclass(omega,singleton(identity_relation)) -> subclass(singleton(least(element_relation,omega)),singleton(identity_relation))*.
% 299.99/300.65  196074[18:Res:190510.1,28.1] || subclass(inverse(identity_relation),complement(u)) member(regular(symmetrization_of(identity_relation)),u)* -> .
% 299.99/300.65  196077[18:Res:190510.1,151988.0] || subclass(inverse(identity_relation),complement(complement(u)))* -> member(regular(symmetrization_of(identity_relation)),u).
% 299.99/300.65  196084[18:Res:190510.1,26.0] || subclass(inverse(identity_relation),intersection(u,v))* -> member(regular(symmetrization_of(identity_relation)),v).
% 299.99/300.65  196085[18:Res:190510.1,25.0] || subclass(inverse(identity_relation),intersection(u,v))* -> member(regular(symmetrization_of(identity_relation)),u).
% 299.99/300.65  196095[18:Res:190510.1,50033.0] || subclass(inverse(identity_relation),subset_relation) equal(complement(regular(symmetrization_of(identity_relation))),ordinal_numbers)** -> .
% 299.99/300.65  196099[18:Res:190510.1,14679.1] || subclass(inverse(identity_relation),inverse(subset_relation)) member(regular(symmetrization_of(identity_relation)),subset_relation)* -> .
% 299.99/300.65  196134[18:Res:156922.1,190532.1] || member(identity_relation,inverse(subset_relation))* equal(complement(complement(subset_relation)),symmetrization_of(identity_relation)) -> .
% 299.99/300.65  196146[18:Res:193179.0,190532.1] || equal(complement(inverse(singleton(identity_relation))),symmetrization_of(identity_relation))** -> asymmetric(singleton(identity_relation),u)*.
% 299.99/300.65  196178[18:MRR:196138.0,13126.0] || equal(complement(union(u,v)),symmetrization_of(identity_relation))** -> member(identity_relation,complement(u)).
% 299.99/300.65  196179[18:MRR:196139.0,13126.0] || equal(complement(union(u,v)),symmetrization_of(identity_relation))** -> member(identity_relation,complement(v)).
% 299.99/300.65  196194[18:SpL:160491.0,196166.1] inductive(symmetric_difference(ordinal_numbers,u)) || equal(union(u,identity_relation),symmetrization_of(identity_relation))** -> .
% 299.99/300.65  196224[18:Res:156922.1,190641.1] || member(identity_relation,inverse(subset_relation))* equal(complement(complement(subset_relation)),inverse(identity_relation)) -> .
% 299.99/300.65  196236[18:Res:193179.0,190641.1] || equal(complement(inverse(singleton(identity_relation))),inverse(identity_relation))** -> asymmetric(singleton(identity_relation),u)*.
% 299.99/300.65  196268[18:MRR:196228.0,13126.0] || equal(complement(union(u,v)),inverse(identity_relation))** -> member(identity_relation,complement(u)).
% 299.99/300.65  196269[18:MRR:196229.0,13126.0] || equal(complement(union(u,v)),inverse(identity_relation))** -> member(identity_relation,complement(v)).
% 299.99/300.65  196286[18:SpL:160491.0,196256.1] inductive(symmetric_difference(ordinal_numbers,u)) || equal(union(u,identity_relation),inverse(identity_relation))** -> .
% 299.99/300.65  196358[21:SpL:117066.0,196356.1] || member(flip(cross_product(u,ordinal_numbers)),ordinal_numbers)* member(v,inverse(u))* -> .
% 299.99/300.65  196359[21:SpL:117142.0,196356.1] || member(restrict(element_relation,ordinal_numbers,u),ordinal_numbers)* member(v,sum_class(u))* -> .
% 299.99/300.65  196557[21:Res:41203.1,196372.0] || member(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers)* -> equal(cantor(least(element_relation,domain_relation)),identity_relation).
% 299.99/300.65  196582[21:Res:80082.1,196372.0] || member(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers)* -> equal(cantor(least(element_relation,rest_relation)),identity_relation).
% 299.99/300.65  196583[21:Res:80198.1,196372.0] || member(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers)* -> equal(cantor(least(element_relation,element_relation)),identity_relation).
% 299.99/300.65  196702[21:Rew:196554.1,160885.2] || member(u,subset_relation) member(u,domain_relation)* -> equal(second(u),identity_relation).
% 299.99/300.65  197519[21:MRR:197518.1,13039.0] operation(u) ||  -> equal(singleton(cantor(u)),identity_relation)** equal(range_of(u),identity_relation).
% 299.99/300.65  198165[21:SpR:197474.0,47.0] ||  -> equal(range_of(u),identity_relation) equal(union(inverse(u),identity_relation),successor(inverse(u)))**.
% 299.99/300.65  39958[5:SpL:43.0,39811.1] || equal(complement(rest_of(inverse(u))),ordinal_numbers)** member(v,range_of(u))* -> .
% 299.99/300.65  195995[16:MRR:195938.0,13126.0] ||  -> member(identity_relation,cantor(element_relation)) equal(power_class(complement(singleton(identity_relation))),complement(range_of(identity_relation)))**.
% 299.99/300.65  194982[15:MRR:194954.0,165460.0] || subclass(ordinal_numbers,complement(union(u,v)))* -> member(range_of(identity_relation),complement(v)).
% 299.99/300.65  194981[15:MRR:194953.0,165460.0] || subclass(ordinal_numbers,complement(union(u,v)))* -> member(range_of(identity_relation),complement(u)).
% 299.99/300.65  194960[15:Res:18819.1,165527.1] || member(range_of(identity_relation),subset_relation) subclass(ordinal_numbers,complement(cross_product(ordinal_numbers,ordinal_numbers)))* -> .
% 299.99/300.65  194949[15:Res:156922.1,165527.1] || member(range_of(identity_relation),inverse(subset_relation))* subclass(ordinal_numbers,complement(complement(subset_relation))) -> .
% 299.99/300.65  14771[8:SpR:14756.0,62.1] || member(ordered_pair(u,v),compose(identity_relation,w))* -> member(v,range_of(identity_relation)).
% 299.99/300.65  165529[15:Res:165526.1,66086.1] || subclass(ordinal_numbers,complement(compose(element_relation,ordinal_numbers)))* member(range_of(identity_relation),element_relation) -> .
% 299.99/300.65  165540[15:Res:165526.1,3617.0] || subclass(ordinal_numbers,symmetric_difference(u,v)) -> member(range_of(identity_relation),union(u,v))*.
% 299.99/300.65  165541[15:Res:165526.1,19559.0] || subclass(ordinal_numbers,symmetric_difference(u,singleton(u)))* -> member(range_of(identity_relation),successor(u)).
% 299.99/300.65  165542[15:Res:165526.1,19676.0] || subclass(ordinal_numbers,symmetric_difference(u,inverse(u)))* -> member(range_of(identity_relation),symmetrization_of(u)).
% 299.99/300.65  165535[15:Res:165526.1,5.0] || subclass(ordinal_numbers,u)* subclass(u,v)* -> member(range_of(identity_relation),v)*.
% 299.99/300.65  191877[15:Res:165442.1,898.0] || subclass(ordinal_numbers,restrict(u,v,w))* -> member(sum_class(range_of(identity_relation)),u).
% 299.99/300.65  17356[7:Rew:59.0,17340.1] || subclass(power_class(u),image(element_relation,complement(u)))* -> equal(power_class(u),identity_relation).
% 299.99/300.65  13366[7:Rew:13036.0,9902.1] || subclass(ordinal_numbers,power_class(u)) member(identity_relation,image(element_relation,complement(u)))* -> .
% 299.99/300.65  13365[7:Rew:13036.0,9939.1] || equal(complement(power_class(u)),ordinal_numbers) -> member(identity_relation,image(element_relation,complement(u)))*.
% 299.99/300.65  167516[7:SpL:59.0,163545.0] || subclass(ordinal_numbers,complement(power_class(u))) -> member(identity_relation,image(element_relation,complement(u)))*.
% 299.99/300.65  8903[5:Rew:8637.0,6928.0] || equal(complement(power_class(u)),ordinal_numbers) -> member(omega,image(element_relation,complement(u)))*.
% 299.99/300.65  152969[5:SpL:59.0,151970.0] || subclass(ordinal_numbers,complement(power_class(u))) -> member(omega,image(element_relation,complement(u)))*.
% 299.99/300.65  8868[5:Rew:8637.0,6721.0] || subclass(ordinal_numbers,power_class(u)) member(omega,image(element_relation,complement(u)))* -> .
% 299.99/300.65  81499[8:SpL:59.0,81412.1] || equal(image(element_relation,complement(u)),domain_relation)** equal(power_class(u),domain_relation) -> .
% 299.99/300.65  81396[8:SpL:59.0,81322.1] || subclass(domain_relation,image(element_relation,complement(u)))* subclass(domain_relation,power_class(u)) -> .
% 299.99/300.65  63446[8:SpL:59.0,63019.1] || subclass(domain_relation,image(element_relation,complement(u)))* subclass(ordinal_numbers,power_class(u)) -> .
% 299.99/300.65  50416[5:SpL:59.0,50032.1] || member(image(element_relation,complement(u)),subset_relation)* subclass(ordinal_numbers,power_class(u)) -> .
% 299.99/300.65  127025[5:SpL:59.0,126665.1] || subclass(omega,image(element_relation,complement(u)))* subclass(omega,power_class(u)) -> .
% 299.99/300.65  127424[5:SpL:59.0,127130.1] || subclass(omega,image(element_relation,complement(u)))* subclass(ordinal_numbers,power_class(u)) -> .
% 299.99/300.65  147799[5:SpL:59.0,147315.1] || equal(image(element_relation,complement(u)),omega)** subclass(omega,power_class(u)) -> .
% 299.99/300.65  147744[5:SpL:59.0,147314.1] || equal(image(element_relation,complement(u)),omega)** subclass(ordinal_numbers,power_class(u)) -> .
% 299.99/300.65  166831[5:SpL:59.0,147805.0] || equal(power_class(u),omega) equal(image(element_relation,complement(u)),omega)** -> .
% 299.99/300.65  134170[5:SpL:59.0,134130.0] || well_ordering(ordinal_numbers,power_class(u)) well_ordering(ordinal_numbers,image(element_relation,complement(u)))* -> .
% 299.99/300.65  151945[5:SpR:59.0,147905.0] ||  -> equal(intersection(image(element_relation,complement(u)),complement(power_class(u))),complement(power_class(u)))**.
% 299.99/300.65  81406[8:SpL:59.0,81326.1] || subclass(ordinal_numbers,image(element_relation,complement(u)))* subclass(domain_relation,power_class(u)) -> .
% 299.99/300.65  9571[5:SpL:59.0,9488.1] || subclass(ordinal_numbers,image(element_relation,complement(u)))* subclass(ordinal_numbers,power_class(u)) -> .
% 299.99/300.65  167290[5:SpL:59.0,126664.1] || subclass(ordinal_numbers,image(element_relation,complement(u)))* subclass(omega,power_class(u)) -> .
% 299.99/300.65  18445[7:Res:13049.1,288.0] || subclass(ordinal_numbers,image(element_relation,complement(u)))* member(identity_relation,power_class(u)) -> .
% 299.99/300.65  81507[8:SpL:59.0,81488.1] || equal(image(element_relation,complement(u)),ordinal_numbers)** equal(power_class(u),domain_relation) -> .
% 299.99/300.65  124987[5:Res:10.1,66645.0] || equal(image(element_relation,complement(u)),ordinal_numbers)** member(omega,power_class(u)) -> .
% 299.99/300.65  167304[5:SpL:59.0,147100.1] || equal(image(element_relation,complement(u)),ordinal_numbers)** subclass(ordinal_numbers,power_class(u)) -> .
% 299.99/300.65  167361[5:SpL:59.0,147101.1] || equal(image(element_relation,complement(u)),ordinal_numbers)** subclass(omega,power_class(u)) -> .
% 299.99/300.65  173852[5:SpL:59.0,167369.0] || equal(power_class(u),omega) equal(image(element_relation,complement(u)),ordinal_numbers)** -> .
% 299.99/300.65  192205[7:Res:192149.1,288.0] || equal(image(element_relation,complement(u)),ordinal_numbers)** member(identity_relation,power_class(u)) -> .
% 299.99/300.65  159458[5:Obv:159449.1] || subclass(u,complement(power_class(v))) -> subclass(u,image(element_relation,complement(v)))*.
% 299.99/300.65  154272[5:SpL:59.0,151988.0] || member(u,complement(power_class(v))) -> member(u,image(element_relation,complement(v)))*.
% 299.99/300.65  193484[14:SpR:162038.0,165172.1] ||  -> member(identity_relation,image(element_relation,symmetrization_of(identity_relation)))* member(identity_relation,power_class(complement(inverse(identity_relation)))).
% 299.99/300.65  142405[8:Rew:141402.0,121626.0] ||  -> subclass(symmetric_difference(ordinal_numbers,image(element_relation,power_class(u))),power_class(image(element_relation,complement(u))))*.
% 299.99/300.65  19198[8:Res:19172.1,13052.1] || equal(image(successor_relation,u),identity_relation)** member(identity_relation,u) -> inductive(u).
% 299.99/300.65  66706[7:Res:66492.1,8979.0] ||  -> equal(integer_of(image(u,singleton(v))),identity_relation)** member(apply(u,v),ordinal_numbers).
% 299.99/300.65  18528[7:Res:18517.1,8979.0] ||  -> equal(singleton(image(u,singleton(v))),identity_relation)** member(apply(u,v),ordinal_numbers).
% 299.99/300.65  195347[16:Rew:195224.0,193320.0] ||  -> member(identity_relation,image(element_relation,singleton(identity_relation)))* member(identity_relation,power_class(complement(singleton(identity_relation)))).
% 299.99/300.65  196288[18:SpL:59.0,196256.1] inductive(image(element_relation,complement(u))) || equal(power_class(u),inverse(identity_relation))** -> .
% 299.99/300.65  196195[18:SpL:59.0,196166.1] inductive(image(element_relation,complement(u))) || equal(power_class(u),symmetrization_of(identity_relation))* -> .
% 299.99/300.65  195139[14:SpL:59.0,195115.1] inductive(image(element_relation,complement(u))) || equal(power_class(u),singleton(identity_relation))** -> .
% 299.99/300.65  96975[5:Rew:59.0,96953.1,59.0,96953.0] ||  -> subclass(singleton(not_subclass_element(power_class(u),v)),power_class(u))* subclass(power_class(u),v).
% 299.99/300.65  146849[5:MRR:146824.0,8956.1] || member(u,ordinal_numbers) subclass(ordinal_numbers,complement(unordered_pair(power_class(u),v)))* -> .
% 299.99/300.65  146850[5:MRR:146825.0,8956.1] || member(u,ordinal_numbers) subclass(ordinal_numbers,complement(unordered_pair(v,power_class(u))))* -> .
% 299.99/300.65  161319[8:MRR:156958.1,94701.1] || member(power_class(u),inverse(subset_relation))* subclass(ordinal_numbers,complement(complement(subset_relation))) -> .
% 299.99/300.65  126676[5:Rew:59.0,126649.0] || subclass(omega,power_class(u)) -> subclass(singleton(least(element_relation,omega)),power_class(u))*.
% 299.99/300.65  96971[5:Rew:59.0,96954.0] || subclass(ordinal_numbers,power_class(u)) -> subclass(singleton(unordered_pair(v,w)),power_class(u))*.
% 299.99/300.65  96972[5:Rew:59.0,96963.0] || subclass(ordinal_numbers,power_class(u)) -> subclass(singleton(ordered_pair(v,w)),power_class(u))*.
% 299.99/300.65  127142[5:Rew:59.0,127114.0] || subclass(ordinal_numbers,power_class(u)) -> subclass(singleton(least(element_relation,omega)),power_class(u))*.
% 299.99/300.65  198633[21:SpR:198454.1,6984.0] || equal(rest_of(apply(choice,omega)),rest_relation)** -> equal(apply(choice,omega),identity_relation).
% 299.99/300.65  190502[18:MRR:167473.1,190496.0] || member(symmetrization_of(identity_relation),ordinal_numbers) -> member(apply(choice,symmetrization_of(identity_relation)),inverse(identity_relation))*.
% 299.99/300.65  61920[7:Res:13069.2,41096.0] || member(u,ordinal_numbers) -> equal(u,identity_relation) member(apply(choice,u),ordinal_numbers)*.
% 299.99/300.65  18515[5:Res:18510.1,5.0] function(u) || subclass(ordinal_numbers,v) -> member(apply(u,w),v)*.
% 299.99/300.65  198753[21:SpR:159.0,196564.1] function(recursion(u,successor_relation,union_of_range_map)) ||  -> equal(cantor(ordinal_add(u,v)),identity_relation)**.
% 299.99/300.65  192207[8:Res:192149.1,14681.0] || equal(regular(u),ordinal_numbers) member(identity_relation,u)* -> equal(u,identity_relation).
% 299.99/300.65  18748[8:Res:13049.1,14681.0] || subclass(ordinal_numbers,regular(u))* member(identity_relation,u) -> equal(u,identity_relation).
% 299.99/300.65  204041[8:Res:192333.1,66086.1] || equal(symmetric_difference(ordinal_numbers,compose(element_relation,ordinal_numbers)),ordinal_numbers)** member(identity_relation,element_relation) -> .
% 299.99/300.65  204147[8:Res:204134.1,7.0] || member(not_subclass_element(u,symmetrization_of(identity_relation)),inverse(identity_relation))* -> subclass(u,symmetrization_of(identity_relation)).
% 299.99/300.65  204165[18:Res:194549.1,28.1] || subclass(symmetrization_of(identity_relation),complement(u)) member(regular(symmetrization_of(identity_relation)),u)* -> .
% 299.99/300.65  204168[18:Res:194549.1,151988.0] || subclass(symmetrization_of(identity_relation),complement(complement(u)))* -> member(regular(symmetrization_of(identity_relation)),u).
% 299.99/300.65  204176[18:Res:194549.1,26.0] || subclass(symmetrization_of(identity_relation),intersection(u,v))* -> member(regular(symmetrization_of(identity_relation)),v).
% 299.99/300.65  204177[18:Res:194549.1,25.0] || subclass(symmetrization_of(identity_relation),intersection(u,v))* -> member(regular(symmetrization_of(identity_relation)),u).
% 299.99/300.65  204190[18:Res:194549.1,50033.0] || subclass(symmetrization_of(identity_relation),subset_relation) equal(complement(regular(symmetrization_of(identity_relation))),ordinal_numbers)** -> .
% 299.99/300.65  204194[18:Res:194549.1,14679.1] || subclass(symmetrization_of(identity_relation),inverse(subset_relation)) member(regular(symmetrization_of(identity_relation)),subset_relation)* -> .
% 299.99/300.65  204627[21:Res:196904.1,28.1] || subclass(domain_relation,complement(u)) member(singleton(singleton(singleton(identity_relation))),u)* -> .
% 299.99/300.65  204630[21:Res:196904.1,151988.0] || subclass(domain_relation,complement(complement(u))) -> member(singleton(singleton(singleton(identity_relation))),u)*.
% 299.99/300.65  204638[21:Res:196904.1,26.0] || subclass(domain_relation,intersection(u,v))* -> member(singleton(singleton(singleton(identity_relation))),v)*.
% 299.99/300.65  204639[21:Res:196904.1,25.0] || subclass(domain_relation,intersection(u,v))* -> member(singleton(singleton(singleton(identity_relation))),u)*.
% 299.99/300.65  204656[21:Res:196904.1,14679.1] || subclass(domain_relation,inverse(subset_relation)) member(singleton(singleton(singleton(identity_relation))),subset_relation)* -> .
% 299.99/300.65  204661[21:Res:196904.1,163154.0] || subclass(domain_relation,symmetrization_of(identity_relation)) -> member(singleton(singleton(singleton(identity_relation))),inverse(identity_relation))*.
% 299.99/300.65  204986[21:SpL:15663.0,198463.1] || member(not_subclass_element(identity_relation,identity_relation),subset_relation)* equal(rest_of(single_valued3(identity_relation)),rest_relation) -> .
% 299.99/300.65  205167[15:Res:195033.1,28.1] || equal(complement(complement(complement(u))),ordinal_numbers)** member(range_of(identity_relation),u) -> .
% 299.99/300.65  205170[15:Res:195033.1,151988.0] || equal(complement(complement(complement(complement(u)))),ordinal_numbers)** -> member(range_of(identity_relation),u).
% 299.99/300.65  205178[15:Res:195033.1,26.0] || equal(complement(complement(intersection(u,v))),ordinal_numbers)** -> member(range_of(identity_relation),v).
% 299.99/300.65  205179[15:Res:195033.1,25.0] || equal(complement(complement(intersection(u,v))),ordinal_numbers)** -> member(range_of(identity_relation),u).
% 299.99/300.65  205196[15:Res:195033.1,14679.1] || equal(complement(complement(inverse(subset_relation))),ordinal_numbers)** member(range_of(identity_relation),subset_relation) -> .
% 299.99/300.65  205201[15:Res:195033.1,163154.0] || equal(complement(complement(symmetrization_of(identity_relation))),ordinal_numbers) -> member(range_of(identity_relation),inverse(identity_relation))*.
% 299.99/300.65  205203[15:Res:195033.1,161.0] || equal(complement(complement(omega)),ordinal_numbers) -> equal(integer_of(range_of(identity_relation)),range_of(identity_relation))**.
% 299.99/300.65  205497[22:Res:148858.1,202348.0] || subclass(singleton(singleton(identity_relation)),inverse(subset_relation))* well_ordering(ordinal_numbers,complement(subset_relation)) -> .
% 299.99/300.65  205521[22:Res:163112.0,205501.0] || well_ordering(ordinal_numbers,complement(inverse(identity_relation))) -> subclass(singleton(singleton(identity_relation)),symmetrization_of(identity_relation))*.
% 299.99/300.65  205522[22:Res:195271.0,205501.0] || well_ordering(ordinal_numbers,complement(singleton(identity_relation))) -> subclass(singleton(singleton(identity_relation)),singleton(identity_relation))*.
% 299.99/300.65  205533[22:Res:193179.0,205501.0] || well_ordering(ordinal_numbers,inverse(singleton(singleton(identity_relation))))* -> asymmetric(singleton(singleton(identity_relation)),u)*.
% 299.99/300.65  205562[22:SpL:160491.0,205502.0] || well_ordering(ordinal_numbers,union(u,identity_relation)) -> member(singleton(identity_relation),symmetric_difference(ordinal_numbers,u))*.
% 299.99/300.65  205565[22:SpL:59.0,205502.0] || well_ordering(ordinal_numbers,power_class(u)) -> member(singleton(identity_relation),image(element_relation,complement(u)))*.
% 299.99/300.65  205573[22:Res:148858.1,202352.0] || subclass(singleton(singleton(identity_relation)),inverse(subset_relation))* -> member(singleton(identity_relation),complement(subset_relation)).
% 299.99/300.65  133835[5:Res:8665.1,130944.0] function(singleton(singleton(singleton(u)))) || well_ordering(ordinal_numbers,cross_product(ordinal_numbers,ordinal_numbers))* -> .
% 299.99/300.65  134009[5:Res:18819.1,133836.0] || member(singleton(singleton(u)),subset_relation)* well_ordering(ordinal_numbers,cross_product(ordinal_numbers,ordinal_numbers))* -> .
% 299.99/300.65  205720[22:MRR:205707.0,8655.0] || well_ordering(ordinal_numbers,image(element_relation,complement(u)))* -> member(singleton(identity_relation),power_class(u)).
% 299.99/300.65  205772[22:SpR:160491.0,205578.1] ||  -> member(singleton(identity_relation),symmetric_difference(ordinal_numbers,u))* member(singleton(identity_relation),union(u,identity_relation)).
% 299.99/300.65  205775[22:SpR:59.0,205578.1] ||  -> member(singleton(identity_relation),image(element_relation,complement(u)))* member(singleton(identity_relation),power_class(u)).
% 299.99/300.65  205983[8:SpL:141394.0,204039.0] || equal(symmetric_difference(u,ordinal_numbers),ordinal_numbers) member(identity_relation,intersection(u,ordinal_numbers))* -> .
% 299.99/300.65  206123[22:Res:205574.1,28.1] || equal(complement(u),singleton(singleton(identity_relation))) member(singleton(identity_relation),u)* -> .
% 299.99/300.65  206126[22:Res:205574.1,151988.0] || equal(complement(complement(u)),singleton(singleton(identity_relation))) -> member(singleton(identity_relation),u)*.
% 299.99/300.65  206134[22:Res:205574.1,26.0] || equal(intersection(u,v),singleton(singleton(identity_relation)))** -> member(singleton(identity_relation),v)*.
% 299.99/300.65  206135[22:Res:205574.1,25.0] || equal(intersection(u,v),singleton(singleton(identity_relation)))** -> member(singleton(identity_relation),u)*.
% 299.99/300.65  206505[5:MRR:206461.0,8655.0] || equal(complement(union(u,v)),ordinal_numbers)** -> member(singleton(w),complement(u))*.
% 299.99/300.65  206506[5:MRR:206462.0,8655.0] || equal(complement(union(u,v)),ordinal_numbers)** -> member(singleton(w),complement(v))*.
% 299.99/300.65  206529[7:Con:206528.1] || member(u,singleton(v))* -> equal(integer_of(v),identity_relation) member(u,omega).
% 299.99/300.65  206543[7:SpR:154737.1,165795.1] || subclass(u,singleton(v))* -> equal(integer_of(v),identity_relation) subclass(u,omega).
% 299.99/300.65  206649[7:SpR:13600.1,154737.1] || subclass(u,singleton(u))* -> equal(singleton(u),identity_relation) equal(identity_relation,u).
% 299.99/300.65  207879[24:Rew:207558.1,207670.2] operation(u) || member(singleton(singleton(identity_relation)),element_relation)* -> member(identity_relation,u)*.
% 299.99/300.65  207952[24:Res:8976.2,207853.1] function(u) operation(image(u,v)) || member(v,ordinal_numbers)* -> .
% 299.99/300.65  208025[24:MRR:207960.2,8638.0] operation(apply(choice,u)) || member(u,ordinal_numbers)* -> equal(u,identity_relation).
% 299.99/300.65  208104[24:Res:13237.2,207872.1] operation(least(u,subset_relation)) || well_ordering(u,ordinal_numbers)* -> equal(subset_relation,identity_relation).
% 299.99/300.65  208176[24:Rew:208168.1,208004.2] operation(regular(omega)) ||  -> equal(regular(identity_relation),identity_relation) equal(range_of(identity_relation),identity_relation)**.
% 299.99/300.65  208205[24:Res:207562.1,5.0] operation(u) || subclass(ordered_pair(u,v),w)* -> member(identity_relation,w).
% 299.99/300.65  208245[24:SpR:207565.1,66293.0] operation(u) ||  -> equal(intersection(successor(u),ordinal_numbers),symmetric_difference(complement(u),ordinal_numbers))**.
% 299.99/300.65  208246[24:SpR:207565.1,189823.1] operation(u) || equal(complement(u),ordinal_numbers)** -> equal(successor(u),identity_relation).
% 299.99/300.65  208515[7:SpL:13260.1,132439.0] || well_ordering(ordinal_numbers,regular(cross_product(u,v)))* -> equal(cross_product(u,v),identity_relation).
% 299.99/300.65  208518[8:SpL:13260.1,162891.0] || equal(regular(cross_product(u,v)),identity_relation)** -> equal(cross_product(u,v),identity_relation).
% 299.99/300.65  208519[8:SpL:13260.1,162248.0] || subclass(regular(cross_product(u,v)),identity_relation)* -> equal(cross_product(u,v),identity_relation).
% 299.99/300.65  208747[8:SpR:208708.1,69395.0] ||  -> equal(singleton(u),identity_relation) equal(complement(symmetric_difference(u,ordinal_numbers)),union(u,identity_relation))**.
% 299.99/300.65  208881[25:SpR:208820.0,13101.0] ||  -> equal(second(not_subclass_element(restrict(u,identity_relation,v),identity_relation)),range__dfg(u,ordinal_numbers,v))**.
% 299.99/300.65  208888[25:SpR:208820.0,13100.0] ||  -> equal(first(not_subclass_element(restrict(u,v,identity_relation),identity_relation)),domain__dfg(u,v,ordinal_numbers))**.
% 299.99/300.65  208943[25:SpL:208820.0,160735.1] || member(ordinal_numbers,cantor(u)) equal(restrict(u,identity_relation,ordinal_numbers),identity_relation)** -> .
% 299.99/300.65  208971[25:Rew:208885.0,198206.1] ||  -> equal(range_of(u),identity_relation) equal(apply(v,inverse(u)),apply(v,ordinal_numbers))**.
% 299.99/300.65  208984[25:Rew:208873.0,198198.1] ||  -> equal(range_of(u),identity_relation) equal(ordered_pair(v,inverse(u)),ordered_pair(v,ordinal_numbers))**.
% 299.99/300.65  208987[25:Rew:208887.0,207633.1] operation(u) ||  -> equal(segment(v,w,ordinal_numbers),segment(v,w,u))*.
% 299.99/300.65  209001[25:Rew:208881.0,207624.1] operation(u) ||  -> equal(range__dfg(v,ordinal_numbers,w),range__dfg(v,u,w))*.
% 299.99/300.65  209003[25:Rew:208888.0,207634.1] operation(u) ||  -> equal(domain__dfg(v,w,ordinal_numbers),domain__dfg(v,w,u))*.
% 299.99/300.65  209011[25:Rew:208820.0,208903.1] || member(singleton(singleton(identity_relation)),compose_class(u))* -> equal(compose(u,identity_relation),ordinal_numbers).
% 299.99/300.65  209341[25:Rew:209323.1,208328.2] operation(u) || member(singleton(singleton(identity_relation)),union_of_range_map)* -> equal(ordinal_numbers,u)*.
% 299.99/300.65  209420[25:SpR:208885.0,196551.1] || member(image(u,identity_relation),ordinal_numbers)* -> equal(cantor(apply(u,ordinal_numbers)),identity_relation).
% 299.99/300.65  209760[23:Res:148858.1,205615.0] || subclass(complement(recursion_equation_functions(u)),inverse(subset_relation))* well_ordering(ordinal_numbers,complement(subset_relation)) -> .
% 299.99/300.65  209771[23:Res:148858.1,205619.0] || subclass(complement(recursion_equation_functions(u)),inverse(subset_relation))* -> member(singleton(identity_relation),complement(subset_relation)).
% 299.99/300.65  209778[24:SpR:207565.1,206259.0] operation(u) ||  -> subclass(symmetric_difference(complement(u),symmetric_difference(ordinal_numbers,u)),successor(u))*.
% 299.99/300.65  209908[15:SpL:163.0,208474.0] || equal(symmetric_difference(u,v),ordinal_numbers) -> member(range_of(identity_relation),union(u,v))*.
% 299.99/300.65  209909[15:SpL:3596.0,208474.0] || equal(symmetric_difference(u,singleton(u)),ordinal_numbers)** -> member(range_of(identity_relation),successor(u))*.
% 299.99/300.65  209910[15:SpL:3597.0,208474.0] || equal(symmetric_difference(u,inverse(u)),ordinal_numbers)** -> member(range_of(identity_relation),symmetrization_of(u))*.
% 299.99/300.65  209955[15:Res:209921.1,5.0] || equal(u,ordinal_numbers) subclass(u,v)* -> member(range_of(identity_relation),v)*.
% 299.99/300.65  210060[15:MRR:210030.0,165460.0] || equal(complement(union(u,v)),ordinal_numbers)** -> member(range_of(identity_relation),complement(u))*.
% 299.99/300.65  210061[15:MRR:210031.0,165460.0] || equal(complement(union(u,v)),ordinal_numbers)** -> member(range_of(identity_relation),complement(v))*.
% 299.99/300.65  210167[25:SpR:207558.1,208873.0] operation(u) ||  -> equal(unordered_pair(identity_relation,unordered_pair(u,identity_relation)),ordered_pair(u,ordinal_numbers))**.
% 299.99/300.65  210301[22:Res:140864.1,205501.0] || member(singleton(identity_relation),complement(u)) well_ordering(ordinal_numbers,symmetric_difference(ordinal_numbers,u))* -> .
% 299.99/300.65  210322[15:Rew:160491.0,210288.1] || member(range_of(identity_relation),complement(u))* subclass(ordinal_numbers,union(u,identity_relation)) -> .
% 299.99/300.65  210324[8:Rew:160491.0,210299.1] || member(singleton(u),complement(v))* subclass(ordinal_numbers,union(v,identity_relation)) -> .
% 299.99/300.65  210325[18:Rew:160491.0,210306.1] || member(identity_relation,complement(u))* equal(union(u,identity_relation),inverse(identity_relation)) -> .
% 299.99/300.65  210326[18:Rew:160491.0,210307.1] || member(identity_relation,complement(u))* equal(union(u,identity_relation),symmetrization_of(identity_relation)) -> .
% 299.99/300.65  210327[14:Rew:160491.0,210308.1] || member(identity_relation,complement(u))* equal(union(u,identity_relation),singleton(identity_relation)) -> .
% 299.99/300.65  210363[15:Res:165442.1,143186.0] || subclass(ordinal_numbers,symmetric_difference(ordinal_numbers,u)) -> member(sum_class(range_of(identity_relation)),complement(u))*.
% 299.99/300.65  210392[5:Res:8642.1,143186.0] || subclass(ordinal_numbers,symmetric_difference(ordinal_numbers,u)) -> member(ordered_pair(v,w),complement(u))*.
% 299.99/300.65  210393[8:Res:15426.1,143186.0] || subclass(domain_relation,symmetric_difference(ordinal_numbers,u)) -> member(ordered_pair(identity_relation,identity_relation),complement(u))*.
% 299.99/300.65  210407[18:Res:190515.1,143186.0] || subclass(ordinal_numbers,symmetric_difference(ordinal_numbers,u)) -> member(regular(symmetrization_of(identity_relation)),complement(u))*.
% 299.99/300.65  210428[14:SpR:69395.0,210404.0] ||  -> member(identity_relation,complement(symmetric_difference(u,ordinal_numbers))) member(identity_relation,complement(intersection(u,ordinal_numbers)))*.
% 299.99/300.65  210465[5:Res:8643.1,143226.0] || subclass(ordinal_numbers,symmetric_difference(ordinal_numbers,u)) member(unordered_pair(v,w),u)* -> .
% 299.99/300.65  210467[7:Res:13072.1,143226.0] || member(regular(symmetric_difference(ordinal_numbers,u)),u)* -> equal(symmetric_difference(ordinal_numbers,u),identity_relation).
% 299.99/300.65  210472[15:Res:165442.1,143226.0] || subclass(ordinal_numbers,symmetric_difference(ordinal_numbers,u)) member(sum_class(range_of(identity_relation)),u)* -> .
% 299.99/300.65  210485[5:Res:143222.1,143226.0] || equal(symmetric_difference(ordinal_numbers,u),omega) member(least(element_relation,omega),u)* -> .
% 299.99/300.65  210486[5:Res:143193.1,143226.0] || equal(symmetric_difference(ordinal_numbers,u),ordinal_numbers) member(least(element_relation,omega),u)* -> .
% 299.99/300.65  210489[5:Res:125731.1,143226.0] || subclass(ordinal_numbers,symmetric_difference(ordinal_numbers,u)) member(least(element_relation,omega),u)* -> .
% 299.99/300.65  210490[5:Res:125725.1,143226.0] || subclass(omega,symmetric_difference(ordinal_numbers,u)) member(least(element_relation,omega),u)* -> .
% 299.99/300.65  210501[5:Res:8642.1,143226.0] || subclass(ordinal_numbers,symmetric_difference(ordinal_numbers,u)) member(ordered_pair(v,w),u)* -> .
% 299.99/300.65  210502[8:Res:15426.1,143226.0] || subclass(domain_relation,symmetric_difference(ordinal_numbers,u)) member(ordered_pair(identity_relation,identity_relation),u)* -> .
% 299.99/300.65  210516[18:Res:190515.1,143226.0] || subclass(ordinal_numbers,symmetric_difference(ordinal_numbers,u)) member(regular(symmetrization_of(identity_relation)),u)* -> .
% 299.99/300.65  210520[8:Rew:160491.0,210495.0] || well_ordering(ordinal_numbers,union(u,identity_relation))* member(singleton(singleton(v)),u)* -> .
% 299.99/300.65  210542[18:Res:210513.1,190641.1] || member(identity_relation,u) equal(complement(union(u,identity_relation)),inverse(identity_relation))** -> .
% 299.99/300.65  210543[18:Res:210513.1,190532.1] || member(identity_relation,u) equal(complement(union(u,identity_relation)),symmetrization_of(identity_relation))** -> .
% 299.99/300.65  210544[14:Res:210513.1,165357.1] || member(identity_relation,u) equal(complement(union(u,identity_relation)),singleton(identity_relation))** -> .
% 299.99/300.65  210607[8:Res:2503.2,210517.1] || subclass(u,v)* equal(complement(v),ordinal_numbers) -> subclass(u,w)*.
% 299.99/300.65  210611[8:Res:13227.2,210517.1] || subclass(u,v)* equal(complement(v),ordinal_numbers) -> equal(u,identity_relation).
% 299.99/300.65  210842[8:Res:210572.1,11.0] || equal(complement(u),ordinal_numbers) subclass(v,u)* -> equal(v,u).
% 299.99/300.65  212236[8:SpL:141394.0,210460.0] || subclass(ordinal_numbers,symmetric_difference(u,ordinal_numbers)) member(omega,intersection(u,ordinal_numbers))* -> .
% 299.99/300.65  212253[8:SpL:141394.0,210511.0] || subclass(ordinal_numbers,symmetric_difference(u,ordinal_numbers)) member(identity_relation,intersection(u,ordinal_numbers))* -> .
% 299.99/300.65  212463[8:Rew:30.0,212444.0] || equal(union(u,v),ordinal_numbers) -> section(element_relation,union(u,v),ordinal_numbers)*.
% 299.99/300.65  212692[8:Rew:30.0,212530.0] || equal(union(u,v),ordinal_numbers) -> equal(complement(union(u,v)),identity_relation)**.
% 299.99/300.65  213009[12:Rew:30.0,212983.0] || equal(union(u,v),ordinal_numbers) -> equal(power_class(union(u,v)),identity_relation)**.
% 299.99/300.65  213191[8:Rew:140603.0,213045.1,66036.0,213045.1] || equal(complement(u),ordinal_numbers) -> equal(symmetric_difference(u,v),union(u,v))**.
% 299.99/300.65  213256[8:SpR:210610.1,163.0] || equal(complement(union(u,v)),ordinal_numbers)** -> equal(symmetric_difference(u,v),identity_relation).
% 299.99/300.65  213257[8:SpR:210610.1,3596.0] || equal(complement(successor(u)),ordinal_numbers) -> equal(symmetric_difference(u,singleton(u)),identity_relation)**.
% 299.99/300.65  213258[8:SpR:210610.1,3597.0] || equal(complement(symmetrization_of(u)),ordinal_numbers) -> equal(symmetric_difference(u,inverse(u)),identity_relation)**.
% 299.99/300.65  213272[8:SpR:210610.1,132293.0] || equal(complement(complement(singleton(u))),ordinal_numbers) -> subclass(complement(successor(u)),identity_relation)*.
% 299.99/300.65  213273[8:SpR:210610.1,132294.0] || equal(complement(complement(inverse(u))),ordinal_numbers) -> subclass(complement(symmetrization_of(u)),identity_relation)*.
% 299.99/300.65  213378[8:Rew:140603.0,213221.1,66036.0,213221.1] || equal(complement(u),ordinal_numbers) -> equal(symmetric_difference(v,u),union(v,u))**.
% 299.99/300.65  213474[24:SpR:207558.1,145761.0] operation(u) ||  -> equal(segment(ordinal_numbers,v,u),cantor(cross_product(v,identity_relation)))**.
% 299.99/300.65  213627[5:SpR:154737.1,151877.0] || subclass(u,singleton(v))* -> subclass(u,complement(recursion_equation_functions(w)))* function(v).
% 299.99/300.65  213645[5:Con:213639.0] || member(u,singleton(v))* -> function(v) member(u,complement(recursion_equation_functions(w)))*.
% 299.99/300.65  214486[25:SpL:208985.1,23.0] operation(u) || member(ordered_pair(v,u),element_relation)* -> member(v,ordinal_numbers).
% 299.99/300.65  214541[25:SpL:208985.1,23.0] operation(u) || member(ordered_pair(v,ordinal_numbers),element_relation)* -> member(v,u)*.
% 299.99/300.65  214852[25:SpR:214376.1,13085.1] operation(u) || member(u,ordinals_with_null_class_as_identity)* -> equal(ordinal_add(identity_relation,ordinal_numbers),u)*.
% 299.99/300.65  214856[25:SpR:214376.1,13085.1] operation(u) || member(ordinal_numbers,ordinals_with_null_class_as_identity) -> equal(ordinal_add(identity_relation,u),ordinal_numbers)**.
% 299.99/300.65  214948[0:Con:214939.2] || member(u,v)* member(w,singleton(u))* -> member(w,v)*.
% 299.99/300.65  214955[16:SpR:195239.0,151502.1] ||  -> member(u,complement(singleton(identity_relation))) subclass(intersection(v,singleton(u)),singleton(identity_relation))*.
% 299.99/300.65  214956[8:SpR:162584.0,151502.1] ||  -> member(u,complement(inverse(identity_relation))) subclass(intersection(v,singleton(u)),symmetrization_of(identity_relation))*.
% 299.99/300.65  214998[5:Con:214991.1] || member(u,singleton(v))* -> member(v,w)* member(u,complement(w))*.
% 299.99/300.65  215016[0:SpR:154737.1,151861.1] || subclass(u,singleton(v))* member(v,w)* -> subclass(u,w)*.
% 299.99/300.65  215085[16:SpR:195239.0,151862.1] ||  -> member(u,complement(singleton(identity_relation))) subclass(intersection(singleton(u),v),singleton(identity_relation))*.
% 299.99/300.65  215086[8:SpR:162584.0,151862.1] ||  -> member(u,complement(inverse(identity_relation))) subclass(intersection(singleton(u),v),symmetrization_of(identity_relation))*.
% 299.99/300.65  215113[5:SpR:154737.1,151862.1] || subclass(u,singleton(v))* -> member(v,w)* subclass(u,complement(w))*.
% 299.99/300.65  215137[16:SpR:195239.0,215108.1] ||  -> member(u,complement(singleton(identity_relation))) subclass(complement(complement(singleton(u))),singleton(identity_relation))*.
% 299.99/300.65  215138[8:SpR:162584.0,215108.1] ||  -> member(u,complement(inverse(identity_relation))) subclass(complement(complement(singleton(u))),symmetrization_of(identity_relation))*.
% 299.99/300.65  215362[8:SpR:160491.0,215271.1] || subclass(symmetric_difference(ordinal_numbers,u),identity_relation)* -> equal(complement(union(u,identity_relation)),identity_relation).
% 299.99/300.65  215366[8:SpR:59.0,215271.1] || subclass(image(element_relation,complement(u)),identity_relation)* -> equal(complement(power_class(u)),identity_relation).
% 299.99/300.65  216303[8:Res:116148.1,216271.1] inductive(cantor(restrict(u,v,identity_relation))) || section(u,identity_relation,v)* -> .
% 299.99/300.65  216639[8:SpR:216188.1,19733.0] || equal(identity_relation,u) -> subclass(symmetric_difference(ordinal_numbers,complement(singleton(u))),successor(u))*.
% 299.99/300.65  216640[8:SpR:216188.1,19734.0] || equal(identity_relation,u) -> subclass(symmetric_difference(ordinal_numbers,complement(inverse(u))),symmetrization_of(u))*.
% 299.99/300.65  216672[8:SpR:216188.1,19421.0] || equal(identity_relation,u) -> subclass(symmetric_difference(complement(v),ordinal_numbers),union(v,u))*.
% 299.99/300.65  216718[8:SpR:216188.1,19733.0] || equal(singleton(u),identity_relation) -> subclass(symmetric_difference(complement(u),ordinal_numbers),successor(u))*.
% 299.99/300.65  216751[8:SpR:216188.1,19734.0] || equal(inverse(u),identity_relation) -> subclass(symmetric_difference(complement(u),ordinal_numbers),symmetrization_of(u))*.
% 299.99/300.65  217175[8:Rew:140613.0,216671.1] || equal(identity_relation,u) -> subclass(complement(union(v,u)),symmetric_difference(ordinal_numbers,v))*.
% 299.99/300.65  217183[8:Rew:140613.0,216723.1] || equal(singleton(u),identity_relation) -> subclass(complement(successor(u)),symmetric_difference(ordinal_numbers,u))*.
% 299.99/300.65  217184[8:Rew:140613.0,216752.1] || equal(inverse(u),identity_relation) -> subclass(complement(symmetrization_of(u)),symmetric_difference(ordinal_numbers,u))*.
% 299.99/300.65  217388[8:Res:216591.1,66086.1] || equal(complement(complement(compose(element_relation,ordinal_numbers))),identity_relation)** member(identity_relation,element_relation) -> .
% 299.99/300.65  217396[8:Res:216591.1,5.0] || equal(complement(u),identity_relation) subclass(u,v)* -> member(identity_relation,v)*.
% 299.99/300.65  217401[8:Res:216591.1,3617.0] || equal(complement(symmetric_difference(u,v)),identity_relation) -> member(identity_relation,union(u,v))*.
% 299.99/300.65  217402[8:Res:216591.1,19559.0] || equal(complement(symmetric_difference(u,singleton(u))),identity_relation)** -> member(identity_relation,successor(u)).
% 299.99/300.65  217403[8:Res:216591.1,19676.0] || equal(complement(symmetric_difference(u,inverse(u))),identity_relation)** -> member(identity_relation,symmetrization_of(u)).
% 299.99/300.65  217458[8:Rew:30.0,217400.0] || equal(union(u,v),identity_relation) member(identity_relation,union(u,v))* -> .
% 299.99/300.65  217537[8:Res:61019.0,162901.0] || equal(regular(complement(complement(subset_relation))),identity_relation)** -> equal(complement(complement(subset_relation)),identity_relation).
% 299.99/300.65  217538[8:Res:61019.0,162888.0] || subclass(regular(complement(complement(subset_relation))),identity_relation)* -> equal(complement(complement(subset_relation)),identity_relation).
% 299.99/300.65  217610[8:Res:216611.1,66086.1] || equal(complement(complement(compose(element_relation,ordinal_numbers))),identity_relation)** member(omega,element_relation) -> .
% 299.99/300.65  217618[8:Res:216611.1,5.0] || equal(complement(u),identity_relation) subclass(u,v)* -> member(omega,v)*.
% 299.99/300.65  217623[8:Res:216611.1,3617.0] || equal(complement(symmetric_difference(u,v)),identity_relation) -> member(omega,union(u,v))*.
% 299.99/300.65  217624[8:Res:216611.1,19559.0] || equal(complement(symmetric_difference(u,singleton(u))),identity_relation)** -> member(omega,successor(u)).
% 299.99/300.65  217625[8:Res:216611.1,19676.0] || equal(complement(symmetric_difference(u,inverse(u))),identity_relation)** -> member(omega,symmetrization_of(u)).
% 299.99/300.65  217666[8:Rew:30.0,217622.0] || equal(union(u,v),identity_relation) member(omega,union(u,v))* -> .
% 299.99/300.65  217713[8:Res:216691.1,50046.1] || equal(complement(complement(unordered_pair(u,v))),identity_relation)** member(u,subset_relation) -> .
% 299.99/300.65  217717[8:Res:216691.1,50058.1] || equal(complement(complement(unordered_pair(u,v))),identity_relation)** member(v,subset_relation) -> .
% 299.99/300.65  217725[8:Res:216691.1,94706.0] || equal(complement(complement(complement(cross_product(u,v)))),identity_relation)** -> member(w,u)*.
% 299.99/300.65  217726[8:Res:216691.1,94705.0] || equal(complement(complement(complement(cross_product(u,v)))),identity_relation)** -> member(w,v)*.
% 299.99/300.65  217730[8:Res:216691.1,116180.0] || equal(complement(complement(complement(rest_of(u)))),identity_relation)** -> member(v,cantor(u))*.
% 299.99/300.65  217733[8:Res:216691.1,116122.1] || equal(complement(complement(rest_of(u))),identity_relation)** member(v,cantor(u))* -> .
% 299.99/300.65  217739[8:Res:216691.1,125985.0] || equal(complement(intersection(u,v)),identity_relation)** -> member(least(element_relation,omega),u)*.
% 299.99/300.65  217740[8:Res:216691.1,125984.0] || equal(complement(intersection(u,v)),identity_relation)** -> member(least(element_relation,omega),v)*.
% 299.99/300.65  217741[8:Res:216691.1,8847.0] || equal(complement(intersection(u,v)),identity_relation)** -> member(unordered_pair(w,x),v)*.
% 299.99/300.65  217742[8:Res:216691.1,8846.0] || equal(complement(intersection(u,v)),identity_relation)** -> member(unordered_pair(w,x),u)*.
% 299.99/300.65  217872[20:Res:217827.0,5.0] || subclass(inverse(identity_relation),u) -> member(regular(complement(complement(symmetrization_of(identity_relation)))),u)*.
% 299.99/300.65  218241[8:Res:8827.2,217144.1] || member(u,ordinal_numbers)* subclass(rest_relation,v)* equal(identity_relation,v) -> .
% 299.99/300.65  218380[21:Res:66492.1,196454.0] || subclass(domain_relation,rest_relation)* -> equal(integer_of(u),identity_relation)** equal(rest_of(u),identity_relation).
% 299.99/300.65  218381[21:Res:18517.1,196454.0] || subclass(domain_relation,rest_relation)* -> equal(singleton(u),identity_relation) equal(rest_of(u),identity_relation)**.
% 299.99/300.65  218394[21:Res:60996.1,196454.0] || subclass(domain_relation,rest_relation) -> equal(u,identity_relation) equal(rest_of(regular(u)),identity_relation)**.
% 299.99/300.65  218396[21:Res:217871.0,196454.0] || subclass(domain_relation,rest_relation) -> equal(rest_of(regular(complement(complement(symmetrization_of(identity_relation))))),identity_relation)**.
% 299.99/300.65  218556[21:Res:66492.1,196455.0] || subclass(rest_relation,domain_relation)* -> equal(integer_of(u),identity_relation)** equal(rest_of(u),identity_relation).
% 299.99/300.65  218557[21:Res:18517.1,196455.0] || subclass(rest_relation,domain_relation)* -> equal(singleton(u),identity_relation) equal(rest_of(u),identity_relation)**.
% 299.99/300.65  218570[21:Res:60996.1,196455.0] || subclass(rest_relation,domain_relation) -> equal(u,identity_relation) equal(rest_of(regular(u)),identity_relation)**.
% 299.99/300.65  218572[21:Res:217871.0,196455.0] || subclass(rest_relation,domain_relation) -> equal(rest_of(regular(complement(complement(symmetrization_of(identity_relation))))),identity_relation)**.
% 299.99/300.65  219016[8:SpR:215491.1,68757.0] || subclass(complement(inverse(identity_relation)),identity_relation)* -> equal(intersection(symmetrization_of(identity_relation),ordinal_numbers),ordinal_numbers).
% 299.99/300.65  219018[8:SpR:215491.1,144460.0] || subclass(symmetric_difference(ordinal_numbers,u),identity_relation)* -> equal(symmetric_difference(complement(u),ordinal_numbers),ordinal_numbers).
% 299.99/300.65  219086[8:Res:8700.2,219073.1] || member(u,ordinal_numbers)* subclass(complement(v),identity_relation)* -> member(u,v)*.
% 299.99/300.65  219202[8:Res:8827.2,219073.1] || member(u,ordinal_numbers)* subclass(rest_relation,v)* subclass(v,identity_relation)* -> .
% 299.99/300.65  219215[8:Res:41098.2,219073.1] || member(u,ordinal_numbers)* member(v,u)* subclass(element_relation,identity_relation) -> .
% 299.99/300.65  219337[15:Res:215659.1,56411.0] || subclass(complement(rest_of(range_of(identity_relation))),identity_relation)* subclass(ordinal_numbers,complement(element_relation)) -> .
% 299.99/300.65  219339[15:Res:215659.1,898.0] || subclass(complement(restrict(u,v,w)),identity_relation)* -> member(range_of(identity_relation),u).
% 299.99/300.65  219681[8:SpR:217115.1,144460.0] || equal(symmetric_difference(ordinal_numbers,u),identity_relation) -> equal(symmetric_difference(complement(u),ordinal_numbers),ordinal_numbers)**.
% 299.99/300.65  219868[15:Res:217197.1,898.0] || equal(complement(restrict(u,v,w)),identity_relation)** -> member(range_of(identity_relation),u).
% 299.99/300.65  220016[8:Res:143200.1,160772.0] || equal(symmetric_difference(ordinal_numbers,u),ordinal_numbers) member(omega,union(u,identity_relation))* -> .
% 299.99/300.65  220069[8:Res:192149.1,160772.0] || equal(symmetric_difference(ordinal_numbers,u),ordinal_numbers) member(identity_relation,union(u,identity_relation))* -> .
% 299.99/300.65  220073[8:Res:13049.1,160772.0] || subclass(ordinal_numbers,symmetric_difference(ordinal_numbers,u)) member(identity_relation,union(u,identity_relation))* -> .
% 299.99/300.65  220130[8:SpL:117066.0,217492.1] operation(flip(cross_product(u,ordinal_numbers))) || equal(complement(inverse(u)),identity_relation)** -> .
% 299.99/300.65  220131[8:SpL:117142.0,217492.1] operation(restrict(element_relation,ordinal_numbers,u)) || equal(complement(sum_class(u)),identity_relation)** -> .
% 299.99/300.65  220288[7:Res:10.1,13243.0] || equal(singleton(u),omega)** -> equal(integer_of(v),identity_relation)** equal(v,u)*.
% 299.99/300.65  220387[25:SpR:208840.0,196656.1] || subclass(domain_relation,flip(u)) -> member(ordered_pair(singleton(singleton(identity_relation)),identity_relation),u)*.
% 299.99/300.65  220434[21:Res:196656.1,152.0] || subclass(domain_relation,flip(recursion_equation_functions(u)))* -> function(ordered_pair(ordered_pair(v,w),identity_relation))*.
% 299.99/300.65  220453[21:Res:196656.1,116129.0] || subclass(domain_relation,flip(rest_of(u))) -> member(ordered_pair(v,w),cantor(u))*.
% 299.99/300.65  220456[21:Res:196656.1,18.0] || subclass(domain_relation,flip(cross_product(u,v)))* -> member(ordered_pair(w,x),u)*.
% 299.99/300.65  220462[21:Res:196656.1,157.0] || subclass(domain_relation,flip(union_of_range_map)) -> equal(sum_class(range_of(ordered_pair(u,v))),identity_relation)**.
% 299.99/300.65  220536[21:Res:196657.1,152.0] || subclass(domain_relation,rotate(recursion_equation_functions(u)))* -> function(ordered_pair(ordered_pair(v,identity_relation),w))*.
% 299.99/300.65  220555[21:Res:196657.1,116129.0] || subclass(domain_relation,rotate(rest_of(u))) -> member(ordered_pair(v,identity_relation),cantor(u))*.
% 299.99/300.65  220558[21:Res:196657.1,18.0] || subclass(domain_relation,rotate(cross_product(u,v)))* -> member(ordered_pair(w,identity_relation),u)*.
% 299.99/300.65  220564[21:Res:196657.1,157.0] || subclass(domain_relation,rotate(union_of_range_map)) -> equal(sum_class(range_of(ordered_pair(u,identity_relation))),v)*.
% 299.99/300.65  220565[21:Res:196657.1,100.0] || subclass(domain_relation,rotate(composition_function)) -> equal(compose(ordered_pair(u,identity_relation),v),w)*.
% 299.99/300.65  220666[7:Res:10.1,17324.0] || equal(singleton(u),v)* -> equal(v,identity_relation) equal(regular(v),u)*.
% 299.99/300.65  220714[15:Res:195033.1,219203.0] || equal(complement(complement(rest_of(range_of(identity_relation)))),ordinal_numbers)** subclass(element_relation,identity_relation) -> .
% 299.99/300.65  220729[8:Res:9632.1,219203.0] || equal(complement(complement(rest_of(singleton(u)))),ordinal_numbers)** subclass(element_relation,identity_relation) -> .
% 299.99/300.65  220731[8:Res:133837.1,219203.0] || well_ordering(ordinal_numbers,complement(rest_of(singleton(singleton(u)))))* subclass(element_relation,identity_relation) -> .
% 299.99/300.65  220733[22:Res:205574.1,219203.0] || equal(rest_of(singleton(identity_relation)),singleton(singleton(identity_relation)))** subclass(element_relation,identity_relation) -> .
% 299.99/300.65  220753[18:Res:194549.1,219203.0] || subclass(symmetrization_of(identity_relation),rest_of(regular(symmetrization_of(identity_relation))))* subclass(element_relation,identity_relation) -> .
% 299.99/300.65  220754[18:Res:190510.1,219203.0] || subclass(inverse(identity_relation),rest_of(regular(symmetrization_of(identity_relation))))* subclass(element_relation,identity_relation) -> .
% 299.99/300.65  220819[8:SpL:117066.0,219206.0] || member(flip(cross_product(u,ordinal_numbers)),inverse(u))* subclass(element_relation,identity_relation) -> .
% 299.99/300.65  221024[8:SpR:219919.1,6984.0] || equal(singleton(apply(choice,omega)),identity_relation)** -> equal(apply(choice,omega),identity_relation).
% 299.99/300.65  221122[7:Res:13236.2,41096.0] || well_ordering(u,v) -> equal(v,identity_relation) member(least(u,v),ordinal_numbers)*.
% 299.99/300.65  221137[24:Res:13236.2,207872.1] operation(least(u,subset_relation)) || well_ordering(u,subset_relation)* -> equal(subset_relation,identity_relation).
% 299.99/300.65  221174[18:MRR:221151.1,190496.0] || well_ordering(u,symmetrization_of(identity_relation)) -> member(least(u,symmetrization_of(identity_relation)),inverse(identity_relation))*.
% 299.99/300.65  221302[8:Res:215662.1,56411.0] || subclass(complement(rest_of(singleton(u))),identity_relation)* subclass(ordinal_numbers,complement(element_relation)) -> .
% 299.99/300.65  221304[8:Res:215662.1,898.0] || subclass(complement(restrict(u,v,w)),identity_relation)* -> member(singleton(x),u)*.
% 299.99/300.65  221337[8:Res:215662.1,3572.0] || subclass(complement(compose_class(u)),identity_relation)* -> equal(compose(u,singleton(v)),v)**.
% 299.99/300.65  221445[8:SpL:160491.0,221330.0] || subclass(union(u,identity_relation),identity_relation) well_ordering(ordinal_numbers,symmetric_difference(ordinal_numbers,u))* -> .
% 299.99/300.65  221449[8:SpL:59.0,221330.0] || subclass(power_class(u),identity_relation) well_ordering(ordinal_numbers,image(element_relation,complement(u)))* -> .
% 299.99/300.65  221561[8:Res:217198.1,898.0] || equal(complement(restrict(u,v,w)),identity_relation)** -> member(singleton(x),u)*.
% 299.99/300.65  221656[8:SpR:218159.1,33.0] || equal(cross_product(u,v),identity_relation) -> equal(restrict(w,u,v),identity_relation)**.
% 299.99/300.65  221661[8:SpR:218159.1,163.0] || equal(complement(intersection(u,v)),identity_relation)** -> equal(symmetric_difference(u,v),identity_relation).
% 299.99/300.65  221698[8:SpR:218159.1,66293.0] || equal(union(u,identity_relation),identity_relation) -> equal(symmetric_difference(complement(u),ordinal_numbers),identity_relation)**.
% 299.99/300.65  222045[8:Rew:217174.1,222044.1,222023.1,222044.1] || equal(image(successor_relation,ordinal_numbers),identity_relation) -> equal(union(singleton(identity_relation),identity_relation),ordinal_numbers)**.
% 299.99/300.65  222091[8:SpR:219120.1,33.0] || subclass(cross_product(u,v),identity_relation)* -> equal(restrict(w,u,v),identity_relation)**.
% 299.99/300.65  222096[8:SpR:219120.1,163.0] || subclass(complement(intersection(u,v)),identity_relation)* -> equal(symmetric_difference(u,v),identity_relation).
% 299.99/300.65  222133[8:SpR:219120.1,66293.0] || subclass(union(u,identity_relation),identity_relation)* -> equal(symmetric_difference(complement(u),ordinal_numbers),identity_relation).
% 299.99/300.65  222539[8:Res:55.1,69474.0] inductive(inverse(subset_relation)) || member(u,subset_relation)* -> equal(integer_of(u),identity_relation).
% 299.99/300.65  222589[24:SpR:217824.0,207931.1] operation(regular(complement(complement(omega)))) ||  -> equal(regular(complement(complement(omega))),identity_relation)**.
% 299.99/300.65  222896[8:Obv:222891.2] || subclass(u,subset_relation) subclass(u,inverse(subset_relation))* -> equal(u,identity_relation).
% 299.99/300.65  222899[8:Obv:222889.1] || subclass(intersection(subset_relation,u),inverse(subset_relation))* -> equal(intersection(subset_relation,u),identity_relation).
% 299.99/300.65  222901[8:Obv:222890.1] || subclass(intersection(u,subset_relation),inverse(subset_relation))* -> equal(intersection(u,subset_relation),identity_relation).
% 299.99/300.65  223010[5:Res:9632.1,974.0] || equal(complement(complement(union_of_range_map)),ordinal_numbers) -> equal(sum_class(range_of(singleton(u))),u)**.
% 299.99/300.65  223150[11:Rew:80200.0,223136.1] || subclass(complement(u),identity_relation) -> equal(complement(image(element_relation,symmetrization_of(u))),identity_relation)**.
% 299.99/300.65  223151[11:Rew:80200.0,223137.1] || equal(complement(u),identity_relation) -> equal(complement(image(element_relation,symmetrization_of(u))),identity_relation)**.
% 299.99/300.65  223473[11:Rew:80200.0,223458.1] || subclass(complement(u),identity_relation) -> equal(complement(image(element_relation,successor(u))),identity_relation)**.
% 299.99/300.65  223474[11:Rew:80200.0,223459.1] || equal(complement(u),identity_relation) -> equal(complement(image(element_relation,successor(u))),identity_relation)**.
% 299.99/300.65  223978[7:Res:55.1,13242.0] inductive(complement(u)) || member(v,u)* -> equal(integer_of(v),identity_relation).
% 299.99/300.65  224745[26:Res:224684.1,18794.1] || subclass(omega,intersection(u,v)) member(identity_relation,symmetric_difference(u,v))* -> .
% 299.99/300.65  224753[26:Res:224684.1,67561.0] || subclass(omega,symmetric_difference(complement(u),ordinal_numbers))* -> member(identity_relation,union(u,identity_relation)).
% 299.99/300.65  224754[26:Res:224684.1,160772.0] || subclass(omega,symmetric_difference(ordinal_numbers,u)) member(identity_relation,union(u,identity_relation))* -> .
% 299.99/300.65  224767[26:Res:224684.1,12.0] || subclass(omega,unordered_pair(u,v))* -> equal(identity_relation,v) equal(identity_relation,u).
% 299.99/300.65  224774[26:Res:224684.1,897.0] || subclass(omega,restrict(u,v,w))* -> member(identity_relation,cross_product(v,w)).
% 299.99/300.65  224783[26:Res:224684.1,14681.0] || subclass(omega,regular(u))* member(identity_relation,u) -> equal(u,identity_relation).
% 299.99/300.65  224785[26:Res:224684.1,288.0] || subclass(omega,image(element_relation,complement(u)))* member(identity_relation,power_class(u)) -> .
% 299.99/300.65  224902[7:Res:55.1,13340.0] inductive(intersection(u,v)) ||  -> equal(integer_of(w),identity_relation) member(w,u)*.
% 299.99/300.65  224967[7:Res:55.1,13341.0] inductive(intersection(u,v)) ||  -> equal(integer_of(w),identity_relation) member(w,v)*.
% 299.99/300.65  225250[26:SpL:160491.0,224734.0] || subclass(omega,union(u,identity_relation)) member(identity_relation,symmetric_difference(ordinal_numbers,u))* -> .
% 299.99/300.65  225254[26:SpL:59.0,224734.0] || subclass(omega,power_class(u)) member(identity_relation,image(element_relation,complement(u)))* -> .
% 299.99/300.65  225273[26:SpL:160491.0,224737.0] || subclass(omega,complement(union(u,identity_relation)))* -> member(identity_relation,symmetric_difference(ordinal_numbers,u)).
% 299.99/300.65  225277[26:SpL:59.0,224737.0] || subclass(omega,complement(power_class(u))) -> member(identity_relation,image(element_relation,complement(u)))*.
% 299.99/300.65  225318[7:Obv:225313.1] || subclass(omega,u) -> equal(integer_of(v),identity_relation) subclass(singleton(v),u)*.
% 299.99/300.65  225355[26:Res:192333.1,225263.1] || equal(symmetric_difference(ordinal_numbers,u),ordinal_numbers)** equal(complement(complement(u)),omega) -> .
% 299.99/300.65  225357[26:Res:193927.1,225263.1] || equal(inverse(subset_relation),inverse(identity_relation)) equal(complement(complement(subset_relation)),omega)** -> .
% 299.99/300.65  225358[26:Res:193924.1,225263.1] || equal(symmetrization_of(identity_relation),inverse(subset_relation)) equal(complement(complement(subset_relation)),omega)** -> .
% 299.99/300.65  225359[26:Res:193906.1,225263.1] || equal(inverse(subset_relation),singleton(identity_relation)) equal(complement(complement(subset_relation)),omega)** -> .
% 299.99/300.65  225376[26:Res:198162.1,225263.1] || equal(complement(ordered_pair(inverse(u),v)),omega)** -> equal(range_of(u),identity_relation).
% 299.99/300.65  225455[7:Obv:225436.2] || subclass(u,v) subclass(u,complement(v))* -> equal(u,identity_relation).
% 299.99/300.65  225464[7:Obv:225429.1] || subclass(intersection(u,v),complement(u))* -> equal(intersection(u,v),identity_relation).
% 299.99/300.65  225466[7:Obv:225435.1] || subclass(intersection(u,v),complement(v))* -> equal(intersection(u,v),identity_relation).
% 299.99/300.65  225497[8:SpL:162584.0,225445.0] || subclass(complement(inverse(identity_relation)),symmetrization_of(identity_relation))* -> equal(complement(inverse(identity_relation)),identity_relation).
% 299.99/300.65  225571[26:SpL:160491.0,225289.0] || equal(complement(union(u,identity_relation)),omega) -> member(identity_relation,symmetric_difference(ordinal_numbers,u))*.
% 299.99/300.65  225575[26:SpL:59.0,225289.0] || equal(complement(power_class(u)),omega) -> member(identity_relation,image(element_relation,complement(u)))*.
% 299.99/300.65  225722[26:SpL:163.0,224747.0] || subclass(omega,symmetric_difference(u,v)) -> member(identity_relation,complement(intersection(u,v)))*.
% 299.99/300.65  225728[26:SpL:155665.0,224747.0] || subclass(omega,symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers)))* -> member(identity_relation,complement(subset_relation)).
% 299.99/300.65  225729[26:SpL:155666.0,224747.0] || subclass(omega,symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation))* -> member(identity_relation,complement(subset_relation)).
% 299.99/300.65  225774[26:SpL:32.0,225707.0] || equal(restrict(u,v,w),omega)** -> member(identity_relation,cross_product(v,w))*.
% 299.99/300.65  225877[26:Res:225794.1,18794.1] || equal(intersection(u,v),omega) member(identity_relation,symmetric_difference(u,v))* -> .
% 299.99/300.65  225885[26:Res:225794.1,67561.0] || equal(symmetric_difference(complement(u),ordinal_numbers),omega) -> member(identity_relation,union(u,identity_relation))*.
% 299.99/300.65  225886[26:Res:225794.1,160772.0] || equal(symmetric_difference(ordinal_numbers,u),omega) member(identity_relation,union(u,identity_relation))* -> .
% 299.99/300.65  225899[26:Res:225794.1,12.0] || equal(unordered_pair(u,v),omega)** -> equal(identity_relation,v) equal(identity_relation,u).
% 299.99/300.65  225915[26:Res:225794.1,14681.0] || equal(regular(u),omega) member(identity_relation,u)* -> equal(u,identity_relation).
% 299.99/300.65  225917[26:Res:225794.1,288.0] || equal(image(element_relation,complement(u)),omega)** member(identity_relation,power_class(u)) -> .
% 299.99/300.65  225957[26:SpL:163.0,225765.0] || equal(symmetric_difference(u,v),omega) -> member(identity_relation,complement(intersection(u,v)))*.
% 299.99/300.65  225963[26:SpL:155665.0,225765.0] || equal(symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers)),omega)** -> member(identity_relation,complement(subset_relation)).
% 299.99/300.65  225964[26:SpL:155666.0,225765.0] || equal(symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation),omega)** -> member(identity_relation,complement(subset_relation)).
% 299.99/300.65  226274[7:Res:132293.0,17322.0] ||  -> equal(complement(successor(u)),identity_relation) member(regular(complement(successor(u))),complement(u))*.
% 299.99/300.65  226275[7:Res:132294.0,17322.0] ||  -> equal(complement(symmetrization_of(u)),identity_relation) member(regular(complement(symmetrization_of(u))),complement(u))*.
% 299.99/300.65  226451[7:Rew:155653.0,226376.0] ||  -> equal(subset_relation,identity_relation) member(regular(subset_relation),complement(compose(complement(element_relation),inverse(element_relation))))*.
% 299.99/300.65  226608[24:SpL:207565.1,216276.1] operation(u) || member(identity_relation,u) subclass(successor(u),identity_relation)* -> .
% 299.99/300.65  227052[8:MRR:226993.1,8638.0] || equal(complement(u),identity_relation) -> equal(integer_of(v),identity_relation) member(v,u)*.
% 299.99/300.65  227053[8:MRR:227011.1,8638.0] || equal(complement(u),identity_relation) -> equal(v,identity_relation) member(regular(v),u)*.
% 299.99/300.65  227085[8:Rew:30.0,227066.1] || equal(union(u,v),identity_relation)** equal(union(u,v),ordinal_numbers) -> .
% 299.99/300.65  227135[21:MRR:227121.0,8655.0] || equal(successor(singleton(identity_relation)),identity_relation) -> member(singleton(singleton(singleton(identity_relation))),successor_relation)*.
% 299.99/300.65  227184[24:SpL:207565.1,217450.0] operation(u) || equal(successor(u),identity_relation) member(identity_relation,u)* -> .
% 299.99/300.65  227216[8:Res:217451.1,66086.1] || equal(union(compose(element_relation,ordinal_numbers),identity_relation),identity_relation)** member(identity_relation,element_relation) -> .
% 299.99/300.65  227229[26:Res:217451.1,225263.1] || equal(union(u,identity_relation),identity_relation)** equal(complement(complement(u)),omega) -> .
% 299.99/300.65  227288[8:MRR:227259.0,13126.0] || subclass(rest_relation,union_of_range_map)* subclass(domain_relation,union_of_range_map) -> equal(rest_of(identity_relation),identity_relation).
% 299.99/300.65  227381[8:SpL:162584.0,217608.0] || equal(complement(symmetrization_of(identity_relation)),identity_relation) member(omega,complement(inverse(identity_relation)))* -> .
% 299.99/300.65  227423[24:SpL:207565.1,217662.0] operation(u) || equal(successor(u),identity_relation) member(omega,u)* -> .
% 299.99/300.65  227455[8:Res:217663.1,66086.1] || equal(union(compose(element_relation,ordinal_numbers),identity_relation),identity_relation)** member(omega,element_relation) -> .
% 299.99/300.65  227532[8:Rew:30.0,227511.0] || equal(union(u,v),identity_relation) equal(union(u,v),omega)** -> .
% 299.99/300.65  227560[8:Rew:30.0,227540.0] || equal(union(u,v),identity_relation) equal(union(u,v),domain_relation)** -> .
% 299.99/300.65  227669[8:SpL:162584.0,217699.0] || equal(complement(symmetrization_of(identity_relation)),identity_relation) subclass(domain_relation,complement(inverse(identity_relation)))* -> .
% 299.99/300.65  227695[8:SpL:162584.0,217700.0] || equal(complement(symmetrization_of(identity_relation)),identity_relation) member(complement(inverse(identity_relation)),subset_relation)* -> .
% 299.99/300.65  227834[21:SpR:18840.1,218385.1] || member(u,subset_relation)* subclass(domain_relation,rest_relation) -> equal(rest_of(u),identity_relation).
% 299.99/300.65  227998[21:SpR:18840.1,218561.1] || member(u,subset_relation)* subclass(rest_relation,domain_relation) -> equal(rest_of(u),identity_relation).
% 299.99/300.65  228103[15:Rew:30.0,228075.0] || equal(union(u,v),identity_relation) subclass(ordinal_numbers,union(u,v))* -> .
% 299.99/300.65  228141[8:SpL:15663.0,219927.1] || member(not_subclass_element(identity_relation,identity_relation),subset_relation)* equal(singleton(single_valued3(identity_relation)),identity_relation) -> .
% 299.99/300.65  228998[8:SpL:13096.1,222292.0] || member(identity_relation,u)* subclass(element_relation,identity_relation) -> equal(singleton(u),identity_relation).
% 299.99/300.65  229049[8:SpL:13096.1,222305.0] || equal(u,ordinal_numbers) subclass(element_relation,identity_relation)* -> equal(singleton(u),identity_relation)**.
% 299.99/300.65  229061[8:SpL:13096.1,222310.0] || subclass(ordinal_numbers,u)* subclass(element_relation,identity_relation)* -> equal(singleton(u),identity_relation).
% 299.99/300.65  229186[16:MRR:229167.2,14676.0] inductive(symmetric_difference(singleton(identity_relation),singleton(identity_relation))) || well_ordering(u,singleton(identity_relation))* -> .
% 299.99/300.65  229284[7:SpR:189.0,229162.0] ||  -> equal(intersection(power_class(image(element_relation,complement(u))),image(element_relation,power_class(u))),identity_relation)**.
% 299.99/300.65  229425[8:SpR:189.0,229346.0] ||  -> equal(union(power_class(image(element_relation,complement(u))),image(element_relation,power_class(u))),ordinal_numbers)**.
% 299.99/300.65  229484[8:SpR:189.0,229359.0] ||  -> equal(symmetric_difference(power_class(image(element_relation,complement(u))),image(element_relation,power_class(u))),ordinal_numbers)**.
% 299.99/300.65  229740[8:Rew:66036.0,229620.0] ||  -> equal(union(image(element_relation,power_class(u)),power_class(image(element_relation,complement(u)))),ordinal_numbers)**.
% 299.99/300.65  229761[8:MRR:229633.2,14676.0] inductive(symmetric_difference(inverse(identity_relation),inverse(identity_relation))) || well_ordering(u,symmetrization_of(identity_relation))* -> .
% 299.99/300.65  229912[7:SpR:189.0,229590.0] ||  -> equal(intersection(image(element_relation,power_class(u)),power_class(image(element_relation,complement(u)))),identity_relation)**.
% 299.99/300.65  230087[8:SpR:189.0,229733.0] ||  -> equal(symmetric_difference(image(element_relation,power_class(u)),power_class(image(element_relation,complement(u)))),ordinal_numbers)**.
% 299.99/300.65  230180[7:SpR:30.0,229638.0] ||  -> equal(symmetric_difference(intersection(complement(u),complement(v)),complement(union(u,v))),identity_relation)**.
% 299.99/300.65  230191[8:SpR:162038.0,229638.0] ||  -> equal(symmetric_difference(image(element_relation,symmetrization_of(identity_relation)),complement(power_class(complement(inverse(identity_relation))))),identity_relation)**.
% 299.99/300.65  230192[16:SpR:195257.0,229638.0] ||  -> equal(symmetric_difference(image(element_relation,singleton(identity_relation)),complement(power_class(complement(singleton(identity_relation))))),identity_relation)**.
% 299.99/300.65  230458[22:MRR:230431.0,8655.0] || well_ordering(ordinal_numbers,symmetric_difference(ordinal_numbers,u)) -> member(singleton(identity_relation),union(u,identity_relation))*.
% 299.99/300.65  230664[8:Res:8643.1,18754.1] || subclass(ordinal_numbers,u) subclass(ordinal_numbers,regular(u))* -> equal(u,identity_relation).
% 299.99/300.65  230764[8:SpL:13260.1,230706.0] || subclass(ordinal_numbers,regular(cross_product(u,v)))* -> equal(cross_product(u,v),identity_relation).
% 299.99/300.65  230782[8:SpL:13260.1,230770.0] || equal(regular(cross_product(u,v)),ordinal_numbers)** -> equal(cross_product(u,v),identity_relation).
% 299.99/300.65  231043[8:Res:61019.0,230762.0] || subclass(ordinal_numbers,regular(complement(complement(subset_relation))))* -> equal(complement(complement(subset_relation)),identity_relation).
% 299.99/300.65  231044[8:Res:13248.1,230762.0] || subclass(ordinal_numbers,regular(intersection(subset_relation,u)))* -> equal(intersection(subset_relation,u),identity_relation).
% 299.99/300.65  231057[8:Res:13210.1,230762.0] || subclass(ordinal_numbers,regular(intersection(u,subset_relation)))* -> equal(intersection(u,subset_relation),identity_relation).
% 299.99/300.65  231058[8:Res:13227.2,230762.0] || subclass(u,subset_relation) subclass(ordinal_numbers,regular(u))* -> equal(u,identity_relation).
% 299.99/300.65  231066[8:Res:127147.1,230762.0] || subclass(ordinal_numbers,complement(complement(subset_relation))) subclass(ordinal_numbers,least(element_relation,omega))* -> .
% 299.99/300.65  231067[8:Res:126679.1,230762.0] || subclass(omega,complement(complement(subset_relation)))* subclass(ordinal_numbers,least(element_relation,omega)) -> .
% 299.99/300.65  231121[8:Res:61019.0,230780.0] || equal(regular(complement(complement(subset_relation))),ordinal_numbers)** -> equal(complement(complement(subset_relation)),identity_relation).
% 299.99/300.65  231122[8:Res:13248.1,230780.0] || equal(regular(intersection(subset_relation,u)),ordinal_numbers)** -> equal(intersection(subset_relation,u),identity_relation).
% 299.99/300.65  231135[8:Res:13210.1,230780.0] || equal(regular(intersection(u,subset_relation)),ordinal_numbers)** -> equal(intersection(u,subset_relation),identity_relation).
% 299.99/300.65  231136[8:Res:13227.2,230780.0] || subclass(u,subset_relation)* equal(regular(u),ordinal_numbers) -> equal(u,identity_relation).
% 299.99/300.65  231144[8:Res:127147.1,230780.0] || subclass(ordinal_numbers,complement(complement(subset_relation)))* equal(least(element_relation,omega),ordinal_numbers) -> .
% 299.99/300.65  231145[8:Res:126679.1,230780.0] || subclass(omega,complement(complement(subset_relation)))* equal(least(element_relation,omega),ordinal_numbers) -> .
% 299.99/300.65  231550[8:SpR:160491.0,229281.0] ||  -> equal(intersection(power_class(symmetric_difference(ordinal_numbers,u)),image(element_relation,union(u,identity_relation))),identity_relation)**.
% 299.99/300.65  231830[8:MRR:231829.2,227056.0] ||  -> member(not_subclass_element(regular(complement(u)),v),u)* subclass(regular(complement(u)),v).
% 299.99/300.65  231854[8:SpR:162584.0,231812.0] ||  -> subclass(regular(complement(inverse(identity_relation))),symmetrization_of(identity_relation))* equal(complement(inverse(identity_relation)),identity_relation).
% 299.99/300.65  231919[8:SpR:160491.0,229481.0] ||  -> equal(symmetric_difference(power_class(symmetric_difference(ordinal_numbers,u)),image(element_relation,union(u,identity_relation))),ordinal_numbers)**.
% 299.99/300.65  231954[8:Rew:59.0,231910.1] || subclass(image(element_relation,complement(u)),power_class(u))* -> subclass(ordinal_numbers,power_class(u)).
% 299.99/300.65  232243[8:SpR:160491.0,229909.0] ||  -> equal(intersection(image(element_relation,union(u,identity_relation)),power_class(symmetric_difference(ordinal_numbers,u))),identity_relation)**.
% 299.99/300.65  232422[8:SpR:160491.0,230084.0] ||  -> equal(symmetric_difference(image(element_relation,union(u,identity_relation)),power_class(symmetric_difference(ordinal_numbers,u))),ordinal_numbers)**.
% 299.99/300.65  232488[8:Res:51313.1,230867.0] || member(singleton(subset_relation),subset_relation) equal(complement(first(singleton(subset_relation))),identity_relation)** -> .
% 299.99/300.65  232500[8:Res:60219.0,230867.0] || equal(complement(not_subclass_element(u,complement(subset_relation))),identity_relation)** -> subclass(u,complement(subset_relation)).
% 299.99/300.65  232549[18:Res:194549.1,230867.0] || subclass(symmetrization_of(identity_relation),subset_relation) equal(complement(regular(symmetrization_of(identity_relation))),identity_relation)** -> .
% 299.99/300.65  232550[18:Res:190510.1,230867.0] || subclass(inverse(identity_relation),subset_relation) equal(complement(regular(symmetrization_of(identity_relation))),identity_relation)** -> .
% 299.99/300.65  232562[8:Res:51313.1,230939.0] || member(singleton(subset_relation),subset_relation) equal(regular(first(singleton(subset_relation))),ordinal_numbers)** -> .
% 299.99/300.65  232574[8:Res:60219.0,230939.0] || equal(regular(not_subclass_element(u,complement(subset_relation))),ordinal_numbers)** -> subclass(u,complement(subset_relation)).
% 299.99/300.65  232623[18:Res:194549.1,230939.0] || subclass(symmetrization_of(identity_relation),subset_relation) equal(regular(regular(symmetrization_of(identity_relation))),ordinal_numbers)** -> .
% 299.99/300.65  232624[18:Res:190510.1,230939.0] || subclass(inverse(identity_relation),subset_relation) equal(regular(regular(symmetrization_of(identity_relation))),ordinal_numbers)** -> .
% 299.99/300.65  232841[8:SpL:50855.1,232823.0] || member(singleton(u),subset_relation) subclass(ordinal_numbers,regular(unordered_pair(v,u)))* -> .
% 299.99/300.65  232852[8:MRR:232846.1,216061.0] || subclass(ordinal_numbers,u) -> equal(regular(unordered_pair(u,singleton(v))),singleton(v))**.
% 299.99/300.65  232992[8:SpL:50855.1,232850.0] || member(singleton(u),subset_relation) equal(regular(unordered_pair(v,u)),ordinal_numbers)** -> .
% 299.99/300.65  232999[8:MRR:232997.1,216061.0] || equal(u,ordinal_numbers) -> equal(regular(unordered_pair(u,singleton(v))),singleton(v))**.
% 299.99/300.65  233137[8:SpL:50855.1,233123.0] || member(singleton(u),subset_relation) subclass(ordinal_numbers,regular(unordered_pair(u,v)))* -> .
% 299.99/300.65  233150[8:MRR:233145.1,216036.0] || subclass(ordinal_numbers,u) -> equal(regular(unordered_pair(singleton(v),u)),singleton(v))**.
% 299.99/300.65  233226[8:SpL:50855.1,233148.0] || member(singleton(u),subset_relation) equal(regular(unordered_pair(u,v)),ordinal_numbers)** -> .
% 299.99/300.65  233235[8:MRR:233234.1,216036.0] || equal(u,ordinal_numbers) -> equal(regular(unordered_pair(singleton(v),u)),singleton(v))**.
% 299.99/300.65  233288[7:Obv:233270.0] ||  -> equal(intersection(recursion_equation_functions(u),singleton(v)),identity_relation)** subclass(v,cross_product(ordinal_numbers,ordinal_numbers)).
% 299.99/300.65  233296[8:Res:231881.0,13082.1] inductive(u) ||  -> equal(singleton(u),identity_relation) member(identity_relation,complement(singleton(u)))*.
% 299.99/300.65  233305[18:Res:231881.0,219270.0] || subclass(complement(singleton(inverse(identity_relation))),identity_relation)* -> equal(singleton(inverse(identity_relation)),identity_relation).
% 299.99/300.65  233308[18:Res:231881.0,190447.0] || well_ordering(ordinal_numbers,complement(singleton(inverse(identity_relation))))* -> equal(singleton(inverse(identity_relation)),identity_relation).
% 299.99/300.65  233310[18:Res:231881.0,219269.0] || subclass(complement(singleton(symmetrization_of(identity_relation))),identity_relation)* -> equal(singleton(symmetrization_of(identity_relation)),identity_relation).
% 299.99/300.65  233313[18:Res:231881.0,190433.0] || well_ordering(ordinal_numbers,complement(singleton(symmetrization_of(identity_relation))))* -> equal(singleton(symmetrization_of(identity_relation)),identity_relation).
% 299.99/300.65  233437[7:Obv:233423.0] ||  -> equal(intersection(singleton(u),recursion_equation_functions(v)),identity_relation)** subclass(u,cross_product(ordinal_numbers,ordinal_numbers)).
% 299.99/300.65  233564[21:MRR:233510.2,216013.0] || member(u,ordinal_numbers) subclass(domain_relation,complement(singleton(ordered_pair(u,identity_relation))))* -> .
% 299.99/300.65  233885[22:Res:233384.0,9876.0] || subclass(complement(singleton(singleton(singleton(identity_relation)))),u)* well_ordering(ordinal_numbers,u) -> .
% 299.99/300.65  233889[22:Res:233384.0,5.0] || subclass(complement(singleton(singleton(singleton(identity_relation)))),u)* -> member(singleton(identity_relation),u).
% 299.99/300.65  234029[22:Res:13125.2,233883.0] || subclass(omega,singleton(singleton(singleton(identity_relation))))* -> equal(integer_of(singleton(identity_relation)),identity_relation).
% 299.99/300.65  234103[21:SpR:197474.0,233383.0] ||  -> equal(range_of(u),identity_relation) member(identity_relation,complement(singleton(ordered_pair(inverse(u),v))))*.
% 299.99/300.65  234108[8:Res:233383.0,9876.0] || subclass(complement(singleton(ordered_pair(u,v))),w)* well_ordering(ordinal_numbers,w) -> .
% 299.99/300.65  234112[8:Res:233383.0,5.0] || subclass(complement(singleton(ordered_pair(u,v))),w)* -> member(singleton(u),w).
% 299.99/300.65  234185[21:SpL:197474.0,234106.0] || member(identity_relation,singleton(ordered_pair(inverse(u),v)))* -> equal(range_of(u),identity_relation).
% 299.99/300.65  234188[8:Res:13125.2,234106.0] || subclass(omega,singleton(ordered_pair(u,v)))* -> equal(integer_of(singleton(u)),identity_relation).
% 299.99/300.65  234311[25:MRR:234310.2,162904.0] || subclass(element_relation,identity_relation) member(ordered_pair(u,singleton(singleton(identity_relation))),composition_function)* -> .
% 299.99/300.65  234379[18:MRR:234378.2,190496.0] || well_ordering(u,ordinal_numbers) -> subclass(singleton(least(u,symmetrization_of(identity_relation))),symmetrization_of(identity_relation))*.
% 299.99/300.65  234560[8:Res:133837.1,233381.0] || well_ordering(ordinal_numbers,complement(singleton(omega)))* -> equal(integer_of(singleton(singleton(u))),identity_relation)**.
% 299.99/300.65  234561[21:Res:196904.1,233381.0] || subclass(domain_relation,singleton(omega)) -> equal(integer_of(singleton(singleton(singleton(identity_relation)))),identity_relation)**.
% 299.99/300.65  234562[22:Res:205574.1,233381.0] || equal(singleton(singleton(identity_relation)),singleton(omega)) -> equal(integer_of(singleton(identity_relation)),identity_relation)**.
% 299.99/300.65  234584[18:Res:194549.1,233381.0] || subclass(symmetrization_of(identity_relation),singleton(omega))* -> equal(integer_of(regular(symmetrization_of(identity_relation))),identity_relation).
% 299.99/300.65  234585[18:Res:190510.1,233381.0] || subclass(inverse(identity_relation),singleton(omega))* -> equal(integer_of(regular(symmetrization_of(identity_relation))),identity_relation).
% 299.99/300.65  234599[8:Rew:125726.0,234548.1] || subclass(ordinal_numbers,complement(complement(singleton(omega))))* -> equal(least(element_relation,omega),identity_relation).
% 299.99/300.65  234600[8:Rew:125726.0,234549.1] || subclass(omega,complement(complement(singleton(omega))))* -> equal(least(element_relation,omega),identity_relation).
% 299.99/300.65  234854[21:MRR:234787.1,14676.0] || member(u,ordinal_numbers) -> equal(apply(singleton(v),u),sum_class(range_of(identity_relation)))**.
% 299.99/300.65  234855[21:MRR:234802.1,14676.0] || member(u,ordinal_numbers) -> equal(apply(range_of(identity_relation),u),sum_class(range_of(identity_relation)))**.
% 299.99/300.65  234968[7:SpL:229238.0,123.0] || subclass(compose(identity_relation,identity_relation),identity_relation) -> transitive(complement(cross_product(u,u)),u)*.
% 299.99/300.65  234969[7:SpL:229238.0,9777.0] || equal(compose(identity_relation,identity_relation),identity_relation) -> transitive(complement(cross_product(u,u)),u)*.
% 299.99/300.65  235002[7:MRR:235001.1,13039.0] || transitive(complement(cross_product(u,u)),u)* -> equal(compose(identity_relation,identity_relation),identity_relation).
% 299.99/300.65  235022[8:SpR:216188.1,234956.0] || equal(cross_product(u,ordinal_numbers),identity_relation) -> equal(image(ordinal_numbers,u),range_of(identity_relation))**.
% 299.99/300.65  235092[8:Res:41368.0,210517.1] || equal(complement(power_class(u)),ordinal_numbers) -> subclass(v,image(element_relation,complement(u)))*.
% 299.99/300.65  235108[8:Obv:235095.0] ||  -> subclass(regular(power_class(u)),image(element_relation,complement(u)))* equal(power_class(u),identity_relation).
% 299.99/300.65  235141[25:Rew:213477.0,235137.1] || equal(cross_product(u,identity_relation),identity_relation) -> equal(cantor(cross_product(u,identity_relation)),identity_relation)**.
% 299.99/300.65  235161[15:Res:195033.1,234983.0] || equal(complement(complement(cantor(complement(cross_product(singleton(range_of(identity_relation)),ordinal_numbers))))),ordinal_numbers)** -> .
% 299.99/300.65  235178[8:Res:9632.1,234983.0] || equal(complement(complement(cantor(complement(cross_product(singleton(singleton(u)),ordinal_numbers))))),ordinal_numbers)** -> .
% 299.99/300.65  235180[8:Res:133837.1,234983.0] || well_ordering(ordinal_numbers,complement(cantor(complement(cross_product(singleton(singleton(singleton(u))),ordinal_numbers)))))* -> .
% 299.99/300.65  235181[21:Res:196904.1,234983.0] || subclass(domain_relation,cantor(complement(cross_product(singleton(singleton(singleton(singleton(identity_relation)))),ordinal_numbers))))* -> .
% 299.99/300.65  235182[22:Res:205574.1,234983.0] || equal(cantor(complement(cross_product(singleton(singleton(identity_relation)),ordinal_numbers))),singleton(singleton(identity_relation)))** -> .
% 299.99/300.65  235204[18:Res:194549.1,234983.0] || subclass(symmetrization_of(identity_relation),cantor(complement(cross_product(singleton(regular(symmetrization_of(identity_relation))),ordinal_numbers))))* -> .
% 299.99/300.65  235205[18:Res:190510.1,234983.0] || subclass(inverse(identity_relation),cantor(complement(cross_product(singleton(regular(symmetrization_of(identity_relation))),ordinal_numbers))))* -> .
% 299.99/300.65  235213[8:SpL:216188.1,235154.0] || equal(cross_product(singleton(omega),ordinal_numbers),identity_relation)** equal(cantor(ordinal_numbers),ordinal_numbers) -> .
% 299.99/300.65  235216[8:SpL:216188.1,235155.0] || equal(cross_product(singleton(omega),ordinal_numbers),identity_relation)** subclass(ordinal_numbers,cantor(ordinal_numbers)) -> .
% 299.99/300.65  235223[26:SpL:216188.1,235195.0] || equal(cross_product(singleton(identity_relation),ordinal_numbers),identity_relation)** equal(cantor(ordinal_numbers),omega) -> .
% 299.99/300.65  235226[26:SpL:216188.1,235196.0] || equal(cross_product(singleton(identity_relation),ordinal_numbers),identity_relation)** subclass(omega,cantor(ordinal_numbers)) -> .
% 299.99/300.65  235248[8:SpL:216188.1,235198.0] || equal(cross_product(singleton(identity_relation),ordinal_numbers),identity_relation)** equal(cantor(ordinal_numbers),ordinal_numbers) -> .
% 299.99/300.65  235251[8:SpL:216188.1,235202.0] || equal(cross_product(singleton(identity_relation),ordinal_numbers),identity_relation)** subclass(ordinal_numbers,cantor(ordinal_numbers)) -> .
% 299.99/300.65  235265[8:SpR:69395.0,230445.1] || member(u,intersection(v,ordinal_numbers)) -> member(u,complement(symmetric_difference(v,ordinal_numbers)))*.
% 299.99/300.65  235280[15:Res:230445.1,165527.1] || member(range_of(identity_relation),u) subclass(ordinal_numbers,complement(union(u,identity_relation)))* -> .
% 299.99/300.65  235294[8:Res:230445.1,8843.1] || member(singleton(u),v)* subclass(ordinal_numbers,complement(union(v,identity_relation)))* -> .
% 299.99/300.65  235446[8:Res:28980.1,116129.0] || subclass(rest_relation,flip(rest_of(u))) -> member(ordered_pair(v,w),cantor(u))*.
% 299.99/300.65  235449[5:Res:28980.1,18.0] || subclass(rest_relation,flip(cross_product(u,v)))* -> member(ordered_pair(w,x),u)*.
% 299.99/300.65  236351[26:SpL:141394.0,224755.0] || subclass(omega,symmetric_difference(u,ordinal_numbers)) member(identity_relation,intersection(u,ordinal_numbers))* -> .
% 299.99/300.65  236388[26:Res:148858.1,224800.0] || subclass(omega,inverse(subset_relation))* equal(complement(complement(subset_relation)),inverse(identity_relation)) -> .
% 299.99/300.65  236562[26:Res:148858.1,224801.0] || subclass(omega,inverse(subset_relation))* equal(complement(complement(subset_relation)),symmetrization_of(identity_relation)) -> .
% 299.99/300.65  236580[26:Res:148858.1,224802.0] || subclass(omega,inverse(subset_relation))* equal(complement(complement(subset_relation)),singleton(identity_relation)) -> .
% 299.99/300.65  236615[26:SpL:13096.1,225140.0] || subclass(omega,u)* subclass(element_relation,identity_relation) -> equal(singleton(u),identity_relation).
% 299.99/300.65  236632[26:SpL:13096.1,225241.0] || equal(u,omega) subclass(element_relation,identity_relation)* -> equal(singleton(u),identity_relation)**.
% 299.99/300.65  236956[26:SpL:141394.0,225887.0] || equal(symmetric_difference(u,ordinal_numbers),omega) member(identity_relation,intersection(u,ordinal_numbers))* -> .
% 299.99/300.65  236982[26:Res:225888.1,66086.1] || equal(symmetric_difference(ordinal_numbers,compose(element_relation,ordinal_numbers)),omega)** member(identity_relation,element_relation) -> .
% 299.99/300.65  236995[26:Res:225888.1,225263.1] || equal(symmetric_difference(ordinal_numbers,u),omega)** equal(complement(complement(u)),omega) -> .
% 299.99/300.65  237646[8:MRR:237573.2,14676.0] || member(u,restrict(subset_relation,v,w))* member(u,inverse(subset_relation)) -> .
% 299.99/300.65  238191[7:SpR:3616.0,237830.0] ||  -> equal(intersection(complement(union(u,v)),symmetric_difference(complement(u),complement(v))),identity_relation)**.
% 299.99/300.65  238468[8:MRR:238349.2,14676.0] || member(u,symmetric_difference(ordinal_numbers,v))* member(u,complement(complement(v))) -> .
% 299.99/300.65  238878[8:MRR:238808.2,14676.0] || member(u,symmetric_difference(ordinal_numbers,inverse(identity_relation)))* member(u,symmetrization_of(identity_relation)) -> .
% 299.99/300.65  238939[8:SpR:160491.0,237395.0] ||  -> equal(intersection(union(u,identity_relation),restrict(symmetric_difference(ordinal_numbers,u),v,w)),identity_relation)**.
% 299.99/300.65  238943[7:SpR:59.0,237395.0] ||  -> equal(intersection(power_class(u),restrict(image(element_relation,complement(u)),v,w)),identity_relation)**.
% 299.99/300.65  239014[8:MRR:238913.2,14676.0] || member(u,restrict(v,w,x))* member(u,complement(v)) -> .
% 299.99/300.65  239865[7:SpR:3616.0,239340.0] ||  -> equal(intersection(symmetric_difference(complement(u),complement(v)),complement(union(u,v))),identity_relation)**.
% 299.99/300.65  19404[0:SpR:163.0,19069.0] ||  -> subclass(symmetric_difference(complement(intersection(u,v)),union(u,v)),complement(symmetric_difference(u,v)))*.
% 299.99/300.65  9935[5:SpL:30.0,9922.1] inductive(intersection(complement(u),complement(v))) || equal(union(u,v),ordinal_numbers)** -> .
% 299.99/300.65  68297[5:SpL:3616.0,8735.0] || equal(symmetric_difference(complement(u),complement(v)),ordinal_numbers)** -> member(omega,union(u,v)).
% 299.99/300.65  68320[5:SpL:3616.0,8732.0] || subclass(ordinal_numbers,symmetric_difference(complement(u),complement(v)))* -> member(omega,union(u,v)).
% 299.99/300.65  69374[8:Res:69184.1,7.0] || member(not_subclass_element(u,compose(element_relation,ordinal_numbers)),element_relation)* -> subclass(u,compose(element_relation,ordinal_numbers)).
% 299.99/300.65  50037[5:SpL:18840.1,23.0] || member(u,subset_relation) member(u,element_relation) -> member(first(u),second(u))*.
% 299.99/300.65  50066[5:MRR:50003.1,50064.1] || member(u,subset_relation) member(first(u),second(u))* -> member(u,element_relation).
% 299.99/300.65  69369[8:Res:69184.1,5.0] || member(u,element_relation)* subclass(compose(element_relation,ordinal_numbers),v)* -> member(u,v)*.
% 299.99/300.65  69164[8:Res:8642.1,66086.1] || subclass(ordinal_numbers,complement(compose(element_relation,ordinal_numbers)))* member(ordered_pair(u,v),element_relation)* -> .
% 299.99/300.65  41118[5:MRR:40591.1,41096.1] || member(u,ordinal_numbers)* member(v,u)* subclass(ordinal_numbers,complement(element_relation))* -> .
% 299.99/300.65  56417[5:Res:9632.1,56411.0] || equal(complement(complement(rest_of(singleton(u)))),ordinal_numbers)** subclass(ordinal_numbers,complement(element_relation)) -> .
% 299.99/300.65  56510[5:SpL:8647.0,56480.0] || member(flip(cross_product(u,ordinal_numbers)),inverse(u))* subclass(ordinal_numbers,complement(element_relation)) -> .
% 299.99/300.65  56509[5:SpL:8648.0,56480.0] || member(restrict(element_relation,ordinal_numbers,u),sum_class(u))* subclass(ordinal_numbers,complement(element_relation)) -> .
% 299.99/300.65  70002[5:SpR:8648.0,39971.1] || equal(complement(rest_of(restrict(element_relation,ordinal_numbers,u))),ordinal_numbers)** -> subclass(sum_class(u),v)*.
% 299.99/300.65  10082[5:SpL:163.0,8848.0] || subclass(ordinal_numbers,symmetric_difference(u,v)) -> member(singleton(w),complement(intersection(u,v)))*.
% 299.99/300.65  10161[5:SpL:163.0,10088.0] || equal(symmetric_difference(u,v),ordinal_numbers) -> member(singleton(w),complement(intersection(u,v)))*.
% 299.99/300.65  10728[0:Res:10714.1,11.0] || member(u,v) subclass(v,singleton(u))* -> equal(v,singleton(u)).
% 299.99/300.65  56771[5:SpL:3596.0,8847.0] || subclass(ordinal_numbers,symmetric_difference(u,singleton(u)))* -> member(unordered_pair(v,w),successor(u))*.
% 299.99/300.65  57119[5:Res:8642.1,19559.0] || subclass(ordinal_numbers,symmetric_difference(u,singleton(u)))* -> member(ordered_pair(v,w),successor(u))*.
% 299.99/300.65  10081[5:SpL:33.0,8848.0] || subclass(ordinal_numbers,restrict(u,v,w))* -> member(singleton(x),cross_product(v,w))*.
% 299.99/300.65  10160[5:SpL:33.0,10088.0] || equal(restrict(u,v,w),ordinal_numbers)** -> member(singleton(x),cross_product(v,w))*.
% 299.99/300.65  9687[5:Res:9632.1,898.0] || equal(complement(complement(restrict(u,v,w))),ordinal_numbers)** -> member(singleton(x),u)*.
% 299.99/300.65  50031[5:SpL:18840.1,2486.0] || member(u,subset_relation) subclass(u,v) -> member(singleton(first(u)),v)*.
% 299.99/300.65  50053[5:SpL:18840.1,10702.0] || member(u,subset_relation) equal(v,u) -> member(singleton(first(u)),v)*.
% 299.99/300.65  50851[5:Res:49995.1,25.0] || member(intersection(u,v),subset_relation) -> member(singleton(first(intersection(u,v))),u)*.
% 299.99/300.65  50850[5:Res:49995.1,26.0] || member(intersection(u,v),subset_relation) -> member(singleton(first(intersection(u,v))),v)*.
% 299.99/300.65  51485[5:Res:51313.1,28.1] || member(singleton(complement(u)),subset_relation) member(first(singleton(complement(u))),u)* -> .
% 299.99/300.65  51510[8:Res:51313.1,14679.1] || member(singleton(inverse(subset_relation)),subset_relation) member(first(singleton(inverse(subset_relation))),subset_relation)* -> .
% 299.99/300.65  39262[5:Res:18819.1,8841.1] || member(ordered_pair(u,v),subset_relation)* subclass(ordinal_numbers,complement(cross_product(ordinal_numbers,ordinal_numbers)))* -> .
% 299.99/300.65  57186[5:Res:8642.1,19676.0] || subclass(ordinal_numbers,symmetric_difference(u,inverse(u)))* -> member(ordered_pair(v,w),symmetrization_of(u))*.
% 299.99/300.65  18210[5:Res:8642.1,3617.0] || subclass(ordinal_numbers,symmetric_difference(u,v)) -> member(ordered_pair(w,x),union(u,v))*.
% 299.99/300.65  8812[5:Rew:8637.0,6941.0] || subclass(ordinal_numbers,u)* subclass(u,v)* -> member(ordered_pair(w,x),v)*.
% 299.99/300.65  40057[5:Res:18819.1,8842.1] || member(unordered_pair(u,v),subset_relation)* subclass(ordinal_numbers,complement(cross_product(ordinal_numbers,ordinal_numbers)))* -> .
% 299.99/300.65  56772[5:SpL:3597.0,8847.0] || subclass(ordinal_numbers,symmetric_difference(u,inverse(u)))* -> member(unordered_pair(v,w),symmetrization_of(u))*.
% 299.99/300.65  47535[5:Obv:47531.1] || member(not_subclass_element(u,intersection(v,ordinal_numbers)),v)* -> subclass(u,intersection(v,ordinal_numbers)).
% 299.99/300.65  18849[5:Res:18819.1,7.0] || member(not_subclass_element(u,cross_product(ordinal_numbers,ordinal_numbers)),subset_relation)* -> subclass(u,cross_product(ordinal_numbers,ordinal_numbers)).
% 299.99/300.65  18839[5:Res:18819.1,5.0] || member(u,subset_relation)* subclass(cross_product(ordinal_numbers,ordinal_numbers),v)* -> member(u,v)*.
% 299.99/300.65  50054[5:SpL:18840.1,8841.1] || member(u,subset_relation)* subclass(ordinal_numbers,complement(v))* member(u,v)* -> .
% 299.99/300.65  28965[8:Res:8827.2,15935.1] || member(u,ordinal_numbers)* subclass(rest_relation,subset_relation) subclass(ordinal_numbers,inverse(subset_relation))* -> .
% 299.99/300.65  39290[5:Res:8827.2,8841.1] || member(u,ordinal_numbers)* subclass(rest_relation,v) subclass(ordinal_numbers,complement(v))* -> .
% 299.99/300.65  15425[8:Res:15380.0,129.0] || subclass(domain_relation,u) well_ordering(v,u)* -> member(least(v,domain_relation),domain_relation)*.
% 299.99/300.65  70005[5:SpR:8647.0,39971.1] || equal(complement(rest_of(flip(cross_product(u,ordinal_numbers)))),ordinal_numbers)** -> subclass(inverse(u),v)*.
% 299.99/300.65  18991[0:Res:18949.0,11.0] || subclass(u,restrict(u,v,w))* -> equal(restrict(u,v,w),u).
% 299.99/300.65  79537[5:Res:60219.0,28.1] || member(not_subclass_element(u,complement(complement(v))),v)* -> subclass(u,complement(complement(v))).
% 299.99/300.65  79554[8:Res:60219.0,14679.1] || member(not_subclass_element(u,complement(inverse(subset_relation))),subset_relation)* -> subclass(u,complement(inverse(subset_relation))).
% 299.99/300.65  79569[5:SpR:30.0,79560.1] ||  -> member(u,intersection(complement(v),complement(w)))* subclass(singleton(u),union(v,w)).
% 299.99/300.65  94663[5:SpR:18840.1,39298.1] || member(u,subset_relation)* subclass(ordinal_numbers,complement(complement(v)))* -> member(u,v)*.
% 299.99/300.65  94665[5:Res:39298.1,28.1] || subclass(ordinal_numbers,complement(complement(complement(u))))* member(ordered_pair(v,w),u)* -> .
% 299.99/300.65  94674[5:Res:39298.1,26.0] || subclass(ordinal_numbers,complement(complement(intersection(u,v))))* -> member(ordered_pair(w,x),v)*.
% 299.99/300.65  94675[5:Res:39298.1,25.0] || subclass(ordinal_numbers,complement(complement(intersection(u,v))))* -> member(ordered_pair(w,x),u)*.
% 299.99/300.65  94685[8:Res:39298.1,14679.1] || subclass(ordinal_numbers,complement(complement(inverse(subset_relation))))* member(ordered_pair(u,v),subset_relation)* -> .
% 299.99/300.65  94703[5:Res:39298.1,8651.0] || subclass(ordinal_numbers,complement(complement(rest_of(u))))* -> equal(restrict(u,v,ordinal_numbers),w)*.
% 299.99/300.65  96353[5:Res:40074.1,28.1] || subclass(ordinal_numbers,complement(complement(complement(u))))* member(unordered_pair(v,w),u)* -> .
% 299.99/300.65  96362[5:Res:40074.1,26.0] || subclass(ordinal_numbers,complement(complement(intersection(u,v))))* -> member(unordered_pair(w,x),v)*.
% 299.99/300.65  96363[5:Res:40074.1,25.0] || subclass(ordinal_numbers,complement(complement(intersection(u,v))))* -> member(unordered_pair(w,x),u)*.
% 299.99/300.65  96373[8:Res:40074.1,14679.1] || subclass(ordinal_numbers,complement(complement(inverse(subset_relation))))* member(unordered_pair(u,v),subset_relation)* -> .
% 299.99/300.65  125213[8:Res:8827.2,28976.1] || member(u,ordinal_numbers)* subclass(rest_relation,subset_relation) subclass(rest_relation,inverse(subset_relation))* -> .
% 299.99/300.65  125898[8:Res:125725.1,66086.1] || subclass(omega,complement(compose(element_relation,ordinal_numbers)))* member(least(element_relation,omega),element_relation) -> .
% 299.99/300.65  125906[5:Res:125725.1,5.0] || subclass(omega,u)* subclass(u,v)* -> member(least(element_relation,omega),v)*.
% 299.99/300.65  125910[5:Res:125725.1,3617.0] || subclass(omega,symmetric_difference(u,v)) -> member(least(element_relation,omega),union(u,v))*.
% 299.99/300.65  125911[5:Res:125725.1,19559.0] || subclass(omega,symmetric_difference(u,singleton(u)))* -> member(least(element_relation,omega),successor(u))*.
% 299.99/300.65  125912[5:Res:125725.1,19676.0] || subclass(omega,symmetric_difference(u,inverse(u)))* -> member(least(element_relation,omega),symmetrization_of(u))*.
% 299.99/300.65  125975[8:Res:125731.1,66086.1] || subclass(ordinal_numbers,complement(compose(element_relation,ordinal_numbers)))* member(least(element_relation,omega),element_relation) -> .
% 299.99/300.65  125983[5:Res:125731.1,5.0] || subclass(ordinal_numbers,u)* subclass(u,v)* -> member(least(element_relation,omega),v)*.
% 299.99/300.65  125987[5:Res:125731.1,3617.0] || subclass(ordinal_numbers,symmetric_difference(u,v)) -> member(least(element_relation,omega),union(u,v))*.
% 299.99/300.65  125988[5:Res:125731.1,19559.0] || subclass(ordinal_numbers,symmetric_difference(u,singleton(u)))* -> member(least(element_relation,omega),successor(u))*.
% 299.99/300.65  125989[5:Res:125731.1,19676.0] || subclass(ordinal_numbers,symmetric_difference(u,inverse(u)))* -> member(least(element_relation,omega),symmetrization_of(u))*.
% 299.99/300.65  126647[5:Res:18819.1,125896.1] || member(least(element_relation,omega),subset_relation) subclass(omega,complement(cross_product(ordinal_numbers,ordinal_numbers)))* -> .
% 299.99/300.65  127112[5:Res:18819.1,125973.1] || member(least(element_relation,omega),subset_relation) subclass(ordinal_numbers,complement(cross_product(ordinal_numbers,ordinal_numbers)))* -> .
% 299.99/300.65  127976[5:Res:126679.1,28.1] || subclass(omega,complement(complement(complement(u))))* member(least(element_relation,omega),u) -> .
% 299.99/300.65  127987[5:Res:126679.1,26.0] || subclass(omega,complement(complement(intersection(u,v))))* -> member(least(element_relation,omega),v).
% 299.99/300.65  127988[5:Res:126679.1,25.0] || subclass(omega,complement(complement(intersection(u,v))))* -> member(least(element_relation,omega),u).
% 299.99/300.65  128004[5:Res:126679.1,50033.0] || subclass(omega,complement(complement(subset_relation)))* equal(complement(least(element_relation,omega)),ordinal_numbers) -> .
% 299.99/300.65  128008[8:Res:126679.1,14679.1] || subclass(omega,complement(complement(inverse(subset_relation))))* member(least(element_relation,omega),subset_relation) -> .
% 299.99/300.65  128310[5:Res:127147.1,28.1] || subclass(ordinal_numbers,complement(complement(complement(u))))* member(least(element_relation,omega),u) -> .
% 299.99/300.65  128321[5:Res:127147.1,26.0] || subclass(ordinal_numbers,complement(complement(intersection(u,v))))* -> member(least(element_relation,omega),v).
% 299.99/300.65  128322[5:Res:127147.1,25.0] || subclass(ordinal_numbers,complement(complement(intersection(u,v))))* -> member(least(element_relation,omega),u).
% 299.99/300.65  128343[8:Res:127147.1,14679.1] || subclass(ordinal_numbers,complement(complement(inverse(subset_relation))))* member(least(element_relation,omega),subset_relation) -> .
% 299.99/300.65  130727[5:Res:130678.0,8787.1] single_valued_class(complement(complement(cross_product(ordinal_numbers,ordinal_numbers)))) ||  -> function(complement(complement(cross_product(ordinal_numbers,ordinal_numbers))))*.
% 299.99/300.65  130958[5:Res:41112.1,9876.0] || member(u,rest_of(u))* subclass(element_relation,v) well_ordering(ordinal_numbers,v)* -> .
% 299.99/300.65  130964[8:Res:117318.1,9876.0] || member(u,cantor(u))* subclass(element_relation,v) well_ordering(ordinal_numbers,v)* -> .
% 299.99/300.65  131474[5:Res:8645.1,18794.1] || subclass(ordinal_numbers,intersection(u,v)) member(singleton(w),symmetric_difference(u,v))* -> .
% 299.99/300.65  131563[0:Res:2504.1,3700.0] || subclass(ordered_pair(u,v),singleton(w))* -> equal(unordered_pair(u,singleton(v)),w).
% 299.99/300.65  132446[5:SpL:6355.1,132439.0] || well_ordering(ordinal_numbers,not_subclass_element(cross_product(u,v),w))* -> subclass(cross_product(u,v),w).
% 299.99/300.65  132829[5:SpL:163.0,130481.0] || equal(symmetric_difference(u,v),omega) -> member(least(element_relation,omega),union(u,v))*.
% 299.99/300.65  132830[5:SpL:3596.0,130481.0] || equal(symmetric_difference(u,singleton(u)),omega)** -> member(least(element_relation,omega),successor(u))*.
% 299.99/300.65  132831[5:SpL:3597.0,130481.0] || equal(symmetric_difference(u,inverse(u)),omega)** -> member(least(element_relation,omega),symmetrization_of(u))*.
% 299.99/300.65  133398[5:SpL:163.0,130610.0] || equal(symmetric_difference(u,v),ordinal_numbers) -> member(least(element_relation,omega),union(u,v))*.
% 299.99/300.65  133399[5:SpL:3596.0,130610.0] || equal(symmetric_difference(u,singleton(u)),ordinal_numbers)** -> member(least(element_relation,omega),successor(u))*.
% 299.99/300.65  133400[5:SpL:3597.0,130610.0] || equal(symmetric_difference(u,inverse(u)),ordinal_numbers)** -> member(least(element_relation,omega),symmetrization_of(u))*.
% 299.99/300.65  133487[5:Res:10.1,40321.0] || equal(u,rest_relation) well_ordering(v,u)* -> member(least(v,rest_relation),rest_relation)*.
% 299.99/300.65  134075[5:Res:133837.1,9876.0] || well_ordering(ordinal_numbers,complement(u))* subclass(u,v)* well_ordering(ordinal_numbers,v)* -> .
% 299.99/300.65  134110[5:Res:133837.1,56411.0] || well_ordering(ordinal_numbers,complement(rest_of(singleton(singleton(u)))))* subclass(ordinal_numbers,complement(element_relation)) -> .
% 299.99/300.65  134112[5:Res:133837.1,898.0] || well_ordering(ordinal_numbers,complement(restrict(u,v,w)))* -> member(singleton(singleton(x)),u)*.
% 299.99/300.65  134119[5:Res:133837.1,161.0] || well_ordering(ordinal_numbers,complement(omega)) -> equal(integer_of(singleton(singleton(u))),singleton(singleton(u)))**.
% 299.99/300.65  135272[5:Res:10.1,28959.1] || equal(cross_product(u,v),rest_relation)** member(w,ordinal_numbers)* -> member(w,u)*.
% 299.99/300.65  135338[5:Res:10.1,28680.1] || equal(cross_product(u,v),domain_relation)** member(w,ordinal_numbers)* -> member(w,u)*.
% 299.99/300.65  137008[5:Res:18211.1,8842.1] || subclass(ordinal_numbers,symmetric_difference(u,v)) subclass(ordinal_numbers,complement(union(u,v)))* -> .
% 299.99/300.65  66818[5:Res:51313.1,161.0] || member(singleton(omega),subset_relation) -> equal(integer_of(first(singleton(omega))),first(singleton(omega)))**.
% 299.99/300.65  139355[5:Res:10.1,8813.0] || equal(u,ordinal_numbers) subclass(u,v)* -> member(unordered_pair(w,x),v)*.
% 299.99/300.65  139760[5:SpR:47.0,39529.1] || member(u,ordinal_numbers) -> member(u,successor(v)) member(u,complement(singleton(v)))*.
% 299.99/300.65  139761[5:SpR:117.0,39529.1] || member(u,ordinal_numbers) -> member(u,symmetrization_of(v)) member(u,complement(inverse(v)))*.
% 299.99/300.65  139817[5:MRR:139783.0,8666.0] || subclass(ordinal_numbers,complement(union(u,v)))* -> member(unordered_pair(w,x),complement(v))*.
% 299.99/300.65  139819[5:MRR:139791.0,125724.0] || subclass(ordinal_numbers,complement(union(u,v)))* -> member(least(element_relation,omega),complement(v))*.
% 299.99/300.65  139820[5:MRR:139792.0,125724.0] || subclass(omega,complement(union(u,v)))* -> member(least(element_relation,omega),complement(v))*.
% 299.99/300.65  139821[5:MRR:139799.0,8667.0] || subclass(ordinal_numbers,complement(union(u,v)))* -> member(ordered_pair(w,x),complement(v))*.
% 299.99/300.65  139824[5:MRR:139789.0,41183.1] ||  -> member(not_subclass_element(u,union(v,w)),complement(w))* subclass(u,union(v,w)).
% 299.99/300.65  139900[5:MRR:139869.0,8666.0] || subclass(ordinal_numbers,complement(union(u,v)))* -> member(unordered_pair(w,x),complement(u))*.
% 299.99/300.65  139902[5:MRR:139877.0,125724.0] || subclass(ordinal_numbers,complement(union(u,v)))* -> member(least(element_relation,omega),complement(u))*.
% 299.99/300.65  139903[5:MRR:139878.0,125724.0] || subclass(omega,complement(union(u,v)))* -> member(least(element_relation,omega),complement(u))*.
% 299.99/300.65  139904[5:MRR:139885.0,8667.0] || subclass(ordinal_numbers,complement(union(u,v)))* -> member(ordered_pair(w,x),complement(u))*.
% 299.99/300.65  139907[5:MRR:139875.0,41183.1] ||  -> member(not_subclass_element(u,union(v,w)),complement(v))* subclass(u,union(v,w)).
% 299.99/300.65  140279[0:Res:10.1,19124.0] || equal(singleton(u),v)* -> subclass(v,w) equal(not_subclass_element(v,w),u)*.
% 299.99/300.65  140865[8:Rew:140603.0,131402.0] || member(u,symmetric_difference(complement(v),ordinal_numbers))* member(u,symmetric_difference(ordinal_numbers,v)) -> .
% 299.99/300.65  143524[5:Res:143160.0,11.0] || subclass(complement(u),symmetric_difference(ordinal_numbers,u))* -> equal(symmetric_difference(ordinal_numbers,u),complement(u)).
% 299.99/300.65  144394[8:SpR:30.0,140613.0] ||  -> equal(symmetric_difference(ordinal_numbers,intersection(complement(u),complement(v))),intersection(union(u,v),ordinal_numbers))**.
% 299.99/300.65  144463[8:Rew:140613.0,144381.0] ||  -> subclass(symmetric_difference(ordinal_numbers,u),v) member(not_subclass_element(symmetric_difference(ordinal_numbers,u),v),complement(u))*.
% 299.99/300.65  147058[5:Res:143193.1,5.0] || equal(u,ordinal_numbers) subclass(u,v)* -> member(least(element_relation,omega),v)*.
% 299.99/300.65  147262[8:Res:143222.1,66086.1] || equal(complement(compose(element_relation,ordinal_numbers)),omega) member(least(element_relation,omega),element_relation)* -> .
% 299.99/300.65  147272[5:Res:143222.1,5.0] || equal(u,omega) subclass(u,v)* -> member(least(element_relation,omega),v)*.
% 299.99/300.65  148167[5:Res:9632.1,3572.0] || equal(complement(complement(compose_class(u))),ordinal_numbers) -> equal(compose(u,singleton(v)),v)**.
% 299.99/300.65  152915[0:Res:55.1,19121.0] inductive(intersection(u,v)) ||  -> subclass(omega,w) member(not_subclass_element(omega,w),u)*.
% 299.99/300.65  152928[5:Res:132293.0,19121.0] ||  -> subclass(complement(successor(u)),v) member(not_subclass_element(complement(successor(u)),v),complement(u))*.
% 299.99/300.65  152929[5:Res:132294.0,19121.0] ||  -> subclass(complement(symmetrization_of(u)),v) member(not_subclass_element(complement(symmetrization_of(u)),v),complement(u))*.
% 299.99/300.65  153039[0:Res:55.1,19120.0] inductive(intersection(u,v)) ||  -> subclass(omega,w) member(not_subclass_element(omega,w),v)*.
% 299.99/300.65  153486[8:Res:153473.0,8825.1] || member(u,ordinal_numbers) -> member(u,compose(element_relation,ordinal_numbers))* member(u,complement(element_relation)).
% 299.99/300.65  154290[5:Res:40074.1,151988.0] || subclass(ordinal_numbers,complement(complement(complement(complement(u)))))* -> member(unordered_pair(v,w),u)*.
% 299.99/300.65  154320[5:Res:127147.1,151988.0] || subclass(ordinal_numbers,complement(complement(complement(complement(u)))))* -> member(least(element_relation,omega),u).
% 299.99/300.65  154321[5:Res:126679.1,151988.0] || subclass(omega,complement(complement(complement(complement(u)))))* -> member(least(element_relation,omega),u).
% 299.99/300.65  154329[5:Res:49995.1,151988.0] || member(complement(complement(u)),subset_relation) -> member(singleton(first(complement(complement(u)))),u)*.
% 299.99/300.65  154337[5:Res:39298.1,151988.0] || subclass(ordinal_numbers,complement(complement(complement(complement(u)))))* -> member(ordered_pair(v,w),u)*.
% 299.99/300.65  155188[0:SpR:154737.1,30.0] || subclass(complement(u),complement(v))* -> equal(union(v,u),complement(complement(u))).
% 299.99/300.65  155857[5:Rew:155653.0,155823.0] ||  -> subclass(subset_relation,u) member(not_subclass_element(subset_relation,u),complement(compose(complement(element_relation),inverse(element_relation))))*.
% 299.99/300.65  156425[5:SpL:155665.0,10088.0] || equal(symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers)),ordinal_numbers)** -> member(singleton(u),complement(subset_relation))*.
% 299.99/300.65  156435[5:SpL:155665.0,8848.0] || subclass(ordinal_numbers,symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers)))* -> member(singleton(u),complement(subset_relation))*.
% 299.99/300.65  156534[5:SpL:155666.0,10088.0] || equal(symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation),ordinal_numbers)** -> member(singleton(u),complement(subset_relation))*.
% 299.99/300.65  156544[5:SpL:155666.0,8848.0] || subclass(ordinal_numbers,symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation))* -> member(singleton(u),complement(subset_relation))*.
% 299.99/300.65  156845[5:MRR:156841.1,8655.0] || well_ordering(ordinal_numbers,complement(singleton(u))) -> member(singleton(singleton(singleton(singleton(u)))),element_relation)*.
% 299.99/300.65  156942[8:Res:156922.1,5.0] || member(u,inverse(subset_relation))* subclass(complement(subset_relation),v)* -> member(u,v)*.
% 299.99/300.65  156961[8:Res:156922.1,125896.1] || member(least(element_relation,omega),inverse(subset_relation))* subclass(omega,complement(complement(subset_relation))) -> .
% 299.99/300.65  157065[8:Res:157036.0,8825.1] || member(u,ordinal_numbers) -> member(u,complement(inverse(subset_relation)))* member(u,complement(subset_relation)).
% 299.99/300.65  159636[5:Res:133837.1,8785.0] || well_ordering(ordinal_numbers,complement(rest_of(u))) -> equal(restrict(u,singleton(v),ordinal_numbers),v)**.
% 299.99/300.65  128504[5:Res:8665.1,8840.1] function(singleton(u)) || member(u,ordinal_numbers) -> member(u,cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.65  134784[8:MRR:134744.1,8667.0] operation(u) || subclass(rest_relation,rest_of(u)) -> member(v,cantor(cantor(u)))*.
% 299.99/300.65  116849[8:Rew:116078.0,19407.1] operation(u) ||  -> subclass(symmetric_difference(cantor(u),v),complement(intersection(v,cantor(u))))*.
% 299.99/300.65  116850[8:Rew:116078.0,19420.1] operation(u) ||  -> subclass(symmetric_difference(v,cantor(u)),complement(intersection(cantor(u),v)))*.
% 299.99/300.65  10867[5:Res:10714.1,8787.1] single_valued_class(singleton(u)) || member(u,cross_product(ordinal_numbers,ordinal_numbers))* -> function(singleton(u)).
% 299.99/300.65  50841[5:Res:49995.1,8788.0] || member(recursion_equation_functions(u),subset_relation) -> subclass(singleton(first(recursion_equation_functions(u))),cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.65  130630[5:Res:41371.0,152.0] ||  -> subclass(complement(complement(recursion_equation_functions(u))),v) function(not_subclass_element(complement(complement(recursion_equation_functions(u))),v))*.
% 299.99/300.65  125723[5:Res:125717.0,129.0] || subclass(omega,u) well_ordering(v,u)* -> member(least(v,omega),omega)*.
% 299.99/300.65  160831[8:Rew:160496.0,16802.1] inductive(intersection(diagonalise(u),complement(v))) || equal(complement(complement(v)),ordinal_numbers)** -> .
% 299.99/300.65  96369[5:Res:40074.1,50033.0] || subclass(ordinal_numbers,complement(complement(subset_relation)))* equal(complement(unordered_pair(u,v)),ordinal_numbers)** -> .
% 299.99/300.65  128339[5:Res:127147.1,50033.0] || subclass(ordinal_numbers,complement(complement(subset_relation)))* equal(complement(least(element_relation,omega)),ordinal_numbers) -> .
% 299.99/300.65  156947[8:Res:156922.1,8842.1] || member(unordered_pair(u,v),inverse(subset_relation))* subclass(ordinal_numbers,complement(complement(subset_relation))) -> .
% 299.99/300.65  156960[8:Res:156922.1,125973.1] || member(least(element_relation,omega),inverse(subset_relation))* subclass(ordinal_numbers,complement(complement(subset_relation))) -> .
% 299.99/300.65  156969[8:Res:156922.1,8841.1] || member(ordered_pair(u,v),inverse(subset_relation))* subclass(ordinal_numbers,complement(complement(subset_relation))) -> .
% 299.99/300.65  165637[5:Res:143198.1,18794.1] || equal(intersection(u,v),ordinal_numbers) member(singleton(w),symmetric_difference(u,v))* -> .
% 299.99/300.65  166757[5:SpL:30.0,166753.1] inductive(intersection(complement(u),complement(v))) || equal(union(u,v),omega)** -> .
% 299.99/300.65  177021[8:SpL:117066.0,161304.1] || subclass(rest_relation,rest_of(flip(cross_product(u,ordinal_numbers))))* well_ordering(ordinal_numbers,inverse(u)) -> .
% 299.99/300.65  177022[8:SpL:117142.0,161304.1] || subclass(rest_relation,rest_of(restrict(element_relation,ordinal_numbers,u)))* well_ordering(ordinal_numbers,sum_class(u)) -> .
% 299.99/300.65  186574[8:SpL:144460.0,176785.0] || equal(symmetric_difference(complement(u),ordinal_numbers),ordinal_numbers) member(omega,symmetric_difference(ordinal_numbers,u))* -> .
% 299.99/300.65  166262[7:Res:132294.0,13082.1] inductive(complement(symmetrization_of(u))) ||  -> member(identity_relation,intersection(complement(u),complement(inverse(u))))*.
% 299.99/300.65  166261[7:Res:132293.0,13082.1] inductive(complement(successor(u))) ||  -> member(identity_relation,intersection(complement(u),complement(singleton(u))))*.
% 299.99/300.65  165050[8:Res:303.1,162901.0] || equal(not_subclass_element(intersection(u,subset_relation),v),identity_relation)** -> subclass(intersection(u,subset_relation),v).
% 299.99/300.65  165049[8:Res:2503.2,162901.0] || subclass(u,subset_relation) equal(not_subclass_element(u,v),identity_relation)** -> subclass(u,v).
% 299.99/300.65  165040[8:Res:313.1,162901.0] || equal(not_subclass_element(intersection(subset_relation,u),v),identity_relation)** -> subclass(intersection(subset_relation,u),v).
% 299.99/300.65  165039[8:Res:41371.0,162901.0] || equal(not_subclass_element(complement(complement(subset_relation)),u),identity_relation)** -> subclass(complement(complement(subset_relation)),u).
% 299.99/300.65  164978[8:Res:303.1,162888.0] || subclass(not_subclass_element(intersection(u,subset_relation),v),identity_relation)* -> subclass(intersection(u,subset_relation),v).
% 299.99/300.65  164977[8:Res:2503.2,162888.0] || subclass(u,subset_relation) subclass(not_subclass_element(u,v),identity_relation)* -> subclass(u,v).
% 299.99/300.65  164968[8:Res:313.1,162888.0] || subclass(not_subclass_element(intersection(subset_relation,u),v),identity_relation)* -> subclass(intersection(subset_relation,u),v).
% 299.99/300.65  164967[8:Res:41371.0,162888.0] || subclass(not_subclass_element(complement(complement(subset_relation)),u),identity_relation)* -> subclass(complement(complement(subset_relation)),u).
% 299.99/300.65  162902[8:SpL:6355.1,162891.0] || equal(not_subclass_element(cross_product(u,v),w),identity_relation)** -> subclass(cross_product(u,v),w).
% 299.99/300.65  162889[8:SpL:6355.1,162248.0] || subclass(not_subclass_element(cross_product(u,v),w),identity_relation)* -> subclass(cross_product(u,v),w).
% 299.99/300.65  162405[7:Res:13061.0,47534.0] ||  -> equal(integer_of(not_subclass_element(u,intersection(omega,u))),identity_relation)** subclass(u,intersection(omega,u)).
% 299.99/300.65  166496[7:Res:13248.1,9876.0] || subclass(u,v)* well_ordering(ordinal_numbers,v)* -> equal(intersection(u,w),identity_relation)**.
% 299.99/300.65  166686[7:Res:13210.1,9876.0] || subclass(u,v)* well_ordering(ordinal_numbers,v)* -> equal(intersection(w,u),identity_relation)**.
% 299.99/300.65  166260[7:Res:130703.0,13082.1] inductive(complement(union(u,v))) ||  -> member(identity_relation,intersection(complement(u),complement(v)))*.
% 299.99/300.65  167604[14:SpL:30.0,167597.0] || well_ordering(ordinal_numbers,union(u,v)) -> member(identity_relation,intersection(complement(u),complement(v)))*.
% 299.99/300.65  160897[8:Rew:160491.0,81797.1] inductive(symmetric_difference(union(identity_relation,u),ordinal_numbers)) ||  -> member(identity_relation,union(complement(u),identity_relation))*.
% 299.99/300.65  83878[7:Res:66696.2,26.0] || subclass(ordinal_numbers,intersection(u,v))* -> equal(integer_of(w),identity_relation) member(w,v)*.
% 299.99/300.65  83879[7:Res:66696.2,25.0] || subclass(ordinal_numbers,intersection(u,v))* -> equal(integer_of(w),identity_relation) member(w,u)*.
% 299.99/300.65  160790[8:Rew:160498.0,69582.1] inductive(symmetric_difference(ordinal_numbers,union(identity_relation,u))) ||  -> member(identity_relation,complement(complement(complement(u))))*.
% 299.99/300.65  69635[8:SpL:68698.0,9922.1] inductive(symmetric_difference(domain_of(u),ordinal_numbers)) || equal(union(cantor(u),identity_relation),ordinal_numbers)** -> .
% 299.99/300.65  69726[8:SpR:66293.0,69395.0] ||  -> equal(union(symmetric_difference(complement(u),ordinal_numbers),identity_relation),complement(symmetric_difference(union(u,identity_relation),ordinal_numbers)))**.
% 299.99/300.65  64208[7:Res:13210.1,50033.0] || equal(complement(regular(intersection(u,subset_relation))),ordinal_numbers)** -> equal(intersection(u,subset_relation),identity_relation).
% 299.99/300.65  64297[7:Res:13248.1,50033.0] || equal(complement(regular(intersection(subset_relation,u))),ordinal_numbers)** -> equal(intersection(subset_relation,u),identity_relation).
% 299.99/300.65  83906[7:Res:66696.2,7.0] || subclass(ordinal_numbers,u) -> equal(integer_of(not_subclass_element(v,u)),identity_relation)** subclass(v,u).
% 299.99/300.65  69782[8:Res:69706.0,13082.1] inductive(symmetric_difference(intersection(u,ordinal_numbers),identity_relation)) ||  -> member(identity_relation,complement(symmetric_difference(u,ordinal_numbers)))*.
% 299.99/300.65  16570[8:Obv:16569.2] || connected(identity_relation,u) member(v,not_well_ordering(identity_relation,u))* -> well_ordering(identity_relation,u).
% 299.99/300.65  83290[7:Res:61019.0,50033.0] || equal(complement(regular(complement(complement(subset_relation)))),ordinal_numbers)** -> equal(complement(complement(subset_relation)),identity_relation).
% 299.99/300.65  166147[8:Res:156922.1,13105.0] || member(regular(complement(complement(subset_relation))),inverse(subset_relation))* -> equal(complement(complement(subset_relation)),identity_relation).
% 299.99/300.65  83291[7:Res:61019.0,3700.0] ||  -> equal(complement(complement(singleton(u))),identity_relation) equal(regular(complement(complement(singleton(u)))),u)**.
% 299.99/300.65  164875[8:SpR:160491.0,130703.0] ||  -> subclass(complement(union(u,symmetric_difference(ordinal_numbers,v))),intersection(complement(u),union(v,identity_relation)))*.
% 299.99/300.65  160767[8:Rew:116078.0,15892.2,116078.0,15892.2,116078.0,15892.1] operation(u) || equal(cantor(u),domain_relation) -> member(identity_relation,cantor(cantor(u)))*.
% 299.99/300.65  160768[8:Rew:116078.0,15884.2,116078.0,15884.2,116078.0,15884.1] operation(u) || subclass(domain_relation,cantor(u)) -> member(identity_relation,cantor(cantor(u)))*.
% 299.99/300.65  14682[8:MRR:13650.3,14676.0] || member(u,v) member(u,singleton(v))* -> equal(singleton(v),identity_relation).
% 299.99/300.65  160921[8:Rew:160491.0,81766.1] inductive(symmetric_difference(complement(intersection(ordinal_numbers,u)),ordinal_numbers)) ||  -> member(identity_relation,union(u,identity_relation))*.
% 299.99/300.65  82301[8:Res:81336.1,8651.0] || subclass(domain_relation,complement(complement(rest_of(u))))* -> equal(restrict(u,identity_relation,ordinal_numbers),identity_relation).
% 299.99/300.65  83869[7:Res:66696.2,28.1] || subclass(ordinal_numbers,complement(u))* member(v,u)* -> equal(integer_of(v),identity_relation).
% 299.99/300.65  166326[7:Res:13125.2,151988.0] || subclass(omega,complement(complement(u)))* -> equal(integer_of(v),identity_relation) member(v,u)*.
% 299.99/300.65  167466[8:Res:51313.1,163154.0] || member(singleton(symmetrization_of(identity_relation)),subset_relation) -> member(first(singleton(symmetrization_of(identity_relation))),inverse(identity_relation))*.
% 299.99/300.65  163161[8:Rew:162584.0,163137.1] || member(not_subclass_element(symmetrization_of(identity_relation),u),complement(inverse(identity_relation)))* -> subclass(symmetrization_of(identity_relation),u).
% 299.99/300.65  163095[8:SpR:162584.0,19734.0] ||  -> subclass(symmetric_difference(symmetrization_of(identity_relation),complement(inverse(complement(inverse(identity_relation))))),symmetrization_of(complement(inverse(identity_relation))))*.
% 299.99/300.65  163094[8:SpR:162584.0,19733.0] ||  -> subclass(symmetric_difference(symmetrization_of(identity_relation),complement(singleton(complement(inverse(identity_relation))))),successor(complement(inverse(identity_relation))))*.
% 299.99/300.65  167475[8:Res:60219.0,163154.0] ||  -> subclass(u,complement(symmetrization_of(identity_relation))) member(not_subclass_element(u,complement(symmetrization_of(identity_relation))),inverse(identity_relation))*.
% 299.99/300.65  167498[8:Res:39298.1,163154.0] || subclass(ordinal_numbers,complement(complement(symmetrization_of(identity_relation)))) -> member(ordered_pair(u,v),inverse(identity_relation))*.
% 299.99/300.65  167464[8:Res:40074.1,163154.0] || subclass(ordinal_numbers,complement(complement(symmetrization_of(identity_relation)))) -> member(unordered_pair(u,v),inverse(identity_relation))*.
% 299.99/300.65  167485[8:Res:127147.1,163154.0] || subclass(ordinal_numbers,complement(complement(symmetrization_of(identity_relation)))) -> member(least(element_relation,omega),inverse(identity_relation))*.
% 299.99/300.65  167486[8:Res:126679.1,163154.0] || subclass(omega,complement(complement(symmetrization_of(identity_relation)))) -> member(least(element_relation,omega),inverse(identity_relation))*.
% 299.99/300.65  61476[5:SpR:105.0,50063.1] || member(not_subclass_element(compose(u,inverse(u)),identity_relation),subset_relation)* -> member(single_valued1(u),ordinal_numbers).
% 299.99/300.65  61487[5:SpR:106.0,50064.1] || member(not_subclass_element(compose(u,inverse(u)),identity_relation),subset_relation)* -> member(single_valued2(u),ordinal_numbers).
% 299.99/300.65  160775[8:Rew:116078.0,19732.2,116078.0,19732.2,116078.0,19732.1] operation(u) || equal(cantor(u),identity_relation) -> connected(v,cantor(cantor(u)))*.
% 299.99/300.65  63820[7:SpL:3616.0,13045.0] || subclass(ordinal_numbers,symmetric_difference(complement(u),complement(v)))* -> member(identity_relation,union(u,v)).
% 299.99/300.65  63789[7:SpL:3616.0,13051.0] || equal(symmetric_difference(complement(u),complement(v)),ordinal_numbers)** -> member(identity_relation,union(u,v)).
% 299.99/300.65  163883[8:Res:19172.1,155663.1] || equal(subset_relation,identity_relation) transitive(subset_relation,ordinal_numbers) -> equal(compose(subset_relation,subset_relation),subset_relation)**.
% 299.99/300.65  164851[8:SpR:160491.0,130703.0] ||  -> subclass(complement(union(symmetric_difference(ordinal_numbers,u),v)),intersection(union(u,identity_relation),complement(v)))*.
% 299.99/300.65  160990[8:Rew:140613.0,66165.0] || subclass(union(u,identity_relation),symmetric_difference(ordinal_numbers,u))* -> equal(union(u,identity_relation),identity_relation).
% 299.99/300.65  68878[8:SpL:66293.0,10088.0] || equal(symmetric_difference(complement(u),ordinal_numbers),ordinal_numbers) -> member(singleton(v),union(u,identity_relation))*.
% 299.99/300.65  68885[8:SpL:66293.0,8848.0] || subclass(ordinal_numbers,symmetric_difference(complement(u),ordinal_numbers)) -> member(singleton(v),union(u,identity_relation))*.
% 299.99/300.65  164854[8:SpR:160491.0,147905.0] ||  -> equal(intersection(symmetric_difference(ordinal_numbers,u),complement(union(u,identity_relation))),complement(union(u,identity_relation)))**.
% 299.99/300.65  160993[8:Rew:140613.0,67584.1] || subclass(ordinal_numbers,complement(union(u,identity_relation))) -> member(singleton(v),symmetric_difference(ordinal_numbers,u))*.
% 299.99/300.65  16746[8:SpL:15354.0,9922.1] inductive(intersection(complement(u),diagonalise(v))) || equal(union(u,identity_relation),ordinal_numbers)** -> .
% 299.99/300.65  13390[7:Rew:13036.0,10719.1] || subclass(omega,singleton(u))* -> equal(integer_of(u),identity_relation) equal(singleton(u),omega).
% 299.99/300.65  167458[8:Res:13125.2,163154.0] || subclass(omega,symmetrization_of(identity_relation)) -> equal(integer_of(u),identity_relation) member(u,inverse(identity_relation))*.
% 299.99/300.65  18746[8:Res:8645.1,14681.0] || subclass(ordinal_numbers,regular(u)) member(singleton(v),u)* -> equal(u,identity_relation).
% 299.99/300.65  64362[7:Res:13227.2,50033.0] || subclass(u,subset_relation) equal(complement(regular(u)),ordinal_numbers)** -> equal(u,identity_relation).
% 299.99/300.65  166790[7:Res:13227.2,151988.0] || subclass(u,complement(complement(v)))* -> equal(u,identity_relation) member(regular(u),v).
% 299.99/300.65  167262[8:Res:143198.1,14681.0] || equal(regular(u),ordinal_numbers) member(singleton(v),u)* -> equal(u,identity_relation).
% 299.99/300.65  167481[8:Res:13227.2,163154.0] || subclass(u,symmetrization_of(identity_relation)) -> equal(u,identity_relation) member(regular(u),inverse(identity_relation))*.
% 299.99/300.65  61581[8:SpR:15663.0,49995.1] || member(not_subclass_element(identity_relation,identity_relation),subset_relation) -> member(singleton(single_valued3(identity_relation)),not_subclass_element(identity_relation,identity_relation))*.
% 299.99/300.65  64621[7:SpR:15265.1,50064.1] function(u) || member(not_subclass_element(identity_relation,identity_relation),subset_relation)* -> member(single_valued2(u),ordinal_numbers)*.
% 299.99/300.65  64640[7:SpR:15272.1,50064.1] single_valued_class(u) || member(not_subclass_element(identity_relation,identity_relation),subset_relation)* -> member(single_valued2(u),ordinal_numbers)*.
% 299.99/300.65  161074[8:Rew:140603.0,66125.1] ||  -> equal(singleton(u),identity_relation) equal(symmetric_difference(singleton(u),u),union(singleton(u),u))**.
% 299.99/300.65  165361[14:Res:165168.1,9876.0] || equal(u,singleton(identity_relation)) subclass(u,v)* well_ordering(ordinal_numbers,v)* -> .
% 299.99/300.65  165384[14:Res:165168.1,897.0] || equal(restrict(u,v,w),singleton(identity_relation))** -> member(identity_relation,cross_product(v,w))*.
% 299.99/300.65  165366[14:Res:165168.1,18794.1] || equal(intersection(u,v),singleton(identity_relation)) member(identity_relation,symmetric_difference(u,v))* -> .
% 299.99/300.65  69165[8:Res:15426.1,66086.1] || subclass(domain_relation,complement(compose(element_relation,ordinal_numbers)))* member(ordered_pair(identity_relation,identity_relation),element_relation) -> .
% 299.99/300.65  62996[8:Res:15426.1,19559.0] || subclass(domain_relation,symmetric_difference(u,singleton(u)))* -> member(ordered_pair(identity_relation,identity_relation),successor(u))*.
% 299.99/300.65  83618[8:SpL:3596.0,83166.0] || equal(symmetric_difference(u,singleton(u)),domain_relation)** -> member(ordered_pair(identity_relation,identity_relation),successor(u))*.
% 299.99/300.65  62997[8:Res:15426.1,19676.0] || subclass(domain_relation,symmetric_difference(u,inverse(u)))* -> member(ordered_pair(identity_relation,identity_relation),symmetrization_of(u))*.
% 299.99/300.65  83619[8:SpL:3597.0,83166.0] || equal(symmetric_difference(u,inverse(u)),domain_relation)** -> member(ordered_pair(identity_relation,identity_relation),symmetrization_of(u))*.
% 299.99/300.65  18209[8:Res:15426.1,3617.0] || subclass(domain_relation,symmetric_difference(u,v)) -> member(ordered_pair(identity_relation,identity_relation),union(u,v))*.
% 299.99/300.65  83617[8:SpL:163.0,83166.0] || equal(symmetric_difference(u,v),domain_relation) -> member(ordered_pair(identity_relation,identity_relation),union(u,v))*.
% 299.99/300.65  82284[8:Res:81336.1,14679.1] || subclass(domain_relation,complement(complement(inverse(subset_relation))))* member(ordered_pair(identity_relation,identity_relation),subset_relation) -> .
% 299.99/300.65  15569[8:Res:15426.1,5.0] || subclass(domain_relation,u)* subclass(u,v)* -> member(ordered_pair(identity_relation,identity_relation),v)*.
% 299.99/300.65  82274[8:Res:81336.1,26.0] || subclass(domain_relation,complement(complement(intersection(u,v))))* -> member(ordered_pair(identity_relation,identity_relation),v).
% 299.99/300.65  15645[8:Res:15628.1,5.0] || equal(rest_relation,domain_relation) subclass(rest_relation,u) -> member(ordered_pair(identity_relation,identity_relation),u)*.
% 299.99/300.65  82265[8:Res:81336.1,28.1] || subclass(domain_relation,complement(complement(complement(u))))* member(ordered_pair(identity_relation,identity_relation),u) -> .
% 299.99/300.65  82275[8:Res:81336.1,25.0] || subclass(domain_relation,complement(complement(intersection(u,v))))* -> member(ordered_pair(identity_relation,identity_relation),u).
% 299.99/300.65  189789[8:SpL:160491.0,134026.0] || equal(complement(union(u,identity_relation)),ordinal_numbers) well_ordering(ordinal_numbers,symmetric_difference(ordinal_numbers,u))* -> .
% 299.99/300.65  189807[8:SpL:160491.0,176788.0] || equal(symmetric_difference(ordinal_numbers,union(u,identity_relation)),ordinal_numbers)** -> member(omega,symmetric_difference(ordinal_numbers,u)).
% 299.99/300.65  190536[18:Res:190442.1,9876.0] || equal(u,symmetrization_of(identity_relation)) subclass(u,v)* well_ordering(ordinal_numbers,v)* -> .
% 299.99/300.65  190541[18:Res:190442.1,18794.1] || equal(intersection(u,v),symmetrization_of(identity_relation)) member(identity_relation,symmetric_difference(u,v))* -> .
% 299.99/300.65  190560[18:Res:190442.1,897.0] || equal(restrict(u,v,w),symmetrization_of(identity_relation))** -> member(identity_relation,cross_product(v,w))*.
% 299.99/300.65  190645[18:Res:190593.1,9876.0] || equal(u,inverse(identity_relation)) subclass(u,v)* well_ordering(ordinal_numbers,v)* -> .
% 299.99/300.65  190650[18:Res:190593.1,18794.1] || equal(intersection(u,v),inverse(identity_relation)) member(identity_relation,symmetric_difference(u,v))* -> .
% 299.99/300.65  190669[18:Res:190593.1,897.0] || equal(restrict(u,v,w),inverse(identity_relation))** -> member(identity_relation,cross_product(v,w))*.
% 299.99/300.65  191934[18:Res:190515.1,66086.1] || subclass(ordinal_numbers,complement(compose(element_relation,ordinal_numbers)))* member(regular(symmetrization_of(identity_relation)),element_relation) -> .
% 299.99/300.65  191940[18:Res:190515.1,5.0] || subclass(ordinal_numbers,u)* subclass(u,v)* -> member(regular(symmetrization_of(identity_relation)),v)*.
% 299.99/300.65  191945[18:Res:190515.1,3617.0] || subclass(ordinal_numbers,symmetric_difference(u,v)) -> member(regular(symmetrization_of(identity_relation)),union(u,v))*.
% 299.99/300.65  191946[18:Res:190515.1,19559.0] || subclass(ordinal_numbers,symmetric_difference(u,singleton(u)))* -> member(regular(symmetrization_of(identity_relation)),successor(u))*.
% 299.99/300.65  191947[18:Res:190515.1,19676.0] || subclass(ordinal_numbers,symmetric_difference(u,inverse(u)))* -> member(regular(symmetrization_of(identity_relation)),symmetrization_of(u))*.
% 299.99/300.65  192606[8:Rew:140603.0,192544.1,66036.0,192544.1] ||  -> function(u) equal(symmetric_difference(recursion_equation_functions(v),singleton(u)),union(recursion_equation_functions(v),singleton(u)))**.
% 299.99/300.65  192799[8:Rew:140603.0,192738.1,66036.0,192738.1] ||  -> function(u) equal(symmetric_difference(singleton(u),recursion_equation_functions(v)),union(singleton(u),recursion_equation_functions(v)))**.
% 299.99/300.65  193180[7:Rew:193044.1,193150.2] || member(not_subclass_element(u,identity_relation),singleton(v))* -> member(v,u) subclass(u,identity_relation).
% 299.99/300.65  193203[8:Res:193179.0,5.0] || subclass(inverse(singleton(u)),v)* -> asymmetric(singleton(u),w)* member(u,v).
% 299.99/300.65  193211[8:Res:193179.0,8843.1] || subclass(ordinal_numbers,complement(inverse(singleton(singleton(u)))))* -> asymmetric(singleton(singleton(u)),v)*.
% 299.99/300.65  193569[8:SpL:68757.0,176785.0] || equal(intersection(symmetrization_of(identity_relation),ordinal_numbers),ordinal_numbers) member(omega,complement(inverse(identity_relation)))* -> .
% 299.99/300.65  193621[8:SpR:140603.0,15320.1] || asymmetric(ordinal_numbers,singleton(u)) -> equal(segment(inverse(ordinal_numbers),singleton(u),u),identity_relation)**.
% 299.99/300.65  39265[5:Res:8801.1,8841.1] || member(ordered_pair(u,v),cross_product(ordinal_numbers,ordinal_numbers))* subclass(ordinal_numbers,complement(composition_function)) -> .
% 299.99/300.65  130881[5:Res:51313.1,9876.0] || member(singleton(u),subset_relation)* subclass(u,v)* well_ordering(ordinal_numbers,v)* -> .
% 299.99/300.65  130862[5:Res:8705.1,9876.0] || member(u,ordinal_numbers) subclass(singleton(u),v)* well_ordering(ordinal_numbers,v) -> .
% 299.99/300.65  133503[5:Res:133488.1,5.0] || well_ordering(u,rest_relation) subclass(rest_relation,v) -> member(least(u,rest_relation),v)*.
% 299.99/300.65  133524[5:Res:133502.1,5.0] || well_ordering(u,rest_relation) subclass(ordinal_numbers,v) -> member(least(u,rest_relation),v)*.
% 299.99/300.65  19688[5:Res:19525.1,5.0] || well_ordering(u,ordinal_numbers) subclass(ordinal_numbers,v) -> member(least(u,ordinal_numbers),v)*.
% 299.99/300.65  133496[5:Res:133486.1,5.0] || well_ordering(u,ordinal_numbers) subclass(rest_relation,v) -> member(least(u,rest_relation),v)*.
% 299.99/300.65  133510[5:Res:133495.1,5.0] || well_ordering(u,ordinal_numbers) subclass(ordinal_numbers,v) -> member(least(u,rest_relation),v)*.
% 299.99/300.65  167334[8:Res:13237.2,162901.0] || well_ordering(u,ordinal_numbers) equal(least(u,subset_relation),identity_relation)** -> equal(subset_relation,identity_relation).
% 299.99/300.65  167335[8:Res:13237.2,162888.0] || well_ordering(u,ordinal_numbers) subclass(least(u,subset_relation),identity_relation)* -> equal(subset_relation,identity_relation).
% 299.99/300.65  131178[5:Res:39607.2,152.0] inductive(recursion_equation_functions(u)) || well_ordering(v,ordinal_numbers) -> function(least(v,recursion_equation_functions(u)))*.
% 299.99/300.65  148929[8:Res:148858.1,130944.0] || subclass(singleton(singleton(singleton(u))),inverse(subset_relation))* well_ordering(ordinal_numbers,complement(subset_relation)) -> .
% 299.99/300.65  193833[19:Res:138.1,193816.0] || member(cross_product(ordinal_numbers,cross_product(ordinal_numbers,ordinal_numbers)),ordinal_numbers)* -> member(least(element_relation,composition_function),composition_function).
% 299.99/300.65  165858[8:Res:163152.1,5.0] || subclass(ordinal_numbers,symmetrization_of(identity_relation)) subclass(inverse(identity_relation),u)* -> member(omega,u).
% 299.99/300.65  194504[8:Res:163112.0,133836.0] || well_ordering(ordinal_numbers,complement(inverse(identity_relation))) -> subclass(singleton(singleton(singleton(u))),symmetrization_of(identity_relation))*.
% 299.99/300.65  194738[8:SpR:66293.0,154945.0] ||  -> equal(intersection(union(u,identity_relation),symmetric_difference(complement(u),ordinal_numbers)),symmetric_difference(complement(u),ordinal_numbers))**.
% 299.99/300.65  195065[14:SpL:160491.0,165360.0] || equal(complement(union(u,identity_relation)),singleton(identity_relation)) -> member(identity_relation,symmetric_difference(ordinal_numbers,u))*.
% 299.99/300.65  195105[18:Res:193927.1,165357.1] || equal(inverse(subset_relation),inverse(identity_relation)) equal(complement(complement(subset_relation)),singleton(identity_relation))** -> .
% 299.99/300.65  195106[18:Res:193924.1,165357.1] || equal(symmetrization_of(identity_relation),inverse(subset_relation)) equal(complement(complement(subset_relation)),singleton(identity_relation))** -> .
% 299.99/300.65  195107[14:Res:193906.1,165357.1] || equal(inverse(subset_relation),singleton(identity_relation)) equal(complement(complement(subset_relation)),singleton(identity_relation))** -> .
% 299.99/300.65  195577[16:Rew:195224.0,195213.1] || well_ordering(ordinal_numbers,complement(singleton(identity_relation))) -> subclass(singleton(singleton(singleton(u))),singleton(identity_relation))*.
% 299.99/300.65  195308[16:Rew:195224.0,193278.0] || equal(intersection(singleton(identity_relation),ordinal_numbers),ordinal_numbers) member(omega,complement(singleton(identity_relation)))* -> .
% 299.99/300.65  195456[16:Rew:195224.0,163181.0] ||  -> subclass(symmetric_difference(singleton(identity_relation),complement(singleton(complement(singleton(identity_relation))))),successor(complement(singleton(identity_relation))))*.
% 299.99/300.65  195457[16:Rew:195224.0,163182.0] ||  -> subclass(symmetric_difference(singleton(identity_relation),complement(inverse(complement(singleton(identity_relation))))),symmetrization_of(complement(singleton(identity_relation))))*.
% 299.99/300.65  196078[18:Res:190510.1,9876.0] || subclass(inverse(identity_relation),u)* subclass(u,v)* well_ordering(ordinal_numbers,v)* -> .
% 299.99/300.65  196101[18:Res:190510.1,56411.0] || subclass(inverse(identity_relation),rest_of(regular(symmetrization_of(identity_relation))))* subclass(ordinal_numbers,complement(element_relation)) -> .
% 299.99/300.65  196103[18:Res:190510.1,898.0] || subclass(inverse(identity_relation),restrict(u,v,w))* -> member(regular(symmetrization_of(identity_relation)),u).
% 299.99/300.65  196106[18:Res:190510.1,161.0] || subclass(inverse(identity_relation),omega) -> equal(integer_of(regular(symmetrization_of(identity_relation))),regular(symmetrization_of(identity_relation)))**.
% 299.99/300.65  196107[18:Res:190510.1,8788.0] || subclass(inverse(identity_relation),recursion_equation_functions(u))* -> subclass(regular(symmetrization_of(identity_relation)),cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.65  196158[18:Res:193927.1,190532.1] || equal(inverse(subset_relation),inverse(identity_relation)) equal(complement(complement(subset_relation)),symmetrization_of(identity_relation))** -> .
% 299.99/300.65  196159[18:Res:193924.1,190532.1] || equal(symmetrization_of(identity_relation),inverse(subset_relation)) equal(complement(complement(subset_relation)),symmetrization_of(identity_relation))** -> .
% 299.99/300.65  196160[18:Res:193906.1,190532.1] || equal(inverse(subset_relation),singleton(identity_relation)) equal(complement(complement(subset_relation)),symmetrization_of(identity_relation))** -> .
% 299.99/300.65  196204[18:SpL:160491.0,190535.0] || equal(complement(union(u,identity_relation)),symmetrization_of(identity_relation)) -> member(identity_relation,symmetric_difference(ordinal_numbers,u))*.
% 299.99/300.65  196248[18:Res:193927.1,190641.1] || equal(inverse(subset_relation),inverse(identity_relation)) equal(complement(complement(subset_relation)),inverse(identity_relation))** -> .
% 299.99/300.65  196249[18:Res:193924.1,190641.1] || equal(symmetrization_of(identity_relation),inverse(subset_relation)) equal(complement(complement(subset_relation)),inverse(identity_relation))** -> .
% 299.99/300.65  196250[18:Res:193906.1,190641.1] || equal(inverse(subset_relation),singleton(identity_relation)) equal(complement(complement(subset_relation)),inverse(identity_relation))** -> .
% 299.99/300.65  196297[18:SpL:160491.0,190644.0] || equal(complement(union(u,identity_relation)),inverse(identity_relation)) -> member(identity_relation,symmetric_difference(ordinal_numbers,u))*.
% 299.99/300.65  196354[21:MRR:196349.1,94705.1] || subclass(ordinal_numbers,complement(complement(cross_product(ordinal_numbers,ordinal_numbers))))* member(u,cantor(v))* -> .
% 299.99/300.65  197602[21:Res:13237.2,197211.0] || well_ordering(u,ordinal_numbers) -> equal(subset_relation,identity_relation) equal(cantor(least(u,subset_relation)),identity_relation)**.
% 299.99/300.65  197982[21:SpR:15528.0,196555.1] || member(not_subclass_element(identity_relation,identity_relation),subset_relation) -> equal(cantor(range__dfg(identity_relation,u,v)),identity_relation)**.
% 299.99/300.65  198466[21:Res:41203.1,197870.1] || member(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers)* equal(rest_of(least(element_relation,domain_relation)),rest_relation) -> .
% 299.99/300.65  198489[21:Res:80082.1,197870.1] || member(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers)* equal(rest_of(least(element_relation,rest_relation)),rest_relation) -> .
% 299.99/300.65  198490[21:Res:80198.1,197870.1] || member(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers)* equal(rest_of(least(element_relation,element_relation)),rest_relation) -> .
% 299.99/300.65  198286[21:Rew:66036.0,198169.1] ||  -> equal(range_of(u),identity_relation) subclass(symmetric_difference(complement(inverse(u)),ordinal_numbers),successor(inverse(u)))*.
% 299.99/300.65  198290[21:Rew:140613.0,198170.1,66036.0,198170.1] ||  -> equal(range_of(u),identity_relation) subclass(complement(successor(inverse(u))),symmetric_difference(ordinal_numbers,inverse(u)))*.
% 299.99/300.65  160899[8:Rew:160491.0,160898.1] inductive(symmetric_difference(cantor(inverse(u)),identity_relation)) ||  -> member(identity_relation,union(range_of(u),identity_relation))*.
% 299.99/300.65  125786[8:SpL:116239.0,116738.1] || subclass(domain_relation,inverse(subset_relation)) member(ordered_pair(inverse(u),range_of(u)),subset_relation)* -> .
% 299.99/300.65  56485[5:Rew:43.0,56453.0] || member(inverse(u),range_of(u)) -> member(ordered_pair(inverse(u),range_of(u)),element_relation)*.
% 299.99/300.65  195023[15:SpL:59.0,165530.0] || subclass(ordinal_numbers,complement(power_class(u))) -> member(range_of(identity_relation),image(element_relation,complement(u)))*.
% 299.99/300.65  195021[15:SpL:160491.0,165530.0] || subclass(ordinal_numbers,complement(union(u,identity_relation))) -> member(range_of(identity_relation),symmetric_difference(ordinal_numbers,u))*.
% 299.99/300.65  194961[15:Res:193179.0,165527.1] || subclass(ordinal_numbers,complement(inverse(singleton(range_of(identity_relation)))))* -> asymmetric(singleton(range_of(identity_relation)),u)*.
% 299.99/300.65  165536[15:Res:165526.1,18794.1] || subclass(ordinal_numbers,intersection(u,v)) member(range_of(identity_relation),symmetric_difference(u,v))* -> .
% 299.99/300.65  165554[15:Res:165526.1,897.0] || subclass(ordinal_numbers,restrict(u,v,w))* -> member(range_of(identity_relation),cross_product(v,w))*.
% 299.99/300.65  165556[15:Res:165526.1,288.0] || subclass(ordinal_numbers,image(element_relation,complement(u)))* member(range_of(identity_relation),power_class(u)) -> .
% 299.99/300.65  167246[15:Res:165526.1,14681.0] || subclass(ordinal_numbers,regular(u)) member(range_of(identity_relation),u)* -> equal(u,identity_relation).
% 299.99/300.65  191863[15:Res:165442.1,19676.0] || subclass(ordinal_numbers,symmetric_difference(u,inverse(u)))* -> member(sum_class(range_of(identity_relation)),symmetrization_of(u))*.
% 299.99/300.65  191862[15:Res:165442.1,19559.0] || subclass(ordinal_numbers,symmetric_difference(u,singleton(u)))* -> member(sum_class(range_of(identity_relation)),successor(u))*.
% 299.99/300.65  191861[15:Res:165442.1,3617.0] || subclass(ordinal_numbers,symmetric_difference(u,v)) -> member(sum_class(range_of(identity_relation)),union(u,v))*.
% 299.99/300.65  191850[15:Res:165442.1,66086.1] || subclass(ordinal_numbers,complement(compose(element_relation,ordinal_numbers)))* member(sum_class(range_of(identity_relation)),element_relation) -> .
% 299.99/300.65  191856[15:Res:165442.1,5.0] || subclass(ordinal_numbers,u)* subclass(u,v)* -> member(sum_class(range_of(identity_relation)),v)*.
% 299.99/300.65  190677[18:Res:190593.1,288.0] || equal(image(element_relation,complement(u)),inverse(identity_relation))** member(identity_relation,power_class(u)) -> .
% 299.99/300.65  190568[18:Res:190442.1,288.0] || equal(image(element_relation,complement(u)),symmetrization_of(identity_relation))** member(identity_relation,power_class(u)) -> .
% 299.99/300.65  165386[14:Res:165168.1,288.0] || equal(image(element_relation,complement(u)),singleton(identity_relation))** member(identity_relation,power_class(u)) -> .
% 299.99/300.65  195067[14:SpL:59.0,165360.0] || equal(complement(power_class(u)),singleton(identity_relation)) -> member(identity_relation,image(element_relation,complement(u)))*.
% 299.99/300.65  196206[18:SpL:59.0,190535.0] || equal(complement(power_class(u)),symmetrization_of(identity_relation)) -> member(identity_relation,image(element_relation,complement(u)))*.
% 299.99/300.65  196299[18:SpL:59.0,190644.0] || equal(complement(power_class(u)),inverse(identity_relation)) -> member(identity_relation,image(element_relation,complement(u)))*.
% 299.99/300.65  19457[0:SpR:487.0,18950.0] ||  -> subclass(symmetric_difference(image(element_relation,complement(u)),v),complement(intersection(power_class(u),complement(v))))*.
% 299.99/300.65  9628[5:SpL:59.0,9496.0] || subclass(ordinal_numbers,complement(power_class(u))) -> member(singleton(v),image(element_relation,complement(u)))*.
% 299.99/300.65  186585[8:SpL:59.0,176788.0] || equal(symmetric_difference(ordinal_numbers,power_class(u)),ordinal_numbers) -> member(omega,image(element_relation,complement(u)))*.
% 299.99/300.65  134032[5:MRR:134012.0,8655.0] || well_ordering(ordinal_numbers,image(element_relation,complement(u)))* -> member(singleton(singleton(v)),power_class(u))*.
% 299.99/300.65  176985[5:SpL:59.0,134026.0] || equal(complement(power_class(u)),ordinal_numbers) well_ordering(ordinal_numbers,image(element_relation,complement(u)))* -> .
% 299.99/300.65  18443[5:Res:8645.1,288.0] || subclass(ordinal_numbers,image(element_relation,complement(u)))* member(singleton(v),power_class(u))* -> .
% 299.99/300.65  165657[5:Res:143198.1,288.0] || equal(image(element_relation,complement(u)),ordinal_numbers) member(singleton(v),power_class(u))* -> .
% 299.99/300.65  19384[0:SpR:485.0,18950.0] ||  -> subclass(symmetric_difference(u,image(element_relation,complement(v))),complement(intersection(complement(u),power_class(v))))*.
% 299.99/300.65  79563[5:Rew:59.0,79535.1] ||  -> member(not_subclass_element(u,power_class(v)),image(element_relation,complement(v)))* subclass(u,power_class(v)).
% 299.99/300.65  159464[5:Obv:159437.0] ||  -> member(u,power_class(v)) subclass(intersection(singleton(u),w),image(element_relation,complement(v)))*.
% 299.99/300.65  159465[5:Obv:159436.0] ||  -> member(u,power_class(v)) subclass(intersection(w,singleton(u)),image(element_relation,complement(v)))*.
% 299.99/300.65  193479[8:SpR:162038.0,66340.0] ||  -> subclass(symmetric_difference(power_class(complement(inverse(identity_relation))),ordinal_numbers),union(image(element_relation,symmetrization_of(identity_relation)),identity_relation))*.
% 299.99/300.65  193477[8:SpR:162038.0,140613.0] ||  -> equal(intersection(power_class(complement(inverse(identity_relation))),ordinal_numbers),symmetric_difference(ordinal_numbers,image(element_relation,symmetrization_of(identity_relation))))**.
% 299.99/300.65  193455[8:Res:163093.0,13082.1] inductive(complement(power_class(complement(inverse(identity_relation))))) ||  -> member(identity_relation,image(element_relation,symmetrization_of(identity_relation)))*.
% 299.99/300.65  193531[14:SpL:162038.0,167597.0] || well_ordering(ordinal_numbers,power_class(complement(inverse(identity_relation))))* -> member(identity_relation,image(element_relation,symmetrization_of(identity_relation))).
% 299.99/300.65  163113[8:SpR:162584.0,79577.0] ||  -> member(u,image(element_relation,symmetrization_of(identity_relation))) subclass(singleton(u),power_class(complement(inverse(identity_relation))))*.
% 299.99/300.65  165179[14:SpR:189.0,165172.1] ||  -> member(identity_relation,image(element_relation,power_class(u))) member(identity_relation,power_class(image(element_relation,complement(u))))*.
% 299.99/300.65  163091[8:SpR:162584.0,130711.0] ||  -> subclass(complement(power_class(image(element_relation,symmetrization_of(identity_relation)))),image(element_relation,power_class(complement(inverse(identity_relation)))))*.
% 299.99/300.65  130712[5:SpR:481.0,130678.0] ||  -> subclass(complement(power_class(intersection(complement(u),complement(v)))),image(element_relation,union(u,v)))*.
% 299.99/300.65  194684[14:SpR:160491.0,165178.0] ||  -> member(identity_relation,image(element_relation,union(u,identity_relation)))* member(identity_relation,power_class(symmetric_difference(ordinal_numbers,u))).
% 299.99/300.65  196565[21:Res:8976.2,196372.0] function(u) || member(v,ordinal_numbers) -> equal(cantor(image(u,v)),identity_relation)**.
% 299.99/300.65  123288[8:Rew:8649.0,123284.0] || equal(image(u,v),domain_relation) subclass(domain_relation,complement(image(u,v)))* -> .
% 299.99/300.65  197885[21:SpR:72.0,196551.1] || member(image(u,singleton(v)),ordinal_numbers)* -> equal(cantor(apply(u,v)),identity_relation).
% 299.99/300.65  195348[16:Rew:195224.0,193315.0] ||  -> subclass(symmetric_difference(power_class(complement(singleton(identity_relation))),ordinal_numbers),union(image(element_relation,singleton(identity_relation)),identity_relation))*.
% 299.99/300.65  195320[16:Rew:195224.0,163200.0] ||  -> member(u,image(element_relation,singleton(identity_relation))) subclass(singleton(u),power_class(complement(singleton(identity_relation))))*.
% 299.99/300.65  195310[16:Rew:195224.0,163178.0] ||  -> subclass(complement(power_class(image(element_relation,singleton(identity_relation)))),image(element_relation,power_class(complement(singleton(identity_relation)))))*.
% 299.99/300.65  195342[16:Rew:195224.0,193397.1] inductive(complement(power_class(complement(singleton(identity_relation))))) ||  -> member(identity_relation,image(element_relation,singleton(identity_relation)))*.
% 299.99/300.65  195346[16:Rew:195224.0,193367.1] || well_ordering(ordinal_numbers,power_class(complement(singleton(identity_relation))))* -> member(identity_relation,image(element_relation,singleton(identity_relation))).
% 299.99/300.65  195336[16:Rew:195224.0,193313.0] ||  -> equal(intersection(power_class(complement(singleton(identity_relation))),ordinal_numbers),symmetric_difference(ordinal_numbers,image(element_relation,singleton(identity_relation))))**.
% 299.99/300.65  193536[8:SpL:162038.0,166753.1] inductive(image(element_relation,symmetrization_of(identity_relation))) || equal(power_class(complement(inverse(identity_relation))),omega)** -> .
% 299.99/300.65  193504[8:SpL:162038.0,9922.1] inductive(image(element_relation,symmetrization_of(identity_relation))) || equal(power_class(complement(inverse(identity_relation))),ordinal_numbers)** -> .
% 299.99/300.65  193372[8:SpL:162037.0,166753.1] inductive(image(element_relation,successor(identity_relation))) || equal(power_class(complement(singleton(identity_relation))),omega)** -> .
% 299.99/300.65  195978[16:SpL:195257.0,166753.1] inductive(image(element_relation,singleton(identity_relation))) || equal(power_class(complement(singleton(identity_relation))),omega)** -> .
% 299.99/300.65  193340[8:SpL:162037.0,9922.1] inductive(image(element_relation,successor(identity_relation))) || equal(power_class(complement(singleton(identity_relation))),ordinal_numbers)** -> .
% 299.99/300.65  195944[16:SpL:195257.0,9922.1] inductive(image(element_relation,singleton(identity_relation))) || equal(power_class(complement(singleton(identity_relation))),ordinal_numbers)** -> .
% 299.99/300.65  123319[8:Rew:72.0,123311.0] || equal(apply(u,v),domain_relation) subclass(domain_relation,complement(apply(u,v)))* -> .
% 299.99/300.65  165047[8:Res:13069.2,162901.0] || member(subset_relation,ordinal_numbers) equal(apply(choice,subset_relation),identity_relation)** -> equal(subset_relation,identity_relation).
% 299.99/300.65  164975[8:Res:13069.2,162888.0] || member(subset_relation,ordinal_numbers) subclass(apply(choice,subset_relation),identity_relation)* -> equal(subset_relation,identity_relation).
% 299.99/300.65  194668[18:MRR:194667.2,190496.0] || member(symmetrization_of(identity_relation),ordinal_numbers) -> subclass(singleton(apply(choice,symmetrization_of(identity_relation))),symmetrization_of(identity_relation))*.
% 299.99/300.65  196730[21:MRR:196577.1,8638.0] || member(u,ordinal_numbers) -> equal(u,identity_relation) equal(cantor(apply(choice,u)),identity_relation)**.
% 299.99/300.65  191373[18:Res:190442.1,14681.0] || equal(regular(u),symmetrization_of(identity_relation)) member(identity_relation,u)* -> equal(u,identity_relation).
% 299.99/300.65  191372[18:Res:190593.1,14681.0] || equal(regular(u),inverse(identity_relation)) member(identity_relation,u)* -> equal(u,identity_relation).
% 299.99/300.65  167240[14:Res:165168.1,14681.0] || equal(regular(u),singleton(identity_relation)) member(identity_relation,u)* -> equal(u,identity_relation).
% 299.99/300.65  190664[18:Res:190593.1,12.0] || equal(unordered_pair(u,v),inverse(identity_relation))** -> equal(identity_relation,v) equal(identity_relation,u).
% 299.99/300.65  190555[18:Res:190442.1,12.0] || equal(unordered_pair(u,v),symmetrization_of(identity_relation))** -> equal(identity_relation,v) equal(identity_relation,u).
% 299.99/300.65  165379[14:Res:165168.1,12.0] || equal(unordered_pair(u,v),singleton(identity_relation))** -> equal(identity_relation,v) equal(identity_relation,u).
% 299.99/300.65  204051[18:Res:192333.1,190641.1] || equal(symmetric_difference(ordinal_numbers,u),ordinal_numbers)** equal(complement(complement(u)),inverse(identity_relation)) -> .
% 299.99/300.65  204052[18:Res:192333.1,190532.1] || equal(symmetric_difference(ordinal_numbers,u),ordinal_numbers)** equal(complement(complement(u)),symmetrization_of(identity_relation)) -> .
% 299.99/300.65  204053[14:Res:192333.1,165357.1] || equal(symmetric_difference(ordinal_numbers,u),ordinal_numbers)** equal(complement(complement(u)),singleton(identity_relation)) -> .
% 299.99/300.65  204141[8:Res:204134.1,5.0] || member(u,inverse(identity_relation))* subclass(symmetrization_of(identity_relation),v)* -> member(u,v)*.
% 299.99/300.65  204146[8:Res:204134.1,13105.0] || member(regular(complement(symmetrization_of(identity_relation))),inverse(identity_relation))* -> equal(complement(symmetrization_of(identity_relation)),identity_relation).
% 299.99/300.65  204170[18:Res:194549.1,9876.0] || subclass(symmetrization_of(identity_relation),u)* subclass(u,v)* well_ordering(ordinal_numbers,v)* -> .
% 299.99/300.65  204196[18:Res:194549.1,56411.0] || subclass(symmetrization_of(identity_relation),rest_of(regular(symmetrization_of(identity_relation))))* subclass(ordinal_numbers,complement(element_relation)) -> .
% 299.99/300.65  204198[18:Res:194549.1,898.0] || subclass(symmetrization_of(identity_relation),restrict(u,v,w))* -> member(regular(symmetrization_of(identity_relation)),u).
% 299.99/300.65  204201[18:Res:194549.1,161.0] || subclass(symmetrization_of(identity_relation),omega) -> equal(integer_of(regular(symmetrization_of(identity_relation))),regular(symmetrization_of(identity_relation)))**.
% 299.99/300.65  204202[18:Res:194549.1,8788.0] || subclass(symmetrization_of(identity_relation),recursion_equation_functions(u))* -> subclass(regular(symmetrization_of(identity_relation)),cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.65  204331[14:SpL:160491.0,195109.1] || equal(symmetric_difference(ordinal_numbers,u),ordinal_numbers)** equal(union(u,identity_relation),singleton(identity_relation)) -> .
% 299.99/300.65  204334[14:SpL:59.0,195109.1] || equal(image(element_relation,complement(u)),ordinal_numbers)** equal(power_class(u),singleton(identity_relation)) -> .
% 299.99/300.65  204451[18:SpL:160491.0,196161.1] || equal(symmetric_difference(ordinal_numbers,u),ordinal_numbers)** equal(union(u,identity_relation),symmetrization_of(identity_relation)) -> .
% 299.99/300.65  204452[18:SpL:59.0,196161.1] || equal(image(element_relation,complement(u)),ordinal_numbers)** equal(power_class(u),symmetrization_of(identity_relation)) -> .
% 299.99/300.65  204470[18:SpL:160491.0,196251.1] || equal(symmetric_difference(ordinal_numbers,u),ordinal_numbers)** equal(union(u,identity_relation),inverse(identity_relation)) -> .
% 299.99/300.65  204473[18:SpL:59.0,196251.1] || equal(image(element_relation,complement(u)),ordinal_numbers)** equal(power_class(u),inverse(identity_relation)) -> .
% 299.99/300.65  204660[21:Res:196904.1,898.0] || subclass(domain_relation,restrict(u,v,w))* -> member(singleton(singleton(singleton(identity_relation))),u)*.
% 299.99/300.65  204664[21:Res:196904.1,8788.0] || subclass(domain_relation,recursion_equation_functions(u))* -> subclass(singleton(singleton(singleton(identity_relation))),cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.65  205198[15:Res:195033.1,56411.0] || equal(complement(complement(rest_of(range_of(identity_relation)))),ordinal_numbers)** subclass(ordinal_numbers,complement(element_relation)) -> .
% 299.99/300.65  205200[15:Res:195033.1,898.0] || equal(complement(complement(restrict(u,v,w))),ordinal_numbers)** -> member(range_of(identity_relation),u).
% 299.99/300.65  205785[22:Res:205578.1,9876.0] || subclass(complement(u),v)* well_ordering(ordinal_numbers,v) -> member(singleton(identity_relation),u)*.
% 299.99/300.65  205789[22:Res:205578.1,5.0] || subclass(complement(u),v)* -> member(singleton(identity_relation),u)* member(singleton(identity_relation),v)*.
% 299.99/300.65  205987[8:SpL:144460.0,204039.0] || equal(symmetric_difference(complement(u),ordinal_numbers),ordinal_numbers) member(identity_relation,symmetric_difference(ordinal_numbers,u))* -> .
% 299.99/300.65  205996[8:SpL:160491.0,204042.0] || equal(symmetric_difference(ordinal_numbers,union(u,identity_relation)),ordinal_numbers)** -> member(identity_relation,symmetric_difference(ordinal_numbers,u)).
% 299.99/300.65  205999[8:SpL:59.0,204042.0] || equal(symmetric_difference(ordinal_numbers,power_class(u)),ordinal_numbers) -> member(identity_relation,image(element_relation,complement(u)))*.
% 299.99/300.65  206154[22:Res:205574.1,56411.0] || equal(rest_of(singleton(identity_relation)),singleton(singleton(identity_relation))) subclass(ordinal_numbers,complement(element_relation))* -> .
% 299.99/300.65  206156[22:Res:205574.1,898.0] || equal(restrict(u,v,w),singleton(singleton(identity_relation)))** -> member(singleton(identity_relation),u).
% 299.99/300.65  206310[7:Res:151910.0,13082.1] inductive(symmetric_difference(u,complement(complement(u)))) ||  -> member(identity_relation,complement(complement(complement(u))))*.
% 299.99/300.65  207269[14:SpL:163.0,165368.0] || equal(symmetric_difference(u,v),singleton(identity_relation)) -> member(identity_relation,complement(intersection(u,v)))*.
% 299.99/300.65  207275[14:SpL:155665.0,165368.0] || equal(symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers)),singleton(identity_relation))** -> member(identity_relation,complement(subset_relation)).
% 299.99/300.65  207276[14:SpL:155666.0,165368.0] || equal(symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation),singleton(identity_relation))** -> member(identity_relation,complement(subset_relation)).
% 299.99/300.65  207291[14:SpL:66293.0,165368.0] || equal(symmetric_difference(complement(u),ordinal_numbers),singleton(identity_relation)) -> member(identity_relation,union(u,identity_relation))*.
% 299.99/300.65  207359[18:SpL:163.0,190543.0] || equal(symmetric_difference(u,v),symmetrization_of(identity_relation)) -> member(identity_relation,complement(intersection(u,v)))*.
% 299.99/300.65  207365[18:SpL:155665.0,190543.0] || equal(symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers)),symmetrization_of(identity_relation))** -> member(identity_relation,complement(subset_relation)).
% 299.99/300.65  207366[18:SpL:155666.0,190543.0] || equal(symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation),symmetrization_of(identity_relation))** -> member(identity_relation,complement(subset_relation)).
% 299.99/300.65  207381[18:SpL:66293.0,190543.0] || equal(symmetric_difference(complement(u),ordinal_numbers),symmetrization_of(identity_relation)) -> member(identity_relation,union(u,identity_relation))*.
% 299.99/300.65  207478[18:SpL:163.0,190652.0] || equal(symmetric_difference(u,v),inverse(identity_relation)) -> member(identity_relation,complement(intersection(u,v)))*.
% 299.99/300.65  207484[18:SpL:155665.0,190652.0] || equal(symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers)),inverse(identity_relation))** -> member(identity_relation,complement(subset_relation)).
% 299.99/300.65  207485[18:SpL:155666.0,190652.0] || equal(symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation),inverse(identity_relation))** -> member(identity_relation,complement(subset_relation)).
% 299.99/300.65  207500[18:SpL:66293.0,190652.0] || equal(symmetric_difference(complement(u),ordinal_numbers),inverse(identity_relation)) -> member(identity_relation,union(u,identity_relation))*.
% 299.99/300.65  207537[8:Res:192400.1,13082.1] inductive(symmetric_difference(u,ordinal_numbers)) || member(u,ordinals_with_null_class_as_identity) -> member(identity_relation,complement(u))*.
% 299.99/300.65  207573[24:SpR:207558.1,17.0] operation(u) ||  -> equal(unordered_pair(identity_relation,unordered_pair(u,singleton(v))),ordered_pair(u,v))**.
% 299.99/300.65  208007[24:Rew:207947.1,197793.1] operation(regular(omega)) ||  -> equal(regular(identity_relation),identity_relation) equal(cross_product(identity_relation,identity_relation),identity_relation)**.
% 299.99/300.65  208195[8:MRR:208194.0,8658.0] || subclass(composition_function,u) well_ordering(v,u)* -> member(least(v,composition_function),composition_function)*.
% 299.99/300.65  208264[24:Rew:140613.0,208242.1,66036.0,208242.1] operation(u) ||  -> equal(complement(image(element_relation,successor(u))),power_class(symmetric_difference(ordinal_numbers,u)))**.
% 299.99/300.65  208425[21:Res:198162.1,190641.1] || equal(complement(ordered_pair(inverse(u),v)),inverse(identity_relation))** -> equal(range_of(u),identity_relation).
% 299.99/300.65  208426[21:Res:198162.1,190532.1] || equal(complement(ordered_pair(inverse(u),v)),symmetrization_of(identity_relation))** -> equal(range_of(u),identity_relation).
% 299.99/300.65  208427[21:Res:198162.1,165357.1] || equal(complement(ordered_pair(inverse(u),v)),singleton(identity_relation))** -> equal(range_of(u),identity_relation).
% 299.99/300.65  208495[7:SpL:13260.1,9529.0] || equal(complement(regular(cross_product(u,v))),ordinal_numbers)** -> equal(cross_product(u,v),identity_relation).
% 299.99/300.65  208496[7:SpL:13260.1,9486.0] || subclass(ordinal_numbers,complement(regular(cross_product(u,v))))* -> equal(cross_product(u,v),identity_relation).
% 299.99/300.65  208555[15:SpL:163.0,165538.0] || subclass(ordinal_numbers,symmetric_difference(u,v)) -> member(range_of(identity_relation),complement(intersection(u,v)))*.
% 299.99/300.65  208561[15:SpL:155665.0,165538.0] || subclass(ordinal_numbers,symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers)))* -> member(range_of(identity_relation),complement(subset_relation)).
% 299.99/300.65  208562[15:SpL:155666.0,165538.0] || subclass(ordinal_numbers,symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation))* -> member(range_of(identity_relation),complement(subset_relation)).
% 299.99/300.65  208577[15:SpL:66293.0,165538.0] || subclass(ordinal_numbers,symmetric_difference(complement(u),ordinal_numbers)) -> member(range_of(identity_relation),union(u,identity_relation))*.
% 299.99/300.65  208610[21:SpL:159.0,198470.1] function(recursion(u,successor_relation,union_of_range_map)) || equal(rest_of(ordinal_add(u,v)),rest_relation)** -> .
% 299.99/300.65  209012[25:Rew:209011.1,207890.2] operation(u) || member(singleton(singleton(identity_relation)),compose_class(v))* -> equal(ordinal_numbers,u)*.
% 299.99/300.65  209014[25:Rew:208820.0,208882.0] || asymmetric(u,identity_relation) -> equal(segment(intersection(u,inverse(u)),identity_relation,ordinal_numbers),identity_relation)**.
% 299.99/300.65  209015[25:Rew:208820.0,208886.0] || member(image(u,identity_relation),ordinal_numbers) -> subclass(apply(u,ordinal_numbers),image(u,identity_relation))*.
% 299.99/300.65  209016[25:Rew:208820.0,208901.1] || member(singleton(singleton(identity_relation)),rest_of(u))* -> equal(restrict(u,identity_relation,ordinal_numbers),ordinal_numbers).
% 299.99/300.65  209017[25:Rew:209016.1,207893.2] operation(u) || member(singleton(singleton(identity_relation)),rest_of(v))* -> equal(ordinal_numbers,u)*.
% 299.99/300.65  209334[25:SpL:208840.0,100.0] || member(ordered_pair(u,singleton(singleton(identity_relation))),composition_function)* -> equal(compose(u,identity_relation),ordinal_numbers).
% 299.99/300.65  209344[25:MRR:209343.0,13126.0] || member(singleton(singleton(identity_relation)),cross_product(ordinal_numbers,ordinal_numbers))* -> member(singleton(singleton(identity_relation)),element_relation).
% 299.99/300.65  209433[25:SpL:208885.0,198460.1] || member(image(u,identity_relation),ordinal_numbers)* equal(rest_of(apply(u,ordinal_numbers)),rest_relation) -> .
% 299.99/300.65  209434[25:Rew:208885.0,209413.0] || equal(apply(u,ordinal_numbers),identity_relation) -> subclass(apply(u,ordinal_numbers),image(u,identity_relation))*.
% 299.99/300.65  209807[8:Res:206259.0,13082.1] inductive(symmetric_difference(complement(u),symmetric_difference(ordinal_numbers,u))) ||  -> member(identity_relation,union(u,identity_relation))*.
% 299.99/300.65  209822[8:Rew:69395.0,209789.0] ||  -> subclass(symmetric_difference(complement(intersection(u,ordinal_numbers)),symmetric_difference(u,ordinal_numbers)),complement(symmetric_difference(u,ordinal_numbers)))*.
% 299.99/300.65  209873[24:Res:207863.1,13082.1] operation(u) inductive(symmetric_difference(complement(u),ordinal_numbers)) ||  -> member(identity_relation,successor(u))*.
% 299.99/300.65  209892[24:Res:207866.1,13082.1] operation(u) inductive(complement(successor(u))) ||  -> member(identity_relation,symmetric_difference(ordinal_numbers,u))*.
% 299.99/300.65  209902[15:SpL:32.0,208474.0] || equal(restrict(u,v,w),ordinal_numbers)** -> member(range_of(identity_relation),cross_product(v,w))*.
% 299.99/300.65  209956[15:Res:209921.1,18794.1] || equal(intersection(u,v),ordinal_numbers) member(range_of(identity_relation),symmetric_difference(u,v))* -> .
% 299.99/300.65  209988[15:Res:209921.1,14681.0] || equal(regular(u),ordinal_numbers) member(range_of(identity_relation),u)* -> equal(u,identity_relation).
% 299.99/300.65  209990[15:Res:209921.1,288.0] || equal(image(element_relation,complement(u)),ordinal_numbers) member(range_of(identity_relation),power_class(u))* -> .
% 299.99/300.65  210071[15:SpL:163.0,208593.0] || equal(symmetric_difference(u,v),ordinal_numbers) -> member(range_of(identity_relation),complement(intersection(u,v)))*.
% 299.99/300.65  210077[15:SpL:155665.0,208593.0] || equal(symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers)),ordinal_numbers)** -> member(range_of(identity_relation),complement(subset_relation)).
% 299.99/300.65  210078[15:SpL:155666.0,208593.0] || equal(symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation),ordinal_numbers)** -> member(range_of(identity_relation),complement(subset_relation)).
% 299.99/300.65  210094[15:SpL:66293.0,208593.0] || equal(symmetric_difference(complement(u),ordinal_numbers),ordinal_numbers) -> member(range_of(identity_relation),union(u,identity_relation))*.
% 299.99/300.65  210134[8:Res:208722.1,13082.1] inductive(symmetric_difference(u,ordinal_numbers)) ||  -> equal(singleton(u),identity_relation) member(identity_relation,complement(u))*.
% 299.99/300.65  210297[8:Res:140864.1,133836.0] || member(singleton(singleton(u)),complement(v))* well_ordering(ordinal_numbers,symmetric_difference(ordinal_numbers,v)) -> .
% 299.99/300.65  210328[8:Rew:160491.0,210285.1] || member(unordered_pair(u,v),complement(w))* subclass(ordinal_numbers,union(w,identity_relation)) -> .
% 299.99/300.65  210329[8:Rew:160491.0,210294.1] || member(least(element_relation,omega),complement(u))* subclass(ordinal_numbers,union(u,identity_relation)) -> .
% 299.99/300.65  210330[8:Rew:160491.0,210295.1] || member(least(element_relation,omega),complement(u))* subclass(omega,union(u,identity_relation)) -> .
% 299.99/300.65  210331[8:Rew:160491.0,210303.1] || member(ordered_pair(u,v),complement(w))* subclass(ordinal_numbers,union(w,identity_relation)) -> .
% 299.99/300.65  210333[8:Rew:160491.0,210286.1,160491.0,210286.0] || member(regular(union(u,identity_relation)),complement(u))* -> equal(union(u,identity_relation),identity_relation).
% 299.99/300.65  210387[21:Res:196904.1,143186.0] || subclass(domain_relation,symmetric_difference(ordinal_numbers,u)) -> member(singleton(singleton(singleton(identity_relation))),complement(u))*.
% 299.99/300.65  210388[22:Res:205574.1,143186.0] || equal(symmetric_difference(ordinal_numbers,u),singleton(singleton(identity_relation))) -> member(singleton(identity_relation),complement(u))*.
% 299.99/300.65  210405[18:Res:194549.1,143186.0] || subclass(symmetrization_of(identity_relation),symmetric_difference(ordinal_numbers,u)) -> member(regular(symmetrization_of(identity_relation)),complement(u))*.
% 299.99/300.65  210406[18:Res:190510.1,143186.0] || subclass(inverse(identity_relation),symmetric_difference(ordinal_numbers,u)) -> member(regular(symmetrization_of(identity_relation)),complement(u))*.
% 299.99/300.65  210435[14:Res:210404.0,5.0] || subclass(union(u,identity_relation),v)* -> member(identity_relation,complement(u)) member(identity_relation,v).
% 299.99/300.65  210441[14:Rew:30.0,210424.1,66036.0,210424.0] ||  -> member(identity_relation,complement(intersection(union(u,v),ordinal_numbers)))* member(identity_relation,union(u,v)).
% 299.99/300.65  210452[8:SpL:68757.0,143226.0] || member(u,intersection(symmetrization_of(identity_relation),ordinal_numbers))* member(u,complement(inverse(identity_relation))) -> .
% 299.99/300.65  210461[5:Res:6.1,143226.0] || member(not_subclass_element(symmetric_difference(ordinal_numbers,u),v),u)* -> subclass(symmetric_difference(ordinal_numbers,u),v).
% 299.99/300.65  210496[21:Res:196904.1,143226.0] || subclass(domain_relation,symmetric_difference(ordinal_numbers,u)) member(singleton(singleton(singleton(identity_relation))),u)* -> .
% 299.99/300.65  210497[22:Res:205574.1,143226.0] || equal(symmetric_difference(ordinal_numbers,u),singleton(singleton(identity_relation))) member(singleton(identity_relation),u)* -> .
% 299.99/300.65  210514[18:Res:194549.1,143226.0] || subclass(symmetrization_of(identity_relation),symmetric_difference(ordinal_numbers,u))* member(regular(symmetrization_of(identity_relation)),u) -> .
% 299.99/300.65  210515[18:Res:190510.1,143226.0] || subclass(inverse(identity_relation),symmetric_difference(ordinal_numbers,u))* member(regular(symmetrization_of(identity_relation)),u) -> .
% 299.99/300.65  210521[8:Rew:160491.0,210464.0] || subclass(ordinal_numbers,complement(union(u,identity_relation)))* member(unordered_pair(v,w),u)* -> .
% 299.99/300.65  210522[8:Rew:160491.0,210487.0] || subclass(ordinal_numbers,complement(union(u,identity_relation)))* member(least(element_relation,omega),u) -> .
% 299.99/300.65  210523[8:Rew:160491.0,210488.0] || subclass(omega,complement(union(u,identity_relation)))* member(least(element_relation,omega),u) -> .
% 299.99/300.65  210524[8:Rew:160491.0,210500.0] || subclass(ordinal_numbers,complement(union(u,identity_relation)))* member(ordered_pair(v,w),u)* -> .
% 299.99/300.65  210526[8:Rew:160491.0,210475.1,160491.0,210475.0] || member(not_subclass_element(u,union(v,identity_relation)),v)* -> subclass(u,union(v,identity_relation)).
% 299.99/300.65  210547[8:Res:8700.2,210517.1] || member(u,ordinal_numbers)* equal(complement(complement(v)),ordinal_numbers)** -> member(u,v)*.
% 299.99/300.65  210659[8:Res:8827.2,210517.1] || member(u,ordinal_numbers)* subclass(rest_relation,v)* equal(complement(v),ordinal_numbers) -> .
% 299.99/300.65  210661[8:Res:8801.1,210517.1] || member(ordered_pair(u,v),cross_product(ordinal_numbers,ordinal_numbers))* equal(complement(composition_function),ordinal_numbers) -> .
% 299.99/300.65  210785[8:SpL:30.0,210578.0] || equal(union(u,v),ordinal_numbers) -> equal(intersection(complement(u),complement(v)),identity_relation)**.
% 299.99/300.65  210792[8:SpL:162038.0,210578.0] || equal(power_class(complement(inverse(identity_relation))),ordinal_numbers) -> equal(image(element_relation,symmetrization_of(identity_relation)),identity_relation)**.
% 299.99/300.65  210793[16:SpL:195257.0,210578.0] || equal(power_class(complement(singleton(identity_relation))),ordinal_numbers) -> equal(image(element_relation,singleton(identity_relation)),identity_relation)**.
% 299.99/300.65  210845[8:Res:210572.1,1301.1] || equal(complement(u),ordinal_numbers) member(u,ordinal_numbers)* -> equal(sum_class(u),u).
% 299.99/300.65  210859[8:Res:210572.1,13052.1] || equal(complement(image(successor_relation,u)),ordinal_numbers)** member(identity_relation,u) -> inductive(u).
% 299.99/300.65  211449[8:Con:211380.2] || equal(complement(u),ordinal_numbers) member(v,w)* -> member(v,complement(u))*.
% 299.99/300.65  211591[8:Con:211572.2] || equal(symmetrization_of(identity_relation),ordinal_numbers) member(u,v)* -> member(u,symmetrization_of(identity_relation))*.
% 299.99/300.65  211676[8:Con:211656.2] || equal(power_class(u),ordinal_numbers) member(v,w)* -> member(v,power_class(u))*.
% 299.99/300.65  212036[8:SpR:211586.1,79560.1] || equal(symmetrization_of(identity_relation),ordinal_numbers) -> member(u,symmetrization_of(identity_relation))* subclass(singleton(u),identity_relation).
% 299.99/300.65  212238[8:SpL:68757.0,210460.0] || subclass(ordinal_numbers,intersection(symmetrization_of(identity_relation),ordinal_numbers))* member(omega,complement(inverse(identity_relation))) -> .
% 299.99/300.65  212239[16:SpL:195256.0,210460.0] || subclass(ordinal_numbers,intersection(singleton(identity_relation),ordinal_numbers))* member(omega,complement(singleton(identity_relation))) -> .
% 299.99/300.65  212240[8:SpL:144460.0,210460.0] || subclass(ordinal_numbers,symmetric_difference(complement(u),ordinal_numbers))* member(omega,symmetric_difference(ordinal_numbers,u)) -> .
% 299.99/300.65  212257[8:SpL:144460.0,210511.0] || subclass(ordinal_numbers,symmetric_difference(complement(u),ordinal_numbers))* member(identity_relation,symmetric_difference(ordinal_numbers,u)) -> .
% 299.99/300.65  212512[8:SpR:211432.1,79560.1] || equal(complement(u),ordinal_numbers) -> member(v,complement(u))* subclass(singleton(v),identity_relation).
% 299.99/300.65  212807[8:SpR:211670.1,79560.1] || equal(power_class(u),ordinal_numbers) -> member(v,power_class(u))* subclass(singleton(v),identity_relation).
% 299.99/300.65  213075[8:SpR:210579.1,33.0] || equal(complement(cross_product(u,v)),ordinal_numbers) -> equal(restrict(w,u,v),identity_relation)**.
% 299.99/300.65  213080[8:SpR:210579.1,163.0] || equal(complement(complement(intersection(u,v))),ordinal_numbers)** -> equal(symmetric_difference(u,v),identity_relation).
% 299.99/300.65  213113[8:SpR:210579.1,66293.0] || equal(complement(union(u,identity_relation)),ordinal_numbers) -> equal(symmetric_difference(complement(u),ordinal_numbers),identity_relation)**.
% 299.99/300.65  213468[21:SpR:145761.0,196546.1] ||  -> equal(singleton(cross_product(u,singleton(v))),identity_relation)** equal(segment(ordinal_numbers,u,v),identity_relation).
% 299.99/300.65  213479[8:SpL:145761.0,164088.1] operation(cross_product(u,singleton(v))) || equal(segment(ordinal_numbers,u,v),ordinal_numbers)** -> .
% 299.99/300.65  213483[8:SpL:145761.0,164087.1] operation(cross_product(u,singleton(v))) || subclass(ordinal_numbers,segment(ordinal_numbers,u,v))* -> .
% 299.99/300.65  213632[7:Res:151877.0,13082.1] inductive(intersection(singleton(u),v)) ||  -> function(u)* member(identity_relation,complement(recursion_equation_functions(w)))*.
% 299.99/300.65  213654[7:Res:213622.0,13082.1] inductive(complement(complement(singleton(u)))) ||  -> function(u)* member(identity_relation,complement(recursion_equation_functions(v)))*.
% 299.99/300.65  213688[7:Res:151512.0,13082.1] inductive(intersection(u,singleton(v))) ||  -> function(v)* member(identity_relation,complement(recursion_equation_functions(w)))*.
% 299.99/300.65  214276[25:SpR:208887.0,196546.1] ||  -> equal(singleton(restrict(u,v,identity_relation)),identity_relation)** equal(segment(u,v,ordinal_numbers),identity_relation).
% 299.99/300.65  214294[25:SpL:208887.0,164088.1] operation(restrict(u,v,identity_relation)) || equal(segment(u,v,ordinal_numbers),ordinal_numbers)** -> .
% 299.99/300.65  214298[25:SpL:208887.0,164087.1] operation(restrict(u,v,identity_relation)) || subclass(ordinal_numbers,segment(u,v,ordinal_numbers))* -> .
% 299.99/300.65  214330[25:SpR:208972.1,13099.0] operation(u) ||  -> equal(recursion(identity_relation,apply(add_relation,u),union_of_range_map),ordinal_multiply(ordinal_numbers,v))*.
% 299.99/300.65  214340[25:SpR:208972.1,208972.1] operation(u) operation(v) ||  -> equal(apply(w,u),apply(w,v))*.
% 299.99/300.65  214351[25:SpR:208972.1,13099.0] operation(u) ||  -> equal(recursion(identity_relation,apply(add_relation,ordinal_numbers),union_of_range_map),ordinal_multiply(u,v))*.
% 299.99/300.65  214427[25:SpR:208985.1,208985.1] operation(u) operation(v) ||  -> equal(ordered_pair(w,u),ordered_pair(w,v))*.
% 299.99/300.65  214501[25:SpL:208985.1,116160.0] operation(u) || member(ordered_pair(v,u),domain_relation)* -> equal(cantor(v),ordinal_numbers).
% 299.99/300.65  214503[25:SpL:208985.1,49.0] operation(u) || member(ordered_pair(v,u),successor_relation)* -> equal(successor(v),ordinal_numbers).
% 299.99/300.65  214556[25:SpL:208985.1,116160.0] operation(u) || member(ordered_pair(v,ordinal_numbers),domain_relation)* -> equal(cantor(v),u)*.
% 299.99/300.65  214558[25:SpL:208985.1,49.0] operation(u) || member(ordered_pair(v,ordinal_numbers),successor_relation)* -> equal(successor(v),u)*.
% 299.99/300.65  214769[25:Res:13125.2,214618.1] operation(u) || subclass(omega,rest_relation) -> equal(integer_of(ordered_pair(v,u)),identity_relation)**.
% 299.99/300.65  214858[25:SpR:214376.1,214376.1] operation(u) operation(v) ||  -> equal(ordinal_add(w,v),ordinal_add(w,u))*.
% 299.99/300.65  214925[7:Res:151501.1,13082.1] inductive(intersection(u,singleton(v))) || member(v,w)* -> member(identity_relation,w)*.
% 299.99/300.65  214957[8:SpR:160491.0,151502.1] ||  -> member(u,symmetric_difference(ordinal_numbers,v)) subclass(intersection(w,singleton(u)),union(v,identity_relation))*.
% 299.99/300.65  214961[5:SpR:59.0,151502.1] ||  -> member(u,image(element_relation,complement(v))) subclass(intersection(w,singleton(u)),power_class(v))*.
% 299.99/300.65  214983[7:Res:151502.1,13082.1] inductive(intersection(u,singleton(v))) ||  -> member(v,w)* member(identity_relation,complement(w))*.
% 299.99/300.65  215021[7:Res:151861.1,13082.1] inductive(intersection(singleton(u),v)) || member(u,w)* -> member(identity_relation,w)*.
% 299.99/300.65  215055[7:Res:215011.1,13082.1] inductive(complement(complement(singleton(u)))) || member(u,v)* -> member(identity_relation,v)*.
% 299.99/300.65  215087[8:SpR:160491.0,151862.1] ||  -> member(u,symmetric_difference(ordinal_numbers,v)) subclass(intersection(singleton(u),w),union(v,identity_relation))*.
% 299.99/300.65  215091[5:SpR:59.0,151862.1] ||  -> member(u,image(element_relation,complement(v))) subclass(intersection(singleton(u),w),power_class(v))*.
% 299.99/300.65  215118[7:Res:151862.1,13082.1] inductive(intersection(singleton(u),v)) ||  -> member(u,w)* member(identity_relation,complement(w))*.
% 299.99/300.65  215139[8:SpR:160491.0,215108.1] ||  -> member(u,symmetric_difference(ordinal_numbers,v)) subclass(complement(complement(singleton(u))),union(v,identity_relation))*.
% 299.99/300.65  215143[5:SpR:59.0,215108.1] ||  -> member(u,image(element_relation,complement(v))) subclass(complement(complement(singleton(u))),power_class(v))*.
% 299.99/300.65  215155[7:Res:215108.1,13082.1] inductive(complement(complement(singleton(u)))) ||  -> member(u,v)* member(identity_relation,complement(v))*.
% 299.99/300.65  215205[7:Res:155157.1,13082.1] inductive(symmetric_difference(u,v)) || subclass(v,u)* -> member(identity_relation,complement(v))*.
% 299.99/300.65  215599[8:SpR:30.0,215487.1] || subclass(intersection(complement(u),complement(v)),identity_relation)* -> subclass(ordinal_numbers,union(u,v)).
% 299.99/300.65  215609[8:SpR:162038.0,215487.1] || subclass(image(element_relation,symmetrization_of(identity_relation)),identity_relation)* -> subclass(ordinal_numbers,power_class(complement(inverse(identity_relation)))).
% 299.99/300.65  215610[16:SpR:195257.0,215487.1] || subclass(image(element_relation,singleton(identity_relation)),identity_relation)* -> subclass(ordinal_numbers,power_class(complement(singleton(identity_relation)))).
% 299.99/300.65  216007[8:SpL:13260.1,215642.0] || subclass(singleton(regular(cross_product(u,v))),identity_relation)* -> equal(cross_product(u,v),identity_relation).
% 299.99/300.65  216231[8:SpL:481.0,216213.0] || equal(power_class(intersection(complement(u),complement(v))),image(element_relation,union(u,v)))** -> .
% 299.99/300.65  216285[8:MRR:216239.0,13126.0] || subclass(intersection(complement(u),complement(v)),identity_relation)* -> member(identity_relation,union(u,v)).
% 299.99/300.65  216558[8:MRR:216525.0,8652.0] || subclass(intersection(complement(u),complement(v)),identity_relation)* -> member(omega,union(u,v)).
% 299.99/300.65  216576[8:SpL:30.0,215660.0] || subclass(union(u,v),identity_relation) -> member(identity_relation,intersection(complement(u),complement(v)))*.
% 299.99/300.65  216585[8:SpL:162038.0,215660.0] || subclass(power_class(complement(inverse(identity_relation))),identity_relation) -> member(identity_relation,image(element_relation,symmetrization_of(identity_relation)))*.
% 299.99/300.65  216586[16:SpL:195257.0,215660.0] || subclass(power_class(complement(singleton(identity_relation))),identity_relation) -> member(identity_relation,image(element_relation,singleton(identity_relation)))*.
% 299.99/300.65  216596[8:SpL:30.0,215661.0] || subclass(union(u,v),identity_relation) -> member(omega,intersection(complement(u),complement(v)))*.
% 299.99/300.65  216605[8:SpL:162038.0,215661.0] || subclass(power_class(complement(inverse(identity_relation))),identity_relation) -> member(omega,image(element_relation,symmetrization_of(identity_relation)))*.
% 299.99/300.65  216606[16:SpL:195257.0,215661.0] || subclass(power_class(complement(singleton(identity_relation))),identity_relation) -> member(omega,image(element_relation,singleton(identity_relation)))*.
% 299.99/300.65  216683[8:SpR:216188.1,30.0] || equal(intersection(complement(u),complement(v)),identity_relation)** -> equal(union(u,v),ordinal_numbers).
% 299.99/300.65  216764[8:SpR:216188.1,132293.0] || equal(successor(u),identity_relation) -> subclass(ordinal_numbers,intersection(complement(u),complement(singleton(u))))*.
% 299.99/300.65  216765[24:SpR:216188.1,207866.1] operation(u) || equal(successor(u),identity_relation) -> subclass(ordinal_numbers,symmetric_difference(ordinal_numbers,u))*.
% 299.99/300.65  216766[8:SpR:216188.1,132294.0] || equal(symmetrization_of(u),identity_relation) -> subclass(ordinal_numbers,intersection(complement(u),complement(inverse(u))))*.
% 299.99/300.65  216780[8:SpR:216188.1,162038.0] || equal(image(element_relation,symmetrization_of(identity_relation)),identity_relation)** -> equal(power_class(complement(inverse(identity_relation))),ordinal_numbers).
% 299.99/300.65  216781[16:SpR:216188.1,195257.0] || equal(image(element_relation,singleton(identity_relation)),identity_relation)** -> equal(power_class(complement(singleton(identity_relation))),ordinal_numbers).
% 299.99/300.65  217145[8:MRR:63501.3,217144.1] || equal(sum_class(u),identity_relation) well_ordering(v,u)* -> subclass(sum_class(u),w)*.
% 299.99/300.65  217209[8:Rew:143170.0,216746.1] || equal(compose(complement(element_relation),inverse(element_relation)),identity_relation)** -> equal(cross_product(ordinal_numbers,ordinal_numbers),subset_relation).
% 299.99/300.65  217210[11:Rew:140613.0,216784.1] || equal(image(successor_relation,ordinal_numbers),identity_relation) -> equal(power_class(symmetric_difference(ordinal_numbers,singleton(identity_relation))),identity_relation)**.
% 299.99/300.65  217228[8:Rew:140603.0,216684.1] || equal(intersection(u,v),identity_relation)** -> equal(symmetric_difference(u,v),union(u,v)).
% 299.99/300.65  217333[8:SpL:162038.0,216227.0] || equal(image(element_relation,power_class(complement(inverse(identity_relation)))),power_class(image(element_relation,symmetrization_of(identity_relation))))** -> .
% 299.99/300.65  217334[16:SpL:195257.0,216227.0] || equal(image(element_relation,power_class(complement(singleton(identity_relation)))),power_class(image(element_relation,singleton(identity_relation))))** -> .
% 299.99/300.65  217392[8:Res:216591.1,9876.0] || equal(complement(u),identity_relation) subclass(u,v)* well_ordering(ordinal_numbers,v)* -> .
% 299.99/300.65  217421[8:Res:216591.1,897.0] || equal(complement(restrict(u,v,w)),identity_relation)** -> member(identity_relation,cross_product(v,w)).
% 299.99/300.65  217430[8:Res:216591.1,14681.0] || equal(complement(regular(u)),identity_relation)** member(identity_relation,u) -> equal(u,identity_relation).
% 299.99/300.65  217518[7:Res:61019.0,9876.0] || subclass(u,v)* well_ordering(ordinal_numbers,v)* -> equal(complement(complement(u)),identity_relation)**.
% 299.99/300.65  217643[8:Res:216611.1,897.0] || equal(complement(restrict(u,v,w)),identity_relation)** -> member(omega,cross_product(v,w)).
% 299.99/300.65  217652[8:Res:216611.1,14681.0] || equal(complement(regular(u)),identity_relation)** member(omega,u) -> equal(u,identity_relation).
% 299.99/300.65  217774[8:Res:216691.1,8854.0] || equal(complement(restrict(u,v,w)),identity_relation)** -> member(unordered_pair(x,y),u)*.
% 299.99/300.65  218036[8:SpL:30.0,217692.0] || equal(union(u,v),identity_relation) -> equal(intersection(complement(u),complement(v)),ordinal_numbers)**.
% 299.99/300.65  218045[8:SpL:162038.0,217692.0] || equal(power_class(complement(inverse(identity_relation))),identity_relation) -> equal(image(element_relation,symmetrization_of(identity_relation)),ordinal_numbers)**.
% 299.99/300.65  218046[16:SpL:195257.0,217692.0] || equal(power_class(complement(singleton(identity_relation))),identity_relation) -> equal(image(element_relation,singleton(identity_relation)),ordinal_numbers)**.
% 299.99/300.65  218386[21:Res:8955.1,196454.0] || member(u,ordinal_numbers) subclass(domain_relation,rest_relation) -> equal(rest_of(sum_class(u)),identity_relation)**.
% 299.99/300.65  218388[21:Res:50063.1,196454.0] || member(u,subset_relation) subclass(domain_relation,rest_relation) -> equal(rest_of(first(u)),identity_relation)**.
% 299.99/300.65  218389[21:Res:50064.1,196454.0] || member(u,subset_relation) subclass(domain_relation,rest_relation) -> equal(rest_of(second(u)),identity_relation)**.
% 299.99/300.65  218390[21:Res:41183.1,196454.0] || subclass(domain_relation,rest_relation) -> subclass(u,v) equal(rest_of(not_subclass_element(u,v)),identity_relation)**.
% 299.99/300.65  218398[21:Res:8956.1,196454.0] || member(u,ordinal_numbers) subclass(domain_relation,rest_relation) -> equal(rest_of(power_class(u)),identity_relation)**.
% 299.99/300.65  218399[21:Res:18510.1,196454.0] function(u) || subclass(domain_relation,rest_relation) -> equal(rest_of(apply(u,v)),identity_relation)**.
% 299.99/300.65  218515[21:MRR:218463.1,8652.0] || equal(rest_relation,domain_relation) subclass(rest_relation,u) -> member(ordered_pair(omega,identity_relation),u)*.
% 299.99/300.65  218562[21:Res:8955.1,196455.0] || member(u,ordinal_numbers) subclass(rest_relation,domain_relation) -> equal(rest_of(sum_class(u)),identity_relation)**.
% 299.99/300.65  218564[21:Res:50063.1,196455.0] || member(u,subset_relation) subclass(rest_relation,domain_relation) -> equal(rest_of(first(u)),identity_relation)**.
% 299.99/300.65  218565[21:Res:50064.1,196455.0] || member(u,subset_relation) subclass(rest_relation,domain_relation) -> equal(rest_of(second(u)),identity_relation)**.
% 299.99/300.65  218566[21:Res:41183.1,196455.0] || subclass(rest_relation,domain_relation) -> subclass(u,v) equal(rest_of(not_subclass_element(u,v)),identity_relation)**.
% 299.99/300.65  218574[21:Res:8956.1,196455.0] || member(u,ordinal_numbers) subclass(rest_relation,domain_relation) -> equal(rest_of(power_class(u)),identity_relation)**.
% 299.99/300.65  218575[21:Res:18510.1,196455.0] function(u) || subclass(rest_relation,domain_relation) -> equal(rest_of(apply(u,v)),identity_relation)**.
% 299.99/300.65  218989[8:Obv:218981.2] || subclass(ordinal_numbers,u) member(omega,singleton(u))* -> equal(singleton(u),identity_relation).
% 299.99/300.65  219305[15:Res:215659.1,66086.1] || subclass(complement(complement(compose(element_relation,ordinal_numbers))),identity_relation)* member(range_of(identity_relation),element_relation) -> .
% 299.99/300.65  219307[15:Res:215659.1,152274.0] || subclass(complement(complement(singleton(range_of(identity_relation)))),identity_relation)* -> subclass(singleton(range_of(identity_relation)),u)*.
% 299.99/300.65  219309[15:Res:215659.1,9876.0] || subclass(complement(u),identity_relation)* subclass(u,v)* well_ordering(ordinal_numbers,v)* -> .
% 299.99/300.65  219313[15:Res:215659.1,5.0] || subclass(complement(u),identity_relation)* subclass(u,v)* -> member(range_of(identity_relation),v)*.
% 299.99/300.65  219318[15:Res:215659.1,3617.0] || subclass(complement(symmetric_difference(u,v)),identity_relation) -> member(range_of(identity_relation),union(u,v))*.
% 299.99/300.65  219319[15:Res:215659.1,19559.0] || subclass(complement(symmetric_difference(u,singleton(u))),identity_relation)* -> member(range_of(identity_relation),successor(u)).
% 299.99/300.65  219320[15:Res:215659.1,19676.0] || subclass(complement(symmetric_difference(u,inverse(u))),identity_relation)* -> member(range_of(identity_relation),symmetrization_of(u)).
% 299.99/300.65  219578[8:Res:216611.1,67561.0] || equal(complement(symmetric_difference(complement(u),ordinal_numbers)),identity_relation)** -> member(omega,union(u,identity_relation)).
% 299.99/300.65  219630[8:Res:216591.1,67561.0] || equal(complement(symmetric_difference(complement(u),ordinal_numbers)),identity_relation)** -> member(identity_relation,union(u,identity_relation)).
% 299.99/300.65  219790[8:Res:67614.1,219073.1] || member(u,union(v,identity_relation))* subclass(symmetric_difference(complement(v),ordinal_numbers),identity_relation)* -> .
% 299.99/300.65  219791[8:Res:67614.1,217144.1] || member(u,union(v,identity_relation))* equal(symmetric_difference(complement(v),ordinal_numbers),identity_relation) -> .
% 299.99/300.65  219832[15:Res:217197.1,66086.1] || equal(complement(complement(compose(element_relation,ordinal_numbers))),identity_relation)** member(range_of(identity_relation),element_relation) -> .
% 299.99/300.65  219840[15:Res:217197.1,5.0] || equal(complement(u),identity_relation) subclass(u,v)* -> member(range_of(identity_relation),v)*.
% 299.99/300.65  219845[15:Res:217197.1,3617.0] || equal(complement(symmetric_difference(u,v)),identity_relation) -> member(range_of(identity_relation),union(u,v))*.
% 299.99/300.65  219846[15:Res:217197.1,19559.0] || equal(complement(symmetric_difference(u,singleton(u))),identity_relation)** -> member(range_of(identity_relation),successor(u)).
% 299.99/300.65  219847[15:Res:217197.1,19676.0] || equal(complement(symmetric_difference(u,inverse(u))),identity_relation)** -> member(range_of(identity_relation),symmetrization_of(u)).
% 299.99/300.65  219896[15:Rew:30.0,219844.0] || equal(union(u,v),identity_relation) member(range_of(identity_relation),union(u,v))* -> .
% 299.99/300.65  219930[8:Res:41203.1,217200.1] || member(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers)* equal(singleton(least(element_relation,domain_relation)),identity_relation) -> .
% 299.99/300.65  219953[8:Res:80082.1,217200.1] || member(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers)* equal(singleton(least(element_relation,rest_relation)),identity_relation) -> .
% 299.99/300.65  219954[10:Res:80198.1,217200.1] || member(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers)* equal(singleton(least(element_relation,element_relation)),identity_relation) -> .
% 299.99/300.65  220029[15:Res:209921.1,160772.0] || equal(symmetric_difference(ordinal_numbers,u),ordinal_numbers) member(range_of(identity_relation),union(u,identity_relation))* -> .
% 299.99/300.65  220031[15:Res:165526.1,160772.0] || subclass(ordinal_numbers,symmetric_difference(ordinal_numbers,u)) member(range_of(identity_relation),union(u,identity_relation))* -> .
% 299.99/300.65  220051[8:Res:143198.1,160772.0] || equal(symmetric_difference(ordinal_numbers,u),ordinal_numbers) member(singleton(v),union(u,identity_relation))* -> .
% 299.99/300.65  220053[8:Res:8645.1,160772.0] || subclass(ordinal_numbers,symmetric_difference(ordinal_numbers,u)) member(singleton(v),union(u,identity_relation))* -> .
% 299.99/300.65  220070[18:Res:190593.1,160772.0] || equal(symmetric_difference(ordinal_numbers,u),inverse(identity_relation)) member(identity_relation,union(u,identity_relation))* -> .
% 299.99/300.65  220071[18:Res:190442.1,160772.0] || equal(symmetric_difference(ordinal_numbers,u),symmetrization_of(identity_relation)) member(identity_relation,union(u,identity_relation))* -> .
% 299.99/300.65  220072[14:Res:165168.1,160772.0] || equal(symmetric_difference(ordinal_numbers,u),singleton(identity_relation)) member(identity_relation,union(u,identity_relation))* -> .
% 299.99/300.65  220215[8:SpL:50855.1,217709.0] || member(singleton(u),subset_relation) equal(complement(complement(unordered_pair(u,v))),identity_relation)** -> .
% 299.99/300.65  220243[8:SpL:50855.1,217710.0] || member(singleton(u),subset_relation) equal(complement(complement(unordered_pair(v,u))),identity_relation)** -> .
% 299.99/300.65  220379[21:SpR:963.0,196656.1] || subclass(domain_relation,flip(u)) -> member(ordered_pair(singleton(singleton(singleton(v))),identity_relation),u)*.
% 299.99/300.65  220395[21:Res:196656.1,9876.0] || subclass(domain_relation,flip(u))* subclass(u,v)* well_ordering(ordinal_numbers,v)* -> .
% 299.99/300.65  220421[21:Res:196656.1,3700.0] || subclass(domain_relation,flip(singleton(u)))* -> equal(ordered_pair(ordered_pair(v,w),identity_relation),u)*.
% 299.99/300.65  220460[21:Res:196656.1,97.0] || subclass(domain_relation,flip(compose_class(u))) -> equal(compose(u,ordered_pair(v,w)),identity_relation)**.
% 299.99/300.65  220467[21:Res:196656.1,37.0] || subclass(domain_relation,flip(rotate(u))) -> member(ordered_pair(ordered_pair(v,identity_relation),w),u)*.
% 299.99/300.65  220468[21:Res:196656.1,40.0] || subclass(domain_relation,flip(flip(u))) -> member(ordered_pair(ordered_pair(v,w),identity_relation),u)*.
% 299.99/300.65  220486[21:SpR:963.0,196657.1] || subclass(domain_relation,rotate(u)) -> member(ordered_pair(singleton(singleton(singleton(identity_relation))),v),u)*.
% 299.99/300.65  220497[21:Res:196657.1,9876.0] || subclass(domain_relation,rotate(u))* subclass(u,v)* well_ordering(ordinal_numbers,v)* -> .
% 299.99/300.65  220523[21:Res:196657.1,3700.0] || subclass(domain_relation,rotate(singleton(u)))* -> equal(ordered_pair(ordered_pair(v,identity_relation),w),u)*.
% 299.99/300.65  220562[21:Res:196657.1,97.0] || subclass(domain_relation,rotate(compose_class(u))) -> equal(compose(u,ordered_pair(v,identity_relation)),w)*.
% 299.99/300.65  220573[21:Res:196657.1,37.0] || subclass(domain_relation,rotate(rotate(u))) -> member(ordered_pair(ordered_pair(identity_relation,v),w),u)*.
% 299.99/300.65  220574[21:Res:196657.1,40.0] || subclass(domain_relation,rotate(flip(u))) -> member(ordered_pair(ordered_pair(identity_relation,v),w),u)*.
% 299.99/300.65  220705[8:Res:13125.2,219203.0] || subclass(omega,rest_of(u))* subclass(element_relation,identity_relation) -> equal(integer_of(u),identity_relation).
% 299.99/300.65  220709[8:Res:40074.1,219203.0] || subclass(ordinal_numbers,complement(complement(rest_of(unordered_pair(u,v)))))* subclass(element_relation,identity_relation) -> .
% 299.99/300.65  220719[8:Res:13227.2,219203.0] || subclass(u,rest_of(regular(u)))* subclass(element_relation,identity_relation) -> equal(u,identity_relation).
% 299.99/300.65  220724[8:Res:127147.1,219203.0] || subclass(ordinal_numbers,complement(complement(rest_of(least(element_relation,omega)))))* subclass(element_relation,identity_relation) -> .
% 299.99/300.65  220725[8:Res:126679.1,219203.0] || subclass(omega,complement(complement(rest_of(least(element_relation,omega)))))* subclass(element_relation,identity_relation) -> .
% 299.99/300.65  220736[8:Res:39298.1,219203.0] || subclass(ordinal_numbers,complement(complement(rest_of(ordered_pair(u,v)))))* subclass(element_relation,identity_relation) -> .
% 299.99/300.65  221140[21:Res:13236.2,197211.0] || well_ordering(u,subset_relation) -> equal(subset_relation,identity_relation) equal(cantor(least(u,subset_relation)),identity_relation)**.
% 299.99/300.65  221141[8:Res:13236.2,162901.0] || well_ordering(u,subset_relation) equal(least(u,subset_relation),identity_relation)** -> equal(subset_relation,identity_relation).
% 299.99/300.65  221142[8:Res:13236.2,162888.0] || well_ordering(u,subset_relation) subclass(least(u,subset_relation),identity_relation)* -> equal(subset_relation,identity_relation).
% 299.99/300.65  221260[8:SpR:50855.1,215662.1] || member(singleton(u),subset_relation)* subclass(complement(v),identity_relation)* -> member(u,v)*.
% 299.99/300.65  221265[8:Res:215662.1,66086.1] || subclass(complement(complement(compose(element_relation,ordinal_numbers))),identity_relation)* member(singleton(u),element_relation)* -> .
% 299.99/300.65  221267[8:Res:215662.1,152274.0] || subclass(complement(complement(singleton(singleton(u)))),identity_relation)* -> subclass(singleton(singleton(u)),v)*.
% 299.99/300.65  221273[8:Res:215662.1,5.0] || subclass(complement(u),identity_relation)* subclass(u,v)* -> member(singleton(w),v)*.
% 299.99/300.65  221278[8:Res:215662.1,3617.0] || subclass(complement(symmetric_difference(u,v)),identity_relation) -> member(singleton(w),union(u,v))*.
% 299.99/300.65  221279[8:Res:215662.1,19559.0] || subclass(complement(symmetric_difference(u,singleton(u))),identity_relation)* -> member(singleton(v),successor(u))*.
% 299.99/300.65  221280[8:Res:215662.1,19676.0] || subclass(complement(symmetric_difference(u,inverse(u))),identity_relation)* -> member(singleton(v),symmetrization_of(u))*.
% 299.99/300.65  221335[8:Res:215662.1,8785.0] || subclass(complement(rest_of(u)),identity_relation) -> equal(restrict(u,singleton(v),ordinal_numbers),v)**.
% 299.99/300.65  221517[8:SpR:50855.1,217198.1] || member(singleton(u),subset_relation)* equal(complement(v),identity_relation) -> member(u,v)*.
% 299.99/300.65  221522[8:Res:217198.1,66086.1] || equal(complement(complement(compose(element_relation,ordinal_numbers))),identity_relation)** member(singleton(u),element_relation)* -> .
% 299.99/300.65  221530[8:Res:217198.1,5.0] || equal(complement(u),identity_relation) subclass(u,v)* -> member(singleton(w),v)*.
% 299.99/300.65  221535[8:Res:217198.1,3617.0] || equal(complement(symmetric_difference(u,v)),identity_relation) -> member(singleton(w),union(u,v))*.
% 299.99/300.65  221536[8:Res:217198.1,19559.0] || equal(complement(symmetric_difference(u,singleton(u))),identity_relation)** -> member(singleton(v),successor(u))*.
% 299.99/300.65  221537[8:Res:217198.1,19676.0] || equal(complement(symmetric_difference(u,inverse(u))),identity_relation)** -> member(singleton(v),symmetrization_of(u))*.
% 299.99/300.65  221617[8:Rew:30.0,221534.0] || equal(union(u,v),identity_relation) member(singleton(w),union(u,v))* -> .
% 299.99/300.65  221684[8:SpR:218159.1,3616.0] || equal(union(u,v),identity_relation) -> equal(symmetric_difference(complement(u),complement(v)),identity_relation)**.
% 299.99/300.65  222119[8:SpR:219120.1,3616.0] || subclass(union(u,v),identity_relation) -> equal(symmetric_difference(complement(u),complement(v)),identity_relation)**.
% 299.99/300.65  222538[8:Res:10.1,69474.0] || equal(inverse(subset_relation),omega) member(u,subset_relation)* -> equal(integer_of(u),identity_relation).
% 299.99/300.65  222581[21:MRR:222567.2,13039.0] || member(u,ordinal_numbers) subclass(domain_relation,union_of_range_map) -> section(element_relation,range_of(u),ordinal_numbers)*.
% 299.99/300.65  222592[21:SpR:217824.0,196545.0] ||  -> equal(regular(complement(complement(omega))),identity_relation) equal(cantor(regular(complement(complement(omega)))),identity_relation)**.
% 299.99/300.65  222683[7:Res:66492.1,31610.0] || subclass(rest_relation,successor_relation)* -> equal(integer_of(u),identity_relation)** equal(rest_of(u),successor(u)).
% 299.99/300.65  222684[7:Res:18517.1,31610.0] || subclass(rest_relation,successor_relation)* -> equal(singleton(u),identity_relation) equal(rest_of(u),successor(u))**.
% 299.99/300.65  222686[5:Res:8666.0,31610.0] || subclass(rest_relation,successor_relation) -> equal(rest_of(unordered_pair(u,v)),successor(unordered_pair(u,v)))**.
% 299.99/300.65  222688[5:Res:8667.0,31610.0] || subclass(rest_relation,successor_relation) -> equal(rest_of(ordered_pair(u,v)),successor(ordered_pair(u,v)))**.
% 299.99/300.65  222690[15:Res:165431.0,31610.0] || subclass(rest_relation,successor_relation) -> equal(rest_of(sum_class(range_of(identity_relation))),successor(sum_class(range_of(identity_relation))))**.
% 299.99/300.65  222698[18:Res:190509.0,31610.0] || subclass(rest_relation,successor_relation) -> equal(rest_of(regular(symmetrization_of(identity_relation))),successor(regular(symmetrization_of(identity_relation))))**.
% 299.99/300.65  222720[5:Res:125724.0,31610.0] || subclass(rest_relation,successor_relation) -> equal(rest_of(least(element_relation,omega)),successor(least(element_relation,omega)))**.
% 299.99/300.65  222991[21:Res:10.1,196425.1] || equal(recursion_equation_functions(u),domain_relation)** member(v,ordinal_numbers) -> function(ordered_pair(v,identity_relation))*.
% 299.99/300.65  223152[11:Rew:80200.0,223138.1] || equal(complement(complement(u)),ordinal_numbers) -> equal(complement(image(element_relation,symmetrization_of(u))),identity_relation)**.
% 299.99/300.65  223153[11:Rew:80200.0,223139.1] || subclass(complement(inverse(u)),identity_relation) -> equal(complement(image(element_relation,symmetrization_of(u))),identity_relation)**.
% 299.99/300.65  223154[11:Rew:80200.0,223140.1] || equal(complement(inverse(u)),identity_relation) -> equal(complement(image(element_relation,symmetrization_of(u))),identity_relation)**.
% 299.99/300.65  223165[11:Rew:80200.0,223123.1,17401.0,223123.1] || equal(complement(u),ordinal_numbers) -> equal(complement(image(element_relation,symmetrization_of(complement(u)))),identity_relation)**.
% 299.99/300.65  223166[11:Rew:80200.0,223127.1,17401.0,223127.1] || equal(symmetrization_of(identity_relation),ordinal_numbers) -> equal(complement(image(element_relation,symmetrization_of(symmetrization_of(identity_relation)))),identity_relation)**.
% 299.99/300.65  223167[11:Rew:80200.0,223135.1,17401.0,223135.1] || equal(power_class(u),ordinal_numbers) -> equal(complement(image(element_relation,symmetrization_of(power_class(u)))),identity_relation)**.
% 299.99/300.65  223475[11:Rew:80200.0,223460.1] || equal(complement(complement(u)),ordinal_numbers) -> equal(complement(image(element_relation,successor(u))),identity_relation)**.
% 299.99/300.65  223476[11:Rew:80200.0,223461.1] || subclass(complement(singleton(u)),identity_relation) -> equal(complement(image(element_relation,successor(u))),identity_relation)**.
% 299.99/300.65  223490[11:Rew:80200.0,223445.1,17401.0,223445.1] || equal(complement(u),ordinal_numbers) -> equal(complement(image(element_relation,successor(complement(u)))),identity_relation)**.
% 299.99/300.65  223491[11:Rew:80200.0,223449.1,17401.0,223449.1] || equal(symmetrization_of(identity_relation),ordinal_numbers) -> equal(complement(image(element_relation,successor(symmetrization_of(identity_relation)))),identity_relation)**.
% 299.99/300.65  223492[11:Rew:80200.0,223457.1,17401.0,223457.1] || equal(power_class(u),ordinal_numbers) -> equal(complement(image(element_relation,successor(power_class(u)))),identity_relation)**.
% 299.99/300.65  223860[8:SpL:160927.0,216213.0] || equal(intersection(complement(u),union(v,identity_relation)),union(u,symmetric_difference(ordinal_numbers,v)))** -> .
% 299.99/300.65  223886[8:Rew:66036.0,223797.1] || subclass(union(u,identity_relation),identity_relation) -> equal(union(v,symmetric_difference(ordinal_numbers,u)),ordinal_numbers)**.
% 299.99/300.65  223977[7:Res:10.1,13242.0] || equal(complement(u),omega) member(v,u)* -> equal(integer_of(v),identity_relation).
% 299.99/300.65  224179[8:SpL:160992.0,216213.0] || equal(intersection(union(u,identity_relation),complement(v)),union(symmetric_difference(ordinal_numbers,u),v))** -> .
% 299.99/300.65  224203[8:Rew:66036.0,224111.1] || subclass(union(u,identity_relation),identity_relation) -> equal(union(symmetric_difference(ordinal_numbers,u),v),ordinal_numbers)**.
% 299.99/300.65  224310[25:MRR:224284.2,216168.0] || member(regular(regular(complement(subset_relation))),inverse(subset_relation))* -> equal(regular(complement(subset_relation)),identity_relation).
% 299.99/300.65  224311[18:MRR:224298.2,190496.0] || member(regular(regular(symmetrization_of(identity_relation))),inverse(identity_relation))* -> equal(regular(symmetrization_of(identity_relation)),identity_relation).
% 299.99/300.65  224313[8:Rew:13098.1,224312.1] || member(regular(u),singleton(u))* -> equal(u,identity_relation) equal(singleton(u),identity_relation).
% 299.99/300.65  224557[25:Rew:208885.0,224449.1] || subclass(element_relation,identity_relation) -> equal(apply(u,cross_product(ordinal_numbers,ordinal_numbers)),apply(u,ordinal_numbers))**.
% 299.99/300.65  224571[25:Rew:208873.0,224434.1] || subclass(element_relation,identity_relation) -> equal(ordered_pair(u,cross_product(ordinal_numbers,ordinal_numbers)),ordered_pair(u,ordinal_numbers))**.
% 299.99/300.65  224646[7:Obv:224642.1] || subclass(singleton(u),omega)* -> equal(singleton(u),identity_relation) equal(integer_of(u),u).
% 299.99/300.65  224752[26:Res:224684.1,18791.0] || subclass(omega,symmetric_difference(complement(u),complement(v)))* -> member(identity_relation,union(u,v)).
% 299.99/300.65  224901[7:Res:10.1,13340.0] || equal(intersection(u,v),omega)** -> equal(integer_of(w),identity_relation) member(w,u)*.
% 299.99/300.65  224966[7:Res:10.1,13341.0] || equal(intersection(u,v),omega)** -> equal(integer_of(w),identity_relation) member(w,v)*.
% 299.99/300.65  224988[26:SpL:208887.0,224842.1] operation(restrict(u,v,identity_relation)) || subclass(omega,segment(u,v,ordinal_numbers))* -> .
% 299.99/300.65  225010[26:SpL:145761.0,224842.1] operation(cross_product(u,singleton(v))) || subclass(omega,segment(ordinal_numbers,u,v))* -> .
% 299.99/300.65  225020[26:SpL:208887.0,224910.1] operation(restrict(u,v,identity_relation)) || equal(segment(u,v,ordinal_numbers),omega)** -> .
% 299.99/300.65  225042[26:SpL:145761.0,224910.1] operation(cross_product(u,singleton(v))) || equal(segment(ordinal_numbers,u,v),omega)** -> .
% 299.99/300.65  225424[7:Res:13061.0,17312.1] || subclass(u,complement(omega))* -> equal(integer_of(regular(u)),identity_relation) equal(u,identity_relation).
% 299.99/300.65  225498[8:SpL:160491.0,225445.0] || subclass(symmetric_difference(ordinal_numbers,u),union(u,identity_relation))* -> equal(symmetric_difference(ordinal_numbers,u),identity_relation).
% 299.99/300.65  225884[26:Res:225794.1,18791.0] || equal(symmetric_difference(complement(u),complement(v)),omega)** -> member(identity_relation,union(u,v)).
% 299.99/300.65  226150[7:Res:10.1,17321.0] || equal(intersection(u,v),w)* -> equal(w,identity_relation) member(regular(w),v)*.
% 299.99/300.65  226169[7:Res:132293.0,17321.0] ||  -> equal(complement(successor(u)),identity_relation) member(regular(complement(successor(u))),complement(singleton(u)))*.
% 299.99/300.65  226170[7:Res:132294.0,17321.0] ||  -> equal(complement(symmetrization_of(u)),identity_relation) member(regular(complement(symmetrization_of(u))),complement(inverse(u)))*.
% 299.99/300.65  226255[7:Res:10.1,17322.0] || equal(intersection(u,v),w)* -> equal(w,identity_relation) member(regular(w),u)*.
% 299.99/300.65  226350[25:Res:226327.1,5.0] || subclass(rest_relation,domain_relation) subclass(rest_relation,u) -> member(ordered_pair(identity_relation,identity_relation),u)*.
% 299.99/300.65  226463[8:Obv:226462.1] || subclass(complement(compose(element_relation,ordinal_numbers)),element_relation)* -> equal(complement(compose(element_relation,ordinal_numbers)),identity_relation).
% 299.99/300.65  226521[8:Obv:226511.1] || subclass(intersection(u,inverse(subset_relation)),subset_relation)* -> equal(intersection(u,inverse(subset_relation)),identity_relation).
% 299.99/300.65  226615[14:SpL:69395.0,216276.1] || member(identity_relation,intersection(u,ordinal_numbers)) subclass(complement(symmetric_difference(u,ordinal_numbers)),identity_relation)* -> .
% 299.99/300.65  226624[8:SpL:117066.0,216284.1] || subclass(rest_relation,rest_of(flip(cross_product(u,ordinal_numbers))))* subclass(inverse(u),identity_relation) -> .
% 299.99/300.65  226625[8:SpL:117142.0,216284.1] || subclass(rest_relation,rest_of(restrict(element_relation,ordinal_numbers,u)))* subclass(sum_class(u),identity_relation) -> .
% 299.99/300.65  226653[8:Res:116148.1,216284.1] || section(u,identity_relation,v) subclass(rest_relation,rest_of(restrict(u,v,identity_relation)))* -> .
% 299.99/300.65  226712[8:Obv:226698.1] || subclass(intersection(inverse(subset_relation),u),subset_relation)* -> equal(intersection(inverse(subset_relation),u),identity_relation).
% 299.99/300.65  226742[7:Res:55.1,13238.0] inductive(recursion_equation_functions(u)) ||  -> equal(integer_of(v),identity_relation) subclass(v,cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.65  226955[8:SpR:216692.1,66293.0] || equal(complement(union(u,identity_relation)),identity_relation) -> equal(symmetric_difference(complement(u),ordinal_numbers),ordinal_numbers)**.
% 299.99/300.65  227056[8:MRR:227014.1,8638.0] || equal(complement(u),identity_relation) -> subclass(v,w) member(not_subclass_element(v,w),u)*.
% 299.99/300.65  227057[8:MRR:227016.2,295.0] || equal(complement(u),identity_relation) member(v,ordinal_numbers) -> member(sum_class(v),u)*.
% 299.99/300.65  227130[21:Res:196520.2,219073.1] || member(u,ordinal_numbers)* equal(successor(u),identity_relation) subclass(successor_relation,identity_relation) -> .
% 299.99/300.65  227143[8:SpL:160491.0,217386.0] || equal(complement(union(u,identity_relation)),identity_relation) member(identity_relation,symmetric_difference(ordinal_numbers,u))* -> .
% 299.99/300.65  227147[8:SpL:59.0,217386.0] || equal(complement(power_class(u)),identity_relation) member(identity_relation,image(element_relation,complement(u)))* -> .
% 299.99/300.65  227165[8:SpL:160491.0,217389.0] || equal(complement(complement(union(u,identity_relation))),identity_relation)** -> member(identity_relation,symmetric_difference(ordinal_numbers,u)).
% 299.99/300.65  227169[8:SpL:59.0,217389.0] || equal(complement(complement(power_class(u))),identity_relation) -> member(identity_relation,image(element_relation,complement(u)))*.
% 299.99/300.65  227191[8:SpL:69395.0,217450.0] || equal(complement(symmetric_difference(u,ordinal_numbers)),identity_relation) member(identity_relation,intersection(u,ordinal_numbers))* -> .
% 299.99/300.65  227230[18:Res:217451.1,190641.1] || equal(union(u,identity_relation),identity_relation)** equal(complement(complement(u)),inverse(identity_relation)) -> .
% 299.99/300.65  227231[18:Res:217451.1,190532.1] || equal(union(u,identity_relation),identity_relation)** equal(complement(complement(u)),symmetrization_of(identity_relation)) -> .
% 299.99/300.65  227232[14:Res:217451.1,165357.1] || equal(union(u,identity_relation),identity_relation)** equal(complement(complement(u)),singleton(identity_relation)) -> .
% 299.99/300.65  227291[21:MRR:227263.0,8655.0] || subclass(rest_relation,union_of_range_map) subclass(domain_relation,union_of_range_map) -> equal(rest_of(singleton(identity_relation)),identity_relation)**.
% 299.99/300.65  227382[8:SpL:160491.0,217608.0] || equal(complement(union(u,identity_relation)),identity_relation) member(omega,symmetric_difference(ordinal_numbers,u))* -> .
% 299.99/300.65  227386[8:SpL:59.0,217608.0] || equal(complement(power_class(u)),identity_relation) member(omega,image(element_relation,complement(u)))* -> .
% 299.99/300.65  227404[8:SpL:160491.0,217611.0] || equal(complement(complement(union(u,identity_relation))),identity_relation)** -> member(omega,symmetric_difference(ordinal_numbers,u)).
% 299.99/300.65  227408[8:SpL:59.0,217611.0] || equal(complement(complement(power_class(u))),identity_relation) -> member(omega,image(element_relation,complement(u)))*.
% 299.99/300.65  227430[8:SpL:69395.0,217662.0] || equal(complement(symmetric_difference(u,ordinal_numbers)),identity_relation) member(omega,intersection(u,ordinal_numbers))* -> .
% 299.99/300.65  227574[8:SpL:160491.0,217695.0] || equal(complement(union(u,identity_relation)),identity_relation)** equal(symmetric_difference(ordinal_numbers,u),ordinal_numbers) -> .
% 299.99/300.65  227578[8:SpL:59.0,217695.0] || equal(complement(power_class(u)),identity_relation) equal(image(element_relation,complement(u)),ordinal_numbers)** -> .
% 299.99/300.65  227604[8:SpL:160491.0,217696.0] || equal(complement(union(u,identity_relation)),identity_relation) subclass(ordinal_numbers,symmetric_difference(ordinal_numbers,u))* -> .
% 299.99/300.65  227608[8:SpL:59.0,217696.0] || equal(complement(power_class(u)),identity_relation) subclass(ordinal_numbers,image(element_relation,complement(u)))* -> .
% 299.99/300.65  227626[8:SpL:160491.0,217697.0] || equal(complement(union(u,identity_relation)),identity_relation)** equal(symmetric_difference(ordinal_numbers,u),omega) -> .
% 299.99/300.65  227630[8:SpL:59.0,217697.0] || equal(complement(power_class(u)),identity_relation) equal(image(element_relation,complement(u)),omega)** -> .
% 299.99/300.65  227648[8:SpL:160491.0,217698.0] || equal(complement(union(u,identity_relation)),identity_relation) subclass(omega,symmetric_difference(ordinal_numbers,u))* -> .
% 299.99/300.65  227652[8:SpL:59.0,217698.0] || equal(complement(power_class(u)),identity_relation) subclass(omega,image(element_relation,complement(u)))* -> .
% 299.99/300.65  227670[8:SpL:160491.0,217699.0] || equal(complement(union(u,identity_relation)),identity_relation) subclass(domain_relation,symmetric_difference(ordinal_numbers,u))* -> .
% 299.99/300.65  227674[8:SpL:59.0,217699.0] || equal(complement(power_class(u)),identity_relation) subclass(domain_relation,image(element_relation,complement(u)))* -> .
% 299.99/300.65  227696[8:SpL:160491.0,217700.0] || equal(complement(union(u,identity_relation)),identity_relation) member(symmetric_difference(ordinal_numbers,u),subset_relation)* -> .
% 299.99/300.65  227700[8:SpL:59.0,217700.0] || equal(complement(power_class(u)),identity_relation) member(image(element_relation,complement(u)),subset_relation)* -> .
% 299.99/300.65  228138[25:SpL:208885.0,219925.1] || member(image(u,identity_relation),ordinal_numbers)* equal(singleton(apply(u,ordinal_numbers)),identity_relation) -> .
% 299.99/300.65  228373[8:SpL:145758.0,220841.0] || member(inverse(cross_product(u,ordinal_numbers)),image(ordinal_numbers,u))* subclass(element_relation,identity_relation) -> .
% 299.99/300.65  228564[8:MRR:228529.3,14676.0] || equal(complement(u),identity_relation) member(v,ordinal_numbers) -> member(v,successor(u))*.
% 299.99/300.65  228574[8:Res:228546.1,5.0] || equal(complement(u),identity_relation) subclass(successor(u),v)* -> member(omega,v).
% 299.99/300.65  228606[8:Res:228547.1,5.0] || equal(complement(u),identity_relation) subclass(successor(u),v)* -> member(identity_relation,v).
% 299.99/300.65  228664[8:MRR:228629.3,14676.0] || equal(complement(u),identity_relation) member(v,ordinal_numbers) -> member(v,symmetrization_of(u))*.
% 299.99/300.65  228673[8:Res:228646.1,5.0] || equal(complement(u),identity_relation) subclass(symmetrization_of(u),v)* -> member(omega,v).
% 299.99/300.65  228685[8:Res:228647.1,5.0] || equal(complement(u),identity_relation) subclass(symmetrization_of(u),v)* -> member(identity_relation,v).
% 299.99/300.65  228823[8:MRR:228788.3,14676.0] || subclass(complement(u),identity_relation) member(v,ordinal_numbers) -> member(v,successor(u))*.
% 299.99/300.65  228833[8:Res:228806.1,5.0] || subclass(complement(u),identity_relation)* subclass(successor(u),v)* -> member(omega,v).
% 299.99/300.65  228846[8:Res:228807.1,5.0] || subclass(complement(u),identity_relation)* subclass(successor(u),v)* -> member(identity_relation,v).
% 299.99/300.65  228961[8:MRR:228927.3,14676.0] || subclass(complement(u),identity_relation) member(v,ordinal_numbers) -> member(v,symmetrization_of(u))*.
% 299.99/300.65  228970[8:Res:228945.1,5.0] || subclass(complement(u),identity_relation) subclass(symmetrization_of(u),v)* -> member(omega,v).
% 299.99/300.65  228983[8:Res:228946.1,5.0] || subclass(complement(u),identity_relation) subclass(symmetrization_of(u),v)* -> member(identity_relation,v).
% 299.99/300.65  229199[7:Obv:229158.1] || subclass(intersection(complement(u),v),u)* -> equal(intersection(complement(u),v),identity_relation).
% 299.99/300.65  229774[7:Obv:229587.1] || subclass(intersection(u,complement(v)),v)* -> equal(intersection(u,complement(v)),identity_relation).
% 299.99/300.65  230193[7:SpR:189.0,229638.0] ||  -> equal(symmetric_difference(image(element_relation,power_class(u)),complement(power_class(image(element_relation,complement(u))))),identity_relation)**.
% 299.99/300.65  230257[8:MRR:230225.2,14676.0] inductive(symmetric_difference(inverse(identity_relation),symmetrization_of(identity_relation))) || well_ordering(u,complement(symmetrization_of(identity_relation)))* -> .
% 299.99/300.65  230465[8:MRR:230428.0,8655.0] || well_ordering(ordinal_numbers,symmetric_difference(ordinal_numbers,u)) -> member(singleton(singleton(v)),union(u,identity_relation))*.
% 299.99/300.65  230679[25:MRR:230639.2,216168.0] || member(unordered_pair(u,v),inverse(subset_relation))* subclass(ordinal_numbers,regular(complement(subset_relation))) -> .
% 299.99/300.65  230680[18:MRR:230659.2,190496.0] || member(unordered_pair(u,v),inverse(identity_relation))* subclass(ordinal_numbers,regular(symmetrization_of(identity_relation))) -> .
% 299.99/300.65  230681[10:MRR:230653.2,217111.0] || member(unordered_pair(u,v),element_relation)* subclass(ordinal_numbers,regular(compose(element_relation,ordinal_numbers)))* -> .
% 299.99/300.65  230682[13:MRR:230654.2,160479.0] || member(unordered_pair(u,v),subset_relation)* subclass(ordinal_numbers,regular(cross_product(ordinal_numbers,ordinal_numbers)))* -> .
% 299.99/300.65  230763[8:SpL:6355.1,230706.0] || subclass(ordinal_numbers,not_subclass_element(cross_product(u,v),w))* -> subclass(cross_product(u,v),w).
% 299.99/300.65  230781[8:SpL:6355.1,230770.0] || equal(not_subclass_element(cross_product(u,v),w),ordinal_numbers)** -> subclass(cross_product(u,v),w).
% 299.99/300.65  230791[8:SpL:13260.1,230675.0] || subclass(ordinal_numbers,regular(regular(cross_product(u,v))))* -> equal(cross_product(u,v),identity_relation).
% 299.99/300.65  230869[8:SpL:13260.1,230771.0] || equal(complement(regular(cross_product(u,v))),identity_relation)** -> equal(cross_product(u,v),identity_relation).
% 299.99/300.65  230941[8:SpL:13260.1,230797.0] || equal(regular(regular(cross_product(u,v))),ordinal_numbers)** -> equal(cross_product(u,v),identity_relation).
% 299.99/300.65  231031[8:MRR:230999.2,295.0] || equal(complement(u),identity_relation) member(v,ordinal_numbers) -> member(power_class(v),u)*.
% 299.99/300.65  231037[8:Res:41371.0,230762.0] || subclass(ordinal_numbers,not_subclass_element(complement(complement(subset_relation)),u))* -> subclass(complement(complement(subset_relation)),u).
% 299.99/300.65  231038[8:Res:313.1,230762.0] || subclass(ordinal_numbers,not_subclass_element(intersection(subset_relation,u),v))* -> subclass(intersection(subset_relation,u),v).
% 299.99/300.65  231051[8:Res:13069.2,230762.0] || member(subset_relation,ordinal_numbers) subclass(ordinal_numbers,apply(choice,subset_relation))* -> equal(subset_relation,identity_relation).
% 299.99/300.65  231054[8:Res:2503.2,230762.0] || subclass(u,subset_relation) subclass(ordinal_numbers,not_subclass_element(u,v))* -> subclass(u,v).
% 299.99/300.65  231055[8:Res:303.1,230762.0] || subclass(ordinal_numbers,not_subclass_element(intersection(u,subset_relation),v))* -> subclass(intersection(u,subset_relation),v).
% 299.99/300.65  231062[8:Res:13236.2,230762.0] || well_ordering(u,subset_relation) subclass(ordinal_numbers,least(u,subset_relation))* -> equal(subset_relation,identity_relation).
% 299.99/300.65  231063[8:Res:13237.2,230762.0] || well_ordering(u,ordinal_numbers) subclass(ordinal_numbers,least(u,subset_relation))* -> equal(subset_relation,identity_relation).
% 299.99/300.65  231115[8:Res:41371.0,230780.0] || equal(not_subclass_element(complement(complement(subset_relation)),u),ordinal_numbers)** -> subclass(complement(complement(subset_relation)),u).
% 299.99/300.65  231116[8:Res:313.1,230780.0] || equal(not_subclass_element(intersection(subset_relation,u),v),ordinal_numbers)** -> subclass(intersection(subset_relation,u),v).
% 299.99/300.65  231129[8:Res:13069.2,230780.0] || member(subset_relation,ordinal_numbers) equal(apply(choice,subset_relation),ordinal_numbers)** -> equal(subset_relation,identity_relation).
% 299.99/300.65  231132[8:Res:2503.2,230780.0] || subclass(u,subset_relation) equal(not_subclass_element(u,v),ordinal_numbers)** -> subclass(u,v).
% 299.99/300.65  231133[8:Res:303.1,230780.0] || equal(not_subclass_element(intersection(u,subset_relation),v),ordinal_numbers)** -> subclass(intersection(u,subset_relation),v).
% 299.99/300.65  231140[8:Res:13236.2,230780.0] || well_ordering(u,subset_relation) equal(least(u,subset_relation),ordinal_numbers)** -> equal(subset_relation,identity_relation).
% 299.99/300.65  231141[8:Res:13237.2,230780.0] || well_ordering(u,ordinal_numbers) equal(least(u,subset_relation),ordinal_numbers)** -> equal(subset_relation,identity_relation).
% 299.99/300.65  231197[7:Res:55.1,13418.0] inductive(restrict(u,v,w)) ||  -> equal(integer_of(x),identity_relation) member(x,u)*.
% 299.99/300.65  231762[8:Rew:160491.0,231716.1] || subclass(symmetric_difference(ordinal_numbers,u),union(u,identity_relation))* -> subclass(ordinal_numbers,union(u,identity_relation)).
% 299.99/300.65  231855[8:SpR:160491.0,231812.0] ||  -> subclass(regular(symmetric_difference(ordinal_numbers,u)),union(u,identity_relation))* equal(symmetric_difference(ordinal_numbers,u),identity_relation).
% 299.99/300.65  231885[8:Obv:231866.0] ||  -> subclass(u,complement(intersection(singleton(u),v)))* equal(intersection(singleton(u),v),identity_relation).
% 299.99/300.65  231886[8:Obv:231867.0] ||  -> subclass(u,complement(intersection(v,singleton(u))))* equal(intersection(v,singleton(u)),identity_relation).
% 299.99/300.65  231899[16:Res:231880.0,17324.0] ||  -> equal(regular(complement(singleton(identity_relation))),identity_relation) equal(regular(regular(complement(singleton(identity_relation)))),identity_relation)**.
% 299.99/300.65  232490[8:Res:61019.0,230867.0] || equal(complement(regular(complement(complement(subset_relation)))),identity_relation)** -> equal(complement(complement(subset_relation)),identity_relation).
% 299.99/300.65  232491[8:Res:13248.1,230867.0] || equal(complement(regular(intersection(subset_relation,u))),identity_relation)** -> equal(intersection(subset_relation,u),identity_relation).
% 299.99/300.65  232504[8:Res:13210.1,230867.0] || equal(complement(regular(intersection(u,subset_relation))),identity_relation)** -> equal(intersection(u,subset_relation),identity_relation).
% 299.99/300.65  232505[8:Res:13227.2,230867.0] || subclass(u,subset_relation) equal(complement(regular(u)),identity_relation)** -> equal(u,identity_relation).
% 299.99/300.65  232513[8:Res:127147.1,230867.0] || subclass(ordinal_numbers,complement(complement(subset_relation)))* equal(complement(least(element_relation,omega)),identity_relation) -> .
% 299.99/300.65  232514[8:Res:126679.1,230867.0] || subclass(omega,complement(complement(subset_relation)))* equal(complement(least(element_relation,omega)),identity_relation) -> .
% 299.99/300.65  232560[8:Res:40074.1,230939.0] || subclass(ordinal_numbers,complement(complement(subset_relation)))* equal(regular(unordered_pair(u,v)),ordinal_numbers)** -> .
% 299.99/300.65  232564[8:Res:61019.0,230939.0] || equal(regular(regular(complement(complement(subset_relation)))),ordinal_numbers)** -> equal(complement(complement(subset_relation)),identity_relation).
% 299.99/300.65  232565[8:Res:13248.1,230939.0] || equal(regular(regular(intersection(subset_relation,u))),ordinal_numbers)** -> equal(intersection(subset_relation,u),identity_relation).
% 299.99/300.65  232578[8:Res:13210.1,230939.0] || equal(regular(regular(intersection(u,subset_relation))),ordinal_numbers)** -> equal(intersection(u,subset_relation),identity_relation).
% 299.99/300.65  232579[8:Res:13227.2,230939.0] || subclass(u,subset_relation) equal(regular(regular(u)),ordinal_numbers)** -> equal(u,identity_relation).
% 299.99/300.65  232587[8:Res:127147.1,230939.0] || subclass(ordinal_numbers,complement(complement(subset_relation)))* equal(regular(least(element_relation,omega)),ordinal_numbers) -> .
% 299.99/300.65  232588[8:Res:126679.1,230939.0] || subclass(omega,complement(complement(subset_relation)))* equal(regular(least(element_relation,omega)),ordinal_numbers) -> .
% 299.99/300.65  233079[8:SpL:50855.1,232851.0] || member(singleton(u),subset_relation) equal(complement(regular(unordered_pair(v,u))),identity_relation)** -> .
% 299.99/300.65  233087[8:MRR:233084.1,216061.0] || equal(complement(u),identity_relation) -> equal(regular(unordered_pair(u,singleton(v))),singleton(v))**.
% 299.99/300.65  233110[21:MRR:233096.0,8655.0] || equal(sum_class(range_of(singleton(identity_relation))),identity_relation) -> member(singleton(singleton(singleton(identity_relation))),union_of_range_map)*.
% 299.99/300.65  233237[8:SpL:50855.1,233149.0] || member(singleton(u),subset_relation) equal(complement(regular(unordered_pair(u,v))),identity_relation)** -> .
% 299.99/300.65  233247[8:MRR:233245.1,216036.0] || equal(complement(u),identity_relation) -> equal(regular(unordered_pair(singleton(v),u)),singleton(v))**.
% 299.99/300.65  233307[18:Res:231881.0,210719.0] || equal(complement(complement(singleton(inverse(identity_relation)))),ordinal_numbers)** -> equal(singleton(inverse(identity_relation)),identity_relation).
% 299.99/300.65  233312[18:Res:231881.0,210718.0] || equal(complement(complement(singleton(symmetrization_of(identity_relation)))),ordinal_numbers)** -> equal(singleton(symmetrization_of(identity_relation)),identity_relation).
% 299.99/300.65  233559[21:MRR:233515.1,18843.1] || member(ordered_pair(u,identity_relation),subset_relation)* subclass(domain_relation,complement(cross_product(ordinal_numbers,ordinal_numbers)))* -> .
% 299.99/300.65  233566[21:MRR:233512.0,8667.0] || member(u,ordinal_numbers) subclass(domain_relation,complement(unordered_pair(ordered_pair(u,identity_relation),v)))* -> .
% 299.99/300.65  233567[21:MRR:233513.0,8667.0] || member(u,ordinal_numbers) subclass(domain_relation,complement(unordered_pair(v,ordered_pair(u,identity_relation))))* -> .
% 299.99/300.65  234105[10:SpR:223660.1,233383.0] || subclass(element_relation,identity_relation) -> member(identity_relation,complement(singleton(ordered_pair(cross_product(ordinal_numbers,ordinal_numbers),u))))*.
% 299.99/300.65  234187[10:SpL:223660.1,234106.0] || subclass(element_relation,identity_relation) member(identity_relation,singleton(ordered_pair(cross_product(ordinal_numbers,ordinal_numbers),u)))* -> .
% 299.99/300.65  234321[8:SpL:50855.1,233387.0] || member(singleton(u),subset_relation) well_ordering(ordinal_numbers,complement(singleton(singleton(singleton(u)))))* -> .
% 299.99/300.65  234373[18:MRR:234372.2,190496.0] || well_ordering(u,ordinal_numbers) member(least(u,symmetrization_of(identity_relation)),complement(inverse(identity_relation)))* -> .
% 299.99/300.65  234374[8:MRR:234359.2,217454.0] || member(least(u,complement(cross_product(ordinal_numbers,ordinal_numbers))),subset_relation)* well_ordering(u,ordinal_numbers) -> .
% 299.99/300.65  234401[8:SpL:50855.1,234119.0] || member(singleton(u),subset_relation) subclass(complement(singleton(singleton(singleton(u)))),identity_relation)* -> .
% 299.99/300.65  234521[8:Res:40074.1,233381.0] || subclass(ordinal_numbers,complement(complement(singleton(omega))))* -> equal(integer_of(unordered_pair(u,v)),identity_relation)**.
% 299.99/300.65  234540[8:Res:13227.2,233381.0] || subclass(u,singleton(omega))* -> equal(u,identity_relation) equal(integer_of(regular(u)),identity_relation).
% 299.99/300.65  234565[8:Res:39298.1,233381.0] || subclass(ordinal_numbers,complement(complement(singleton(omega))))* -> equal(integer_of(ordered_pair(u,v)),identity_relation)**.
% 299.99/300.65  234856[21:MRR:234785.1,14676.0] || member(u,ordinal_numbers) -> equal(apply(sum_class(range_of(identity_relation)),u),sum_class(range_of(identity_relation)))**.
% 299.99/300.65  234857[21:MRR:234788.1,14676.0] || member(u,ordinal_numbers) -> equal(apply(regular(symmetrization_of(identity_relation)),u),sum_class(range_of(identity_relation)))**.
% 299.99/300.65  234858[21:MRR:234791.1,14676.0] || member(u,ordinal_numbers) -> equal(apply(least(element_relation,omega),u),sum_class(range_of(identity_relation)))**.
% 299.99/300.65  234859[21:MRR:234795.1,14676.0] || member(u,ordinal_numbers) -> equal(apply(unordered_pair(v,w),u),sum_class(range_of(identity_relation)))**.
% 299.99/300.65  234860[21:MRR:234796.1,14676.0] || member(u,ordinal_numbers) -> equal(apply(ordered_pair(v,w),u),sum_class(range_of(identity_relation)))**.
% 299.99/300.65  234861[26:MRR:234846.0,13126.0] || equal(complement(cantor(u)),omega) -> equal(apply(u,identity_relation),sum_class(range_of(identity_relation)))**.
% 299.99/300.65  234865[22:MRR:234837.0,8655.0] || well_ordering(ordinal_numbers,cantor(u)) -> equal(apply(u,singleton(identity_relation)),sum_class(range_of(identity_relation)))**.
% 299.99/300.65  234951[7:SpR:229238.0,13101.0] ||  -> equal(range__dfg(complement(cross_product(singleton(u),v)),u,v),second(not_subclass_element(identity_relation,identity_relation)))**.
% 299.99/300.65  235145[21:SpL:197474.0,234983.0] || member(inverse(u),cantor(complement(cross_product(identity_relation,ordinal_numbers))))* -> equal(range_of(u),identity_relation).
% 299.99/300.65  235151[8:Res:116403.2,234983.0] || member(u,ordinal_numbers) subclass(rest_relation,rest_of(complement(cross_product(singleton(u),ordinal_numbers))))* -> .
% 299.99/300.65  235152[8:Res:13125.2,234983.0] || subclass(omega,cantor(complement(cross_product(singleton(u),ordinal_numbers))))* -> equal(integer_of(u),identity_relation).
% 299.99/300.65  235156[8:Res:40074.1,234983.0] || subclass(ordinal_numbers,complement(complement(cantor(complement(cross_product(singleton(unordered_pair(u,v)),ordinal_numbers))))))* -> .
% 299.99/300.65  235166[8:Res:13227.2,234983.0] || subclass(u,cantor(complement(cross_product(singleton(regular(u)),ordinal_numbers))))* -> equal(u,identity_relation).
% 299.99/300.65  235171[8:Res:127147.1,234983.0] || subclass(ordinal_numbers,complement(complement(cantor(complement(cross_product(singleton(least(element_relation,omega)),ordinal_numbers))))))* -> .
% 299.99/300.65  235172[8:Res:126679.1,234983.0] || subclass(omega,complement(complement(cantor(complement(cross_product(singleton(least(element_relation,omega)),ordinal_numbers))))))* -> .
% 299.99/300.65  235185[8:Res:39298.1,234983.0] || subclass(ordinal_numbers,complement(complement(cantor(complement(cross_product(singleton(ordered_pair(u,v)),ordinal_numbers))))))* -> .
% 299.99/300.65  235272[8:Res:230445.1,5.0] || member(u,v)* subclass(union(v,identity_relation),w)* -> member(u,w)*.
% 299.99/300.65  235312[8:MRR:235277.2,235274.1] || member(unordered_pair(u,v),w)* subclass(ordinal_numbers,regular(union(w,identity_relation)))* -> .
% 299.99/300.65  235379[5:Res:28980.1,9876.0] || subclass(rest_relation,flip(u))* subclass(u,v)* well_ordering(ordinal_numbers,v)* -> .
% 299.99/300.65  235442[5:Res:28980.1,23.0] || subclass(rest_relation,flip(element_relation)) -> member(ordered_pair(u,v),rest_of(ordered_pair(v,u)))*.
% 299.99/300.65  235448[5:Res:28980.1,19.0] || subclass(rest_relation,flip(cross_product(u,v)))* -> member(rest_of(ordered_pair(w,x)),v)*.
% 299.99/300.65  235507[5:Res:28979.1,9876.0] || subclass(rest_relation,rotate(u))* subclass(u,v)* well_ordering(ordinal_numbers,v)* -> .
% 299.99/300.65  235570[5:Res:28979.1,23.0] || subclass(rest_relation,rotate(element_relation)) -> member(ordered_pair(u,rest_of(ordered_pair(v,u))),v)*.
% 299.99/300.65  235853[8:MRR:235850.1,216561.0] || subclass(complement(singleton(omega)),u)* -> equal(integer_of(v),identity_relation) member(v,u)*.
% 299.99/300.65  235978[25:SpR:235012.0,208972.1] operation(u) ||  -> equal(apply(complement(cross_product(identity_relation,ordinal_numbers)),u),sum_class(range_of(identity_relation)))**.
% 299.99/300.65  235980[25:SpR:216188.1,235012.0] || equal(cross_product(identity_relation,ordinal_numbers),identity_relation) -> equal(apply(ordinal_numbers,ordinal_numbers),sum_class(range_of(identity_relation)))**.
% 299.99/300.65  235989[8:SpL:216188.1,235153.0] || equal(cross_product(singleton(omega),ordinal_numbers),identity_relation)** equal(complement(cantor(ordinal_numbers)),identity_relation) -> .
% 299.99/300.65  235993[15:SpL:216188.1,235160.0] || equal(cross_product(singleton(range_of(identity_relation)),ordinal_numbers),identity_relation)** equal(cantor(ordinal_numbers),ordinal_numbers) -> .
% 299.99/300.65  235996[15:SpL:216188.1,235162.0] || equal(cross_product(singleton(range_of(identity_relation)),ordinal_numbers),identity_relation)** subclass(ordinal_numbers,cantor(ordinal_numbers)) -> .
% 299.99/300.65  236009[8:SpL:216188.1,235197.0] || equal(cross_product(singleton(identity_relation),ordinal_numbers),identity_relation)** equal(complement(cantor(ordinal_numbers)),identity_relation) -> .
% 299.99/300.65  236013[18:SpL:216188.1,235199.0] || equal(cross_product(singleton(identity_relation),ordinal_numbers),identity_relation)** equal(cantor(ordinal_numbers),inverse(identity_relation)) -> .
% 299.99/300.65  236016[18:SpL:216188.1,235200.0] || equal(cross_product(singleton(identity_relation),ordinal_numbers),identity_relation)** equal(symmetrization_of(identity_relation),cantor(ordinal_numbers)) -> .
% 299.99/300.65  236019[14:SpL:216188.1,235201.0] || equal(cross_product(singleton(identity_relation),ordinal_numbers),identity_relation)** equal(cantor(ordinal_numbers),singleton(identity_relation)) -> .
% 299.99/300.65  236208[8:SpL:216188.1,235177.0] || equal(cross_product(singleton(singleton(u)),ordinal_numbers),identity_relation)** equal(cantor(ordinal_numbers),ordinal_numbers) -> .
% 299.99/300.65  236339[8:SpL:216188.1,235179.0] || equal(cross_product(singleton(singleton(u)),ordinal_numbers),identity_relation)** subclass(ordinal_numbers,cantor(ordinal_numbers)) -> .
% 299.99/300.65  236355[26:SpL:144460.0,224755.0] || subclass(omega,symmetric_difference(complement(u),ordinal_numbers))* member(identity_relation,symmetric_difference(ordinal_numbers,u)) -> .
% 299.99/300.65  236651[26:SpL:160491.0,225363.1] || equal(symmetric_difference(ordinal_numbers,u),inverse(identity_relation))** equal(union(u,identity_relation),omega) -> .
% 299.99/300.65  236655[26:SpL:59.0,225363.1] || equal(image(element_relation,complement(u)),inverse(identity_relation))** equal(power_class(u),omega) -> .
% 299.99/300.65  236698[26:SpL:160491.0,225365.1] || equal(symmetric_difference(ordinal_numbers,u),singleton(identity_relation))** equal(union(u,identity_relation),omega) -> .
% 299.99/300.65  236702[26:SpL:59.0,225365.1] || equal(image(element_relation,complement(u)),singleton(identity_relation))** equal(power_class(u),omega) -> .
% 299.99/300.65  236715[16:SpL:160491.0,225450.0] || subclass(singleton(identity_relation),union(u,identity_relation))* member(identity_relation,symmetric_difference(ordinal_numbers,u)) -> .
% 299.99/300.65  236719[16:SpL:59.0,225450.0] || subclass(singleton(identity_relation),power_class(u)) member(identity_relation,image(element_relation,complement(u)))* -> .
% 299.99/300.65  236742[18:SpL:160491.0,225452.1] || subclass(ordinal_numbers,symmetric_difference(ordinal_numbers,u)) subclass(symmetrization_of(identity_relation),union(u,identity_relation))* -> .
% 299.99/300.65  236746[18:SpL:59.0,225452.1] || subclass(ordinal_numbers,image(element_relation,complement(u)))* subclass(symmetrization_of(identity_relation),power_class(u)) -> .
% 299.99/300.65  236877[8:Res:17392.2,219073.1] || subclass(u,v)* subclass(v,identity_relation)* -> equal(intersection(u,w),identity_relation)**.
% 299.99/300.65  236878[8:Res:17392.2,217144.1] || subclass(u,v)* equal(identity_relation,v) -> equal(intersection(u,w),identity_relation)**.
% 299.99/300.65  236922[7:Obv:236818.1] || subclass(u,v)* -> equal(intersection(u,singleton(w)),identity_relation)** member(w,v)*.
% 299.99/300.65  236960[26:SpL:144460.0,225887.0] || equal(symmetric_difference(complement(u),ordinal_numbers),omega) member(identity_relation,symmetric_difference(ordinal_numbers,u))* -> .
% 299.99/300.65  236996[26:Res:225888.1,190641.1] || equal(symmetric_difference(ordinal_numbers,u),omega)** equal(complement(complement(u)),inverse(identity_relation)) -> .
% 299.99/300.65  236997[26:Res:225888.1,190532.1] || equal(symmetric_difference(ordinal_numbers,u),omega)** equal(complement(complement(u)),symmetrization_of(identity_relation)) -> .
% 299.99/300.65  236998[26:Res:225888.1,165357.1] || equal(symmetric_difference(ordinal_numbers,u),omega)** equal(complement(complement(u)),singleton(identity_relation)) -> .
% 299.99/300.65  237348[8:Rew:140603.0,237237.0,66036.0,237237.0] ||  -> equal(symmetric_difference(inverse(subset_relation),intersection(u,subset_relation)),union(inverse(subset_relation),intersection(u,subset_relation)))**.
% 299.99/300.65  237448[7:SpR:30.0,237181.0] ||  -> equal(intersection(union(u,v),intersection(w,intersection(complement(u),complement(v)))),identity_relation)**.
% 299.99/300.65  237459[8:SpR:162038.0,237181.0] ||  -> equal(intersection(power_class(complement(inverse(identity_relation))),intersection(u,image(element_relation,symmetrization_of(identity_relation)))),identity_relation)**.
% 299.99/300.65  237460[16:SpR:195257.0,237181.0] ||  -> equal(intersection(power_class(complement(singleton(identity_relation))),intersection(u,image(element_relation,singleton(identity_relation)))),identity_relation)**.
% 299.99/300.65  237544[8:Rew:140603.0,237358.0,66036.0,237358.0] ||  -> equal(symmetric_difference(complement(u),intersection(v,u)),union(complement(u),intersection(v,u)))**.
% 299.99/300.65  238009[8:Rew:140603.0,237890.0,66036.0,237890.0] ||  -> equal(symmetric_difference(inverse(subset_relation),intersection(subset_relation,u)),union(inverse(subset_relation),intersection(subset_relation,u)))**.
% 299.99/300.65  238121[8:Rew:140603.0,238020.0,66036.0,238020.0] ||  -> equal(symmetric_difference(inverse(subset_relation),complement(complement(subset_relation))),union(inverse(subset_relation),complement(complement(subset_relation))))**.
% 299.99/300.65  238230[7:SpR:30.0,237830.0] ||  -> equal(intersection(union(u,v),intersection(intersection(complement(u),complement(v)),w)),identity_relation)**.
% 299.99/300.65  238241[8:SpR:162038.0,237830.0] ||  -> equal(intersection(power_class(complement(inverse(identity_relation))),intersection(image(element_relation,symmetrization_of(identity_relation)),u)),identity_relation)**.
% 299.99/300.65  238242[16:SpR:195257.0,237830.0] ||  -> equal(intersection(power_class(complement(singleton(identity_relation))),intersection(image(element_relation,singleton(identity_relation)),u)),identity_relation)**.
% 299.99/300.65  238316[8:Rew:140603.0,238132.0,66036.0,238132.0] ||  -> equal(symmetric_difference(complement(u),intersection(u,v)),union(complement(u),intersection(u,v)))**.
% 299.99/300.65  238350[8:SpR:238174.0,154737.1] || subclass(symmetric_difference(ordinal_numbers,u),complement(complement(u)))* -> equal(symmetric_difference(ordinal_numbers,u),identity_relation).
% 299.99/300.65  238611[8:Res:13572.2,219073.1] || subclass(u,v)* subclass(v,identity_relation)* -> equal(intersection(w,u),identity_relation)**.
% 299.99/300.65  238612[8:Res:13572.2,217144.1] || subclass(u,v)* equal(identity_relation,v) -> equal(intersection(w,u),identity_relation)**.
% 299.99/300.65  238658[7:Obv:238551.1] || subclass(u,v)* -> equal(intersection(singleton(w),u),identity_relation)** member(w,v)*.
% 299.99/300.65  239149[16:MRR:239052.2,14676.0] || member(u,intersection(v,complement(singleton(identity_relation))))* member(u,singleton(identity_relation)) -> .
% 299.99/300.65  239531[8:Rew:140603.0,239413.0,66036.0,239413.0] ||  -> equal(symmetric_difference(intersection(subset_relation,u),inverse(subset_relation)),union(intersection(subset_relation,u),inverse(subset_relation)))**.
% 299.99/300.65  239536[8:Rew:239339.0,239524.1] || member(not_subclass_element(inverse(subset_relation),identity_relation),intersection(subset_relation,u))* -> subclass(inverse(subset_relation),identity_relation).
% 299.99/300.65  239646[8:Rew:140603.0,239543.0,66036.0,239543.0] ||  -> equal(symmetric_difference(complement(complement(subset_relation)),inverse(subset_relation)),union(complement(complement(subset_relation)),inverse(subset_relation)))**.
% 299.99/300.65  239651[8:Rew:239454.0,239638.1] || member(not_subclass_element(inverse(subset_relation),identity_relation),complement(complement(subset_relation)))* -> subclass(inverse(subset_relation),identity_relation).
% 299.99/300.65  239773[8:Rew:140603.0,239658.0,66036.0,239658.0] ||  -> equal(symmetric_difference(intersection(u,subset_relation),inverse(subset_relation)),union(intersection(u,subset_relation),inverse(subset_relation)))**.
% 299.99/300.65  239778[8:Rew:239452.0,239766.1] || member(not_subclass_element(inverse(subset_relation),identity_relation),intersection(u,subset_relation))* -> subclass(inverse(subset_relation),identity_relation).
% 299.99/300.65  239820[7:SpR:30.0,239340.0] ||  -> equal(intersection(intersection(intersection(complement(u),complement(v)),w),union(u,v)),identity_relation)**.
% 299.99/300.65  239831[8:SpR:162038.0,239340.0] ||  -> equal(intersection(intersection(image(element_relation,symmetrization_of(identity_relation)),u),power_class(complement(inverse(identity_relation)))),identity_relation)**.
% 299.99/300.65  239832[16:SpR:195257.0,239340.0] ||  -> equal(intersection(intersection(image(element_relation,singleton(identity_relation)),u),power_class(complement(singleton(identity_relation)))),identity_relation)**.
% 299.99/300.65  239978[8:Rew:140603.0,239785.0,66036.0,239785.0] ||  -> equal(symmetric_difference(intersection(u,v),complement(u)),union(intersection(u,v),complement(u)))**.
% 299.99/300.65  239983[7:Rew:239340.0,239967.1] || member(not_subclass_element(complement(u),identity_relation),intersection(u,v))* -> subclass(complement(u),identity_relation).
% 299.99/300.65  9574[5:SpL:30.0,9488.1] || subclass(ordinal_numbers,intersection(complement(u),complement(v)))* subclass(ordinal_numbers,union(u,v)) -> .
% 299.99/300.65  8869[5:Rew:8637.0,6724.0] || subclass(ordinal_numbers,union(u,v)) member(omega,intersection(complement(u),complement(v)))* -> .
% 299.99/300.65  8904[5:Rew:8637.0,6931.0] || equal(complement(union(u,v)),ordinal_numbers) -> member(omega,intersection(complement(u),complement(v)))*.
% 299.99/300.65  69158[8:Res:9632.1,66086.1] || equal(complement(complement(complement(compose(element_relation,ordinal_numbers)))),ordinal_numbers)** member(singleton(u),element_relation)* -> .
% 299.99/300.65  39960[5:SpL:8648.0,39811.1] || equal(complement(rest_of(restrict(element_relation,ordinal_numbers,u))),ordinal_numbers)** member(v,sum_class(u))* -> .
% 299.99/300.65  57176[5:Res:9632.1,19676.0] || equal(complement(complement(symmetric_difference(u,inverse(u)))),ordinal_numbers)** -> member(singleton(v),symmetrization_of(u))*.
% 299.99/300.65  18361[5:Res:9632.1,3617.0] || equal(complement(complement(symmetric_difference(u,v))),ordinal_numbers) -> member(singleton(w),union(u,v))*.
% 299.99/300.65  36359[5:SpL:3616.0,10088.0] || equal(symmetric_difference(complement(u),complement(v)),ordinal_numbers) -> member(singleton(w),union(u,v))*.
% 299.99/300.65  36362[5:SpL:3616.0,8848.0] || subclass(ordinal_numbers,symmetric_difference(complement(u),complement(v)))* -> member(singleton(w),union(u,v))*.
% 299.99/300.65  9683[5:Res:9632.1,5.0] || equal(complement(complement(u)),ordinal_numbers)** subclass(u,v)* -> member(singleton(w),v)*.
% 299.99/300.65  47542[0:Rew:3705.1,47541.1] || member(u,v) member(u,w) -> subclass(singleton(u),intersection(w,v))*.
% 299.99/300.65  19533[0:SpR:3596.0,19069.0] ||  -> subclass(symmetric_difference(complement(intersection(u,singleton(u))),successor(u)),complement(symmetric_difference(u,singleton(u))))*.
% 299.99/300.65  51209[5:SpR:50855.1,10714.1] || member(singleton(u),subset_relation) member(first(singleton(u)),v)* -> subclass(u,v).
% 299.99/300.65  51229[5:SpR:50855.1,964.0] || member(singleton(u),subset_relation) -> member(unordered_pair(v,u),ordered_pair(v,first(singleton(u))))*.
% 299.99/300.65  51232[5:SpR:50855.1,9632.1] || member(singleton(u),subset_relation)* equal(complement(complement(v)),ordinal_numbers)** -> member(u,v)*.
% 299.99/300.65  51295[5:SpL:50855.1,3700.0] || member(singleton(u),subset_relation)* member(v,u)* -> equal(v,first(singleton(u)))*.
% 299.99/300.65  51494[5:Res:51313.1,5.0] || member(singleton(u),subset_relation) subclass(u,v) -> member(first(singleton(u)),v)*.
% 299.99/300.65  57109[5:Res:9632.1,19559.0] || equal(complement(complement(symmetric_difference(u,singleton(u)))),ordinal_numbers)** -> member(singleton(v),successor(u))*.
% 299.99/300.65  51205[5:SpR:50855.1,963.0] || member(singleton(u),subset_relation) -> equal(ordered_pair(u,first(singleton(u))),singleton(singleton(u)))**.
% 299.99/300.65  51497[5:Res:51313.1,26.0] || member(singleton(intersection(u,v)),subset_relation) -> member(first(singleton(intersection(u,v))),v)*.
% 299.99/300.65  51498[5:Res:51313.1,25.0] || member(singleton(intersection(u,v)),subset_relation) -> member(first(singleton(intersection(u,v))),u)*.
% 299.99/300.65  18828[5:Res:8642.1,897.0] || subclass(ordinal_numbers,restrict(u,v,w))* -> member(ordered_pair(x,y),cross_product(v,w))*.
% 299.99/300.65  56814[5:SpL:163.0,8846.0] || subclass(ordinal_numbers,symmetric_difference(u,v)) -> member(unordered_pair(w,x),complement(intersection(u,v)))*.
% 299.99/300.65  50450[5:Res:2503.2,50033.0] || subclass(u,subset_relation) equal(complement(not_subclass_element(u,v)),ordinal_numbers)** -> subclass(u,v).
% 299.99/300.65  49649[5:SpL:6355.1,9529.0] || equal(complement(not_subclass_element(cross_product(u,v),w)),ordinal_numbers)** -> subclass(cross_product(u,v),w).
% 299.99/300.65  49648[5:SpL:6355.1,9486.0] || subclass(ordinal_numbers,complement(not_subclass_element(cross_product(u,v),w)))* -> subclass(cross_product(u,v),w).
% 299.99/300.65  50433[5:Res:313.1,50033.0] || equal(complement(not_subclass_element(intersection(subset_relation,u),v)),ordinal_numbers)** -> subclass(intersection(subset_relation,u),v).
% 299.99/300.65  50449[5:Res:303.1,50033.0] || equal(complement(not_subclass_element(intersection(u,subset_relation),v)),ordinal_numbers)** -> subclass(intersection(u,subset_relation),v).
% 299.99/300.65  50034[5:SpL:18840.1,149.0] || member(u,subset_relation) member(u,rest_relation) -> equal(rest_of(first(u)),second(u))**.
% 299.99/300.65  50026[5:SpL:18840.1,18.0] || member(u,subset_relation) member(u,cross_product(v,w))* -> member(first(u),v).
% 299.99/300.65  50025[5:SpL:18840.1,19.0] || member(u,subset_relation) member(u,cross_product(v,w))* -> member(second(u),w).
% 299.99/300.65  50410[5:SpL:30.0,50032.1] || member(intersection(complement(u),complement(v)),subset_relation)* subclass(ordinal_numbers,union(u,v)) -> .
% 299.99/300.65  63442[8:SpL:30.0,63019.1] || subclass(domain_relation,intersection(complement(u),complement(v)))* subclass(ordinal_numbers,union(u,v)) -> .
% 299.99/300.65  39961[5:SpL:8647.0,39811.1] || equal(complement(rest_of(flip(cross_product(u,ordinal_numbers)))),ordinal_numbers)** member(v,inverse(u))* -> .
% 299.99/300.65  19651[0:SpR:3597.0,19069.0] ||  -> subclass(symmetric_difference(complement(intersection(u,inverse(u))),symmetrization_of(u)),complement(symmetric_difference(u,inverse(u))))*.
% 299.99/300.65  79543[5:Res:60219.0,5.0] || subclass(u,v) -> subclass(w,complement(u)) member(not_subclass_element(w,complement(u)),v)*.
% 299.99/300.65  79544[5:Res:60219.0,26.0] ||  -> subclass(u,complement(intersection(v,w))) member(not_subclass_element(u,complement(intersection(v,w))),w)*.
% 299.99/300.65  79545[5:Res:60219.0,25.0] ||  -> subclass(u,complement(intersection(v,w))) member(not_subclass_element(u,complement(intersection(v,w))),v)*.
% 299.99/300.65  79579[5:Res:79560.1,11.0] || subclass(complement(u),singleton(v))* -> member(v,u) equal(complement(u),singleton(v)).
% 299.99/300.65  81390[8:SpL:30.0,81322.1] || subclass(domain_relation,intersection(complement(u),complement(v)))* subclass(domain_relation,union(u,v)) -> .
% 299.99/300.65  81400[8:SpL:30.0,81326.1] || subclass(ordinal_numbers,intersection(complement(u),complement(v)))* subclass(domain_relation,union(u,v)) -> .
% 299.99/300.65  81493[8:SpL:30.0,81412.1] || equal(intersection(complement(u),complement(v)),domain_relation)** equal(union(u,v),domain_relation) -> .
% 299.99/300.65  82883[5:SpR:50855.1,79560.1] || member(singleton(u),subset_relation) -> member(first(singleton(u)),v)* subclass(u,complement(v)).
% 299.99/300.65  94690[5:Res:39298.1,56411.0] || subclass(ordinal_numbers,complement(complement(rest_of(ordered_pair(u,v)))))* subclass(ordinal_numbers,complement(element_relation)) -> .
% 299.99/300.65  94692[5:Res:39298.1,898.0] || subclass(ordinal_numbers,complement(complement(restrict(u,v,w))))* -> member(ordered_pair(x,y),u)*.
% 299.99/300.65  94719[5:Res:39298.1,37.0] || subclass(ordinal_numbers,complement(complement(rotate(u)))) -> member(ordered_pair(ordered_pair(v,w),x),u)*.
% 299.99/300.65  94720[5:Res:39298.1,40.0] || subclass(ordinal_numbers,complement(complement(flip(u)))) -> member(ordered_pair(ordered_pair(v,w),x),u)*.
% 299.99/300.65  96378[5:Res:40074.1,56411.0] || subclass(ordinal_numbers,complement(complement(rest_of(unordered_pair(u,v)))))* subclass(ordinal_numbers,complement(element_relation)) -> .
% 299.99/300.65  96380[5:Res:40074.1,898.0] || subclass(ordinal_numbers,complement(complement(restrict(u,v,w))))* -> member(unordered_pair(x,y),u)*.
% 299.99/300.65  79549[5:Res:60219.0,161.0] ||  -> subclass(u,complement(omega)) equal(integer_of(not_subclass_element(u,complement(omega))),not_subclass_element(u,complement(omega)))**.
% 299.99/300.65  94678[5:Res:39298.1,161.0] || subclass(ordinal_numbers,complement(complement(omega)))* -> equal(integer_of(ordered_pair(u,v)),ordered_pair(u,v))**.
% 299.99/300.65  96366[5:Res:40074.1,161.0] || subclass(ordinal_numbers,complement(complement(omega)))* -> equal(integer_of(unordered_pair(u,v)),unordered_pair(u,v))**.
% 299.99/300.65  116466[8:Rew:116078.0,50024.2] || member(u,subset_relation) member(u,rest_of(v)) -> member(first(u),cantor(v))*.
% 299.99/300.65  117086[8:Rew:117064.0,82175.0] || subclass(ordinal_numbers,inverse(u)) equal(complement(rest_of(flip(cross_product(u,ordinal_numbers)))),ordinal_numbers)** -> .
% 299.99/300.65  117162[8:Rew:117140.0,82174.0] || subclass(ordinal_numbers,sum_class(u)) equal(complement(rest_of(restrict(element_relation,ordinal_numbers,u))),ordinal_numbers)** -> .
% 299.99/300.65  125926[5:Res:125725.1,897.0] || subclass(omega,restrict(u,v,w))* -> member(least(element_relation,omega),cross_product(v,w))*.
% 299.99/300.65  126003[5:Res:125731.1,897.0] || subclass(ordinal_numbers,restrict(u,v,w))* -> member(least(element_relation,omega),cross_product(v,w))*.
% 299.99/300.65  127018[5:SpL:30.0,126665.1] || subclass(omega,intersection(complement(u),complement(v)))* subclass(omega,union(u,v)) -> .
% 299.99/300.65  127417[5:SpL:30.0,127130.1] || subclass(omega,intersection(complement(u),complement(v)))* subclass(ordinal_numbers,union(u,v)) -> .
% 299.99/300.65  128010[5:Res:126679.1,56411.0] || subclass(omega,complement(complement(rest_of(least(element_relation,omega)))))* subclass(ordinal_numbers,complement(element_relation)) -> .
% 299.99/300.65  128012[5:Res:126679.1,898.0] || subclass(omega,complement(complement(restrict(u,v,w))))* -> member(least(element_relation,omega),u).
% 299.99/300.65  128345[5:Res:127147.1,56411.0] || subclass(ordinal_numbers,complement(complement(rest_of(least(element_relation,omega)))))* subclass(ordinal_numbers,complement(element_relation)) -> .
% 299.99/300.65  128347[5:Res:127147.1,898.0] || subclass(ordinal_numbers,complement(complement(restrict(u,v,w))))* -> member(least(element_relation,omega),u).
% 299.99/300.65  130513[5:SpL:163.0,125908.0] || subclass(omega,symmetric_difference(u,v)) -> member(least(element_relation,omega),complement(intersection(u,v)))*.
% 299.99/300.65  130654[5:Res:41371.0,50033.0] || equal(complement(not_subclass_element(complement(complement(subset_relation)),u)),ordinal_numbers)** -> subclass(complement(complement(subset_relation)),u).
% 299.99/300.65  130655[5:Res:41371.0,3700.0] ||  -> subclass(complement(complement(singleton(u))),v) equal(not_subclass_element(complement(complement(singleton(u))),v),u)**.
% 299.99/300.65  130865[8:Res:69184.1,9876.0] || member(u,element_relation)* subclass(compose(element_relation,ordinal_numbers),v)* well_ordering(ordinal_numbers,v) -> .
% 299.99/300.65  131041[8:AED:130968.1] || member(u,cantor(v))* subclass(rest_of(v),w)* well_ordering(ordinal_numbers,w) -> .
% 299.99/300.65  131433[0:Res:27.2,18794.1] || member(u,v) member(u,w) member(u,symmetric_difference(w,v))* -> .
% 299.99/300.65  131446[5:Res:8643.1,18794.1] || subclass(ordinal_numbers,intersection(u,v)) member(unordered_pair(w,x),symmetric_difference(u,v))* -> .
% 299.99/300.65  131469[5:Res:125731.1,18794.1] || subclass(ordinal_numbers,intersection(u,v)) member(least(element_relation,omega),symmetric_difference(u,v))* -> .
% 299.99/300.65  131470[5:Res:125725.1,18794.1] || subclass(omega,intersection(u,v)) member(least(element_relation,omega),symmetric_difference(u,v))* -> .
% 299.99/300.65  131482[5:Res:8642.1,18794.1] || subclass(ordinal_numbers,intersection(u,v)) member(ordered_pair(w,x),symmetric_difference(u,v))* -> .
% 299.99/300.65  131531[0:Res:2504.1,28.1] || subclass(ordered_pair(u,v),complement(w)) member(unordered_pair(u,singleton(v)),w)* -> .
% 299.99/300.65  131537[5:Res:2504.1,9876.0] || subclass(ordered_pair(u,v),w)* subclass(w,x)* well_ordering(ordinal_numbers,x)* -> .
% 299.99/300.65  131544[0:Res:2504.1,26.0] || subclass(ordered_pair(u,v),intersection(w,x))* -> member(unordered_pair(u,singleton(v)),x).
% 299.99/300.65  131545[0:Res:2504.1,25.0] || subclass(ordered_pair(u,v),intersection(w,x))* -> member(unordered_pair(u,singleton(v)),w).
% 299.99/300.65  131566[8:Res:2504.1,14679.1] || subclass(ordered_pair(u,v),inverse(subset_relation)) member(unordered_pair(u,singleton(v)),subset_relation)* -> .
% 299.99/300.65  132781[5:SpL:163.0,125985.0] || subclass(ordinal_numbers,symmetric_difference(u,v)) -> member(least(element_relation,omega),complement(intersection(u,v)))*.
% 299.99/300.65  132825[5:SpL:32.0,130481.0] || equal(restrict(u,v,w),omega)** -> member(least(element_relation,omega),cross_product(v,w))*.
% 299.99/300.65  132875[5:SpL:163.0,130556.0] || equal(symmetric_difference(u,v),omega) -> member(least(element_relation,omega),complement(intersection(u,v)))*.
% 299.99/300.65  133394[5:SpL:32.0,130610.0] || equal(restrict(u,v,w),ordinal_numbers)** -> member(least(element_relation,omega),cross_product(v,w))*.
% 299.99/300.65  134071[8:Res:133837.1,66086.1] || well_ordering(ordinal_numbers,complement(complement(compose(element_relation,ordinal_numbers))))* member(singleton(singleton(u)),element_relation)* -> .
% 299.99/300.65  134080[5:Res:133837.1,5.0] || well_ordering(ordinal_numbers,complement(u))* subclass(u,v)* -> member(singleton(singleton(w)),v)*.
% 299.99/300.65  134087[5:Res:133837.1,3617.0] || well_ordering(ordinal_numbers,complement(symmetric_difference(u,v))) -> member(singleton(singleton(w)),union(u,v))*.
% 299.99/300.65  134088[5:Res:133837.1,19559.0] || well_ordering(ordinal_numbers,complement(symmetric_difference(u,singleton(u))))* -> member(singleton(singleton(v)),successor(u))*.
% 299.99/300.65  134089[5:Res:133837.1,19676.0] || well_ordering(ordinal_numbers,complement(symmetric_difference(u,inverse(u))))* -> member(singleton(singleton(v)),symmetrization_of(u))*.
% 299.99/300.65  134163[5:SpL:30.0,134130.0] || well_ordering(ordinal_numbers,union(u,v)) well_ordering(ordinal_numbers,intersection(complement(u),complement(v)))* -> .
% 299.99/300.65  134405[5:SpL:163.0,132824.0] || equal(symmetric_difference(u,v),ordinal_numbers) -> member(least(element_relation,omega),complement(intersection(u,v)))*.
% 299.99/300.65  140464[5:MRR:140382.0,41183.1] ||  -> member(not_subclass_element(u,intersection(complement(v),u)),v)* subclass(u,intersection(complement(v),u)).
% 299.99/300.65  140863[8:Rew:140603.0,68971.0] || member(u,complement(v))* subclass(symmetric_difference(ordinal_numbers,v),w)* -> member(u,w)*.
% 299.99/300.65  146789[5:MRR:146743.0,8955.1] || member(u,ordinal_numbers) subclass(ordinal_numbers,complement(complement(v)))* -> member(sum_class(u),v)*.
% 299.99/300.65  147273[5:Res:143222.1,18794.1] || equal(intersection(u,v),omega) member(least(element_relation,omega),symmetric_difference(u,v))* -> .
% 299.99/300.65  147738[5:SpL:30.0,147314.1] || equal(intersection(complement(u),complement(v)),omega)** subclass(ordinal_numbers,union(u,v)) -> .
% 299.99/300.65  147793[5:SpL:30.0,147315.1] || equal(intersection(complement(u),complement(v)),omega)** subclass(omega,union(u,v)) -> .
% 299.99/300.65  147850[5:Res:10.1,18580.1] || equal(intersection(u,v),ordinal_numbers)** member(w,ordinal_numbers) -> member(sum_class(w),v)*.
% 299.99/300.65  147953[5:Res:10.1,18581.1] || equal(intersection(u,v),ordinal_numbers)** member(w,ordinal_numbers) -> member(sum_class(w),u)*.
% 299.99/300.65  148876[8:Res:148858.1,11.0] || subclass(u,inverse(subset_relation))* subclass(complement(subset_relation),u)* -> equal(complement(subset_relation),u).
% 299.99/300.65  148925[8:Res:148858.1,8840.1] || subclass(singleton(u),inverse(subset_relation))* member(u,ordinal_numbers) -> member(u,complement(subset_relation)).
% 299.99/300.65  148962[5:Res:10.1,28958.1] || equal(cross_product(u,v),rest_relation)** member(w,ordinal_numbers) -> member(rest_of(w),v)*.
% 299.99/300.65  151922[5:SpR:147905.0,33.0] ||  -> equal(restrict(complement(complement(cross_product(u,v))),u,v),complement(complement(cross_product(u,v))))**.
% 299.99/300.65  152063[5:Res:10.1,18829.0] || equal(restrict(u,v,w),ordinal_numbers)** -> member(unordered_pair(x,y),cross_product(v,w))*.
% 299.99/300.65  152245[5:MRR:152186.0,41183.1] || subclass(u,complement(complement(v))) -> member(not_subclass_element(u,w),v)* subclass(u,w).
% 299.99/300.65  152912[0:Res:10.1,19121.0] || equal(intersection(u,v),w)* -> subclass(w,x) member(not_subclass_element(w,x),u)*.
% 299.99/300.65  152963[5:SpL:30.0,151970.0] || subclass(ordinal_numbers,complement(union(u,v))) -> member(omega,intersection(complement(u),complement(v)))*.
% 299.99/300.65  153036[0:Res:10.1,19120.0] || equal(intersection(u,v),w)* -> subclass(w,x) member(not_subclass_element(w,x),v)*.
% 299.99/300.65  153052[5:Res:132293.0,19120.0] ||  -> subclass(complement(successor(u)),v) member(not_subclass_element(complement(successor(u)),v),complement(singleton(u)))*.
% 299.99/300.65  153053[5:Res:132294.0,19120.0] ||  -> subclass(complement(symmetrization_of(u)),v) member(not_subclass_element(complement(symmetrization_of(u)),v),complement(inverse(u)))*.
% 299.99/300.65  154266[5:SpL:30.0,151988.0] || member(u,complement(union(v,w))) -> member(u,intersection(complement(v),complement(w)))*.
% 299.99/300.65  154292[5:Res:51313.1,151988.0] || member(singleton(complement(complement(u))),subset_relation) -> member(first(singleton(complement(complement(u)))),u)*.
% 299.99/300.65  154307[5:Res:60219.0,151988.0] ||  -> subclass(u,complement(complement(complement(v)))) member(not_subclass_element(u,complement(complement(complement(v)))),v)*.
% 299.99/300.65  154352[5:Res:2504.1,151988.0] || subclass(ordered_pair(u,v),complement(complement(w)))* -> member(unordered_pair(u,singleton(v)),w).
% 299.99/300.65  155156[0:SpR:154737.1,163.0] || subclass(u,v) -> equal(intersection(complement(u),union(v,u)),symmetric_difference(v,u))**.
% 299.99/300.65  155169[0:SpR:154737.1,32.0] || subclass(cross_product(u,v),w)* -> equal(restrict(w,u,v),cross_product(u,v)).
% 299.99/300.65  155170[8:SpR:154737.1,15308.1] || subclass(inverse(u),u)* asymmetric(u,v) -> section(inverse(u),v,v)*.
% 299.99/300.65  155186[0:SpR:154737.1,3618.1] || subclass(u,v) member(w,symmetric_difference(v,u))* -> member(w,complement(u)).
% 299.99/300.65  155211[5:SpR:154737.1,132293.0] || subclass(complement(singleton(u)),complement(u)) -> subclass(complement(successor(u)),complement(singleton(u)))*.
% 299.99/300.65  155213[5:SpR:154737.1,132294.0] || subclass(complement(inverse(u)),complement(u)) -> subclass(complement(symmetrization_of(u)),complement(inverse(u)))*.
% 299.99/300.65  155293[0:SpL:154737.1,18794.1] || subclass(u,v) member(w,symmetric_difference(v,u))* member(w,u) -> .
% 299.99/300.65  155531[0:SpR:154945.0,3618.1] || member(u,symmetric_difference(v,intersection(v,w)))* -> member(u,complement(intersection(v,w))).
% 299.99/300.65  155629[0:SpL:154945.0,18794.1] || member(u,symmetric_difference(v,intersection(v,w)))* member(u,intersection(v,w)) -> .
% 299.99/300.65  155951[0:SpR:155147.0,3618.1] || member(u,symmetric_difference(v,intersection(w,v)))* -> member(u,complement(intersection(w,v))).
% 299.99/300.65  156051[0:SpL:155147.0,18794.1] || member(u,symmetric_difference(v,intersection(w,v)))* member(u,intersection(w,v)) -> .
% 299.99/300.65  156411[5:SpR:155665.0,154945.0] ||  -> equal(intersection(complement(subset_relation),symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers))),symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers)))**.
% 299.99/300.65  156420[5:SpL:155665.0,132824.0] || equal(symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers)),ordinal_numbers) -> member(least(element_relation,omega),complement(subset_relation))*.
% 299.99/300.65  156429[5:SpL:155665.0,125985.0] || subclass(ordinal_numbers,symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers)))* -> member(least(element_relation,omega),complement(subset_relation)).
% 299.99/300.65  156432[5:SpL:155665.0,8846.0] || subclass(ordinal_numbers,symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers)))* -> member(unordered_pair(u,v),complement(subset_relation))*.
% 299.99/300.65  156445[5:SpL:155665.0,125908.0] || subclass(omega,symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers)))* -> member(least(element_relation,omega),complement(subset_relation)).
% 299.99/300.65  156449[5:SpL:155665.0,130556.0] || equal(symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers)),omega) -> member(least(element_relation,omega),complement(subset_relation))*.
% 299.99/300.65  156520[5:SpR:155666.0,154945.0] ||  -> equal(intersection(complement(subset_relation),symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation)),symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation))**.
% 299.99/300.65  156529[5:SpL:155666.0,132824.0] || equal(symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation),ordinal_numbers) -> member(least(element_relation,omega),complement(subset_relation))*.
% 299.99/300.65  156538[5:SpL:155666.0,125985.0] || subclass(ordinal_numbers,symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation))* -> member(least(element_relation,omega),complement(subset_relation)).
% 299.99/300.65  156541[5:SpL:155666.0,8846.0] || subclass(ordinal_numbers,symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation))* -> member(unordered_pair(u,v),complement(subset_relation))*.
% 299.99/300.65  156554[5:SpL:155666.0,125908.0] || subclass(omega,symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation))* -> member(least(element_relation,omega),complement(subset_relation)).
% 299.99/300.65  156558[5:SpL:155666.0,130556.0] || equal(symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation),omega) -> member(least(element_relation,omega),complement(subset_relation))*.
% 299.99/300.65  156839[5:Res:8645.1,40594.1] || subclass(ordinal_numbers,u) member(u,ordinal_numbers) -> member(singleton(singleton(singleton(u))),element_relation)*.
% 299.99/300.65  156944[8:Res:156922.1,290.0] || member(not_subclass_element(complement(complement(subset_relation)),u),inverse(subset_relation))* -> subclass(complement(complement(subset_relation)),u).
% 299.99/300.65  159633[5:Res:9632.1,8785.0] || equal(complement(complement(rest_of(u))),ordinal_numbers) -> equal(restrict(u,singleton(v),ordinal_numbers),v)**.
% 299.99/300.65  147328[5:Res:10.1,28934.1] || equal(recursion_equation_functions(u),rest_relation)** member(v,ordinal_numbers) -> function(ordered_pair(v,rest_of(v)))*.
% 299.99/300.65  134240[8:SpL:117380.1,134134.0] operation(u) || well_ordering(ordinal_numbers,complement(cantor(u)))* -> member(v,cantor(cantor(u)))*.
% 299.99/300.65  155202[8:SpR:154737.1,116209.1] operation(u) || subclass(v,cantor(u)) -> equal(intersection(v,cantor(u)),v)**.
% 299.99/300.65  127980[5:Res:126679.1,8788.0] || subclass(omega,complement(complement(recursion_equation_functions(u))))* -> subclass(least(element_relation,omega),cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.65  51488[5:Res:51313.1,8788.0] || member(singleton(recursion_equation_functions(u)),subset_relation) -> subclass(first(singleton(recursion_equation_functions(u))),cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.65  79539[5:Res:60219.0,8788.0] ||  -> subclass(u,complement(recursion_equation_functions(v))) subclass(not_subclass_element(u,complement(recursion_equation_functions(v))),cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.65  96908[5:SpR:50855.1,96837.0] || member(singleton(u),subset_relation) -> subclass(u,complement(recursion_equation_functions(v)))* function(first(singleton(u))).
% 299.99/300.65  147349[5:SoR:19832.0,75.1] one_to_one(unordered_pair(u,v)) || member(v,ordinal_numbers) -> member(v,cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.65  147379[5:SoR:19790.0,75.1] one_to_one(unordered_pair(u,v)) || member(u,ordinal_numbers) -> member(u,cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.65  50035[5:SpL:18840.1,49.0] || member(u,subset_relation) member(u,successor_relation) -> equal(successor(first(u)),second(u))**.
% 299.99/300.65  50073[5:MRR:50072.2,18819.1] || member(u,subset_relation) equal(successor(first(u)),second(u))** -> member(u,successor_relation).
% 299.99/300.65  51296[5:SpL:50855.1,8843.1] || member(singleton(u),subset_relation)* subclass(ordinal_numbers,complement(v))* member(u,v)* -> .
% 299.99/300.65  81501[8:SpL:30.0,81488.1] || equal(intersection(complement(u),complement(v)),ordinal_numbers)** equal(union(u,v),domain_relation) -> .
% 299.99/300.65  146657[5:Res:10.1,66637.0] || equal(intersection(complement(u),complement(v)),ordinal_numbers)** member(omega,union(u,v)) -> .
% 299.99/300.65  147059[5:Res:143193.1,18794.1] || equal(intersection(u,v),ordinal_numbers) member(least(element_relation,omega),symmetric_difference(u,v))* -> .
% 299.99/300.65  156937[8:Res:156922.1,9876.0] || member(u,inverse(subset_relation))* subclass(complement(subset_relation),v)* well_ordering(ordinal_numbers,v) -> .
% 299.99/300.65  165078[8:SpL:116154.0,164087.1] operation(restrict(u,v,singleton(w))) || subclass(ordinal_numbers,segment(u,v,w))* -> .
% 299.99/300.65  165087[8:SpL:116154.0,164088.1] operation(restrict(u,v,singleton(w))) || equal(segment(u,v,w),ordinal_numbers)** -> .
% 299.99/300.65  165676[5:Res:143198.1,40594.1] || equal(u,ordinal_numbers) member(u,ordinal_numbers) -> member(singleton(singleton(singleton(u))),element_relation)*.
% 299.99/300.65  166827[5:SpL:30.0,147805.0] || equal(union(u,v),omega) equal(intersection(complement(u),complement(v)),omega)** -> .
% 299.99/300.65  167286[5:SpL:30.0,126664.1] || subclass(ordinal_numbers,intersection(complement(u),complement(v)))* subclass(omega,union(u,v)) -> .
% 299.99/300.65  167300[5:SpL:30.0,147100.1] || equal(intersection(complement(u),complement(v)),ordinal_numbers)** subclass(ordinal_numbers,union(u,v)) -> .
% 299.99/300.65  167357[5:SpL:30.0,147101.1] || equal(intersection(complement(u),complement(v)),ordinal_numbers)** subclass(omega,union(u,v)) -> .
% 299.99/300.65  173848[5:SpL:30.0,167369.0] || equal(union(u,v),omega) equal(intersection(complement(u),complement(v)),ordinal_numbers)** -> .
% 299.99/300.65  176793[8:Res:144409.1,5.0] || equal(symmetric_difference(ordinal_numbers,u),ordinal_numbers) subclass(complement(u),v)* -> member(omega,v).
% 299.99/300.65  162404[7:Res:13061.0,19111.1] || subclass(u,complement(omega)) -> equal(integer_of(not_subclass_element(u,v)),identity_relation)** subclass(u,v).
% 299.99/300.65  166178[7:MRR:166151.0,60996.1] ||  -> member(regular(complement(union(u,v))),complement(v))* equal(complement(union(u,v)),identity_relation).
% 299.99/300.65  166179[7:MRR:166150.0,60996.1] ||  -> member(regular(complement(union(u,v))),complement(u))* equal(complement(union(u,v)),identity_relation).
% 299.99/300.65  13367[7:Rew:13036.0,9942.1] || equal(complement(union(u,v)),ordinal_numbers) -> member(identity_relation,intersection(complement(u),complement(v)))*.
% 299.99/300.65  13368[7:Rew:13036.0,9905.1] || subclass(ordinal_numbers,union(u,v)) member(identity_relation,intersection(complement(u),complement(v)))* -> .
% 299.99/300.65  167512[7:SpL:30.0,163545.0] || subclass(ordinal_numbers,complement(union(u,v))) -> member(identity_relation,intersection(complement(u),complement(v)))*.
% 299.99/300.65  66845[7:SpR:50855.1,13059.1] || member(singleton(u),subset_relation) -> equal(integer_of(first(singleton(u))),identity_relation)** subclass(u,omega).
% 299.99/300.65  19700[8:Res:19277.2,77.1] single_valued_class(inverse(u)) function(u) || equal(inverse(u),identity_relation)** -> one_to_one(u).
% 299.99/300.65  83895[7:Res:66696.2,898.0] || subclass(ordinal_numbers,restrict(u,v,w))* -> equal(integer_of(x),identity_relation) member(x,u)*.
% 299.99/300.65  81644[8:Res:67606.0,13082.1] inductive(symmetric_difference(union(u,identity_relation),ordinal_numbers)) ||  -> member(identity_relation,complement(symmetric_difference(complement(u),ordinal_numbers)))*.
% 299.99/300.65  83275[7:Res:61019.0,28.1] || member(regular(complement(complement(complement(u)))),u)* -> equal(complement(complement(complement(u))),identity_relation).
% 299.99/300.65  83294[8:Res:61019.0,14679.1] || member(regular(complement(complement(inverse(subset_relation)))),subset_relation)* -> equal(complement(complement(inverse(subset_relation))),identity_relation).
% 299.99/300.65  160973[8:Rew:160480.0,82636.1] inductive(symmetric_difference(identity_relation,intersection(complement(u),ordinal_numbers))) ||  -> member(identity_relation,complement(union(u,identity_relation)))*.
% 299.99/300.65  160972[8:Rew:160498.0,82242.1] inductive(symmetric_difference(identity_relation,intersection(ordinal_numbers,complement(u)))) ||  -> member(identity_relation,complement(complement(complement(u))))*.
% 299.99/300.65  81729[8:Res:69385.0,13082.1] inductive(symmetric_difference(complement(intersection(u,ordinal_numbers)),ordinal_numbers)) ||  -> member(identity_relation,complement(symmetric_difference(u,ordinal_numbers)))*.
% 299.99/300.65  161065[8:Rew:140613.0,79564.0] ||  -> member(not_subclass_element(u,union(v,identity_relation)),symmetric_difference(ordinal_numbers,v))* subclass(u,union(v,identity_relation)).
% 299.99/300.65  162661[7:Res:13072.1,18794.1] || member(regular(intersection(u,v)),symmetric_difference(u,v))* -> equal(intersection(u,v),identity_relation).
% 299.99/300.65  83584[8:Res:79233.1,13082.1] operation(u) inductive(symmetric_difference(ordinal_numbers,domain_of(u))) ||  -> member(identity_relation,complement(cantor(u)))*.
% 299.99/300.65  167480[8:Res:13210.1,163154.0] ||  -> equal(intersection(u,symmetrization_of(identity_relation)),identity_relation) member(regular(intersection(u,symmetrization_of(identity_relation))),inverse(identity_relation))*.
% 299.99/300.65  167472[8:Res:13248.1,163154.0] ||  -> equal(intersection(symmetrization_of(identity_relation),u),identity_relation) member(regular(intersection(symmetrization_of(identity_relation),u)),inverse(identity_relation))*.
% 299.99/300.65  163098[8:SpR:162584.0,132294.0] ||  -> subclass(complement(symmetrization_of(complement(inverse(identity_relation)))),intersection(symmetrization_of(identity_relation),complement(inverse(complement(inverse(identity_relation))))))*.
% 299.99/300.65  163096[8:SpR:162584.0,132293.0] ||  -> subclass(complement(successor(complement(inverse(identity_relation)))),intersection(symmetrization_of(identity_relation),complement(singleton(complement(inverse(identity_relation))))))*.
% 299.99/300.65  167502[8:Res:2504.1,163154.0] || subclass(ordered_pair(u,v),symmetrization_of(identity_relation)) -> member(unordered_pair(u,singleton(v)),inverse(identity_relation))*.
% 299.99/300.65  164150[8:SpL:163119.0,19121.0] || subclass(u,symmetrization_of(identity_relation)) -> subclass(u,v) member(not_subclass_element(u,v),inverse(identity_relation))*.
% 299.99/300.65  15616[8:SpR:15614.1,154.1] || equal(rest_relation,domain_relation) member(identity_relation,recursion_equation_functions(u))* -> equal(compose(u,identity_relation),identity_relation).
% 299.99/300.65  61970[7:Res:13049.1,490.0] || subclass(ordinal_numbers,intersection(complement(u),complement(v)))* member(identity_relation,union(u,v)) -> .
% 299.99/300.65  83901[7:Res:66696.2,13105.0] || subclass(ordinal_numbers,u) -> equal(integer_of(regular(complement(u))),identity_relation)** equal(complement(u),identity_relation).
% 299.99/300.65  19722[8:Res:19531.1,11.0] || equal(sum_class(u),identity_relation) subclass(u,sum_class(u))* -> equal(sum_class(u),u).
% 299.99/300.65  161226[8:Rew:140613.0,67542.0] ||  -> subclass(symmetric_difference(union(u,identity_relation),complement(singleton(symmetric_difference(ordinal_numbers,u)))),successor(symmetric_difference(ordinal_numbers,u)))*.
% 299.99/300.65  161225[8:Rew:140613.0,67543.0] ||  -> subclass(symmetric_difference(union(u,identity_relation),complement(inverse(symmetric_difference(ordinal_numbers,u)))),symmetrization_of(symmetric_difference(ordinal_numbers,u)))*.
% 299.99/300.65  68883[8:SpL:66293.0,8846.0] || subclass(ordinal_numbers,symmetric_difference(complement(u),ordinal_numbers)) -> member(unordered_pair(v,w),union(u,identity_relation))*.
% 299.99/300.65  83182[8:SpL:66293.0,15572.0] || subclass(domain_relation,symmetric_difference(complement(u),ordinal_numbers)) -> member(ordered_pair(identity_relation,identity_relation),union(u,identity_relation))*.
% 299.99/300.65  83660[8:SpL:66293.0,83195.0] || equal(symmetric_difference(complement(u),ordinal_numbers),domain_relation) -> member(ordered_pair(identity_relation,identity_relation),union(u,identity_relation))*.
% 299.99/300.65  69482[7:Res:13125.2,56411.0] || subclass(omega,rest_of(u))* subclass(ordinal_numbers,complement(element_relation)) -> equal(integer_of(u),identity_relation).
% 299.99/300.65  64372[7:Res:13227.2,56411.0] || subclass(u,rest_of(regular(u)))* subclass(ordinal_numbers,complement(element_relation)) -> equal(u,identity_relation).
% 299.99/300.65  18753[8:Res:8642.1,14681.0] || subclass(ordinal_numbers,regular(u)) member(ordered_pair(v,w),u)* -> equal(u,identity_relation).
% 299.99/300.65  167254[8:Res:143222.1,14681.0] || equal(regular(u),omega) member(least(element_relation,omega),u)* -> equal(u,identity_relation).
% 299.99/300.65  167255[8:Res:143193.1,14681.0] || equal(regular(u),ordinal_numbers) member(least(element_relation,omega),u)* -> equal(u,identity_relation).
% 299.99/300.65  167258[8:Res:125731.1,14681.0] || subclass(ordinal_numbers,regular(u)) member(least(element_relation,omega),u)* -> equal(u,identity_relation).
% 299.99/300.65  167259[8:Res:125725.1,14681.0] || subclass(omega,regular(u)) member(least(element_relation,omega),u)* -> equal(u,identity_relation).
% 299.99/300.65  165373[14:Res:165168.1,18791.0] || equal(symmetric_difference(complement(u),complement(v)),singleton(identity_relation))** -> member(identity_relation,union(u,v)).
% 299.99/300.65  166902[8:Res:15426.1,18794.1] || subclass(domain_relation,intersection(u,v)) member(ordered_pair(identity_relation,identity_relation),symmetric_difference(u,v))* -> .
% 299.99/300.65  18827[8:Res:15426.1,897.0] || subclass(domain_relation,restrict(u,v,w))* -> member(ordered_pair(identity_relation,identity_relation),cross_product(v,w))*.
% 299.99/300.65  83615[8:SpL:32.0,83166.0] || equal(restrict(u,v,w),domain_relation)** -> member(ordered_pair(identity_relation,identity_relation),cross_product(v,w))*.
% 299.99/300.65  83171[8:SpL:163.0,15572.0] || subclass(domain_relation,symmetric_difference(u,v)) -> member(ordered_pair(identity_relation,identity_relation),complement(intersection(u,v)))*.
% 299.99/300.65  83647[8:SpL:163.0,83195.0] || equal(symmetric_difference(u,v),domain_relation) -> member(ordered_pair(identity_relation,identity_relation),complement(intersection(u,v)))*.
% 299.99/300.65  160968[8:Rew:141390.0,83658.0,116078.0,83658.0] || equal(symmetric_difference(ordinal_numbers,cantor(u)),domain_relation) -> member(ordered_pair(identity_relation,identity_relation),complement(cantor(u)))*.
% 299.99/300.65  160966[8:Rew:160496.0,83659.1] || equal(symmetric_difference(ordinal_numbers,complement(u)),domain_relation) -> member(ordered_pair(identity_relation,identity_relation),complement(complement(u)))*.
% 299.99/300.65  82289[8:Res:81336.1,56411.0] || subclass(domain_relation,complement(complement(rest_of(ordered_pair(identity_relation,identity_relation)))))* subclass(ordinal_numbers,complement(element_relation)) -> .
% 299.99/300.65  82279[8:Res:81336.1,161.0] || subclass(domain_relation,complement(complement(omega)))* -> equal(integer_of(ordered_pair(identity_relation,identity_relation)),ordered_pair(identity_relation,identity_relation)).
% 299.99/300.65  82268[8:Res:81336.1,8788.0] || subclass(domain_relation,complement(complement(recursion_equation_functions(u))))* -> subclass(ordered_pair(identity_relation,identity_relation),cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.65  18752[8:Res:15426.1,14681.0] || subclass(domain_relation,regular(u)) member(ordered_pair(identity_relation,identity_relation),u)* -> equal(u,identity_relation).
% 299.99/300.65  82290[8:Res:81336.1,898.0] || subclass(domain_relation,complement(complement(restrict(u,v,w))))* -> member(ordered_pair(identity_relation,identity_relation),u).
% 299.99/300.65  190548[18:Res:190442.1,18791.0] || equal(symmetric_difference(complement(u),complement(v)),symmetrization_of(identity_relation))** -> member(identity_relation,union(u,v)).
% 299.99/300.65  190657[18:Res:190593.1,18791.0] || equal(symmetric_difference(complement(u),complement(v)),inverse(identity_relation))** -> member(identity_relation,union(u,v)).
% 299.99/300.65  191941[18:Res:190515.1,18794.1] || subclass(ordinal_numbers,intersection(u,v)) member(regular(symmetrization_of(identity_relation)),symmetric_difference(u,v))* -> .
% 299.99/300.65  191960[18:Res:190515.1,897.0] || subclass(ordinal_numbers,restrict(u,v,w))* -> member(regular(symmetrization_of(identity_relation)),cross_product(v,w))*.
% 299.99/300.65  191972[18:Res:190515.1,14681.0] || subclass(ordinal_numbers,regular(u)) member(regular(symmetrization_of(identity_relation)),u)* -> equal(u,identity_relation).
% 299.99/300.65  192179[7:Res:192149.1,490.0] || equal(intersection(complement(u),complement(v)),ordinal_numbers)** member(identity_relation,union(u,v)) -> .
% 299.99/300.65  192409[8:SpR:188530.1,3618.1] || member(u,ordinals_with_null_class_as_identity) member(v,symmetric_difference(u,ordinal_numbers))* -> member(v,complement(u)).
% 299.99/300.65  192453[8:SpL:188530.1,18794.1] || member(u,ordinals_with_null_class_as_identity) member(v,symmetric_difference(u,ordinal_numbers))* member(v,u) -> .
% 299.99/300.65  192476[8:MRR:192475.1,41096.1] || member(u,ordinals_with_null_class_as_identity) member(v,complement(u)) -> member(v,symmetric_difference(u,ordinal_numbers))*.
% 299.99/300.65  192477[8:Rew:140613.0,192401.1,66141.0,192401.1,66141.0,192401.1] || member(u,ordinals_with_null_class_as_identity) -> equal(symmetric_difference(ordinal_numbers,symmetric_difference(u,ordinal_numbers)),symmetric_difference(complement(u),ordinal_numbers))**.
% 299.99/300.65  192800[7:Rew:192639.1,192790.2] || member(not_subclass_element(recursion_equation_functions(u),identity_relation),singleton(v))* -> function(v) subclass(recursion_equation_functions(u),identity_relation).
% 299.99/300.65  193199[8:Res:193179.0,9876.0] || subclass(inverse(singleton(u)),v)* well_ordering(ordinal_numbers,v) -> asymmetric(singleton(u),w)*.
% 299.99/300.65  193210[8:Res:193179.0,133836.0] || well_ordering(ordinal_numbers,inverse(singleton(singleton(singleton(u)))))* -> asymmetric(singleton(singleton(singleton(u))),v)*.
% 299.99/300.65  193215[8:Rew:50855.1,193197.2] || member(singleton(u),subset_relation) -> member(first(singleton(u)),inverse(u))* asymmetric(u,v)*.
% 299.99/300.65  193417[7:Res:13125.2,162318.0] || subclass(omega,inverse(subset_relation)) -> equal(integer_of(not_subclass_element(subset_relation,identity_relation)),identity_relation)** subclass(subset_relation,identity_relation).
% 299.99/300.65  133978[5:SpL:50855.1,133836.0] || member(singleton(u),subset_relation)* member(singleton(u),v)* well_ordering(ordinal_numbers,v) -> .
% 299.99/300.65  134060[5:SpR:50855.1,133837.1] || member(singleton(u),subset_relation)* well_ordering(ordinal_numbers,complement(v))* -> member(singleton(u),v)*.
% 299.99/300.65  19451[7:Res:19442.0,13070.0] || well_ordering(u,cross_product(ordinal_numbers,ordinal_numbers))* -> equal(subset_relation,identity_relation) member(least(u,subset_relation),subset_relation).
% 299.99/300.65  19450[7:Res:19442.0,13113.0] || well_ordering(u,cross_product(ordinal_numbers,ordinal_numbers)) -> equal(segment(u,subset_relation,least(u,subset_relation)),identity_relation)**.
% 299.99/300.65  130863[5:Res:8703.1,9876.0] || member(u,ordinal_numbers) subclass(unordered_pair(u,v),w)* well_ordering(ordinal_numbers,w) -> .
% 299.99/300.65  130864[5:Res:8704.1,9876.0] || member(u,ordinal_numbers) subclass(unordered_pair(v,u),w)* well_ordering(ordinal_numbers,w) -> .
% 299.99/300.65  130929[10:Res:76912.1,9876.0] || member(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers)* subclass(element_relation,u) well_ordering(ordinal_numbers,u)* -> .
% 299.99/300.65  65412[7:Res:13237.2,50033.0] || well_ordering(u,ordinal_numbers) equal(complement(least(u,subset_relation)),ordinal_numbers)** -> equal(subset_relation,identity_relation).
% 299.99/300.65  131204[5:Res:39607.2,3700.0] inductive(singleton(u)) || well_ordering(v,ordinal_numbers) -> equal(least(v,singleton(u)),u)**.
% 299.99/300.65  132204[2:Res:39609.2,152.0] inductive(recursion_equation_functions(u)) || well_ordering(v,recursion_equation_functions(u)) -> function(least(v,recursion_equation_functions(u)))*.
% 299.99/300.65  193981[14:Res:193906.1,5.0] || equal(inverse(subset_relation),singleton(identity_relation)) subclass(complement(subset_relation),u)* -> member(identity_relation,u).
% 299.99/300.65  193988[18:Res:193924.1,5.0] || equal(symmetrization_of(identity_relation),inverse(subset_relation)) subclass(complement(subset_relation),u)* -> member(identity_relation,u).
% 299.99/300.65  193995[18:Res:193927.1,5.0] || equal(inverse(subset_relation),inverse(identity_relation)) subclass(complement(subset_relation),u)* -> member(identity_relation,u).
% 299.99/300.65  194068[7:SpR:50855.1,162411.1] || member(singleton(u),subset_relation)* well_ordering(ordinal_numbers,omega) -> equal(integer_of(singleton(u)),identity_relation).
% 299.99/300.65  164154[8:SpL:163119.0,18581.1] || member(u,ordinal_numbers) subclass(ordinal_numbers,symmetrization_of(identity_relation)) -> member(sum_class(u),inverse(identity_relation))*.
% 299.99/300.65  194071[8:SpR:50855.1,163153.1] || member(singleton(u),subset_relation)* subclass(ordinal_numbers,symmetrization_of(identity_relation)) -> member(u,inverse(identity_relation)).
% 299.99/300.65  194076[8:Res:163153.1,5.0] || subclass(ordinal_numbers,symmetrization_of(identity_relation)) subclass(inverse(identity_relation),u) -> member(singleton(v),u)*.
% 299.99/300.65  194463[14:Res:165177.0,5.0] || subclass(symmetric_difference(ordinal_numbers,u),v)* -> member(identity_relation,union(u,identity_relation))* member(identity_relation,v).
% 299.99/300.65  194492[8:Res:163112.0,5.0] || subclass(complement(inverse(identity_relation)),u)* -> subclass(singleton(v),symmetrization_of(identity_relation))* member(v,u)*.
% 299.99/300.65  194497[8:Res:163112.0,7.0] ||  -> subclass(singleton(not_subclass_element(u,complement(inverse(identity_relation)))),symmetrization_of(identity_relation))* subclass(u,complement(inverse(identity_relation))).
% 299.99/300.65  194757[8:SpL:66293.0,132824.0] || equal(symmetric_difference(complement(u),ordinal_numbers),ordinal_numbers) -> member(least(element_relation,omega),union(u,identity_relation))*.
% 299.99/300.65  194765[8:SpL:66293.0,125985.0] || subclass(ordinal_numbers,symmetric_difference(complement(u),ordinal_numbers)) -> member(least(element_relation,omega),union(u,identity_relation))*.
% 299.99/300.65  194773[8:SpL:66293.0,125908.0] || subclass(omega,symmetric_difference(complement(u),ordinal_numbers)) -> member(least(element_relation,omega),union(u,identity_relation))*.
% 299.99/300.65  194775[8:SpL:66293.0,130556.0] || equal(symmetric_difference(complement(u),ordinal_numbers),omega) -> member(least(element_relation,omega),union(u,identity_relation))*.
% 299.99/300.65  194992[7:SpR:140603.0,13344.2] || asymmetric(ordinal_numbers,u) subclass(compose(identity_relation,identity_relation),identity_relation)* -> transitive(inverse(ordinal_numbers),u)*.
% 299.99/300.65  195134[14:SpL:30.0,195115.1] inductive(intersection(complement(u),complement(v))) || equal(union(u,v),singleton(identity_relation))** -> .
% 299.99/300.65  195590[16:Rew:195224.0,195199.1] || subclass(complement(singleton(identity_relation)),u)* -> subclass(singleton(v),singleton(identity_relation))* member(v,u)*.
% 299.99/300.65  195466[16:Rew:195224.0,163183.0] ||  -> subclass(complement(successor(complement(singleton(identity_relation)))),intersection(singleton(identity_relation),complement(singleton(complement(singleton(identity_relation))))))*.
% 299.99/300.65  195468[16:Rew:195224.0,163185.0] ||  -> subclass(complement(symmetrization_of(complement(singleton(identity_relation)))),intersection(singleton(identity_relation),complement(inverse(complement(singleton(identity_relation))))))*.
% 299.99/300.65  195841[8:SpR:140603.0,15666.1] || asymmetric(ordinal_numbers,singleton(u)) -> equal(domain__dfg(inverse(ordinal_numbers),singleton(u),u),single_valued3(identity_relation))**.
% 299.99/300.65  196071[8:Rew:66036.0,196045.1,30.0,196045.0] || equal(union(u,v),ordinal_numbers) -> equal(complement(intersection(union(u,v),ordinal_numbers)),identity_relation)**.
% 299.99/300.65  196076[18:Res:190510.1,66086.1] || subclass(inverse(identity_relation),complement(compose(element_relation,ordinal_numbers)))* member(regular(symmetrization_of(identity_relation)),element_relation) -> .
% 299.99/300.65  196082[18:Res:190510.1,5.0] || subclass(inverse(identity_relation),u)* subclass(u,v)* -> member(regular(symmetrization_of(identity_relation)),v)*.
% 299.99/300.65  196087[18:Res:190510.1,3617.0] || subclass(inverse(identity_relation),symmetric_difference(u,v)) -> member(regular(symmetrization_of(identity_relation)),union(u,v))*.
% 299.99/300.65  196088[18:Res:190510.1,19559.0] || subclass(inverse(identity_relation),symmetric_difference(u,singleton(u)))* -> member(regular(symmetrization_of(identity_relation)),successor(u)).
% 299.99/300.65  196089[18:Res:190510.1,19676.0] || subclass(inverse(identity_relation),symmetric_difference(u,inverse(u)))* -> member(regular(symmetrization_of(identity_relation)),symmetrization_of(u)).
% 299.99/300.65  196191[18:SpL:30.0,196166.1] inductive(intersection(complement(u),complement(v))) || equal(union(u,v),symmetrization_of(identity_relation))** -> .
% 299.99/300.65  196283[18:SpL:30.0,196256.1] inductive(intersection(complement(u),complement(v))) || equal(union(u,v),inverse(identity_relation))** -> .
% 299.99/300.65  197183[7:Obv:197166.0] ||  -> equal(regular(unordered_pair(u,v)),u)** equal(unordered_pair(u,v),identity_relation) member(v,ordinal_numbers).
% 299.99/300.65  197184[7:Obv:197174.0] ||  -> equal(regular(unordered_pair(u,v)),v)** equal(unordered_pair(u,v),identity_relation) member(u,ordinal_numbers).
% 299.99/300.65  197470[21:SpR:196546.1,116154.0] ||  -> equal(singleton(restrict(u,v,singleton(w))),identity_relation)** equal(segment(u,v,w),identity_relation).
% 299.99/300.65  197932[21:SpR:105.0,196554.1] || member(not_subclass_element(compose(u,inverse(u)),identity_relation),subset_relation)* -> equal(cantor(single_valued1(u)),identity_relation).
% 299.99/300.65  197977[21:SpR:106.0,196555.1] || member(not_subclass_element(compose(u,inverse(u)),identity_relation),subset_relation)* -> equal(cantor(single_valued2(u)),identity_relation).
% 299.99/300.65  197980[21:SpR:15272.1,196555.1] single_valued_class(u) || member(not_subclass_element(identity_relation,identity_relation),subset_relation)* -> equal(cantor(single_valued2(u)),identity_relation)**.
% 299.99/300.65  197981[21:SpR:15265.1,196555.1] function(u) || member(not_subclass_element(identity_relation,identity_relation),subset_relation)* -> equal(cantor(single_valued2(u)),identity_relation)**.
% 299.99/300.65  198703[21:Res:13237.2,198565.0] || well_ordering(u,ordinal_numbers) equal(rest_of(least(u,subset_relation)),rest_relation)** -> equal(subset_relation,identity_relation).
% 299.99/300.65  198299[21:Rew:197474.0,198219.2] || member(singleton(singleton(identity_relation)),element_relation)* -> equal(range_of(u),identity_relation) member(identity_relation,inverse(u))*.
% 299.99/300.65  134694[8:SpR:116239.0,116403.2] || member(u,ordinal_numbers) subclass(rest_relation,rest_of(inverse(v)))* -> member(u,range_of(v))*.
% 299.99/300.65  14770[8:SpR:14756.0,62.1] || member(ordered_pair(u,v),compose(w,identity_relation))* -> member(v,image(w,range_of(identity_relation))).
% 299.99/300.65  165543[15:Res:165526.1,18791.0] || subclass(ordinal_numbers,symmetric_difference(complement(u),complement(v)))* -> member(range_of(identity_relation),union(u,v)).
% 299.99/300.65  193613[15:Res:167474.1,5.0] || subclass(ordinal_numbers,symmetrization_of(identity_relation)) subclass(inverse(identity_relation),u) -> member(range_of(identity_relation),u)*.
% 299.99/300.65  191886[15:Res:165442.1,288.0] || subclass(ordinal_numbers,image(element_relation,complement(u))) member(sum_class(range_of(identity_relation)),power_class(u))* -> .
% 299.99/300.65  191876[15:Res:165442.1,897.0] || subclass(ordinal_numbers,restrict(u,v,w))* -> member(sum_class(range_of(identity_relation)),cross_product(v,w))*.
% 299.99/300.65  191857[15:Res:165442.1,18794.1] || subclass(ordinal_numbers,intersection(u,v)) member(sum_class(range_of(identity_relation)),symmetric_difference(u,v))* -> .
% 299.99/300.65  191888[15:Res:165442.1,14681.0] || subclass(ordinal_numbers,regular(u)) member(sum_class(range_of(identity_relation)),u)* -> equal(u,identity_relation).
% 299.99/300.65  145884[5:SpL:145758.0,56504.0] || member(inverse(cross_product(u,ordinal_numbers)),image(ordinal_numbers,u))* subclass(ordinal_numbers,complement(element_relation)) -> .
% 299.99/300.65  145880[8:SpR:145758.0,117217.1] operation(cross_product(u,ordinal_numbers)) ||  -> subclass(image(ordinal_numbers,u),cantor(cantor(cross_product(u,ordinal_numbers))))*.
% 299.99/300.65  83305[7:Rew:59.0,83272.1] ||  -> member(regular(complement(power_class(u))),image(element_relation,complement(u)))* equal(complement(power_class(u)),identity_relation).
% 299.99/300.65  194696[14:Res:165178.0,5.0] || subclass(image(element_relation,complement(u)),v)* -> member(identity_relation,power_class(u)) member(identity_relation,v).
% 299.99/300.65  18449[8:Res:15426.1,288.0] || subclass(domain_relation,image(element_relation,complement(u))) member(ordered_pair(identity_relation,identity_relation),power_class(u))* -> .
% 299.99/300.65  125928[5:Res:125725.1,288.0] || subclass(omega,image(element_relation,complement(u))) member(least(element_relation,omega),power_class(u))* -> .
% 299.99/300.65  147300[5:Res:143222.1,288.0] || equal(image(element_relation,complement(u)),omega) member(least(element_relation,omega),power_class(u))* -> .
% 299.99/300.65  134011[5:Res:79577.0,133836.0] || well_ordering(ordinal_numbers,image(element_relation,complement(u))) -> subclass(singleton(singleton(singleton(v))),power_class(u))*.
% 299.99/300.65  126005[5:Res:125731.1,288.0] || subclass(ordinal_numbers,image(element_relation,complement(u))) member(least(element_relation,omega),power_class(u))* -> .
% 299.99/300.65  18450[5:Res:8642.1,288.0] || subclass(ordinal_numbers,image(element_relation,complement(u))) member(ordered_pair(v,w),power_class(u))* -> .
% 299.99/300.65  191970[18:Res:190515.1,288.0] || subclass(ordinal_numbers,image(element_relation,complement(u))) member(regular(symmetrization_of(identity_relation)),power_class(u))* -> .
% 299.99/300.65  147086[5:Res:143193.1,288.0] || equal(image(element_relation,complement(u)),ordinal_numbers) member(least(element_relation,omega),power_class(u))* -> .
% 299.99/300.65  9933[5:SpL:189.0,9922.1] inductive(image(element_relation,power_class(u))) || equal(power_class(image(element_relation,complement(u))),ordinal_numbers)** -> .
% 299.99/300.65  166762[5:SpL:189.0,166753.1] inductive(image(element_relation,power_class(u))) || equal(power_class(image(element_relation,complement(u))),omega)** -> .
% 299.99/300.65  193532[8:SpL:162038.0,134130.0] || well_ordering(ordinal_numbers,power_class(complement(inverse(identity_relation)))) well_ordering(ordinal_numbers,image(element_relation,symmetrization_of(identity_relation)))* -> .
% 299.99/300.65  193513[8:SpL:162038.0,8712.0] || subclass(ordinal_numbers,power_class(complement(inverse(identity_relation)))) member(omega,image(element_relation,symmetrization_of(identity_relation)))* -> .
% 299.99/300.65  193516[8:SpL:162038.0,8738.0] || equal(complement(power_class(complement(inverse(identity_relation)))),ordinal_numbers) -> member(omega,image(element_relation,symmetrization_of(identity_relation)))*.
% 299.99/300.65  193518[8:SpL:162038.0,151970.0] || subclass(ordinal_numbers,complement(power_class(complement(inverse(identity_relation)))))* -> member(omega,image(element_relation,symmetrization_of(identity_relation))).
% 299.99/300.65  193512[8:SpL:162038.0,50032.1] || member(image(element_relation,symmetrization_of(identity_relation)),subset_relation)* subclass(ordinal_numbers,power_class(complement(inverse(identity_relation)))) -> .
% 299.99/300.65  193511[8:SpL:162038.0,63019.1] || subclass(domain_relation,image(element_relation,symmetrization_of(identity_relation)))* subclass(ordinal_numbers,power_class(complement(inverse(identity_relation)))) -> .
% 299.99/300.65  193521[8:SpL:162038.0,81322.1] || subclass(domain_relation,image(element_relation,symmetrization_of(identity_relation)))* subclass(domain_relation,power_class(complement(inverse(identity_relation)))) -> .
% 299.99/300.65  193510[8:SpL:162038.0,127130.1] || subclass(omega,image(element_relation,symmetrization_of(identity_relation)))* subclass(ordinal_numbers,power_class(complement(inverse(identity_relation)))) -> .
% 299.99/300.65  193530[8:SpL:162038.0,126665.1] || subclass(omega,image(element_relation,symmetrization_of(identity_relation)))* subclass(omega,power_class(complement(inverse(identity_relation)))) -> .
% 299.99/300.65  193508[8:SpL:162038.0,9488.1] || subclass(ordinal_numbers,image(element_relation,symmetrization_of(identity_relation)))* subclass(ordinal_numbers,power_class(complement(inverse(identity_relation)))) -> .
% 299.99/300.65  193520[8:SpL:162038.0,81326.1] || subclass(ordinal_numbers,image(element_relation,symmetrization_of(identity_relation))) subclass(domain_relation,power_class(complement(inverse(identity_relation))))* -> .
% 299.99/300.65  193528[8:SpL:162038.0,126664.1] || subclass(ordinal_numbers,image(element_relation,symmetrization_of(identity_relation))) subclass(omega,power_class(complement(inverse(identity_relation))))* -> .
% 299.99/300.65  193523[8:SpL:162038.0,81412.1] || equal(image(element_relation,symmetrization_of(identity_relation)),domain_relation)** equal(power_class(complement(inverse(identity_relation))),domain_relation) -> .
% 299.99/300.65  193509[8:SpL:162038.0,147314.1] || equal(image(element_relation,symmetrization_of(identity_relation)),omega) subclass(ordinal_numbers,power_class(complement(inverse(identity_relation))))* -> .
% 299.99/300.65  193529[8:SpL:162038.0,147315.1] || equal(image(element_relation,symmetrization_of(identity_relation)),omega) subclass(omega,power_class(complement(inverse(identity_relation))))* -> .
% 299.99/300.65  193535[8:SpL:162038.0,147805.0] || equal(power_class(complement(inverse(identity_relation))),omega) equal(image(element_relation,symmetrization_of(identity_relation)),omega)** -> .
% 299.99/300.65  193507[8:SpL:162038.0,147100.1] || equal(image(element_relation,symmetrization_of(identity_relation)),ordinal_numbers) subclass(ordinal_numbers,power_class(complement(inverse(identity_relation))))* -> .
% 299.99/300.65  193522[8:SpL:162038.0,81488.1] || equal(image(element_relation,symmetrization_of(identity_relation)),ordinal_numbers)** equal(power_class(complement(inverse(identity_relation))),domain_relation) -> .
% 299.99/300.65  193527[8:SpL:162038.0,147101.1] || equal(image(element_relation,symmetrization_of(identity_relation)),ordinal_numbers) subclass(omega,power_class(complement(inverse(identity_relation))))* -> .
% 299.99/300.65  193534[8:SpL:162038.0,167369.0] || equal(power_class(complement(inverse(identity_relation))),omega) equal(image(element_relation,symmetrization_of(identity_relation)),ordinal_numbers)** -> .
% 299.99/300.65  193505[8:SpL:162038.0,13048.0] || subclass(ordinal_numbers,power_class(complement(inverse(identity_relation)))) member(identity_relation,image(element_relation,symmetrization_of(identity_relation)))* -> .
% 299.99/300.65  193514[8:SpL:162038.0,13046.0] || equal(complement(power_class(complement(inverse(identity_relation)))),ordinal_numbers) -> member(identity_relation,image(element_relation,symmetrization_of(identity_relation)))*.
% 299.99/300.65  193517[8:SpL:162038.0,163545.0] || subclass(ordinal_numbers,complement(power_class(complement(inverse(identity_relation)))))* -> member(identity_relation,image(element_relation,symmetrization_of(identity_relation))).
% 299.99/300.65  193470[8:SpR:162038.0,19421.0] ||  -> subclass(symmetric_difference(power_class(complement(inverse(identity_relation))),complement(u)),union(image(element_relation,symmetrization_of(identity_relation)),u))*.
% 299.99/300.65  193489[8:SpR:162038.0,19421.0] ||  -> subclass(symmetric_difference(complement(u),power_class(complement(inverse(identity_relation)))),union(u,image(element_relation,symmetrization_of(identity_relation))))*.
% 299.99/300.65  163145[8:SpL:162584.0,288.0] || member(u,image(element_relation,symmetrization_of(identity_relation)))* member(u,power_class(complement(inverse(identity_relation)))) -> .
% 299.99/300.65  193545[8:SpL:162038.0,151988.0] || member(u,complement(power_class(complement(inverse(identity_relation)))))* -> member(u,image(element_relation,symmetrization_of(identity_relation))).
% 299.99/300.65  66983[8:SpR:189.0,66340.0] ||  -> subclass(symmetric_difference(power_class(image(element_relation,complement(u))),ordinal_numbers),union(image(element_relation,power_class(u)),identity_relation))*.
% 299.99/300.65  162358[7:Res:13056.1,941.1] inductive(power_class(image(element_relation,complement(u)))) || member(identity_relation,image(element_relation,power_class(u)))* -> .
% 299.99/300.65  166263[7:Res:130711.0,13082.1] inductive(complement(power_class(image(element_relation,complement(u))))) ||  -> member(identity_relation,image(element_relation,power_class(u)))*.
% 299.99/300.65  167609[14:SpL:189.0,167597.0] || well_ordering(ordinal_numbers,power_class(image(element_relation,complement(u))))* -> member(identity_relation,image(element_relation,power_class(u))).
% 299.99/300.65  144398[8:SpR:189.0,140613.0] ||  -> equal(intersection(power_class(image(element_relation,complement(u))),ordinal_numbers),symmetric_difference(ordinal_numbers,image(element_relation,power_class(u))))**.
% 299.99/300.65  81131[5:SpR:189.0,79560.1] ||  -> member(u,image(element_relation,power_class(v))) subclass(singleton(u),power_class(image(element_relation,complement(v))))*.
% 299.99/300.65  130744[5:SpR:189.0,130710.0] ||  -> subclass(complement(power_class(image(element_relation,power_class(u)))),image(element_relation,power_class(image(element_relation,complement(u)))))*.
% 299.99/300.65  142402[8:Rew:141402.0,121627.0] ||  -> subclass(symmetric_difference(ordinal_numbers,image(element_relation,union(u,v))),power_class(intersection(complement(u),complement(v))))*.
% 299.99/300.65  164859[8:SpR:160491.0,130711.0] ||  -> subclass(complement(power_class(image(element_relation,union(u,identity_relation)))),image(element_relation,power_class(symmetric_difference(ordinal_numbers,u))))*.
% 299.99/300.65  164882[8:SpR:160491.0,79577.0] ||  -> member(u,image(element_relation,union(v,identity_relation)))* subclass(singleton(u),power_class(symmetric_difference(ordinal_numbers,v))).
% 299.99/300.65  198471[21:Res:8976.2,197870.1] function(u) || member(v,ordinal_numbers) equal(rest_of(image(u,v)),rest_relation)** -> .
% 299.99/300.65  136327[8:SpR:8649.0,135061.1] || equal(rest_of(inverse(restrict(u,v,ordinal_numbers))),rest_relation)** -> subclass(w,image(u,v))*.
% 299.99/300.65  19730[8:Rew:72.0,19716.0] || equal(apply(u,v),identity_relation) -> subclass(apply(u,v),image(u,singleton(v)))*.
% 299.99/300.65  49191[5:Res:8642.1,9471.0] || subclass(ordinal_numbers,compose(u,v)) -> subclass(w,image(u,image(v,singleton(x))))*.
% 299.99/300.65  195375[16:Rew:195224.0,193368.1] || well_ordering(ordinal_numbers,power_class(complement(singleton(identity_relation)))) well_ordering(ordinal_numbers,image(element_relation,singleton(identity_relation)))* -> .
% 299.99/300.65  195371[16:Rew:195224.0,193354.1] || subclass(ordinal_numbers,complement(power_class(complement(singleton(identity_relation)))))* -> member(omega,image(element_relation,singleton(identity_relation))).
% 299.99/300.65  195372[16:Rew:195224.0,193352.1] || equal(complement(power_class(complement(singleton(identity_relation)))),ordinal_numbers) -> member(omega,image(element_relation,singleton(identity_relation)))*.
% 299.99/300.65  195373[16:Rew:195224.0,193349.1] || subclass(ordinal_numbers,power_class(complement(singleton(identity_relation)))) member(omega,image(element_relation,singleton(identity_relation)))* -> .
% 299.99/300.65  195369[16:Rew:195224.0,193348.0] || member(image(element_relation,singleton(identity_relation)),subset_relation)* subclass(ordinal_numbers,power_class(complement(singleton(identity_relation)))) -> .
% 299.99/300.65  195367[16:Rew:195224.0,193357.0] || subclass(domain_relation,image(element_relation,singleton(identity_relation)))* subclass(domain_relation,power_class(complement(singleton(identity_relation)))) -> .
% 299.99/300.65  195368[16:Rew:195224.0,193347.0] || subclass(domain_relation,image(element_relation,singleton(identity_relation)))* subclass(ordinal_numbers,power_class(complement(singleton(identity_relation)))) -> .
% 299.99/300.65  195365[16:Rew:195224.0,193366.0] || subclass(omega,image(element_relation,singleton(identity_relation)))* subclass(omega,power_class(complement(singleton(identity_relation)))) -> .
% 299.99/300.65  195366[16:Rew:195224.0,193346.0] || subclass(omega,image(element_relation,singleton(identity_relation)))* subclass(ordinal_numbers,power_class(complement(singleton(identity_relation)))) -> .
% 299.99/300.65  195362[16:Rew:195224.0,193364.0] || subclass(ordinal_numbers,image(element_relation,singleton(identity_relation))) subclass(omega,power_class(complement(singleton(identity_relation))))* -> .
% 299.99/300.65  195363[16:Rew:195224.0,193356.0] || subclass(ordinal_numbers,image(element_relation,singleton(identity_relation))) subclass(domain_relation,power_class(complement(singleton(identity_relation))))* -> .
% 299.99/300.65  195364[16:Rew:195224.0,193344.0] || subclass(ordinal_numbers,image(element_relation,singleton(identity_relation)))* subclass(ordinal_numbers,power_class(complement(singleton(identity_relation)))) -> .
% 299.99/300.65  195360[16:Rew:195224.0,193359.0] || equal(image(element_relation,singleton(identity_relation)),domain_relation)** equal(power_class(complement(singleton(identity_relation))),domain_relation) -> .
% 299.99/300.65  195356[16:Rew:195224.0,193371.1] || equal(power_class(complement(singleton(identity_relation))),omega) equal(image(element_relation,singleton(identity_relation)),omega)** -> .
% 299.99/300.65  195357[16:Rew:195224.0,193365.0] || equal(image(element_relation,singleton(identity_relation)),omega) subclass(omega,power_class(complement(singleton(identity_relation))))* -> .
% 299.99/300.65  195358[16:Rew:195224.0,193345.0] || equal(image(element_relation,singleton(identity_relation)),omega) subclass(ordinal_numbers,power_class(complement(singleton(identity_relation))))* -> .
% 299.99/300.65  195351[16:Rew:195224.0,193370.1] || equal(power_class(complement(singleton(identity_relation))),omega) equal(image(element_relation,singleton(identity_relation)),ordinal_numbers)** -> .
% 299.99/300.65  195352[16:Rew:195224.0,193363.0] || equal(image(element_relation,singleton(identity_relation)),ordinal_numbers) subclass(omega,power_class(complement(singleton(identity_relation))))* -> .
% 299.99/300.65  195353[16:Rew:195224.0,193358.0] || equal(image(element_relation,singleton(identity_relation)),ordinal_numbers)** equal(power_class(complement(singleton(identity_relation))),domain_relation) -> .
% 299.99/300.65  195354[16:Rew:195224.0,193343.0] || equal(image(element_relation,singleton(identity_relation)),ordinal_numbers) subclass(ordinal_numbers,power_class(complement(singleton(identity_relation))))* -> .
% 299.99/300.65  195328[16:Rew:195224.0,193325.0] ||  -> subclass(symmetric_difference(complement(u),power_class(complement(singleton(identity_relation)))),union(u,image(element_relation,singleton(identity_relation))))*.
% 299.99/300.65  195322[16:Rew:195224.0,193306.0] ||  -> subclass(symmetric_difference(power_class(complement(singleton(identity_relation))),complement(u)),union(image(element_relation,singleton(identity_relation)),u))*.
% 299.99/300.65  195317[16:Rew:195224.0,193381.1] || member(u,complement(power_class(complement(singleton(identity_relation)))))* -> member(u,image(element_relation,singleton(identity_relation))).
% 299.99/300.65  195319[16:Rew:195224.0,163232.0] || member(u,image(element_relation,singleton(identity_relation)))* member(u,power_class(complement(singleton(identity_relation)))) -> .
% 299.99/300.65  195343[16:Rew:195224.0,193353.1] || subclass(ordinal_numbers,complement(power_class(complement(singleton(identity_relation)))))* -> member(identity_relation,image(element_relation,singleton(identity_relation))).
% 299.99/300.65  195344[16:Rew:195224.0,193350.1] || equal(complement(power_class(complement(singleton(identity_relation)))),ordinal_numbers) -> member(identity_relation,image(element_relation,singleton(identity_relation)))*.
% 299.99/300.65  195345[16:Rew:195224.0,193341.1] || subclass(ordinal_numbers,power_class(complement(singleton(identity_relation)))) member(identity_relation,image(element_relation,singleton(identity_relation)))* -> .
% 299.99/300.65  164152[8:SpL:163119.0,18545.1] || member(u,ordinal_numbers) subclass(ordinal_numbers,symmetrization_of(identity_relation)) -> member(power_class(u),inverse(identity_relation))*.
% 299.99/300.65  146859[5:MRR:146813.0,8956.1] || member(u,ordinal_numbers) subclass(ordinal_numbers,complement(complement(v)))* -> member(power_class(u),v)*.
% 299.99/300.65  196291[18:SpL:162038.0,196256.1] inductive(image(element_relation,symmetrization_of(identity_relation))) || equal(power_class(complement(inverse(identity_relation))),inverse(identity_relation))** -> .
% 299.99/300.65  196198[18:SpL:162038.0,196166.1] inductive(image(element_relation,symmetrization_of(identity_relation))) || equal(power_class(complement(inverse(identity_relation))),symmetrization_of(identity_relation))** -> .
% 299.99/300.65  195143[14:SpL:162038.0,195115.1] inductive(image(element_relation,symmetrization_of(identity_relation))) || equal(power_class(complement(inverse(identity_relation))),singleton(identity_relation))** -> .
% 299.99/300.65  196292[18:SpL:195257.0,196256.1] inductive(image(element_relation,singleton(identity_relation))) || equal(power_class(complement(singleton(identity_relation))),inverse(identity_relation))** -> .
% 299.99/300.65  196199[18:SpL:195257.0,196166.1] inductive(image(element_relation,singleton(identity_relation))) || equal(power_class(complement(singleton(identity_relation))),symmetrization_of(identity_relation))** -> .
% 299.99/300.65  195142[14:SpL:162037.0,195115.1] inductive(image(element_relation,successor(identity_relation))) || equal(power_class(complement(singleton(identity_relation))),singleton(identity_relation))** -> .
% 299.99/300.65  195983[16:SpL:195257.0,195115.1] inductive(image(element_relation,singleton(identity_relation))) || equal(power_class(complement(singleton(identity_relation))),singleton(identity_relation))** -> .
% 299.99/300.65  148270[5:Res:10.1,18544.1] || equal(intersection(u,v),ordinal_numbers)** member(w,ordinal_numbers) -> member(power_class(w),v)*.
% 299.99/300.65  148543[5:Res:10.1,18545.1] || equal(intersection(u,v),ordinal_numbers)** member(w,ordinal_numbers) -> member(power_class(w),u)*.
% 299.99/300.65  61930[7:Res:13069.2,50033.0] || member(subset_relation,ordinal_numbers) equal(complement(apply(choice,subset_relation)),ordinal_numbers)** -> equal(subset_relation,identity_relation).
% 299.99/300.65  194664[18:MRR:194663.2,190496.0] || member(symmetrization_of(identity_relation),ordinal_numbers) member(apply(choice,symmetrization_of(identity_relation)),complement(inverse(identity_relation)))* -> .
% 299.99/300.65  198525[21:MRR:198483.1,8638.0] || member(u,ordinal_numbers) equal(rest_of(apply(choice,u)),rest_relation)** -> equal(u,identity_relation).
% 299.99/300.65  65624[7:Rew:63616.2,65623.2] || member(singleton(u),subset_relation)* -> equal(u,identity_relation) equal(apply(choice,u),regular(u)).
% 299.99/300.65  197466[21:SpR:196546.1,117380.1] operation(u) ||  -> equal(singleton(cantor(u)),identity_relation)** equal(cross_product(identity_relation,identity_relation),cantor(u))*.
% 299.99/300.65  63616[7:Rew:50855.1,63612.1] || member(singleton(u),subset_relation)* -> equal(u,identity_relation) equal(first(singleton(u)),regular(u)).
% 299.99/300.65  194744[8:SpR:66293.0,188530.1] || member(union(u,identity_relation),ordinals_with_null_class_as_identity)* -> equal(symmetric_difference(complement(u),ordinal_numbers),union(u,identity_relation)).
% 299.99/300.65  165006[8:SpR:161038.2,143170.0] || member(u,ordinal_numbers) -> member(u,cantor(ordinal_numbers)) equal(cross_product(singleton(u),ordinal_numbers),identity_relation)**.
% 299.99/300.65  136419[8:Rew:136362.1,136380.2] operation(u) || equal(rest_of(inverse(u)),rest_relation)** -> equal(cantor(cantor(u)),ordinal_numbers).
% 299.99/300.65  204048[8:Res:192333.1,5.0] || equal(symmetric_difference(ordinal_numbers,u),ordinal_numbers) subclass(complement(u),v)* -> member(identity_relation,v).
% 299.99/300.65  204144[8:Res:204134.1,290.0] || member(not_subclass_element(complement(symmetrization_of(identity_relation)),u),inverse(identity_relation))* -> subclass(complement(symmetrization_of(identity_relation)),u).
% 299.99/300.65  204167[18:Res:194549.1,66086.1] || subclass(symmetrization_of(identity_relation),complement(compose(element_relation,ordinal_numbers)))* member(regular(symmetrization_of(identity_relation)),element_relation) -> .
% 299.99/300.65  204174[18:Res:194549.1,5.0] || subclass(symmetrization_of(identity_relation),u)* subclass(u,v)* -> member(regular(symmetrization_of(identity_relation)),v)*.
% 299.99/300.65  204179[18:Res:194549.1,3617.0] || subclass(symmetrization_of(identity_relation),symmetric_difference(u,v)) -> member(regular(symmetrization_of(identity_relation)),union(u,v))*.
% 299.99/300.65  204180[18:Res:194549.1,19559.0] || subclass(symmetrization_of(identity_relation),symmetric_difference(u,singleton(u)))* -> member(regular(symmetrization_of(identity_relation)),successor(u)).
% 299.99/300.65  204181[18:Res:194549.1,19676.0] || subclass(symmetrization_of(identity_relation),symmetric_difference(u,inverse(u)))* -> member(regular(symmetrization_of(identity_relation)),symmetrization_of(u)).
% 299.99/300.65  204629[21:Res:196904.1,66086.1] || subclass(domain_relation,complement(compose(element_relation,ordinal_numbers))) member(singleton(singleton(singleton(identity_relation))),element_relation)* -> .
% 299.99/300.65  204636[21:Res:196904.1,5.0] || subclass(domain_relation,u)* subclass(u,v)* -> member(singleton(singleton(singleton(identity_relation))),v)*.
% 299.99/300.65  204641[21:Res:196904.1,3617.0] || subclass(domain_relation,symmetric_difference(u,v)) -> member(singleton(singleton(singleton(identity_relation))),union(u,v))*.
% 299.99/300.65  204642[21:Res:196904.1,19559.0] || subclass(domain_relation,symmetric_difference(u,singleton(u)))* -> member(singleton(singleton(singleton(identity_relation))),successor(u))*.
% 299.99/300.65  204643[21:Res:196904.1,19676.0] || subclass(domain_relation,symmetric_difference(u,inverse(u)))* -> member(singleton(singleton(singleton(identity_relation))),symmetrization_of(u))*.
% 299.99/300.65  204663[21:Res:196904.1,161.0] || subclass(domain_relation,omega) -> equal(integer_of(singleton(singleton(singleton(identity_relation)))),singleton(singleton(singleton(identity_relation))))**.
% 299.99/300.65  204687[21:MRR:204684.1,8655.0] || subclass(domain_relation,singleton(singleton(identity_relation))) -> member(singleton(singleton(singleton(singleton(singleton(identity_relation))))),element_relation)*.
% 299.99/300.65  204975[21:SpL:72.0,198460.1] || member(image(u,singleton(v)),ordinal_numbers)* equal(rest_of(apply(u,v)),rest_relation) -> .
% 299.99/300.65  204994[21:SpL:15528.0,198464.1] || member(not_subclass_element(identity_relation,identity_relation),subset_relation) equal(rest_of(range__dfg(identity_relation,u,v)),rest_relation)** -> .
% 299.99/300.65  205169[15:Res:195033.1,66086.1] || equal(complement(complement(complement(compose(element_relation,ordinal_numbers)))),ordinal_numbers)** member(range_of(identity_relation),element_relation) -> .
% 299.99/300.65  205176[15:Res:195033.1,5.0] || equal(complement(complement(u)),ordinal_numbers)** subclass(u,v)* -> member(range_of(identity_relation),v)*.
% 299.99/300.65  205181[15:Res:195033.1,3617.0] || equal(complement(complement(symmetric_difference(u,v))),ordinal_numbers) -> member(range_of(identity_relation),union(u,v))*.
% 299.99/300.65  205182[15:Res:195033.1,19559.0] || equal(complement(complement(symmetric_difference(u,singleton(u)))),ordinal_numbers)** -> member(range_of(identity_relation),successor(u)).
% 299.99/300.65  205183[15:Res:195033.1,19676.0] || equal(complement(complement(symmetric_difference(u,inverse(u)))),ordinal_numbers)** -> member(range_of(identity_relation),symmetrization_of(u)).
% 299.99/300.65  205461[21:Res:13125.2,196624.0] || subclass(omega,domain_relation) -> equal(integer_of(singleton(singleton(singleton(u)))),identity_relation)** equal(identity_relation,u).
% 299.99/300.65  205519[22:Res:3618.1,205501.0] || member(singleton(identity_relation),symmetric_difference(u,v)) well_ordering(ordinal_numbers,complement(intersection(u,v)))* -> .
% 299.99/300.65  205555[22:MRR:205524.0,8655.0] || well_ordering(ordinal_numbers,intersection(complement(u),complement(v)))* -> member(singleton(identity_relation),union(u,v)).
% 299.99/300.65  205559[22:SpL:30.0,205502.0] || well_ordering(ordinal_numbers,union(u,v)) -> member(singleton(identity_relation),intersection(complement(u),complement(v)))*.
% 299.99/300.65  205566[22:SpL:162038.0,205502.0] || well_ordering(ordinal_numbers,power_class(complement(inverse(identity_relation)))) -> member(singleton(identity_relation),image(element_relation,symmetrization_of(identity_relation)))*.
% 299.99/300.65  205567[22:SpL:195257.0,205502.0] || well_ordering(ordinal_numbers,power_class(complement(singleton(identity_relation)))) -> member(singleton(identity_relation),image(element_relation,singleton(identity_relation)))*.
% 299.99/300.65  13624[7:Rew:13036.0,13435.2] inductive(regular(recursion_equation_functions(u))) ||  -> equal(recursion_equation_functions(u),identity_relation)** member(identity_relation,cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.65  130866[5:Res:18819.1,9876.0] || member(u,subset_relation)* subclass(cross_product(ordinal_numbers,ordinal_numbers),v)* well_ordering(ordinal_numbers,v) -> .
% 299.99/300.65  205769[22:SpR:30.0,205578.1] ||  -> member(singleton(identity_relation),intersection(complement(u),complement(v)))* member(singleton(identity_relation),union(u,v)).
% 299.99/300.65  205776[22:SpR:162038.0,205578.1] ||  -> member(singleton(identity_relation),image(element_relation,symmetrization_of(identity_relation)))* member(singleton(identity_relation),power_class(complement(inverse(identity_relation)))).
% 299.99/300.65  205777[22:SpR:195257.0,205578.1] ||  -> member(singleton(identity_relation),image(element_relation,singleton(identity_relation)))* member(singleton(identity_relation),power_class(complement(singleton(identity_relation)))).
% 299.99/300.65  206125[22:Res:205574.1,66086.1] || equal(complement(compose(element_relation,ordinal_numbers)),singleton(singleton(identity_relation)))** member(singleton(identity_relation),element_relation) -> .
% 299.99/300.65  206128[22:Res:205574.1,9876.0] || equal(u,singleton(singleton(identity_relation)))* subclass(u,v)* well_ordering(ordinal_numbers,v)* -> .
% 299.99/300.65  206132[22:Res:205574.1,5.0] || equal(u,singleton(singleton(identity_relation)))* subclass(u,v)* -> member(singleton(identity_relation),v)*.
% 299.99/300.65  206137[22:Res:205574.1,3617.0] || equal(symmetric_difference(u,v),singleton(singleton(identity_relation))) -> member(singleton(identity_relation),union(u,v))*.
% 299.99/300.65  206138[22:Res:205574.1,19559.0] || equal(symmetric_difference(u,singleton(u)),singleton(singleton(identity_relation)))** -> member(singleton(identity_relation),successor(u))*.
% 299.99/300.65  206139[22:Res:205574.1,19676.0] || equal(symmetric_difference(u,inverse(u)),singleton(singleton(identity_relation)))** -> member(singleton(identity_relation),symmetrization_of(u))*.
% 299.99/300.65  206267[8:Rew:160491.0,206196.1] || member(u,symmetric_difference(complement(v),symmetric_difference(ordinal_numbers,v)))* -> member(u,union(v,identity_relation)).
% 299.99/300.65  207617[24:SpR:207558.1,2504.1] operation(u) || subclass(ordered_pair(v,u),w)* -> member(unordered_pair(v,identity_relation),w)*.
% 299.99/300.65  207673[24:SpL:207558.1,2557.0] operation(u) || member(singleton(singleton(identity_relation)),cross_product(v,w))* -> member(u,w)*.
% 299.99/300.65  207780[24:SpL:207558.1,8979.0] operation(u) || member(image(v,identity_relation),ordinal_numbers) -> member(apply(v,u),ordinal_numbers)*.
% 299.99/300.65  207885[24:Rew:207558.1,207621.1] operation(u) || section(v,identity_relation,w) -> subclass(segment(v,w,u),identity_relation)*.
% 299.99/300.65  207896[24:MRR:207895.1,13039.0] operation(u) || subclass(segment(v,w,u),identity_relation)* -> section(v,identity_relation,w).
% 299.99/300.65  208006[24:Rew:207947.1,197797.1] operation(regular(omega)) ||  -> equal(regular(identity_relation),identity_relation) equal(restrict(u,identity_relation,identity_relation),identity_relation)**.
% 299.99/300.65  208255[24:SpR:207565.1,69395.0] operation(intersection(u,ordinal_numbers)) ||  -> equal(complement(symmetric_difference(u,ordinal_numbers)),successor(intersection(u,ordinal_numbers)))**.
% 299.99/300.65  208279[24:SpR:207572.1,41112.1] operation(rest_of(identity_relation)) || member(identity_relation,rest_of(identity_relation)) -> member(singleton(singleton(identity_relation)),element_relation)*.
% 299.99/300.65  208423[21:Res:198162.1,5.0] || subclass(ordered_pair(inverse(u),v),w)* -> equal(range_of(u),identity_relation) member(identity_relation,w).
% 299.99/300.65  208497[7:SpL:13260.1,39306.0] || equal(complement(singleton(regular(cross_product(u,v)))),ordinal_numbers)** -> equal(cross_product(u,v),identity_relation).
% 299.99/300.65  208498[7:SpL:13260.1,39295.0] || subclass(ordinal_numbers,complement(singleton(regular(cross_product(u,v)))))* -> equal(cross_product(u,v),identity_relation).
% 299.99/300.65  208733[8:SpR:208708.1,3618.1] || member(u,symmetric_difference(v,ordinal_numbers))* -> equal(singleton(v),identity_relation) member(u,complement(v)).
% 299.99/300.65  208753[8:SpR:208708.1,66293.0] ||  -> equal(singleton(union(u,identity_relation)),identity_relation) equal(symmetric_difference(complement(u),ordinal_numbers),union(u,identity_relation))**.
% 299.99/300.65  208791[8:SpL:208708.1,18794.1] || member(u,symmetric_difference(v,ordinal_numbers))* member(u,v) -> equal(singleton(v),identity_relation).
% 299.99/300.65  208815[8:MRR:208814.0,41096.1] || member(u,complement(v)) -> equal(singleton(v),identity_relation) member(u,symmetric_difference(v,ordinal_numbers))*.
% 299.99/300.65  208818[8:Rew:140613.0,208723.1,66141.0,208723.1,66141.0,208723.1] ||  -> equal(singleton(u),identity_relation) equal(symmetric_difference(ordinal_numbers,symmetric_difference(u,ordinal_numbers)),symmetric_difference(complement(u),ordinal_numbers))**.
% 299.99/300.65  208986[25:Rew:208887.0,198212.1] ||  -> equal(range_of(u),identity_relation) equal(segment(v,w,inverse(u)),segment(v,w,ordinal_numbers))**.
% 299.99/300.65  209000[25:Rew:208881.0,198208.1] ||  -> equal(range_of(u),identity_relation) equal(range__dfg(v,inverse(u),w),range__dfg(v,ordinal_numbers,w))**.
% 299.99/300.65  209002[25:Rew:208888.0,198213.1] ||  -> equal(range_of(u),identity_relation) equal(domain__dfg(v,w,inverse(u)),domain__dfg(v,w,ordinal_numbers))**.
% 299.99/300.65  209021[25:Rew:208820.0,208883.0] || asymmetric(u,identity_relation) -> equal(domain__dfg(intersection(u,inverse(u)),identity_relation,ordinal_numbers),single_valued3(identity_relation))**.
% 299.99/300.65  209342[25:Rew:209334.1,208344.2] operation(u) || member(ordered_pair(v,singleton(singleton(identity_relation))),composition_function)* -> equal(ordinal_numbers,u)*.
% 299.99/300.65  209428[25:SpL:208885.0,9586.0] || subclass(apply(u,ordinal_numbers),image(u,identity_relation))* -> section(element_relation,image(u,identity_relation),ordinal_numbers).
% 299.99/300.65  209738[25:SpL:209659.0,12.0] || member(u,ordered_pair(ordinal_numbers,ordinal_numbers))* -> equal(u,unordered_pair(ordinal_numbers,identity_relation)) equal(u,identity_relation).
% 299.99/300.65  209750[21:SpL:117380.1,204678.0] operation(u) || subclass(domain_relation,cantor(u)) -> member(singleton(identity_relation),cantor(cantor(u)))*.
% 299.99/300.65  209833[8:Rew:160759.0,209832.0] ||  -> subclass(symmetric_difference(union(u,identity_relation),symmetric_difference(complement(u),ordinal_numbers)),complement(symmetric_difference(complement(u),ordinal_numbers)))*.
% 299.99/300.65  209862[24:SpR:195239.0,207863.1] operation(complement(singleton(identity_relation))) ||  -> subclass(symmetric_difference(singleton(identity_relation),ordinal_numbers),successor(complement(singleton(identity_relation))))*.
% 299.99/300.65  209863[24:SpR:162584.0,207863.1] operation(complement(inverse(identity_relation))) ||  -> subclass(symmetric_difference(symmetrization_of(identity_relation),ordinal_numbers),successor(complement(inverse(identity_relation))))*.
% 299.99/300.65  209883[24:SpR:141394.0,207866.1] operation(intersection(u,ordinal_numbers)) ||  -> subclass(complement(successor(intersection(u,ordinal_numbers))),symmetric_difference(u,ordinal_numbers))*.
% 299.99/300.65  209963[15:Res:209921.1,18791.0] || equal(symmetric_difference(complement(u),complement(v)),ordinal_numbers) -> member(range_of(identity_relation),union(u,v))*.
% 299.99/300.65  210212[21:SpL:117380.1,209753.0] operation(u) || equal(cantor(u),domain_relation) -> member(singleton(identity_relation),cantor(cantor(u)))*.
% 299.99/300.65  210290[8:Res:140864.1,7.0] || member(not_subclass_element(u,symmetric_difference(ordinal_numbers,v)),complement(v))* -> subclass(u,symmetric_difference(ordinal_numbers,v)).
% 299.99/300.65  210334[8:Rew:160491.0,210284.1,160491.0,210284.0] || member(not_subclass_element(union(u,identity_relation),v),complement(u))* -> subclass(union(u,identity_relation),v).
% 299.99/300.65  210349[7:Res:13125.2,143186.0] || subclass(omega,symmetric_difference(ordinal_numbers,u))* -> equal(integer_of(v),identity_relation) member(v,complement(u))*.
% 299.99/300.65  210371[7:Res:13227.2,143186.0] || subclass(u,symmetric_difference(ordinal_numbers,v)) -> equal(u,identity_relation) member(regular(u),complement(v))*.
% 299.99/300.65  210385[5:Res:49995.1,143186.0] || member(symmetric_difference(ordinal_numbers,u),subset_relation) -> member(singleton(first(symmetric_difference(ordinal_numbers,u))),complement(u))*.
% 299.99/300.65  210431[14:Res:210404.0,9876.0] || subclass(union(u,identity_relation),v)* well_ordering(ordinal_numbers,v) -> member(identity_relation,complement(u)).
% 299.99/300.65  210458[7:Res:13125.2,143226.0] || subclass(omega,symmetric_difference(ordinal_numbers,u))* member(v,u)* -> equal(integer_of(v),identity_relation).
% 299.99/300.65  210480[7:Res:13227.2,143226.0] || subclass(u,symmetric_difference(ordinal_numbers,v))* member(regular(u),v) -> equal(u,identity_relation).
% 299.99/300.65  210494[5:Res:49995.1,143226.0] || member(symmetric_difference(ordinal_numbers,u),subset_relation) member(singleton(first(symmetric_difference(ordinal_numbers,u))),u)* -> .
% 299.99/300.65  210794[8:SpL:189.0,210578.0] || equal(power_class(image(element_relation,complement(u))),ordinal_numbers)** -> equal(image(element_relation,power_class(u)),identity_relation).
% 299.99/300.65  211065[8:Res:210572.1,161194.1] operation(u) || equal(complement(cantor(u)),ordinal_numbers) -> connected(v,cantor(cantor(u)))*.
% 299.99/300.65  211085[8:Res:210572.1,155663.1] || equal(complement(subset_relation),ordinal_numbers) transitive(subset_relation,ordinal_numbers) -> equal(compose(subset_relation,subset_relation),subset_relation)**.
% 299.99/300.65  211306[8:Res:210606.1,11.0] || equal(complement(u),ordinal_numbers) subclass(complement(u),v)* -> equal(complement(u),v).
% 299.99/300.65  211541[8:Res:211438.1,11.0] || equal(symmetrization_of(identity_relation),ordinal_numbers) subclass(symmetrization_of(identity_relation),u)* -> equal(symmetrization_of(identity_relation),u).
% 299.99/300.65  211625[8:Res:211441.1,11.0] || equal(power_class(u),ordinal_numbers) subclass(power_class(u),v)* -> equal(power_class(u),v).
% 299.99/300.65  211920[8:Rew:211812.1,211919.1] || equal(symmetrization_of(identity_relation),ordinal_numbers) -> member(not_subclass_element(ordinal_numbers,u),ordinal_numbers)* subclass(symmetrization_of(identity_relation),u).
% 299.99/300.65  212167[8:Rew:211586.1,212035.2] || equal(symmetrization_of(identity_relation),ordinal_numbers) -> member(not_subclass_element(u,identity_relation),symmetrization_of(identity_relation))* subclass(u,identity_relation).
% 299.99/300.65  212171[8:Rew:66036.0,211997.2,211586.1,211997.2,66036.0,211997.1] || equal(symmetrization_of(identity_relation),ordinal_numbers) -> member(not_subclass_element(ordinal_numbers,u),symmetrization_of(identity_relation))* subclass(ordinal_numbers,u).
% 299.99/300.65  212700[24:Rew:66036.0,212488.2,17351.0,212488.2,160498.0,212488.2] operation(complement(u)) || equal(complement(u),ordinal_numbers) -> subclass(ordinal_numbers,successor(complement(u)))*.
% 299.99/300.65  212706[8:Rew:211432.1,212511.2] || equal(complement(u),ordinal_numbers) -> member(not_subclass_element(v,identity_relation),complement(u))* subclass(v,identity_relation).
% 299.99/300.65  212711[8:Rew:66036.0,212471.2,211432.1,212471.2,66036.0,212471.1] || equal(complement(u),ordinal_numbers) -> member(not_subclass_element(ordinal_numbers,v),complement(u))* subclass(ordinal_numbers,v).
% 299.99/300.65  212926[24:Rew:66036.0,212783.2,17351.0,212783.2,160498.0,212783.2] operation(power_class(u)) || equal(power_class(u),ordinal_numbers) -> subclass(ordinal_numbers,successor(power_class(u)))*.
% 299.99/300.65  212930[8:Rew:211670.1,212806.2] || equal(power_class(u),ordinal_numbers) -> member(not_subclass_element(v,identity_relation),power_class(u))* subclass(v,identity_relation).
% 299.99/300.65  212934[8:Rew:66036.0,212766.2,211670.1,212766.2,66036.0,212766.1] || equal(power_class(u),ordinal_numbers) -> member(not_subclass_element(ordinal_numbers,v),power_class(u))* subclass(ordinal_numbers,v).
% 299.99/300.65  213099[8:SpR:210579.1,3616.0] || equal(complement(union(u,v)),ordinal_numbers) -> equal(symmetric_difference(complement(u),complement(v)),identity_relation)**.
% 299.99/300.65  213489[14:SpL:145761.0,165401.1] operation(cross_product(u,singleton(v))) || equal(segment(ordinal_numbers,u,v),singleton(identity_relation))** -> .
% 299.99/300.65  213490[18:SpL:145761.0,190588.1] operation(cross_product(u,singleton(v))) || equal(segment(ordinal_numbers,u,v),symmetrization_of(identity_relation))** -> .
% 299.99/300.65  213491[18:SpL:145761.0,190699.1] operation(cross_product(u,singleton(v))) || equal(segment(ordinal_numbers,u,v),inverse(identity_relation))** -> .
% 299.99/300.65  214037[7:Res:13125.2,152274.0] || subclass(omega,complement(singleton(u)))* -> equal(integer_of(u),identity_relation) subclass(singleton(u),v)*.
% 299.99/300.65  214043[15:Res:195033.1,152274.0] || equal(complement(complement(complement(singleton(range_of(identity_relation))))),ordinal_numbers)** -> subclass(singleton(range_of(identity_relation)),u)*.
% 299.99/300.65  214045[15:Res:165442.1,152274.0] || subclass(ordinal_numbers,complement(singleton(sum_class(range_of(identity_relation)))))* -> subclass(singleton(sum_class(range_of(identity_relation))),u)*.
% 299.99/300.65  214058[5:Res:9632.1,152274.0] || equal(complement(complement(complement(singleton(singleton(u))))),ordinal_numbers)** -> subclass(singleton(singleton(u)),v)*.
% 299.99/300.65  214084[18:Res:190515.1,152274.0] || subclass(ordinal_numbers,complement(singleton(regular(symmetrization_of(identity_relation)))))* -> subclass(singleton(regular(symmetrization_of(identity_relation))),u)*.
% 299.99/300.65  214287[25:SpR:916.0,208887.0] ||  -> equal(cantor(restrict(cross_product(u,identity_relation),v,w)),segment(cross_product(v,w),u,ordinal_numbers))**.
% 299.99/300.65  214304[25:SpL:208887.0,165401.1] operation(restrict(u,v,identity_relation)) || equal(segment(u,v,ordinal_numbers),singleton(identity_relation))** -> .
% 299.99/300.65  214305[25:SpL:208887.0,190588.1] operation(restrict(u,v,identity_relation)) || equal(segment(u,v,ordinal_numbers),symmetrization_of(identity_relation))** -> .
% 299.99/300.65  214306[25:SpL:208887.0,190699.1] operation(restrict(u,v,identity_relation)) || equal(segment(u,v,ordinal_numbers),inverse(identity_relation))** -> .
% 299.99/300.65  214315[25:Rew:160429.0,214289.1] ||  -> equal(cross_product(u,identity_relation),identity_relation) equal(segment(regular(cross_product(u,identity_relation)),u,ordinal_numbers),identity_relation)**.
% 299.99/300.65  214438[25:SpR:208985.1,41112.1] operation(rest_of(u)) || member(u,rest_of(u))* -> member(ordered_pair(u,ordinal_numbers),element_relation)*.
% 299.99/300.65  214441[25:SpR:208985.1,117318.1] operation(cantor(u)) || member(u,cantor(u))* -> member(ordered_pair(u,ordinal_numbers),element_relation)*.
% 299.99/300.65  214494[25:SpL:208985.1,19.0] operation(u) || member(ordered_pair(v,u),cross_product(w,x))* -> member(ordinal_numbers,x).
% 299.99/300.65  214513[25:SpL:208985.1,157.0] operation(u) || member(ordered_pair(v,u),union_of_range_map)* -> equal(sum_class(range_of(v)),ordinal_numbers).
% 299.99/300.65  214549[25:SpL:208985.1,19.0] operation(u) || member(ordered_pair(v,ordinal_numbers),cross_product(w,x))* -> member(u,x)*.
% 299.99/300.65  214568[25:SpL:208985.1,157.0] operation(u) || member(ordered_pair(v,ordinal_numbers),union_of_range_map)* -> equal(sum_class(range_of(v)),u)*.
% 299.99/300.65  215174[16:SpR:195239.0,155157.1] || subclass(complement(singleton(identity_relation)),u) -> subclass(symmetric_difference(u,complement(singleton(identity_relation))),singleton(identity_relation))*.
% 299.99/300.65  215175[8:SpR:162584.0,155157.1] || subclass(complement(inverse(identity_relation)),u) -> subclass(symmetric_difference(u,complement(inverse(identity_relation))),symmetrization_of(identity_relation))*.
% 299.99/300.65  215358[8:SpR:30.0,215271.1] || subclass(intersection(complement(u),complement(v)),identity_relation)* -> equal(complement(union(u,v)),identity_relation).
% 299.99/300.65  215367[8:SpR:162038.0,215271.1] || subclass(image(element_relation,symmetrization_of(identity_relation)),identity_relation)* -> equal(complement(power_class(complement(inverse(identity_relation)))),identity_relation).
% 299.99/300.65  215368[16:SpR:195257.0,215271.1] || subclass(image(element_relation,singleton(identity_relation)),identity_relation)* -> equal(complement(power_class(complement(singleton(identity_relation)))),identity_relation).
% 299.99/300.65  215470[8:SpL:215271.1,160667.0] || subclass(symmetrization_of(u),identity_relation)* subclass(cross_product(v,v),identity_relation)* -> connected(u,v)*.
% 299.99/300.65  215595[8:MRR:215594.2,13039.0] || subclass(symmetrization_of(u),identity_relation)* connected(u,v)* -> equal(cross_product(v,v),identity_relation)**.
% 299.99/300.65  215611[8:SpR:189.0,215487.1] || subclass(image(element_relation,power_class(u)),identity_relation) -> subclass(ordinal_numbers,power_class(image(element_relation,complement(u))))*.
% 299.99/300.65  216006[8:SpL:6355.1,215642.0] || subclass(singleton(not_subclass_element(cross_product(u,v),w)),identity_relation)* -> subclass(cross_product(u,v),w).
% 299.99/300.65  216587[8:SpL:189.0,215660.0] || subclass(power_class(image(element_relation,complement(u))),identity_relation)* -> member(identity_relation,image(element_relation,power_class(u))).
% 299.99/300.65  216607[8:SpL:189.0,215661.0] || subclass(power_class(image(element_relation,complement(u))),identity_relation)* -> member(omega,image(element_relation,power_class(u))).
% 299.99/300.65  216750[8:SpR:216188.1,155824.0] || equal(compose(complement(element_relation),inverse(element_relation)),identity_relation)** -> equal(image(ordinal_numbers,ordinal_numbers),range_of(subset_relation)).
% 299.99/300.65  216782[8:SpR:216188.1,189.0] || equal(image(element_relation,power_class(u)),identity_relation) -> equal(power_class(image(element_relation,complement(u))),ordinal_numbers)**.
% 299.99/300.65  217234[8:Rew:17351.0,217059.1] || equal(symmetrization_of(u),identity_relation) subclass(cross_product(v,v),identity_relation)* -> connected(u,v)*.
% 299.99/300.65  217248[8:Rew:66141.0,216675.1] || equal(identity_relation,u) -> equal(intersection(union(v,u),ordinal_numbers),symmetric_difference(complement(v),ordinal_numbers))**.
% 299.99/300.65  217276[8:MRR:217275.2,13039.0] || equal(symmetrization_of(u),identity_relation) connected(u,v)* -> equal(cross_product(v,v),identity_relation)**.
% 299.99/300.65  217335[8:SpL:189.0,216227.0] || equal(image(element_relation,power_class(image(element_relation,complement(u)))),power_class(image(element_relation,power_class(u))))** -> .
% 299.99/300.65  217404[8:Res:216591.1,18791.0] || equal(complement(symmetric_difference(complement(u),complement(v))),identity_relation)** -> member(identity_relation,union(u,v)).
% 299.99/300.65  217460[8:EmS:13166.0,13166.1,75.1,214833.1] one_to_one(symmetrization_of(u)) || equal(symmetrization_of(u),ordinal_numbers)** -> member(identity_relation,cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.65  217462[8:EmS:13166.0,13166.1,82.1,214833.1] operation(symmetrization_of(u)) || equal(symmetrization_of(u),ordinal_numbers)** -> member(identity_relation,cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.65  217464[8:EmS:13166.0,13166.1,75.1,214832.1] one_to_one(successor(u)) || equal(successor(u),ordinal_numbers)** -> member(identity_relation,cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.65  217466[8:EmS:13166.0,13166.1,82.1,214832.1] operation(successor(u)) || equal(successor(u),ordinal_numbers)** -> member(identity_relation,cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.65  217472[8:EmS:13166.0,13166.1,75.1,211493.1] one_to_one(power_class(u)) || equal(power_class(u),ordinal_numbers)** -> member(identity_relation,cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.65  217474[8:EmS:13166.0,13166.1,82.1,211493.1] operation(power_class(u)) || equal(power_class(u),ordinal_numbers)** -> member(identity_relation,cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.65  217480[8:EmS:13166.0,13166.1,75.1,211442.1] one_to_one(complement(u)) || equal(complement(u),ordinal_numbers)** -> member(identity_relation,cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.65  217482[8:EmS:13166.0,13166.1,82.1,211442.1] operation(complement(u)) || equal(complement(u),ordinal_numbers)** -> member(identity_relation,cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.65  217576[8:Rew:160491.0,217531.1,160491.0,217531.0] || member(regular(complement(union(u,identity_relation))),u)* -> equal(complement(union(u,identity_relation)),identity_relation).
% 299.99/300.65  217626[8:Res:216611.1,18791.0] || equal(complement(symmetric_difference(complement(u),complement(v))),identity_relation)** -> member(omega,union(u,v)).
% 299.99/300.65  217686[8:Res:216691.1,9649.0] || equal(complement(u),identity_relation) well_ordering(v,u)* -> member(least(v,ordinal_numbers),ordinal_numbers)*.
% 299.99/300.65  217690[8:Res:216691.1,8813.0] || equal(complement(u),identity_relation) subclass(u,v)* -> member(unordered_pair(w,x),v)*.
% 299.99/300.65  217731[8:Res:216691.1,69166.0] || equal(complement(complement(compose(element_relation,ordinal_numbers))),identity_relation)** member(unordered_pair(u,v),element_relation)* -> .
% 299.99/300.65  217944[7:Res:18949.0,17315.0] ||  -> equal(restrict(recursion_equation_functions(u),v,w),identity_relation) function(regular(restrict(recursion_equation_functions(u),v,w)))*.
% 299.99/300.65  218047[8:SpL:189.0,217692.0] || equal(power_class(image(element_relation,complement(u))),identity_relation)** -> equal(image(element_relation,power_class(u)),ordinal_numbers).
% 299.99/300.65  218069[8:SpL:13260.1,217708.0] || equal(complement(complement(regular(cross_product(u,v)))),identity_relation)** -> equal(cross_product(u,v),identity_relation).
% 299.99/300.65  218082[8:SpL:13260.1,215649.0] || subclass(unordered_pair(u,regular(cross_product(v,w))),identity_relation)* -> equal(cross_product(v,w),identity_relation).
% 299.99/300.65  218108[8:SpL:13260.1,215653.0] || subclass(unordered_pair(regular(cross_product(u,v)),w),identity_relation)* -> equal(cross_product(u,v),identity_relation).
% 299.99/300.65  218130[8:Res:27.2,217144.1] || member(u,v)* member(u,w)* equal(intersection(w,v),identity_relation)** -> .
% 299.99/300.65  218133[8:Res:39530.1,217144.1] || member(u,ordinal_numbers) equal(union(v,w),identity_relation)** -> member(u,complement(v))*.
% 299.99/300.65  218134[8:Res:39529.1,217144.1] || member(u,ordinal_numbers) equal(union(v,w),identity_relation)** -> member(u,complement(w))*.
% 299.99/300.65  218251[8:Res:20.2,217144.1] || member(u,v)* member(w,x)* equal(cross_product(x,v),identity_relation)** -> .
% 299.99/300.65  218340[8:Con:218258.2] operation(u) || member(v,cantor(cantor(u)))* equal(cantor(u),identity_relation) -> .
% 299.99/300.65  218346[8:SpL:13260.1,217155.0] || equal(unordered_pair(u,regular(cross_product(v,w))),identity_relation)** -> equal(cross_product(v,w),identity_relation).
% 299.99/300.65  218411[21:Res:19525.1,196454.0] || well_ordering(u,ordinal_numbers) subclass(domain_relation,rest_relation) -> equal(rest_of(least(u,ordinal_numbers)),identity_relation)**.
% 299.99/300.65  218412[21:Res:133502.1,196454.0] || well_ordering(u,rest_relation) subclass(domain_relation,rest_relation) -> equal(rest_of(least(u,rest_relation)),identity_relation)**.
% 299.99/300.65  218413[21:Res:133495.1,196454.0] || well_ordering(u,ordinal_numbers) subclass(domain_relation,rest_relation) -> equal(rest_of(least(u,rest_relation)),identity_relation)**.
% 299.99/300.65  218466[21:SpR:218460.1,154.1] || equal(rest_relation,domain_relation) member(omega,recursion_equation_functions(u))* -> equal(compose(u,identity_relation),omega).
% 299.99/300.65  218526[8:SpL:13260.1,217160.0] || equal(unordered_pair(regular(cross_product(u,v)),w),identity_relation)** -> equal(cross_product(u,v),identity_relation).
% 299.99/300.65  218587[21:Res:19525.1,196455.0] || well_ordering(u,ordinal_numbers) subclass(rest_relation,domain_relation) -> equal(rest_of(least(u,ordinal_numbers)),identity_relation)**.
% 299.99/300.65  218588[21:Res:133502.1,196455.0] || well_ordering(u,rest_relation) subclass(rest_relation,domain_relation) -> equal(rest_of(least(u,rest_relation)),identity_relation)**.
% 299.99/300.65  218589[21:Res:133495.1,196455.0] || well_ordering(u,ordinal_numbers) subclass(rest_relation,domain_relation) -> equal(rest_of(least(u,rest_relation)),identity_relation)**.
% 299.99/300.65  218644[16:SpL:195239.0,66645.0] || subclass(ordinal_numbers,image(element_relation,singleton(identity_relation))) member(omega,power_class(complement(singleton(identity_relation))))* -> .
% 299.99/300.65  218645[8:SpL:162584.0,66645.0] || subclass(ordinal_numbers,image(element_relation,symmetrization_of(identity_relation))) member(omega,power_class(complement(inverse(identity_relation))))* -> .
% 299.99/300.65  218831[21:MRR:218778.1,165460.0] || subclass(rest_relation,domain_relation) subclass(rest_relation,u) -> member(ordered_pair(range_of(identity_relation),identity_relation),u)*.
% 299.99/300.65  218972[21:MRR:218913.1,8655.0] || subclass(rest_relation,domain_relation) subclass(rest_relation,u) -> member(ordered_pair(singleton(v),identity_relation),u)*.
% 299.99/300.65  219091[8:Res:27.2,219073.1] || member(u,v)* member(u,w)* subclass(intersection(w,v),identity_relation)* -> .
% 299.99/300.65  219094[8:Res:39530.1,219073.1] || member(u,ordinal_numbers) subclass(union(v,w),identity_relation)* -> member(u,complement(v))*.
% 299.99/300.65  219095[8:Res:39529.1,219073.1] || member(u,ordinal_numbers) subclass(union(v,w),identity_relation)* -> member(u,complement(w))*.
% 299.99/300.65  219212[8:Res:20.2,219073.1] || member(u,v)* member(w,x)* subclass(cross_product(x,v),identity_relation)* -> .
% 299.99/300.65  219294[8:Con:219219.2] operation(u) || member(v,cantor(cantor(u)))* subclass(cantor(u),identity_relation) -> .
% 299.99/300.65  219338[15:Res:215659.1,897.0] || subclass(complement(restrict(u,v,w)),identity_relation)* -> member(range_of(identity_relation),cross_product(v,w)).
% 299.99/300.65  219347[15:Res:215659.1,14681.0] || subclass(complement(regular(u)),identity_relation)* member(range_of(identity_relation),u) -> equal(u,identity_relation).
% 299.99/300.65  219371[24:SpR:66834.1,207931.1] operation(least(u,omega)) || well_ordering(u,ordinal_numbers) -> equal(least(u,omega),identity_relation)**.
% 299.99/300.65  219418[8:Res:13237.2,216107.0] || well_ordering(u,ordinal_numbers) equal(singleton(least(u,subset_relation)),identity_relation)** -> equal(subset_relation,identity_relation).
% 299.99/300.65  219590[15:Res:215659.1,67561.0] || subclass(complement(symmetric_difference(complement(u),ordinal_numbers)),identity_relation)* -> member(range_of(identity_relation),union(u,identity_relation)).
% 299.99/300.65  219594[15:Res:165442.1,67561.0] || subclass(ordinal_numbers,symmetric_difference(complement(u),ordinal_numbers)) -> member(sum_class(range_of(identity_relation)),union(u,identity_relation))*.
% 299.99/300.65  219623[8:Res:8642.1,67561.0] || subclass(ordinal_numbers,symmetric_difference(complement(u),ordinal_numbers)) -> member(ordered_pair(v,w),union(u,identity_relation))*.
% 299.99/300.65  219639[18:Res:190515.1,67561.0] || subclass(ordinal_numbers,symmetric_difference(complement(u),ordinal_numbers)) -> member(regular(symmetrization_of(identity_relation)),union(u,identity_relation))*.
% 299.99/300.65  219792[8:Res:67614.1,210517.1] || member(u,union(v,identity_relation))* equal(complement(symmetric_difference(complement(v),ordinal_numbers)),ordinal_numbers)** -> .
% 299.99/300.65  219808[22:Res:67614.1,205501.0] || member(singleton(identity_relation),union(u,identity_relation)) well_ordering(ordinal_numbers,symmetric_difference(complement(u),ordinal_numbers))* -> .
% 299.99/300.65  219849[15:Res:217197.1,67561.0] || equal(complement(symmetric_difference(complement(u),ordinal_numbers)),identity_relation) -> member(range_of(identity_relation),union(u,identity_relation))*.
% 299.99/300.65  219867[15:Res:217197.1,897.0] || equal(complement(restrict(u,v,w)),identity_relation)** -> member(range_of(identity_relation),cross_product(v,w))*.
% 299.99/300.65  219876[15:Res:217197.1,14681.0] || equal(complement(regular(u)),identity_relation) member(range_of(identity_relation),u)* -> equal(u,identity_relation).
% 299.99/300.65  219939[8:Res:8976.2,217200.1] function(u) || member(v,ordinal_numbers) equal(singleton(image(u,v)),identity_relation)** -> .
% 299.99/300.65  219996[8:MRR:219947.1,8638.0] || member(u,ordinal_numbers) equal(singleton(apply(choice,u)),identity_relation)** -> equal(u,identity_relation).
% 299.99/300.65  220022[8:Res:8643.1,160772.0] || subclass(ordinal_numbers,symmetric_difference(ordinal_numbers,u)) member(unordered_pair(v,w),union(u,identity_relation))* -> .
% 299.99/300.65  220024[8:Res:13072.1,160772.0] || member(regular(symmetric_difference(ordinal_numbers,u)),union(u,identity_relation))* -> equal(symmetric_difference(ordinal_numbers,u),identity_relation).
% 299.99/300.65  220032[15:Res:165442.1,160772.0] || subclass(ordinal_numbers,symmetric_difference(ordinal_numbers,u)) member(sum_class(range_of(identity_relation)),union(u,identity_relation))* -> .
% 299.99/300.65  220045[8:Res:143222.1,160772.0] || equal(symmetric_difference(ordinal_numbers,u),omega) member(least(element_relation,omega),union(u,identity_relation))* -> .
% 299.99/300.65  220046[8:Res:143193.1,160772.0] || equal(symmetric_difference(ordinal_numbers,u),ordinal_numbers) member(least(element_relation,omega),union(u,identity_relation))* -> .
% 299.99/300.65  220049[8:Res:125731.1,160772.0] || subclass(ordinal_numbers,symmetric_difference(ordinal_numbers,u)) member(least(element_relation,omega),union(u,identity_relation))* -> .
% 299.99/300.65  220050[8:Res:125725.1,160772.0] || subclass(omega,symmetric_difference(ordinal_numbers,u)) member(least(element_relation,omega),union(u,identity_relation))* -> .
% 299.99/300.65  220061[8:Res:8642.1,160772.0] || subclass(ordinal_numbers,symmetric_difference(ordinal_numbers,u)) member(ordered_pair(v,w),union(u,identity_relation))* -> .
% 299.99/300.65  220062[8:Res:15426.1,160772.0] || subclass(domain_relation,symmetric_difference(ordinal_numbers,u)) member(ordered_pair(identity_relation,identity_relation),union(u,identity_relation))* -> .
% 299.99/300.65  220078[18:Res:190515.1,160772.0] || subclass(ordinal_numbers,symmetric_difference(ordinal_numbers,u)) member(regular(symmetrization_of(identity_relation)),union(u,identity_relation))* -> .
% 299.99/300.65  220133[25:SpL:208887.0,217492.1] operation(restrict(u,v,identity_relation)) || equal(complement(segment(u,v,ordinal_numbers)),identity_relation)** -> .
% 299.99/300.65  220156[8:SpL:145761.0,217492.1] operation(cross_product(u,singleton(v))) || equal(complement(segment(ordinal_numbers,u,v)),identity_relation)** -> .
% 299.99/300.65  220352[8:Rew:66036.0,220331.1] || subclass(image(element_relation,complement(u)),identity_relation)* -> equal(complement(intersection(power_class(u),ordinal_numbers)),identity_relation).
% 299.99/300.65  220382[21:SpR:18840.1,196656.1] || member(u,subset_relation) subclass(domain_relation,flip(v)) -> member(ordered_pair(u,identity_relation),v)*.
% 299.99/300.65  220389[21:Res:196656.1,28.1] || subclass(domain_relation,flip(complement(u))) member(ordered_pair(ordered_pair(v,w),identity_relation),u)* -> .
% 299.99/300.65  220392[21:Res:196656.1,151988.0] || subclass(domain_relation,flip(complement(complement(u)))) -> member(ordered_pair(ordered_pair(v,w),identity_relation),u)*.
% 299.99/300.65  220401[21:Res:196656.1,26.0] || subclass(domain_relation,flip(intersection(u,v)))* -> member(ordered_pair(ordered_pair(w,x),identity_relation),v)*.
% 299.99/300.65  220402[21:Res:196656.1,25.0] || subclass(domain_relation,flip(intersection(u,v)))* -> member(ordered_pair(ordered_pair(w,x),identity_relation),u)*.
% 299.99/300.65  220424[21:Res:196656.1,14679.1] || subclass(domain_relation,flip(inverse(subset_relation))) member(ordered_pair(ordered_pair(u,v),identity_relation),subset_relation)* -> .
% 299.99/300.65  220429[21:Res:196656.1,163154.0] || subclass(domain_relation,flip(symmetrization_of(identity_relation))) -> member(ordered_pair(ordered_pair(u,v),identity_relation),inverse(identity_relation))*.
% 299.99/300.65  220454[21:Res:196656.1,8651.0] || subclass(domain_relation,flip(rest_of(u))) -> equal(restrict(u,ordered_pair(v,w),ordinal_numbers),identity_relation)**.
% 299.99/300.65  220464[21:Res:196656.1,117450.1] operation(u) || subclass(domain_relation,flip(cantor(u))) -> member(identity_relation,cantor(cantor(u)))*.
% 299.99/300.65  220491[21:Res:196657.1,28.1] || subclass(domain_relation,rotate(complement(u))) member(ordered_pair(ordered_pair(v,identity_relation),w),u)* -> .
% 299.99/300.65  220494[21:Res:196657.1,151988.0] || subclass(domain_relation,rotate(complement(complement(u)))) -> member(ordered_pair(ordered_pair(v,identity_relation),w),u)*.
% 299.99/300.65  220503[21:Res:196657.1,26.0] || subclass(domain_relation,rotate(intersection(u,v)))* -> member(ordered_pair(ordered_pair(w,identity_relation),x),v)*.
% 299.99/300.65  220504[21:Res:196657.1,25.0] || subclass(domain_relation,rotate(intersection(u,v)))* -> member(ordered_pair(ordered_pair(w,identity_relation),x),u)*.
% 299.99/300.65  220526[21:Res:196657.1,14679.1] || subclass(domain_relation,rotate(inverse(subset_relation))) member(ordered_pair(ordered_pair(u,identity_relation),v),subset_relation)* -> .
% 299.99/300.65  220531[21:Res:196657.1,163154.0] || subclass(domain_relation,rotate(symmetrization_of(identity_relation))) -> member(ordered_pair(ordered_pair(u,identity_relation),v),inverse(identity_relation))*.
% 299.99/300.65  220556[21:Res:196657.1,8651.0] || subclass(domain_relation,rotate(rest_of(u))) -> equal(restrict(u,ordered_pair(v,identity_relation),ordinal_numbers),w)*.
% 299.99/300.65  220570[21:Res:196657.1,117450.1] operation(u) || subclass(domain_relation,rotate(cantor(u))) -> member(v,cantor(cantor(u)))*.
% 299.99/300.65  220717[8:Res:2503.2,219203.0] || subclass(u,rest_of(not_subclass_element(u,v)))* subclass(element_relation,identity_relation) -> subclass(u,v).
% 299.99/300.65  220738[21:Res:196657.1,219203.0] || subclass(domain_relation,rotate(rest_of(ordered_pair(ordered_pair(u,identity_relation),v))))* subclass(element_relation,identity_relation) -> .
% 299.99/300.65  220741[21:Res:196656.1,219203.0] || subclass(domain_relation,flip(rest_of(ordered_pair(ordered_pair(u,v),identity_relation))))* subclass(element_relation,identity_relation) -> .
% 299.99/300.65  220744[8:Res:2504.1,219203.0] || subclass(ordered_pair(u,v),rest_of(unordered_pair(u,singleton(v))))* subclass(element_relation,identity_relation) -> .
% 299.99/300.65  220822[25:SpL:208887.0,219206.0] || member(restrict(u,v,identity_relation),segment(u,v,ordinal_numbers))* subclass(element_relation,identity_relation) -> .
% 299.99/300.65  220845[8:SpL:145761.0,219206.0] || member(cross_product(u,singleton(v)),segment(ordinal_numbers,u,v))* subclass(element_relation,identity_relation) -> .
% 299.99/300.65  221136[8:Res:13236.2,216107.0] || well_ordering(u,subset_relation) equal(singleton(least(u,subset_relation)),identity_relation)** -> equal(subset_relation,identity_relation).
% 299.99/300.65  221138[21:Res:13236.2,198565.0] || well_ordering(u,subset_relation) equal(rest_of(least(u,subset_relation)),rest_relation)** -> equal(subset_relation,identity_relation).
% 299.99/300.65  221144[7:Res:13236.2,50033.0] || well_ordering(u,subset_relation) equal(complement(least(u,subset_relation)),ordinal_numbers)** -> equal(subset_relation,identity_relation).
% 299.99/300.65  221156[7:Res:13236.2,152.0] || well_ordering(u,recursion_equation_functions(v)) -> equal(recursion_equation_functions(v),identity_relation) function(least(u,recursion_equation_functions(v)))*.
% 299.99/300.65  221282[8:Res:215662.1,67561.0] || subclass(complement(symmetric_difference(complement(u),ordinal_numbers)),identity_relation)* -> member(singleton(v),union(u,identity_relation))*.
% 299.99/300.65  221303[8:Res:215662.1,897.0] || subclass(complement(restrict(u,v,w)),identity_relation)* -> member(singleton(x),cross_product(v,w))*.
% 299.99/300.65  221312[8:Res:215662.1,14681.0] || subclass(complement(regular(u)),identity_relation)* member(singleton(v),u)* -> equal(u,identity_relation).
% 299.99/300.65  221441[8:SpL:30.0,221330.0] || subclass(union(u,v),identity_relation) well_ordering(ordinal_numbers,intersection(complement(u),complement(v)))* -> .
% 299.99/300.65  221450[8:SpL:162038.0,221330.0] || subclass(power_class(complement(inverse(identity_relation))),identity_relation) well_ordering(ordinal_numbers,image(element_relation,symmetrization_of(identity_relation)))* -> .
% 299.99/300.65  221451[16:SpL:195257.0,221330.0] || subclass(power_class(complement(singleton(identity_relation))),identity_relation) well_ordering(ordinal_numbers,image(element_relation,singleton(identity_relation)))* -> .
% 299.99/300.65  221539[8:Res:217198.1,67561.0] || equal(complement(symmetric_difference(complement(u),ordinal_numbers)),identity_relation) -> member(singleton(v),union(u,identity_relation))*.
% 299.99/300.65  221560[8:Res:217198.1,897.0] || equal(complement(restrict(u,v,w)),identity_relation)** -> member(singleton(x),cross_product(v,w))*.
% 299.99/300.65  221569[8:Res:217198.1,14681.0] || equal(complement(regular(u)),identity_relation) member(singleton(v),u)* -> equal(u,identity_relation).
% 299.99/300.65  222532[8:Res:217645.1,5.0] || equal(complement(symmetrization_of(identity_relation)),identity_relation) subclass(inverse(identity_relation),u)* -> member(omega,u).
% 299.99/300.65  222588[8:SpR:217824.0,219919.1] || equal(singleton(regular(complement(complement(omega)))),identity_relation)** -> equal(regular(complement(complement(omega))),identity_relation).
% 299.99/300.65  222590[21:SpR:217824.0,198454.1] || equal(rest_of(regular(complement(complement(omega)))),rest_relation)** -> equal(regular(complement(complement(omega))),identity_relation).
% 299.99/300.65  222697[7:Res:60996.1,31610.0] || subclass(rest_relation,successor_relation) -> equal(u,identity_relation) equal(rest_of(regular(u)),successor(regular(u)))**.
% 299.99/300.65  223018[25:Rew:209323.1,223017.2] || member(singleton(singleton(identity_relation)),union_of_range_map)* -> equal(range_of(u),identity_relation)** equal(inverse(u),ordinal_numbers).
% 299.99/300.65  223155[11:Rew:80200.0,223141.1] || equal(complement(complement(inverse(u))),ordinal_numbers) -> equal(complement(image(element_relation,symmetrization_of(u))),identity_relation)**.
% 299.99/300.65  223159[8:Rew:140603.0,223121.1] || equal(identity_relation,u) -> equal(complement(image(element_relation,symmetrization_of(u))),power_class(complement(inverse(u))))**.
% 299.99/300.65  223479[11:Rew:80200.0,223463.1] || equal(complement(complement(singleton(u))),ordinal_numbers) -> equal(complement(image(element_relation,successor(u))),identity_relation)**.
% 299.99/300.65  223483[8:Rew:140603.0,223443.1] || equal(identity_relation,u) -> equal(complement(image(element_relation,successor(u))),power_class(complement(singleton(u))))**.
% 299.99/300.65  223892[8:Rew:66036.0,223799.1] || equal(complement(union(u,identity_relation)),ordinal_numbers) -> equal(union(v,symmetric_difference(ordinal_numbers,u)),ordinal_numbers)**.
% 299.99/300.65  224210[8:Rew:66036.0,224113.1] || equal(complement(union(u,identity_relation)),ordinal_numbers) -> equal(union(symmetric_difference(ordinal_numbers,u),v),ordinal_numbers)**.
% 299.99/300.65  224314[10:MRR:224293.2,217111.0] || member(regular(regular(compose(element_relation,ordinal_numbers))),element_relation)* -> equal(regular(compose(element_relation,ordinal_numbers)),identity_relation).
% 299.99/300.65  224315[13:MRR:224294.2,160479.0] || member(regular(regular(cross_product(ordinal_numbers,ordinal_numbers))),subset_relation)* -> equal(regular(cross_product(ordinal_numbers,ordinal_numbers)),identity_relation).
% 299.99/300.65  224318[8:MRR:224296.0,60996.1] || subclass(rest_relation,rest_of(u))* -> equal(regular(cantor(u)),identity_relation) equal(cantor(u),identity_relation).
% 299.99/300.65  224380[10:SpR:223660.1,47.0] || subclass(element_relation,identity_relation) -> equal(union(cross_product(ordinal_numbers,ordinal_numbers),identity_relation),successor(cross_product(ordinal_numbers,ordinal_numbers)))**.
% 299.99/300.65  224748[26:Res:224684.1,490.0] || subclass(omega,intersection(complement(u),complement(v)))* member(identity_relation,union(u,v)) -> .
% 299.99/300.65  224972[26:SpL:50855.1,224766.0] || member(singleton(u),subset_relation)* subclass(omega,u) -> equal(first(singleton(u)),identity_relation).
% 299.99/300.65  224982[26:Rew:224972.2,126419.2] || member(singleton(u),subset_relation)* subclass(omega,u) -> equal(least(element_relation,omega),identity_relation).
% 299.99/300.65  224987[26:SpL:116154.0,224842.1] operation(restrict(u,v,singleton(w))) || subclass(omega,segment(u,v,w))* -> .
% 299.99/300.65  225019[26:SpL:116154.0,224910.1] operation(restrict(u,v,singleton(w))) || equal(segment(u,v,w),omega)** -> .
% 299.99/300.65  225109[7:Obv:225044.0] ||  -> equal(intersection(u,singleton(v)),identity_relation) equal(intersection(intersection(u,singleton(v)),v),identity_relation)**.
% 299.99/300.65  225122[26:SpL:50855.1,224978.0] || member(singleton(u),subset_relation)* equal(u,omega) -> equal(first(singleton(u)),identity_relation).
% 299.99/300.65  225126[26:Rew:225122.2,126489.2] || member(singleton(u),subset_relation)* equal(u,omega) -> equal(least(element_relation,omega),identity_relation).
% 299.99/300.65  225224[7:Obv:225147.0] ||  -> equal(intersection(singleton(u),v),identity_relation) equal(intersection(intersection(singleton(u),v),u),identity_relation)**.
% 299.99/300.65  225244[26:SpL:30.0,224734.0] || subclass(omega,union(u,v)) member(identity_relation,intersection(complement(u),complement(v)))* -> .
% 299.99/300.65  225255[26:SpL:162038.0,224734.0] || subclass(omega,power_class(complement(inverse(identity_relation)))) member(identity_relation,image(element_relation,symmetrization_of(identity_relation)))* -> .
% 299.99/300.65  225256[26:SpL:195257.0,224734.0] || subclass(omega,power_class(complement(singleton(identity_relation)))) member(identity_relation,image(element_relation,singleton(identity_relation)))* -> .
% 299.99/300.65  225267[26:SpL:30.0,224737.0] || subclass(omega,complement(union(u,v))) -> member(identity_relation,intersection(complement(u),complement(v)))*.
% 299.99/300.65  225278[26:SpL:162038.0,224737.0] || subclass(omega,complement(power_class(complement(inverse(identity_relation)))))* -> member(identity_relation,image(element_relation,symmetrization_of(identity_relation))).
% 299.99/300.65  225279[26:SpL:195257.0,224737.0] || subclass(omega,complement(power_class(complement(singleton(identity_relation)))))* -> member(identity_relation,image(element_relation,singleton(identity_relation))).
% 299.99/300.65  225319[7:Obv:225315.1] || subclass(omega,u) -> equal(integer_of(v),identity_relation) subclass(intersection(singleton(v),w),u)*.
% 299.99/300.65  225320[7:Obv:225314.1] || subclass(omega,u) -> equal(integer_of(v),identity_relation) subclass(intersection(w,singleton(v)),u)*.
% 299.99/300.65  225326[26:Res:3618.1,225263.1] || member(identity_relation,symmetric_difference(u,v)) equal(complement(complement(intersection(u,v))),omega)** -> .
% 299.99/300.65  225332[26:Res:67614.1,225263.1] || member(identity_relation,union(u,identity_relation)) equal(complement(symmetric_difference(complement(u),ordinal_numbers)),omega)** -> .
% 299.99/300.65  225454[18:Rew:225453.1,214082.1] || subclass(symmetrization_of(identity_relation),complement(singleton(regular(symmetrization_of(identity_relation)))))* -> subclass(singleton(regular(identity_relation)),u)*.
% 299.99/300.65  225458[8:Rew:162584.0,225405.0] || subclass(u,symmetrization_of(identity_relation)) -> subclass(singleton(regular(u)),symmetrization_of(identity_relation))* equal(u,identity_relation).
% 299.99/300.65  225459[16:Rew:195239.0,225406.0] || subclass(u,singleton(identity_relation)) -> subclass(singleton(regular(u)),singleton(identity_relation))* equal(u,identity_relation).
% 299.99/300.65  225468[7:Obv:225397.2] || subclass(singleton(u),complement(v))* member(u,v) -> equal(singleton(u),identity_relation).
% 299.99/300.65  225502[7:SpL:59.0,225445.0] || subclass(image(element_relation,complement(u)),power_class(u))* -> equal(image(element_relation,complement(u)),identity_relation).
% 299.99/300.65  225514[7:Res:151501.1,225445.0] || member(u,complement(intersection(v,singleton(u))))* -> equal(intersection(v,singleton(u)),identity_relation).
% 299.99/300.65  225515[7:Res:151861.1,225445.0] || member(u,complement(intersection(singleton(u),v)))* -> equal(intersection(singleton(u),v),identity_relation).
% 299.99/300.65  225523[7:Res:215011.1,225445.0] || member(u,complement(complement(complement(singleton(u)))))* -> equal(complement(complement(singleton(u))),identity_relation).
% 299.99/300.65  225565[26:SpL:30.0,225289.0] || equal(complement(union(u,v)),omega) -> member(identity_relation,intersection(complement(u),complement(v)))*.
% 299.99/300.65  225576[26:SpL:162038.0,225289.0] || equal(complement(power_class(complement(inverse(identity_relation)))),omega) -> member(identity_relation,image(element_relation,symmetrization_of(identity_relation)))*.
% 299.99/300.65  225577[26:SpL:195257.0,225289.0] || equal(complement(power_class(complement(singleton(identity_relation)))),omega) -> member(identity_relation,image(element_relation,singleton(identity_relation)))*.
% 299.99/300.66  225880[26:Res:225794.1,490.0] || equal(intersection(complement(u),complement(v)),omega)** member(identity_relation,union(u,v)) -> .
% 299.99/300.66  226075[7:Obv:226052.1] || subclass(symmetric_difference(u,v),complement(union(u,v)))* -> equal(symmetric_difference(u,v),identity_relation).
% 299.99/300.66  226085[25:Res:13125.2,224596.1] || subclass(omega,union_of_range_map) subclass(element_relation,identity_relation) -> equal(integer_of(singleton(singleton(identity_relation))),identity_relation)**.
% 299.99/300.66  226325[21:SpR:50855.1,218966.1] || member(singleton(u),subset_relation) subclass(rest_relation,domain_relation) -> member(ordered_pair(u,identity_relation),rest_relation)*.
% 299.99/300.66  226365[21:Res:226329.1,5.0] || subclass(rest_relation,domain_relation) subclass(rest_relation,u) -> member(singleton(singleton(singleton(identity_relation))),u)*.
% 299.99/300.66  226387[7:Res:13258.1,9876.0] || subclass(u,v)* well_ordering(ordinal_numbers,v)* -> equal(restrict(u,w,x),identity_relation)**.
% 299.99/300.66  226409[8:Res:13258.1,162901.0] || equal(regular(restrict(subset_relation,u,v)),identity_relation)** -> equal(restrict(subset_relation,u,v),identity_relation).
% 299.99/300.66  226410[8:Res:13258.1,162888.0] || subclass(regular(restrict(subset_relation,u,v)),identity_relation)* -> equal(restrict(subset_relation,u,v),identity_relation).
% 299.99/300.66  226446[8:Obv:226441.1] || subclass(restrict(subset_relation,u,v),inverse(subset_relation))* -> equal(restrict(subset_relation,u,v),identity_relation).
% 299.99/300.66  226448[7:Obv:226440.1] || subclass(restrict(u,v,w),complement(u))* -> equal(restrict(u,v,w),identity_relation).
% 299.99/300.66  226741[7:Res:10.1,13238.0] || equal(recursion_equation_functions(u),omega)** -> equal(integer_of(v),identity_relation) subclass(v,cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.66  227132[21:Res:196520.2,210517.1] || member(u,ordinal_numbers)* equal(successor(u),identity_relation) equal(complement(successor_relation),ordinal_numbers) -> .
% 299.99/300.66  227134[21:Res:196520.2,8841.1] || member(u,ordinal_numbers)* equal(successor(u),identity_relation) subclass(ordinal_numbers,complement(successor_relation))* -> .
% 299.99/300.66  227223[8:Res:217451.1,5.0] || equal(union(u,identity_relation),identity_relation) subclass(complement(u),v)* -> member(identity_relation,v).
% 299.99/300.66  227462[8:Res:217663.1,5.0] || equal(union(u,identity_relation),identity_relation) subclass(complement(u),v)* -> member(omega,v).
% 299.99/300.66  228137[8:SpL:72.0,219925.1] || member(image(u,singleton(v)),ordinal_numbers)* equal(singleton(apply(u,v)),identity_relation) -> .
% 299.99/300.66  228153[8:SpL:15528.0,219928.1] || member(not_subclass_element(identity_relation,identity_relation),subset_relation) equal(singleton(range__dfg(identity_relation,u,v)),identity_relation)** -> .
% 299.99/300.66  228229[7:Res:10.1,17313.0] || equal(recursion_equation_functions(u),v)* -> equal(v,identity_relation) subclass(regular(v),cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.66  228367[21:Res:10.1,196427.1] || equal(singleton(u),domain_relation)** member(v,ordinal_numbers) -> equal(ordered_pair(v,identity_relation),u)*.
% 299.99/300.66  228371[8:SpL:8649.0,220841.0] || member(inverse(restrict(u,v,ordinal_numbers)),image(u,v))* subclass(element_relation,identity_relation) -> .
% 299.99/300.66  228407[21:Res:10.1,196457.1] || equal(compose_class(u),domain_relation) member(v,ordinal_numbers) -> equal(compose(u,v),identity_relation)**.
% 299.99/300.66  228570[8:Res:228546.1,9876.0] || equal(complement(u),identity_relation) subclass(successor(u),v)* well_ordering(ordinal_numbers,v) -> .
% 299.99/300.66  228594[5:Res:40074.1,18451.1] || subclass(ordinal_numbers,complement(complement(power_class(u)))) subclass(ordinal_numbers,image(element_relation,complement(u)))* -> .
% 299.99/300.66  228596[5:Res:2504.1,18451.1] || subclass(ordered_pair(u,v),power_class(w))* subclass(ordinal_numbers,image(element_relation,complement(w))) -> .
% 299.99/300.66  228669[8:Res:228646.1,9876.0] || equal(complement(u),identity_relation) subclass(symmetrization_of(u),v)* well_ordering(ordinal_numbers,v) -> .
% 299.99/300.66  228829[8:Res:228806.1,9876.0] || subclass(complement(u),identity_relation)* subclass(successor(u),v)* well_ordering(ordinal_numbers,v) -> .
% 299.99/300.66  228893[25:MRR:228870.2,216168.0] || member(apply(choice,regular(complement(subset_relation))),inverse(subset_relation))* -> equal(regular(complement(subset_relation)),identity_relation).
% 299.99/300.66  228894[18:MRR:228884.2,190496.0] || member(apply(choice,regular(symmetrization_of(identity_relation))),inverse(identity_relation))* -> equal(regular(symmetrization_of(identity_relation)),identity_relation).
% 299.99/300.66  228898[8:Rew:13098.1,228897.1] || member(apply(choice,u),singleton(u))* -> equal(u,identity_relation) equal(singleton(u),identity_relation).
% 299.99/300.66  228966[8:Res:228945.1,9876.0] || subclass(complement(u),identity_relation) subclass(symmetrization_of(u),v)* well_ordering(ordinal_numbers,v) -> .
% 299.99/300.66  229151[7:Res:13061.0,17387.0] ||  -> equal(integer_of(regular(intersection(complement(omega),u))),identity_relation)** equal(intersection(complement(omega),u),identity_relation).
% 299.99/300.66  229192[7:Rew:163.0,229111.1] || member(regular(symmetric_difference(u,v)),intersection(u,v))* -> equal(symmetric_difference(u,v),identity_relation).
% 299.99/300.66  229272[8:SpR:160927.0,229162.0] ||  -> equal(intersection(union(u,symmetric_difference(ordinal_numbers,v)),intersection(complement(u),union(v,identity_relation))),identity_relation)**.
% 299.99/300.66  229273[8:SpR:160992.0,229162.0] ||  -> equal(intersection(union(symmetric_difference(ordinal_numbers,u),v),intersection(union(u,identity_relation),complement(v))),identity_relation)**.
% 299.99/300.66  229285[7:SpR:481.0,229162.0] ||  -> equal(intersection(power_class(intersection(complement(u),complement(v))),image(element_relation,union(u,v))),identity_relation)**.
% 299.99/300.66  229373[16:MRR:229351.2,14676.0] inductive(symmetric_difference(complement(singleton(identity_relation)),complement(singleton(identity_relation)))) || well_ordering(u,singleton(identity_relation))* -> .
% 299.99/300.66  229413[8:SpR:160927.0,229346.0] ||  -> equal(union(union(u,symmetric_difference(ordinal_numbers,v)),intersection(complement(u),union(v,identity_relation))),ordinal_numbers)**.
% 299.99/300.66  229414[8:SpR:160992.0,229346.0] ||  -> equal(union(union(symmetric_difference(ordinal_numbers,u),v),intersection(union(u,identity_relation),complement(v))),ordinal_numbers)**.
% 299.99/300.66  229426[8:SpR:481.0,229346.0] ||  -> equal(union(power_class(intersection(complement(u),complement(v))),image(element_relation,union(u,v))),ordinal_numbers)**.
% 299.99/300.66  229472[8:SpR:160927.0,229359.0] ||  -> equal(symmetric_difference(union(u,symmetric_difference(ordinal_numbers,v)),intersection(complement(u),union(v,identity_relation))),ordinal_numbers)**.
% 299.99/300.66  229473[8:SpR:160992.0,229359.0] ||  -> equal(symmetric_difference(union(symmetric_difference(ordinal_numbers,u),v),intersection(union(u,identity_relation),complement(v))),ordinal_numbers)**.
% 299.99/300.66  229485[8:SpR:481.0,229359.0] ||  -> equal(symmetric_difference(power_class(intersection(complement(u),complement(v))),image(element_relation,union(u,v))),ordinal_numbers)**.
% 299.99/300.66  229580[7:Res:13061.0,13571.0] ||  -> equal(integer_of(regular(intersection(u,complement(omega)))),identity_relation)** equal(intersection(u,complement(omega)),identity_relation).
% 299.99/300.66  229753[8:Rew:66036.0,229616.0] ||  -> equal(union(image(element_relation,union(u,v)),power_class(intersection(complement(u),complement(v)))),ordinal_numbers)**.
% 299.99/300.66  229775[8:MRR:229598.2,14676.0] inductive(symmetric_difference(complement(inverse(identity_relation)),complement(inverse(identity_relation)))) || well_ordering(u,symmetrization_of(identity_relation))* -> .
% 299.99/300.66  229777[8:MRR:229719.2,14676.0] inductive(symmetric_difference(u,complement(complement(u)))) || well_ordering(v,complement(complement(complement(u))))* -> .
% 299.99/300.66  229900[8:SpR:160927.0,229590.0] ||  -> equal(intersection(intersection(complement(u),union(v,identity_relation)),union(u,symmetric_difference(ordinal_numbers,v))),identity_relation)**.
% 299.99/300.66  229901[8:SpR:160992.0,229590.0] ||  -> equal(intersection(intersection(union(u,identity_relation),complement(v)),union(symmetric_difference(ordinal_numbers,u),v)),identity_relation)**.
% 299.99/300.66  229913[7:SpR:481.0,229590.0] ||  -> equal(intersection(image(element_relation,union(u,v)),power_class(intersection(complement(u),complement(v)))),identity_relation)**.
% 299.99/300.66  230024[8:SpR:160927.0,229711.0] ||  -> equal(union(intersection(complement(u),union(v,identity_relation)),union(u,symmetric_difference(ordinal_numbers,v))),ordinal_numbers)**.
% 299.99/300.66  230025[8:SpR:160992.0,229711.0] ||  -> equal(union(intersection(union(u,identity_relation),complement(v)),union(symmetric_difference(ordinal_numbers,u),v)),ordinal_numbers)**.
% 299.99/300.66  230075[8:SpR:160927.0,229733.0] ||  -> equal(symmetric_difference(intersection(complement(u),union(v,identity_relation)),union(u,symmetric_difference(ordinal_numbers,v))),ordinal_numbers)**.
% 299.99/300.66  230076[8:SpR:160992.0,229733.0] ||  -> equal(symmetric_difference(intersection(union(u,identity_relation),complement(v)),union(symmetric_difference(ordinal_numbers,u),v)),ordinal_numbers)**.
% 299.99/300.66  230088[8:SpR:481.0,229733.0] ||  -> equal(symmetric_difference(image(element_relation,union(u,v)),power_class(intersection(complement(u),complement(v)))),ordinal_numbers)**.
% 299.99/300.66  230256[8:MRR:230219.2,14676.0] || member(u,union(inverse(identity_relation),symmetrization_of(identity_relation)))* member(u,complement(symmetrization_of(identity_relation))) -> .
% 299.99/300.66  230356[8:Rew:229276.0,230349.1] || member(not_subclass_element(complement(inverse(identity_relation)),identity_relation),symmetrization_of(identity_relation))* -> subclass(complement(inverse(identity_relation)),identity_relation).
% 299.99/300.66  230473[8:MRR:230419.0,41183.1] ||  -> member(not_subclass_element(u,symmetric_difference(ordinal_numbers,v)),union(v,identity_relation))* subclass(u,symmetric_difference(ordinal_numbers,v)).
% 299.99/300.66  230663[8:Res:40074.1,18754.1] || subclass(ordinal_numbers,complement(complement(u)))* subclass(ordinal_numbers,regular(u)) -> equal(u,identity_relation).
% 299.99/300.66  230673[8:Res:2504.1,18754.1] || subclass(ordered_pair(u,v),w)* subclass(ordinal_numbers,regular(w)) -> equal(w,identity_relation).
% 299.99/300.66  230683[16:MRR:230641.2,215767.0] || subclass(ordinal_numbers,regular(complement(singleton(identity_relation)))) -> subclass(singleton(unordered_pair(u,v)),singleton(identity_relation))*.
% 299.99/300.66  230684[8:MRR:230646.2,218132.1] || member(unordered_pair(u,v),complement(w))* subclass(ordinal_numbers,regular(symmetric_difference(ordinal_numbers,w))) -> .
% 299.99/300.66  230790[8:SpL:6355.1,230675.0] || subclass(ordinal_numbers,regular(not_subclass_element(cross_product(u,v),w)))* -> subclass(cross_product(u,v),w).
% 299.99/300.66  230868[8:SpL:6355.1,230771.0] || equal(complement(not_subclass_element(cross_product(u,v),w)),identity_relation)** -> subclass(cross_product(u,v),w).
% 299.99/300.66  230940[8:SpL:6355.1,230797.0] || equal(regular(not_subclass_element(cross_product(u,v),w)),ordinal_numbers)** -> subclass(cross_product(u,v),w).
% 299.99/300.66  231105[8:Res:13258.1,230762.0] || subclass(ordinal_numbers,regular(restrict(subset_relation,u,v)))* -> equal(restrict(subset_relation,u,v),identity_relation).
% 299.99/300.66  231183[8:Res:13258.1,230780.0] || equal(regular(restrict(subset_relation,u,v)),ordinal_numbers)** -> equal(restrict(subset_relation,u,v),identity_relation).
% 299.99/300.66  231196[7:Res:10.1,13418.0] || equal(restrict(u,v,w),omega)** -> equal(integer_of(x),identity_relation) member(x,u)*.
% 299.99/300.66  231203[8:SpL:13260.1,230798.0] || equal(complement(regular(regular(cross_product(u,v)))),identity_relation)** -> equal(cross_product(u,v),identity_relation).
% 299.99/300.66  231555[8:SpR:162038.0,229281.0] ||  -> equal(intersection(power_class(image(element_relation,symmetrization_of(identity_relation))),image(element_relation,power_class(complement(inverse(identity_relation))))),identity_relation)**.
% 299.99/300.66  231556[16:SpR:195257.0,229281.0] ||  -> equal(intersection(power_class(image(element_relation,singleton(identity_relation))),image(element_relation,power_class(complement(singleton(identity_relation))))),identity_relation)**.
% 299.99/300.66  231819[25:MRR:231783.2,216168.0] || member(not_subclass_element(regular(complement(subset_relation)),u),inverse(subset_relation))* -> subclass(regular(complement(subset_relation)),u).
% 299.99/300.66  231820[18:MRR:231798.2,190496.0] || member(not_subclass_element(regular(symmetrization_of(identity_relation)),u),inverse(identity_relation))* -> subclass(regular(symmetrization_of(identity_relation)),u).
% 299.99/300.66  231824[8:Rew:13098.1,231823.1] || member(not_subclass_element(u,v),singleton(u))* -> subclass(u,v) equal(singleton(u),identity_relation).
% 299.99/300.66  231859[8:SpR:59.0,231812.0] ||  -> subclass(regular(image(element_relation,complement(u))),power_class(u))* equal(image(element_relation,complement(u)),identity_relation).
% 299.99/300.66  231878[8:Res:231812.0,11.0] || subclass(complement(u),regular(u))* -> equal(u,identity_relation) equal(complement(u),regular(u)).
% 299.99/300.66  231900[16:Res:231880.0,19124.0] ||  -> subclass(regular(complement(singleton(identity_relation))),u) equal(not_subclass_element(regular(complement(singleton(identity_relation))),u),identity_relation)**.
% 299.99/300.66  231924[8:SpR:162038.0,229481.0] ||  -> equal(symmetric_difference(power_class(image(element_relation,symmetrization_of(identity_relation))),image(element_relation,power_class(complement(inverse(identity_relation))))),ordinal_numbers)**.
% 299.99/300.66  231925[16:SpR:195257.0,229481.0] ||  -> equal(symmetric_difference(power_class(image(element_relation,singleton(identity_relation))),image(element_relation,power_class(complement(singleton(identity_relation))))),ordinal_numbers)**.
% 299.99/300.66  232044[7:Res:10.1,17323.0] || equal(restrict(u,v,w),x)* -> equal(x,identity_relation) member(regular(x),u)*.
% 299.99/300.66  232248[8:SpR:162038.0,229909.0] ||  -> equal(intersection(image(element_relation,power_class(complement(inverse(identity_relation)))),power_class(image(element_relation,symmetrization_of(identity_relation)))),identity_relation)**.
% 299.99/300.66  232249[16:SpR:195257.0,229909.0] ||  -> equal(intersection(image(element_relation,power_class(complement(singleton(identity_relation)))),power_class(image(element_relation,singleton(identity_relation)))),identity_relation)**.
% 299.99/300.66  232427[8:SpR:162038.0,230084.0] ||  -> equal(symmetric_difference(image(element_relation,power_class(complement(inverse(identity_relation)))),power_class(image(element_relation,symmetrization_of(identity_relation)))),ordinal_numbers)**.
% 299.99/300.66  232428[16:SpR:195257.0,230084.0] ||  -> equal(symmetric_difference(image(element_relation,power_class(complement(singleton(identity_relation)))),power_class(image(element_relation,singleton(identity_relation)))),ordinal_numbers)**.
% 299.99/300.66  232461[8:Res:55.1,69457.0] inductive(complement(compose(element_relation,ordinal_numbers))) || member(u,element_relation)* -> equal(integer_of(u),identity_relation).
% 299.99/300.66  232484[8:Res:41371.0,230867.0] || equal(complement(not_subclass_element(complement(complement(subset_relation)),u)),identity_relation)** -> subclass(complement(complement(subset_relation)),u).
% 299.99/300.66  232485[8:Res:313.1,230867.0] || equal(complement(not_subclass_element(intersection(subset_relation,u),v)),identity_relation)** -> subclass(intersection(subset_relation,u),v).
% 299.99/300.66  232498[8:Res:13069.2,230867.0] || member(subset_relation,ordinal_numbers) equal(complement(apply(choice,subset_relation)),identity_relation)** -> equal(subset_relation,identity_relation).
% 299.99/300.66  232501[8:Res:2503.2,230867.0] || subclass(u,subset_relation) equal(complement(not_subclass_element(u,v)),identity_relation)** -> subclass(u,v).
% 299.99/300.66  232502[8:Res:303.1,230867.0] || equal(complement(not_subclass_element(intersection(u,subset_relation),v)),identity_relation)** -> subclass(intersection(u,subset_relation),v).
% 299.99/300.66  232509[8:Res:13236.2,230867.0] || well_ordering(u,subset_relation) equal(complement(least(u,subset_relation)),identity_relation)** -> equal(subset_relation,identity_relation).
% 299.99/300.66  232510[8:Res:13237.2,230867.0] || well_ordering(u,ordinal_numbers) equal(complement(least(u,subset_relation)),identity_relation)** -> equal(subset_relation,identity_relation).
% 299.99/300.66  232558[8:Res:41371.0,230939.0] || equal(regular(not_subclass_element(complement(complement(subset_relation)),u)),ordinal_numbers)** -> subclass(complement(complement(subset_relation)),u).
% 299.99/300.66  232559[8:Res:313.1,230939.0] || equal(regular(not_subclass_element(intersection(subset_relation,u),v)),ordinal_numbers)** -> subclass(intersection(subset_relation,u),v).
% 299.99/300.66  232572[8:Res:13069.2,230939.0] || member(subset_relation,ordinal_numbers) equal(regular(apply(choice,subset_relation)),ordinal_numbers)** -> equal(subset_relation,identity_relation).
% 299.99/300.66  232575[8:Res:2503.2,230939.0] || subclass(u,subset_relation) equal(regular(not_subclass_element(u,v)),ordinal_numbers)** -> subclass(u,v).
% 299.99/300.66  232576[8:Res:303.1,230939.0] || equal(regular(not_subclass_element(intersection(u,subset_relation),v)),ordinal_numbers)** -> subclass(intersection(u,subset_relation),v).
% 299.99/300.66  232583[8:Res:13236.2,230939.0] || well_ordering(u,subset_relation) equal(regular(least(u,subset_relation)),ordinal_numbers)** -> equal(subset_relation,identity_relation).
% 299.99/300.66  232584[8:Res:13237.2,230939.0] || well_ordering(u,ordinal_numbers) equal(regular(least(u,subset_relation)),ordinal_numbers)** -> equal(subset_relation,identity_relation).
% 299.99/300.66  232745[7:MRR:232742.1,13039.0] || subclass(singleton(least(element_relation,omega)),omega) -> section(element_relation,singleton(least(element_relation,omega)),omega)*.
% 299.99/300.66  232839[8:MRR:232833.1,217156.0] || subclass(ordinal_numbers,u) -> equal(regular(unordered_pair(u,unordered_pair(v,w))),unordered_pair(v,w))**.
% 299.99/300.66  233005[8:SpL:13260.1,232981.0] || subclass(ordinal_numbers,regular(singleton(regular(cross_product(u,v)))))* -> equal(cross_product(u,v),identity_relation).
% 299.99/300.66  233072[8:SpL:13260.1,233013.0] || equal(regular(singleton(regular(cross_product(u,v)))),ordinal_numbers)** -> equal(cross_product(u,v),identity_relation).
% 299.99/300.66  233105[21:Res:196525.2,219073.1] || member(u,ordinal_numbers) equal(sum_class(range_of(u)),identity_relation)** subclass(union_of_range_map,identity_relation) -> .
% 299.99/300.66  233135[8:MRR:233130.1,217161.0] || subclass(ordinal_numbers,u) -> equal(regular(unordered_pair(unordered_pair(v,w),u)),unordered_pair(v,w))**.
% 299.99/300.66  233371[23:Res:231881.0,205619.0] ||  -> equal(singleton(complement(recursion_equation_functions(u))),identity_relation) member(singleton(identity_relation),complement(singleton(complement(recursion_equation_functions(u)))))*.
% 299.99/300.66  233372[23:Res:231881.0,205615.0] || well_ordering(ordinal_numbers,complement(singleton(complement(recursion_equation_functions(u)))))* -> equal(singleton(complement(recursion_equation_functions(u))),identity_relation).
% 299.99/300.66  233565[21:Obv:233549.0] || equal(successor(u),identity_relation) member(u,ordinal_numbers)* subclass(domain_relation,complement(successor_relation))* -> .
% 299.99/300.66  233974[8:Res:13056.1,161200.0] inductive(image(element_relation,union(u,identity_relation))) || member(identity_relation,power_class(symmetric_difference(ordinal_numbers,u)))* -> .
% 299.99/300.66  234075[8:Res:55.1,161050.0] inductive(rest_of(u)) ||  -> equal(integer_of(ordered_pair(v,w)),identity_relation)** member(v,cantor(u))*.
% 299.99/300.66  234084[8:SpL:13260.1,233382.0] || well_ordering(ordinal_numbers,complement(singleton(regular(cross_product(u,v)))))* -> equal(cross_product(u,v),identity_relation).
% 299.99/300.66  234102[8:SpR:50855.1,233383.0] || member(singleton(u),subset_relation) -> member(u,complement(singleton(ordered_pair(first(singleton(u)),v))))*.
% 299.99/300.66  234124[8:SpL:13260.1,234113.0] || subclass(complement(singleton(regular(cross_product(u,v)))),identity_relation)* -> equal(cross_product(u,v),identity_relation).
% 299.99/300.66  234184[8:SpL:50855.1,234106.0] || member(singleton(u),subset_relation) member(u,singleton(ordered_pair(first(singleton(u)),v)))* -> .
% 299.99/300.66  234494[21:MRR:234460.2,8638.0] || equal(complement(u),identity_relation) member(v,ordinal_numbers) -> member(ordered_pair(v,identity_relation),u)*.
% 299.99/300.66  234536[8:Res:2503.2,233381.0] || subclass(u,singleton(omega)) -> subclass(u,v) equal(integer_of(not_subclass_element(u,v)),identity_relation)**.
% 299.99/300.66  234567[21:Res:196657.1,233381.0] || subclass(domain_relation,rotate(singleton(omega))) -> equal(integer_of(ordered_pair(ordered_pair(u,identity_relation),v)),identity_relation)**.
% 299.99/300.66  234569[21:Res:196656.1,233381.0] || subclass(domain_relation,flip(singleton(omega))) -> equal(integer_of(ordered_pair(ordered_pair(u,v),identity_relation)),identity_relation)**.
% 299.99/300.66  234572[8:Res:2504.1,233381.0] || subclass(ordered_pair(u,v),singleton(omega))* -> equal(integer_of(unordered_pair(u,singleton(v))),identity_relation).
% 299.99/300.66  234738[8:MRR:234732.1,217155.0] || subclass(ordinal_numbers,u) -> equal(regular(unordered_pair(u,ordered_pair(v,w))),ordered_pair(v,w))**.
% 299.99/300.66  234751[8:MRR:234749.1,217156.0] || equal(u,ordinal_numbers) -> equal(regular(unordered_pair(u,unordered_pair(v,w))),unordered_pair(v,w))**.
% 299.99/300.66  234768[8:MRR:234763.1,217160.0] || subclass(ordinal_numbers,u) -> equal(regular(unordered_pair(ordered_pair(v,w),u)),ordered_pair(v,w))**.
% 299.99/300.66  234777[8:MRR:234776.1,217161.0] || equal(u,ordinal_numbers) -> equal(regular(unordered_pair(unordered_pair(v,w),u)),unordered_pair(v,w))**.
% 299.99/300.66  234866[18:MRR:234847.0,13126.0] || equal(complement(cantor(u)),inverse(identity_relation)) -> equal(apply(u,identity_relation),sum_class(range_of(identity_relation)))**.
% 299.99/300.66  234867[18:MRR:234848.0,13126.0] || equal(complement(cantor(u)),symmetrization_of(identity_relation)) -> equal(apply(u,identity_relation),sum_class(range_of(identity_relation)))**.
% 299.99/300.66  234868[14:MRR:234849.0,13126.0] || equal(complement(cantor(u)),singleton(identity_relation)) -> equal(apply(u,identity_relation),sum_class(range_of(identity_relation)))**.
% 299.99/300.66  234876[15:MRR:234821.0,165460.0] || subclass(ordinal_numbers,complement(cantor(u)))* -> equal(apply(u,range_of(identity_relation)),sum_class(range_of(identity_relation))).
% 299.99/300.66  234877[8:MRR:234835.0,8655.0] || subclass(ordinal_numbers,complement(cantor(u)))* -> equal(apply(u,singleton(v)),sum_class(range_of(identity_relation)))**.
% 299.99/300.66  234878[8:MRR:234834.0,8655.0] || well_ordering(ordinal_numbers,cantor(u)) -> equal(apply(u,singleton(singleton(v))),sum_class(range_of(identity_relation)))**.
% 299.99/300.66  234885[8:MRR:234824.0,41183.1] ||  -> equal(apply(u,not_subclass_element(v,cantor(u))),sum_class(range_of(identity_relation)))** subclass(v,cantor(u)).
% 299.99/300.66  234921[8:MRR:234919.1,217155.0] || equal(u,ordinal_numbers) -> equal(regular(unordered_pair(u,ordered_pair(v,w))),ordered_pair(v,w))**.
% 299.99/300.66  234934[8:MRR:234933.1,217160.0] || equal(u,ordinal_numbers) -> equal(regular(unordered_pair(ordered_pair(v,w),u)),ordered_pair(v,w))**.
% 299.99/300.66  235147[10:SpL:223660.1,234983.0] || subclass(element_relation,identity_relation) member(cross_product(ordinal_numbers,ordinal_numbers),cantor(complement(cross_product(identity_relation,ordinal_numbers))))* -> .
% 299.99/300.66  235164[8:Res:2503.2,234983.0] || subclass(u,cantor(complement(cross_product(singleton(not_subclass_element(u,v)),ordinal_numbers))))* -> subclass(u,v).
% 299.99/300.66  235165[8:Res:8978.2,234983.0] || member(u,ordinal_numbers) subclass(ordinal_numbers,cantor(complement(cross_product(singleton(sum_class(u)),ordinal_numbers))))* -> .
% 299.99/300.66  235167[8:Res:8977.2,234983.0] || member(u,ordinal_numbers) subclass(ordinal_numbers,cantor(complement(cross_product(singleton(power_class(u)),ordinal_numbers))))* -> .
% 299.99/300.66  235187[21:Res:196657.1,234983.0] || subclass(domain_relation,rotate(cantor(complement(cross_product(singleton(ordered_pair(ordered_pair(u,identity_relation),v)),ordinal_numbers)))))* -> .
% 299.99/300.66  235190[21:Res:196656.1,234983.0] || subclass(domain_relation,flip(cantor(complement(cross_product(singleton(ordered_pair(ordered_pair(u,v),identity_relation)),ordinal_numbers)))))* -> .
% 299.99/300.66  235193[8:Res:2504.1,234983.0] || subclass(ordered_pair(u,v),cantor(complement(cross_product(singleton(unordered_pair(u,singleton(v))),ordinal_numbers))))* -> .
% 299.99/300.66  235268[8:Res:230445.1,9876.0] || member(u,v)* subclass(union(v,identity_relation),w)* well_ordering(ordinal_numbers,w) -> .
% 299.99/300.66  235310[8:Rew:66036.0,235266.1] || member(u,image(element_relation,complement(v))) -> member(u,complement(intersection(power_class(v),ordinal_numbers)))*.
% 299.99/300.66  235313[8:MRR:235307.2,235274.1] || member(regular(regular(union(u,identity_relation))),u)* -> equal(regular(union(u,identity_relation)),identity_relation).
% 299.99/300.66  235443[5:Res:28980.1,149.0] || subclass(rest_relation,flip(rest_relation)) -> equal(rest_of(ordered_pair(u,v)),rest_of(ordered_pair(v,u)))*.
% 299.99/300.66  235455[5:Res:28980.1,49.0] || subclass(rest_relation,flip(successor_relation)) -> equal(rest_of(ordered_pair(u,v)),successor(ordered_pair(v,u)))**.
% 299.99/300.66  235571[5:Res:28979.1,149.0] || subclass(rest_relation,rotate(rest_relation)) -> equal(rest_of(ordered_pair(u,rest_of(ordered_pair(v,u)))),v)**.
% 299.99/300.66  235583[5:Res:28979.1,49.0] || subclass(rest_relation,rotate(successor_relation)) -> equal(successor(ordered_pair(u,rest_of(ordered_pair(v,u)))),v)**.
% 299.99/300.66  235590[8:Res:28979.1,117450.1] operation(u) || subclass(rest_relation,rotate(cantor(u))) -> member(v,cantor(cantor(u)))*.
% 299.99/300.66  235790[5:Res:55.1,19113.0] inductive(recursion_equation_functions(u)) ||  -> subclass(omega,v) subclass(not_subclass_element(omega,v),cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.66  235848[7:Res:55.1,13339.0] inductive(u) || subclass(u,v)* -> equal(integer_of(w),identity_relation) member(w,v)*.
% 299.99/300.66  236175[8:SpL:50855.1,234409.0] || member(singleton(u),subset_relation) equal(complement(complement(singleton(singleton(singleton(u))))),ordinal_numbers)** -> .
% 299.99/300.66  236187[8:SpL:50855.1,234639.0] || member(singleton(u),subset_relation) subclass(ordinal_numbers,complement(complement(singleton(singleton(singleton(u))))))* -> .
% 299.99/300.66  236203[8:SpL:50855.1,235177.0] || member(singleton(u),subset_relation) equal(cantor(complement(cross_product(singleton(u),ordinal_numbers))),ordinal_numbers)** -> .
% 299.99/300.66  236334[8:SpL:50855.1,235179.0] || member(singleton(u),subset_relation) subclass(ordinal_numbers,cantor(complement(cross_product(singleton(u),ordinal_numbers))))* -> .
% 299.99/300.66  236879[8:Res:17392.2,210517.1] || subclass(u,v)* equal(complement(v),ordinal_numbers) -> equal(intersection(u,w),identity_relation)**.
% 299.99/300.66  236989[26:Res:225888.1,5.0] || equal(symmetric_difference(ordinal_numbers,u),omega) subclass(complement(u),v)* -> member(identity_relation,v).
% 299.99/300.66  237351[8:Rew:237182.0,237340.1] || member(not_subclass_element(intersection(u,subset_relation),identity_relation),inverse(subset_relation))* -> subclass(intersection(u,subset_relation),identity_relation).
% 299.99/300.66  237461[7:SpR:189.0,237181.0] ||  -> equal(intersection(power_class(image(element_relation,complement(u))),intersection(v,image(element_relation,power_class(u)))),identity_relation)**.
% 299.99/300.66  237547[7:Rew:237181.0,237522.1] || member(not_subclass_element(intersection(u,v),identity_relation),complement(v))* -> subclass(intersection(u,v),identity_relation).
% 299.99/300.66  238013[8:Rew:237831.0,238001.1] || member(not_subclass_element(intersection(subset_relation,u),identity_relation),inverse(subset_relation))* -> subclass(intersection(subset_relation,u),identity_relation).
% 299.99/300.66  238180[7:SpR:3606.0,237830.0] ||  -> equal(intersection(complement(complement(restrict(u,v,w))),symmetric_difference(cross_product(v,w),u)),identity_relation)**.
% 299.99/300.66  238181[7:SpR:3603.0,237830.0] ||  -> equal(intersection(complement(complement(restrict(u,v,w))),symmetric_difference(u,cross_product(v,w))),identity_relation)**.
% 299.99/300.66  238243[7:SpR:189.0,237830.0] ||  -> equal(intersection(power_class(image(element_relation,complement(u))),intersection(image(element_relation,power_class(u)),v)),identity_relation)**.
% 299.99/300.66  238320[7:Rew:237830.0,238304.1] || member(not_subclass_element(intersection(u,v),identity_relation),complement(u))* -> subclass(intersection(u,v),identity_relation).
% 299.99/300.66  238380[8:SpR:162038.0,238174.0] ||  -> equal(intersection(complement(power_class(complement(inverse(identity_relation)))),symmetric_difference(ordinal_numbers,image(element_relation,symmetrization_of(identity_relation)))),identity_relation)**.
% 299.99/300.66  238381[16:SpR:195257.0,238174.0] ||  -> equal(intersection(complement(power_class(complement(singleton(identity_relation)))),symmetric_difference(ordinal_numbers,image(element_relation,singleton(identity_relation)))),identity_relation)**.
% 299.99/300.66  238613[8:Res:13572.2,210517.1] || subclass(u,v)* equal(complement(v),ordinal_numbers) -> equal(intersection(w,u),identity_relation)**.
% 299.99/300.66  238702[16:SpR:238387.0,154737.1] || subclass(symmetric_difference(ordinal_numbers,singleton(identity_relation)),singleton(identity_relation))* -> equal(symmetric_difference(ordinal_numbers,singleton(identity_relation)),identity_relation).
% 299.99/300.66  238810[8:SpR:238388.0,154737.1] || subclass(symmetric_difference(ordinal_numbers,inverse(identity_relation)),symmetrization_of(identity_relation))* -> equal(symmetric_difference(ordinal_numbers,inverse(identity_relation)),identity_relation).
% 299.99/300.66  238933[7:SpR:30.0,237395.0] ||  -> equal(intersection(union(u,v),restrict(intersection(complement(u),complement(v)),w,x)),identity_relation)**.
% 299.99/300.66  238944[8:SpR:162038.0,237395.0] ||  -> equal(intersection(power_class(complement(inverse(identity_relation))),restrict(image(element_relation,symmetrization_of(identity_relation)),u,v)),identity_relation)**.
% 299.99/300.66  238945[16:SpR:195257.0,237395.0] ||  -> equal(intersection(power_class(complement(singleton(identity_relation))),restrict(image(element_relation,singleton(identity_relation)),u,v)),identity_relation)**.
% 299.99/300.66  239833[7:SpR:189.0,239340.0] ||  -> equal(intersection(intersection(image(element_relation,power_class(u)),v),power_class(image(element_relation,complement(u)))),identity_relation)**.
% 299.99/300.66  239853[7:SpR:3606.0,239340.0] ||  -> equal(intersection(symmetric_difference(cross_product(u,v),w),complement(complement(restrict(w,u,v)))),identity_relation)**.
% 299.99/300.66  239854[7:SpR:3603.0,239340.0] ||  -> equal(intersection(symmetric_difference(u,cross_product(v,w)),complement(complement(restrict(u,v,w)))),identity_relation)**.
% 299.99/300.66  19325[0:Res:18950.0,11.0] || subclass(union(u,v),symmetric_difference(u,v))* -> equal(symmetric_difference(u,v),union(u,v)).
% 299.99/300.66  36170[0:SpR:482.0,18950.0] ||  -> subclass(symmetric_difference(intersection(complement(u),complement(v)),w),complement(intersection(union(u,v),complement(w))))*.
% 299.99/300.66  36222[0:SpR:483.0,18950.0] ||  -> subclass(symmetric_difference(u,intersection(complement(v),complement(w))),complement(intersection(complement(u),union(v,w))))*.
% 299.99/300.66  56409[5:Res:41112.1,5.0] || member(u,rest_of(u)) subclass(element_relation,v) -> member(ordered_pair(u,rest_of(u)),v)*.
% 299.99/300.66  18743[8:Res:17124.1,5.0] || member(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers) subclass(domain_relation,u) -> member(least(element_relation,domain_relation),u)*.
% 299.99/300.66  46484[8:Res:41203.1,5.0] || member(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers) subclass(ordinal_numbers,u) -> member(least(element_relation,domain_relation),u)*.
% 299.99/300.66  18846[5:Res:18819.1,8800.1] || member(ordered_pair(u,v),subset_relation)* member(u,v) -> member(ordered_pair(u,v),element_relation).
% 299.99/300.66  56442[5:Res:2503.2,56411.0] || subclass(u,rest_of(not_subclass_element(u,v)))* subclass(ordinal_numbers,complement(element_relation)) -> subclass(u,v).
% 299.99/300.66  9631[5:SpL:30.0,9496.0] || subclass(ordinal_numbers,complement(union(u,v))) -> member(singleton(w),intersection(complement(u),complement(v)))*.
% 299.99/300.66  29146[5:Res:8645.1,490.0] || subclass(ordinal_numbers,intersection(complement(u),complement(v)))* member(singleton(w),union(u,v))* -> .
% 299.99/300.66  18797[5:Res:3618.1,8843.1] || member(singleton(u),symmetric_difference(v,w))* subclass(ordinal_numbers,complement(complement(intersection(v,w))))* -> .
% 299.99/300.66  51207[5:SpR:50855.1,47.0] || member(singleton(u),subset_relation) -> equal(union(first(singleton(u)),u),successor(first(singleton(u))))**.
% 299.99/300.66  51215[5:SpR:50855.1,19314.0] || member(singleton(u),subset_relation) -> subclass(symmetric_difference(first(singleton(u)),u),successor(first(singleton(u))))*.
% 299.99/300.66  51317[5:Rew:50855.1,51210.1] || member(singleton(u),subset_relation)* -> subclass(u,v) equal(not_subclass_element(u,v),first(singleton(u)))**.
% 299.99/300.66  19341[0:Res:19314.0,11.0] || subclass(successor(u),symmetric_difference(u,singleton(u)))* -> equal(symmetric_difference(u,singleton(u)),successor(u)).
% 299.99/300.66  51568[5:Res:51204.1,5.0] || member(singleton(u),subset_relation) subclass(singleton(singleton(u)),v)* -> member(singleton(u),v).
% 299.99/300.66  18820[5:Res:9632.1,897.0] || equal(complement(complement(restrict(u,v,w))),ordinal_numbers)** -> member(singleton(x),cross_product(v,w))*.
% 299.99/300.66  51530[5:Rew:51324.2,51529.2] || member(singleton(u),subset_relation) member(u,subset_relation) -> member(first(u),singleton(first(u)))*.
% 299.99/300.66  50854[5:Res:49995.1,898.0] || member(restrict(u,v,w),subset_relation) -> member(singleton(first(restrict(u,v,w))),u)*.
% 299.99/300.66  50866[5:Res:49995.1,3617.0] || member(symmetric_difference(u,v),subset_relation) -> member(singleton(first(symmetric_difference(u,v))),union(u,v))*.
% 299.99/300.66  49661[5:SpL:6355.1,39306.0] || equal(complement(singleton(not_subclass_element(cross_product(u,v),w))),ordinal_numbers)** -> subclass(cross_product(u,v),w).
% 299.99/300.66  49660[5:SpL:6355.1,39295.0] || subclass(ordinal_numbers,complement(singleton(not_subclass_element(cross_product(u,v),w))))* -> subclass(cross_product(u,v),w).
% 299.99/300.66  45609[5:Obv:45598.0] ||  -> equal(not_subclass_element(unordered_pair(u,v),w),v)** subclass(unordered_pair(u,v),w) member(u,ordinal_numbers).
% 299.99/300.66  45610[5:Obv:45589.0] ||  -> equal(not_subclass_element(unordered_pair(u,v),w),u)** subclass(unordered_pair(u,v),w) member(v,ordinal_numbers).
% 299.99/300.66  56845[5:SpL:3616.0,8846.0] || subclass(ordinal_numbers,symmetric_difference(complement(u),complement(v))) -> member(unordered_pair(w,x),union(u,v))*.
% 299.99/300.66  19123[0:Res:2503.2,898.0] || subclass(u,restrict(v,w,x))* -> subclass(u,y) member(not_subclass_element(u,y),v)*.
% 299.99/300.66  18850[5:Res:18819.1,290.0] || member(not_subclass_element(complement(cross_product(ordinal_numbers,ordinal_numbers)),u),subset_relation)* -> subclass(complement(cross_product(ordinal_numbers,ordinal_numbers)),u).
% 299.99/300.66  19063[0:Rew:163.0,18999.0] ||  -> subclass(symmetric_difference(u,v),w) member(not_subclass_element(symmetric_difference(u,v),w),complement(intersection(u,v)))*.
% 299.99/300.66  18993[5:Res:18949.0,8787.1] single_valued_class(restrict(cross_product(ordinal_numbers,ordinal_numbers),u,v)) ||  -> function(restrict(cross_product(ordinal_numbers,ordinal_numbers),u,v))*.
% 299.99/300.66  18773[0:SpR:33.0,3618.1] || member(u,symmetric_difference(cross_product(v,w),x))* -> member(u,complement(restrict(x,v,w))).
% 299.99/300.66  68294[5:SpL:3606.0,8735.0] || equal(symmetric_difference(cross_product(u,v),w),ordinal_numbers) -> member(omega,complement(restrict(w,u,v)))*.
% 299.99/300.66  68317[5:SpL:3606.0,8732.0] || subclass(ordinal_numbers,symmetric_difference(cross_product(u,v),w)) -> member(omega,complement(restrict(w,u,v)))*.
% 299.99/300.66  18770[0:SpR:32.0,3618.1] || member(u,symmetric_difference(v,cross_product(w,x)))* -> member(u,complement(restrict(v,w,x))).
% 299.99/300.66  68293[5:SpL:3603.0,8735.0] || equal(symmetric_difference(u,cross_product(v,w)),ordinal_numbers) -> member(omega,complement(restrict(u,v,w)))*.
% 299.99/300.66  68316[5:SpL:3603.0,8732.0] || subclass(ordinal_numbers,symmetric_difference(u,cross_product(v,w))) -> member(omega,complement(restrict(u,v,w)))*.
% 299.99/300.66  39270[5:Res:20.2,8841.1] || member(u,v)* member(w,x)* subclass(ordinal_numbers,complement(cross_product(x,v)))* -> .
% 299.99/300.66  19352[0:Res:19315.0,11.0] || subclass(symmetrization_of(u),symmetric_difference(u,inverse(u)))* -> equal(symmetric_difference(u,inverse(u)),symmetrization_of(u)).
% 299.99/300.66  80083[8:Res:64007.1,5.0] || member(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers) subclass(rest_relation,u) -> member(least(element_relation,rest_relation),u)*.
% 299.99/300.66  80199[10:Res:76912.1,5.0] || member(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers) subclass(element_relation,u) -> member(least(element_relation,element_relation),u)*.
% 299.99/300.66  81042[8:Res:80082.1,5.0] || member(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers) subclass(ordinal_numbers,u) -> member(least(element_relation,rest_relation),u)*.
% 299.99/300.66  81060[10:Res:80198.1,5.0] || member(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers) subclass(ordinal_numbers,u) -> member(least(element_relation,element_relation),u)*.
% 299.99/300.66  83819[5:Res:8881.1,5.0] || subclass(ordinal_numbers,symmetric_difference(u,v)) subclass(union(u,v),w)* -> member(omega,w).
% 299.99/300.66  83839[5:Res:8892.1,5.0] || equal(symmetric_difference(u,v),ordinal_numbers) subclass(union(u,v),w)* -> member(omega,w).
% 299.99/300.66  94667[8:Res:39298.1,66086.1] || subclass(ordinal_numbers,complement(complement(complement(compose(element_relation,ordinal_numbers)))))* member(ordered_pair(u,v),element_relation)* -> .
% 299.99/300.66  94673[5:Res:39298.1,5.0] || subclass(ordinal_numbers,complement(complement(u)))* subclass(u,v)* -> member(ordered_pair(w,x),v)*.
% 299.99/300.66  94677[5:Res:39298.1,3617.0] || subclass(ordinal_numbers,complement(complement(symmetric_difference(u,v)))) -> member(ordered_pair(w,x),union(u,v))*.
% 299.99/300.66  96355[8:Res:40074.1,66086.1] || subclass(ordinal_numbers,complement(complement(complement(compose(element_relation,ordinal_numbers)))))* member(unordered_pair(u,v),element_relation)* -> .
% 299.99/300.66  96361[5:Res:40074.1,5.0] || subclass(ordinal_numbers,complement(complement(u)))* subclass(u,v)* -> member(unordered_pair(w,x),v)*.
% 299.99/300.66  96365[5:Res:40074.1,3617.0] || subclass(ordinal_numbers,complement(complement(symmetric_difference(u,v)))) -> member(unordered_pair(w,x),union(u,v))*.
% 299.99/300.66  115509[5:Res:40074.1,19559.0] || subclass(ordinal_numbers,complement(complement(symmetric_difference(u,singleton(u)))))* -> member(unordered_pair(v,w),successor(u))*.
% 299.99/300.66  115538[5:Res:39298.1,19559.0] || subclass(ordinal_numbers,complement(complement(symmetric_difference(u,singleton(u)))))* -> member(ordered_pair(v,w),successor(u))*.
% 299.99/300.66  116625[8:Rew:116078.0,19856.0] ||  -> equal(cantor(restrict(cross_product(u,singleton(v)),w,x)),segment(cross_product(w,x),u,v))**.
% 299.99/300.66  117466[8:Rew:116078.0,116737.2] || member(u,cantor(u)) subclass(element_relation,v) -> member(ordered_pair(u,cantor(u)),v)*.
% 299.99/300.66  116864[8:Rew:116078.0,82924.1] || member(singleton(u),subset_relation)* equal(cantor(u),ordinal_numbers) subclass(ordinal_numbers,complement(element_relation)) -> .
% 299.99/300.66  124625[5:Res:40074.1,19676.0] || subclass(ordinal_numbers,complement(complement(symmetric_difference(u,inverse(u)))))* -> member(unordered_pair(v,w),symmetrization_of(u))*.
% 299.99/300.66  124656[5:Res:39298.1,19676.0] || subclass(ordinal_numbers,complement(complement(symmetric_difference(u,inverse(u)))))* -> member(ordered_pair(v,w),symmetrization_of(u))*.
% 299.99/300.66  125803[8:SpL:117066.0,116738.1] || subclass(domain_relation,inverse(subset_relation)) member(ordered_pair(flip(cross_product(u,ordinal_numbers)),inverse(u)),subset_relation)* -> .
% 299.99/300.66  125804[8:SpL:117142.0,116738.1] || subclass(domain_relation,inverse(subset_relation)) member(ordered_pair(restrict(element_relation,ordinal_numbers,u),sum_class(u)),subset_relation)* -> .
% 299.99/300.66  127978[8:Res:126679.1,66086.1] || subclass(omega,complement(complement(complement(compose(element_relation,ordinal_numbers)))))* member(least(element_relation,omega),element_relation) -> .
% 299.99/300.66  127986[5:Res:126679.1,5.0] || subclass(omega,complement(complement(u)))* subclass(u,v)* -> member(least(element_relation,omega),v)*.
% 299.99/300.66  127990[5:Res:126679.1,3617.0] || subclass(omega,complement(complement(symmetric_difference(u,v)))) -> member(least(element_relation,omega),union(u,v))*.
% 299.99/300.66  127991[5:Res:126679.1,19559.0] || subclass(omega,complement(complement(symmetric_difference(u,singleton(u)))))* -> member(least(element_relation,omega),successor(u)).
% 299.99/300.66  127992[5:Res:126679.1,19676.0] || subclass(omega,complement(complement(symmetric_difference(u,inverse(u)))))* -> member(least(element_relation,omega),symmetrization_of(u)).
% 299.99/300.66  128312[8:Res:127147.1,66086.1] || subclass(ordinal_numbers,complement(complement(complement(compose(element_relation,ordinal_numbers)))))* member(least(element_relation,omega),element_relation) -> .
% 299.99/300.66  128320[5:Res:127147.1,5.0] || subclass(ordinal_numbers,complement(complement(u)))* subclass(u,v)* -> member(least(element_relation,omega),v)*.
% 299.99/300.66  128324[5:Res:127147.1,3617.0] || subclass(ordinal_numbers,complement(complement(symmetric_difference(u,v)))) -> member(least(element_relation,omega),union(u,v))*.
% 299.99/300.66  128325[5:Res:127147.1,19559.0] || subclass(ordinal_numbers,complement(complement(symmetric_difference(u,singleton(u)))))* -> member(least(element_relation,omega),successor(u)).
% 299.99/300.66  128326[5:Res:127147.1,19676.0] || subclass(ordinal_numbers,complement(complement(symmetric_difference(u,inverse(u)))))* -> member(least(element_relation,omega),symmetrization_of(u)).
% 299.99/300.66  130521[5:SpL:3616.0,125908.0] || subclass(omega,symmetric_difference(complement(u),complement(v))) -> member(least(element_relation,omega),union(u,v))*.
% 299.99/300.66  130625[5:Res:41371.0,28.1] || member(not_subclass_element(complement(complement(complement(u))),v),u)* -> subclass(complement(complement(complement(u))),v).
% 299.99/300.66  130658[8:Res:41371.0,14679.1] || member(not_subclass_element(complement(complement(inverse(subset_relation))),u),subset_relation)* -> subclass(complement(complement(inverse(subset_relation))),u).
% 299.99/300.66  130909[5:Res:2503.2,9876.0] || subclass(u,v)* subclass(v,w)* well_ordering(ordinal_numbers,w)* -> subclass(u,x)*.
% 299.99/300.66  131387[0:SpL:32.0,18794.1] || member(u,symmetric_difference(v,cross_product(w,x)))* member(u,restrict(v,w,x)) -> .
% 299.99/300.66  131390[0:SpL:33.0,18794.1] || member(u,symmetric_difference(cross_product(v,w),x))* member(u,restrict(x,v,w)) -> .
% 299.99/300.66  131442[0:Res:6.1,18794.1] || member(not_subclass_element(intersection(u,v),w),symmetric_difference(u,v))* -> subclass(intersection(u,v),w).
% 299.99/300.66  131568[5:Res:2504.1,56411.0] || subclass(ordered_pair(u,v),rest_of(unordered_pair(u,singleton(v))))* subclass(ordinal_numbers,complement(element_relation)) -> .
% 299.99/300.66  131570[0:Res:2504.1,898.0] || subclass(ordered_pair(u,v),restrict(w,x,y))* -> member(unordered_pair(u,singleton(v)),w).
% 299.99/300.66  132789[5:SpL:3616.0,125985.0] || subclass(ordinal_numbers,symmetric_difference(complement(u),complement(v))) -> member(least(element_relation,omega),union(u,v))*.
% 299.99/300.66  132883[5:SpL:3616.0,130556.0] || equal(symmetric_difference(complement(u),complement(v)),omega) -> member(least(element_relation,omega),union(u,v))*.
% 299.99/300.66  133988[5:Res:3618.1,133836.0] || member(singleton(singleton(u)),symmetric_difference(v,w))* well_ordering(ordinal_numbers,complement(intersection(v,w))) -> .
% 299.99/300.66  134033[5:MRR:133990.0,8655.0] || well_ordering(ordinal_numbers,intersection(complement(u),complement(v)))* -> member(singleton(singleton(w)),union(u,v))*.
% 299.99/300.66  134111[5:Res:133837.1,897.0] || well_ordering(ordinal_numbers,complement(restrict(u,v,w)))* -> member(singleton(singleton(x)),cross_product(v,w))*.
% 299.99/300.66  134413[5:SpL:3616.0,132824.0] || equal(symmetric_difference(complement(u),complement(v)),ordinal_numbers) -> member(least(element_relation,omega),union(u,v))*.
% 299.99/300.66  135082[8:SpR:116154.0,135059.1] || equal(rest_of(restrict(u,v,singleton(w))),rest_relation)** -> subclass(x,segment(u,v,w))*.
% 299.99/300.66  136694[5:Res:8642.1,18791.0] || subclass(ordinal_numbers,symmetric_difference(complement(u),complement(v))) -> member(ordered_pair(w,x),union(u,v))*.
% 299.99/300.66  139827[5:MRR:139782.0,41183.1] ||  -> member(not_subclass_element(complement(union(u,v)),w),complement(v))* subclass(complement(union(u,v)),w).
% 299.99/300.66  139910[5:MRR:139868.0,41183.1] ||  -> member(not_subclass_element(complement(union(u,v)),w),complement(u))* subclass(complement(union(u,v)),w).
% 299.99/300.66  140441[5:Rew:33.0,140402.1,33.0,140402.0] || member(not_subclass_element(u,restrict(u,ordinal_numbers,ordinal_numbers)),subset_relation)* -> subclass(u,restrict(u,ordinal_numbers,ordinal_numbers)).
% 299.99/300.66  145764[5:SpR:143170.0,122.1] || transitive(ordinal_numbers,u) -> subclass(compose(cross_product(u,u),cross_product(u,u)),cross_product(u,u))*.
% 299.99/300.66  145782[8:SpL:143170.0,116152.0] || equal(cantor(cross_product(u,v)),v)** subclass(v,u) -> section(ordinal_numbers,v,u).
% 299.99/300.66  145783[5:SpL:143170.0,123.0] || subclass(compose(cross_product(u,u),cross_product(u,u)),cross_product(u,u))* -> transitive(ordinal_numbers,u).
% 299.99/300.66  145784[5:SpL:143170.0,9777.0] || equal(compose(cross_product(u,u),cross_product(u,u)),cross_product(u,u))** -> transitive(ordinal_numbers,u).
% 299.99/300.66  145792[8:SpL:143170.0,116155.1] || subclass(u,v) subclass(cantor(cross_product(v,u)),u)* -> section(ordinal_numbers,u,v).
% 299.99/300.66  147944[8:SpL:140613.0,18581.1] || member(u,ordinal_numbers) subclass(ordinal_numbers,symmetric_difference(ordinal_numbers,v)) -> member(sum_class(u),complement(v))*.
% 299.99/300.66  148895[8:Res:148858.1,8836.1] || subclass(unordered_pair(u,v),inverse(subset_relation))* member(u,ordinal_numbers) -> member(u,complement(subset_relation)).
% 299.99/300.66  148897[8:Res:148858.1,8837.1] || subclass(unordered_pair(u,v),inverse(subset_relation))* member(v,ordinal_numbers) -> member(v,complement(subset_relation)).
% 299.99/300.66  148942[8:Res:148858.1,40321.0] || subclass(rest_relation,inverse(subset_relation)) well_ordering(u,complement(subset_relation)) -> member(least(u,rest_relation),rest_relation)*.
% 299.99/300.66  151528[0:Obv:151477.1] || member(u,v) -> subclass(intersection(w,singleton(u)),intersection(v,intersection(w,singleton(u))))*.
% 299.99/300.66  151892[0:Obv:151835.1] || member(u,v) -> subclass(intersection(singleton(u),w),intersection(v,intersection(singleton(u),w)))*.
% 299.99/300.66  151939[5:SpR:30.0,147905.0] ||  -> equal(intersection(intersection(complement(u),complement(v)),complement(union(u,v))),complement(union(u,v)))**.
% 299.99/300.66  152897[8:SpL:140613.0,19121.0] || subclass(u,symmetric_difference(ordinal_numbers,v)) -> subclass(u,w) member(not_subclass_element(u,w),complement(v))*.
% 299.99/300.66  153484[8:Res:153473.0,11.0] || subclass(complement(element_relation),complement(compose(element_relation,ordinal_numbers)))* -> equal(complement(compose(element_relation,ordinal_numbers)),complement(element_relation)).
% 299.99/300.66  155563[0:SpR:3616.0,154945.0] ||  -> equal(intersection(union(u,v),symmetric_difference(complement(u),complement(v))),symmetric_difference(complement(u),complement(v)))**.
% 299.99/300.66  156400[5:SpR:155665.0,19069.0] ||  -> subclass(symmetric_difference(complement(subset_relation),union(subset_relation,cross_product(ordinal_numbers,ordinal_numbers))),complement(symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers))))*.
% 299.99/300.66  156509[5:SpR:155666.0,19069.0] ||  -> subclass(symmetric_difference(complement(subset_relation),union(cross_product(ordinal_numbers,ordinal_numbers),subset_relation)),complement(symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation)))*.
% 299.99/300.66  156919[8:Res:156893.0,11.0] || subclass(complement(subset_relation),intersection(u,inverse(subset_relation)))* -> equal(intersection(u,inverse(subset_relation)),complement(subset_relation)).
% 299.99/300.66  157049[8:Res:157013.0,11.0] || subclass(complement(subset_relation),intersection(inverse(subset_relation),u))* -> equal(intersection(inverse(subset_relation),u),complement(subset_relation)).
% 299.99/300.66  157063[8:Res:157036.0,11.0] || subclass(complement(subset_relation),complement(complement(inverse(subset_relation))))* -> equal(complement(complement(inverse(subset_relation))),complement(subset_relation)).
% 299.99/300.66  159556[5:Res:10.1,28944.1] || equal(singleton(u),rest_relation)** member(v,ordinal_numbers) -> equal(ordered_pair(v,rest_of(v)),u)*.
% 299.99/300.66  159674[5:Res:10.1,28963.1] || equal(compose_class(u),rest_relation) member(v,ordinal_numbers) -> equal(compose(u,v),rest_of(v))**.
% 299.99/300.66  147325[5:SoR:10704.0,28934.2] || subclass(rest_relation,recursion_equation_functions(u))* member(v,ordinal_numbers) -> member(singleton(v),cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.66  117453[8:Rew:116078.0,116540.2,116078.0,116540.1] operation(u) || subclass(ordinal_numbers,complement(complement(cantor(u))))* -> member(v,cantor(cantor(u)))*.
% 299.99/300.66  117454[8:Rew:116078.0,116547.2,116078.0,116547.1] operation(u) || member(v,cantor(cantor(u)))* subclass(ordinal_numbers,complement(cantor(u))) -> .
% 299.99/300.66  155251[8:SpR:154737.1,116209.1] operation(u) || subclass(cantor(u),v) -> equal(intersection(cantor(u),v),cantor(u))**.
% 299.99/300.66  131535[5:Res:2504.1,8788.0] || subclass(ordered_pair(u,v),recursion_equation_functions(w))* -> subclass(unordered_pair(u,singleton(v)),cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.66  132037[0:Res:18949.0,19115.0] ||  -> subclass(restrict(recursion_equation_functions(u),v,w),x) function(not_subclass_element(restrict(recursion_equation_functions(u),v,w),x))*.
% 299.99/300.66  96917[5:Res:96837.0,11.0] || subclass(complement(recursion_equation_functions(u)),singleton(v))* -> function(v) equal(complement(recursion_equation_functions(u)),singleton(v)).
% 299.99/300.66  161103[8:Rew:116078.0,82923.1] || member(singleton(u),subset_relation)* subclass(ordinal_numbers,cantor(u)) subclass(ordinal_numbers,complement(element_relation)) -> .
% 299.99/300.66  117308[8:Rew:116154.0,83712.0] || equal(segment(u,v,w),domain_relation) subclass(domain_relation,complement(segment(u,v,w)))* -> .
% 299.99/300.66  165640[5:Res:143198.1,490.0] || equal(intersection(complement(u),complement(v)),ordinal_numbers) member(singleton(w),union(u,v))* -> .
% 299.99/300.66  174944[0:Res:151497.0,8559.2] || member(u,singleton(v))* member(u,recursion_equation_functions(w))* -> function(v) member(u,x)*.
% 299.99/300.66  175429[0:Res:151488.0,8559.2] || member(u,singleton(v))* member(u,w)* -> member(v,w)* member(u,x)*.
% 299.99/300.66  176789[8:Res:144409.1,9876.0] || equal(symmetric_difference(ordinal_numbers,u),ordinal_numbers) subclass(complement(u),v)* well_ordering(ordinal_numbers,v) -> .
% 299.99/300.66  176981[5:SpL:30.0,134026.0] || equal(complement(union(u,v)),ordinal_numbers) well_ordering(ordinal_numbers,intersection(complement(u),complement(v)))* -> .
% 299.99/300.66  186579[8:SpL:30.0,176788.0] || equal(symmetric_difference(ordinal_numbers,union(u,v)),ordinal_numbers) -> member(omega,intersection(complement(u),complement(v)))*.
% 299.99/300.66  167403[8:SpR:160659.1,141399.0] || subclass(ordinal_numbers,segment(u,v,w)) -> equal(symmetric_difference(ordinal_numbers,segment(u,v,w)),identity_relation)**.
% 299.99/300.66  166685[7:Res:13210.1,151988.0] ||  -> equal(intersection(u,complement(complement(v))),identity_relation) member(regular(intersection(u,complement(complement(v)))),v)*.
% 299.99/300.66  166495[7:Res:13248.1,151988.0] ||  -> equal(intersection(complement(complement(u)),v),identity_relation) member(regular(intersection(complement(complement(u)),v)),u)*.
% 299.99/300.66  165071[8:Res:919.1,162901.0] || equal(not_subclass_element(restrict(subset_relation,u,v),w),identity_relation)** -> subclass(restrict(subset_relation,u,v),w).
% 299.99/300.66  164999[8:Res:919.1,162888.0] || subclass(not_subclass_element(restrict(subset_relation,u,v),w),identity_relation)* -> subclass(restrict(subset_relation,u,v),w).
% 299.99/300.66  17360[7:Rew:30.0,17344.1] || subclass(union(u,v),intersection(complement(u),complement(v)))* -> equal(union(u,v),identity_relation).
% 299.99/300.66  13420[7:Rew:13036.0,10930.1] || subclass(omega,element_relation) -> equal(integer_of(singleton(singleton(singleton(u)))),identity_relation)** member(singleton(u),u)*.
% 299.99/300.66  83902[7:Res:66696.2,290.0] || subclass(ordinal_numbers,u) -> equal(integer_of(not_subclass_element(complement(u),v)),identity_relation)** subclass(complement(u),v).
% 299.99/300.66  19275[8:Res:19172.1,123.0] || equal(compose(restrict(u,v,v),restrict(u,v,v)),identity_relation)** -> transitive(u,v).
% 299.99/300.66  63770[7:SpL:3606.0,13051.0] || equal(symmetric_difference(cross_product(u,v),w),ordinal_numbers) -> member(identity_relation,complement(restrict(w,u,v)))*.
% 299.99/300.66  63801[7:SpL:3606.0,13045.0] || subclass(ordinal_numbers,symmetric_difference(cross_product(u,v),w)) -> member(identity_relation,complement(restrict(w,u,v)))*.
% 299.99/300.66  63769[7:SpL:3603.0,13051.0] || equal(symmetric_difference(u,cross_product(v,w)),ordinal_numbers) -> member(identity_relation,complement(restrict(u,v,w)))*.
% 299.99/300.66  63800[7:SpL:3603.0,13045.0] || subclass(ordinal_numbers,symmetric_difference(u,cross_product(v,w))) -> member(identity_relation,complement(restrict(u,v,w)))*.
% 299.99/300.66  13357[7:Rew:13036.0,9787.2] inductive(domain_of(restrict(u,v,w))) || section(u,w,v)* -> member(identity_relation,w).
% 299.99/300.66  166207[8:Res:116148.1,13082.1] inductive(cantor(restrict(u,v,w))) || section(u,w,v)* -> member(identity_relation,w).
% 299.99/300.66  83284[7:Res:61019.0,26.0] ||  -> equal(complement(complement(intersection(u,v))),identity_relation) member(regular(complement(complement(intersection(u,v)))),v)*.
% 299.99/300.66  83285[7:Res:61019.0,25.0] ||  -> equal(complement(complement(intersection(u,v))),identity_relation) member(regular(complement(complement(intersection(u,v)))),u)*.
% 299.99/300.66  81697[8:Res:81695.0,13113.0] || well_ordering(u,complement(subset_relation)) -> equal(segment(u,inverse(subset_relation),least(u,inverse(subset_relation))),identity_relation)**.
% 299.99/300.66  83877[7:Res:66696.2,5.0] || subclass(ordinal_numbers,u)* subclass(u,v)* -> equal(integer_of(w),identity_relation) member(w,v)*.
% 299.99/300.66  83881[7:Res:66696.2,3617.0] || subclass(ordinal_numbers,symmetric_difference(u,v)) -> equal(integer_of(w),identity_relation) member(w,union(u,v))*.
% 299.99/300.66  13256[7:Rew:13036.0,13032.0] ||  -> equal(restrict(u,v,w),identity_relation) member(regular(restrict(u,v,w)),cross_product(v,w))*.
% 299.99/300.66  68865[8:SpR:66293.0,3618.1] || member(u,symmetric_difference(union(v,identity_relation),ordinal_numbers))* -> member(u,complement(symmetric_difference(complement(v),ordinal_numbers))).
% 299.99/300.66  68908[8:MRR:68907.0,41096.1] || member(u,complement(symmetric_difference(complement(v),ordinal_numbers))) -> member(u,symmetric_difference(union(v,identity_relation),ordinal_numbers))*.
% 299.99/300.66  161058[8:Rew:116078.0,83597.2,116078.0,83597.2,116078.0,83597.1] operation(u) || subclass(domain_relation,complement(complement(cantor(u))))* -> member(identity_relation,cantor(cantor(u))).
% 299.99/300.66  161059[8:Rew:116078.0,83740.2,116078.0,83740.2,116078.0,83740.1] operation(u) || equal(complement(complement(cantor(u))),domain_relation) -> member(identity_relation,cantor(cantor(u)))*.
% 299.99/300.66  83278[7:Res:61019.0,8788.0] ||  -> equal(complement(complement(recursion_equation_functions(u))),identity_relation) subclass(regular(complement(complement(recursion_equation_functions(u)))),cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.66  81316[8:Res:13125.2,15565.1] || subclass(omega,u) subclass(domain_relation,complement(u))* -> equal(integer_of(ordered_pair(identity_relation,identity_relation)),identity_relation)**.
% 299.99/300.66  83283[7:Res:61019.0,5.0] || subclass(u,v) -> equal(complement(complement(u)),identity_relation) member(regular(complement(complement(u))),v)*.
% 299.99/300.66  69479[7:Res:13125.2,19559.0] || subclass(omega,symmetric_difference(u,singleton(u)))* -> equal(integer_of(v),identity_relation) member(v,successor(u))*.
% 299.99/300.66  69480[7:Res:13125.2,19676.0] || subclass(omega,symmetric_difference(u,inverse(u)))* -> equal(integer_of(v),identity_relation) member(v,symmetrization_of(u))*.
% 299.99/300.66  167477[8:Res:303.1,163154.0] ||  -> subclass(intersection(u,symmetrization_of(identity_relation)),v) member(not_subclass_element(intersection(u,symmetrization_of(identity_relation)),v),inverse(identity_relation))*.
% 299.99/300.66  167463[8:Res:313.1,163154.0] ||  -> subclass(intersection(symmetrization_of(identity_relation),u),v) member(not_subclass_element(intersection(symmetrization_of(identity_relation),u),v),inverse(identity_relation))*.
% 299.99/300.66  167462[8:Res:41371.0,163154.0] ||  -> subclass(complement(complement(symmetrization_of(identity_relation))),u) member(not_subclass_element(complement(complement(symmetrization_of(identity_relation))),u),inverse(identity_relation))*.
% 299.99/300.66  163079[8:Res:162023.0,11.0] || subclass(complement(inverse(identity_relation)),complement(symmetrization_of(identity_relation)))* -> equal(complement(symmetrization_of(identity_relation)),complement(inverse(identity_relation))).
% 299.99/300.66  165149[8:Res:163118.0,13113.0] || well_ordering(u,inverse(identity_relation)) -> equal(segment(u,symmetrization_of(identity_relation),least(u,symmetrization_of(identity_relation))),identity_relation)**.
% 299.99/300.66  163156[8:SpL:162584.0,18791.0] || member(u,symmetric_difference(complement(v),symmetrization_of(identity_relation)))* -> member(u,union(v,complement(inverse(identity_relation)))).
% 299.99/300.66  163149[8:SpL:162584.0,18791.0] || member(u,symmetric_difference(symmetrization_of(identity_relation),complement(v)))* -> member(u,union(complement(inverse(identity_relation)),v)).
% 299.99/300.66  13354[7:Rew:13036.0,9788.3] inductive(not_well_ordering(u,v)) || connected(u,v) -> well_ordering(u,v)* member(identity_relation,v).
% 299.99/300.66  164866[8:SpR:160491.0,132294.0] ||  -> subclass(complement(symmetrization_of(symmetric_difference(ordinal_numbers,u))),intersection(union(u,identity_relation),complement(inverse(symmetric_difference(ordinal_numbers,u)))))*.
% 299.99/300.66  164864[8:SpR:160491.0,132293.0] ||  -> subclass(complement(successor(symmetric_difference(ordinal_numbers,u))),intersection(union(u,identity_relation),complement(singleton(symmetric_difference(ordinal_numbers,u)))))*.
% 299.99/300.66  68899[8:Rew:66293.0,68864.0] ||  -> equal(symmetric_difference(complement(u),ordinal_numbers),identity_relation) member(regular(symmetric_difference(complement(u),ordinal_numbers)),union(u,identity_relation))*.
% 299.99/300.66  161227[8:Rew:140613.0,83306.0] ||  -> member(regular(complement(union(u,identity_relation))),symmetric_difference(ordinal_numbers,u))* equal(complement(union(u,identity_relation)),identity_relation).
% 299.99/300.66  83871[8:Res:66696.2,66086.1] || subclass(ordinal_numbers,complement(compose(element_relation,ordinal_numbers)))* member(u,element_relation)* -> equal(integer_of(u),identity_relation).
% 299.99/300.66  64369[7:Res:13227.2,19559.0] || subclass(u,symmetric_difference(v,singleton(v)))* -> equal(u,identity_relation) member(regular(u),successor(v)).
% 299.99/300.66  18745[8:Res:9632.1,14681.0] || equal(complement(complement(regular(u))),ordinal_numbers)** member(singleton(v),u)* -> equal(u,identity_relation).
% 299.99/300.66  65561[8:Res:49995.1,14681.0] || member(regular(u),subset_relation) member(singleton(first(regular(u))),u)* -> equal(u,identity_relation).
% 299.99/300.66  64370[7:Res:13227.2,19676.0] || subclass(u,symmetric_difference(v,inverse(v)))* -> equal(u,identity_relation) member(regular(u),symmetrization_of(v)).
% 299.99/300.66  18215[7:Res:13227.2,3617.0] || subclass(u,symmetric_difference(v,w)) -> equal(u,identity_relation) member(regular(u),union(v,w))*.
% 299.99/300.66  17317[7:Res:13227.2,5.0] || subclass(u,v)* subclass(v,w)* -> equal(u,identity_relation) member(regular(u),w)*.
% 299.99/300.66  166791[7:Res:13227.2,9876.0] || subclass(u,v)* subclass(v,w)* well_ordering(ordinal_numbers,w)* -> equal(u,identity_relation).
% 299.99/300.66  167266[8:Res:133837.1,14681.0] || well_ordering(ordinal_numbers,complement(regular(u)))* member(singleton(singleton(v)),u)* -> equal(u,identity_relation).
% 299.99/300.66  167632[14:SpL:116154.0,165401.1] operation(restrict(u,v,singleton(w))) || equal(segment(u,v,w),singleton(identity_relation))** -> .
% 299.99/300.66  165369[14:Res:165168.1,490.0] || equal(intersection(complement(u),complement(v)),singleton(identity_relation))** member(identity_relation,union(u,v)) -> .
% 299.99/300.66  167627[14:SpL:50855.1,165378.0] || member(singleton(u),subset_relation)* equal(u,singleton(identity_relation)) -> equal(first(singleton(u)),identity_relation).
% 299.99/300.66  161362[8:Rew:116154.0,83663.0] || equal(segment(u,v,w),domain_relation) -> member(ordered_pair(identity_relation,identity_relation),segment(u,v,w))*.
% 299.99/300.66  82267[8:Res:81336.1,66086.1] || subclass(domain_relation,complement(complement(complement(compose(element_relation,ordinal_numbers)))))* member(ordered_pair(identity_relation,identity_relation),element_relation) -> .
% 299.99/300.66  82277[8:Res:81336.1,3617.0] || subclass(domain_relation,complement(complement(symmetric_difference(u,v)))) -> member(ordered_pair(identity_relation,identity_relation),union(u,v))*.
% 299.99/300.66  83175[8:SpL:3616.0,15572.0] || subclass(domain_relation,symmetric_difference(complement(u),complement(v))) -> member(ordered_pair(identity_relation,identity_relation),union(u,v))*.
% 299.99/300.66  83653[8:SpL:3616.0,83195.0] || equal(symmetric_difference(complement(u),complement(v)),domain_relation) -> member(ordered_pair(identity_relation,identity_relation),union(u,v))*.
% 299.99/300.66  163976[8:SpL:15614.1,28976.1] || equal(rest_relation,domain_relation) subclass(rest_relation,inverse(subset_relation)) member(ordered_pair(identity_relation,identity_relation),subset_relation)* -> .
% 299.99/300.66  82273[8:Res:81336.1,5.0] || subclass(domain_relation,complement(complement(u)))* subclass(u,v)* -> member(ordered_pair(identity_relation,identity_relation),v)*.
% 299.99/300.66  161081[8:Rew:116078.0,83680.1] || equal(cantor(u),domain_relation) subclass(cantor(u),v)* -> member(ordered_pair(identity_relation,identity_relation),v)*.
% 299.99/300.66  190544[18:Res:190442.1,490.0] || equal(intersection(complement(u),complement(v)),symmetrization_of(identity_relation))** member(identity_relation,union(u,v)) -> .
% 299.99/300.66  190653[18:Res:190593.1,490.0] || equal(intersection(complement(u),complement(v)),inverse(identity_relation))** member(identity_relation,union(u,v)) -> .
% 299.99/300.66  191948[18:Res:190515.1,18791.0] || subclass(ordinal_numbers,symmetric_difference(complement(u),complement(v))) -> member(regular(symmetrization_of(identity_relation)),union(u,v))*.
% 299.99/300.66  191995[18:SpL:50855.1,190554.0] || member(singleton(u),subset_relation)* equal(u,symmetrization_of(identity_relation)) -> equal(first(singleton(u)),identity_relation).
% 299.99/300.66  192007[18:SpL:116154.0,190588.1] operation(restrict(u,v,singleton(w))) || equal(segment(u,v,w),symmetrization_of(identity_relation))** -> .
% 299.99/300.66  192009[18:SpL:50855.1,190663.0] || member(singleton(u),subset_relation)* equal(u,inverse(identity_relation)) -> equal(first(singleton(u)),identity_relation).
% 299.99/300.66  192013[18:SpL:116154.0,190699.1] operation(restrict(u,v,singleton(w))) || equal(segment(u,v,w),inverse(identity_relation))** -> .
% 299.99/300.66  192561[7:SpR:50855.1,192514.1] || member(singleton(u),subset_relation) -> function(first(singleton(u))) equal(intersection(recursion_equation_functions(v),u),identity_relation)**.
% 299.99/300.66  192755[7:SpR:50855.1,192639.1] || member(singleton(u),subset_relation) -> function(first(singleton(u))) equal(intersection(u,recursion_equation_functions(v)),identity_relation)**.
% 299.99/300.66  192893[7:SpR:50855.1,192834.1] || member(singleton(u),subset_relation) -> member(first(singleton(u)),v)* equal(intersection(v,u),identity_relation).
% 299.99/300.66  193113[7:SpR:50855.1,193044.1] || member(singleton(u),subset_relation) -> member(first(singleton(u)),v)* equal(intersection(u,v),identity_relation).
% 299.99/300.66  193205[8:Res:193179.0,8842.1] || subclass(ordinal_numbers,complement(inverse(singleton(unordered_pair(u,v)))))* -> asymmetric(singleton(unordered_pair(u,v)),w)*.
% 299.99/300.66  193208[8:Res:193179.0,125973.1] || subclass(ordinal_numbers,complement(inverse(singleton(least(element_relation,omega)))))* -> asymmetric(singleton(least(element_relation,omega)),u)*.
% 299.99/300.66  193209[8:Res:193179.0,125896.1] || subclass(omega,complement(inverse(singleton(least(element_relation,omega)))))* -> asymmetric(singleton(least(element_relation,omega)),u)*.
% 299.99/300.66  193212[8:Res:193179.0,8841.1] || subclass(ordinal_numbers,complement(inverse(singleton(ordered_pair(u,v)))))* -> asymmetric(singleton(ordered_pair(u,v)),w)*.
% 299.99/300.66  130943[5:Res:51204.1,9876.0] || member(singleton(u),subset_relation) subclass(singleton(singleton(u)),v)* well_ordering(ordinal_numbers,v) -> .
% 299.99/300.66  134391[5:SpL:50855.1,132463.0] || member(singleton(u),subset_relation)* equal(v,singleton(singleton(u)))* well_ordering(ordinal_numbers,v)* -> .
% 299.99/300.66  131207[8:Res:39607.2,14679.1] inductive(inverse(subset_relation)) || well_ordering(u,ordinal_numbers) member(least(u,inverse(subset_relation)),subset_relation)* -> .
% 299.99/300.66  131176[8:Res:39607.2,116166.0] inductive(recursion_equation_functions(u)) || well_ordering(v,ordinal_numbers) -> member(cantor(least(v,recursion_equation_functions(u))),ordinal_numbers)*.
% 299.99/300.66  19200[8:Res:19172.1,141.1] || equal(sum_class(u),identity_relation) well_ordering(element_relation,u)* -> equal(u,ordinal_numbers) member(u,ordinal_numbers).
% 299.99/300.66  131173[5:Res:39607.2,28.1] inductive(complement(u)) || well_ordering(v,ordinal_numbers) member(least(v,complement(u)),u)* -> .
% 299.99/300.66  132233[2:Res:39609.2,3700.0] inductive(singleton(u)) || well_ordering(v,singleton(u)) -> equal(least(v,singleton(u)),u)**.
% 299.99/300.66  193977[14:Res:193906.1,9876.0] || equal(inverse(subset_relation),singleton(identity_relation)) subclass(complement(subset_relation),u)* well_ordering(ordinal_numbers,u) -> .
% 299.99/300.66  193984[18:Res:193924.1,9876.0] || equal(symmetrization_of(identity_relation),inverse(subset_relation)) subclass(complement(subset_relation),u)* well_ordering(ordinal_numbers,u) -> .
% 299.99/300.66  193991[18:Res:193927.1,9876.0] || equal(inverse(subset_relation),inverse(identity_relation)) subclass(complement(subset_relation),u)* well_ordering(ordinal_numbers,u) -> .
% 299.99/300.66  194372[21:MRR:194353.2,14676.0] || subclass(ordinal_numbers,complement(complement(cross_product(ordinal_numbers,cross_product(ordinal_numbers,ordinal_numbers)))))* member(u,cantor(v))* -> .
% 299.99/300.66  194459[14:Res:165177.0,9876.0] || subclass(symmetric_difference(ordinal_numbers,u),v)* well_ordering(ordinal_numbers,v) -> member(identity_relation,union(u,identity_relation))*.
% 299.99/300.66  194488[8:Res:163112.0,9876.0] || subclass(complement(inverse(identity_relation)),u)* well_ordering(ordinal_numbers,u) -> subclass(singleton(v),symmetrization_of(identity_relation))*.
% 299.99/300.66  194523[8:Rew:162584.0,194498.0] || subclass(u,symmetrization_of(identity_relation)) -> subclass(singleton(not_subclass_element(u,v)),symmetrization_of(identity_relation))* subclass(u,v).
% 299.99/300.66  194524[8:Rew:162584.0,194500.1] || member(u,ordinal_numbers) subclass(ordinal_numbers,symmetrization_of(identity_relation)) -> subclass(singleton(sum_class(u)),symmetrization_of(identity_relation))*.
% 299.99/300.66  194528[20:Res:194511.0,13113.0] || well_ordering(u,symmetrization_of(identity_relation)) -> equal(segment(u,singleton(identity_relation),least(u,singleton(identity_relation))),identity_relation)**.
% 299.99/300.66  194541[18:Res:194513.0,11.0] || subclass(symmetrization_of(identity_relation),singleton(regular(symmetrization_of(identity_relation))))* -> equal(singleton(regular(symmetrization_of(identity_relation))),symmetrization_of(identity_relation)).
% 299.99/300.66  194777[8:SpL:66293.0,18794.1] || member(u,symmetric_difference(union(v,identity_relation),ordinal_numbers))* member(u,symmetric_difference(complement(v),ordinal_numbers)) -> .
% 299.99/300.66  194802[8:Rew:140613.0,194733.0,66141.0,194733.0,66141.0,194733.0] ||  -> equal(symmetric_difference(complement(symmetric_difference(complement(u),ordinal_numbers)),ordinal_numbers),symmetric_difference(ordinal_numbers,symmetric_difference(union(u,identity_relation),ordinal_numbers)))**.
% 299.99/300.66  195062[14:SpL:30.0,165360.0] || equal(complement(union(u,v)),singleton(identity_relation)) -> member(identity_relation,intersection(complement(u),complement(v)))*.
% 299.99/300.66  195079[14:Res:3618.1,165357.1] || member(identity_relation,symmetric_difference(u,v)) equal(complement(complement(intersection(u,v))),singleton(identity_relation))** -> .
% 299.99/300.66  195602[16:Rew:195224.0,195195.2] || subclass(complement(singleton(identity_relation)),u)* well_ordering(ordinal_numbers,u) -> subclass(singleton(v),singleton(identity_relation))*.
% 299.99/300.66  195452[16:Rew:195224.0,194294.2] || well_ordering(u,complement(v))* -> member(identity_relation,v) member(least(u,singleton(identity_relation)),singleton(identity_relation))*.
% 299.99/300.66  195479[16:Rew:195224.0,163236.0] || member(u,symmetric_difference(singleton(identity_relation),complement(v)))* -> member(u,union(complement(singleton(identity_relation)),v)).
% 299.99/300.66  195480[16:Rew:195224.0,163244.0] || member(u,symmetric_difference(complement(v),singleton(identity_relation)))* -> member(u,union(v,complement(singleton(identity_relation)))).
% 299.99/300.66  195481[16:Rew:195224.0,194272.2] || member(identity_relation,u) well_ordering(v,u)* -> member(least(v,singleton(identity_relation)),singleton(identity_relation))*.
% 299.99/300.66  195616[16:Rew:195224.0,195207.1,195239.0,195207.0] || subclass(u,singleton(identity_relation)) -> subclass(singleton(not_subclass_element(u,v)),singleton(identity_relation))* subclass(u,v).
% 299.99/300.66  196083[18:Res:190510.1,18794.1] || subclass(inverse(identity_relation),intersection(u,v)) member(regular(symmetrization_of(identity_relation)),symmetric_difference(u,v))* -> .
% 299.99/300.66  196102[18:Res:190510.1,897.0] || subclass(inverse(identity_relation),restrict(u,v,w))* -> member(regular(symmetrization_of(identity_relation)),cross_product(v,w))*.
% 299.99/300.66  196113[18:Res:190510.1,14681.0] || subclass(inverse(identity_relation),regular(u)) member(regular(symmetrization_of(identity_relation)),u)* -> equal(u,identity_relation).
% 299.99/300.66  196133[18:Res:3618.1,190532.1] || member(identity_relation,symmetric_difference(u,v)) equal(complement(complement(intersection(u,v))),symmetrization_of(identity_relation))** -> .
% 299.99/300.66  196201[18:SpL:30.0,190535.0] || equal(complement(union(u,v)),symmetrization_of(identity_relation)) -> member(identity_relation,intersection(complement(u),complement(v)))*.
% 299.99/300.66  196223[18:Res:3618.1,190641.1] || member(identity_relation,symmetric_difference(u,v)) equal(complement(complement(intersection(u,v))),inverse(identity_relation))** -> .
% 299.99/300.66  196294[18:SpL:30.0,190644.0] || equal(complement(union(u,v)),inverse(identity_relation)) -> member(identity_relation,intersection(complement(u),complement(v)))*.
% 299.99/300.66  196360[21:SpL:116154.0,196356.1] || member(restrict(u,v,singleton(w)),ordinal_numbers)* member(x,segment(u,v,w))* -> .
% 299.99/300.66  196422[21:Rew:196372.1,174444.2] || member(u,ordinal_numbers) subclass(domain_relation,complement(complement(v))) -> member(ordered_pair(u,identity_relation),v)*.
% 299.99/300.66  196450[21:Rew:196372.1,192702.2] || member(u,ordinal_numbers) subclass(domain_relation,symmetrization_of(identity_relation)) -> member(ordered_pair(u,identity_relation),inverse(identity_relation))*.
% 299.99/300.66  197161[7:EqF:13263.1,13263.2] || equal(u,v) -> equal(unordered_pair(v,u),identity_relation) equal(regular(unordered_pair(v,u)),v)**.
% 299.99/300.66  197521[21:MRR:197499.1,13039.0] || subclass(u,v) -> equal(singleton(restrict(w,v,u)),identity_relation)** section(w,u,v).
% 299.99/300.66  197572[21:Obv:197544.0] ||  -> equal(regular(unordered_pair(u,v)),u)** equal(unordered_pair(u,v),identity_relation) equal(cantor(v),identity_relation).
% 299.99/300.66  197573[21:Obv:197543.0] ||  -> equal(regular(unordered_pair(u,v)),v)** equal(unordered_pair(u,v),identity_relation) equal(cantor(u),identity_relation).
% 299.99/300.66  194714[8:Res:19172.1,117508.1] operation(u) || equal(cantor(cantor(u)),identity_relation)** -> equal(cantor(cantor(u)),range_of(u)).
% 299.99/300.66  195403[16:Rew:195224.0,195026.1] || subclass(ordinal_numbers,complement(power_class(complement(singleton(identity_relation))))) -> member(range_of(identity_relation),image(element_relation,singleton(identity_relation)))*.
% 299.99/300.66  195027[15:SpL:162038.0,165530.0] || subclass(ordinal_numbers,complement(power_class(complement(inverse(identity_relation))))) -> member(range_of(identity_relation),image(element_relation,symmetrization_of(identity_relation)))*.
% 299.99/300.66  195018[15:SpL:30.0,165530.0] || subclass(ordinal_numbers,complement(union(u,v))) -> member(range_of(identity_relation),intersection(complement(u),complement(v)))*.
% 299.99/300.66  61462[8:Rew:14756.0,61456.1] || member(ordered_pair(u,not_subclass_element(v,range_of(identity_relation))),compose(identity_relation,w))* -> subclass(v,range_of(identity_relation)).
% 299.99/300.66  194948[15:Res:3618.1,165527.1] || member(range_of(identity_relation),symmetric_difference(u,v)) subclass(ordinal_numbers,complement(complement(intersection(u,v))))* -> .
% 299.99/300.66  165539[15:Res:165526.1,490.0] || subclass(ordinal_numbers,intersection(complement(u),complement(v)))* member(range_of(identity_relation),union(u,v)) -> .
% 299.99/300.66  191864[15:Res:165442.1,18791.0] || subclass(ordinal_numbers,symmetric_difference(complement(u),complement(v))) -> member(sum_class(range_of(identity_relation)),union(u,v))*.
% 299.99/300.66  18694[8:Res:16042.1,5.0] || equal(sum_class(range_of(identity_relation)),identity_relation) subclass(union_of_range_map,u) -> member(ordered_pair(identity_relation,identity_relation),u)*.
% 299.99/300.66  196916[21:SpR:196549.0,116203.2] function(singleton(u)) || subclass(range_of(singleton(u)),v) -> maps(singleton(u),identity_relation,v)*.
% 299.99/300.66  61724[5:SpL:18840.1,157.0] || member(u,subset_relation) member(u,union_of_range_map) -> equal(sum_class(range_of(first(u))),second(u))**.
% 299.99/300.66  62891[5:MRR:62890.2,18819.1] || member(u,subset_relation) equal(sum_class(range_of(first(u))),second(u))** -> member(u,union_of_range_map).
% 299.99/300.66  196801[21:SpR:196567.0,116203.2] function(range_of(identity_relation)) || subclass(range_of(range_of(identity_relation)),u) -> maps(range_of(identity_relation),identity_relation,u)*.
% 299.99/300.66  196110[18:Res:190510.1,288.0] || subclass(inverse(identity_relation),image(element_relation,complement(u)))* member(regular(symmetrization_of(identity_relation)),power_class(u)) -> .
% 299.99/300.66  19809[0:SpR:59.0,19734.0] ||  -> subclass(symmetric_difference(power_class(u),complement(inverse(image(element_relation,complement(u))))),symmetrization_of(image(element_relation,complement(u))))*.
% 299.99/300.66  19792[0:SpR:59.0,19733.0] ||  -> subclass(symmetric_difference(power_class(u),complement(singleton(image(element_relation,complement(u))))),successor(image(element_relation,complement(u))))*.
% 299.99/300.66  130684[5:Rew:59.0,130619.1] ||  -> member(not_subclass_element(complement(power_class(u)),v),image(element_relation,complement(u)))* subclass(complement(power_class(u)),v).
% 299.99/300.66  159440[5:Res:41368.0,9876.0] || subclass(power_class(u),v)* well_ordering(ordinal_numbers,v) -> subclass(w,image(element_relation,complement(u)))*.
% 299.99/300.66  96950[5:Res:79577.0,5.0] || subclass(image(element_relation,complement(u)),v)* -> subclass(singleton(w),power_class(u))* member(w,v)*.
% 299.99/300.66  194692[14:Res:165178.0,9876.0] || subclass(image(element_relation,complement(u)),v)* well_ordering(ordinal_numbers,v) -> member(identity_relation,power_class(u)).
% 299.99/300.66  196289[18:SpL:189.0,196256.1] inductive(image(element_relation,power_class(u))) || equal(power_class(image(element_relation,complement(u))),inverse(identity_relation))** -> .
% 299.99/300.66  196196[18:SpL:189.0,196166.1] inductive(image(element_relation,power_class(u))) || equal(power_class(image(element_relation,complement(u))),symmetrization_of(identity_relation))** -> .
% 299.99/300.66  195140[14:SpL:189.0,195115.1] inductive(image(element_relation,power_class(u))) || equal(power_class(image(element_relation,complement(u))),singleton(identity_relation))** -> .
% 299.99/300.66  193519[8:SpL:162038.0,9496.0] || subclass(ordinal_numbers,complement(power_class(complement(inverse(identity_relation))))) -> member(singleton(u),image(element_relation,symmetrization_of(identity_relation)))*.
% 299.99/300.66  193515[8:SpL:162038.0,134026.0] || equal(complement(power_class(complement(inverse(identity_relation)))),ordinal_numbers) well_ordering(ordinal_numbers,image(element_relation,symmetrization_of(identity_relation)))* -> .
% 299.99/300.66  193537[8:SpL:162038.0,176788.0] || equal(symmetric_difference(ordinal_numbers,power_class(complement(inverse(identity_relation)))),ordinal_numbers)** -> member(omega,image(element_relation,symmetrization_of(identity_relation))).
% 299.99/300.66  193480[8:SpR:162038.0,144409.1] || equal(symmetric_difference(ordinal_numbers,image(element_relation,symmetrization_of(identity_relation))),ordinal_numbers)** -> member(omega,power_class(complement(inverse(identity_relation)))).
% 299.99/300.66  193506[8:SpL:162038.0,155244.0] || subclass(ordinal_numbers,power_class(complement(inverse(identity_relation)))) -> equal(symmetric_difference(ordinal_numbers,image(element_relation,symmetrization_of(identity_relation))),ordinal_numbers)**.
% 299.99/300.66  195071[14:SpL:162038.0,165360.0] || equal(complement(power_class(complement(inverse(identity_relation)))),singleton(identity_relation)) -> member(identity_relation,image(element_relation,symmetrization_of(identity_relation)))*.
% 299.99/300.66  196209[18:SpL:162038.0,190535.0] || equal(complement(power_class(complement(inverse(identity_relation)))),symmetrization_of(identity_relation)) -> member(identity_relation,image(element_relation,symmetrization_of(identity_relation)))*.
% 299.99/300.66  196302[18:SpL:162038.0,190644.0] || equal(complement(power_class(complement(inverse(identity_relation)))),inverse(identity_relation)) -> member(identity_relation,image(element_relation,symmetrization_of(identity_relation)))*.
% 299.99/300.66  193465[8:SpR:162038.0,130703.0] ||  -> subclass(complement(union(image(element_relation,symmetrization_of(identity_relation)),u)),intersection(power_class(complement(inverse(identity_relation))),complement(u)))*.
% 299.99/300.66  163092[8:SpR:162584.0,487.0] ||  -> equal(complement(intersection(power_class(complement(inverse(identity_relation))),complement(u))),union(image(element_relation,symmetrization_of(identity_relation)),u))**.
% 299.99/300.66  193488[8:SpR:162038.0,130703.0] ||  -> subclass(complement(union(u,image(element_relation,symmetrization_of(identity_relation)))),intersection(complement(u),power_class(complement(inverse(identity_relation)))))*.
% 299.99/300.66  163115[8:SpR:162584.0,485.0] ||  -> equal(complement(intersection(complement(u),power_class(complement(inverse(identity_relation))))),union(u,image(element_relation,symmetrization_of(identity_relation))))**.
% 299.99/300.66  13369[7:Rew:13036.0,9940.1] || equal(complement(power_class(image(element_relation,complement(u)))),ordinal_numbers)** -> member(identity_relation,image(element_relation,power_class(u))).
% 299.99/300.66  13370[7:Rew:13036.0,9903.1] || subclass(ordinal_numbers,power_class(image(element_relation,complement(u))))* member(identity_relation,image(element_relation,power_class(u))) -> .
% 299.99/300.66  167517[7:SpL:189.0,163545.0] || subclass(ordinal_numbers,complement(power_class(image(element_relation,complement(u)))))* -> member(identity_relation,image(element_relation,power_class(u))).
% 299.99/300.66  19753[0:SpR:189.0,19421.0] ||  -> subclass(symmetric_difference(power_class(image(element_relation,complement(u))),complement(v)),union(image(element_relation,power_class(u)),v))*.
% 299.99/300.66  81500[8:SpL:189.0,81412.1] || equal(image(element_relation,power_class(u)),domain_relation) equal(power_class(image(element_relation,complement(u))),domain_relation)** -> .
% 299.99/300.66  8905[5:Rew:8637.0,6929.0] || equal(complement(power_class(image(element_relation,complement(u)))),ordinal_numbers)** -> member(omega,image(element_relation,power_class(u))).
% 299.99/300.66  8870[5:Rew:8637.0,6722.0] || subclass(ordinal_numbers,power_class(image(element_relation,complement(u))))* member(omega,image(element_relation,power_class(u))) -> .
% 299.99/300.66  152970[5:SpL:189.0,151970.0] || subclass(ordinal_numbers,complement(power_class(image(element_relation,complement(u)))))* -> member(omega,image(element_relation,power_class(u))).
% 299.99/300.66  50417[5:SpL:189.0,50032.1] || member(image(element_relation,power_class(u)),subset_relation) subclass(ordinal_numbers,power_class(image(element_relation,complement(u))))* -> .
% 299.99/300.66  63447[8:SpL:189.0,63019.1] || subclass(domain_relation,image(element_relation,power_class(u))) subclass(ordinal_numbers,power_class(image(element_relation,complement(u))))* -> .
% 299.99/300.66  81397[8:SpL:189.0,81322.1] || subclass(domain_relation,image(element_relation,power_class(u))) subclass(domain_relation,power_class(image(element_relation,complement(u))))* -> .
% 299.99/300.66  147745[5:SpL:189.0,147314.1] || equal(image(element_relation,power_class(u)),omega) subclass(ordinal_numbers,power_class(image(element_relation,complement(u))))* -> .
% 299.99/300.66  147800[5:SpL:189.0,147315.1] || equal(image(element_relation,power_class(u)),omega) subclass(omega,power_class(image(element_relation,complement(u))))* -> .
% 299.99/300.66  166832[5:SpL:189.0,147805.0] || equal(power_class(image(element_relation,complement(u))),omega)** equal(image(element_relation,power_class(u)),omega) -> .
% 299.99/300.66  127026[5:SpL:189.0,126665.1] || subclass(omega,image(element_relation,power_class(u))) subclass(omega,power_class(image(element_relation,complement(u))))* -> .
% 299.99/300.66  127425[5:SpL:189.0,127130.1] || subclass(omega,image(element_relation,power_class(u))) subclass(ordinal_numbers,power_class(image(element_relation,complement(u))))* -> .
% 299.99/300.66  134171[5:SpL:189.0,134130.0] || well_ordering(ordinal_numbers,power_class(image(element_relation,complement(u))))* well_ordering(ordinal_numbers,image(element_relation,power_class(u))) -> .
% 299.99/300.66  81508[8:SpL:189.0,81488.1] || equal(image(element_relation,power_class(u)),ordinal_numbers) equal(power_class(image(element_relation,complement(u))),domain_relation)** -> .
% 299.99/300.66  167305[5:SpL:189.0,147100.1] || equal(image(element_relation,power_class(u)),ordinal_numbers) subclass(ordinal_numbers,power_class(image(element_relation,complement(u))))* -> .
% 299.99/300.66  167362[5:SpL:189.0,147101.1] || equal(image(element_relation,power_class(u)),ordinal_numbers) subclass(omega,power_class(image(element_relation,complement(u))))* -> .
% 299.99/300.66  173853[5:SpL:189.0,167369.0] || equal(power_class(image(element_relation,complement(u))),omega)** equal(image(element_relation,power_class(u)),ordinal_numbers) -> .
% 299.99/300.66  124981[5:SpL:59.0,66645.0] || subclass(ordinal_numbers,image(element_relation,power_class(u))) member(omega,power_class(image(element_relation,complement(u))))* -> .
% 299.99/300.66  81407[8:SpL:189.0,81326.1] || subclass(ordinal_numbers,image(element_relation,power_class(u))) subclass(domain_relation,power_class(image(element_relation,complement(u))))* -> .
% 299.99/300.66  9572[5:SpL:189.0,9488.1] || subclass(ordinal_numbers,image(element_relation,power_class(u))) subclass(ordinal_numbers,power_class(image(element_relation,complement(u))))* -> .
% 299.99/300.66  167291[5:SpL:189.0,126664.1] || subclass(ordinal_numbers,image(element_relation,power_class(u))) subclass(omega,power_class(image(element_relation,complement(u))))* -> .
% 299.99/300.66  19742[0:SpR:189.0,19421.0] ||  -> subclass(symmetric_difference(complement(u),power_class(image(element_relation,complement(v)))),union(u,image(element_relation,power_class(v))))*.
% 299.99/300.66  154273[5:SpL:189.0,151988.0] || member(u,complement(power_class(image(element_relation,complement(v)))))* -> member(u,image(element_relation,power_class(v))).
% 299.99/300.66  142404[8:Rew:141402.0,121658.0] ||  -> subclass(symmetric_difference(ordinal_numbers,image(element_relation,power_class(image(element_relation,complement(u))))),power_class(image(element_relation,power_class(u))))*.
% 299.99/300.66  194690[14:SpR:162038.0,165178.0] ||  -> member(identity_relation,image(element_relation,power_class(complement(inverse(identity_relation)))))* member(identity_relation,power_class(image(element_relation,symmetrization_of(identity_relation)))).
% 299.99/300.66  165180[14:SpR:481.0,165172.1] ||  -> member(identity_relation,image(element_relation,union(u,v))) member(identity_relation,power_class(intersection(complement(u),complement(v))))*.
% 299.99/300.66  51230[5:SpR:50855.1,72.0] || member(singleton(u),subset_relation) -> equal(apply(v,first(singleton(u))),sum_class(image(v,u)))**.
% 299.99/300.66  81198[5:SpL:8649.0,56504.0] || member(inverse(restrict(u,v,ordinal_numbers)),image(u,v))* subclass(ordinal_numbers,complement(element_relation)) -> .
% 299.99/300.66  195376[16:Rew:195224.0,193355.1] || subclass(ordinal_numbers,complement(power_class(complement(singleton(identity_relation))))) -> member(singleton(u),image(element_relation,singleton(identity_relation)))*.
% 299.99/300.66  195374[16:Rew:195224.0,193351.1] || equal(complement(power_class(complement(singleton(identity_relation)))),ordinal_numbers) well_ordering(ordinal_numbers,image(element_relation,singleton(identity_relation)))* -> .
% 299.99/300.66  195370[16:Rew:195224.0,193373.1] || equal(symmetric_difference(ordinal_numbers,power_class(complement(singleton(identity_relation)))),ordinal_numbers)** -> member(omega,image(element_relation,singleton(identity_relation))).
% 299.99/300.66  195329[16:Rew:195224.0,193324.0] ||  -> subclass(complement(union(u,image(element_relation,singleton(identity_relation)))),intersection(complement(u),power_class(complement(singleton(identity_relation)))))*.
% 299.99/300.66  195327[16:Rew:195224.0,163202.0] ||  -> equal(complement(intersection(complement(u),power_class(complement(singleton(identity_relation))))),union(u,image(element_relation,singleton(identity_relation))))**.
% 299.99/300.66  195323[16:Rew:195224.0,193301.0] ||  -> subclass(complement(union(image(element_relation,singleton(identity_relation)),u)),intersection(power_class(complement(singleton(identity_relation))),complement(u)))*.
% 299.99/300.66  195321[16:Rew:195224.0,163179.0] ||  -> equal(complement(intersection(power_class(complement(singleton(identity_relation))),complement(u))),union(image(element_relation,singleton(identity_relation)),u))**.
% 299.99/300.66  195315[16:Rew:195224.0,194689.1] ||  -> member(identity_relation,image(element_relation,power_class(complement(singleton(identity_relation)))))* member(identity_relation,power_class(image(element_relation,singleton(identity_relation)))).
% 299.99/300.66  195339[16:Rew:195224.0,195070.1] || equal(complement(power_class(complement(singleton(identity_relation)))),singleton(identity_relation)) -> member(identity_relation,image(element_relation,singleton(identity_relation)))*.
% 299.99/300.66  196210[18:SpL:195257.0,190535.0] || equal(complement(power_class(complement(singleton(identity_relation)))),symmetrization_of(identity_relation)) -> member(identity_relation,image(element_relation,singleton(identity_relation)))*.
% 299.99/300.66  196303[18:SpL:195257.0,190644.0] || equal(complement(power_class(complement(singleton(identity_relation)))),inverse(identity_relation)) -> member(identity_relation,image(element_relation,singleton(identity_relation)))*.
% 299.99/300.66  195337[16:Rew:195224.0,193342.1] || subclass(ordinal_numbers,power_class(complement(singleton(identity_relation)))) -> equal(symmetric_difference(ordinal_numbers,image(element_relation,singleton(identity_relation))),ordinal_numbers)**.
% 299.99/300.66  195338[16:Rew:195224.0,193316.0] || equal(symmetric_difference(ordinal_numbers,image(element_relation,singleton(identity_relation))),ordinal_numbers)** -> member(omega,power_class(complement(singleton(identity_relation)))).
% 299.99/300.66  148532[8:SpL:140613.0,18545.1] || member(u,ordinal_numbers) subclass(ordinal_numbers,symmetric_difference(ordinal_numbers,v)) -> member(power_class(u),complement(v))*.
% 299.99/300.66  146784[5:Rew:59.0,146762.1] || member(u,ordinal_numbers) subclass(ordinal_numbers,power_class(v)) -> subclass(singleton(sum_class(u)),power_class(v))*.
% 299.99/300.66  146854[5:Rew:59.0,146832.1] || member(u,ordinal_numbers) subclass(ordinal_numbers,power_class(v)) -> subclass(singleton(power_class(u)),power_class(v))*.
% 299.99/300.66  152240[5:Rew:59.0,152206.0] || subclass(u,power_class(v)) -> subclass(singleton(not_subclass_element(u,w)),power_class(v))* subclass(u,w).
% 299.99/300.66  97002[5:SpR:50855.1,96970.1] || member(singleton(u),subset_relation) subclass(ordinal_numbers,power_class(v)) -> subclass(singleton(u),power_class(v))*.
% 299.99/300.66  198658[7:SSi:198650.0,73.0] ||  -> equal(unordered_pair(u,v),identity_relation) equal(apply(choice,unordered_pair(u,v)),v)** member(u,ordinal_numbers).
% 299.99/300.66  198657[7:SSi:198642.0,73.0] ||  -> equal(unordered_pair(u,v),identity_relation) equal(apply(choice,unordered_pair(u,v)),u)** member(v,ordinal_numbers).
% 299.99/300.66  13637[7:Rew:13036.0,13317.1] ||  -> equal(singleton(cross_product(u,v)),identity_relation) equal(restrict(singleton(cross_product(u,v)),u,v),identity_relation)**.
% 299.99/300.66  204037[8:SpR:162038.0,192333.1] || equal(symmetric_difference(ordinal_numbers,image(element_relation,symmetrization_of(identity_relation))),ordinal_numbers)** -> member(identity_relation,power_class(complement(inverse(identity_relation)))).
% 299.99/300.66  204038[16:SpR:195257.0,192333.1] || equal(symmetric_difference(ordinal_numbers,image(element_relation,singleton(identity_relation))),ordinal_numbers)** -> member(identity_relation,power_class(complement(singleton(identity_relation)))).
% 299.99/300.66  204175[18:Res:194549.1,18794.1] || subclass(symmetrization_of(identity_relation),intersection(u,v)) member(regular(symmetrization_of(identity_relation)),symmetric_difference(u,v))* -> .
% 299.99/300.66  204197[18:Res:194549.1,897.0] || subclass(symmetrization_of(identity_relation),restrict(u,v,w))* -> member(regular(symmetrization_of(identity_relation)),cross_product(v,w))*.
% 299.99/300.66  204206[18:Res:194549.1,14681.0] || subclass(symmetrization_of(identity_relation),regular(u)) member(regular(symmetrization_of(identity_relation)),u)* -> equal(u,identity_relation).
% 299.99/300.66  204328[14:SpL:30.0,195109.1] || equal(intersection(complement(u),complement(v)),ordinal_numbers)** equal(union(u,v),singleton(identity_relation)) -> .
% 299.99/300.66  204335[14:SpL:162038.0,195109.1] || equal(image(element_relation,symmetrization_of(identity_relation)),ordinal_numbers)** equal(power_class(complement(inverse(identity_relation))),singleton(identity_relation)) -> .
% 299.99/300.66  204336[16:SpL:195257.0,195109.1] || equal(image(element_relation,singleton(identity_relation)),ordinal_numbers)** equal(power_class(complement(singleton(identity_relation))),singleton(identity_relation)) -> .
% 299.99/300.66  204448[18:SpL:30.0,196161.1] || equal(intersection(complement(u),complement(v)),ordinal_numbers)** equal(union(u,v),symmetrization_of(identity_relation)) -> .
% 299.99/300.66  204453[18:SpL:162038.0,196161.1] || equal(image(element_relation,symmetrization_of(identity_relation)),ordinal_numbers)** equal(power_class(complement(inverse(identity_relation))),symmetrization_of(identity_relation)) -> .
% 299.99/300.66  204454[18:SpL:195257.0,196161.1] || equal(image(element_relation,singleton(identity_relation)),ordinal_numbers)** equal(power_class(complement(singleton(identity_relation))),symmetrization_of(identity_relation)) -> .
% 299.99/300.66  204467[18:SpL:30.0,196251.1] || equal(intersection(complement(u),complement(v)),ordinal_numbers)** equal(union(u,v),inverse(identity_relation)) -> .
% 299.99/300.66  204474[18:SpL:162038.0,196251.1] || equal(image(element_relation,symmetrization_of(identity_relation)),ordinal_numbers)** equal(power_class(complement(inverse(identity_relation))),inverse(identity_relation)) -> .
% 299.99/300.66  204475[18:SpL:195257.0,196251.1] || equal(image(element_relation,singleton(identity_relation)),ordinal_numbers)** equal(power_class(complement(singleton(identity_relation))),inverse(identity_relation)) -> .
% 299.99/300.66  204637[21:Res:196904.1,18794.1] || subclass(domain_relation,intersection(u,v)) member(singleton(singleton(singleton(identity_relation))),symmetric_difference(u,v))* -> .
% 299.99/300.66  204659[21:Res:196904.1,897.0] || subclass(domain_relation,restrict(u,v,w))* -> member(singleton(singleton(singleton(identity_relation))),cross_product(v,w))*.
% 299.99/300.66  204668[21:Res:196904.1,14681.0] || subclass(domain_relation,regular(u)) member(singleton(singleton(singleton(identity_relation))),u)* -> equal(u,identity_relation).
% 299.99/300.66  204935[21:Res:196904.1,288.0] || subclass(domain_relation,image(element_relation,complement(u))) member(singleton(singleton(singleton(identity_relation))),power_class(u))* -> .
% 299.99/300.66  204949[18:Res:194549.1,288.0] || subclass(symmetrization_of(identity_relation),image(element_relation,complement(u)))* member(regular(symmetrization_of(identity_relation)),power_class(u)) -> .
% 299.99/300.66  204987[21:SpL:105.0,198463.1] || member(not_subclass_element(compose(u,inverse(u)),identity_relation),subset_relation)* equal(rest_of(single_valued1(u)),rest_relation) -> .
% 299.99/300.66  204989[21:SpL:106.0,198464.1] || member(not_subclass_element(compose(u,inverse(u)),identity_relation),subset_relation)* equal(rest_of(single_valued2(u)),rest_relation) -> .
% 299.99/300.66  204992[21:SpL:15272.1,198464.1] single_valued_class(u) || member(not_subclass_element(identity_relation,identity_relation),subset_relation)* equal(rest_of(single_valued2(u)),rest_relation)** -> .
% 299.99/300.66  204993[21:SpL:15265.1,198464.1] function(u) || member(not_subclass_element(identity_relation,identity_relation),subset_relation)* equal(rest_of(single_valued2(u)),rest_relation)** -> .
% 299.99/300.66  205199[15:Res:195033.1,897.0] || equal(complement(complement(restrict(u,v,w))),ordinal_numbers)** -> member(range_of(identity_relation),cross_product(v,w)).
% 299.99/300.66  205208[15:Res:195033.1,14681.0] || equal(complement(complement(regular(u))),ordinal_numbers)** member(range_of(identity_relation),u) -> equal(u,identity_relation).
% 299.99/300.66  205568[22:SpL:189.0,205502.0] || well_ordering(ordinal_numbers,power_class(image(element_relation,complement(u))))* -> member(singleton(identity_relation),image(element_relation,power_class(u))).
% 299.99/300.66  147324[5:SoR:132440.0,28934.2] || well_ordering(ordinal_numbers,cross_product(ordinal_numbers,ordinal_numbers))* subclass(rest_relation,recursion_equation_functions(u))* member(v,ordinal_numbers)* -> .
% 299.99/300.66  205778[22:SpR:189.0,205578.1] ||  -> member(singleton(identity_relation),image(element_relation,power_class(u))) member(singleton(identity_relation),power_class(image(element_relation,complement(u))))*.
% 299.99/300.66  205993[8:SpL:30.0,204042.0] || equal(symmetric_difference(ordinal_numbers,union(u,v)),ordinal_numbers) -> member(identity_relation,intersection(complement(u),complement(v)))*.
% 299.99/300.66  206000[8:SpL:162038.0,204042.0] || equal(symmetric_difference(ordinal_numbers,power_class(complement(inverse(identity_relation)))),ordinal_numbers)** -> member(identity_relation,image(element_relation,symmetrization_of(identity_relation))).
% 299.99/300.66  206001[16:SpL:195257.0,204042.0] || equal(symmetric_difference(ordinal_numbers,power_class(complement(singleton(identity_relation)))),ordinal_numbers)** -> member(identity_relation,image(element_relation,singleton(identity_relation))).
% 299.99/300.66  206133[22:Res:205574.1,18794.1] || equal(intersection(u,v),singleton(singleton(identity_relation))) member(singleton(identity_relation),symmetric_difference(u,v))* -> .
% 299.99/300.66  206155[22:Res:205574.1,897.0] || equal(restrict(u,v,w),singleton(singleton(identity_relation)))** -> member(singleton(identity_relation),cross_product(v,w))*.
% 299.99/300.66  206164[22:Res:205574.1,14681.0] || equal(regular(u),singleton(singleton(identity_relation))) member(singleton(identity_relation),u)* -> equal(u,identity_relation).
% 299.99/300.66  206166[22:Res:205574.1,288.0] || equal(image(element_relation,complement(u)),singleton(singleton(identity_relation))) member(singleton(identity_relation),power_class(u))* -> .
% 299.99/300.66  206244[8:SpL:155582.0,18794.1] || member(u,symmetric_difference(complement(v),symmetric_difference(ordinal_numbers,v)))* member(u,symmetric_difference(ordinal_numbers,v)) -> .
% 299.99/300.66  207665[24:SpR:207558.1,107.0] operation(single_valued1(u)) ||  -> equal(domain__dfg(u,image(inverse(u),identity_relation),single_valued2(u)),single_valued3(u))**.
% 299.99/300.66  207718[24:SpL:207558.1,160735.1] operation(u) || member(u,cantor(v))* equal(restrict(v,identity_relation,ordinal_numbers),identity_relation)** -> .
% 299.99/300.66  208359[24:Con:208343.0] operation(u) || member(singleton(singleton(identity_relation)),cantor(u))* -> member(identity_relation,cantor(cantor(u))).
% 299.99/300.66  208501[7:SpL:13260.1,39562.0] || equal(complement(unordered_pair(regular(cross_product(u,v)),w)),ordinal_numbers)** -> equal(cross_product(u,v),identity_relation).
% 299.99/300.66  208502[7:SpL:13260.1,39297.0] || subclass(ordinal_numbers,complement(unordered_pair(regular(cross_product(u,v)),w)))* -> equal(cross_product(u,v),identity_relation).
% 299.99/300.66  208529[7:SpL:13260.1,39499.0] || equal(complement(unordered_pair(u,regular(cross_product(v,w)))),ordinal_numbers)** -> equal(cross_product(v,w),identity_relation).
% 299.99/300.66  208530[7:SpL:13260.1,39296.0] || subclass(ordinal_numbers,complement(unordered_pair(u,regular(cross_product(v,w)))))* -> equal(cross_product(v,w),identity_relation).
% 299.99/300.66  208868[25:SpR:208820.0,62.1] || member(ordered_pair(ordinal_numbers,u),compose(v,w))* -> member(u,image(v,image(w,identity_relation))).
% 299.99/300.66  209013[25:Rew:209011.1,198311.2] || member(singleton(singleton(identity_relation)),compose_class(u))* -> equal(range_of(v),identity_relation)** equal(inverse(v),ordinal_numbers).
% 299.99/300.66  209018[25:Rew:209016.1,198312.2] || member(singleton(singleton(identity_relation)),rest_of(u))* -> equal(range_of(v),identity_relation)** equal(inverse(v),ordinal_numbers).
% 299.99/300.66  209281[25:SpR:208840.0,20.2] || member(ordinal_numbers,u) member(identity_relation,v) -> member(singleton(singleton(identity_relation)),cross_product(v,u))*.
% 299.99/300.66  209332[25:SpL:208840.0,117450.1] operation(u) || member(singleton(singleton(identity_relation)),cantor(u))* -> member(ordinal_numbers,cantor(cantor(u))).
% 299.99/300.66  209416[25:SpR:208885.0,8978.2] || member(image(u,identity_relation),ordinal_numbers) subclass(ordinal_numbers,v) -> member(apply(u,ordinal_numbers),v)*.
% 299.99/300.66  209435[25:Rew:208885.0,209414.0] || equal(apply(u,ordinal_numbers),image(u,identity_relation)) -> subclass(apply(u,ordinal_numbers),image(u,identity_relation))*.
% 299.99/300.66  209686[25:SpL:208841.0,12.0] || member(u,ordered_pair(ordinal_numbers,v))* -> equal(u,unordered_pair(ordinal_numbers,singleton(v))) equal(u,identity_relation).
% 299.99/300.66  209864[24:SpR:160491.0,207863.1] operation(symmetric_difference(ordinal_numbers,u)) ||  -> subclass(symmetric_difference(union(u,identity_relation),ordinal_numbers),successor(symmetric_difference(ordinal_numbers,u)))*.
% 299.99/300.66  209885[24:SpR:68757.0,207866.1] operation(complement(inverse(identity_relation))) ||  -> subclass(complement(successor(complement(inverse(identity_relation)))),intersection(symmetrization_of(identity_relation),ordinal_numbers))*.
% 299.99/300.66  209886[24:SpR:195256.0,207866.1] operation(complement(singleton(identity_relation))) ||  -> subclass(complement(successor(complement(singleton(identity_relation)))),intersection(singleton(identity_relation),ordinal_numbers))*.
% 299.99/300.66  209887[24:SpR:144460.0,207866.1] operation(symmetric_difference(ordinal_numbers,u)) ||  -> subclass(complement(successor(symmetric_difference(ordinal_numbers,u))),symmetric_difference(complement(u),ordinal_numbers))*.
% 299.99/300.66  209959[15:Res:209921.1,490.0] || equal(intersection(complement(u),complement(v)),ordinal_numbers) member(range_of(identity_relation),union(u,v))* -> .
% 299.99/300.66  210169[25:SpR:197474.0,208873.0] ||  -> equal(range_of(u),identity_relation) equal(unordered_pair(identity_relation,unordered_pair(inverse(u),identity_relation)),ordered_pair(inverse(u),ordinal_numbers))**.
% 299.99/300.66  210196[25:SpL:208873.0,12.0] || member(u,ordered_pair(v,ordinal_numbers))* -> equal(u,unordered_pair(v,identity_relation)) equal(u,singleton(v)).
% 299.99/300.66  210202[25:MRR:210201.0,162891.0] ||  -> equal(regular(ordered_pair(u,ordinal_numbers)),unordered_pair(u,identity_relation))** equal(regular(ordered_pair(u,ordinal_numbers)),singleton(u)).
% 299.99/300.66  210275[8:Res:140864.1,9876.0] || member(u,complement(v))* subclass(symmetric_difference(ordinal_numbers,v),w)* well_ordering(ordinal_numbers,w) -> .
% 299.99/300.66  210357[5:Res:51313.1,143186.0] || member(singleton(symmetric_difference(ordinal_numbers,u)),subset_relation) -> member(first(singleton(symmetric_difference(ordinal_numbers,u))),complement(u))*.
% 299.99/300.66  210395[5:Res:2504.1,143186.0] || subclass(ordered_pair(u,v),symmetric_difference(ordinal_numbers,w)) -> member(unordered_pair(u,singleton(v)),complement(w))*.
% 299.99/300.66  210466[5:Res:51313.1,143226.0] || member(singleton(symmetric_difference(ordinal_numbers,u)),subset_relation) member(first(singleton(symmetric_difference(ordinal_numbers,u))),u)* -> .
% 299.99/300.66  210476[5:Res:2503.2,143226.0] || subclass(u,symmetric_difference(ordinal_numbers,v)) member(not_subclass_element(u,w),v)* -> subclass(u,w).
% 299.99/300.66  210478[5:Res:8978.2,143226.0] || member(u,ordinal_numbers) subclass(ordinal_numbers,symmetric_difference(ordinal_numbers,v))* member(sum_class(u),v)* -> .
% 299.99/300.66  210481[5:Res:8977.2,143226.0] || member(u,ordinal_numbers) subclass(ordinal_numbers,symmetric_difference(ordinal_numbers,v))* member(power_class(u),v)* -> .
% 299.99/300.66  210504[5:Res:2504.1,143226.0] || subclass(ordered_pair(u,v),symmetric_difference(ordinal_numbers,w))* member(unordered_pair(u,singleton(v)),w) -> .
% 299.99/300.66  210527[8:Rew:160491.0,210462.1,160491.0,210462.0] || member(not_subclass_element(complement(union(u,identity_relation)),v),u)* -> subclass(complement(union(u,identity_relation)),v).
% 299.99/300.66  210552[8:Res:27.2,210517.1] || member(u,v)* member(u,w)* equal(complement(intersection(w,v)),ordinal_numbers)** -> .
% 299.99/300.66  210555[8:Res:39530.1,210517.1] || member(u,ordinal_numbers) equal(complement(union(v,w)),ordinal_numbers)** -> member(u,complement(v))*.
% 299.99/300.66  210556[8:Res:39529.1,210517.1] || member(u,ordinal_numbers) equal(complement(union(v,w)),ordinal_numbers)** -> member(u,complement(w))*.
% 299.99/300.66  210667[8:Res:20.2,210517.1] || member(u,v)* member(w,x)* equal(complement(cross_product(x,v)),ordinal_numbers)** -> .
% 299.99/300.66  210761[8:Con:210672.2] operation(u) || member(v,cantor(cantor(u)))* equal(complement(cantor(u)),ordinal_numbers) -> .
% 299.99/300.66  211314[8:Res:210606.1,116155.1] || equal(complement(u),ordinal_numbers) subclass(complement(u),v) -> section(w,complement(u),v)*.
% 299.99/300.66  211394[8:Res:210606.1,8990.1] function(complement(u)) || equal(complement(u),ordinal_numbers) -> equal(cross_product(ordinal_numbers,ordinal_numbers),complement(u))*.
% 299.99/300.66  211431[8:Res:210606.1,40321.0] || equal(complement(u),ordinal_numbers) well_ordering(v,complement(u))* -> member(least(v,rest_relation),rest_relation)*.
% 299.99/300.66  211548[8:Res:211438.1,116155.1] || equal(symmetrization_of(identity_relation),ordinal_numbers) subclass(symmetrization_of(identity_relation),u) -> section(v,symmetrization_of(identity_relation),u)*.
% 299.99/300.66  211585[8:Res:211438.1,40321.0] || equal(symmetrization_of(identity_relation),ordinal_numbers) well_ordering(u,symmetrization_of(identity_relation)) -> member(least(u,rest_relation),rest_relation)*.
% 299.99/300.66  211632[8:Res:211441.1,116155.1] || equal(power_class(u),ordinal_numbers) subclass(power_class(u),v) -> section(w,power_class(u),v)*.
% 299.99/300.66  211665[8:Res:211441.1,8990.1] function(power_class(u)) || equal(power_class(u),ordinal_numbers) -> equal(cross_product(ordinal_numbers,ordinal_numbers),power_class(u))*.
% 299.99/300.66  211669[8:Res:211441.1,40321.0] || equal(power_class(u),ordinal_numbers) well_ordering(v,power_class(u))* -> member(least(v,rest_relation),rest_relation)*.
% 299.99/300.66  212147[8:Rew:160498.0,212004.1] || equal(symmetrization_of(identity_relation),ordinal_numbers) -> subclass(complement(complement(complement(singleton(symmetrization_of(identity_relation))))),successor(symmetrization_of(identity_relation)))*.
% 299.99/300.66  212148[8:Rew:160498.0,212005.1] || equal(symmetrization_of(identity_relation),ordinal_numbers) -> subclass(complement(complement(complement(inverse(symmetrization_of(identity_relation))))),symmetrization_of(symmetrization_of(identity_relation)))*.
% 299.99/300.66  212681[8:Rew:160498.0,212479.1] || equal(complement(u),ordinal_numbers) -> subclass(complement(complement(complement(singleton(complement(u))))),successor(complement(u)))*.
% 299.99/300.66  212682[8:Rew:160498.0,212480.1] || equal(complement(u),ordinal_numbers) -> subclass(complement(complement(complement(inverse(complement(u))))),symmetrization_of(complement(u)))*.
% 299.99/300.66  212638[8:SpL:211432.1,160667.0] || equal(complement(symmetrization_of(u)),ordinal_numbers)** subclass(cross_product(v,v),identity_relation)* -> connected(u,v)*.
% 299.99/300.66  212749[8:MRR:212748.2,13039.0] || equal(complement(symmetrization_of(u)),ordinal_numbers)** connected(u,v)* -> equal(cross_product(v,v),identity_relation)**.
% 299.99/300.66  212910[8:Rew:160498.0,212774.1] || equal(power_class(u),ordinal_numbers) -> subclass(complement(complement(complement(singleton(power_class(u))))),successor(power_class(u)))*.
% 299.99/300.66  212911[8:Rew:160498.0,212775.1] || equal(power_class(u),ordinal_numbers) -> subclass(complement(complement(complement(inverse(power_class(u))))),symmetrization_of(power_class(u)))*.
% 299.99/300.66  213478[8:SpL:145761.0,56525.0] || member(cross_product(u,singleton(v)),segment(ordinal_numbers,u,v))* subclass(ordinal_numbers,complement(element_relation)) -> .
% 299.99/300.66  213487[8:SpL:145761.0,161304.1] || subclass(rest_relation,rest_of(cross_product(u,singleton(v))))* well_ordering(ordinal_numbers,segment(ordinal_numbers,u,v)) -> .
% 299.99/300.66  214060[5:Res:133837.1,152274.0] || well_ordering(ordinal_numbers,complement(complement(singleton(singleton(singleton(u))))))* -> subclass(singleton(singleton(singleton(u))),v)*.
% 299.99/300.66  214083[18:Res:190510.1,152274.0] || subclass(inverse(identity_relation),complement(singleton(regular(symmetrization_of(identity_relation)))))* -> subclass(singleton(regular(symmetrization_of(identity_relation))),u)*.
% 299.99/300.66  214089[5:Rew:50855.1,214032.2] || member(singleton(u),subset_relation) member(first(singleton(u)),complement(u))* -> subclass(u,v)*.
% 299.99/300.66  214293[25:SpL:208887.0,56525.0] || member(restrict(u,v,identity_relation),segment(u,v,ordinal_numbers))* subclass(ordinal_numbers,complement(element_relation)) -> .
% 299.99/300.66  214302[25:SpL:208887.0,161304.1] || subclass(rest_relation,rest_of(restrict(u,v,identity_relation)))* well_ordering(ordinal_numbers,segment(u,v,ordinal_numbers)) -> .
% 299.99/300.66  214496[25:SpL:208985.1,97.0] operation(u) || member(ordered_pair(v,u),compose_class(w))* -> equal(compose(w,v),ordinal_numbers).
% 299.99/300.66  214551[25:SpL:208985.1,97.0] operation(u) || member(ordered_pair(v,ordinal_numbers),compose_class(w))* -> equal(compose(w,v),u)*.
% 299.99/300.66  214953[5:SpR:30.0,151502.1] ||  -> member(u,intersection(complement(v),complement(w))) subclass(intersection(x,singleton(u)),union(v,w))*.
% 299.99/300.66  214954[8:SpR:211432.1,151502.1] || equal(complement(u),ordinal_numbers) -> member(v,complement(u))* subclass(intersection(w,singleton(v)),identity_relation)*.
% 299.99/300.66  214958[8:SpR:211586.1,151502.1] || equal(symmetrization_of(identity_relation),ordinal_numbers) -> member(u,symmetrization_of(identity_relation)) subclass(intersection(v,singleton(u)),identity_relation)*.
% 299.99/300.66  214962[8:SpR:162038.0,151502.1] ||  -> member(u,image(element_relation,symmetrization_of(identity_relation))) subclass(intersection(v,singleton(u)),power_class(complement(inverse(identity_relation))))*.
% 299.99/300.66  214963[16:SpR:195257.0,151502.1] ||  -> member(u,image(element_relation,singleton(identity_relation))) subclass(intersection(v,singleton(u)),power_class(complement(singleton(identity_relation))))*.
% 299.99/300.66  214966[8:SpR:211670.1,151502.1] || equal(power_class(u),ordinal_numbers) -> member(v,power_class(u))* subclass(intersection(w,singleton(v)),identity_relation)*.
% 299.99/300.66  215083[5:SpR:30.0,151862.1] ||  -> member(u,intersection(complement(v),complement(w))) subclass(intersection(singleton(u),x),union(v,w))*.
% 299.99/300.66  215084[8:SpR:211432.1,151862.1] || equal(complement(u),ordinal_numbers) -> member(v,complement(u))* subclass(intersection(singleton(v),w),identity_relation)*.
% 299.99/300.66  215088[8:SpR:211586.1,151862.1] || equal(symmetrization_of(identity_relation),ordinal_numbers) -> member(u,symmetrization_of(identity_relation)) subclass(intersection(singleton(u),v),identity_relation)*.
% 299.99/300.66  215092[8:SpR:162038.0,151862.1] ||  -> member(u,image(element_relation,symmetrization_of(identity_relation))) subclass(intersection(singleton(u),v),power_class(complement(inverse(identity_relation))))*.
% 299.99/300.66  215093[16:SpR:195257.0,151862.1] ||  -> member(u,image(element_relation,singleton(identity_relation))) subclass(intersection(singleton(u),v),power_class(complement(singleton(identity_relation))))*.
% 299.99/300.66  215096[8:SpR:211670.1,151862.1] || equal(power_class(u),ordinal_numbers) -> member(v,power_class(u))* subclass(intersection(singleton(v),w),identity_relation)*.
% 299.99/300.66  215135[5:SpR:30.0,215108.1] ||  -> member(u,intersection(complement(v),complement(w))) subclass(complement(complement(singleton(u))),union(v,w))*.
% 299.99/300.66  215136[8:SpR:211432.1,215108.1] || equal(complement(u),ordinal_numbers) -> member(v,complement(u))* subclass(complement(complement(singleton(v))),identity_relation)*.
% 299.99/300.66  215140[8:SpR:211586.1,215108.1] || equal(symmetrization_of(identity_relation),ordinal_numbers) -> member(u,symmetrization_of(identity_relation)) subclass(complement(complement(singleton(u))),identity_relation)*.
% 299.99/300.66  215144[8:SpR:162038.0,215108.1] ||  -> member(u,image(element_relation,symmetrization_of(identity_relation))) subclass(complement(complement(singleton(u))),power_class(complement(inverse(identity_relation))))*.
% 299.99/300.66  215145[16:SpR:195257.0,215108.1] ||  -> member(u,image(element_relation,singleton(identity_relation))) subclass(complement(complement(singleton(u))),power_class(complement(singleton(identity_relation))))*.
% 299.99/300.66  215148[8:SpR:211670.1,215108.1] || equal(power_class(u),ordinal_numbers) -> member(v,power_class(u))* subclass(complement(complement(singleton(v))),identity_relation)*.
% 299.99/300.66  215176[8:SpR:160491.0,155157.1] || subclass(symmetric_difference(ordinal_numbers,u),v) -> subclass(symmetric_difference(v,symmetric_difference(ordinal_numbers,u)),union(u,identity_relation))*.
% 299.99/300.66  215369[8:SpR:189.0,215271.1] || subclass(image(element_relation,power_class(u)),identity_relation) -> equal(complement(power_class(image(element_relation,complement(u)))),identity_relation)**.
% 299.99/300.66  217516[7:Res:61019.0,151988.0] ||  -> equal(complement(complement(complement(complement(u)))),identity_relation) member(regular(complement(complement(complement(complement(u))))),u)*.
% 299.99/300.66  217678[8:Res:216691.1,19120.0] || equal(complement(intersection(u,v)),identity_relation)** -> subclass(ordinal_numbers,w) member(not_subclass_element(ordinal_numbers,w),v)*.
% 299.99/300.66  217679[8:Res:216691.1,19121.0] || equal(complement(intersection(u,v)),identity_relation)** -> subclass(ordinal_numbers,w) member(not_subclass_element(ordinal_numbers,w),u)*.
% 299.99/300.66  217748[8:Res:216691.1,18581.1] || equal(complement(intersection(u,v)),identity_relation)** member(w,ordinal_numbers) -> member(sum_class(w),u)*.
% 299.99/300.66  217749[8:Res:216691.1,18580.1] || equal(complement(intersection(u,v)),identity_relation)** member(w,ordinal_numbers) -> member(sum_class(w),v)*.
% 299.99/300.66  217773[8:Res:216691.1,18829.0] || equal(complement(restrict(u,v,w)),identity_relation)** -> member(unordered_pair(x,y),cross_product(v,w))*.
% 299.99/300.66  217947[7:Res:139.1,17315.0] || member(recursion_equation_functions(u),ordinal_numbers) -> equal(sum_class(recursion_equation_functions(u)),identity_relation) function(regular(sum_class(recursion_equation_functions(u))))*.
% 299.99/300.66  217965[7:MRR:217954.2,13102.1] || connected(u,recursion_equation_functions(v)) -> well_ordering(u,recursion_equation_functions(v)) function(regular(not_well_ordering(u,recursion_equation_functions(v))))*.
% 299.99/300.66  218068[8:SpL:6355.1,217708.0] || equal(complement(complement(not_subclass_element(cross_product(u,v),w))),identity_relation)** -> subclass(cross_product(u,v),w).
% 299.99/300.66  218081[8:SpL:6355.1,215649.0] || subclass(unordered_pair(u,not_subclass_element(cross_product(v,w),x)),identity_relation)* -> subclass(cross_product(v,w),x).
% 299.99/300.66  218107[8:SpL:6355.1,215653.0] || subclass(unordered_pair(not_subclass_element(cross_product(u,v),w),x),identity_relation)* -> subclass(cross_product(u,v),w).
% 299.99/300.66  218345[8:SpL:6355.1,217155.0] || equal(unordered_pair(u,not_subclass_element(cross_product(v,w),x)),identity_relation)** -> subclass(cross_product(v,w),x).
% 299.99/300.66  218475[21:SpL:218460.1,28976.1] || equal(rest_relation,domain_relation) subclass(rest_relation,inverse(subset_relation)) member(ordered_pair(omega,identity_relation),subset_relation)* -> .
% 299.99/300.66  218525[8:SpL:6355.1,217160.0] || equal(unordered_pair(not_subclass_element(cross_product(u,v),w),x),identity_relation)** -> subclass(cross_product(u,v),w).
% 299.99/300.66  218646[8:SpL:160491.0,66645.0] || subclass(ordinal_numbers,image(element_relation,union(u,identity_relation)))* member(omega,power_class(symmetric_difference(ordinal_numbers,u))) -> .
% 299.99/300.66  219107[8:Res:8835.1,219073.1] || member(u,ordinal_numbers) subclass(image(element_relation,complement(v)),identity_relation)* -> member(u,power_class(v))*.
% 299.99/300.66  219321[15:Res:215659.1,18791.0] || subclass(complement(symmetric_difference(complement(u),complement(v))),identity_relation)* -> member(range_of(identity_relation),union(u,v)).
% 299.99/300.66  219333[15:Res:215659.1,12.0] || subclass(complement(unordered_pair(u,v)),identity_relation)* -> equal(range_of(identity_relation),v) equal(range_of(identity_relation),u).
% 299.99/300.66  219374[21:SpR:66834.1,196545.0] || well_ordering(u,ordinal_numbers) -> equal(least(u,omega),identity_relation) equal(cantor(least(u,omega)),identity_relation)**.
% 299.99/300.66  219454[7:Res:9461.1,13082.1] inductive(not_subclass_element(recursion_equation_functions(u),v)) ||  -> subclass(recursion_equation_functions(u),v)* member(identity_relation,cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.66  219592[15:Res:195033.1,67561.0] || equal(complement(complement(symmetric_difference(complement(u),ordinal_numbers))),ordinal_numbers)** -> member(range_of(identity_relation),union(u,identity_relation)).
% 299.99/300.66  219614[8:Res:9632.1,67561.0] || equal(complement(complement(symmetric_difference(complement(u),ordinal_numbers))),ordinal_numbers)** -> member(singleton(v),union(u,identity_relation))*.
% 299.99/300.66  219617[8:Res:133837.1,67561.0] || well_ordering(ordinal_numbers,complement(symmetric_difference(complement(u),ordinal_numbers)))* -> member(singleton(singleton(v)),union(u,identity_relation))*.
% 299.99/300.66  219618[21:Res:196904.1,67561.0] || subclass(domain_relation,symmetric_difference(complement(u),ordinal_numbers)) -> member(singleton(singleton(singleton(identity_relation))),union(u,identity_relation))*.
% 299.99/300.66  219619[22:Res:205574.1,67561.0] || equal(symmetric_difference(complement(u),ordinal_numbers),singleton(singleton(identity_relation))) -> member(singleton(identity_relation),union(u,identity_relation))*.
% 299.99/300.66  219637[18:Res:194549.1,67561.0] || subclass(symmetrization_of(identity_relation),symmetric_difference(complement(u),ordinal_numbers)) -> member(regular(symmetrization_of(identity_relation)),union(u,identity_relation))*.
% 299.99/300.66  219638[18:Res:190510.1,67561.0] || subclass(inverse(identity_relation),symmetric_difference(complement(u),ordinal_numbers)) -> member(regular(symmetrization_of(identity_relation)),union(u,identity_relation))*.
% 299.99/300.66  219796[15:Res:67614.1,165527.1] || member(range_of(identity_relation),union(u,identity_relation)) subclass(ordinal_numbers,complement(symmetric_difference(complement(u),ordinal_numbers)))* -> .
% 299.99/300.66  219805[8:Res:67614.1,133836.0] || member(singleton(singleton(u)),union(v,identity_relation))* well_ordering(ordinal_numbers,symmetric_difference(complement(v),ordinal_numbers)) -> .
% 299.99/300.66  219806[8:Res:67614.1,8843.1] || member(singleton(u),union(v,identity_relation))* subclass(ordinal_numbers,complement(symmetric_difference(complement(v),ordinal_numbers)))* -> .
% 299.99/300.66  219813[18:Res:67614.1,190641.1] || member(identity_relation,union(u,identity_relation)) equal(complement(symmetric_difference(complement(u),ordinal_numbers)),inverse(identity_relation))** -> .
% 299.99/300.66  219814[18:Res:67614.1,190532.1] || member(identity_relation,union(u,identity_relation)) equal(complement(symmetric_difference(complement(u),ordinal_numbers)),symmetrization_of(identity_relation))** -> .
% 299.99/300.66  219815[14:Res:67614.1,165357.1] || member(identity_relation,union(u,identity_relation)) equal(complement(symmetric_difference(complement(u),ordinal_numbers)),singleton(identity_relation))** -> .
% 299.99/300.66  219848[15:Res:217197.1,18791.0] || equal(complement(symmetric_difference(complement(u),complement(v))),identity_relation)** -> member(range_of(identity_relation),union(u,v)).
% 299.99/300.66  220018[8:Res:6.1,160772.0] || member(not_subclass_element(symmetric_difference(ordinal_numbers,u),v),union(u,identity_relation))* -> subclass(symmetric_difference(ordinal_numbers,u),v).
% 299.99/300.66  220056[21:Res:196904.1,160772.0] || subclass(domain_relation,symmetric_difference(ordinal_numbers,u)) member(singleton(singleton(singleton(identity_relation))),union(u,identity_relation))* -> .
% 299.99/300.66  220057[22:Res:205574.1,160772.0] || equal(symmetric_difference(ordinal_numbers,u),singleton(singleton(identity_relation))) member(singleton(identity_relation),union(u,identity_relation))* -> .
% 299.99/300.66  220076[18:Res:194549.1,160772.0] || subclass(symmetrization_of(identity_relation),symmetric_difference(ordinal_numbers,u)) member(regular(symmetrization_of(identity_relation)),union(u,identity_relation))* -> .
% 299.99/300.66  220077[18:Res:190510.1,160772.0] || subclass(inverse(identity_relation),symmetric_difference(ordinal_numbers,u)) member(regular(symmetrization_of(identity_relation)),union(u,identity_relation))* -> .
% 299.99/300.66  220132[8:SpL:116154.0,217492.1] operation(restrict(u,v,singleton(w))) || equal(complement(segment(u,v,w)),identity_relation)** -> .
% 299.99/300.66  220195[8:SpL:13260.1,217704.0] || equal(complement(complement(singleton(regular(cross_product(u,v))))),identity_relation)** -> equal(cross_product(u,v),identity_relation).
% 299.99/300.66  220378[8:Rew:51324.2,220367.2] || member(singleton(u),subset_relation) member(u,subset_relation) subclass(singleton(first(u)),identity_relation)* -> .
% 299.99/300.66  220410[21:Res:196656.1,143226.0] || subclass(domain_relation,flip(symmetric_difference(ordinal_numbers,u))) member(ordered_pair(ordered_pair(v,w),identity_relation),u)* -> .
% 299.99/300.66  220411[21:Res:196656.1,143186.0] || subclass(domain_relation,flip(symmetric_difference(ordinal_numbers,u))) -> member(ordered_pair(ordered_pair(v,w),identity_relation),complement(u))*.
% 299.99/300.66  220426[21:Res:196656.1,56411.0] || subclass(domain_relation,flip(rest_of(ordered_pair(ordered_pair(u,v),identity_relation))))* subclass(ordinal_numbers,complement(element_relation)) -> .
% 299.99/300.66  220428[21:Res:196656.1,898.0] || subclass(domain_relation,flip(restrict(u,v,w)))* -> member(ordered_pair(ordered_pair(x,y),identity_relation),u)*.
% 299.99/300.66  220432[21:Res:196656.1,8788.0] || subclass(domain_relation,flip(recursion_equation_functions(u)))* -> subclass(ordered_pair(ordered_pair(v,w),identity_relation),cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.66  220512[21:Res:196657.1,143226.0] || subclass(domain_relation,rotate(symmetric_difference(ordinal_numbers,u))) member(ordered_pair(ordered_pair(v,identity_relation),w),u)* -> .
% 299.99/300.66  220513[21:Res:196657.1,143186.0] || subclass(domain_relation,rotate(symmetric_difference(ordinal_numbers,u))) -> member(ordered_pair(ordered_pair(v,identity_relation),w),complement(u))*.
% 299.99/300.66  220528[21:Res:196657.1,56411.0] || subclass(domain_relation,rotate(rest_of(ordered_pair(ordered_pair(u,identity_relation),v))))* subclass(ordinal_numbers,complement(element_relation)) -> .
% 299.99/300.66  220530[21:Res:196657.1,898.0] || subclass(domain_relation,rotate(restrict(u,v,w)))* -> member(ordered_pair(ordered_pair(x,identity_relation),y),u)*.
% 299.99/300.66  220534[21:Res:196657.1,8788.0] || subclass(domain_relation,rotate(recursion_equation_functions(u)))* -> subclass(ordered_pair(ordered_pair(v,identity_relation),w),cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.66  220670[7:Res:18949.0,17324.0] ||  -> equal(restrict(singleton(u),v,w),identity_relation) equal(regular(restrict(singleton(u),v,w)),u)**.
% 299.99/300.66  220821[8:SpL:116154.0,219206.0] || member(restrict(u,v,singleton(w)),segment(u,v,w))* subclass(element_relation,identity_relation) -> .
% 299.99/300.66  221145[7:Res:13236.2,3700.0] || well_ordering(u,singleton(v)) -> equal(singleton(v),identity_relation) equal(least(u,singleton(v)),v)**.
% 299.99/300.66  221281[8:Res:215662.1,18791.0] || subclass(complement(symmetric_difference(complement(u),complement(v))),identity_relation)* -> member(singleton(w),union(u,v))*.
% 299.99/300.66  221296[8:Res:215662.1,12.0] || subclass(complement(unordered_pair(u,v)),identity_relation)* -> equal(singleton(w),v)* equal(singleton(w),u)*.
% 299.99/300.66  221344[8:Res:215662.1,40594.1] || subclass(complement(u),identity_relation) member(u,ordinal_numbers) -> member(singleton(singleton(singleton(u))),element_relation)*.
% 299.99/300.66  221452[8:SpL:189.0,221330.0] || subclass(power_class(image(element_relation,complement(u))),identity_relation)* well_ordering(ordinal_numbers,image(element_relation,power_class(u))) -> .
% 299.99/300.66  221538[8:Res:217198.1,18791.0] || equal(complement(symmetric_difference(complement(u),complement(v))),identity_relation)** -> member(singleton(w),union(u,v))*.
% 299.99/300.66  221601[8:Res:217198.1,40594.1] || equal(complement(u),identity_relation) member(u,ordinal_numbers) -> member(singleton(singleton(singleton(u))),element_relation)*.
% 299.99/300.66  221665[8:SpR:218159.1,3606.0] || equal(complement(restrict(u,v,w)),identity_relation) -> equal(symmetric_difference(cross_product(v,w),u),identity_relation)**.
% 299.99/300.66  221666[8:SpR:218159.1,3603.0] || equal(complement(restrict(u,v,w)),identity_relation) -> equal(symmetric_difference(u,cross_product(v,w)),identity_relation)**.
% 299.99/300.66  222100[8:SpR:219120.1,3606.0] || subclass(complement(restrict(u,v,w)),identity_relation)* -> equal(symmetric_difference(cross_product(v,w),u),identity_relation).
% 299.99/300.66  222101[8:SpR:219120.1,3603.0] || subclass(complement(restrict(u,v,w)),identity_relation)* -> equal(symmetric_difference(u,cross_product(v,w)),identity_relation).
% 299.99/300.66  222689[5:Res:8955.1,31610.0] || member(u,ordinal_numbers) subclass(rest_relation,successor_relation) -> equal(rest_of(sum_class(u)),successor(sum_class(u)))**.
% 299.99/300.66  222691[5:Res:50063.1,31610.0] || member(u,subset_relation) subclass(rest_relation,successor_relation) -> equal(rest_of(first(u)),successor(first(u)))**.
% 299.99/300.66  222692[5:Res:50064.1,31610.0] || member(u,subset_relation) subclass(rest_relation,successor_relation) -> equal(rest_of(second(u)),successor(second(u)))**.
% 299.99/300.66  222772[5:Rew:31610.2,222695.2] || member(u,ordinal_numbers) subclass(rest_relation,successor_relation) -> equal(rest_of(successor(u)),successor(successor(u)))**.
% 299.99/300.66  222701[5:Res:8956.1,31610.0] || member(u,ordinal_numbers) subclass(rest_relation,successor_relation) -> equal(rest_of(power_class(u)),successor(power_class(u)))**.
% 299.99/300.66  223158[8:Rew:140613.0,223120.1] || equal(inverse(u),identity_relation) -> equal(complement(image(element_relation,symmetrization_of(u))),power_class(symmetric_difference(ordinal_numbers,u)))**.
% 299.99/300.66  223354[21:MRR:223294.1,165431.0] || subclass(rest_relation,domain_relation) subclass(rest_relation,u) -> member(ordered_pair(sum_class(range_of(identity_relation)),identity_relation),u)*.
% 299.99/300.66  223420[21:MRR:223362.1,190509.0] || subclass(rest_relation,domain_relation) subclass(rest_relation,u) -> member(ordered_pair(regular(symmetrization_of(identity_relation)),identity_relation),u)*.
% 299.99/300.66  223482[8:Rew:140613.0,223442.1] || equal(singleton(u),identity_relation) -> equal(complement(image(element_relation,successor(u))),power_class(symmetric_difference(ordinal_numbers,u)))**.
% 299.99/300.66  223551[21:MRR:223496.1,125724.0] || subclass(rest_relation,domain_relation) subclass(rest_relation,u) -> member(ordered_pair(least(element_relation,omega),identity_relation),u)*.
% 299.99/300.66  223727[14:SpR:160927.0,165172.1] ||  -> member(identity_relation,intersection(complement(u),union(v,identity_relation)))* member(identity_relation,union(u,symmetric_difference(ordinal_numbers,v))).
% 299.99/300.66  223768[24:SpR:207565.1,160927.0] operation(u) ||  -> equal(complement(intersection(complement(v),successor(u))),union(v,symmetric_difference(ordinal_numbers,u)))**.
% 299.99/300.66  223780[16:SpR:195239.0,160927.0] ||  -> equal(union(complement(singleton(identity_relation)),symmetric_difference(ordinal_numbers,u)),complement(intersection(singleton(identity_relation),union(u,identity_relation))))**.
% 299.99/300.66  223781[8:SpR:162584.0,160927.0] ||  -> equal(union(complement(inverse(identity_relation)),symmetric_difference(ordinal_numbers,u)),complement(intersection(symmetrization_of(identity_relation),union(u,identity_relation))))**.
% 299.99/300.66  223962[16:SpL:195239.0,13242.0] || subclass(omega,singleton(identity_relation)) member(u,complement(singleton(identity_relation)))* -> equal(integer_of(u),identity_relation).
% 299.99/300.66  223963[8:SpL:162584.0,13242.0] || subclass(omega,symmetrization_of(identity_relation)) member(u,complement(inverse(identity_relation)))* -> equal(integer_of(u),identity_relation).
% 299.99/300.66  224044[14:SpR:160992.0,165172.1] ||  -> member(identity_relation,intersection(union(u,identity_relation),complement(v)))* member(identity_relation,union(symmetric_difference(ordinal_numbers,u),v)).
% 299.99/300.66  224090[16:SpR:195239.0,160992.0] ||  -> equal(union(symmetric_difference(ordinal_numbers,u),complement(singleton(identity_relation))),complement(intersection(union(u,identity_relation),singleton(identity_relation))))**.
% 299.99/300.66  224091[8:SpR:162584.0,160992.0] ||  -> equal(union(symmetric_difference(ordinal_numbers,u),complement(inverse(identity_relation))),complement(intersection(union(u,identity_relation),symmetrization_of(identity_relation))))**.
% 299.99/300.66  224102[24:SpR:207565.1,160992.0] operation(u) ||  -> equal(complement(intersection(successor(u),complement(v))),union(symmetric_difference(ordinal_numbers,u),v))**.
% 299.99/300.66  224114[8:SpR:147905.0,160992.0] ||  -> equal(union(symmetric_difference(ordinal_numbers,u),complement(union(u,identity_relation))),complement(complement(complement(union(u,identity_relation)))))**.
% 299.99/300.66  224214[8:Rew:66293.0,224086.1] || equal(identity_relation,u) -> equal(union(symmetric_difference(ordinal_numbers,v),u),complement(symmetric_difference(complement(v),ordinal_numbers)))**.
% 299.99/300.66  224316[8:MRR:224290.2,218132.1] || member(regular(regular(symmetric_difference(ordinal_numbers,u))),complement(u))* -> equal(regular(symmetric_difference(ordinal_numbers,u)),identity_relation).
% 299.99/300.66  224321[8:MRR:224282.0,60996.1] ||  -> member(regular(regular(complement(u))),u)* equal(regular(complement(u)),identity_relation) equal(complement(u),identity_relation).
% 299.99/300.66  224569[10:Rew:66036.0,224384.1] || subclass(element_relation,identity_relation) -> subclass(symmetric_difference(complement(cross_product(ordinal_numbers,ordinal_numbers)),ordinal_numbers),successor(cross_product(ordinal_numbers,ordinal_numbers)))*.
% 299.99/300.66  224574[25:Rew:208887.0,224452.1] || subclass(element_relation,identity_relation) -> equal(segment(u,v,cross_product(ordinal_numbers,ordinal_numbers)),segment(u,v,ordinal_numbers))**.
% 299.99/300.66  224577[10:Rew:140613.0,224389.1,66036.0,224389.1] || subclass(element_relation,identity_relation) -> subclass(complement(successor(cross_product(ordinal_numbers,ordinal_numbers))),symmetric_difference(ordinal_numbers,cross_product(ordinal_numbers,ordinal_numbers)))*.
% 299.99/300.66  224584[25:Rew:208881.0,224445.1] || subclass(element_relation,identity_relation) -> equal(range__dfg(u,cross_product(ordinal_numbers,ordinal_numbers),v),range__dfg(u,ordinal_numbers,v))**.
% 299.99/300.66  224585[25:Rew:208888.0,224453.1] || subclass(element_relation,identity_relation) -> equal(domain__dfg(u,v,cross_product(ordinal_numbers,ordinal_numbers)),domain__dfg(u,v,ordinal_numbers))**.
% 299.99/300.66  224685[26:Rew:224682.1,224683.2] inductive(successor(identity_relation)) || member(identity_relation,image(successor_relation,omega))* -> equal(image(successor_relation,omega),omega).
% 299.99/300.66  225257[26:SpL:189.0,224734.0] || subclass(omega,power_class(image(element_relation,complement(u))))* member(identity_relation,image(element_relation,power_class(u))) -> .
% 299.99/300.66  225280[26:SpL:189.0,224737.0] || subclass(omega,complement(power_class(image(element_relation,complement(u)))))* -> member(identity_relation,image(element_relation,power_class(u))).
% 299.99/300.66  225330[26:Res:27.2,225263.1] || member(identity_relation,u) member(identity_relation,v) equal(complement(intersection(v,u)),omega)** -> .
% 299.99/300.66  225404[8:Res:156922.1,17312.1] || member(regular(u),inverse(subset_relation))* subclass(u,complement(complement(subset_relation))) -> equal(u,identity_relation).
% 299.99/300.66  225418[7:Res:18819.1,17312.1] || member(regular(u),subset_relation) subclass(u,complement(cross_product(ordinal_numbers,ordinal_numbers)))* -> equal(u,identity_relation).
% 299.99/300.66  225423[8:Res:204134.1,17312.1] || member(regular(u),inverse(identity_relation))* subclass(u,complement(symmetrization_of(identity_relation))) -> equal(u,identity_relation).
% 299.99/300.66  225460[8:Rew:160491.0,225410.1] || member(regular(u),complement(v))* subclass(u,union(v,identity_relation)) -> equal(u,identity_relation).
% 299.99/300.66  225472[7:MRR:225412.0,60996.1] || subclass(u,complement(union(v,w)))* -> member(regular(u),complement(w)) equal(u,identity_relation).
% 299.99/300.66  225473[7:MRR:225411.0,60996.1] || subclass(u,complement(union(v,w)))* -> member(regular(u),complement(v)) equal(u,identity_relation).
% 299.99/300.66  225578[26:SpL:189.0,225289.0] || equal(complement(power_class(image(element_relation,complement(u)))),omega)** -> member(identity_relation,image(element_relation,power_class(u))).
% 299.99/300.66  225726[26:SpL:3606.0,224747.0] || subclass(omega,symmetric_difference(cross_product(u,v),w)) -> member(identity_relation,complement(restrict(w,u,v)))*.
% 299.99/300.66  225727[26:SpL:3603.0,224747.0] || subclass(omega,symmetric_difference(u,cross_product(v,w))) -> member(identity_relation,complement(restrict(u,v,w)))*.
% 299.99/300.66  225961[26:SpL:3606.0,225765.0] || equal(symmetric_difference(cross_product(u,v),w),omega) -> member(identity_relation,complement(restrict(w,u,v)))*.
% 299.99/300.66  225962[26:SpL:3603.0,225765.0] || equal(symmetric_difference(u,cross_product(v,w)),omega) -> member(identity_relation,complement(restrict(u,v,w)))*.
% 299.99/300.66  226044[7:Res:13578.1,9876.0] || subclass(union(u,v),w)* well_ordering(ordinal_numbers,w) -> equal(symmetric_difference(u,v),identity_relation).
% 299.99/300.66  226412[7:Res:13258.1,50033.0] || equal(complement(regular(restrict(subset_relation,u,v))),ordinal_numbers)** -> equal(restrict(subset_relation,u,v),identity_relation).
% 299.99/300.66  226620[14:Rew:66036.0,226616.1] || member(identity_relation,image(element_relation,complement(u))) subclass(complement(intersection(power_class(u),ordinal_numbers)),identity_relation)* -> .
% 299.99/300.66  226627[25:SpL:208887.0,216284.1] || subclass(rest_relation,rest_of(restrict(u,v,identity_relation)))* subclass(segment(u,v,ordinal_numbers),identity_relation) -> .
% 299.99/300.66  226649[8:SpL:145761.0,216284.1] || subclass(rest_relation,rest_of(cross_product(u,singleton(v))))* subclass(segment(ordinal_numbers,u,v),identity_relation) -> .
% 299.99/300.66  226887[24:Rew:207565.1,226871.2] operation(u) || member(regular(successor(u)),symmetric_difference(ordinal_numbers,u))* -> equal(successor(u),identity_relation).
% 299.99/300.66  227137[8:SpL:30.0,217386.0] || equal(complement(union(u,v)),identity_relation) member(identity_relation,intersection(complement(u),complement(v)))* -> .
% 299.99/300.66  227148[8:SpL:162038.0,217386.0] || equal(complement(power_class(complement(inverse(identity_relation)))),identity_relation) member(identity_relation,image(element_relation,symmetrization_of(identity_relation)))* -> .
% 299.99/300.66  227149[16:SpL:195257.0,217386.0] || equal(complement(power_class(complement(singleton(identity_relation)))),identity_relation) member(identity_relation,image(element_relation,singleton(identity_relation)))* -> .
% 299.99/300.66  227159[8:SpL:30.0,217389.0] || equal(complement(complement(union(u,v))),identity_relation) -> member(identity_relation,intersection(complement(u),complement(v)))*.
% 299.99/300.66  227170[8:SpL:162038.0,217389.0] || equal(complement(complement(power_class(complement(inverse(identity_relation))))),identity_relation)** -> member(identity_relation,image(element_relation,symmetrization_of(identity_relation))).
% 299.99/300.66  227171[16:SpL:195257.0,217389.0] || equal(complement(complement(power_class(complement(singleton(identity_relation))))),identity_relation)** -> member(identity_relation,image(element_relation,singleton(identity_relation))).
% 299.99/300.66  227195[8:Rew:66036.0,227192.0] || equal(complement(intersection(power_class(u),ordinal_numbers)),identity_relation) member(identity_relation,image(element_relation,complement(u)))* -> .
% 299.99/300.66  227209[8:SpR:162038.0,217451.1] || equal(union(image(element_relation,symmetrization_of(identity_relation)),identity_relation),identity_relation)** -> member(identity_relation,power_class(complement(inverse(identity_relation)))).
% 299.99/300.66  227210[16:SpR:195257.0,217451.1] || equal(union(image(element_relation,singleton(identity_relation)),identity_relation),identity_relation)** -> member(identity_relation,power_class(complement(singleton(identity_relation)))).
% 299.99/300.66  227219[8:Res:217451.1,9876.0] || equal(union(u,identity_relation),identity_relation) subclass(complement(u),v)* well_ordering(ordinal_numbers,v) -> .
% 299.99/300.66  227248[8:SpR:61728.2,117140.0] || member(u,ordinal_numbers) subclass(rest_relation,union_of_range_map) -> equal(intersection(rest_of(u),ordinal_numbers),rest_of(u))**.
% 299.99/300.66  227336[25:SpR:192979.1,208885.0] ||  -> equal(cross_product(identity_relation,ordinal_numbers),identity_relation) equal(apply(regular(cross_product(identity_relation,ordinal_numbers)),ordinal_numbers),sum_class(range_of(identity_relation)))**.
% 299.99/300.66  227376[8:SpL:30.0,217608.0] || equal(complement(union(u,v)),identity_relation) member(omega,intersection(complement(u),complement(v)))* -> .
% 299.99/300.66  227387[8:SpL:162038.0,217608.0] || equal(complement(power_class(complement(inverse(identity_relation)))),identity_relation) member(omega,image(element_relation,symmetrization_of(identity_relation)))* -> .
% 299.99/300.66  227388[16:SpL:195257.0,217608.0] || equal(complement(power_class(complement(singleton(identity_relation)))),identity_relation) member(omega,image(element_relation,singleton(identity_relation)))* -> .
% 299.99/300.66  227398[8:SpL:30.0,217611.0] || equal(complement(complement(union(u,v))),identity_relation) -> member(omega,intersection(complement(u),complement(v)))*.
% 299.99/300.66  227409[8:SpL:162038.0,217611.0] || equal(complement(complement(power_class(complement(inverse(identity_relation))))),identity_relation)** -> member(omega,image(element_relation,symmetrization_of(identity_relation))).
% 299.99/300.66  227410[16:SpL:195257.0,217611.0] || equal(complement(complement(power_class(complement(singleton(identity_relation))))),identity_relation)** -> member(omega,image(element_relation,singleton(identity_relation))).
% 299.99/300.66  227434[8:Rew:66036.0,227431.0] || equal(complement(intersection(power_class(u),ordinal_numbers)),identity_relation) member(omega,image(element_relation,complement(u)))* -> .
% 299.99/300.66  227448[8:SpR:162038.0,217663.1] || equal(union(image(element_relation,symmetrization_of(identity_relation)),identity_relation),identity_relation)** -> member(omega,power_class(complement(inverse(identity_relation)))).
% 299.99/300.66  227449[16:SpR:195257.0,217663.1] || equal(union(image(element_relation,singleton(identity_relation)),identity_relation),identity_relation)** -> member(omega,power_class(complement(singleton(identity_relation)))).
% 299.99/300.66  227568[8:SpL:30.0,217695.0] || equal(complement(union(u,v)),identity_relation) equal(intersection(complement(u),complement(v)),ordinal_numbers)** -> .
% 299.99/300.66  227579[8:SpL:162038.0,217695.0] || equal(complement(power_class(complement(inverse(identity_relation)))),identity_relation)** equal(image(element_relation,symmetrization_of(identity_relation)),ordinal_numbers) -> .
% 299.99/300.66  227580[16:SpL:195257.0,217695.0] || equal(complement(power_class(complement(singleton(identity_relation)))),identity_relation)** equal(image(element_relation,singleton(identity_relation)),ordinal_numbers) -> .
% 299.99/300.66  227598[8:SpL:30.0,217696.0] || equal(complement(union(u,v)),identity_relation) subclass(ordinal_numbers,intersection(complement(u),complement(v)))* -> .
% 299.99/300.66  227609[8:SpL:162038.0,217696.0] || equal(complement(power_class(complement(inverse(identity_relation)))),identity_relation) subclass(ordinal_numbers,image(element_relation,symmetrization_of(identity_relation)))* -> .
% 299.99/300.66  227610[16:SpL:195257.0,217696.0] || equal(complement(power_class(complement(singleton(identity_relation)))),identity_relation) subclass(ordinal_numbers,image(element_relation,singleton(identity_relation)))* -> .
% 299.99/300.66  227620[8:SpL:30.0,217697.0] || equal(complement(union(u,v)),identity_relation) equal(intersection(complement(u),complement(v)),omega)** -> .
% 299.99/300.66  227631[8:SpL:162038.0,217697.0] || equal(complement(power_class(complement(inverse(identity_relation)))),identity_relation)** equal(image(element_relation,symmetrization_of(identity_relation)),omega) -> .
% 299.99/300.66  227632[16:SpL:195257.0,217697.0] || equal(complement(power_class(complement(singleton(identity_relation)))),identity_relation)** equal(image(element_relation,singleton(identity_relation)),omega) -> .
% 299.99/300.66  227642[8:SpL:30.0,217698.0] || equal(complement(union(u,v)),identity_relation) subclass(omega,intersection(complement(u),complement(v)))* -> .
% 299.99/300.66  227653[8:SpL:162038.0,217698.0] || equal(complement(power_class(complement(inverse(identity_relation)))),identity_relation) subclass(omega,image(element_relation,symmetrization_of(identity_relation)))* -> .
% 299.99/300.66  227654[16:SpL:195257.0,217698.0] || equal(complement(power_class(complement(singleton(identity_relation)))),identity_relation) subclass(omega,image(element_relation,singleton(identity_relation)))* -> .
% 299.99/300.66  227664[8:SpL:30.0,217699.0] || equal(complement(union(u,v)),identity_relation) subclass(domain_relation,intersection(complement(u),complement(v)))* -> .
% 299.99/300.66  227675[8:SpL:162038.0,217699.0] || equal(complement(power_class(complement(inverse(identity_relation)))),identity_relation) subclass(domain_relation,image(element_relation,symmetrization_of(identity_relation)))* -> .
% 299.99/300.66  227676[16:SpL:195257.0,217699.0] || equal(complement(power_class(complement(singleton(identity_relation)))),identity_relation) subclass(domain_relation,image(element_relation,singleton(identity_relation)))* -> .
% 299.99/300.66  227690[8:SpL:30.0,217700.0] || equal(complement(union(u,v)),identity_relation) member(intersection(complement(u),complement(v)),subset_relation)* -> .
% 299.99/300.66  227701[8:SpL:162038.0,217700.0] || equal(complement(power_class(complement(inverse(identity_relation)))),identity_relation) member(image(element_relation,symmetrization_of(identity_relation)),subset_relation)* -> .
% 299.99/300.66  227702[16:SpL:195257.0,217700.0] || equal(complement(power_class(complement(singleton(identity_relation)))),identity_relation) member(image(element_relation,singleton(identity_relation)),subset_relation)* -> .
% 299.99/300.66  227958[21:MRR:227894.1,8666.0] || subclass(rest_relation,domain_relation) subclass(rest_relation,u) -> member(ordered_pair(unordered_pair(v,w),identity_relation),u)*.
% 299.99/300.66  228052[21:MRR:227984.1,8667.0] || subclass(rest_relation,domain_relation) subclass(rest_relation,u) -> member(ordered_pair(ordered_pair(v,w),identity_relation),u)*.
% 299.99/300.66  228142[8:SpL:105.0,219927.1] || member(not_subclass_element(compose(u,inverse(u)),identity_relation),subset_relation)* equal(singleton(single_valued1(u)),identity_relation) -> .
% 299.99/300.66  228148[8:SpL:106.0,219928.1] || member(not_subclass_element(compose(u,inverse(u)),identity_relation),subset_relation)* equal(singleton(single_valued2(u)),identity_relation) -> .
% 299.99/300.66  228151[8:SpL:15272.1,219928.1] single_valued_class(u) || member(not_subclass_element(identity_relation,identity_relation),subset_relation)* equal(singleton(single_valued2(u)),identity_relation)** -> .
% 299.99/300.66  228152[8:SpL:15265.1,219928.1] function(u) || member(not_subclass_element(identity_relation,identity_relation),subset_relation)* equal(singleton(single_valued2(u)),identity_relation)** -> .
% 299.99/300.66  228742[8:Rew:162584.0,228711.1] || member(u,ordinal_numbers) subclass(ordinal_numbers,symmetrization_of(identity_relation)) -> subclass(singleton(power_class(u)),symmetrization_of(identity_relation))*.
% 299.99/300.66  228762[8:SpL:162038.0,222095.0] || subclass(power_class(complement(inverse(identity_relation))),identity_relation) -> equal(symmetric_difference(ordinal_numbers,image(element_relation,symmetrization_of(identity_relation))),identity_relation)**.
% 299.99/300.66  228763[16:SpL:195257.0,222095.0] || subclass(power_class(complement(singleton(identity_relation))),identity_relation) -> equal(symmetric_difference(ordinal_numbers,image(element_relation,singleton(identity_relation))),identity_relation)**.
% 299.99/300.66  228895[13:MRR:228880.2,160479.0] || member(apply(choice,regular(cross_product(ordinal_numbers,ordinal_numbers))),subset_relation)* -> equal(regular(cross_product(ordinal_numbers,ordinal_numbers)),identity_relation).
% 299.99/300.66  228896[10:MRR:228879.2,217111.0] || member(apply(choice,regular(compose(element_relation,ordinal_numbers))),element_relation)* -> equal(regular(compose(element_relation,ordinal_numbers)),identity_relation).
% 299.99/300.66  229029[7:Res:19563.1,9876.0] || subclass(successor(u),v)* well_ordering(ordinal_numbers,v) -> equal(symmetric_difference(u,singleton(u)),identity_relation)**.
% 299.99/300.66  229042[7:Obv:229037.1] || subclass(symmetric_difference(u,singleton(u)),complement(successor(u)))* -> equal(symmetric_difference(u,singleton(u)),identity_relation).
% 299.99/300.66  229195[8:Rew:162584.0,229137.1,162584.0,229137.0] ||  -> subclass(singleton(regular(intersection(symmetrization_of(identity_relation),u))),symmetrization_of(identity_relation))* equal(intersection(symmetrization_of(identity_relation),u),identity_relation).
% 299.99/300.66  229770[8:Rew:162584.0,229566.1,162584.0,229566.0] ||  -> subclass(singleton(regular(intersection(u,symmetrization_of(identity_relation)))),symmetrization_of(identity_relation))* equal(intersection(u,symmetrization_of(identity_relation)),identity_relation).
% 299.99/300.66  230146[7:Res:19679.1,9876.0] || subclass(symmetrization_of(u),v)* well_ordering(ordinal_numbers,v) -> equal(symmetric_difference(u,inverse(u)),identity_relation)**.
% 299.99/300.66  230159[7:Obv:230155.1] || subclass(symmetric_difference(u,inverse(u)),complement(symmetrization_of(u)))* -> equal(symmetric_difference(u,inverse(u)),identity_relation).
% 299.99/300.66  230181[8:SpR:160927.0,229638.0] ||  -> equal(symmetric_difference(intersection(complement(u),union(v,identity_relation)),complement(union(u,symmetric_difference(ordinal_numbers,v)))),identity_relation)**.
% 299.99/300.66  230182[8:SpR:160992.0,229638.0] ||  -> equal(symmetric_difference(intersection(union(u,identity_relation),complement(v)),complement(union(symmetric_difference(ordinal_numbers,u),v))),identity_relation)**.
% 299.99/300.66  230194[7:SpR:481.0,229638.0] ||  -> equal(symmetric_difference(image(element_relation,union(u,v)),complement(power_class(intersection(complement(u),complement(v))))),identity_relation)**.
% 299.99/300.66  230410[8:Res:161066.1,219073.1] || member(u,ordinal_numbers) subclass(symmetric_difference(ordinal_numbers,v),identity_relation) -> member(u,union(v,identity_relation))*.
% 299.99/300.66  230693[8:MRR:230655.2,217162.0] || subclass(ordinal_numbers,regular(inverse(singleton(unordered_pair(u,v)))))* -> asymmetric(singleton(unordered_pair(u,v)),w)*.
% 299.99/300.66  230752[7:Obv:230737.0] || well_ordering(u,ordinal_numbers) -> equal(singleton(v),identity_relation) equal(segment(u,singleton(v),v),identity_relation)**.
% 299.99/300.66  230932[8:Res:216691.1,18544.1] || equal(complement(intersection(u,v)),identity_relation)** member(w,ordinal_numbers) -> member(power_class(w),v)*.
% 299.99/300.66  231027[8:Res:216691.1,18545.1] || equal(complement(intersection(u,v)),identity_relation)** member(w,ordinal_numbers) -> member(power_class(w),u)*.
% 299.99/300.66  231092[8:Res:919.1,230762.0] || subclass(ordinal_numbers,not_subclass_element(restrict(subset_relation,u,v),w))* -> subclass(restrict(subset_relation,u,v),w).
% 299.99/300.66  231170[8:Res:919.1,230780.0] || equal(not_subclass_element(restrict(subset_relation,u,v),w),ordinal_numbers)** -> subclass(restrict(subset_relation,u,v),w).
% 299.99/300.66  231202[8:SpL:6355.1,230798.0] || equal(complement(regular(not_subclass_element(cross_product(u,v),w))),identity_relation)** -> subclass(cross_product(u,v),w).
% 299.99/300.66  231378[7:Obv:231331.1] || subclass(symmetric_difference(u,v),complement(complement(intersection(u,v))))* -> equal(symmetric_difference(u,v),identity_relation).
% 299.99/300.66  231557[7:SpR:189.0,229281.0] ||  -> equal(intersection(power_class(image(element_relation,power_class(u))),image(element_relation,power_class(image(element_relation,complement(u))))),identity_relation)**.
% 299.99/300.66  231821[13:MRR:231794.2,160479.0] || member(not_subclass_element(regular(cross_product(ordinal_numbers,ordinal_numbers)),u),subset_relation)* -> subclass(regular(cross_product(ordinal_numbers,ordinal_numbers)),u).
% 299.99/300.66  231822[10:MRR:231793.2,217111.0] || member(not_subclass_element(regular(compose(element_relation,ordinal_numbers)),u),element_relation)* -> subclass(regular(compose(element_relation,ordinal_numbers)),u).
% 299.99/300.66  231898[16:Res:231880.0,11.0] || subclass(singleton(identity_relation),regular(complement(singleton(identity_relation))))* -> equal(regular(complement(singleton(identity_relation))),singleton(identity_relation)).
% 299.99/300.66  231926[8:SpR:189.0,229481.0] ||  -> equal(symmetric_difference(power_class(image(element_relation,power_class(u))),image(element_relation,power_class(image(element_relation,complement(u))))),ordinal_numbers)**.
% 299.99/300.66  232250[7:SpR:189.0,229909.0] ||  -> equal(intersection(image(element_relation,power_class(image(element_relation,complement(u)))),power_class(image(element_relation,power_class(u)))),identity_relation)**.
% 299.99/300.66  232429[8:SpR:189.0,230084.0] ||  -> equal(symmetric_difference(image(element_relation,power_class(image(element_relation,complement(u)))),power_class(image(element_relation,power_class(u)))),ordinal_numbers)**.
% 299.99/300.66  232460[8:Res:10.1,69457.0] || equal(complement(compose(element_relation,ordinal_numbers)),omega)** member(u,element_relation)* -> equal(integer_of(u),identity_relation).
% 299.99/300.66  232552[8:Res:13258.1,230867.0] || equal(complement(regular(restrict(subset_relation,u,v))),identity_relation)** -> equal(restrict(subset_relation,u,v),identity_relation).
% 299.99/300.66  232626[8:Res:13258.1,230939.0] || equal(regular(regular(restrict(subset_relation,u,v))),ordinal_numbers)** -> equal(restrict(subset_relation,u,v),identity_relation).
% 299.99/300.66  232810[8:Rew:30.0,232751.1] || subclass(intersection(complement(u),complement(v)),union(u,v))* -> subclass(ordinal_numbers,union(u,v)).
% 299.99/300.66  233004[8:SpL:6355.1,232981.0] || subclass(ordinal_numbers,regular(singleton(not_subclass_element(cross_product(u,v),w))))* -> subclass(cross_product(u,v),w).
% 299.99/300.66  233018[8:Res:10.1,69182.0] || equal(complement(compose(element_relation,ordinal_numbers)),u)* member(regular(u),element_relation)* -> equal(u,identity_relation).
% 299.99/300.66  233071[8:SpL:6355.1,233013.0] || equal(regular(singleton(not_subclass_element(cross_product(u,v),w))),ordinal_numbers)** -> subclass(cross_product(u,v),w).
% 299.99/300.66  233107[21:Res:196525.2,210517.1] || member(u,ordinal_numbers) equal(sum_class(range_of(u)),identity_relation)** equal(complement(union_of_range_map),ordinal_numbers) -> .
% 299.99/300.66  233109[21:Res:196525.2,8841.1] || member(u,ordinal_numbers) equal(sum_class(range_of(u)),identity_relation)** subclass(ordinal_numbers,complement(union_of_range_map))* -> .
% 299.99/300.66  233116[8:SpL:13260.1,233014.0] || equal(complement(regular(singleton(regular(cross_product(u,v))))),identity_relation)** -> equal(cross_product(u,v),identity_relation).
% 299.99/300.66  233301[8:Res:231881.0,11.0] || subclass(complement(singleton(u)),u)* -> equal(singleton(u),identity_relation) equal(complement(singleton(u)),u).
% 299.99/300.66  233370[8:Res:231881.0,40321.0] || well_ordering(u,complement(singleton(rest_relation)))* -> equal(singleton(rest_relation),identity_relation) member(least(u,rest_relation),rest_relation).
% 299.99/300.66  233476[24:Res:161057.2,207853.1] operation(cantor(least(u,recursion_equation_functions(v)))) || well_ordering(u,ordinal_numbers)* -> equal(recursion_equation_functions(v),identity_relation)**.
% 299.99/300.66  233521[21:Res:13061.0,196424.2] || member(u,ordinal_numbers) subclass(domain_relation,complement(omega)) -> equal(integer_of(ordered_pair(u,identity_relation)),identity_relation)**.
% 299.99/300.66  233568[21:MRR:233532.2,41096.1] || member(identity_relation,u) member(v,w)* subclass(domain_relation,complement(cross_product(w,u)))* -> .
% 299.99/300.66  233569[21:Obv:233550.0] || equal(sum_class(range_of(u)),identity_relation)** member(u,ordinal_numbers) subclass(domain_relation,complement(union_of_range_map))* -> .
% 299.99/300.66  233728[25:SpR:208840.0,13409.1] || subclass(omega,union_of_range_map) -> equal(integer_of(singleton(singleton(identity_relation))),identity_relation)** equal(sum_class(range_of(identity_relation)),ordinal_numbers).
% 299.99/300.66  233844[26:Res:225794.1,941.1] || equal(power_class(image(element_relation,complement(u))),omega) member(identity_relation,image(element_relation,power_class(u)))* -> .
% 299.99/300.66  233907[8:Res:143200.1,161200.0] || equal(image(element_relation,union(u,identity_relation)),ordinal_numbers) member(omega,power_class(symmetric_difference(ordinal_numbers,u)))* -> .
% 299.99/300.66  233966[26:Res:225794.1,161200.0] || equal(image(element_relation,union(u,identity_relation)),omega) member(identity_relation,power_class(symmetric_difference(ordinal_numbers,u)))* -> .
% 299.99/300.66  233967[26:Res:224684.1,161200.0] || subclass(omega,image(element_relation,union(u,identity_relation)))* member(identity_relation,power_class(symmetric_difference(ordinal_numbers,u))) -> .
% 299.99/300.66  233969[8:Res:192149.1,161200.0] || equal(image(element_relation,union(u,identity_relation)),ordinal_numbers) member(identity_relation,power_class(symmetric_difference(ordinal_numbers,u)))* -> .
% 299.99/300.66  233973[8:Res:13049.1,161200.0] || subclass(ordinal_numbers,image(element_relation,union(u,identity_relation)))* member(identity_relation,power_class(symmetric_difference(ordinal_numbers,u))) -> .
% 299.99/300.66  234074[8:Res:10.1,161050.0] || equal(rest_of(u),omega) -> equal(integer_of(ordered_pair(v,w)),identity_relation)** member(v,cantor(u))*.
% 299.99/300.66  234083[8:SpL:6355.1,233382.0] || well_ordering(ordinal_numbers,complement(singleton(not_subclass_element(cross_product(u,v),w))))* -> subclass(cross_product(u,v),w).
% 299.99/300.66  234123[8:SpL:6355.1,234113.0] || subclass(complement(singleton(not_subclass_element(cross_product(u,v),w))),identity_relation)* -> subclass(cross_product(u,v),w).
% 299.99/300.66  234490[21:Res:10.1,196423.1] || equal(intersection(u,v),domain_relation)** member(w,ordinal_numbers) -> member(ordered_pair(w,identity_relation),u)*.
% 299.99/300.66  234564[21:Res:196416.2,233381.0] || member(u,ordinal_numbers) subclass(domain_relation,singleton(omega)) -> equal(integer_of(ordered_pair(u,identity_relation)),identity_relation)**.
% 299.99/300.66  234630[8:SpL:13260.1,234115.0] || equal(complement(complement(singleton(regular(cross_product(u,v))))),ordinal_numbers)** -> equal(cross_product(u,v),identity_relation).
% 299.99/300.66  234644[8:SpL:13260.1,234117.0] || subclass(ordinal_numbers,complement(complement(singleton(regular(cross_product(u,v))))))* -> equal(cross_product(u,v),identity_relation).
% 299.99/300.66  234718[21:Res:10.1,196432.1] || equal(intersection(u,v),domain_relation)** member(w,ordinal_numbers) -> member(ordered_pair(w,identity_relation),v)*.
% 299.99/300.66  234727[8:SpL:13260.1,232824.0] || subclass(ordinal_numbers,regular(unordered_pair(u,regular(cross_product(v,w)))))* -> equal(cross_product(v,w),identity_relation).
% 299.99/300.66  234757[8:SpL:13260.1,233124.0] || subclass(ordinal_numbers,regular(unordered_pair(regular(cross_product(u,v)),w)))* -> equal(cross_product(u,v),identity_relation).
% 299.99/300.66  234812[8:Res:193440.1,219206.0] || member(u,ordinal_numbers) subclass(element_relation,identity_relation) -> equal(apply(u,u),sum_class(range_of(identity_relation)))**.
% 299.99/300.66  234862[21:MRR:234779.2,14676.0] || member(u,ordinal_numbers) -> equal(singleton(v),identity_relation) equal(apply(v,u),sum_class(range_of(identity_relation)))**.
% 299.99/300.66  234863[21:MRR:234789.2,14676.0] || member(u,ordinal_numbers) -> equal(v,identity_relation) equal(apply(regular(v),u),sum_class(range_of(identity_relation)))**.
% 299.99/300.66  234864[21:MRR:234790.1,14676.0] || member(u,ordinal_numbers) -> equal(apply(regular(complement(complement(symmetrization_of(identity_relation)))),u),sum_class(range_of(identity_relation)))**.
% 299.99/300.66  234882[8:MRR:234840.0,8667.0] || subclass(ordinal_numbers,complement(cantor(u))) -> equal(apply(u,ordered_pair(v,w)),sum_class(range_of(identity_relation)))**.
% 299.99/300.66  234883[8:MRR:234831.0,125724.0] || subclass(omega,complement(cantor(u))) -> equal(apply(u,least(element_relation,omega)),sum_class(range_of(identity_relation)))**.
% 299.99/300.66  234884[8:MRR:234830.0,125724.0] || subclass(ordinal_numbers,complement(cantor(u))) -> equal(apply(u,least(element_relation,omega)),sum_class(range_of(identity_relation)))**.
% 299.99/300.66  234886[8:MRR:234819.0,8666.0] || subclass(ordinal_numbers,complement(cantor(u))) -> equal(apply(u,unordered_pair(v,w)),sum_class(range_of(identity_relation)))**.
% 299.99/300.66  234888[8:MRR:234820.0,60996.1] ||  -> equal(apply(u,regular(complement(cantor(u)))),sum_class(range_of(identity_relation)))** equal(complement(cantor(u)),identity_relation).
% 299.99/300.66  234914[8:SpL:13260.1,234736.0] || equal(regular(unordered_pair(u,regular(cross_product(v,w)))),ordinal_numbers)** -> equal(cross_product(v,w),identity_relation).
% 299.99/300.66  234927[8:SpL:13260.1,234766.0] || equal(regular(unordered_pair(regular(cross_product(u,v)),w)),ordinal_numbers)** -> equal(cross_product(u,v),identity_relation).
% 299.99/300.66  235144[8:SpL:50855.1,234983.0] || member(singleton(u),subset_relation) member(first(singleton(u)),cantor(complement(cross_product(u,ordinal_numbers))))* -> .
% 299.99/300.66  235184[21:Res:196416.2,234983.0] || member(u,ordinal_numbers) subclass(domain_relation,cantor(complement(cross_product(singleton(ordered_pair(u,identity_relation)),ordinal_numbers))))* -> .
% 299.99/300.66  235245[5:Res:10.1,18582.1] || equal(restrict(u,v,w),ordinal_numbers)** member(x,ordinal_numbers) -> member(sum_class(x),u)*.
% 299.99/300.66  235287[8:Res:230445.1,17312.1] || member(regular(u),v) subclass(u,complement(union(v,identity_relation)))* -> equal(u,identity_relation).
% 299.99/300.66  235314[8:MRR:235302.2,235274.1] || member(not_subclass_element(regular(union(u,identity_relation)),v),u)* -> subclass(regular(union(u,identity_relation)),v).
% 299.99/300.66  235315[8:MRR:235282.2,235274.1] || member(apply(choice,regular(union(u,identity_relation))),u)* -> equal(regular(union(u,identity_relation)),identity_relation).
% 299.99/300.66  235361[25:SpR:208840.0,28980.1] || subclass(rest_relation,flip(u)) -> member(ordered_pair(ordered_pair(ordinal_numbers,identity_relation),rest_of(singleton(singleton(identity_relation)))),u)*.
% 299.99/300.66  235372[25:SpR:208840.0,28980.1] || subclass(rest_relation,flip(u)) -> member(ordered_pair(singleton(singleton(identity_relation)),rest_of(ordered_pair(ordinal_numbers,identity_relation))),u)*.
% 299.99/300.66  235425[5:Res:28980.1,152.0] || subclass(rest_relation,flip(recursion_equation_functions(u)))* -> function(ordered_pair(ordered_pair(v,w),rest_of(ordered_pair(w,v))))*.
% 299.99/300.66  235456[5:Res:28980.1,157.0] || subclass(rest_relation,flip(union_of_range_map)) -> equal(sum_class(range_of(ordered_pair(u,v))),rest_of(ordered_pair(v,u)))**.
% 299.99/300.66  235495[25:SpR:208840.0,28979.1] || subclass(rest_relation,rotate(u)) -> member(ordered_pair(ordered_pair(ordinal_numbers,rest_of(singleton(singleton(identity_relation)))),identity_relation),u)*.
% 299.99/300.66  235553[5:Res:28979.1,152.0] || subclass(rest_relation,rotate(recursion_equation_functions(u)))* -> function(ordered_pair(ordered_pair(v,rest_of(ordered_pair(w,v))),w))*.
% 299.99/300.66  235574[8:Res:28979.1,116129.0] || subclass(rest_relation,rotate(rest_of(u))) -> member(ordered_pair(v,rest_of(ordered_pair(w,v))),cantor(u))*.
% 299.99/300.66  235577[5:Res:28979.1,18.0] || subclass(rest_relation,rotate(cross_product(u,v)))* -> member(ordered_pair(w,rest_of(ordered_pair(x,w))),u)*.
% 299.99/300.66  235584[5:Res:28979.1,157.0] || subclass(rest_relation,rotate(union_of_range_map)) -> equal(sum_class(range_of(ordered_pair(u,rest_of(ordered_pair(v,u))))),v)**.
% 299.99/300.66  235787[5:Res:10.1,19113.0] || equal(recursion_equation_functions(u),v)* -> subclass(v,w) subclass(not_subclass_element(v,w),cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.66  235846[7:Res:10.1,13339.0] || equal(u,omega) subclass(u,v)* -> equal(integer_of(w),identity_relation) member(w,v)*.
% 299.99/300.66  236034[5:Res:10.1,18546.1] || equal(restrict(u,v,w),ordinal_numbers)** member(x,ordinal_numbers) -> member(power_class(x),u)*.
% 299.99/300.66  236070[18:MRR:236055.3,190496.0] || equal(symmetrization_of(identity_relation),ordinal_numbers) subclass(symmetrization_of(identity_relation),complement(u))* member(identity_relation,u) -> .
% 299.99/300.66  236265[7:Res:13061.0,18897.0] ||  -> equal(integer_of(not_subclass_element(intersection(u,complement(omega)),v)),identity_relation)** subclass(intersection(u,complement(omega)),v).
% 299.99/300.66  236469[7:Res:13061.0,19016.0] ||  -> equal(integer_of(not_subclass_element(intersection(complement(omega),u),v)),identity_relation)** subclass(intersection(complement(omega),u),v).
% 299.99/300.66  236511[8:Rew:217694.1,236510.2] || equal(complement(complement(u)),identity_relation) member(not_subclass_element(ordinal_numbers,v),u)* -> subclass(ordinal_numbers,v).
% 299.99/300.66  236530[0:Rew:163.0,236425.1] || member(not_subclass_element(symmetric_difference(u,v),w),intersection(u,v))* -> subclass(symmetric_difference(u,v),w).
% 299.99/300.66  236645[26:SpL:30.0,225363.1] || equal(intersection(complement(u),complement(v)),inverse(identity_relation))** equal(union(u,v),omega) -> .
% 299.99/300.66  236656[26:SpL:162038.0,225363.1] || equal(image(element_relation,symmetrization_of(identity_relation)),inverse(identity_relation))** equal(power_class(complement(inverse(identity_relation))),omega) -> .
% 299.99/300.66  236657[26:SpL:195257.0,225363.1] || equal(image(element_relation,singleton(identity_relation)),inverse(identity_relation))** equal(power_class(complement(singleton(identity_relation))),omega) -> .
% 299.99/300.66  236692[26:SpL:30.0,225365.1] || equal(intersection(complement(u),complement(v)),singleton(identity_relation))** equal(union(u,v),omega) -> .
% 299.99/300.66  236703[26:SpL:162038.0,225365.1] || equal(image(element_relation,symmetrization_of(identity_relation)),singleton(identity_relation))** equal(power_class(complement(inverse(identity_relation))),omega) -> .
% 299.99/300.66  236704[26:SpL:195257.0,225365.1] || equal(image(element_relation,singleton(identity_relation)),singleton(identity_relation))** equal(power_class(complement(singleton(identity_relation))),omega) -> .
% 299.99/300.66  236709[16:SpL:30.0,225450.0] || subclass(singleton(identity_relation),union(u,v)) member(identity_relation,intersection(complement(u),complement(v)))* -> .
% 299.99/300.66  236720[16:SpL:162038.0,225450.0] || subclass(singleton(identity_relation),power_class(complement(inverse(identity_relation))))* member(identity_relation,image(element_relation,symmetrization_of(identity_relation))) -> .
% 299.99/300.66  236721[16:SpL:195257.0,225450.0] || subclass(singleton(identity_relation),power_class(complement(singleton(identity_relation))))* member(identity_relation,image(element_relation,singleton(identity_relation))) -> .
% 299.99/300.66  236736[18:SpL:30.0,225452.1] || subclass(ordinal_numbers,intersection(complement(u),complement(v)))* subclass(symmetrization_of(identity_relation),union(u,v)) -> .
% 299.99/300.66  236747[18:SpL:162038.0,225452.1] || subclass(ordinal_numbers,image(element_relation,symmetrization_of(identity_relation))) subclass(symmetrization_of(identity_relation),power_class(complement(inverse(identity_relation))))* -> .
% 299.99/300.66  236748[18:SpL:195257.0,225452.1] || subclass(ordinal_numbers,image(element_relation,singleton(identity_relation))) subclass(symmetrization_of(identity_relation),power_class(complement(singleton(identity_relation))))* -> .
% 299.99/300.66  236870[7:Res:17392.2,152.0] || subclass(u,recursion_equation_functions(v))* -> equal(intersection(u,w),identity_relation) function(regular(intersection(u,w)))*.
% 299.99/300.66  236975[26:SpR:162038.0,225888.1] || equal(symmetric_difference(ordinal_numbers,image(element_relation,symmetrization_of(identity_relation))),omega)** -> member(identity_relation,power_class(complement(inverse(identity_relation)))).
% 299.99/300.66  236976[26:SpR:195257.0,225888.1] || equal(symmetric_difference(ordinal_numbers,image(element_relation,singleton(identity_relation))),omega)** -> member(identity_relation,power_class(complement(singleton(identity_relation)))).
% 299.99/300.66  236985[26:Res:225888.1,9876.0] || equal(symmetric_difference(ordinal_numbers,u),omega) subclass(complement(u),v)* well_ordering(ordinal_numbers,v) -> .
% 299.99/300.66  237649[8:Rew:140603.0,237554.0,66036.0,237554.0] ||  -> equal(symmetric_difference(inverse(subset_relation),restrict(subset_relation,u,v)),union(inverse(subset_relation),restrict(subset_relation,u,v)))**.
% 299.99/300.66  238382[8:SpR:189.0,238174.0] ||  -> equal(intersection(complement(power_class(image(element_relation,complement(u)))),symmetric_difference(ordinal_numbers,image(element_relation,power_class(u)))),identity_relation)**.
% 299.99/300.66  238474[8:Rew:140603.0,238327.0,66036.0,238327.0] ||  -> equal(symmetric_difference(complement(complement(u)),symmetric_difference(ordinal_numbers,u)),union(complement(complement(u)),symmetric_difference(ordinal_numbers,u)))**.
% 299.99/300.66  238478[8:Rew:238174.0,238447.1] || member(not_subclass_element(symmetric_difference(ordinal_numbers,u),identity_relation),complement(complement(u)))* -> subclass(symmetric_difference(ordinal_numbers,u),identity_relation).
% 299.99/300.66  238604[7:Res:13572.2,152.0] || subclass(u,recursion_equation_functions(v))* -> equal(intersection(w,u),identity_relation) function(regular(intersection(w,u)))*.
% 299.99/300.66  238776[16:Rew:140603.0,238674.0,66036.0,238674.0] ||  -> equal(symmetric_difference(singleton(identity_relation),symmetric_difference(ordinal_numbers,singleton(identity_relation))),union(singleton(identity_relation),symmetric_difference(ordinal_numbers,singleton(identity_relation))))**.
% 299.99/300.66  238880[8:Rew:140603.0,238787.0,66036.0,238787.0] ||  -> equal(symmetric_difference(symmetrization_of(identity_relation),symmetric_difference(ordinal_numbers,inverse(identity_relation))),union(symmetrization_of(identity_relation),symmetric_difference(ordinal_numbers,inverse(identity_relation))))**.
% 299.99/300.66  238946[7:SpR:189.0,237395.0] ||  -> equal(intersection(power_class(image(element_relation,complement(u))),restrict(image(element_relation,power_class(u)),v,w)),identity_relation)**.
% 299.99/300.66  239017[8:Rew:140603.0,238891.0,66036.0,238891.0] ||  -> equal(symmetric_difference(complement(u),restrict(u,v,w)),union(complement(u),restrict(u,v,w)))**.
% 299.99/300.66  18796[0:Res:3618.1,5.0] || member(u,symmetric_difference(v,w))* subclass(complement(intersection(v,w)),x)* -> member(u,x)*.
% 299.99/300.66  29144[0:Res:27.2,490.0] || member(u,complement(v)) member(u,complement(w)) member(u,union(w,v))* -> .
% 299.99/300.66  36303[0:SpR:3616.0,19069.0] ||  -> subclass(symmetric_difference(union(u,v),union(complement(u),complement(v))),complement(symmetric_difference(complement(u),complement(v))))*.
% 299.99/300.66  43748[5:MRR:43713.0,41096.1] || member(u,union(v,w)) -> member(u,intersection(v,w))* member(u,symmetric_difference(v,w)).
% 299.99/300.66  69447[8:MRR:69430.0,41096.1] || member(u,complement(intersection(v,ordinal_numbers)))* subclass(symmetric_difference(v,ordinal_numbers),w)* -> member(u,w)*.
% 299.99/300.66  69162[8:Res:49995.1,66086.1] || member(complement(compose(element_relation,ordinal_numbers)),subset_relation) member(singleton(first(complement(compose(element_relation,ordinal_numbers)))),element_relation)* -> .
% 299.99/300.66  69178[8:Res:2503.2,66086.1] || subclass(u,complement(compose(element_relation,ordinal_numbers)))* member(not_subclass_element(u,v),element_relation)* -> subclass(u,v).
% 299.99/300.66  69176[8:Res:8978.2,66086.1] || member(u,ordinal_numbers) subclass(ordinal_numbers,complement(compose(element_relation,ordinal_numbers)))* member(sum_class(u),element_relation)* -> .
% 299.99/300.66  51325[5:Rew:50855.1,51257.2] || member(singleton(u),subset_relation) member(singleton(singleton(u)),element_relation)* -> member(u,first(singleton(u)))*.
% 299.99/300.66  56508[5:SpL:126.0,56480.0] || member(restrict(u,v,singleton(w)),segment(u,v,w))* subclass(ordinal_numbers,complement(element_relation)) -> .
% 299.99/300.66  57207[5:Res:8978.2,19676.0] || member(u,ordinal_numbers) subclass(ordinal_numbers,symmetric_difference(v,inverse(v)))* -> member(sum_class(u),symmetrization_of(v))*.
% 299.99/300.66  57140[5:Res:8978.2,19559.0] || member(u,ordinal_numbers) subclass(ordinal_numbers,symmetric_difference(v,singleton(v)))* -> member(sum_class(u),successor(v))*.
% 299.99/300.66  18590[5:Res:8978.2,3617.0] || member(u,ordinal_numbers) subclass(ordinal_numbers,symmetric_difference(v,w)) -> member(sum_class(u),union(v,w))*.
% 299.99/300.66  18577[5:Res:8978.2,5.0] || member(u,ordinal_numbers) subclass(ordinal_numbers,v)* subclass(v,w)* -> member(sum_class(u),w)*.
% 299.99/300.66  57142[0:Res:2503.2,19559.0] || subclass(u,symmetric_difference(v,singleton(v)))* -> subclass(u,w) member(not_subclass_element(u,w),successor(v))*.
% 299.99/300.66  9689[5:Res:9632.1,12.0] || equal(complement(complement(unordered_pair(u,v))),ordinal_numbers)** -> equal(singleton(w),v)* equal(singleton(w),u)*.
% 299.99/300.66  70001[5:SpR:126.0,39971.1] || equal(complement(rest_of(restrict(u,v,singleton(w)))),ordinal_numbers)** -> subclass(segment(u,v,w),x)*.
% 299.99/300.66  51280[5:SpL:50855.1,50044.1] || member(singleton(u),subset_relation) member(first(singleton(u)),subset_relation)* subclass(ordinal_numbers,complement(u)) -> .
% 299.99/300.66  36337[0:SpR:47.0,3616.0] ||  -> equal(intersection(successor(u),union(complement(u),complement(singleton(u)))),symmetric_difference(complement(u),complement(singleton(u))))**.
% 299.99/300.66  41025[5:SpL:3606.0,10088.0] || equal(symmetric_difference(cross_product(u,v),w),ordinal_numbers) -> member(singleton(x),complement(restrict(w,u,v)))*.
% 299.99/300.66  41028[5:SpL:3606.0,8848.0] || subclass(ordinal_numbers,symmetric_difference(cross_product(u,v),w)) -> member(singleton(x),complement(restrict(w,u,v)))*.
% 299.99/300.66  40906[5:SpL:3603.0,10088.0] || equal(symmetric_difference(u,cross_product(v,w)),ordinal_numbers) -> member(singleton(x),complement(restrict(u,v,w)))*.
% 299.99/300.66  40909[5:SpL:3603.0,8848.0] || subclass(ordinal_numbers,symmetric_difference(u,cross_product(v,w))) -> member(singleton(x),complement(restrict(u,v,w)))*.
% 299.99/300.66  51514[5:Res:51313.1,3617.0] || member(singleton(symmetric_difference(u,v)),subset_relation) -> member(first(singleton(symmetric_difference(u,v))),union(u,v))*.
% 299.99/300.66  51501[5:Res:51313.1,898.0] || member(singleton(restrict(u,v,w)),subset_relation) -> member(first(singleton(restrict(u,v,w))),u)*.
% 299.99/300.66  51324[5:Rew:50855.1,51227.1] || member(singleton(u),subset_relation)* member(u,subset_relation) -> equal(first(singleton(u)),singleton(first(u))).
% 299.99/300.66  57116[5:Res:49995.1,19559.0] || member(symmetric_difference(u,singleton(u)),subset_relation) -> member(singleton(first(symmetric_difference(u,singleton(u)))),successor(u))*.
% 299.99/300.66  57183[5:Res:49995.1,19676.0] || member(symmetric_difference(u,inverse(u)),subset_relation) -> member(singleton(first(symmetric_difference(u,inverse(u)))),symmetrization_of(u))*.
% 299.99/300.66  39255[5:Res:3618.1,8841.1] || member(ordered_pair(u,v),symmetric_difference(w,x))* subclass(ordinal_numbers,complement(complement(intersection(w,x)))) -> .
% 299.99/300.66  28940[5:Res:8827.2,26.0] || member(u,ordinal_numbers) subclass(rest_relation,intersection(v,w))* -> member(ordered_pair(u,rest_of(u)),w)*.
% 299.99/300.66  28930[5:Res:8827.2,28.1] || member(u,ordinal_numbers) subclass(rest_relation,complement(v)) member(ordered_pair(u,rest_of(u)),v)* -> .
% 299.99/300.66  28941[5:Res:8827.2,25.0] || member(u,ordinal_numbers) subclass(rest_relation,intersection(v,w))* -> member(ordered_pair(u,rest_of(u)),v)*.
% 299.99/300.66  29150[5:Res:8642.1,490.0] || subclass(ordinal_numbers,intersection(complement(u),complement(v))) member(ordered_pair(w,x),union(u,v))* -> .
% 299.99/300.66  40048[5:Res:3618.1,8842.1] || member(unordered_pair(u,v),symmetric_difference(w,x))* subclass(ordinal_numbers,complement(complement(intersection(w,x)))) -> .
% 299.99/300.66  45611[0:Obv:45606.1] || member(u,v) -> equal(not_subclass_element(unordered_pair(u,w),v),w)** subclass(unordered_pair(u,w),v).
% 299.99/300.66  49675[5:SpL:6355.1,39499.0] || equal(complement(unordered_pair(u,not_subclass_element(cross_product(v,w),x))),ordinal_numbers)** -> subclass(cross_product(v,w),x).
% 299.99/300.66  49674[5:SpL:6355.1,39296.0] || subclass(ordinal_numbers,complement(unordered_pair(u,not_subclass_element(cross_product(v,w),x))))* -> subclass(cross_product(v,w),x).
% 299.99/300.66  45585[0:EqF:3695.1,3695.2] || equal(u,v) -> subclass(unordered_pair(v,u),w) equal(not_subclass_element(unordered_pair(v,u),w),v)**.
% 299.99/300.66  29152[5:Res:8643.1,490.0] || subclass(ordinal_numbers,intersection(complement(u),complement(v))) member(unordered_pair(w,x),union(u,v))* -> .
% 299.99/300.66  45612[0:Obv:45605.1] || member(u,v) -> equal(not_subclass_element(unordered_pair(w,u),v),w)** subclass(unordered_pair(w,u),v).
% 299.99/300.66  49663[5:SpL:6355.1,39562.0] || equal(complement(unordered_pair(not_subclass_element(cross_product(u,v),w),x)),ordinal_numbers)** -> subclass(cross_product(u,v),w).
% 299.99/300.66  49662[5:SpL:6355.1,39297.0] || subclass(ordinal_numbers,complement(unordered_pair(not_subclass_element(cross_product(u,v),w),x)))* -> subclass(cross_product(u,v),w).
% 299.99/300.66  18822[0:Res:6.1,897.0] ||  -> subclass(restrict(u,v,w),x) member(not_subclass_element(restrict(u,v,w),x),cross_product(v,w))*.
% 299.99/300.66  18903[0:Res:303.1,5.0] || subclass(u,v) -> subclass(intersection(w,u),x) member(not_subclass_element(intersection(w,u),x),v)*.
% 299.99/300.66  18907[0:Res:303.1,25.0] ||  -> subclass(intersection(u,intersection(v,w)),x) member(not_subclass_element(intersection(u,intersection(v,w)),x),v)*.
% 299.99/300.66  18906[0:Res:303.1,26.0] ||  -> subclass(intersection(u,intersection(v,w)),x) member(not_subclass_element(intersection(u,intersection(v,w)),x),w)*.
% 299.99/300.66  19022[0:Res:313.1,5.0] || subclass(u,v) -> subclass(intersection(u,w),x) member(not_subclass_element(intersection(u,w),x),v)*.
% 299.99/300.66  19026[0:Res:313.1,25.0] ||  -> subclass(intersection(intersection(u,v),w),x) member(not_subclass_element(intersection(intersection(u,v),w),x),u)*.
% 299.99/300.66  19025[0:Res:313.1,26.0] ||  -> subclass(intersection(intersection(u,v),w),x) member(not_subclass_element(intersection(intersection(u,v),w),x),v)*.
% 299.99/300.66  19131[0:Res:2503.2,3617.0] || subclass(u,symmetric_difference(v,w)) -> subclass(u,x) member(not_subclass_element(u,x),union(v,w))*.
% 299.99/300.66  19117[0:Res:2503.2,5.0] || subclass(u,v)* subclass(v,w)* -> subclass(u,x) member(not_subclass_element(u,x),w)*.
% 299.99/300.66  57209[0:Res:2503.2,19676.0] || subclass(u,symmetric_difference(v,inverse(v)))* -> subclass(u,w) member(not_subclass_element(u,w),symmetrization_of(v))*.
% 299.99/300.66  50027[5:SpL:18840.1,97.0] || member(u,subset_relation) member(u,compose_class(v)) -> equal(compose(v,first(u)),second(u))**.
% 299.99/300.66  50075[5:MRR:50074.2,18819.1] || member(u,subset_relation) equal(compose(v,first(u)),second(u))** -> member(u,compose_class(v)).
% 299.99/300.66  36859[5:Res:8665.1,8825.1] function(complement(u)) || member(v,ordinal_numbers) -> member(v,u)* member(v,cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.66  28956[5:Res:8827.2,8651.0] || member(u,ordinal_numbers) subclass(rest_relation,rest_of(v)) -> equal(restrict(v,u,ordinal_numbers),rest_of(u))**.
% 299.99/300.66  18229[8:SpR:33.0,15308.1] || asymmetric(cross_product(u,v),w) -> section(restrict(inverse(cross_product(u,v)),u,v),w,w)*.
% 299.99/300.66  36338[0:SpR:117.0,3616.0] ||  -> equal(intersection(symmetrization_of(u),union(complement(u),complement(inverse(u)))),symmetric_difference(complement(u),complement(inverse(u))))**.
% 299.99/300.66  9881[5:Res:8642.1,131.3] || subclass(ordinal_numbers,u) member(v,w)* subclass(w,x)* well_ordering(u,x)* -> .
% 299.99/300.66  39816[0:Res:10.1,9661.0] || equal(u,v)* well_ordering(w,u)* -> subclass(v,x)* member(least(w,v),v)*.
% 299.99/300.66  39608[2:Res:10.1,9665.1] inductive(u) || equal(v,u)* well_ordering(w,v)* -> member(least(w,u),u)*.
% 299.99/300.66  79547[5:Res:60219.0,3617.0] ||  -> subclass(u,complement(symmetric_difference(v,w))) member(not_subclass_element(u,complement(symmetric_difference(v,w))),union(v,w))*.
% 299.99/300.66  79567[5:Rew:30.0,79527.1] ||  -> member(not_subclass_element(u,union(v,w)),intersection(complement(v),complement(w)))* subclass(u,union(v,w)).
% 299.99/300.66  79638[5:Res:60219.0,898.0] ||  -> subclass(u,complement(restrict(v,w,x))) member(not_subclass_element(u,complement(restrict(v,w,x))),v)*.
% 299.99/300.66  94691[5:Res:39298.1,897.0] || subclass(ordinal_numbers,complement(complement(restrict(u,v,w))))* -> member(ordered_pair(x,y),cross_product(v,w))*.
% 299.99/300.66  96379[5:Res:40074.1,897.0] || subclass(ordinal_numbers,complement(complement(restrict(u,v,w))))* -> member(unordered_pair(x,y),cross_product(v,w))*.
% 299.99/300.66  96901[8:Res:81695.0,9665.1] inductive(inverse(subset_relation)) || well_ordering(u,complement(subset_relation)) -> member(least(u,inverse(subset_relation)),inverse(subset_relation))*.
% 299.99/300.66  116621[8:Rew:116078.0,19861.1] || section(cross_product(u,v),w,x) -> subclass(cantor(restrict(cross_product(x,w),u,v)),w)*.
% 299.99/300.66  125909[5:Res:125725.1,490.0] || subclass(omega,intersection(complement(u),complement(v))) member(least(element_relation,omega),union(u,v))* -> .
% 299.99/300.66  125921[5:Res:125725.1,12.0] || subclass(omega,unordered_pair(u,v))* -> equal(least(element_relation,omega),v) equal(least(element_relation,omega),u).
% 299.99/300.66  125986[5:Res:125731.1,490.0] || subclass(ordinal_numbers,intersection(complement(u),complement(v))) member(least(element_relation,omega),union(u,v))* -> .
% 299.99/300.66  126635[5:Res:3618.1,125896.1] || member(least(element_relation,omega),symmetric_difference(u,v))* subclass(omega,complement(complement(intersection(u,v)))) -> .
% 299.99/300.66  127098[5:Res:3618.1,125973.1] || member(least(element_relation,omega),symmetric_difference(u,v))* subclass(ordinal_numbers,complement(complement(intersection(u,v)))) -> .
% 299.99/300.66  128011[5:Res:126679.1,897.0] || subclass(omega,complement(complement(restrict(u,v,w))))* -> member(least(element_relation,omega),cross_product(v,w)).
% 299.99/300.66  128346[5:Res:127147.1,897.0] || subclass(ordinal_numbers,complement(complement(restrict(u,v,w))))* -> member(least(element_relation,omega),cross_product(v,w)).
% 299.99/300.66  130635[5:Res:41371.0,5.0] || subclass(u,v) -> subclass(complement(complement(u)),w) member(not_subclass_element(complement(complement(u)),w),v)*.
% 299.99/300.66  130636[5:Res:41371.0,26.0] ||  -> subclass(complement(complement(intersection(u,v))),w) member(not_subclass_element(complement(complement(intersection(u,v))),w),v)*.
% 299.99/300.66  130637[5:Res:41371.0,25.0] ||  -> subclass(complement(complement(intersection(u,v))),w) member(not_subclass_element(complement(complement(intersection(u,v))),w),u)*.
% 299.99/300.66  131475[5:Res:49995.1,18794.1] || member(intersection(u,v),subset_relation) member(singleton(first(intersection(u,v))),symmetric_difference(u,v))* -> .
% 299.99/300.66  131533[8:Res:2504.1,66086.1] || subclass(ordered_pair(u,v),complement(compose(element_relation,ordinal_numbers)))* member(unordered_pair(u,singleton(v)),element_relation) -> .
% 299.99/300.66  131542[0:Res:2504.1,5.0] || subclass(ordered_pair(u,v),w)* subclass(w,x)* -> member(unordered_pair(u,singleton(v)),x)*.
% 299.99/300.66  131547[0:Res:2504.1,3617.0] || subclass(ordered_pair(u,v),symmetric_difference(w,x)) -> member(unordered_pair(u,singleton(v)),union(w,x))*.
% 299.99/300.66  131548[0:Res:2504.1,19559.0] || subclass(ordered_pair(u,v),symmetric_difference(w,singleton(w)))* -> member(unordered_pair(u,singleton(v)),successor(w)).
% 299.99/300.66  131549[0:Res:2504.1,19676.0] || subclass(ordered_pair(u,v),symmetric_difference(w,inverse(w)))* -> member(unordered_pair(u,singleton(v)),symmetrization_of(w)).
% 299.99/300.66  131577[0:Res:2504.1,161.0] || subclass(ordered_pair(u,v),omega) -> equal(integer_of(unordered_pair(u,singleton(v))),unordered_pair(u,singleton(v)))**.
% 299.99/300.66  132376[5:Res:132293.0,8825.1] || member(u,ordinal_numbers) -> member(u,successor(v)) member(u,intersection(complement(v),complement(singleton(v))))*.
% 299.99/300.66  132419[5:Res:132294.0,8825.1] || member(u,ordinal_numbers) -> member(u,symmetrization_of(v)) member(u,intersection(complement(v),complement(inverse(v))))*.
% 299.99/300.66  134713[8:SpR:117066.0,116403.2] || member(u,ordinal_numbers) subclass(rest_relation,rest_of(flip(cross_product(v,ordinal_numbers))))* -> member(u,inverse(v))*.
% 299.99/300.66  134714[8:SpR:117142.0,116403.2] || member(u,ordinal_numbers) subclass(rest_relation,rest_of(restrict(element_relation,ordinal_numbers,v)))* -> member(u,sum_class(v))*.
% 299.99/300.66  134920[8:Rew:50855.1,134896.2] || member(singleton(u),subset_relation) member(singleton(singleton(u)),rest_of(v))* -> member(u,cantor(v)).
% 299.99/300.66  135190[8:Rew:135117.1,135136.2] || equal(rest_of(restrict(u,v,w)),rest_relation)** section(u,w,v) -> equal(ordinal_numbers,w).
% 299.99/300.66  135249[5:Rew:50855.1,135224.2] || member(singleton(u),subset_relation) member(singleton(singleton(u)),cross_product(v,w))* -> member(u,v).
% 299.99/300.66  136684[5:Res:9632.1,18791.0] || equal(complement(complement(symmetric_difference(complement(u),complement(v)))),ordinal_numbers)** -> member(singleton(w),union(u,v))*.
% 299.99/300.66  136688[5:Res:133837.1,18791.0] || well_ordering(ordinal_numbers,complement(symmetric_difference(complement(u),complement(v))))* -> member(singleton(singleton(w)),union(u,v))*.
% 299.99/300.66  140283[0:Res:18949.0,19124.0] ||  -> subclass(restrict(singleton(u),v,w),x) equal(not_subclass_element(restrict(singleton(u),v,w),x),u)**.
% 299.99/300.66  140457[8:Rew:66423.0,140346.1] || member(not_subclass_element(ordinal_numbers,symmetric_difference(u,ordinal_numbers)),complement(intersection(u,ordinal_numbers)))* -> subclass(ordinal_numbers,symmetric_difference(u,ordinal_numbers)).
% 299.99/300.66  146757[5:Res:18819.1,18571.2] || member(sum_class(u),subset_relation)* member(u,ordinal_numbers) subclass(ordinal_numbers,complement(cross_product(ordinal_numbers,ordinal_numbers)))* -> .
% 299.99/300.66  146792[5:MRR:146751.0,8955.1] || member(u,ordinal_numbers) subclass(ordinal_numbers,complement(union(v,w)))* -> member(sum_class(u),complement(w))*.
% 299.99/300.66  146793[5:MRR:146750.0,8955.1] || member(u,ordinal_numbers) subclass(ordinal_numbers,complement(union(v,w)))* -> member(sum_class(u),complement(v))*.
% 299.99/300.66  147276[5:Res:143222.1,490.0] || equal(intersection(complement(u),complement(v)),omega) member(least(element_relation,omega),union(u,v))* -> .
% 299.99/300.66  147293[5:Res:143222.1,12.0] || equal(unordered_pair(u,v),omega)** -> equal(least(element_relation,omega),v)* equal(least(element_relation,omega),u)*.
% 299.99/300.66  151531[0:Rew:18910.1,151530.1] || member(u,v) member(u,w) -> subclass(intersection(x,singleton(u)),intersection(w,v))*.
% 299.99/300.66  151895[0:Rew:19029.1,151894.1] || member(u,v) member(u,w) -> subclass(intersection(singleton(u),x),intersection(w,v))*.
% 299.99/300.66  152201[5:Res:18819.1,19111.1] || member(not_subclass_element(u,v),subset_relation)* subclass(u,complement(cross_product(ordinal_numbers,ordinal_numbers)))* -> subclass(u,v).
% 299.99/300.66  152246[5:MRR:152195.0,41183.1] || subclass(u,complement(union(v,w)))* -> member(not_subclass_element(u,x),complement(w))* subclass(u,x).
% 299.99/300.66  152247[5:MRR:152194.0,41183.1] || subclass(u,complement(union(v,w)))* -> member(not_subclass_element(u,x),complement(v))* subclass(u,x).
% 299.99/300.66  153367[5:Res:919.1,50033.0] || equal(complement(not_subclass_element(restrict(subset_relation,u,v),w)),ordinal_numbers)** -> subclass(restrict(subset_relation,u,v),w).
% 299.99/300.66  154287[5:Res:41371.0,151988.0] ||  -> subclass(complement(complement(complement(complement(u)))),v) member(not_subclass_element(complement(complement(complement(complement(u)))),v),u)*.
% 299.99/300.66  154288[5:Res:313.1,151988.0] ||  -> subclass(intersection(complement(complement(u)),v),w) member(not_subclass_element(intersection(complement(complement(u)),v),w),u)*.
% 299.99/300.66  154309[5:Res:303.1,151988.0] ||  -> subclass(intersection(u,complement(complement(v))),w) member(not_subclass_element(intersection(u,complement(complement(v))),w),v)*.
% 299.99/300.66  154334[5:Res:8827.2,151988.0] || member(u,ordinal_numbers) subclass(rest_relation,complement(complement(v))) -> member(ordered_pair(u,rest_of(u)),v)*.
% 299.99/300.66  155171[0:SpR:154737.1,3597.0] || subclass(inverse(u),u) -> equal(intersection(complement(inverse(u)),symmetrization_of(u)),symmetric_difference(u,inverse(u)))**.
% 299.99/300.66  155178[0:SpR:154737.1,3596.0] || subclass(singleton(u),u) -> equal(intersection(complement(singleton(u)),successor(u)),symmetric_difference(u,singleton(u)))**.
% 299.99/300.66  155191[0:SpR:154737.1,163.0] || subclass(union(u,v),complement(intersection(u,v)))* -> equal(symmetric_difference(u,v),union(u,v)).
% 299.99/300.66  155192[0:SpR:154737.1,3596.0] || subclass(successor(u),complement(intersection(u,singleton(u))))* -> equal(symmetric_difference(u,singleton(u)),successor(u)).
% 299.99/300.66  155193[0:SpR:154737.1,3597.0] || subclass(symmetrization_of(u),complement(intersection(u,inverse(u))))* -> equal(symmetric_difference(u,inverse(u)),symmetrization_of(u)).
% 299.99/300.66  155517[0:SpR:154945.0,163.0] ||  -> equal(intersection(complement(intersection(u,v)),union(u,intersection(u,v))),symmetric_difference(u,intersection(u,v)))**.
% 299.99/300.66  155936[0:SpR:155147.0,163.0] ||  -> equal(intersection(complement(intersection(u,v)),union(v,intersection(u,v))),symmetric_difference(v,intersection(u,v)))**.
% 299.99/300.66  156838[5:Res:9632.1,40594.1] || equal(complement(complement(u)),ordinal_numbers) member(u,ordinal_numbers) -> member(singleton(singleton(singleton(u))),element_relation)*.
% 299.99/300.66  156851[5:MRR:156850.1,50063.1] || member(singleton(u),subset_relation) member(u,first(singleton(u)))* -> member(singleton(singleton(u)),element_relation)*.
% 299.99/300.66  156955[8:Res:156922.1,19111.1] || member(not_subclass_element(u,v),inverse(subset_relation))* subclass(u,complement(complement(subset_relation))) -> subclass(u,v).
% 299.99/300.66  156956[8:Res:156922.1,47534.0] || member(not_subclass_element(u,intersection(complement(subset_relation),u)),inverse(subset_relation))* -> subclass(u,intersection(complement(subset_relation),u)).
% 299.99/300.66  132040[0:Res:139.1,19115.0] || member(recursion_equation_functions(u),ordinal_numbers) -> subclass(sum_class(recursion_equation_functions(u)),v) function(not_subclass_element(sum_class(recursion_equation_functions(u)),v))*.
% 299.99/300.66  117512[8:Rew:116078.0,116546.2,116078.0,116546.1] operation(u) || member(singleton(singleton(singleton(v))),cantor(u))* -> member(v,cantor(cantor(u))).
% 299.99/300.66  19018[5:Res:313.1,8788.0] ||  -> subclass(intersection(recursion_equation_functions(u),v),w) subclass(not_subclass_element(intersection(recursion_equation_functions(u),v),w),cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.66  130629[5:Res:41371.0,8788.0] ||  -> subclass(complement(complement(recursion_equation_functions(u))),v) subclass(not_subclass_element(complement(complement(recursion_equation_functions(u))),v),cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.66  18899[5:Res:303.1,8788.0] ||  -> subclass(intersection(u,recursion_equation_functions(v)),w) subclass(not_subclass_element(intersection(u,recursion_equation_functions(v)),w),cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.66  36046[5:Rew:154.1,36040.2] || member(u,recursion_equation_functions(v))* subclass(cross_product(ordinal_numbers,ordinal_numbers),u)* -> equal(u,cross_product(ordinal_numbers,ordinal_numbers)).
% 299.99/300.66  161198[8:Rew:160496.0,161197.1] operation(u) || equal(complement(complement(symmetrization_of(v))),cantor(u)) -> connected(v,cantor(cantor(u)))*.
% 299.99/300.66  32145[5:MRR:32143.1,8657.0] || member(u,ordinal_numbers) equal(rest_of(u),successor(u)) -> member(ordered_pair(u,rest_of(u)),successor_relation)*.
% 299.99/300.66  18845[5:Res:18819.1,8799.1] || member(ordered_pair(u,v),subset_relation)* equal(successor(u),v) -> member(ordered_pair(u,v),successor_relation).
% 299.99/300.66  42244[5:MRR:42235.1,8655.0] || member(u,ordinal_numbers) equal(successor(singleton(u)),u) -> member(singleton(singleton(singleton(u))),successor_relation)*.
% 299.99/300.66  147062[5:Res:143193.1,490.0] || equal(intersection(complement(u),complement(v)),ordinal_numbers) member(least(element_relation,omega),union(u,v))* -> .
% 299.99/300.66  162892[8:MRR:61015.0,162891.0] ||  -> equal(unordered_pair(u,singleton(v)),regular(ordered_pair(u,v)))** equal(regular(ordered_pair(u,v)),singleton(u)).
% 299.99/300.66  177023[8:SpL:116154.0,161304.1] || subclass(rest_relation,rest_of(restrict(u,v,singleton(w))))* well_ordering(ordinal_numbers,segment(u,v,w)) -> .
% 299.99/300.66  166549[7:Rew:155665.0,166471.0] ||  -> equal(symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers)),identity_relation) member(regular(symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers))),complement(subset_relation))*.
% 299.99/300.66  166550[7:Rew:155666.0,166472.0] ||  -> equal(symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation),identity_relation) member(regular(symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation)),complement(subset_relation))*.
% 299.99/300.66  165099[7:Res:130678.0,13113.0] || well_ordering(u,v) -> equal(segment(u,complement(complement(v)),least(u,complement(complement(v)))),identity_relation)**.
% 299.99/300.66  164616[7:SpL:154737.1,13103.0] || subclass(inverse(u),u)* equal(restrict(inverse(u),v,v),identity_relation)** -> asymmetric(u,v).
% 299.99/300.66  164710[7:SpR:154737.1,13104.1] || subclass(inverse(u),u)* asymmetric(u,v) -> equal(restrict(inverse(u),v,v),identity_relation)**.
% 299.99/300.66  164922[8:SpL:160491.0,18791.0] || member(u,symmetric_difference(complement(v),union(w,identity_relation)))* -> member(u,union(v,symmetric_difference(ordinal_numbers,w))).
% 299.99/300.66  161191[8:Rew:116078.0,18637.2,116078.0,18637.1] operation(u) ||  -> equal(intersection(cantor(u),v),identity_relation) member(regular(intersection(v,cantor(u))),v)*.
% 299.99/300.66  19844[7:Res:3652.1,13082.1] inductive(segment(u,v,w)) || section(u,singleton(w),v)* -> member(identity_relation,singleton(w)).
% 299.99/300.66  19087[7:Res:19045.0,13113.0] || well_ordering(u,v) -> equal(segment(u,intersection(v,w),least(u,intersection(v,w))),identity_relation)**.
% 299.99/300.66  18968[7:Res:18926.0,13113.0] || well_ordering(u,v) -> equal(segment(u,intersection(w,v),least(u,intersection(w,v))),identity_relation)**.
% 299.99/300.66  62039[8:Res:19172.1,9010.0] || equal(cross_product(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers),identity_relation) -> equal(cross_product(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers),rotate(u))*.
% 299.99/300.66  62038[8:Res:19172.1,9009.0] || equal(cross_product(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers),identity_relation) -> equal(cross_product(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers),flip(u))*.
% 299.99/300.66  161180[8:Rew:116078.0,19199.0] || equal(cantor(restrict(u,v,w)),identity_relation)** subclass(w,v) -> section(u,w,v).
% 299.99/300.66  161179[8:Rew:116078.0,18645.2,116078.0,18645.1] operation(u) ||  -> equal(intersection(v,cantor(u)),identity_relation) member(regular(intersection(cantor(u),v)),v)*.
% 299.99/300.66  13309[7:Rew:13036.0,8609.1] || member(regular(union(u,v)),intersection(complement(u),complement(v)))* -> equal(union(u,v),identity_relation).
% 299.99/300.66  166378[7:Res:13125.2,971.0] || subclass(omega,rest_relation) -> equal(integer_of(singleton(singleton(singleton(u)))),identity_relation)** equal(rest_of(singleton(u)),u).
% 299.99/300.66  13423[7:Rew:13036.0,10947.1] || subclass(omega,compose_class(u))* -> equal(integer_of(ordered_pair(v,w)),identity_relation)** equal(compose(u,v),w)*.
% 299.99/300.66  69469[7:Res:13125.2,897.0] || subclass(omega,restrict(u,v,w))* -> equal(integer_of(x),identity_relation) member(x,cross_product(v,w))*.
% 299.99/300.66  83894[7:Res:66696.2,897.0] || subclass(ordinal_numbers,restrict(u,v,w))* -> equal(integer_of(x),identity_relation) member(x,cross_product(v,w))*.
% 299.99/300.66  13338[7:Rew:13036.0,10917.1] || subclass(omega,unordered_pair(u,v))* -> equal(integer_of(w),identity_relation)** equal(w,v)* equal(w,u)*.
% 299.99/300.66  166332[7:Res:13125.2,18794.1] || subclass(omega,intersection(u,v)) member(w,symmetric_difference(u,v))* -> equal(integer_of(w),identity_relation).
% 299.99/300.66  62524[7:SpR:13101.0,50064.1] || member(not_subclass_element(restrict(u,singleton(v),w),identity_relation),subset_relation)* -> member(range__dfg(u,v,w),ordinal_numbers).
% 299.99/300.66  62554[7:SpR:13100.0,50063.1] || member(not_subclass_element(restrict(u,v,singleton(w)),identity_relation),subset_relation)* -> member(domain__dfg(u,v,w),ordinal_numbers).
% 299.99/300.66  164919[8:SpL:160491.0,18791.0] || member(u,symmetric_difference(union(v,identity_relation),complement(w)))* -> member(u,union(symmetric_difference(ordinal_numbers,v),w)).
% 299.99/300.66  68906[8:MRR:68893.0,41096.1] || member(u,union(v,identity_relation))* subclass(symmetric_difference(complement(v),ordinal_numbers),w)* -> member(u,w)*.
% 299.99/300.66  82117[8:Res:60219.0,14681.0] || member(not_subclass_element(u,complement(regular(v))),v)* -> subclass(u,complement(regular(v))) equal(v,identity_relation).
% 299.99/300.66  67229[7:Obv:67227.0] ||  -> equal(not_subclass_element(unordered_pair(u,v),omega),u)** equal(integer_of(v),identity_relation) subclass(unordered_pair(u,v),omega).
% 299.99/300.66  167496[8:Res:8827.2,163154.0] || member(u,ordinal_numbers) subclass(rest_relation,symmetrization_of(identity_relation)) -> member(ordered_pair(u,rest_of(u)),inverse(identity_relation))*.
% 299.99/300.66  163155[8:SpL:162584.0,490.0] || member(u,intersection(complement(v),symmetrization_of(identity_relation)))* member(u,union(v,complement(inverse(identity_relation)))) -> .
% 299.99/300.66  163144[8:SpL:162584.0,490.0] || member(u,intersection(symmetrization_of(identity_relation),complement(v)))* member(u,union(complement(inverse(identity_relation)),v)) -> .
% 299.99/300.66  163143[8:SpL:162584.0,66637.0] || subclass(ordinal_numbers,intersection(complement(u),symmetrization_of(identity_relation))) member(omega,union(u,complement(inverse(identity_relation))))* -> .
% 299.99/300.66  163123[8:SpL:162584.0,66637.0] || subclass(ordinal_numbers,intersection(symmetrization_of(identity_relation),complement(u))) member(omega,union(complement(inverse(identity_relation)),u))* -> .
% 299.99/300.66  62416[7:SpL:13104.1,9777.0] || asymmetric(u,v) equal(compose(identity_relation,identity_relation),identity_relation) -> transitive(intersection(u,inverse(u)),v)*.
% 299.99/300.66  62429[7:MRR:62428.2,13039.0] || asymmetric(u,v) transitive(intersection(u,inverse(u)),v)* -> equal(compose(identity_relation,identity_relation),identity_relation).
% 299.99/300.66  81696[8:Res:81695.0,13070.0] || well_ordering(u,complement(subset_relation)) -> equal(inverse(subset_relation),identity_relation) member(least(u,inverse(subset_relation)),inverse(subset_relation))*.
% 299.99/300.66  68904[8:Rew:66293.0,68860.0] ||  -> subclass(symmetric_difference(complement(u),ordinal_numbers),v) member(not_subclass_element(symmetric_difference(complement(u),ordinal_numbers),v),union(u,identity_relation))*.
% 299.99/300.66  164932[8:Rew:160491.0,164852.1] ||  -> member(not_subclass_element(complement(union(u,identity_relation)),v),symmetric_difference(ordinal_numbers,u))* subclass(complement(union(u,identity_relation)),v).
% 299.99/300.66  67230[7:Obv:67226.0] ||  -> equal(not_subclass_element(unordered_pair(u,v),omega),v)** equal(integer_of(u),identity_relation) subclass(unordered_pair(u,v),omega).
% 299.99/300.66  65569[8:Res:51313.1,14681.0] || member(singleton(regular(u)),subset_relation) member(first(singleton(regular(u))),u)* -> equal(u,identity_relation).
% 299.99/300.66  18833[7:Res:13227.2,897.0] || subclass(u,restrict(v,w,x))* -> equal(u,identity_relation) member(regular(u),cross_product(w,x))*.
% 299.99/300.66  18758[8:Res:13227.2,14681.0] || subclass(u,regular(v)) member(regular(u),v)* -> equal(u,identity_relation) equal(v,identity_relation).
% 299.99/300.66  69484[8:Res:13125.2,14681.0] || subclass(omega,regular(u))* member(v,u)* -> equal(integer_of(v),identity_relation) equal(u,identity_relation).
% 299.99/300.66  83898[8:Res:66696.2,14681.0] || subclass(ordinal_numbers,regular(u))* member(v,u)* -> equal(integer_of(v),identity_relation) equal(u,identity_relation).
% 299.99/300.66  166796[7:Res:13227.2,18794.1] || subclass(u,intersection(v,w)) member(regular(u),symmetric_difference(v,w))* -> equal(u,identity_relation).
% 299.99/300.66  167236[8:Res:40074.1,14681.0] || subclass(ordinal_numbers,complement(complement(regular(u))))* member(unordered_pair(v,w),u)* -> equal(u,identity_relation).
% 299.99/300.66  167256[8:Res:127147.1,14681.0] || subclass(ordinal_numbers,complement(complement(regular(u))))* member(least(element_relation,omega),u) -> equal(u,identity_relation).
% 299.99/300.66  167257[8:Res:126679.1,14681.0] || subclass(omega,complement(complement(regular(u))))* member(least(element_relation,omega),u) -> equal(u,identity_relation).
% 299.99/300.66  167269[8:Res:39298.1,14681.0] || subclass(ordinal_numbers,complement(complement(regular(u))))* member(ordered_pair(v,w),u)* -> equal(u,identity_relation).
% 299.99/300.66  19193[8:Res:19172.1,13113.0] || equal(identity_relation,u) well_ordering(v,w)* -> equal(segment(v,u,least(v,u)),identity_relation)**.
% 299.99/300.66  62027[8:Res:19172.1,3729.1] || equal(identity_relation,u) connected(v,u) -> well_ordering(v,u) equal(not_well_ordering(v,u),u)**.
% 299.99/300.66  163881[8:Res:19172.1,117594.1] || equal(identity_relation,u) section(v,u,w) -> equal(cantor(restrict(v,w,u)),u)**.
% 299.99/300.66  164501[14:Res:164498.0,129.0] || subclass(singleton(identity_relation),u)* well_ordering(v,u)* -> member(least(v,singleton(identity_relation)),singleton(identity_relation))*.
% 299.99/300.66  64660[8:SpL:50855.1,15574.0] || member(singleton(u),subset_relation)* subclass(domain_relation,u) -> equal(ordered_pair(identity_relation,identity_relation),first(singleton(u))).
% 299.99/300.66  64663[8:SpL:50855.1,18039.0] || member(singleton(u),subset_relation)* equal(u,domain_relation) -> equal(ordered_pair(identity_relation,identity_relation),first(singleton(u))).
% 299.99/300.66  81304[8:Res:3618.1,15565.1] || member(ordered_pair(identity_relation,identity_relation),symmetric_difference(u,v))* subclass(domain_relation,complement(complement(intersection(u,v)))) -> .
% 299.99/300.66  82757[8:Res:81336.1,897.0] || subclass(domain_relation,complement(complement(restrict(u,v,w))))* -> member(ordered_pair(identity_relation,identity_relation),cross_product(v,w)).
% 299.99/300.66  62984[8:Res:15426.1,490.0] || subclass(domain_relation,intersection(complement(u),complement(v))) member(ordered_pair(identity_relation,identity_relation),union(u,v))* -> .
% 299.99/300.66  15575[8:Res:15426.1,12.0] || subclass(domain_relation,unordered_pair(u,v))* -> equal(ordered_pair(identity_relation,identity_relation),v) equal(ordered_pair(identity_relation,identity_relation),u).
% 299.99/300.66  82293[8:Res:81336.1,14681.0] || subclass(domain_relation,complement(complement(regular(u))))* member(ordered_pair(identity_relation,identity_relation),u) -> equal(u,identity_relation).
% 299.99/300.66  190435[18:Res:190432.0,129.0] || subclass(symmetrization_of(identity_relation),u)* well_ordering(v,u)* -> member(least(v,symmetrization_of(identity_relation)),symmetrization_of(identity_relation))*.
% 299.99/300.66  190449[18:Res:190445.0,129.0] || subclass(inverse(identity_relation),u)* well_ordering(v,u)* -> member(least(v,inverse(identity_relation)),inverse(identity_relation))*.
% 299.99/300.66  191944[18:Res:190515.1,490.0] || subclass(ordinal_numbers,intersection(complement(u),complement(v))) member(regular(symmetrization_of(identity_relation)),union(u,v))* -> .
% 299.99/300.66  192536[8:MRR:192519.4,14676.0] || member(u,singleton(v))* member(u,recursion_equation_functions(w))* well_ordering(x,y)* -> function(v).
% 299.99/300.66  192862[8:MRR:192841.4,14676.0] || member(u,singleton(v))* member(u,w)* well_ordering(x,y)* -> member(v,w)*.
% 299.99/300.66  192996[8:Rew:160429.0,192971.1] ||  -> equal(cross_product(u,singleton(v)),identity_relation) equal(segment(regular(cross_product(u,singleton(v))),u,v),identity_relation)**.
% 299.99/300.66  193001[8:MRR:193000.1,13039.0] || subclass(u,v) -> equal(cross_product(v,u),identity_relation) section(regular(cross_product(v,u)),u,v)*.
% 299.99/300.66  130959[5:Res:8801.1,9876.0] || member(ordered_pair(u,v),cross_product(ordinal_numbers,ordinal_numbers))* subclass(composition_function,w) well_ordering(ordinal_numbers,w)* -> .
% 299.99/300.66  132236[8:Res:39609.2,14679.1] inductive(inverse(subset_relation)) || well_ordering(u,inverse(subset_relation)) member(least(u,inverse(subset_relation)),subset_relation)* -> .
% 299.99/300.66  130845[5:Res:8700.2,9876.0] || member(u,ordinal_numbers)* subclass(complement(v),w)* well_ordering(ordinal_numbers,w) -> member(u,v)*.
% 299.99/300.66  130957[5:Res:8827.2,9876.0] || member(u,ordinal_numbers)* subclass(rest_relation,v)* subclass(v,w)* well_ordering(ordinal_numbers,w)* -> .
% 299.99/300.66  130972[5:Res:41098.2,9876.0] || member(u,ordinal_numbers)* member(v,u)* subclass(element_relation,w) well_ordering(ordinal_numbers,w)* -> .
% 299.99/300.66  132202[8:Res:39609.2,116166.0] inductive(recursion_equation_functions(u)) || well_ordering(v,recursion_equation_functions(u)) -> member(cantor(least(v,recursion_equation_functions(u))),ordinal_numbers)*.
% 299.99/300.66  167320[7:Res:13237.2,151988.0] || well_ordering(u,ordinal_numbers) -> equal(complement(complement(v)),identity_relation) member(least(u,complement(complement(v))),v)*.
% 299.99/300.66  18705[7:Res:13237.2,26.0] || well_ordering(u,ordinal_numbers) -> equal(intersection(v,w),identity_relation) member(least(u,intersection(v,w)),w)*.
% 299.99/300.66  18706[7:Res:13237.2,25.0] || well_ordering(u,ordinal_numbers) -> equal(intersection(v,w),identity_relation) member(least(u,intersection(v,w)),v)*.
% 299.99/300.66  18698[7:Res:13237.2,8788.0] || well_ordering(u,ordinal_numbers) -> equal(recursion_equation_functions(v),identity_relation) subclass(least(u,recursion_equation_functions(v)),cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.66  18702[7:Res:13237.2,5.0] || well_ordering(u,ordinal_numbers) subclass(v,w) -> equal(v,identity_relation) member(least(u,v),w)*.
% 299.99/300.66  167336[7:Res:13237.2,50007.0] || well_ordering(u,ordinal_numbers) subclass(ordinal_numbers,v) -> equal(subset_relation,identity_relation) member(least(u,subset_relation),v)*.
% 299.99/300.66  131184[5:Res:39607.2,5.0] inductive(u) || well_ordering(v,ordinal_numbers) subclass(u,w) -> member(least(v,u),w)*.
% 299.99/300.66  154325[5:Res:39607.2,151988.0] inductive(complement(complement(u))) || well_ordering(v,ordinal_numbers) -> member(least(v,complement(complement(u))),u)*.
% 299.99/300.66  131177[5:Res:39607.2,8788.0] inductive(recursion_equation_functions(u)) || well_ordering(v,ordinal_numbers) -> subclass(least(v,recursion_equation_functions(u)),cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.66  131185[5:Res:39607.2,26.0] inductive(intersection(u,v)) || well_ordering(w,ordinal_numbers) -> member(least(w,intersection(u,v)),v)*.
% 299.99/300.66  131186[5:Res:39607.2,25.0] inductive(intersection(u,v)) || well_ordering(w,ordinal_numbers) -> member(least(w,intersection(u,v)),u)*.
% 299.99/300.66  132210[2:Res:39609.2,5.0] inductive(u) || well_ordering(v,u) subclass(u,w) -> member(least(v,u),w)*.
% 299.99/300.66  132199[2:Res:39609.2,28.1] inductive(complement(u)) || well_ordering(v,complement(u)) member(least(v,complement(u)),u)* -> .
% 299.99/300.66  194551[7:Res:138.1,13496.0] || member(cross_product(ordinal_numbers,cross_product(ordinal_numbers,ordinal_numbers)),ordinal_numbers)* -> equal(segment(element_relation,composition_function,least(element_relation,composition_function)),identity_relation).
% 299.99/300.66  194573[8:SpR:69395.0,39530.1] || member(u,ordinal_numbers) -> member(u,complement(symmetric_difference(v,ordinal_numbers))) member(u,complement(intersection(v,ordinal_numbers)))*.
% 299.99/300.66  195082[14:Res:27.2,165357.1] || member(identity_relation,u) member(identity_relation,v) equal(complement(intersection(v,u)),singleton(identity_relation))** -> .
% 299.99/300.66  195438[16:Rew:195224.0,163210.0] || subclass(ordinal_numbers,intersection(singleton(identity_relation),complement(u))) member(omega,union(complement(singleton(identity_relation)),u))* -> .
% 299.99/300.66  195442[16:Rew:195224.0,163230.0] || subclass(ordinal_numbers,intersection(complement(u),singleton(identity_relation))) member(omega,union(u,complement(singleton(identity_relation))))* -> .
% 299.99/300.66  195493[16:Rew:195224.0,163231.0] || member(u,intersection(singleton(identity_relation),complement(v)))* member(u,union(complement(singleton(identity_relation)),v)) -> .
% 299.99/300.66  195496[16:Rew:195224.0,163243.0] || member(u,intersection(complement(v),singleton(identity_relation)))* member(u,union(v,complement(singleton(identity_relation)))) -> .
% 299.99/300.66  196090[18:Res:190510.1,18791.0] || subclass(inverse(identity_relation),symmetric_difference(complement(u),complement(v)))* -> member(regular(symmetrization_of(identity_relation)),union(u,v)).
% 299.99/300.66  196136[18:Res:27.2,190532.1] || member(identity_relation,u) member(identity_relation,v) equal(complement(intersection(v,u)),symmetrization_of(identity_relation))** -> .
% 299.99/300.66  196219[7:Res:13501.2,41096.0] || well_ordering(u,cross_product(ordinal_numbers,ordinal_numbers)) -> equal(compose_class(v),identity_relation) member(least(u,compose_class(v)),ordinal_numbers)*.
% 299.99/300.66  196226[18:Res:27.2,190641.1] || member(identity_relation,u) member(identity_relation,v) equal(complement(intersection(v,u)),inverse(identity_relation))** -> .
% 299.99/300.66  196280[7:Res:13500.2,41096.0] || well_ordering(u,cross_product(ordinal_numbers,ordinal_numbers)) -> equal(rest_of(v),identity_relation) member(least(u,rest_of(v)),ordinal_numbers)*.
% 299.99/300.66  196421[21:Rew:196372.1,161327.2] || member(u,ordinal_numbers) subclass(domain_relation,restrict(v,w,x))* -> member(ordered_pair(u,identity_relation),v)*.
% 299.99/300.66  196433[21:Rew:196372.1,161325.2] || member(u,ordinal_numbers) subclass(domain_relation,recursion_equation_functions(v))* -> subclass(ordered_pair(u,identity_relation),cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.66  196437[21:Rew:196372.1,161403.2] || member(u,ordinal_numbers) subclass(domain_relation,omega) -> equal(integer_of(ordered_pair(u,identity_relation)),ordered_pair(u,identity_relation))**.
% 299.99/300.66  196526[21:Rew:196372.1,196443.1] || member(u,ordinal_numbers) equal(compose(v,u),identity_relation) -> member(ordered_pair(u,identity_relation),compose_class(v))*.
% 299.99/300.66  197185[7:Obv:197172.0] ||  -> equal(regular(unordered_pair(u,v)),v) equal(unordered_pair(u,v),identity_relation) member(u,unordered_pair(u,v))*.
% 299.99/300.66  197186[7:Obv:197164.0] ||  -> equal(regular(unordered_pair(u,v)),u) equal(unordered_pair(u,v),identity_relation) member(v,unordered_pair(u,v))*.
% 299.99/300.66  197291[7:SpR:140603.0,13299.1] || asymmetric(ordinal_numbers,singleton(u)) -> equal(range__dfg(inverse(ordinal_numbers),u,singleton(u)),second(not_subclass_element(identity_relation,identity_relation)))**.
% 299.99/300.66  198677[21:Obv:198675.1] || equal(rest_of(u),rest_relation) -> equal(regular(unordered_pair(v,u)),v)** equal(unordered_pair(v,u),identity_relation).
% 299.99/300.66  198678[21:Obv:198674.1] || equal(rest_of(u),rest_relation) -> equal(regular(unordered_pair(u,v)),v)** equal(unordered_pair(u,v),identity_relation).
% 299.99/300.66  198834[21:Obv:198804.0] ||  -> equal(not_subclass_element(unordered_pair(u,v),w),u)** subclass(unordered_pair(u,v),w) equal(cantor(v),identity_relation).
% 299.99/300.66  198835[21:Obv:198803.0] ||  -> equal(not_subclass_element(unordered_pair(u,v),w),v)** subclass(unordered_pair(u,v),w) equal(cantor(u),identity_relation).
% 299.99/300.66  198986[7:Res:8652.0,13362.0] || subclass(ordinal_numbers,u) well_ordering(omega,u)* -> equal(integer_of(ordered_pair(omega,least(omega,ordinal_numbers))),identity_relation)**.
% 299.99/300.66  199002[7:Res:13126.0,13362.0] || subclass(ordinal_numbers,u) well_ordering(omega,u)* -> equal(integer_of(ordered_pair(identity_relation,least(omega,ordinal_numbers))),identity_relation)**.
% 299.99/300.66  198172[21:SpR:197474.0,17.0] ||  -> equal(range_of(u),identity_relation) equal(unordered_pair(identity_relation,unordered_pair(inverse(u),singleton(v))),ordered_pair(inverse(u),v))**.
% 299.99/300.66  198222[21:SpL:197474.0,2557.0] || member(singleton(singleton(identity_relation)),cross_product(u,v))* -> equal(range_of(w),identity_relation) member(inverse(w),v)*.
% 299.99/300.66  36713[0:SpL:43.0,4392.1] operation(inverse(u)) || member(v,range_of(u))* -> equal(ordered_pair(first(v),second(v)),v)**.
% 299.99/300.66  116336[8:Rew:116078.0,36570.2] operation(inverse(u)) || member(ordered_pair(v,w),range_of(u))* -> member(v,cantor(range_of(u))).
% 299.99/300.66  116337[8:Rew:116078.0,36426.2] operation(inverse(u)) || member(ordered_pair(v,w),range_of(u))* -> member(w,cantor(range_of(u))).
% 299.99/300.66  197462[21:SpR:196546.1,116203.2] function(u) || subclass(range_of(u),v) -> equal(singleton(u),identity_relation) maps(u,identity_relation,v)*.
% 299.99/300.66  39310[0:SoR:8530.0,82.1] operation(inverse(u)) || subclass(range_of(inverse(u)),v) -> maps(inverse(u),range_of(u),v)*.
% 299.99/300.66  39309[0:SoR:8530.0,75.1] one_to_one(inverse(u)) || subclass(range_of(inverse(u)),v) -> maps(inverse(u),range_of(u),v)*.
% 299.99/300.66  61455[8:SpL:14756.0,9470.1] || member(ordered_pair(u,v),compose(identity_relation,w))* subclass(range_of(identity_relation),x)* -> member(v,x)*.
% 299.99/300.66  165558[15:Res:165526.1,941.1] || subclass(ordinal_numbers,power_class(image(element_relation,complement(u)))) member(range_of(identity_relation),image(element_relation,power_class(u)))* -> .
% 299.99/300.66  195024[15:SpL:189.0,165530.0] || subclass(ordinal_numbers,complement(power_class(image(element_relation,complement(u)))))* -> member(range_of(identity_relation),image(element_relation,power_class(u))).
% 299.99/300.66  167624[7:SpR:154737.1,13311.1] || subclass(inverse(u),u)* asymmetric(u,ordinal_numbers) -> equal(image(inverse(u),ordinal_numbers),range_of(identity_relation))**.
% 299.99/300.66  191860[15:Res:165442.1,490.0] || subclass(ordinal_numbers,intersection(complement(u),complement(v))) member(sum_class(range_of(identity_relation)),union(u,v))* -> .
% 299.99/300.66  197812[8:Obv:197811.1] || member(u,ordinal_numbers) -> member(u,image(ordinal_numbers,singleton(u)))* asymmetric(cross_product(singleton(u),ordinal_numbers),v)*.
% 299.99/300.66  193234[8:SpR:161207.0,160491.0] ||  -> equal(union(intersection(singleton(identity_relation),image(successor_relation,ordinal_numbers)),identity_relation),complement(symmetric_difference(singleton(identity_relation),image(successor_relation,ordinal_numbers))))**.
% 299.99/300.66  164004[8:Res:148858.1,13052.1] || subclass(image(successor_relation,complement(subset_relation)),inverse(subset_relation))* member(identity_relation,complement(subset_relation)) -> inductive(complement(subset_relation)).
% 299.99/300.66  19455[0:SpR:487.0,117.0] ||  -> equal(complement(intersection(power_class(u),complement(inverse(image(element_relation,complement(u)))))),symmetrization_of(image(element_relation,complement(u))))**.
% 299.99/300.66  132403[5:SpR:59.0,132294.0] ||  -> subclass(complement(symmetrization_of(image(element_relation,complement(u)))),intersection(power_class(u),complement(inverse(image(element_relation,complement(u))))))*.
% 299.99/300.66  19454[0:SpR:487.0,47.0] ||  -> equal(complement(intersection(power_class(u),complement(singleton(image(element_relation,complement(u)))))),successor(image(element_relation,complement(u))))**.
% 299.99/300.66  132360[5:SpR:59.0,132293.0] ||  -> subclass(complement(successor(image(element_relation,complement(u)))),intersection(power_class(u),complement(singleton(image(element_relation,complement(u))))))*.
% 299.99/300.66  130868[5:Res:79577.0,9876.0] || subclass(image(element_relation,complement(u)),v)* well_ordering(ordinal_numbers,v) -> subclass(singleton(w),power_class(u))*.
% 299.99/300.66  18444[0:Res:6.1,288.0] || member(not_subclass_element(image(element_relation,complement(u)),v),power_class(u))* -> subclass(image(element_relation,complement(u)),v).
% 299.99/300.66  69476[7:Res:13125.2,288.0] || subclass(omega,image(element_relation,complement(u)))* member(v,power_class(u))* -> equal(integer_of(v),identity_relation).
% 299.99/300.66  83897[7:Res:66696.2,288.0] || subclass(ordinal_numbers,image(element_relation,complement(u)))* member(v,power_class(u))* -> equal(integer_of(v),identity_relation).
% 299.99/300.66  96960[5:Res:79577.0,7.0] ||  -> subclass(singleton(not_subclass_element(u,image(element_relation,complement(v)))),power_class(v))* subclass(u,image(element_relation,complement(v))).
% 299.99/300.66  18455[7:Res:13227.2,288.0] || subclass(u,image(element_relation,complement(v)))* member(regular(u),power_class(v)) -> equal(u,identity_relation).
% 299.99/300.66  132728[5:SpR:19486.0,8956.1] || member(intersection(complement(u),complement(inverse(u))),ordinal_numbers)* -> member(complement(image(element_relation,symmetrization_of(u))),ordinal_numbers).
% 299.99/300.66  193552[8:Rew:162038.0,193539.1] || subclass(power_class(complement(inverse(identity_relation))),image(element_relation,symmetrization_of(identity_relation)))* -> equal(power_class(complement(inverse(identity_relation))),identity_relation).
% 299.99/300.66  193468[8:SpR:162038.0,147905.0] ||  -> equal(intersection(image(element_relation,symmetrization_of(identity_relation)),complement(power_class(complement(inverse(identity_relation))))),complement(power_class(complement(inverse(identity_relation)))))**.
% 299.99/300.66  163114[8:SpR:162584.0,8835.1] || member(u,ordinal_numbers) -> member(u,image(element_relation,symmetrization_of(identity_relation)))* member(u,power_class(complement(inverse(identity_relation)))).
% 299.99/300.66  165388[14:Res:165168.1,941.1] || equal(power_class(image(element_relation,complement(u))),singleton(identity_relation)) member(identity_relation,image(element_relation,power_class(u)))* -> .
% 299.99/300.66  195068[14:SpL:189.0,165360.0] || equal(complement(power_class(image(element_relation,complement(u)))),singleton(identity_relation))** -> member(identity_relation,image(element_relation,power_class(u))).
% 299.99/300.66  196207[18:SpL:189.0,190535.0] || equal(complement(power_class(image(element_relation,complement(u)))),symmetrization_of(identity_relation))** -> member(identity_relation,image(element_relation,power_class(u))).
% 299.99/300.66  196300[18:SpL:189.0,190644.0] || equal(complement(power_class(image(element_relation,complement(u)))),inverse(identity_relation))** -> member(identity_relation,image(element_relation,power_class(u))).
% 299.99/300.66  9629[5:SpL:189.0,9496.0] || subclass(ordinal_numbers,complement(power_class(image(element_relation,complement(u)))))* -> member(singleton(v),image(element_relation,power_class(u)))*.
% 299.99/300.66  155438[5:Res:8645.1,941.1] || subclass(ordinal_numbers,power_class(image(element_relation,complement(u)))) member(singleton(v),image(element_relation,power_class(u)))* -> .
% 299.99/300.66  937[0:SpR:189.0,30.0] ||  -> equal(complement(intersection(power_class(image(element_relation,complement(u))),complement(v))),union(image(element_relation,power_class(u)),v))**.
% 299.99/300.66  132286[5:SpR:189.0,130703.0] ||  -> subclass(complement(union(image(element_relation,power_class(u)),v)),intersection(power_class(image(element_relation,complement(u))),complement(v)))*.
% 299.99/300.66  186588[8:SpL:189.0,176788.0] || equal(symmetric_difference(ordinal_numbers,power_class(image(element_relation,complement(u)))),ordinal_numbers)** -> member(omega,image(element_relation,power_class(u))).
% 299.99/300.66  176986[5:SpL:189.0,134026.0] || equal(complement(power_class(image(element_relation,complement(u)))),ordinal_numbers)** well_ordering(ordinal_numbers,image(element_relation,power_class(u))) -> .
% 299.99/300.66  176779[8:SpR:189.0,144409.1] || equal(symmetric_difference(ordinal_numbers,image(element_relation,power_class(u))),ordinal_numbers) -> member(omega,power_class(image(element_relation,complement(u))))*.
% 299.99/300.66  176856[8:SpL:189.0,155244.0] || subclass(ordinal_numbers,power_class(image(element_relation,complement(u))))* -> equal(symmetric_difference(ordinal_numbers,image(element_relation,power_class(u))),ordinal_numbers).
% 299.99/300.66  939[0:SpR:189.0,30.0] ||  -> equal(complement(intersection(complement(u),power_class(image(element_relation,complement(v))))),union(u,image(element_relation,power_class(v))))**.
% 299.99/300.66  132273[5:SpR:189.0,130703.0] ||  -> subclass(complement(union(u,image(element_relation,power_class(v)))),intersection(complement(u),power_class(image(element_relation,complement(v)))))*.
% 299.99/300.66  194687[14:SpR:189.0,165178.0] ||  -> member(identity_relation,image(element_relation,power_class(image(element_relation,complement(u)))))* member(identity_relation,power_class(image(element_relation,power_class(u)))).
% 299.99/300.66  66984[8:SpR:481.0,66340.0] ||  -> subclass(symmetric_difference(power_class(intersection(complement(u),complement(v))),ordinal_numbers),union(image(element_relation,union(u,v)),identity_relation))*.
% 299.99/300.66  167610[14:SpL:481.0,167597.0] || well_ordering(ordinal_numbers,power_class(intersection(complement(u),complement(v))))* -> member(identity_relation,image(element_relation,union(u,v))).
% 299.99/300.66  130745[5:SpR:481.0,130710.0] ||  -> subclass(complement(power_class(image(element_relation,union(u,v)))),image(element_relation,power_class(intersection(complement(u),complement(v)))))*.
% 299.99/300.66  144399[8:SpR:481.0,140613.0] ||  -> equal(intersection(power_class(intersection(complement(u),complement(v))),ordinal_numbers),symmetric_difference(ordinal_numbers,image(element_relation,union(u,v))))**.
% 299.99/300.66  161369[8:Rew:140613.0,67538.0] ||  -> equal(complement(intersection(power_class(symmetric_difference(ordinal_numbers,u)),complement(v))),union(image(element_relation,union(u,identity_relation)),v))**.
% 299.99/300.66  82975[5:SpR:481.0,79560.1] ||  -> member(u,image(element_relation,union(v,w))) subclass(singleton(u),power_class(intersection(complement(v),complement(w))))*.
% 299.99/300.66  161351[8:Rew:140613.0,67555.0] ||  -> equal(complement(intersection(complement(u),power_class(symmetric_difference(ordinal_numbers,v)))),union(u,image(element_relation,union(v,identity_relation))))**.
% 299.99/300.66  132973[5:SpR:19485.0,8956.1] || member(intersection(complement(u),complement(singleton(u))),ordinal_numbers)* -> member(complement(image(element_relation,successor(u))),ordinal_numbers).
% 299.99/300.66  9590[5:SpL:72.0,9586.0] || subclass(apply(u,v),image(u,singleton(v)))* -> section(element_relation,image(u,singleton(v)),ordinal_numbers).
% 299.99/300.66  18568[5:SpR:72.0,8978.2] || member(image(u,singleton(v)),ordinal_numbers)* subclass(ordinal_numbers,w) -> member(apply(u,v),w)*.
% 299.99/300.66  15684[8:SpR:15667.1,107.0] single_valued_class(u) ||  -> equal(domain__dfg(u,image(inverse(u),singleton(single_valued3(identity_relation))),single_valued2(u)),single_valued3(u))**.
% 299.99/300.66  15688[8:SpR:15668.1,107.0] function(u) ||  -> equal(domain__dfg(u,image(inverse(u),singleton(single_valued3(identity_relation))),single_valued2(u)),single_valued3(u))**.
% 299.99/300.66  107350[5:Res:39298.1,9471.0] || subclass(ordinal_numbers,complement(complement(compose(u,v)))) -> subclass(w,image(u,image(v,singleton(x))))*.
% 299.99/300.66  195385[16:Rew:195224.0,193388.0] || subclass(power_class(complement(singleton(identity_relation))),image(element_relation,singleton(identity_relation)))* -> equal(power_class(complement(singleton(identity_relation))),identity_relation).
% 299.99/300.66  195377[16:Rew:195224.0,193304.0] ||  -> equal(intersection(image(element_relation,singleton(identity_relation)),complement(power_class(complement(singleton(identity_relation))))),complement(power_class(complement(singleton(identity_relation)))))**.
% 299.99/300.66  195318[16:Rew:195224.0,163201.1] || member(u,ordinal_numbers) -> member(u,image(element_relation,singleton(identity_relation)))* member(u,power_class(complement(singleton(identity_relation)))).
% 299.99/300.66  69175[8:Res:8977.2,66086.1] || member(u,ordinal_numbers) subclass(ordinal_numbers,complement(compose(element_relation,ordinal_numbers)))* member(power_class(u),element_relation)* -> .
% 299.99/300.66  57139[5:Res:8977.2,19559.0] || member(u,ordinal_numbers) subclass(ordinal_numbers,symmetric_difference(v,singleton(v)))* -> member(power_class(u),successor(v))*.
% 299.99/300.66  57206[5:Res:8977.2,19676.0] || member(u,ordinal_numbers) subclass(ordinal_numbers,symmetric_difference(v,inverse(v)))* -> member(power_class(u),symmetrization_of(v))*.
% 299.99/300.66  18554[5:Res:8977.2,3617.0] || member(u,ordinal_numbers) subclass(ordinal_numbers,symmetric_difference(v,w)) -> member(power_class(u),union(v,w))*.
% 299.99/300.66  146827[5:Res:18819.1,18535.2] || member(power_class(u),subset_relation)* member(u,ordinal_numbers) subclass(ordinal_numbers,complement(cross_product(ordinal_numbers,ordinal_numbers)))* -> .
% 299.99/300.66  146862[5:MRR:146821.0,8956.1] || member(u,ordinal_numbers) subclass(ordinal_numbers,complement(union(v,w)))* -> member(power_class(u),complement(w))*.
% 299.99/300.66  146863[5:MRR:146820.0,8956.1] || member(u,ordinal_numbers) subclass(ordinal_numbers,complement(union(v,w)))* -> member(power_class(u),complement(v))*.
% 299.99/300.66  18541[5:Res:8977.2,5.0] || member(u,ordinal_numbers) subclass(ordinal_numbers,v)* subclass(v,w)* -> member(power_class(u),w)*.
% 299.99/300.66  139767[5:SpR:487.0,39529.1] || member(u,ordinal_numbers) -> member(u,complement(intersection(power_class(v),complement(w))))* member(u,complement(w)).
% 299.99/300.66  139899[5:Rew:59.0,139853.2] || member(u,ordinal_numbers) -> member(u,complement(intersection(power_class(v),complement(w))))* member(u,power_class(v)).
% 299.99/300.66  19495[5:SpL:481.0,9922.1] inductive(image(element_relation,union(u,v))) || equal(power_class(intersection(complement(u),complement(v))),ordinal_numbers)** -> .
% 299.99/300.66  166763[5:SpL:481.0,166753.1] inductive(image(element_relation,union(u,v))) || equal(power_class(intersection(complement(u),complement(v))),omega)** -> .
% 299.99/300.66  139848[5:SpR:485.0,39530.1] || member(u,ordinal_numbers) -> member(u,complement(intersection(complement(v),power_class(w))))* member(u,complement(v)).
% 299.99/300.66  139816[5:Rew:59.0,139762.2] || member(u,ordinal_numbers) -> member(u,complement(intersection(complement(v),power_class(w))))* member(u,power_class(w)).
% 299.99/300.66  163950[7:Res:13069.2,50007.0] || member(subset_relation,ordinal_numbers) subclass(ordinal_numbers,u) -> equal(subset_relation,identity_relation) member(apply(choice,subset_relation),u)*.
% 299.99/300.66  15263[8:Res:13069.2,14679.1] || member(inverse(subset_relation),ordinal_numbers) member(apply(choice,inverse(subset_relation)),subset_relation)* -> equal(inverse(subset_relation),identity_relation).
% 299.99/300.66  198637[7:EqF:13262.1,13262.2] || equal(u,v) -> equal(unordered_pair(v,u),identity_relation) equal(apply(choice,unordered_pair(v,u)),v)**.
% 299.99/300.66  198778[21:SSi:198751.0,73.0] ||  -> equal(unordered_pair(u,v),identity_relation) equal(apply(choice,unordered_pair(u,v)),v)** equal(cantor(u),identity_relation).
% 299.99/300.66  198779[21:SSi:198752.0,73.0] ||  -> equal(unordered_pair(u,v),identity_relation) equal(apply(choice,unordered_pair(u,v)),u)** equal(cantor(v),identity_relation).
% 299.99/300.66  195706[7:Res:13225.3,152.0] || member(u,ordinal_numbers) subclass(u,recursion_equation_functions(v))* -> equal(u,identity_relation) function(apply(choice,u))*.
% 299.99/300.66  197512[21:Rew:197467.2,161188.2] operation(u) ||  -> equal(singleton(cantor(u)),identity_relation) equal(restrict(singleton(cantor(u)),identity_relation,identity_relation),identity_relation)**.
% 299.99/300.66  204122[8:SpR:50855.1,194487.1] || member(singleton(u),subset_relation) member(first(singleton(u)),inverse(identity_relation))* -> subclass(u,symmetrization_of(identity_relation)).
% 299.99/300.66  204129[8:Res:194487.1,11.0] || member(u,inverse(identity_relation)) subclass(symmetrization_of(identity_relation),singleton(u))* -> equal(symmetrization_of(identity_relation),singleton(u)).
% 299.99/300.66  204148[8:Res:204134.1,19111.1] || member(not_subclass_element(u,v),inverse(identity_relation))* subclass(u,complement(symmetrization_of(identity_relation))) -> subclass(u,v).
% 299.99/300.66  204149[8:Res:204134.1,47534.0] || member(not_subclass_element(u,intersection(symmetrization_of(identity_relation),u)),inverse(identity_relation))* -> subclass(u,intersection(symmetrization_of(identity_relation),u)).
% 299.99/300.66  204182[18:Res:194549.1,18791.0] || subclass(symmetrization_of(identity_relation),symmetric_difference(complement(u),complement(v)))* -> member(regular(symmetrization_of(identity_relation)),union(u,v)).
% 299.99/300.66  204644[21:Res:196904.1,18791.0] || subclass(domain_relation,symmetric_difference(complement(u),complement(v))) -> member(singleton(singleton(singleton(identity_relation))),union(u,v))*.
% 299.99/300.66  204732[21:Rew:963.0,204701.2] || subclass(domain_relation,rest_relation) subclass(rest_relation,inverse(subset_relation)) member(singleton(singleton(singleton(identity_relation))),subset_relation)* -> .
% 299.99/300.66  204761[8:SpR:189.0,192333.1] || equal(symmetric_difference(ordinal_numbers,image(element_relation,power_class(u))),ordinal_numbers) -> member(identity_relation,power_class(image(element_relation,complement(u))))*.
% 299.99/300.66  204825[14:SpL:189.0,195109.1] || equal(image(element_relation,power_class(u)),ordinal_numbers) equal(power_class(image(element_relation,complement(u))),singleton(identity_relation))** -> .
% 299.99/300.66  204827[18:SpL:189.0,196161.1] || equal(image(element_relation,power_class(u)),ordinal_numbers) equal(power_class(image(element_relation,complement(u))),symmetrization_of(identity_relation))** -> .
% 299.99/300.66  204829[18:SpL:189.0,196251.1] || equal(image(element_relation,power_class(u)),ordinal_numbers) equal(power_class(image(element_relation,complement(u))),inverse(identity_relation))** -> .
% 299.99/300.66  205184[15:Res:195033.1,18791.0] || equal(complement(complement(symmetric_difference(complement(u),complement(v)))),ordinal_numbers)** -> member(range_of(identity_relation),union(u,v)).
% 299.99/300.66  205194[15:Res:195033.1,12.0] || equal(complement(complement(unordered_pair(u,v))),ordinal_numbers)** -> equal(range_of(identity_relation),v) equal(range_of(identity_relation),u).
% 299.99/300.66  205459[21:SpL:50855.1,196624.0] || member(singleton(u),subset_relation) member(singleton(singleton(u)),domain_relation)* -> equal(first(singleton(u)),identity_relation).
% 299.99/300.66  205523[22:Res:27.2,205501.0] || member(singleton(identity_relation),u) member(singleton(identity_relation),v) well_ordering(ordinal_numbers,intersection(v,u))* -> .
% 299.99/300.66  206002[8:SpL:189.0,204042.0] || equal(symmetric_difference(ordinal_numbers,power_class(image(element_relation,complement(u)))),ordinal_numbers)** -> member(identity_relation,image(element_relation,power_class(u))).
% 299.99/300.66  206140[22:Res:205574.1,18791.0] || equal(symmetric_difference(complement(u),complement(v)),singleton(singleton(identity_relation))) -> member(singleton(identity_relation),union(u,v))*.
% 299.99/300.66  206150[22:Res:205574.1,12.0] || equal(unordered_pair(u,v),singleton(singleton(identity_relation)))** -> equal(singleton(identity_relation),v) equal(singleton(identity_relation),u).
% 299.99/300.66  206509[7:SpR:50855.1,165794.1] || member(singleton(u),subset_relation) -> equal(integer_of(first(singleton(u))),identity_relation) subclass(intersection(v,u),omega)*.
% 299.99/300.66  206526[7:Res:165794.1,1303.1] inductive(intersection(u,singleton(v))) ||  -> equal(integer_of(v),identity_relation) equal(intersection(u,singleton(v)),omega)**.
% 299.99/300.66  206532[7:SpR:50855.1,165795.1] || member(singleton(u),subset_relation) -> equal(integer_of(first(singleton(u))),identity_relation) subclass(intersection(u,v),omega)*.
% 299.99/300.66  206553[7:Res:165795.1,1303.1] inductive(intersection(singleton(u),v)) ||  -> equal(integer_of(u),identity_relation) equal(intersection(singleton(u),v),omega)**.
% 299.99/300.66  206559[7:SpR:50855.1,206540.1] || member(singleton(u),subset_relation) -> equal(integer_of(first(singleton(u))),identity_relation) subclass(complement(complement(u)),omega)*.
% 299.99/300.66  206568[7:Res:206540.1,1303.1] inductive(complement(complement(singleton(u)))) ||  -> equal(integer_of(u),identity_relation) equal(complement(complement(singleton(u))),omega)**.
% 299.99/300.66  206569[7:Res:206540.1,8825.1] || member(u,ordinal_numbers) -> equal(integer_of(v),identity_relation) member(u,complement(singleton(v)))* member(u,omega).
% 299.99/300.66  207273[14:SpL:3606.0,165368.0] || equal(symmetric_difference(cross_product(u,v),w),singleton(identity_relation)) -> member(identity_relation,complement(restrict(w,u,v)))*.
% 299.99/300.66  207274[14:SpL:3603.0,165368.0] || equal(symmetric_difference(u,cross_product(v,w)),singleton(identity_relation)) -> member(identity_relation,complement(restrict(u,v,w)))*.
% 299.99/300.66  207363[18:SpL:3606.0,190543.0] || equal(symmetric_difference(cross_product(u,v),w),symmetrization_of(identity_relation)) -> member(identity_relation,complement(restrict(w,u,v)))*.
% 299.99/300.66  207364[18:SpL:3603.0,190543.0] || equal(symmetric_difference(u,cross_product(v,w)),symmetrization_of(identity_relation)) -> member(identity_relation,complement(restrict(u,v,w)))*.
% 299.99/300.66  207482[18:SpL:3606.0,190652.0] || equal(symmetric_difference(cross_product(u,v),w),inverse(identity_relation)) -> member(identity_relation,complement(restrict(w,u,v)))*.
% 299.99/300.66  207483[18:SpL:3603.0,190652.0] || equal(symmetric_difference(u,cross_product(v,w)),inverse(identity_relation)) -> member(identity_relation,complement(restrict(u,v,w)))*.
% 299.99/300.66  207848[24:MRR:196951.3,207847.0] function(singleton(u)) || subclass(range_of(singleton(u)),identity_relation)* equal(cross_product(identity_relation,identity_relation),identity_relation) -> .
% 299.99/300.66  207852[24:MRR:196835.3,207851.0] function(range_of(identity_relation)) || subclass(range_of(range_of(identity_relation)),identity_relation)* equal(cross_product(identity_relation,identity_relation),identity_relation) -> .
% 299.99/300.66  207891[24:Rew:207558.1,207625.1] operation(u) || asymmetric(v,identity_relation) -> equal(segment(intersection(v,inverse(v)),identity_relation,u),identity_relation)**.
% 299.99/300.66  207892[24:Rew:207558.1,207629.1] operation(u) || member(image(v,identity_relation),ordinal_numbers) -> subclass(apply(v,u),image(v,identity_relation))*.
% 299.99/300.66  208478[7:SpR:13260.1,962.0] ||  -> equal(cross_product(u,v),identity_relation) member(singleton(first(regular(cross_product(u,v)))),regular(cross_product(u,v)))*.
% 299.99/300.66  208510[7:SpL:13260.1,130942.0] || subclass(regular(cross_product(u,v)),w)* well_ordering(ordinal_numbers,w) -> equal(cross_product(u,v),identity_relation).
% 299.99/300.66  208532[7:SpL:13260.1,132438.0] || equal(u,regular(cross_product(v,w)))* well_ordering(ordinal_numbers,u)* -> equal(cross_product(v,w),identity_relation).
% 299.99/300.66  208559[15:SpL:3606.0,165538.0] || subclass(ordinal_numbers,symmetric_difference(cross_product(u,v),w)) -> member(range_of(identity_relation),complement(restrict(w,u,v)))*.
% 299.99/300.66  208560[15:SpL:3603.0,165538.0] || subclass(ordinal_numbers,symmetric_difference(u,cross_product(v,w))) -> member(range_of(identity_relation),complement(restrict(u,v,w)))*.
% 299.99/300.66  209022[25:Rew:208820.0,208884.0] || asymmetric(u,identity_relation) -> equal(range__dfg(intersection(u,inverse(u)),ordinal_numbers,identity_relation),second(not_subclass_element(identity_relation,identity_relation)))**.
% 299.99/300.66  209309[25:SpL:208840.0,37.0] || member(ordered_pair(singleton(singleton(identity_relation)),u),rotate(v))* -> member(ordered_pair(ordered_pair(ordinal_numbers,u),identity_relation),v).
% 299.99/300.66  209310[25:SpL:208840.0,40.0] || member(ordered_pair(singleton(singleton(identity_relation)),u),flip(v))* -> member(ordered_pair(ordered_pair(ordinal_numbers,identity_relation),u),v).
% 299.99/300.66  209340[25:MRR:208361.3,209339.0] operation(u) || equal(singleton(identity_relation),u)* member(singleton(singleton(identity_relation)),cross_product(ordinal_numbers,ordinal_numbers))* -> .
% 299.99/300.66  209657[25:SpR:50855.1,208841.0] || member(singleton(u),subset_relation) -> equal(unordered_pair(identity_relation,unordered_pair(ordinal_numbers,u)),ordered_pair(ordinal_numbers,first(singleton(u))))**.
% 299.99/300.66  209746[25:MRR:209745.0,162891.0] ||  -> equal(apply(choice,ordered_pair(ordinal_numbers,ordinal_numbers)),unordered_pair(ordinal_numbers,identity_relation))** equal(apply(choice,ordered_pair(ordinal_numbers,ordinal_numbers)),identity_relation).
% 299.99/300.66  209867[24:SpR:59.0,207863.1] operation(image(element_relation,complement(u))) ||  -> subclass(symmetric_difference(power_class(u),ordinal_numbers),successor(image(element_relation,complement(u))))*.
% 299.99/300.66  209899[24:Res:207866.1,8825.1] operation(u) || member(v,ordinal_numbers) -> member(v,successor(u)) member(v,symmetric_difference(ordinal_numbers,u))*.
% 299.99/300.66  210075[15:SpL:3606.0,208593.0] || equal(symmetric_difference(cross_product(u,v),w),ordinal_numbers) -> member(range_of(identity_relation),complement(restrict(w,u,v)))*.
% 299.99/300.66  210076[15:SpL:3603.0,208593.0] || equal(symmetric_difference(u,cross_product(v,w)),ordinal_numbers) -> member(range_of(identity_relation),complement(restrict(u,v,w)))*.
% 299.99/300.66  210335[8:Rew:160491.0,210291.1] || member(not_subclass_element(u,v),complement(w))* subclass(u,union(w,identity_relation)) -> subclass(u,v).
% 299.99/300.66  210336[8:Rew:160491.0,210293.2] || member(sum_class(u),complement(v))* member(u,ordinal_numbers) subclass(ordinal_numbers,union(v,identity_relation)) -> .
% 299.99/300.66  210359[7:Res:13248.1,143186.0] ||  -> equal(intersection(symmetric_difference(ordinal_numbers,u),v),identity_relation) member(regular(intersection(symmetric_difference(ordinal_numbers,u),v)),complement(u))*.
% 299.99/300.66  210370[7:Res:13210.1,143186.0] ||  -> equal(intersection(u,symmetric_difference(ordinal_numbers,v)),identity_relation) member(regular(intersection(u,symmetric_difference(ordinal_numbers,v))),complement(v))*.
% 299.99/300.66  210390[21:Res:196416.2,143186.0] || member(u,ordinal_numbers) subclass(domain_relation,symmetric_difference(ordinal_numbers,v)) -> member(ordered_pair(u,identity_relation),complement(v))*.
% 299.99/300.66  210468[7:Res:13248.1,143226.0] || member(regular(intersection(symmetric_difference(ordinal_numbers,u),v)),u)* -> equal(intersection(symmetric_difference(ordinal_numbers,u),v),identity_relation).
% 299.99/300.66  210479[7:Res:13210.1,143226.0] || member(regular(intersection(u,symmetric_difference(ordinal_numbers,v))),v)* -> equal(intersection(u,symmetric_difference(ordinal_numbers,v)),identity_relation).
% 299.99/300.66  210499[21:Res:196416.2,143226.0] || member(u,ordinal_numbers) subclass(domain_relation,symmetric_difference(ordinal_numbers,v)) member(ordered_pair(u,identity_relation),v)* -> .
% 299.99/300.66  210795[8:SpL:481.0,210578.0] || equal(power_class(intersection(complement(u),complement(v))),ordinal_numbers)** -> equal(image(element_relation,union(u,v)),identity_relation).
% 299.99/300.66  210852[8:Res:210572.1,141.1] || equal(complement(sum_class(u)),ordinal_numbers)** well_ordering(element_relation,u) -> equal(u,ordinal_numbers) member(u,ordinal_numbers).
% 299.99/300.66  211046[8:Res:210572.1,8998.0] || equal(complement(cross_product(ordinal_numbers,cross_product(ordinal_numbers,ordinal_numbers))),ordinal_numbers)** -> equal(cross_product(ordinal_numbers,cross_product(ordinal_numbers,ordinal_numbers)),composition_function).
% 299.99/300.66  211051[8:Res:210572.1,123.0] || equal(complement(compose(restrict(u,v,v),restrict(u,v,v))),ordinal_numbers)** -> transitive(u,v).
% 299.99/300.66  211137[8:Res:210572.1,8664.1] || equal(complement(compose(u,inverse(u))),ordinal_numbers)** subclass(u,cross_product(ordinal_numbers,ordinal_numbers)) -> function(u).
% 299.99/300.66  211157[8:Res:210572.1,117508.1] operation(u) || equal(complement(cantor(cantor(u))),ordinal_numbers)** -> equal(cantor(cantor(u)),range_of(u)).
% 299.99/300.66  212338[8:Rew:51324.2,212326.2] || member(singleton(u),subset_relation) member(u,subset_relation) equal(complement(singleton(first(u))),ordinal_numbers)** -> .
% 299.99/300.66  213084[8:SpR:210579.1,3606.0] || equal(complement(complement(restrict(u,v,w))),ordinal_numbers)** -> equal(symmetric_difference(cross_product(v,w),u),identity_relation).
% 299.99/300.66  213085[8:SpR:210579.1,3603.0] || equal(complement(complement(restrict(u,v,w))),ordinal_numbers)** -> equal(symmetric_difference(u,cross_product(v,w)),identity_relation).
% 299.99/300.66  213612[5:SpR:50855.1,151877.0] || member(singleton(u),subset_relation) -> subclass(intersection(u,v),complement(recursion_equation_functions(w)))* function(first(singleton(u))).
% 299.99/300.66  213649[5:SpR:50855.1,213622.0] || member(singleton(u),subset_relation) -> subclass(complement(complement(u)),complement(recursion_equation_functions(v)))* function(first(singleton(u))).
% 299.99/300.66  213661[5:Res:213622.0,8825.1] || member(u,ordinal_numbers) -> function(v) member(u,complement(singleton(v)))* member(u,complement(recursion_equation_functions(w)))*.
% 299.99/300.66  213673[5:SpR:50855.1,151512.0] || member(singleton(u),subset_relation) -> subclass(intersection(v,u),complement(recursion_equation_functions(w)))* function(first(singleton(u))).
% 299.99/300.66  214040[5:Res:40074.1,152274.0] || subclass(ordinal_numbers,complement(complement(complement(singleton(unordered_pair(u,v))))))* -> subclass(singleton(unordered_pair(u,v)),w)*.
% 299.99/300.66  214053[5:Res:127147.1,152274.0] || subclass(ordinal_numbers,complement(complement(complement(singleton(least(element_relation,omega))))))* -> subclass(singleton(least(element_relation,omega)),u)*.
% 299.99/300.66  214054[5:Res:126679.1,152274.0] || subclass(omega,complement(complement(complement(singleton(least(element_relation,omega))))))* -> subclass(singleton(least(element_relation,omega)),u)*.
% 299.99/300.66  214061[21:Res:196904.1,152274.0] || subclass(domain_relation,complement(singleton(singleton(singleton(singleton(identity_relation))))))* -> subclass(singleton(singleton(singleton(singleton(identity_relation)))),u)*.
% 299.99/300.66  214066[5:Res:39298.1,152274.0] || subclass(ordinal_numbers,complement(complement(complement(singleton(ordered_pair(u,v))))))* -> subclass(singleton(ordered_pair(u,v)),w)*.
% 299.99/300.66  214493[25:SpL:208985.1,8651.0] operation(u) || member(ordered_pair(v,u),rest_of(w))* -> equal(restrict(w,v,ordinal_numbers),ordinal_numbers).
% 299.99/300.66  214529[25:SpL:208985.1,100.0] operation(u) || member(ordered_pair(v,ordered_pair(w,u)),composition_function)* -> equal(compose(v,w),ordinal_numbers).
% 299.99/300.66  214548[25:SpL:208985.1,8651.0] operation(u) || member(ordered_pair(v,ordinal_numbers),rest_of(w))* -> equal(restrict(w,v,ordinal_numbers),u)*.
% 299.99/300.66  214591[25:SpL:208985.1,100.0] operation(u) || member(ordered_pair(v,ordered_pair(w,ordinal_numbers)),composition_function)* -> equal(compose(v,w),u)*.
% 299.99/300.66  214622[25:MRR:214509.1,18.1] operation(u) || member(ordered_pair(v,u),cross_product(ordinal_numbers,ordinal_numbers))* -> member(ordered_pair(v,ordinal_numbers),element_relation).
% 299.99/300.66  214910[5:SpR:50855.1,151501.1] || member(singleton(u),subset_relation) member(first(singleton(u)),v)* -> subclass(intersection(w,u),v)*.
% 299.99/300.66  214931[0:Res:151501.1,1303.1] inductive(intersection(u,singleton(v))) || member(v,omega) -> equal(intersection(u,singleton(v)),omega)**.
% 299.99/300.66  214964[5:SpR:189.0,151502.1] ||  -> member(u,image(element_relation,power_class(v))) subclass(intersection(w,singleton(u)),power_class(image(element_relation,complement(v))))*.
% 299.99/300.66  214968[5:SpR:50855.1,151502.1] || member(singleton(u),subset_relation) -> member(first(singleton(u)),v) subclass(intersection(w,u),complement(v))*.
% 299.99/300.66  215001[5:SpR:50855.1,151861.1] || member(singleton(u),subset_relation) member(first(singleton(u)),v)* -> subclass(intersection(u,w),v)*.
% 299.99/300.66  215027[0:Res:151861.1,1303.1] inductive(intersection(singleton(u),v)) || member(u,omega) -> equal(intersection(singleton(u),v),omega)**.
% 299.99/300.66  215050[5:SpR:50855.1,215011.1] || member(singleton(u),subset_relation) member(first(singleton(u)),v)* -> subclass(complement(complement(u)),v).
% 299.99/300.66  215061[5:Res:215011.1,1303.1] inductive(complement(complement(singleton(u)))) || member(u,omega) -> equal(complement(complement(singleton(u))),omega)**.
% 299.99/300.66  215069[5:Res:215011.1,8825.1] || member(u,v)* member(w,ordinal_numbers) -> member(w,complement(singleton(u)))* member(w,v)*.
% 299.99/300.66  215094[5:SpR:189.0,151862.1] ||  -> member(u,image(element_relation,power_class(v))) subclass(intersection(singleton(u),w),power_class(image(element_relation,complement(v))))*.
% 299.99/300.66  215098[5:SpR:50855.1,151862.1] || member(singleton(u),subset_relation) -> member(first(singleton(u)),v) subclass(intersection(u,w),complement(v))*.
% 299.99/300.66  215146[5:SpR:189.0,215108.1] ||  -> member(u,image(element_relation,power_class(v))) subclass(complement(complement(singleton(u))),power_class(image(element_relation,complement(v))))*.
% 299.99/300.66  215150[5:SpR:50855.1,215108.1] || member(singleton(u),subset_relation) -> member(first(singleton(u)),v) subclass(complement(complement(u)),complement(v))*.
% 299.99/300.66  215163[5:Res:215108.1,8825.1] || member(u,ordinal_numbers) -> member(v,w)* member(u,complement(singleton(v)))* member(u,complement(w))*.
% 299.99/300.66  215173[8:SpR:211432.1,155157.1] || equal(complement(u),ordinal_numbers) subclass(complement(u),v) -> subclass(symmetric_difference(v,complement(u)),identity_relation)*.
% 299.99/300.66  215177[8:SpR:211586.1,155157.1] || equal(symmetrization_of(identity_relation),ordinal_numbers) subclass(symmetrization_of(identity_relation),u) -> subclass(symmetric_difference(u,symmetrization_of(identity_relation)),identity_relation)*.
% 299.99/300.66  215180[0:SpR:59.0,155157.1] || subclass(image(element_relation,complement(u)),v) -> subclass(symmetric_difference(v,image(element_relation,complement(u))),power_class(u))*.
% 299.99/300.66  215185[8:SpR:211670.1,155157.1] || equal(power_class(u),ordinal_numbers) subclass(power_class(u),v) -> subclass(symmetric_difference(v,power_class(u)),identity_relation)*.
% 299.99/300.66  215612[8:SpR:481.0,215487.1] || subclass(image(element_relation,union(u,v)),identity_relation) -> subclass(ordinal_numbers,power_class(intersection(complement(u),complement(v))))*.
% 299.99/300.66  216346[11:SpR:154737.1,80250.0] || subclass(complement(image(successor_relation,ordinal_numbers)),complement(singleton(identity_relation)))* -> equal(power_class(complement(image(successor_relation,ordinal_numbers))),identity_relation).
% 299.99/300.66  216588[8:SpL:481.0,215660.0] || subclass(power_class(intersection(complement(u),complement(v))),identity_relation)* -> member(identity_relation,image(element_relation,union(u,v))).
% 299.99/300.66  216608[8:SpL:481.0,215661.0] || subclass(power_class(intersection(complement(u),complement(v))),identity_relation)* -> member(omega,image(element_relation,union(u,v))).
% 299.99/300.66  216783[8:SpR:216188.1,481.0] || equal(image(element_relation,union(u,v)),identity_relation) -> equal(power_class(intersection(complement(u),complement(v))),ordinal_numbers)**.
% 299.99/300.66  216903[8:SpL:216188.1,18791.0] || equal(identity_relation,u) member(v,symmetric_difference(complement(w),ordinal_numbers))* -> member(v,union(w,u))*.
% 299.99/300.66  217256[8:Rew:140613.0,216848.1] || equal(identity_relation,u) subclass(ordinal_numbers,symmetric_difference(ordinal_numbers,v)) member(omega,union(v,u))* -> .
% 299.99/300.66  217259[8:Rew:140613.0,216902.1] || equal(identity_relation,u) member(v,symmetric_difference(ordinal_numbers,w))* member(v,union(w,u))* -> .
% 299.99/300.66  217336[8:SpL:481.0,216227.0] || equal(image(element_relation,power_class(intersection(complement(u),complement(v)))),power_class(image(element_relation,union(u,v))))** -> .
% 299.99/300.66  217457[8:MRR:194652.2,217454.0] || member(apply(choice,complement(cross_product(ordinal_numbers,ordinal_numbers))),subset_relation)* member(complement(cross_product(ordinal_numbers,ordinal_numbers)),ordinal_numbers) -> .
% 299.99/300.66  217468[8:EmS:13166.0,13166.1,75.1,211494.1] one_to_one(union(u,v)) || equal(union(u,v),ordinal_numbers)** -> member(identity_relation,cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.66  217470[8:EmS:13166.0,13166.1,82.1,211494.1] operation(union(u,v)) || equal(union(u,v),ordinal_numbers)** -> member(identity_relation,cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.66  217840[8:Rew:17351.0,217828.2] || equal(complement(complement(symmetrization_of(u))),identity_relation)** connected(u,v)* -> equal(cross_product(v,v),identity_relation)**.
% 299.99/300.66  217950[7:Res:52.1,17315.0] inductive(recursion_equation_functions(u)) ||  -> equal(image(successor_relation,recursion_equation_functions(u)),identity_relation) function(regular(image(successor_relation,recursion_equation_functions(u))))*.
% 299.99/300.66  218048[8:SpL:481.0,217692.0] || equal(power_class(intersection(complement(u),complement(v))),identity_relation)** -> equal(image(element_relation,union(u,v)),ordinal_numbers).
% 299.99/300.66  218278[8:Res:9618.2,217144.1] || member(ordered_pair(u,v),cross_product(ordinal_numbers,ordinal_numbers))* subclass(composition_function,w)* equal(identity_relation,w) -> .
% 299.99/300.66  218391[21:Res:41203.1,196454.0] || member(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers)* subclass(domain_relation,rest_relation) -> equal(rest_of(least(element_relation,domain_relation)),identity_relation).
% 299.99/300.66  218414[21:Res:80082.1,196454.0] || member(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers)* subclass(domain_relation,rest_relation) -> equal(rest_of(least(element_relation,rest_relation)),identity_relation).
% 299.99/300.66  218415[21:Res:80198.1,196454.0] || member(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers)* subclass(domain_relation,rest_relation) -> equal(rest_of(least(element_relation,element_relation)),identity_relation).
% 299.99/300.66  218567[21:Res:41203.1,196455.0] || member(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers)* subclass(rest_relation,domain_relation) -> equal(rest_of(least(element_relation,domain_relation)),identity_relation).
% 299.99/300.66  218590[21:Res:80082.1,196455.0] || member(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers)* subclass(rest_relation,domain_relation) -> equal(rest_of(least(element_relation,rest_relation)),identity_relation).
% 299.99/300.66  218591[21:Res:80198.1,196455.0] || member(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers)* subclass(rest_relation,domain_relation) -> equal(rest_of(least(element_relation,element_relation)),identity_relation).
% 299.99/300.66  218699[7:Res:13125.2,973.0] || subclass(omega,successor_relation) -> equal(integer_of(singleton(singleton(singleton(u)))),identity_relation)** equal(successor(singleton(u)),u).
% 299.99/300.66  218711[21:SpR:218397.1,154.1] || subclass(domain_relation,rest_relation) member(range_of(identity_relation),recursion_equation_functions(u))* -> equal(compose(u,identity_relation),range_of(identity_relation)).
% 299.99/300.66  218720[21:SpL:218397.1,28976.1] || subclass(domain_relation,rest_relation) subclass(rest_relation,inverse(subset_relation)) member(ordered_pair(range_of(identity_relation),identity_relation),subset_relation)* -> .
% 299.99/300.66  218781[21:SpR:218573.1,154.1] || subclass(rest_relation,domain_relation) member(range_of(identity_relation),recursion_equation_functions(u))* -> equal(compose(u,identity_relation),range_of(identity_relation)).
% 299.99/300.66  218791[21:SpL:218573.1,28976.1] || subclass(rest_relation,domain_relation) subclass(rest_relation,inverse(subset_relation)) member(ordered_pair(range_of(identity_relation),identity_relation),subset_relation)* -> .
% 299.99/300.66  218852[21:SpR:218384.1,154.1] || subclass(domain_relation,rest_relation) member(singleton(u),recursion_equation_functions(v))* -> equal(compose(v,identity_relation),singleton(u)).
% 299.99/300.66  218865[21:SpL:218384.1,28976.1] || subclass(domain_relation,rest_relation) subclass(rest_relation,inverse(subset_relation)) member(ordered_pair(singleton(u),identity_relation),subset_relation)* -> .
% 299.99/300.66  218916[21:SpR:218560.1,154.1] || subclass(rest_relation,domain_relation) member(singleton(u),recursion_equation_functions(v))* -> equal(compose(v,identity_relation),singleton(u)).
% 299.99/300.66  218930[21:SpL:218560.1,28976.1] || subclass(rest_relation,domain_relation) subclass(rest_relation,inverse(subset_relation)) member(ordered_pair(singleton(u),identity_relation),subset_relation)* -> .
% 299.99/300.66  219240[8:Res:9618.2,219073.1] || member(ordered_pair(u,v),cross_product(ordinal_numbers,ordinal_numbers))* subclass(composition_function,w)* subclass(w,identity_relation)* -> .
% 299.99/300.66  219372[21:SpR:66834.1,198454.1] || well_ordering(u,ordinal_numbers) equal(rest_of(least(u,omega)),rest_relation)** -> equal(least(u,omega),identity_relation).
% 299.99/300.66  219577[8:Res:13125.2,67561.0] || subclass(omega,symmetric_difference(complement(u),ordinal_numbers))* -> equal(integer_of(v),identity_relation) member(v,union(u,identity_relation))*.
% 299.99/300.66  219584[8:Res:40074.1,67561.0] || subclass(ordinal_numbers,complement(complement(symmetric_difference(complement(u),ordinal_numbers))))* -> member(unordered_pair(v,w),union(u,identity_relation))*.
% 299.99/300.66  219602[8:Res:13227.2,67561.0] || subclass(u,symmetric_difference(complement(v),ordinal_numbers)) -> equal(u,identity_relation) member(regular(u),union(v,identity_relation))*.
% 299.99/300.66  219609[8:Res:127147.1,67561.0] || subclass(ordinal_numbers,complement(complement(symmetric_difference(complement(u),ordinal_numbers))))* -> member(least(element_relation,omega),union(u,identity_relation)).
% 299.99/300.66  219610[8:Res:126679.1,67561.0] || subclass(omega,complement(complement(symmetric_difference(complement(u),ordinal_numbers))))* -> member(least(element_relation,omega),union(u,identity_relation)).
% 299.99/300.66  219622[8:Res:39298.1,67561.0] || subclass(ordinal_numbers,complement(complement(symmetric_difference(complement(u),ordinal_numbers))))* -> member(ordered_pair(v,w),union(u,identity_relation))*.
% 299.99/300.66  219794[8:Res:67614.1,8842.1] || member(unordered_pair(u,v),union(w,identity_relation))* subclass(ordinal_numbers,complement(symmetric_difference(complement(w),ordinal_numbers))) -> .
% 299.99/300.66  219802[8:Res:67614.1,125973.1] || member(least(element_relation,omega),union(u,identity_relation))* subclass(ordinal_numbers,complement(symmetric_difference(complement(u),ordinal_numbers))) -> .
% 299.99/300.66  219803[8:Res:67614.1,125896.1] || member(least(element_relation,omega),union(u,identity_relation))* subclass(omega,complement(symmetric_difference(complement(u),ordinal_numbers))) -> .
% 299.99/300.66  219810[8:Res:67614.1,8841.1] || member(ordered_pair(u,v),union(w,identity_relation))* subclass(ordinal_numbers,complement(symmetric_difference(complement(w),ordinal_numbers))) -> .
% 299.99/300.66  219989[18:MRR:194537.1,219934.0] || well_ordering(u,symmetrization_of(identity_relation)) -> member(least(u,singleton(regular(symmetrization_of(identity_relation)))),singleton(regular(symmetrization_of(identity_relation))))*.
% 299.99/300.66  220014[8:Res:13125.2,160772.0] || subclass(omega,symmetric_difference(ordinal_numbers,u)) member(v,union(u,identity_relation))* -> equal(integer_of(v),identity_relation).
% 299.99/300.66  220040[8:Res:13227.2,160772.0] || subclass(u,symmetric_difference(ordinal_numbers,v)) member(regular(u),union(v,identity_relation))* -> equal(u,identity_relation).
% 299.99/300.66  220054[8:Res:49995.1,160772.0] || member(symmetric_difference(ordinal_numbers,u),subset_relation) member(singleton(first(symmetric_difference(ordinal_numbers,u))),union(u,identity_relation))* -> .
% 299.99/300.66  220194[8:SpL:6355.1,217704.0] || equal(complement(complement(singleton(not_subclass_element(cross_product(u,v),w)))),identity_relation)** -> subclass(cross_product(u,v),w).
% 299.99/300.66  220355[8:Rew:66036.0,220325.1] || subclass(intersection(complement(u),complement(v)),identity_relation)* -> equal(complement(intersection(union(u,v),ordinal_numbers)),identity_relation).
% 299.99/300.66  220391[21:Res:196656.1,66086.1] || subclass(domain_relation,flip(complement(compose(element_relation,ordinal_numbers)))) member(ordered_pair(ordered_pair(u,v),identity_relation),element_relation)* -> .
% 299.99/300.66  220399[21:Res:196656.1,5.0] || subclass(domain_relation,flip(u))* subclass(u,v)* -> member(ordered_pair(ordered_pair(w,x),identity_relation),v)*.
% 299.99/300.66  220404[21:Res:196656.1,3617.0] || subclass(domain_relation,flip(symmetric_difference(u,v))) -> member(ordered_pair(ordered_pair(w,x),identity_relation),union(u,v))*.
% 299.99/300.66  220405[21:Res:196656.1,19559.0] || subclass(domain_relation,flip(symmetric_difference(u,singleton(u))))* -> member(ordered_pair(ordered_pair(v,w),identity_relation),successor(u))*.
% 299.99/300.66  220406[21:Res:196656.1,19676.0] || subclass(domain_relation,flip(symmetric_difference(u,inverse(u))))* -> member(ordered_pair(ordered_pair(v,w),identity_relation),symmetrization_of(u))*.
% 299.99/300.66  220465[21:Res:196656.1,117449.1] operation(u) || subclass(domain_relation,flip(cantor(u))) -> member(ordered_pair(v,w),cantor(cantor(u)))*.
% 299.99/300.66  220493[21:Res:196657.1,66086.1] || subclass(domain_relation,rotate(complement(compose(element_relation,ordinal_numbers)))) member(ordered_pair(ordered_pair(u,identity_relation),v),element_relation)* -> .
% 299.99/300.66  220501[21:Res:196657.1,5.0] || subclass(domain_relation,rotate(u))* subclass(u,v)* -> member(ordered_pair(ordered_pair(w,identity_relation),x),v)*.
% 299.99/300.66  220506[21:Res:196657.1,3617.0] || subclass(domain_relation,rotate(symmetric_difference(u,v))) -> member(ordered_pair(ordered_pair(w,identity_relation),x),union(u,v))*.
% 299.99/300.66  220507[21:Res:196657.1,19559.0] || subclass(domain_relation,rotate(symmetric_difference(u,singleton(u))))* -> member(ordered_pair(ordered_pair(v,identity_relation),w),successor(u))*.
% 299.99/300.66  220508[21:Res:196657.1,19676.0] || subclass(domain_relation,rotate(symmetric_difference(u,inverse(u))))* -> member(ordered_pair(ordered_pair(v,identity_relation),w),symmetrization_of(u))*.
% 299.99/300.66  220694[7:MRR:220680.2,13102.1] || connected(u,singleton(v)) -> well_ordering(u,singleton(v)) equal(regular(not_well_ordering(u,singleton(v))),v)**.
% 299.99/300.66  221018[8:SpR:219919.1,66834.1] || equal(singleton(least(u,omega)),identity_relation)** well_ordering(u,ordinal_numbers) -> equal(least(u,omega),identity_relation).
% 299.99/300.66  221037[8:Obv:221034.1] || equal(singleton(u),identity_relation) -> equal(regular(unordered_pair(v,u)),v)** equal(unordered_pair(v,u),identity_relation).
% 299.99/300.66  221038[8:Obv:221033.1] || equal(singleton(u),identity_relation) -> equal(regular(unordered_pair(u,v)),v)** equal(unordered_pair(u,v),identity_relation).
% 299.99/300.66  221114[7:Res:13236.2,28.1] || well_ordering(u,complement(v)) member(least(u,complement(v)),v)* -> equal(complement(v),identity_relation).
% 299.99/300.66  221123[7:Res:13236.2,5.0] || well_ordering(u,v) subclass(v,w) -> equal(v,identity_relation) member(least(u,v),w)*.
% 299.99/300.66  221143[7:Res:13236.2,50007.0] || well_ordering(u,subset_relation) subclass(ordinal_numbers,v) -> equal(subset_relation,identity_relation) member(least(u,subset_relation),v)*.
% 299.99/300.66  221148[8:Res:13236.2,14679.1] || well_ordering(u,inverse(subset_relation)) member(least(u,inverse(subset_relation)),subset_relation)* -> equal(inverse(subset_relation),identity_relation).
% 299.99/300.66  221155[8:Res:13236.2,116166.0] || well_ordering(u,recursion_equation_functions(v)) -> equal(recursion_equation_functions(v),identity_relation) member(cantor(least(u,recursion_equation_functions(v))),ordinal_numbers)*.
% 299.99/300.66  222565[21:SpR:145758.0,196460.2] || member(cross_product(u,ordinal_numbers),ordinal_numbers)* subclass(domain_relation,union_of_range_map) -> equal(sum_class(image(ordinal_numbers,u)),identity_relation).
% 299.99/300.66  222693[5:Res:41183.1,31610.0] || subclass(rest_relation,successor_relation) -> subclass(u,v) equal(rest_of(not_subclass_element(u,v)),successor(not_subclass_element(u,v)))**.
% 299.99/300.66  222702[5:Res:18510.1,31610.0] function(u) || subclass(rest_relation,successor_relation) -> equal(rest_of(apply(u,v)),successor(apply(u,v)))**.
% 299.99/300.66  223118[11:SpR:19486.0,217117.1] || equal(intersection(complement(u),complement(inverse(u))),identity_relation)** -> equal(complement(image(element_relation,symmetrization_of(u))),identity_relation).
% 299.99/300.66  223436[11:SpR:19485.0,217117.1] || equal(intersection(complement(u),complement(singleton(u))),identity_relation)** -> equal(complement(image(element_relation,successor(u))),identity_relation).
% 299.99/300.66  223488[21:Rew:140613.0,223440.1,66036.0,223440.1] ||  -> equal(range_of(u),identity_relation) equal(complement(image(element_relation,successor(inverse(u)))),power_class(symmetric_difference(ordinal_numbers,inverse(u))))**.
% 299.99/300.66  223679[25:SpR:208985.1,13413.1] operation(u) || subclass(omega,element_relation) -> equal(integer_of(ordered_pair(v,ordinal_numbers)),identity_relation)** member(v,u)*.
% 299.99/300.66  223680[24:SpR:207572.1,13413.1] operation(u) || subclass(omega,element_relation) -> equal(integer_of(singleton(singleton(identity_relation))),identity_relation)** member(identity_relation,u)*.
% 299.99/300.66  223685[25:SpR:208985.1,13413.1] operation(u) || subclass(omega,element_relation) -> equal(integer_of(ordered_pair(v,u)),identity_relation)** member(v,ordinal_numbers).
% 299.99/300.66  223703[8:SpR:160927.0,216188.1] || equal(intersection(complement(u),union(v,identity_relation)),identity_relation)** -> equal(union(u,symmetric_difference(ordinal_numbers,v)),ordinal_numbers).
% 299.99/300.66  223721[8:SpR:160927.0,140613.0] ||  -> equal(symmetric_difference(ordinal_numbers,intersection(complement(u),union(v,identity_relation))),intersection(union(u,symmetric_difference(ordinal_numbers,v)),ordinal_numbers))**.
% 299.99/300.66  223723[8:SpR:160927.0,66340.0] ||  -> subclass(symmetric_difference(union(u,symmetric_difference(ordinal_numbers,v)),ordinal_numbers),union(intersection(complement(u),union(v,identity_relation)),identity_relation))*.
% 299.99/300.66  223729[8:SpR:160927.0,130710.0] ||  -> subclass(complement(power_class(intersection(complement(u),union(v,identity_relation)))),image(element_relation,union(u,symmetric_difference(ordinal_numbers,v))))*.
% 299.99/300.66  223754[8:SpR:160927.0,79560.1] ||  -> member(u,intersection(complement(v),union(w,identity_relation)))* subclass(singleton(u),union(v,symmetric_difference(ordinal_numbers,w))).
% 299.99/300.66  223782[8:SpR:160491.0,160927.0] ||  -> equal(complement(intersection(union(u,identity_relation),union(v,identity_relation))),union(symmetric_difference(ordinal_numbers,u),symmetric_difference(ordinal_numbers,v)))**.
% 299.99/300.66  223803[8:SpL:160927.0,210578.0] || equal(union(u,symmetric_difference(ordinal_numbers,v)),ordinal_numbers) -> equal(intersection(complement(u),union(v,identity_relation)),identity_relation)**.
% 299.99/300.66  223809[8:SpL:160927.0,9922.1] inductive(intersection(complement(u),union(v,identity_relation))) || equal(union(u,symmetric_difference(ordinal_numbers,v)),ordinal_numbers)** -> .
% 299.99/300.66  223839[14:SpL:160927.0,167597.0] || well_ordering(ordinal_numbers,union(u,symmetric_difference(ordinal_numbers,v))) -> member(identity_relation,intersection(complement(u),union(v,identity_relation)))*.
% 299.99/300.66  223844[8:SpL:160927.0,166753.1] inductive(intersection(complement(u),union(v,identity_relation))) || equal(union(u,symmetric_difference(ordinal_numbers,v)),omega)** -> .
% 299.99/300.66  223848[8:SpL:160927.0,217692.0] || equal(union(u,symmetric_difference(ordinal_numbers,v)),identity_relation) -> equal(intersection(complement(u),union(v,identity_relation)),ordinal_numbers)**.
% 299.99/300.66  223856[8:SpL:160927.0,216227.0] || equal(image(element_relation,union(u,symmetric_difference(ordinal_numbers,v))),power_class(intersection(complement(u),union(v,identity_relation))))** -> .
% 299.99/300.66  223862[8:SpL:160927.0,215661.0] || subclass(union(u,symmetric_difference(ordinal_numbers,v)),identity_relation) -> member(omega,intersection(complement(u),union(v,identity_relation)))*.
% 299.99/300.66  223863[8:SpL:160927.0,215660.0] || subclass(union(u,symmetric_difference(ordinal_numbers,v)),identity_relation) -> member(identity_relation,intersection(complement(u),union(v,identity_relation)))*.
% 299.99/300.66  223964[8:SpL:160491.0,13242.0] || subclass(omega,union(u,identity_relation)) member(v,symmetric_difference(ordinal_numbers,u))* -> equal(integer_of(v),identity_relation).
% 299.99/300.66  223968[7:SpL:59.0,13242.0] || subclass(omega,power_class(u)) member(v,image(element_relation,complement(u)))* -> equal(integer_of(v),identity_relation).
% 299.99/300.66  224020[8:SpR:160992.0,216188.1] || equal(intersection(union(u,identity_relation),complement(v)),identity_relation)** -> equal(union(symmetric_difference(ordinal_numbers,u),v),ordinal_numbers).
% 299.99/300.66  224038[8:SpR:160992.0,140613.0] ||  -> equal(symmetric_difference(ordinal_numbers,intersection(union(u,identity_relation),complement(v))),intersection(union(symmetric_difference(ordinal_numbers,u),v),ordinal_numbers))**.
% 299.99/300.66  224040[8:SpR:160992.0,66340.0] ||  -> subclass(symmetric_difference(union(symmetric_difference(ordinal_numbers,u),v),ordinal_numbers),union(intersection(union(u,identity_relation),complement(v)),identity_relation))*.
% 299.99/300.66  224046[8:SpR:160992.0,130710.0] ||  -> subclass(complement(power_class(intersection(union(u,identity_relation),complement(v)))),image(element_relation,union(symmetric_difference(ordinal_numbers,u),v)))*.
% 299.99/300.66  224071[8:SpR:160992.0,79560.1] ||  -> member(u,intersection(union(v,identity_relation),complement(w)))* subclass(singleton(u),union(symmetric_difference(ordinal_numbers,v),w)).
% 299.99/300.66  224118[8:SpR:154737.1,160992.0] || subclass(complement(u),union(v,identity_relation))* -> equal(union(symmetric_difference(ordinal_numbers,v),u),complement(complement(u))).
% 299.99/300.66  224121[8:SpL:160992.0,210578.0] || equal(union(symmetric_difference(ordinal_numbers,u),v),ordinal_numbers) -> equal(intersection(union(u,identity_relation),complement(v)),identity_relation)**.
% 299.99/300.66  224127[8:SpL:160992.0,9922.1] inductive(intersection(union(u,identity_relation),complement(v))) || equal(union(symmetric_difference(ordinal_numbers,u),v),ordinal_numbers)** -> .
% 299.99/300.66  224158[14:SpL:160992.0,167597.0] || well_ordering(ordinal_numbers,union(symmetric_difference(ordinal_numbers,u),v)) -> member(identity_relation,intersection(union(u,identity_relation),complement(v)))*.
% 299.99/300.66  224163[8:SpL:160992.0,166753.1] inductive(intersection(union(u,identity_relation),complement(v))) || equal(union(symmetric_difference(ordinal_numbers,u),v),omega)** -> .
% 299.99/300.66  224167[8:SpL:160992.0,217692.0] || equal(union(symmetric_difference(ordinal_numbers,u),v),identity_relation) -> equal(intersection(union(u,identity_relation),complement(v)),ordinal_numbers)**.
% 299.99/300.66  224175[8:SpL:160992.0,216227.0] || equal(image(element_relation,union(symmetric_difference(ordinal_numbers,u),v)),power_class(intersection(union(u,identity_relation),complement(v))))** -> .
% 299.99/300.66  224181[8:SpL:160992.0,215661.0] || subclass(union(symmetric_difference(ordinal_numbers,u),v),identity_relation) -> member(omega,intersection(union(u,identity_relation),complement(v)))*.
% 299.99/300.66  224182[8:SpL:160992.0,215660.0] || subclass(union(symmetric_difference(ordinal_numbers,u),v),identity_relation) -> member(identity_relation,intersection(union(u,identity_relation),complement(v)))*.
% 299.99/300.66  224687[26:Res:224681.0,13362.0] || subclass(omega,u) well_ordering(omega,u)* -> equal(integer_of(ordered_pair(identity_relation,least(omega,omega))),identity_relation)**.
% 299.99/300.66  224703[25:SpL:208985.1,194371.0] operation(u) || member(ordered_pair(v,ordinal_numbers),cross_product(ordinal_numbers,ordinal_numbers))* member(u,cantor(v))* -> .
% 299.99/300.66  224709[25:SpL:208985.1,194371.0] operation(u) || member(ordered_pair(v,u),cross_product(ordinal_numbers,ordinal_numbers))* member(ordinal_numbers,cantor(v)) -> .
% 299.99/300.66  224858[7:SpL:163.0,13340.0] || subclass(omega,symmetric_difference(u,v)) -> equal(integer_of(w),identity_relation) member(w,complement(intersection(u,v)))*.
% 299.99/300.66  224864[7:SpL:155665.0,13340.0] || subclass(omega,symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers)))* -> equal(integer_of(u),identity_relation) member(u,complement(subset_relation))*.
% 299.99/300.66  224865[7:SpL:155666.0,13340.0] || subclass(omega,symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation))* -> equal(integer_of(u),identity_relation) member(u,complement(subset_relation))*.
% 299.99/300.66  224981[26:Rew:224972.2,220283.3] || member(singleton(u),subset_relation)* subclass(omega,u) -> equal(integer_of(v),identity_relation)** equal(v,identity_relation).
% 299.99/300.66  225111[7:Obv:225046.1] || subclass(intersection(u,singleton(v)),w)* -> equal(intersection(u,singleton(v)),identity_relation) member(v,w).
% 299.99/300.66  225226[7:Obv:225149.1] || subclass(intersection(singleton(u),v),w)* -> equal(intersection(singleton(u),v),identity_relation) member(u,w).
% 299.99/300.66  225419[8:Res:193179.0,17312.1] || subclass(u,complement(inverse(singleton(regular(u)))))* -> asymmetric(singleton(regular(u)),v)* equal(u,identity_relation).
% 299.99/300.66  225503[8:SpL:162038.0,225445.0] || subclass(image(element_relation,symmetrization_of(identity_relation)),power_class(complement(inverse(identity_relation))))* -> equal(image(element_relation,symmetrization_of(identity_relation)),identity_relation).
% 299.99/300.66  225504[16:SpL:195257.0,225445.0] || subclass(image(element_relation,singleton(identity_relation)),power_class(complement(singleton(identity_relation))))* -> equal(image(element_relation,singleton(identity_relation)),identity_relation).
% 299.99/300.66  226212[7:SpL:163.0,17322.0] || subclass(u,symmetric_difference(v,w)) -> equal(u,identity_relation) member(regular(u),complement(intersection(v,w)))*.
% 299.99/300.66  226218[7:SpL:155665.0,17322.0] || subclass(u,symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers)))* -> equal(u,identity_relation) member(regular(u),complement(subset_relation)).
% 299.99/300.66  226219[7:SpL:155666.0,17322.0] || subclass(u,symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation))* -> equal(u,identity_relation) member(regular(u),complement(subset_relation)).
% 299.99/300.66  226382[7:Res:13258.1,28.1] || member(regular(restrict(complement(u),v,w)),u)* -> equal(restrict(complement(u),v,w),identity_relation).
% 299.99/300.66  226416[8:Res:13258.1,14679.1] || member(regular(restrict(inverse(subset_relation),u,v)),subset_relation)* -> equal(restrict(inverse(subset_relation),u,v),identity_relation).
% 299.99/300.66  226419[8:Res:13258.1,163154.0] ||  -> equal(restrict(symmetrization_of(identity_relation),u,v),identity_relation) member(regular(restrict(symmetrization_of(identity_relation),u,v)),inverse(identity_relation))*.
% 299.99/300.66  226626[8:SpL:116154.0,216284.1] || subclass(rest_relation,rest_of(restrict(u,v,singleton(w))))* subclass(segment(u,v,w),identity_relation) -> .
% 299.99/300.66  226860[21:Obv:226848.1] || subclass(rest_relation,rest_of(u)) -> equal(regular(unordered_pair(v,u)),v)** equal(unordered_pair(v,u),identity_relation).
% 299.99/300.66  226861[21:Obv:226847.1] || subclass(rest_relation,rest_of(u)) -> equal(regular(unordered_pair(u,v)),v)** equal(unordered_pair(u,v),identity_relation).
% 299.99/300.66  227150[8:SpL:189.0,217386.0] || equal(complement(power_class(image(element_relation,complement(u)))),identity_relation)** member(identity_relation,image(element_relation,power_class(u))) -> .
% 299.99/300.66  227172[8:SpL:189.0,217389.0] || equal(complement(complement(power_class(image(element_relation,complement(u))))),identity_relation)** -> member(identity_relation,image(element_relation,power_class(u))).
% 299.99/300.66  227211[8:SpR:189.0,217451.1] || equal(union(image(element_relation,power_class(u)),identity_relation),identity_relation) -> member(identity_relation,power_class(image(element_relation,complement(u))))*.
% 299.99/300.66  227293[21:Obv:227261.0] || subclass(rest_relation,union_of_range_map) member(u,ordinal_numbers)* subclass(domain_relation,union_of_range_map) -> equal(rest_of(u),identity_relation).
% 299.99/300.66  227389[8:SpL:189.0,217608.0] || equal(complement(power_class(image(element_relation,complement(u)))),identity_relation)** member(omega,image(element_relation,power_class(u))) -> .
% 299.99/300.66  227411[8:SpL:189.0,217611.0] || equal(complement(complement(power_class(image(element_relation,complement(u))))),identity_relation)** -> member(omega,image(element_relation,power_class(u))).
% 299.99/300.66  227450[8:SpR:189.0,217663.1] || equal(union(image(element_relation,power_class(u)),identity_relation),identity_relation) -> member(omega,power_class(image(element_relation,complement(u))))*.
% 299.99/300.66  227581[8:SpL:189.0,217695.0] || equal(complement(power_class(image(element_relation,complement(u)))),identity_relation)** equal(image(element_relation,power_class(u)),ordinal_numbers) -> .
% 299.99/300.66  227611[8:SpL:189.0,217696.0] || equal(complement(power_class(image(element_relation,complement(u)))),identity_relation)** subclass(ordinal_numbers,image(element_relation,power_class(u))) -> .
% 299.99/300.66  227633[8:SpL:189.0,217697.0] || equal(complement(power_class(image(element_relation,complement(u)))),identity_relation)** equal(image(element_relation,power_class(u)),omega) -> .
% 299.99/300.66  227655[8:SpL:189.0,217698.0] || equal(complement(power_class(image(element_relation,complement(u)))),identity_relation)** subclass(omega,image(element_relation,power_class(u))) -> .
% 299.99/300.66  227677[8:SpL:189.0,217699.0] || equal(complement(power_class(image(element_relation,complement(u)))),identity_relation)** subclass(domain_relation,image(element_relation,power_class(u))) -> .
% 299.99/300.66  227703[8:SpL:189.0,217700.0] || equal(complement(power_class(image(element_relation,complement(u)))),identity_relation)** member(image(element_relation,power_class(u)),subset_relation) -> .
% 299.99/300.66  228062[15:SpL:50855.1,219332.0] || member(singleton(u),subset_relation)* subclass(complement(u),identity_relation) -> equal(first(singleton(u)),range_of(identity_relation)).
% 299.99/300.66  228130[21:Rew:196554.1,228123.3] || member(u,subset_relation)* subclass(omega,domain_relation) -> equal(integer_of(u),identity_relation) equal(second(u),identity_relation).
% 299.99/300.66  228744[8:Rew:160491.0,228716.2] || member(power_class(u),complement(v))* member(u,ordinal_numbers) subclass(ordinal_numbers,union(v,identity_relation)) -> .
% 299.99/300.66  228764[8:SpL:189.0,222095.0] || subclass(power_class(image(element_relation,complement(u))),identity_relation)* -> equal(symmetric_difference(ordinal_numbers,image(element_relation,power_class(u))),identity_relation).
% 299.99/300.66  228900[8:MRR:228876.2,218132.1] || member(apply(choice,regular(symmetric_difference(ordinal_numbers,u))),complement(u))* -> equal(regular(symmetric_difference(ordinal_numbers,u)),identity_relation).
% 299.99/300.66  228901[16:MRR:228872.2,215767.0] ||  -> subclass(singleton(apply(choice,regular(complement(singleton(identity_relation))))),singleton(identity_relation))* equal(regular(complement(singleton(identity_relation))),identity_relation).
% 299.99/300.66  229077[8:SpL:50855.1,222904.0] || member(singleton(u),subset_relation) subclass(u,inverse(subset_relation)) member(first(singleton(u)),subset_relation)* -> .
% 299.99/300.66  229189[8:Rew:162584.0,229091.1] || member(regular(intersection(symmetrization_of(identity_relation),u)),complement(inverse(identity_relation)))* -> equal(intersection(symmetrization_of(identity_relation),u),identity_relation).
% 299.99/300.66  229193[7:Rew:155665.0,229117.1] || member(regular(symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers))),subset_relation)* -> equal(symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers)),identity_relation).
% 299.99/300.66  229194[7:Rew:155666.0,229118.1] || member(regular(symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation)),subset_relation)* -> equal(symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation),identity_relation).
% 299.99/300.66  229767[8:Rew:162584.0,229534.1] || member(regular(intersection(u,symmetrization_of(identity_relation))),complement(inverse(identity_relation)))* -> equal(intersection(u,symmetrization_of(identity_relation)),identity_relation).
% 299.99/300.66  230696[8:MRR:230644.2,219791.1] || member(unordered_pair(u,v),union(w,identity_relation))* subclass(ordinal_numbers,regular(symmetric_difference(complement(w),ordinal_numbers))) -> .
% 299.99/300.66  231265[8:SpR:208708.1,17447.1] ||  -> equal(singleton(u),identity_relation) equal(symmetric_difference(u,ordinal_numbers),identity_relation) member(regular(symmetric_difference(u,ordinal_numbers)),complement(u))*.
% 299.99/300.66  231266[8:SpR:188530.1,17447.1] || member(u,ordinals_with_null_class_as_identity) -> equal(symmetric_difference(u,ordinal_numbers),identity_relation) member(regular(symmetric_difference(u,ordinal_numbers)),complement(u))*.
% 299.99/300.66  231280[7:SpR:154737.1,17447.1] || subclass(u,v) -> equal(symmetric_difference(v,u),identity_relation) member(regular(symmetric_difference(v,u)),complement(u))*.
% 299.99/300.66  231323[7:Res:17447.1,9876.0] || subclass(complement(intersection(u,v)),w)* well_ordering(ordinal_numbers,w) -> equal(symmetric_difference(u,v),identity_relation).
% 299.99/300.66  231825[8:MRR:231790.2,218132.1] || member(not_subclass_element(regular(symmetric_difference(ordinal_numbers,u)),v),complement(u))* -> subclass(regular(symmetric_difference(ordinal_numbers,u)),v).
% 299.99/300.66  231860[8:SpR:162038.0,231812.0] ||  -> subclass(regular(image(element_relation,symmetrization_of(identity_relation))),power_class(complement(inverse(identity_relation))))* equal(image(element_relation,symmetrization_of(identity_relation)),identity_relation).
% 299.99/300.66  231861[16:SpR:195257.0,231812.0] ||  -> subclass(regular(image(element_relation,singleton(identity_relation))),power_class(complement(singleton(identity_relation))))* equal(image(element_relation,singleton(identity_relation)),identity_relation).
% 299.99/300.66  232036[7:SpL:155653.0,17323.0] || subclass(u,subset_relation) -> equal(u,identity_relation) member(regular(u),complement(compose(complement(element_relation),inverse(element_relation))))*.
% 299.99/300.66  232477[8:MRR:232469.2,162901.1] || member(unordered_pair(u,v),subset_relation)* subclass(ordinal_numbers,v) -> equal(regular(unordered_pair(u,v)),u).
% 299.99/300.66  232478[8:MRR:232468.2,162901.1] || member(unordered_pair(u,v),subset_relation)* subclass(ordinal_numbers,u) -> equal(regular(unordered_pair(u,v)),v).
% 299.99/300.66  232539[8:Res:919.1,230867.0] || equal(complement(not_subclass_element(restrict(subset_relation,u,v),w)),identity_relation)** -> subclass(restrict(subset_relation,u,v),w).
% 299.99/300.66  232613[8:Res:919.1,230939.0] || equal(regular(not_subclass_element(restrict(subset_relation,u,v),w)),ordinal_numbers)** -> subclass(restrict(subset_relation,u,v),w).
% 299.99/300.66  232808[8:Rew:162038.0,232762.1] || subclass(image(element_relation,symmetrization_of(identity_relation)),power_class(complement(inverse(identity_relation))))* -> subclass(ordinal_numbers,power_class(complement(inverse(identity_relation)))).
% 299.99/300.66  232809[16:Rew:195257.0,232763.1] || subclass(image(element_relation,singleton(identity_relation)),power_class(complement(singleton(identity_relation))))* -> subclass(ordinal_numbers,power_class(complement(singleton(identity_relation)))).
% 299.99/300.66  233035[8:Res:143160.0,69182.0] || member(regular(symmetric_difference(ordinal_numbers,compose(element_relation,ordinal_numbers))),element_relation)* -> equal(symmetric_difference(ordinal_numbers,compose(element_relation,ordinal_numbers)),identity_relation).
% 299.99/300.66  233115[8:SpL:6355.1,233014.0] || equal(complement(regular(singleton(not_subclass_element(cross_product(u,v),w)))),identity_relation)** -> subclass(cross_product(u,v),w).
% 299.99/300.66  233479[21:Res:161057.2,196372.0] || well_ordering(u,ordinal_numbers) -> equal(recursion_equation_functions(v),identity_relation) equal(cantor(cantor(least(u,recursion_equation_functions(v)))),identity_relation)**.
% 299.99/300.66  233561[21:Rew:162584.0,233501.1] || member(u,ordinal_numbers) subclass(domain_relation,symmetrization_of(identity_relation)) -> subclass(singleton(ordered_pair(u,identity_relation)),symmetrization_of(identity_relation))*.
% 299.99/300.66  233562[21:Rew:195239.0,233502.1] || member(u,ordinal_numbers) subclass(domain_relation,singleton(identity_relation)) -> subclass(singleton(ordered_pair(u,identity_relation)),singleton(identity_relation))*.
% 299.99/300.66  233578[21:MRR:233577.0,13126.0] || equal(compose(u,v),identity_relation)** member(v,ordinal_numbers) subclass(domain_relation,complement(compose_class(u)))* -> .
% 299.99/300.66  233729[25:Rew:233728.2,233722.3] operation(u) || subclass(omega,union_of_range_map) -> equal(integer_of(singleton(singleton(identity_relation))),identity_relation)** equal(ordinal_numbers,u)*.
% 299.99/300.66  233848[18:Res:190593.1,941.1] || equal(power_class(image(element_relation,complement(u))),inverse(identity_relation)) member(identity_relation,image(element_relation,power_class(u)))* -> .
% 299.99/300.66  233849[18:Res:190442.1,941.1] || equal(power_class(image(element_relation,complement(u))),symmetrization_of(identity_relation)) member(identity_relation,image(element_relation,power_class(u)))* -> .
% 299.99/300.66  233920[15:Res:209921.1,161200.0] || equal(image(element_relation,union(u,identity_relation)),ordinal_numbers) member(range_of(identity_relation),power_class(symmetric_difference(ordinal_numbers,u)))* -> .
% 299.99/300.66  233922[15:Res:165526.1,161200.0] || subclass(ordinal_numbers,image(element_relation,union(u,identity_relation))) member(range_of(identity_relation),power_class(symmetric_difference(ordinal_numbers,u)))* -> .
% 299.99/300.66  233947[8:Res:143198.1,161200.0] || equal(image(element_relation,union(u,identity_relation)),ordinal_numbers) member(singleton(v),power_class(symmetric_difference(ordinal_numbers,u)))* -> .
% 299.99/300.66  233949[8:Res:8645.1,161200.0] || subclass(ordinal_numbers,image(element_relation,union(u,identity_relation))) member(singleton(v),power_class(symmetric_difference(ordinal_numbers,u)))* -> .
% 299.99/300.66  233970[18:Res:190593.1,161200.0] || equal(image(element_relation,union(u,identity_relation)),inverse(identity_relation)) member(identity_relation,power_class(symmetric_difference(ordinal_numbers,u)))* -> .
% 299.99/300.66  233971[18:Res:190442.1,161200.0] || equal(image(element_relation,union(u,identity_relation)),symmetrization_of(identity_relation)) member(identity_relation,power_class(symmetric_difference(ordinal_numbers,u)))* -> .
% 299.99/300.66  233972[14:Res:165168.1,161200.0] || equal(image(element_relation,union(u,identity_relation)),singleton(identity_relation)) member(identity_relation,power_class(symmetric_difference(ordinal_numbers,u)))* -> .
% 299.99/300.66  234246[24:Rew:207565.1,234223.2] operation(u) || member(not_subclass_element(successor(u),v),symmetric_difference(ordinal_numbers,u))* -> subclass(successor(u),v).
% 299.99/300.66  234308[25:Rew:209334.1,234307.2] || member(ordered_pair(u,singleton(singleton(identity_relation))),composition_function)* -> equal(range_of(v),identity_relation)** equal(inverse(v),ordinal_numbers).
% 299.99/300.66  234563[8:Res:8827.2,233381.0] || member(u,ordinal_numbers) subclass(rest_relation,singleton(omega)) -> equal(integer_of(ordered_pair(u,rest_of(u))),identity_relation)**.
% 299.99/300.66  234629[8:SpL:6355.1,234115.0] || equal(complement(complement(singleton(not_subclass_element(cross_product(u,v),w)))),ordinal_numbers)** -> subclass(cross_product(u,v),w).
% 299.99/300.66  234643[8:SpL:6355.1,234117.0] || subclass(ordinal_numbers,complement(complement(singleton(not_subclass_element(cross_product(u,v),w)))))* -> subclass(cross_product(u,v),w).
% 299.99/300.66  234726[8:SpL:6355.1,232824.0] || subclass(ordinal_numbers,regular(unordered_pair(u,not_subclass_element(cross_product(v,w),x))))* -> subclass(cross_product(v,w),x).
% 299.99/300.66  234756[8:SpL:6355.1,233124.0] || subclass(ordinal_numbers,regular(unordered_pair(not_subclass_element(cross_product(u,v),w),x)))* -> subclass(cross_product(u,v),w).
% 299.99/300.66  234801[8:SpR:116239.0,193440.1] || member(u,ordinal_numbers) -> member(u,range_of(v)) equal(apply(inverse(v),u),sum_class(range_of(identity_relation)))**.
% 299.99/300.66  234813[8:Res:193440.1,56525.0] || member(u,ordinal_numbers) subclass(ordinal_numbers,complement(element_relation))* -> equal(apply(u,u),sum_class(range_of(identity_relation)))**.
% 299.99/300.66  234814[8:Res:193440.1,219073.1] || member(u,ordinal_numbers) subclass(cantor(v),identity_relation)* -> equal(apply(v,u),sum_class(range_of(identity_relation)))**.
% 299.99/300.66  234815[8:Res:193440.1,217144.1] || member(u,ordinal_numbers) equal(cantor(v),identity_relation) -> equal(apply(v,u),sum_class(range_of(identity_relation)))**.
% 299.99/300.66  234869[21:MRR:234784.2,14676.0] || member(u,ordinal_numbers) member(v,ordinal_numbers) -> equal(apply(sum_class(u),v),sum_class(range_of(identity_relation)))**.
% 299.99/300.66  234870[21:MRR:234797.2,14676.0] || member(u,subset_relation) member(v,ordinal_numbers) -> equal(apply(first(u),v),sum_class(range_of(identity_relation)))**.
% 299.99/300.66  234871[21:MRR:234798.2,14676.0] || member(u,subset_relation) member(v,ordinal_numbers) -> equal(apply(second(u),v),sum_class(range_of(identity_relation)))**.
% 299.99/300.66  234872[21:MRR:234799.2,14676.0] || member(u,ordinal_numbers) member(v,ordinal_numbers) -> equal(apply(rest_of(u),v),sum_class(range_of(identity_relation)))**.
% 299.99/300.66  234873[21:MRR:234800.2,14676.0] || member(u,ordinal_numbers) -> subclass(v,w) equal(apply(not_subclass_element(v,w),u),sum_class(range_of(identity_relation)))**.
% 299.99/300.66  234874[21:MRR:234803.2,14676.0] || member(u,ordinal_numbers) member(v,ordinal_numbers) -> equal(apply(power_class(u),v),sum_class(range_of(identity_relation)))**.
% 299.99/300.66  234875[21:MRR:234804.2,14676.0] function(u) || member(v,ordinal_numbers) -> equal(apply(apply(u,w),v),sum_class(range_of(identity_relation)))**.
% 299.99/300.66  234894[8:MRR:234817.0,41183.1] ||  -> equal(apply(u,not_subclass_element(complement(cantor(u)),v)),sum_class(range_of(identity_relation)))** subclass(complement(cantor(u)),v).
% 299.99/300.66  234913[8:SpL:6355.1,234736.0] || equal(regular(unordered_pair(u,not_subclass_element(cross_product(v,w),x))),ordinal_numbers)** -> subclass(cross_product(v,w),x).
% 299.99/300.66  234926[8:SpL:6355.1,234766.0] || equal(regular(unordered_pair(not_subclass_element(cross_product(u,v),w),x)),ordinal_numbers)** -> subclass(cross_product(u,v),w).
% 299.99/300.66  235183[8:Res:8827.2,234983.0] || member(u,ordinal_numbers) subclass(rest_relation,cantor(complement(cross_product(singleton(ordered_pair(u,rest_of(u))),ordinal_numbers))))* -> .
% 299.99/300.66  235246[8:Res:216691.1,18582.1] || equal(complement(restrict(u,v,w)),identity_relation)** member(x,ordinal_numbers) -> member(sum_class(x),u)*.
% 299.99/300.66  235284[8:Res:230445.1,19111.1] || member(not_subclass_element(u,v),w)* subclass(u,complement(union(w,identity_relation)))* -> subclass(u,v).
% 299.99/300.66  235286[8:Res:230445.1,18571.2] || member(sum_class(u),v)* member(u,ordinal_numbers) subclass(ordinal_numbers,complement(union(v,identity_relation)))* -> .
% 299.99/300.66  235288[8:Res:230445.1,18535.2] || member(power_class(u),v)* member(u,ordinal_numbers) subclass(ordinal_numbers,complement(union(v,identity_relation)))* -> .
% 299.99/300.66  235311[8:Rew:66036.0,235260.1] || member(u,intersection(complement(v),complement(w))) -> member(u,complement(intersection(union(v,w),ordinal_numbers)))*.
% 299.99/300.66  235362[21:SpR:218561.1,28980.1] || subclass(rest_relation,domain_relation) subclass(rest_relation,flip(u)) -> member(ordered_pair(ordered_pair(v,w),identity_relation),u)*.
% 299.99/300.66  235363[21:SpR:218385.1,28980.1] || subclass(domain_relation,rest_relation) subclass(rest_relation,flip(u)) -> member(ordered_pair(ordered_pair(v,w),identity_relation),u)*.
% 299.99/300.66  235408[5:Res:28980.1,3700.0] || subclass(rest_relation,flip(singleton(u)))* -> equal(ordered_pair(ordered_pair(v,w),rest_of(ordered_pair(w,v))),u)*.
% 299.99/300.66  235454[5:Res:28980.1,97.0] || subclass(rest_relation,flip(compose_class(u))) -> equal(compose(u,ordered_pair(v,w)),rest_of(ordered_pair(w,v)))**.
% 299.99/300.66  235459[8:Res:28980.1,117449.1] operation(u) || subclass(rest_relation,flip(cantor(u))) -> member(ordered_pair(v,w),cantor(cantor(u)))*.
% 299.99/300.66  235461[5:Res:28980.1,37.0] || subclass(rest_relation,flip(rotate(u))) -> member(ordered_pair(ordered_pair(v,rest_of(ordered_pair(v,w))),w),u)*.
% 299.99/300.66  235462[5:Res:28980.1,40.0] || subclass(rest_relation,flip(flip(u))) -> member(ordered_pair(ordered_pair(v,w),rest_of(ordered_pair(v,w))),u)*.
% 299.99/300.66  235496[21:SpR:218561.1,28979.1] || subclass(rest_relation,domain_relation) subclass(rest_relation,rotate(u)) -> member(ordered_pair(ordered_pair(v,identity_relation),w),u)*.
% 299.99/300.66  235497[21:SpR:218385.1,28979.1] || subclass(domain_relation,rest_relation) subclass(rest_relation,rotate(u)) -> member(ordered_pair(ordered_pair(v,identity_relation),w),u)*.
% 299.99/300.66  235536[5:Res:28979.1,3700.0] || subclass(rest_relation,rotate(singleton(u)))* -> equal(ordered_pair(ordered_pair(v,rest_of(ordered_pair(w,v))),w),u)*.
% 299.99/300.66  235582[5:Res:28979.1,97.0] || subclass(rest_relation,rotate(compose_class(u))) -> equal(compose(u,ordered_pair(v,rest_of(ordered_pair(w,v)))),w)**.
% 299.99/300.66  235593[5:Res:28979.1,37.0] || subclass(rest_relation,rotate(rotate(u))) -> member(ordered_pair(ordered_pair(rest_of(ordered_pair(v,w)),v),w),u)*.
% 299.99/300.66  235594[5:Res:28979.1,40.0] || subclass(rest_relation,rotate(flip(u))) -> member(ordered_pair(ordered_pair(rest_of(ordered_pair(v,w)),w),v),u)*.
% 299.99/300.66  236035[8:Res:216691.1,18546.1] || equal(complement(restrict(u,v,w)),identity_relation)** member(x,ordinal_numbers) -> member(power_class(x),u)*.
% 299.99/300.66  236313[8:Rew:162584.0,236249.1,162584.0,236249.0] ||  -> subclass(singleton(not_subclass_element(intersection(u,symmetrization_of(identity_relation)),v)),symmetrization_of(identity_relation))* subclass(intersection(u,symmetrization_of(identity_relation)),v).
% 299.99/300.66  236527[8:Rew:162584.0,236453.1,162584.0,236453.0] ||  -> subclass(singleton(not_subclass_element(intersection(symmetrization_of(identity_relation),u),v)),symmetrization_of(identity_relation))* subclass(intersection(symmetrization_of(identity_relation),u),v).
% 299.99/300.66  236658[26:SpL:189.0,225363.1] || equal(image(element_relation,power_class(u)),inverse(identity_relation)) equal(power_class(image(element_relation,complement(u))),omega)** -> .
% 299.99/300.66  236682[7:Obv:236669.2] || subclass(u,omega) subclass(omega,v) -> equal(not_subclass_element(u,v),identity_relation)** subclass(u,v).
% 299.99/300.66  236705[26:SpL:189.0,225365.1] || equal(image(element_relation,power_class(u)),singleton(identity_relation)) equal(power_class(image(element_relation,complement(u))),omega)** -> .
% 299.99/300.66  236722[16:SpL:189.0,225450.0] || subclass(singleton(identity_relation),power_class(image(element_relation,complement(u))))* member(identity_relation,image(element_relation,power_class(u))) -> .
% 299.99/300.66  236749[18:SpL:189.0,225452.1] || subclass(ordinal_numbers,image(element_relation,power_class(u))) subclass(symmetrization_of(identity_relation),power_class(image(element_relation,complement(u))))* -> .
% 299.99/300.66  236843[8:Res:17392.2,230780.0] || subclass(u,subset_relation) equal(regular(intersection(u,v)),ordinal_numbers)** -> equal(intersection(u,v),identity_relation).
% 299.99/300.66  236844[8:Res:17392.2,230762.0] || subclass(u,subset_relation) subclass(ordinal_numbers,regular(intersection(u,v)))* -> equal(intersection(u,v),identity_relation).
% 299.99/300.66  236849[8:Res:17392.2,162901.0] || subclass(u,subset_relation) equal(regular(intersection(u,v)),identity_relation)** -> equal(intersection(u,v),identity_relation).
% 299.99/300.66  236850[8:Res:17392.2,162888.0] || subclass(u,subset_relation) subclass(regular(intersection(u,v)),identity_relation)* -> equal(intersection(u,v),identity_relation).
% 299.99/300.66  236853[7:Res:17392.2,3700.0] || subclass(u,singleton(v))* -> equal(intersection(u,w),identity_relation) equal(regular(intersection(u,w)),v)*.
% 299.99/300.66  236907[8:Rew:140613.0,236796.1] || subclass(complement(u),v) -> equal(symmetric_difference(ordinal_numbers,u),identity_relation) member(regular(symmetric_difference(ordinal_numbers,u)),v)*.
% 299.99/300.66  236927[8:Obv:236888.2] || subclass(u,subset_relation) subclass(intersection(u,v),inverse(subset_relation))* -> equal(intersection(u,v),identity_relation).
% 299.99/300.66  236928[7:Obv:236887.2] || subclass(u,v) subclass(intersection(u,w),complement(v))* -> equal(intersection(u,w),identity_relation).
% 299.99/300.66  236977[26:SpR:189.0,225888.1] || equal(symmetric_difference(ordinal_numbers,image(element_relation,power_class(u))),omega) -> member(identity_relation,power_class(image(element_relation,complement(u))))*.
% 299.99/300.66  237114[8:Res:13574.1,230780.0] || equal(regular(intersection(u,intersection(v,subset_relation))),ordinal_numbers)** -> equal(intersection(u,intersection(v,subset_relation)),identity_relation).
% 299.99/300.66  237115[8:Res:13574.1,230762.0] || subclass(ordinal_numbers,regular(intersection(u,intersection(v,subset_relation))))* -> equal(intersection(u,intersection(v,subset_relation)),identity_relation).
% 299.99/300.66  237120[8:Res:13574.1,162901.0] || equal(regular(intersection(u,intersection(v,subset_relation))),identity_relation)** -> equal(intersection(u,intersection(v,subset_relation)),identity_relation).
% 299.99/300.66  237121[8:Res:13574.1,162888.0] || subclass(regular(intersection(u,intersection(v,subset_relation))),identity_relation)* -> equal(intersection(u,intersection(v,subset_relation)),identity_relation).
% 299.99/300.66  237136[7:Res:13574.1,152.0] ||  -> equal(intersection(u,intersection(v,recursion_equation_functions(w))),identity_relation) function(regular(intersection(u,intersection(v,recursion_equation_functions(w)))))*.
% 299.99/300.66  237227[8:Obv:237154.1] || subclass(intersection(u,intersection(v,subset_relation)),inverse(subset_relation))* -> equal(intersection(u,intersection(v,subset_relation)),identity_relation).
% 299.99/300.66  237228[7:Obv:237153.1] || subclass(intersection(u,intersection(v,w)),complement(w))* -> equal(intersection(u,intersection(v,w)),identity_relation).
% 299.99/300.66  237449[8:SpR:160927.0,237181.0] ||  -> equal(intersection(union(u,symmetric_difference(ordinal_numbers,v)),intersection(w,intersection(complement(u),union(v,identity_relation)))),identity_relation)**.
% 299.99/300.66  237450[8:SpR:160992.0,237181.0] ||  -> equal(intersection(union(symmetric_difference(ordinal_numbers,u),v),intersection(w,intersection(union(u,identity_relation),complement(v)))),identity_relation)**.
% 299.99/300.66  237462[7:SpR:481.0,237181.0] ||  -> equal(intersection(power_class(intersection(complement(u),complement(v))),intersection(w,image(element_relation,union(u,v)))),identity_relation)**.
% 299.99/300.66  237652[8:Rew:237269.0,237642.1] || member(not_subclass_element(restrict(subset_relation,u,v),identity_relation),inverse(subset_relation))* -> subclass(restrict(subset_relation,u,v),identity_relation).
% 299.99/300.66  237765[8:Res:13573.1,230780.0] || equal(regular(intersection(u,intersection(subset_relation,v))),ordinal_numbers)** -> equal(intersection(u,intersection(subset_relation,v)),identity_relation).
% 299.99/300.66  237766[8:Res:13573.1,230762.0] || subclass(ordinal_numbers,regular(intersection(u,intersection(subset_relation,v))))* -> equal(intersection(u,intersection(subset_relation,v)),identity_relation).
% 299.99/300.66  237771[8:Res:13573.1,162901.0] || equal(regular(intersection(u,intersection(subset_relation,v))),identity_relation)** -> equal(intersection(u,intersection(subset_relation,v)),identity_relation).
% 299.99/300.66  237772[8:Res:13573.1,162888.0] || subclass(regular(intersection(u,intersection(subset_relation,v))),identity_relation)* -> equal(intersection(u,intersection(subset_relation,v)),identity_relation).
% 299.99/300.66  237787[7:Res:13573.1,152.0] ||  -> equal(intersection(u,intersection(recursion_equation_functions(v),w)),identity_relation) function(regular(intersection(u,intersection(recursion_equation_functions(v),w))))*.
% 299.99/300.66  237878[8:Obv:237805.1] || subclass(intersection(u,intersection(subset_relation,v)),inverse(subset_relation))* -> equal(intersection(u,intersection(subset_relation,v)),identity_relation).
% 299.99/300.66  237879[7:Obv:237804.1] || subclass(intersection(u,intersection(v,w)),complement(v))* -> equal(intersection(u,intersection(v,w)),identity_relation).
% 299.99/300.66  238179[7:SpR:3594.0,237830.0] ||  -> equal(intersection(complement(complement(symmetric_difference(u,v))),symmetric_difference(complement(intersection(u,v)),union(u,v))),identity_relation)**.
% 299.99/300.66  238231[8:SpR:160927.0,237830.0] ||  -> equal(intersection(union(u,symmetric_difference(ordinal_numbers,v)),intersection(intersection(complement(u),union(v,identity_relation)),w)),identity_relation)**.
% 299.99/300.66  238232[8:SpR:160992.0,237830.0] ||  -> equal(intersection(union(symmetric_difference(ordinal_numbers,u),v),intersection(intersection(union(u,identity_relation),complement(v)),w)),identity_relation)**.
% 299.99/300.66  238244[7:SpR:481.0,237830.0] ||  -> equal(intersection(power_class(intersection(complement(u),complement(v))),intersection(image(element_relation,union(u,v)),w)),identity_relation)**.
% 299.99/300.66  238577[8:Res:13572.2,230780.0] || subclass(u,subset_relation) equal(regular(intersection(v,u)),ordinal_numbers)** -> equal(intersection(v,u),identity_relation).
% 299.99/300.66  238578[8:Res:13572.2,230762.0] || subclass(u,subset_relation) subclass(ordinal_numbers,regular(intersection(v,u)))* -> equal(intersection(v,u),identity_relation).
% 299.99/300.66  238583[8:Res:13572.2,162901.0] || subclass(u,subset_relation) equal(regular(intersection(v,u)),identity_relation)** -> equal(intersection(v,u),identity_relation).
% 299.99/300.66  238584[8:Res:13572.2,162888.0] || subclass(u,subset_relation) subclass(regular(intersection(v,u)),identity_relation)* -> equal(intersection(v,u),identity_relation).
% 299.99/300.66  238587[7:Res:13572.2,3700.0] || subclass(u,singleton(v))* -> equal(intersection(w,u),identity_relation) equal(regular(intersection(w,u)),v)*.
% 299.99/300.66  238663[8:Obv:238622.2] || subclass(u,subset_relation) subclass(intersection(v,u),inverse(subset_relation))* -> equal(intersection(v,u),identity_relation).
% 299.99/300.66  238664[7:Obv:238621.2] || subclass(u,v) subclass(intersection(w,u),complement(v))* -> equal(intersection(w,u),identity_relation).
% 299.99/300.66  238884[8:Rew:238388.0,238874.1] || member(not_subclass_element(symmetric_difference(ordinal_numbers,inverse(identity_relation)),identity_relation),symmetrization_of(identity_relation))* -> subclass(symmetric_difference(ordinal_numbers,inverse(identity_relation)),identity_relation).
% 299.99/300.66  239021[7:Rew:237395.0,239007.1] || member(not_subclass_element(restrict(u,v,w),identity_relation),complement(u))* -> subclass(restrict(u,v,w),identity_relation).
% 299.99/300.66  239277[8:Res:17397.1,230780.0] || equal(regular(intersection(intersection(subset_relation,u),v)),ordinal_numbers)** -> equal(intersection(intersection(subset_relation,u),v),identity_relation).
% 299.99/300.66  239278[8:Res:17397.1,230762.0] || subclass(ordinal_numbers,regular(intersection(intersection(subset_relation,u),v)))* -> equal(intersection(intersection(subset_relation,u),v),identity_relation).
% 299.99/300.66  239283[8:Res:17397.1,162901.0] || equal(regular(intersection(intersection(subset_relation,u),v)),identity_relation)** -> equal(intersection(intersection(subset_relation,u),v),identity_relation).
% 299.99/300.66  239284[8:Res:17397.1,162888.0] || subclass(regular(intersection(intersection(subset_relation,u),v)),identity_relation)* -> equal(intersection(intersection(subset_relation,u),v),identity_relation).
% 299.99/300.66  239299[7:Res:17397.1,152.0] ||  -> equal(intersection(intersection(recursion_equation_functions(u),v),w),identity_relation) function(regular(intersection(intersection(recursion_equation_functions(u),v),w)))*.
% 299.99/300.66  239401[8:Obv:239317.1] || subclass(intersection(intersection(subset_relation,u),v),inverse(subset_relation))* -> equal(intersection(intersection(subset_relation,u),v),identity_relation).
% 299.99/300.66  239402[7:Obv:239316.1] || subclass(intersection(intersection(u,v),w),complement(u))* -> equal(intersection(intersection(u,v),w),identity_relation).
% 299.99/300.66  239821[8:SpR:160927.0,239340.0] ||  -> equal(intersection(intersection(intersection(complement(u),union(v,identity_relation)),w),union(u,symmetric_difference(ordinal_numbers,v))),identity_relation)**.
% 299.99/300.66  239822[8:SpR:160992.0,239340.0] ||  -> equal(intersection(intersection(intersection(union(u,identity_relation),complement(v)),w),union(symmetric_difference(ordinal_numbers,u),v)),identity_relation)**.
% 299.99/300.66  239834[7:SpR:481.0,239340.0] ||  -> equal(intersection(intersection(image(element_relation,union(u,v)),w),power_class(intersection(complement(u),complement(v)))),identity_relation)**.
% 299.99/300.66  239852[7:SpR:3594.0,239340.0] ||  -> equal(intersection(symmetric_difference(complement(intersection(u,v)),union(u,v)),complement(complement(symmetric_difference(u,v)))),identity_relation)**.
% 299.99/300.66  240112[8:Res:17396.1,230780.0] || equal(regular(intersection(intersection(u,subset_relation),v)),ordinal_numbers)** -> equal(intersection(intersection(u,subset_relation),v),identity_relation).
% 299.99/300.66  240113[8:Res:17396.1,230762.0] || subclass(ordinal_numbers,regular(intersection(intersection(u,subset_relation),v)))* -> equal(intersection(intersection(u,subset_relation),v),identity_relation).
% 299.99/300.66  240118[8:Res:17396.1,162901.0] || equal(regular(intersection(intersection(u,subset_relation),v)),identity_relation)** -> equal(intersection(intersection(u,subset_relation),v),identity_relation).
% 299.99/300.66  240119[8:Res:17396.1,162888.0] || subclass(regular(intersection(intersection(u,subset_relation),v)),identity_relation)* -> equal(intersection(intersection(u,subset_relation),v),identity_relation).
% 299.99/300.66  240134[7:Res:17396.1,152.0] ||  -> equal(intersection(intersection(u,recursion_equation_functions(v)),w),identity_relation) function(regular(intersection(intersection(u,recursion_equation_functions(v)),w)))*.
% 299.99/300.66  240243[8:Obv:240152.1] || subclass(intersection(intersection(u,subset_relation),v),inverse(subset_relation))* -> equal(intersection(intersection(u,subset_relation),v),identity_relation).
% 299.99/300.66  240244[7:Obv:240151.1] || subclass(intersection(intersection(u,v),w),complement(v))* -> equal(intersection(intersection(u,v),w),identity_relation).
% 299.99/300.66  18774[0:SpR:163.0,3618.1] || member(u,symmetric_difference(complement(intersection(v,w)),union(v,w)))* -> member(u,complement(symmetric_difference(v,w))).
% 299.99/300.66  19429[0:Res:19069.0,11.0] || subclass(complement(intersection(u,v)),symmetric_difference(u,v))* -> equal(complement(intersection(u,v)),symmetric_difference(u,v)).
% 299.99/300.66  41091[0:Res:10.1,8559.2] || equal(u,intersection(v,w))* member(x,w)* member(x,v)* -> member(x,u)*.
% 299.99/300.66  68295[5:SpL:3594.0,8735.0] || equal(symmetric_difference(complement(intersection(u,v)),union(u,v)),ordinal_numbers)** -> member(omega,complement(symmetric_difference(u,v))).
% 299.99/300.66  68318[5:SpL:3594.0,8732.0] || subclass(ordinal_numbers,symmetric_difference(complement(intersection(u,v)),union(u,v)))* -> member(omega,complement(symmetric_difference(u,v))).
% 299.99/300.66  69167[8:Res:51313.1,66086.1] || member(singleton(complement(compose(element_relation,ordinal_numbers))),subset_relation) member(first(singleton(complement(compose(element_relation,ordinal_numbers)))),element_relation)* -> .
% 299.99/300.66  56501[5:Rew:8647.0,56459.0] || member(flip(cross_product(u,ordinal_numbers)),inverse(u)) -> member(ordered_pair(flip(cross_product(u,ordinal_numbers)),inverse(u)),element_relation)*.
% 299.99/300.66  41119[5:MRR:40588.1,41096.1] || member(u,ordinal_numbers) member(v,u) subclass(element_relation,w) -> member(ordered_pair(v,u),w)*.
% 299.99/300.66  56502[5:Rew:8648.0,56458.0] || member(restrict(element_relation,ordinal_numbers,u),sum_class(u)) -> member(ordered_pair(restrict(element_relation,ordinal_numbers,u),sum_class(u)),element_relation)*.
% 299.99/300.66  18836[5:Res:8978.2,897.0] || member(u,ordinal_numbers) subclass(ordinal_numbers,restrict(v,w,x))* -> member(sum_class(u),cross_product(w,x))*.
% 299.99/300.66  39959[5:SpL:126.0,39811.1] || equal(complement(rest_of(restrict(u,v,singleton(w)))),ordinal_numbers)** member(x,segment(u,v,w))* -> .
% 299.99/300.66  51217[5:SpR:50855.1,19733.0] || member(singleton(u),subset_relation) -> subclass(symmetric_difference(complement(first(singleton(u))),complement(u)),successor(first(singleton(u))))*.
% 299.99/300.66  51228[5:SpR:50855.1,17.0] || member(singleton(u),subset_relation) -> equal(unordered_pair(singleton(v),unordered_pair(v,u)),ordered_pair(v,first(singleton(u))))**.
% 299.99/300.66  51279[5:SpL:50855.1,9688.0] || member(singleton(u),subset_relation)* equal(complement(complement(u)),ordinal_numbers) -> equal(singleton(v),first(singleton(u)))*.
% 299.99/300.66  9478[5:Res:27.2,8843.1] || member(singleton(u),v)* member(singleton(u),w)* subclass(ordinal_numbers,complement(intersection(w,v)))* -> .
% 299.99/300.66  9419[0:SpR:963.0,20.2] || member(u,v) member(singleton(u),w) -> member(singleton(singleton(singleton(u))),cross_product(w,v))*.
% 299.99/300.66  57138[5:Res:51313.1,19559.0] || member(singleton(symmetric_difference(u,singleton(u))),subset_relation) -> member(first(singleton(symmetric_difference(u,singleton(u)))),successor(u))*.
% 299.99/300.66  57205[5:Res:51313.1,19676.0] || member(singleton(symmetric_difference(u,inverse(u))),subset_relation) -> member(first(singleton(symmetric_difference(u,inverse(u)))),symmetrization_of(u))*.
% 299.99/300.66  50853[5:Res:49995.1,897.0] || member(restrict(u,v,w),subset_relation) -> member(singleton(first(restrict(u,v,w))),cross_product(v,w))*.
% 299.99/300.66  28943[5:Res:8827.2,898.0] || member(u,ordinal_numbers) subclass(rest_relation,restrict(v,w,x))* -> member(ordered_pair(u,rest_of(u)),v)*.
% 299.99/300.66  65951[5:Res:8652.0,9421.0] || member(u,v)* -> equal(ordered_pair(first(ordered_pair(u,omega)),second(ordered_pair(u,omega))),ordered_pair(u,omega))**.
% 299.99/300.66  45617[0:Obv:45597.0] ||  -> equal(not_subclass_element(unordered_pair(u,v),w),v)** subclass(unordered_pair(u,v),w) member(u,unordered_pair(u,v))*.
% 299.99/300.66  45618[0:Obv:45588.0] ||  -> equal(not_subclass_element(unordered_pair(u,v),w),u)** subclass(unordered_pair(u,v),w) member(v,unordered_pair(u,v))*.
% 299.99/300.66  56819[5:SpL:3606.0,8846.0] || subclass(ordinal_numbers,symmetric_difference(cross_product(u,v),w)) -> member(unordered_pair(x,y),complement(restrict(w,u,v)))*.
% 299.99/300.66  56818[5:SpL:3603.0,8846.0] || subclass(ordinal_numbers,symmetric_difference(u,cross_product(v,w))) -> member(unordered_pair(x,y),complement(restrict(u,v,w)))*.
% 299.99/300.66  47536[0:Obv:47533.2] || subclass(u,v) member(not_subclass_element(u,intersection(w,v)),w)* -> subclass(u,intersection(w,v)).
% 299.99/300.66  18799[0:Res:3618.1,7.0] || member(not_subclass_element(u,complement(intersection(v,w))),symmetric_difference(v,w))* -> subclass(u,complement(intersection(v,w))).
% 299.99/300.66  19122[0:Res:2503.2,897.0] || subclass(u,restrict(v,w,x))* -> subclass(u,y) member(not_subclass_element(u,y),cross_product(w,x))*.
% 299.99/300.66  1044[0:Rew:30.0,1033.1] || member(not_subclass_element(union(u,v),w),intersection(complement(u),complement(v)))* -> subclass(union(u,v),w).
% 299.99/300.66  47538[0:Obv:47532.1] || member(not_subclass_element(intersection(u,v),intersection(w,v)),w)* -> subclass(intersection(u,v),intersection(w,v)).
% 299.99/300.66  47539[0:Obv:47527.1] || member(not_subclass_element(intersection(u,v),intersection(w,u)),w)* -> subclass(intersection(u,v),intersection(w,u)).
% 299.99/300.66  50023[5:SpL:18840.1,8651.0] || member(u,subset_relation) member(u,rest_of(v)) -> equal(restrict(v,first(u),ordinal_numbers),second(u))**.
% 299.99/300.66  19446[0:Res:18946.0,11.0] || subclass(cross_product(u,v),restrict(w,u,v))* -> equal(restrict(w,u,v),cross_product(u,v)).
% 299.99/300.66  3731[0:Res:133.2,1303.1] inductive(not_well_ordering(u,omega)) || connected(u,omega) -> well_ordering(u,omega) equal(not_well_ordering(u,omega),omega)**.
% 299.99/300.66  39628[5:Res:8662.0,9665.1] inductive(compose_class(u)) || well_ordering(v,cross_product(ordinal_numbers,ordinal_numbers)) -> member(least(v,compose_class(u)),compose_class(u))*.
% 299.99/300.66  39630[5:Res:8665.1,9665.1] function(u) inductive(u) || well_ordering(v,cross_product(ordinal_numbers,ordinal_numbers))* -> member(least(v,u),u)*.
% 299.99/300.66  39838[5:Res:8665.1,9661.0] function(u) || well_ordering(v,cross_product(ordinal_numbers,ordinal_numbers))* -> subclass(u,w)* member(least(v,u),u)*.
% 299.99/300.66  39627[5:Res:8661.0,9665.1] inductive(rest_of(u)) || well_ordering(v,cross_product(ordinal_numbers,ordinal_numbers)) -> member(least(v,rest_of(u)),rest_of(u))*.
% 299.99/300.66  40320[5:Res:10.1,9010.0] || equal(rotate(u),cross_product(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers))* -> equal(cross_product(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers),rotate(u)).
% 299.99/300.66  40275[5:Res:10.1,9009.0] || equal(flip(u),cross_product(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers))* -> equal(cross_product(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers),flip(u)).
% 299.99/300.66  15568[8:Res:15426.1,129.0] || subclass(domain_relation,u) subclass(u,v)* well_ordering(w,v)* -> member(least(w,u),u)*.
% 299.99/300.66  70014[5:Res:39971.1,137.1] || equal(complement(rest_of(restrict(u,v,w))),ordinal_numbers)** subclass(w,v) -> section(u,w,v).
% 299.99/300.66  62423[8:MRR:62408.3,14676.0] || asymmetric(u,v)* member(w,cross_product(v,v))* member(w,intersection(u,inverse(u)))* -> .
% 299.99/300.66  9646[5:Res:8645.1,129.0] || subclass(ordinal_numbers,u) subclass(u,v)* well_ordering(w,v)* -> member(least(w,u),u)*.
% 299.99/300.66  79954[5:Res:60219.0,129.0] || subclass(u,v)* well_ordering(w,v)* -> subclass(x,complement(u))* member(least(w,u),u)*.
% 299.99/300.66  81100[8:Res:60219.0,66086.1] || member(not_subclass_element(u,complement(complement(compose(element_relation,ordinal_numbers)))),element_relation)* -> subclass(u,complement(complement(compose(element_relation,ordinal_numbers)))).
% 299.99/300.66  103274[5:Obv:103259.0] ||  -> equal(not_subclass_element(unordered_pair(u,v),complement(w)),v)** member(u,w) subclass(unordered_pair(u,v),complement(w)).
% 299.99/300.66  103275[5:Obv:103247.0] ||  -> equal(not_subclass_element(unordered_pair(u,v),complement(w)),u)** member(v,w) subclass(unordered_pair(u,v),complement(w)).
% 299.99/300.66  66814[0:Res:313.1,161.0] ||  -> subclass(intersection(omega,u),v) equal(integer_of(not_subclass_element(intersection(omega,u),v)),not_subclass_element(intersection(omega,u),v))**.
% 299.99/300.66  66827[0:Res:303.1,161.0] ||  -> subclass(intersection(u,omega),v) equal(integer_of(not_subclass_element(intersection(u,omega),v)),not_subclass_element(intersection(u,omega),v))**.
% 299.99/300.66  115520[5:Res:60219.0,19559.0] ||  -> subclass(u,complement(symmetric_difference(v,singleton(v)))) member(not_subclass_element(u,complement(symmetric_difference(v,singleton(v)))),successor(v))*.
% 299.99/300.66  116641[8:Rew:116078.0,51245.1] || member(singleton(u),subset_relation) -> equal(segment(v,w,first(singleton(u))),cantor(restrict(v,w,u)))**.
% 299.99/300.66  124637[5:Res:60219.0,19676.0] ||  -> subclass(u,complement(symmetric_difference(v,inverse(v)))) member(not_subclass_element(u,complement(symmetric_difference(v,inverse(v)))),symmetrization_of(v))*.
% 299.99/300.66  125890[5:Rew:50855.1,125873.2] || member(singleton(u),subset_relation) member(singleton(singleton(u)),rest_relation)* -> equal(first(singleton(u)),rest_of(u)).
% 299.99/300.66  130517[5:SpL:3606.0,125908.0] || subclass(omega,symmetric_difference(cross_product(u,v),w)) -> member(least(element_relation,omega),complement(restrict(w,u,v)))*.
% 299.99/300.66  130518[5:SpL:3603.0,125908.0] || subclass(omega,symmetric_difference(u,cross_product(v,w))) -> member(least(element_relation,omega),complement(restrict(u,v,w)))*.
% 299.99/300.66  130667[5:Res:41371.0,161.0] ||  -> subclass(complement(complement(omega)),u) equal(integer_of(not_subclass_element(complement(complement(omega)),u)),not_subclass_element(complement(complement(omega)),u))**.
% 299.99/300.66  130700[5:Obv:130676.1] || member(not_subclass_element(complement(complement(u)),intersection(v,u)),v)* -> subclass(complement(complement(u)),intersection(v,u)).
% 299.99/300.66  131391[0:SpL:163.0,18794.1] || member(u,symmetric_difference(complement(intersection(v,w)),union(v,w)))* member(u,symmetric_difference(v,w)) -> .
% 299.99/300.66  131447[5:Res:51313.1,18794.1] || member(singleton(intersection(u,v)),subset_relation) member(first(singleton(intersection(u,v))),symmetric_difference(u,v))* -> .
% 299.99/300.66  131458[0:Res:2503.2,18794.1] || subclass(u,intersection(v,w)) member(not_subclass_element(u,x),symmetric_difference(v,w))* -> subclass(u,x).
% 299.99/300.66  131460[5:Res:8978.2,18794.1] || member(u,ordinal_numbers) subclass(ordinal_numbers,intersection(v,w)) member(sum_class(u),symmetric_difference(v,w))* -> .
% 299.99/300.66  131543[0:Res:2504.1,18794.1] || subclass(ordered_pair(u,v),intersection(w,x)) member(unordered_pair(u,singleton(v)),symmetric_difference(w,x))* -> .
% 299.99/300.66  131569[0:Res:2504.1,897.0] || subclass(ordered_pair(u,v),restrict(w,x,y))* -> member(unordered_pair(u,singleton(v)),cross_product(x,y))*.
% 299.99/300.66  132432[5:SpL:6355.1,130942.0] || subclass(not_subclass_element(cross_product(u,v),w),x)* well_ordering(ordinal_numbers,x) -> subclass(cross_product(u,v),w).
% 299.99/300.66  132468[5:SpL:6355.1,132438.0] || equal(u,not_subclass_element(cross_product(v,w),x))* well_ordering(ordinal_numbers,u)* -> subclass(cross_product(v,w),x).
% 299.99/300.66  132785[5:SpL:3606.0,125985.0] || subclass(ordinal_numbers,symmetric_difference(cross_product(u,v),w)) -> member(least(element_relation,omega),complement(restrict(w,u,v)))*.
% 299.99/300.66  132786[5:SpL:3603.0,125985.0] || subclass(ordinal_numbers,symmetric_difference(u,cross_product(v,w))) -> member(least(element_relation,omega),complement(restrict(u,v,w)))*.
% 299.99/300.66  132879[5:SpL:3606.0,130556.0] || equal(symmetric_difference(cross_product(u,v),w),omega) -> member(least(element_relation,omega),complement(restrict(w,u,v)))*.
% 299.99/300.66  132880[5:SpL:3603.0,130556.0] || equal(symmetric_difference(u,cross_product(v,w)),omega) -> member(least(element_relation,omega),complement(restrict(u,v,w)))*.
% 299.99/300.66  134106[5:Res:133837.1,12.0] || well_ordering(ordinal_numbers,complement(unordered_pair(u,v)))* -> equal(singleton(singleton(w)),v)* equal(singleton(singleton(w)),u)*.
% 299.99/300.66  134409[5:SpL:3606.0,132824.0] || equal(symmetric_difference(cross_product(u,v),w),ordinal_numbers) -> member(least(element_relation,omega),complement(restrict(w,u,v)))*.
% 299.99/300.66  134410[5:SpL:3603.0,132824.0] || equal(symmetric_difference(u,cross_product(v,w)),ordinal_numbers) -> member(least(element_relation,omega),complement(restrict(u,v,w)))*.
% 299.99/300.66  134722[8:Res:116403.2,5.0] || member(u,ordinal_numbers)* subclass(rest_relation,rest_of(v)) subclass(cantor(v),w)* -> member(u,w)*.
% 299.99/300.66  136654[5:Res:40074.1,18791.0] || subclass(ordinal_numbers,complement(complement(symmetric_difference(complement(u),complement(v)))))* -> member(unordered_pair(w,x),union(u,v))*.
% 299.99/300.66  136677[5:Res:127147.1,18791.0] || subclass(ordinal_numbers,complement(complement(symmetric_difference(complement(u),complement(v)))))* -> member(least(element_relation,omega),union(u,v)).
% 299.99/300.66  136678[5:Res:126679.1,18791.0] || subclass(omega,complement(complement(symmetric_difference(complement(u),complement(v)))))* -> member(least(element_relation,omega),union(u,v)).
% 299.99/300.66  136693[5:Res:39298.1,18791.0] || subclass(ordinal_numbers,complement(complement(symmetric_difference(complement(u),complement(v)))))* -> member(ordered_pair(w,x),union(u,v))*.
% 299.99/300.66  137007[5:Res:18211.1,5.0] || subclass(ordinal_numbers,symmetric_difference(u,v)) subclass(union(u,v),w)* -> member(unordered_pair(x,y),w)*.
% 299.99/300.66  139764[5:SpR:482.0,39529.1] || member(u,ordinal_numbers) -> member(u,complement(intersection(union(v,w),complement(x))))* member(u,complement(x)).
% 299.99/300.66  139780[5:Res:39529.1,5.0] || member(u,ordinal_numbers) subclass(union(v,w),x)* -> member(u,complement(w))* member(u,x)*.
% 299.99/300.66  139844[5:SpR:483.0,39530.1] || member(u,ordinal_numbers) -> member(u,complement(intersection(complement(v),union(w,x))))* member(u,complement(v)).
% 299.99/300.66  139866[5:Res:39530.1,5.0] || member(u,ordinal_numbers) subclass(union(v,w),x)* -> member(u,complement(v))* member(u,x)*.
% 299.99/300.66  140401[8:Res:69184.1,47534.0] || member(not_subclass_element(u,intersection(compose(element_relation,ordinal_numbers),u)),element_relation)* -> subclass(u,intersection(compose(element_relation,ordinal_numbers),u)).
% 299.99/300.66  140442[0:Rew:33.0,140332.1] || member(not_subclass_element(u,restrict(u,v,w)),cross_product(v,w))* -> subclass(u,restrict(u,v,w)).
% 299.99/300.66  140468[5:MRR:140400.0,41183.1] ||  -> member(not_subclass_element(u,intersection(union(v,w),u)),complement(w))* subclass(u,intersection(union(v,w),u)).
% 299.99/300.66  140469[5:MRR:140399.0,41183.1] ||  -> member(not_subclass_element(u,intersection(union(v,w),u)),complement(v))* subclass(u,intersection(union(v,w),u)).
% 299.99/300.66  147919[5:SpL:163.0,18581.1] || member(u,ordinal_numbers) subclass(ordinal_numbers,symmetric_difference(v,w)) -> member(sum_class(u),complement(intersection(v,w)))*.
% 299.99/300.66  148899[8:Res:148858.1,8825.1] || subclass(complement(u),inverse(subset_relation))* member(v,ordinal_numbers) -> member(v,u)* member(v,complement(subset_relation))*.
% 299.99/300.66  152863[0:SpL:163.0,19121.0] || subclass(u,symmetric_difference(v,w)) -> subclass(u,x) member(not_subclass_element(u,x),complement(intersection(v,w)))*.
% 299.99/300.66  153336[0:Res:919.1,28.1] || member(not_subclass_element(restrict(complement(u),v,w),x),u)* -> subclass(restrict(complement(u),v,w),x).
% 299.99/300.66  153371[8:Res:919.1,14679.1] || member(not_subclass_element(restrict(inverse(subset_relation),u,v),w),subset_relation)* -> subclass(restrict(inverse(subset_relation),u,v),w).
% 299.99/300.66  155552[0:SpR:3606.0,154945.0] ||  -> equal(intersection(complement(restrict(u,v,w)),symmetric_difference(cross_product(v,w),u)),symmetric_difference(cross_product(v,w),u))**.
% 299.99/300.66  155553[0:SpR:3603.0,154945.0] ||  -> equal(intersection(complement(restrict(u,v,w)),symmetric_difference(u,cross_product(v,w))),symmetric_difference(u,cross_product(v,w)))**.
% 299.99/300.66  155870[5:Res:155818.0,11.0] || subclass(complement(compose(complement(element_relation),inverse(element_relation))),subset_relation)* -> equal(complement(compose(complement(element_relation),inverse(element_relation))),subset_relation).
% 299.99/300.66  156459[5:SpL:155665.0,19121.0] || subclass(u,symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers)))* -> subclass(u,v) member(not_subclass_element(u,v),complement(subset_relation))*.
% 299.99/300.66  156465[5:SpL:155665.0,18581.1] || member(u,ordinal_numbers) subclass(ordinal_numbers,symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers)))* -> member(sum_class(u),complement(subset_relation))*.
% 299.99/300.66  156473[5:Rew:155665.0,156405.0] ||  -> subclass(symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers)),u) member(not_subclass_element(symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers)),u),complement(subset_relation))*.
% 299.99/300.66  156488[5:Res:156404.0,11.0] || subclass(complement(subset_relation),symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers)))* -> equal(symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers)),complement(subset_relation)).
% 299.99/300.66  156568[5:SpL:155666.0,19121.0] || subclass(u,symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation))* -> subclass(u,v) member(not_subclass_element(u,v),complement(subset_relation))*.
% 299.99/300.66  156574[5:SpL:155666.0,18581.1] || member(u,ordinal_numbers) subclass(ordinal_numbers,symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation))* -> member(sum_class(u),complement(subset_relation))*.
% 299.99/300.66  156582[5:Rew:155666.0,156514.0] ||  -> subclass(symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation),u) member(not_subclass_element(symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation),u),complement(subset_relation))*.
% 299.99/300.66  156597[5:Res:156513.0,11.0] || subclass(complement(subset_relation),symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation))* -> equal(symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation),complement(subset_relation)).
% 299.99/300.66  156848[8:MRR:156825.0,8655.0] || subclass(rest_relation,rest_of(u)) member(cantor(u),ordinal_numbers) -> member(singleton(singleton(singleton(cantor(u)))),element_relation)*.
% 299.99/300.66  156849[5:MRR:156813.0,8655.0] || member(complement(u),ordinal_numbers) -> member(singleton(complement(u)),u)* member(singleton(singleton(singleton(complement(u)))),element_relation)*.
% 299.99/300.66  156933[8:Res:156904.0,11.0] || subclass(complement(subset_relation),restrict(inverse(subset_relation),u,v))* -> equal(restrict(inverse(subset_relation),u,v),complement(subset_relation)).
% 299.99/300.66  28932[5:Res:8827.2,8788.0] || member(u,ordinal_numbers) subclass(rest_relation,recursion_equation_functions(v))* -> subclass(ordered_pair(u,rest_of(u)),cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.66  117542[8:Rew:116078.0,116544.3,116078.0,116544.2] operation(u) || member(v,ordinal_numbers) subclass(domain_relation,cantor(u)) -> member(v,cantor(cantor(u)))*.
% 299.99/300.66  117543[8:Rew:116078.0,116545.3,116078.0,116545.2] operation(u) || member(v,ordinal_numbers) subclass(rest_relation,cantor(u)) -> member(v,cantor(cantor(u)))*.
% 299.99/300.66  117544[8:Rew:116078.0,116554.2,116078.0,116554.1] operation(u) || member(singleton(singleton(singleton(v))),cantor(u))* -> member(singleton(v),cantor(cantor(u))).
% 299.99/300.66  117546[8:Rew:116078.0,116810.1] operation(u) ||  -> subclass(intersection(cantor(u),v),w) member(not_subclass_element(intersection(v,cantor(u)),w),v)*.
% 299.99/300.66  117547[8:Rew:116078.0,116813.2] operation(u) ||  -> subclass(intersection(v,cantor(u)),w) member(not_subclass_element(intersection(cantor(u),v),w),v)*.
% 299.99/300.66  117553[8:Rew:116078.0,116868.2] operation(u) || member(v,symmetric_difference(cantor(u),w)) -> member(v,complement(intersection(w,cantor(u))))*.
% 299.99/300.66  117554[8:Rew:116078.0,116874.2] operation(u) || member(v,symmetric_difference(w,cantor(u))) -> member(v,complement(intersection(cantor(u),w)))*.
% 299.99/300.66  131398[8:SpL:116209.1,18794.1] operation(u) || member(v,symmetric_difference(cantor(u),w)) member(v,intersection(w,cantor(u)))* -> .
% 299.99/300.66  131432[8:SpL:116209.1,18794.1] operation(u) || member(v,symmetric_difference(w,cantor(u))) member(v,intersection(cantor(u),w))* -> .
% 299.99/300.66  125904[5:Res:125725.1,129.0] || subclass(omega,u) subclass(u,v)* well_ordering(w,v)* -> member(least(w,u),u)*.
% 299.99/300.66  147270[5:Res:143222.1,129.0] || equal(u,omega) subclass(u,v)* well_ordering(w,v)* -> member(least(w,u),u)*.
% 299.99/300.66  147056[5:Res:143193.1,129.0] || equal(u,ordinal_numbers) subclass(u,v)* well_ordering(w,v)* -> member(least(w,u),u)*.
% 299.99/300.66  148933[8:Res:148858.1,8990.1] function(complement(subset_relation)) || subclass(cross_product(ordinal_numbers,ordinal_numbers),inverse(subset_relation))* -> equal(cross_product(ordinal_numbers,ordinal_numbers),complement(subset_relation)).
% 299.99/300.66  166382[8:Res:13125.2,116453.0] || subclass(omega,rest_of(u)) -> equal(integer_of(singleton(singleton(singleton(v)))),identity_relation)** member(singleton(v),cantor(u))*.
% 299.99/300.66  166368[7:Res:13125.2,47534.0] || subclass(omega,u) -> equal(integer_of(not_subclass_element(v,intersection(u,v))),identity_relation)** subclass(v,intersection(u,v)).
% 299.99/300.66  165113[7:Res:143160.0,13113.0] || well_ordering(u,complement(v)) -> equal(segment(u,symmetric_difference(ordinal_numbers,v),least(u,symmetric_difference(ordinal_numbers,v))),identity_relation)**.
% 299.99/300.66  167273[8:Res:2504.1,14681.0] || subclass(ordered_pair(u,v),regular(w)) member(unordered_pair(u,singleton(v)),w)* -> equal(w,identity_relation).
% 299.99/300.66  161407[8:Rew:140613.0,67594.1] || member(u,intersection(complement(v),union(w,identity_relation)))* member(u,union(v,symmetric_difference(ordinal_numbers,w))) -> .
% 299.99/300.66  19857[7:SpR:916.0,13100.0] ||  -> equal(first(not_subclass_element(restrict(cross_product(u,singleton(v)),w,x),identity_relation)),domain__dfg(cross_product(w,x),u,v))**.
% 299.99/300.66  62104[8:Res:19172.1,9580.1] || equal(segment(u,v,w),identity_relation) subclass(singleton(w),v) -> section(u,singleton(w),v)*.
% 299.99/300.66  161340[8:Rew:116078.0,19889.0] || member(u,cantor(cross_product(v,w))) equal(restrict(cross_product(singleton(u),ordinal_numbers),v,w),identity_relation)** -> .
% 299.99/300.66  19862[7:SpR:916.0,13101.0] ||  -> equal(second(not_subclass_element(restrict(cross_product(singleton(u),v),w,x),identity_relation)),range__dfg(cross_product(w,x),u,v))**.
% 299.99/300.66  161339[8:Rew:116078.0,68236.1] || member(singleton(u),subset_relation) -> member(first(singleton(u)),cantor(v))* equal(restrict(v,u,ordinal_numbers),identity_relation).
% 299.99/300.66  60663[7:Res:13126.0,9421.0] || member(u,v)* -> equal(ordered_pair(first(ordered_pair(u,identity_relation)),second(ordered_pair(u,identity_relation))),ordered_pair(u,identity_relation))**.
% 299.99/300.66  18214[7:Res:13210.1,3617.0] ||  -> equal(intersection(u,symmetric_difference(v,w)),identity_relation) member(regular(intersection(u,symmetric_difference(v,w))),union(v,w))*.
% 299.99/300.66  13577[7:Rew:13036.0,13016.0] ||  -> equal(intersection(u,restrict(v,w,x)),identity_relation) member(regular(intersection(u,restrict(v,w,x))),v)*.
% 299.99/300.66  18216[7:Res:13248.1,3617.0] ||  -> equal(intersection(symmetric_difference(u,v),w),identity_relation) member(regular(intersection(symmetric_difference(u,v),w)),union(u,v))*.
% 299.99/300.66  17398[7:Res:13248.1,898.0] ||  -> equal(intersection(restrict(u,v,w),x),identity_relation) member(regular(intersection(restrict(u,v,w),x)),u)*.
% 299.99/300.66  64330[7:Rew:3616.0,64277.0] ||  -> equal(symmetric_difference(complement(u),complement(v)),identity_relation) member(regular(symmetric_difference(complement(u),complement(v))),union(u,v))*.
% 299.99/300.66  63802[7:SpL:3594.0,13045.0] || subclass(ordinal_numbers,symmetric_difference(complement(intersection(u,v)),union(u,v)))* -> member(identity_relation,complement(symmetric_difference(u,v))).
% 299.99/300.66  63771[7:SpL:3594.0,13051.0] || equal(symmetric_difference(complement(intersection(u,v)),union(u,v)),ordinal_numbers)** -> member(identity_relation,complement(symmetric_difference(u,v))).
% 299.99/300.66  83287[7:Res:61019.0,3617.0] ||  -> equal(complement(complement(symmetric_difference(u,v))),identity_relation) member(regular(complement(complement(symmetric_difference(u,v)))),union(u,v))*.
% 299.99/300.66  83298[7:Res:61019.0,898.0] ||  -> equal(complement(complement(restrict(u,v,w))),identity_relation) member(regular(complement(complement(restrict(u,v,w)))),u)*.
% 299.99/300.66  83313[7:Rew:30.0,83266.1] ||  -> member(regular(complement(union(u,v))),intersection(complement(u),complement(v)))* equal(complement(union(u,v)),identity_relation).
% 299.99/300.66  161346[8:Rew:116078.0,18638.2,116078.0,18638.1] operation(u) ||  -> equal(intersection(cantor(u),v),identity_relation) member(regular(intersection(v,cantor(u))),cantor(u))*.
% 299.99/300.66  161341[8:Rew:116078.0,18644.2,116078.0,18644.1] operation(u) ||  -> equal(intersection(v,cantor(u)),identity_relation) member(regular(intersection(cantor(u),v)),cantor(u))*.
% 299.99/300.66  13422[7:Rew:13036.0,10940.1] || subclass(omega,rest_of(u)) -> equal(integer_of(ordered_pair(v,w)),identity_relation)** equal(restrict(u,v,ordinal_numbers),w)*.
% 299.99/300.66  166339[7:Res:13125.2,18791.0] || subclass(omega,symmetric_difference(complement(u),complement(v)))* -> equal(integer_of(w),identity_relation) member(w,union(u,v))*.
% 299.99/300.66  161412[8:Rew:140613.0,67589.1] || member(u,intersection(union(v,identity_relation),complement(w)))* member(u,union(symmetric_difference(ordinal_numbers,v),w)) -> .
% 299.99/300.66  164913[8:SpL:160491.0,66637.0] || subclass(ordinal_numbers,intersection(complement(u),union(v,identity_relation)))* member(omega,union(u,symmetric_difference(ordinal_numbers,v))) -> .
% 299.99/300.66  18761[8:Res:8978.2,14681.0] || member(u,ordinal_numbers) subclass(ordinal_numbers,regular(v)) member(sum_class(u),v)* -> equal(v,identity_relation).
% 299.99/300.66  18757[8:Res:13210.1,14681.0] || member(regular(intersection(u,regular(v))),v)* -> equal(intersection(u,regular(v)),identity_relation) equal(v,identity_relation).
% 299.99/300.66  19134[8:Res:2503.2,14681.0] || subclass(u,regular(v)) member(not_subclass_element(u,w),v)* -> subclass(u,w) equal(v,identity_relation).
% 299.99/300.66  167503[8:Res:919.1,163154.0] ||  -> subclass(restrict(symmetrization_of(identity_relation),u,v),w) member(not_subclass_element(restrict(symmetrization_of(identity_relation),u,v),w),inverse(identity_relation))*.
% 299.99/300.66  163110[8:SpR:162584.0,3616.0] ||  -> equal(intersection(union(u,complement(inverse(identity_relation))),union(complement(u),symmetrization_of(identity_relation))),symmetric_difference(complement(u),symmetrization_of(identity_relation)))**.
% 299.99/300.66  163089[8:SpR:162584.0,3616.0] ||  -> equal(intersection(union(complement(inverse(identity_relation)),u),union(symmetrization_of(identity_relation),complement(u))),symmetric_difference(symmetrization_of(identity_relation),complement(u)))**.
% 299.99/300.66  163122[8:SpR:162584.0,483.0] ||  -> equal(complement(intersection(complement(u),union(v,complement(inverse(identity_relation))))),union(u,intersection(complement(v),symmetrization_of(identity_relation))))**.
% 299.99/300.66  163109[8:SpR:162584.0,483.0] ||  -> equal(complement(intersection(complement(u),union(complement(inverse(identity_relation)),v))),union(u,intersection(symmetrization_of(identity_relation),complement(v))))**.
% 299.99/300.66  163105[8:SpR:162584.0,482.0] ||  -> equal(complement(intersection(union(u,complement(inverse(identity_relation))),complement(v))),union(intersection(complement(u),symmetrization_of(identity_relation)),v))**.
% 299.99/300.66  163083[8:SpR:162584.0,482.0] ||  -> equal(complement(intersection(union(complement(inverse(identity_relation)),u),complement(v))),union(intersection(symmetrization_of(identity_relation),complement(u)),v))**.
% 299.99/300.66  163148[8:SpL:162584.0,8825.1] || member(u,ordinal_numbers) subclass(symmetrization_of(identity_relation),v)* -> member(u,complement(inverse(identity_relation)))* member(u,v)*.
% 299.99/300.66  165436[15:MRR:16213.0,165430.0] function(u) || equal(rest_relation,domain_relation) equal(compose(u,identity_relation),identity_relation) -> member(identity_relation,recursion_equation_functions(u))*.
% 299.99/300.66  60858[7:Res:13056.1,8554.1] inductive(complement(intersection(u,v))) || member(identity_relation,union(u,v)) -> member(identity_relation,symmetric_difference(u,v))*.
% 299.99/300.66  66994[8:Res:66340.0,11.0] || subclass(union(u,identity_relation),symmetric_difference(complement(u),ordinal_numbers))* -> equal(symmetric_difference(complement(u),ordinal_numbers),union(u,identity_relation)).
% 299.99/300.66  164893[8:SpL:160491.0,66637.0] || subclass(ordinal_numbers,intersection(union(u,identity_relation),complement(v)))* member(omega,union(symmetric_difference(ordinal_numbers,u),v)) -> .
% 299.99/300.66  164947[8:Res:162025.0,11.0] || subclass(symmetric_difference(ordinal_numbers,u),complement(union(u,identity_relation)))* -> equal(complement(union(u,identity_relation)),symmetric_difference(ordinal_numbers,u)).
% 299.99/300.66  66853[7:Rew:13391.2,66850.3] inductive(singleton(u)) || well_ordering(v,omega) -> equal(integer_of(u),identity_relation)** member(least(v,omega),omega)*.
% 299.99/300.66  17325[7:Res:13227.2,12.0] || subclass(u,unordered_pair(v,w))* -> equal(u,identity_relation) equal(regular(u),w) equal(regular(u),v).
% 299.99/300.66  18759[8:Res:13248.1,14681.0] || member(regular(intersection(regular(u),v)),u)* -> equal(intersection(regular(u),v),identity_relation) equal(u,identity_relation).
% 299.99/300.66  83301[8:Res:61019.0,14681.0] || member(regular(complement(complement(regular(u)))),u)* -> equal(complement(complement(regular(u))),identity_relation) equal(u,identity_relation).
% 299.99/300.66  166803[7:Res:13227.2,18791.0] || subclass(u,symmetric_difference(complement(v),complement(w)))* -> equal(u,identity_relation) member(regular(u),union(v,w)).
% 299.99/300.66  61579[8:SpR:15663.0,18840.1] || member(not_subclass_element(identity_relation,identity_relation),subset_relation) -> equal(ordered_pair(single_valued3(identity_relation),second(not_subclass_element(identity_relation,identity_relation))),not_subclass_element(identity_relation,identity_relation))**.
% 299.99/300.66  62970[8:Rew:15663.0,62965.1] || member(not_subclass_element(identity_relation,identity_relation),subset_relation) -> equal(ordered_pair(single_valued3(identity_relation),range__dfg(identity_relation,u,v)),not_subclass_element(identity_relation,identity_relation))**.
% 299.99/300.66  94707[5:Res:39298.1,8800.1] || subclass(ordinal_numbers,complement(complement(cross_product(ordinal_numbers,ordinal_numbers))))* member(u,v) -> member(ordered_pair(u,v),element_relation)*.
% 299.99/300.66  192986[7:SpL:13621.1,123.0] || subclass(compose(identity_relation,identity_relation),identity_relation) -> equal(cross_product(u,u),identity_relation) transitive(regular(cross_product(u,u)),u)*.
% 299.99/300.66  192987[7:SpL:13621.1,9777.0] || equal(compose(identity_relation,identity_relation),identity_relation) -> equal(cross_product(u,u),identity_relation) transitive(regular(cross_product(u,u)),u)*.
% 299.99/300.66  192998[8:Rew:15663.0,192972.1] ||  -> equal(cross_product(u,singleton(v)),identity_relation) equal(domain__dfg(regular(cross_product(u,singleton(v))),u,v),single_valued3(identity_relation))**.
% 299.99/300.66  193009[7:MRR:193008.1,13039.0] || transitive(regular(cross_product(u,u)),u)* -> equal(cross_product(u,u),identity_relation) equal(compose(identity_relation,identity_relation),identity_relation).
% 299.99/300.66  193207[8:Res:193179.0,18571.2] || member(u,ordinal_numbers) subclass(ordinal_numbers,complement(inverse(singleton(sum_class(u)))))* -> asymmetric(singleton(sum_class(u)),v)*.
% 299.99/300.66  13428[7:Rew:13036.0,10932.1] || subclass(omega,composition_function) -> equal(integer_of(ordered_pair(u,ordered_pair(v,w))),identity_relation)** equal(compose(u,v),w).
% 299.99/300.66  50052[5:SpL:18840.1,100.0] || member(u,subset_relation) member(ordered_pair(v,u),composition_function)* -> equal(compose(v,first(u)),second(u)).
% 299.99/300.66  116343[8:Rew:116078.0,46642.2] || member(ordered_pair(u,v),cross_product(ordinal_numbers,ordinal_numbers))* subclass(composition_function,rest_of(w)) -> member(u,cantor(w))*.
% 299.99/300.66  46650[8:Res:9618.2,15935.1] || member(ordered_pair(u,v),cross_product(ordinal_numbers,ordinal_numbers))* subclass(composition_function,subset_relation) subclass(ordinal_numbers,inverse(subset_relation)) -> .
% 299.99/300.66  46644[5:Res:9618.2,18.0] || member(ordered_pair(u,v),cross_product(ordinal_numbers,ordinal_numbers))* subclass(composition_function,cross_product(w,x))* -> member(u,w)*.
% 299.99/300.66  3996[0:SpL:963.0,100.0] || member(singleton(singleton(singleton(ordered_pair(u,v)))),composition_function)* -> equal(compose(singleton(ordered_pair(u,v)),u),v)**.
% 299.99/300.66  46665[5:Res:9618.2,8841.1] || member(ordered_pair(u,v),cross_product(ordinal_numbers,ordinal_numbers))* subclass(composition_function,w) subclass(ordinal_numbers,complement(w))* -> .
% 299.99/300.66  50846[5:Res:49995.1,129.0] || member(u,subset_relation) subclass(u,v)* well_ordering(w,v)* -> member(least(w,u),u)*.
% 299.99/300.66  165292[7:Res:155818.0,13070.0] || well_ordering(u,complement(compose(complement(element_relation),inverse(element_relation))))* -> equal(subset_relation,identity_relation) member(least(u,subset_relation),subset_relation).
% 299.99/300.66  165145[7:Res:155818.0,13113.0] || well_ordering(u,complement(compose(complement(element_relation),inverse(element_relation))))* -> equal(segment(u,subset_relation,least(u,subset_relation)),identity_relation)**.
% 299.99/300.66  49298[5:Res:8638.0,9640.1] || member(u,ordinal_numbers) well_ordering(v,ordinal_numbers) -> member(least(v,unordered_pair(u,w)),unordered_pair(u,w))*.
% 299.99/300.66  49228[5:Res:8638.0,9639.1] || member(u,ordinal_numbers) well_ordering(v,ordinal_numbers) -> member(least(v,unordered_pair(w,u)),unordered_pair(w,u))*.
% 299.99/300.66  40082[5:SoR:9016.0,75.1] one_to_one(sum_class(cross_product(universal_class,universal_class))) || well_ordering(element_relation,cross_product(ordinal_numbers,ordinal_numbers))* -> member(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers).
% 299.99/300.66  40083[5:SoR:9016.0,82.1] operation(sum_class(cross_product(universal_class,universal_class))) || well_ordering(element_relation,cross_product(ordinal_numbers,ordinal_numbers))* -> member(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers).
% 299.99/300.66  40040[5:SoR:9113.0,75.1] one_to_one(sum_class(cross_product(ordinal_numbers,ordinal_numbers))) || well_ordering(element_relation,cross_product(ordinal_numbers,ordinal_numbers))* -> member(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers).
% 299.99/300.66  132203[5:Res:39609.2,8788.0] inductive(recursion_equation_functions(u)) || well_ordering(v,recursion_equation_functions(u)) -> subclass(least(v,recursion_equation_functions(u)),cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.66  194079[8:Res:163153.1,40594.1] || subclass(ordinal_numbers,symmetrization_of(identity_relation)) member(inverse(identity_relation),ordinal_numbers) -> member(singleton(singleton(singleton(inverse(identity_relation)))),element_relation)*.
% 299.99/300.66  194783[8:SpL:66293.0,19121.0] || subclass(u,symmetric_difference(complement(v),ordinal_numbers)) -> subclass(u,w) member(not_subclass_element(u,w),union(v,identity_relation))*.
% 299.99/300.66  194785[8:SpL:66293.0,18581.1] || member(u,ordinal_numbers) subclass(ordinal_numbers,symmetric_difference(complement(v),ordinal_numbers)) -> member(sum_class(u),union(v,identity_relation))*.
% 299.99/300.66  195439[16:Rew:195224.0,163170.0] ||  -> equal(complement(intersection(union(complement(singleton(identity_relation)),u),complement(v))),union(intersection(singleton(identity_relation),complement(u)),v))**.
% 299.99/300.66  195443[16:Rew:195224.0,163192.0] ||  -> equal(complement(intersection(union(u,complement(singleton(identity_relation))),complement(v))),union(intersection(complement(u),singleton(identity_relation)),v))**.
% 299.99/300.66  195494[16:Rew:195224.0,163196.0] ||  -> equal(complement(intersection(complement(u),union(complement(singleton(identity_relation)),v))),union(u,intersection(singleton(identity_relation),complement(v))))**.
% 299.99/300.66  195497[16:Rew:195224.0,163209.0] ||  -> equal(complement(intersection(complement(u),union(v,complement(singleton(identity_relation))))),union(u,intersection(complement(v),singleton(identity_relation))))**.
% 299.99/300.66  195500[16:Rew:195224.0,163176.0] ||  -> equal(intersection(union(complement(singleton(identity_relation)),u),union(singleton(identity_relation),complement(u))),symmetric_difference(singleton(identity_relation),complement(u)))**.
% 299.99/300.66  195501[16:Rew:195224.0,163197.0] ||  -> equal(intersection(union(u,complement(singleton(identity_relation))),union(complement(u),singleton(identity_relation))),symmetric_difference(complement(u),singleton(identity_relation)))**.
% 299.99/300.66  195504[16:Rew:195224.0,163235.1] || member(u,ordinal_numbers) subclass(singleton(identity_relation),v)* -> member(u,complement(singleton(identity_relation)))* member(u,v)*.
% 299.99/300.66  196086[18:Res:190510.1,490.0] || subclass(inverse(identity_relation),intersection(complement(u),complement(v)))* member(regular(symmetrization_of(identity_relation)),union(u,v)) -> .
% 299.99/300.66  196097[18:Res:190510.1,12.0] || subclass(inverse(identity_relation),unordered_pair(u,v))* -> equal(regular(symmetrization_of(identity_relation)),v) equal(regular(symmetrization_of(identity_relation)),u).
% 299.99/300.66  196323[8:SpR:161356.2,15528.0] || member(u,ordinal_numbers) -> member(u,cantor(v)) equal(range__dfg(v,u,ordinal_numbers),range__dfg(identity_relation,w,x))*.
% 299.99/300.66  196431[21:Rew:196372.1,161399.3] || member(u,ordinal_numbers) subclass(domain_relation,v)* subclass(v,w)* -> member(ordered_pair(u,identity_relation),w)*.
% 299.99/300.66  196435[21:Rew:196372.1,174456.2] || member(u,ordinal_numbers) subclass(domain_relation,symmetric_difference(v,inverse(v)))* -> member(ordered_pair(u,identity_relation),symmetrization_of(v))*.
% 299.99/300.66  196436[21:Rew:196372.1,174455.2] || member(u,ordinal_numbers) subclass(domain_relation,symmetric_difference(v,singleton(v)))* -> member(ordered_pair(u,identity_relation),successor(v))*.
% 299.99/300.66  196438[21:Rew:196372.1,161400.2] || member(u,ordinal_numbers) subclass(domain_relation,complement(compose(element_relation,ordinal_numbers)))* member(ordered_pair(u,identity_relation),element_relation)* -> .
% 299.99/300.66  196442[21:Rew:196372.1,161398.2] || member(u,ordinal_numbers) subclass(domain_relation,symmetric_difference(v,w)) -> member(ordered_pair(u,identity_relation),union(v,w))*.
% 299.99/300.66  197111[7:Res:138.1,13224.1] function(u) || member(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers) -> equal(u,identity_relation) member(least(element_relation,u),u)*.
% 299.99/300.66  197933[21:SpR:13100.0,196554.1] || member(not_subclass_element(restrict(u,v,singleton(w)),identity_relation),subset_relation)* -> equal(cantor(domain__dfg(u,v,w)),identity_relation).
% 299.99/300.66  197978[21:SpR:13101.0,196555.1] || member(not_subclass_element(restrict(u,singleton(v),w),identity_relation),subset_relation)* -> equal(cantor(range__dfg(u,v,w)),identity_relation).
% 299.99/300.66  198988[7:Res:8655.0,13362.0] || subclass(ordinal_numbers,u) well_ordering(omega,u)* -> equal(integer_of(ordered_pair(singleton(v),least(omega,ordinal_numbers))),identity_relation)**.
% 299.99/300.66  198262[21:SpL:197474.0,160735.1] || member(inverse(u),cantor(v))* equal(restrict(v,identity_relation,ordinal_numbers),identity_relation) -> equal(range_of(u),identity_relation).
% 299.99/300.66  62889[5:MRR:62887.1,8657.0] || member(u,ordinal_numbers) equal(sum_class(range_of(u)),rest_of(u)) -> member(ordered_pair(u,rest_of(u)),union_of_range_map)*.
% 299.99/300.66  18844[5:Res:18819.1,8798.1] || member(ordered_pair(u,v),subset_relation)* equal(sum_class(range_of(u)),v) -> member(ordered_pair(u,v),union_of_range_map).
% 299.99/300.66  117042[8:Rew:116239.0,66620.2] inductive(cantor(inverse(u))) || well_ordering(v,range_of(u)) -> member(least(v,range_of(u)),range_of(u))*.
% 299.99/300.66  36429[5:Rew:43.0,36415.2,8647.0,36415.2] operation(flip(cross_product(u,ordinal_numbers))) || member(ordered_pair(v,w),inverse(u))* -> member(w,range_of(u)).
% 299.99/300.66  38146[5:Rew:43.0,38124.1] operation(flip(cross_product(u,ordinal_numbers))) ||  -> equal(restrict(v,range_of(u),range_of(u)),intersection(inverse(u),v))**.
% 299.99/300.66  116338[8:Rew:116078.0,38120.1] operation(inverse(u)) ||  -> equal(restrict(v,cantor(range_of(u)),cantor(range_of(u))),intersection(range_of(u),v))**.
% 299.99/300.66  36572[5:Rew:43.0,36559.2,8647.0,36559.2] operation(flip(cross_product(u,ordinal_numbers))) || member(ordered_pair(v,w),inverse(u))* -> member(v,range_of(u)).
% 299.99/300.66  176977[8:Rew:116239.0,176966.2] operation(inverse(u)) || subclass(range_of(u),complement(complement(symmetrization_of(v))))* -> connected(v,cantor(range_of(u))).
% 299.99/300.66  177010[8:Rew:116239.0,176996.1] operation(inverse(u)) || connected(v,cantor(range_of(u))) -> subclass(range_of(u),complement(complement(symmetrization_of(v))))*.
% 299.99/300.66  199003[15:Res:165460.0,13362.0] || subclass(ordinal_numbers,u) well_ordering(omega,u)* -> equal(integer_of(ordered_pair(range_of(identity_relation),least(omega,ordinal_numbers))),identity_relation)**.
% 299.99/300.66  193452[8:MRR:193444.1,50063.1] || member(singleton(u),subset_relation) -> member(first(singleton(u)),cantor(v))* equal(image(v,u),range_of(identity_relation)).
% 299.99/300.66  193436[8:SpR:161076.2,52.1] inductive(singleton(u)) || member(u,ordinal_numbers) -> member(u,cantor(successor_relation)) subclass(range_of(identity_relation),singleton(u))*.
% 299.99/300.66  194951[15:Res:27.2,165527.1] || member(range_of(identity_relation),u) member(range_of(identity_relation),v) subclass(ordinal_numbers,complement(intersection(v,u)))* -> .
% 299.99/300.66  198339[5:MRR:198327.1,8655.0] || member(u,ordinal_numbers) equal(sum_class(range_of(singleton(u))),u) -> member(singleton(singleton(singleton(u))),union_of_range_map)*.
% 299.99/300.66  166853[5:SpR:145758.0,8859.1] || member(inverse(cross_product(u,ordinal_numbers)),ordinal_numbers) -> member(ordered_pair(inverse(cross_product(u,ordinal_numbers)),image(ordinal_numbers,u)),domain_relation)*.
% 299.99/300.66  161475[8:Rew:140603.0,61059.0] ||  -> equal(symmetric_difference(complement(singleton(identity_relation)),complement(image(successor_relation,ordinal_numbers))),union(complement(singleton(identity_relation)),complement(image(successor_relation,ordinal_numbers))))**.
% 299.99/300.66  130758[5:Res:130710.0,11.0] || subclass(image(element_relation,complement(u)),complement(power_class(u)))* -> equal(image(element_relation,complement(u)),complement(power_class(u))).
% 299.99/300.66  83816[5:SpR:487.0,8881.1] || subclass(ordinal_numbers,symmetric_difference(image(element_relation,complement(u)),v)) -> member(omega,complement(intersection(power_class(u),complement(v))))*.
% 299.99/300.66  83836[5:SpR:487.0,8892.1] || equal(symmetric_difference(image(element_relation,complement(u)),v),ordinal_numbers) -> member(omega,complement(intersection(power_class(u),complement(v))))*.
% 299.99/300.66  50864[5:Res:49995.1,288.0] || member(image(element_relation,complement(u)),subset_relation) member(singleton(first(image(element_relation,complement(u)))),power_class(u))* -> .
% 299.99/300.66  18589[5:Res:8978.2,288.0] || member(u,ordinal_numbers) subclass(ordinal_numbers,image(element_relation,complement(v)))* member(sum_class(u),power_class(v))* -> .
% 299.99/300.66  18553[5:Res:8977.2,288.0] || member(u,ordinal_numbers) subclass(ordinal_numbers,image(element_relation,complement(v)))* member(power_class(u),power_class(v))* -> .
% 299.99/300.66  83806[5:SpR:485.0,8881.1] || subclass(ordinal_numbers,symmetric_difference(u,image(element_relation,complement(v)))) -> member(omega,complement(intersection(complement(u),power_class(v))))*.
% 299.99/300.66  83826[5:SpR:485.0,8892.1] || equal(symmetric_difference(u,image(element_relation,complement(v))),ordinal_numbers) -> member(omega,complement(intersection(complement(u),power_class(v))))*.
% 299.99/300.66  19130[0:Res:2503.2,288.0] || subclass(u,image(element_relation,complement(v))) member(not_subclass_element(u,w),power_class(v))* -> subclass(u,w).
% 299.99/300.66  131571[0:Res:2504.1,288.0] || subclass(ordered_pair(u,v),image(element_relation,complement(w)))* member(unordered_pair(u,singleton(v)),power_class(w)) -> .
% 299.99/300.66  132775[5:Rew:19486.0,132735.0] || subclass(ordinal_numbers,complement(image(element_relation,symmetrization_of(u)))) -> subclass(singleton(singleton(v)),complement(image(element_relation,symmetrization_of(u))))*.
% 299.99/300.66  155214[0:SpR:154737.1,19486.0] || subclass(complement(inverse(u)),complement(u))* -> equal(complement(image(element_relation,symmetrization_of(u))),power_class(complement(inverse(u)))).
% 299.99/300.66  193554[8:Rew:162038.0,193538.1] || member(regular(power_class(complement(inverse(identity_relation)))),image(element_relation,symmetrization_of(identity_relation)))* -> equal(power_class(complement(inverse(identity_relation))),identity_relation).
% 299.99/300.66  193553[8:Rew:162038.0,193493.1] ||  -> member(not_subclass_element(u,power_class(complement(inverse(identity_relation)))),image(element_relation,symmetrization_of(identity_relation)))* subclass(u,power_class(complement(inverse(identity_relation)))).
% 299.99/300.66  193473[8:SpR:162038.0,19734.0] ||  -> subclass(symmetric_difference(power_class(complement(inverse(identity_relation))),complement(inverse(image(element_relation,symmetrization_of(identity_relation))))),symmetrization_of(image(element_relation,symmetrization_of(identity_relation))))*.
% 299.99/300.66  193472[8:SpR:162038.0,19733.0] ||  -> subclass(symmetric_difference(power_class(complement(inverse(identity_relation))),complement(singleton(image(element_relation,symmetrization_of(identity_relation))))),successor(image(element_relation,symmetrization_of(identity_relation))))*.
% 299.99/300.66  163163[8:Rew:162584.0,163116.1] ||  -> member(not_subclass_element(u,image(element_relation,symmetrization_of(identity_relation))),power_class(complement(inverse(identity_relation))))* subclass(u,image(element_relation,symmetrization_of(identity_relation))).
% 299.99/300.66  163099[8:SpR:162584.0,19486.0] ||  -> equal(power_class(intersection(symmetrization_of(identity_relation),complement(inverse(complement(inverse(identity_relation)))))),complement(image(element_relation,symmetrization_of(complement(inverse(identity_relation))))))**.
% 299.99/300.66  195469[16:Rew:195224.0,163186.0] ||  -> equal(power_class(intersection(singleton(identity_relation),complement(inverse(complement(singleton(identity_relation)))))),complement(image(element_relation,symmetrization_of(complement(singleton(identity_relation))))))**.
% 299.99/300.66  166924[8:Res:15426.1,941.1] || subclass(domain_relation,power_class(image(element_relation,complement(u)))) member(ordered_pair(identity_relation,identity_relation),image(element_relation,power_class(u)))* -> .
% 299.99/300.66  81636[8:SpR:189.0,67606.0] ||  -> subclass(symmetric_difference(union(image(element_relation,power_class(u)),identity_relation),ordinal_numbers),complement(symmetric_difference(power_class(image(element_relation,complement(u))),ordinal_numbers)))*.
% 299.99/300.66  155401[5:Res:8643.1,941.1] || subclass(ordinal_numbers,power_class(image(element_relation,complement(u)))) member(unordered_pair(v,w),image(element_relation,power_class(u)))* -> .
% 299.99/300.66  155428[5:Res:143222.1,941.1] || equal(power_class(image(element_relation,complement(u))),omega) member(least(element_relation,omega),image(element_relation,power_class(u)))* -> .
% 299.99/300.66  155432[5:Res:125731.1,941.1] || subclass(ordinal_numbers,power_class(image(element_relation,complement(u)))) member(least(element_relation,omega),image(element_relation,power_class(u)))* -> .
% 299.99/300.66  155433[5:Res:125725.1,941.1] || subclass(omega,power_class(image(element_relation,complement(u)))) member(least(element_relation,omega),image(element_relation,power_class(u)))* -> .
% 299.99/300.66  155448[5:Res:8642.1,941.1] || subclass(ordinal_numbers,power_class(image(element_relation,complement(u)))) member(ordered_pair(v,w),image(element_relation,power_class(u)))* -> .
% 299.99/300.66  8831[5:Rew:8637.0,989.0] || member(u,ordinal_numbers) -> member(u,image(element_relation,power_class(v))) member(u,power_class(image(element_relation,complement(v))))*.
% 299.99/300.66  96944[5:SpR:189.0,79577.0] ||  -> member(u,image(element_relation,power_class(image(element_relation,complement(v)))))* subclass(singleton(u),power_class(image(element_relation,power_class(v)))).
% 299.99/300.66  132504[5:SpR:189.0,130711.0] ||  -> subclass(complement(power_class(image(element_relation,power_class(image(element_relation,complement(u)))))),image(element_relation,power_class(image(element_relation,power_class(u)))))*.
% 299.99/300.66  163146[8:SpL:162584.0,941.1] || member(u,image(element_relation,power_class(complement(inverse(identity_relation)))))* member(u,power_class(image(element_relation,symmetrization_of(identity_relation)))) -> .
% 299.99/300.66  19498[7:SpL:481.0,13048.0] || subclass(ordinal_numbers,power_class(intersection(complement(u),complement(v))))* member(identity_relation,image(element_relation,union(u,v))) -> .
% 299.99/300.66  19500[7:SpL:481.0,13046.0] || equal(complement(power_class(intersection(complement(u),complement(v)))),ordinal_numbers)** -> member(identity_relation,image(element_relation,union(u,v))).
% 299.99/300.66  167518[7:SpL:481.0,163545.0] || subclass(ordinal_numbers,complement(power_class(intersection(complement(u),complement(v)))))* -> member(identity_relation,image(element_relation,union(u,v))).
% 299.99/300.66  67179[5:SpL:481.0,8712.0] || subclass(ordinal_numbers,power_class(intersection(complement(u),complement(v))))* member(omega,image(element_relation,union(u,v))) -> .
% 299.99/300.66  67190[5:SpL:481.0,8738.0] || equal(complement(power_class(intersection(complement(u),complement(v)))),ordinal_numbers)** -> member(omega,image(element_relation,union(u,v))).
% 299.99/300.66  152971[5:SpL:481.0,151970.0] || subclass(ordinal_numbers,complement(power_class(intersection(complement(u),complement(v)))))* -> member(omega,image(element_relation,union(u,v))).
% 299.99/300.66  83008[8:SpL:481.0,81412.1] || equal(image(element_relation,union(u,v)),domain_relation) equal(power_class(intersection(complement(u),complement(v))),domain_relation)** -> .
% 299.99/300.66  63448[8:SpL:481.0,63019.1] || subclass(domain_relation,image(element_relation,union(u,v))) subclass(ordinal_numbers,power_class(intersection(complement(u),complement(v))))* -> .
% 299.99/300.66  83006[8:SpL:481.0,81322.1] || subclass(domain_relation,image(element_relation,union(u,v))) subclass(domain_relation,power_class(intersection(complement(u),complement(v))))* -> .
% 299.99/300.66  50418[5:SpL:481.0,50032.1] || member(image(element_relation,union(u,v)),subset_relation) subclass(ordinal_numbers,power_class(intersection(complement(u),complement(v))))* -> .
% 299.99/300.66  19756[0:SpR:481.0,19421.0] ||  -> subclass(symmetric_difference(power_class(intersection(complement(u),complement(v))),complement(w)),union(image(element_relation,union(u,v)),w))*.
% 299.99/300.66  147746[5:SpL:481.0,147314.1] || equal(image(element_relation,union(u,v)),omega) subclass(ordinal_numbers,power_class(intersection(complement(u),complement(v))))* -> .
% 299.99/300.66  147801[5:SpL:481.0,147315.1] || equal(image(element_relation,union(u,v)),omega) subclass(omega,power_class(intersection(complement(u),complement(v))))* -> .
% 299.99/300.66  166833[5:SpL:481.0,147805.0] || equal(power_class(intersection(complement(u),complement(v))),omega)** equal(image(element_relation,union(u,v)),omega) -> .
% 299.99/300.66  127027[5:SpL:481.0,126665.1] || subclass(omega,image(element_relation,union(u,v))) subclass(omega,power_class(intersection(complement(u),complement(v))))* -> .
% 299.99/300.66  127426[5:SpL:481.0,127130.1] || subclass(omega,image(element_relation,union(u,v))) subclass(ordinal_numbers,power_class(intersection(complement(u),complement(v))))* -> .
% 299.99/300.66  134172[5:SpL:481.0,134130.0] || well_ordering(ordinal_numbers,power_class(intersection(complement(u),complement(v))))* well_ordering(ordinal_numbers,image(element_relation,union(u,v))) -> .
% 299.99/300.66  83007[8:SpL:481.0,81488.1] || equal(image(element_relation,union(u,v)),ordinal_numbers) equal(power_class(intersection(complement(u),complement(v))),domain_relation)** -> .
% 299.99/300.66  167306[5:SpL:481.0,147100.1] || equal(image(element_relation,union(u,v)),ordinal_numbers) subclass(ordinal_numbers,power_class(intersection(complement(u),complement(v))))* -> .
% 299.99/300.66  167363[5:SpL:481.0,147101.1] || equal(image(element_relation,union(u,v)),ordinal_numbers) subclass(omega,power_class(intersection(complement(u),complement(v))))* -> .
% 299.99/300.66  173854[5:SpL:481.0,167369.0] || equal(power_class(intersection(complement(u),complement(v))),omega)** equal(image(element_relation,union(u,v)),ordinal_numbers) -> .
% 299.99/300.66  124974[5:SpL:30.0,66645.0] || subclass(ordinal_numbers,image(element_relation,union(u,v))) member(omega,power_class(intersection(complement(u),complement(v))))* -> .
% 299.99/300.66  83005[8:SpL:481.0,81326.1] || subclass(ordinal_numbers,image(element_relation,union(u,v))) subclass(domain_relation,power_class(intersection(complement(u),complement(v))))* -> .
% 299.99/300.66  19497[5:SpL:481.0,9488.1] || subclass(ordinal_numbers,image(element_relation,union(u,v))) subclass(ordinal_numbers,power_class(intersection(complement(u),complement(v))))* -> .
% 299.99/300.66  167292[5:SpL:481.0,126664.1] || subclass(ordinal_numbers,image(element_relation,union(u,v))) subclass(omega,power_class(intersection(complement(u),complement(v))))* -> .
% 299.99/300.66  142403[8:Rew:141402.0,121659.0] ||  -> subclass(symmetric_difference(ordinal_numbers,image(element_relation,power_class(intersection(complement(u),complement(v))))),power_class(image(element_relation,union(u,v))))*.
% 299.99/300.66  19745[0:SpR:481.0,19421.0] ||  -> subclass(symmetric_difference(complement(u),power_class(intersection(complement(v),complement(w)))),union(u,image(element_relation,union(v,w))))*.
% 299.99/300.66  18436[0:SpL:30.0,288.0] || member(u,image(element_relation,union(v,w))) member(u,power_class(intersection(complement(v),complement(w))))* -> .
% 299.99/300.66  154274[5:SpL:481.0,151988.0] || member(u,complement(power_class(intersection(complement(v),complement(w)))))* -> member(u,image(element_relation,union(v,w))).
% 299.99/300.66  161413[8:Rew:140613.0,67554.2] || member(u,ordinal_numbers) -> member(u,image(element_relation,union(v,identity_relation)))* member(u,power_class(symmetric_difference(ordinal_numbers,v))).
% 299.99/300.66  133034[5:Rew:19485.0,132980.0] || subclass(ordinal_numbers,complement(image(element_relation,successor(u)))) -> subclass(singleton(singleton(v)),complement(image(element_relation,successor(u))))*.
% 299.99/300.66  155212[0:SpR:154737.1,19485.0] || subclass(complement(singleton(u)),complement(u))* -> equal(complement(image(element_relation,successor(u))),power_class(complement(singleton(u)))).
% 299.99/300.66  163097[8:SpR:162584.0,19485.0] ||  -> equal(power_class(intersection(symmetrization_of(identity_relation),complement(singleton(complement(inverse(identity_relation)))))),complement(image(element_relation,successor(complement(inverse(identity_relation))))))**.
% 299.99/300.66  195467[16:Rew:195224.0,163184.0] ||  -> equal(power_class(intersection(singleton(identity_relation),complement(singleton(complement(singleton(identity_relation)))))),complement(image(element_relation,successor(complement(singleton(identity_relation))))))**.
% 299.99/300.66  195387[16:Rew:195224.0,193390.0] || member(regular(power_class(complement(singleton(identity_relation)))),image(element_relation,singleton(identity_relation)))* -> equal(power_class(complement(singleton(identity_relation))),identity_relation).
% 299.99/300.66  195386[16:Rew:195224.0,193389.0] ||  -> member(not_subclass_element(u,power_class(complement(singleton(identity_relation)))),image(element_relation,singleton(identity_relation)))* subclass(u,power_class(complement(singleton(identity_relation)))).
% 299.99/300.66  195383[16:Rew:195224.0,193309.0] ||  -> subclass(symmetric_difference(power_class(complement(singleton(identity_relation))),complement(inverse(image(element_relation,singleton(identity_relation))))),symmetrization_of(image(element_relation,singleton(identity_relation))))*.
% 299.99/300.66  195381[16:Rew:195224.0,193308.0] ||  -> subclass(symmetric_difference(power_class(complement(singleton(identity_relation))),complement(singleton(image(element_relation,singleton(identity_relation))))),successor(image(element_relation,singleton(identity_relation))))*.
% 299.99/300.66  195618[16:Rew:195224.0,195333.1] ||  -> member(not_subclass_element(u,image(element_relation,singleton(identity_relation))),power_class(complement(singleton(identity_relation))))* subclass(u,image(element_relation,singleton(identity_relation))).
% 299.99/300.66  195312[16:Rew:195224.0,163233.1] || member(u,image(element_relation,power_class(complement(singleton(identity_relation)))))* member(u,power_class(image(element_relation,singleton(identity_relation)))) -> .
% 299.99/300.66  49196[0:Obv:49186.1] || member(ordered_pair(u,v),compose(w,x)) -> subclass(singleton(v),image(w,image(x,singleton(u))))*.
% 299.99/300.66  18835[5:Res:8977.2,897.0] || member(u,ordinal_numbers) subclass(ordinal_numbers,restrict(v,w,x))* -> member(power_class(u),cross_product(w,x))*.
% 299.99/300.66  131461[5:Res:8977.2,18794.1] || member(u,ordinal_numbers) subclass(ordinal_numbers,intersection(v,w)) member(power_class(u),symmetric_difference(v,w))* -> .
% 299.99/300.66  148507[5:SpL:163.0,18545.1] || member(u,ordinal_numbers) subclass(ordinal_numbers,symmetric_difference(v,w)) -> member(power_class(u),complement(intersection(v,w)))*.
% 299.99/300.66  156463[5:SpL:155665.0,18545.1] || member(u,ordinal_numbers) subclass(ordinal_numbers,symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers)))* -> member(power_class(u),complement(subset_relation))*.
% 299.99/300.66  156572[5:SpL:155666.0,18545.1] || member(u,ordinal_numbers) subclass(ordinal_numbers,symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation))* -> member(power_class(u),complement(subset_relation))*.
% 299.99/300.66  161381[5:Rew:487.0,146650.1] || subclass(ordinal_numbers,intersection(power_class(u),complement(v))) member(omega,complement(intersection(power_class(u),complement(v))))* -> .
% 299.99/300.66  18760[8:Res:8977.2,14681.0] || member(u,ordinal_numbers) subclass(ordinal_numbers,regular(v)) member(power_class(u),v)* -> equal(v,identity_relation).
% 299.99/300.66  195049[14:MRR:195039.2,165227.0] || equal(power_class(u),ordinal_numbers) well_ordering(v,power_class(u))* -> member(least(v,singleton(identity_relation)),singleton(identity_relation))*.
% 299.99/300.66  161380[5:Rew:485.0,146638.1] || subclass(ordinal_numbers,intersection(complement(u),power_class(v))) member(omega,complement(intersection(complement(u),power_class(v))))* -> .
% 299.99/300.66  196290[18:SpL:481.0,196256.1] inductive(image(element_relation,union(u,v))) || equal(power_class(intersection(complement(u),complement(v))),inverse(identity_relation))** -> .
% 299.99/300.66  196197[18:SpL:481.0,196166.1] inductive(image(element_relation,union(u,v))) || equal(power_class(intersection(complement(u),complement(v))),symmetrization_of(identity_relation))** -> .
% 299.99/300.66  195141[14:SpL:481.0,195115.1] inductive(image(element_relation,union(u,v))) || equal(power_class(intersection(complement(u),complement(v))),singleton(identity_relation))** -> .
% 299.99/300.66  13436[7:Rew:13036.0,9464.1] || member(recursion_equation_functions(u),ordinal_numbers) -> equal(recursion_equation_functions(u),identity_relation) subclass(apply(choice,recursion_equation_functions(u)),cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.66  198651[8:SpR:13262.2,118070.0] ||  -> equal(unordered_pair(u,v),identity_relation) equal(apply(choice,unordered_pair(u,v)),v)** equal(intersection(u,ordinal_numbers),u).
% 299.99/300.66  198662[7:MRR:198661.0,8666.0] ||  -> equal(apply(choice,unordered_pair(u,v)),v)** equal(unordered_pair(u,v),identity_relation) member(u,unordered_pair(u,v))*.
% 299.99/300.66  198643[8:SpR:13262.1,118070.0] ||  -> equal(unordered_pair(u,v),identity_relation) equal(apply(choice,unordered_pair(u,v)),u)** equal(intersection(v,ordinal_numbers),v).
% 299.99/300.66  198664[7:MRR:198663.0,8666.0] ||  -> equal(apply(choice,unordered_pair(u,v)),u)** equal(unordered_pair(u,v),identity_relation) member(v,unordered_pair(u,v))*.
% 299.99/300.66  195693[7:Res:13225.3,3700.0] || member(u,ordinal_numbers) subclass(u,singleton(v))* -> equal(u,identity_relation) equal(apply(choice,u),v).
% 299.99/300.66  195689[8:Res:13225.3,162888.0] || member(u,ordinal_numbers) subclass(u,subset_relation) subclass(apply(choice,u),identity_relation)* -> equal(u,identity_relation).
% 299.99/300.66  195688[8:Res:13225.3,162901.0] || member(u,ordinal_numbers) subclass(u,subset_relation) equal(apply(choice,u),identity_relation)** -> equal(u,identity_relation).
% 299.99/300.66  197467[21:SpR:196546.1,117511.1] operation(u) ||  -> equal(singleton(cantor(u)),identity_relation) equal(intersection(cantor(u),v),restrict(v,identity_relation,identity_relation))**.
% 299.99/300.66  10862[5:Res:139.1,8787.1] single_valued_class(sum_class(cross_product(ordinal_numbers,ordinal_numbers))) || member(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers) -> function(sum_class(cross_product(ordinal_numbers,ordinal_numbers)))*.
% 299.99/300.66  204178[18:Res:194549.1,490.0] || subclass(symmetrization_of(identity_relation),intersection(complement(u),complement(v)))* member(regular(symmetrization_of(identity_relation)),union(u,v)) -> .
% 299.99/300.66  204192[18:Res:194549.1,12.0] || subclass(symmetrization_of(identity_relation),unordered_pair(u,v))* -> equal(regular(symmetrization_of(identity_relation)),v) equal(regular(symmetrization_of(identity_relation)),u).
% 299.99/300.66  204640[21:Res:196904.1,490.0] || subclass(domain_relation,intersection(complement(u),complement(v))) member(singleton(singleton(singleton(identity_relation))),union(u,v))* -> .
% 299.99/300.66  205569[22:SpL:481.0,205502.0] || well_ordering(ordinal_numbers,power_class(intersection(complement(u),complement(v))))* -> member(singleton(identity_relation),image(element_relation,union(u,v))).
% 299.99/300.66  205779[22:SpR:481.0,205578.1] ||  -> member(singleton(identity_relation),image(element_relation,union(u,v))) member(singleton(identity_relation),power_class(intersection(complement(u),complement(v))))*.
% 299.99/300.66  206136[22:Res:205574.1,490.0] || equal(intersection(complement(u),complement(v)),singleton(singleton(identity_relation))) member(singleton(identity_relation),union(u,v))* -> .
% 299.99/300.66  206274[8:Rew:160491.0,206186.0] ||  -> equal(intersection(union(u,identity_relation),union(complement(u),symmetric_difference(ordinal_numbers,u))),symmetric_difference(complement(u),symmetric_difference(ordinal_numbers,u)))**.
% 299.99/300.66  206525[7:Res:165794.1,11.0] || subclass(omega,intersection(u,singleton(v)))* -> equal(integer_of(v),identity_relation) equal(intersection(u,singleton(v)),omega).
% 299.99/300.66  206552[7:Res:165795.1,11.0] || subclass(omega,intersection(singleton(u),v))* -> equal(integer_of(u),identity_relation) equal(intersection(singleton(u),v),omega).
% 299.99/300.66  206567[7:Res:206540.1,11.0] || subclass(omega,complement(complement(singleton(u))))* -> equal(integer_of(u),identity_relation) equal(complement(complement(singleton(u))),omega).
% 299.99/300.66  207542[8:Res:192400.1,11.0] || member(u,ordinals_with_null_class_as_identity) subclass(complement(u),symmetric_difference(u,ordinal_numbers))* -> equal(symmetric_difference(u,ordinal_numbers),complement(u)).
% 299.99/300.66  207894[24:Rew:207558.1,207626.1] operation(u) || asymmetric(v,identity_relation) -> equal(domain__dfg(intersection(v,inverse(v)),identity_relation,u),single_valued3(identity_relation))**.
% 299.99/300.66  208230[8:MRR:208227.1,160668.1] || equal(cross_product(u,u),complement(complement(symmetrization_of(v))))* -> equal(complement(complement(symmetrization_of(v))),cross_product(u,u)).
% 299.99/300.66  208268[24:Rew:66036.0,208256.1] operation(image(element_relation,complement(u))) ||  -> equal(complement(intersection(power_class(u),ordinal_numbers)),successor(image(element_relation,complement(u))))**.
% 299.99/300.66  208487[7:SpR:13260.1,39298.1] || subclass(ordinal_numbers,complement(complement(u))) -> equal(cross_product(v,w),identity_relation) member(regular(cross_product(v,w)),u)*.
% 299.99/300.66  208531[7:SpL:13260.1,8841.1] || subclass(ordinal_numbers,complement(u)) member(regular(cross_product(v,w)),u)* -> equal(cross_product(v,w),identity_relation).
% 299.99/300.66  208611[21:SSi:208608.0,73.0] || equal(rest_of(u),rest_relation) -> equal(unordered_pair(v,u),identity_relation) equal(apply(choice,unordered_pair(v,u)),v)**.
% 299.99/300.66  208612[21:SSi:208607.0,73.0] || equal(rest_of(u),rest_relation) -> equal(unordered_pair(u,v),identity_relation) equal(apply(choice,unordered_pair(u,v)),v)**.
% 299.99/300.66  209336[25:SpL:208840.0,194373.1] || member(identity_relation,cantor(u)) member(ordered_pair(u,singleton(singleton(identity_relation))),cross_product(ordinal_numbers,cross_product(ordinal_numbers,ordinal_numbers)))* -> .
% 299.99/300.66  209429[25:SpL:208885.0,18571.2] || member(image(u,identity_relation),ordinal_numbers) subclass(ordinal_numbers,complement(v)) member(apply(u,ordinal_numbers),v)* -> .
% 299.99/300.66  210139[8:Res:208722.1,11.0] || subclass(complement(u),symmetric_difference(u,ordinal_numbers))* -> equal(singleton(u),identity_relation) equal(symmetric_difference(u,ordinal_numbers),complement(u)).
% 299.99/300.66  210354[5:Res:313.1,143186.0] ||  -> subclass(intersection(symmetric_difference(ordinal_numbers,u),v),w) member(not_subclass_element(intersection(symmetric_difference(ordinal_numbers,u),v),w),complement(u))*.
% 299.99/300.66  210368[5:Res:303.1,143186.0] ||  -> subclass(intersection(u,symmetric_difference(ordinal_numbers,v)),w) member(not_subclass_element(intersection(u,symmetric_difference(ordinal_numbers,v)),w),complement(v))*.
% 299.99/300.66  210375[7:Res:13237.2,143186.0] || well_ordering(u,ordinal_numbers) -> equal(symmetric_difference(ordinal_numbers,v),identity_relation) member(least(u,symmetric_difference(ordinal_numbers,v)),complement(v))*.
% 299.99/300.66  210389[5:Res:8827.2,143186.0] || member(u,ordinal_numbers) subclass(rest_relation,symmetric_difference(ordinal_numbers,v)) -> member(ordered_pair(u,rest_of(u)),complement(v))*.
% 299.99/300.66  210463[5:Res:313.1,143226.0] || member(not_subclass_element(intersection(symmetric_difference(ordinal_numbers,u),v),w),u)* -> subclass(intersection(symmetric_difference(ordinal_numbers,u),v),w).
% 299.99/300.66  210477[5:Res:303.1,143226.0] || member(not_subclass_element(intersection(u,symmetric_difference(ordinal_numbers,v)),w),v)* -> subclass(intersection(u,symmetric_difference(ordinal_numbers,v)),w).
% 299.99/300.66  210484[7:Res:13237.2,143226.0] || well_ordering(u,ordinal_numbers) member(least(u,symmetric_difference(ordinal_numbers,v)),v)* -> equal(symmetric_difference(ordinal_numbers,v),identity_relation).
% 299.99/300.66  210498[5:Res:8827.2,143226.0] || member(u,ordinal_numbers) subclass(rest_relation,symmetric_difference(ordinal_numbers,v)) member(ordered_pair(u,rest_of(u)),v)* -> .
% 299.99/300.66  210690[8:Res:9618.2,210517.1] || member(ordered_pair(u,v),cross_product(ordinal_numbers,ordinal_numbers))* subclass(composition_function,w)* equal(complement(w),ordinal_numbers) -> .
% 299.99/300.66  210839[8:Res:210572.1,13113.0] || equal(complement(u),ordinal_numbers) well_ordering(v,w)* -> equal(segment(v,u,least(v,u)),identity_relation)**.
% 299.99/300.66  210856[8:Res:210572.1,116155.1] || equal(complement(cantor(restrict(u,v,w))),ordinal_numbers)** subclass(w,v) -> section(u,w,v).
% 299.99/300.66  211047[8:Res:210572.1,9010.0] || equal(complement(cross_product(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers)),ordinal_numbers)** -> equal(cross_product(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers),rotate(u))*.
% 299.99/300.66  211048[8:Res:210572.1,9009.0] || equal(complement(cross_product(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers)),ordinal_numbers)** -> equal(cross_product(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers),flip(u))*.
% 299.99/300.66  211081[8:Res:210572.1,3729.1] || equal(complement(u),ordinal_numbers) connected(v,u) -> well_ordering(v,u) equal(not_well_ordering(v,u),u)**.
% 299.99/300.66  211082[8:Res:210572.1,117594.1] || equal(complement(u),ordinal_numbers) section(v,u,w) -> equal(cantor(restrict(v,w,u)),u)**.
% 299.99/300.66  211420[8:Res:210606.1,9470.1] || equal(complement(u),ordinal_numbers) member(ordered_pair(v,w),compose(x,y))* -> member(w,complement(u))*.
% 299.99/300.66  211584[8:Res:211438.1,9470.1] || equal(symmetrization_of(identity_relation),ordinal_numbers) member(ordered_pair(u,v),compose(w,x))* -> member(v,symmetrization_of(identity_relation)).
% 299.99/300.66  211668[8:Res:211441.1,9470.1] || equal(power_class(u),ordinal_numbers) member(ordered_pair(v,w),compose(x,y))* -> member(w,power_class(u))*.
% 299.99/300.66  213462[8:SpR:145761.0,117217.1] operation(cross_product(u,singleton(v))) ||  -> subclass(range_of(cross_product(u,singleton(v))),cantor(segment(ordinal_numbers,u,v)))*.
% 299.99/300.66  213480[8:SpL:145761.0,116738.1] || subclass(domain_relation,inverse(subset_relation)) member(ordered_pair(cross_product(u,singleton(v)),segment(ordinal_numbers,u,v)),subset_relation)* -> .
% 299.99/300.66  214227[21:Obv:214220.1] || equal(rest_of(u),rest_relation) -> equal(not_subclass_element(unordered_pair(v,u),w),v)** subclass(unordered_pair(v,u),w).
% 299.99/300.66  214228[21:Obv:214219.1] || equal(rest_of(u),rest_relation) -> equal(not_subclass_element(unordered_pair(u,v),w),v)** subclass(unordered_pair(u,v),w).
% 299.99/300.66  214270[25:SpR:208887.0,117217.1] operation(restrict(u,v,identity_relation)) ||  -> subclass(range_of(restrict(u,v,identity_relation)),cantor(segment(u,v,ordinal_numbers)))*.
% 299.99/300.66  214295[25:SpL:208887.0,116738.1] || subclass(domain_relation,inverse(subset_relation)) member(ordered_pair(restrict(u,v,identity_relation),segment(u,v,ordinal_numbers)),subset_relation)* -> .
% 299.99/300.66  214930[0:Res:151501.1,11.0] || member(u,v) subclass(v,intersection(w,singleton(u)))* -> equal(v,intersection(w,singleton(u))).
% 299.99/300.66  214940[5:Res:151501.1,8787.1] single_valued_class(intersection(u,singleton(v))) || member(v,cross_product(ordinal_numbers,ordinal_numbers)) -> function(intersection(u,singleton(v)))*.
% 299.99/300.66  215026[0:Res:151861.1,11.0] || member(u,v) subclass(v,intersection(singleton(u),w))* -> equal(v,intersection(singleton(u),w)).
% 299.99/300.66  215036[5:Res:151861.1,8787.1] single_valued_class(intersection(singleton(u),v)) || member(u,cross_product(ordinal_numbers,ordinal_numbers)) -> function(intersection(singleton(u),v))*.
% 299.99/300.66  215060[5:Res:215011.1,11.0] || member(u,v) subclass(v,complement(complement(singleton(u))))* -> equal(v,complement(complement(singleton(u)))).
% 299.99/300.66  215070[5:Res:215011.1,8787.1] single_valued_class(complement(complement(singleton(u)))) || member(u,cross_product(ordinal_numbers,ordinal_numbers)) -> function(complement(complement(singleton(u))))*.
% 299.99/300.66  215210[0:Res:155157.1,11.0] || subclass(u,v) subclass(complement(u),symmetric_difference(v,u))* -> equal(symmetric_difference(v,u),complement(u)).
% 299.99/300.66  215370[8:SpR:481.0,215271.1] || subclass(image(element_relation,union(u,v)),identity_relation) -> equal(complement(power_class(intersection(complement(u),complement(v)))),identity_relation)**.
% 299.99/300.66  216748[8:SpR:216188.1,155846.1] || equal(compose(complement(element_relation),inverse(element_relation)),identity_relation)** equal(compose(subset_relation,subset_relation),subset_relation) -> transitive(ordinal_numbers,ordinal_numbers).
% 299.99/300.66  216749[8:SpR:216188.1,155845.1] || equal(compose(complement(element_relation),inverse(element_relation)),identity_relation)** subclass(compose(subset_relation,subset_relation),subset_relation) -> transitive(ordinal_numbers,ordinal_numbers).
% 299.99/300.66  217031[8:SpL:216188.1,155827.0] || equal(compose(complement(element_relation),inverse(element_relation)),identity_relation)** transitive(ordinal_numbers,ordinal_numbers) -> subclass(compose(subset_relation,subset_relation),subset_relation).
% 299.99/300.66  217262[8:Rew:140613.0,216670.1] || equal(identity_relation,u) -> equal(complement(intersection(union(v,u),complement(w))),union(symmetric_difference(ordinal_numbers,v),w))**.
% 299.99/300.66  217265[8:Rew:140613.0,216708.1] || equal(identity_relation,u) -> equal(complement(intersection(complement(v),union(w,u))),union(v,symmetric_difference(ordinal_numbers,w)))**.
% 299.99/300.66  217671[8:Res:216691.1,13113.0] || equal(complement(u),identity_relation) well_ordering(v,u)* -> equal(segment(v,ordinal_numbers,least(v,ordinal_numbers)),identity_relation)**.
% 299.99/300.66  217946[7:Res:9604.1,17315.0] || equal(sum_class(recursion_equation_functions(u)),recursion_equation_functions(u)) -> equal(sum_class(recursion_equation_functions(u)),identity_relation) function(regular(sum_class(recursion_equation_functions(u))))*.
% 299.99/300.66  218143[8:Res:8551.2,217144.1] || member(u,cross_product(v,w))* member(u,x)* equal(restrict(x,v,w),identity_relation)** -> .
% 299.99/300.66  218277[8:Res:62.1,217144.1] || member(ordered_pair(u,v),compose(w,x))* equal(image(w,image(x,singleton(u))),identity_relation) -> .
% 299.99/300.66  218400[21:Res:8976.2,196454.0] function(u) || member(v,ordinal_numbers) subclass(domain_relation,rest_relation) -> equal(rest_of(image(u,v)),identity_relation)**.
% 299.99/300.66  218457[21:MRR:218408.1,8638.0] || member(u,ordinal_numbers) subclass(domain_relation,rest_relation) -> equal(u,identity_relation) equal(rest_of(apply(choice,u)),identity_relation)**.
% 299.99/300.66  218576[21:Res:8976.2,196455.0] function(u) || member(v,ordinal_numbers) subclass(rest_relation,domain_relation) -> equal(rest_of(image(u,v)),identity_relation)**.
% 299.99/300.66  218633[21:MRR:218584.1,8638.0] || member(u,ordinal_numbers) subclass(rest_relation,domain_relation) -> equal(u,identity_relation) equal(rest_of(apply(choice,u)),identity_relation)**.
% 299.99/300.66  218651[8:SpL:162038.0,66645.0] || subclass(ordinal_numbers,image(element_relation,power_class(complement(inverse(identity_relation)))))* member(omega,power_class(image(element_relation,symmetrization_of(identity_relation)))) -> .
% 299.99/300.66  218652[16:SpL:195257.0,66645.0] || subclass(ordinal_numbers,image(element_relation,power_class(complement(singleton(identity_relation)))))* member(omega,power_class(image(element_relation,singleton(identity_relation)))) -> .
% 299.99/300.66  218705[5:Rew:50855.1,218694.2] || member(singleton(u),subset_relation) member(singleton(singleton(u)),successor_relation)* -> equal(first(singleton(u)),successor(u)).
% 299.99/300.66  219015[8:SpR:215491.1,161207.0] || subclass(intersection(singleton(identity_relation),image(successor_relation,ordinal_numbers)),identity_relation)* -> equal(symmetric_difference(singleton(identity_relation),image(successor_relation,ordinal_numbers)),ordinal_numbers).
% 299.99/300.66  219092[8:Res:8832.1,219073.1] || member(u,ordinal_numbers) subclass(intersection(complement(v),complement(w)),identity_relation)* -> member(u,union(v,w))*.
% 299.99/300.66  219104[8:Res:8551.2,219073.1] || member(u,cross_product(v,w))* member(u,x)* subclass(restrict(x,v,w),identity_relation)* -> .
% 299.99/300.66  219183[8:Res:9563.3,219073.1] || connected(u,v) well_ordering(w,v)* subclass(not_well_ordering(u,v),identity_relation)* -> well_ordering(u,v).
% 299.99/300.66  219217[8:Res:9706.3,219073.1] || member(u,ordinal_numbers)* member(v,ordinal_numbers)* equal(successor(v),u)* subclass(successor_relation,identity_relation) -> .
% 299.99/300.66  219239[8:Res:62.1,219073.1] || member(ordered_pair(u,v),compose(w,x))* subclass(image(w,image(x,singleton(u))),identity_relation)* -> .
% 299.99/300.66  219334[15:Res:215659.1,21.0] || subclass(complement(cross_product(u,v)),identity_relation)* -> equal(ordered_pair(first(range_of(identity_relation)),second(range_of(identity_relation))),range_of(identity_relation))**.
% 299.99/300.66  219571[8:SpL:162038.0,67561.0] || member(u,symmetric_difference(power_class(complement(inverse(identity_relation))),ordinal_numbers))* -> member(u,union(image(element_relation,symmetrization_of(identity_relation)),identity_relation)).
% 299.99/300.66  219572[16:SpL:195257.0,67561.0] || member(u,symmetric_difference(power_class(complement(singleton(identity_relation))),ordinal_numbers))* -> member(u,union(image(element_relation,singleton(identity_relation)),identity_relation)).
% 299.99/300.66  219603[8:Res:8977.2,67561.0] || member(u,ordinal_numbers) subclass(ordinal_numbers,symmetric_difference(complement(v),ordinal_numbers)) -> member(power_class(u),union(v,identity_relation))*.
% 299.99/300.66  219616[8:Res:49995.1,67561.0] || member(symmetric_difference(complement(u),ordinal_numbers),subset_relation) -> member(singleton(first(symmetric_difference(complement(u),ordinal_numbers))),union(u,identity_relation))*.
% 299.99/300.66  219627[8:Res:2504.1,67561.0] || subclass(ordered_pair(u,v),symmetric_difference(complement(w),ordinal_numbers)) -> member(unordered_pair(u,singleton(v)),union(w,identity_relation))*.
% 299.99/300.66  219776[8:SpR:162038.0,67614.1] || member(u,union(image(element_relation,symmetrization_of(identity_relation)),identity_relation)) -> member(u,symmetric_difference(power_class(complement(inverse(identity_relation))),ordinal_numbers))*.
% 299.99/300.66  219777[16:SpR:195257.0,67614.1] || member(u,union(image(element_relation,singleton(identity_relation)),identity_relation)) -> member(u,symmetric_difference(power_class(complement(singleton(identity_relation))),ordinal_numbers))*.
% 299.99/300.66  219783[8:Res:67614.1,9876.0] || member(u,union(v,identity_relation))* subclass(symmetric_difference(complement(v),ordinal_numbers),w)* well_ordering(ordinal_numbers,w) -> .
% 299.99/300.66  219798[8:Res:67614.1,7.0] || member(not_subclass_element(u,symmetric_difference(complement(v),ordinal_numbers)),union(v,identity_relation))* -> subclass(u,symmetric_difference(complement(v),ordinal_numbers)).
% 299.99/300.66  220023[8:Res:51313.1,160772.0] || member(singleton(symmetric_difference(ordinal_numbers,u)),subset_relation) member(first(singleton(symmetric_difference(ordinal_numbers,u))),union(u,identity_relation))* -> .
% 299.99/300.66  220036[8:Res:2503.2,160772.0] || subclass(u,symmetric_difference(ordinal_numbers,v)) member(not_subclass_element(u,w),union(v,identity_relation))* -> subclass(u,w).
% 299.99/300.66  220038[8:Res:8978.2,160772.0] || member(u,ordinal_numbers) subclass(ordinal_numbers,symmetric_difference(ordinal_numbers,v)) member(sum_class(u),union(v,identity_relation))* -> .
% 299.99/300.66  220041[8:Res:8977.2,160772.0] || member(u,ordinal_numbers) subclass(ordinal_numbers,symmetric_difference(ordinal_numbers,v)) member(power_class(u),union(v,identity_relation))* -> .
% 299.99/300.66  220065[8:Res:2504.1,160772.0] || subclass(ordered_pair(u,v),symmetric_difference(ordinal_numbers,w)) member(unordered_pair(u,singleton(v)),union(w,identity_relation))* -> .
% 299.99/300.66  220171[8:SpR:116209.1,17390.1] operation(u) ||  -> equal(intersection(recursion_equation_functions(v),cantor(u)),identity_relation) function(regular(intersection(cantor(u),recursion_equation_functions(v))))*.
% 299.99/300.66  220229[8:SpR:116209.1,13568.1] operation(u) ||  -> equal(intersection(cantor(u),recursion_equation_functions(v)),identity_relation) function(regular(intersection(recursion_equation_functions(v),cantor(u))))*.
% 299.99/300.66  220400[21:Res:196656.1,18794.1] || subclass(domain_relation,flip(intersection(u,v))) member(ordered_pair(ordered_pair(w,x),identity_relation),symmetric_difference(u,v))* -> .
% 299.99/300.66  220408[21:Res:196656.1,67561.0] || subclass(domain_relation,flip(symmetric_difference(complement(u),ordinal_numbers))) -> member(ordered_pair(ordered_pair(v,w),identity_relation),union(u,identity_relation))*.
% 299.99/300.66  220409[21:Res:196656.1,160772.0] || subclass(domain_relation,flip(symmetric_difference(ordinal_numbers,u))) member(ordered_pair(ordered_pair(v,w),identity_relation),union(u,identity_relation))* -> .
% 299.99/300.66  220427[21:Res:196656.1,897.0] || subclass(domain_relation,flip(restrict(u,v,w)))* -> member(ordered_pair(ordered_pair(x,y),identity_relation),cross_product(v,w))*.
% 299.99/300.66  220431[21:Res:196656.1,161.0] || subclass(domain_relation,flip(omega)) -> equal(integer_of(ordered_pair(ordered_pair(u,v),identity_relation)),ordered_pair(ordered_pair(u,v),identity_relation))**.
% 299.99/300.66  220436[21:Res:196656.1,14681.0] || subclass(domain_relation,flip(regular(u))) member(ordered_pair(ordered_pair(v,w),identity_relation),u)* -> equal(u,identity_relation).
% 299.99/300.66  220438[21:Res:196656.1,288.0] || subclass(domain_relation,flip(image(element_relation,complement(u)))) member(ordered_pair(ordered_pair(v,w),identity_relation),power_class(u))* -> .
% 299.99/300.66  220502[21:Res:196657.1,18794.1] || subclass(domain_relation,rotate(intersection(u,v))) member(ordered_pair(ordered_pair(w,identity_relation),x),symmetric_difference(u,v))* -> .
% 299.99/300.66  220510[21:Res:196657.1,67561.0] || subclass(domain_relation,rotate(symmetric_difference(complement(u),ordinal_numbers))) -> member(ordered_pair(ordered_pair(v,identity_relation),w),union(u,identity_relation))*.
% 299.99/300.66  220511[21:Res:196657.1,160772.0] || subclass(domain_relation,rotate(symmetric_difference(ordinal_numbers,u))) member(ordered_pair(ordered_pair(v,identity_relation),w),union(u,identity_relation))* -> .
% 299.99/300.66  220529[21:Res:196657.1,897.0] || subclass(domain_relation,rotate(restrict(u,v,w)))* -> member(ordered_pair(ordered_pair(x,identity_relation),y),cross_product(v,w))*.
% 299.99/300.66  220533[21:Res:196657.1,161.0] || subclass(domain_relation,rotate(omega)) -> equal(integer_of(ordered_pair(ordered_pair(u,identity_relation),v)),ordered_pair(ordered_pair(u,identity_relation),v))**.
% 299.99/300.66  220538[21:Res:196657.1,14681.0] || subclass(domain_relation,rotate(regular(u))) member(ordered_pair(ordered_pair(v,identity_relation),w),u)* -> equal(u,identity_relation).
% 299.99/300.66  220540[21:Res:196657.1,288.0] || subclass(domain_relation,rotate(image(element_relation,complement(u)))) member(ordered_pair(ordered_pair(v,identity_relation),w),power_class(u))* -> .
% 299.99/300.66  220568[21:Res:196657.1,9471.0] || subclass(domain_relation,rotate(compose(u,v))) -> subclass(w,image(u,image(v,singleton(ordered_pair(x,identity_relation)))))*.
% 299.99/300.66  220676[7:Res:52.1,17324.0] inductive(singleton(u)) ||  -> equal(image(successor_relation,singleton(u)),identity_relation) equal(regular(image(successor_relation,singleton(u))),u)**.
% 299.99/300.66  220777[5:Res:39607.2,143226.0] inductive(symmetric_difference(ordinal_numbers,u)) || well_ordering(v,ordinal_numbers) member(least(v,symmetric_difference(ordinal_numbers,u)),u)* -> .
% 299.99/300.66  220778[5:Res:39607.2,143186.0] inductive(symmetric_difference(ordinal_numbers,u)) || well_ordering(v,ordinal_numbers) -> member(least(v,symmetric_difference(ordinal_numbers,u)),complement(u))*.
% 299.99/300.66  220978[8:Res:19531.1,19115.0] || equal(sum_class(recursion_equation_functions(u)),identity_relation) -> subclass(sum_class(recursion_equation_functions(u)),v) function(not_subclass_element(sum_class(recursion_equation_functions(u)),v))*.
% 299.99/300.66  220983[0:Res:52.1,19115.0] inductive(recursion_equation_functions(u)) ||  -> subclass(image(successor_relation,recursion_equation_functions(u)),v) function(not_subclass_element(image(successor_relation,recursion_equation_functions(u)),v))*.
% 299.99/300.66  221154[7:Res:13236.2,8788.0] || well_ordering(u,recursion_equation_functions(v)) -> equal(recursion_equation_functions(v),identity_relation) subclass(least(u,recursion_equation_functions(v)),cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.66  221297[8:Res:215662.1,21.0] || subclass(complement(cross_product(u,v)),identity_relation)* -> equal(ordered_pair(first(singleton(w)),second(singleton(w))),singleton(w))**.
% 299.99/300.66  221453[8:SpL:481.0,221330.0] || subclass(power_class(intersection(complement(u),complement(v))),identity_relation)* well_ordering(ordinal_numbers,image(element_relation,union(u,v))) -> .
% 299.99/300.66  221664[8:SpR:218159.1,3594.0] || equal(complement(symmetric_difference(u,v)),identity_relation) -> equal(symmetric_difference(complement(intersection(u,v)),union(u,v)),identity_relation)**.
% 299.99/300.66  222099[8:SpR:219120.1,3594.0] || subclass(complement(symmetric_difference(u,v)),identity_relation) -> equal(symmetric_difference(complement(intersection(u,v)),union(u,v)),identity_relation)**.
% 299.99/300.66  222564[21:SpR:8649.0,196460.2] || member(restrict(u,v,ordinal_numbers),ordinal_numbers)* subclass(domain_relation,union_of_range_map) -> equal(sum_class(image(u,v)),identity_relation).
% 299.99/300.66  222613[21:SpL:218387.1,28976.1] || subclass(domain_relation,rest_relation) subclass(rest_relation,inverse(subset_relation)) member(ordered_pair(sum_class(range_of(identity_relation)),identity_relation),subset_relation)* -> .
% 299.99/300.66  222699[20:Res:217871.0,31610.0] || subclass(rest_relation,successor_relation) -> equal(rest_of(regular(complement(complement(symmetrization_of(identity_relation))))),successor(regular(complement(complement(symmetrization_of(identity_relation))))))**.
% 299.99/300.66  222715[5:Res:19525.1,31610.0] || well_ordering(u,ordinal_numbers) subclass(rest_relation,successor_relation) -> equal(rest_of(least(u,ordinal_numbers)),successor(least(u,ordinal_numbers)))**.
% 299.99/300.66  222716[5:Res:133502.1,31610.0] || well_ordering(u,rest_relation) subclass(rest_relation,successor_relation) -> equal(rest_of(least(u,rest_relation)),successor(least(u,rest_relation)))**.
% 299.99/300.66  222717[5:Res:133495.1,31610.0] || well_ordering(u,ordinal_numbers) subclass(rest_relation,successor_relation) -> equal(rest_of(least(u,rest_relation)),successor(least(u,rest_relation)))**.
% 299.99/300.66  222906[8:MRR:222905.3,217224.0] || subclass(unordered_pair(u,v),inverse(subset_relation))* member(v,subset_relation) -> equal(regular(unordered_pair(u,v)),u).
% 299.99/300.66  222908[8:MRR:222907.3,217223.0] || subclass(unordered_pair(u,v),inverse(subset_relation))* member(u,subset_relation) -> equal(regular(unordered_pair(u,v)),v).
% 299.99/300.66  223006[7:Res:13125.2,974.0] || subclass(omega,union_of_range_map) -> equal(integer_of(singleton(singleton(singleton(u)))),identity_relation)** equal(sum_class(range_of(singleton(u))),u).
% 299.99/300.66  223090[7:Res:13125.2,13306.0] || subclass(omega,image(element_relation,complement(u)))* -> equal(integer_of(regular(power_class(u))),identity_relation) equal(power_class(u),identity_relation).
% 299.99/300.66  223111[21:SpR:19486.0,196563.1] || member(intersection(complement(u),complement(inverse(u))),ordinal_numbers)* -> equal(cantor(complement(image(element_relation,symmetrization_of(u)))),identity_relation).
% 299.99/300.66  223183[21:SpL:218395.1,28976.1] || subclass(domain_relation,rest_relation) subclass(rest_relation,inverse(subset_relation)) member(ordered_pair(regular(symmetrization_of(identity_relation)),identity_relation),subset_relation)* -> .
% 299.99/300.66  223246[21:SpL:218416.1,28976.1] || subclass(domain_relation,rest_relation) subclass(rest_relation,inverse(subset_relation)) member(ordered_pair(least(element_relation,omega),identity_relation),subset_relation)* -> .
% 299.99/300.66  223309[21:SpL:218563.1,28976.1] || subclass(rest_relation,domain_relation) subclass(rest_relation,inverse(subset_relation)) member(ordered_pair(sum_class(range_of(identity_relation)),identity_relation),subset_relation)* -> .
% 299.99/300.67  223375[21:SpL:218571.1,28976.1] || subclass(rest_relation,domain_relation) subclass(rest_relation,inverse(subset_relation)) member(ordered_pair(regular(symmetrization_of(identity_relation)),identity_relation),subset_relation)* -> .
% 299.99/300.67  223429[21:SpR:19485.0,196563.1] || member(intersection(complement(u),complement(singleton(u))),ordinal_numbers)* -> equal(cantor(complement(image(element_relation,successor(u)))),identity_relation).
% 299.99/300.67  223509[21:SpL:218592.1,28976.1] || subclass(rest_relation,domain_relation) subclass(rest_relation,inverse(subset_relation)) member(ordered_pair(least(element_relation,omega),identity_relation),subset_relation)* -> .
% 299.99/300.67  223681[7:SpR:18840.1,13413.1] || member(u,subset_relation) subclass(omega,element_relation) -> equal(integer_of(u),identity_relation) member(first(u),second(u))*.
% 299.99/300.67  223711[8:SpR:160927.0,19421.0] ||  -> subclass(symmetric_difference(union(u,symmetric_difference(ordinal_numbers,v)),complement(w)),union(intersection(complement(u),union(v,identity_relation)),w))*.
% 299.99/300.67  223732[22:SpR:160927.0,205578.1] ||  -> member(singleton(identity_relation),intersection(complement(u),union(v,identity_relation)))* member(singleton(identity_relation),union(u,symmetric_difference(ordinal_numbers,v))).
% 299.99/300.67  223749[8:SpR:160927.0,19421.0] ||  -> subclass(symmetric_difference(complement(u),union(v,symmetric_difference(ordinal_numbers,w))),union(u,intersection(complement(v),union(w,identity_relation))))*.
% 299.99/300.67  223800[8:SpR:154737.1,160927.0] || subclass(union(u,identity_relation),complement(v))* -> equal(union(v,symmetric_difference(ordinal_numbers,u)),complement(union(u,identity_relation))).
% 299.99/300.67  223810[8:SpL:160927.0,13048.0] || subclass(ordinal_numbers,union(u,symmetric_difference(ordinal_numbers,v))) member(identity_relation,intersection(complement(u),union(v,identity_relation)))* -> .
% 299.99/300.67  223812[8:SpL:160927.0,147100.1] || equal(intersection(complement(u),union(v,identity_relation)),ordinal_numbers) subclass(ordinal_numbers,union(u,symmetric_difference(ordinal_numbers,v)))* -> .
% 299.99/300.67  223813[8:SpL:160927.0,9488.1] || subclass(ordinal_numbers,intersection(complement(u),union(v,identity_relation)))* subclass(ordinal_numbers,union(u,symmetric_difference(ordinal_numbers,v))) -> .
% 299.99/300.67  223814[8:SpL:160927.0,147314.1] || equal(intersection(complement(u),union(v,identity_relation)),omega) subclass(ordinal_numbers,union(u,symmetric_difference(ordinal_numbers,v)))* -> .
% 299.99/300.67  223815[8:SpL:160927.0,127130.1] || subclass(omega,intersection(complement(u),union(v,identity_relation)))* subclass(ordinal_numbers,union(u,symmetric_difference(ordinal_numbers,v))) -> .
% 299.99/300.67  223816[8:SpL:160927.0,63019.1] || subclass(domain_relation,intersection(complement(u),union(v,identity_relation)))* subclass(ordinal_numbers,union(u,symmetric_difference(ordinal_numbers,v))) -> .
% 299.99/300.67  223817[8:SpL:160927.0,50032.1] || member(intersection(complement(u),union(v,identity_relation)),subset_relation)* subclass(ordinal_numbers,union(u,symmetric_difference(ordinal_numbers,v))) -> .
% 299.99/300.67  223818[8:SpL:160927.0,8712.0] || subclass(ordinal_numbers,union(u,symmetric_difference(ordinal_numbers,v))) member(omega,intersection(complement(u),union(v,identity_relation)))* -> .
% 299.99/300.67  223819[8:SpL:160927.0,13046.0] || equal(complement(union(u,symmetric_difference(ordinal_numbers,v))),ordinal_numbers) -> member(identity_relation,intersection(complement(u),union(v,identity_relation)))*.
% 299.99/300.67  223821[8:SpL:160927.0,8738.0] || equal(complement(union(u,symmetric_difference(ordinal_numbers,v))),ordinal_numbers) -> member(omega,intersection(complement(u),union(v,identity_relation)))*.
% 299.99/300.67  223823[8:SpL:160927.0,163545.0] || subclass(ordinal_numbers,complement(union(u,symmetric_difference(ordinal_numbers,v)))) -> member(identity_relation,intersection(complement(u),union(v,identity_relation)))*.
% 299.99/300.67  223824[8:SpL:160927.0,151970.0] || subclass(ordinal_numbers,complement(union(u,symmetric_difference(ordinal_numbers,v)))) -> member(omega,intersection(complement(u),union(v,identity_relation)))*.
% 299.99/300.67  223829[8:SpL:160927.0,81326.1] || subclass(ordinal_numbers,intersection(complement(u),union(v,identity_relation)))* subclass(domain_relation,union(u,symmetric_difference(ordinal_numbers,v))) -> .
% 299.99/300.67  223830[8:SpL:160927.0,81322.1] || subclass(domain_relation,intersection(complement(u),union(v,identity_relation)))* subclass(domain_relation,union(u,symmetric_difference(ordinal_numbers,v))) -> .
% 299.99/300.67  223831[8:SpL:160927.0,81488.1] || equal(intersection(complement(u),union(v,identity_relation)),ordinal_numbers)** equal(union(u,symmetric_difference(ordinal_numbers,v)),domain_relation) -> .
% 299.99/300.67  223832[8:SpL:160927.0,81412.1] || equal(intersection(complement(u),union(v,identity_relation)),domain_relation)** equal(union(u,symmetric_difference(ordinal_numbers,v)),domain_relation) -> .
% 299.99/300.67  223834[8:SpL:160927.0,147101.1] || equal(intersection(complement(u),union(v,identity_relation)),ordinal_numbers) subclass(omega,union(u,symmetric_difference(ordinal_numbers,v)))* -> .
% 299.99/300.67  223835[8:SpL:160927.0,126664.1] || subclass(ordinal_numbers,intersection(complement(u),union(v,identity_relation)))* subclass(omega,union(u,symmetric_difference(ordinal_numbers,v))) -> .
% 299.99/300.67  223836[8:SpL:160927.0,147315.1] || equal(intersection(complement(u),union(v,identity_relation)),omega) subclass(omega,union(u,symmetric_difference(ordinal_numbers,v)))* -> .
% 299.99/300.67  223837[8:SpL:160927.0,126665.1] || subclass(omega,intersection(complement(u),union(v,identity_relation)))* subclass(omega,union(u,symmetric_difference(ordinal_numbers,v))) -> .
% 299.99/300.67  223838[22:SpL:160927.0,205502.0] || well_ordering(ordinal_numbers,union(u,symmetric_difference(ordinal_numbers,v))) -> member(singleton(identity_relation),intersection(complement(u),union(v,identity_relation)))*.
% 299.99/300.67  223840[8:SpL:160927.0,134130.0] || well_ordering(ordinal_numbers,union(u,symmetric_difference(ordinal_numbers,v))) well_ordering(ordinal_numbers,intersection(complement(u),union(v,identity_relation)))* -> .
% 299.99/300.67  223842[8:SpL:160927.0,167369.0] || equal(union(u,symmetric_difference(ordinal_numbers,v)),omega) equal(intersection(complement(u),union(v,identity_relation)),ordinal_numbers)** -> .
% 299.99/300.67  223843[8:SpL:160927.0,147805.0] || equal(union(u,symmetric_difference(ordinal_numbers,v)),omega) equal(intersection(complement(u),union(v,identity_relation)),omega)** -> .
% 299.99/300.67  223851[14:SpL:160927.0,195115.1] inductive(intersection(complement(u),union(v,identity_relation))) || equal(union(u,symmetric_difference(ordinal_numbers,v)),singleton(identity_relation))** -> .
% 299.99/300.67  223853[18:SpL:160927.0,196166.1] inductive(intersection(complement(u),union(v,identity_relation))) || equal(union(u,symmetric_difference(ordinal_numbers,v)),symmetrization_of(identity_relation))** -> .
% 299.99/300.67  223855[18:SpL:160927.0,196256.1] inductive(intersection(complement(u),union(v,identity_relation))) || equal(union(u,symmetric_difference(ordinal_numbers,v)),inverse(identity_relation))** -> .
% 299.99/300.67  223861[8:SpL:160927.0,221330.0] || subclass(union(u,symmetric_difference(ordinal_numbers,v)),identity_relation) well_ordering(ordinal_numbers,intersection(complement(u),union(v,identity_relation)))* -> .
% 299.99/300.67  223870[8:SpL:160927.0,151988.0] || member(u,complement(union(v,symmetric_difference(ordinal_numbers,w)))) -> member(u,intersection(complement(v),union(w,identity_relation)))*.
% 299.99/300.67  224028[8:SpR:160992.0,19421.0] ||  -> subclass(symmetric_difference(union(symmetric_difference(ordinal_numbers,u),v),complement(w)),union(intersection(union(u,identity_relation),complement(v)),w))*.
% 299.99/300.67  224049[22:SpR:160992.0,205578.1] ||  -> member(singleton(identity_relation),intersection(union(u,identity_relation),complement(v)))* member(singleton(identity_relation),union(symmetric_difference(ordinal_numbers,u),v)).
% 299.99/300.67  224066[8:SpR:160992.0,19421.0] ||  -> subclass(symmetric_difference(complement(u),union(symmetric_difference(ordinal_numbers,v),w)),union(u,intersection(union(v,identity_relation),complement(w))))*.
% 299.99/300.67  224128[8:SpL:160992.0,13048.0] || subclass(ordinal_numbers,union(symmetric_difference(ordinal_numbers,u),v)) member(identity_relation,intersection(union(u,identity_relation),complement(v)))* -> .
% 299.99/300.67  224130[8:SpL:160992.0,147100.1] || equal(intersection(union(u,identity_relation),complement(v)),ordinal_numbers) subclass(ordinal_numbers,union(symmetric_difference(ordinal_numbers,u),v))* -> .
% 299.99/300.67  224131[8:SpL:160992.0,9488.1] || subclass(ordinal_numbers,intersection(union(u,identity_relation),complement(v)))* subclass(ordinal_numbers,union(symmetric_difference(ordinal_numbers,u),v)) -> .
% 299.99/300.67  224132[8:SpL:160992.0,147314.1] || equal(intersection(union(u,identity_relation),complement(v)),omega) subclass(ordinal_numbers,union(symmetric_difference(ordinal_numbers,u),v))* -> .
% 299.99/300.67  224133[8:SpL:160992.0,127130.1] || subclass(omega,intersection(union(u,identity_relation),complement(v)))* subclass(ordinal_numbers,union(symmetric_difference(ordinal_numbers,u),v)) -> .
% 299.99/300.67  224134[8:SpL:160992.0,63019.1] || subclass(domain_relation,intersection(union(u,identity_relation),complement(v)))* subclass(ordinal_numbers,union(symmetric_difference(ordinal_numbers,u),v)) -> .
% 299.99/300.67  224135[8:SpL:160992.0,50032.1] || member(intersection(union(u,identity_relation),complement(v)),subset_relation)* subclass(ordinal_numbers,union(symmetric_difference(ordinal_numbers,u),v)) -> .
% 299.99/300.67  224136[8:SpL:160992.0,8712.0] || subclass(ordinal_numbers,union(symmetric_difference(ordinal_numbers,u),v)) member(omega,intersection(union(u,identity_relation),complement(v)))* -> .
% 299.99/300.67  224137[8:SpL:160992.0,13046.0] || equal(complement(union(symmetric_difference(ordinal_numbers,u),v)),ordinal_numbers) -> member(identity_relation,intersection(union(u,identity_relation),complement(v)))*.
% 299.99/300.67  224139[8:SpL:160992.0,8738.0] || equal(complement(union(symmetric_difference(ordinal_numbers,u),v)),ordinal_numbers) -> member(omega,intersection(union(u,identity_relation),complement(v)))*.
% 299.99/300.67  224141[8:SpL:160992.0,163545.0] || subclass(ordinal_numbers,complement(union(symmetric_difference(ordinal_numbers,u),v))) -> member(identity_relation,intersection(union(u,identity_relation),complement(v)))*.
% 299.99/300.67  224142[8:SpL:160992.0,151970.0] || subclass(ordinal_numbers,complement(union(symmetric_difference(ordinal_numbers,u),v))) -> member(omega,intersection(union(u,identity_relation),complement(v)))*.
% 299.99/300.67  224147[8:SpL:160992.0,81326.1] || subclass(ordinal_numbers,intersection(union(u,identity_relation),complement(v)))* subclass(domain_relation,union(symmetric_difference(ordinal_numbers,u),v)) -> .
% 299.99/300.67  224148[8:SpL:160992.0,81322.1] || subclass(domain_relation,intersection(union(u,identity_relation),complement(v)))* subclass(domain_relation,union(symmetric_difference(ordinal_numbers,u),v)) -> .
% 299.99/300.67  224149[8:SpL:160992.0,81488.1] || equal(intersection(union(u,identity_relation),complement(v)),ordinal_numbers)** equal(union(symmetric_difference(ordinal_numbers,u),v),domain_relation) -> .
% 299.99/300.67  224150[8:SpL:160992.0,81412.1] || equal(intersection(union(u,identity_relation),complement(v)),domain_relation)** equal(union(symmetric_difference(ordinal_numbers,u),v),domain_relation) -> .
% 299.99/300.67  224153[8:SpL:160992.0,147101.1] || equal(intersection(union(u,identity_relation),complement(v)),ordinal_numbers) subclass(omega,union(symmetric_difference(ordinal_numbers,u),v))* -> .
% 299.99/300.67  224154[8:SpL:160992.0,126664.1] || subclass(ordinal_numbers,intersection(union(u,identity_relation),complement(v)))* subclass(omega,union(symmetric_difference(ordinal_numbers,u),v)) -> .
% 299.99/300.67  224155[8:SpL:160992.0,147315.1] || equal(intersection(union(u,identity_relation),complement(v)),omega) subclass(omega,union(symmetric_difference(ordinal_numbers,u),v))* -> .
% 299.99/300.67  224156[8:SpL:160992.0,126665.1] || subclass(omega,intersection(union(u,identity_relation),complement(v)))* subclass(omega,union(symmetric_difference(ordinal_numbers,u),v)) -> .
% 299.99/300.67  224157[22:SpL:160992.0,205502.0] || well_ordering(ordinal_numbers,union(symmetric_difference(ordinal_numbers,u),v)) -> member(singleton(identity_relation),intersection(union(u,identity_relation),complement(v)))*.
% 299.99/300.67  224159[8:SpL:160992.0,134130.0] || well_ordering(ordinal_numbers,union(symmetric_difference(ordinal_numbers,u),v)) well_ordering(ordinal_numbers,intersection(union(u,identity_relation),complement(v)))* -> .
% 299.99/300.67  224161[8:SpL:160992.0,167369.0] || equal(union(symmetric_difference(ordinal_numbers,u),v),omega) equal(intersection(union(u,identity_relation),complement(v)),ordinal_numbers)** -> .
% 299.99/300.67  224162[8:SpL:160992.0,147805.0] || equal(union(symmetric_difference(ordinal_numbers,u),v),omega) equal(intersection(union(u,identity_relation),complement(v)),omega)** -> .
% 299.99/300.67  224170[14:SpL:160992.0,195115.1] inductive(intersection(union(u,identity_relation),complement(v))) || equal(union(symmetric_difference(ordinal_numbers,u),v),singleton(identity_relation))** -> .
% 299.99/300.67  224172[18:SpL:160992.0,196166.1] inductive(intersection(union(u,identity_relation),complement(v))) || equal(union(symmetric_difference(ordinal_numbers,u),v),symmetrization_of(identity_relation))** -> .
% 299.99/300.67  224174[18:SpL:160992.0,196256.1] inductive(intersection(union(u,identity_relation),complement(v))) || equal(union(symmetric_difference(ordinal_numbers,u),v),inverse(identity_relation))** -> .
% 299.99/300.67  224180[8:SpL:160992.0,221330.0] || subclass(union(symmetric_difference(ordinal_numbers,u),v),identity_relation) well_ordering(ordinal_numbers,intersection(union(u,identity_relation),complement(v)))* -> .
% 299.99/300.67  224189[8:SpL:160992.0,151988.0] || member(u,complement(union(symmetric_difference(ordinal_numbers,v),w))) -> member(u,intersection(union(v,identity_relation),complement(w)))*.
% 299.99/300.67  224301[8:Res:13125.2,18750.0] || subclass(omega,u) -> equal(integer_of(regular(regular(u))),identity_relation)** equal(regular(u),identity_relation) equal(u,identity_relation).
% 299.99/300.67  224426[25:SpR:223660.1,208873.0] || subclass(element_relation,identity_relation) -> equal(unordered_pair(identity_relation,unordered_pair(cross_product(ordinal_numbers,ordinal_numbers),identity_relation)),ordered_pair(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers))**.
% 299.99/300.67  224466[10:SpL:223660.1,2557.0] || subclass(element_relation,identity_relation) member(singleton(singleton(identity_relation)),cross_product(u,v))* -> member(cross_product(ordinal_numbers,ordinal_numbers),v).
% 299.99/300.67  225113[8:Obv:225082.2] || member(u,v) member(u,intersection(w,singleton(v)))* -> equal(intersection(w,singleton(v)),identity_relation).
% 299.99/300.67  225114[8:Obv:225078.2] || subclass(ordinal_numbers,u) member(omega,intersection(v,singleton(u)))* -> equal(intersection(v,singleton(u)),identity_relation).
% 299.99/300.67  225115[7:Obv:225049.1] || subclass(intersection(u,singleton(v)),omega)* -> equal(intersection(u,singleton(v)),identity_relation) equal(integer_of(v),v).
% 299.99/300.67  225120[8:Rew:13570.1,225119.1] || member(regular(u),intersection(v,singleton(u)))* -> equal(u,identity_relation) equal(intersection(v,singleton(u)),identity_relation).
% 299.99/300.67  225228[8:Obv:225191.2] || member(u,v) member(u,intersection(singleton(v),w))* -> equal(intersection(singleton(v),w),identity_relation).
% 299.99/300.67  225229[8:Obv:225187.2] || subclass(ordinal_numbers,u) member(omega,intersection(singleton(u),v))* -> equal(intersection(singleton(u),v),identity_relation).
% 299.99/300.67  225230[7:Obv:225152.1] || subclass(intersection(singleton(u),v),omega)* -> equal(intersection(singleton(u),v),identity_relation) equal(integer_of(u),u).
% 299.99/300.67  225235[8:Rew:17399.1,225234.1] || member(regular(u),intersection(singleton(u),v))* -> equal(u,identity_relation) equal(intersection(singleton(u),v),identity_relation).
% 299.99/300.67  225245[26:SpL:160927.0,224734.0] || subclass(omega,union(u,symmetric_difference(ordinal_numbers,v))) member(identity_relation,intersection(complement(u),union(v,identity_relation)))* -> .
% 299.99/300.67  225246[26:SpL:160992.0,224734.0] || subclass(omega,union(symmetric_difference(ordinal_numbers,u),v)) member(identity_relation,intersection(union(u,identity_relation),complement(v)))* -> .
% 299.99/300.67  225258[26:SpL:481.0,224734.0] || subclass(omega,power_class(intersection(complement(u),complement(v))))* member(identity_relation,image(element_relation,union(u,v))) -> .
% 299.99/300.67  225268[26:SpL:160927.0,224737.0] || subclass(omega,complement(union(u,symmetric_difference(ordinal_numbers,v)))) -> member(identity_relation,intersection(complement(u),union(v,identity_relation)))*.
% 299.99/300.67  225269[26:SpL:160992.0,224737.0] || subclass(omega,complement(union(symmetric_difference(ordinal_numbers,u),v))) -> member(identity_relation,intersection(union(u,identity_relation),complement(v)))*.
% 299.99/300.67  225281[26:SpL:481.0,224737.0] || subclass(omega,complement(power_class(intersection(complement(u),complement(v)))))* -> member(identity_relation,image(element_relation,union(u,v))).
% 299.99/300.67  225426[7:Res:13125.2,17312.1] || subclass(omega,u) subclass(v,complement(u))* -> equal(integer_of(regular(v)),identity_relation) equal(v,identity_relation).
% 299.99/300.67  225492[7:SpL:30.0,225445.0] || subclass(intersection(complement(u),complement(v)),union(u,v))* -> equal(intersection(complement(u),complement(v)),identity_relation).
% 299.99/300.67  225505[7:SpL:189.0,225445.0] || subclass(image(element_relation,power_class(u)),power_class(image(element_relation,complement(u))))* -> equal(image(element_relation,power_class(u)),identity_relation).
% 299.99/300.67  225566[26:SpL:160927.0,225289.0] || equal(complement(union(u,symmetric_difference(ordinal_numbers,v))),omega) -> member(identity_relation,intersection(complement(u),union(v,identity_relation)))*.
% 299.99/300.67  225567[26:SpL:160992.0,225289.0] || equal(complement(union(symmetric_difference(ordinal_numbers,u),v)),omega) -> member(identity_relation,intersection(union(u,identity_relation),complement(v)))*.
% 299.99/300.67  225579[26:SpL:481.0,225289.0] || equal(complement(power_class(intersection(complement(u),complement(v)))),omega)** -> member(identity_relation,image(element_relation,union(u,v))).
% 299.99/300.67  225725[26:SpL:3594.0,224747.0] || subclass(omega,symmetric_difference(complement(intersection(u,v)),union(u,v)))* -> member(identity_relation,complement(symmetric_difference(u,v))).
% 299.99/300.67  225960[26:SpL:3594.0,225765.0] || equal(symmetric_difference(complement(intersection(u,v)),union(u,v)),omega)** -> member(identity_relation,complement(symmetric_difference(u,v))).
% 299.99/300.67  226048[7:Res:13578.1,5.0] || subclass(union(u,v),w) -> equal(symmetric_difference(u,v),identity_relation) member(regular(symmetric_difference(u,v)),w)*.
% 299.99/300.67  226154[7:Res:18949.0,17321.0] ||  -> equal(restrict(intersection(u,v),w,x),identity_relation) member(regular(restrict(intersection(u,v),w,x)),v)*.
% 299.99/300.67  226259[7:Res:18949.0,17322.0] ||  -> equal(restrict(intersection(u,v),w,x),identity_relation) member(regular(restrict(intersection(u,v),w,x)),u)*.
% 299.99/300.67  226385[7:Res:13258.1,151988.0] ||  -> equal(restrict(complement(complement(u)),v,w),identity_relation) member(regular(restrict(complement(complement(u)),v,w)),u)*.
% 299.99/300.67  226391[7:Res:13258.1,5.0] || subclass(u,v) -> equal(restrict(u,w,x),identity_relation) member(regular(restrict(u,w,x)),v)*.
% 299.99/300.67  226422[7:Res:13258.1,8788.0] ||  -> equal(restrict(recursion_equation_functions(u),v,w),identity_relation) subclass(regular(restrict(recursion_equation_functions(u),v,w)),cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.67  226621[14:Rew:66036.0,226611.1] || member(identity_relation,intersection(complement(u),complement(v))) subclass(complement(intersection(union(u,v),ordinal_numbers)),identity_relation)* -> .
% 299.99/300.67  227125[21:Res:196520.2,9876.0] || member(u,ordinal_numbers)* equal(successor(u),identity_relation) subclass(successor_relation,v) well_ordering(ordinal_numbers,v)* -> .
% 299.99/300.67  227196[8:Rew:66036.0,227187.0] || equal(complement(intersection(union(u,v),ordinal_numbers)),identity_relation) member(identity_relation,intersection(complement(u),complement(v)))* -> .
% 299.99/300.67  227250[8:SpR:61728.2,141387.0] || member(u,ordinal_numbers) subclass(rest_relation,union_of_range_map) -> equal(symmetric_difference(rest_of(u),ordinal_numbers),symmetric_difference(ordinal_numbers,rest_of(u)))**.
% 299.99/300.67  227275[8:SpL:61728.2,222208.0] || member(u,ordinal_numbers) subclass(rest_relation,union_of_range_map) member(identity_relation,rest_of(u))* subclass(element_relation,identity_relation) -> .
% 299.99/300.67  227278[26:SpL:61728.2,224803.0] || member(u,ordinal_numbers) subclass(rest_relation,union_of_range_map) subclass(omega,rest_of(u))* subclass(element_relation,identity_relation) -> .
% 299.99/300.67  227279[26:SpL:61728.2,225144.0] || member(u,ordinal_numbers)* subclass(rest_relation,union_of_range_map) equal(rest_of(u),omega) subclass(element_relation,identity_relation) -> .
% 299.99/300.67  227334[7:SpR:192979.1,72.0] ||  -> equal(cross_product(singleton(u),ordinal_numbers),identity_relation) equal(apply(regular(cross_product(singleton(u),ordinal_numbers)),u),sum_class(range_of(identity_relation)))**.
% 299.99/300.67  227435[8:Rew:66036.0,227426.0] || equal(complement(intersection(union(u,v),ordinal_numbers)),identity_relation) member(omega,intersection(complement(u),complement(v)))* -> .
% 299.99/300.67  227769[21:SpL:218383.1,28976.1] || subclass(domain_relation,rest_relation) subclass(rest_relation,inverse(subset_relation)) member(ordered_pair(unordered_pair(u,v),identity_relation),subset_relation)* -> .
% 299.99/300.67  227842[21:SpL:218385.1,28976.1] || subclass(domain_relation,rest_relation) subclass(rest_relation,inverse(subset_relation)) member(ordered_pair(ordered_pair(u,v),identity_relation),subset_relation)* -> .
% 299.99/300.67  227912[21:SpL:218559.1,28976.1] || subclass(rest_relation,domain_relation) subclass(rest_relation,inverse(subset_relation)) member(ordered_pair(unordered_pair(u,v),identity_relation),subset_relation)* -> .
% 299.99/300.67  227974[25:SpR:208985.1,13410.1] operation(u) || subclass(omega,rest_relation) -> equal(integer_of(ordered_pair(v,ordinal_numbers)),identity_relation)** equal(rest_of(v),u)*.
% 299.99/300.67  228006[21:SpL:218561.1,28976.1] || subclass(rest_relation,domain_relation) subclass(rest_relation,inverse(subset_relation)) member(ordered_pair(ordered_pair(u,v),identity_relation),subset_relation)* -> .
% 299.99/300.67  228121[25:SpR:208985.1,160930.1] operation(u) || subclass(omega,domain_relation) -> equal(integer_of(ordered_pair(v,ordinal_numbers)),identity_relation)** equal(cantor(v),u)*.
% 299.99/300.67  228127[25:SpR:208985.1,160930.1] operation(u) || subclass(omega,domain_relation) -> equal(integer_of(ordered_pair(v,u)),identity_relation)** equal(cantor(v),ordinal_numbers).
% 299.99/300.67  228186[25:SpR:208985.1,13412.1] operation(u) || subclass(omega,successor_relation) -> equal(integer_of(ordered_pair(v,ordinal_numbers)),identity_relation)** equal(successor(v),u)*.
% 299.99/300.67  228192[25:SpR:208985.1,13412.1] operation(u) || subclass(omega,successor_relation) -> equal(integer_of(ordered_pair(v,u)),identity_relation)** equal(successor(v),ordinal_numbers).
% 299.99/300.67  228597[5:Rew:47.0,228584.0,30.0,228584.0] || subclass(ordinal_numbers,image(element_relation,successor(u))) member(unordered_pair(v,w),complement(image(element_relation,successor(u))))* -> .
% 299.99/300.67  228598[5:Rew:117.0,228583.0,30.0,228583.0] || subclass(ordinal_numbers,image(element_relation,symmetrization_of(u))) member(unordered_pair(v,w),complement(image(element_relation,symmetrization_of(u))))* -> .
% 299.99/300.67  228725[8:Res:193179.0,18535.2] || member(u,ordinal_numbers) subclass(ordinal_numbers,complement(inverse(singleton(power_class(u)))))* -> asymmetric(singleton(power_class(u)),v)*.
% 299.99/300.67  229136[8:Res:156922.1,17387.0] || member(regular(intersection(complement(complement(subset_relation)),u)),inverse(subset_relation))* -> equal(intersection(complement(complement(subset_relation)),u),identity_relation).
% 299.99/300.67  229150[8:Res:204134.1,17387.0] || member(regular(intersection(complement(symmetrization_of(identity_relation)),u)),inverse(identity_relation))* -> equal(intersection(complement(symmetrization_of(identity_relation)),u),identity_relation).
% 299.99/300.67  229198[8:Rew:160491.0,229142.1,160491.0,229142.0] || member(regular(intersection(union(u,identity_relation),v)),complement(u))* -> equal(intersection(union(u,identity_relation),v),identity_relation).
% 299.99/300.67  229201[7:Rew:59.0,229096.1] || member(regular(intersection(power_class(u),v)),image(element_relation,complement(u)))* -> equal(intersection(power_class(u),v),identity_relation).
% 299.99/300.67  229565[8:Res:156922.1,13571.0] || member(regular(intersection(u,complement(complement(subset_relation)))),inverse(subset_relation))* -> equal(intersection(u,complement(complement(subset_relation))),identity_relation).
% 299.99/300.67  229579[8:Res:204134.1,13571.0] || member(regular(intersection(u,complement(symmetrization_of(identity_relation)))),inverse(identity_relation))* -> equal(intersection(u,complement(symmetrization_of(identity_relation))),identity_relation).
% 299.99/300.67  229773[8:Rew:160491.0,229571.1,160491.0,229571.0] || member(regular(intersection(u,union(v,identity_relation))),complement(v))* -> equal(intersection(u,union(v,identity_relation)),identity_relation).
% 299.99/300.67  229779[7:Rew:59.0,229539.1] || member(regular(intersection(u,power_class(v))),image(element_relation,complement(v)))* -> equal(intersection(u,power_class(v)),identity_relation).
% 299.99/300.67  231060[8:Res:13225.3,230762.0] || member(u,ordinal_numbers) subclass(u,subset_relation) subclass(ordinal_numbers,apply(choice,u))* -> equal(u,identity_relation).
% 299.99/300.67  231138[8:Res:13225.3,230780.0] || member(u,ordinal_numbers) subclass(u,subset_relation) equal(apply(choice,u),ordinal_numbers)** -> equal(u,identity_relation).
% 299.99/300.67  231545[8:SpR:160927.0,229281.0] ||  -> equal(intersection(power_class(intersection(complement(u),union(v,identity_relation))),image(element_relation,union(u,symmetric_difference(ordinal_numbers,v)))),identity_relation)**.
% 299.99/300.67  231546[8:SpR:160992.0,229281.0] ||  -> equal(intersection(power_class(intersection(union(u,identity_relation),complement(v))),image(element_relation,union(symmetric_difference(ordinal_numbers,u),v))),identity_relation)**.
% 299.99/300.67  231558[7:SpR:481.0,229281.0] ||  -> equal(intersection(power_class(image(element_relation,union(u,v))),image(element_relation,power_class(intersection(complement(u),complement(v))))),identity_relation)**.
% 299.99/300.67  231849[8:SpR:30.0,231812.0] ||  -> subclass(regular(intersection(complement(u),complement(v))),union(u,v))* equal(intersection(complement(u),complement(v)),identity_relation).
% 299.99/300.67  231862[8:SpR:189.0,231812.0] ||  -> subclass(regular(image(element_relation,power_class(u))),power_class(image(element_relation,complement(u))))* equal(image(element_relation,power_class(u)),identity_relation).
% 299.99/300.67  231888[8:Obv:231871.0] ||  -> equal(regular(unordered_pair(u,v)),u) subclass(v,complement(unordered_pair(u,v)))* equal(unordered_pair(u,v),identity_relation).
% 299.99/300.67  231889[8:Obv:231870.0] ||  -> equal(regular(unordered_pair(u,v)),v) subclass(u,complement(unordered_pair(u,v)))* equal(unordered_pair(u,v),identity_relation).
% 299.99/300.67  231914[8:SpR:160927.0,229481.0] ||  -> equal(symmetric_difference(power_class(intersection(complement(u),union(v,identity_relation))),image(element_relation,union(u,symmetric_difference(ordinal_numbers,v)))),ordinal_numbers)**.
% 299.99/300.67  231915[8:SpR:160992.0,229481.0] ||  -> equal(symmetric_difference(power_class(intersection(union(u,identity_relation),complement(v))),image(element_relation,union(symmetric_difference(ordinal_numbers,u),v))),ordinal_numbers)**.
% 299.99/300.67  231927[8:SpR:481.0,229481.0] ||  -> equal(symmetric_difference(power_class(image(element_relation,union(u,v))),image(element_relation,power_class(intersection(complement(u),complement(v))))),ordinal_numbers)**.
% 299.99/300.67  232238[8:SpR:160927.0,229909.0] ||  -> equal(intersection(image(element_relation,union(u,symmetric_difference(ordinal_numbers,v))),power_class(intersection(complement(u),union(v,identity_relation)))),identity_relation)**.
% 299.99/300.67  232239[8:SpR:160992.0,229909.0] ||  -> equal(intersection(image(element_relation,union(symmetric_difference(ordinal_numbers,u),v)),power_class(intersection(union(u,identity_relation),complement(v)))),identity_relation)**.
% 299.99/300.67  232251[7:SpR:481.0,229909.0] ||  -> equal(intersection(image(element_relation,power_class(intersection(complement(u),complement(v)))),power_class(image(element_relation,union(u,v)))),identity_relation)**.
% 299.99/300.67  232417[8:SpR:160927.0,230084.0] ||  -> equal(symmetric_difference(image(element_relation,union(u,symmetric_difference(ordinal_numbers,v))),power_class(intersection(complement(u),union(v,identity_relation)))),ordinal_numbers)**.
% 299.99/300.67  232418[8:SpR:160992.0,230084.0] ||  -> equal(symmetric_difference(image(element_relation,union(symmetric_difference(ordinal_numbers,u),v)),power_class(intersection(union(u,identity_relation),complement(v)))),ordinal_numbers)**.
% 299.99/300.67  232430[8:SpR:481.0,230084.0] ||  -> equal(symmetric_difference(image(element_relation,power_class(intersection(complement(u),complement(v)))),power_class(image(element_relation,union(u,v)))),ordinal_numbers)**.
% 299.99/300.67  233193[16:Rew:195239.0,233176.1] || member(regular(image(element_relation,singleton(identity_relation))),power_class(complement(singleton(identity_relation))))* -> equal(image(element_relation,singleton(identity_relation)),identity_relation).
% 299.99/300.67  233194[8:Rew:162584.0,233177.1] || member(regular(image(element_relation,symmetrization_of(identity_relation))),power_class(complement(inverse(identity_relation))))* -> equal(image(element_relation,symmetrization_of(identity_relation)),identity_relation).
% 299.99/300.67  233473[8:Res:161057.2,217200.1] || well_ordering(u,ordinal_numbers) equal(singleton(cantor(least(u,recursion_equation_functions(v)))),identity_relation)** -> equal(recursion_equation_functions(v),identity_relation).
% 299.99/300.67  233477[21:Res:161057.2,197870.1] || well_ordering(u,ordinal_numbers) equal(rest_of(cantor(least(u,recursion_equation_functions(v)))),rest_relation)** -> equal(recursion_equation_functions(v),identity_relation).
% 299.99/300.67  233500[21:Res:156922.1,196424.2] || member(ordered_pair(u,identity_relation),inverse(subset_relation))* member(u,ordinal_numbers) subclass(domain_relation,complement(complement(subset_relation))) -> .
% 299.99/300.67  233520[21:Res:204134.1,196424.2] || member(ordered_pair(u,identity_relation),inverse(identity_relation))* member(u,ordinal_numbers) subclass(domain_relation,complement(symmetrization_of(identity_relation))) -> .
% 299.99/300.67  233563[21:Rew:160491.0,233507.2] || member(ordered_pair(u,identity_relation),complement(v))* member(u,ordinal_numbers) subclass(domain_relation,union(v,identity_relation)) -> .
% 299.99/300.67  233575[21:MRR:233509.0,8667.0] || member(u,ordinal_numbers) subclass(domain_relation,complement(union(v,w)))* -> member(ordered_pair(u,identity_relation),complement(w))*.
% 299.99/300.67  233576[21:MRR:233508.0,8667.0] || member(u,ordinal_numbers) subclass(domain_relation,complement(union(v,w)))* -> member(ordered_pair(u,identity_relation),complement(v))*.
% 299.99/300.67  233796[15:Res:217197.1,941.1] || equal(complement(power_class(image(element_relation,complement(u)))),identity_relation) member(range_of(identity_relation),image(element_relation,power_class(u)))* -> .
% 299.99/300.67  233797[15:Res:215659.1,941.1] || subclass(complement(power_class(image(element_relation,complement(u)))),identity_relation)* member(range_of(identity_relation),image(element_relation,power_class(u))) -> .
% 299.99/300.67  233801[15:Res:165442.1,941.1] || subclass(ordinal_numbers,power_class(image(element_relation,complement(u)))) member(sum_class(range_of(identity_relation)),image(element_relation,power_class(u)))* -> .
% 299.99/300.67  233823[8:Res:217198.1,941.1] || equal(complement(power_class(image(element_relation,complement(u)))),identity_relation) member(singleton(v),image(element_relation,power_class(u)))* -> .
% 299.99/300.67  233824[8:Res:215662.1,941.1] || subclass(complement(power_class(image(element_relation,complement(u)))),identity_relation)* member(singleton(v),image(element_relation,power_class(u)))* -> .
% 299.99/300.67  233855[18:Res:190515.1,941.1] || subclass(ordinal_numbers,power_class(image(element_relation,complement(u)))) member(regular(symmetrization_of(identity_relation)),image(element_relation,power_class(u)))* -> .
% 299.99/300.67  233895[24:SpL:207565.1,161200.0] operation(u) || member(v,image(element_relation,successor(u)))* member(v,power_class(symmetric_difference(ordinal_numbers,u))) -> .
% 299.99/300.67  233913[8:Res:8643.1,161200.0] || subclass(ordinal_numbers,image(element_relation,union(u,identity_relation))) member(unordered_pair(v,w),power_class(symmetric_difference(ordinal_numbers,u)))* -> .
% 299.99/300.67  233923[15:Res:165442.1,161200.0] || subclass(ordinal_numbers,image(element_relation,union(u,identity_relation))) member(sum_class(range_of(identity_relation)),power_class(symmetric_difference(ordinal_numbers,u)))* -> .
% 299.99/300.67  233937[8:Res:143222.1,161200.0] || equal(image(element_relation,union(u,identity_relation)),omega) member(least(element_relation,omega),power_class(symmetric_difference(ordinal_numbers,u)))* -> .
% 299.99/300.67  233938[8:Res:143193.1,161200.0] || equal(image(element_relation,union(u,identity_relation)),ordinal_numbers) member(least(element_relation,omega),power_class(symmetric_difference(ordinal_numbers,u)))* -> .
% 299.99/300.67  233941[8:Res:125731.1,161200.0] || subclass(ordinal_numbers,image(element_relation,union(u,identity_relation))) member(least(element_relation,omega),power_class(symmetric_difference(ordinal_numbers,u)))* -> .
% 299.99/300.67  233942[8:Res:125725.1,161200.0] || subclass(omega,image(element_relation,union(u,identity_relation))) member(least(element_relation,omega),power_class(symmetric_difference(ordinal_numbers,u)))* -> .
% 299.99/300.67  233957[8:Res:8642.1,161200.0] || subclass(ordinal_numbers,image(element_relation,union(u,identity_relation))) member(ordered_pair(v,w),power_class(symmetric_difference(ordinal_numbers,u)))* -> .
% 299.99/300.67  233959[8:Res:15426.1,161200.0] || subclass(domain_relation,image(element_relation,union(u,identity_relation))) member(ordered_pair(identity_relation,identity_relation),power_class(symmetric_difference(ordinal_numbers,u)))* -> .
% 299.99/300.67  233977[18:Res:190515.1,161200.0] || subclass(ordinal_numbers,image(element_relation,union(u,identity_relation))) member(regular(symmetrization_of(identity_relation)),power_class(symmetric_difference(ordinal_numbers,u)))* -> .
% 299.99/300.67  234816[8:Res:193440.1,210517.1] || member(u,ordinal_numbers) equal(complement(cantor(v)),ordinal_numbers) -> equal(apply(v,u),sum_class(range_of(identity_relation)))**.
% 299.99/300.67  234879[21:MRR:234794.2,14676.0] || well_ordering(u,rest_relation) member(v,ordinal_numbers) -> equal(apply(least(u,rest_relation),v),sum_class(range_of(identity_relation)))**.
% 299.99/300.67  234880[21:MRR:234793.2,14676.0] || well_ordering(u,ordinal_numbers) member(v,ordinal_numbers) -> equal(apply(least(u,rest_relation),v),sum_class(range_of(identity_relation)))**.
% 299.99/300.67  234881[21:MRR:234792.2,14676.0] || well_ordering(u,ordinal_numbers) member(v,ordinal_numbers) -> equal(apply(least(u,ordinal_numbers),v),sum_class(range_of(identity_relation)))**.
% 299.99/300.67  234887[8:MRR:234828.0,60996.1] || subclass(u,complement(cantor(v)))* -> equal(apply(v,regular(u)),sum_class(range_of(identity_relation))) equal(u,identity_relation).
% 299.99/300.67  234889[8:MRR:234842.1,8667.0] operation(u) ||  -> equal(apply(u,ordered_pair(v,w)),sum_class(range_of(identity_relation)))** member(v,cantor(cantor(u))).
% 299.99/300.67  234890[8:MRR:234841.1,8667.0] operation(u) ||  -> equal(apply(u,ordered_pair(v,w)),sum_class(range_of(identity_relation)))** member(w,cantor(cantor(u))).
% 299.99/300.67  235285[8:Res:230445.1,47534.0] || member(not_subclass_element(u,intersection(union(v,identity_relation),u)),v)* -> subclass(u,intersection(union(v,identity_relation),u)).
% 299.99/300.67  235298[21:Res:230445.1,196424.2] || member(ordered_pair(u,identity_relation),v)* member(u,ordinal_numbers) subclass(domain_relation,complement(union(v,identity_relation)))* -> .
% 299.99/300.67  235353[5:SpR:963.0,28980.1] || subclass(rest_relation,flip(u)) -> member(ordered_pair(ordered_pair(v,singleton(v)),rest_of(singleton(singleton(singleton(v))))),u)*.
% 299.99/300.67  235364[5:SpR:963.0,28980.1] || subclass(rest_relation,flip(u)) -> member(ordered_pair(singleton(singleton(singleton(v))),rest_of(ordered_pair(v,singleton(v)))),u)*.
% 299.99/300.67  235374[5:Res:28980.1,28.1] || subclass(rest_relation,flip(complement(u))) member(ordered_pair(ordered_pair(v,w),rest_of(ordered_pair(w,v))),u)* -> .
% 299.99/300.67  235377[5:Res:28980.1,151988.0] || subclass(rest_relation,flip(complement(complement(u)))) -> member(ordered_pair(ordered_pair(v,w),rest_of(ordered_pair(w,v))),u)*.
% 299.99/300.67  235385[5:Res:28980.1,26.0] || subclass(rest_relation,flip(intersection(u,v)))* -> member(ordered_pair(ordered_pair(w,x),rest_of(ordered_pair(x,w))),v)*.
% 299.99/300.67  235386[5:Res:28980.1,25.0] || subclass(rest_relation,flip(intersection(u,v)))* -> member(ordered_pair(ordered_pair(w,x),rest_of(ordered_pair(x,w))),u)*.
% 299.99/300.67  235409[8:Res:28980.1,233381.0] || subclass(rest_relation,flip(singleton(omega))) -> equal(integer_of(ordered_pair(ordered_pair(u,v),rest_of(ordered_pair(v,u)))),identity_relation)**.
% 299.99/300.67  235412[8:Res:28980.1,14679.1] || subclass(rest_relation,flip(inverse(subset_relation))) member(ordered_pair(ordered_pair(u,v),rest_of(ordered_pair(v,u))),subset_relation)* -> .
% 299.99/300.67  235415[8:Res:28980.1,234983.0] || subclass(rest_relation,flip(cantor(complement(cross_product(singleton(ordered_pair(ordered_pair(u,v),rest_of(ordered_pair(v,u)))),ordinal_numbers)))))* -> .
% 299.99/300.67  235416[8:Res:28980.1,219203.0] || subclass(rest_relation,flip(rest_of(ordered_pair(ordered_pair(u,v),rest_of(ordered_pair(v,u))))))* subclass(element_relation,identity_relation) -> .
% 299.99/300.67  235420[8:Res:28980.1,163154.0] || subclass(rest_relation,flip(symmetrization_of(identity_relation))) -> member(ordered_pair(ordered_pair(u,v),rest_of(ordered_pair(v,u))),inverse(identity_relation))*.
% 299.99/300.67  235447[5:Res:28980.1,8651.0] || subclass(rest_relation,flip(rest_of(u))) -> equal(restrict(u,ordered_pair(v,w),ordinal_numbers),rest_of(ordered_pair(w,v)))**.
% 299.99/300.67  235458[8:Res:28980.1,117450.1] operation(u) || subclass(rest_relation,flip(cantor(u))) -> member(rest_of(ordered_pair(v,w)),cantor(cantor(u)))*.
% 299.99/300.67  235487[5:SpR:963.0,28979.1] || subclass(rest_relation,rotate(u)) -> member(ordered_pair(ordered_pair(v,rest_of(singleton(singleton(singleton(v))))),singleton(v)),u)*.
% 299.99/300.67  235502[5:Res:28979.1,28.1] || subclass(rest_relation,rotate(complement(u))) member(ordered_pair(ordered_pair(v,rest_of(ordered_pair(w,v))),w),u)* -> .
% 299.99/300.67  235505[5:Res:28979.1,151988.0] || subclass(rest_relation,rotate(complement(complement(u)))) -> member(ordered_pair(ordered_pair(v,rest_of(ordered_pair(w,v))),w),u)*.
% 299.99/300.67  235513[5:Res:28979.1,26.0] || subclass(rest_relation,rotate(intersection(u,v)))* -> member(ordered_pair(ordered_pair(w,rest_of(ordered_pair(x,w))),x),v)*.
% 299.99/300.67  235514[5:Res:28979.1,25.0] || subclass(rest_relation,rotate(intersection(u,v)))* -> member(ordered_pair(ordered_pair(w,rest_of(ordered_pair(x,w))),x),u)*.
% 299.99/300.67  235537[8:Res:28979.1,233381.0] || subclass(rest_relation,rotate(singleton(omega))) -> equal(integer_of(ordered_pair(ordered_pair(u,rest_of(ordered_pair(v,u))),v)),identity_relation)**.
% 299.99/300.67  235540[8:Res:28979.1,14679.1] || subclass(rest_relation,rotate(inverse(subset_relation))) member(ordered_pair(ordered_pair(u,rest_of(ordered_pair(v,u))),v),subset_relation)* -> .
% 299.99/300.67  235543[8:Res:28979.1,234983.0] || subclass(rest_relation,rotate(cantor(complement(cross_product(singleton(ordered_pair(ordered_pair(u,rest_of(ordered_pair(v,u))),v)),ordinal_numbers)))))* -> .
% 299.99/300.67  235544[8:Res:28979.1,219203.0] || subclass(rest_relation,rotate(rest_of(ordered_pair(ordered_pair(u,rest_of(ordered_pair(v,u))),v))))* subclass(element_relation,identity_relation) -> .
% 299.99/300.67  235548[8:Res:28979.1,163154.0] || subclass(rest_relation,rotate(symmetrization_of(identity_relation))) -> member(ordered_pair(ordered_pair(u,rest_of(ordered_pair(v,u))),v),inverse(identity_relation))*.
% 299.99/300.67  235575[5:Res:28979.1,8651.0] || subclass(rest_relation,rotate(rest_of(u))) -> equal(restrict(u,ordered_pair(v,rest_of(ordered_pair(w,v))),ordinal_numbers),w)**.
% 299.99/300.67  235585[5:Res:28979.1,100.0] || subclass(rest_relation,rotate(composition_function)) -> equal(compose(ordered_pair(u,rest_of(ordered_pair(ordered_pair(v,w),u))),v),w)**.
% 299.99/300.67  235844[8:Res:148858.1,13339.0] || subclass(omega,inverse(subset_relation)) subclass(complement(subset_relation),u)* -> equal(integer_of(v),identity_relation) member(v,u)*.
% 299.99/300.67  235845[8:Res:211438.1,13339.0] || equal(symmetrization_of(identity_relation),ordinal_numbers) subclass(symmetrization_of(identity_relation),u)* -> equal(integer_of(v),identity_relation) member(v,u)*.
% 299.99/300.67  235851[8:Res:210606.1,13339.0] || equal(complement(u),ordinal_numbers) subclass(complement(u),v)* -> equal(integer_of(w),identity_relation) member(w,v)*.
% 299.99/300.67  235852[8:Res:211441.1,13339.0] || equal(power_class(u),ordinal_numbers) subclass(power_class(u),v)* -> equal(integer_of(w),identity_relation) member(w,v)*.
% 299.99/300.67  235946[22:Res:69478.2,205501.0] || subclass(omega,symmetric_difference(u,v)) well_ordering(ordinal_numbers,union(u,v))* -> equal(integer_of(singleton(identity_relation)),identity_relation).
% 299.99/300.67  236305[8:Rew:162584.0,236216.1] || member(not_subclass_element(intersection(u,symmetrization_of(identity_relation)),v),complement(inverse(identity_relation)))* -> subclass(intersection(u,symmetrization_of(identity_relation)),v).
% 299.99/300.67  236520[8:Rew:162584.0,236405.1] || member(not_subclass_element(intersection(symmetrization_of(identity_relation),u),v),complement(inverse(identity_relation)))* -> subclass(intersection(symmetrization_of(identity_relation),u),v).
% 299.99/300.67  236528[5:Rew:155666.0,236432.1] || member(not_subclass_element(symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation),u),subset_relation)* -> subclass(symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation),u).
% 299.99/300.67  236529[5:Rew:155665.0,236431.1] || member(not_subclass_element(symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers)),u),subset_relation)* -> subclass(symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers)),u).
% 299.99/300.67  236597[16:SpL:195239.0,36857.0] || equal(u,singleton(identity_relation)) member(v,ordinal_numbers) -> member(v,complement(singleton(identity_relation)))* member(v,u)*.
% 299.99/300.67  236598[8:SpL:162584.0,36857.0] || equal(u,symmetrization_of(identity_relation)) member(v,ordinal_numbers) -> member(v,complement(inverse(identity_relation)))* member(v,u)*.
% 299.99/300.67  236819[7:Res:17392.2,28.1] || subclass(u,complement(v)) member(regular(intersection(u,w)),v)* -> equal(intersection(u,w),identity_relation).
% 299.99/300.67  236822[7:Res:17392.2,151988.0] || subclass(u,complement(complement(v))) -> equal(intersection(u,w),identity_relation) member(regular(intersection(u,w)),v)*.
% 299.99/300.67  236824[7:Res:17392.2,9876.0] || subclass(u,v)* subclass(v,w)* well_ordering(ordinal_numbers,w)* -> equal(intersection(u,x),identity_relation)**.
% 299.99/300.67  236830[7:Res:17392.2,26.0] || subclass(u,intersection(v,w))* -> equal(intersection(u,x),identity_relation) member(regular(intersection(u,x)),w)*.
% 299.99/300.67  236831[7:Res:17392.2,25.0] || subclass(u,intersection(v,w))* -> equal(intersection(u,x),identity_relation) member(regular(intersection(u,x)),v)*.
% 299.99/300.67  236841[8:Res:17392.2,230939.0] || subclass(u,subset_relation) equal(regular(regular(intersection(u,v))),ordinal_numbers)** -> equal(intersection(u,v),identity_relation).
% 299.99/300.67  236842[8:Res:17392.2,230867.0] || subclass(u,subset_relation) equal(complement(regular(intersection(u,v))),identity_relation)** -> equal(intersection(u,v),identity_relation).
% 299.99/300.67  236852[7:Res:17392.2,50033.0] || subclass(u,subset_relation) equal(complement(regular(intersection(u,v))),ordinal_numbers)** -> equal(intersection(u,v),identity_relation).
% 299.99/300.67  236854[8:Res:17392.2,233381.0] || subclass(u,singleton(omega)) -> equal(intersection(u,v),identity_relation) equal(integer_of(regular(intersection(u,v))),identity_relation)**.
% 299.99/300.67  236857[8:Res:17392.2,14679.1] || subclass(u,inverse(subset_relation)) member(regular(intersection(u,v)),subset_relation)* -> equal(intersection(u,v),identity_relation).
% 299.99/300.67  236860[8:Res:17392.2,234983.0] || subclass(u,cantor(complement(cross_product(singleton(regular(intersection(u,v))),ordinal_numbers))))* -> equal(intersection(u,v),identity_relation).
% 299.99/300.67  236861[8:Res:17392.2,219203.0] || subclass(u,rest_of(regular(intersection(u,v))))* subclass(element_relation,identity_relation) -> equal(intersection(u,v),identity_relation).
% 299.99/300.67  236865[8:Res:17392.2,163154.0] || subclass(u,symmetrization_of(identity_relation)) -> equal(intersection(u,v),identity_relation) member(regular(intersection(u,v)),inverse(identity_relation))*.
% 299.99/300.67  237112[8:Res:13574.1,230939.0] || equal(regular(regular(intersection(u,intersection(v,subset_relation)))),ordinal_numbers)** -> equal(intersection(u,intersection(v,subset_relation)),identity_relation).
% 299.99/300.67  237113[8:Res:13574.1,230867.0] || equal(complement(regular(intersection(u,intersection(v,subset_relation)))),identity_relation)** -> equal(intersection(u,intersection(v,subset_relation)),identity_relation).
% 299.99/300.67  237123[7:Res:13574.1,50033.0] || equal(complement(regular(intersection(u,intersection(v,subset_relation)))),ordinal_numbers)** -> equal(intersection(u,intersection(v,subset_relation)),identity_relation).
% 299.99/300.67  237124[7:Res:13574.1,3700.0] ||  -> equal(intersection(u,intersection(v,singleton(w))),identity_relation) equal(regular(intersection(u,intersection(v,singleton(w)))),w)**.
% 299.99/300.67  237763[8:Res:13573.1,230939.0] || equal(regular(regular(intersection(u,intersection(subset_relation,v)))),ordinal_numbers)** -> equal(intersection(u,intersection(subset_relation,v)),identity_relation).
% 299.99/300.67  237764[8:Res:13573.1,230867.0] || equal(complement(regular(intersection(u,intersection(subset_relation,v)))),identity_relation)** -> equal(intersection(u,intersection(subset_relation,v)),identity_relation).
% 299.99/300.67  237774[7:Res:13573.1,50033.0] || equal(complement(regular(intersection(u,intersection(subset_relation,v)))),ordinal_numbers)** -> equal(intersection(u,intersection(subset_relation,v)),identity_relation).
% 299.99/300.67  237775[7:Res:13573.1,3700.0] ||  -> equal(intersection(u,intersection(singleton(v),w)),identity_relation) equal(regular(intersection(u,intersection(singleton(v),w))),v)**.
% 299.99/300.67  238383[8:SpR:481.0,238174.0] ||  -> equal(intersection(complement(power_class(intersection(complement(u),complement(v)))),symmetric_difference(ordinal_numbers,image(element_relation,union(u,v)))),identity_relation)**.
% 299.99/300.67  238553[7:Res:13572.2,28.1] || subclass(u,complement(v)) member(regular(intersection(w,u)),v)* -> equal(intersection(w,u),identity_relation).
% 299.99/300.67  238556[7:Res:13572.2,151988.0] || subclass(u,complement(complement(v))) -> equal(intersection(w,u),identity_relation) member(regular(intersection(w,u)),v)*.
% 299.99/300.67  238558[7:Res:13572.2,9876.0] || subclass(u,v)* subclass(v,w)* well_ordering(ordinal_numbers,w)* -> equal(intersection(x,u),identity_relation)**.
% 299.99/300.67  238564[7:Res:13572.2,26.0] || subclass(u,intersection(v,w))* -> equal(intersection(x,u),identity_relation) member(regular(intersection(x,u)),w)*.
% 299.99/300.67  238565[7:Res:13572.2,25.0] || subclass(u,intersection(v,w))* -> equal(intersection(x,u),identity_relation) member(regular(intersection(x,u)),v)*.
% 299.99/300.67  238575[8:Res:13572.2,230939.0] || subclass(u,subset_relation) equal(regular(regular(intersection(v,u))),ordinal_numbers)** -> equal(intersection(v,u),identity_relation).
% 299.99/300.67  238576[8:Res:13572.2,230867.0] || subclass(u,subset_relation) equal(complement(regular(intersection(v,u))),identity_relation)** -> equal(intersection(v,u),identity_relation).
% 299.99/300.67  238586[7:Res:13572.2,50033.0] || subclass(u,subset_relation) equal(complement(regular(intersection(v,u))),ordinal_numbers)** -> equal(intersection(v,u),identity_relation).
% 299.99/300.67  238588[8:Res:13572.2,233381.0] || subclass(u,singleton(omega)) -> equal(intersection(v,u),identity_relation) equal(integer_of(regular(intersection(v,u))),identity_relation)**.
% 299.99/300.67  238591[8:Res:13572.2,14679.1] || subclass(u,inverse(subset_relation)) member(regular(intersection(v,u)),subset_relation)* -> equal(intersection(v,u),identity_relation).
% 299.99/300.67  238594[8:Res:13572.2,234983.0] || subclass(u,cantor(complement(cross_product(singleton(regular(intersection(v,u))),ordinal_numbers))))* -> equal(intersection(v,u),identity_relation).
% 299.99/300.67  238595[8:Res:13572.2,219203.0] || subclass(u,rest_of(regular(intersection(v,u))))* subclass(element_relation,identity_relation) -> equal(intersection(v,u),identity_relation).
% 299.99/300.67  238599[8:Res:13572.2,163154.0] || subclass(u,symmetrization_of(identity_relation)) -> equal(intersection(v,u),identity_relation) member(regular(intersection(v,u)),inverse(identity_relation))*.
% 299.99/300.67  238934[8:SpR:160927.0,237395.0] ||  -> equal(intersection(union(u,symmetric_difference(ordinal_numbers,v)),restrict(intersection(complement(u),union(v,identity_relation)),w,x)),identity_relation)**.
% 299.99/300.67  238935[8:SpR:160992.0,237395.0] ||  -> equal(intersection(union(symmetric_difference(ordinal_numbers,u),v),restrict(intersection(union(u,identity_relation),complement(v)),w,x)),identity_relation)**.
% 299.99/300.67  238947[7:SpR:481.0,237395.0] ||  -> equal(intersection(power_class(intersection(complement(u),complement(v))),restrict(image(element_relation,union(u,v)),w,x)),identity_relation)**.
% 299.99/300.67  239152[16:Rew:140603.0,239028.0,66036.0,239028.0] ||  -> equal(symmetric_difference(singleton(identity_relation),intersection(u,complement(singleton(identity_relation)))),union(singleton(identity_relation),intersection(u,complement(singleton(identity_relation)))))**.
% 299.99/300.67  239275[8:Res:17397.1,230939.0] || equal(regular(regular(intersection(intersection(subset_relation,u),v))),ordinal_numbers)** -> equal(intersection(intersection(subset_relation,u),v),identity_relation).
% 299.99/300.67  239276[8:Res:17397.1,230867.0] || equal(complement(regular(intersection(intersection(subset_relation,u),v))),identity_relation)** -> equal(intersection(intersection(subset_relation,u),v),identity_relation).
% 299.99/300.67  239286[7:Res:17397.1,50033.0] || equal(complement(regular(intersection(intersection(subset_relation,u),v))),ordinal_numbers)** -> equal(intersection(intersection(subset_relation,u),v),identity_relation).
% 299.99/300.67  239287[7:Res:17397.1,3700.0] ||  -> equal(intersection(intersection(singleton(u),v),w),identity_relation) equal(regular(intersection(intersection(singleton(u),v),w)),u)**.
% 299.99/300.67  240110[8:Res:17396.1,230939.0] || equal(regular(regular(intersection(intersection(u,subset_relation),v))),ordinal_numbers)** -> equal(intersection(intersection(u,subset_relation),v),identity_relation).
% 299.99/300.67  240111[8:Res:17396.1,230867.0] || equal(complement(regular(intersection(intersection(u,subset_relation),v))),identity_relation)** -> equal(intersection(intersection(u,subset_relation),v),identity_relation).
% 299.99/300.67  240121[7:Res:17396.1,50033.0] || equal(complement(regular(intersection(intersection(u,subset_relation),v))),ordinal_numbers)** -> equal(intersection(intersection(u,subset_relation),v),identity_relation).
% 299.99/300.67  240122[7:Res:17396.1,3700.0] ||  -> equal(intersection(intersection(u,singleton(v)),w),identity_relation) equal(regular(intersection(intersection(u,singleton(v)),w)),v)**.
% 299.99/300.67  66627[5:Res:8646.1,8554.1] || subclass(ordinal_numbers,complement(intersection(u,v)))* member(omega,union(u,v)) -> member(omega,symmetric_difference(u,v)).
% 299.99/300.67  69179[8:Res:8827.2,66086.1] || member(u,ordinal_numbers) subclass(rest_relation,complement(compose(element_relation,ordinal_numbers))) member(ordered_pair(u,rest_of(u)),element_relation)* -> .
% 299.99/300.67  56408[5:Res:41112.1,129.0] || member(u,rest_of(u))* subclass(element_relation,v) well_ordering(w,v)* -> member(least(w,element_relation),element_relation)*.
% 299.99/300.67  57144[5:Res:8827.2,19559.0] || member(u,ordinal_numbers) subclass(rest_relation,symmetric_difference(v,singleton(v)))* -> member(ordered_pair(u,rest_of(u)),successor(v))*.
% 299.99/300.67  19540[0:SpR:3596.0,3618.1] || member(u,symmetric_difference(complement(intersection(v,singleton(v))),successor(v)))* -> member(u,complement(symmetric_difference(v,singleton(v)))).
% 299.99/300.67  48563[5:SpL:3594.0,10088.0] || equal(symmetric_difference(complement(intersection(u,v)),union(u,v)),ordinal_numbers)** -> member(singleton(w),complement(symmetric_difference(u,v)))*.
% 299.99/300.67  48566[5:SpL:3594.0,8848.0] || subclass(ordinal_numbers,symmetric_difference(complement(intersection(u,v)),union(u,v)))* -> member(singleton(w),complement(symmetric_difference(u,v)))*.
% 299.99/300.67  39783[0:SpL:126.0,9583.0] || equal(segment(u,v,w),singleton(w)) subclass(singleton(w),v) -> section(u,singleton(w),v)*.
% 299.99/300.67  9696[5:Res:9632.1,21.0] || equal(complement(complement(cross_product(u,v))),ordinal_numbers)** -> equal(ordered_pair(first(singleton(w)),second(singleton(w))),singleton(w))**.
% 299.99/300.67  9443[0:SpL:963.0,37.0] || member(ordered_pair(singleton(singleton(singleton(u))),v),rotate(w))* -> member(ordered_pair(ordered_pair(u,v),singleton(u)),w)*.
% 299.99/300.67  9434[0:SpL:963.0,40.0] || member(ordered_pair(singleton(singleton(singleton(u))),v),flip(w))* -> member(ordered_pair(ordered_pair(u,singleton(u)),v),w)*.
% 299.99/300.67  45740[5:MRR:45730.1,8655.0] || member(u,ordinal_numbers) equal(compose(v,singleton(u)),u) -> member(singleton(singleton(singleton(u))),compose_class(v))*.
% 299.99/300.67  19797[0:SpR:30.0,19733.0] ||  -> subclass(symmetric_difference(union(u,v),complement(singleton(intersection(complement(u),complement(v))))),successor(intersection(complement(u),complement(v))))*.
% 299.99/300.67  51500[5:Res:51313.1,897.0] || member(singleton(restrict(u,v,w)),subset_relation) -> member(first(singleton(restrict(u,v,w))),cross_product(v,w))*.
% 299.99/300.67  49620[0:SpR:6355.1,962.0] ||  -> subclass(cross_product(u,v),w) member(singleton(first(not_subclass_element(cross_product(u,v),w))),not_subclass_element(cross_product(u,v),w))*.
% 299.99/300.67  18848[5:Res:18819.1,8802.1] || member(ordered_pair(u,v),subset_relation) equal(compose(w,u),v) -> member(ordered_pair(u,v),compose_class(w))*.
% 299.99/300.67  57211[5:Res:8827.2,19676.0] || member(u,ordinal_numbers) subclass(rest_relation,symmetric_difference(v,inverse(v)))* -> member(ordered_pair(u,rest_of(u)),symmetrization_of(v))*.
% 299.99/300.67  28982[5:MRR:28970.1,8657.0] || member(u,ordinal_numbers) equal(compose(v,u),rest_of(u)) -> member(ordered_pair(u,rest_of(u)),compose_class(v))*.
% 299.99/300.67  28950[5:Res:8827.2,3617.0] || member(u,ordinal_numbers) subclass(rest_relation,symmetric_difference(v,w)) -> member(ordered_pair(u,rest_of(u)),union(v,w))*.
% 299.99/300.67  28936[5:Res:8827.2,5.0] || member(u,ordinal_numbers) subclass(rest_relation,v)* subclass(v,w)* -> member(ordered_pair(u,rest_of(u)),w)*.
% 299.99/300.67  18917[0:Res:303.1,3617.0] ||  -> subclass(intersection(u,symmetric_difference(v,w)),x) member(not_subclass_element(intersection(u,symmetric_difference(v,w)),x),union(v,w))*.
% 299.99/300.67  19036[0:Res:313.1,3617.0] ||  -> subclass(intersection(symmetric_difference(u,v),w),x) member(not_subclass_element(intersection(symmetric_difference(u,v),w),x),union(u,v))*.
% 299.99/300.67  49670[5:SpL:6355.1,8841.1] || subclass(ordinal_numbers,complement(u)) member(not_subclass_element(cross_product(v,w),x),u)* -> subclass(cross_product(v,w),x).
% 299.99/300.67  41369[5:MRR:39534.0,41183.1] ||  -> member(not_subclass_element(u,intersection(complement(v),complement(w))),union(v,w))* subclass(u,intersection(complement(v),complement(w))).
% 299.99/300.67  36389[0:Rew:3616.0,36305.0] ||  -> subclass(symmetric_difference(complement(u),complement(v)),w) member(not_subclass_element(symmetric_difference(complement(u),complement(v)),w),union(u,v))*.
% 299.99/300.67  18909[0:Res:303.1,898.0] ||  -> subclass(intersection(u,restrict(v,w,x)),y) member(not_subclass_element(intersection(u,restrict(v,w,x)),y),v)*.
% 299.99/300.67  19028[0:Res:313.1,898.0] ||  -> subclass(intersection(restrict(u,v,w),x),y) member(not_subclass_element(intersection(restrict(u,v,w),x),y),u)*.
% 299.99/300.67  41095[5:Res:8665.1,8559.2] function(intersection(u,v)) || member(w,v)* member(w,u)* -> member(w,cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.67  19814[0:SpR:30.0,19734.0] ||  -> subclass(symmetric_difference(union(u,v),complement(inverse(intersection(complement(u),complement(v))))),symmetrization_of(intersection(complement(u),complement(v))))*.
% 299.99/300.67  40994[0:SpR:3606.0,19069.0] ||  -> subclass(symmetric_difference(complement(restrict(u,v,w)),union(cross_product(v,w),u)),complement(symmetric_difference(cross_product(v,w),u)))*.
% 299.99/300.67  40878[0:SpR:3603.0,19069.0] ||  -> subclass(symmetric_difference(complement(restrict(u,v,w)),union(u,cross_product(v,w))),complement(symmetric_difference(u,cross_product(v,w))))*.
% 299.99/300.67  19658[0:SpR:3597.0,3618.1] || member(u,symmetric_difference(complement(intersection(v,inverse(v))),symmetrization_of(v)))* -> member(u,complement(symmetric_difference(v,inverse(v)))).
% 299.99/300.67  39621[2:Res:18926.0,9665.1] inductive(intersection(u,v)) || well_ordering(w,v) -> member(least(w,intersection(u,v)),intersection(u,v))*.
% 299.99/300.67  39614[2:Res:19045.0,9665.1] inductive(intersection(u,v)) || well_ordering(w,u) -> member(least(w,intersection(u,v)),intersection(u,v))*.
% 299.99/300.67  82748[5:Res:60219.0,897.0] ||  -> subclass(u,complement(restrict(v,w,x))) member(not_subclass_element(u,complement(restrict(v,w,x))),cross_product(w,x))*.
% 299.99/300.67  94683[5:Res:39298.1,12.0] || subclass(ordinal_numbers,complement(complement(unordered_pair(u,v))))* -> equal(ordered_pair(w,x),v)* equal(ordered_pair(w,x),u)*.
% 299.99/300.67  94714[5:Res:39298.1,131.3] || subclass(ordinal_numbers,complement(complement(u)))* member(v,w)* subclass(w,x)* well_ordering(u,x)* -> .
% 299.99/300.67  96371[5:Res:40074.1,12.0] || subclass(ordinal_numbers,complement(complement(unordered_pair(u,v))))* -> equal(unordered_pair(w,x),v)* equal(unordered_pair(w,x),u)*.
% 299.99/300.67  107725[5:SpR:6355.1,39298.1] || subclass(ordinal_numbers,complement(complement(u))) -> subclass(cross_product(v,w),x) member(not_subclass_element(cross_product(v,w),x),u)*.
% 299.99/300.67  66829[5:Res:8827.2,161.0] || member(u,ordinal_numbers) subclass(rest_relation,omega) -> equal(integer_of(ordered_pair(u,rest_of(u))),ordered_pair(u,rest_of(u)))**.
% 299.99/300.67  116398[8:Rew:116078.0,48736.0] || member(u,cantor(v)) subclass(rest_of(v),w) -> member(ordered_pair(u,restrict(v,u,ordinal_numbers)),w)*.
% 299.99/300.67  116736[8:Rew:116078.0,56477.0] || member(u,cantor(u))* subclass(element_relation,v) well_ordering(w,v)* -> member(least(w,element_relation),element_relation)*.
% 299.99/300.67  125805[8:SpL:116154.0,116738.1] || subclass(domain_relation,inverse(subset_relation)) member(ordered_pair(restrict(u,v,singleton(w)),segment(u,v,w)),subset_relation)* -> .
% 299.99/300.67  128006[5:Res:126679.1,12.0] || subclass(omega,complement(complement(unordered_pair(u,v))))* -> equal(least(element_relation,omega),v) equal(least(element_relation,omega),u).
% 299.99/300.67  128341[5:Res:127147.1,12.0] || subclass(ordinal_numbers,complement(complement(unordered_pair(u,v))))* -> equal(least(element_relation,omega),v) equal(least(element_relation,omega),u).
% 299.99/300.67  130485[5:SpL:50855.1,2557.0] || member(singleton(u),subset_relation) member(singleton(singleton(u)),cross_product(v,w))* -> member(first(singleton(u)),w).
% 299.99/300.67  130639[5:Res:41371.0,3617.0] ||  -> subclass(complement(complement(symmetric_difference(u,v))),w) member(not_subclass_element(complement(complement(symmetric_difference(u,v))),w),union(u,v))*.
% 299.99/300.67  130660[5:Res:41371.0,898.0] ||  -> subclass(complement(complement(restrict(u,v,w))),x) member(not_subclass_element(complement(complement(restrict(u,v,w))),x),u)*.
% 299.99/300.67  130698[5:Rew:30.0,130612.1] ||  -> member(not_subclass_element(complement(union(u,v)),w),intersection(complement(u),complement(v)))* subclass(complement(union(u,v)),w).
% 299.99/300.67  130717[5:Res:130678.0,9665.1] inductive(complement(complement(u))) || well_ordering(v,u) -> member(least(v,complement(complement(u))),complement(complement(u)))*.
% 299.99/300.67  130847[5:Res:27.2,9876.0] || member(u,v)* member(u,w)* subclass(intersection(w,v),x)* well_ordering(ordinal_numbers,x) -> .
% 299.99/300.67  130969[5:Res:20.2,9876.0] || member(u,v)* member(w,x)* subclass(cross_product(x,v),y)* well_ordering(ordinal_numbers,y) -> .
% 299.99/300.67  131392[0:SpL:3596.0,18794.1] || member(u,symmetric_difference(complement(intersection(v,singleton(v))),successor(v)))* member(u,symmetric_difference(v,singleton(v))) -> .
% 299.99/300.67  131393[0:SpL:3597.0,18794.1] || member(u,symmetric_difference(complement(intersection(v,inverse(v))),symmetrization_of(v)))* member(u,symmetric_difference(v,inverse(v))) -> .
% 299.99/300.67  131522[5:SpR:50855.1,2504.1] || member(singleton(u),subset_relation) subclass(ordered_pair(v,first(singleton(u))),w)* -> member(unordered_pair(v,u),w).
% 299.99/300.67  132343[5:SpR:50855.1,132293.0] || member(singleton(u),subset_relation) -> subclass(complement(successor(first(singleton(u)))),intersection(complement(first(singleton(u))),complement(u)))*.
% 299.99/300.67  133989[5:Res:27.2,133836.0] || member(singleton(singleton(u)),v)* member(singleton(singleton(u)),w)* well_ordering(ordinal_numbers,intersection(w,v))* -> .
% 299.99/300.67  134078[5:Res:133837.1,129.0] || well_ordering(ordinal_numbers,complement(u)) subclass(u,v)* well_ordering(w,v)* -> member(least(w,u),u)*.
% 299.99/300.67  134786[8:MRR:134741.0,8667.0] || subclass(rest_relation,rest_of(u)) member(v,w)* subclass(w,x)* well_ordering(cantor(u),x)* -> .
% 299.99/300.67  136667[0:Res:2503.2,18791.0] || subclass(u,symmetric_difference(complement(v),complement(w))) -> subclass(u,x) member(not_subclass_element(u,x),union(v,w))*.
% 299.99/300.67  136669[5:Res:8978.2,18791.0] || member(u,ordinal_numbers) subclass(ordinal_numbers,symmetric_difference(complement(v),complement(w)))* -> member(sum_class(u),union(v,w))*.
% 299.99/300.67  136704[0:Res:2504.1,18791.0] || subclass(ordered_pair(u,v),symmetric_difference(complement(w),complement(x)))* -> member(unordered_pair(u,singleton(v)),union(w,x)).
% 299.99/300.67  139825[5:Rew:30.0,139758.2] || member(u,ordinal_numbers) -> member(u,complement(intersection(complement(v),union(w,x))))* member(u,union(w,x)).
% 299.99/300.67  139908[5:Rew:30.0,139850.2] || member(u,ordinal_numbers) -> member(u,complement(intersection(union(v,w),complement(x))))* member(u,union(v,w)).
% 299.99/300.67  145798[8:Rew:143170.0,145786.2] || section(ordinal_numbers,u,v) subclass(u,cantor(cross_product(v,u)))* -> equal(cantor(cross_product(v,u)),u).
% 299.99/300.67  148871[8:Res:148858.1,9661.0] || subclass(u,inverse(subset_relation)) well_ordering(v,complement(subset_relation)) -> subclass(u,w)* member(least(v,u),u)*.
% 299.99/300.67  148872[8:Res:148858.1,9665.1] inductive(u) || subclass(u,inverse(subset_relation)) well_ordering(v,complement(subset_relation)) -> member(least(v,u),u)*.
% 299.99/300.67  152916[0:Res:18949.0,19121.0] ||  -> subclass(restrict(intersection(u,v),w,x),y) member(not_subclass_element(restrict(intersection(u,v),w,x),y),u)*.
% 299.99/300.67  153040[0:Res:18949.0,19120.0] ||  -> subclass(restrict(intersection(u,v),w,x),y) member(not_subclass_element(restrict(intersection(u,v),w,x),y),v)*.
% 299.99/300.67  153252[0:Res:18204.1,5.0] || subclass(union(u,v),w) -> subclass(symmetric_difference(u,v),x) member(not_subclass_element(symmetric_difference(u,v),x),w)*.
% 299.99/300.67  153347[0:Res:919.1,5.0] || subclass(u,v) -> subclass(restrict(u,w,x),y) member(not_subclass_element(restrict(u,w,x),y),v)*.
% 299.99/300.67  153565[5:Res:8551.2,39751.0] || member(u,cross_product(ordinal_numbers,ordinal_numbers)) member(u,complement(compose(complement(element_relation),inverse(element_relation))))* -> member(u,subset_relation).
% 299.99/300.67  154353[5:Res:919.1,151988.0] ||  -> subclass(restrict(complement(complement(u)),v,w),x) member(not_subclass_element(restrict(complement(complement(u)),v,w),x),u)*.
% 299.99/300.67  117564[8:Rew:116078.0,116556.3,116078.0,116556.2] operation(u) || member(v,subset_relation) member(v,cantor(u)) -> member(first(v),cantor(cantor(u)))*.
% 299.99/300.67  117565[8:Rew:116078.0,116557.3,116078.0,116557.2] operation(u) || member(v,subset_relation) member(v,cantor(u)) -> member(second(v),cantor(cantor(u)))*.
% 299.99/300.67  117566[8:Rew:116078.0,116558.3,116078.0,116558.2] operation(u) || member(v,ordinal_numbers) subclass(rest_relation,cantor(u)) -> member(rest_of(v),cantor(cantor(u)))*.
% 299.99/300.67  117569[8:Rew:116078.0,116812.2] operation(u) ||  -> subclass(intersection(v,cantor(u)),w) member(not_subclass_element(intersection(cantor(u),v),w),cantor(u))*.
% 299.99/300.67  117570[8:Rew:116078.0,116824.2] operation(u) ||  -> subclass(intersection(cantor(u),v),w) member(not_subclass_element(intersection(v,cantor(u)),w),cantor(u))*.
% 299.99/300.67  116875[8:Rew:116078.0,18636.1] operation(u) ||  -> equal(intersection(complement(intersection(v,cantor(u))),union(cantor(u),v)),symmetric_difference(cantor(u),v))**.
% 299.99/300.67  116877[8:Rew:116078.0,18643.1] operation(u) ||  -> equal(intersection(complement(intersection(cantor(u),v)),union(v,cantor(u))),symmetric_difference(v,cantor(u)))**.
% 299.99/300.67  139425[8:SpR:116209.1,18901.1] operation(u) ||  -> subclass(intersection(cantor(u),recursion_equation_functions(v)),w) function(not_subclass_element(intersection(recursion_equation_functions(v),cantor(u)),w))*.
% 299.99/300.67  139510[8:SpR:116209.1,19020.1] operation(u) ||  -> subclass(intersection(recursion_equation_functions(v),cantor(u)),w) function(not_subclass_element(intersection(cantor(u),recursion_equation_functions(v)),w))*.
% 299.99/300.67  36717[5:SpL:8647.0,4392.1] operation(flip(cross_product(u,ordinal_numbers))) || member(v,inverse(u))* -> equal(ordered_pair(first(v),second(v)),v)**.
% 299.99/300.67  36716[5:SpL:8648.0,4392.1] operation(restrict(element_relation,ordinal_numbers,u)) || member(v,sum_class(u))* -> equal(ordered_pair(first(v),second(v)),v)**.
% 299.99/300.67  116321[8:Rew:116078.0,36430.2] operation(restrict(element_relation,ordinal_numbers,u)) || member(ordered_pair(v,w),sum_class(u))* -> member(w,cantor(sum_class(u))).
% 299.99/300.67  116322[8:Rew:116078.0,36573.2] operation(restrict(element_relation,ordinal_numbers,u)) || member(ordered_pair(v,w),sum_class(u))* -> member(v,cantor(sum_class(u))).
% 299.99/300.67  132039[5:Res:9604.1,19115.0] || equal(sum_class(recursion_equation_functions(u)),recursion_equation_functions(u)) -> subclass(sum_class(recursion_equation_functions(u)),v) function(not_subclass_element(sum_class(recursion_equation_functions(u)),v))*.
% 299.99/300.67  153340[5:Res:919.1,8788.0] ||  -> subclass(restrict(recursion_equation_functions(u),v,w),x) subclass(not_subclass_element(restrict(recursion_equation_functions(u),v,w),x),cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.67  103279[5:Obv:103248.0] ||  -> equal(not_subclass_element(unordered_pair(u,v),complement(recursion_equation_functions(w))),u)** subclass(unordered_pair(u,v),complement(recursion_equation_functions(w))) function(v).
% 299.99/300.67  103276[5:Obv:103260.0] ||  -> equal(not_subclass_element(unordered_pair(u,v),complement(recursion_equation_functions(w))),v)** subclass(unordered_pair(u,v),complement(recursion_equation_functions(w))) function(u).
% 299.99/300.67  161410[8:Rew:160496.0,62159.2] function(union(identity_relation,symmetrization_of(u))) || connected(u,ordinal_numbers) -> equal(complement(complement(symmetrization_of(u))),cross_product(ordinal_numbers,ordinal_numbers))**.
% 299.99/300.67  163581[5:Res:143200.1,8554.1] || equal(complement(intersection(u,v)),ordinal_numbers) member(omega,union(u,v)) -> member(omega,symmetric_difference(u,v))*.
% 299.99/300.67  164044[8:Res:160669.1,8990.1] function(complement(complement(symmetrization_of(u)))) || connected(u,ordinal_numbers) -> equal(complement(complement(symmetrization_of(u))),cross_product(ordinal_numbers,ordinal_numbers))**.
% 299.99/300.67  42241[5:Res:9706.3,8841.1] || member(u,ordinal_numbers)* member(v,ordinal_numbers)* equal(successor(v),u)* subclass(ordinal_numbers,complement(successor_relation))* -> .
% 299.99/300.67  166367[7:Res:13125.2,19111.1] || subclass(omega,u) subclass(v,complement(u))* -> equal(integer_of(not_subclass_element(v,w)),identity_relation)** subclass(v,w).
% 299.99/300.67  166383[7:Res:13125.2,3572.0] || subclass(omega,compose_class(u)) -> equal(integer_of(singleton(singleton(singleton(v)))),identity_relation)** equal(compose(u,singleton(v)),v)**.
% 299.99/300.67  165246[7:Res:130678.0,13070.0] || well_ordering(u,v) -> equal(complement(complement(v)),identity_relation) member(least(u,complement(complement(v))),complement(complement(v)))*.
% 299.99/300.67  69181[8:Res:13210.1,66086.1] || member(regular(intersection(u,complement(compose(element_relation,ordinal_numbers)))),element_relation)* -> equal(intersection(u,complement(compose(element_relation,ordinal_numbers))),identity_relation).
% 299.99/300.67  69171[8:Res:13248.1,66086.1] || member(regular(intersection(complement(compose(element_relation,ordinal_numbers)),u)),element_relation)* -> equal(intersection(complement(compose(element_relation,ordinal_numbers)),u),identity_relation).
% 299.99/300.67  64215[7:Res:13210.1,19559.0] ||  -> equal(intersection(u,symmetric_difference(v,singleton(v))),identity_relation) member(regular(intersection(u,symmetric_difference(v,singleton(v)))),successor(v))*.
% 299.99/300.67  13394[7:Rew:13036.0,10727.2] || member(u,v)* well_ordering(w,v)* -> equal(segment(w,singleton(u),least(w,singleton(u))),identity_relation)**.
% 299.99/300.67  64304[7:Res:13248.1,19559.0] ||  -> equal(intersection(symmetric_difference(u,singleton(u)),v),identity_relation) member(regular(intersection(symmetric_difference(u,singleton(u)),v)),successor(u))*.
% 299.99/300.67  161462[8:Rew:140613.0,67563.0] ||  -> equal(complement(intersection(complement(u),union(v,symmetric_difference(ordinal_numbers,w)))),union(u,intersection(complement(v),union(w,identity_relation))))**.
% 299.99/300.67  64305[7:Res:13248.1,19676.0] ||  -> equal(intersection(symmetric_difference(u,inverse(u)),v),identity_relation) member(regular(intersection(symmetric_difference(u,inverse(u)),v)),symmetrization_of(u))*.
% 299.99/300.67  64216[7:Res:13210.1,19676.0] ||  -> equal(intersection(u,symmetric_difference(v,inverse(v))),identity_relation) member(regular(intersection(u,symmetric_difference(v,inverse(v)))),symmetrization_of(v))*.
% 299.99/300.67  61001[7:Res:13072.1,490.0] || member(regular(intersection(complement(u),complement(v))),union(u,v))* -> equal(intersection(complement(u),complement(v)),identity_relation).
% 299.99/300.67  19323[7:Res:18950.0,13113.0] || well_ordering(u,union(v,w)) -> equal(segment(u,symmetric_difference(v,w),least(u,symmetric_difference(v,w))),identity_relation)**.
% 299.99/300.67  18989[7:Res:18949.0,13113.0] || well_ordering(u,v) -> equal(segment(u,restrict(v,w,x),least(u,restrict(v,w,x))),identity_relation)**.
% 299.99/300.67  13579[7:Rew:13036.0,13011.2] || subclass(u,v)* well_ordering(w,v)* -> equal(intersection(x,u),identity_relation)** member(least(w,u),u)*.
% 299.99/300.67  17391[7:Res:13248.1,129.0] || subclass(u,v)* well_ordering(w,v)* -> equal(intersection(u,x),identity_relation)** member(least(w,u),u)*.
% 299.99/300.67  18969[7:Res:18926.0,13070.0] || well_ordering(u,v) -> equal(intersection(w,v),identity_relation) member(least(u,intersection(w,v)),intersection(w,v))*.
% 299.99/300.67  79707[7:Res:79560.1,13113.0] || well_ordering(u,complement(v))* -> member(w,v)* equal(segment(u,singleton(w),least(u,singleton(w))),identity_relation)**.
% 299.99/300.67  165419[7:Res:96837.0,13113.0] || well_ordering(u,complement(recursion_equation_functions(v)))* -> function(w) equal(segment(u,singleton(w),least(u,singleton(w))),identity_relation)**.
% 299.99/300.67  83277[8:Res:61019.0,66086.1] || member(regular(complement(complement(complement(compose(element_relation,ordinal_numbers))))),element_relation)* -> equal(complement(complement(complement(compose(element_relation,ordinal_numbers)))),identity_relation).
% 299.99/300.67  165091[8:Res:148858.1,13113.0] || subclass(u,inverse(subset_relation)) well_ordering(v,complement(subset_relation)) -> equal(segment(v,u,least(v,u)),identity_relation)**.
% 299.99/300.67  19088[7:Res:19045.0,13070.0] || well_ordering(u,v) -> equal(intersection(v,w),identity_relation) member(least(u,intersection(v,w)),intersection(v,w))*.
% 299.99/300.67  166691[7:Res:13210.1,18794.1] || member(regular(intersection(u,intersection(v,w))),symmetric_difference(v,w))* -> equal(intersection(u,intersection(v,w)),identity_relation).
% 299.99/300.67  166501[7:Res:13248.1,18794.1] || member(regular(intersection(intersection(u,v),w)),symmetric_difference(u,v))* -> equal(intersection(intersection(u,v),w),identity_relation).
% 299.99/300.67  18802[7:Res:3618.1,13105.0] || member(regular(complement(complement(intersection(u,v)))),symmetric_difference(u,v))* -> equal(complement(complement(intersection(u,v))),identity_relation).
% 299.99/300.67  69468[7:Res:13125.2,490.0] || subclass(omega,intersection(complement(u),complement(v)))* member(w,union(u,v))* -> equal(integer_of(w),identity_relation).
% 299.99/300.67  83880[7:Res:66696.2,490.0] || subclass(ordinal_numbers,intersection(complement(u),complement(v)))* member(w,union(u,v))* -> equal(integer_of(w),identity_relation).
% 299.99/300.67  161471[8:Rew:140613.0,67592.2] || member(u,ordinal_numbers) subclass(union(v,identity_relation),w)* -> member(u,symmetric_difference(ordinal_numbers,v))* member(u,w)*.
% 299.99/300.67  161472[8:Rew:140613.0,67553.0] ||  -> equal(complement(intersection(complement(u),union(symmetric_difference(ordinal_numbers,v),w))),union(u,intersection(union(v,identity_relation),complement(w))))**.
% 299.99/300.67  161473[8:Rew:140613.0,67550.0] ||  -> equal(complement(intersection(union(u,symmetric_difference(ordinal_numbers,v)),complement(w))),union(intersection(complement(u),union(v,identity_relation)),w))**.
% 299.99/300.67  18920[8:Res:303.1,14681.0] || member(not_subclass_element(intersection(u,regular(v)),w),v)* -> subclass(intersection(u,regular(v)),w) equal(v,identity_relation).
% 299.99/300.67  83281[7:Res:61019.0,129.0] || subclass(u,v)* well_ordering(w,v)* -> equal(complement(complement(u)),identity_relation) member(least(w,u),u)*.
% 299.99/300.67  13653[7:Rew:13036.0,13245.2] || well_ordering(u,omega) -> equal(integer_of(v),identity_relation) equal(segment(u,singleton(v),least(u,singleton(v))),identity_relation)**.
% 299.99/300.67  163121[8:SpR:162584.0,8832.1] || member(u,ordinal_numbers) -> member(u,intersection(complement(v),symmetrization_of(identity_relation)))* member(u,union(v,complement(inverse(identity_relation)))).
% 299.99/300.67  163108[8:SpR:162584.0,8832.1] || member(u,ordinal_numbers) -> member(u,intersection(symmetrization_of(identity_relation),complement(v)))* member(u,union(complement(inverse(identity_relation)),v)).
% 299.99/300.67  165160[8:Res:162023.0,13113.0] || well_ordering(u,complement(inverse(identity_relation))) -> equal(segment(u,complement(symmetrization_of(identity_relation)),least(u,complement(symmetrization_of(identity_relation)))),identity_relation)**.
% 299.99/300.67  61958[7:Res:13049.1,8554.1] || subclass(ordinal_numbers,complement(intersection(u,v)))* member(identity_relation,union(u,v)) -> member(identity_relation,symmetric_difference(u,v)).
% 299.99/300.67  161485[8:Rew:140613.0,67540.0] ||  -> equal(complement(intersection(union(symmetric_difference(ordinal_numbers,u),v),complement(w))),union(intersection(union(u,identity_relation),complement(v)),w))**.
% 299.99/300.67  19039[8:Res:313.1,14681.0] || member(not_subclass_element(intersection(regular(u),v),w),u)* -> subclass(intersection(regular(u),v),w) equal(u,identity_relation).
% 299.99/300.67  64357[7:Res:13227.2,490.0] || subclass(u,intersection(complement(v),complement(w)))* member(regular(u),union(v,w)) -> equal(u,identity_relation).
% 299.99/300.67  165238[8:Res:148858.1,13070.0] || subclass(u,inverse(subset_relation)) well_ordering(v,complement(subset_relation)) -> equal(u,identity_relation) member(least(v,u),u)*.
% 299.99/300.67  167234[8:Res:41371.0,14681.0] || member(not_subclass_element(complement(complement(regular(u))),v),u)* -> subclass(complement(complement(regular(u))),v) equal(u,identity_relation).
% 299.99/300.67  64638[8:Rew:15663.0,64620.2] function(u) || member(not_subclass_element(identity_relation,identity_relation),subset_relation) -> equal(ordered_pair(single_valued3(identity_relation),single_valued2(u)),not_subclass_element(identity_relation,identity_relation))**.
% 299.99/300.67  64659[8:Rew:15663.0,64639.2] single_valued_class(u) || member(not_subclass_element(identity_relation,identity_relation),subset_relation) -> equal(ordered_pair(single_valued3(identity_relation),single_valued2(u)),not_subclass_element(identity_relation,identity_relation))**.
% 299.99/300.67  165363[14:Res:165168.1,129.0] || equal(u,singleton(identity_relation)) subclass(u,v)* well_ordering(w,v)* -> member(least(w,u),u)*.
% 299.99/300.67  82282[8:Res:81336.1,12.0] || subclass(domain_relation,complement(complement(unordered_pair(u,v))))* -> equal(ordered_pair(identity_relation,identity_relation),v) equal(ordered_pair(identity_relation,identity_relation),u).
% 299.99/300.67  165351[5:Res:39298.1,8799.1] || subclass(ordinal_numbers,complement(complement(cross_product(ordinal_numbers,ordinal_numbers))))* equal(successor(u),v) -> member(ordered_pair(u,v),successor_relation)*.
% 299.99/300.67  189708[8:SpL:117511.1,13103.0] operation(u) || equal(intersection(cantor(u),intersection(v,inverse(v))),identity_relation)** -> asymmetric(v,cantor(cantor(u))).
% 299.99/300.67  189901[8:SpR:13104.1,117511.1] operation(u) || asymmetric(v,cantor(cantor(u))) -> equal(intersection(cantor(u),intersection(v,inverse(v))),identity_relation)**.
% 299.99/300.67  190538[18:Res:190442.1,129.0] || equal(u,symmetrization_of(identity_relation)) subclass(u,v)* well_ordering(w,v)* -> member(least(w,u),u)*.
% 299.99/300.67  190647[18:Res:190593.1,129.0] || equal(u,inverse(identity_relation)) subclass(u,v)* well_ordering(w,v)* -> member(least(w,u),u)*.
% 299.99/300.67  192168[7:Res:192149.1,8554.1] || equal(complement(intersection(u,v)),ordinal_numbers) member(identity_relation,union(u,v)) -> member(identity_relation,symmetric_difference(u,v))*.
% 299.99/300.67  193206[8:Res:193179.0,19111.1] || subclass(u,complement(inverse(singleton(not_subclass_element(u,v)))))* -> asymmetric(singleton(not_subclass_element(u,v)),w)* subclass(u,v).
% 299.99/300.67  193623[8:SpR:154737.1,15320.1] || subclass(inverse(u),u)* asymmetric(u,singleton(v)) -> equal(segment(inverse(u),singleton(v),v),identity_relation)**.
% 299.99/300.67  51493[5:Res:51313.1,129.0] || member(singleton(u),subset_relation) subclass(u,v)* well_ordering(w,v)* -> member(least(w,u),u)*.
% 299.99/300.67  49062[5:Res:8638.0,9633.1] || member(u,ordinal_numbers)* well_ordering(v,ordinal_numbers) -> member(u,w)* member(least(v,complement(w)),complement(w))*.
% 299.99/300.67  134717[8:Res:116403.2,9876.0] || member(u,ordinal_numbers)* subclass(rest_relation,rest_of(v)) subclass(cantor(v),w)* well_ordering(ordinal_numbers,w) -> .
% 299.99/300.67  139775[5:Res:39529.1,9876.0] || member(u,ordinal_numbers) subclass(union(v,w),x)* well_ordering(ordinal_numbers,x) -> member(u,complement(w))*.
% 299.99/300.67  139861[5:Res:39530.1,9876.0] || member(u,ordinal_numbers) subclass(union(v,w),x)* well_ordering(ordinal_numbers,x) -> member(u,complement(v))*.
% 299.99/300.67  46167[5:Res:9563.3,41096.0] || connected(u,v) well_ordering(w,v) -> well_ordering(u,v) member(least(w,not_well_ordering(u,v)),ordinal_numbers)*.
% 299.99/300.67  65159[7:MRR:65157.2,13039.0] || well_ordering(u,ordinal_numbers) subclass(singleton(least(u,v)),v) -> section(u,singleton(least(u,v)),v)*.
% 299.99/300.67  18707[7:Res:13237.2,898.0] || well_ordering(u,ordinal_numbers) -> equal(restrict(v,w,x),identity_relation) member(least(u,restrict(v,w,x)),v)*.
% 299.99/300.67  18715[7:Res:13237.2,3617.0] || well_ordering(u,ordinal_numbers) -> equal(symmetric_difference(v,w),identity_relation) member(least(u,symmetric_difference(v,w)),union(v,w))*.
% 299.99/300.67  18762[8:Res:13237.2,14681.0] || well_ordering(u,ordinal_numbers) member(least(u,regular(v)),v)* -> equal(regular(v),identity_relation) equal(v,identity_relation).
% 299.99/300.67  167261[8:Res:39607.2,14681.0] inductive(regular(u)) || well_ordering(v,ordinal_numbers) member(least(v,regular(u)),u)* -> equal(u,identity_relation).
% 299.99/300.67  131188[5:Res:39607.2,3617.0] inductive(symmetric_difference(u,v)) || well_ordering(w,ordinal_numbers) -> member(least(w,symmetric_difference(u,v)),union(u,v))*.
% 299.99/300.67  131209[5:Res:39607.2,898.0] inductive(restrict(u,v,w)) || well_ordering(x,ordinal_numbers) -> member(least(x,restrict(u,v,w)),u)*.
% 299.99/300.67  154324[5:Res:39609.2,151988.0] inductive(complement(complement(u))) || well_ordering(v,complement(complement(u))) -> member(least(v,complement(complement(u))),u)*.
% 299.99/300.67  132212[2:Res:39609.2,26.0] inductive(intersection(u,v)) || well_ordering(w,intersection(u,v)) -> member(least(w,intersection(u,v)),v)*.
% 299.99/300.67  132213[2:Res:39609.2,25.0] inductive(intersection(u,v)) || well_ordering(w,intersection(u,v)) -> member(least(w,intersection(u,v)),u)*.
% 299.99/300.67  194499[8:Res:163112.0,47534.0] ||  -> subclass(singleton(not_subclass_element(u,intersection(complement(inverse(identity_relation)),u))),symmetrization_of(identity_relation))* subclass(u,intersection(complement(inverse(identity_relation)),u)).
% 299.99/300.67  195622[16:Rew:195224.0,195208.0] ||  -> subclass(singleton(not_subclass_element(u,intersection(complement(singleton(identity_relation)),u))),singleton(identity_relation))* subclass(u,intersection(complement(singleton(identity_relation)),u)).
% 299.99/300.67  195492[16:Rew:195224.0,163195.1] || member(u,ordinal_numbers) -> member(u,intersection(singleton(identity_relation),complement(v)))* member(u,union(complement(singleton(identity_relation)),v)).
% 299.99/300.67  195495[16:Rew:195224.0,163208.1] || member(u,ordinal_numbers) -> member(u,intersection(complement(v),singleton(identity_relation)))* member(u,union(v,complement(singleton(identity_relation)))).
% 299.99/300.67  196080[18:Res:190510.1,129.0] || subclass(inverse(identity_relation),u) subclass(u,v)* well_ordering(w,v)* -> member(least(w,u),u)*.
% 299.99/300.67  196324[8:SpR:161356.2,15272.1] single_valued_class(u) || member(v,ordinal_numbers) -> member(v,cantor(w)) equal(range__dfg(w,v,ordinal_numbers),single_valued2(u))*.
% 299.99/300.67  196325[8:SpR:161356.2,15265.1] function(u) || member(v,ordinal_numbers) -> member(v,cantor(w)) equal(range__dfg(w,v,ordinal_numbers),single_valued2(u))*.
% 299.99/300.67  196420[21:Rew:196372.1,192712.2] || member(u,ordinal_numbers) subclass(domain_relation,regular(v)) member(ordered_pair(u,identity_relation),v)* -> equal(v,identity_relation).
% 299.99/300.67  196444[21:Rew:196372.1,174450.2] || member(u,ordinal_numbers) subclass(domain_relation,intersection(v,w)) member(ordered_pair(u,identity_relation),symmetric_difference(v,w))* -> .
% 299.99/300.67  196446[21:Rew:196372.1,161447.2] || member(u,ordinal_numbers) subclass(domain_relation,restrict(v,w,x))* -> member(ordered_pair(u,identity_relation),cross_product(w,x))*.
% 299.99/300.67  197187[7:Obv:197173.0] ||  -> equal(regular(unordered_pair(u,v)),v) equal(unordered_pair(u,v),identity_relation) equal(intersection(unordered_pair(u,v),u),identity_relation)**.
% 299.99/300.67  197188[7:Obv:197165.0] ||  -> equal(regular(unordered_pair(u,v)),u) equal(unordered_pair(u,v),identity_relation) equal(intersection(unordered_pair(u,v),v),identity_relation)**.
% 299.99/300.67  198557[7:Res:13511.3,41096.0] || member(u,ordinal_numbers) well_ordering(v,u) -> equal(sum_class(u),identity_relation) member(least(v,sum_class(u)),ordinal_numbers)*.
% 299.99/300.67  198987[7:Res:8666.0,13362.0] || subclass(ordinal_numbers,u) well_ordering(omega,u)* -> equal(integer_of(ordered_pair(unordered_pair(v,w),least(omega,ordinal_numbers))),identity_relation)**.
% 299.99/300.67  198989[7:Res:8667.0,13362.0] || subclass(ordinal_numbers,u) well_ordering(omega,u)* -> equal(integer_of(ordered_pair(ordered_pair(v,w),least(omega,ordinal_numbers))),identity_relation)**.
% 299.99/300.67  199005[18:Res:190509.0,13362.0] || subclass(ordinal_numbers,u) well_ordering(omega,u)* -> equal(integer_of(ordered_pair(regular(symmetrization_of(identity_relation)),least(omega,ordinal_numbers))),identity_relation)**.
% 299.99/300.67  199028[7:Res:125717.0,13362.0] || subclass(omega,u) well_ordering(omega,u)* -> equal(integer_of(ordered_pair(least(element_relation,omega),least(omega,omega))),identity_relation)**.
% 299.99/300.67  199029[7:Res:125724.0,13362.0] || subclass(ordinal_numbers,u) well_ordering(omega,u)* -> equal(integer_of(ordered_pair(least(element_relation,omega),least(omega,ordinal_numbers))),identity_relation)**.
% 299.99/300.67  199065[8:Res:15380.0,13362.0] || subclass(domain_relation,u) well_ordering(omega,u)* -> equal(integer_of(ordered_pair(ordered_pair(identity_relation,identity_relation),least(omega,domain_relation))),identity_relation)**.
% 299.99/300.67  199082[14:Res:164498.0,13362.0] || subclass(singleton(identity_relation),u)* well_ordering(omega,u) -> equal(integer_of(ordered_pair(identity_relation,least(omega,singleton(identity_relation)))),identity_relation)**.
% 299.99/300.67  199094[18:Res:190432.0,13362.0] || subclass(symmetrization_of(identity_relation),u)* well_ordering(omega,u) -> equal(integer_of(ordered_pair(identity_relation,least(omega,symmetrization_of(identity_relation)))),identity_relation)**.
% 299.99/300.67  199095[18:Res:190445.0,13362.0] || subclass(inverse(identity_relation),u)* well_ordering(omega,u) -> equal(integer_of(ordered_pair(identity_relation,least(omega,inverse(identity_relation)))),identity_relation)**.
% 299.99/300.67  199121[7:Res:13515.2,41096.0] || well_ordering(u,cross_product(ordinal_numbers,ordinal_numbers)) -> equal(compose(v,w),identity_relation) member(least(u,compose(v,w)),ordinal_numbers)*.
% 299.99/300.67  176979[8:Rew:116239.0,176967.2,117066.0,176967.2] operation(flip(cross_product(u,ordinal_numbers))) || subclass(inverse(u),complement(complement(symmetrization_of(v))))* -> connected(v,range_of(u)).
% 299.99/300.67  177012[8:Rew:116239.0,176997.1,117066.0,176997.1] operation(flip(cross_product(u,ordinal_numbers))) || connected(v,range_of(u)) -> subclass(inverse(u),complement(complement(symmetrization_of(v))))*.
% 299.99/300.67  195025[15:SpL:481.0,165530.0] || subclass(ordinal_numbers,complement(power_class(intersection(complement(u),complement(v)))))* -> member(range_of(identity_relation),image(element_relation,union(u,v))).
% 299.99/300.67  19345[7:SpR:33.0,13311.1] || asymmetric(cross_product(u,v),ordinal_numbers) -> equal(image(restrict(inverse(cross_product(u,v)),u,v),ordinal_numbers),range_of(identity_relation))**.
% 299.99/300.67  61450[8:SpL:14756.0,9470.1] || member(ordered_pair(u,v),compose(w,identity_relation))* subclass(image(w,range_of(identity_relation)),x)* -> member(v,x)*.
% 299.99/300.67  198991[15:Res:165431.0,13362.0] || subclass(ordinal_numbers,u) well_ordering(omega,u)* -> equal(integer_of(ordered_pair(sum_class(range_of(identity_relation)),least(omega,ordinal_numbers))),identity_relation)**.
% 299.99/300.67  196960[21:SpR:196552.0,116203.2] function(sum_class(range_of(identity_relation))) || subclass(range_of(sum_class(range_of(identity_relation))),u) -> maps(sum_class(range_of(identity_relation)),identity_relation,u)*.
% 299.99/300.67  197004[21:SpR:196569.0,116203.2] function(regular(symmetrization_of(identity_relation))) || subclass(range_of(regular(symmetrization_of(identity_relation))),u) -> maps(regular(symmetrization_of(identity_relation)),identity_relation,u)*.
% 299.99/300.67  197534[21:SpR:196568.1,116203.2] function(regular(u)) || subclass(range_of(regular(u)),v) -> equal(u,identity_relation) maps(regular(u),identity_relation,v)*.
% 299.99/300.67  197046[21:SpR:196584.0,116203.2] function(least(element_relation,omega)) || subclass(range_of(least(element_relation,omega)),u) -> maps(least(element_relation,omega),identity_relation,u)*.
% 299.99/300.67  197125[21:SpR:196548.0,116203.2] function(unordered_pair(u,v)) || subclass(range_of(unordered_pair(u,v)),w) -> maps(unordered_pair(u,v),identity_relation,w)*.
% 299.99/300.67  197206[21:SpR:196550.0,116203.2] function(ordered_pair(u,v)) || subclass(range_of(ordered_pair(u,v)),w) -> maps(ordered_pair(u,v),identity_relation,w)*.
% 299.99/300.67  161474[8:Rew:140613.0,66142.0] ||  -> equal(symmetric_difference(complement(intersection(singleton(identity_relation),image(successor_relation,ordinal_numbers))),ordinal_numbers),symmetric_difference(ordinal_numbers,symmetric_difference(singleton(identity_relation),image(successor_relation,ordinal_numbers))))**.
% 299.99/300.67  193231[8:SpR:161207.0,176865.1] || equal(complement(intersection(singleton(identity_relation),image(successor_relation,ordinal_numbers))),ordinal_numbers)** -> equal(symmetric_difference(singleton(identity_relation),image(successor_relation,ordinal_numbers)),ordinal_numbers).
% 299.99/300.67  193239[8:SpL:161207.0,176785.0] || equal(symmetric_difference(singleton(identity_relation),image(successor_relation,ordinal_numbers)),ordinal_numbers) member(omega,intersection(singleton(identity_relation),image(successor_relation,ordinal_numbers)))* -> .
% 299.99/300.67  51512[5:Res:51313.1,288.0] || member(singleton(image(element_relation,complement(u))),subset_relation) member(first(singleton(image(element_relation,complement(u)))),power_class(u))* -> .
% 299.99/300.67  166427[7:Res:13125.2,1042.0] || subclass(omega,image(element_relation,complement(u)))* -> equal(integer_of(not_subclass_element(power_class(u),v)),identity_relation)** subclass(power_class(u),v).
% 299.99/300.67  196445[21:Rew:196372.1,161448.2] || member(u,ordinal_numbers) subclass(domain_relation,image(element_relation,complement(v))) member(ordered_pair(u,identity_relation),power_class(v))* -> .
% 299.99/300.67  29091[5:Res:8835.1,5.0] || member(u,ordinal_numbers) subclass(image(element_relation,complement(v)),w)* -> member(u,power_class(v))* member(u,w)*.
% 299.99/300.67  36852[5:SpL:59.0,8825.1] || member(u,ordinal_numbers) subclass(power_class(v),w)* -> member(u,image(element_relation,complement(v)))* member(u,w)*.
% 299.99/300.67  159476[5:Rew:117.0,159416.1,30.0,159416.1,117.0,159416.0,30.0,159416.0] ||  -> member(not_subclass_element(u,image(element_relation,symmetrization_of(v))),complement(image(element_relation,symmetrization_of(v))))* subclass(u,image(element_relation,symmetrization_of(v))).
% 299.99/300.67  193548[8:SpL:162038.0,18791.0] || member(u,symmetric_difference(complement(v),power_class(complement(inverse(identity_relation)))))* -> member(u,union(v,image(element_relation,symmetrization_of(identity_relation)))).
% 299.99/300.67  193544[8:SpL:162038.0,18791.0] || member(u,symmetric_difference(power_class(complement(inverse(identity_relation))),complement(v)))* -> member(u,union(image(element_relation,symmetrization_of(identity_relation)),v)).
% 299.99/300.67  193475[8:SpR:162038.0,132294.0] ||  -> subclass(complement(symmetrization_of(image(element_relation,symmetrization_of(identity_relation)))),intersection(power_class(complement(inverse(identity_relation))),complement(inverse(image(element_relation,symmetrization_of(identity_relation))))))*.
% 299.99/300.67  193474[8:SpR:162038.0,132293.0] ||  -> subclass(complement(successor(image(element_relation,symmetrization_of(identity_relation)))),intersection(power_class(complement(inverse(identity_relation))),complement(singleton(image(element_relation,symmetrization_of(identity_relation))))))*.
% 299.99/300.67  163134[8:SpL:162584.0,1042.0] || member(not_subclass_element(power_class(complement(inverse(identity_relation))),u),image(element_relation,symmetrization_of(identity_relation)))* -> subclass(power_class(complement(inverse(identity_relation))),u).
% 299.99/300.67  164867[8:SpR:160491.0,19486.0] ||  -> equal(power_class(intersection(union(u,identity_relation),complement(inverse(symmetric_difference(ordinal_numbers,u))))),complement(image(element_relation,symmetrization_of(symmetric_difference(ordinal_numbers,u)))))**.
% 299.99/300.67  17359[7:Rew:189.0,17341.1] || subclass(power_class(image(element_relation,complement(u))),image(element_relation,power_class(u)))* -> equal(power_class(image(element_relation,complement(u))),identity_relation).
% 299.99/300.67  19810[0:SpR:189.0,19734.0] ||  -> subclass(symmetric_difference(power_class(image(element_relation,complement(u))),complement(inverse(image(element_relation,power_class(u))))),symmetrization_of(image(element_relation,power_class(u))))*.
% 299.99/300.67  19793[0:SpR:189.0,19733.0] ||  -> subclass(symmetric_difference(power_class(image(element_relation,complement(u))),complement(singleton(image(element_relation,power_class(u))))),successor(image(element_relation,power_class(u))))*.
% 299.99/300.67  151946[5:SpR:189.0,147905.0] ||  -> equal(intersection(image(element_relation,power_class(u)),complement(power_class(image(element_relation,complement(u))))),complement(power_class(image(element_relation,complement(u)))))**.
% 299.99/300.67  155441[5:Res:133837.1,941.1] || well_ordering(ordinal_numbers,complement(power_class(image(element_relation,complement(u)))))* member(singleton(singleton(v)),image(element_relation,power_class(u)))* -> .
% 299.99/300.67  155437[5:Res:9632.1,941.1] || equal(complement(complement(power_class(image(element_relation,complement(u))))),ordinal_numbers)** member(singleton(v),image(element_relation,power_class(u)))* -> .
% 299.99/300.67  159463[5:Rew:59.0,159428.1] ||  -> member(not_subclass_element(u,image(element_relation,power_class(v))),power_class(image(element_relation,complement(v))))* subclass(u,image(element_relation,power_class(v))).
% 299.99/300.67  124982[5:SpL:189.0,66645.0] || subclass(ordinal_numbers,image(element_relation,power_class(image(element_relation,complement(u)))))* member(omega,power_class(image(element_relation,power_class(u)))) -> .
% 299.99/300.67  18433[0:SpL:189.0,288.0] || member(u,image(element_relation,power_class(image(element_relation,complement(v)))))* member(u,power_class(image(element_relation,power_class(v)))) -> .
% 299.99/300.67  193496[8:SpR:162038.0,485.0] ||  -> equal(complement(intersection(complement(u),power_class(image(element_relation,symmetrization_of(identity_relation))))),union(u,image(element_relation,power_class(complement(inverse(identity_relation))))))**.
% 299.99/300.67  193483[8:SpR:162038.0,487.0] ||  -> equal(complement(intersection(power_class(image(element_relation,symmetrization_of(identity_relation))),complement(u))),union(image(element_relation,power_class(complement(inverse(identity_relation)))),u))**.
% 299.99/300.67  195069[14:SpL:481.0,165360.0] || equal(complement(power_class(intersection(complement(u),complement(v)))),singleton(identity_relation))** -> member(identity_relation,image(element_relation,union(u,v))).
% 299.99/300.67  196208[18:SpL:481.0,190535.0] || equal(complement(power_class(intersection(complement(u),complement(v)))),symmetrization_of(identity_relation))** -> member(identity_relation,image(element_relation,union(u,v))).
% 299.99/300.67  196301[18:SpL:481.0,190644.0] || equal(complement(power_class(intersection(complement(u),complement(v)))),inverse(identity_relation))** -> member(identity_relation,image(element_relation,union(u,v))).
% 299.99/300.67  19501[5:SpL:481.0,9496.0] || subclass(ordinal_numbers,complement(power_class(intersection(complement(u),complement(v)))))* -> member(singleton(w),image(element_relation,union(u,v)))*.
% 299.99/300.67  187417[8:SpL:481.0,176788.0] || equal(symmetric_difference(ordinal_numbers,power_class(intersection(complement(u),complement(v)))),ordinal_numbers)** -> member(omega,image(element_relation,union(u,v))).
% 299.99/300.67  19466[0:SpR:30.0,487.0] ||  -> equal(complement(intersection(power_class(intersection(complement(u),complement(v))),complement(w))),union(image(element_relation,union(u,v)),w))**.
% 299.99/300.67  132287[5:SpR:481.0,130703.0] ||  -> subclass(complement(union(image(element_relation,union(u,v)),w)),intersection(power_class(intersection(complement(u),complement(v))),complement(w)))*.
% 299.99/300.67  176987[5:SpL:481.0,134026.0] || equal(complement(power_class(intersection(complement(u),complement(v)))),ordinal_numbers)** well_ordering(ordinal_numbers,image(element_relation,union(u,v))) -> .
% 299.99/300.67  194688[14:SpR:481.0,165178.0] ||  -> member(identity_relation,image(element_relation,power_class(intersection(complement(u),complement(v)))))* member(identity_relation,power_class(image(element_relation,union(u,v)))).
% 299.99/300.67  176780[8:SpR:481.0,144409.1] || equal(symmetric_difference(ordinal_numbers,image(element_relation,union(u,v))),ordinal_numbers) -> member(omega,power_class(intersection(complement(u),complement(v))))*.
% 299.99/300.67  176857[8:SpL:481.0,155244.0] || subclass(ordinal_numbers,power_class(intersection(complement(u),complement(v))))* -> equal(symmetric_difference(ordinal_numbers,image(element_relation,union(u,v))),ordinal_numbers).
% 299.99/300.67  19392[0:SpR:30.0,485.0] ||  -> equal(complement(intersection(complement(u),power_class(intersection(complement(v),complement(w))))),union(u,image(element_relation,union(v,w))))**.
% 299.99/300.67  132274[5:SpR:481.0,130703.0] ||  -> subclass(complement(union(u,image(element_relation,union(v,w)))),intersection(complement(u),power_class(intersection(complement(v),complement(w)))))*.
% 299.99/300.67  164916[8:SpL:160491.0,941.1] || member(u,image(element_relation,power_class(symmetric_difference(ordinal_numbers,v))))* member(u,power_class(image(element_relation,union(v,identity_relation)))) -> .
% 299.99/300.67  159475[5:Rew:47.0,159417.1,30.0,159417.1,47.0,159417.0,30.0,159417.0] ||  -> member(not_subclass_element(u,image(element_relation,successor(v))),complement(image(element_relation,successor(v))))* subclass(u,image(element_relation,successor(v))).
% 299.99/300.67  164865[8:SpR:160491.0,19485.0] ||  -> equal(power_class(intersection(union(u,identity_relation),complement(singleton(symmetric_difference(ordinal_numbers,u))))),complement(image(element_relation,successor(symmetric_difference(ordinal_numbers,u)))))**.
% 299.99/300.67  167501[8:Res:9006.3,163154.0] function(u) || member(v,ordinal_numbers) subclass(ordinal_numbers,symmetrization_of(identity_relation)) -> member(image(u,v),inverse(identity_relation))*.
% 299.99/300.67  39332[5:Res:9006.3,26.0] function(u) || member(v,ordinal_numbers) subclass(ordinal_numbers,intersection(w,x))* -> member(image(u,v),x)*.
% 299.99/300.67  39322[5:Res:9006.3,28.1] function(u) || member(v,ordinal_numbers) subclass(ordinal_numbers,complement(w)) member(image(u,v),w)* -> .
% 299.99/300.67  39333[5:Res:9006.3,25.0] function(u) || member(v,ordinal_numbers) subclass(ordinal_numbers,intersection(w,x))* -> member(image(u,v),w)*.
% 299.99/300.67  154351[5:Res:9006.3,151988.0] function(u) || member(v,ordinal_numbers) subclass(ordinal_numbers,complement(complement(w))) -> member(image(u,v),w)*.
% 299.99/300.67  146740[5:SpL:72.0,18571.2] || member(image(u,singleton(v)),ordinal_numbers)* subclass(ordinal_numbers,complement(w)) member(apply(u,v),w)* -> .
% 299.99/300.67  63880[7:Res:284.1,13082.1] inductive(apply(u,v)) || member(image(u,singleton(v)),ordinal_numbers)* -> member(identity_relation,image(u,singleton(v))).
% 299.99/300.67  17978[7:SpR:15265.1,107.0] function(u) ||  -> equal(domain__dfg(u,image(inverse(u),singleton(single_valued1(u))),second(not_subclass_element(identity_relation,identity_relation))),single_valued3(u))**.
% 299.99/300.67  18036[7:SpR:15272.1,107.0] single_valued_class(u) ||  -> equal(domain__dfg(u,image(inverse(u),singleton(single_valued1(u))),second(not_subclass_element(identity_relation,identity_relation))),single_valued3(u))**.
% 299.99/300.67  18600[8:SpR:17976.1,107.0] function(u) ||  -> equal(domain__dfg(u,image(inverse(u),singleton(single_valued1(u))),range__dfg(identity_relation,v,w)),single_valued3(u))**.
% 299.99/300.67  18610[8:SpR:18033.1,107.0] single_valued_class(u) ||  -> equal(domain__dfg(u,image(inverse(u),singleton(single_valued1(u))),range__dfg(identity_relation,v,w)),single_valued3(u))**.
% 299.99/300.67  35802[0:Res:10714.1,1300.1] inductive(singleton(u)) || member(u,image(successor_relation,singleton(u)))* -> equal(image(successor_relation,singleton(u)),singleton(u)).
% 299.99/300.67  162882[0:Res:52.1,19124.0] inductive(singleton(u)) ||  -> subclass(image(successor_relation,singleton(u)),v) equal(not_subclass_element(image(successor_relation,singleton(u)),v),u)**.
% 299.99/300.67  195394[16:Rew:195224.0,193384.1] || member(u,symmetric_difference(complement(v),power_class(complement(singleton(identity_relation)))))* -> member(u,union(v,image(element_relation,singleton(identity_relation)))).
% 299.99/300.67  195390[16:Rew:195224.0,193380.1] || member(u,symmetric_difference(power_class(complement(singleton(identity_relation))),complement(v)))* -> member(u,union(image(element_relation,singleton(identity_relation)),v)).
% 299.99/300.67  195334[16:Rew:195224.0,163221.0] || member(not_subclass_element(power_class(complement(singleton(identity_relation))),u),image(element_relation,singleton(identity_relation)))* -> subclass(power_class(complement(singleton(identity_relation))),u).
% 299.99/300.67  195384[16:Rew:195224.0,193311.0] ||  -> subclass(complement(symmetrization_of(image(element_relation,singleton(identity_relation)))),intersection(power_class(complement(singleton(identity_relation))),complement(inverse(image(element_relation,singleton(identity_relation))))))*.
% 299.99/300.67  195382[16:Rew:195224.0,193310.0] ||  -> subclass(complement(successor(image(element_relation,singleton(identity_relation)))),intersection(power_class(complement(singleton(identity_relation))),complement(singleton(image(element_relation,singleton(identity_relation))))))*.
% 299.99/300.67  195314[16:Rew:195224.0,193332.0] ||  -> equal(complement(intersection(complement(u),power_class(image(element_relation,singleton(identity_relation))))),union(u,image(element_relation,power_class(complement(singleton(identity_relation))))))**.
% 299.99/300.67  195313[16:Rew:195224.0,193319.0] ||  -> equal(complement(intersection(power_class(image(element_relation,singleton(identity_relation))),complement(u))),union(image(element_relation,power_class(complement(singleton(identity_relation)))),u))**.
% 299.99/300.67  136670[5:Res:8977.2,18791.0] || member(u,ordinal_numbers) subclass(ordinal_numbers,symmetric_difference(complement(v),complement(w)))* -> member(power_class(u),union(v,w))*.
% 299.99/300.67  97011[5:Res:96970.1,11.0] || subclass(ordinal_numbers,power_class(u)) subclass(power_class(u),singleton(singleton(v)))* -> equal(power_class(u),singleton(singleton(v))).
% 299.99/300.67  162893[8:MRR:61942.0,162891.0] ||  -> equal(apply(choice,ordered_pair(u,v)),unordered_pair(u,singleton(v)))** equal(apply(choice,ordered_pair(u,v)),singleton(u)).
% 299.99/300.67  163936[7:Res:13069.2,151988.0] || member(complement(complement(u)),ordinal_numbers) -> equal(complement(complement(u)),identity_relation) member(apply(choice,complement(complement(u))),u)*.
% 299.99/300.67  195701[8:Res:13225.3,163154.0] || member(u,ordinal_numbers) subclass(u,symmetrization_of(identity_relation)) -> equal(u,identity_relation) member(apply(choice,u),inverse(identity_relation))*.
% 299.99/300.67  195696[8:Res:13225.3,14679.1] || member(u,ordinal_numbers) subclass(u,inverse(subset_relation)) member(apply(choice,u),subset_relation)* -> equal(u,identity_relation).
% 299.99/300.67  195692[7:Res:13225.3,50033.0] || member(u,ordinal_numbers) subclass(u,subset_relation) equal(complement(apply(choice,u)),ordinal_numbers)** -> equal(u,identity_relation).
% 299.99/300.67  195681[7:Res:13225.3,26.0] || member(u,ordinal_numbers) subclass(u,intersection(v,w))* -> equal(u,identity_relation) member(apply(choice,u),w)*.
% 299.99/300.67  195671[7:Res:13225.3,28.1] || member(u,ordinal_numbers) subclass(u,complement(v)) member(apply(choice,u),v)* -> equal(u,identity_relation).
% 299.99/300.67  195674[7:Res:13225.3,151988.0] || member(u,ordinal_numbers) subclass(u,complement(complement(v))) -> equal(u,identity_relation) member(apply(choice,u),v)*.
% 299.99/300.67  195682[7:Res:13225.3,25.0] || member(u,ordinal_numbers) subclass(u,intersection(v,w))* -> equal(u,identity_relation) member(apply(choice,u),v)*.
% 299.99/300.67  63699[8:SoR:18511.0,19277.2] single_valued_class(recursion(u,successor_relation,union_of_range_map)) || equal(recursion(u,successor_relation,union_of_range_map),identity_relation) -> member(ordinal_add(u,v),ordinal_numbers)*.
% 299.99/300.67  145797[5:Rew:143170.0,145760.0] || member(cross_product(u,singleton(v)),ordinal_numbers) -> member(ordered_pair(cross_product(u,singleton(v)),segment(ordinal_numbers,u,v)),domain_relation)*.
% 299.99/300.67  204172[18:Res:194549.1,129.0] || subclass(symmetrization_of(identity_relation),u) subclass(u,v)* well_ordering(w,v)* -> member(least(w,u),u)*.
% 299.99/300.67  204654[21:Res:196904.1,12.0] || subclass(domain_relation,unordered_pair(u,v))* -> equal(singleton(singleton(singleton(identity_relation))),v) equal(singleton(singleton(singleton(identity_relation))),u).
% 299.99/300.67  204988[21:SpL:13100.0,198463.1] || member(not_subclass_element(restrict(u,v,singleton(w)),identity_relation),subset_relation)* equal(rest_of(domain__dfg(u,v,w)),rest_relation) -> .
% 299.99/300.67  204990[21:SpL:13101.0,198464.1] || member(not_subclass_element(restrict(u,singleton(v),w),identity_relation),subset_relation)* equal(rest_of(range__dfg(u,v,w)),rest_relation) -> .
% 299.99/300.67  205195[15:Res:195033.1,21.0] || equal(complement(complement(cross_product(u,v))),ordinal_numbers)** -> equal(ordered_pair(first(range_of(identity_relation)),second(range_of(identity_relation))),range_of(identity_relation))**.
% 299.99/300.67  205340[8:SpR:481.0,192333.1] || equal(symmetric_difference(ordinal_numbers,image(element_relation,union(u,v))),ordinal_numbers) -> member(identity_relation,power_class(intersection(complement(u),complement(v))))*.
% 299.99/300.67  205419[14:SpL:481.0,195109.1] || equal(image(element_relation,union(u,v)),ordinal_numbers) equal(power_class(intersection(complement(u),complement(v))),singleton(identity_relation))** -> .
% 299.99/300.67  205421[18:SpL:481.0,196161.1] || equal(image(element_relation,union(u,v)),ordinal_numbers) equal(power_class(intersection(complement(u),complement(v))),symmetrization_of(identity_relation))** -> .
% 299.99/300.67  205423[18:SpL:481.0,196251.1] || equal(image(element_relation,union(u,v)),ordinal_numbers) equal(power_class(intersection(complement(u),complement(v))),inverse(identity_relation))** -> .
% 299.99/300.67  205550[22:Res:62.1,205501.0] || member(ordered_pair(u,singleton(identity_relation)),compose(v,w)) well_ordering(ordinal_numbers,image(v,image(w,singleton(u))))* -> .
% 299.99/300.67  205622[23:MRR:204737.4,205613.0] function(singleton(identity_relation)) function(u) || subclass(domain_relation,rest_relation) equal(compose(u,identity_relation),singleton(identity_relation))** -> .
% 299.99/300.67  205984[8:SpL:161207.0,204039.0] || equal(symmetric_difference(singleton(identity_relation),image(successor_relation,ordinal_numbers)),ordinal_numbers) member(identity_relation,intersection(singleton(identity_relation),image(successor_relation,ordinal_numbers)))* -> .
% 299.99/300.67  206003[8:SpL:481.0,204042.0] || equal(symmetric_difference(ordinal_numbers,power_class(intersection(complement(u),complement(v)))),ordinal_numbers)** -> member(identity_relation,image(element_relation,union(u,v))).
% 299.99/300.67  206151[22:Res:205574.1,21.0] || equal(cross_product(u,v),singleton(singleton(identity_relation)))** -> equal(ordered_pair(first(singleton(identity_relation)),second(singleton(identity_relation))),singleton(identity_relation))**.
% 299.99/300.67  206218[8:SpR:162038.0,155582.0] ||  -> equal(intersection(power_class(complement(inverse(identity_relation))),symmetric_difference(ordinal_numbers,image(element_relation,symmetrization_of(identity_relation)))),symmetric_difference(ordinal_numbers,image(element_relation,symmetrization_of(identity_relation))))**.
% 299.99/300.67  206219[16:SpR:195257.0,155582.0] ||  -> equal(intersection(power_class(complement(singleton(identity_relation))),symmetric_difference(ordinal_numbers,image(element_relation,singleton(identity_relation)))),symmetric_difference(ordinal_numbers,image(element_relation,singleton(identity_relation))))**.
% 299.99/300.67  207272[14:SpL:3594.0,165368.0] || equal(symmetric_difference(complement(intersection(u,v)),union(u,v)),singleton(identity_relation))** -> member(identity_relation,complement(symmetric_difference(u,v))).
% 299.99/300.67  207362[18:SpL:3594.0,190543.0] || equal(symmetric_difference(complement(intersection(u,v)),union(u,v)),symmetrization_of(identity_relation))** -> member(identity_relation,complement(symmetric_difference(u,v))).
% 299.99/300.67  207481[18:SpL:3594.0,190652.0] || equal(symmetric_difference(complement(intersection(u,v)),union(u,v)),inverse(identity_relation))** -> member(identity_relation,complement(symmetric_difference(u,v))).
% 299.99/300.67  207559[24:MRR:197525.4,207558.0] function(u) || subclass(range_of(u),identity_relation)* equal(cross_product(identity_relation,identity_relation),identity_relation) -> equal(singleton(u),identity_relation).
% 299.99/300.67  207600[24:SpR:207558.1,62.1] operation(u) || member(ordered_pair(u,v),compose(w,x))* -> member(v,image(w,image(x,identity_relation))).
% 299.99/300.67  207856[24:MRR:197242.3,207855.0] function(ordered_pair(u,v)) || subclass(range_of(ordered_pair(u,v)),identity_relation)* equal(cross_product(identity_relation,identity_relation),identity_relation) -> .
% 299.99/300.67  207859[24:MRR:197160.3,207858.0] function(unordered_pair(u,v)) || subclass(range_of(unordered_pair(u,v)),identity_relation)* equal(cross_product(identity_relation,identity_relation),identity_relation) -> .
% 299.99/300.67  207862[24:MRR:197079.3,207861.0] function(least(element_relation,omega)) || subclass(range_of(least(element_relation,omega)),identity_relation)* equal(cross_product(identity_relation,identity_relation),identity_relation) -> .
% 299.99/300.67  207999[24:MRR:196995.3,207938.0] function(sum_class(range_of(identity_relation))) || subclass(range_of(sum_class(range_of(identity_relation))),identity_relation)* equal(cross_product(identity_relation,identity_relation),identity_relation) -> .
% 299.99/300.67  208000[24:MRR:197037.3,207948.0] function(regular(symmetrization_of(identity_relation))) || subclass(range_of(regular(symmetrization_of(identity_relation))),identity_relation)* equal(cross_product(identity_relation,identity_relation),identity_relation) -> .
% 299.99/300.67  208284[24:SpR:207572.1,20.2] operation(u) || member(u,v)* member(identity_relation,w) -> member(singleton(singleton(identity_relation)),cross_product(w,v))*.
% 299.99/300.67  208342[24:SpL:207572.1,117450.1] operation(u) operation(v) || member(singleton(singleton(identity_relation)),cantor(v))* -> member(u,cantor(cantor(v)))*.
% 299.99/300.67  208412[8:Con:208400.2] operation(u) || member(v,cantor(cantor(u)))* subclass(cantor(u),w)* well_ordering(ordinal_numbers,w) -> .
% 299.99/300.67  208481[24:SpR:13260.1,207562.1] operation(first(regular(cross_product(u,v)))) ||  -> equal(cross_product(u,v),identity_relation) member(identity_relation,regular(cross_product(u,v)))*.
% 299.99/300.67  208558[15:SpL:3594.0,165538.0] || subclass(ordinal_numbers,symmetric_difference(complement(intersection(u,v)),union(u,v)))* -> member(range_of(identity_relation),complement(symmetric_difference(u,v))).
% 299.99/300.67  209025[25:Rew:208820.0,208889.0] || member(restrict(u,v,identity_relation),ordinal_numbers) -> member(ordered_pair(restrict(u,v,identity_relation),segment(u,v,ordinal_numbers)),domain_relation)*.
% 299.99/300.67  209289[25:SpR:208840.0,116123.2] || member(identity_relation,cantor(u)) equal(restrict(u,identity_relation,ordinal_numbers),ordinal_numbers) -> member(singleton(singleton(identity_relation)),rest_of(u))*.
% 299.99/300.67  209803[8:SpR:162038.0,206259.0] ||  -> subclass(symmetric_difference(power_class(complement(inverse(identity_relation))),symmetric_difference(ordinal_numbers,image(element_relation,symmetrization_of(identity_relation)))),union(image(element_relation,symmetrization_of(identity_relation)),identity_relation))*.
% 299.99/300.67  209804[16:SpR:195257.0,206259.0] ||  -> subclass(symmetric_difference(power_class(complement(singleton(identity_relation))),symmetric_difference(ordinal_numbers,image(element_relation,singleton(identity_relation)))),union(image(element_relation,singleton(identity_relation)),identity_relation))*.
% 299.99/300.67  209868[24:SpR:162038.0,207863.1] operation(image(element_relation,symmetrization_of(identity_relation))) ||  -> subclass(symmetric_difference(power_class(complement(inverse(identity_relation))),ordinal_numbers),successor(image(element_relation,symmetrization_of(identity_relation))))*.
% 299.99/300.67  209869[24:SpR:195257.0,207863.1] operation(image(element_relation,singleton(identity_relation))) ||  -> subclass(symmetric_difference(power_class(complement(singleton(identity_relation))),ordinal_numbers),successor(image(element_relation,singleton(identity_relation))))*.
% 299.99/300.67  209878[24:Res:207863.1,11.0] operation(u) || subclass(successor(u),symmetric_difference(complement(u),ordinal_numbers))* -> equal(symmetric_difference(complement(u),ordinal_numbers),successor(u)).
% 299.99/300.67  209897[24:Res:207866.1,11.0] operation(u) || subclass(symmetric_difference(ordinal_numbers,u),complement(successor(u)))* -> equal(symmetric_difference(ordinal_numbers,u),complement(successor(u))).
% 299.99/300.67  210074[15:SpL:3594.0,208593.0] || equal(symmetric_difference(complement(intersection(u,v)),union(u,v)),ordinal_numbers)** -> member(range_of(identity_relation),complement(symmetric_difference(u,v))).
% 299.99/300.67  210168[25:SpR:50855.1,208873.0] || member(singleton(u),subset_relation) -> equal(unordered_pair(u,unordered_pair(first(singleton(u)),identity_relation)),ordered_pair(first(singleton(u)),ordinal_numbers))**.
% 299.99/300.67  210268[8:SpR:161207.0,140864.1] || member(u,complement(intersection(singleton(identity_relation),image(successor_relation,ordinal_numbers))))* -> member(u,symmetric_difference(singleton(identity_relation),image(successor_relation,ordinal_numbers))).
% 299.99/300.67  210292[8:Res:140864.1,47534.0] || member(not_subclass_element(u,intersection(symmetric_difference(ordinal_numbers,v),u)),complement(v))* -> subclass(u,intersection(symmetric_difference(ordinal_numbers,v),u)).
% 299.99/300.67  210565[8:Res:8551.2,210517.1] || member(u,cross_product(v,w))* member(u,x)* equal(complement(restrict(x,v,w)),ordinal_numbers)** -> .
% 299.99/300.67  210640[8:Res:9563.3,210517.1] || connected(u,v) well_ordering(w,v)* equal(complement(not_well_ordering(u,v)),ordinal_numbers)** -> well_ordering(u,v).
% 299.99/300.67  210670[8:Res:9706.3,210517.1] || member(u,ordinal_numbers)* member(v,ordinal_numbers)* equal(successor(v),u)* equal(complement(successor_relation),ordinal_numbers) -> .
% 299.99/300.67  210689[8:Res:62.1,210517.1] || member(ordered_pair(u,v),compose(w,x))* equal(complement(image(w,image(x,singleton(u)))),ordinal_numbers)** -> .
% 299.99/300.67  211080[8:Res:210572.1,9580.1] || equal(complement(segment(u,v,w)),ordinal_numbers)** subclass(singleton(w),v) -> section(u,singleton(w),v).
% 299.99/300.67  211302[8:Res:210606.1,13070.0] || equal(complement(u),ordinal_numbers) well_ordering(v,complement(u))* -> equal(w,identity_relation) member(least(v,w),w)*.
% 299.99/300.67  211303[8:Res:210606.1,13113.0] || equal(complement(u),ordinal_numbers) well_ordering(v,complement(u))* -> equal(segment(v,w,least(v,w)),identity_relation)**.
% 299.99/300.67  211304[8:Res:210606.1,9661.0] || equal(complement(u),ordinal_numbers) well_ordering(v,complement(u))* -> subclass(w,x)* member(least(v,w),w)*.
% 299.99/300.67  211305[8:Res:210606.1,9665.1] inductive(u) || equal(complement(v),ordinal_numbers) well_ordering(w,complement(v))* -> member(least(w,u),u)*.
% 299.99/300.67  211537[8:Res:211438.1,13070.0] || equal(symmetrization_of(identity_relation),ordinal_numbers) well_ordering(u,symmetrization_of(identity_relation)) -> equal(v,identity_relation) member(least(u,v),v)*.
% 299.99/300.67  211538[8:Res:211438.1,13113.0] || equal(symmetrization_of(identity_relation),ordinal_numbers) well_ordering(u,symmetrization_of(identity_relation)) -> equal(segment(u,v,least(u,v)),identity_relation)**.
% 299.99/300.67  211539[8:Res:211438.1,9661.0] || equal(symmetrization_of(identity_relation),ordinal_numbers) well_ordering(u,symmetrization_of(identity_relation)) -> subclass(v,w)* member(least(u,v),v)*.
% 299.99/300.67  211540[8:Res:211438.1,9665.1] inductive(u) || equal(symmetrization_of(identity_relation),ordinal_numbers) well_ordering(v,symmetrization_of(identity_relation)) -> member(least(v,u),u)*.
% 299.99/300.67  211621[8:Res:211441.1,13070.0] || equal(power_class(u),ordinal_numbers) well_ordering(v,power_class(u))* -> equal(w,identity_relation) member(least(v,w),w)*.
% 299.99/300.67  211622[8:Res:211441.1,13113.0] || equal(power_class(u),ordinal_numbers) well_ordering(v,power_class(u))* -> equal(segment(v,w,least(v,w)),identity_relation)**.
% 299.99/300.67  211623[8:Res:211441.1,9661.0] || equal(power_class(u),ordinal_numbers) well_ordering(v,power_class(u))* -> subclass(w,x)* member(least(v,w),w)*.
% 299.99/300.67  211624[8:Res:211441.1,9665.1] inductive(u) || equal(power_class(v),ordinal_numbers) well_ordering(w,power_class(v))* -> member(least(w,u),u)*.
% 299.99/300.67  212237[8:SpL:161207.0,210460.0] || subclass(ordinal_numbers,symmetric_difference(singleton(identity_relation),image(successor_relation,ordinal_numbers))) member(omega,intersection(singleton(identity_relation),image(successor_relation,ordinal_numbers)))* -> .
% 299.99/300.67  212254[8:SpL:161207.0,210511.0] || subclass(ordinal_numbers,symmetric_difference(singleton(identity_relation),image(successor_relation,ordinal_numbers))) member(identity_relation,intersection(singleton(identity_relation),image(successor_relation,ordinal_numbers)))* -> .
% 299.99/300.67  213083[8:SpR:210579.1,3594.0] || equal(complement(complement(symmetric_difference(u,v))),ordinal_numbers) -> equal(symmetric_difference(complement(intersection(u,v)),union(u,v)),identity_relation)**.
% 299.99/300.67  213472[8:SpR:145761.0,116403.2] || member(u,ordinal_numbers) subclass(rest_relation,rest_of(cross_product(v,singleton(w))))* -> member(u,segment(ordinal_numbers,v,w))*.
% 299.99/300.67  213588[25:MRR:213584.0,66422.0] || member(ordinal_numbers,not_well_ordering(ordinal_numbers,u)) equal(cantor(cross_product(not_well_ordering(ordinal_numbers,u),identity_relation)),identity_relation)** -> well_ordering(ordinal_numbers,u).
% 299.99/300.67  214072[0:Res:2504.1,152274.0] || subclass(ordered_pair(u,v),complement(singleton(unordered_pair(u,singleton(v)))))* -> subclass(singleton(unordered_pair(u,singleton(v))),w)*.
% 299.99/300.67  214285[25:SpR:208887.0,116403.2] || member(u,ordinal_numbers) subclass(rest_relation,rest_of(restrict(v,w,identity_relation)))* -> member(u,segment(v,w,ordinal_numbers))*.
% 299.99/300.67  214317[25:Rew:160429.0,214291.1] || asymmetric(cross_product(u,v),identity_relation) -> equal(segment(restrict(inverse(cross_product(u,v)),u,v),identity_relation,ordinal_numbers),identity_relation)**.
% 299.99/300.67  214410[25:SpR:208985.1,20.2] operation(u) || member(ordinal_numbers,v) member(w,x) -> member(ordered_pair(w,u),cross_product(x,v))*.
% 299.99/300.67  214447[25:SpR:208985.1,20.2] operation(u) || member(u,v)* member(w,x) -> member(ordered_pair(w,ordinal_numbers),cross_product(x,v))*.
% 299.99/300.67  214527[25:SpL:208985.1,117450.1] operation(u) operation(v) || member(ordered_pair(w,u),cantor(v))* -> member(ordinal_numbers,cantor(cantor(v))).
% 299.99/300.67  214589[25:SpL:208985.1,117450.1] operation(u) operation(v) || member(ordered_pair(w,ordinal_numbers),cantor(v))* -> member(u,cantor(cantor(v)))*.
% 299.99/300.67  214620[25:Rew:208820.0,214526.2] operation(u) || member(v,ordered_pair(w,u))* -> equal(v,unordered_pair(w,identity_relation)) equal(v,singleton(w)).
% 299.99/300.67  214965[5:SpR:481.0,151502.1] ||  -> member(u,image(element_relation,union(v,w))) subclass(intersection(x,singleton(u)),power_class(intersection(complement(v),complement(w))))*.
% 299.99/300.67  214988[5:Res:151502.1,11.0] || subclass(complement(u),intersection(v,singleton(w)))* -> member(w,u) equal(complement(u),intersection(v,singleton(w))).
% 299.99/300.67  215095[5:SpR:481.0,151862.1] ||  -> member(u,image(element_relation,union(v,w))) subclass(intersection(singleton(u),x),power_class(intersection(complement(v),complement(w))))*.
% 299.99/300.67  215123[5:Res:151862.1,11.0] || subclass(complement(u),intersection(singleton(v),w))* -> member(v,u) equal(complement(u),intersection(singleton(v),w)).
% 299.99/300.67  215147[5:SpR:481.0,215108.1] ||  -> member(u,image(element_relation,union(v,w))) subclass(complement(complement(singleton(u))),power_class(intersection(complement(v),complement(w))))*.
% 299.99/300.67  215160[5:Res:215108.1,11.0] || subclass(complement(u),complement(complement(singleton(v))))* -> member(v,u) equal(complement(u),complement(complement(singleton(v)))).
% 299.99/300.67  215181[8:SpR:162038.0,155157.1] || subclass(image(element_relation,symmetrization_of(identity_relation)),u) -> subclass(symmetric_difference(u,image(element_relation,symmetrization_of(identity_relation))),power_class(complement(inverse(identity_relation))))*.
% 299.99/300.67  215182[16:SpR:195257.0,155157.1] || subclass(image(element_relation,singleton(identity_relation)),u) -> subclass(symmetric_difference(u,image(element_relation,singleton(identity_relation))),power_class(complement(singleton(identity_relation))))*.
% 299.99/300.67  215353[8:SpR:215271.1,161196.2] operation(u) || subclass(symmetrization_of(v),identity_relation) connected(v,cantor(cantor(u)))* -> subclass(cantor(u),identity_relation).
% 299.99/300.67  215471[8:SpL:215271.1,161194.1] operation(u) || subclass(symmetrization_of(v),identity_relation) subclass(cantor(u),identity_relation) -> connected(v,cantor(cantor(u)))*.
% 299.99/300.67  217267[8:Rew:140613.0,216707.2] || equal(identity_relation,u) member(v,ordinal_numbers) -> member(v,symmetric_difference(ordinal_numbers,w))* member(v,union(w,u))*.
% 299.99/300.67  217268[8:Rew:17351.0,216768.3] operation(u) || equal(symmetrization_of(v),identity_relation) connected(v,cantor(cantor(u)))* -> subclass(cantor(u),identity_relation).
% 299.99/300.67  217269[8:Rew:17351.0,217060.2] operation(u) || equal(symmetrization_of(v),identity_relation) subclass(cantor(u),identity_relation) -> connected(v,cantor(cantor(u)))*.
% 299.99/300.67  217270[8:Rew:140603.0,216761.1] || equal(restrict(u,v,w),identity_relation) -> equal(symmetric_difference(u,cross_product(v,w)),union(u,cross_product(v,w)))**.
% 299.99/300.67  217271[8:Rew:140603.0,216760.1] || equal(restrict(u,v,w),identity_relation) -> equal(symmetric_difference(cross_product(v,w),u),union(cross_product(v,w),u))**.
% 299.99/300.67  217394[8:Res:216591.1,129.0] || equal(complement(u),identity_relation) subclass(u,v)* well_ordering(w,v)* -> member(least(w,u),u)*.
% 299.99/300.67  217528[7:Res:61019.0,19559.0] ||  -> equal(complement(complement(symmetric_difference(u,singleton(u)))),identity_relation) member(regular(complement(complement(symmetric_difference(u,singleton(u))))),successor(u))*.
% 299.99/300.67  217529[7:Res:61019.0,19676.0] ||  -> equal(complement(complement(symmetric_difference(u,inverse(u)))),identity_relation) member(regular(complement(complement(symmetric_difference(u,inverse(u))))),symmetrization_of(u))*.
% 299.99/300.67  217582[8:Rew:162038.0,217504.1] ||  -> member(regular(complement(power_class(complement(inverse(identity_relation))))),image(element_relation,symmetrization_of(identity_relation)))* equal(complement(power_class(complement(inverse(identity_relation)))),identity_relation).
% 299.99/300.67  217583[16:Rew:195257.0,217505.1] ||  -> member(regular(complement(power_class(complement(singleton(identity_relation))))),image(element_relation,singleton(identity_relation)))* equal(complement(power_class(complement(singleton(identity_relation)))),identity_relation).
% 299.99/300.67  219218[8:Res:9837.3,219073.1] || member(u,ordinal_numbers)* member(v,ordinal_numbers) equal(sum_class(range_of(v)),u)* subclass(union_of_range_map,identity_relation) -> .
% 299.99/300.67  219311[15:Res:215659.1,129.0] || subclass(complement(u),identity_relation) subclass(u,v)* well_ordering(w,v)* -> member(least(w,u),u)*.
% 299.99/300.67  219573[8:SpL:189.0,67561.0] || member(u,symmetric_difference(power_class(image(element_relation,complement(v))),ordinal_numbers))* -> member(u,union(image(element_relation,power_class(v)),identity_relation)).
% 299.99/300.67  219586[8:Res:51313.1,67561.0] || member(singleton(symmetric_difference(complement(u),ordinal_numbers)),subset_relation) -> member(first(singleton(symmetric_difference(complement(u),ordinal_numbers))),union(u,identity_relation))*.
% 299.99/300.67  219597[8:Res:60219.0,67561.0] ||  -> subclass(u,complement(symmetric_difference(complement(v),ordinal_numbers))) member(not_subclass_element(u,complement(symmetric_difference(complement(v),ordinal_numbers))),union(v,identity_relation))*.
% 299.99/300.67  219621[21:Res:196416.2,67561.0] || member(u,ordinal_numbers) subclass(domain_relation,symmetric_difference(complement(v),ordinal_numbers)) -> member(ordered_pair(u,identity_relation),union(v,identity_relation))*.
% 299.99/300.67  219778[8:SpR:189.0,67614.1] || member(u,union(image(element_relation,power_class(v)),identity_relation)) -> member(u,symmetric_difference(power_class(image(element_relation,complement(v))),ordinal_numbers))*.
% 299.99/300.67  219795[8:Res:67614.1,13105.0] || member(regular(complement(symmetric_difference(complement(u),ordinal_numbers))),union(u,identity_relation))* -> equal(complement(symmetric_difference(complement(u),ordinal_numbers)),identity_relation).
% 299.99/300.67  220026[8:Res:13248.1,160772.0] || member(regular(intersection(symmetric_difference(ordinal_numbers,u),v)),union(u,identity_relation))* -> equal(intersection(symmetric_difference(ordinal_numbers,u),v),identity_relation).
% 299.99/300.67  220039[8:Res:13210.1,160772.0] || member(regular(intersection(u,symmetric_difference(ordinal_numbers,v))),union(v,identity_relation))* -> equal(intersection(u,symmetric_difference(ordinal_numbers,v)),identity_relation).
% 299.99/300.67  220059[21:Res:196416.2,160772.0] || member(u,ordinal_numbers) subclass(domain_relation,symmetric_difference(ordinal_numbers,v)) member(ordered_pair(u,identity_relation),union(v,identity_relation))* -> .
% 299.99/300.67  220384[21:SpR:13260.1,196656.1] || subclass(domain_relation,flip(u)) -> equal(cross_product(v,w),identity_relation) member(ordered_pair(regular(cross_product(v,w)),identity_relation),u)*.
% 299.99/300.67  220397[21:Res:196656.1,129.0] || subclass(domain_relation,flip(u)) subclass(u,v)* well_ordering(w,v)* -> member(least(w,u),u)*.
% 299.99/300.67  220407[21:Res:196656.1,18791.0] || subclass(domain_relation,flip(symmetric_difference(complement(u),complement(v)))) -> member(ordered_pair(ordered_pair(w,x),identity_relation),union(u,v))*.
% 299.99/300.67  220499[21:Res:196657.1,129.0] || subclass(domain_relation,rotate(u)) subclass(u,v)* well_ordering(w,v)* -> member(least(w,u),u)*.
% 299.99/300.67  220509[21:Res:196657.1,18791.0] || subclass(domain_relation,rotate(symmetric_difference(complement(u),complement(v)))) -> member(ordered_pair(ordered_pair(w,identity_relation),x),union(u,v))*.
% 299.99/300.67  220661[7:SpL:50855.1,17324.0] || member(singleton(u),subset_relation)* subclass(v,u)* -> equal(v,identity_relation) equal(regular(v),first(singleton(u)))*.
% 299.99/300.67  220721[8:Res:13225.3,219203.0] || member(u,ordinal_numbers) subclass(u,rest_of(apply(choice,u)))* subclass(element_relation,identity_relation) -> equal(u,identity_relation).
% 299.99/300.67  221076[7:MRR:221072.2,13039.0] || well_ordering(u,v) subclass(singleton(least(u,v)),v) -> section(u,singleton(least(u,v)),v)*.
% 299.99/300.67  221117[7:Res:13236.2,151988.0] || well_ordering(u,complement(complement(v))) -> equal(complement(complement(v)),identity_relation) member(least(u,complement(complement(v))),v)*.
% 299.99/300.67  221125[7:Res:13236.2,26.0] || well_ordering(u,intersection(v,w)) -> equal(intersection(v,w),identity_relation) member(least(u,intersection(v,w)),w)*.
% 299.99/300.67  221126[7:Res:13236.2,25.0] || well_ordering(u,intersection(v,w)) -> equal(intersection(v,w),identity_relation) member(least(u,intersection(v,w)),v)*.
% 299.99/300.67  222602[21:SpR:218387.1,154.1] || subclass(domain_relation,rest_relation) member(sum_class(range_of(identity_relation)),recursion_equation_functions(u))* -> equal(compose(u,identity_relation),sum_class(range_of(identity_relation))).
% 299.99/300.67  223019[5:Rew:50855.1,223001.2] || member(singleton(u),subset_relation) member(singleton(singleton(u)),union_of_range_map)* -> equal(first(singleton(u)),sum_class(range_of(u))).
% 299.99/300.67  223072[8:SpL:160491.0,13306.0] || member(regular(power_class(symmetric_difference(ordinal_numbers,u))),image(element_relation,union(u,identity_relation)))* -> equal(power_class(symmetric_difference(ordinal_numbers,u)),identity_relation).
% 299.99/300.67  223143[21:SpL:19486.0,198469.1] || member(intersection(complement(u),complement(inverse(u))),ordinal_numbers)* equal(rest_of(complement(image(element_relation,symmetrization_of(u)))),rest_relation) -> .
% 299.99/300.67  223146[21:SpL:19486.0,202345.1] || member(intersection(complement(u),complement(inverse(u))),ordinal_numbers)* subclass(rest_relation,rest_of(complement(image(element_relation,symmetrization_of(u))))) -> .
% 299.99/300.67  223174[21:SpR:218395.1,154.1] || subclass(domain_relation,rest_relation) member(regular(symmetrization_of(identity_relation)),recursion_equation_functions(u))* -> equal(compose(u,identity_relation),regular(symmetrization_of(identity_relation))).
% 299.99/300.67  223237[21:SpR:218416.1,154.1] || subclass(domain_relation,rest_relation) member(least(element_relation,omega),recursion_equation_functions(u))* -> equal(compose(u,identity_relation),least(element_relation,omega)).
% 299.99/300.67  223297[21:SpR:218563.1,154.1] || subclass(rest_relation,domain_relation) member(sum_class(range_of(identity_relation)),recursion_equation_functions(u))* -> equal(compose(u,identity_relation),sum_class(range_of(identity_relation))).
% 299.99/300.67  223365[21:SpR:218571.1,154.1] || subclass(rest_relation,domain_relation) member(regular(symmetrization_of(identity_relation)),recursion_equation_functions(u))* -> equal(compose(u,identity_relation),regular(symmetrization_of(identity_relation))).
% 299.99/300.67  223465[21:SpL:19485.0,198469.1] || member(intersection(complement(u),complement(singleton(u))),ordinal_numbers)* equal(rest_of(complement(image(element_relation,successor(u)))),rest_relation) -> .
% 299.99/300.67  223468[21:SpL:19485.0,202345.1] || member(intersection(complement(u),complement(singleton(u))),ordinal_numbers)* subclass(rest_relation,rest_of(complement(image(element_relation,successor(u))))) -> .
% 299.99/300.67  223499[21:SpR:218592.1,154.1] || subclass(rest_relation,domain_relation) member(least(element_relation,omega),recursion_equation_functions(u))* -> equal(compose(u,identity_relation),least(element_relation,omega)).
% 299.99/300.67  223702[8:SpR:160927.0,130703.0] ||  -> subclass(complement(union(intersection(complement(u),union(v,identity_relation)),w)),intersection(union(u,symmetric_difference(ordinal_numbers,v)),complement(w)))*.
% 299.99/300.67  223731[14:SpR:160927.0,165178.0] ||  -> member(identity_relation,image(element_relation,union(u,symmetric_difference(ordinal_numbers,v))))* member(identity_relation,power_class(intersection(complement(u),union(v,identity_relation)))).
% 299.99/300.67  223748[8:SpR:160927.0,130703.0] ||  -> subclass(complement(union(u,intersection(complement(v),union(w,identity_relation)))),intersection(complement(u),union(v,symmetric_difference(ordinal_numbers,w))))*.
% 299.99/300.67  223757[8:SpR:160927.0,151502.1] ||  -> member(u,intersection(complement(v),union(w,identity_relation))) subclass(intersection(x,singleton(u)),union(v,symmetric_difference(ordinal_numbers,w)))*.
% 299.99/300.67  223758[8:SpR:160927.0,151862.1] ||  -> member(u,intersection(complement(v),union(w,identity_relation))) subclass(intersection(singleton(u),x),union(v,symmetric_difference(ordinal_numbers,w)))*.
% 299.99/300.67  223759[8:SpR:160927.0,215108.1] ||  -> member(u,intersection(complement(v),union(w,identity_relation))) subclass(complement(complement(singleton(u))),union(v,symmetric_difference(ordinal_numbers,w)))*.
% 299.99/300.67  223787[8:SpR:162038.0,160927.0] ||  -> equal(complement(intersection(power_class(complement(inverse(identity_relation))),union(u,identity_relation))),union(image(element_relation,symmetrization_of(identity_relation)),symmetric_difference(ordinal_numbers,u)))**.
% 299.99/300.67  223788[16:SpR:195257.0,160927.0] ||  -> equal(complement(intersection(power_class(complement(singleton(identity_relation))),union(u,identity_relation))),union(image(element_relation,singleton(identity_relation)),symmetric_difference(ordinal_numbers,u)))**.
% 299.99/300.67  223820[8:SpL:160927.0,134026.0] || equal(complement(union(u,symmetric_difference(ordinal_numbers,v))),ordinal_numbers) well_ordering(ordinal_numbers,intersection(complement(u),union(v,identity_relation)))* -> .
% 299.99/300.67  223822[15:SpL:160927.0,165530.0] || subclass(ordinal_numbers,complement(union(u,symmetric_difference(ordinal_numbers,v)))) -> member(range_of(identity_relation),intersection(complement(u),union(v,identity_relation)))*.
% 299.99/300.67  223825[8:SpL:160927.0,9496.0] || subclass(ordinal_numbers,complement(union(u,symmetric_difference(ordinal_numbers,v)))) -> member(singleton(w),intersection(complement(u),union(v,identity_relation)))*.
% 299.99/300.67  223826[14:SpL:160927.0,165360.0] || equal(complement(union(u,symmetric_difference(ordinal_numbers,v))),singleton(identity_relation)) -> member(identity_relation,intersection(complement(u),union(v,identity_relation)))*.
% 299.99/300.67  223827[18:SpL:160927.0,190535.0] || equal(complement(union(u,symmetric_difference(ordinal_numbers,v))),symmetrization_of(identity_relation)) -> member(identity_relation,intersection(complement(u),union(v,identity_relation)))*.
% 299.99/300.67  223828[18:SpL:160927.0,190644.0] || equal(complement(union(u,symmetric_difference(ordinal_numbers,v))),inverse(identity_relation)) -> member(identity_relation,intersection(complement(u),union(v,identity_relation)))*.
% 299.99/300.67  223845[8:SpL:160927.0,204042.0] || equal(symmetric_difference(ordinal_numbers,union(u,symmetric_difference(ordinal_numbers,v))),ordinal_numbers) -> member(identity_relation,intersection(complement(u),union(v,identity_relation)))*.
% 299.99/300.67  223846[8:SpL:160927.0,176788.0] || equal(symmetric_difference(ordinal_numbers,union(u,symmetric_difference(ordinal_numbers,v))),ordinal_numbers) -> member(omega,intersection(complement(u),union(v,identity_relation)))*.
% 299.99/300.67  223850[14:SpL:160927.0,195109.1] || equal(intersection(complement(u),union(v,identity_relation)),ordinal_numbers)** equal(union(u,symmetric_difference(ordinal_numbers,v)),singleton(identity_relation)) -> .
% 299.99/300.67  223852[18:SpL:160927.0,196161.1] || equal(intersection(complement(u),union(v,identity_relation)),ordinal_numbers)** equal(union(u,symmetric_difference(ordinal_numbers,v)),symmetrization_of(identity_relation)) -> .
% 299.99/300.67  223854[18:SpL:160927.0,196251.1] || equal(intersection(complement(u),union(v,identity_relation)),ordinal_numbers)** equal(union(u,symmetric_difference(ordinal_numbers,v)),inverse(identity_relation)) -> .
% 299.99/300.67  223959[7:SpL:30.0,13242.0] || subclass(omega,union(u,v)) member(w,intersection(complement(u),complement(v)))* -> equal(integer_of(w),identity_relation).
% 299.99/300.67  223969[8:SpL:162038.0,13242.0] || subclass(omega,power_class(complement(inverse(identity_relation)))) member(u,image(element_relation,symmetrization_of(identity_relation)))* -> equal(integer_of(u),identity_relation).
% 299.99/300.67  223970[16:SpL:195257.0,13242.0] || subclass(omega,power_class(complement(singleton(identity_relation)))) member(u,image(element_relation,singleton(identity_relation)))* -> equal(integer_of(u),identity_relation).
% 299.99/300.67  224019[8:SpR:160992.0,130703.0] ||  -> subclass(complement(union(intersection(union(u,identity_relation),complement(v)),w)),intersection(union(symmetric_difference(ordinal_numbers,u),v),complement(w)))*.
% 299.99/300.67  224048[14:SpR:160992.0,165178.0] ||  -> member(identity_relation,image(element_relation,union(symmetric_difference(ordinal_numbers,u),v)))* member(identity_relation,power_class(intersection(union(u,identity_relation),complement(v)))).
% 299.99/300.67  224065[8:SpR:160992.0,130703.0] ||  -> subclass(complement(union(u,intersection(union(v,identity_relation),complement(w)))),intersection(complement(u),union(symmetric_difference(ordinal_numbers,v),w)))*.
% 299.99/300.67  224074[8:SpR:160992.0,151502.1] ||  -> member(u,intersection(union(v,identity_relation),complement(w))) subclass(intersection(x,singleton(u)),union(symmetric_difference(ordinal_numbers,v),w))*.
% 299.99/300.67  224075[8:SpR:160992.0,151862.1] ||  -> member(u,intersection(union(v,identity_relation),complement(w))) subclass(intersection(singleton(u),x),union(symmetric_difference(ordinal_numbers,v),w))*.
% 299.99/300.67  224076[8:SpR:160992.0,215108.1] ||  -> member(u,intersection(union(v,identity_relation),complement(w))) subclass(complement(complement(singleton(u))),union(symmetric_difference(ordinal_numbers,v),w))*.
% 299.99/300.67  224097[8:SpR:162038.0,160992.0] ||  -> equal(complement(intersection(union(u,identity_relation),power_class(complement(inverse(identity_relation))))),union(symmetric_difference(ordinal_numbers,u),image(element_relation,symmetrization_of(identity_relation))))**.
% 299.99/300.67  224098[16:SpR:195257.0,160992.0] ||  -> equal(complement(intersection(union(u,identity_relation),power_class(complement(singleton(identity_relation))))),union(symmetric_difference(ordinal_numbers,u),image(element_relation,singleton(identity_relation))))**.
% 299.99/300.67  224138[8:SpL:160992.0,134026.0] || equal(complement(union(symmetric_difference(ordinal_numbers,u),v)),ordinal_numbers) well_ordering(ordinal_numbers,intersection(union(u,identity_relation),complement(v)))* -> .
% 299.99/300.67  224140[15:SpL:160992.0,165530.0] || subclass(ordinal_numbers,complement(union(symmetric_difference(ordinal_numbers,u),v))) -> member(range_of(identity_relation),intersection(union(u,identity_relation),complement(v)))*.
% 299.99/300.67  224143[8:SpL:160992.0,9496.0] || subclass(ordinal_numbers,complement(union(symmetric_difference(ordinal_numbers,u),v))) -> member(singleton(w),intersection(union(u,identity_relation),complement(v)))*.
% 299.99/300.67  224144[14:SpL:160992.0,165360.0] || equal(complement(union(symmetric_difference(ordinal_numbers,u),v)),singleton(identity_relation)) -> member(identity_relation,intersection(union(u,identity_relation),complement(v)))*.
% 299.99/300.67  224145[18:SpL:160992.0,190535.0] || equal(complement(union(symmetric_difference(ordinal_numbers,u),v)),symmetrization_of(identity_relation)) -> member(identity_relation,intersection(union(u,identity_relation),complement(v)))*.
% 299.99/300.67  224146[18:SpL:160992.0,190644.0] || equal(complement(union(symmetric_difference(ordinal_numbers,u),v)),inverse(identity_relation)) -> member(identity_relation,intersection(union(u,identity_relation),complement(v)))*.
% 299.99/300.67  224164[8:SpL:160992.0,204042.0] || equal(symmetric_difference(ordinal_numbers,union(symmetric_difference(ordinal_numbers,u),v)),ordinal_numbers) -> member(identity_relation,intersection(union(u,identity_relation),complement(v)))*.
% 299.99/300.67  224165[8:SpL:160992.0,176788.0] || equal(symmetric_difference(ordinal_numbers,union(symmetric_difference(ordinal_numbers,u),v)),ordinal_numbers) -> member(omega,intersection(union(u,identity_relation),complement(v)))*.
% 299.99/300.67  224169[14:SpL:160992.0,195109.1] || equal(intersection(union(u,identity_relation),complement(v)),ordinal_numbers)** equal(union(symmetric_difference(ordinal_numbers,u),v),singleton(identity_relation)) -> .
% 299.99/300.67  224171[18:SpL:160992.0,196161.1] || equal(intersection(union(u,identity_relation),complement(v)),ordinal_numbers)** equal(union(symmetric_difference(ordinal_numbers,u),v),symmetrization_of(identity_relation)) -> .
% 299.99/300.67  224173[18:SpL:160992.0,196251.1] || equal(intersection(union(u,identity_relation),complement(v)),ordinal_numbers)** equal(union(symmetric_difference(ordinal_numbers,u),v),inverse(identity_relation)) -> .
% 299.99/300.67  224322[8:MRR:224289.2,219791.1] || member(regular(regular(symmetric_difference(complement(u),ordinal_numbers))),union(u,identity_relation))* -> equal(regular(symmetric_difference(complement(u),ordinal_numbers)),identity_relation).
% 299.99/300.67  224392[10:SpR:223660.1,17.0] || subclass(element_relation,identity_relation) -> equal(unordered_pair(identity_relation,unordered_pair(cross_product(ordinal_numbers,ordinal_numbers),singleton(u))),ordered_pair(cross_product(ordinal_numbers,ordinal_numbers),u))**.
% 299.99/300.67  224524[10:SpL:223660.1,160735.1] || subclass(element_relation,identity_relation) member(cross_product(ordinal_numbers,ordinal_numbers),cantor(u))* equal(restrict(u,identity_relation,ordinal_numbers),identity_relation) -> .
% 299.99/300.67  224599[10:Rew:140613.0,224390.1,66036.0,224390.1] || subclass(element_relation,identity_relation) -> equal(complement(image(element_relation,successor(cross_product(ordinal_numbers,ordinal_numbers)))),power_class(symmetric_difference(ordinal_numbers,cross_product(ordinal_numbers,ordinal_numbers))))**.
% 299.99/300.67  224735[26:Res:224684.1,8554.1] || subclass(omega,complement(intersection(u,v)))* member(identity_relation,union(u,v)) -> member(identity_relation,symmetric_difference(u,v)).
% 299.99/300.67  225064[8:SpR:116209.1,13570.1] operation(u) ||  -> equal(intersection(cantor(u),singleton(v)),identity_relation) equal(regular(intersection(singleton(v),cantor(u))),v)**.
% 299.99/300.67  225110[7:Rew:50855.1,225055.1] || member(singleton(u),subset_relation) -> equal(intersection(v,u),identity_relation) equal(regular(intersection(v,u)),first(singleton(u)))**.
% 299.99/300.67  225116[8:Obv:225080.2] || subclass(intersection(u,singleton(v)),inverse(subset_relation))* member(v,subset_relation) -> equal(intersection(u,singleton(v)),identity_relation).
% 299.99/300.67  225180[8:SpR:116209.1,17399.1] operation(u) ||  -> equal(intersection(singleton(v),cantor(u)),identity_relation) equal(regular(intersection(cantor(u),singleton(v))),v)**.
% 299.99/300.67  225225[7:Rew:50855.1,225159.1] || member(singleton(u),subset_relation) -> equal(intersection(u,v),identity_relation) equal(regular(intersection(u,v)),first(singleton(u)))**.
% 299.99/300.67  225231[8:Obv:225189.2] || subclass(intersection(singleton(u),v),inverse(subset_relation))* member(u,subset_relation) -> equal(intersection(singleton(u),v),identity_relation).
% 299.99/300.67  225345[26:Res:8551.2,225263.1] || member(identity_relation,cross_product(u,v)) member(identity_relation,w) equal(complement(restrict(w,u,v)),omega)** -> .
% 299.99/300.67  225353[26:Res:62.1,225263.1] || member(ordered_pair(u,identity_relation),compose(v,w)) equal(complement(image(v,image(w,singleton(u)))),omega)** -> .
% 299.99/300.67  225403[7:Res:3618.1,17312.1] || member(regular(u),symmetric_difference(v,w)) subclass(u,complement(complement(intersection(v,w))))* -> equal(u,identity_relation).
% 299.99/300.67  225409[8:Res:67614.1,17312.1] || member(regular(u),union(v,identity_relation)) subclass(u,complement(symmetric_difference(complement(v),ordinal_numbers)))* -> equal(u,identity_relation).
% 299.99/300.67  225476[7:Obv:225396.2] || subclass(intersection(u,singleton(v)),complement(w))* member(v,w) -> equal(intersection(u,singleton(v)),identity_relation).
% 299.99/300.67  225478[7:Obv:225395.2] || subclass(intersection(singleton(u),v),complement(w))* member(u,w) -> equal(intersection(singleton(u),v),identity_relation).
% 299.99/300.67  225868[26:Res:225794.1,8554.1] || equal(complement(intersection(u,v)),omega) member(identity_relation,union(u,v)) -> member(identity_relation,symmetric_difference(u,v))*.
% 299.99/300.67  226402[7:Res:13258.1,143226.0] || member(regular(restrict(symmetric_difference(ordinal_numbers,u),v,w)),u)* -> equal(restrict(symmetric_difference(ordinal_numbers,u),v,w),identity_relation).
% 299.99/300.67  226403[7:Res:13258.1,143186.0] ||  -> equal(restrict(symmetric_difference(ordinal_numbers,u),v,w),identity_relation) member(regular(restrict(symmetric_difference(ordinal_numbers,u),v,w)),complement(u))*.
% 299.99/300.67  226421[7:Res:13258.1,161.0] ||  -> equal(restrict(omega,u,v),identity_relation) equal(integer_of(regular(restrict(omega,u,v))),regular(restrict(omega,u,v)))**.
% 299.99/300.67  226461[8:Res:13125.2,69170.0] || subclass(omega,element_relation) -> equal(integer_of(regular(complement(compose(element_relation,ordinal_numbers)))),identity_relation)** equal(complement(compose(element_relation,ordinal_numbers)),identity_relation).
% 299.99/300.67  226796[8:Rew:160491.0,226786.2] || subclass(omega,symmetric_difference(ordinal_numbers,u)) -> equal(integer_of(regular(union(u,identity_relation))),identity_relation)** equal(union(u,identity_relation),identity_relation).
% 299.99/300.67  226800[7:Obv:226778.2] || subclass(omega,u) subclass(complement(u),omega)* -> equal(complement(u),identity_relation) equal(regular(complement(u)),identity_relation).
% 299.99/300.67  227129[21:Res:196520.2,5.0] || member(u,ordinal_numbers) equal(successor(u),identity_relation) subclass(successor_relation,v) -> member(ordered_pair(u,identity_relation),v)*.
% 299.99/300.67  227138[8:SpL:160927.0,217386.0] || equal(complement(union(u,symmetric_difference(ordinal_numbers,v))),identity_relation) member(identity_relation,intersection(complement(u),union(v,identity_relation)))* -> .
% 299.99/300.67  227139[8:SpL:160992.0,217386.0] || equal(complement(union(symmetric_difference(ordinal_numbers,u),v)),identity_relation) member(identity_relation,intersection(union(u,identity_relation),complement(v)))* -> .
% 299.99/300.67  227151[8:SpL:481.0,217386.0] || equal(complement(power_class(intersection(complement(u),complement(v)))),identity_relation)** member(identity_relation,image(element_relation,union(u,v))) -> .
% 299.99/300.67  227160[8:SpL:160927.0,217389.0] || equal(complement(complement(union(u,symmetric_difference(ordinal_numbers,v)))),identity_relation) -> member(identity_relation,intersection(complement(u),union(v,identity_relation)))*.
% 299.99/300.67  227161[8:SpL:160992.0,217389.0] || equal(complement(complement(union(symmetric_difference(ordinal_numbers,u),v))),identity_relation) -> member(identity_relation,intersection(union(u,identity_relation),complement(v)))*.
% 299.99/300.67  227173[8:SpL:481.0,217389.0] || equal(complement(complement(power_class(intersection(complement(u),complement(v))))),identity_relation)** -> member(identity_relation,image(element_relation,union(u,v))).
% 299.99/300.67  227199[8:SpR:160927.0,217451.1] || equal(union(intersection(complement(u),union(v,identity_relation)),identity_relation),identity_relation)** -> member(identity_relation,union(u,symmetric_difference(ordinal_numbers,v))).
% 299.99/300.67  227200[8:SpR:160992.0,217451.1] || equal(union(intersection(union(u,identity_relation),complement(v)),identity_relation),identity_relation)** -> member(identity_relation,union(symmetric_difference(ordinal_numbers,u),v)).
% 299.99/300.67  227212[8:SpR:481.0,217451.1] || equal(union(image(element_relation,union(u,v)),identity_relation),identity_relation) -> member(identity_relation,power_class(intersection(complement(u),complement(v))))*.
% 299.99/300.67  227246[5:SpR:61728.2,139.1] || member(u,ordinal_numbers) subclass(rest_relation,union_of_range_map) member(range_of(u),ordinal_numbers) -> subclass(rest_of(u),range_of(u))*.
% 299.99/300.67  227280[18:SpL:61728.2,222297.0] || member(u,ordinal_numbers)* subclass(rest_relation,union_of_range_map) equal(rest_of(u),inverse(identity_relation)) subclass(element_relation,identity_relation) -> .
% 299.99/300.67  227281[18:SpL:61728.2,222298.0] || member(u,ordinal_numbers)* subclass(rest_relation,union_of_range_map) equal(rest_of(u),symmetrization_of(identity_relation)) subclass(element_relation,identity_relation) -> .
% 299.99/300.67  227282[14:SpL:61728.2,222299.0] || member(u,ordinal_numbers)* subclass(rest_relation,union_of_range_map) equal(rest_of(u),singleton(identity_relation)) subclass(element_relation,identity_relation) -> .
% 299.99/300.67  227292[8:Rew:61728.2,227244.2] || member(u,ordinal_numbers) subclass(rest_relation,union_of_range_map) equal(rest_of(u),identity_relation) -> subclass(rest_of(u),range_of(u))*.
% 299.99/300.67  227377[8:SpL:160927.0,217608.0] || equal(complement(union(u,symmetric_difference(ordinal_numbers,v))),identity_relation) member(omega,intersection(complement(u),union(v,identity_relation)))* -> .
% 299.99/300.67  227378[8:SpL:160992.0,217608.0] || equal(complement(union(symmetric_difference(ordinal_numbers,u),v)),identity_relation) member(omega,intersection(union(u,identity_relation),complement(v)))* -> .
% 299.99/300.67  227390[8:SpL:481.0,217608.0] || equal(complement(power_class(intersection(complement(u),complement(v)))),identity_relation)** member(omega,image(element_relation,union(u,v))) -> .
% 299.99/300.67  227399[8:SpL:160927.0,217611.0] || equal(complement(complement(union(u,symmetric_difference(ordinal_numbers,v)))),identity_relation) -> member(omega,intersection(complement(u),union(v,identity_relation)))*.
% 299.99/300.67  227400[8:SpL:160992.0,217611.0] || equal(complement(complement(union(symmetric_difference(ordinal_numbers,u),v))),identity_relation) -> member(omega,intersection(union(u,identity_relation),complement(v)))*.
% 299.99/300.67  227412[8:SpL:481.0,217611.0] || equal(complement(complement(power_class(intersection(complement(u),complement(v))))),identity_relation)** -> member(omega,image(element_relation,union(u,v))).
% 299.99/300.67  227438[8:SpR:160927.0,217663.1] || equal(union(intersection(complement(u),union(v,identity_relation)),identity_relation),identity_relation)** -> member(omega,union(u,symmetric_difference(ordinal_numbers,v))).
% 299.99/300.67  227439[8:SpR:160992.0,217663.1] || equal(union(intersection(union(u,identity_relation),complement(v)),identity_relation),identity_relation)** -> member(omega,union(symmetric_difference(ordinal_numbers,u),v)).
% 299.99/300.67  227451[8:SpR:481.0,217663.1] || equal(union(image(element_relation,union(u,v)),identity_relation),identity_relation) -> member(omega,power_class(intersection(complement(u),complement(v))))*.
% 299.99/300.67  227569[8:SpL:160927.0,217695.0] || equal(complement(union(u,symmetric_difference(ordinal_numbers,v))),identity_relation) equal(intersection(complement(u),union(v,identity_relation)),ordinal_numbers)** -> .
% 299.99/300.67  227570[8:SpL:160992.0,217695.0] || equal(complement(union(symmetric_difference(ordinal_numbers,u),v)),identity_relation) equal(intersection(union(u,identity_relation),complement(v)),ordinal_numbers)** -> .
% 299.99/300.67  227582[8:SpL:481.0,217695.0] || equal(complement(power_class(intersection(complement(u),complement(v)))),identity_relation)** equal(image(element_relation,union(u,v)),ordinal_numbers) -> .
% 299.99/300.67  227599[8:SpL:160927.0,217696.0] || equal(complement(union(u,symmetric_difference(ordinal_numbers,v))),identity_relation) subclass(ordinal_numbers,intersection(complement(u),union(v,identity_relation)))* -> .
% 299.99/300.67  227600[8:SpL:160992.0,217696.0] || equal(complement(union(symmetric_difference(ordinal_numbers,u),v)),identity_relation) subclass(ordinal_numbers,intersection(union(u,identity_relation),complement(v)))* -> .
% 299.99/300.67  227612[8:SpL:481.0,217696.0] || equal(complement(power_class(intersection(complement(u),complement(v)))),identity_relation)** subclass(ordinal_numbers,image(element_relation,union(u,v))) -> .
% 299.99/300.67  227621[8:SpL:160927.0,217697.0] || equal(complement(union(u,symmetric_difference(ordinal_numbers,v))),identity_relation) equal(intersection(complement(u),union(v,identity_relation)),omega)** -> .
% 299.99/300.67  227622[8:SpL:160992.0,217697.0] || equal(complement(union(symmetric_difference(ordinal_numbers,u),v)),identity_relation) equal(intersection(union(u,identity_relation),complement(v)),omega)** -> .
% 299.99/300.67  227634[8:SpL:481.0,217697.0] || equal(complement(power_class(intersection(complement(u),complement(v)))),identity_relation)** equal(image(element_relation,union(u,v)),omega) -> .
% 299.99/300.67  227643[8:SpL:160927.0,217698.0] || equal(complement(union(u,symmetric_difference(ordinal_numbers,v))),identity_relation) subclass(omega,intersection(complement(u),union(v,identity_relation)))* -> .
% 299.99/300.67  227644[8:SpL:160992.0,217698.0] || equal(complement(union(symmetric_difference(ordinal_numbers,u),v)),identity_relation) subclass(omega,intersection(union(u,identity_relation),complement(v)))* -> .
% 299.99/300.67  227656[8:SpL:481.0,217698.0] || equal(complement(power_class(intersection(complement(u),complement(v)))),identity_relation)** subclass(omega,image(element_relation,union(u,v))) -> .
% 299.99/300.67  227665[8:SpL:160927.0,217699.0] || equal(complement(union(u,symmetric_difference(ordinal_numbers,v))),identity_relation) subclass(domain_relation,intersection(complement(u),union(v,identity_relation)))* -> .
% 299.99/300.67  227666[8:SpL:160992.0,217699.0] || equal(complement(union(symmetric_difference(ordinal_numbers,u),v)),identity_relation) subclass(domain_relation,intersection(union(u,identity_relation),complement(v)))* -> .
% 299.99/300.67  227678[8:SpL:481.0,217699.0] || equal(complement(power_class(intersection(complement(u),complement(v)))),identity_relation)** subclass(domain_relation,image(element_relation,union(u,v))) -> .
% 299.99/300.67  227691[8:SpL:160927.0,217700.0] || equal(complement(union(u,symmetric_difference(ordinal_numbers,v))),identity_relation) member(intersection(complement(u),union(v,identity_relation)),subset_relation)* -> .
% 299.99/300.67  227692[8:SpL:160992.0,217700.0] || equal(complement(union(symmetric_difference(ordinal_numbers,u),v)),identity_relation) member(intersection(union(u,identity_relation),complement(v)),subset_relation)* -> .
% 299.99/300.67  227704[8:SpL:481.0,217700.0] || equal(complement(power_class(intersection(complement(u),complement(v)))),identity_relation)** member(image(element_relation,union(u,v)),subset_relation) -> .
% 299.99/300.67  227755[21:SpR:218383.1,154.1] || subclass(domain_relation,rest_relation) member(unordered_pair(u,v),recursion_equation_functions(w))* -> equal(compose(w,identity_relation),unordered_pair(u,v)).
% 299.99/300.67  227824[21:SpR:218385.1,154.1] || subclass(domain_relation,rest_relation) member(ordered_pair(u,v),recursion_equation_functions(w))* -> equal(compose(w,identity_relation),ordered_pair(u,v)).
% 299.99/300.67  227897[21:SpR:218559.1,154.1] || subclass(rest_relation,domain_relation) member(unordered_pair(u,v),recursion_equation_functions(w))* -> equal(compose(w,identity_relation),unordered_pair(u,v)).
% 299.99/300.67  227976[7:SpR:18840.1,13410.1] || member(u,subset_relation) subclass(omega,rest_relation) -> equal(integer_of(u),identity_relation) equal(rest_of(first(u)),second(u))**.
% 299.99/300.67  227987[21:SpR:218561.1,154.1] || subclass(rest_relation,domain_relation) member(ordered_pair(u,v),recursion_equation_functions(w))* -> equal(compose(w,identity_relation),ordered_pair(u,v)).
% 299.99/300.67  228143[8:SpL:13100.0,219927.1] || member(not_subclass_element(restrict(u,v,singleton(w)),identity_relation),subset_relation)* equal(singleton(domain__dfg(u,v,w)),identity_relation) -> .
% 299.99/300.67  228149[8:SpL:13101.0,219928.1] || member(not_subclass_element(restrict(u,singleton(v),w),identity_relation),subset_relation)* equal(singleton(range__dfg(u,v,w)),identity_relation) -> .
% 299.99/300.67  228188[7:SpR:18840.1,13412.1] || member(u,subset_relation) subclass(omega,successor_relation) -> equal(integer_of(u),identity_relation) equal(successor(first(u)),second(u))**.
% 299.99/300.67  228198[8:SpL:19486.0,219937.1] || member(intersection(complement(u),complement(inverse(u))),ordinal_numbers)* equal(singleton(complement(image(element_relation,symmetrization_of(u)))),identity_relation) -> .
% 299.99/300.67  228199[8:SpL:19485.0,219937.1] || member(intersection(complement(u),complement(singleton(u))),ordinal_numbers)* equal(singleton(complement(image(element_relation,successor(u)))),identity_relation) -> .
% 299.99/300.67  228236[7:Res:139.1,17313.0] || member(recursion_equation_functions(u),ordinal_numbers) -> equal(sum_class(recursion_equation_functions(u)),identity_relation) subclass(regular(sum_class(recursion_equation_functions(u))),cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.67  228253[7:MRR:228243.2,13102.1] || connected(u,recursion_equation_functions(v)) -> well_ordering(u,recursion_equation_functions(v)) subclass(regular(not_well_ordering(u,recursion_equation_functions(v))),cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.67  228372[8:SpL:19860.0,220841.0] || member(inverse(restrict(cross_product(u,ordinal_numbers),v,w)),image(cross_product(v,w),u))* subclass(element_relation,identity_relation) -> .
% 299.99/300.67  228765[8:SpL:481.0,222095.0] || subclass(power_class(intersection(complement(u),complement(v))),identity_relation)* -> equal(symmetric_difference(ordinal_numbers,image(element_relation,union(u,v))),identity_relation).
% 299.99/300.67  228887[8:Res:13125.2,61018.0] || subclass(omega,u) -> equal(integer_of(apply(choice,regular(u))),identity_relation)** equal(regular(u),identity_relation) equal(u,identity_relation).
% 299.99/300.67  228905[8:Rew:13570.1,228904.1] || member(apply(choice,u),intersection(v,singleton(u)))* -> equal(u,identity_relation) equal(intersection(v,singleton(u)),identity_relation).
% 299.99/300.67  228907[8:Rew:17399.1,228906.1] || member(apply(choice,u),intersection(singleton(u),v))* -> equal(u,identity_relation) equal(intersection(singleton(u),v),identity_relation).
% 299.99/300.67  229033[7:Res:19563.1,5.0] || subclass(successor(u),v) -> equal(symmetric_difference(u,singleton(u)),identity_relation) member(regular(symmetric_difference(u,singleton(u))),v)*.
% 299.99/300.67  229146[7:Res:18819.1,17387.0] || member(regular(intersection(complement(cross_product(ordinal_numbers,ordinal_numbers)),u)),subset_relation)* -> equal(intersection(complement(cross_product(ordinal_numbers,ordinal_numbers)),u),identity_relation).
% 299.99/300.67  229153[7:Res:13125.2,17387.0] || subclass(omega,u) -> equal(integer_of(regular(intersection(complement(u),v))),identity_relation)** equal(intersection(complement(u),v),identity_relation).
% 299.99/300.67  229191[8:Rew:160491.0,229092.1] || member(regular(intersection(union(u,identity_relation),v)),symmetric_difference(ordinal_numbers,u))* -> equal(intersection(union(u,identity_relation),v),identity_relation).
% 299.99/300.67  229217[7:MRR:229144.0,60996.1] ||  -> member(regular(intersection(complement(union(u,v)),w)),complement(v))* equal(intersection(complement(union(u,v)),w),identity_relation).
% 299.99/300.67  229218[7:MRR:229143.0,60996.1] ||  -> member(regular(intersection(complement(union(u,v)),w)),complement(u))* equal(intersection(complement(union(u,v)),w),identity_relation).
% 299.99/300.67  229575[7:Res:18819.1,13571.0] || member(regular(intersection(u,complement(cross_product(ordinal_numbers,ordinal_numbers)))),subset_relation)* -> equal(intersection(u,complement(cross_product(ordinal_numbers,ordinal_numbers))),identity_relation).
% 299.99/300.67  229582[7:Res:13125.2,13571.0] || subclass(omega,u) -> equal(integer_of(regular(intersection(v,complement(u)))),identity_relation)** equal(intersection(v,complement(u)),identity_relation).
% 299.99/300.67  229769[8:Rew:160491.0,229535.1] || member(regular(intersection(u,union(v,identity_relation))),symmetric_difference(ordinal_numbers,v))* -> equal(intersection(u,union(v,identity_relation)),identity_relation).
% 299.99/300.67  229804[7:MRR:229573.0,60996.1] ||  -> member(regular(intersection(u,complement(union(v,w)))),complement(w))* equal(intersection(u,complement(union(v,w))),identity_relation).
% 299.99/300.67  229805[7:MRR:229572.0,60996.1] ||  -> member(regular(intersection(u,complement(union(v,w)))),complement(v))* equal(intersection(u,complement(union(v,w))),identity_relation).
% 299.99/300.67  230150[7:Res:19679.1,5.0] || subclass(symmetrization_of(u),v) -> equal(symmetric_difference(u,inverse(u)),identity_relation) member(regular(symmetric_difference(u,inverse(u))),v)*.
% 299.99/300.67  230403[8:Res:161066.1,5.0] || member(u,ordinal_numbers) subclass(symmetric_difference(ordinal_numbers,v),w)* -> member(u,union(v,identity_relation))* member(u,w)*.
% 299.99/300.67  230479[8:MRR:230421.0,41183.1] ||  -> member(not_subclass_element(u,intersection(symmetric_difference(ordinal_numbers,v),u)),union(v,identity_relation))* subclass(u,intersection(symmetric_difference(ordinal_numbers,v),u)).
% 299.99/300.67  230662[8:Res:13125.2,18754.1] || subclass(omega,u) subclass(ordinal_numbers,regular(u))* -> equal(integer_of(unordered_pair(v,w)),identity_relation)** equal(u,identity_relation).
% 299.99/300.67  230670[8:Res:18211.1,18754.1] || subclass(ordinal_numbers,symmetric_difference(u,v)) subclass(ordinal_numbers,regular(union(u,v)))* -> equal(union(u,v),identity_relation).
% 299.99/300.67  230697[8:MRR:230648.0,8666.0] || subclass(ordinal_numbers,regular(union(u,v)))* -> member(unordered_pair(w,x),complement(v))* equal(union(u,v),identity_relation).
% 299.99/300.67  230698[8:MRR:230647.0,8666.0] || subclass(ordinal_numbers,regular(union(u,v)))* -> member(unordered_pair(w,x),complement(u))* equal(union(u,v),identity_relation).
% 299.99/300.67  230757[7:Rew:63616.2,230756.3] || member(singleton(u),subset_relation)* well_ordering(v,ordinal_numbers) -> equal(u,identity_relation) equal(least(v,u),regular(u))**.
% 299.99/300.67  231239[7:SpR:154945.0,17447.1] ||  -> equal(symmetric_difference(u,intersection(u,v)),identity_relation) member(regular(symmetric_difference(u,intersection(u,v))),complement(intersection(u,v)))*.
% 299.99/300.67  231240[7:SpR:155147.0,17447.1] ||  -> equal(symmetric_difference(u,intersection(v,u)),identity_relation) member(regular(symmetric_difference(u,intersection(v,u))),complement(intersection(v,u)))*.
% 299.99/300.67  231327[7:Res:17447.1,5.0] || subclass(complement(intersection(u,v)),w) -> equal(symmetric_difference(u,v),identity_relation) member(regular(symmetric_difference(u,v)),w)*.
% 299.99/300.67  231801[8:Res:13125.2,18747.0] || subclass(omega,u) -> equal(integer_of(not_subclass_element(regular(u),v)),identity_relation)** subclass(regular(u),v) equal(u,identity_relation).
% 299.99/300.67  231833[8:Rew:13570.1,231832.1] || member(not_subclass_element(u,v),intersection(w,singleton(u)))* -> subclass(u,v) equal(intersection(w,singleton(u)),identity_relation).
% 299.99/300.67  231835[8:Rew:17399.1,231834.1] || member(not_subclass_element(u,v),intersection(singleton(u),w))* -> subclass(u,v) equal(intersection(singleton(u),w),identity_relation).
% 299.99/300.67  231875[8:Res:231812.0,13113.0] || well_ordering(u,complement(v)) -> equal(v,identity_relation) equal(segment(u,regular(v),least(u,regular(v))),identity_relation)**.
% 299.99/300.67  232507[8:Res:13225.3,230867.0] || member(u,ordinal_numbers) subclass(u,subset_relation) equal(complement(apply(choice,u)),identity_relation)** -> equal(u,identity_relation).
% 299.99/300.67  232581[8:Res:13225.3,230939.0] || member(u,ordinal_numbers) subclass(u,subset_relation) equal(regular(apply(choice,u)),ordinal_numbers)** -> equal(u,identity_relation).
% 299.99/300.67  232811[8:Rew:189.0,232764.1] || subclass(image(element_relation,power_class(u)),power_class(image(element_relation,complement(u))))* -> subclass(ordinal_numbers,power_class(image(element_relation,complement(u)))).
% 299.99/300.67  233100[21:Res:196525.2,9876.0] || member(u,ordinal_numbers) equal(sum_class(range_of(u)),identity_relation)** subclass(union_of_range_map,v) well_ordering(ordinal_numbers,v)* -> .
% 299.99/300.67  233198[7:Rew:59.0,233182.1] || member(regular(image(element_relation,power_class(u))),power_class(image(element_relation,complement(u))))* -> equal(image(element_relation,power_class(u)),identity_relation).
% 299.99/300.67  233208[7:Rew:47.0,233167.1,30.0,233167.1,47.0,233167.0,30.0,233167.0] || member(regular(image(element_relation,successor(u))),complement(image(element_relation,successor(u))))* -> equal(image(element_relation,successor(u)),identity_relation).
% 299.99/300.67  233209[7:Rew:117.0,233166.1,30.0,233166.1,117.0,233166.0,30.0,233166.0] || member(regular(image(element_relation,symmetrization_of(u))),complement(image(element_relation,symmetrization_of(u))))* -> equal(image(element_relation,symmetrization_of(u)),identity_relation).
% 299.99/300.67  233271[7:Res:17388.1,13082.1] inductive(regular(intersection(recursion_equation_functions(u),v))) ||  -> equal(intersection(recursion_equation_functions(u),v),identity_relation)** member(identity_relation,cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.67  233297[8:Res:231881.0,13070.0] || well_ordering(u,complement(singleton(v)))* -> equal(singleton(v),identity_relation) equal(v,identity_relation) member(least(u,v),v)*.
% 299.99/300.67  233298[8:Res:231881.0,13113.0] || well_ordering(u,complement(singleton(v))) -> equal(singleton(v),identity_relation) equal(segment(u,v,least(u,v)),identity_relation)**.
% 299.99/300.67  233299[8:Res:231881.0,9661.0] || well_ordering(u,complement(singleton(v)))* -> equal(singleton(v),identity_relation) subclass(v,w)* member(least(u,v),v)*.
% 299.99/300.67  233300[8:Res:231881.0,9665.1] inductive(u) || well_ordering(v,complement(singleton(u)))* -> equal(singleton(u),identity_relation) member(least(v,u),u)*.
% 299.99/300.67  233322[8:Res:231881.0,8825.1] || member(u,ordinal_numbers) -> equal(singleton(complement(v)),identity_relation) member(u,v) member(u,complement(singleton(complement(v))))*.
% 299.99/300.67  233424[7:Res:13566.1,13082.1] inductive(regular(intersection(u,recursion_equation_functions(v)))) ||  -> equal(intersection(u,recursion_equation_functions(v)),identity_relation)** member(identity_relation,cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.67  233573[21:MRR:233531.2,41096.1] || member(u,cantor(v)) equal(restrict(v,u,ordinal_numbers),identity_relation)** subclass(domain_relation,complement(rest_of(v)))* -> .
% 299.99/300.67  233721[25:SpR:208985.1,13409.1] operation(u) || subclass(omega,union_of_range_map) -> equal(integer_of(ordered_pair(v,ordinal_numbers)),identity_relation)** equal(sum_class(range_of(v)),u)*.
% 299.99/300.67  233727[25:SpR:208985.1,13409.1] operation(u) || subclass(omega,union_of_range_map) -> equal(integer_of(ordered_pair(v,u)),identity_relation)** equal(sum_class(range_of(v)),ordinal_numbers).
% 299.99/300.67  233799[15:Res:195033.1,941.1] || equal(complement(complement(power_class(image(element_relation,complement(u))))),ordinal_numbers)** member(range_of(identity_relation),image(element_relation,power_class(u))) -> .
% 299.99/300.67  233830[21:Res:196904.1,941.1] || subclass(domain_relation,power_class(image(element_relation,complement(u)))) member(singleton(singleton(singleton(identity_relation))),image(element_relation,power_class(u)))* -> .
% 299.99/300.67  233831[22:Res:205574.1,941.1] || equal(power_class(image(element_relation,complement(u))),singleton(singleton(identity_relation))) member(singleton(identity_relation),image(element_relation,power_class(u)))* -> .
% 299.99/300.67  233853[18:Res:194549.1,941.1] || subclass(symmetrization_of(identity_relation),power_class(image(element_relation,complement(u)))) member(regular(symmetrization_of(identity_relation)),image(element_relation,power_class(u)))* -> .
% 299.99/300.67  233854[18:Res:190510.1,941.1] || subclass(inverse(identity_relation),power_class(image(element_relation,complement(u)))) member(regular(symmetrization_of(identity_relation)),image(element_relation,power_class(u)))* -> .
% 299.99/300.67  233952[21:Res:196904.1,161200.0] || subclass(domain_relation,image(element_relation,union(u,identity_relation))) member(singleton(singleton(singleton(identity_relation))),power_class(symmetric_difference(ordinal_numbers,u)))* -> .
% 299.99/300.67  233953[22:Res:205574.1,161200.0] || equal(image(element_relation,union(u,identity_relation)),singleton(singleton(identity_relation))) member(singleton(identity_relation),power_class(symmetric_difference(ordinal_numbers,u)))* -> .
% 299.99/300.67  233975[18:Res:194549.1,161200.0] || subclass(symmetrization_of(identity_relation),image(element_relation,union(u,identity_relation))) member(regular(symmetrization_of(identity_relation)),power_class(symmetric_difference(ordinal_numbers,u)))* -> .
% 299.99/300.67  233976[18:Res:190510.1,161200.0] || subclass(inverse(identity_relation),image(element_relation,union(u,identity_relation))) member(regular(symmetrization_of(identity_relation)),power_class(symmetric_difference(ordinal_numbers,u)))* -> .
% 299.99/300.67  234095[8:SpR:13260.1,233383.0] ||  -> equal(cross_product(u,v),identity_relation) member(singleton(first(regular(cross_product(u,v)))),complement(singleton(regular(cross_product(u,v)))))*.
% 299.99/300.67  234178[8:SpL:13260.1,234106.0] || member(singleton(first(regular(cross_product(u,v)))),singleton(regular(cross_product(u,v))))* -> equal(cross_product(u,v),identity_relation).
% 299.99/300.67  234348[8:Res:156922.1,18696.1] || member(least(u,complement(complement(subset_relation))),inverse(subset_relation))* well_ordering(u,ordinal_numbers) -> equal(complement(complement(subset_relation)),identity_relation).
% 299.99/300.67  234362[8:Res:204134.1,18696.1] || member(least(u,complement(symmetrization_of(identity_relation))),inverse(identity_relation))* well_ordering(u,ordinal_numbers) -> equal(complement(symmetrization_of(identity_relation)),identity_relation).
% 299.99/300.67  234375[8:Rew:160491.0,234355.2,160491.0,234355.0] || member(least(u,union(v,identity_relation)),complement(v))* well_ordering(u,ordinal_numbers) -> equal(union(v,identity_relation),identity_relation).
% 299.99/300.67  234381[7:Rew:59.0,234340.2] || well_ordering(u,ordinal_numbers) member(least(u,power_class(v)),image(element_relation,complement(v)))* -> equal(power_class(v),identity_relation).
% 299.99/300.67  234439[21:SpL:163.0,196423.1] || member(u,ordinal_numbers) subclass(domain_relation,symmetric_difference(v,w)) -> member(ordered_pair(u,identity_relation),complement(intersection(v,w)))*.
% 299.99/300.67  234445[21:SpL:155665.0,196423.1] || member(u,ordinal_numbers) subclass(domain_relation,symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers)))* -> member(ordered_pair(u,identity_relation),complement(subset_relation))*.
% 299.99/300.67  234446[21:SpL:155666.0,196423.1] || member(u,ordinal_numbers) subclass(domain_relation,symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation))* -> member(ordered_pair(u,identity_relation),complement(subset_relation))*.
% 299.99/300.67  234542[8:Res:13225.3,233381.0] || member(u,ordinal_numbers) subclass(u,singleton(omega)) -> equal(u,identity_relation) equal(integer_of(apply(choice,u)),identity_relation)**.
% 299.99/300.67  234780[8:SpR:117066.0,193440.1] || member(u,ordinal_numbers) -> member(u,inverse(v)) equal(apply(flip(cross_product(v,ordinal_numbers)),u),sum_class(range_of(identity_relation)))**.
% 299.99/300.67  234781[8:SpR:117142.0,193440.1] || member(u,ordinal_numbers) -> member(u,sum_class(v)) equal(apply(restrict(element_relation,ordinal_numbers,v),u),sum_class(range_of(identity_relation)))**.
% 299.99/300.67  234891[8:MRR:234829.0,8956.1] || member(u,ordinal_numbers) subclass(ordinal_numbers,complement(cantor(v)))* -> equal(apply(v,power_class(u)),sum_class(range_of(identity_relation)))**.
% 299.99/300.67  234892[8:MRR:234827.0,8955.1] || member(u,ordinal_numbers) subclass(ordinal_numbers,complement(cantor(v)))* -> equal(apply(v,sum_class(u)),sum_class(range_of(identity_relation)))**.
% 299.99/300.67  234893[8:MRR:234825.0,41183.1] || subclass(u,complement(cantor(v))) -> equal(apply(v,not_subclass_element(u,w)),sum_class(range_of(identity_relation)))** subclass(u,w).
% 299.99/300.67  234899[8:MRR:234826.0,41183.1] ||  -> equal(apply(u,not_subclass_element(v,intersection(cantor(u),v))),sum_class(range_of(identity_relation)))** subclass(v,intersection(cantor(u),v)).
% 299.99/300.67  235013[7:SpR:234956.0,62.1] || member(ordered_pair(u,v),compose(w,complement(cross_product(singleton(u),ordinal_numbers))))* -> member(v,image(w,range_of(identity_relation))).
% 299.99/300.67  235018[7:SpR:234956.0,62.1] || member(ordered_pair(u,v),compose(complement(cross_product(image(w,singleton(u)),ordinal_numbers)),w))* -> member(v,range_of(identity_relation)).
% 299.99/300.67  235168[8:Res:13225.3,234983.0] || member(u,ordinal_numbers) subclass(u,cantor(complement(cross_product(singleton(apply(choice,u)),ordinal_numbers))))* -> equal(u,identity_relation).
% 299.99/300.67  235194[8:Res:9006.3,234983.0] function(u) || member(v,ordinal_numbers) subclass(ordinal_numbers,cantor(complement(cross_product(singleton(image(u,v)),ordinal_numbers))))* -> .
% 299.99/300.67  235308[8:Res:230445.1,17387.0] || member(regular(intersection(complement(union(u,identity_relation)),v)),u)* -> equal(intersection(complement(union(u,identity_relation)),v),identity_relation).
% 299.99/300.67  235309[8:Res:230445.1,13571.0] || member(regular(intersection(u,complement(union(v,identity_relation)))),v)* -> equal(intersection(u,complement(union(v,identity_relation))),identity_relation).
% 299.99/300.67  235354[25:SpR:208985.1,28980.1] operation(u) || subclass(rest_relation,flip(v)) -> member(ordered_pair(ordered_pair(u,w),rest_of(ordered_pair(w,ordinal_numbers))),v)*.
% 299.99/300.67  235355[24:SpR:207572.1,28980.1] operation(u) || subclass(rest_relation,flip(v)) -> member(ordered_pair(ordered_pair(u,identity_relation),rest_of(singleton(singleton(identity_relation)))),v)*.
% 299.99/300.67  235360[25:SpR:208985.1,28980.1] operation(u) || subclass(rest_relation,flip(v)) -> member(ordered_pair(ordered_pair(ordinal_numbers,w),rest_of(ordered_pair(w,u))),v)*.
% 299.99/300.67  235365[25:SpR:208985.1,28980.1] operation(u) || subclass(rest_relation,flip(v)) -> member(ordered_pair(ordered_pair(w,ordinal_numbers),rest_of(ordered_pair(u,w))),v)*.
% 299.99/300.67  235366[24:SpR:207572.1,28980.1] operation(u) || subclass(rest_relation,flip(v)) -> member(ordered_pair(singleton(singleton(identity_relation)),rest_of(ordered_pair(u,identity_relation))),v)*.
% 299.99/300.67  235371[25:SpR:208985.1,28980.1] operation(u) || subclass(rest_relation,flip(v)) -> member(ordered_pair(ordered_pair(w,u),rest_of(ordered_pair(ordinal_numbers,w))),v)*.
% 299.99/300.67  235373[25:SpR:208985.1,28980.1] operation(rest_of(ordered_pair(u,v))) || subclass(rest_relation,flip(w)) -> member(ordered_pair(ordered_pair(v,u),ordinal_numbers),w)*.
% 299.99/300.67  235381[5:Res:28980.1,129.0] || subclass(rest_relation,flip(u)) subclass(u,v)* well_ordering(w,v)* -> member(least(w,u),u)*.
% 299.99/300.67  235394[5:Res:28980.1,143226.0] || subclass(rest_relation,flip(symmetric_difference(ordinal_numbers,u))) member(ordered_pair(ordered_pair(v,w),rest_of(ordered_pair(w,v))),u)* -> .
% 299.99/300.67  235395[5:Res:28980.1,143186.0] || subclass(rest_relation,flip(symmetric_difference(ordinal_numbers,u))) -> member(ordered_pair(ordered_pair(v,w),rest_of(ordered_pair(w,v))),complement(u))*.
% 299.99/300.67  235417[5:Res:28980.1,56411.0] || subclass(rest_relation,flip(rest_of(ordered_pair(ordered_pair(u,v),rest_of(ordered_pair(v,u))))))* subclass(ordinal_numbers,complement(element_relation)) -> .
% 299.99/300.67  235419[5:Res:28980.1,898.0] || subclass(rest_relation,flip(restrict(u,v,w)))* -> member(ordered_pair(ordered_pair(x,y),rest_of(ordered_pair(y,x))),u)*.
% 299.99/300.67  235423[5:Res:28980.1,8788.0] || subclass(rest_relation,flip(recursion_equation_functions(u)))* -> subclass(ordered_pair(ordered_pair(v,w),rest_of(ordered_pair(w,v))),cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.67  235488[25:SpR:208985.1,28979.1] operation(u) || subclass(rest_relation,rotate(v)) -> member(ordered_pair(ordered_pair(u,rest_of(ordered_pair(w,ordinal_numbers))),w),v)*.
% 299.99/300.67  235489[24:SpR:207572.1,28979.1] operation(u) || subclass(rest_relation,rotate(v)) -> member(ordered_pair(ordered_pair(u,rest_of(singleton(singleton(identity_relation)))),identity_relation),v)*.
% 299.99/300.67  235494[25:SpR:208985.1,28979.1] operation(u) || subclass(rest_relation,rotate(v)) -> member(ordered_pair(ordered_pair(ordinal_numbers,rest_of(ordered_pair(w,u))),w),v)*.
% 299.99/300.67  235498[25:SpR:208985.1,28979.1] operation(rest_of(ordered_pair(u,v))) || subclass(rest_relation,rotate(w)) -> member(ordered_pair(ordered_pair(v,ordinal_numbers),u),w)*.
% 299.99/300.67  235499[24:SpR:207572.1,28979.1] operation(rest_of(ordered_pair(u,identity_relation))) || subclass(rest_relation,rotate(v)) -> member(ordered_pair(singleton(singleton(identity_relation)),u),v)*.
% 299.99/300.67  235500[25:SpR:208985.1,28979.1] operation(u) || subclass(rest_relation,rotate(v)) -> member(ordered_pair(ordered_pair(w,rest_of(ordered_pair(u,w))),ordinal_numbers),v)*.
% 299.99/300.67  235501[25:SpR:208985.1,28979.1] operation(u) || subclass(rest_relation,rotate(v)) -> member(ordered_pair(ordered_pair(w,rest_of(ordered_pair(ordinal_numbers,w))),u),v)*.
% 299.99/300.67  235509[5:Res:28979.1,129.0] || subclass(rest_relation,rotate(u)) subclass(u,v)* well_ordering(w,v)* -> member(least(w,u),u)*.
% 299.99/300.67  235522[5:Res:28979.1,143226.0] || subclass(rest_relation,rotate(symmetric_difference(ordinal_numbers,u))) member(ordered_pair(ordered_pair(v,rest_of(ordered_pair(w,v))),w),u)* -> .
% 299.99/300.67  235523[5:Res:28979.1,143186.0] || subclass(rest_relation,rotate(symmetric_difference(ordinal_numbers,u))) -> member(ordered_pair(ordered_pair(v,rest_of(ordered_pair(w,v))),w),complement(u))*.
% 299.99/300.67  235545[5:Res:28979.1,56411.0] || subclass(rest_relation,rotate(rest_of(ordered_pair(ordered_pair(u,rest_of(ordered_pair(v,u))),v))))* subclass(ordinal_numbers,complement(element_relation)) -> .
% 299.99/300.67  235547[5:Res:28979.1,898.0] || subclass(rest_relation,rotate(restrict(u,v,w)))* -> member(ordered_pair(ordered_pair(x,rest_of(ordered_pair(y,x))),y),u)*.
% 299.99/300.67  235551[5:Res:28979.1,8788.0] || subclass(rest_relation,rotate(recursion_equation_functions(u)))* -> subclass(ordered_pair(ordered_pair(v,rest_of(ordered_pair(w,v))),w),cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.67  235930[15:Res:69478.2,165527.1] || subclass(omega,symmetric_difference(u,v)) subclass(ordinal_numbers,complement(union(u,v)))* -> equal(integer_of(range_of(identity_relation)),identity_relation).
% 299.99/300.67  235943[7:Res:69478.2,133836.0] || subclass(omega,symmetric_difference(u,v)) well_ordering(ordinal_numbers,union(u,v))* -> equal(integer_of(singleton(singleton(w))),identity_relation)**.
% 299.99/300.67  235944[7:Res:69478.2,8843.1] || subclass(omega,symmetric_difference(u,v)) subclass(ordinal_numbers,complement(union(u,v)))* -> equal(integer_of(singleton(w)),identity_relation)**.
% 299.99/300.67  235969[7:Rew:125726.0,235939.2] || subclass(omega,symmetric_difference(u,v)) subclass(ordinal_numbers,complement(union(u,v)))* -> equal(least(element_relation,omega),identity_relation).
% 299.99/300.67  235970[7:Rew:125726.0,235940.2] || subclass(omega,symmetric_difference(u,v)) subclass(omega,complement(union(u,v)))* -> equal(least(element_relation,omega),identity_relation).
% 299.99/300.67  236248[8:Res:156922.1,18897.0] || member(not_subclass_element(intersection(u,complement(complement(subset_relation))),v),inverse(subset_relation))* -> subclass(intersection(u,complement(complement(subset_relation))),v).
% 299.99/300.67  236264[8:Res:204134.1,18897.0] || member(not_subclass_element(intersection(u,complement(symmetrization_of(identity_relation))),v),inverse(identity_relation))* -> subclass(intersection(u,complement(symmetrization_of(identity_relation))),v).
% 299.99/300.67  236310[8:Rew:160491.0,236255.1,160491.0,236255.0] || member(not_subclass_element(intersection(u,union(v,identity_relation)),w),complement(v))* -> subclass(intersection(u,union(v,identity_relation)),w).
% 299.99/300.67  236316[0:Rew:59.0,236221.1] || member(not_subclass_element(intersection(u,power_class(v)),w),image(element_relation,complement(v)))* -> subclass(intersection(u,power_class(v)),w).
% 299.99/300.67  236352[26:SpL:161207.0,224755.0] || subclass(omega,symmetric_difference(singleton(identity_relation),image(successor_relation,ordinal_numbers))) member(identity_relation,intersection(singleton(identity_relation),image(successor_relation,ordinal_numbers)))* -> .
% 299.99/300.67  236452[8:Res:156922.1,19016.0] || member(not_subclass_element(intersection(complement(complement(subset_relation)),u),v),inverse(subset_relation))* -> subclass(intersection(complement(complement(subset_relation)),u),v).
% 299.99/300.67  236468[8:Res:204134.1,19016.0] || member(not_subclass_element(intersection(complement(symmetrization_of(identity_relation)),u),v),inverse(identity_relation))* -> subclass(intersection(complement(symmetrization_of(identity_relation)),u),v).
% 299.99/300.67  236524[8:Rew:160491.0,236459.1,160491.0,236459.0] || member(not_subclass_element(intersection(union(u,identity_relation),v),w),complement(u))* -> subclass(intersection(union(u,identity_relation),v),w).
% 299.99/300.67  236533[0:Rew:59.0,236410.1] || member(not_subclass_element(intersection(power_class(u),v),w),image(element_relation,complement(u)))* -> subclass(intersection(power_class(u),v),w).
% 299.99/300.67  236599[8:SpL:160491.0,36857.0] || equal(u,union(v,identity_relation))* member(w,ordinal_numbers) -> member(w,symmetric_difference(ordinal_numbers,v))* member(w,u)*.
% 299.99/300.67  236603[5:SpL:59.0,36857.0] || equal(u,power_class(v))* member(w,ordinal_numbers) -> member(w,image(element_relation,complement(v)))* member(w,u)*.
% 299.99/300.67  236646[26:SpL:160927.0,225363.1] || equal(intersection(complement(u),union(v,identity_relation)),inverse(identity_relation))** equal(union(u,symmetric_difference(ordinal_numbers,v)),omega) -> .
% 299.99/300.67  236647[26:SpL:160992.0,225363.1] || equal(intersection(union(u,identity_relation),complement(v)),inverse(identity_relation))** equal(union(symmetric_difference(ordinal_numbers,u),v),omega) -> .
% 299.99/300.67  236659[26:SpL:481.0,225363.1] || equal(image(element_relation,union(u,v)),inverse(identity_relation)) equal(power_class(intersection(complement(u),complement(v))),omega)** -> .
% 299.99/300.67  236693[26:SpL:160927.0,225365.1] || equal(intersection(complement(u),union(v,identity_relation)),singleton(identity_relation))** equal(union(u,symmetric_difference(ordinal_numbers,v)),omega) -> .
% 299.99/300.67  236694[26:SpL:160992.0,225365.1] || equal(intersection(union(u,identity_relation),complement(v)),singleton(identity_relation))** equal(union(symmetric_difference(ordinal_numbers,u),v),omega) -> .
% 299.99/300.67  236706[26:SpL:481.0,225365.1] || equal(image(element_relation,union(u,v)),singleton(identity_relation)) equal(power_class(intersection(complement(u),complement(v))),omega)** -> .
% 299.99/300.67  236710[16:SpL:160927.0,225450.0] || subclass(singleton(identity_relation),union(u,symmetric_difference(ordinal_numbers,v))) member(identity_relation,intersection(complement(u),union(v,identity_relation)))* -> .
% 299.99/300.67  236711[16:SpL:160992.0,225450.0] || subclass(singleton(identity_relation),union(symmetric_difference(ordinal_numbers,u),v)) member(identity_relation,intersection(union(u,identity_relation),complement(v)))* -> .
% 299.99/300.67  236723[16:SpL:481.0,225450.0] || subclass(singleton(identity_relation),power_class(intersection(complement(u),complement(v))))* member(identity_relation,image(element_relation,union(u,v))) -> .
% 299.99/300.67  236737[18:SpL:160927.0,225452.1] || subclass(ordinal_numbers,intersection(complement(u),union(v,identity_relation))) subclass(symmetrization_of(identity_relation),union(u,symmetric_difference(ordinal_numbers,v)))* -> .
% 299.99/300.67  236738[18:SpL:160992.0,225452.1] || subclass(ordinal_numbers,intersection(union(u,identity_relation),complement(v))) subclass(symmetrization_of(identity_relation),union(symmetric_difference(ordinal_numbers,u),v))* -> .
% 299.99/300.67  236750[18:SpL:481.0,225452.1] || subclass(ordinal_numbers,image(element_relation,union(u,v))) subclass(symmetrization_of(identity_relation),power_class(intersection(complement(u),complement(v))))* -> .
% 299.99/300.67  236839[7:Res:17392.2,143226.0] || subclass(u,symmetric_difference(ordinal_numbers,v)) member(regular(intersection(u,w)),v)* -> equal(intersection(u,w),identity_relation).
% 299.99/300.67  236840[7:Res:17392.2,143186.0] || subclass(u,symmetric_difference(ordinal_numbers,v)) -> equal(intersection(u,w),identity_relation) member(regular(intersection(u,w)),complement(v))*.
% 299.99/300.67  236862[7:Res:17392.2,56411.0] || subclass(u,rest_of(regular(intersection(u,v))))* subclass(ordinal_numbers,complement(element_relation)) -> equal(intersection(u,v),identity_relation).
% 299.99/300.67  236864[7:Res:17392.2,898.0] || subclass(u,restrict(v,w,x))* -> equal(intersection(u,y),identity_relation) member(regular(intersection(u,y)),v)*.
% 299.99/300.67  236868[7:Res:17392.2,8788.0] || subclass(u,recursion_equation_functions(v))* -> equal(intersection(u,w),identity_relation) subclass(regular(intersection(u,w)),cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.67  236957[26:SpL:161207.0,225887.0] || equal(symmetric_difference(singleton(identity_relation),image(successor_relation,ordinal_numbers)),omega) member(identity_relation,intersection(singleton(identity_relation),image(successor_relation,ordinal_numbers)))* -> .
% 299.99/300.67  236978[26:SpR:481.0,225888.1] || equal(symmetric_difference(ordinal_numbers,image(element_relation,union(u,v))),omega) -> member(identity_relation,power_class(intersection(complement(u),complement(v))))*.
% 299.99/300.67  237090[7:Res:13574.1,28.1] || member(regular(intersection(u,intersection(v,complement(w)))),w)* -> equal(intersection(u,intersection(v,complement(w))),identity_relation).
% 299.99/300.67  237128[8:Res:13574.1,14679.1] || member(regular(intersection(u,intersection(v,inverse(subset_relation)))),subset_relation)* -> equal(intersection(u,intersection(v,inverse(subset_relation))),identity_relation).
% 299.99/300.67  237131[8:Res:13574.1,163154.0] ||  -> equal(intersection(u,intersection(v,symmetrization_of(identity_relation))),identity_relation) member(regular(intersection(u,intersection(v,symmetrization_of(identity_relation)))),inverse(identity_relation))*.
% 299.99/300.67  237741[7:Res:13573.1,28.1] || member(regular(intersection(u,intersection(complement(v),w))),v)* -> equal(intersection(u,intersection(complement(v),w)),identity_relation).
% 299.99/300.67  237779[8:Res:13573.1,14679.1] || member(regular(intersection(u,intersection(inverse(subset_relation),v))),subset_relation)* -> equal(intersection(u,intersection(inverse(subset_relation),v)),identity_relation).
% 299.99/300.67  237782[8:Res:13573.1,163154.0] ||  -> equal(intersection(u,intersection(symmetrization_of(identity_relation),v)),identity_relation) member(regular(intersection(u,intersection(symmetrization_of(identity_relation),v))),inverse(identity_relation))*.
% 299.99/300.67  237882[7:Rew:163.0,237670.0] ||  -> equal(intersection(u,symmetric_difference(v,w)),identity_relation) member(regular(intersection(u,symmetric_difference(v,w))),complement(intersection(v,w)))*.
% 299.99/300.67  238573[7:Res:13572.2,143226.0] || subclass(u,symmetric_difference(ordinal_numbers,v)) member(regular(intersection(w,u)),v)* -> equal(intersection(w,u),identity_relation).
% 299.99/300.67  238574[7:Res:13572.2,143186.0] || subclass(u,symmetric_difference(ordinal_numbers,v)) -> equal(intersection(w,u),identity_relation) member(regular(intersection(w,u)),complement(v))*.
% 299.99/300.67  238596[7:Res:13572.2,56411.0] || subclass(u,rest_of(regular(intersection(v,u))))* subclass(ordinal_numbers,complement(element_relation)) -> equal(intersection(v,u),identity_relation).
% 299.99/300.67  238598[7:Res:13572.2,898.0] || subclass(u,restrict(v,w,x))* -> equal(intersection(y,u),identity_relation) member(regular(intersection(y,u)),v)*.
% 299.99/300.67  238602[7:Res:13572.2,8788.0] || subclass(u,recursion_equation_functions(v))* -> equal(intersection(w,u),identity_relation) subclass(regular(intersection(w,u)),cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.67  239253[7:Res:17397.1,28.1] || member(regular(intersection(intersection(complement(u),v),w)),u)* -> equal(intersection(intersection(complement(u),v),w),identity_relation).
% 299.99/300.67  239291[8:Res:17397.1,14679.1] || member(regular(intersection(intersection(inverse(subset_relation),u),v)),subset_relation)* -> equal(intersection(intersection(inverse(subset_relation),u),v),identity_relation).
% 299.99/300.67  239294[8:Res:17397.1,163154.0] ||  -> equal(intersection(intersection(symmetrization_of(identity_relation),u),v),identity_relation) member(regular(intersection(intersection(symmetrization_of(identity_relation),u),v)),inverse(identity_relation))*.
% 299.99/300.67  239405[7:Rew:163.0,239175.0] ||  -> equal(intersection(symmetric_difference(u,v),w),identity_relation) member(regular(intersection(symmetric_difference(u,v),w)),complement(intersection(u,v)))*.
% 299.99/300.67  240088[7:Res:17396.1,28.1] || member(regular(intersection(intersection(u,complement(v)),w)),v)* -> equal(intersection(intersection(u,complement(v)),w),identity_relation).
% 299.99/300.67  240126[8:Res:17396.1,14679.1] || member(regular(intersection(intersection(u,inverse(subset_relation)),v)),subset_relation)* -> equal(intersection(intersection(u,inverse(subset_relation)),v),identity_relation).
% 299.99/300.67  240129[8:Res:17396.1,163154.0] ||  -> equal(intersection(intersection(u,symmetrization_of(identity_relation)),v),identity_relation) member(regular(intersection(intersection(u,symmetrization_of(identity_relation)),v)),inverse(identity_relation))*.
% 299.99/300.67  19766[0:Res:19421.0,11.0] || subclass(union(u,v),symmetric_difference(complement(u),complement(v)))* -> equal(symmetric_difference(complement(u),complement(v)),union(u,v)).
% 299.99/300.67  69177[8:Res:303.1,66086.1] || member(not_subclass_element(intersection(u,complement(compose(element_relation,ordinal_numbers))),v),element_relation)* -> subclass(intersection(u,complement(compose(element_relation,ordinal_numbers))),v).
% 299.99/300.67  69163[8:Res:313.1,66086.1] || member(not_subclass_element(intersection(complement(compose(element_relation,ordinal_numbers)),u),v),element_relation)* -> subclass(intersection(complement(compose(element_relation,ordinal_numbers)),u),v).
% 299.99/300.67  29161[5:Res:8978.2,490.0] || member(u,ordinal_numbers) subclass(ordinal_numbers,intersection(complement(v),complement(w)))* member(sum_class(u),union(v,w))* -> .
% 299.99/300.67  57141[0:Res:303.1,19559.0] ||  -> subclass(intersection(u,symmetric_difference(v,singleton(v))),w) member(not_subclass_element(intersection(u,symmetric_difference(v,singleton(v))),w),successor(v))*.
% 299.99/300.67  19542[0:SpR:3596.0,27.2] || member(u,successor(v)) member(u,complement(intersection(v,singleton(v))))* -> member(u,symmetric_difference(v,singleton(v))).
% 299.99/300.67  51203[5:SpR:50855.1,17.0] || member(singleton(u),subset_relation) -> equal(unordered_pair(u,unordered_pair(first(singleton(u)),singleton(v))),ordered_pair(first(singleton(u)),v))**.
% 299.99/300.67  57102[5:SpL:50855.1,19559.0] || member(singleton(u),subset_relation) member(v,symmetric_difference(first(singleton(u)),u))* -> member(v,successor(first(singleton(u)))).
% 299.99/300.67  19806[0:Res:19733.0,11.0] || subclass(successor(u),symmetric_difference(complement(u),complement(singleton(u))))* -> equal(symmetric_difference(complement(u),complement(singleton(u))),successor(u)).
% 299.99/300.67  39620[2:Res:10714.1,9665.1] inductive(singleton(u)) || member(u,v)* well_ordering(w,v)* -> member(least(w,singleton(u)),singleton(u))*.
% 299.99/300.67  57117[0:Res:313.1,19559.0] ||  -> subclass(intersection(symmetric_difference(u,singleton(u)),v),w) member(not_subclass_element(intersection(symmetric_difference(u,singleton(u)),v),w),successor(u))*.
% 299.99/300.67  36167[0:SpR:482.0,47.0] ||  -> equal(complement(intersection(union(u,v),complement(singleton(intersection(complement(u),complement(v)))))),successor(intersection(complement(u),complement(v))))**.
% 299.99/300.67  39257[5:Res:27.2,8841.1] || member(ordered_pair(u,v),w)* member(ordered_pair(u,v),x)* subclass(ordinal_numbers,complement(intersection(x,w)))* -> .
% 299.99/300.67  9644[0:Res:962.0,129.0] || subclass(ordered_pair(u,v),w)* well_ordering(x,w)* -> member(least(x,ordered_pair(u,v)),ordered_pair(u,v))*.
% 299.99/300.67  28942[5:Res:8827.2,897.0] || member(u,ordinal_numbers) subclass(rest_relation,restrict(v,w,x))* -> member(ordered_pair(u,rest_of(u)),cross_product(w,x))*.
% 299.99/300.67  45464[0:Res:10.1,9420.2] || equal(u,cross_product(v,w))* member(x,w)* member(y,v)* -> member(ordered_pair(y,x),u)*.
% 299.99/300.67  40050[5:Res:27.2,8842.1] || member(unordered_pair(u,v),w)* member(unordered_pair(u,v),x)* subclass(ordinal_numbers,complement(intersection(x,w)))* -> .
% 299.99/300.67  19125[0:Res:2503.2,12.0] || subclass(u,unordered_pair(v,w))* -> subclass(u,x) equal(not_subclass_element(u,x),w)* equal(not_subclass_element(u,x),v)*.
% 299.99/300.67  56820[5:SpL:3594.0,8846.0] || subclass(ordinal_numbers,symmetric_difference(complement(intersection(u,v)),union(u,v)))* -> member(unordered_pair(w,x),complement(symmetric_difference(u,v)))*.
% 299.99/300.67  29163[0:Res:2503.2,490.0] || subclass(u,intersection(complement(v),complement(w))) member(not_subclass_element(u,x),union(v,w))* -> subclass(u,x).
% 299.99/300.67  29147[0:Res:6.1,490.0] || member(not_subclass_element(intersection(complement(u),complement(v)),w),union(u,v))* -> subclass(intersection(complement(u),complement(v)),w).
% 299.99/300.67  18800[0:Res:3618.1,290.0] || member(not_subclass_element(complement(complement(intersection(u,v))),w),symmetric_difference(u,v))* -> subclass(complement(complement(intersection(u,v))),w).
% 299.99/300.67  57184[0:Res:313.1,19676.0] ||  -> subclass(intersection(symmetric_difference(u,inverse(u)),v),w) member(not_subclass_element(intersection(symmetric_difference(u,inverse(u)),v),w),symmetrization_of(u))*.
% 299.99/300.67  57208[0:Res:303.1,19676.0] ||  -> subclass(intersection(u,symmetric_difference(v,inverse(v))),w) member(not_subclass_element(intersection(u,symmetric_difference(v,inverse(v))),w),symmetrization_of(v))*.
% 299.99/300.67  50002[5:SpR:18840.1,20.2] || member(u,subset_relation) member(second(u),v) member(first(u),w) -> member(u,cross_product(w,v))*.
% 299.99/300.67  39637[5:Res:8689.0,9665.1] inductive(flip(u)) || well_ordering(v,cross_product(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers))* -> member(least(v,flip(u)),flip(u))*.
% 299.99/300.67  39638[5:Res:8690.0,9665.1] inductive(rotate(u)) || well_ordering(v,cross_product(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers))* -> member(least(v,rotate(u)),rotate(u))*.
% 299.99/300.67  36168[0:SpR:482.0,117.0] ||  -> equal(complement(intersection(union(u,v),complement(inverse(intersection(complement(u),complement(v)))))),symmetrization_of(intersection(complement(u),complement(v))))**.
% 299.99/300.67  19823[0:Res:19734.0,11.0] || subclass(symmetrization_of(u),symmetric_difference(complement(u),complement(inverse(u))))* -> equal(symmetric_difference(complement(u),complement(inverse(u))),symmetrization_of(u)).
% 299.99/300.67  19660[0:SpR:3597.0,27.2] || member(u,symmetrization_of(v)) member(u,complement(intersection(v,inverse(v))))* -> member(u,symmetric_difference(v,inverse(v))).
% 299.99/300.67  83087[5:SpL:50855.1,66648.0] || member(singleton(u),subset_relation) subclass(ordinal_numbers,symmetric_difference(first(singleton(u)),u))* -> member(omega,successor(first(singleton(u)))).
% 299.99/300.67  83093[5:SpL:50855.1,68244.0] || member(singleton(u),subset_relation) equal(symmetric_difference(first(singleton(u)),u),ordinal_numbers)** -> member(omega,successor(first(singleton(u))))*.
% 299.99/300.67  83802[5:SpR:483.0,8881.1] || subclass(ordinal_numbers,symmetric_difference(u,intersection(complement(v),complement(w)))) -> member(omega,complement(intersection(complement(u),union(v,w))))*.
% 299.99/300.67  83807[5:SpR:482.0,8881.1] || subclass(ordinal_numbers,symmetric_difference(intersection(complement(u),complement(v)),w)) -> member(omega,complement(intersection(union(u,v),complement(w))))*.
% 299.99/300.67  83822[5:SpR:483.0,8892.1] || equal(symmetric_difference(u,intersection(complement(v),complement(w))),ordinal_numbers) -> member(omega,complement(intersection(complement(u),union(v,w))))*.
% 299.99/300.67  83827[5:SpR:482.0,8892.1] || equal(symmetric_difference(intersection(complement(u),complement(v)),w),ordinal_numbers) -> member(omega,complement(intersection(union(u,v),complement(w))))*.
% 299.99/300.67  96894[5:Res:79560.1,9665.1] inductive(singleton(u)) || well_ordering(v,complement(w))* -> member(u,w)* member(least(v,singleton(u)),singleton(u))*.
% 299.99/300.67  116635[8:Rew:116078.0,3655.2] inductive(domain_of(restrict(u,v,omega))) || section(u,omega,v) -> equal(cantor(restrict(u,v,omega)),omega)**.
% 299.99/300.67  118991[8:Res:116148.1,1303.1] inductive(cantor(restrict(u,v,omega))) || section(u,omega,v) -> equal(cantor(restrict(u,v,omega)),omega)**.
% 299.99/300.67  126636[5:Res:27.2,125896.1] || member(least(element_relation,omega),u) member(least(element_relation,omega),v) subclass(omega,complement(intersection(v,u)))* -> .
% 299.99/300.67  127099[5:Res:27.2,125973.1] || member(least(element_relation,omega),u) member(least(element_relation,omega),v) subclass(ordinal_numbers,complement(intersection(v,u)))* -> .
% 299.99/300.67  130516[5:SpL:3594.0,125908.0] || subclass(omega,symmetric_difference(complement(intersection(u,v)),union(u,v)))* -> member(least(element_relation,omega),complement(symmetric_difference(u,v))).
% 299.99/300.67  130627[8:Res:41371.0,66086.1] || member(not_subclass_element(complement(complement(complement(compose(element_relation,ordinal_numbers)))),u),element_relation)* -> subclass(complement(complement(complement(compose(element_relation,ordinal_numbers)))),u).
% 299.99/300.67  130640[5:Res:41371.0,19559.0] ||  -> subclass(complement(complement(symmetric_difference(u,singleton(u)))),v) member(not_subclass_element(complement(complement(symmetric_difference(u,singleton(u)))),v),successor(u))*.
% 299.99/300.67  130641[5:Res:41371.0,19676.0] ||  -> subclass(complement(complement(symmetric_difference(u,inverse(u)))),v) member(not_subclass_element(complement(complement(symmetric_difference(u,inverse(u)))),v),symmetrization_of(u))*.
% 299.99/300.67  131444[0:Res:313.1,18794.1] || member(not_subclass_element(intersection(intersection(u,v),w),x),symmetric_difference(u,v))* -> subclass(intersection(intersection(u,v),w),x).
% 299.99/300.67  131459[0:Res:303.1,18794.1] || member(not_subclass_element(intersection(u,intersection(v,w)),x),symmetric_difference(v,w))* -> subclass(intersection(u,intersection(v,w)),x).
% 299.99/300.67  131478[5:Res:8827.2,18794.1] || member(u,ordinal_numbers) subclass(rest_relation,intersection(v,w)) member(ordered_pair(u,rest_of(u)),symmetric_difference(v,w))* -> .
% 299.99/300.67  131540[0:Res:2504.1,129.0] || subclass(ordered_pair(u,v),w)* subclass(w,x)* well_ordering(y,x)* -> member(least(y,w),w)*.
% 299.99/300.67  131546[0:Res:2504.1,490.0] || subclass(ordered_pair(u,v),intersection(complement(w),complement(x)))* member(unordered_pair(u,singleton(v)),union(w,x)) -> .
% 299.99/300.67  132353[5:SpR:30.0,132293.0] ||  -> subclass(complement(successor(intersection(complement(u),complement(v)))),intersection(union(u,v),complement(singleton(intersection(complement(u),complement(v))))))*.
% 299.99/300.67  132396[5:SpR:30.0,132294.0] ||  -> subclass(complement(symmetrization_of(intersection(complement(u),complement(v)))),intersection(union(u,v),complement(inverse(intersection(complement(u),complement(v))))))*.
% 299.99/300.67  132784[5:SpL:3594.0,125985.0] || subclass(ordinal_numbers,symmetric_difference(complement(intersection(u,v)),union(u,v)))* -> member(least(element_relation,omega),complement(symmetric_difference(u,v))).
% 299.99/300.67  132878[5:SpL:3594.0,130556.0] || equal(symmetric_difference(complement(intersection(u,v)),union(u,v)),omega)** -> member(least(element_relation,omega),complement(symmetric_difference(u,v))).
% 299.99/300.67  134408[5:SpL:3594.0,132824.0] || equal(symmetric_difference(complement(intersection(u,v)),union(u,v)),ordinal_numbers)** -> member(least(element_relation,omega),complement(symmetric_difference(u,v))).
% 299.99/300.67  134715[8:SpR:116154.0,116403.2] || member(u,ordinal_numbers) subclass(rest_relation,rest_of(restrict(v,w,singleton(x))))* -> member(u,segment(v,w,x))*.
% 299.99/300.67  136686[5:Res:49995.1,18791.0] || member(symmetric_difference(complement(u),complement(v)),subset_relation) -> member(singleton(first(symmetric_difference(complement(u),complement(v)))),union(u,v))*.
% 299.99/300.67  140270[5:SpL:50855.1,19124.0] || member(singleton(u),subset_relation)* subclass(v,u)* -> subclass(v,w) equal(not_subclass_element(v,w),first(singleton(u)))*.
% 299.99/300.67  140463[0:Rew:32.0,140328.1] || member(not_subclass_element(cross_product(u,v),restrict(w,u,v)),w)* -> subclass(cross_product(u,v),restrict(w,u,v)).
% 299.99/300.67  143520[5:Res:143160.0,9665.1] inductive(symmetric_difference(ordinal_numbers,u)) || well_ordering(v,complement(u)) -> member(least(v,symmetric_difference(ordinal_numbers,u)),symmetric_difference(ordinal_numbers,u))*.
% 299.99/300.67  146744[5:Res:3618.1,18571.2] || member(sum_class(u),symmetric_difference(v,w))* member(u,ordinal_numbers) subclass(ordinal_numbers,complement(complement(intersection(v,w))))* -> .
% 299.99/300.67  148182[5:Rew:50855.1,148153.2] || member(singleton(u),subset_relation) member(singleton(singleton(u)),compose_class(v))* -> equal(compose(v,u),first(singleton(u))).
% 299.99/300.67  148920[8:Res:148858.1,8559.2] || subclass(intersection(u,v),inverse(subset_relation))* member(w,v)* member(w,u)* -> member(w,complement(subset_relation))*.
% 299.99/300.67  151521[5:Rew:50855.1,151450.1] || member(singleton(u),subset_relation) -> subclass(intersection(v,u),w) equal(not_subclass_element(intersection(v,u),w),first(singleton(u)))**.
% 299.99/300.67  151885[5:Rew:50855.1,151803.1] || member(singleton(u),subset_relation) -> subclass(intersection(u,v),w) equal(not_subclass_element(intersection(u,v),w),first(singleton(u)))**.
% 299.99/300.67  152187[0:Res:3618.1,19111.1] || member(not_subclass_element(u,v),symmetric_difference(w,x))* subclass(u,complement(complement(intersection(w,x)))) -> subclass(u,v).
% 299.99/300.67  153412[0:Obv:153394.1] || member(not_subclass_element(restrict(u,v,w),intersection(x,u)),x)* -> subclass(restrict(u,v,w),intersection(x,u)).
% 299.99/300.67  155796[8:Rew:155653.0,155671.2] || member(ordinal_numbers,cantor(subset_relation)) equal(subset_relation,u) subclass(rest_of(subset_relation),v) -> member(ordered_pair(ordinal_numbers,u),v)*.
% 299.99/300.67  156412[5:SpR:155665.0,3618.1] || member(u,symmetric_difference(complement(subset_relation),union(subset_relation,cross_product(ordinal_numbers,ordinal_numbers))))* -> member(u,complement(symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers)))).
% 299.99/300.67  156453[5:SpL:155665.0,18794.1] || member(u,symmetric_difference(complement(subset_relation),union(subset_relation,cross_product(ordinal_numbers,ordinal_numbers))))* member(u,symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers))) -> .
% 299.99/300.67  156521[5:SpR:155666.0,3618.1] || member(u,symmetric_difference(complement(subset_relation),union(cross_product(ordinal_numbers,ordinal_numbers),subset_relation)))* -> member(u,complement(symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation))).
% 299.99/300.67  156562[5:SpL:155666.0,18794.1] || member(u,symmetric_difference(complement(subset_relation),union(cross_product(ordinal_numbers,ordinal_numbers),subset_relation)))* member(u,symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation)) -> .
% 299.99/300.67  156966[8:Res:156922.1,40594.1] || member(singleton(complement(subset_relation)),inverse(subset_relation)) member(complement(subset_relation),ordinal_numbers) -> member(singleton(singleton(singleton(complement(subset_relation)))),element_relation)*.
% 299.99/300.67  140340[8:SpL:116209.1,47534.0] operation(u) || member(not_subclass_element(v,intersection(v,cantor(u))),cantor(u))* -> subclass(v,intersection(cantor(u),v)).
% 299.99/300.67  151460[8:SpR:116209.1,18910.1] operation(u) ||  -> subclass(intersection(cantor(u),singleton(v)),w) equal(not_subclass_element(intersection(singleton(v),cantor(u)),w),v)**.
% 299.99/300.67  151826[8:SpR:116209.1,19029.1] operation(u) ||  -> subclass(intersection(singleton(v),cantor(u)),w) equal(not_subclass_element(intersection(cantor(u),singleton(v)),w),v)**.
% 299.99/300.67  116323[8:Rew:116078.0,38123.1] operation(restrict(element_relation,ordinal_numbers,u)) ||  -> equal(restrict(v,cantor(sum_class(u)),cantor(sum_class(u))),intersection(sum_class(u),v))**.
% 299.99/300.67  96913[5:Res:96837.0,9665.1] inductive(singleton(u)) || well_ordering(v,complement(recursion_equation_functions(w)))* -> function(u) member(least(v,singleton(u)),singleton(u))*.
% 299.99/300.67  161513[5:Rew:483.0,146632.1] || subclass(ordinal_numbers,intersection(complement(u),union(v,w))) member(omega,complement(intersection(complement(u),union(v,w))))* -> .
% 299.99/300.67  161514[5:Rew:482.0,146644.1] || subclass(ordinal_numbers,intersection(union(u,v),complement(w))) member(omega,complement(intersection(union(u,v),complement(w))))* -> .
% 299.99/300.67  176786[8:Res:144409.1,8554.1] || equal(symmetric_difference(ordinal_numbers,intersection(u,v)),ordinal_numbers)** member(omega,union(u,v)) -> member(omega,symmetric_difference(u,v)).
% 299.99/300.67  176978[8:Rew:117142.0,176968.2] operation(restrict(element_relation,ordinal_numbers,u)) || subclass(sum_class(u),complement(complement(symmetrization_of(v))))* -> connected(v,cantor(sum_class(u))).
% 299.99/300.67  177011[8:Rew:117142.0,176998.1] operation(restrict(element_relation,ordinal_numbers,u)) || connected(v,cantor(sum_class(u))) -> subclass(sum_class(u),complement(complement(symmetrization_of(v))))*.
% 299.99/300.67  166430[8:Res:13125.2,69161.0] || subclass(omega,element_relation) -> equal(integer_of(not_subclass_element(complement(compose(element_relation,ordinal_numbers)),u)),identity_relation)** subclass(complement(compose(element_relation,ordinal_numbers)),u).
% 299.99/300.67  166381[7:Res:13125.2,8785.0] || subclass(omega,rest_of(u)) -> equal(integer_of(singleton(singleton(singleton(v)))),identity_relation) equal(restrict(u,singleton(v),ordinal_numbers),v)**.
% 299.99/300.67  165260[7:Res:143160.0,13070.0] || well_ordering(u,complement(v)) -> equal(symmetric_difference(ordinal_numbers,v),identity_relation) member(least(u,symmetric_difference(ordinal_numbers,v)),symmetric_difference(ordinal_numbers,v))*.
% 299.99/300.67  165159[8:Res:157036.0,13113.0] || well_ordering(u,complement(subset_relation)) -> equal(segment(u,complement(complement(inverse(subset_relation))),least(u,complement(complement(inverse(subset_relation))))),identity_relation)**.
% 299.99/300.67  165158[8:Res:153473.0,13113.0] || well_ordering(u,complement(element_relation)) -> equal(segment(u,complement(compose(element_relation,ordinal_numbers)),least(u,complement(compose(element_relation,ordinal_numbers)))),identity_relation)**.
% 299.99/300.67  165143[8:Res:157013.0,13113.0] || well_ordering(u,complement(subset_relation)) -> equal(segment(u,intersection(inverse(subset_relation),v),least(u,intersection(inverse(subset_relation),v))),identity_relation)**.
% 299.99/300.67  165142[8:Res:156893.0,13113.0] || well_ordering(u,complement(subset_relation)) -> equal(segment(u,intersection(v,inverse(subset_relation)),least(u,intersection(v,inverse(subset_relation)))),identity_relation)**.
% 299.99/300.67  19339[7:Res:19314.0,13113.0] || well_ordering(u,successor(v)) -> equal(segment(u,symmetric_difference(v,singleton(v)),least(u,symmetric_difference(v,singleton(v)))),identity_relation)**.
% 299.99/300.67  62527[7:SpR:50855.1,13101.0] || member(singleton(u),subset_relation) -> equal(second(not_subclass_element(restrict(v,u,w),identity_relation)),range__dfg(v,first(singleton(u)),w))**.
% 299.99/300.67  62558[7:SpR:50855.1,13100.0] || member(singleton(u),subset_relation) -> equal(first(not_subclass_element(restrict(v,w,u),identity_relation)),domain__dfg(v,w,first(singleton(u))))**.
% 299.99/300.67  64334[7:Rew:3603.0,64255.0] ||  -> equal(symmetric_difference(u,cross_product(v,w)),identity_relation) member(regular(symmetric_difference(u,cross_product(v,w))),complement(restrict(u,v,w)))*.
% 299.99/300.67  64333[7:Rew:3606.0,64256.0] ||  -> equal(symmetric_difference(cross_product(u,v),w),identity_relation) member(regular(symmetric_difference(cross_product(u,v),w)),complement(restrict(w,u,v)))*.
% 299.99/300.67  19350[7:Res:19315.0,13113.0] || well_ordering(u,symmetrization_of(v)) -> equal(segment(u,symmetric_difference(v,inverse(v)),least(u,symmetric_difference(v,inverse(v)))),identity_relation)**.
% 299.99/300.67  79794[7:Res:79560.1,13070.0] || well_ordering(u,complement(v))* -> member(w,v)* equal(singleton(w),identity_relation) member(least(u,singleton(w)),singleton(w))*.
% 299.99/300.67  165418[7:Res:96837.0,13070.0] || well_ordering(u,complement(recursion_equation_functions(v)))* -> function(w) equal(singleton(w),identity_relation) member(least(u,singleton(w)),singleton(w))*.
% 299.99/300.67  83047[7:SpL:50855.1,19558.0] || member(singleton(u),subset_relation) subclass(ordinal_numbers,symmetric_difference(first(singleton(u)),u))* -> member(identity_relation,successor(first(singleton(u)))).
% 299.99/300.67  83091[7:SpL:50855.1,19549.0] || member(singleton(u),subset_relation) equal(symmetric_difference(first(singleton(u)),u),ordinal_numbers)** -> member(identity_relation,successor(first(singleton(u))))*.
% 299.99/300.67  161562[8:Rew:140613.0,67562.2] || member(u,ordinal_numbers) -> member(u,intersection(complement(v),union(w,identity_relation)))* member(u,union(v,symmetric_difference(ordinal_numbers,w))).
% 299.99/300.67  19427[7:Res:19069.0,13113.0] || well_ordering(u,complement(intersection(v,w))) -> equal(segment(u,symmetric_difference(v,w),least(u,symmetric_difference(v,w))),identity_relation)**.
% 299.99/300.67  161464[8:Rew:116078.0,68107.1] || member(singleton(u),subset_relation) member(first(singleton(u)),cantor(v))* equal(restrict(v,u,ordinal_numbers),identity_relation) -> .
% 299.99/300.67  18832[7:Res:13210.1,897.0] ||  -> equal(intersection(u,restrict(v,w,x)),identity_relation) member(regular(intersection(u,restrict(v,w,x))),cross_product(w,x))*.
% 299.99/300.67  18834[7:Res:13248.1,897.0] ||  -> equal(intersection(restrict(u,v,w),x),identity_relation) member(regular(intersection(restrict(u,v,w),x)),cross_product(v,w))*.
% 299.99/300.67  83297[7:Res:61019.0,897.0] ||  -> equal(complement(complement(restrict(u,v,w))),identity_relation) member(regular(complement(complement(restrict(u,v,w)))),cross_product(v,w))*.
% 299.99/300.67  166385[7:Res:13125.2,40594.1] || subclass(omega,u) member(u,ordinal_numbers) -> equal(integer_of(singleton(u)),identity_relation) member(singleton(singleton(singleton(u))),element_relation)*.
% 299.99/300.67  161556[8:Rew:140613.0,67556.0] ||  -> equal(intersection(union(u,symmetric_difference(ordinal_numbers,v)),union(complement(u),union(v,identity_relation))),symmetric_difference(complement(u),union(v,identity_relation)))**.
% 299.99/300.67  161555[8:Rew:140613.0,67552.2] || member(u,ordinal_numbers) -> member(u,intersection(union(v,identity_relation),complement(w)))* member(u,union(symmetric_difference(ordinal_numbers,v),w)).
% 299.99/300.67  65579[8:Res:8827.2,14681.0] || member(u,ordinal_numbers) subclass(rest_relation,regular(v)) member(ordered_pair(u,rest_of(u)),v)* -> equal(v,identity_relation).
% 299.99/300.67  13658[7:Rew:13036.0,13244.2] || well_ordering(u,omega) -> equal(integer_of(v),identity_relation) equal(singleton(v),identity_relation) member(least(u,singleton(v)),singleton(v))*.
% 299.99/300.67  161540[8:Rew:140613.0,67544.0] ||  -> equal(intersection(union(symmetric_difference(ordinal_numbers,u),v),union(union(u,identity_relation),complement(v))),symmetric_difference(union(u,identity_relation),complement(v)))**.
% 299.99/300.67  17328[7:Res:13227.2,21.0] || subclass(u,cross_product(v,w))* -> equal(u,identity_relation) equal(ordered_pair(first(regular(u)),second(regular(u))),regular(u))**.
% 299.99/300.67  13266[7:Rew:13036.0,10726.2] || member(u,v)* well_ordering(w,v)* -> equal(singleton(u),identity_relation) member(least(w,singleton(u)),singleton(u))*.
% 299.99/300.67  165189[14:Res:165172.1,129.0] || subclass(complement(u),v)* well_ordering(w,v)* -> member(identity_relation,u) member(least(w,complement(u)),complement(u))*.
% 299.99/300.67  13434[7:Rew:13036.0,12822.1] || subclass(cross_product(ordinal_numbers,ordinal_numbers),regular(recursion_equation_functions(u)))* -> equal(recursion_equation_functions(u),identity_relation) equal(cross_product(ordinal_numbers,ordinal_numbers),regular(recursion_equation_functions(u))).
% 299.99/300.67  165358[14:Res:165168.1,8554.1] || equal(complement(intersection(u,v)),singleton(identity_relation)) member(identity_relation,union(u,v)) -> member(identity_relation,symmetric_difference(u,v))*.
% 299.99/300.67  15659[8:Res:15426.1,21.0] || subclass(domain_relation,cross_product(u,v))* -> equal(ordered_pair(first(ordered_pair(identity_relation,identity_relation)),second(ordered_pair(identity_relation,identity_relation))),ordered_pair(identity_relation,identity_relation))**.
% 299.99/300.67  83172[8:SpL:3594.0,15572.0] || subclass(domain_relation,symmetric_difference(complement(intersection(u,v)),union(u,v)))* -> member(ordered_pair(identity_relation,identity_relation),complement(symmetric_difference(u,v))).
% 299.99/300.67  83650[8:SpL:3594.0,83195.0] || equal(symmetric_difference(complement(intersection(u,v)),union(u,v)),domain_relation)** -> member(ordered_pair(identity_relation,identity_relation),complement(symmetric_difference(u,v))).
% 299.99/300.67  81305[8:Res:27.2,15565.1] || member(ordered_pair(identity_relation,identity_relation),u) member(ordered_pair(identity_relation,identity_relation),v) subclass(domain_relation,complement(intersection(v,u)))* -> .
% 299.99/300.67  190533[18:Res:190442.1,8554.1] || equal(complement(intersection(u,v)),symmetrization_of(identity_relation)) member(identity_relation,union(u,v)) -> member(identity_relation,symmetric_difference(u,v))*.
% 299.99/300.67  190642[18:Res:190593.1,8554.1] || equal(complement(intersection(u,v)),inverse(identity_relation)) member(identity_relation,union(u,v)) -> member(identity_relation,symmetric_difference(u,v))*.
% 299.99/300.67  192615[7:Rew:192514.1,192589.3,192514.1,192589.1] || member(not_subclass_element(u,identity_relation),singleton(v))* member(not_subclass_element(u,identity_relation),recursion_equation_functions(w))* -> function(v) subclass(u,identity_relation).
% 299.99/300.67  192963[7:Rew:192834.1,192920.3,192834.1,192920.1] || member(not_subclass_element(u,identity_relation),singleton(v))* member(not_subclass_element(u,identity_relation),w)* -> member(v,w)* subclass(u,identity_relation).
% 299.99/300.67  192975[7:SpR:13621.1,13101.0] ||  -> equal(cross_product(singleton(u),v),identity_relation) equal(range__dfg(regular(cross_product(singleton(u),v)),u,v),second(not_subclass_element(identity_relation,identity_relation)))**.
% 299.99/300.67  166406[7:Res:13125.2,3995.0] || subclass(omega,composition_function) -> equal(integer_of(ordered_pair(u,singleton(singleton(singleton(v))))),identity_relation)** equal(compose(u,singleton(v)),v).
% 299.99/300.67  46649[5:Res:9618.2,23.0] || member(ordered_pair(u,v),cross_product(ordinal_numbers,ordinal_numbers))* subclass(composition_function,element_relation) -> member(u,ordered_pair(v,compose(u,v)))*.
% 299.99/300.67  39612[2:Res:139.1,9665.1] inductive(sum_class(u)) || member(u,ordinal_numbers) well_ordering(v,u) -> member(least(v,sum_class(u)),sum_class(u))*.
% 299.99/300.67  49300[5:Res:295.0,9640.1] || member(u,ordinal_numbers) well_ordering(v,unordered_pair(u,w)) -> member(least(v,unordered_pair(u,w)),unordered_pair(u,w))*.
% 299.99/300.67  49230[5:Res:295.0,9639.1] || member(u,ordinal_numbers) well_ordering(v,unordered_pair(w,u)) -> member(least(v,unordered_pair(w,u)),unordered_pair(w,u))*.
% 299.99/300.67  49064[5:Res:295.0,9633.1] || member(u,ordinal_numbers)* well_ordering(v,complement(w)) -> member(u,w)* member(least(v,complement(w)),complement(w))*.
% 299.99/300.67  80197[10:Res:76912.1,129.0] || member(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers) subclass(element_relation,u) well_ordering(v,u)* -> member(least(v,element_relation),element_relation)*.
% 299.99/300.67  131175[8:Res:39607.2,66086.1] inductive(complement(compose(element_relation,ordinal_numbers))) || well_ordering(u,ordinal_numbers) member(least(u,complement(compose(element_relation,ordinal_numbers))),element_relation)* -> .
% 299.99/300.67  65419[7:Res:13237.2,19559.0] || well_ordering(u,ordinal_numbers) -> equal(symmetric_difference(v,singleton(v)),identity_relation) member(least(u,symmetric_difference(v,singleton(v))),successor(v))*.
% 299.99/300.67  65420[7:Res:13237.2,19676.0] || well_ordering(u,ordinal_numbers) -> equal(symmetric_difference(v,inverse(v)),identity_relation) member(least(u,symmetric_difference(v,inverse(v))),symmetrization_of(v))*.
% 299.99/300.67  167326[7:Res:13237.2,18794.1] || well_ordering(u,ordinal_numbers) member(least(u,intersection(v,w)),symmetric_difference(v,w))* -> equal(intersection(v,w),identity_relation).
% 299.99/300.67  69180[8:Res:13237.2,66086.1] || well_ordering(u,ordinal_numbers) member(least(u,complement(compose(element_relation,ordinal_numbers))),element_relation)* -> equal(complement(compose(element_relation,ordinal_numbers)),identity_relation).
% 299.99/300.67  131189[5:Res:39607.2,19559.0] inductive(symmetric_difference(u,singleton(u))) || well_ordering(v,ordinal_numbers) -> member(least(v,symmetric_difference(u,singleton(u))),successor(u))*.
% 299.99/300.67  131190[5:Res:39607.2,19676.0] inductive(symmetric_difference(u,inverse(u))) || well_ordering(v,ordinal_numbers) -> member(least(v,symmetric_difference(u,inverse(u))),symmetrization_of(u))*.
% 299.99/300.67  131471[5:Res:39607.2,18794.1] inductive(intersection(u,v)) || well_ordering(w,ordinal_numbers) member(least(w,intersection(u,v)),symmetric_difference(u,v))* -> .
% 299.99/300.67  167260[8:Res:39609.2,14681.0] inductive(regular(u)) || well_ordering(v,regular(u)) member(least(v,regular(u)),u)* -> equal(u,identity_relation).
% 299.99/300.67  194376[21:MRR:194356.2,14676.0] || member(singleton(u),cantor(v)) member(ordered_pair(v,singleton(singleton(singleton(u)))),cross_product(ordinal_numbers,cross_product(ordinal_numbers,ordinal_numbers)))* -> .
% 299.99/300.67  194538[18:Res:194513.0,13113.0] || well_ordering(u,symmetrization_of(identity_relation)) -> equal(segment(u,singleton(regular(symmetrization_of(identity_relation))),least(u,singleton(regular(symmetrization_of(identity_relation))))),identity_relation)**.
% 299.99/300.67  194994[7:SpR:154737.1,13344.2] || subclass(inverse(u),u)* asymmetric(u,v) subclass(compose(identity_relation,identity_relation),identity_relation)* -> transitive(inverse(u),v)*.
% 299.99/300.67  195094[14:Res:8551.2,165357.1] || member(identity_relation,cross_product(u,v)) member(identity_relation,w) equal(complement(restrict(w,u,v)),singleton(identity_relation))** -> .
% 299.99/300.67  195843[8:SpR:154737.1,15666.1] || subclass(inverse(u),u)* asymmetric(u,singleton(v)) -> equal(domain__dfg(inverse(u),singleton(v),v),single_valued3(identity_relation))**.
% 299.99/300.67  196148[18:Res:8551.2,190532.1] || member(identity_relation,cross_product(u,v)) member(identity_relation,w) equal(complement(restrict(w,u,v)),symmetrization_of(identity_relation))** -> .
% 299.99/300.67  196238[18:Res:8551.2,190641.1] || member(identity_relation,cross_product(u,v)) member(identity_relation,w) equal(complement(restrict(w,u,v)),inverse(identity_relation))** -> .
% 299.99/300.67  196441[21:Rew:196372.1,174457.2] || member(u,ordinal_numbers) subclass(domain_relation,symmetric_difference(complement(v),complement(w))) -> member(ordered_pair(u,identity_relation),union(v,w))*.
% 299.99/300.67  197314[7:SpR:154.1,13505.1] || member(u,recursion_equation_functions(v))* well_ordering(w,cross_product(ordinal_numbers,ordinal_numbers)) -> equal(segment(w,u,least(w,u)),identity_relation)**.
% 299.99/300.67  198013[7:Res:138.1,13513.0] || member(cross_product(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers),ordinal_numbers)* -> equal(rotate(u),identity_relation) member(least(element_relation,rotate(u)),rotate(u))*.
% 299.99/300.67  198107[7:Res:138.1,13512.0] || member(cross_product(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers),ordinal_numbers)* -> equal(flip(u),identity_relation) member(least(element_relation,flip(u)),flip(u))*.
% 299.99/300.67  199044[21:Res:196792.0,13362.0] || subclass(domain_relation,u) well_ordering(omega,u)* -> equal(integer_of(ordered_pair(singleton(singleton(singleton(identity_relation))),least(omega,domain_relation))),identity_relation)**.
% 299.99/300.67  199092[7:Res:13056.1,13362.0] inductive(u) || subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(identity_relation,least(omega,u))),identity_relation)**.
% 299.99/300.67  199124[7:Rew:154.1,199116.2] || member(u,recursion_equation_functions(v))* well_ordering(w,cross_product(ordinal_numbers,ordinal_numbers))* -> equal(u,identity_relation) member(least(w,u),u)*.
% 299.99/300.67  198939[8:Res:161565.3,41096.0] operation(u) || well_ordering(v,cantor(cantor(u))) -> equal(range_of(u),identity_relation) member(least(v,range_of(u)),ordinal_numbers)*.
% 299.99/300.67  161458[8:Rew:116078.0,16145.2,116078.0,16145.2,116078.0,16145.2] function(u) || subclass(range_of(u),identity_relation) equal(cantor(cantor(v)),cantor(u)) -> compatible(u,v,identity_relation)*.
% 299.99/300.67  196779[21:Rew:160429.0,196765.1] function(u) || subclass(range_of(u),identity_relation) equal(cantor(cantor(v)),cantor(u)) -> compatible(u,v,omega)*.
% 299.99/300.67  161459[8:Rew:116078.0,19203.2,116078.0,19203.2,116078.0,19203.2] function(u) || equal(range_of(u),identity_relation) equal(cantor(cantor(v)),cantor(u)) -> compatible(u,v,w)*.
% 299.99/300.67  165410[5:Res:39298.1,8798.1] || subclass(ordinal_numbers,complement(complement(cross_product(ordinal_numbers,ordinal_numbers))))* equal(sum_class(range_of(u)),v) -> member(ordered_pair(u,v),union_of_range_map)*.
% 299.99/300.67  198337[5:Res:9837.3,8841.1] || member(u,ordinal_numbers)* member(v,ordinal_numbers) equal(sum_class(range_of(v)),u)* subclass(ordinal_numbers,complement(union_of_range_map))* -> .
% 299.99/300.67  117580[8:Rew:116078.0,116339.2] operation(inverse(u)) || subclass(cantor(range_of(u)),range_of(inverse(u)))* -> equal(range_of(inverse(u)),cantor(range_of(u))).
% 299.99/300.67  193451[8:Rew:116239.0,193441.1] || member(single_valued1(u),ordinal_numbers) -> member(single_valued1(u),range_of(u)) equal(domain__dfg(u,range_of(identity_relation),single_valued2(u)),single_valued3(u))**.
% 299.99/300.67  194971[15:Res:62.1,165527.1] || member(ordered_pair(u,range_of(identity_relation)),compose(v,w)) subclass(ordinal_numbers,complement(image(v,image(w,singleton(u)))))* -> .
% 299.99/300.67  165018[8:SpR:161038.2,19860.0] || member(u,ordinal_numbers) -> member(u,cantor(cross_product(v,ordinal_numbers))) equal(image(cross_product(singleton(u),ordinal_numbers),v),range_of(identity_relation))**.
% 299.99/300.67  61463[8:Rew:14756.0,61451.1] || member(ordered_pair(u,not_subclass_element(v,image(w,range_of(identity_relation)))),compose(w,identity_relation))* -> subclass(v,image(w,range_of(identity_relation))).
% 299.99/300.67  18693[8:Res:16042.1,129.0] || equal(sum_class(range_of(identity_relation)),identity_relation) subclass(union_of_range_map,u) well_ordering(v,u)* -> member(least(v,union_of_range_map),union_of_range_map)*.
% 299.99/300.67  197926[21:SpR:196554.1,116203.2] function(first(u)) || member(u,subset_relation) subclass(range_of(first(u)),v) -> maps(first(u),identity_relation,v)*.
% 299.99/300.67  197879[21:SpR:196551.1,116203.2] function(sum_class(u)) || member(u,ordinal_numbers) subclass(range_of(sum_class(u)),v) -> maps(sum_class(u),identity_relation,v)*.
% 299.99/300.67  197972[21:SpR:196555.1,116203.2] function(second(u)) || member(u,subset_relation) subclass(range_of(second(u)),v) -> maps(second(u),identity_relation,v)*.
% 299.99/300.67  198022[21:SpR:196558.1,116203.2] function(rest_of(u)) || member(u,ordinal_numbers) subclass(range_of(rest_of(u)),v) -> maps(rest_of(u),identity_relation,v)*.
% 299.99/300.67  198066[21:SpR:196563.1,116203.2] function(power_class(u)) || member(u,ordinal_numbers) subclass(range_of(power_class(u)),v) -> maps(power_class(u),identity_relation,v)*.
% 299.99/300.67  193237[8:SpR:154737.1,161207.0] || subclass(image(successor_relation,ordinal_numbers),singleton(identity_relation)) -> equal(symmetric_difference(singleton(identity_relation),image(successor_relation,ordinal_numbers)),symmetric_difference(ordinal_numbers,image(successor_relation,ordinal_numbers)))**.
% 299.99/300.67  194670[7:Rew:59.0,194637.2,59.0,194637.0] || member(power_class(u),ordinal_numbers) member(apply(choice,power_class(u)),image(element_relation,complement(u)))* -> equal(power_class(u),identity_relation).
% 299.99/300.67  18456[7:Res:13248.1,288.0] || member(regular(intersection(image(element_relation,complement(u)),v)),power_class(u))* -> equal(intersection(image(element_relation,complement(u)),v),identity_relation).
% 299.99/300.67  159445[5:Res:41368.0,5.0] || subclass(power_class(u),v) -> subclass(w,image(element_relation,complement(u))) member(not_subclass_element(w,image(element_relation,complement(u))),v)*.
% 299.99/300.67  136988[5:SpR:487.0,18211.1] || subclass(ordinal_numbers,symmetric_difference(image(element_relation,complement(u)),v)) -> member(unordered_pair(w,x),complement(intersection(power_class(u),complement(v))))*.
% 299.99/300.67  165153[7:Res:130710.0,13113.0] || well_ordering(u,image(element_relation,complement(v))) -> equal(segment(u,complement(power_class(v)),least(u,complement(power_class(v)))),identity_relation)**.
% 299.99/300.67  18454[7:Res:13210.1,288.0] || member(regular(intersection(u,image(element_relation,complement(v)))),power_class(v))* -> equal(intersection(u,image(element_relation,complement(v))),identity_relation).
% 299.99/300.67  28949[5:Res:8827.2,288.0] || member(u,ordinal_numbers) subclass(rest_relation,image(element_relation,complement(v))) member(ordered_pair(u,rest_of(u)),power_class(v))* -> .
% 299.99/300.67  140470[5:MRR:140407.0,41183.1] ||  -> member(not_subclass_element(u,intersection(image(element_relation,complement(v)),u)),power_class(v))* subclass(u,intersection(image(element_relation,complement(v)),u)).
% 299.99/300.67  130869[5:Res:8835.1,9876.0] || member(u,ordinal_numbers) subclass(image(element_relation,complement(v)),w)* well_ordering(ordinal_numbers,w) -> member(u,power_class(v))*.
% 299.99/300.67  136983[5:SpR:485.0,18211.1] || subclass(ordinal_numbers,symmetric_difference(u,image(element_relation,complement(v)))) -> member(unordered_pair(w,x),complement(intersection(complement(u),power_class(v))))*.
% 299.99/300.67  132754[0:SpR:59.0,19486.0] ||  -> equal(power_class(intersection(power_class(u),complement(inverse(image(element_relation,complement(u)))))),complement(image(element_relation,symmetrization_of(image(element_relation,complement(u))))))**.
% 299.99/300.67  193556[8:Rew:162038.0,193466.1] ||  -> member(not_subclass_element(complement(power_class(complement(inverse(identity_relation)))),u),image(element_relation,symmetrization_of(identity_relation)))* subclass(complement(power_class(complement(inverse(identity_relation)))),u).
% 299.99/300.67  193547[8:SpL:162038.0,490.0] || member(u,intersection(complement(v),power_class(complement(inverse(identity_relation)))))* member(u,union(v,image(element_relation,symmetrization_of(identity_relation)))) -> .
% 299.99/300.67  193542[8:SpL:162038.0,490.0] || member(u,intersection(power_class(complement(inverse(identity_relation))),complement(v)))* member(u,union(image(element_relation,symmetrization_of(identity_relation)),v)) -> .
% 299.99/300.67  193500[8:SpL:162038.0,66637.0] || subclass(ordinal_numbers,intersection(power_class(complement(inverse(identity_relation))),complement(u)))* member(omega,union(image(element_relation,symmetrization_of(identity_relation)),u)) -> .
% 299.99/300.67  193541[8:SpL:162038.0,66637.0] || subclass(ordinal_numbers,intersection(complement(u),power_class(complement(inverse(identity_relation)))))* member(omega,union(u,image(element_relation,symmetrization_of(identity_relation)))) -> .
% 299.99/300.67  166354[7:Res:13125.2,941.1] || subclass(omega,power_class(image(element_relation,complement(u))))* member(v,image(element_relation,power_class(u)))* -> equal(integer_of(v),identity_relation).
% 299.99/300.67  13307[7:Rew:13036.0,8607.1] || member(regular(power_class(image(element_relation,complement(u)))),image(element_relation,power_class(u)))* -> equal(power_class(image(element_relation,complement(u))),identity_relation).
% 299.99/300.67  132404[5:SpR:189.0,132294.0] ||  -> subclass(complement(symmetrization_of(image(element_relation,power_class(u)))),intersection(power_class(image(element_relation,complement(u))),complement(inverse(image(element_relation,power_class(u))))))*.
% 299.99/300.67  132361[5:SpR:189.0,132293.0] ||  -> subclass(complement(successor(image(element_relation,power_class(u)))),intersection(power_class(image(element_relation,complement(u))),complement(singleton(image(element_relation,power_class(u))))))*.
% 299.99/300.67  155400[5:Res:40074.1,941.1] || subclass(ordinal_numbers,complement(complement(power_class(image(element_relation,complement(u))))))* member(unordered_pair(v,w),image(element_relation,power_class(u)))* -> .
% 299.99/300.67  155430[5:Res:127147.1,941.1] || subclass(ordinal_numbers,complement(complement(power_class(image(element_relation,complement(u))))))* member(least(element_relation,omega),image(element_relation,power_class(u))) -> .
% 299.99/300.67  155431[5:Res:126679.1,941.1] || subclass(omega,complement(complement(power_class(image(element_relation,complement(u))))))* member(least(element_relation,omega),image(element_relation,power_class(u))) -> .
% 299.99/300.67  155447[5:Res:39298.1,941.1] || subclass(ordinal_numbers,complement(complement(power_class(image(element_relation,complement(u))))))* member(ordered_pair(v,w),image(element_relation,power_class(u)))* -> .
% 299.99/300.67  166818[7:Res:13227.2,941.1] || subclass(u,power_class(image(element_relation,complement(v)))) member(regular(u),image(element_relation,power_class(v)))* -> equal(u,identity_relation).
% 299.99/300.67  136642[0:SpL:189.0,18791.0] || member(u,symmetric_difference(power_class(image(element_relation,complement(v))),complement(w)))* -> member(u,union(image(element_relation,power_class(v)),w)).
% 299.99/300.67  81160[5:Rew:189.0,81130.1] ||  -> member(not_subclass_element(u,power_class(image(element_relation,complement(v)))),image(element_relation,power_class(v)))* subclass(u,power_class(image(element_relation,complement(v)))).
% 299.99/300.67  19463[0:SpR:189.0,487.0] ||  -> equal(union(image(element_relation,power_class(image(element_relation,complement(u)))),v),complement(intersection(power_class(image(element_relation,power_class(u))),complement(v))))**.
% 299.99/300.67  19389[0:SpR:189.0,485.0] ||  -> equal(union(u,image(element_relation,power_class(image(element_relation,complement(v))))),complement(intersection(complement(u),power_class(image(element_relation,power_class(v))))))**.
% 299.99/300.67  136629[0:SpL:189.0,18791.0] || member(u,symmetric_difference(complement(v),power_class(image(element_relation,complement(w)))))* -> member(u,union(v,image(element_relation,power_class(w)))).
% 299.99/300.67  193495[8:SpR:162038.0,8835.1] || member(u,ordinal_numbers) -> member(u,image(element_relation,power_class(complement(inverse(identity_relation)))))* member(u,power_class(image(element_relation,symmetrization_of(identity_relation)))).
% 299.99/300.67  82962[8:SpR:481.0,67606.0] ||  -> subclass(symmetric_difference(union(image(element_relation,union(u,v)),identity_relation),ordinal_numbers),complement(symmetric_difference(power_class(intersection(complement(u),complement(v))),ordinal_numbers)))*.
% 299.99/300.67  132505[5:SpR:481.0,130711.0] ||  -> subclass(complement(power_class(image(element_relation,power_class(intersection(complement(u),complement(v)))))),image(element_relation,power_class(image(element_relation,union(u,v)))))*.
% 299.99/300.67  164904[8:SpL:160491.0,1042.0] || member(not_subclass_element(power_class(symmetric_difference(ordinal_numbers,u)),v),image(element_relation,union(u,identity_relation)))* -> subclass(power_class(symmetric_difference(ordinal_numbers,u)),v).
% 299.99/300.67  96945[5:SpR:481.0,79577.0] ||  -> member(u,image(element_relation,power_class(intersection(complement(v),complement(w)))))* subclass(singleton(u),power_class(image(element_relation,union(v,w)))).
% 299.99/300.67  19482[5:SpR:481.0,8700.2] || member(u,ordinal_numbers) -> member(u,image(element_relation,union(v,w))) member(u,power_class(intersection(complement(v),complement(w))))*.
% 299.99/300.67  164933[8:Rew:160491.0,164885.1] ||  -> member(not_subclass_element(u,image(element_relation,union(v,identity_relation))),power_class(symmetric_difference(ordinal_numbers,v)))* subclass(u,image(element_relation,union(v,identity_relation))).
% 299.99/300.67  133008[0:SpR:59.0,19485.0] ||  -> equal(power_class(intersection(power_class(u),complement(singleton(image(element_relation,complement(u)))))),complement(image(element_relation,successor(image(element_relation,complement(u))))))**.
% 299.99/300.67  139666[5:SpL:19860.0,56504.0] || member(inverse(restrict(cross_product(u,ordinal_numbers),v,w)),image(cross_product(v,w),u))* subclass(ordinal_numbers,complement(element_relation)) -> .
% 299.99/300.67  18378[5:SpR:8649.0,8859.1] || member(inverse(restrict(u,v,ordinal_numbers)),ordinal_numbers) -> member(ordered_pair(inverse(restrict(u,v,ordinal_numbers)),image(u,v)),domain_relation)*.
% 299.99/300.67  39336[5:Res:9006.3,898.0] function(u) || member(v,ordinal_numbers) subclass(ordinal_numbers,restrict(w,x,y))* -> member(image(u,v),w)*.
% 299.99/300.67  40438[7:SpR:17977.2,107.0] function(u) function(v) ||  -> equal(domain__dfg(u,image(inverse(u),singleton(single_valued1(u))),single_valued2(v)),single_valued3(u))**.
% 299.99/300.67  49897[7:SpR:18034.2,107.0] single_valued_class(u) single_valued_class(v) ||  -> equal(domain__dfg(u,image(inverse(u),singleton(single_valued1(u))),single_valued2(v)),single_valued3(u))**.
% 299.99/300.67  49931[7:SpR:18035.2,107.0] single_valued_class(u) function(v) ||  -> equal(domain__dfg(u,image(inverse(u),singleton(single_valued1(u))),single_valued2(v)),single_valued3(u))**.
% 299.99/300.67  40110[8:SpR:15683.2,107.0] single_valued_class(u) single_valued_class(v) ||  -> equal(domain__dfg(u,image(inverse(u),singleton(single_valued1(v))),single_valued2(u)),single_valued3(u))**.
% 299.99/300.67  40133[8:SpR:15686.2,107.0] function(u) function(v) ||  -> equal(domain__dfg(u,image(inverse(u),singleton(single_valued1(v))),single_valued2(u)),single_valued3(u))**.
% 299.99/300.67  40159[8:SpR:15687.2,107.0] function(u) single_valued_class(v) ||  -> equal(domain__dfg(u,image(inverse(u),singleton(single_valued1(v))),single_valued2(u)),single_valued3(u))**.
% 299.99/300.67  40168[8:SpR:15687.2,107.0] function(u) single_valued_class(v) ||  -> equal(domain__dfg(v,image(inverse(v),singleton(single_valued1(u))),single_valued2(v)),single_valued3(v))**.
% 299.99/300.67  49942[7:SpR:18035.2,107.0] single_valued_class(u) function(v) ||  -> equal(domain__dfg(v,image(inverse(v),singleton(single_valued1(v))),single_valued2(u)),single_valued3(v))**.
% 299.99/300.67  65616[7:SpR:13096.1,284.1] || member(image(choice,singleton(singleton(u))),ordinal_numbers)* -> equal(singleton(u),identity_relation) subclass(u,image(choice,singleton(singleton(u))))*.
% 299.99/300.67  195396[16:Rew:195224.0,193392.0] ||  -> member(not_subclass_element(complement(power_class(complement(singleton(identity_relation)))),u),image(element_relation,singleton(identity_relation)))* subclass(complement(power_class(complement(singleton(identity_relation)))),u).
% 299.99/300.67  195393[16:Rew:195224.0,193383.1] || member(u,intersection(complement(v),power_class(complement(singleton(identity_relation)))))* member(u,union(v,image(element_relation,singleton(identity_relation)))) -> .
% 299.99/300.67  195389[16:Rew:195224.0,193378.1] || member(u,intersection(power_class(complement(singleton(identity_relation))),complement(v)))* member(u,union(image(element_relation,singleton(identity_relation)),v)) -> .
% 299.99/300.67  195330[16:Rew:195224.0,193377.1] || subclass(ordinal_numbers,intersection(complement(u),power_class(complement(singleton(identity_relation)))))* member(omega,union(u,image(element_relation,singleton(identity_relation)))) -> .
% 299.99/300.67  195324[16:Rew:195224.0,193336.1] || subclass(ordinal_numbers,intersection(power_class(complement(singleton(identity_relation))),complement(u)))* member(omega,union(image(element_relation,singleton(identity_relation)),u)) -> .
% 299.99/300.67  195311[16:Rew:195224.0,193331.2] || member(u,ordinal_numbers) -> member(u,image(element_relation,power_class(complement(singleton(identity_relation)))))* member(u,power_class(image(element_relation,singleton(identity_relation)))).
% 299.99/300.67  9491[5:Res:62.1,8843.1] || member(ordered_pair(u,singleton(v)),compose(w,x))* subclass(ordinal_numbers,complement(image(w,image(x,singleton(u)))))* -> .
% 299.99/300.67  134029[5:Res:62.1,133836.0] || member(ordered_pair(u,singleton(singleton(v))),compose(w,x))* well_ordering(ordinal_numbers,image(w,image(x,singleton(u)))) -> .
% 299.99/300.67  151529[0:Obv:151478.1] || member(ordered_pair(u,v),compose(w,x)) -> subclass(intersection(y,singleton(v)),image(w,image(x,singleton(u))))*.
% 299.99/300.67  151893[0:Obv:151836.1] || member(ordered_pair(u,v),compose(w,x)) -> subclass(intersection(singleton(v),y),image(w,image(x,singleton(u))))*.
% 299.99/300.67  196245[18:Res:62.1,190641.1] || member(ordered_pair(u,identity_relation),compose(v,w)) equal(complement(image(v,image(w,singleton(u)))),inverse(identity_relation))** -> .
% 299.99/300.67  196155[18:Res:62.1,190532.1] || member(ordered_pair(u,identity_relation),compose(v,w)) equal(complement(image(v,image(w,singleton(u)))),symmetrization_of(identity_relation))** -> .
% 299.99/300.67  195101[14:Res:62.1,165357.1] || member(ordered_pair(u,identity_relation),compose(v,w)) equal(complement(image(v,image(w,singleton(u)))),singleton(identity_relation))** -> .
% 299.99/300.67  146814[5:Res:3618.1,18535.2] || member(power_class(u),symmetric_difference(v,w))* member(u,ordinal_numbers) subclass(ordinal_numbers,complement(complement(intersection(v,w))))* -> .
% 299.99/300.67  29160[5:Res:8977.2,490.0] || member(u,ordinal_numbers) subclass(ordinal_numbers,intersection(complement(v),complement(w)))* member(power_class(u),union(v,w))* -> .
% 299.99/300.67  197401[8:Res:13246.2,162888.0] || member(intersection(subset_relation,u),ordinal_numbers) subclass(apply(choice,intersection(subset_relation,u)),identity_relation)* -> equal(intersection(subset_relation,u),identity_relation).
% 299.99/300.67  197400[8:Res:13246.2,162901.0] || member(intersection(subset_relation,u),ordinal_numbers) equal(apply(choice,intersection(subset_relation,u)),identity_relation)** -> equal(intersection(subset_relation,u),identity_relation).
% 299.99/300.67  197690[8:Res:13247.2,162888.0] || member(intersection(u,subset_relation),ordinal_numbers) subclass(apply(choice,intersection(u,subset_relation)),identity_relation)* -> equal(intersection(u,subset_relation),identity_relation).
% 299.99/300.67  197689[8:Res:13247.2,162901.0] || member(intersection(u,subset_relation),ordinal_numbers) equal(apply(choice,intersection(u,subset_relation)),identity_relation)** -> equal(intersection(u,subset_relation),identity_relation).
% 299.99/300.67  197430[8:Rew:140613.0,197369.1,140613.0,197369.0] || member(symmetric_difference(ordinal_numbers,u),ordinal_numbers) -> equal(symmetric_difference(ordinal_numbers,u),identity_relation) member(apply(choice,symmetric_difference(ordinal_numbers,u)),complement(u))*.
% 299.99/300.67  195704[7:Res:13225.3,8788.0] || member(u,ordinal_numbers) subclass(u,recursion_equation_functions(v))* -> equal(u,identity_relation) subclass(apply(choice,u),cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.67  195703[7:Res:13225.3,161.0] || member(u,ordinal_numbers) subclass(u,omega) -> equal(u,identity_relation) equal(integer_of(apply(choice,u)),apply(choice,u))**.
% 299.99/300.67  195698[7:Res:13225.3,56411.0] || member(u,ordinal_numbers) subclass(u,rest_of(apply(choice,u)))* subclass(ordinal_numbers,complement(element_relation)) -> equal(u,identity_relation).
% 299.99/300.67  195700[7:Res:13225.3,898.0] || member(u,ordinal_numbers) subclass(u,restrict(v,w,x))* -> equal(u,identity_relation) member(apply(choice,u),v).
% 299.99/300.67  161465[8:Rew:116078.0,19864.1] || member(u,ordinal_numbers) -> member(u,cantor(cross_product(v,w))) equal(restrict(cross_product(singleton(u),ordinal_numbers),v,w),identity_relation)**.
% 299.99/300.67  116344[8:Rew:116078.0,68235.3] || member(u,ordinal_numbers) member(v,cross_product(singleton(u),ordinal_numbers))* member(v,w)* -> member(u,cantor(w))*.
% 299.99/300.67  202350[22:Res:202344.0,129.0] || subclass(singleton(singleton(identity_relation)),u)* well_ordering(v,u)* -> member(least(v,singleton(singleton(identity_relation))),singleton(singleton(identity_relation)))*.
% 299.99/300.67  204040[8:Res:192333.1,8554.1] || equal(symmetric_difference(ordinal_numbers,intersection(u,v)),ordinal_numbers)** member(identity_relation,union(u,v)) -> member(identity_relation,symmetric_difference(u,v)).
% 299.99/300.67  204156[8:Res:204134.1,40594.1] || member(singleton(symmetrization_of(identity_relation)),inverse(identity_relation)) member(symmetrization_of(identity_relation),ordinal_numbers) -> member(singleton(singleton(singleton(symmetrization_of(identity_relation)))),element_relation)*.
% 299.99/300.67  205535[22:Res:8551.2,205501.0] || member(singleton(identity_relation),cross_product(u,v)) member(singleton(identity_relation),w) well_ordering(ordinal_numbers,restrict(w,u,v))* -> .
% 299.99/300.67  205617[23:Res:205609.0,129.0] || subclass(complement(recursion_equation_functions(u)),v)* well_ordering(w,v)* -> member(least(w,complement(recursion_equation_functions(u))),complement(recursion_equation_functions(u)))*.
% 299.99/300.67  206130[22:Res:205574.1,129.0] || equal(u,singleton(singleton(identity_relation))) subclass(u,v)* well_ordering(w,v)* -> member(least(w,u),u)*.
% 299.99/300.67  206220[8:SpR:189.0,155582.0] ||  -> equal(intersection(power_class(image(element_relation,complement(u))),symmetric_difference(ordinal_numbers,image(element_relation,power_class(u)))),symmetric_difference(ordinal_numbers,image(element_relation,power_class(u))))**.
% 299.99/300.67  206530[7:Rew:206526.2,206524.3] inductive(intersection(u,singleton(v))) || well_ordering(w,omega) -> equal(integer_of(v),identity_relation)** member(least(w,omega),omega)*.
% 299.99/300.67  206557[7:Rew:206553.2,206551.3] inductive(intersection(singleton(u),v)) || well_ordering(w,omega) -> equal(integer_of(u),identity_relation)** member(least(w,omega),omega)*.
% 299.99/300.67  206570[7:Rew:206568.2,206566.3] inductive(complement(complement(singleton(u)))) || well_ordering(v,omega) -> equal(integer_of(u),identity_relation)** member(least(v,omega),omega)*.
% 299.99/300.67  207897[24:Rew:207558.1,207627.1] operation(u) || asymmetric(v,identity_relation) -> equal(range__dfg(intersection(v,inverse(v)),u,identity_relation),second(not_subclass_element(identity_relation,identity_relation)))**.
% 299.99/300.67  208003[24:MRR:197578.4,207947.0] function(regular(u)) || subclass(range_of(regular(u)),identity_relation)* equal(cross_product(identity_relation,identity_relation),identity_relation) -> equal(u,identity_relation).
% 299.99/300.67  208217[7:Res:13333.3,41096.0] inductive(u) || well_ordering(v,u) -> equal(image(successor_relation,u),identity_relation) member(least(v,image(successor_relation,u)),ordinal_numbers)*.
% 299.99/300.67  208314[24:SpL:207572.1,37.0] operation(u) || member(ordered_pair(singleton(singleton(identity_relation)),v),rotate(w))* -> member(ordered_pair(ordered_pair(u,v),identity_relation),w)*.
% 299.99/300.67  208315[24:SpL:207572.1,40.0] operation(u) || member(ordered_pair(singleton(singleton(identity_relation)),v),flip(w))* -> member(ordered_pair(ordered_pair(u,identity_relation),v),w)*.
% 299.99/300.67  208946[25:SpL:208820.0,9470.1] || member(ordered_pair(ordinal_numbers,u),compose(v,w))* subclass(image(v,image(w,identity_relation)),x)* -> member(u,x)*.
% 299.99/300.67  209346[25:Rew:208840.0,209317.2] || equal(sum_class(range_of(identity_relation)),ordinal_numbers) member(singleton(singleton(identity_relation)),cross_product(ordinal_numbers,ordinal_numbers))* -> member(singleton(singleton(identity_relation)),union_of_range_map).
% 299.99/300.67  209805[8:SpR:189.0,206259.0] ||  -> subclass(symmetric_difference(power_class(image(element_relation,complement(u))),symmetric_difference(ordinal_numbers,image(element_relation,power_class(u)))),union(image(element_relation,power_class(u)),identity_relation))*.
% 299.99/300.67  209861[24:SpR:30.0,207863.1] operation(intersection(complement(u),complement(v))) ||  -> subclass(symmetric_difference(union(u,v),ordinal_numbers),successor(intersection(complement(u),complement(v))))*.
% 299.99/300.67  209870[24:SpR:189.0,207863.1] operation(image(element_relation,power_class(u))) ||  -> subclass(symmetric_difference(power_class(image(element_relation,complement(u))),ordinal_numbers),successor(image(element_relation,power_class(u))))*.
% 299.99/300.67  210235[8:SpR:117142.0,161701.2] || section(element_relation,u,ordinal_numbers) well_ordering(v,u) -> equal(segment(v,sum_class(u),least(v,sum_class(u))),identity_relation)**.
% 299.99/300.67  210373[7:Res:13225.3,143186.0] || member(u,ordinal_numbers) subclass(u,symmetric_difference(ordinal_numbers,v)) -> equal(u,identity_relation) member(apply(choice,u),complement(v))*.
% 299.99/300.67  210396[5:Res:9006.3,143186.0] function(u) || member(v,ordinal_numbers) subclass(ordinal_numbers,symmetric_difference(ordinal_numbers,w)) -> member(image(u,v),complement(w))*.
% 299.99/300.67  210397[5:Res:919.1,143186.0] ||  -> subclass(restrict(symmetric_difference(ordinal_numbers,u),v,w),x) member(not_subclass_element(restrict(symmetric_difference(ordinal_numbers,u),v,w),x),complement(u))*.
% 299.99/300.67  210473[7:Res:13069.2,143226.0] || member(symmetric_difference(ordinal_numbers,u),ordinal_numbers) member(apply(choice,symmetric_difference(ordinal_numbers,u)),u)* -> equal(symmetric_difference(ordinal_numbers,u),identity_relation).
% 299.99/300.67  210482[7:Res:13225.3,143226.0] || member(u,ordinal_numbers) subclass(u,symmetric_difference(ordinal_numbers,v)) member(apply(choice,u),v)* -> equal(u,identity_relation).
% 299.99/300.67  210505[5:Res:9006.3,143226.0] function(u) || member(v,ordinal_numbers) subclass(ordinal_numbers,symmetric_difference(ordinal_numbers,w)) member(image(u,v),w)* -> .
% 299.99/300.67  210506[5:Res:919.1,143226.0] || member(not_subclass_element(restrict(symmetric_difference(ordinal_numbers,u),v,w),x),u)* -> subclass(restrict(symmetric_difference(ordinal_numbers,u),v,w),x).
% 299.99/300.67  210671[8:Res:9837.3,210517.1] || member(u,ordinal_numbers)* member(v,ordinal_numbers) equal(sum_class(range_of(v)),u)* equal(complement(union_of_range_map),ordinal_numbers) -> .
% 299.99/300.67  211396[8:Res:210606.1,9420.2] || equal(complement(u),ordinal_numbers) member(v,w)* member(x,y)* -> member(ordered_pair(x,v),complement(u))*.
% 299.99/300.67  211583[8:Res:211438.1,9420.2] || equal(symmetrization_of(identity_relation),ordinal_numbers) member(u,v)* member(w,x)* -> member(ordered_pair(w,u),symmetrization_of(identity_relation))*.
% 299.99/300.67  211667[8:Res:211441.1,9420.2] || equal(power_class(u),ordinal_numbers) member(v,w)* member(x,y)* -> member(ordered_pair(x,v),power_class(u))*.
% 299.99/300.67  212393[7:SpL:13259.2,132439.0] || member(cross_product(u,v),ordinal_numbers) well_ordering(ordinal_numbers,apply(choice,cross_product(u,v)))* -> equal(cross_product(u,v),identity_relation).
% 299.99/300.67  212396[8:SpL:13259.2,162891.0] || member(cross_product(u,v),ordinal_numbers) equal(apply(choice,cross_product(u,v)),identity_relation)** -> equal(cross_product(u,v),identity_relation).
% 299.99/300.67  212397[8:SpL:13259.2,162248.0] || member(cross_product(u,v),ordinal_numbers) subclass(apply(choice,cross_product(u,v)),identity_relation)* -> equal(cross_product(u,v),identity_relation).
% 299.99/300.67  212525[8:SpR:211432.1,161196.2] operation(u) || equal(complement(symmetrization_of(v)),ordinal_numbers) connected(v,cantor(cantor(u)))* -> subclass(cantor(u),identity_relation).
% 299.99/300.67  212639[8:SpL:211432.1,161194.1] operation(u) || equal(complement(symmetrization_of(v)),ordinal_numbers) subclass(cantor(u),identity_relation) -> connected(v,cantor(cantor(u)))*.
% 299.99/300.67  213464[8:SpR:145761.0,116209.1] operation(cross_product(u,singleton(v))) ||  -> equal(intersection(segment(ordinal_numbers,u,v),w),intersection(w,segment(ordinal_numbers,u,v)))*.
% 299.99/300.67  213637[5:Res:151877.0,11.0] || subclass(complement(recursion_equation_functions(u)),intersection(singleton(v),w))* -> function(v) equal(complement(recursion_equation_functions(u)),intersection(singleton(v),w)).
% 299.99/300.67  213659[5:Res:213622.0,11.0] || subclass(complement(recursion_equation_functions(u)),complement(complement(singleton(v))))* -> function(v) equal(complement(recursion_equation_functions(u)),complement(complement(singleton(v)))).
% 299.99/300.67  213693[5:Res:151512.0,11.0] || subclass(complement(recursion_equation_functions(u)),intersection(v,singleton(w)))* -> function(w) equal(complement(recursion_equation_functions(u)),intersection(v,singleton(w))).
% 299.99/300.67  214272[25:SpR:208887.0,116209.1] operation(restrict(u,v,identity_relation)) ||  -> equal(intersection(segment(u,v,ordinal_numbers),w),intersection(w,segment(u,v,ordinal_numbers)))*.
% 299.99/300.67  214474[25:SpR:208985.1,9004.1] operation(inverse(u)) || member(flip(cross_product(u,ordinal_numbers)),ordinal_numbers) -> member(ordered_pair(flip(cross_product(u,ordinal_numbers)),ordinal_numbers),domain_relation)*.
% 299.99/300.67  214480[25:SpR:208985.1,9005.1] operation(sum_class(u)) || member(restrict(element_relation,ordinal_numbers,u),ordinal_numbers) -> member(ordered_pair(restrict(element_relation,ordinal_numbers,u),ordinal_numbers),domain_relation)*.
% 299.99/300.67  214499[25:SpL:208985.1,37.0] operation(u) || member(ordered_pair(ordered_pair(v,u),w),rotate(x))* -> member(ordered_pair(ordered_pair(ordinal_numbers,w),v),x).
% 299.99/300.67  214500[25:SpL:208985.1,40.0] operation(u) || member(ordered_pair(ordered_pair(v,u),w),flip(x))* -> member(ordered_pair(ordered_pair(ordinal_numbers,v),w),x).
% 299.99/300.67  214531[25:SpL:208985.1,37.0] operation(u) || member(ordered_pair(ordered_pair(v,w),u),rotate(x))* -> member(ordered_pair(ordered_pair(w,ordinal_numbers),v),x).
% 299.99/300.67  214532[25:SpL:208985.1,40.0] operation(u) || member(ordered_pair(ordered_pair(v,w),u),flip(x))* -> member(ordered_pair(ordered_pair(w,v),ordinal_numbers),x).
% 299.99/300.67  214554[25:SpL:208985.1,37.0] operation(u) || member(ordered_pair(ordered_pair(v,ordinal_numbers),w),rotate(x))* -> member(ordered_pair(ordered_pair(u,w),v),x)*.
% 299.99/300.67  214555[25:SpL:208985.1,40.0] operation(u) || member(ordered_pair(ordered_pair(v,ordinal_numbers),w),flip(x))* -> member(ordered_pair(ordered_pair(u,v),w),x)*.
% 299.99/300.67  214593[25:SpL:208985.1,37.0] operation(u) || member(ordered_pair(ordered_pair(v,w),ordinal_numbers),rotate(x))* -> member(ordered_pair(ordered_pair(w,u),v),x)*.
% 299.99/300.67  214594[25:SpL:208985.1,40.0] operation(u) || member(ordered_pair(ordered_pair(v,w),ordinal_numbers),flip(x))* -> member(ordered_pair(ordered_pair(w,v),u),x)*.
% 299.99/300.67  214765[25:SpL:13260.1,214618.1] operation(second(regular(cross_product(u,v)))) || member(regular(cross_product(u,v)),rest_relation)* -> equal(cross_product(u,v),identity_relation).
% 299.99/300.67  215172[0:SpR:30.0,155157.1] || subclass(intersection(complement(u),complement(v)),w) -> subclass(symmetric_difference(w,intersection(complement(u),complement(v))),union(u,v))*.
% 299.99/300.67  215183[0:SpR:189.0,155157.1] || subclass(image(element_relation,power_class(u)),v) -> subclass(symmetric_difference(v,image(element_relation,power_class(u))),power_class(image(element_relation,complement(u))))*.
% 299.99/300.67  215785[8:MRR:165281.2,215781.0] || subclass(ordinal_numbers,power_class(u)) well_ordering(v,power_class(u))* -> member(least(v,singleton(singleton(w))),singleton(singleton(w)))*.
% 299.99/300.67  217387[8:Res:216591.1,8554.1] || equal(complement(complement(intersection(u,v))),identity_relation)** member(identity_relation,union(u,v)) -> member(identity_relation,symmetric_difference(u,v)).
% 299.99/300.67  217463[8:EmS:13166.0,13166.1,19277.2,214833.1] single_valued_class(symmetrization_of(u)) || equal(symmetrization_of(u),identity_relation)** equal(symmetrization_of(u),ordinal_numbers) -> member(identity_relation,cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.67  217467[8:EmS:13166.0,13166.1,19277.2,214832.1] single_valued_class(successor(u)) || equal(successor(u),identity_relation)** equal(successor(u),ordinal_numbers) -> member(identity_relation,cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.67  217609[8:Res:216611.1,8554.1] || equal(complement(complement(intersection(u,v))),identity_relation)** member(omega,union(u,v)) -> member(omega,symmetric_difference(u,v)).
% 299.99/300.67  218255[8:Res:9865.3,217144.1] || member(u,ordinal_numbers)* member(v,ordinal_numbers) equal(compose(w,v),u)* equal(compose_class(w),identity_relation) -> .
% 299.99/300.67  219216[8:Res:9865.3,219073.1] || member(u,ordinal_numbers)* member(v,ordinal_numbers) equal(compose(w,v),u)* subclass(compose_class(w),identity_relation)* -> .
% 299.99/300.67  219341[15:Res:215659.1,3689.0] || subclass(complement(ordered_pair(u,v)),identity_relation)* -> equal(unordered_pair(u,singleton(v)),range_of(identity_relation)) equal(range_of(identity_relation),singleton(u)).
% 299.99/300.67  219588[8:Res:61019.0,67561.0] ||  -> equal(complement(complement(symmetric_difference(complement(u),ordinal_numbers))),identity_relation) member(regular(complement(complement(symmetric_difference(complement(u),ordinal_numbers)))),union(u,identity_relation))*.
% 299.99/300.67  219589[8:Res:13248.1,67561.0] ||  -> equal(intersection(symmetric_difference(complement(u),ordinal_numbers),v),identity_relation) member(regular(intersection(symmetric_difference(complement(u),ordinal_numbers),v)),union(u,identity_relation))*.
% 299.99/300.67  219601[8:Res:13210.1,67561.0] ||  -> equal(intersection(u,symmetric_difference(complement(v),ordinal_numbers)),identity_relation) member(regular(intersection(u,symmetric_difference(complement(v),ordinal_numbers))),union(v,identity_relation))*.
% 299.99/300.67  219620[8:Res:8827.2,67561.0] || member(u,ordinal_numbers) subclass(rest_relation,symmetric_difference(complement(v),ordinal_numbers)) -> member(ordered_pair(u,rest_of(u)),union(v,identity_relation))*.
% 299.99/300.67  219793[8:Res:67614.1,290.0] || member(not_subclass_element(complement(symmetric_difference(complement(u),ordinal_numbers)),v),union(u,identity_relation))* -> subclass(complement(symmetric_difference(complement(u),ordinal_numbers)),v).
% 299.99/300.67  219799[8:Res:67614.1,19111.1] || member(not_subclass_element(u,v),union(w,identity_relation))* subclass(u,complement(symmetric_difference(complement(w),ordinal_numbers))) -> subclass(u,v).
% 299.99/300.67  219801[8:Res:67614.1,18571.2] || member(sum_class(u),union(v,identity_relation))* member(u,ordinal_numbers) subclass(ordinal_numbers,complement(symmetric_difference(complement(v),ordinal_numbers)))* -> .
% 299.99/300.67  220020[8:Res:313.1,160772.0] || member(not_subclass_element(intersection(symmetric_difference(ordinal_numbers,u),v),w),union(u,identity_relation))* -> subclass(intersection(symmetric_difference(ordinal_numbers,u),v),w).
% 299.99/300.67  220037[8:Res:303.1,160772.0] || member(not_subclass_element(intersection(u,symmetric_difference(ordinal_numbers,v)),w),union(v,identity_relation))* -> subclass(intersection(u,symmetric_difference(ordinal_numbers,v)),w).
% 299.99/300.67  220044[8:Res:13237.2,160772.0] || well_ordering(u,ordinal_numbers) member(least(u,symmetric_difference(ordinal_numbers,v)),union(v,identity_relation))* -> equal(symmetric_difference(ordinal_numbers,v),identity_relation).
% 299.99/300.67  220058[8:Res:8827.2,160772.0] || member(u,ordinal_numbers) subclass(rest_relation,symmetric_difference(ordinal_numbers,v)) member(ordered_pair(u,rest_of(u)),union(v,identity_relation))* -> .
% 299.99/300.67  220383[21:SpR:6355.1,196656.1] || subclass(domain_relation,flip(u)) -> subclass(cross_product(v,w),x) member(ordered_pair(not_subclass_element(cross_product(v,w),x),identity_relation),u)*.
% 299.99/300.67  220393[21:Res:196656.1,152274.0] || subclass(domain_relation,flip(complement(singleton(ordered_pair(ordered_pair(u,v),identity_relation)))))* -> subclass(singleton(ordered_pair(ordered_pair(u,v),identity_relation)),w)*.
% 299.99/300.67  220403[21:Res:196656.1,490.0] || subclass(domain_relation,flip(intersection(complement(u),complement(v)))) member(ordered_pair(ordered_pair(w,x),identity_relation),union(u,v))* -> .
% 299.99/300.67  220495[21:Res:196657.1,152274.0] || subclass(domain_relation,rotate(complement(singleton(ordered_pair(ordered_pair(u,identity_relation),v)))))* -> subclass(singleton(ordered_pair(ordered_pair(u,identity_relation),v)),w)*.
% 299.99/300.67  220505[21:Res:196657.1,490.0] || subclass(domain_relation,rotate(intersection(complement(u),complement(v)))) member(ordered_pair(ordered_pair(w,identity_relation),x),union(u,v))* -> .
% 299.99/300.67  220567[21:Res:196657.1,131.3] || subclass(domain_relation,rotate(u))* member(ordered_pair(v,identity_relation),w)* subclass(w,x)* well_ordering(u,x)* -> .
% 299.99/300.67  220685[7:Res:3652.1,17324.0] || section(u,singleton(v),w) -> equal(segment(u,w,v),identity_relation) equal(regular(segment(u,w,v)),v)**.
% 299.99/300.67  220776[8:Res:39607.2,160772.0] inductive(symmetric_difference(ordinal_numbers,u)) || well_ordering(v,ordinal_numbers) member(least(v,symmetric_difference(ordinal_numbers,u)),union(u,identity_relation))* -> .
% 299.99/300.67  221134[7:Res:13236.2,143226.0] || well_ordering(u,symmetric_difference(ordinal_numbers,v)) member(least(u,symmetric_difference(ordinal_numbers,v)),v)* -> equal(symmetric_difference(ordinal_numbers,v),identity_relation).
% 299.99/300.67  221135[7:Res:13236.2,143186.0] || well_ordering(u,symmetric_difference(ordinal_numbers,v)) -> equal(symmetric_difference(ordinal_numbers,v),identity_relation) member(least(u,symmetric_difference(ordinal_numbers,v)),complement(v))*.
% 299.99/300.67  221158[8:Res:13236.2,14681.0] || well_ordering(u,regular(v)) member(least(u,regular(v)),v)* -> equal(regular(v),identity_relation) equal(v,identity_relation).
% 299.99/300.67  221306[8:Res:215662.1,3689.0] || subclass(complement(ordered_pair(u,v)),identity_relation)* -> equal(singleton(w),unordered_pair(u,singleton(v)))* equal(singleton(w),singleton(u)).
% 299.99/300.67  221400[5:Res:39609.2,143226.0] inductive(symmetric_difference(ordinal_numbers,u)) || well_ordering(v,symmetric_difference(ordinal_numbers,u)) member(least(v,symmetric_difference(ordinal_numbers,u)),u)* -> .
% 299.99/300.67  221401[5:Res:39609.2,143186.0] inductive(symmetric_difference(ordinal_numbers,u)) || well_ordering(v,symmetric_difference(ordinal_numbers,u)) -> member(least(v,symmetric_difference(ordinal_numbers,u)),complement(u))*.
% 299.99/300.67  222694[8:Res:41203.1,31610.0] || member(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers)* subclass(rest_relation,successor_relation) -> equal(rest_of(least(element_relation,domain_relation)),successor(least(element_relation,domain_relation))).
% 299.99/300.67  222718[8:Res:80082.1,31610.0] || member(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers)* subclass(rest_relation,successor_relation) -> equal(rest_of(least(element_relation,rest_relation)),successor(least(element_relation,rest_relation))).
% 299.99/300.67  222719[10:Res:80198.1,31610.0] || member(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers)* subclass(rest_relation,successor_relation) -> equal(rest_of(least(element_relation,element_relation)),successor(least(element_relation,element_relation))).
% 299.99/300.67  223789[8:SpR:189.0,160927.0] ||  -> equal(complement(intersection(power_class(image(element_relation,complement(u))),union(v,identity_relation))),union(image(element_relation,power_class(u)),symmetric_difference(ordinal_numbers,v)))**.
% 299.99/300.67  224099[8:SpR:189.0,160992.0] ||  -> equal(complement(intersection(union(u,identity_relation),power_class(image(element_relation,complement(v))))),union(symmetric_difference(ordinal_numbers,u),image(element_relation,power_class(v))))**.
% 299.99/300.67  224323[8:MRR:224292.0,60996.1] ||  -> member(regular(regular(union(u,v))),complement(v))* equal(regular(union(u,v)),identity_relation) equal(union(u,v),identity_relation).
% 299.99/300.67  224324[8:MRR:224291.0,60996.1] ||  -> member(regular(regular(union(u,v))),complement(u))* equal(regular(union(u,v)),identity_relation) equal(union(u,v),identity_relation).
% 299.99/300.67  224811[26:Rew:224810.1,125933.2] || subclass(omega,ordered_pair(u,v))* -> equal(unordered_pair(u,singleton(v)),least(element_relation,omega)) equal(least(element_relation,omega),identity_relation).
% 299.99/300.67  224812[26:Rew:224810.1,69481.3] || subclass(omega,ordered_pair(u,v))* -> equal(integer_of(w),identity_relation)** equal(w,unordered_pair(u,singleton(v)))* equal(w,identity_relation).
% 299.99/300.67  224862[7:SpL:3606.0,13340.0] || subclass(omega,symmetric_difference(cross_product(u,v),w)) -> equal(integer_of(x),identity_relation) member(x,complement(restrict(w,u,v)))*.
% 299.99/300.67  224863[7:SpL:3603.0,13340.0] || subclass(omega,symmetric_difference(u,cross_product(v,w))) -> equal(integer_of(x),identity_relation) member(x,complement(restrict(u,v,w)))*.
% 299.99/300.67  225118[8:Obv:225047.0] ||  -> equal(intersection(u,singleton(v)),identity_relation) equal(symmetric_difference(intersection(u,singleton(v)),v),union(intersection(u,singleton(v)),v))**.
% 299.99/300.67  225233[8:Obv:225150.0] ||  -> equal(intersection(singleton(u),v),identity_relation) equal(symmetric_difference(intersection(singleton(u),v),u),union(intersection(singleton(u),v),u))**.
% 299.99/300.67  225945[26:Rew:225944.1,147304.2] || equal(ordered_pair(u,v),omega) -> equal(unordered_pair(u,singleton(v)),least(element_relation,omega))** equal(least(element_relation,omega),identity_relation).
% 299.99/300.67  226157[7:Res:139.1,17321.0] || member(intersection(u,v),ordinal_numbers) -> equal(sum_class(intersection(u,v)),identity_relation) member(regular(sum_class(intersection(u,v))),v)*.
% 299.99/300.67  226181[7:MRR:226164.2,13102.1] || connected(u,intersection(v,w)) -> well_ordering(u,intersection(v,w)) member(regular(not_well_ordering(u,intersection(v,w))),w)*.
% 299.99/300.67  226216[7:SpL:3606.0,17322.0] || subclass(u,symmetric_difference(cross_product(v,w),x)) -> equal(u,identity_relation) member(regular(u),complement(restrict(x,v,w)))*.
% 299.99/300.67  226217[7:SpL:3603.0,17322.0] || subclass(u,symmetric_difference(v,cross_product(w,x))) -> equal(u,identity_relation) member(regular(u),complement(restrict(v,w,x)))*.
% 299.99/300.67  226262[7:Res:139.1,17322.0] || member(intersection(u,v),ordinal_numbers) -> equal(sum_class(intersection(u,v)),identity_relation) member(regular(sum_class(intersection(u,v))),u)*.
% 299.99/300.67  226286[7:MRR:226269.2,13102.1] || connected(u,intersection(v,w)) -> well_ordering(u,intersection(v,w)) member(regular(not_well_ordering(u,intersection(v,w))),v)*.
% 299.99/300.67  226373[7:SpR:916.0,13258.1] ||  -> equal(restrict(cross_product(u,v),w,x),identity_relation) member(regular(restrict(cross_product(w,x),u,v)),cross_product(u,v))*.
% 299.99/300.67  226389[7:Res:13258.1,129.0] || subclass(u,v)* well_ordering(w,v)* -> equal(restrict(u,x,y),identity_relation)** member(least(w,u),u)*.
% 299.99/300.67  226396[7:Res:13258.1,3617.0] ||  -> equal(restrict(symmetric_difference(u,v),w,x),identity_relation) member(regular(restrict(symmetric_difference(u,v),w,x)),union(u,v))*.
% 299.99/300.67  226418[7:Res:13258.1,898.0] ||  -> equal(restrict(restrict(u,v,w),x,y),identity_relation) member(regular(restrict(restrict(u,v,w),x,y)),u)*.
% 299.99/300.67  226426[8:Res:13258.1,14681.0] || member(regular(restrict(regular(u),v,w)),u)* -> equal(restrict(regular(u),v,w),identity_relation) equal(u,identity_relation).
% 299.99/300.67  227215[8:Res:217451.1,8554.1] || equal(union(intersection(u,v),identity_relation),identity_relation)** member(identity_relation,union(u,v)) -> member(identity_relation,symmetric_difference(u,v)).
% 299.99/300.67  227266[5:SpR:145758.0,61728.2] || member(cross_product(u,ordinal_numbers),ordinal_numbers)* subclass(rest_relation,union_of_range_map) -> equal(rest_of(cross_product(u,ordinal_numbers)),sum_class(image(ordinal_numbers,u))).
% 299.99/300.67  227268[5:SpL:61728.2,9586.0] || member(u,ordinal_numbers) subclass(rest_relation,union_of_range_map) subclass(rest_of(u),range_of(u))* -> section(element_relation,range_of(u),ordinal_numbers)*.
% 299.99/300.67  227454[8:Res:217663.1,8554.1] || equal(union(intersection(u,v),identity_relation),identity_relation)** member(omega,union(u,v)) -> member(omega,symmetric_difference(u,v)).
% 299.99/300.67  228239[7:Res:52.1,17313.0] inductive(recursion_equation_functions(u)) ||  -> equal(image(successor_relation,recursion_equation_functions(u)),identity_relation) subclass(regular(image(successor_relation,recursion_equation_functions(u))),cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.67  228715[8:Res:67614.1,18535.2] || member(power_class(u),union(v,identity_relation))* member(u,ordinal_numbers) subclass(ordinal_numbers,complement(symmetric_difference(complement(v),ordinal_numbers)))* -> .
% 299.99/300.67  228903[8:MRR:228875.2,219791.1] || member(apply(choice,regular(symmetric_difference(complement(u),ordinal_numbers))),union(u,identity_relation))* -> equal(regular(symmetric_difference(complement(u),ordinal_numbers)),identity_relation).
% 299.99/300.67  229131[8:SpL:116209.1,17387.0] operation(u) || member(regular(intersection(cantor(u),complement(v))),v)* -> equal(intersection(complement(v),cantor(u)),identity_relation).
% 299.99/300.67  229212[7:Rew:3603.0,229116.1] || member(regular(symmetric_difference(u,cross_product(v,w))),restrict(u,v,w))* -> equal(symmetric_difference(u,cross_product(v,w)),identity_relation).
% 299.99/300.67  229213[7:Rew:3606.0,229115.1] || member(regular(symmetric_difference(cross_product(u,v),w)),restrict(w,u,v))* -> equal(symmetric_difference(cross_product(u,v),w),identity_relation).
% 299.99/300.67  229550[8:SpL:116209.1,13571.0] operation(u) || member(regular(intersection(complement(v),cantor(u))),v)* -> equal(intersection(cantor(u),complement(v)),identity_relation).
% 299.99/300.67  230258[8:Rew:140603.0,230226.0,66036.0,230226.0] ||  -> equal(symmetric_difference(complement(symmetrization_of(identity_relation)),union(inverse(identity_relation),symmetrization_of(identity_relation))),union(complement(symmetrization_of(identity_relation)),union(inverse(identity_relation),symmetrization_of(identity_relation))))**.
% 299.99/300.67  230399[8:Res:161066.1,9876.0] || member(u,ordinal_numbers) subclass(symmetric_difference(ordinal_numbers,v),w)* well_ordering(ordinal_numbers,w) -> member(u,union(v,identity_relation))*.
% 299.99/300.67  230640[8:Res:163112.0,18754.1] || subclass(ordinal_numbers,regular(complement(inverse(identity_relation)))) -> subclass(singleton(unordered_pair(u,v)),symmetrization_of(identity_relation))* equal(complement(inverse(identity_relation)),identity_relation).
% 299.99/300.67  230699[8:MRR:230642.3,218130.2] || member(unordered_pair(u,v),w)* member(unordered_pair(u,v),x)* subclass(ordinal_numbers,regular(intersection(x,w)))* -> .
% 299.99/300.67  230700[8:MRR:230645.0,8666.0] || subclass(ordinal_numbers,regular(symmetric_difference(ordinal_numbers,u))) -> member(unordered_pair(v,w),union(u,identity_relation))* equal(symmetric_difference(ordinal_numbers,u),identity_relation).
% 299.99/300.67  230765[8:SpL:13259.2,230706.0] || member(cross_product(u,v),ordinal_numbers) subclass(ordinal_numbers,apply(choice,cross_product(u,v)))* -> equal(cross_product(u,v),identity_relation).
% 299.99/300.67  230783[8:SpL:13259.2,230770.0] || member(cross_product(u,v),ordinal_numbers) equal(apply(choice,cross_product(u,v)),ordinal_numbers)** -> equal(cross_product(u,v),identity_relation).
% 299.99/300.67  231052[8:Res:13246.2,230762.0] || member(intersection(subset_relation,u),ordinal_numbers) subclass(ordinal_numbers,apply(choice,intersection(subset_relation,u)))* -> equal(intersection(subset_relation,u),identity_relation).
% 299.99/300.67  231061[8:Res:13247.2,230762.0] || member(intersection(u,subset_relation),ordinal_numbers) subclass(ordinal_numbers,apply(choice,intersection(u,subset_relation)))* -> equal(intersection(u,subset_relation),identity_relation).
% 299.99/300.67  231130[8:Res:13246.2,230780.0] || member(intersection(subset_relation,u),ordinal_numbers) equal(apply(choice,intersection(subset_relation,u)),ordinal_numbers)** -> equal(intersection(subset_relation,u),identity_relation).
% 299.99/300.67  231139[8:Res:13247.2,230780.0] || member(intersection(u,subset_relation),ordinal_numbers) equal(apply(choice,intersection(u,subset_relation)),ordinal_numbers)** -> equal(intersection(u,subset_relation),identity_relation).
% 299.99/300.67  231272[8:SpR:66293.0,17447.1] ||  -> equal(symmetric_difference(union(u,identity_relation),ordinal_numbers),identity_relation) member(regular(symmetric_difference(union(u,identity_relation),ordinal_numbers)),complement(symmetric_difference(complement(u),ordinal_numbers)))*.
% 299.99/300.67  231381[8:Rew:160491.0,231243.1] ||  -> equal(symmetric_difference(complement(u),symmetric_difference(ordinal_numbers,u)),identity_relation) member(regular(symmetric_difference(complement(u),symmetric_difference(ordinal_numbers,u))),union(u,identity_relation))*.
% 299.99/300.67  231831[8:MRR:231788.2,219791.1] || member(not_subclass_element(regular(symmetric_difference(complement(u),ordinal_numbers)),v),union(u,identity_relation))* -> subclass(regular(symmetric_difference(complement(u),ordinal_numbers)),v).
% 299.99/300.67  231874[8:Res:231812.0,13070.0] || well_ordering(u,complement(v)) -> equal(v,identity_relation) equal(regular(v),identity_relation) member(least(u,regular(v)),regular(v))*.
% 299.99/300.67  231877[8:Res:231812.0,9665.1] inductive(regular(u)) || well_ordering(v,complement(u)) -> equal(u,identity_relation) member(least(v,regular(u)),regular(u))*.
% 299.99/300.67  231895[16:Res:231880.0,13113.0] || well_ordering(u,singleton(identity_relation)) -> equal(segment(u,regular(complement(singleton(identity_relation))),least(u,regular(complement(singleton(identity_relation))))),identity_relation)**.
% 299.99/300.67  233104[21:Res:196525.2,5.0] || member(u,ordinal_numbers) equal(sum_class(range_of(u)),identity_relation) subclass(union_of_range_map,v) -> member(ordered_pair(u,identity_relation),v)*.
% 299.99/300.67  233188[7:Res:13125.2,18447.0] || subclass(omega,power_class(u)) -> equal(integer_of(regular(image(element_relation,complement(u)))),identity_relation)** equal(image(element_relation,complement(u)),identity_relation).
% 299.99/300.67  233196[8:Rew:160491.0,233178.1] || member(regular(image(element_relation,union(u,identity_relation))),power_class(symmetric_difference(ordinal_numbers,u)))* -> equal(image(element_relation,union(u,identity_relation)),identity_relation).
% 299.99/300.67  233468[8:Res:161057.2,5.0] || well_ordering(u,ordinal_numbers) subclass(ordinal_numbers,v) -> equal(recursion_equation_functions(w),identity_relation) member(cantor(least(u,recursion_equation_functions(w))),v)*.
% 299.99/300.67  233516[21:Res:193179.0,196424.2] || member(u,ordinal_numbers) subclass(domain_relation,complement(inverse(singleton(ordered_pair(u,identity_relation)))))* -> asymmetric(singleton(ordered_pair(u,identity_relation)),v)*.
% 299.99/300.67  233523[21:Res:13125.2,196424.2] || subclass(omega,u) member(v,ordinal_numbers) subclass(domain_relation,complement(u))* -> equal(integer_of(ordered_pair(v,identity_relation)),identity_relation)**.
% 299.99/300.67  233723[7:SpR:18840.1,13409.1] || member(u,subset_relation) subclass(omega,union_of_range_map) -> equal(integer_of(u),identity_relation) equal(sum_class(range_of(first(u))),second(u))**.
% 299.99/300.67  233905[8:Res:13125.2,161200.0] || subclass(omega,image(element_relation,union(u,identity_relation)))* member(v,power_class(symmetric_difference(ordinal_numbers,u)))* -> equal(integer_of(v),identity_relation).
% 299.99/300.67  233931[8:Res:13227.2,161200.0] || subclass(u,image(element_relation,union(v,identity_relation))) member(regular(u),power_class(symmetric_difference(ordinal_numbers,v)))* -> equal(u,identity_relation).
% 299.99/300.67  234161[8:Rew:160491.0,234150.2] || subclass(omega,symmetric_difference(ordinal_numbers,u)) -> equal(integer_of(not_subclass_element(union(u,identity_relation),v)),identity_relation)** subclass(union(u,identity_relation),v).
% 299.99/300.67  234365[7:Res:13125.2,18696.1] || subclass(omega,u) well_ordering(v,ordinal_numbers) -> equal(integer_of(least(v,complement(u))),identity_relation)** equal(complement(u),identity_relation).
% 299.99/300.67  234380[8:Rew:160491.0,234336.2] || well_ordering(u,ordinal_numbers) member(least(u,union(v,identity_relation)),symmetric_difference(ordinal_numbers,v))* -> equal(union(v,identity_relation),identity_relation).
% 299.99/300.67  234387[7:MRR:234357.0,65402.2] || well_ordering(u,ordinal_numbers) -> member(least(u,complement(union(v,w))),complement(w))* equal(complement(union(v,w)),identity_relation).
% 299.99/300.67  234388[7:MRR:234356.0,65402.2] || well_ordering(u,ordinal_numbers) -> member(least(u,complement(union(v,w))),complement(v))* equal(complement(union(v,w)),identity_relation).
% 299.99/300.67  234811[8:Res:193440.1,5.0] || member(u,ordinal_numbers) subclass(cantor(v),w)* -> equal(apply(v,u),sum_class(range_of(identity_relation)))** member(u,w)*.
% 299.99/300.67  234895[21:MRR:234839.0,8667.0] || member(u,ordinal_numbers) subclass(domain_relation,complement(cantor(v))) -> equal(apply(v,ordered_pair(u,identity_relation)),sum_class(range_of(identity_relation)))**.
% 299.99/300.67  234896[8:MRR:234818.0,8666.0] || subclass(ordinal_numbers,regular(cantor(u))) -> equal(apply(u,unordered_pair(v,w)),sum_class(range_of(identity_relation)))** equal(cantor(u),identity_relation).
% 299.99/300.67  234897[8:MRR:234850.0,60996.1] ||  -> equal(apply(u,regular(regular(cantor(u)))),sum_class(range_of(identity_relation)))** equal(regular(cantor(u)),identity_relation) equal(cantor(u),identity_relation).
% 299.99/300.67  234900[8:MRR:234852.0,60996.1] ||  -> equal(apply(u,regular(intersection(v,complement(cantor(u))))),sum_class(range_of(identity_relation)))** equal(intersection(v,complement(cantor(u))),identity_relation).
% 299.99/300.67  234901[8:MRR:234851.0,60996.1] ||  -> equal(apply(u,regular(intersection(complement(cantor(u)),v))),sum_class(range_of(identity_relation)))** equal(intersection(complement(cantor(u)),v),identity_relation).
% 299.99/300.67  235292[8:Res:230445.1,18696.1] || member(least(u,complement(union(v,identity_relation))),v)* well_ordering(u,ordinal_numbers) -> equal(complement(union(v,identity_relation)),identity_relation).
% 299.99/300.67  235356[5:SpR:18840.1,28980.1] || member(u,subset_relation) subclass(rest_relation,flip(v)) -> member(ordered_pair(ordered_pair(second(u),first(u)),rest_of(u)),v)*.
% 299.99/300.67  235367[5:SpR:18840.1,28980.1] || member(u,subset_relation) subclass(rest_relation,flip(v)) -> member(ordered_pair(u,rest_of(ordered_pair(second(u),first(u)))),v)*.
% 299.99/300.67  235376[8:Res:28980.1,66086.1] || subclass(rest_relation,flip(complement(compose(element_relation,ordinal_numbers)))) member(ordered_pair(ordered_pair(u,v),rest_of(ordered_pair(v,u))),element_relation)* -> .
% 299.99/300.67  235383[5:Res:28980.1,5.0] || subclass(rest_relation,flip(u))* subclass(u,v)* -> member(ordered_pair(ordered_pair(w,x),rest_of(ordered_pair(x,w))),v)*.
% 299.99/300.67  235388[5:Res:28980.1,3617.0] || subclass(rest_relation,flip(symmetric_difference(u,v))) -> member(ordered_pair(ordered_pair(w,x),rest_of(ordered_pair(x,w))),union(u,v))*.
% 299.99/300.67  235389[5:Res:28980.1,19559.0] || subclass(rest_relation,flip(symmetric_difference(u,singleton(u))))* -> member(ordered_pair(ordered_pair(v,w),rest_of(ordered_pair(w,v))),successor(u))*.
% 299.99/300.67  235390[5:Res:28980.1,19676.0] || subclass(rest_relation,flip(symmetric_difference(u,inverse(u))))* -> member(ordered_pair(ordered_pair(v,w),rest_of(ordered_pair(w,v))),symmetrization_of(u))*.
% 299.99/300.67  235490[5:SpR:18840.1,28979.1] || member(u,subset_relation) subclass(rest_relation,rotate(v)) -> member(ordered_pair(ordered_pair(second(u),rest_of(u)),first(u)),v)*.
% 299.99/300.67  235504[8:Res:28979.1,66086.1] || subclass(rest_relation,rotate(complement(compose(element_relation,ordinal_numbers)))) member(ordered_pair(ordered_pair(u,rest_of(ordered_pair(v,u))),v),element_relation)* -> .
% 299.99/300.67  235511[5:Res:28979.1,5.0] || subclass(rest_relation,rotate(u))* subclass(u,v)* -> member(ordered_pair(ordered_pair(w,rest_of(ordered_pair(x,w))),x),v)*.
% 299.99/300.67  235516[5:Res:28979.1,3617.0] || subclass(rest_relation,rotate(symmetric_difference(u,v))) -> member(ordered_pair(ordered_pair(w,rest_of(ordered_pair(x,w))),x),union(u,v))*.
% 299.99/300.67  235517[5:Res:28979.1,19559.0] || subclass(rest_relation,rotate(symmetric_difference(u,singleton(u))))* -> member(ordered_pair(ordered_pair(v,rest_of(ordered_pair(w,v))),w),successor(u))*.
% 299.99/300.67  235518[5:Res:28979.1,19676.0] || subclass(rest_relation,rotate(symmetric_difference(u,inverse(u))))* -> member(ordered_pair(ordered_pair(v,rest_of(ordered_pair(w,v))),w),symmetrization_of(u))*.
% 299.99/300.67  235588[5:Res:28979.1,3995.0] || subclass(rest_relation,rotate(composition_function)) -> equal(compose(ordered_pair(u,rest_of(ordered_pair(singleton(singleton(singleton(v))),u))),singleton(v)),v)**.
% 299.99/300.67  235647[8:Res:116403.2,36719.1] operation(u) || member(v,ordinal_numbers) subclass(rest_relation,rest_of(u))* -> equal(ordered_pair(first(v),second(v)),v)**.
% 299.99/300.67  235662[15:Res:215659.1,36719.1] operation(u) || subclass(complement(cantor(u)),identity_relation)* -> equal(ordered_pair(first(range_of(identity_relation)),second(range_of(identity_relation))),range_of(identity_relation))**.
% 299.99/300.67  235690[8:Res:215662.1,36719.1] operation(u) || subclass(complement(cantor(u)),identity_relation)* -> equal(ordered_pair(first(singleton(v)),second(singleton(v))),singleton(v))**.
% 299.99/300.67  235794[5:Res:139.1,19113.0] || member(recursion_equation_functions(u),ordinal_numbers) -> subclass(sum_class(recursion_equation_functions(u)),v) subclass(not_subclass_element(sum_class(recursion_equation_functions(u)),v),cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.67  235922[7:Res:69478.2,5.0] || subclass(omega,symmetric_difference(u,v)) subclass(union(u,v),w)* -> equal(integer_of(x),identity_relation) member(x,w)*.
% 299.99/300.67  235928[7:Res:69478.2,8842.1] || subclass(omega,symmetric_difference(u,v)) subclass(ordinal_numbers,complement(union(u,v)))* -> equal(integer_of(unordered_pair(w,x)),identity_relation)**.
% 299.99/300.67  235933[7:Res:69478.2,7.0] || subclass(omega,symmetric_difference(u,v)) -> equal(integer_of(not_subclass_element(w,union(u,v))),identity_relation)** subclass(w,union(u,v)).
% 299.99/300.67  235949[7:Res:69478.2,8841.1] || subclass(omega,symmetric_difference(u,v)) subclass(ordinal_numbers,complement(union(u,v)))* -> equal(integer_of(ordered_pair(w,x)),identity_relation)**.
% 299.99/300.67  236092[0:Res:19564.1,5.0] || subclass(successor(u),v) -> subclass(symmetric_difference(u,singleton(u)),w) member(not_subclass_element(symmetric_difference(u,singleton(u)),w),v)*.
% 299.99/300.67  236144[0:Res:19680.1,5.0] || subclass(symmetrization_of(u),v) -> subclass(symmetric_difference(u,inverse(u)),w) member(not_subclass_element(symmetric_difference(u,inverse(u)),w),v)*.
% 299.99/300.67  236258[8:Res:230445.1,18897.0] || member(not_subclass_element(intersection(u,complement(union(v,identity_relation))),w),v)* -> subclass(intersection(u,complement(union(v,identity_relation))),w).
% 299.99/300.67  236260[5:Res:18819.1,18897.0] || member(not_subclass_element(intersection(u,complement(cross_product(ordinal_numbers,ordinal_numbers))),v),subset_relation)* -> subclass(intersection(u,complement(cross_product(ordinal_numbers,ordinal_numbers))),v).
% 299.99/300.67  236267[7:Res:13125.2,18897.0] || subclass(omega,u) -> equal(integer_of(not_subclass_element(intersection(v,complement(u)),w)),identity_relation)** subclass(intersection(v,complement(u)),w).
% 299.99/300.67  236314[8:Rew:160491.0,236217.1] || member(not_subclass_element(intersection(u,union(v,identity_relation)),w),symmetric_difference(ordinal_numbers,v))* -> subclass(intersection(u,union(v,identity_relation)),w).
% 299.99/300.67  236328[5:MRR:236257.0,41183.1] ||  -> member(not_subclass_element(intersection(u,complement(union(v,w))),x),complement(w))* subclass(intersection(u,complement(union(v,w))),x).
% 299.99/300.67  236329[5:MRR:236256.0,41183.1] ||  -> member(not_subclass_element(intersection(u,complement(union(v,w))),x),complement(v))* subclass(intersection(u,complement(union(v,w))),x).
% 299.99/300.67  236462[8:Res:230445.1,19016.0] || member(not_subclass_element(intersection(complement(union(u,identity_relation)),v),w),u)* -> subclass(intersection(complement(union(u,identity_relation)),v),w).
% 299.99/300.67  236464[5:Res:18819.1,19016.0] || member(not_subclass_element(intersection(complement(cross_product(ordinal_numbers,ordinal_numbers)),u),v),subset_relation)* -> subclass(intersection(complement(cross_product(ordinal_numbers,ordinal_numbers)),u),v).
% 299.99/300.67  236471[7:Res:13125.2,19016.0] || subclass(omega,u) -> equal(integer_of(not_subclass_element(intersection(complement(u),v),w)),identity_relation)** subclass(intersection(complement(u),v),w).
% 299.99/300.67  236531[8:Rew:160491.0,236406.1] || member(not_subclass_element(intersection(union(u,identity_relation),v),w),symmetric_difference(ordinal_numbers,u))* -> subclass(intersection(union(u,identity_relation),v),w).
% 299.99/300.67  236549[5:MRR:236461.0,41183.1] ||  -> member(not_subclass_element(intersection(complement(union(u,v)),w),x),complement(v))* subclass(intersection(complement(union(u,v)),w),x).
% 299.99/300.67  236550[5:MRR:236460.0,41183.1] ||  -> member(not_subclass_element(intersection(complement(union(u,v)),w),x),complement(u))* subclass(intersection(complement(union(u,v)),w),x).
% 299.99/300.67  236687[7:Obv:236671.2] || subclass(complement(u),omega) subclass(omega,u) -> equal(not_subclass_element(complement(u),v),identity_relation)** subclass(complement(u),v).
% 299.99/300.67  236821[8:Res:17392.2,66086.1] || subclass(u,complement(compose(element_relation,ordinal_numbers))) member(regular(intersection(u,v)),element_relation)* -> equal(intersection(u,v),identity_relation).
% 299.99/300.67  236828[7:Res:17392.2,5.0] || subclass(u,v)* subclass(v,w)* -> equal(intersection(u,x),identity_relation) member(regular(intersection(u,x)),w)*.
% 299.99/300.67  236833[7:Res:17392.2,3617.0] || subclass(u,symmetric_difference(v,w)) -> equal(intersection(u,x),identity_relation) member(regular(intersection(u,x)),union(v,w))*.
% 299.99/300.67  236834[7:Res:17392.2,19559.0] || subclass(u,symmetric_difference(v,singleton(v)))* -> equal(intersection(u,w),identity_relation) member(regular(intersection(u,w)),successor(v))*.
% 299.99/300.67  236835[7:Res:17392.2,19676.0] || subclass(u,symmetric_difference(v,inverse(v)))* -> equal(intersection(u,w),identity_relation) member(regular(intersection(u,w)),symmetrization_of(v))*.
% 299.99/300.67  236867[7:Res:17392.2,161.0] || subclass(u,omega) -> equal(intersection(u,v),identity_relation) equal(integer_of(regular(intersection(u,v))),regular(intersection(u,v)))**.
% 299.99/300.67  236925[8:Rew:66293.0,236797.1] || subclass(union(u,identity_relation),v) -> equal(symmetric_difference(complement(u),ordinal_numbers),identity_relation) member(regular(symmetric_difference(complement(u),ordinal_numbers)),v)*.
% 299.99/300.67  236926[7:Rew:33.0,236766.1] || subclass(cross_product(u,v),w) -> equal(restrict(x,u,v),identity_relation) member(regular(restrict(x,u,v)),w)*.
% 299.99/300.67  236981[26:Res:225888.1,8554.1] || equal(symmetric_difference(ordinal_numbers,intersection(u,v)),omega)** member(identity_relation,union(u,v)) -> member(identity_relation,symmetric_difference(u,v)).
% 299.99/300.67  237093[7:Res:13574.1,151988.0] ||  -> equal(intersection(u,intersection(v,complement(complement(w)))),identity_relation) member(regular(intersection(u,intersection(v,complement(complement(w))))),w)*.
% 299.99/300.67  237099[7:Res:13574.1,5.0] || subclass(u,v) -> equal(intersection(w,intersection(x,u)),identity_relation) member(regular(intersection(w,intersection(x,u))),v)*.
% 299.99/300.67  237101[7:Res:13574.1,26.0] ||  -> equal(intersection(u,intersection(v,intersection(w,x))),identity_relation) member(regular(intersection(u,intersection(v,intersection(w,x)))),x)*.
% 299.99/300.67  237102[7:Res:13574.1,25.0] ||  -> equal(intersection(u,intersection(v,intersection(w,x))),identity_relation) member(regular(intersection(u,intersection(v,intersection(w,x)))),w)*.
% 299.99/300.67  237134[7:Res:13574.1,8788.0] ||  -> equal(intersection(u,intersection(v,recursion_equation_functions(w))),identity_relation) subclass(regular(intersection(u,intersection(v,recursion_equation_functions(w)))),cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.67  237744[7:Res:13573.1,151988.0] ||  -> equal(intersection(u,intersection(complement(complement(v)),w)),identity_relation) member(regular(intersection(u,intersection(complement(complement(v)),w))),v)*.
% 299.99/300.67  237750[7:Res:13573.1,5.0] || subclass(u,v) -> equal(intersection(w,intersection(u,x)),identity_relation) member(regular(intersection(w,intersection(u,x))),v)*.
% 299.99/300.67  237752[7:Res:13573.1,26.0] ||  -> equal(intersection(u,intersection(intersection(v,w),x)),identity_relation) member(regular(intersection(u,intersection(intersection(v,w),x))),w)*.
% 299.99/300.67  237753[7:Res:13573.1,25.0] ||  -> equal(intersection(u,intersection(intersection(v,w),x)),identity_relation) member(regular(intersection(u,intersection(intersection(v,w),x))),v)*.
% 299.99/300.67  237785[7:Res:13573.1,8788.0] ||  -> equal(intersection(u,intersection(recursion_equation_functions(v),w)),identity_relation) subclass(regular(intersection(u,intersection(recursion_equation_functions(v),w))),cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.67  238555[8:Res:13572.2,66086.1] || subclass(u,complement(compose(element_relation,ordinal_numbers))) member(regular(intersection(v,u)),element_relation)* -> equal(intersection(v,u),identity_relation).
% 299.99/300.67  238562[7:Res:13572.2,5.0] || subclass(u,v)* subclass(v,w)* -> equal(intersection(x,u),identity_relation) member(regular(intersection(x,u)),w)*.
% 299.99/300.67  238567[7:Res:13572.2,3617.0] || subclass(u,symmetric_difference(v,w)) -> equal(intersection(x,u),identity_relation) member(regular(intersection(x,u)),union(v,w))*.
% 299.99/300.67  238568[7:Res:13572.2,19559.0] || subclass(u,symmetric_difference(v,singleton(v)))* -> equal(intersection(w,u),identity_relation) member(regular(intersection(w,u)),successor(v))*.
% 299.99/300.67  238569[7:Res:13572.2,19676.0] || subclass(u,symmetric_difference(v,inverse(v)))* -> equal(intersection(w,u),identity_relation) member(regular(intersection(w,u)),symmetrization_of(v))*.
% 299.99/300.67  238601[7:Res:13572.2,161.0] || subclass(u,omega) -> equal(intersection(v,u),identity_relation) equal(integer_of(regular(intersection(v,u))),regular(intersection(v,u)))**.
% 299.99/300.67  239256[7:Res:17397.1,151988.0] ||  -> equal(intersection(intersection(complement(complement(u)),v),w),identity_relation) member(regular(intersection(intersection(complement(complement(u)),v),w)),u)*.
% 299.99/300.67  239262[7:Res:17397.1,5.0] || subclass(u,v) -> equal(intersection(intersection(u,w),x),identity_relation) member(regular(intersection(intersection(u,w),x)),v)*.
% 299.99/300.67  239264[7:Res:17397.1,26.0] ||  -> equal(intersection(intersection(intersection(u,v),w),x),identity_relation) member(regular(intersection(intersection(intersection(u,v),w),x)),v)*.
% 299.99/300.67  239265[7:Res:17397.1,25.0] ||  -> equal(intersection(intersection(intersection(u,v),w),x),identity_relation) member(regular(intersection(intersection(intersection(u,v),w),x)),u)*.
% 299.99/300.67  239297[7:Res:17397.1,8788.0] ||  -> equal(intersection(intersection(recursion_equation_functions(u),v),w),identity_relation) subclass(regular(intersection(intersection(recursion_equation_functions(u),v),w)),cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.67  240091[7:Res:17396.1,151988.0] ||  -> equal(intersection(intersection(u,complement(complement(v))),w),identity_relation) member(regular(intersection(intersection(u,complement(complement(v))),w)),v)*.
% 299.99/300.67  240097[7:Res:17396.1,5.0] || subclass(u,v) -> equal(intersection(intersection(w,u),x),identity_relation) member(regular(intersection(intersection(w,u),x)),v)*.
% 299.99/300.67  240099[7:Res:17396.1,26.0] ||  -> equal(intersection(intersection(u,intersection(v,w)),x),identity_relation) member(regular(intersection(intersection(u,intersection(v,w)),x)),w)*.
% 299.99/300.67  240100[7:Res:17396.1,25.0] ||  -> equal(intersection(intersection(u,intersection(v,w)),x),identity_relation) member(regular(intersection(intersection(u,intersection(v,w)),x)),v)*.
% 299.99/300.67  240132[7:Res:17396.1,8788.0] ||  -> equal(intersection(intersection(u,recursion_equation_functions(v)),w),identity_relation) subclass(regular(intersection(intersection(u,recursion_equation_functions(v)),w)),cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.67  36310[0:SpR:3616.0,3618.1] || member(u,symmetric_difference(union(v,w),union(complement(v),complement(w))))* -> member(u,complement(symmetric_difference(complement(v),complement(w)))).
% 299.99/300.67  39642[2:Res:18950.0,9665.1] inductive(symmetric_difference(u,v)) || well_ordering(w,union(u,v)) -> member(least(w,symmetric_difference(u,v)),symmetric_difference(u,v))*.
% 299.99/300.67  19116[0:Res:2503.2,129.0] || subclass(u,v)* subclass(v,w)* well_ordering(x,w)* -> subclass(u,y)* member(least(x,v),v)*.
% 299.99/300.67  39528[5:Res:8832.1,5.0] || member(u,ordinal_numbers) subclass(intersection(complement(v),complement(w)),x)* -> member(u,union(v,w))* member(u,x)*.
% 299.99/300.67  36843[5:SpL:30.0,8825.1] || member(u,ordinal_numbers) subclass(union(v,w),x)* -> member(u,intersection(complement(v),complement(w)))* member(u,x)*.
% 299.99/300.67  39736[0:Res:8551.2,5.0] || member(u,cross_product(v,w))* member(u,x)* subclass(restrict(x,v,w),y)* -> member(u,y)*.
% 299.99/300.67  45736[5:Res:9865.3,8841.1] || member(u,ordinal_numbers)* member(v,ordinal_numbers) equal(compose(w,v),u)* subclass(ordinal_numbers,complement(compose_class(w)))* -> .
% 299.99/300.67  39629[5:Res:8663.0,9665.1] inductive(compose(u,v)) || well_ordering(w,cross_product(ordinal_numbers,ordinal_numbers)) -> member(least(w,compose(u,v)),compose(u,v))*.
% 299.99/300.67  19027[0:Res:313.1,897.0] ||  -> subclass(intersection(restrict(u,v,w),x),y) member(not_subclass_element(intersection(restrict(u,v,w),x),y),cross_product(v,w))*.
% 299.99/300.67  18908[0:Res:303.1,897.0] ||  -> subclass(intersection(u,restrict(v,w,x)),y) member(not_subclass_element(intersection(u,restrict(v,w,x)),y),cross_product(w,x))*.
% 299.99/300.67  41047[0:Rew:3606.0,40996.0] ||  -> subclass(symmetric_difference(cross_product(u,v),w),x) member(not_subclass_element(symmetric_difference(cross_product(u,v),w),x),complement(restrict(w,u,v)))*.
% 299.99/300.67  40927[0:Rew:3603.0,40880.0] ||  -> subclass(symmetric_difference(u,cross_product(v,w)),x) member(not_subclass_element(symmetric_difference(u,cross_product(v,w)),x),complement(restrict(u,v,w)))*.
% 299.99/300.67  50028[5:SpL:18840.1,40.0] || member(u,subset_relation) member(ordered_pair(u,v),flip(w)) -> member(ordered_pair(ordered_pair(second(u),first(u)),v),w)*.
% 299.99/300.67  50029[5:SpL:18840.1,37.0] || member(u,subset_relation) member(ordered_pair(u,v),rotate(w)) -> member(ordered_pair(ordered_pair(second(u),v),first(u)),w)*.
% 299.99/300.67  50856[5:Res:49995.1,12.0] || member(unordered_pair(u,v),subset_relation) -> equal(singleton(first(unordered_pair(u,v))),v)** equal(singleton(first(unordered_pair(u,v))),u)**.
% 299.99/300.67  50852[5:Res:49995.1,490.0] || member(intersection(complement(u),complement(v)),subset_relation) member(singleton(first(intersection(complement(u),complement(v)))),union(u,v))* -> .
% 299.99/300.67  39570[5:Res:9632.1,3689.0] || equal(complement(complement(ordered_pair(u,v))),ordinal_numbers)** -> equal(singleton(w),unordered_pair(u,singleton(v)))* equal(singleton(w),singleton(u)).
% 299.99/300.67  39739[5:Res:8551.2,8843.1] || member(singleton(u),cross_product(v,w))* member(singleton(u),x)* subclass(ordinal_numbers,complement(restrict(x,v,w)))* -> .
% 299.99/300.67  46154[0:Rew:126.0,46146.2,126.0,46146.0] || member(u,segment(v,w,u))* section(v,singleton(u),w) -> equal(segment(v,w,u),singleton(u)).
% 299.99/300.67  43716[5:Res:8645.1,8554.1] || subclass(ordinal_numbers,complement(intersection(u,v))) member(singleton(w),union(u,v)) -> member(singleton(w),symmetric_difference(u,v))*.
% 299.99/300.67  46932[5:Res:8655.0,9421.0] || member(u,v)* -> equal(ordered_pair(first(ordered_pair(u,singleton(w))),second(ordered_pair(u,singleton(w)))),ordered_pair(u,singleton(w)))**.
% 299.99/300.67  9602[5:Rew:963.0,9599.2] || member(singleton(u),u)* member(singleton(singleton(singleton(u))),cross_product(ordinal_numbers,ordinal_numbers))* -> member(singleton(singleton(singleton(u))),element_relation).
% 299.99/300.67  116623[8:Rew:116078.0,19901.1] || subclass(u,v) subclass(cantor(restrict(cross_product(v,u),w,x)),u)* -> section(cross_product(w,x),u,v).
% 299.99/300.67  116624[8:Rew:116078.0,39781.0] || equal(cantor(restrict(cross_product(u,v),w,x)),v)** subclass(v,u) -> section(cross_product(w,x),v,u).
% 299.99/300.67  130659[5:Res:41371.0,897.0] ||  -> subclass(complement(complement(restrict(u,v,w))),x) member(not_subclass_element(complement(complement(restrict(u,v,w))),x),cross_product(v,w))*.
% 299.99/300.67  131399[0:SpL:3616.0,18794.1] || member(u,symmetric_difference(union(v,w),union(complement(v),complement(w))))* member(u,symmetric_difference(complement(v),complement(w))) -> .
% 299.99/300.67  131564[0:Res:2504.1,12.0] || subclass(ordered_pair(u,v),unordered_pair(w,x))* -> equal(unordered_pair(u,singleton(v)),x) equal(unordered_pair(u,singleton(v)),w).
% 299.99/300.67  134107[5:Res:133837.1,21.0] || well_ordering(ordinal_numbers,complement(cross_product(u,v)))* -> equal(ordered_pair(first(singleton(singleton(w))),second(singleton(singleton(w)))),singleton(singleton(w)))**.
% 299.99/300.67  134787[8:MRR:134747.0,41183.1] || subclass(rest_relation,rest_of(u)) member(not_subclass_element(v,intersection(w,cantor(u))),w)* -> subclass(v,intersection(w,cantor(u))).
% 299.99/300.67  136690[5:Res:8827.2,18791.0] || member(u,ordinal_numbers) subclass(rest_relation,symmetric_difference(complement(v),complement(w))) -> member(ordered_pair(u,rest_of(u)),union(v,w))*.
% 299.99/300.67  136666[5:Res:60219.0,18791.0] ||  -> subclass(u,complement(symmetric_difference(complement(v),complement(w)))) member(not_subclass_element(u,complement(symmetric_difference(complement(v),complement(w)))),union(v,w))*.
% 299.99/300.67  136656[5:Res:51313.1,18791.0] || member(singleton(symmetric_difference(complement(u),complement(v))),subset_relation) -> member(first(singleton(symmetric_difference(complement(u),complement(v)))),union(u,v))*.
% 299.99/300.67  140294[0:Res:3652.1,19124.0] || section(u,singleton(v),w) -> subclass(segment(u,w,v),x) equal(not_subclass_element(segment(u,w,v),x),v)**.
% 299.99/300.67  140467[0:Rew:163.0,140333.1] || member(not_subclass_element(union(u,v),symmetric_difference(u,v)),complement(intersection(u,v)))* -> subclass(union(u,v),symmetric_difference(u,v)).
% 299.99/300.67  147924[5:SpL:3603.0,18581.1] || member(u,ordinal_numbers) subclass(ordinal_numbers,symmetric_difference(v,cross_product(w,x))) -> member(sum_class(u),complement(restrict(v,w,x)))*.
% 299.99/300.67  147923[5:SpL:3606.0,18581.1] || member(u,ordinal_numbers) subclass(ordinal_numbers,symmetric_difference(cross_product(v,w),x)) -> member(sum_class(u),complement(restrict(x,v,w)))*.
% 299.99/300.67  148887[8:Res:148858.1,116155.1] || subclass(cantor(restrict(u,v,complement(subset_relation))),inverse(subset_relation))* subclass(complement(subset_relation),v) -> section(u,complement(subset_relation),v).
% 299.99/300.67  152919[0:Res:139.1,19121.0] || member(intersection(u,v),ordinal_numbers) -> subclass(sum_class(intersection(u,v)),w) member(not_subclass_element(sum_class(intersection(u,v)),w),u)*.
% 299.99/300.67  152868[0:SpL:3603.0,19121.0] || subclass(u,symmetric_difference(v,cross_product(w,x))) -> subclass(u,y) member(not_subclass_element(u,y),complement(restrict(v,w,x)))*.
% 299.99/300.67  152867[0:SpL:3606.0,19121.0] || subclass(u,symmetric_difference(cross_product(v,w),x)) -> subclass(u,y) member(not_subclass_element(u,y),complement(restrict(x,v,w)))*.
% 299.99/300.67  153043[0:Res:139.1,19120.0] || member(intersection(u,v),ordinal_numbers) -> subclass(sum_class(intersection(u,v)),w) member(not_subclass_element(sum_class(intersection(u,v)),w),v)*.
% 299.99/300.67  153380[0:Res:919.1,161.0] ||  -> subclass(restrict(omega,u,v),w) equal(integer_of(not_subclass_element(restrict(omega,u,v),w)),not_subclass_element(restrict(omega,u,v),w))**.
% 299.99/300.67  153373[0:Res:919.1,898.0] ||  -> subclass(restrict(restrict(u,v,w),x,y),z) member(not_subclass_element(restrict(restrict(u,v,w),x,y),z),u)*.
% 299.99/300.67  153352[0:Res:919.1,3617.0] ||  -> subclass(restrict(symmetric_difference(u,v),w,x),y) member(not_subclass_element(restrict(symmetric_difference(u,v),w,x),y),union(u,v))*.
% 299.99/300.67  153333[0:SpR:916.0,919.1] ||  -> subclass(restrict(cross_product(u,v),w,x),y) member(not_subclass_element(restrict(cross_product(w,x),u,v),y),cross_product(u,v))*.
% 299.99/300.67  155296[0:SpL:154737.1,8554.1] || subclass(u,v) member(w,union(v,u)) member(w,complement(u)) -> member(w,symmetric_difference(v,u))*.
% 299.99/300.67  155861[5:Rew:155653.0,155847.2] || transitive(complement(compose(complement(element_relation),inverse(element_relation))),ordinal_numbers)* subclass(subset_relation,compose(subset_relation,subset_relation)) -> equal(compose(subset_relation,subset_relation),subset_relation).
% 299.99/300.67  156415[5:SpR:155665.0,154737.1] || subclass(union(subset_relation,cross_product(ordinal_numbers,ordinal_numbers)),complement(subset_relation))* -> equal(symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers)),union(subset_relation,cross_product(ordinal_numbers,ordinal_numbers))).
% 299.99/300.67  156414[5:SpR:155665.0,27.2] || member(u,union(subset_relation,cross_product(ordinal_numbers,ordinal_numbers))) member(u,complement(subset_relation)) -> member(u,symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers)))*.
% 299.99/300.67  156524[5:SpR:155666.0,154737.1] || subclass(union(cross_product(ordinal_numbers,ordinal_numbers),subset_relation),complement(subset_relation))* -> equal(symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation),union(cross_product(ordinal_numbers,ordinal_numbers),subset_relation)).
% 299.99/300.67  156523[5:SpR:155666.0,27.2] || member(u,union(cross_product(ordinal_numbers,ordinal_numbers),subset_relation)) member(u,complement(subset_relation)) -> member(u,symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation))*.
% 299.99/300.67  159648[5:Rew:50855.1,159619.2] || member(singleton(u),subset_relation) member(singleton(singleton(u)),rest_of(v))* -> equal(restrict(v,u,ordinal_numbers),first(singleton(u))).
% 299.99/300.67  161557[8:Rew:160496.0,62161.3] || connected(u,v)* member(w,v)* member(x,v)* -> member(ordered_pair(x,w),complement(complement(symmetrization_of(u))))*.
% 299.99/300.67  28650[5:SpR:8647.0,8826.2] || member(flip(cross_product(u,ordinal_numbers)),ordinal_numbers) subclass(domain_relation,v) -> member(ordered_pair(flip(cross_product(u,ordinal_numbers)),inverse(u)),v)*.
% 299.99/300.67  18659[0:SpR:126.0,3767.1] operation(restrict(u,v,singleton(w))) ||  -> equal(intersection(segment(u,v,w),x),intersection(x,segment(u,v,w)))*.
% 299.99/300.67  140377[8:SpL:116209.1,47534.0] operation(u) || member(not_subclass_element(cantor(u),intersection(cantor(u),v)),v)* -> subclass(cantor(u),intersection(v,cantor(u))).
% 299.99/300.67  116739[8:Rew:116078.0,36720.1] operation(u) || equal(complement(complement(cantor(u))),ordinal_numbers)** -> equal(ordered_pair(first(singleton(v)),second(singleton(v))),singleton(v))**.
% 299.99/300.67  165629[5:Res:143198.1,8554.1] || equal(complement(intersection(u,v)),ordinal_numbers) member(singleton(w),union(u,v)) -> member(singleton(w),symmetric_difference(u,v))*.
% 299.99/300.67  176376[5:Res:39298.1,8802.1] || subclass(ordinal_numbers,complement(complement(cross_product(ordinal_numbers,ordinal_numbers))))* equal(compose(u,v),w) -> member(ordered_pair(v,w),compose_class(u))*.
% 299.99/300.67  62998[8:Res:15426.1,3689.0] || subclass(domain_relation,ordered_pair(u,v))* -> equal(unordered_pair(u,singleton(v)),ordered_pair(identity_relation,identity_relation)) equal(ordered_pair(identity_relation,identity_relation),singleton(u)).
% 299.99/300.67  167274[8:Res:919.1,14681.0] || member(not_subclass_element(restrict(regular(u),v,w),x),u)* -> subclass(restrict(regular(u),v,w),x) equal(u,identity_relation).
% 299.99/300.67  17316[7:Res:13227.2,129.0] || subclass(u,v)* subclass(v,w)* well_ordering(x,w)* -> equal(u,identity_relation) member(least(x,v),v)*.
% 299.99/300.67  13510[7:Rew:13036.0,9606.2] || equal(sum_class(u),u) well_ordering(v,u) -> equal(sum_class(u),identity_relation) member(least(v,sum_class(u)),sum_class(u))*.
% 299.99/300.67  165307[8:Res:162023.0,13070.0] || well_ordering(u,complement(inverse(identity_relation))) -> equal(complement(symmetrization_of(identity_relation)),identity_relation) member(least(u,complement(symmetrization_of(identity_relation))),complement(symmetrization_of(identity_relation)))*.
% 299.99/300.67  66991[8:Res:66340.0,13113.0] || well_ordering(u,union(v,identity_relation)) -> equal(segment(u,symmetric_difference(complement(v),ordinal_numbers),least(u,symmetric_difference(complement(v),ordinal_numbers))),identity_relation)**.
% 299.99/300.67  19324[7:Res:18950.0,13070.0] || well_ordering(u,union(v,w)) -> equal(symmetric_difference(v,w),identity_relation) member(least(u,symmetric_difference(v,w)),symmetric_difference(v,w))*.
% 299.99/300.67  19444[7:Res:18946.0,13113.0] || well_ordering(u,cross_product(v,w)) -> equal(segment(u,restrict(x,v,w),least(u,restrict(x,v,w))),identity_relation)**.
% 299.99/300.67  13430[7:Rew:13036.0,10952.1] || subclass(omega,flip(u)) -> equal(integer_of(ordered_pair(ordered_pair(v,w),x)),identity_relation) member(ordered_pair(ordered_pair(w,v),x),u)*.
% 299.99/300.67  13431[7:Rew:13036.0,10953.1] || subclass(omega,rotate(u)) -> equal(integer_of(ordered_pair(ordered_pair(v,w),x)),identity_relation) member(ordered_pair(ordered_pair(w,x),v),u)*.
% 299.99/300.67  165162[8:Res:162025.0,13113.0] || well_ordering(u,symmetric_difference(ordinal_numbers,v)) -> equal(segment(u,complement(union(v,identity_relation)),least(u,complement(union(v,identity_relation)))),identity_relation)**.
% 299.99/300.67  165137[7:Res:155657.1,13113.0] || transitive(subset_relation,ordinal_numbers) well_ordering(u,subset_relation) -> equal(segment(u,compose(subset_relation,subset_relation),least(u,compose(subset_relation,subset_relation))),identity_relation)**.
% 299.99/300.67  191898[7:MRR:191896.2,13039.0] || well_ordering(u,cross_product(ordinal_numbers,ordinal_numbers)) subclass(singleton(least(u,element_relation)),element_relation) -> section(u,singleton(least(u,element_relation)),element_relation)*.
% 299.99/300.67  191924[7:MRR:191922.2,13039.0] || well_ordering(u,cross_product(ordinal_numbers,ordinal_numbers)) subclass(singleton(least(u,successor_relation)),successor_relation) -> section(u,singleton(least(u,successor_relation)),successor_relation)*.
% 299.99/300.67  191982[7:MRR:191980.2,13039.0] || well_ordering(u,cross_product(ordinal_numbers,ordinal_numbers)) subclass(singleton(least(u,domain_relation)),domain_relation) -> section(u,singleton(least(u,domain_relation)),domain_relation)*.
% 299.99/300.67  192004[7:MRR:192002.2,13039.0] || well_ordering(u,cross_product(ordinal_numbers,ordinal_numbers)) subclass(singleton(least(u,rest_relation)),rest_relation) -> section(u,singleton(least(u,rest_relation)),rest_relation)*.
% 299.99/300.67  192024[7:MRR:192022.2,13039.0] || well_ordering(u,cross_product(ordinal_numbers,ordinal_numbers)) subclass(singleton(least(u,union_of_range_map)),union_of_range_map) -> section(u,singleton(least(u,union_of_range_map)),union_of_range_map)*.
% 299.99/300.67  193619[8:SpR:33.0,15320.1] || asymmetric(cross_product(u,v),singleton(w)) -> equal(segment(restrict(inverse(cross_product(u,v)),u,v),singleton(w),w),identity_relation)**.
% 299.99/300.67  132215[2:Res:39609.2,3617.0] inductive(symmetric_difference(u,v)) || well_ordering(w,symmetric_difference(u,v)) -> member(least(w,symmetric_difference(u,v)),union(u,v))*.
% 299.99/300.67  49993[5:MRR:49991.2,41096.1] || well_ordering(cross_product(u,ordinal_numbers),ordinal_numbers)* member(v,u)* subclass(ordinal_numbers,w) well_ordering(cross_product(u,ordinal_numbers),w)* -> .
% 299.99/300.67  131208[5:Res:39607.2,897.0] inductive(restrict(u,v,w)) || well_ordering(x,ordinal_numbers) -> member(least(x,restrict(u,v,w)),cross_product(v,w))*.
% 299.99/300.67  141694[8:Rew:141387.0,131196.2] inductive(symmetric_difference(sum_class(u),ordinal_numbers)) || well_ordering(v,ordinal_numbers) -> member(least(v,symmetric_difference(ordinal_numbers,sum_class(u))),complement(sum_class(u)))*.
% 299.99/300.67  141866[8:Rew:141388.0,131195.2] inductive(symmetric_difference(inverse(u),ordinal_numbers)) || well_ordering(v,ordinal_numbers) -> member(least(v,symmetric_difference(ordinal_numbers,inverse(u))),complement(inverse(u)))*.
% 299.99/300.67  142293[8:Rew:141390.0,131193.2] inductive(symmetric_difference(cantor(u),ordinal_numbers)) || well_ordering(v,ordinal_numbers) -> member(least(v,symmetric_difference(ordinal_numbers,cantor(u))),complement(cantor(u)))*.
% 299.99/300.67  18837[7:Res:13237.2,897.0] || well_ordering(u,ordinal_numbers) -> equal(restrict(v,w,x),identity_relation) member(least(u,restrict(v,w,x)),cross_product(w,x))*.
% 299.99/300.67  148882[8:Res:148858.1,141.1] || subclass(sum_class(complement(subset_relation)),inverse(subset_relation))* well_ordering(element_relation,complement(subset_relation)) -> equal(complement(subset_relation),ordinal_numbers) member(complement(subset_relation),ordinal_numbers).
% 299.99/300.67  9637[5:Res:8705.1,129.0] || member(u,ordinal_numbers) subclass(singleton(u),v)* well_ordering(w,v)* -> member(least(w,singleton(u)),singleton(u))*.
% 299.99/300.67  161743[5:Rew:155653.0,153610.2] inductive(restrict(complement(compose(complement(element_relation),inverse(element_relation))),ordinal_numbers,ordinal_numbers)) || well_ordering(u,ordinal_numbers) -> member(least(u,subset_relation),subset_relation)*.
% 299.99/300.67  161818[5:Rew:155653.0,153609.2,155653.0,153609.1] inductive(restrict(complement(compose(complement(element_relation),inverse(element_relation))),ordinal_numbers,ordinal_numbers)) || well_ordering(u,subset_relation) -> member(least(u,subset_relation),subset_relation)*.
% 299.99/300.67  45467[5:Res:8665.1,9420.2] function(cross_product(u,v)) || member(w,v)* member(x,u)* -> member(ordered_pair(x,w),cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.67  130960[5:Res:9618.2,9876.0] || member(ordered_pair(u,v),cross_product(ordinal_numbers,ordinal_numbers))* subclass(composition_function,w)* subclass(w,x)* well_ordering(ordinal_numbers,x)* -> .
% 299.99/300.67  46647[5:Res:9618.2,149.0] || member(ordered_pair(u,v),cross_product(ordinal_numbers,ordinal_numbers))* subclass(composition_function,rest_relation) -> equal(ordered_pair(v,compose(u,v)),rest_of(u))**.
% 299.99/300.67  116908[8:Rew:116078.0,46640.2] || member(ordered_pair(u,v),cross_product(ordinal_numbers,ordinal_numbers))* subclass(composition_function,domain_relation) -> equal(ordered_pair(v,compose(u,v)),cantor(u))**.
% 299.99/300.67  159828[0:SpL:963.0,3995.0] || member(singleton(singleton(singleton(singleton(singleton(singleton(u)))))),composition_function)* -> equal(compose(singleton(singleton(singleton(singleton(u)))),singleton(u)),u)**.
% 299.99/300.67  159847[5:Rew:50855.1,159818.2] || member(singleton(u),subset_relation) member(ordered_pair(v,singleton(singleton(u))),composition_function)* -> equal(compose(v,u),first(singleton(u))).
% 299.99/300.67  46648[5:Res:9618.2,49.0] || member(ordered_pair(u,v),cross_product(ordinal_numbers,ordinal_numbers))* subclass(composition_function,successor_relation) -> equal(ordered_pair(v,compose(u,v)),successor(u))**.
% 299.99/300.67  18258[8:SpR:18040.1,8801.1] || equal(compose_class(u),domain_relation) member(ordered_pair(u,identity_relation),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(u,ordered_pair(identity_relation,identity_relation)),composition_function)*.
% 299.99/300.67  15914[7:SpR:13585.1,8801.1] single_valued_class(u) || member(ordered_pair(u,inverse(u)),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(u,ordered_pair(inverse(u),identity_relation)),composition_function)*.
% 299.99/300.67  15915[7:SpR:13584.1,8801.1] function(u) || member(ordered_pair(u,inverse(u)),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(u,ordered_pair(inverse(u),identity_relation)),composition_function)*.
% 299.99/300.67  194377[21:MRR:194357.3,14676.0] || member(u,subset_relation) member(first(u),cantor(v)) member(ordered_pair(v,u),cross_product(ordinal_numbers,cross_product(ordinal_numbers,ordinal_numbers)))* -> .
% 299.99/300.67  196098[18:Res:190510.1,21.0] || subclass(inverse(identity_relation),cross_product(u,v))* -> equal(ordered_pair(first(regular(symmetrization_of(identity_relation))),second(regular(symmetrization_of(identity_relation)))),regular(symmetrization_of(identity_relation)))**.
% 299.99/300.67  196321[8:SpR:161356.2,50064.1] || member(u,ordinal_numbers) member(not_subclass_element(identity_relation,identity_relation),subset_relation) -> member(u,cantor(v)) member(range__dfg(v,u,ordinal_numbers),ordinal_numbers)*.
% 299.99/300.67  196440[21:Rew:196372.1,161598.2] || member(u,ordinal_numbers) subclass(domain_relation,intersection(complement(v),complement(w))) member(ordered_pair(u,identity_relation),union(v,w))* -> .
% 299.99/300.67  196527[21:Rew:196372.1,196426.2] || member(u,ordinal_numbers) subclass(domain_relation,unordered_pair(v,w))* -> equal(ordered_pair(u,identity_relation),w)* equal(ordered_pair(u,identity_relation),v)*.
% 299.99/300.67  197190[7:Obv:197175.1] || subclass(unordered_pair(u,v),w)* -> equal(regular(unordered_pair(u,v)),v) equal(unordered_pair(u,v),identity_relation) member(u,w).
% 299.99/300.67  197192[7:Obv:197167.1] || subclass(unordered_pair(u,v),w)* -> equal(regular(unordered_pair(u,v)),u) equal(unordered_pair(u,v),identity_relation) member(v,w).
% 299.99/300.67  199101[18:Res:194543.0,13362.0] || subclass(symmetrization_of(identity_relation),u)* well_ordering(omega,u) -> equal(integer_of(ordered_pair(regular(symmetrization_of(identity_relation)),least(omega,symmetrization_of(identity_relation)))),identity_relation)**.
% 299.99/300.67  199098[18:Res:190499.0,13362.0] || subclass(inverse(identity_relation),u)* well_ordering(omega,u) -> equal(integer_of(ordered_pair(regular(symmetrization_of(identity_relation)),least(omega,inverse(identity_relation)))),identity_relation)**.
% 299.99/300.67  199091[7:Res:13049.1,13362.0] || subclass(ordinal_numbers,u) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(identity_relation,least(omega,u))),identity_relation)**.
% 299.99/300.67  199087[7:Res:192149.1,13362.0] || equal(u,ordinal_numbers) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(identity_relation,least(omega,u))),identity_relation)**.
% 299.99/300.67  199004[7:Res:60996.1,13362.0] || subclass(ordinal_numbers,u) well_ordering(omega,u)* -> equal(v,identity_relation) equal(integer_of(ordered_pair(regular(v),least(omega,ordinal_numbers))),identity_relation)**.
% 299.99/300.67  198985[7:Res:18517.1,13362.0] || subclass(ordinal_numbers,u) well_ordering(omega,u)* -> equal(singleton(v),identity_relation) equal(integer_of(ordered_pair(v,least(omega,ordinal_numbers))),identity_relation)**.
% 299.99/300.67  198984[7:Res:66492.1,13362.0] || subclass(ordinal_numbers,u) well_ordering(omega,u)* -> equal(integer_of(v),identity_relation) equal(integer_of(ordered_pair(v,least(omega,ordinal_numbers))),identity_relation)**.
% 299.99/300.67  198978[7:Res:13072.1,13362.0] || subclass(u,v)* well_ordering(omega,v)* -> equal(u,identity_relation) equal(integer_of(ordered_pair(regular(u),least(omega,u))),identity_relation)**.
% 299.99/300.67  198971[7:Res:8646.1,13362.0] || subclass(ordinal_numbers,u) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(omega,least(omega,u))),identity_relation)**.
% 299.99/300.67  198970[7:Res:143200.1,13362.0] || equal(u,ordinal_numbers) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(omega,least(omega,u))),identity_relation)**.
% 299.99/300.67  198967[7:Res:13061.0,13362.0] || subclass(omega,u) well_ordering(omega,u)* -> equal(integer_of(v),identity_relation) equal(integer_of(ordered_pair(v,least(omega,omega))),identity_relation)**.
% 299.99/300.67  28649[5:SpR:8648.0,8826.2] || member(restrict(element_relation,ordinal_numbers,u),ordinal_numbers) subclass(domain_relation,v) -> member(ordered_pair(restrict(element_relation,ordinal_numbers,u),sum_class(u)),v)*.
% 299.99/300.67  135128[8:Res:135059.1,117602.1] function(u) || equal(rest_of(cantor(v)),rest_relation) equal(cantor(cantor(w)),cantor(u)) -> compatible(u,w,v)*.
% 299.99/300.67  37694[5:SoR:18511.0,10858.2] single_valued_class(recursion(u,successor_relation,union_of_range_map)) || equal(recursion(u,successor_relation,union_of_range_map),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordinal_add(u,v),ordinal_numbers)*.
% 299.99/300.67  195691[7:Res:13225.3,50007.0] || member(u,ordinal_numbers) subclass(u,subset_relation) subclass(ordinal_numbers,v) -> equal(u,identity_relation) member(apply(choice,u),v)*.
% 299.99/300.67  195679[7:Res:13225.3,5.0] || member(u,ordinal_numbers) subclass(u,v)* subclass(v,w)* -> equal(u,identity_relation) member(apply(choice,u),w)*.
% 299.99/300.67  195686[7:Res:13225.3,19676.0] || member(u,ordinal_numbers) subclass(u,symmetric_difference(v,inverse(v)))* -> equal(u,identity_relation) member(apply(choice,u),symmetrization_of(v))*.
% 299.99/300.67  195685[7:Res:13225.3,19559.0] || member(u,ordinal_numbers) subclass(u,symmetric_difference(v,singleton(v)))* -> equal(u,identity_relation) member(apply(choice,u),successor(v))*.
% 299.99/300.67  195684[7:Res:13225.3,3617.0] || member(u,ordinal_numbers) subclass(u,symmetric_difference(v,w)) -> equal(u,identity_relation) member(apply(choice,u),union(v,w))*.
% 299.99/300.67  195673[8:Res:13225.3,66086.1] || member(u,ordinal_numbers) subclass(u,complement(compose(element_relation,ordinal_numbers)))* member(apply(choice,u),element_relation) -> equal(u,identity_relation).
% 299.99/300.67  18208[7:Res:13069.2,3617.0] || member(symmetric_difference(u,v),ordinal_numbers) -> equal(symmetric_difference(u,v),identity_relation) member(apply(choice,symmetric_difference(u,v)),union(u,v))*.
% 299.99/300.67  197705[7:Res:13247.2,152.0] || member(intersection(u,recursion_equation_functions(v)),ordinal_numbers) -> equal(intersection(u,recursion_equation_functions(v)),identity_relation) function(apply(choice,intersection(u,recursion_equation_functions(v))))*.
% 299.99/300.67  197693[7:Res:13247.2,50033.0] || member(intersection(u,subset_relation),ordinal_numbers) equal(complement(apply(choice,intersection(u,subset_relation))),ordinal_numbers)** -> equal(intersection(u,subset_relation),identity_relation).
% 299.99/300.67  197404[7:Res:13246.2,50033.0] || member(intersection(subset_relation,u),ordinal_numbers) equal(complement(apply(choice,intersection(subset_relation,u))),ordinal_numbers)** -> equal(intersection(subset_relation,u),identity_relation).
% 299.99/300.67  197416[7:Res:13246.2,152.0] || member(intersection(recursion_equation_functions(u),v),ordinal_numbers) -> equal(intersection(recursion_equation_functions(u),v),identity_relation) function(apply(choice,intersection(recursion_equation_functions(u),v)))*.
% 299.99/300.67  194657[7:Res:13125.2,13313.1] || subclass(omega,u) member(complement(u),ordinal_numbers) -> equal(integer_of(apply(choice,complement(u))),identity_relation)** equal(complement(u),identity_relation).
% 299.99/300.67  194645[8:Res:156922.1,13313.1] || member(apply(choice,complement(complement(subset_relation))),inverse(subset_relation))* member(complement(complement(subset_relation)),ordinal_numbers) -> equal(complement(complement(subset_relation)),identity_relation).
% 299.99/300.67  148512[5:SpL:3603.0,18545.1] || member(u,ordinal_numbers) subclass(ordinal_numbers,symmetric_difference(v,cross_product(w,x))) -> member(power_class(u),complement(restrict(v,w,x)))*.
% 299.99/300.67  148511[5:SpL:3606.0,18545.1] || member(u,ordinal_numbers) subclass(ordinal_numbers,symmetric_difference(cross_product(v,w),x)) -> member(power_class(u),complement(restrict(x,v,w)))*.
% 299.99/300.67  40061[5:Res:62.1,8842.1] || member(ordered_pair(u,unordered_pair(v,w)),compose(x,y))* subclass(ordinal_numbers,complement(image(x,image(y,singleton(u))))) -> .
% 299.99/300.67  39282[5:Res:62.1,8841.1] || member(ordered_pair(u,ordered_pair(v,w)),compose(x,y))* subclass(ordinal_numbers,complement(image(x,image(y,singleton(u))))) -> .
% 299.99/300.67  46048[0:Res:10.1,9470.1] || equal(u,image(v,image(w,singleton(x))))* member(ordered_pair(x,y),compose(v,w))* -> member(y,u)*.
% 299.99/300.67  127131[5:Res:62.1,125973.1] || member(ordered_pair(u,least(element_relation,omega)),compose(v,w))* subclass(ordinal_numbers,complement(image(v,image(w,singleton(u))))) -> .
% 299.99/300.67  126666[5:Res:62.1,125896.1] || member(ordered_pair(u,least(element_relation,omega)),compose(v,w))* subclass(omega,complement(image(v,image(w,singleton(u))))) -> .
% 299.99/300.67  81329[8:Res:62.1,15565.1] || member(ordered_pair(u,ordered_pair(identity_relation,identity_relation)),compose(v,w))* subclass(domain_relation,complement(image(v,image(w,singleton(u))))) -> .
% 299.99/300.67  195316[16:Rew:195224.0,193379.2] || member(u,ordinal_numbers) subclass(power_class(complement(singleton(identity_relation))),v)* -> member(u,image(element_relation,singleton(identity_relation)))* member(u,v)*.
% 299.99/300.67  195325[16:Rew:195224.0,193300.0] ||  -> equal(complement(intersection(union(image(element_relation,singleton(identity_relation)),u),complement(v))),union(intersection(power_class(complement(singleton(identity_relation))),complement(u)),v))**.
% 299.99/300.67  195331[16:Rew:195224.0,193323.0] ||  -> equal(complement(intersection(union(u,image(element_relation,singleton(identity_relation))),complement(v))),union(intersection(complement(u),power_class(complement(singleton(identity_relation)))),v))**.
% 299.99/300.67  195391[16:Rew:195224.0,193327.0] ||  -> equal(complement(intersection(complement(u),union(image(element_relation,singleton(identity_relation)),v))),union(u,intersection(power_class(complement(singleton(identity_relation))),complement(v))))**.
% 299.99/300.67  195395[16:Rew:195224.0,193334.0] ||  -> equal(complement(intersection(complement(u),union(v,image(element_relation,singleton(identity_relation))))),union(u,intersection(complement(v),power_class(complement(singleton(identity_relation))))))**.
% 299.99/300.67  46050[0:Res:52.1,9470.1] inductive(image(u,singleton(v))) || member(ordered_pair(v,w),compose(successor_relation,u))* -> member(w,image(u,singleton(v))).
% 299.99/300.67  39328[5:Res:9006.3,5.0] function(u) || member(v,ordinal_numbers) subclass(ordinal_numbers,w)* subclass(w,x)* -> member(image(u,v),x)*.
% 299.99/300.67  39345[5:Res:9006.3,3617.0] function(u) || member(v,ordinal_numbers) subclass(ordinal_numbers,symmetric_difference(w,x)) -> member(image(u,v),union(w,x))*.
% 299.99/300.67  57220[5:Res:9006.3,19676.0] function(u) || member(v,ordinal_numbers) subclass(ordinal_numbers,symmetric_difference(w,inverse(w)))* -> member(image(u,v),symmetrization_of(w))*.
% 299.99/300.67  57153[5:Res:9006.3,19559.0] function(u) || member(v,ordinal_numbers) subclass(ordinal_numbers,symmetric_difference(w,singleton(w)))* -> member(image(u,v),successor(w))*.
% 299.99/300.67  69183[8:Res:9006.3,66086.1] function(u) || member(v,ordinal_numbers) subclass(ordinal_numbers,complement(compose(element_relation,ordinal_numbers)))* member(image(u,v),element_relation)* -> .
% 299.99/300.67  132976[5:SpR:19485.0,8977.2] || member(intersection(complement(u),complement(singleton(u))),ordinal_numbers)* subclass(ordinal_numbers,v) -> member(complement(image(element_relation,successor(u))),v)*.
% 299.99/300.67  19506[0:SpL:481.0,288.0] || member(u,image(element_relation,power_class(intersection(complement(v),complement(w)))))* member(u,power_class(image(element_relation,union(v,w)))) -> .
% 299.99/300.67  124983[5:SpL:481.0,66645.0] || subclass(ordinal_numbers,image(element_relation,power_class(intersection(complement(u),complement(v)))))* member(omega,power_class(image(element_relation,union(u,v)))) -> .
% 299.99/300.67  29131[0:SpL:189.0,490.0] || member(u,intersection(complement(v),power_class(image(element_relation,complement(w)))))* member(u,union(v,image(element_relation,power_class(w)))) -> .
% 299.99/300.67  155461[0:Res:2504.1,941.1] || subclass(ordered_pair(u,v),power_class(image(element_relation,complement(w)))) member(unordered_pair(u,singleton(v)),image(element_relation,power_class(w)))* -> .
% 299.99/300.67  29088[5:SpR:189.0,8835.1] || member(u,ordinal_numbers) -> member(u,image(element_relation,power_class(image(element_relation,complement(v)))))* member(u,power_class(image(element_relation,power_class(v)))).
% 299.99/300.67  146639[5:SpL:189.0,66637.0] || subclass(ordinal_numbers,intersection(complement(u),power_class(image(element_relation,complement(v)))))* member(omega,union(u,image(element_relation,power_class(v)))) -> .
% 299.99/300.67  29142[0:SpL:189.0,490.0] || member(u,intersection(power_class(image(element_relation,complement(v))),complement(w)))* member(u,union(image(element_relation,power_class(v)),w)) -> .
% 299.99/300.67  155421[5:Res:8977.2,941.1] || member(u,ordinal_numbers) subclass(ordinal_numbers,power_class(image(element_relation,complement(v)))) member(power_class(u),image(element_relation,power_class(v)))* -> .
% 299.99/300.67  155420[5:Res:8978.2,941.1] || member(u,ordinal_numbers) subclass(ordinal_numbers,power_class(image(element_relation,complement(v)))) member(sum_class(u),image(element_relation,power_class(v)))* -> .
% 299.99/300.67  155418[0:Res:2503.2,941.1] || subclass(u,power_class(image(element_relation,complement(v)))) member(not_subclass_element(u,w),image(element_relation,power_class(v)))* -> subclass(u,w).
% 299.99/300.67  146651[5:SpL:189.0,66637.0] || subclass(ordinal_numbers,intersection(power_class(image(element_relation,complement(u))),complement(v)))* member(omega,union(image(element_relation,power_class(u)),v)) -> .
% 299.99/300.67  1046[0:Rew:189.0,1029.1] || member(not_subclass_element(power_class(image(element_relation,complement(u))),v),image(element_relation,power_class(u)))* -> subclass(power_class(image(element_relation,complement(u))),v).
% 299.99/300.67  83312[7:Rew:189.0,83273.1] ||  -> member(regular(complement(power_class(image(element_relation,complement(u))))),image(element_relation,power_class(u)))* equal(complement(power_class(image(element_relation,complement(u)))),identity_relation).
% 299.99/300.67  193543[8:SpL:162038.0,8825.1] || member(u,ordinal_numbers) subclass(power_class(complement(inverse(identity_relation))),v)* -> member(u,image(element_relation,symmetrization_of(identity_relation)))* member(u,v)*.
% 299.99/300.67  193487[8:SpR:162038.0,482.0] ||  -> equal(complement(intersection(union(u,image(element_relation,symmetrization_of(identity_relation))),complement(v))),union(intersection(complement(u),power_class(complement(inverse(identity_relation)))),v))**.
% 299.99/300.67  193464[8:SpR:162038.0,482.0] ||  -> equal(complement(intersection(union(image(element_relation,symmetrization_of(identity_relation)),u),complement(v))),union(intersection(power_class(complement(inverse(identity_relation))),complement(u)),v))**.
% 299.99/300.67  193491[8:SpR:162038.0,483.0] ||  -> equal(complement(intersection(complement(u),union(image(element_relation,symmetrization_of(identity_relation)),v))),union(u,intersection(power_class(complement(inverse(identity_relation))),complement(v))))**.
% 299.99/300.67  193498[8:SpR:162038.0,483.0] ||  -> equal(complement(intersection(complement(u),union(v,image(element_relation,symmetrization_of(identity_relation))))),union(u,intersection(complement(v),power_class(complement(inverse(identity_relation))))))**.
% 299.99/300.67  132731[5:SpR:19486.0,8977.2] || member(intersection(complement(u),complement(inverse(u))),ordinal_numbers)* subclass(ordinal_numbers,v) -> member(complement(image(element_relation,symmetrization_of(u))),v)*.
% 299.99/300.67  140406[5:Res:79577.0,47534.0] ||  -> subclass(singleton(not_subclass_element(u,intersection(image(element_relation,complement(v)),u))),power_class(v))* subclass(u,intersection(image(element_relation,complement(v)),u)).
% 299.99/300.67  18916[0:Res:303.1,288.0] || member(not_subclass_element(intersection(u,image(element_relation,complement(v))),w),power_class(v))* -> subclass(intersection(u,image(element_relation,complement(v))),w).
% 299.99/300.67  19035[0:Res:313.1,288.0] || member(not_subclass_element(intersection(image(element_relation,complement(u)),v),w),power_class(u))* -> subclass(intersection(image(element_relation,complement(u)),v),w).
% 299.99/300.67  131210[5:Res:39607.2,288.0] inductive(image(element_relation,complement(u))) || well_ordering(v,ordinal_numbers) member(least(v,image(element_relation,complement(u))),power_class(u))* -> .
% 299.99/300.67  18714[7:Res:13237.2,288.0] || well_ordering(u,ordinal_numbers) member(least(u,image(element_relation,complement(v))),power_class(v))* -> equal(image(element_relation,complement(v)),identity_relation).
% 299.99/300.67  165528[15:Res:165526.1,8554.1] || subclass(ordinal_numbers,complement(intersection(u,v))) member(range_of(identity_relation),union(u,v)) -> member(range_of(identity_relation),symmetric_difference(u,v))*.
% 299.99/300.67  165523[15:Res:165460.0,9421.0] || member(u,v)* -> equal(ordered_pair(first(ordered_pair(u,range_of(identity_relation))),second(ordered_pair(u,range_of(identity_relation)))),ordered_pair(u,range_of(identity_relation)))**.
% 299.99/300.67  16623[8:SpL:14756.0,8803.0] || member(u,range_of(identity_relation)) member(ordered_pair(v,u),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(v,u),compose(identity_relation,w))*.
% 299.99/300.67  194963[15:Res:8551.2,165527.1] || member(range_of(identity_relation),cross_product(u,v)) member(range_of(identity_relation),w) subclass(ordinal_numbers,complement(restrict(w,u,v)))* -> .
% 299.99/300.67  196834[21:Rew:160429.0,196820.1] function(u) || subclass(range_of(u),identity_relation) equal(cantor(cantor(v)),cantor(u)) -> compatible(u,v,range_of(identity_relation))*.
% 299.99/300.67  142045[8:Rew:141389.0,131194.2] inductive(symmetric_difference(range_of(u),ordinal_numbers)) || well_ordering(v,ordinal_numbers) -> member(least(v,symmetric_difference(ordinal_numbers,range_of(u))),complement(range_of(u)))*.
% 299.99/300.67  117596[8:Rew:116078.0,116565.2] operation(u) inductive(range_of(u)) || well_ordering(v,cantor(cantor(u))) -> member(least(v,range_of(u)),range_of(u))*.
% 299.99/300.67  196950[21:Rew:160429.0,196935.1] function(u) || subclass(range_of(u),identity_relation) equal(cantor(cantor(v)),cantor(u)) -> compatible(u,v,singleton(w))*.
% 299.99/300.67  198185[21:SpR:197474.0,62.1] || member(ordered_pair(inverse(u),v),compose(w,x))* -> equal(range_of(u),identity_relation) member(v,image(w,image(x,identity_relation))).
% 299.99/300.67  204126[8:Res:194487.1,13113.0] || member(u,inverse(identity_relation)) well_ordering(v,symmetrization_of(identity_relation)) -> equal(segment(v,singleton(u),least(v,singleton(u))),identity_relation)**.
% 299.99/300.67  204193[18:Res:194549.1,21.0] || subclass(symmetrization_of(identity_relation),cross_product(u,v))* -> equal(ordered_pair(first(regular(symmetrization_of(identity_relation))),second(regular(symmetrization_of(identity_relation)))),regular(symmetrization_of(identity_relation)))**.
% 299.99/300.67  205202[15:Res:195033.1,3689.0] || equal(complement(complement(ordered_pair(u,v))),ordinal_numbers)** -> equal(unordered_pair(u,singleton(v)),range_of(identity_relation)) equal(range_of(identity_relation),singleton(u)).
% 299.99/300.67  205787[22:Res:205578.1,129.0] || subclass(complement(u),v)* well_ordering(w,v)* -> member(singleton(identity_relation),u) member(least(w,complement(u)),complement(u))*.
% 299.99/300.67  205958[8:Res:204134.1,13313.1] || member(apply(choice,complement(symmetrization_of(identity_relation))),inverse(identity_relation))* member(complement(symmetrization_of(identity_relation)),ordinal_numbers) -> equal(complement(symmetrization_of(identity_relation)),identity_relation).
% 299.99/300.67  206158[22:Res:205574.1,3689.0] || equal(ordered_pair(u,v),singleton(singleton(identity_relation))) -> equal(unordered_pair(u,singleton(v)),singleton(identity_relation))** equal(singleton(identity_relation),singleton(u)).
% 299.99/300.67  208009[24:MRR:197917.4,207937.0] function(sum_class(u)) || member(u,ordinal_numbers) subclass(range_of(sum_class(u)),identity_relation)* equal(cross_product(identity_relation,identity_relation),identity_relation) -> .
% 299.99/300.67  208011[24:MRR:197963.4,207940.0] function(first(u)) || member(u,subset_relation) subclass(range_of(first(u)),identity_relation)* equal(cross_product(identity_relation,identity_relation),identity_relation) -> .
% 299.99/300.67  208012[24:MRR:198012.4,207941.0] function(second(u)) || member(u,subset_relation) subclass(range_of(second(u)),identity_relation)* equal(cross_product(identity_relation,identity_relation),identity_relation) -> .
% 299.99/300.67  208014[24:MRR:198057.4,207944.0] function(rest_of(u)) || member(u,ordinal_numbers) subclass(range_of(rest_of(u)),identity_relation)* equal(cross_product(identity_relation,identity_relation),identity_relation) -> .
% 299.99/300.67  208015[24:MRR:198102.4,207950.0] function(power_class(u)) || member(u,ordinal_numbers) subclass(range_of(power_class(u)),identity_relation)* equal(cross_product(identity_relation,identity_relation),identity_relation) -> .
% 299.99/300.67  208199[24:SpR:6355.1,207562.1] operation(first(not_subclass_element(cross_product(u,v),w))) ||  -> subclass(cross_product(u,v),w) member(identity_relation,not_subclass_element(cross_product(u,v),w))*.
% 299.99/300.67  208270[24:Rew:66036.0,208250.1] operation(intersection(complement(u),complement(v))) ||  -> equal(complement(intersection(union(u,v),ordinal_numbers)),successor(intersection(complement(u),complement(v))))**.
% 299.99/300.67  208293[24:SpR:207572.1,8801.1] operation(compose(u,identity_relation)) || member(ordered_pair(u,identity_relation),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(u,singleton(singleton(identity_relation))),composition_function)*.
% 299.99/300.67  208533[7:SpL:13260.1,10702.0] || equal(u,regular(cross_product(v,w))) -> equal(cross_product(v,w),identity_relation) member(singleton(first(regular(cross_product(v,w)))),u)*.
% 299.99/300.67  208511[7:SpL:13260.1,2486.0] || subclass(regular(cross_product(u,v)),w) -> equal(cross_product(u,v),identity_relation) member(singleton(first(regular(cross_product(u,v)))),w)*.
% 299.99/300.67  208540[8:Rew:117380.1,208494.1] operation(u) ||  -> equal(cantor(u),identity_relation) equal(ordered_pair(first(regular(cantor(u))),second(regular(cantor(u)))),regular(cantor(u)))**.
% 299.99/300.67  209119[8:Res:13056.1,119943.0] inductive(cantor(u)) || subclass(rest_of(u),v)* well_ordering(w,v)* -> member(least(w,rest_of(u)),rest_of(u))*.
% 299.99/300.67  209073[8:Res:13072.1,119943.0] || subclass(rest_of(u),v)* well_ordering(w,v)* -> equal(cantor(u),identity_relation) member(least(w,rest_of(u)),rest_of(u))*.
% 299.99/300.67  209221[25:Res:208830.0,13362.0] || subclass(ordered_pair(ordinal_numbers,u),v)* well_ordering(omega,v) -> equal(integer_of(ordered_pair(identity_relation,least(omega,ordered_pair(ordinal_numbers,u)))),identity_relation)**.
% 299.99/300.67  209347[25:Rew:208840.0,209335.2] || equal(compose(u,identity_relation),ordinal_numbers) member(singleton(singleton(identity_relation)),cross_product(ordinal_numbers,ordinal_numbers))* -> member(singleton(singleton(identity_relation)),compose_class(u))*.
% 299.99/300.67  209406[21:SpL:196567.0,117617.1] function(u) || subclass(range_of(u),identity_relation) equal(cantor(cantor(v)),cantor(u)) -> compatible(u,v,inverse(identity_relation))*.
% 299.99/300.67  209947[15:Res:209921.1,8554.1] || equal(complement(intersection(u,v)),ordinal_numbers) member(range_of(identity_relation),union(u,v)) -> member(range_of(identity_relation),symmetric_difference(u,v))*.
% 299.99/300.67  210337[8:Rew:160491.0,210289.2,160491.0,210289.1,160491.0,210289.0] || member(apply(choice,union(u,identity_relation)),complement(u))* member(union(u,identity_relation),ordinal_numbers) -> equal(union(u,identity_relation),identity_relation).
% 299.99/300.67  210669[8:Res:9865.3,210517.1] || member(u,ordinal_numbers)* member(v,ordinal_numbers) equal(compose(w,v),u)* equal(complement(compose_class(w)),ordinal_numbers) -> .
% 299.99/300.67  211155[8:Res:210572.1,117602.1] function(u) || equal(complement(range_of(u)),ordinal_numbers) equal(cantor(cantor(v)),cantor(u)) -> compatible(u,v,w)*.
% 299.99/300.67  211133[8:Res:210572.1,161591.1] || equal(complement(complement(complement(symmetrization_of(u)))),ordinal_numbers)** connected(u,v)* -> equal(complement(complement(symmetrization_of(u))),cross_product(v,v))*.
% 299.99/300.67  212301[8:Rew:117142.0,212291.2] || section(element_relation,u,ordinal_numbers) well_ordering(v,u) -> equal(sum_class(u),identity_relation) member(least(v,sum_class(u)),sum_class(u))*.
% 299.99/300.67  212374[7:SpL:13259.2,9486.0] || member(cross_product(u,v),ordinal_numbers) subclass(ordinal_numbers,complement(apply(choice,cross_product(u,v))))* -> equal(cross_product(u,v),identity_relation).
% 299.99/300.67  212373[7:SpL:13259.2,9529.0] || member(cross_product(u,v),ordinal_numbers) equal(complement(apply(choice,cross_product(u,v))),ordinal_numbers)** -> equal(cross_product(u,v),identity_relation).
% 299.99/300.67  213547[8:Res:116127.5,14676.0] operation(u) operation(v) || compatible(w,v,u) subclass(cantor(v),identity_relation) -> homomorphism(w,v,u)*.
% 299.99/300.67  214064[5:Res:8827.2,152274.0] || member(u,ordinal_numbers) subclass(rest_relation,complement(singleton(ordered_pair(u,rest_of(u)))))* -> subclass(singleton(ordered_pair(u,rest_of(u))),v)*.
% 299.99/300.67  214564[25:SpL:208985.1,8800.1] operation(u) || member(v,u) member(ordered_pair(v,ordinal_numbers),cross_product(ordinal_numbers,ordinal_numbers))* -> member(ordered_pair(v,u),element_relation)*.
% 299.99/300.67  214468[25:SpR:208985.1,8801.1] operation(compose(u,v)) || member(ordered_pair(u,v),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(u,ordered_pair(v,ordinal_numbers)),composition_function)*.
% 299.99/300.67  216008[8:SpL:13259.2,215642.0] || member(cross_product(u,v),ordinal_numbers) subclass(singleton(apply(choice,cross_product(u,v))),identity_relation)* -> equal(cross_product(u,v),identity_relation).
% 299.99/300.67  217829[8:MRR:217548.0,217708.0] ||  -> equal(regular(complement(complement(ordered_pair(u,v)))),unordered_pair(u,singleton(v)))** equal(regular(complement(complement(ordered_pair(u,v)))),singleton(u)).
% 299.99/300.67  217880[20:Res:217871.0,13362.0] || subclass(ordinal_numbers,u) well_ordering(omega,u)* -> equal(integer_of(ordered_pair(regular(complement(complement(symmetrization_of(identity_relation)))),least(omega,ordinal_numbers))),identity_relation)**.
% 299.99/300.67  219606[8:Res:13237.2,67561.0] || well_ordering(u,ordinal_numbers) -> equal(symmetric_difference(complement(v),ordinal_numbers),identity_relation) member(least(u,symmetric_difference(complement(v),ordinal_numbers)),union(v,identity_relation))*.
% 299.99/300.67  219599[8:Res:303.1,67561.0] ||  -> subclass(intersection(u,symmetric_difference(complement(v),ordinal_numbers)),w) member(not_subclass_element(intersection(u,symmetric_difference(complement(v),ordinal_numbers)),w),union(v,identity_relation))*.
% 299.99/300.67  219583[8:Res:313.1,67561.0] ||  -> subclass(intersection(symmetric_difference(complement(u),ordinal_numbers),v),w) member(not_subclass_element(intersection(symmetric_difference(complement(u),ordinal_numbers),v),w),union(u,identity_relation))*.
% 299.99/300.67  219582[8:Res:41371.0,67561.0] ||  -> subclass(complement(complement(symmetric_difference(complement(u),ordinal_numbers))),v) member(not_subclass_element(complement(complement(symmetric_difference(complement(u),ordinal_numbers))),v),union(u,identity_relation))*.
% 299.99/300.67  219574[8:SpL:481.0,67561.0] || member(u,symmetric_difference(power_class(intersection(complement(v),complement(w))),ordinal_numbers))* -> member(u,union(image(element_relation,union(v,w)),identity_relation)).
% 299.99/300.67  219779[8:SpR:481.0,67614.1] || member(u,union(image(element_relation,union(v,w)),identity_relation)) -> member(u,symmetric_difference(power_class(intersection(complement(v),complement(w))),ordinal_numbers))*.
% 299.99/300.67  220561[21:Res:196657.1,8800.1] || subclass(domain_relation,rotate(cross_product(ordinal_numbers,ordinal_numbers))) member(ordered_pair(u,identity_relation),v) -> member(ordered_pair(ordered_pair(u,identity_relation),v),element_relation)*.
% 299.99/300.67  220775[8:Res:39607.2,67561.0] inductive(symmetric_difference(complement(u),ordinal_numbers)) || well_ordering(v,ordinal_numbers) -> member(least(v,symmetric_difference(complement(u),ordinal_numbers)),union(u,identity_relation))*.
% 299.99/300.67  221128[7:Res:13236.2,3617.0] || well_ordering(u,symmetric_difference(v,w)) -> equal(symmetric_difference(v,w),identity_relation) member(least(u,symmetric_difference(v,w)),union(v,w))*.
% 299.99/300.67  222703[5:Res:8976.2,31610.0] function(u) || member(v,ordinal_numbers) subclass(rest_relation,successor_relation) -> equal(rest_of(image(u,v)),successor(image(u,v)))**.
% 299.99/300.67  222775[7:MRR:222711.1,8638.0] || member(u,ordinal_numbers) subclass(rest_relation,successor_relation) -> equal(u,identity_relation) equal(rest_of(apply(choice,u)),successor(apply(choice,u)))**.
% 299.99/300.67  223872[8:SpL:160927.0,67561.0] || member(u,symmetric_difference(union(v,symmetric_difference(ordinal_numbers,w)),ordinal_numbers)) -> member(u,union(intersection(complement(v),union(w,identity_relation)),identity_relation))*.
% 299.99/300.67  223871[8:SpL:160927.0,288.0] || member(u,image(element_relation,union(v,symmetric_difference(ordinal_numbers,w))))* member(u,power_class(intersection(complement(v),union(w,identity_relation)))) -> .
% 299.99/300.67  223857[8:SpL:160927.0,66645.0] || subclass(ordinal_numbers,image(element_relation,union(u,symmetric_difference(ordinal_numbers,v)))) member(omega,power_class(intersection(complement(u),union(v,identity_relation))))* -> .
% 299.99/300.67  223760[8:SpR:160927.0,67614.1] || member(u,union(intersection(complement(v),union(w,identity_relation)),identity_relation))* -> member(u,symmetric_difference(union(v,symmetric_difference(ordinal_numbers,w)),ordinal_numbers)).
% 299.99/300.67  223706[8:SpR:160927.0,147905.0] ||  -> equal(intersection(intersection(complement(u),union(v,identity_relation)),complement(union(u,symmetric_difference(ordinal_numbers,v)))),complement(union(u,symmetric_difference(ordinal_numbers,v))))**.
% 299.99/300.67  223925[8:Rew:160927.0,223849.1] || subclass(union(u,symmetric_difference(ordinal_numbers,v)),intersection(complement(u),union(v,identity_relation)))* -> equal(union(u,symmetric_difference(ordinal_numbers,v)),identity_relation).
% 299.99/300.67  224191[8:SpL:160992.0,67561.0] || member(u,symmetric_difference(union(symmetric_difference(ordinal_numbers,v),w),ordinal_numbers)) -> member(u,union(intersection(union(v,identity_relation),complement(w)),identity_relation))*.
% 299.99/300.67  224190[8:SpL:160992.0,288.0] || member(u,image(element_relation,union(symmetric_difference(ordinal_numbers,v),w)))* member(u,power_class(intersection(union(v,identity_relation),complement(w)))) -> .
% 299.99/300.67  224176[8:SpL:160992.0,66645.0] || subclass(ordinal_numbers,image(element_relation,union(symmetric_difference(ordinal_numbers,u),v))) member(omega,power_class(intersection(union(u,identity_relation),complement(v))))* -> .
% 299.99/300.67  224077[8:SpR:160992.0,67614.1] || member(u,union(intersection(union(v,identity_relation),complement(w)),identity_relation))* -> member(u,symmetric_difference(union(symmetric_difference(ordinal_numbers,v),w),ordinal_numbers)).
% 299.99/300.67  224023[8:SpR:160992.0,147905.0] ||  -> equal(intersection(intersection(union(u,identity_relation),complement(v)),complement(union(symmetric_difference(ordinal_numbers,u),v))),complement(union(symmetric_difference(ordinal_numbers,u),v)))**.
% 299.99/300.67  224240[8:Rew:160992.0,224168.1] || subclass(union(symmetric_difference(ordinal_numbers,u),v),intersection(union(u,identity_relation),complement(v)))* -> equal(union(symmetric_difference(ordinal_numbers,u),v),identity_relation).
% 299.99/300.67  224285[8:Res:163112.0,18750.0] ||  -> subclass(singleton(regular(regular(complement(inverse(identity_relation))))),symmetrization_of(identity_relation))* equal(regular(complement(inverse(identity_relation))),identity_relation) equal(complement(inverse(identity_relation)),identity_relation).
% 299.99/300.67  224362[21:MRR:224349.2,13039.0] || subclass(domain_relation,union_of_range_map) well_ordering(element_relation,range_of(singleton(identity_relation)))* -> equal(range_of(singleton(identity_relation)),ordinal_numbers) member(range_of(singleton(identity_relation)),ordinal_numbers).
% 299.99/300.67  224739[26:Res:224684.1,13362.0] || subclass(omega,u) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(identity_relation,least(omega,u))),identity_relation)**.
% 299.99/300.67  225321[7:Obv:225317.1] || subclass(omega,u) -> equal(not_subclass_element(unordered_pair(v,w),u),v)** equal(integer_of(w),identity_relation) subclass(unordered_pair(v,w),u).
% 299.99/300.67  225322[7:Obv:225316.1] || subclass(omega,u) -> equal(not_subclass_element(unordered_pair(v,w),u),w)** equal(integer_of(v),identity_relation) subclass(unordered_pair(v,w),u).
% 299.99/300.67  225407[7:Res:27.2,17312.1] || member(regular(u),v) member(regular(u),w) subclass(u,complement(intersection(w,v)))* -> equal(u,identity_relation).
% 299.99/300.67  225506[7:SpL:481.0,225445.0] || subclass(image(element_relation,union(u,v)),power_class(intersection(complement(u),complement(v))))* -> equal(image(element_relation,union(u,v)),identity_relation).
% 299.99/300.67  225871[26:Res:225794.1,13362.0] || equal(u,omega) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(identity_relation,least(omega,u))),identity_relation)**.
% 299.99/300.67  226160[7:Res:52.1,17321.0] inductive(intersection(u,v)) ||  -> equal(image(successor_relation,intersection(u,v)),identity_relation) member(regular(image(successor_relation,intersection(u,v))),v)*.
% 299.99/300.67  226265[7:Res:52.1,17322.0] inductive(intersection(u,v)) ||  -> equal(image(successor_relation,intersection(u,v)),identity_relation) member(regular(image(successor_relation,intersection(u,v))),u)*.
% 299.99/300.67  226401[8:Res:13258.1,160772.0] || member(regular(restrict(symmetric_difference(ordinal_numbers,u),v,w)),union(u,identity_relation))* -> equal(restrict(symmetric_difference(ordinal_numbers,u),v,w),identity_relation).
% 299.99/300.67  226398[7:Res:13258.1,19676.0] ||  -> equal(restrict(symmetric_difference(u,inverse(u)),v,w),identity_relation) member(regular(restrict(symmetric_difference(u,inverse(u)),v,w)),symmetrization_of(u))*.
% 299.99/300.67  226397[7:Res:13258.1,19559.0] ||  -> equal(restrict(symmetric_difference(u,singleton(u)),v,w),identity_relation) member(regular(restrict(symmetric_difference(u,singleton(u)),v,w)),successor(u))*.
% 299.99/300.67  226392[7:Res:13258.1,18794.1] || member(regular(restrict(intersection(u,v),w,x)),symmetric_difference(u,v))* -> equal(restrict(intersection(u,v),w,x),identity_relation).
% 299.99/300.67  226384[8:Res:13258.1,66086.1] || member(regular(restrict(complement(compose(element_relation,ordinal_numbers)),u,v)),element_relation)* -> equal(restrict(complement(compose(element_relation,ordinal_numbers)),u,v),identity_relation).
% 299.99/300.67  226802[7:Rew:30.0,226780.2] || subclass(omega,intersection(complement(u),complement(v)))* -> equal(integer_of(regular(union(u,v))),identity_relation) equal(union(u,v),identity_relation).
% 299.99/300.67  226812[21:SpL:13259.2,226662.0] || member(cross_product(u,v),ordinal_numbers) subclass(rest_relation,rest_of(apply(choice,cross_product(u,v))))* -> equal(cross_product(u,v),identity_relation).
% 299.99/300.67  228235[7:Res:9604.1,17313.0] || equal(sum_class(recursion_equation_functions(u)),recursion_equation_functions(u)) -> equal(sum_class(recursion_equation_functions(u)),identity_relation) subclass(regular(sum_class(recursion_equation_functions(u))),cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.67  228361[21:SpL:50855.1,196427.1] || member(singleton(u),subset_relation)* member(v,ordinal_numbers) subclass(domain_relation,u) -> equal(ordered_pair(v,identity_relation),first(singleton(u)))*.
% 299.99/300.67  228902[8:MRR:228868.3,62127.0] || member(apply(choice,regular(complement(u))),ordinal_numbers)* -> member(apply(choice,regular(complement(u))),u)* equal(regular(complement(u)),identity_relation).
% 299.99/300.67  229000[8:SpL:13262.1,222292.0] || member(identity_relation,u) subclass(element_relation,identity_relation) -> equal(unordered_pair(v,u),identity_relation) equal(apply(choice,unordered_pair(v,u)),v)**.
% 299.99/300.67  228999[8:SpL:13262.2,222292.0] || member(identity_relation,u) subclass(element_relation,identity_relation) -> equal(unordered_pair(u,v),identity_relation) equal(apply(choice,unordered_pair(u,v)),v)**.
% 299.99/300.67  229051[8:SpL:13262.1,222305.0] || equal(u,ordinal_numbers) subclass(element_relation,identity_relation) -> equal(unordered_pair(v,u),identity_relation) equal(apply(choice,unordered_pair(v,u)),v)**.
% 299.99/300.67  229050[8:SpL:13262.2,222305.0] || equal(u,ordinal_numbers) subclass(element_relation,identity_relation) -> equal(unordered_pair(u,v),identity_relation) equal(apply(choice,unordered_pair(u,v)),v)**.
% 299.99/300.67  229063[8:SpL:13262.1,222310.0] || subclass(ordinal_numbers,u) subclass(element_relation,identity_relation) -> equal(unordered_pair(v,u),identity_relation) equal(apply(choice,unordered_pair(v,u)),v)**.
% 299.99/300.67  229062[8:SpL:13262.2,222310.0] || subclass(ordinal_numbers,u) subclass(element_relation,identity_relation) -> equal(unordered_pair(u,v),identity_relation) equal(apply(choice,unordered_pair(u,v)),v)**.
% 299.99/300.67  229211[7:Rew:30.0,229086.1] || member(regular(intersection(union(u,v),w)),intersection(complement(u),complement(v)))* -> equal(intersection(union(u,v),w),identity_relation).
% 299.99/300.67  229797[7:Rew:30.0,229529.1] || member(regular(intersection(u,union(v,w))),intersection(complement(v),complement(w)))* -> equal(intersection(u,union(v,w)),identity_relation).
% 299.99/300.67  230478[8:MRR:230440.0,60996.1] ||  -> member(regular(regular(symmetric_difference(ordinal_numbers,u))),union(u,identity_relation))* equal(regular(symmetric_difference(ordinal_numbers,u)),identity_relation) equal(symmetric_difference(ordinal_numbers,u),identity_relation).
% 299.99/300.67  230701[8:MRR:230661.0,8666.0] || subclass(ordinal_numbers,regular(image(element_relation,complement(u))))* -> member(unordered_pair(v,w),power_class(u))* equal(image(element_relation,complement(u)),identity_relation).
% 299.99/300.67  230702[8:MRR:230672.2,218277.1] || member(ordered_pair(u,unordered_pair(v,w)),compose(x,y))* subclass(ordinal_numbers,regular(image(x,image(y,singleton(u))))) -> .
% 299.99/300.67  230792[8:SpL:13259.2,230675.0] || member(cross_product(u,v),ordinal_numbers) subclass(ordinal_numbers,regular(apply(choice,cross_product(u,v))))* -> equal(cross_product(u,v),identity_relation).
% 299.99/300.67  230870[8:SpL:13259.2,230771.0] || member(cross_product(u,v),ordinal_numbers) equal(complement(apply(choice,cross_product(u,v))),identity_relation)** -> equal(cross_product(u,v),identity_relation).
% 299.99/300.67  230942[8:SpL:13259.2,230797.0] || member(cross_product(u,v),ordinal_numbers) equal(regular(apply(choice,cross_product(u,v))),ordinal_numbers)** -> equal(cross_product(u,v),identity_relation).
% 299.99/300.67  231281[8:SpR:116209.1,17447.1] operation(u) ||  -> equal(symmetric_difference(v,cantor(u)),identity_relation) member(regular(symmetric_difference(v,cantor(u))),complement(intersection(cantor(u),v)))*.
% 299.99/300.67  231255[8:SpR:116209.1,17447.1] operation(u) ||  -> equal(symmetric_difference(cantor(u),v),identity_relation) member(regular(symmetric_difference(cantor(u),v)),complement(intersection(v,cantor(u))))*.
% 299.99/300.67  231836[8:MRR:231792.0,41183.1] ||  -> member(not_subclass_element(regular(union(u,v)),w),complement(v))* subclass(regular(union(u,v)),w) equal(union(u,v),identity_relation).
% 299.99/300.67  231837[8:MRR:231791.0,41183.1] ||  -> member(not_subclass_element(regular(union(u,v)),w),complement(u))* subclass(regular(union(u,v)),w) equal(union(u,v),identity_relation).
% 299.99/300.67  231863[8:SpR:481.0,231812.0] ||  -> subclass(regular(image(element_relation,union(u,v))),power_class(intersection(complement(u),complement(v))))* equal(image(element_relation,union(u,v)),identity_relation).
% 299.99/300.67  232508[8:Res:13247.2,230867.0] || member(intersection(u,subset_relation),ordinal_numbers) equal(complement(apply(choice,intersection(u,subset_relation))),identity_relation)** -> equal(intersection(u,subset_relation),identity_relation).
% 299.99/300.67  232499[8:Res:13246.2,230867.0] || member(intersection(subset_relation,u),ordinal_numbers) equal(complement(apply(choice,intersection(subset_relation,u))),identity_relation)** -> equal(intersection(subset_relation,u),identity_relation).
% 299.99/300.67  232582[8:Res:13247.2,230939.0] || member(intersection(u,subset_relation),ordinal_numbers) equal(regular(apply(choice,intersection(u,subset_relation))),ordinal_numbers)** -> equal(intersection(u,subset_relation),identity_relation).
% 299.99/300.67  232573[8:Res:13246.2,230939.0] || member(intersection(subset_relation,u),ordinal_numbers) equal(regular(apply(choice,intersection(subset_relation,u))),ordinal_numbers)** -> equal(intersection(subset_relation,u),identity_relation).
% 299.99/300.67  232813[8:Rew:160992.0,232753.1] || subclass(intersection(union(u,identity_relation),complement(v)),union(symmetric_difference(ordinal_numbers,u),v))* -> subclass(ordinal_numbers,union(symmetric_difference(ordinal_numbers,u),v)).
% 299.99/300.67  232814[8:Rew:160927.0,232752.1] || subclass(intersection(complement(u),union(v,identity_relation)),union(u,symmetric_difference(ordinal_numbers,v)))* -> subclass(ordinal_numbers,union(u,symmetric_difference(ordinal_numbers,v))).
% 299.99/300.67  233267[8:SpR:116209.1,17388.1] operation(u) ||  -> equal(intersection(recursion_equation_functions(v),cantor(u)),identity_relation) subclass(regular(intersection(cantor(u),recursion_equation_functions(v))),cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.67  233412[8:SpR:116209.1,13566.1] operation(u) ||  -> equal(intersection(cantor(u),recursion_equation_functions(v)),identity_relation) subclass(regular(intersection(recursion_equation_functions(v),cantor(u))),cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.67  233475[21:Res:161057.2,196454.0] || well_ordering(u,ordinal_numbers) subclass(domain_relation,rest_relation) -> equal(recursion_equation_functions(v),identity_relation) equal(rest_of(cantor(least(u,recursion_equation_functions(v)))),identity_relation)**.
% 299.99/300.67  233474[21:Res:161057.2,196455.0] || well_ordering(u,ordinal_numbers) subclass(rest_relation,domain_relation) -> equal(recursion_equation_functions(v),identity_relation) equal(rest_of(cantor(least(u,recursion_equation_functions(v)))),identity_relation)**.
% 299.99/300.67  233505[21:Res:67614.1,196424.2] || member(ordered_pair(u,identity_relation),union(v,identity_relation))* member(u,ordinal_numbers) subclass(domain_relation,complement(symmetric_difference(complement(v),ordinal_numbers))) -> .
% 299.99/300.67  233499[21:Res:3618.1,196424.2] || member(ordered_pair(u,identity_relation),symmetric_difference(v,w))* member(u,ordinal_numbers) subclass(domain_relation,complement(complement(intersection(v,w)))) -> .
% 299.99/300.67  233838[21:Res:196656.1,941.1] || subclass(domain_relation,flip(power_class(image(element_relation,complement(u))))) member(ordered_pair(ordered_pair(v,w),identity_relation),image(element_relation,power_class(u)))* -> .
% 299.99/300.67  233836[21:Res:196657.1,941.1] || subclass(domain_relation,rotate(power_class(image(element_relation,complement(u))))) member(ordered_pair(ordered_pair(v,identity_relation),w),image(element_relation,power_class(u)))* -> .
% 299.99/300.67  233778[16:SpL:195257.0,941.1] || member(u,image(element_relation,power_class(image(element_relation,singleton(identity_relation)))))* member(u,power_class(image(element_relation,power_class(complement(singleton(identity_relation)))))) -> .
% 299.99/300.67  233777[8:SpL:162038.0,941.1] || member(u,image(element_relation,power_class(image(element_relation,symmetrization_of(identity_relation)))))* member(u,power_class(image(element_relation,power_class(complement(inverse(identity_relation)))))) -> .
% 299.99/300.67  233963[8:Res:2504.1,161200.0] || subclass(ordered_pair(u,v),image(element_relation,union(w,identity_relation))) member(unordered_pair(u,singleton(v)),power_class(symmetric_difference(ordinal_numbers,w)))* -> .
% 299.99/300.67  233960[21:Res:196656.1,161200.0] || subclass(domain_relation,flip(image(element_relation,union(u,identity_relation)))) member(ordered_pair(ordered_pair(v,w),identity_relation),power_class(symmetric_difference(ordinal_numbers,u)))* -> .
% 299.99/300.67  233958[21:Res:196657.1,161200.0] || subclass(domain_relation,rotate(image(element_relation,union(u,identity_relation)))) member(ordered_pair(ordered_pair(v,identity_relation),w),power_class(symmetric_difference(ordinal_numbers,u)))* -> .
% 299.99/300.67  233932[8:Res:8977.2,161200.0] || member(u,ordinal_numbers) subclass(ordinal_numbers,image(element_relation,union(v,identity_relation))) member(power_class(u),power_class(symmetric_difference(ordinal_numbers,v)))* -> .
% 299.99/300.67  233929[8:Res:8978.2,161200.0] || member(u,ordinal_numbers) subclass(ordinal_numbers,image(element_relation,union(v,identity_relation))) member(sum_class(u),power_class(symmetric_difference(ordinal_numbers,v)))* -> .
% 299.99/300.67  233927[8:Res:2503.2,161200.0] || subclass(u,image(element_relation,union(v,identity_relation))) member(not_subclass_element(u,w),power_class(symmetric_difference(ordinal_numbers,v)))* -> subclass(u,w).
% 299.99/300.67  233909[8:Res:6.1,161200.0] || member(not_subclass_element(image(element_relation,union(u,identity_relation)),v),power_class(symmetric_difference(ordinal_numbers,u)))* -> subclass(image(element_relation,union(u,identity_relation)),v).
% 299.99/300.67  234094[8:SpR:6355.1,233383.0] ||  -> subclass(cross_product(u,v),w) member(singleton(first(not_subclass_element(cross_product(u,v),w))),complement(singleton(not_subclass_element(cross_product(u,v),w))))*.
% 299.99/300.67  234177[8:SpL:6355.1,234106.0] || member(singleton(first(not_subclass_element(cross_product(u,v),w))),singleton(not_subclass_element(cross_product(u,v),w)))* -> subclass(cross_product(u,v),w).
% 299.99/300.67  234807[8:Res:193440.1,9876.0] || member(u,ordinal_numbers) subclass(cantor(v),w)* well_ordering(ordinal_numbers,w) -> equal(apply(v,u),sum_class(range_of(identity_relation)))**.
% 299.99/300.67  234805[8:SpR:145761.0,193440.1] || member(u,ordinal_numbers) -> member(u,segment(ordinal_numbers,v,w)) equal(apply(cross_product(v,singleton(w)),u),sum_class(range_of(identity_relation)))**.
% 299.99/300.67  234783[25:SpR:208887.0,193440.1] || member(u,ordinal_numbers) -> member(u,segment(v,w,ordinal_numbers)) equal(apply(restrict(v,w,identity_relation),u),sum_class(range_of(identity_relation)))**.
% 299.99/300.67  234902[8:MRR:234845.0,41183.1] ||  -> equal(apply(u,not_subclass_element(regular(cantor(u)),v)),sum_class(range_of(identity_relation)))** subclass(regular(cantor(u)),v) equal(cantor(u),identity_relation).
% 299.99/300.67  234903[8:MRR:234833.0,65402.2] || well_ordering(u,ordinal_numbers) -> equal(apply(v,least(u,complement(cantor(v)))),sum_class(range_of(identity_relation)))** equal(complement(cantor(v)),identity_relation).
% 299.99/300.67  235429[5:Res:28980.1,288.0] || subclass(rest_relation,flip(image(element_relation,complement(u)))) member(ordered_pair(ordered_pair(v,w),rest_of(ordered_pair(w,v))),power_class(u))* -> .
% 299.99/300.67  235427[8:Res:28980.1,14681.0] || subclass(rest_relation,flip(regular(u))) member(ordered_pair(ordered_pair(v,w),rest_of(ordered_pair(w,v))),u)* -> equal(u,identity_relation).
% 299.99/300.67  235418[5:Res:28980.1,897.0] || subclass(rest_relation,flip(restrict(u,v,w)))* -> member(ordered_pair(ordered_pair(x,y),rest_of(ordered_pair(y,x))),cross_product(v,w))*.
% 299.99/300.67  235393[8:Res:28980.1,160772.0] || subclass(rest_relation,flip(symmetric_difference(ordinal_numbers,u))) member(ordered_pair(ordered_pair(v,w),rest_of(ordered_pair(w,v))),union(u,identity_relation))* -> .
% 299.99/300.67  235392[8:Res:28980.1,67561.0] || subclass(rest_relation,flip(symmetric_difference(complement(u),ordinal_numbers))) -> member(ordered_pair(ordered_pair(v,w),rest_of(ordered_pair(w,v))),union(u,identity_relation))*.
% 299.99/300.67  235384[5:Res:28980.1,18794.1] || subclass(rest_relation,flip(intersection(u,v))) member(ordered_pair(ordered_pair(w,x),rest_of(ordered_pair(x,w))),symmetric_difference(u,v))* -> .
% 299.99/300.67  235557[5:Res:28979.1,288.0] || subclass(rest_relation,rotate(image(element_relation,complement(u)))) member(ordered_pair(ordered_pair(v,rest_of(ordered_pair(w,v))),w),power_class(u))* -> .
% 299.99/300.67  235555[8:Res:28979.1,14681.0] || subclass(rest_relation,rotate(regular(u))) member(ordered_pair(ordered_pair(v,rest_of(ordered_pair(w,v))),w),u)* -> equal(u,identity_relation).
% 299.99/300.67  235546[5:Res:28979.1,897.0] || subclass(rest_relation,rotate(restrict(u,v,w)))* -> member(ordered_pair(ordered_pair(x,rest_of(ordered_pair(y,x))),y),cross_product(v,w))*.
% 299.99/300.67  235521[8:Res:28979.1,160772.0] || subclass(rest_relation,rotate(symmetric_difference(ordinal_numbers,u))) member(ordered_pair(ordered_pair(v,rest_of(ordered_pair(w,v))),w),union(u,identity_relation))* -> .
% 299.99/300.67  235520[8:Res:28979.1,67561.0] || subclass(rest_relation,rotate(symmetric_difference(complement(u),ordinal_numbers))) -> member(ordered_pair(ordered_pair(v,rest_of(ordered_pair(w,v))),w),union(u,identity_relation))*.
% 299.99/300.67  235512[5:Res:28979.1,18794.1] || subclass(rest_relation,rotate(intersection(u,v))) member(ordered_pair(ordered_pair(w,rest_of(ordered_pair(x,w))),x),symmetric_difference(u,v))* -> .
% 299.99/300.67  235697[22:Res:205574.1,36719.1] operation(u) || equal(cantor(u),singleton(singleton(identity_relation)))* -> equal(ordered_pair(first(singleton(identity_relation)),second(singleton(identity_relation))),singleton(identity_relation))**.
% 299.99/300.67  235664[15:Res:195033.1,36719.1] operation(u) || equal(complement(complement(cantor(u))),ordinal_numbers)** -> equal(ordered_pair(first(range_of(identity_relation)),second(range_of(identity_relation))),range_of(identity_relation))**.
% 299.99/300.67  235645[8:SpL:145761.0,36719.1] operation(cross_product(u,singleton(v))) || member(w,segment(ordinal_numbers,u,v))* -> equal(ordered_pair(first(w),second(w)),w)**.
% 299.99/300.67  235623[25:SpL:208887.0,36719.1] operation(restrict(u,v,identity_relation)) || member(w,segment(u,v,ordinal_numbers))* -> equal(ordered_pair(first(w),second(w)),w)**.
% 299.99/300.67  235797[5:Res:52.1,19113.0] inductive(recursion_equation_functions(u)) ||  -> subclass(image(successor_relation,recursion_equation_functions(u)),v) subclass(not_subclass_element(image(successor_relation,recursion_equation_functions(u)),v),cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.67  235792[8:Res:19531.1,19113.0] || equal(sum_class(recursion_equation_functions(u)),identity_relation) -> subclass(sum_class(recursion_equation_functions(u)),v) subclass(not_subclass_element(sum_class(recursion_equation_functions(u)),v),cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.67  235929[7:Res:69478.2,13105.0] || subclass(omega,symmetric_difference(u,v)) -> equal(integer_of(regular(complement(union(u,v)))),identity_relation)** equal(complement(union(u,v)),identity_relation).
% 299.99/300.67  236232[8:SpL:116209.1,18897.0] operation(u) || member(not_subclass_element(intersection(complement(v),cantor(u)),w),v)* -> subclass(intersection(cantor(u),complement(v)),w).
% 299.99/300.67  236327[8:MRR:236261.0,41183.1] ||  -> equal(apply(u,not_subclass_element(intersection(v,complement(cantor(u))),w)),sum_class(range_of(identity_relation)))** subclass(intersection(v,complement(cantor(u))),w).
% 299.99/300.67  236447[8:SpL:116209.1,19016.0] operation(u) || member(not_subclass_element(intersection(cantor(u),complement(v)),w),v)* -> subclass(intersection(complement(v),cantor(u)),w).
% 299.99/300.67  236543[0:Rew:3603.0,236430.1] || member(not_subclass_element(symmetric_difference(u,cross_product(v,w)),x),restrict(u,v,w))* -> subclass(symmetric_difference(u,cross_product(v,w)),x).
% 299.99/300.67  236544[0:Rew:3606.0,236429.1] || member(not_subclass_element(symmetric_difference(cross_product(u,v),w),x),restrict(w,u,v))* -> subclass(symmetric_difference(cross_product(u,v),w),x).
% 299.99/300.67  236548[8:MRR:236465.0,41183.1] ||  -> equal(apply(u,not_subclass_element(intersection(complement(cantor(u)),v),w)),sum_class(range_of(identity_relation)))** subclass(intersection(complement(cantor(u)),v),w).
% 299.99/300.67  236605[16:SpL:195257.0,36857.0] || equal(u,power_class(complement(singleton(identity_relation))))* member(v,ordinal_numbers) -> member(v,image(element_relation,singleton(identity_relation)))* member(v,u)*.
% 299.99/300.67  236604[8:SpL:162038.0,36857.0] || equal(u,power_class(complement(inverse(identity_relation))))* member(v,ordinal_numbers) -> member(v,image(element_relation,symmetrization_of(identity_relation)))* member(v,u)*.
% 299.99/300.67  236593[5:SpL:30.0,36857.0] || equal(u,union(v,w))* member(x,ordinal_numbers) -> member(x,intersection(complement(v),complement(w)))* member(x,u)*.
% 299.99/300.67  236617[26:SpL:13262.1,225140.0] || subclass(omega,u) subclass(element_relation,identity_relation) -> equal(unordered_pair(v,u),identity_relation) equal(apply(choice,unordered_pair(v,u)),v)**.
% 299.99/300.67  236616[26:SpL:13262.2,225140.0] || subclass(omega,u) subclass(element_relation,identity_relation) -> equal(unordered_pair(u,v),identity_relation) equal(apply(choice,unordered_pair(u,v)),v)**.
% 299.99/300.67  236634[26:SpL:13262.1,225241.0] || equal(u,omega) subclass(element_relation,identity_relation) -> equal(unordered_pair(v,u),identity_relation) equal(apply(choice,unordered_pair(v,u)),v)**.
% 299.99/300.67  236633[26:SpL:13262.2,225241.0] || equal(u,omega) subclass(element_relation,identity_relation) -> equal(unordered_pair(u,v),identity_relation) equal(apply(choice,unordered_pair(u,v)),v)**.
% 299.99/300.67  236874[7:Res:17392.2,288.0] || subclass(u,image(element_relation,complement(v))) member(regular(intersection(u,w)),power_class(v))* -> equal(intersection(u,w),identity_relation).
% 299.99/300.67  236872[8:Res:17392.2,14681.0] || subclass(u,regular(v)) member(regular(intersection(u,w)),v)* -> equal(intersection(u,w),identity_relation) equal(v,identity_relation).
% 299.99/300.67  236863[7:Res:17392.2,897.0] || subclass(u,restrict(v,w,x))* -> equal(intersection(u,y),identity_relation) member(regular(intersection(u,y)),cross_product(w,x))*.
% 299.99/300.67  236838[8:Res:17392.2,160772.0] || subclass(u,symmetric_difference(ordinal_numbers,v)) member(regular(intersection(u,w)),union(v,identity_relation))* -> equal(intersection(u,w),identity_relation).
% 299.99/300.67  236837[8:Res:17392.2,67561.0] || subclass(u,symmetric_difference(complement(v),ordinal_numbers)) -> equal(intersection(u,w),identity_relation) member(regular(intersection(u,w)),union(v,identity_relation))*.
% 299.99/300.67  236829[7:Res:17392.2,18794.1] || subclass(u,intersection(v,w)) member(regular(intersection(u,x)),symmetric_difference(v,w))* -> equal(intersection(u,x),identity_relation).
% 299.99/300.67  236806[8:SpR:116209.1,17392.2] operation(u) || subclass(v,w) -> equal(intersection(v,cantor(u)),identity_relation) member(regular(intersection(cantor(u),v)),w)*.
% 299.99/300.67  236930[7:Rew:155666.0,236775.1] || subclass(complement(subset_relation),u) -> equal(symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation),identity_relation) member(regular(symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation)),u)*.
% 299.99/300.67  236931[7:Rew:155665.0,236774.1] || subclass(complement(subset_relation),u) -> equal(symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers)),identity_relation) member(regular(symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers))),u)*.
% 299.99/300.67  237111[7:Res:13574.1,143186.0] ||  -> equal(intersection(u,intersection(v,symmetric_difference(ordinal_numbers,w))),identity_relation) member(regular(intersection(u,intersection(v,symmetric_difference(ordinal_numbers,w)))),complement(w))*.
% 299.99/300.67  237110[7:Res:13574.1,143226.0] || member(regular(intersection(u,intersection(v,symmetric_difference(ordinal_numbers,w)))),w)* -> equal(intersection(u,intersection(v,symmetric_difference(ordinal_numbers,w))),identity_relation).
% 299.99/300.67  237079[8:SpR:116209.1,13574.1] operation(u) ||  -> equal(intersection(cantor(u),intersection(v,w)),identity_relation) member(regular(intersection(intersection(v,w),cantor(u))),w)*.
% 299.99/300.67  237034[8:SpR:116209.1,13574.1] operation(u) ||  -> equal(intersection(v,intersection(cantor(u),w)),identity_relation) member(regular(intersection(v,intersection(w,cantor(u)))),w)*.
% 299.99/300.67  237762[7:Res:13573.1,143186.0] ||  -> equal(intersection(u,intersection(symmetric_difference(ordinal_numbers,v),w)),identity_relation) member(regular(intersection(u,intersection(symmetric_difference(ordinal_numbers,v),w))),complement(v))*.
% 299.99/300.67  237761[7:Res:13573.1,143226.0] || member(regular(intersection(u,intersection(symmetric_difference(ordinal_numbers,v),w))),v)* -> equal(intersection(u,intersection(symmetric_difference(ordinal_numbers,v),w)),identity_relation).
% 299.99/300.67  237729[8:SpR:116209.1,13573.1] operation(u) ||  -> equal(intersection(cantor(u),intersection(v,w)),identity_relation) member(regular(intersection(intersection(v,w),cantor(u))),v)*.
% 299.99/300.68  237708[8:SpR:116209.1,13573.1] operation(u) ||  -> equal(intersection(v,intersection(w,cantor(u))),identity_relation) member(regular(intersection(v,intersection(cantor(u),w))),w)*.
% 299.99/300.68  237880[7:Rew:155666.0,237677.0] ||  -> equal(intersection(u,symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation)),identity_relation) member(regular(intersection(u,symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation))),complement(subset_relation))*.
% 299.99/300.68  237881[7:Rew:155665.0,237676.0] ||  -> equal(intersection(u,symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers))),identity_relation) member(regular(intersection(u,symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers)))),complement(subset_relation))*.
% 299.99/300.68  238608[7:Res:13572.2,288.0] || subclass(u,image(element_relation,complement(v))) member(regular(intersection(w,u)),power_class(v))* -> equal(intersection(w,u),identity_relation).
% 299.99/300.68  238606[8:Res:13572.2,14681.0] || subclass(u,regular(v)) member(regular(intersection(w,u)),v)* -> equal(intersection(w,u),identity_relation) equal(v,identity_relation).
% 299.99/300.68  238597[7:Res:13572.2,897.0] || subclass(u,restrict(v,w,x))* -> equal(intersection(y,u),identity_relation) member(regular(intersection(y,u)),cross_product(w,x))*.
% 299.99/300.68  238572[8:Res:13572.2,160772.0] || subclass(u,symmetric_difference(ordinal_numbers,v)) member(regular(intersection(w,u)),union(v,identity_relation))* -> equal(intersection(w,u),identity_relation).
% 299.99/300.68  238571[8:Res:13572.2,67561.0] || subclass(u,symmetric_difference(complement(v),ordinal_numbers)) -> equal(intersection(w,u),identity_relation) member(regular(intersection(w,u)),union(v,identity_relation))*.
% 299.99/300.68  238563[7:Res:13572.2,18794.1] || subclass(u,intersection(v,w)) member(regular(intersection(x,u)),symmetric_difference(v,w))* -> equal(intersection(x,u),identity_relation).
% 299.99/300.68  238509[8:SpR:116209.1,13572.2] operation(u) || subclass(v,w) -> equal(intersection(cantor(u),v),identity_relation) member(regular(intersection(v,cantor(u))),w)*.
% 299.99/300.68  239274[7:Res:17397.1,143186.0] ||  -> equal(intersection(intersection(symmetric_difference(ordinal_numbers,u),v),w),identity_relation) member(regular(intersection(intersection(symmetric_difference(ordinal_numbers,u),v),w)),complement(u))*.
% 299.99/300.68  239273[7:Res:17397.1,143226.0] || member(regular(intersection(intersection(symmetric_difference(ordinal_numbers,u),v),w)),u)* -> equal(intersection(intersection(symmetric_difference(ordinal_numbers,u),v),w),identity_relation).
% 299.99/300.68  239250[8:SpR:116209.1,17397.1] operation(u) ||  -> equal(intersection(intersection(v,w),cantor(u)),identity_relation) member(regular(intersection(cantor(u),intersection(v,w))),v)*.
% 299.99/300.68  239214[8:SpR:116209.1,17397.1] operation(u) ||  -> equal(intersection(intersection(v,cantor(u)),w),identity_relation) member(regular(intersection(intersection(cantor(u),v),w)),v)*.
% 299.99/300.68  239403[7:Rew:155666.0,239182.0] ||  -> equal(intersection(symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation),u),identity_relation) member(regular(intersection(symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation),u)),complement(subset_relation))*.
% 299.99/300.68  239404[7:Rew:155665.0,239181.0] ||  -> equal(intersection(symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers)),u),identity_relation) member(regular(intersection(symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers)),u)),complement(subset_relation))*.
% 299.99/300.68  240109[7:Res:17396.1,143186.0] ||  -> equal(intersection(intersection(u,symmetric_difference(ordinal_numbers,v)),w),identity_relation) member(regular(intersection(intersection(u,symmetric_difference(ordinal_numbers,v)),w)),complement(v))*.
% 299.99/300.68  240108[7:Res:17396.1,143226.0] || member(regular(intersection(intersection(u,symmetric_difference(ordinal_numbers,v)),w)),v)* -> equal(intersection(intersection(u,symmetric_difference(ordinal_numbers,v)),w),identity_relation).
% 299.99/300.68  240083[8:SpR:116209.1,17396.1] operation(u) ||  -> equal(intersection(intersection(v,w),cantor(u)),identity_relation) member(regular(intersection(cantor(u),intersection(v,w))),w)*.
% 299.99/300.68  240015[8:SpR:116209.1,17396.1] operation(u) ||  -> equal(intersection(intersection(cantor(u),v),w),identity_relation) member(regular(intersection(intersection(v,cantor(u)),w)),v)*.
% 299.99/300.68  36311[0:SpR:3616.0,27.2] || member(u,union(complement(v),complement(w))) member(u,union(v,w)) -> member(u,symmetric_difference(complement(v),complement(w)))*.
% 299.99/300.68  39643[2:Res:19069.0,9665.1] inductive(symmetric_difference(u,v)) || well_ordering(w,complement(intersection(u,v))) -> member(least(w,symmetric_difference(u,v)),symmetric_difference(u,v))*.
% 299.99/300.68  50362[0:Res:19045.0,9636.2] || member(u,v)* member(u,w)* well_ordering(x,w) -> member(least(x,intersection(w,v)),intersection(w,v))*.
% 299.99/300.68  50363[0:Res:18926.0,9636.2] || member(u,v)* member(u,w)* well_ordering(x,v) -> member(least(x,intersection(w,v)),intersection(w,v))*.
% 299.99/300.68  39613[2:Res:18949.0,9665.1] inductive(restrict(u,v,w)) || well_ordering(x,u) -> member(least(x,restrict(u,v,w)),restrict(u,v,w))*.
% 299.99/300.68  46170[5:SoR:9585.0,75.1] one_to_one(domain_of(restrict(u,v,cross_product(ordinal_numbers,ordinal_numbers)))) || subclass(cross_product(ordinal_numbers,ordinal_numbers),v) -> section(u,cross_product(ordinal_numbers,ordinal_numbers),v)*.
% 299.99/300.68  45622[0:Obv:45593.1] || subclass(unordered_pair(u,v),w)* -> equal(not_subclass_element(unordered_pair(u,v),x),u)** subclass(unordered_pair(u,v),x) member(v,w).
% 299.99/300.68  45621[0:Obv:45602.1] || subclass(unordered_pair(u,v),w)* -> equal(not_subclass_element(unordered_pair(u,v),x),v)** subclass(unordered_pair(u,v),x) member(u,w).
% 299.99/300.68  29168[5:Res:8827.2,490.0] || member(u,ordinal_numbers) subclass(rest_relation,intersection(complement(v),complement(w))) member(ordered_pair(u,rest_of(u)),union(v,w))* -> .
% 299.99/300.68  50060[5:SpL:18840.1,3689.0] || member(u,subset_relation) member(v,u)* -> equal(v,unordered_pair(first(u),singleton(second(u))))* equal(v,singleton(first(u))).
% 299.99/300.68  51503[5:Res:51313.1,12.0] || member(singleton(unordered_pair(u,v)),subset_relation)* -> equal(first(singleton(unordered_pair(u,v))),v) equal(first(singleton(unordered_pair(u,v))),u).
% 299.99/300.68  51499[5:Res:51313.1,490.0] || member(singleton(intersection(complement(u),complement(v))),subset_relation) member(first(singleton(intersection(complement(u),complement(v)))),union(u,v))* -> .
% 299.99/300.68  19847[0:Res:3652.1,11.0] || section(u,singleton(v),w) subclass(singleton(v),segment(u,w,v))* -> equal(segment(u,w,v),singleton(v)).
% 299.99/300.68  94684[5:Res:39298.1,21.0] || subclass(ordinal_numbers,complement(complement(cross_product(u,v))))* -> equal(ordered_pair(first(ordered_pair(w,x)),second(ordered_pair(w,x))),ordered_pair(w,x))**.
% 299.99/300.68  96372[5:Res:40074.1,21.0] || subclass(ordinal_numbers,complement(complement(cross_product(u,v))))* -> equal(ordered_pair(first(unordered_pair(w,x)),second(unordered_pair(w,x))),unordered_pair(w,x))**.
% 299.99/300.68  116452[8:Rew:116078.0,9742.0] || member(singleton(u),cantor(v)) equal(restrict(v,singleton(u),ordinal_numbers),u) -> member(singleton(singleton(singleton(u))),rest_of(v))*.
% 299.99/300.68  123051[8:SoR:119376.0,75.1] one_to_one(cantor(restrict(u,v,cross_product(ordinal_numbers,ordinal_numbers)))) || subclass(cross_product(ordinal_numbers,ordinal_numbers),v) -> section(u,cross_product(ordinal_numbers,ordinal_numbers),v)*.
% 299.99/300.68  128007[5:Res:126679.1,21.0] || subclass(omega,complement(complement(cross_product(u,v))))* -> equal(ordered_pair(first(least(element_relation,omega)),second(least(element_relation,omega))),least(element_relation,omega))**.
% 299.99/300.68  128342[5:Res:127147.1,21.0] || subclass(ordinal_numbers,complement(complement(cross_product(u,v))))* -> equal(ordered_pair(first(least(element_relation,omega)),second(least(element_relation,omega))),least(element_relation,omega))**.
% 299.99/300.68  130867[5:Res:8551.2,9876.0] || member(u,cross_product(v,w))* member(u,x)* subclass(restrict(x,v,w),y)* well_ordering(ordinal_numbers,y) -> .
% 299.99/300.68  132314[5:Res:130703.0,11.0] || subclass(intersection(complement(u),complement(v)),complement(union(u,v)))* -> equal(intersection(complement(u),complement(v)),complement(union(u,v))).
% 299.99/300.68  132374[5:Res:132293.0,11.0] || subclass(intersection(complement(u),complement(singleton(u))),complement(successor(u)))* -> equal(intersection(complement(u),complement(singleton(u))),complement(successor(u))).
% 299.99/300.68  132417[5:Res:132294.0,11.0] || subclass(intersection(complement(u),complement(inverse(u))),complement(symmetrization_of(u)))* -> equal(intersection(complement(u),complement(inverse(u))),complement(symmetrization_of(u))).
% 299.99/300.68  134010[5:Res:8551.2,133836.0] || member(singleton(singleton(u)),cross_product(v,w))* member(singleton(singleton(u)),x)* well_ordering(ordinal_numbers,restrict(x,v,w))* -> .
% 299.99/300.68  134118[5:Res:133837.1,3689.0] || well_ordering(ordinal_numbers,complement(ordered_pair(u,v)))* -> equal(singleton(singleton(w)),unordered_pair(u,singleton(v)))* equal(singleton(singleton(w)),singleton(u)).
% 299.99/300.68  136985[5:SpR:482.0,18211.1] || subclass(ordinal_numbers,symmetric_difference(intersection(complement(u),complement(v)),w)) -> member(unordered_pair(x,y),complement(intersection(union(u,v),complement(w))))*.
% 299.99/300.68  136979[5:SpR:483.0,18211.1] || subclass(ordinal_numbers,symmetric_difference(u,intersection(complement(v),complement(w)))) -> member(unordered_pair(x,y),complement(intersection(complement(u),union(v,w))))*.
% 299.99/300.68  140383[0:Res:3618.1,47534.0] || member(not_subclass_element(u,intersection(complement(intersection(v,w)),u)),symmetric_difference(v,w))* -> subclass(u,intersection(complement(intersection(v,w)),u)).
% 299.99/300.68  140465[0:Rew:3597.0,140335.1] || member(not_subclass_element(symmetrization_of(u),symmetric_difference(u,inverse(u))),complement(intersection(u,inverse(u))))* -> subclass(symmetrization_of(u),symmetric_difference(u,inverse(u))).
% 299.99/300.68  140466[0:Rew:3596.0,140334.1] || member(not_subclass_element(successor(u),symmetric_difference(u,singleton(u))),complement(intersection(u,singleton(u))))* -> subclass(successor(u),symmetric_difference(u,singleton(u))).
% 299.99/300.68  140889[8:Rew:140603.0,66137.1] || asymmetric(u,v) -> equal(symmetric_difference(cross_product(v,v),intersection(u,inverse(u))),union(cross_product(v,v),intersection(u,inverse(u))))**.
% 299.99/300.68  140893[8:Rew:140603.0,66136.1] || asymmetric(u,v) -> equal(symmetric_difference(intersection(u,inverse(u)),cross_product(v,v)),union(intersection(u,inverse(u)),cross_product(v,v)))**.
% 299.99/300.68  145790[8:SpL:143170.0,116117.1] || member(u,cantor(ordinal_numbers)) equal(cross_product(u,ordinal_numbers),v) subclass(rest_of(ordinal_numbers),w) -> member(ordered_pair(u,v),w)*.
% 299.99/300.68  146745[5:Res:27.2,18571.2] || member(sum_class(u),v)* member(sum_class(u),w)* member(u,ordinal_numbers) subclass(ordinal_numbers,complement(intersection(w,v)))* -> .
% 299.99/300.68  148935[8:Res:148858.1,9420.2] || subclass(cross_product(u,v),inverse(subset_relation))* member(w,v)* member(x,u)* -> member(ordered_pair(x,w),complement(subset_relation))*.
% 299.99/300.68  153301[0:Obv:153256.1] || member(not_subclass_element(symmetric_difference(u,v),intersection(w,union(u,v))),w)* -> subclass(symmetric_difference(u,v),intersection(w,union(u,v))).
% 299.99/300.68  153354[0:Res:919.1,19676.0] ||  -> subclass(restrict(symmetric_difference(u,inverse(u)),v,w),x) member(not_subclass_element(restrict(symmetric_difference(u,inverse(u)),v,w),x),symmetrization_of(u))*.
% 299.99/300.68  153353[0:Res:919.1,19559.0] ||  -> subclass(restrict(symmetric_difference(u,singleton(u)),v,w),x) member(not_subclass_element(restrict(symmetric_difference(u,singleton(u)),v,w),x),successor(u))*.
% 299.99/300.68  153348[0:Res:919.1,18794.1] || member(not_subclass_element(restrict(intersection(u,v),w,x),y),symmetric_difference(u,v))* -> subclass(restrict(intersection(u,v),w,x),y).
% 299.99/300.68  153338[8:Res:919.1,66086.1] || member(not_subclass_element(restrict(complement(compose(element_relation,ordinal_numbers)),u,v),w),element_relation)* -> subclass(restrict(complement(compose(element_relation,ordinal_numbers)),u,v),w).
% 299.99/300.68  155220[0:SpR:154737.1,3616.0] || subclass(union(complement(u),complement(v)),union(u,v))* -> equal(symmetric_difference(complement(u),complement(v)),union(complement(u),complement(v))).
% 299.99/300.68  156823[8:Res:69184.1,40594.1] || member(singleton(compose(element_relation,ordinal_numbers)),element_relation) member(compose(element_relation,ordinal_numbers),ordinal_numbers) -> member(singleton(singleton(singleton(compose(element_relation,ordinal_numbers)))),element_relation)*.
% 299.99/300.68  156852[5:MRR:156822.0,8655.0] || member(union(u,v),ordinal_numbers) -> member(singleton(union(u,v)),complement(v))* member(singleton(singleton(singleton(union(u,v)))),element_relation)*.
% 299.99/300.68  156853[5:MRR:156821.0,8655.0] || member(union(u,v),ordinal_numbers) -> member(singleton(union(u,v)),complement(u))* member(singleton(singleton(singleton(union(u,v)))),element_relation)*.
% 299.99/300.68  159546[5:SpL:50855.1,28944.1] || member(singleton(u),subset_relation)* member(v,ordinal_numbers) subclass(rest_relation,u) -> equal(ordered_pair(v,rest_of(v)),first(singleton(u)))*.
% 299.99/300.68  156940[8:Res:156922.1,129.0] || member(u,inverse(subset_relation))* subclass(complement(subset_relation),v)* well_ordering(w,v)* -> member(least(w,complement(subset_relation)),complement(subset_relation))*.
% 299.99/300.68  9708[5:Rew:963.0,9705.2] || equal(successor(singleton(u)),u) member(singleton(singleton(singleton(u))),cross_product(ordinal_numbers,ordinal_numbers))* -> member(singleton(singleton(singleton(u))),successor_relation).
% 299.99/300.68  126573[5:Res:9461.1,11.0] || subclass(cross_product(ordinal_numbers,ordinal_numbers),not_subclass_element(recursion_equation_functions(u),v))* -> subclass(recursion_equation_functions(u),v) equal(not_subclass_element(recursion_equation_functions(u),v),cross_product(ordinal_numbers,ordinal_numbers)).
% 299.99/300.68  123052[8:SoR:119376.0,82.1] operation(cantor(restrict(u,v,cross_product(ordinal_numbers,ordinal_numbers)))) || subclass(cross_product(ordinal_numbers,ordinal_numbers),v) -> section(u,cross_product(ordinal_numbers,ordinal_numbers),v)*.
% 299.99/300.68  46171[5:SoR:9585.0,82.1] operation(domain_of(restrict(u,v,cross_product(ordinal_numbers,ordinal_numbers)))) || subclass(cross_product(ordinal_numbers,ordinal_numbers),v) -> section(u,cross_product(ordinal_numbers,ordinal_numbers),v)*.
% 299.99/300.68  36715[0:SpL:126.0,4392.1] operation(restrict(u,v,singleton(w))) || member(x,segment(u,v,w))* -> equal(ordered_pair(first(x),second(x)),x)**.
% 299.99/300.68  117613[8:Rew:116078.0,116571.2,116078.0,116571.2,116078.0,116571.2,116078.0,116571.1] operation(u) || section(v,cantor(cantor(u)),cantor(cantor(u))) -> subclass(cantor(intersection(cantor(u),v)),cantor(cantor(u)))*.
% 299.99/300.68  117612[8:Rew:116078.0,116570.2,116078.0,116570.1,116078.0,116570.1,116078.0,116570.1] operation(u) || subclass(cantor(intersection(cantor(u),v)),cantor(cantor(u)))* -> section(v,cantor(cantor(u)),cantor(cantor(u))).
% 299.99/300.68  117611[8:Rew:116078.0,116567.2,116078.0,116567.2,116078.0,116567.1,116078.0,116567.1] operation(u) || equal(cantor(intersection(cantor(u),v)),cantor(cantor(u))) -> section(v,cantor(cantor(u)),cantor(cantor(u)))*.
% 299.99/300.68  83700[8:Res:83681.1,129.0] || equal(cantor(u),domain_relation) subclass(cantor(u),v)* well_ordering(w,v)* -> member(least(w,cantor(u)),cantor(u))*.
% 299.99/300.68  82283[8:Res:81336.1,21.0] || subclass(domain_relation,complement(complement(cross_product(u,v))))* -> equal(ordered_pair(first(ordered_pair(identity_relation,identity_relation)),second(ordered_pair(identity_relation,identity_relation))),ordered_pair(identity_relation,identity_relation))**.
% 299.99/300.68  64371[7:Res:13227.2,3689.0] || subclass(u,ordered_pair(v,w))* -> equal(u,identity_relation) equal(regular(u),unordered_pair(v,singleton(w))) equal(regular(u),singleton(v)).
% 299.99/300.68  61480[5:Rew:106.0,61475.1] || member(not_subclass_element(compose(u,inverse(u)),identity_relation),subset_relation)* -> equal(not_subclass_element(compose(u,inverse(u)),identity_relation),ordered_pair(single_valued1(u),single_valued2(u))).
% 299.99/300.68  66491[7:Res:13061.0,9421.0] || member(u,v)* -> equal(integer_of(w),identity_relation) equal(ordered_pair(first(ordered_pair(u,w)),second(ordered_pair(u,w))),ordered_pair(u,w))**.
% 299.99/300.68  19428[7:Res:19069.0,13070.0] || well_ordering(u,complement(intersection(v,w))) -> equal(symmetric_difference(v,w),identity_relation) member(least(u,symmetric_difference(v,w)),symmetric_difference(v,w))*.
% 299.99/300.68  18990[7:Res:18949.0,13070.0] || well_ordering(u,v) -> equal(restrict(v,w,x),identity_relation) member(least(u,restrict(v,w,x)),restrict(v,w,x))*.
% 299.99/300.68  61886[7:Res:18517.1,9421.0] || member(u,v)* -> equal(singleton(w),identity_relation) equal(ordered_pair(first(ordered_pair(u,w)),second(ordered_pair(u,w))),ordered_pair(u,w))**.
% 299.99/300.68  13359[7:Rew:13036.0,9819.2] inductive(compose(restrict(u,v,v),restrict(u,v,v))) || transitive(u,v) -> member(identity_relation,restrict(u,v,v))*.
% 299.99/300.68  66498[7:Res:13061.0,8562.0] || member(not_subclass_element(u,intersection(v,omega)),v)* -> equal(integer_of(not_subclass_element(u,intersection(v,omega))),identity_relation) subclass(u,intersection(v,omega)).
% 299.99/300.68  165156[7:Res:132294.0,13113.0] || well_ordering(u,intersection(complement(v),complement(inverse(v)))) -> equal(segment(u,complement(symmetrization_of(v)),least(u,complement(symmetrization_of(v)))),identity_relation)**.
% 299.99/300.68  165155[7:Res:132293.0,13113.0] || well_ordering(u,intersection(complement(v),complement(singleton(v)))) -> equal(segment(u,complement(successor(v)),least(u,complement(successor(v)))),identity_relation)**.
% 299.99/300.68  165144[8:Res:156904.0,13113.0] || well_ordering(u,complement(subset_relation)) -> equal(segment(u,restrict(inverse(subset_relation),v,w),least(u,restrict(inverse(subset_relation),v,w))),identity_relation)**.
% 299.99/300.68  165141[7:Res:156513.0,13113.0] || well_ordering(u,complement(subset_relation)) -> equal(segment(u,symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation),least(u,symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation))),identity_relation)**.
% 299.99/300.68  165140[7:Res:156404.0,13113.0] || well_ordering(u,complement(subset_relation)) -> equal(segment(u,symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers)),least(u,symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers)))),identity_relation)**.
% 299.99/300.68  166508[7:Res:13248.1,18791.0] ||  -> equal(intersection(symmetric_difference(complement(u),complement(v)),w),identity_relation) member(regular(intersection(symmetric_difference(complement(u),complement(v)),w)),union(u,v))*.
% 299.99/300.68  166698[7:Res:13210.1,18791.0] ||  -> equal(intersection(u,symmetric_difference(complement(v),complement(w))),identity_relation) member(regular(intersection(u,symmetric_difference(complement(v),complement(w)))),union(v,w))*.
% 299.99/300.68  192080[8:Res:19531.1,19121.0] || equal(sum_class(intersection(u,v)),identity_relation) -> subclass(sum_class(intersection(u,v)),w) member(not_subclass_element(sum_class(intersection(u,v)),w),u)*.
% 299.99/300.68  192079[8:Res:19531.1,19120.0] || equal(sum_class(intersection(u,v)),identity_relation) -> subclass(sum_class(intersection(u,v)),w) member(not_subclass_element(sum_class(intersection(u,v)),w),v)*.
% 299.99/300.68  130940[5:Res:9563.3,9876.0] || connected(u,v) well_ordering(w,v)* subclass(not_well_ordering(u,v),x)* well_ordering(ordinal_numbers,x) -> well_ordering(u,v).
% 299.99/300.68  132238[2:Res:39609.2,898.0] inductive(restrict(u,v,w)) || well_ordering(x,restrict(u,v,w)) -> member(least(x,restrict(u,v,w)),u)*.
% 299.99/300.68  132211[2:Res:39609.2,18794.1] inductive(intersection(u,v)) || well_ordering(w,intersection(u,v)) member(least(w,intersection(u,v)),symmetric_difference(u,v))* -> .
% 299.99/300.68  50242[5:Res:8638.0,9660.2] || member(u,v)* member(w,x)* well_ordering(y,ordinal_numbers) -> member(least(y,cross_product(x,v)),cross_product(x,v))*.
% 299.99/300.68  50359[5:Res:8638.0,9636.2] || member(u,v)* member(u,w)* well_ordering(x,ordinal_numbers) -> member(least(x,intersection(w,v)),intersection(w,v))*.
% 299.99/300.68  18731[7:Obv:18730.3] || well_ordering(u,ordinal_numbers) connected(u,v) member(least(u,not_well_ordering(u,v)),not_well_ordering(u,v))* -> well_ordering(u,v).
% 299.99/300.68  179443[5:Res:9706.3,9876.0] || member(u,ordinal_numbers)* member(v,ordinal_numbers)* equal(successor(v),u)* subclass(successor_relation,w) well_ordering(ordinal_numbers,w)* -> .
% 299.99/300.68  41120[5:MRR:40587.1,41096.1] || member(u,ordinal_numbers)* member(v,u)* subclass(element_relation,w) well_ordering(x,w)* -> member(least(x,element_relation),element_relation)*.
% 299.99/300.68  28935[5:Res:8827.2,129.0] || member(u,ordinal_numbers)* subclass(rest_relation,v) subclass(v,w)* well_ordering(x,w)* -> member(least(x,v),v)*.
% 299.99/300.68  130725[5:Res:130678.0,9633.1] || member(u,ordinal_numbers) well_ordering(v,w) -> member(u,complement(w))* member(least(v,complement(complement(w))),complement(complement(w)))*.
% 299.99/300.68  130848[5:Res:8832.1,9876.0] || member(u,ordinal_numbers) subclass(intersection(complement(v),complement(w)),x)* well_ordering(ordinal_numbers,x) -> member(u,union(v,w))*.
% 299.99/300.68  46643[5:Res:9618.2,19.0] || member(ordered_pair(u,v),cross_product(ordinal_numbers,ordinal_numbers)) subclass(composition_function,cross_product(w,x))* -> member(ordered_pair(v,compose(u,v)),x)*.
% 299.99/300.68  46616[5:Res:9618.2,152.0] || member(ordered_pair(u,v),cross_product(ordinal_numbers,ordinal_numbers)) subclass(composition_function,recursion_equation_functions(w))* -> function(ordered_pair(u,ordered_pair(v,compose(u,v))))*.
% 299.99/300.68  117609[8:Rew:116078.0,116541.3,116078.0,116541.2] operation(u) || member(ordered_pair(v,w),cross_product(ordinal_numbers,ordinal_numbers))* subclass(composition_function,cantor(u)) -> member(v,cantor(cantor(u)))*.
% 299.99/300.68  194990[7:SpR:33.0,13344.2] || asymmetric(cross_product(u,v),w) subclass(compose(identity_relation,identity_relation),identity_relation) -> transitive(restrict(inverse(cross_product(u,v)),u,v),w)*.
% 299.99/300.68  195839[8:SpR:33.0,15666.1] || asymmetric(cross_product(u,v),singleton(w)) -> equal(domain__dfg(restrict(inverse(cross_product(u,v)),u,v),singleton(w),w),single_valued3(identity_relation))**.
% 299.99/300.68  195845[8:Rew:50855.1,195838.1] || member(singleton(u),subset_relation) asymmetric(v,u) -> equal(domain__dfg(intersection(v,inverse(v)),u,first(singleton(u))),single_valued3(identity_relation))**.
% 299.99/300.68  196105[18:Res:190510.1,3689.0] || subclass(inverse(identity_relation),ordered_pair(u,v))* -> equal(unordered_pair(u,singleton(v)),regular(symmetrization_of(identity_relation))) equal(regular(symmetrization_of(identity_relation)),singleton(u)).
% 299.99/300.68  196220[7:Res:13501.2,5.0] || well_ordering(u,cross_product(ordinal_numbers,ordinal_numbers)) subclass(compose_class(v),w) -> equal(compose_class(v),identity_relation) member(least(u,compose_class(v)),w)*.
% 299.99/300.68  196281[7:Res:13500.2,5.0] || well_ordering(u,cross_product(ordinal_numbers,ordinal_numbers)) subclass(rest_of(v),w) -> equal(rest_of(v),identity_relation) member(least(u,rest_of(v)),w)*.
% 299.99/300.68  197193[8:Obv:197180.2] || member(u,v) member(u,unordered_pair(v,w))* -> equal(regular(unordered_pair(v,w)),w) equal(unordered_pair(v,w),identity_relation).
% 299.99/300.68  197194[8:Obv:197179.2] || member(u,v) member(u,unordered_pair(w,v))* -> equal(regular(unordered_pair(w,v)),w) equal(unordered_pair(w,v),identity_relation).
% 299.99/300.68  197293[7:SpR:154737.1,13299.1] || subclass(inverse(u),u)* asymmetric(u,singleton(v)) -> equal(range__dfg(inverse(u),v,singleton(v)),second(not_subclass_element(identity_relation,identity_relation)))**.
% 299.99/300.68  197845[7:SpL:13302.1,9777.0] || asymmetric(cross_product(u,v),w) equal(compose(identity_relation,identity_relation),identity_relation) -> transitive(restrict(inverse(cross_product(u,v)),u,v),w)*.
% 299.99/300.68  197865[7:MRR:197864.2,13039.0] || asymmetric(cross_product(u,v),w) transitive(restrict(inverse(cross_product(u,v)),u,v),w)* -> equal(compose(identity_relation,identity_relation),identity_relation).
% 299.99/300.68  197979[21:SpR:161356.2,196555.1] || member(u,ordinal_numbers) member(not_subclass_element(identity_relation,identity_relation),subset_relation) -> member(u,cantor(v)) equal(cantor(range__dfg(v,u,ordinal_numbers)),identity_relation)**.
% 299.99/300.68  199090[14:Res:165168.1,13362.0] || equal(u,singleton(identity_relation)) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(identity_relation,least(omega,u))),identity_relation)**.
% 299.99/300.68  199089[18:Res:190442.1,13362.0] || equal(u,symmetrization_of(identity_relation)) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(identity_relation,least(omega,u))),identity_relation)**.
% 299.99/300.68  199088[18:Res:190593.1,13362.0] || equal(u,inverse(identity_relation)) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(identity_relation,least(omega,u))),identity_relation)**.
% 299.99/300.68  199083[14:Res:165172.1,13362.0] || subclass(complement(u),v)* well_ordering(omega,v) -> member(identity_relation,u) equal(integer_of(ordered_pair(identity_relation,least(omega,complement(u)))),identity_relation)**.
% 299.99/300.68  199047[7:Res:8645.1,13362.0] || subclass(ordinal_numbers,u) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(singleton(w),least(omega,u))),identity_relation)**.
% 299.99/300.68  199045[7:Res:143198.1,13362.0] || equal(u,ordinal_numbers) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(singleton(w),least(omega,u))),identity_relation)**.
% 299.99/300.68  199038[7:Res:962.0,13362.0] || subclass(ordered_pair(u,v),w)* well_ordering(omega,w) -> equal(integer_of(ordered_pair(singleton(u),least(omega,ordered_pair(u,v)))),identity_relation)**.
% 299.99/300.68  198997[7:Res:148963.1,13362.0] || member(u,ordinal_numbers) subclass(ordinal_numbers,v) well_ordering(omega,v)* -> equal(integer_of(ordered_pair(rest_of(u),least(omega,ordinal_numbers))),identity_relation)**.
% 299.99/300.68  198995[7:Res:41183.1,13362.0] || subclass(ordinal_numbers,u) well_ordering(omega,u)* -> subclass(v,w) equal(integer_of(ordered_pair(not_subclass_element(v,w),least(omega,ordinal_numbers))),identity_relation)**.
% 299.99/300.68  198994[7:Res:50064.1,13362.0] || member(u,subset_relation) subclass(ordinal_numbers,v) well_ordering(omega,v)* -> equal(integer_of(ordered_pair(second(u),least(omega,ordinal_numbers))),identity_relation)**.
% 299.99/300.68  198993[7:Res:50063.1,13362.0] || member(u,subset_relation) subclass(ordinal_numbers,v) well_ordering(omega,v)* -> equal(integer_of(ordered_pair(first(u),least(omega,ordinal_numbers))),identity_relation)**.
% 299.99/300.68  198990[7:Res:8955.1,13362.0] || member(u,ordinal_numbers) subclass(ordinal_numbers,v) well_ordering(omega,v)* -> equal(integer_of(ordered_pair(sum_class(u),least(omega,ordinal_numbers))),identity_relation)**.
% 299.99/300.68  198972[7:Res:6.1,13362.0] || subclass(u,v)* well_ordering(omega,v)* -> subclass(u,w) equal(integer_of(ordered_pair(not_subclass_element(u,w),least(omega,u))),identity_relation)**.
% 299.99/300.68  39968[5:Res:94.3,39811.1] operation(u) operation(v) || compatible(w,v,u) equal(complement(rest_of(v)),ordinal_numbers) -> homomorphism(w,v,u)*.
% 299.99/300.68  116421[8:Rew:116078.0,39271.3] operation(u) operation(v) || compatible(w,v,u) subclass(ordinal_numbers,complement(cantor(v)))* -> homomorphism(w,v,u)*.
% 299.99/300.68  156824[5:Res:18819.1,40594.1] || member(singleton(cross_product(ordinal_numbers,ordinal_numbers)),subset_relation) member(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers) -> member(singleton(singleton(singleton(cross_product(ordinal_numbers,ordinal_numbers)))),element_relation)*.
% 299.99/300.68  140887[8:Rew:140603.0,116397.2] || member(u,ordinal_numbers) -> member(u,cantor(v)) equal(symmetric_difference(cross_product(singleton(u),ordinal_numbers),v),union(cross_product(singleton(u),ordinal_numbers),v))**.
% 299.99/300.68  140890[8:Rew:140603.0,116396.2] || member(u,ordinal_numbers) -> member(u,cantor(v)) equal(symmetric_difference(v,cross_product(singleton(u),ordinal_numbers)),union(v,cross_product(singleton(u),ordinal_numbers)))**.
% 299.99/300.68  46051[5:Res:8665.1,9470.1] function(image(u,image(v,singleton(w)))) || member(ordered_pair(w,x),compose(u,v))* -> member(x,cross_product(ordinal_numbers,ordinal_numbers)).
% 299.99/300.68  199000[7:Res:18510.1,13362.0] function(u) || subclass(ordinal_numbers,v) well_ordering(omega,v)* -> equal(integer_of(ordered_pair(apply(u,w),least(omega,ordinal_numbers))),identity_relation)**.
% 299.99/300.68  195710[8:Res:13225.3,14681.0] || member(u,ordinal_numbers) subclass(u,regular(v)) member(apply(choice,u),v)* -> equal(u,identity_relation) equal(v,identity_relation).
% 299.99/300.68  195699[7:Res:13225.3,897.0] || member(u,ordinal_numbers) subclass(u,restrict(v,w,x))* -> equal(u,identity_relation) member(apply(choice,u),cross_product(w,x))*.
% 299.99/300.68  195680[7:Res:13225.3,18794.1] || member(u,ordinal_numbers) subclass(u,intersection(v,w)) member(apply(choice,u),symmetric_difference(v,w))* -> equal(u,identity_relation).
% 299.99/300.68  198669[7:MRR:198668.0,8666.0] || subclass(unordered_pair(u,v),w)* -> equal(apply(choice,unordered_pair(u,v)),u)** equal(unordered_pair(u,v),identity_relation) member(v,w).
% 299.99/300.68  198667[7:MRR:198666.0,8666.0] || subclass(unordered_pair(u,v),w)* -> equal(apply(choice,unordered_pair(u,v)),v)** equal(unordered_pair(u,v),identity_relation) member(u,w).
% 299.99/300.68  194669[8:Rew:160491.0,194635.2,160491.0,194635.0] || member(union(u,identity_relation),ordinal_numbers) member(apply(choice,union(u,identity_relation)),symmetric_difference(ordinal_numbers,u))* -> equal(union(u,identity_relation),identity_relation).
% 299.99/300.68  13257[7:Rew:13036.0,8915.1] || member(restrict(u,v,w),ordinal_numbers) -> equal(restrict(u,v,w),identity_relation) member(apply(choice,restrict(u,v,w)),u)*.
% 299.99/300.68  197445[7:Rew:163.0,197348.1,163.0,197348.0] || member(symmetric_difference(u,v),ordinal_numbers) -> equal(symmetric_difference(u,v),identity_relation) member(apply(choice,symmetric_difference(u,v)),complement(intersection(u,v)))*.
% 299.99/300.68  197694[7:Res:13247.2,3700.0] || member(intersection(u,singleton(v)),ordinal_numbers) -> equal(intersection(u,singleton(v)),identity_relation) equal(apply(choice,intersection(u,singleton(v))),v)**.
% 299.99/300.68  197405[7:Res:13246.2,3700.0] || member(intersection(singleton(u),v),ordinal_numbers) -> equal(intersection(singleton(u),v),identity_relation) equal(apply(choice,intersection(singleton(u),v)),u)**.
% 299.99/300.68  163942[7:Res:13069.2,18794.1] || member(intersection(u,v),ordinal_numbers) member(apply(choice,intersection(u,v)),symmetric_difference(u,v))* -> equal(intersection(u,v),identity_relation).
% 299.99/300.68  146815[5:Res:27.2,18535.2] || member(power_class(u),v)* member(power_class(u),w)* member(u,ordinal_numbers) subclass(ordinal_numbers,complement(intersection(w,v)))* -> .
% 299.99/300.68  198999[7:Res:8956.1,13362.0] || member(u,ordinal_numbers) subclass(ordinal_numbers,v) well_ordering(omega,v)* -> equal(integer_of(ordered_pair(power_class(u),least(omega,ordinal_numbers))),identity_relation)**.
% 299.99/300.68  131001[5:Res:62.1,9876.0] || member(ordered_pair(u,v),compose(w,x))* subclass(image(w,image(x,singleton(u))),y)* well_ordering(ordinal_numbers,y) -> .
% 299.99/300.68  195388[16:Rew:195224.0,193326.2] || member(u,ordinal_numbers) -> member(u,intersection(power_class(complement(singleton(identity_relation))),complement(v)))* member(u,union(image(element_relation,singleton(identity_relation)),v)).
% 299.99/300.68  195392[16:Rew:195224.0,193333.2] || member(u,ordinal_numbers) -> member(u,intersection(complement(v),power_class(complement(singleton(identity_relation)))))* member(u,union(v,image(element_relation,singleton(identity_relation)))).
% 299.99/300.68  195628[16:Rew:195224.0,195398.1] || subclass(image(element_relation,singleton(identity_relation)),complement(power_class(complement(singleton(identity_relation)))))* -> equal(complement(power_class(complement(singleton(identity_relation)))),image(element_relation,singleton(identity_relation))).
% 299.99/300.68  36688[0:SpR:159.0,284.1] || member(image(recursion(u,successor_relation,union_of_range_map),singleton(v)),ordinal_numbers) -> subclass(ordinal_add(u,v),image(recursion(u,successor_relation,union_of_range_map),singleton(v)))*.
% 299.99/300.68  65583[8:Res:9006.3,14681.0] function(u) || member(v,ordinal_numbers) subclass(ordinal_numbers,regular(w)) member(image(u,v),w)* -> equal(w,identity_relation).
% 299.99/300.68  39335[5:Res:9006.3,897.0] function(u) || member(v,ordinal_numbers) subclass(ordinal_numbers,restrict(w,x,y))* -> member(image(u,v),cross_product(x,y))*.
% 299.99/300.68  131491[5:Res:9006.3,18794.1] function(u) || member(v,ordinal_numbers) subclass(ordinal_numbers,intersection(w,x)) member(image(u,v),symmetric_difference(w,x))* -> .
% 299.99/300.68  39341[5:Res:9006.3,288.0] function(u) || member(v,ordinal_numbers) subclass(ordinal_numbers,image(element_relation,complement(w))) member(image(u,v),power_class(w))* -> .
% 299.99/300.68  39616[2:Res:52.1,9665.1] inductive(u) inductive(image(successor_relation,u)) || well_ordering(v,u) -> member(least(v,image(successor_relation,u)),image(successor_relation,u))*.
% 299.99/300.68  132991[5:SpR:50855.1,19485.0] || member(singleton(u),subset_relation) -> equal(power_class(intersection(complement(first(singleton(u))),complement(u))),complement(image(element_relation,successor(first(singleton(u))))))**.
% 299.99/300.68  136630[0:SpL:481.0,18791.0] || member(u,symmetric_difference(complement(v),power_class(intersection(complement(w),complement(x)))))* -> member(u,union(v,image(element_relation,union(w,x)))).
% 299.99/300.68  19484[0:SpR:481.0,485.0] ||  -> equal(union(u,image(element_relation,power_class(intersection(complement(v),complement(w))))),complement(intersection(complement(u),power_class(image(element_relation,union(v,w))))))**.
% 299.99/300.68  136643[0:SpL:481.0,18791.0] || member(u,symmetric_difference(power_class(intersection(complement(v),complement(w))),complement(x)))* -> member(u,union(image(element_relation,union(v,w)),x)).
% 299.99/300.68  159470[5:Rew:30.0,159422.1] ||  -> member(not_subclass_element(u,image(element_relation,union(v,w))),power_class(intersection(complement(v),complement(w))))* subclass(u,image(element_relation,union(v,w))).
% 299.99/300.68  19477[0:SpR:481.0,487.0] ||  -> equal(union(image(element_relation,power_class(intersection(complement(u),complement(v)))),w),complement(intersection(power_class(image(element_relation,union(u,v))),complement(w))))**.
% 299.99/300.68  19796[0:SpR:481.0,19733.0] ||  -> subclass(symmetric_difference(power_class(intersection(complement(u),complement(v))),complement(singleton(image(element_relation,union(u,v))))),successor(image(element_relation,union(u,v))))*.
% 299.99/300.68  19813[0:SpR:481.0,19734.0] ||  -> subclass(symmetric_difference(power_class(intersection(complement(u),complement(v))),complement(inverse(image(element_relation,union(u,v))))),symmetrization_of(image(element_relation,union(u,v))))*.
% 299.99/300.68  151947[5:SpR:481.0,147905.0] ||  -> equal(intersection(image(element_relation,union(u,v)),complement(power_class(intersection(complement(u),complement(v))))),complement(power_class(intersection(complement(u),complement(v)))))**.
% 299.99/300.68  19514[7:Rew:481.0,19503.1] || subclass(power_class(intersection(complement(u),complement(v))),image(element_relation,union(u,v)))* -> equal(power_class(intersection(complement(u),complement(v))),identity_relation).
% 299.99/300.68  36243[0:SpR:189.0,483.0] ||  -> equal(union(u,intersection(complement(v),power_class(image(element_relation,complement(w))))),complement(intersection(complement(u),union(v,image(element_relation,power_class(w))))))**.
% 299.99/300.68  155386[0:SpL:189.0,941.1] || member(u,image(element_relation,power_class(image(element_relation,power_class(v))))) member(u,power_class(image(element_relation,power_class(image(element_relation,complement(v))))))* -> .
% 299.99/300.68  36853[5:SpL:189.0,8825.1] || member(u,ordinal_numbers) subclass(power_class(image(element_relation,complement(v))),w)* -> member(u,image(element_relation,power_class(v)))* member(u,w)*.
% 299.99/300.68  36191[0:SpR:189.0,482.0] ||  -> equal(union(intersection(complement(u),power_class(image(element_relation,complement(v)))),w),complement(intersection(union(u,image(element_relation,power_class(v))),complement(w))))**.
% 299.99/300.68  36255[0:SpR:189.0,483.0] ||  -> equal(union(u,intersection(power_class(image(element_relation,complement(v))),complement(w))),complement(intersection(complement(u),union(image(element_relation,power_class(v)),w))))**.
% 299.99/300.68  196447[21:Rew:196372.1,174472.2] || member(u,ordinal_numbers) subclass(domain_relation,power_class(image(element_relation,complement(v)))) member(ordered_pair(u,identity_relation),image(element_relation,power_class(v)))* -> .
% 299.99/300.68  36203[0:SpR:189.0,482.0] ||  -> equal(union(intersection(power_class(image(element_relation,complement(u))),complement(v)),w),complement(intersection(union(image(element_relation,power_class(u)),v),complement(w))))**.
% 299.99/300.68  130697[5:Rew:189.0,130620.1] ||  -> member(not_subclass_element(complement(power_class(image(element_relation,complement(u)))),v),image(element_relation,power_class(u)))* subclass(complement(power_class(image(element_relation,complement(u)))),v).
% 299.99/300.68  155439[5:Res:49995.1,941.1] || member(power_class(image(element_relation,complement(u))),subset_relation) member(singleton(first(power_class(image(element_relation,complement(u))))),image(element_relation,power_class(u)))* -> .
% 299.99/300.68  193460[8:Res:163093.0,11.0] || subclass(image(element_relation,symmetrization_of(identity_relation)),complement(power_class(complement(inverse(identity_relation)))))* -> equal(complement(power_class(complement(inverse(identity_relation)))),image(element_relation,symmetrization_of(identity_relation))).
% 299.99/300.68  193490[8:SpR:162038.0,8832.1] || member(u,ordinal_numbers) -> member(u,intersection(power_class(complement(inverse(identity_relation))),complement(v)))* member(u,union(image(element_relation,symmetrization_of(identity_relation)),v)).
% 299.99/300.68  193497[8:SpR:162038.0,8832.1] || member(u,ordinal_numbers) -> member(u,intersection(complement(v),power_class(complement(inverse(identity_relation)))))* member(u,union(v,image(element_relation,symmetrization_of(identity_relation)))).
% 299.99/300.68  195707[7:Res:13225.3,288.0] || member(u,ordinal_numbers) subclass(u,image(element_relation,complement(v))) member(apply(choice,u),power_class(v))* -> equal(u,identity_relation).
% 299.99/300.68  19383[0:SpR:485.0,163.0] ||  -> equal(intersection(complement(intersection(u,image(element_relation,complement(v)))),complement(intersection(complement(u),power_class(v)))),symmetric_difference(u,image(element_relation,complement(v))))**.
% 299.99/300.68  165300[7:Res:130710.0,13070.0] || well_ordering(u,image(element_relation,complement(v))) -> equal(complement(power_class(v)),identity_relation) member(least(u,complement(power_class(v))),complement(power_class(v)))*.
% 299.99/300.68  19456[0:SpR:487.0,163.0] ||  -> equal(intersection(complement(intersection(image(element_relation,complement(u)),v)),complement(intersection(power_class(u),complement(v)))),symmetric_difference(image(element_relation,complement(u)),v))**.
% 299.99/300.68  130754[5:Res:130710.0,9665.1] inductive(complement(power_class(u))) || well_ordering(v,image(element_relation,complement(u))) -> member(least(v,complement(power_class(u))),complement(power_class(u)))*.
% 299.99/300.68  162881[0:Res:52.1,19121.0] inductive(intersection(u,v)) ||  -> subclass(image(successor_relation,intersection(u,v)),w) member(not_subclass_element(image(successor_relation,intersection(u,v)),w),u)*.
% 299.99/300.68  162880[0:Res:52.1,19120.0] inductive(intersection(u,v)) ||  -> subclass(image(successor_relation,intersection(u,v)),w) member(not_subclass_element(image(successor_relation,intersection(u,v)),w),v)*.
% 299.99/300.68  69373[8:Res:69184.1,9471.0] || member(ordered_pair(u,not_subclass_element(v,image(element_relation,image(ordinal_numbers,singleton(u))))),element_relation)* -> subclass(v,image(element_relation,image(ordinal_numbers,singleton(u)))).
% 299.99/300.68  198795[21:SpR:196556.1,116203.2] function(not_subclass_element(u,v)) || subclass(range_of(not_subclass_element(u,v)),w) -> subclass(u,v) maps(not_subclass_element(u,v),identity_relation,w)*.
% 299.99/300.68  198745[21:SpR:196564.1,116203.2] function(u) function(apply(u,v)) || subclass(range_of(apply(u,v)),w) -> maps(apply(u,v),identity_relation,w)*.
% 299.99/300.68  196991[21:Rew:160429.0,196980.1] function(u) || subclass(range_of(u),identity_relation) equal(cantor(cantor(v)),cantor(u)) -> compatible(u,v,sum_class(range_of(identity_relation)))*.
% 299.99/300.68  198982[15:Res:165526.1,13362.0] || subclass(ordinal_numbers,u) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(range_of(identity_relation),least(omega,u))),identity_relation)**.
% 299.99/300.68  63694[8:SoR:8530.0,19277.2] single_valued_class(inverse(u)) || subclass(range_of(inverse(u)),v) equal(inverse(u),identity_relation) -> maps(inverse(u),range_of(u),v)*.
% 299.99/300.68  135130[8:Res:135059.1,117617.1] function(u) || equal(rest_of(range_of(v)),rest_relation) equal(cantor(cantor(w)),cantor(u)) -> compatible(u,w,inverse(v))*.
% 299.99/300.68  61726[5:Res:9618.2,157.0] || member(ordered_pair(u,v),cross_product(ordinal_numbers,ordinal_numbers))* subclass(composition_function,union_of_range_map) -> equal(ordered_pair(v,compose(u,v)),sum_class(range_of(u)))**.
% 299.99/300.68  197238[21:Rew:160429.0,197227.1] function(u) || subclass(range_of(u),identity_relation) equal(cantor(cantor(v)),cantor(u)) -> compatible(u,v,ordered_pair(w,x))*.
% 299.99/300.68  197156[21:Rew:160429.0,197145.1] function(u) || subclass(range_of(u),identity_relation) equal(cantor(cantor(v)),cantor(u)) -> compatible(u,v,unordered_pair(w,x))*.
% 299.99/300.68  197075[21:Rew:160429.0,197064.1] function(u) || subclass(range_of(u),identity_relation) equal(cantor(cantor(v)),cantor(u)) -> compatible(u,v,least(element_relation,omega))*.
% 299.99/300.68  197033[21:Rew:160429.0,197022.1] function(u) || subclass(range_of(u),identity_relation) equal(cantor(cantor(v)),cantor(u)) -> compatible(u,v,regular(symmetrization_of(identity_relation)))*.
% 299.99/300.68  202347[22:Res:202344.0,13362.0] || subclass(singleton(singleton(identity_relation)),u)* well_ordering(omega,u) -> equal(integer_of(ordered_pair(singleton(identity_relation),least(omega,singleton(singleton(identity_relation))))),identity_relation)**.
% 299.99/300.68  204128[8:Res:194487.1,9665.1] inductive(singleton(u)) || member(u,inverse(identity_relation)) well_ordering(v,symmetrization_of(identity_relation)) -> member(least(v,singleton(u)),singleton(u))*.
% 299.99/300.68  204125[8:Res:194487.1,13070.0] || member(u,inverse(identity_relation)) well_ordering(v,symmetrization_of(identity_relation)) -> equal(singleton(u),identity_relation) member(least(v,singleton(u)),singleton(u))*.
% 299.99/300.68  204200[18:Res:194549.1,3689.0] || subclass(symmetrization_of(identity_relation),ordered_pair(u,v))* -> equal(unordered_pair(u,singleton(v)),regular(symmetrization_of(identity_relation))) equal(regular(symmetrization_of(identity_relation)),singleton(u)).
% 299.99/300.68  192250[8:Rew:8637.0,192242.2] single_valued_class(image(successor_relation,cross_product(universal_class,universal_class))) || member(identity_relation,cross_product(ordinal_numbers,ordinal_numbers)) equal(image(successor_relation,cross_product(ordinal_numbers,ordinal_numbers)),identity_relation)** -> .
% 299.99/300.68  192243[8:SoR:162899.0,19277.2] single_valued_class(image(successor_relation,cross_product(ordinal_numbers,ordinal_numbers))) || member(identity_relation,cross_product(ordinal_numbers,ordinal_numbers)) equal(image(successor_relation,cross_product(ordinal_numbers,ordinal_numbers)),identity_relation)** -> .
% 299.99/300.68  205614[23:Res:205609.0,13362.0] || subclass(complement(recursion_equation_functions(u)),v)* well_ordering(omega,v) -> equal(integer_of(ordered_pair(singleton(identity_relation),least(omega,complement(recursion_equation_functions(u))))),identity_relation)**.
% 299.99/300.68  207539[8:Res:192400.1,13113.0] || member(u,ordinals_with_null_class_as_identity) well_ordering(v,complement(u)) -> equal(segment(v,symmetric_difference(u,ordinal_numbers),least(v,symmetric_difference(u,ordinal_numbers))),identity_relation)**.
% 299.99/300.68  208013[24:MRR:198842.4,207942.0] function(not_subclass_element(u,v)) || subclass(range_of(not_subclass_element(u,v)),identity_relation)* equal(cross_product(identity_relation,identity_relation),identity_relation) -> subclass(u,v).
% 299.99/300.68  208016[24:MRR:198786.4,207951.1] function(u) function(apply(u,v)) || subclass(range_of(apply(u,v)),identity_relation)* equal(cross_product(identity_relation,identity_relation),identity_relation) -> .
% 299.99/300.68  208066[24:Rew:207558.1,208045.1] operation(u) || member(restrict(v,w,identity_relation),ordinal_numbers) -> member(ordered_pair(restrict(v,w,identity_relation),segment(v,w,u)),domain_relation)*.
% 299.99/300.68  208292[24:SpR:207572.1,116123.2] operation(u) || member(identity_relation,cantor(v)) equal(restrict(v,identity_relation,ordinal_numbers),u)* -> member(singleton(singleton(identity_relation)),rest_of(v))*.
% 299.99/300.68  208508[7:SpL:13260.1,18.0] || member(regular(cross_product(u,v)),cross_product(w,x))* -> equal(cross_product(u,v),identity_relation) member(first(regular(cross_product(u,v))),w).
% 299.99/300.68  208507[7:SpL:13260.1,19.0] || member(regular(cross_product(u,v)),cross_product(w,x))* -> equal(cross_product(u,v),identity_relation) member(second(regular(cross_product(u,v))),x).
% 299.99/300.68  208505[8:SpL:13260.1,116129.0] || member(regular(cross_product(u,v)),rest_of(w)) -> equal(cross_product(u,v),identity_relation) member(first(regular(cross_product(u,v))),cantor(w))*.
% 299.99/300.68  209290[25:SpR:208840.0,117604.3] operation(u) || member(ordinal_numbers,cantor(cantor(u))) member(identity_relation,cantor(cantor(u))) -> member(singleton(singleton(identity_relation)),cantor(u))*.
% 299.99/300.68  209423[25:SpR:208885.0,9005.1] || member(restrict(element_relation,ordinal_numbers,image(u,identity_relation)),ordinal_numbers) -> member(ordered_pair(restrict(element_relation,ordinal_numbers,image(u,identity_relation)),apply(u,ordinal_numbers)),domain_relation)*.
% 299.99/300.68  209436[25:Rew:208885.0,209430.2] || member(image(u,identity_relation),ordinal_numbers) subclass(image(u,identity_relation),apply(u,ordinal_numbers))* -> equal(apply(u,ordinal_numbers),image(u,identity_relation)).
% 299.99/300.68  209634[25:Rew:208820.0,209618.1] || member(ordered_pair(ordinal_numbers,not_subclass_element(u,image(v,image(w,identity_relation)))),compose(v,w))* -> subclass(u,image(v,image(w,identity_relation))).
% 299.99/300.68  209747[25:Rew:209659.0,209702.2,209659.0,209702.0] ||  -> subclass(ordered_pair(ordinal_numbers,ordinal_numbers),u) equal(not_subclass_element(ordered_pair(ordinal_numbers,ordinal_numbers),u),unordered_pair(ordinal_numbers,identity_relation))** equal(not_subclass_element(ordered_pair(ordinal_numbers,ordinal_numbers),u),identity_relation).
% 299.99/300.68  209812[8:Res:206259.0,11.0] || subclass(union(u,identity_relation),symmetric_difference(complement(u),symmetric_difference(ordinal_numbers,u)))* -> equal(symmetric_difference(complement(u),symmetric_difference(ordinal_numbers,u)),union(u,identity_relation)).
% 299.99/300.68  209894[24:Res:207866.1,13113.0] operation(u) || well_ordering(v,symmetric_difference(ordinal_numbers,u)) -> equal(segment(v,complement(successor(u)),least(v,complement(successor(u)))),identity_relation)**.
% 299.99/300.68  209950[15:Res:209921.1,13362.0] || equal(u,ordinal_numbers) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(range_of(identity_relation),least(omega,u))),identity_relation)**.
% 299.99/300.68  210136[8:Res:208722.1,13113.0] || well_ordering(u,complement(v)) -> equal(singleton(v),identity_relation) equal(segment(u,symmetric_difference(v,ordinal_numbers),least(u,symmetric_difference(v,ordinal_numbers))),identity_relation)**.
% 299.99/300.68  212376[7:SpL:13259.2,39295.0] || member(cross_product(u,v),ordinal_numbers) subclass(ordinal_numbers,complement(singleton(apply(choice,cross_product(u,v)))))* -> equal(cross_product(u,v),identity_relation).
% 299.99/300.68  212375[7:SpL:13259.2,39306.0] || member(cross_product(u,v),ordinal_numbers) equal(complement(singleton(apply(choice,cross_product(u,v)))),ordinal_numbers)** -> equal(cross_product(u,v),identity_relation).
% 299.99/300.68  213496[8:Rew:145761.0,213460.0] || member(cross_product(u,singleton(v)),segment(ordinal_numbers,u,v)) -> member(ordered_pair(cross_product(u,singleton(v)),segment(ordinal_numbers,u,v)),element_relation)*.
% 299.99/300.68  214073[5:Res:9006.3,152274.0] function(u) || member(v,ordinal_numbers) subclass(ordinal_numbers,complement(singleton(image(u,v))))* -> subclass(singleton(image(u,v)),w)*.
% 299.99/300.68  214050[7:Res:13225.3,152274.0] || member(u,ordinal_numbers) subclass(u,complement(singleton(apply(choice,u))))* -> equal(u,identity_relation) subclass(singleton(apply(choice,u)),v)*.
% 299.99/300.68  214319[25:Rew:208887.0,214268.0] || member(restrict(u,v,identity_relation),segment(u,v,ordinal_numbers)) -> member(ordered_pair(restrict(u,v,identity_relation),segment(u,v,ordinal_numbers)),element_relation)*.
% 299.99/300.68  214563[25:SpL:208985.1,8799.1] operation(u) || equal(successor(v),u) member(ordered_pair(v,ordinal_numbers),cross_product(ordinal_numbers,ordinal_numbers))* -> member(ordered_pair(v,u),successor_relation)*.
% 299.99/300.68  214508[25:SpL:208985.1,8799.1] operation(u) || equal(successor(v),ordinal_numbers) member(ordered_pair(v,u),cross_product(ordinal_numbers,ordinal_numbers))* -> member(ordered_pair(v,ordinal_numbers),successor_relation).
% 299.99/300.68  214463[25:SpR:208985.1,116123.2] operation(u) || member(v,cantor(w)) equal(restrict(w,v,ordinal_numbers),u)* -> member(ordered_pair(v,ordinal_numbers),rest_of(w))*.
% 299.99/300.68  214426[25:SpR:208985.1,116123.2] operation(u) || member(v,cantor(w)) equal(restrict(w,v,ordinal_numbers),ordinal_numbers) -> member(ordered_pair(v,u),rest_of(w))*.
% 299.99/300.68  214764[25:SpL:6355.1,214618.1] operation(second(not_subclass_element(cross_product(u,v),w))) || member(not_subclass_element(cross_product(u,v),w),rest_relation)* -> subclass(cross_product(u,v),w).
% 299.99/300.68  215207[7:Res:155157.1,13113.0] || subclass(u,v) well_ordering(w,complement(u)) -> equal(segment(w,symmetric_difference(v,u),least(w,symmetric_difference(v,u))),identity_relation)**.
% 299.99/300.68  217391[8:Res:216591.1,13362.0] || equal(complement(u),identity_relation) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(identity_relation,least(omega,u))),identity_relation)**.
% 299.99/300.68  217481[8:EmS:13166.0,13166.1,10858.2,211442.1] single_valued_class(complement(u)) || equal(cross_product(ordinal_numbers,ordinal_numbers),complement(u))* equal(complement(u),ordinal_numbers) -> member(identity_relation,cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.68  217473[8:EmS:13166.0,13166.1,10858.2,211493.1] single_valued_class(power_class(u)) || equal(cross_product(ordinal_numbers,ordinal_numbers),power_class(u))* equal(power_class(u),ordinal_numbers) -> member(identity_relation,cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.68  217465[8:EmS:13166.0,13166.1,10858.2,214832.1] single_valued_class(successor(u)) || equal(cross_product(ordinal_numbers,ordinal_numbers),successor(u))* equal(successor(u),ordinal_numbers) -> member(identity_relation,cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.68  217461[8:EmS:13166.0,13166.1,10858.2,214833.1] single_valued_class(symmetrization_of(u)) || equal(cross_product(ordinal_numbers,ordinal_numbers),symmetrization_of(u))* equal(symmetrization_of(u),ordinal_numbers) -> member(identity_relation,cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.68  217530[7:Res:61019.0,18791.0] ||  -> equal(complement(complement(symmetric_difference(complement(u),complement(v)))),identity_relation) member(regular(complement(complement(symmetric_difference(complement(u),complement(v))))),union(u,v))*.
% 299.99/300.68  217613[8:Res:216611.1,13362.0] || equal(complement(u),identity_relation) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(omega,least(omega,u))),identity_relation)**.
% 299.99/300.68  218070[8:SpL:13259.2,217708.0] || member(cross_product(u,v),ordinal_numbers) equal(complement(complement(apply(choice,cross_product(u,v)))),identity_relation)** -> equal(cross_product(u,v),identity_relation).
% 299.99/300.68  218083[8:SpL:13259.2,215649.0] || member(cross_product(u,v),ordinal_numbers) subclass(unordered_pair(w,apply(choice,cross_product(u,v))),identity_relation)* -> equal(cross_product(u,v),identity_relation).
% 299.99/300.68  218109[8:SpL:13259.2,215653.0] || member(cross_product(u,v),ordinal_numbers) subclass(unordered_pair(apply(choice,cross_product(u,v)),w),identity_relation)* -> equal(cross_product(u,v),identity_relation).
% 299.99/300.68  218347[8:SpL:13259.2,217155.0] || member(cross_product(u,v),ordinal_numbers) equal(unordered_pair(w,apply(choice,cross_product(u,v))),identity_relation)** -> equal(cross_product(u,v),identity_relation).
% 299.99/300.68  218527[8:SpL:13259.2,217160.0] || member(cross_product(u,v),ordinal_numbers) equal(unordered_pair(apply(choice,cross_product(u,v)),w),identity_relation)** -> equal(cross_product(u,v),identity_relation).
% 299.99/300.68  218990[8:Obv:218984.2] || subclass(ordinal_numbers,u) member(omega,unordered_pair(v,u))* -> equal(regular(unordered_pair(v,u)),v) equal(unordered_pair(v,u),identity_relation).
% 299.99/300.68  218991[8:Obv:218983.2] || subclass(ordinal_numbers,u) member(omega,unordered_pair(u,v))* -> equal(regular(unordered_pair(u,v)),v) equal(unordered_pair(u,v),identity_relation).
% 299.99/300.68  219304[15:Res:215659.1,8554.1] || subclass(complement(complement(intersection(u,v))),identity_relation)* member(range_of(identity_relation),union(u,v)) -> member(range_of(identity_relation),symmetric_difference(u,v)).
% 299.99/300.68  219628[8:Res:9006.3,67561.0] function(u) || member(v,ordinal_numbers) subclass(ordinal_numbers,symmetric_difference(complement(w),ordinal_numbers)) -> member(image(u,v),union(w,identity_relation))*.
% 299.99/300.68  219604[8:Res:13225.3,67561.0] || member(u,ordinal_numbers) subclass(u,symmetric_difference(complement(v),ordinal_numbers)) -> equal(u,identity_relation) member(apply(choice,u),union(v,identity_relation))*.
% 299.99/300.68  219800[8:Res:67614.1,47534.0] || member(not_subclass_element(u,intersection(symmetric_difference(complement(v),ordinal_numbers),u)),union(v,identity_relation))* -> subclass(u,intersection(symmetric_difference(complement(v),ordinal_numbers),u)).
% 299.99/300.68  219831[15:Res:217197.1,8554.1] || equal(complement(complement(intersection(u,v))),identity_relation) member(range_of(identity_relation),union(u,v)) -> member(range_of(identity_relation),symmetric_difference(u,v))*.
% 299.99/300.68  220067[8:Res:919.1,160772.0] || member(not_subclass_element(restrict(symmetric_difference(ordinal_numbers,u),v,w),x),union(u,identity_relation))* -> subclass(restrict(symmetric_difference(ordinal_numbers,u),v,w),x).
% 299.99/300.68  220066[8:Res:9006.3,160772.0] function(u) || member(v,ordinal_numbers) subclass(ordinal_numbers,symmetric_difference(ordinal_numbers,w)) member(image(u,v),union(w,identity_relation))* -> .
% 299.99/300.68  220042[8:Res:13225.3,160772.0] || member(u,ordinal_numbers) subclass(u,symmetric_difference(ordinal_numbers,v)) member(apply(choice,u),union(v,identity_relation))* -> equal(u,identity_relation).
% 299.99/300.68  220033[8:Res:13069.2,160772.0] || member(symmetric_difference(ordinal_numbers,u),ordinal_numbers) member(apply(choice,symmetric_difference(ordinal_numbers,u)),union(u,identity_relation))* -> equal(symmetric_difference(ordinal_numbers,u),identity_relation).
% 299.99/300.68  220458[21:Res:196656.1,8799.1] || subclass(domain_relation,flip(cross_product(ordinal_numbers,ordinal_numbers))) equal(successor(ordered_pair(u,v)),identity_relation) -> member(ordered_pair(ordered_pair(u,v),identity_relation),successor_relation)*.
% 299.99/300.68  220422[21:Res:196656.1,12.0] || subclass(domain_relation,flip(unordered_pair(u,v)))* -> equal(ordered_pair(ordered_pair(w,x),identity_relation),v)* equal(ordered_pair(ordered_pair(w,x),identity_relation),u)*.
% 299.99/300.68  220560[21:Res:196657.1,8799.1] || subclass(domain_relation,rotate(cross_product(ordinal_numbers,ordinal_numbers))) equal(successor(ordered_pair(u,identity_relation)),v) -> member(ordered_pair(ordered_pair(u,identity_relation),v),successor_relation)*.
% 299.99/300.68  220524[21:Res:196657.1,12.0] || subclass(domain_relation,rotate(unordered_pair(u,v)))* -> equal(ordered_pair(ordered_pair(w,identity_relation),x),v)* equal(ordered_pair(ordered_pair(w,identity_relation),x),u)*.
% 299.99/300.68  221150[7:Res:13236.2,898.0] || well_ordering(u,restrict(v,w,x)) -> equal(restrict(v,w,x),identity_relation) member(least(u,restrict(v,w,x)),v)*.
% 299.99/300.68  221133[8:Res:13236.2,160772.0] || well_ordering(u,symmetric_difference(ordinal_numbers,v)) member(least(u,symmetric_difference(ordinal_numbers,v)),union(v,identity_relation))* -> equal(symmetric_difference(ordinal_numbers,v),identity_relation).
% 299.99/300.68  221124[7:Res:13236.2,18794.1] || well_ordering(u,intersection(v,w)) member(least(u,intersection(v,w)),symmetric_difference(v,w))* -> equal(intersection(v,w),identity_relation).
% 299.99/300.68  221264[8:Res:215662.1,8554.1] || subclass(complement(complement(intersection(u,v))),identity_relation)* member(singleton(w),union(u,v)) -> member(singleton(w),symmetric_difference(u,v))*.
% 299.99/300.68  221399[8:Res:39609.2,160772.0] inductive(symmetric_difference(ordinal_numbers,u)) || well_ordering(v,symmetric_difference(ordinal_numbers,u)) member(least(v,symmetric_difference(ordinal_numbers,u)),union(u,identity_relation))* -> .
% 299.99/300.68  221521[8:Res:217198.1,8554.1] || equal(complement(complement(intersection(u,v))),identity_relation) member(singleton(w),union(u,v)) -> member(singleton(w),symmetric_difference(u,v))*.
% 299.99/300.68  222583[21:MRR:222566.3,13039.0] || member(u,ordinal_numbers) subclass(domain_relation,union_of_range_map) well_ordering(element_relation,range_of(u))* -> equal(range_of(u),ordinal_numbers) member(range_of(u),ordinal_numbers).
% 299.99/300.68  223078[16:SpL:195257.0,13306.0] || member(regular(power_class(image(element_relation,singleton(identity_relation)))),image(element_relation,power_class(complement(singleton(identity_relation)))))* -> equal(power_class(image(element_relation,singleton(identity_relation))),identity_relation).
% 299.99/300.68  223077[8:SpL:162038.0,13306.0] || member(regular(power_class(image(element_relation,symmetrization_of(identity_relation)))),image(element_relation,power_class(complement(inverse(identity_relation)))))* -> equal(power_class(image(element_relation,symmetrization_of(identity_relation))),identity_relation).
% 299.99/300.68  223132[16:SpR:195257.0,19486.0] ||  -> equal(power_class(intersection(power_class(complement(singleton(identity_relation))),complement(inverse(image(element_relation,singleton(identity_relation)))))),complement(image(element_relation,symmetrization_of(image(element_relation,singleton(identity_relation))))))**.
% 299.99/300.68  223131[8:SpR:162038.0,19486.0] ||  -> equal(power_class(intersection(power_class(complement(inverse(identity_relation))),complement(inverse(image(element_relation,symmetrization_of(identity_relation)))))),complement(image(element_relation,symmetrization_of(image(element_relation,symmetrization_of(identity_relation))))))**.
% 299.99/300.68  223454[16:SpR:195257.0,19485.0] ||  -> equal(power_class(intersection(power_class(complement(singleton(identity_relation))),complement(singleton(image(element_relation,singleton(identity_relation)))))),complement(image(element_relation,successor(image(element_relation,singleton(identity_relation))))))**.
% 299.99/300.68  223453[8:SpR:162038.0,19485.0] ||  -> equal(power_class(intersection(power_class(complement(inverse(identity_relation))),complement(singleton(image(element_relation,symmetrization_of(identity_relation)))))),complement(image(element_relation,successor(image(element_relation,symmetrization_of(identity_relation))))))**.
% 299.99/300.68  223875[8:SpL:160927.0,18791.0] || member(u,symmetric_difference(complement(v),union(w,symmetric_difference(ordinal_numbers,x))))* -> member(u,union(v,intersection(complement(w),union(x,identity_relation)))).
% 299.99/300.68  223869[8:SpL:160927.0,18791.0] || member(u,symmetric_difference(union(v,symmetric_difference(ordinal_numbers,w)),complement(x)))* -> member(u,union(intersection(complement(v),union(w,identity_relation)),x)).
% 299.99/300.68  223790[8:SpR:481.0,160927.0] ||  -> equal(complement(intersection(power_class(intersection(complement(u),complement(v))),union(w,identity_relation))),union(image(element_relation,union(u,v)),symmetric_difference(ordinal_numbers,w)))**.
% 299.99/300.68  223756[8:SpR:160927.0,485.0] ||  -> equal(complement(intersection(complement(u),power_class(intersection(complement(v),union(w,identity_relation))))),union(u,image(element_relation,union(v,symmetric_difference(ordinal_numbers,w)))))**.
% 299.99/300.68  223744[8:SpR:160927.0,160927.0] ||  -> equal(union(intersection(complement(u),union(v,identity_relation)),symmetric_difference(ordinal_numbers,w)),complement(intersection(union(u,symmetric_difference(ordinal_numbers,v)),union(w,identity_relation))))**.
% 299.99/300.68  223730[8:SpR:160927.0,487.0] ||  -> equal(complement(intersection(power_class(intersection(complement(u),union(v,identity_relation))),complement(w))),union(image(element_relation,union(u,symmetric_difference(ordinal_numbers,v))),w))**.
% 299.99/300.68  223926[8:Rew:160927.0,223847.1] || member(regular(union(u,symmetric_difference(ordinal_numbers,v))),intersection(complement(u),union(v,identity_relation)))* -> equal(union(u,symmetric_difference(ordinal_numbers,v)),identity_relation).
% 299.99/300.68  223928[8:Rew:160927.0,223753.1] ||  -> member(not_subclass_element(u,union(v,symmetric_difference(ordinal_numbers,w))),intersection(complement(v),union(w,identity_relation)))* subclass(u,union(v,symmetric_difference(ordinal_numbers,w))).
% 299.99/300.68  223972[7:SpL:481.0,13242.0] || subclass(omega,power_class(intersection(complement(u),complement(v))))* member(w,image(element_relation,union(u,v)))* -> equal(integer_of(w),identity_relation).
% 299.99/300.68  223960[8:SpL:160927.0,13242.0] || subclass(omega,union(u,symmetric_difference(ordinal_numbers,v))) member(w,intersection(complement(u),union(v,identity_relation)))* -> equal(integer_of(w),identity_relation).
% 299.99/300.68  224194[8:SpL:160992.0,18791.0] || member(u,symmetric_difference(complement(v),union(symmetric_difference(ordinal_numbers,w),x)))* -> member(u,union(v,intersection(union(w,identity_relation),complement(x)))).
% 299.99/300.68  224188[8:SpL:160992.0,18791.0] || member(u,symmetric_difference(union(symmetric_difference(ordinal_numbers,v),w),complement(x)))* -> member(u,union(intersection(union(v,identity_relation),complement(w)),x)).
% 299.99/300.68  224152[8:SpL:160992.0,13242.0] || subclass(omega,union(symmetric_difference(ordinal_numbers,u),v)) member(w,intersection(union(u,identity_relation),complement(v)))* -> equal(integer_of(w),identity_relation).
% 299.99/300.68  224100[8:SpR:481.0,160992.0] ||  -> equal(complement(intersection(union(u,identity_relation),power_class(intersection(complement(v),complement(w))))),union(symmetric_difference(ordinal_numbers,u),image(element_relation,union(v,w))))**.
% 299.99/300.68  224088[8:SpR:160927.0,160992.0] ||  -> equal(union(symmetric_difference(ordinal_numbers,u),intersection(complement(v),union(w,identity_relation))),complement(intersection(union(u,identity_relation),union(v,symmetric_difference(ordinal_numbers,w)))))**.
% 299.99/300.68  224078[8:SpR:160992.0,160992.0] ||  -> equal(union(symmetric_difference(ordinal_numbers,u),intersection(union(v,identity_relation),complement(w))),complement(intersection(union(u,identity_relation),union(symmetric_difference(ordinal_numbers,v),w))))**.
% 299.99/300.68  224073[8:SpR:160992.0,485.0] ||  -> equal(complement(intersection(complement(u),power_class(intersection(union(v,identity_relation),complement(w))))),union(u,image(element_relation,union(symmetric_difference(ordinal_numbers,v),w))))**.
% 299.99/300.68  224061[8:SpR:160992.0,160927.0] ||  -> equal(union(intersection(union(u,identity_relation),complement(v)),symmetric_difference(ordinal_numbers,w)),complement(intersection(union(symmetric_difference(ordinal_numbers,u),v),union(w,identity_relation))))**.
% 299.99/300.68  224047[8:SpR:160992.0,487.0] ||  -> equal(complement(intersection(power_class(intersection(union(u,identity_relation),complement(v))),complement(w))),union(image(element_relation,union(symmetric_difference(ordinal_numbers,u),v)),w))**.
% 299.99/300.68  224241[8:Rew:160992.0,224166.1] || member(regular(union(symmetric_difference(ordinal_numbers,u),v)),intersection(union(u,identity_relation),complement(v)))* -> equal(union(symmetric_difference(ordinal_numbers,u),v),identity_relation).
% 299.99/300.68  224243[8:Rew:160992.0,224070.1] ||  -> member(not_subclass_element(u,union(symmetric_difference(ordinal_numbers,v),w)),intersection(union(v,identity_relation),complement(w)))* subclass(u,union(symmetric_difference(ordinal_numbers,v),w)).
% 299.99/300.68  224327[8:Rew:13263.1,224326.2] || member(regular(u),unordered_pair(v,u))* -> equal(regular(unordered_pair(v,u)),v) equal(u,identity_relation) equal(unordered_pair(v,u),identity_relation).
% 299.99/300.68  224329[8:Rew:13263.2,224328.2] || member(regular(u),unordered_pair(u,v))* -> equal(regular(unordered_pair(u,v)),v) equal(u,identity_relation) equal(unordered_pair(u,v),identity_relation).
% 299.99/300.68  224421[10:SpR:223660.1,62.1] || subclass(element_relation,identity_relation) member(ordered_pair(cross_product(ordinal_numbers,ordinal_numbers),u),compose(v,w))* -> member(u,image(v,image(w,identity_relation))).
% 299.99/300.68  224647[7:Obv:224645.1] || subclass(unordered_pair(u,v),omega)* -> equal(regular(unordered_pair(u,v)),u) equal(unordered_pair(u,v),identity_relation) equal(integer_of(v),v).
% 299.99/300.68  224648[7:Obv:224644.1] || subclass(unordered_pair(u,v),omega)* -> equal(regular(unordered_pair(u,v)),v) equal(unordered_pair(u,v),identity_relation) equal(integer_of(u),u).
% 299.99/300.68  224861[7:SpL:3594.0,13340.0] || subclass(omega,symmetric_difference(complement(intersection(u,v)),union(u,v)))* -> equal(integer_of(w),identity_relation) member(w,complement(symmetric_difference(u,v)))*.
% 299.99/300.68  225494[8:SpL:160992.0,225445.0] || subclass(intersection(union(u,identity_relation),complement(v)),union(symmetric_difference(ordinal_numbers,u),v))* -> equal(intersection(union(u,identity_relation),complement(v)),identity_relation).
% 299.99/300.68  225493[8:SpL:160927.0,225445.0] || subclass(intersection(complement(u),union(v,identity_relation)),union(u,symmetric_difference(ordinal_numbers,v)))* -> equal(intersection(complement(u),union(v,identity_relation)),identity_relation).
% 299.99/300.68  226215[7:SpL:3594.0,17322.0] || subclass(u,symmetric_difference(complement(intersection(v,w)),union(v,w)))* -> equal(u,identity_relation) member(regular(u),complement(symmetric_difference(v,w))).
% 299.99/300.68  226306[21:SpR:19860.0,196460.2] || member(restrict(cross_product(u,ordinal_numbers),v,w),ordinal_numbers)* subclass(domain_relation,union_of_range_map) -> equal(sum_class(image(cross_product(v,w),u)),identity_relation).
% 299.99/300.68  226428[7:Res:13258.1,288.0] || member(regular(restrict(image(element_relation,complement(u)),v,w)),power_class(u))* -> equal(restrict(image(element_relation,complement(u)),v,w),identity_relation).
% 299.99/300.68  226417[7:Res:13258.1,897.0] ||  -> equal(restrict(restrict(u,v,w),x,y),identity_relation) member(regular(restrict(restrict(u,v,w),x,y)),cross_product(v,w))*.
% 299.99/300.68  226400[8:Res:13258.1,67561.0] ||  -> equal(restrict(symmetric_difference(complement(u),ordinal_numbers),v,w),identity_relation) member(regular(restrict(symmetric_difference(complement(u),ordinal_numbers),v,w)),union(u,identity_relation))*.
% 299.99/300.68  226798[16:Rew:195257.0,226792.2] || subclass(omega,image(element_relation,singleton(identity_relation))) -> equal(integer_of(regular(power_class(complement(singleton(identity_relation))))),identity_relation)** equal(power_class(complement(singleton(identity_relation))),identity_relation).
% 299.99/300.68  226799[8:Rew:162038.0,226791.2] || subclass(omega,image(element_relation,symmetrization_of(identity_relation))) -> equal(integer_of(regular(power_class(complement(inverse(identity_relation))))),identity_relation)** equal(power_class(complement(inverse(identity_relation))),identity_relation).
% 299.99/300.68  227264[5:SpR:8649.0,61728.2] || member(restrict(u,v,ordinal_numbers),ordinal_numbers)* subclass(rest_relation,union_of_range_map) -> equal(rest_of(restrict(u,v,ordinal_numbers)),sum_class(image(u,v))).
% 299.99/300.68  228572[8:Res:228546.1,129.0] || equal(complement(u),identity_relation) subclass(successor(u),v)* well_ordering(w,v)* -> member(least(w,successor(u)),successor(u))*.
% 299.99/300.68  228671[8:Res:228646.1,129.0] || equal(complement(u),identity_relation) subclass(symmetrization_of(u),v)* well_ordering(w,v)* -> member(least(w,symmetrization_of(u)),symmetrization_of(u))*.
% 299.99/300.68  228831[8:Res:228806.1,129.0] || subclass(complement(u),identity_relation) subclass(successor(u),v)* well_ordering(w,v)* -> member(least(w,successor(u)),successor(u))*.
% 299.99/300.68  228871[8:Res:163112.0,61018.0] ||  -> subclass(singleton(apply(choice,regular(complement(inverse(identity_relation))))),symmetrization_of(identity_relation))* equal(regular(complement(inverse(identity_relation))),identity_relation) equal(complement(inverse(identity_relation)),identity_relation).
% 299.99/300.68  228968[8:Res:228945.1,129.0] || subclass(complement(u),identity_relation) subclass(symmetrization_of(u),v)* well_ordering(w,v)* -> member(least(w,symmetrization_of(u)),symmetrization_of(u))*.
% 299.99/300.68  229208[16:Rew:195257.0,229098.1] || member(regular(intersection(power_class(complement(singleton(identity_relation))),u)),image(element_relation,singleton(identity_relation)))* -> equal(intersection(power_class(complement(singleton(identity_relation))),u),identity_relation).
% 299.99/300.68  229209[8:Rew:162038.0,229097.1] || member(regular(intersection(power_class(complement(inverse(identity_relation))),u)),image(element_relation,symmetrization_of(identity_relation)))* -> equal(intersection(power_class(complement(inverse(identity_relation))),u),identity_relation).
% 299.99/300.68  229792[16:Rew:195257.0,229541.1] || member(regular(intersection(u,power_class(complement(singleton(identity_relation))))),image(element_relation,singleton(identity_relation)))* -> equal(intersection(u,power_class(complement(singleton(identity_relation)))),identity_relation).
% 299.99/300.68  229793[8:Rew:162038.0,229540.1] || member(regular(intersection(u,power_class(complement(inverse(identity_relation))))),image(element_relation,symmetrization_of(identity_relation)))* -> equal(intersection(u,power_class(complement(inverse(identity_relation)))),identity_relation).
% 299.99/300.68  231204[8:SpL:13259.2,230798.0] || member(cross_product(u,v),ordinal_numbers) equal(complement(regular(apply(choice,cross_product(u,v)))),identity_relation)** -> equal(cross_product(u,v),identity_relation).
% 299.99/300.68  231292[8:SpR:160992.0,17447.1] ||  -> equal(symmetric_difference(union(u,identity_relation),complement(v)),identity_relation) member(regular(symmetric_difference(union(u,identity_relation),complement(v))),union(symmetric_difference(ordinal_numbers,u),v))*.
% 299.99/300.68  231291[8:SpR:160927.0,17447.1] ||  -> equal(symmetric_difference(complement(u),union(v,identity_relation)),identity_relation) member(regular(symmetric_difference(complement(u),union(v,identity_relation))),union(u,symmetric_difference(ordinal_numbers,v)))*.
% 299.99/300.68  231784[8:Res:163112.0,18747.0] ||  -> subclass(singleton(not_subclass_element(regular(complement(inverse(identity_relation))),u)),symmetrization_of(identity_relation))* subclass(regular(complement(inverse(identity_relation))),u) equal(complement(inverse(identity_relation)),identity_relation).
% 299.99/300.68  231839[8:MRR:231789.0,41183.1] ||  -> member(not_subclass_element(regular(symmetric_difference(ordinal_numbers,u)),v),union(u,identity_relation))* subclass(regular(symmetric_difference(ordinal_numbers,u)),v) equal(symmetric_difference(ordinal_numbers,u),identity_relation).
% 299.99/300.68  231851[8:SpR:160992.0,231812.0] ||  -> subclass(regular(intersection(union(u,identity_relation),complement(v))),union(symmetric_difference(ordinal_numbers,u),v))* equal(intersection(union(u,identity_relation),complement(v)),identity_relation).
% 299.99/300.68  231850[8:SpR:160927.0,231812.0] ||  -> subclass(regular(intersection(complement(u),union(v,identity_relation))),union(u,symmetric_difference(ordinal_numbers,v)))* equal(intersection(complement(u),union(v,identity_relation)),identity_relation).
% 299.99/300.68  232812[8:Rew:481.0,232765.1] || subclass(image(element_relation,union(u,v)),power_class(intersection(complement(u),complement(v))))* -> subclass(ordinal_numbers,power_class(intersection(complement(u),complement(v)))).
% 299.99/300.68  233006[8:SpL:13259.2,232981.0] || member(cross_product(u,v),ordinal_numbers) subclass(ordinal_numbers,regular(singleton(apply(choice,cross_product(u,v)))))* -> equal(cross_product(u,v),identity_relation).
% 299.99/300.68  233073[8:SpL:13259.2,233013.0] || member(cross_product(u,v),ordinal_numbers) equal(regular(singleton(apply(choice,cross_product(u,v)))),ordinal_numbers)** -> equal(cross_product(u,v),identity_relation).
% 299.99/300.68  233204[7:Rew:30.0,233172.1] || member(regular(image(element_relation,union(u,v))),power_class(intersection(complement(u),complement(v))))* -> equal(image(element_relation,union(u,v)),identity_relation).
% 299.99/300.68  233347[8:Res:231881.0,8559.2] || member(u,v) member(u,w) -> equal(singleton(intersection(w,v)),identity_relation) member(u,complement(singleton(intersection(w,v))))*.
% 299.99/300.68  233392[8:MRR:233319.2,216024.0] || member(u,ordinal_numbers) well_ordering(v,complement(singleton(unordered_pair(w,u)))) -> member(least(v,unordered_pair(w,u)),unordered_pair(w,u))*.
% 299.99/300.68  233393[8:MRR:233317.2,216024.0] || member(u,ordinal_numbers) well_ordering(v,complement(singleton(unordered_pair(u,w)))) -> member(least(v,unordered_pair(u,w)),unordered_pair(u,w))*.
% 299.99/300.68  233581[21:MRR:233539.3,41096.1] operation(u) || member(identity_relation,cantor(cantor(u)))* member(v,cantor(cantor(u)))* subclass(domain_relation,complement(cantor(u))) -> .
% 299.99/300.68  233955[21:Res:196416.2,161200.0] || member(u,ordinal_numbers) subclass(domain_relation,image(element_relation,union(v,identity_relation))) member(ordered_pair(u,identity_relation),power_class(symmetric_difference(ordinal_numbers,v)))* -> .
% 299.99/300.68  233950[8:Res:49995.1,161200.0] || member(image(element_relation,union(u,identity_relation)),subset_relation) member(singleton(first(image(element_relation,union(u,identity_relation)))),power_class(symmetric_difference(ordinal_numbers,u)))* -> .
% 299.99/300.68  234085[8:SpL:13259.2,233382.0] || member(cross_product(u,v),ordinal_numbers) well_ordering(ordinal_numbers,complement(singleton(apply(choice,cross_product(u,v)))))* -> equal(cross_product(u,v),identity_relation).
% 299.99/300.68  234125[8:SpL:13259.2,234113.0] || member(cross_product(u,v),ordinal_numbers) subclass(complement(singleton(apply(choice,cross_product(u,v)))),identity_relation)* -> equal(cross_product(u,v),identity_relation).
% 299.99/300.68  234169[7:Rew:30.0,234144.2] || subclass(omega,intersection(complement(u),complement(v)))* -> equal(integer_of(not_subclass_element(union(u,v),w)),identity_relation)** subclass(union(u,v),w).
% 299.99/300.68  234385[7:Rew:30.0,234330.2] || well_ordering(u,ordinal_numbers) member(least(u,union(v,w)),intersection(complement(v),complement(w)))* -> equal(union(v,w),identity_relation).
% 299.99/300.68  234444[21:SpL:3603.0,196423.1] || member(u,ordinal_numbers) subclass(domain_relation,symmetric_difference(v,cross_product(w,x))) -> member(ordered_pair(u,identity_relation),complement(restrict(v,w,x)))*.
% 299.99/300.68  234443[21:SpL:3606.0,196423.1] || member(u,ordinal_numbers) subclass(domain_relation,symmetric_difference(cross_product(v,w),x)) -> member(ordered_pair(u,identity_relation),complement(restrict(x,v,w)))*.
% 299.99/300.68  234782[8:SpR:116154.0,193440.1] || member(u,ordinal_numbers) -> member(u,segment(v,w,x)) equal(apply(restrict(v,w,singleton(x)),u),sum_class(range_of(identity_relation)))**.
% 299.99/300.68  234898[8:MRR:234836.0,8655.0] || member(cantor(u),ordinal_numbers) -> equal(apply(u,singleton(cantor(u))),sum_class(range_of(identity_relation)))** member(singleton(singleton(singleton(cantor(u)))),element_relation)*.
% 299.99/300.68  235039[7:Rew:234956.0,235032.1] || member(ordered_pair(u,not_subclass_element(v,range_of(identity_relation))),compose(complement(cross_product(image(w,singleton(u)),ordinal_numbers)),w))* -> subclass(v,range_of(identity_relation)).
% 299.99/300.68  235295[8:Res:230445.1,40594.1] || member(singleton(union(u,identity_relation)),u)* member(union(u,identity_relation),ordinal_numbers) -> member(singleton(singleton(singleton(union(u,identity_relation)))),element_relation)*.
% 299.99/300.68  235391[5:Res:28980.1,18791.0] || subclass(rest_relation,flip(symmetric_difference(complement(u),complement(v)))) -> member(ordered_pair(ordered_pair(w,x),rest_of(ordered_pair(x,w))),union(u,v))*.
% 299.99/300.68  235519[5:Res:28979.1,18791.0] || subclass(rest_relation,rotate(symmetric_difference(complement(u),complement(v)))) -> member(ordered_pair(ordered_pair(w,rest_of(ordered_pair(x,w))),x),union(u,v))*.
% 299.99/300.68  235705[8:Res:15426.1,36719.1] operation(u) || subclass(domain_relation,cantor(u))* -> equal(ordered_pair(first(ordered_pair(identity_relation,identity_relation)),second(ordered_pair(identity_relation,identity_relation))),ordered_pair(identity_relation,identity_relation))**.
% 299.99/300.68  235674[7:Res:13227.2,36719.1] operation(u) || subclass(v,cantor(u))* -> equal(v,identity_relation) equal(ordered_pair(first(regular(v)),second(regular(v))),regular(v))**.
% 299.99/300.68  235646[8:Res:193440.1,36719.1] operation(u) || member(v,ordinal_numbers) -> equal(apply(u,v),sum_class(range_of(identity_relation)))** equal(ordered_pair(first(v),second(v)),v)**.
% 299.99/300.68  235793[5:Res:9604.1,19113.0] || equal(sum_class(recursion_equation_functions(u)),recursion_equation_functions(u)) -> subclass(sum_class(recursion_equation_functions(u)),v) subclass(not_subclass_element(sum_class(recursion_equation_functions(u)),v),cross_product(ordinal_numbers,ordinal_numbers))*.
% 299.99/300.68  235937[7:Res:69478.2,17312.1] || subclass(omega,symmetric_difference(u,v)) subclass(w,complement(union(u,v)))* -> equal(integer_of(regular(w)),identity_relation) equal(w,identity_relation).
% 299.99/300.68  235926[7:Res:69478.2,290.0] || subclass(omega,symmetric_difference(u,v)) -> equal(integer_of(not_subclass_element(complement(union(u,v)),w)),identity_relation)** subclass(complement(union(u,v)),w).
% 299.99/300.68  235913[7:SpR:487.0,69478.2] || subclass(omega,symmetric_difference(image(element_relation,complement(u)),v)) -> equal(integer_of(w),identity_relation) member(w,complement(intersection(power_class(u),complement(v))))*.
% 299.99/300.68  235903[7:SpR:485.0,69478.2] || subclass(omega,symmetric_difference(u,image(element_relation,complement(v)))) -> equal(integer_of(w),identity_relation) member(w,complement(intersection(complement(u),power_class(v))))*.
% 299.99/300.68  236119[0:Obv:236099.1] || member(not_subclass_element(symmetric_difference(u,singleton(u)),intersection(v,successor(u))),v)* -> subclass(symmetric_difference(u,singleton(u)),intersection(v,successor(u))).
% 299.99/300.68  236167[0:Obv:236152.1] || member(not_subclass_element(symmetric_difference(u,inverse(u)),intersection(v,symmetrization_of(u))),v)* -> subclass(symmetric_difference(u,inverse(u)),intersection(v,symmetrization_of(u))).
% 299.99/300.68  236323[0:Rew:30.0,236211.1] || member(not_subclass_element(intersection(u,union(v,w)),x),intersection(complement(v),complement(w)))* -> subclass(intersection(u,union(v,w)),x).
% 299.99/300.68  236542[0:Rew:30.0,236400.1] || member(not_subclass_element(intersection(union(u,v),w),x),intersection(complement(u),complement(v)))* -> subclass(intersection(union(u,v),w),x).
% 299.99/300.68  236606[5:SpL:189.0,36857.0] || equal(u,power_class(image(element_relation,complement(v))))* member(w,ordinal_numbers) -> member(w,image(element_relation,power_class(v)))* member(w,u)*.
% 299.99/300.68  236836[7:Res:17392.2,18791.0] || subclass(u,symmetric_difference(complement(v),complement(w))) -> equal(intersection(u,x),identity_relation) member(regular(intersection(u,x)),union(v,w))*.
% 299.99/300.68  236779[8:SpR:116209.1,17392.2] operation(u) || subclass(cantor(u),v) -> equal(intersection(cantor(u),w),identity_relation) member(regular(intersection(w,cantor(u))),v)*.
% 299.99/300.68  236933[7:Rew:3616.0,236783.1] || subclass(union(u,v),w) -> equal(symmetric_difference(complement(u),complement(v)),identity_relation) member(regular(symmetric_difference(complement(u),complement(v))),w)*.
% 299.99/300.68  237138[8:Res:13574.1,14681.0] || member(regular(intersection(u,intersection(v,regular(w)))),w)* -> equal(intersection(u,intersection(v,regular(w))),identity_relation) equal(w,identity_relation).
% 299.99/300.68  237133[7:Res:13574.1,161.0] ||  -> equal(intersection(u,intersection(v,omega)),identity_relation) equal(integer_of(regular(intersection(u,intersection(v,omega)))),regular(intersection(u,intersection(v,omega))))**.
% 299.99/300.68  237130[7:Res:13574.1,898.0] ||  -> equal(intersection(u,intersection(v,restrict(w,x,y))),identity_relation) member(regular(intersection(u,intersection(v,restrict(w,x,y)))),w)*.
% 299.99/300.68  237104[7:Res:13574.1,3617.0] ||  -> equal(intersection(u,intersection(v,symmetric_difference(w,x))),identity_relation) member(regular(intersection(u,intersection(v,symmetric_difference(w,x)))),union(w,x))*.
% 299.99/300.68  237061[8:SpR:116209.1,13574.1] operation(u) ||  -> equal(intersection(v,intersection(w,cantor(u))),identity_relation) member(regular(intersection(v,intersection(cantor(u),w))),cantor(u))*.
% 299.99/300.68  237789[8:Res:13573.1,14681.0] || member(regular(intersection(u,intersection(regular(v),w))),v)* -> equal(intersection(u,intersection(regular(v),w)),identity_relation) equal(v,identity_relation).
% 299.99/300.68  237784[7:Res:13573.1,161.0] ||  -> equal(intersection(u,intersection(omega,v)),identity_relation) equal(integer_of(regular(intersection(u,intersection(omega,v)))),regular(intersection(u,intersection(omega,v))))**.
% 299.99/300.68  237781[7:Res:13573.1,898.0] ||  -> equal(intersection(u,intersection(restrict(v,w,x),y)),identity_relation) member(regular(intersection(u,intersection(restrict(v,w,x),y))),v)*.
% 299.99/300.68  237755[7:Res:13573.1,3617.0] ||  -> equal(intersection(u,intersection(symmetric_difference(v,w),x)),identity_relation) member(regular(intersection(u,intersection(symmetric_difference(v,w),x))),union(v,w))*.
% 299.99/300.68  237681[8:SpR:116209.1,13573.1] operation(u) ||  -> equal(intersection(v,intersection(cantor(u),w)),identity_relation) member(regular(intersection(v,intersection(w,cantor(u)))),cantor(u))*.
% 299.99/300.68  238570[7:Res:13572.2,18791.0] || subclass(u,symmetric_difference(complement(v),complement(w))) -> equal(intersection(x,u),identity_relation) member(regular(intersection(x,u)),union(v,w))*.
% 299.99/300.68  238536[8:SpR:116209.1,13572.2] operation(u) || subclass(cantor(u),v) -> equal(intersection(w,cantor(u)),identity_relation) member(regular(intersection(cantor(u),w)),v)*.
% 299.99/300.68  239301[8:Res:17397.1,14681.0] || member(regular(intersection(intersection(regular(u),v),w)),u)* -> equal(intersection(intersection(regular(u),v),w),identity_relation) equal(u,identity_relation).
% 299.99/300.68  239296[7:Res:17397.1,161.0] ||  -> equal(intersection(intersection(omega,u),v),identity_relation) equal(integer_of(regular(intersection(intersection(omega,u),v))),regular(intersection(intersection(omega,u),v)))**.
% 299.99/300.68  239293[7:Res:17397.1,898.0] ||  -> equal(intersection(intersection(restrict(u,v,w),x),y),identity_relation) member(regular(intersection(intersection(restrict(u,v,w),x),y)),u)*.
% 299.99/300.68  239267[7:Res:17397.1,3617.0] ||  -> equal(intersection(intersection(symmetric_difference(u,v),w),x),identity_relation) member(regular(intersection(intersection(symmetric_difference(u,v),w),x)),union(u,v))*.
% 299.99/300.68  239187[8:SpR:116209.1,17397.1] operation(u) ||  -> equal(intersection(intersection(cantor(u),v),w),identity_relation) member(regular(intersection(intersection(v,cantor(u)),w)),cantor(u))*.
% 299.99/300.68  240136[8:Res:17396.1,14681.0] || member(regular(intersection(intersection(u,regular(v)),w)),v)* -> equal(intersection(intersection(u,regular(v)),w),identity_relation) equal(v,identity_relation).
% 299.99/300.68  240131[7:Res:17396.1,161.0] ||  -> equal(intersection(intersection(u,omega),v),identity_relation) equal(integer_of(regular(intersection(intersection(u,omega),v))),regular(intersection(intersection(u,omega),v)))**.
% 299.99/300.68  240128[7:Res:17396.1,898.0] ||  -> equal(intersection(intersection(u,restrict(v,w,x)),y),identity_relation) member(regular(intersection(intersection(u,restrict(v,w,x)),y)),v)*.
% 299.99/300.68  240102[7:Res:17396.1,3617.0] ||  -> equal(intersection(intersection(u,symmetric_difference(v,w)),x),identity_relation) member(regular(intersection(intersection(u,symmetric_difference(v,w)),x)),union(v,w))*.
% 299.99/300.68  240043[8:SpR:116209.1,17396.1] operation(u) ||  -> equal(intersection(intersection(v,cantor(u)),w),identity_relation) member(regular(intersection(intersection(cantor(u),v),w)),cantor(u))*.
% 299.99/300.68  41059[0:SpL:163.0,8559.2] || member(u,union(v,w)) member(u,complement(intersection(v,w)))* subclass(symmetric_difference(v,w),x)* -> member(u,x)*.
% 299.99/300.68  39645[2:Res:19315.0,9665.1] inductive(symmetric_difference(u,inverse(u))) || well_ordering(v,symmetrization_of(u)) -> member(least(v,symmetric_difference(u,inverse(u))),symmetric_difference(u,inverse(u)))*.
% 299.99/300.68  40885[0:SpR:3603.0,3618.1] || member(u,symmetric_difference(complement(restrict(v,w,x)),union(v,cross_product(w,x))))* -> member(u,complement(symmetric_difference(v,cross_product(w,x)))).
% 299.99/300.68  41001[0:SpR:3606.0,3618.1] || member(u,symmetric_difference(complement(restrict(v,w,x)),union(cross_product(w,x),v)))* -> member(u,complement(symmetric_difference(cross_product(w,x),v))).
% 299.99/300.68  19662[0:SpR:33.0,3597.0] ||  -> equal(intersection(complement(restrict(inverse(cross_product(u,v)),u,v)),symmetrization_of(cross_product(u,v))),symmetric_difference(cross_product(u,v),inverse(cross_product(u,v))))**.
% 299.99/300.68  43724[5:Res:8643.1,8554.1] || subclass(ordinal_numbers,complement(intersection(u,v))) member(unordered_pair(w,x),union(u,v)) -> member(unordered_pair(w,x),symmetric_difference(u,v))*.
% 299.99/300.68  40052[5:Res:8551.2,8842.1] || member(unordered_pair(u,v),cross_product(w,x))* member(unordered_pair(u,v),y)* subclass(ordinal_numbers,complement(restrict(y,w,x)))* -> .
% 299.99/300.68  19128[0:Res:2503.2,21.0] || subclass(u,cross_product(v,w))* -> subclass(u,x) equal(ordered_pair(first(not_subclass_element(u,x)),second(not_subclass_element(u,x))),not_subclass_element(u,x))**.
% 299.99/300.68  43721[5:Res:8642.1,8554.1] || subclass(ordinal_numbers,complement(intersection(u,v))) member(ordered_pair(w,x),union(u,v)) -> member(ordered_pair(w,x),symmetric_difference(u,v))*.
% 299.99/300.68  28945[5:Res:8827.2,12.0] || member(u,ordinal_numbers) subclass(rest_relation,unordered_pair(v,w))* -> equal(ordered_pair(u,rest_of(u)),w)* equal(ordered_pair(u,rest_of(u)),v)*.
% 299.99/300.68  39743[5:Res:8551.2,8841.1] || member(ordered_pair(u,v),cross_product(w,x))* member(ordered_pair(u,v),y)* subclass(ordinal_numbers,complement(restrict(y,w,x)))* -> .
% 299.99/300.68  49669[0:SpL:6355.1,10702.0] || equal(u,not_subclass_element(cross_product(v,w),x)) -> subclass(cross_product(v,w),x) member(singleton(first(not_subclass_element(cross_product(v,w),x))),u)*.
% 299.99/300.68  49647[0:SpL:6355.1,2486.0] || subclass(not_subclass_element(cross_product(u,v),w),x) -> subclass(cross_product(u,v),w) member(singleton(first(not_subclass_element(cross_product(u,v),w))),x)*.
% 299.99/300.68  19545[0:SpR:33.0,3596.0] ||  -> equal(intersection(complement(restrict(singleton(cross_product(u,v)),u,v)),successor(cross_product(u,v))),symmetric_difference(cross_product(u,v),singleton(cross_product(u,v))))**.
% 299.99/300.68  9645[0:Res:967.0,129.0] || subclass(singleton(singleton(singleton(u))),v)* well_ordering(w,v)* -> member(least(w,singleton(singleton(singleton(u)))),singleton(singleton(singleton(u))))*.
% 299.99/300.68  39644[2:Res:19314.0,9665.1] inductive(symmetric_difference(u,singleton(u))) || well_ordering(v,successor(u)) -> member(least(v,symmetric_difference(u,singleton(u))),symmetric_difference(u,singleton(u)))*.
% 299.99/300.68  51216[5:SpR:50855.1,3596.0] || member(singleton(u),subset_relation) -> equal(intersection(complement(intersection(first(singleton(u)),u)),successor(first(singleton(u)))),symmetric_difference(first(singleton(u)),u))**.
% 299.99/300.68  43715[5:Res:9632.1,8554.1] || equal(complement(complement(complement(intersection(u,v)))),ordinal_numbers)** member(singleton(w),union(u,v)) -> member(singleton(w),symmetric_difference(u,v))*.
% 299.99/300.68  79552[5:Res:60219.0,12.0] ||  -> subclass(u,complement(unordered_pair(v,w))) equal(not_subclass_element(u,complement(unordered_pair(v,w))),w)** equal(not_subclass_element(u,complement(unordered_pair(v,w))),v)**.
% 299.99/300.68  96707[5:Res:39298.1,3689.0] || subclass(ordinal_numbers,complement(complement(ordered_pair(u,v))))* -> equal(ordered_pair(w,x),unordered_pair(u,singleton(v)))* equal(ordered_pair(w,x),singleton(u)).
% 299.99/300.68  96683[5:Res:40074.1,3689.0] || subclass(ordinal_numbers,complement(complement(ordered_pair(u,v))))* -> equal(unordered_pair(w,x),unordered_pair(u,singleton(v)))* equal(unordered_pair(w,x),singleton(u)).
% 299.99/300.68  125897[5:Res:125725.1,8554.1] || subclass(omega,complement(intersection(u,v))) member(least(element_relation,omega),union(u,v)) -> member(least(element_relation,omega),symmetric_difference(u,v))*.
% 299.99/300.68  125974[5:Res:125731.1,8554.1] || subclass(ordinal_numbers,complement(intersection(u,v))) member(least(element_relation,omega),union(u,v)) -> member(least(element_relation,omega),symmetric_difference(u,v))*.
% 299.99/300.68  126648[5:Res:8551.2,125896.1] || member(least(element_relation,omega),cross_product(u,v))* member(least(element_relation,omega),w) subclass(omega,complement(restrict(w,u,v)))* -> .
% 299.99/300.68  127113[5:Res:8551.2,125973.1] || member(least(element_relation,omega),cross_product(u,v))* member(least(element_relation,omega),w) subclass(ordinal_numbers,complement(restrict(w,u,v)))* -> .
% 299.99/300.68  128018[5:Res:126679.1,3689.0] || subclass(omega,complement(complement(ordered_pair(u,v))))* -> equal(unordered_pair(u,singleton(v)),least(element_relation,omega)) equal(least(element_relation,omega),singleton(u)).
% 299.99/300.68  128353[5:Res:127147.1,3689.0] || subclass(ordinal_numbers,complement(complement(ordered_pair(u,v))))* -> equal(unordered_pair(u,singleton(v)),least(element_relation,omega)) equal(least(element_relation,omega),singleton(u)).
% 299.99/300.68  131396[0:SpL:3603.0,18794.1] || member(u,symmetric_difference(complement(restrict(v,w,x)),union(v,cross_product(w,x))))* member(u,symmetric_difference(v,cross_product(w,x))) -> .
% 299.99/300.68  131395[0:SpL:3606.0,18794.1] || member(u,symmetric_difference(complement(restrict(v,w,x)),union(cross_product(w,x),v)))* member(u,symmetric_difference(cross_product(w,x),v)) -> .
% 299.99/300.68  136668[0:Res:303.1,18791.0] ||  -> subclass(intersection(u,symmetric_difference(complement(v),complement(w))),x) member(not_subclass_element(intersection(u,symmetric_difference(complement(v),complement(w))),x),union(v,w))*.
% 299.99/300.68  136653[0:Res:313.1,18791.0] ||  -> subclass(intersection(symmetric_difference(complement(u),complement(v)),w),x) member(not_subclass_element(intersection(symmetric_difference(complement(u),complement(v)),w),x),union(u,v))*.
% 299.99/300.68  136652[5:Res:41371.0,18791.0] ||  -> subclass(complement(complement(symmetric_difference(complement(u),complement(v)))),w) member(not_subclass_element(complement(complement(symmetric_difference(complement(u),complement(v)))),w),union(u,v))*.
% 299.99/300.68  140474[5:MRR:140385.0,41183.1] ||  -> member(not_subclass_element(u,intersection(intersection(complement(v),complement(w)),u)),union(v,w))* subclass(u,intersection(intersection(complement(v),complement(w)),u)).
% 299.99/300.68  147047[5:Res:143193.1,8554.1] || equal(complement(intersection(u,v)),ordinal_numbers) member(least(element_relation,omega),union(u,v)) -> member(least(element_relation,omega),symmetric_difference(u,v))*.
% 299.99/300.68  147261[5:Res:143222.1,8554.1] || equal(complement(intersection(u,v)),omega) member(least(element_relation,omega),union(u,v)) -> member(least(element_relation,omega),symmetric_difference(u,v))*.
% 299.99/300.68  147922[5:SpL:3594.0,18581.1] || member(u,ordinal_numbers) subclass(ordinal_numbers,symmetric_difference(complement(intersection(v,w)),union(v,w)))* -> member(sum_class(u),complement(symmetric_difference(v,w)))*.
% 299.99/300.68  152188[0:Res:27.2,19111.1] || member(not_subclass_element(u,v),w)* member(not_subclass_element(u,v),x)* subclass(u,complement(intersection(x,w)))* -> subclass(u,v).
% 299.99/300.68  152866[0:SpL:3594.0,19121.0] || subclass(u,symmetric_difference(complement(intersection(v,w)),union(v,w)))* -> subclass(u,x) member(not_subclass_element(u,x),complement(symmetric_difference(v,w)))*.
% 299.99/300.68  153372[0:Res:919.1,897.0] ||  -> subclass(restrict(restrict(u,v,w),x,y),z) member(not_subclass_element(restrict(restrict(u,v,w),x,y),z),cross_product(v,w))*.
% 299.99/300.68  153480[8:Res:153473.0,9665.1] inductive(complement(compose(element_relation,ordinal_numbers))) || well_ordering(u,complement(element_relation)) -> member(least(u,complement(compose(element_relation,ordinal_numbers))),complement(compose(element_relation,ordinal_numbers)))*.
% 299.99/300.68  155158[0:SpR:154737.1,3594.0] || subclass(u,v) -> equal(intersection(complement(symmetric_difference(v,u)),union(complement(u),union(v,u))),symmetric_difference(complement(u),union(v,u)))**.
% 299.99/300.68  155632[0:SpL:154945.0,8554.1] || member(u,union(v,intersection(v,w))) member(u,complement(intersection(v,w))) -> member(u,symmetric_difference(v,intersection(v,w)))*.
% 299.99/300.68  155551[0:SpR:3594.0,154945.0] ||  -> equal(intersection(complement(symmetric_difference(u,v)),symmetric_difference(complement(intersection(u,v)),union(u,v))),symmetric_difference(complement(intersection(u,v)),union(u,v)))**.
% 299.99/300.68  156054[0:SpL:155147.0,8554.1] || member(u,union(v,intersection(w,v))) member(u,complement(intersection(w,v))) -> member(u,symmetric_difference(v,intersection(w,v)))*.
% 299.99/300.68  156915[8:Res:156893.0,9665.1] inductive(intersection(u,inverse(subset_relation))) || well_ordering(v,complement(subset_relation)) -> member(least(v,intersection(u,inverse(subset_relation))),intersection(u,inverse(subset_relation)))*.
% 299.99/300.68  157045[8:Res:157013.0,9665.1] inductive(intersection(inverse(subset_relation),u)) || well_ordering(v,complement(subset_relation)) -> member(least(v,intersection(inverse(subset_relation),u)),intersection(inverse(subset_relation),u))*.
% 299.99/300.68  157059[8:Res:157036.0,9665.1] inductive(complement(complement(inverse(subset_relation)))) || well_ordering(u,complement(subset_relation)) -> member(least(u,complement(complement(inverse(subset_relation)))),complement(complement(inverse(subset_relation))))*.
% 299.99/300.68  42238[5:Res:9706.3,5.0] || member(u,ordinal_numbers) member(v,ordinal_numbers) equal(successor(v),u) subclass(successor_relation,w) -> member(ordered_pair(v,u),w)*.
% 299.99/300.68  132044[0:Res:133.2,19115.0] || connected(u,recursion_equation_functions(v)) -> well_ordering(u,recursion_equation_functions(v)) subclass(not_well_ordering(u,recursion_equation_functions(v)),w) function(not_subclass_element(not_well_ordering(u,recursion_equation_functions(v)),w))*.
% 299.99/300.68  176791[8:Res:144409.1,129.0] || equal(symmetric_difference(ordinal_numbers,u),ordinal_numbers) subclass(complement(u),v)* well_ordering(w,v)* -> member(least(w,complement(u)),complement(u))*.
% 299.99/300.68  62972[8:Res:15426.1,8554.1] || subclass(domain_relation,complement(intersection(u,v))) member(ordered_pair(identity_relation,identity_relation),union(u,v)) -> member(ordered_pair(identity_relation,identity_relation),symmetric_difference(u,v))*.
% 299.99/300.68  161737[8:Rew:160480.0,161736.2,160491.0,161736.1] inductive(symmetric_difference(intersection(ordinal_numbers,u),identity_relation)) || well_ordering(v,union(u,identity_relation)) -> member(least(v,union(u,identity_relation)),union(u,identity_relation))*.
% 299.99/300.68  13662[7:Rew:13036.0,13486.2] || well_ordering(u,cross_product(ordinal_numbers,ordinal_numbers)) -> equal(recursion_equation_functions(v),identity_relation) equal(segment(u,regular(recursion_equation_functions(v)),least(u,regular(recursion_equation_functions(v)))),identity_relation)**.
% 299.99/300.68  69456[7:Res:13125.2,8554.1] || subclass(omega,complement(intersection(u,v)))* member(w,union(u,v)) -> equal(integer_of(w),identity_relation) member(w,symmetric_difference(u,v))*.
% 299.99/300.68  83870[7:Res:66696.2,8554.1] || subclass(ordinal_numbers,complement(intersection(u,v)))* member(w,union(u,v)) -> equal(integer_of(w),identity_relation) member(w,symmetric_difference(u,v))*.
% 299.99/300.68  165306[8:Res:157036.0,13070.0] || well_ordering(u,complement(subset_relation)) -> equal(complement(complement(inverse(subset_relation))),identity_relation) member(least(u,complement(complement(inverse(subset_relation)))),complement(complement(inverse(subset_relation))))*.
% 299.99/300.68  165305[8:Res:153473.0,13070.0] || well_ordering(u,complement(element_relation)) -> equal(complement(compose(element_relation,ordinal_numbers)),identity_relation) member(least(u,complement(compose(element_relation,ordinal_numbers))),complement(compose(element_relation,ordinal_numbers)))*.
% 299.99/300.68  19351[7:Res:19315.0,13070.0] || well_ordering(u,symmetrization_of(v)) -> equal(symmetric_difference(v,inverse(v)),identity_relation) member(least(u,symmetric_difference(v,inverse(v))),symmetric_difference(v,inverse(v)))*.
% 299.99/300.68  19340[7:Res:19314.0,13070.0] || well_ordering(u,successor(v)) -> equal(symmetric_difference(v,singleton(v)),identity_relation) member(least(u,symmetric_difference(v,singleton(v))),symmetric_difference(v,singleton(v)))*.
% 299.99/300.68  19764[7:Res:19421.0,13113.0] || well_ordering(u,union(v,w)) -> equal(segment(u,symmetric_difference(complement(v),complement(w)),least(u,symmetric_difference(complement(v),complement(w)))),identity_relation)**.
% 299.99/300.68  64292[7:Res:13248.1,490.0] || member(regular(intersection(intersection(complement(u),complement(v)),w)),union(u,v))* -> equal(intersection(intersection(complement(u),complement(v)),w),identity_relation).
% 299.99/300.68  64203[7:Res:13210.1,490.0] || member(regular(intersection(u,intersection(complement(v),complement(w)))),union(v,w))* -> equal(intersection(u,intersection(complement(v),complement(w))),identity_relation).
% 299.99/300.68  13310[7:Rew:13036.0,8599.2] || member(regular(complement(intersection(u,v))),v)* member(regular(complement(intersection(u,v))),u)* -> equal(complement(intersection(u,v)),identity_relation).
% 299.99/300.68  165284[7:Res:155657.1,13070.0] || transitive(subset_relation,ordinal_numbers) well_ordering(u,subset_relation) -> equal(compose(subset_relation,subset_relation),identity_relation) member(least(u,compose(subset_relation,subset_relation)),compose(subset_relation,subset_relation))*.
% 299.99/300.68  165154[7:Res:130703.0,13113.0] || well_ordering(u,intersection(complement(v),complement(w))) -> equal(segment(u,complement(union(v,w)),least(u,complement(union(v,w)))),identity_relation)**.
% 299.99/300.68  165290[8:Res:157013.0,13070.0] || well_ordering(u,complement(subset_relation)) -> equal(intersection(inverse(subset_relation),v),identity_relation) member(least(u,intersection(inverse(subset_relation),v)),intersection(inverse(subset_relation),v))*.
% 299.99/300.68  165289[8:Res:156893.0,13070.0] || well_ordering(u,complement(subset_relation)) -> equal(intersection(v,inverse(subset_relation)),identity_relation) member(least(u,intersection(v,inverse(subset_relation))),intersection(v,inverse(subset_relation)))*.
% 299.99/300.68  191933[18:Res:190515.1,8554.1] || subclass(ordinal_numbers,complement(intersection(u,v))) member(regular(symmetrization_of(identity_relation)),union(u,v)) -> member(regular(symmetrization_of(identity_relation)),symmetric_difference(u,v))*.
% 299.99/300.68  193005[8:Rew:140603.0,192969.1,66036.0,192969.1] ||  -> equal(cross_product(u,v),identity_relation) equal(symmetric_difference(regular(cross_product(u,v)),cross_product(u,v)),union(regular(cross_product(u,v)),cross_product(u,v)))**.
% 299.99/300.68  132217[2:Res:39609.2,19676.0] inductive(symmetric_difference(u,inverse(u))) || well_ordering(v,symmetric_difference(u,inverse(u))) -> member(least(v,symmetric_difference(u,inverse(u))),symmetrization_of(u))*.
% 299.99/300.68  132216[2:Res:39609.2,19559.0] inductive(symmetric_difference(u,singleton(u))) || well_ordering(v,symmetric_difference(u,singleton(u))) -> member(least(v,symmetric_difference(u,singleton(u))),successor(u))*.
% 299.99/300.68  132201[8:Res:39609.2,66086.1] inductive(complement(compose(element_relation,ordinal_numbers))) || well_ordering(u,complement(compose(element_relation,ordinal_numbers))) member(least(u,complement(compose(element_relation,ordinal_numbers))),element_relation)* -> .
% 299.99/300.68  136682[5:Res:39607.2,18791.0] inductive(symmetric_difference(complement(u),complement(v))) || well_ordering(w,ordinal_numbers) -> member(least(w,symmetric_difference(complement(u),complement(v))),union(u,v))*.
% 299.99/300.68  167333[7:Res:13237.2,18791.0] || well_ordering(u,ordinal_numbers) -> equal(symmetric_difference(complement(v),complement(w)),identity_relation) member(least(u,symmetric_difference(complement(v),complement(w))),union(v,w))*.
% 299.99/300.68  162896[8:MRR:65421.1,162891.0] || well_ordering(u,ordinal_numbers) -> equal(least(u,ordered_pair(v,w)),unordered_pair(v,singleton(w)))** equal(least(u,ordered_pair(v,w)),singleton(v)).
% 299.99/300.68  46645[5:Res:9618.2,97.0] || member(ordered_pair(u,v),cross_product(ordinal_numbers,ordinal_numbers))* subclass(composition_function,compose_class(w))* -> equal(compose(w,u),ordered_pair(v,compose(u,v)))*.
% 299.99/300.68  46627[5:Res:9618.2,3700.0] || member(ordered_pair(u,v),cross_product(ordinal_numbers,ordinal_numbers)) subclass(composition_function,singleton(w))* -> equal(ordered_pair(u,ordered_pair(v,compose(u,v))),w)*.
% 299.99/300.68  193979[14:Res:193906.1,129.0] || equal(inverse(subset_relation),singleton(identity_relation)) subclass(complement(subset_relation),u)* well_ordering(v,u)* -> member(least(v,complement(subset_relation)),complement(subset_relation))*.
% 299.99/300.68  193986[18:Res:193924.1,129.0] || equal(symmetrization_of(identity_relation),inverse(subset_relation)) subclass(complement(subset_relation),u)* well_ordering(v,u)* -> member(least(v,complement(subset_relation)),complement(subset_relation))*.
% 299.99/300.68  193993[18:Res:193927.1,129.0] || equal(inverse(subset_relation),inverse(identity_relation)) subclass(complement(subset_relation),u)* well_ordering(v,u)* -> member(least(v,complement(subset_relation)),complement(subset_relation))*.
% 299.99/300.68  194506[8:Res:163112.0,40594.1] || member(complement(inverse(identity_relation)),ordinal_numbers) -> subclass(singleton(singleton(complement(inverse(identity_relation)))),symmetrization_of(identity_relation)) member(singleton(singleton(singleton(complement(inverse(identity_relation))))),element_relation)*.
% 299.99/300.68  195630[16:Rew:195224.0,195215.1] || member(complement(singleton(identity_relation)),ordinal_numbers) -> subclass(singleton(singleton(complement(singleton(identity_relation)))),singleton(identity_relation)) member(singleton(singleton(singleton(complement(singleton(identity_relation))))),element_relation)*.
% 299.99/300.68  197195[8:Obv:197176.0] ||  -> equal(regular(unordered_pair(u,v)),v) equal(unordered_pair(u,v),identity_relation) equal(symmetric_difference(unordered_pair(u,v),u),union(unordered_pair(u,v),u))**.
% 299.99/300.68  197196[8:Obv:197168.0] ||  -> equal(regular(unordered_pair(u,v)),u) equal(unordered_pair(u,v),identity_relation) equal(symmetric_difference(unordered_pair(u,v),v),union(unordered_pair(u,v),v))**.
% 299.99/300.68  197857[8:MRR:197833.3,14676.0] || asymmetric(cross_product(u,v),w)* member(x,cross_product(w,w))* member(x,restrict(inverse(cross_product(u,v)),u,v))* -> .
% 299.99/300.68  199100[18:Res:190515.1,13362.0] || subclass(ordinal_numbers,u) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(regular(symmetrization_of(identity_relation)),least(omega,u))),identity_relation)**.
% 299.99/300.68  199069[8:Res:15426.1,13362.0] || subclass(domain_relation,u) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(ordered_pair(identity_relation,identity_relation),least(omega,u))),identity_relation)**.
% 299.99/300.68  199068[8:Res:15628.1,13362.0] || equal(rest_relation,domain_relation) subclass(rest_relation,u) well_ordering(omega,u)* -> equal(integer_of(ordered_pair(ordered_pair(identity_relation,identity_relation),least(omega,rest_relation))),identity_relation)**.
% 299.99/300.68  199066[21:Res:196415.1,13362.0] || member(u,ordinal_numbers) subclass(domain_relation,v) well_ordering(omega,v)* -> equal(integer_of(ordered_pair(ordered_pair(u,identity_relation),least(omega,domain_relation))),identity_relation)**.
% 299.99/300.68  199057[7:Res:8642.1,13362.0] || subclass(ordinal_numbers,u) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(ordered_pair(w,x),least(omega,u))),identity_relation)**.
% 299.99/300.68  199048[7:Res:49995.1,13362.0] || member(u,subset_relation) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(singleton(first(u)),least(omega,u))),identity_relation)**.
% 299.99/300.68  199035[7:Res:125725.1,13362.0] || subclass(omega,u) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(least(element_relation,omega),least(omega,u))),identity_relation)**.
% 299.99/300.68  199034[7:Res:125731.1,13362.0] || subclass(ordinal_numbers,u) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(least(element_relation,omega),least(omega,u))),identity_relation)**.
% 299.99/300.68  199031[7:Res:143193.1,13362.0] || equal(u,ordinal_numbers) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(least(element_relation,omega),least(omega,u))),identity_relation)**.
% 299.99/300.68  199030[7:Res:143222.1,13362.0] || equal(u,omega) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(least(element_relation,omega),least(omega,u))),identity_relation)**.
% 299.99/300.68  199020[7:Res:133495.1,13362.0] || well_ordering(u,ordinal_numbers) subclass(ordinal_numbers,v) well_ordering(omega,v)* -> equal(integer_of(ordered_pair(least(u,rest_relation),least(omega,ordinal_numbers))),identity_relation)**.
% 299.99/300.68  199019[7:Res:133502.1,13362.0] || well_ordering(u,rest_relation) subclass(ordinal_numbers,v) well_ordering(omega,v)* -> equal(integer_of(ordered_pair(least(u,rest_relation),least(omega,ordinal_numbers))),identity_relation)**.
% 299.99/300.68  199018[7:Res:19525.1,13362.0] || well_ordering(u,ordinal_numbers) subclass(ordinal_numbers,v) well_ordering(omega,v)* -> equal(integer_of(ordered_pair(least(u,ordinal_numbers),least(omega,ordinal_numbers))),identity_relation)**.
% 299.99/300.68  199016[7:Res:133488.1,13362.0] || well_ordering(u,rest_relation) subclass(rest_relation,v) well_ordering(omega,v)* -> equal(integer_of(ordered_pair(least(u,rest_relation),least(omega,rest_relation))),identity_relation)**.
% 299.99/300.68  199015[7:Res:133486.1,13362.0] || well_ordering(u,ordinal_numbers) subclass(rest_relation,v) well_ordering(omega,v)* -> equal(integer_of(ordered_pair(least(u,rest_relation),least(omega,rest_relation))),identity_relation)**.
% 299.99/300.68  198976[7:Res:8643.1,13362.0] || subclass(ordinal_numbers,u) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(unordered_pair(w,x),least(omega,u))),identity_relation)**.
% 299.99/300.68  198959[7:Res:8705.1,13362.0] || member(u,ordinal_numbers) subclass(singleton(u),v)* well_ordering(omega,v) -> equal(integer_of(ordered_pair(u,least(omega,singleton(u)))),identity_relation)**.
% 299.99/300.68  198958[7:Res:13094.1,13362.0] || subclass(singleton(u),v)* well_ordering(omega,v) -> equal(singleton(u),identity_relation) equal(integer_of(ordered_pair(u,least(omega,singleton(u)))),identity_relation)**.
% 299.99/300.68  195687[7:Res:13225.3,18791.0] || member(u,ordinal_numbers) subclass(u,symmetric_difference(complement(v),complement(w))) -> equal(u,identity_relation) member(apply(choice,u),union(v,w))*.
% 299.99/300.68  61937[7:Res:13069.2,19559.0] || member(symmetric_difference(u,singleton(u)),ordinal_numbers) -> equal(symmetric_difference(u,singleton(u)),identity_relation) member(apply(choice,symmetric_difference(u,singleton(u))),successor(u))*.
% 299.99/300.68  61938[7:Res:13069.2,19676.0] || member(symmetric_difference(u,inverse(u)),ordinal_numbers) -> equal(symmetric_difference(u,inverse(u)),identity_relation) member(apply(choice,symmetric_difference(u,inverse(u))),symmetrization_of(u))*.
% 299.99/300.68  197671[7:Res:13247.2,28.1] || member(intersection(u,complement(v)),ordinal_numbers) member(apply(choice,intersection(u,complement(v))),v)* -> equal(intersection(u,complement(v)),identity_relation).
% 299.99/300.68  197697[8:Res:13247.2,14679.1] || member(intersection(u,inverse(subset_relation)),ordinal_numbers) member(apply(choice,intersection(u,inverse(subset_relation))),subset_relation)* -> equal(intersection(u,inverse(subset_relation)),identity_relation).
% 299.99/300.68  197700[8:Res:13247.2,163154.0] || member(intersection(u,symmetrization_of(identity_relation)),ordinal_numbers) -> equal(intersection(u,symmetrization_of(identity_relation)),identity_relation) member(apply(choice,intersection(u,symmetrization_of(identity_relation))),inverse(identity_relation))*.
% 299.99/300.68  197692[7:Res:13247.2,50007.0] || member(intersection(u,subset_relation),ordinal_numbers) subclass(ordinal_numbers,v) -> equal(intersection(u,subset_relation),identity_relation) member(apply(choice,intersection(u,subset_relation)),v)*.
% 299.99/300.68  197408[8:Res:13246.2,14679.1] || member(intersection(inverse(subset_relation),u),ordinal_numbers) member(apply(choice,intersection(inverse(subset_relation),u)),subset_relation)* -> equal(intersection(inverse(subset_relation),u),identity_relation).
% 299.99/300.68  197411[8:Res:13246.2,163154.0] || member(intersection(symmetrization_of(identity_relation),u),ordinal_numbers) -> equal(intersection(symmetrization_of(identity_relation),u),identity_relation) member(apply(choice,intersection(symmetrization_of(identity_relation),u)),inverse(identity_relation))*.
% 299.99/300.68  197403[7:Res:13246.2,50007.0] || member(intersection(subset_relation,u),ordinal_numbers) subclass(ordinal_numbers,v) -> equal(intersection(subset_relation,u),identity_relation) member(apply(choice,intersection(subset_relation,u)),v)*.
% 299.99/300.68  197383[7:Res:13246.2,28.1] || member(intersection(complement(u),v),ordinal_numbers) member(apply(choice,intersection(complement(u),v)),u)* -> equal(intersection(complement(u),v),identity_relation).
% 299.99/300.68  197679[7:Res:13247.2,5.0] || member(intersection(u,v),ordinal_numbers) subclass(v,w) -> equal(intersection(u,v),identity_relation) member(apply(choice,intersection(u,v)),w)*.
% 299.99/300.68  197391[7:Res:13246.2,5.0] || member(intersection(u,v),ordinal_numbers) subclass(u,w) -> equal(intersection(u,v),identity_relation) member(apply(choice,intersection(u,v)),w)*.
% 299.99/300.68  194675[7:MRR:194650.0,61920.2] || member(complement(union(u,v)),ordinal_numbers) -> member(apply(choice,complement(union(u,v))),complement(v))* equal(complement(union(u,v)),identity_relation).
% 299.99/300.68  194676[7:MRR:194649.0,61920.2] || member(complement(union(u,v)),ordinal_numbers) -> member(apply(choice,complement(union(u,v))),complement(u))* equal(complement(union(u,v)),identity_relation).
% 299.99/300.68  69173[8:Res:13069.2,66086.1] || member(complement(compose(element_relation,ordinal_numbers)),ordinal_numbers) member(apply(choice,complement(compose(element_relation,ordinal_numbers))),element_relation)* -> equal(complement(compose(element_relation,ordinal_numbers)),identity_relation).
% 299.99/300.68  160459[7:Rew:13068.1,97007.3] inductive(singleton(singleton(u))) || subclass(ordinal_numbers,power_class(v)) well_ordering(w,power_class(v))* -> member(least(w,singleton(identity_relation)),singleton(identity_relation))*.
% 299.99/300.68  165134[7:Res:96970.1,13113.0] || subclass(ordinal_numbers,power_class(u)) well_ordering(v,power_class(u))* -> equal(segment(v,singleton(singleton(w)),least(v,singleton(singleton(w)))),identity_relation)**.
% 299.99/300.68  148510[5:SpL:3594.0,18545.1] || member(u,ordinal_numbers) subclass(ordinal_numbers,symmetric_difference(complement(intersection(v,w)),union(v,w)))* -> member(power_class(u),complement(symmetric_difference(v,w)))*.
% 299.99/300.68  51208[5:SpR:50855.1,62.1] || member(singleton(u),subset_relation) member(ordered_pair(first(singleton(u)),v),compose(w,x))* -> member(v,image(w,image(x,u))).
% 299.99/300.68  195326[16:Rew:195224.0,193307.0] ||  -> equal(intersection(union(image(element_relation,singleton(identity_relation)),u),union(power_class(complement(singleton(identity_relation))),complement(u))),symmetric_difference(power_class(complement(singleton(identity_relation))),complement(u)))**.
% 299.99/300.68  195332[16:Rew:195224.0,193328.0] ||  -> equal(intersection(union(u,image(element_relation,singleton(identity_relation))),union(complement(u),power_class(complement(singleton(identity_relation))))),symmetric_difference(complement(u),power_class(complement(singleton(identity_relation)))))**.
% 299.99/300.68  148937[8:Res:148858.1,9470.1] || subclass(image(u,image(v,singleton(w))),inverse(subset_relation))* member(ordered_pair(w,x),compose(u,v))* -> member(x,complement(subset_relation)).
% 299.99/300.68  136703[5:Res:9006.3,18791.0] function(u) || member(v,ordinal_numbers) subclass(ordinal_numbers,symmetric_difference(complement(w),complement(x))) -> member(image(u,v),union(w,x))*.
% 299.99/300.68  139652[8:SpR:19860.0,117217.1] operation(restrict(cross_product(u,ordinal_numbers),v,w)) ||  -> subclass(image(cross_product(v,w),u),cantor(cantor(restrict(cross_product(u,ordinal_numbers),v,w))))*.
% 299.99/300.68  133001[0:SpR:30.0,19485.0] ||  -> equal(power_class(intersection(union(u,v),complement(singleton(intersection(complement(u),complement(v)))))),complement(image(element_relation,successor(intersection(complement(u),complement(v))))))**.
% 299.99/300.68  133009[0:SpR:189.0,19485.0] ||  -> equal(power_class(intersection(power_class(image(element_relation,complement(u))),complement(singleton(image(element_relation,power_class(u)))))),complement(image(element_relation,successor(image(element_relation,power_class(u))))))**.
% 299.99/300.68  146809[5:SpL:19485.0,18535.2] || member(intersection(complement(u),complement(singleton(u))),ordinal_numbers)* subclass(ordinal_numbers,complement(v)) member(complement(image(element_relation,successor(u))),v)* -> .
% 299.99/300.68  29132[0:SpL:481.0,490.0] || member(u,intersection(complement(v),power_class(intersection(complement(w),complement(x)))))* member(u,union(v,image(element_relation,union(w,x)))) -> .
% 299.99/300.68  146640[5:SpL:481.0,66637.0] || subclass(ordinal_numbers,intersection(complement(u),power_class(intersection(complement(v),complement(w)))))* member(omega,union(u,image(element_relation,union(v,w)))) -> .
% 299.99/300.68  29089[5:SpR:481.0,8835.1] || member(u,ordinal_numbers) -> member(u,image(element_relation,power_class(intersection(complement(v),complement(w)))))* member(u,power_class(image(element_relation,union(v,w)))).
% 299.99/300.68  29143[0:SpL:481.0,490.0] || member(u,intersection(power_class(intersection(complement(v),complement(w))),complement(x)))* member(u,union(image(element_relation,union(v,w)),x)) -> .
% 299.99/300.68  83029[5:Rew:481.0,82974.1] ||  -> member(not_subclass_element(u,power_class(intersection(complement(v),complement(w)))),image(element_relation,union(v,w)))* subclass(u,power_class(intersection(complement(v),complement(w)))).
% 299.99/300.68  146652[5:SpL:481.0,66637.0] || subclass(ordinal_numbers,intersection(power_class(intersection(complement(u),complement(v))),complement(w)))* member(omega,union(image(element_relation,union(u,v)),w)) -> .
% 299.99/300.68  132362[5:SpR:481.0,132293.0] ||  -> subclass(complement(successor(image(element_relation,union(u,v)))),intersection(power_class(intersection(complement(u),complement(v))),complement(singleton(image(element_relation,union(u,v))))))*.
% 299.99/300.68  132405[5:SpR:481.0,132294.0] ||  -> subclass(complement(symmetrization_of(image(element_relation,union(u,v)))),intersection(power_class(intersection(complement(u),complement(v))),complement(inverse(image(element_relation,union(u,v))))))*.
% 299.99/300.68  19515[7:Rew:481.0,19502.1] || member(regular(power_class(intersection(complement(u),complement(v)))),image(element_relation,union(u,v)))* -> equal(power_class(intersection(complement(u),complement(v))),identity_relation).
% 299.99/300.68  39511[5:SpR:189.0,8832.1] || member(u,ordinal_numbers) -> member(u,intersection(complement(v),power_class(image(element_relation,complement(w)))))* member(u,union(v,image(element_relation,power_class(w)))).
% 299.99/300.68  39524[5:SpR:189.0,8832.1] || member(u,ordinal_numbers) -> member(u,intersection(power_class(image(element_relation,complement(v))),complement(w)))* member(u,union(image(element_relation,power_class(v)),w)).
% 299.99/300.68  155443[5:Res:8827.2,941.1] || member(u,ordinal_numbers) subclass(rest_relation,power_class(image(element_relation,complement(v)))) member(ordered_pair(u,rest_of(u)),image(element_relation,power_class(v)))* -> .
% 299.99/300.68  155417[5:Res:60219.0,941.1] || member(not_subclass_element(u,complement(power_class(image(element_relation,complement(v))))),image(element_relation,power_class(v)))* -> subclass(u,complement(power_class(image(element_relation,complement(v))))).
% 299.99/300.68  132755[0:SpR:189.0,19486.0] ||  -> equal(power_class(intersection(power_class(image(element_relation,complement(u))),complement(inverse(image(element_relation,power_class(u)))))),complement(image(element_relation,symmetrization_of(image(element_relation,power_class(u))))))**.
% 299.99/300.68  155402[5:Res:51313.1,941.1] || member(singleton(power_class(image(element_relation,complement(u)))),subset_relation) member(first(singleton(power_class(image(element_relation,complement(u))))),image(element_relation,power_class(u)))* -> .
% 299.99/300.68  193492[8:SpR:162038.0,3616.0] ||  -> equal(intersection(union(u,image(element_relation,symmetrization_of(identity_relation))),union(complement(u),power_class(complement(inverse(identity_relation))))),symmetric_difference(complement(u),power_class(complement(inverse(identity_relation)))))**.
% 299.99/300.68  193471[8:SpR:162038.0,3616.0] ||  -> equal(intersection(union(image(element_relation,symmetrization_of(identity_relation)),u),union(power_class(complement(inverse(identity_relation))),complement(u))),symmetric_difference(power_class(complement(inverse(identity_relation))),complement(u)))**.
% 299.99/300.68  132747[0:SpR:30.0,19486.0] ||  -> equal(power_class(intersection(union(u,v),complement(inverse(intersection(complement(u),complement(v)))))),complement(image(element_relation,symmetrization_of(intersection(complement(u),complement(v))))))**.
% 299.99/300.68  146808[5:SpL:19486.0,18535.2] || member(intersection(complement(u),complement(inverse(u))),ordinal_numbers)* subclass(ordinal_numbers,complement(v)) member(complement(image(element_relation,symmetrization_of(u))),v)* -> .
% 299.99/300.68  159477[5:Obv:159439.0] ||  -> equal(not_subclass_element(unordered_pair(u,v),image(element_relation,complement(w))),u)** member(v,power_class(w)) subclass(unordered_pair(u,v),image(element_relation,complement(w))).
% 299.99/300.68  159478[5:Obv:159438.0] ||  -> equal(not_subclass_element(unordered_pair(u,v),image(element_relation,complement(w))),v)** member(u,power_class(w)) subclass(unordered_pair(u,v),image(element_relation,complement(w))).
% 299.99/300.68  153374[0:Res:919.1,288.0] || member(not_subclass_element(restrict(image(element_relation,complement(u)),v,w),x),power_class(u))* -> subclass(restrict(image(element_relation,complement(u)),v,w),x).
% 299.99/300.68  159443[5:Res:41368.0,129.0] || subclass(power_class(u),v)* well_ordering(w,v)* -> subclass(x,image(element_relation,complement(u)))* member(least(w,power_class(u)),power_class(u))*.
% 299.99/300.68  9839[5:Rew:963.0,9836.2] || equal(sum_class(range_of(singleton(u))),u) member(singleton(singleton(singleton(u))),cross_product(ordinal_numbers,ordinal_numbers))* -> member(singleton(singleton(singleton(u))),union_of_range_map).
% 299.99/300.68  191849[15:Res:165442.1,8554.1] || subclass(ordinal_numbers,complement(intersection(u,v))) member(sum_class(range_of(identity_relation)),union(u,v)) -> member(sum_class(range_of(identity_relation)),symmetric_difference(u,v))*.
% 299.99/300.68  198983[15:Res:165442.1,13362.0] || subclass(ordinal_numbers,u) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(sum_class(range_of(identity_relation)),least(omega,u))),identity_relation)**.
% 299.99/300.68  193442[8:SpR:161076.2,62.1] || member(u,ordinal_numbers) member(ordered_pair(u,v),compose(w,x))* -> member(u,cantor(x)) member(v,image(w,range_of(identity_relation))).
% 299.99/300.68  193446[8:SpL:161076.2,13280.0] || member(u,ordinal_numbers) equal(range_of(identity_relation),singleton(u)) member(identity_relation,singleton(u))* -> member(u,cantor(successor_relation))* inductive(singleton(u)).
% 299.99/300.68  193445[8:SpL:161076.2,13052.1] || member(u,ordinal_numbers) member(identity_relation,singleton(u)) subclass(range_of(identity_relation),singleton(u))* -> member(u,cantor(successor_relation)) inductive(singleton(u)).
% 299.99/300.68  16622[8:SpL:14756.0,8803.0] || member(u,image(v,range_of(identity_relation))) member(ordered_pair(w,u),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(w,u),compose(v,identity_relation))*.
% 299.99/300.68  47640[5:SoR:9013.0,75.1] one_to_one(flip(cross_product(u,universal_class))) || subclass(range_of(flip(cross_product(u,ordinal_numbers))),v) -> maps(flip(cross_product(u,ordinal_numbers)),inverse(u),v)*.
% 299.99/300.68  47704[5:SoR:9087.0,75.1] one_to_one(flip(cross_product(u,ordinal_numbers))) || subclass(range_of(flip(cross_product(u,ordinal_numbers))),v) -> maps(flip(cross_product(u,ordinal_numbers)),inverse(u),v)*.
% 299.99/300.68  47705[5:SoR:9087.0,82.1] operation(flip(cross_product(u,ordinal_numbers))) || subclass(range_of(flip(cross_product(u,ordinal_numbers))),v) -> maps(flip(cross_product(u,ordinal_numbers)),inverse(u),v)*.
% 299.99/300.68  47641[5:SoR:9013.0,82.1] operation(flip(cross_product(u,universal_class))) || subclass(range_of(flip(cross_product(u,ordinal_numbers))),v) -> maps(flip(cross_product(u,ordinal_numbers)),inverse(u),v)*.
% 299.99/300.68  117618[8:Rew:116078.0,116330.2,116078.0,116330.2,116078.0,116330.2] function(u) || equal(cantor(range_of(v)),range_of(u)) equal(cantor(cantor(w)),cantor(u)) -> compatible(u,w,inverse(v))*.
% 299.99/300.68  198330[5:Res:9837.3,9876.0] || member(u,ordinal_numbers)* member(v,ordinal_numbers) equal(sum_class(range_of(v)),u)* subclass(union_of_range_map,w) well_ordering(ordinal_numbers,w)* -> .
% 299.99/300.68  47882[5:SoR:9014.0,75.1] one_to_one(restrict(element_relation,universal_class,u)) || subclass(range_of(restrict(element_relation,ordinal_numbers,u)),v) -> maps(restrict(element_relation,ordinal_numbers,u),sum_class(u),v)*.
% 299.99/300.68  47897[5:SoR:9101.0,75.1] one_to_one(restrict(element_relation,ordinal_numbers,u)) || subclass(range_of(restrict(element_relation,ordinal_numbers,u)),v) -> maps(restrict(element_relation,ordinal_numbers,u),sum_class(u),v)*.
% 299.99/300.68  47898[5:SoR:9101.0,82.1] operation(restrict(element_relation,ordinal_numbers,u)) || subclass(range_of(restrict(element_relation,ordinal_numbers,u)),v) -> maps(restrict(element_relation,ordinal_numbers,u),sum_class(u),v)*.
% 299.99/300.68  47883[5:SoR:9014.0,82.1] operation(restrict(element_relation,universal_class,u)) || subclass(range_of(restrict(element_relation,ordinal_numbers,u)),v) -> maps(restrict(element_relation,ordinal_numbers,u),sum_class(u),v)*.
% 299.99/300.68  117619[8:Rew:116078.0,116335.2] operation(inverse(u)) || member(v,cantor(range_of(u))) member(w,cantor(range_of(u))) -> member(ordered_pair(w,v),range_of(u))*.
% 299.99/300.68  46414[5:Rew:43.0,46385.2,8647.0,46385.2,43.0,46385.1,8647.0,46385.1] operation(flip(cross_product(u,ordinal_numbers))) || member(v,range_of(u)) member(w,range_of(u)) -> member(ordered_pair(w,v),inverse(u))*.
% 299.99/300.68  197524[21:Rew:196546.1,197497.1] function(u) || subclass(range_of(u),identity_relation)* equal(cross_product(identity_relation,identity_relation),cantor(u)) -> equal(singleton(cantor(u)),identity_relation) operation(u).
% 299.99/300.68  204516[21:SpR:196579.1,116203.2] function(least(u,ordinal_numbers)) || well_ordering(u,ordinal_numbers) subclass(range_of(least(u,ordinal_numbers)),v) -> maps(least(u,ordinal_numbers),identity_relation,v)*.
% 299.99/300.68  204555[21:SpR:196580.1,116203.2] function(least(u,rest_relation)) || well_ordering(u,rest_relation) subclass(range_of(least(u,rest_relation)),v) -> maps(least(u,rest_relation),identity_relation,v)*.
% 299.99/300.68  204597[21:SpR:196581.1,116203.2] function(least(u,rest_relation)) || well_ordering(u,ordinal_numbers) subclass(range_of(least(u,rest_relation)),v) -> maps(least(u,rest_relation),identity_relation,v)*.
% 299.99/300.68  204662[21:Res:196904.1,3689.0] || subclass(domain_relation,ordered_pair(u,v))* -> equal(unordered_pair(u,singleton(v)),singleton(singleton(singleton(identity_relation)))) equal(singleton(singleton(singleton(identity_relation))),singleton(u)).
% 299.99/300.68  204655[21:Res:196904.1,21.0] || subclass(domain_relation,cross_product(u,v))* -> equal(ordered_pair(first(singleton(singleton(singleton(identity_relation)))),second(singleton(singleton(singleton(identity_relation))))),singleton(singleton(singleton(identity_relation))))**.
% 299.99/300.68  204991[21:SpL:161356.2,198464.1] || member(u,ordinal_numbers) member(not_subclass_element(identity_relation,identity_relation),subset_relation) equal(rest_of(range__dfg(v,u,ordinal_numbers)),rest_relation)** -> member(u,cantor(v)).
% 299.99/300.68  205168[15:Res:195033.1,8554.1] || equal(complement(complement(complement(intersection(u,v)))),ordinal_numbers)** member(range_of(identity_relation),union(u,v)) -> member(range_of(identity_relation),symmetric_difference(u,v)).
% 299.99/300.68  206124[22:Res:205574.1,8554.1] || equal(complement(intersection(u,v)),singleton(singleton(identity_relation))) member(singleton(identity_relation),union(u,v)) -> member(singleton(identity_relation),symmetric_difference(u,v))*.
% 299.99/300.68  206221[8:SpR:481.0,155582.0] ||  -> equal(intersection(power_class(intersection(complement(u),complement(v))),symmetric_difference(ordinal_numbers,image(element_relation,union(u,v)))),symmetric_difference(ordinal_numbers,image(element_relation,union(u,v))))**.
% 299.99/300.68  206522[7:Res:165794.1,13113.0] || well_ordering(u,omega) -> equal(integer_of(v),identity_relation) equal(segment(u,intersection(w,singleton(v)),least(u,intersection(w,singleton(v)))),identity_relation)**.
% 299.99/300.68  206549[7:Res:165795.1,13113.0] || well_ordering(u,omega) -> equal(integer_of(v),identity_relation) equal(segment(u,intersection(singleton(v),w),least(u,intersection(singleton(v),w))),identity_relation)**.
% 299.99/300.68  206564[7:Res:206540.1,13113.0] || well_ordering(u,omega) -> equal(integer_of(v),identity_relation) equal(segment(u,complement(complement(singleton(v))),least(u,complement(complement(singleton(v))))),identity_relation)**.
% 299.99/300.68  208019[24:MRR:204544.4,207963.0] function(least(u,ordinal_numbers)) || well_ordering(u,ordinal_numbers) subclass(range_of(least(u,ordinal_numbers)),identity_relation)* equal(cross_product(identity_relation,identity_relation),identity_relation) -> .
% 299.99/300.68  208020[24:MRR:204583.4,207964.0] function(least(u,rest_relation)) || well_ordering(u,rest_relation) subclass(range_of(least(u,rest_relation)),identity_relation)* equal(cross_product(identity_relation,identity_relation),identity_relation) -> .
% 299.99/300.68  208021[24:MRR:204626.4,207965.0] function(least(u,rest_relation)) || well_ordering(u,ordinal_numbers) subclass(range_of(least(u,rest_relation)),identity_relation)* equal(cross_product(identity_relation,identity_relation),identity_relation) -> .
% 299.99/300.68  208135[24:SpL:207558.1,9470.1] operation(u) || member(ordered_pair(u,v),compose(w,x))* subclass(image(w,image(x,identity_relation)),y)* -> member(v,y)*.
% 299.99/300.68  208362[24:Rew:207572.1,208322.3] operation(u) || equal(sum_class(range_of(identity_relation)),u)* member(singleton(singleton(identity_relation)),cross_product(ordinal_numbers,ordinal_numbers))* -> member(singleton(singleton(identity_relation)),union_of_range_map).
% 299.99/300.68  208479[7:SpR:13260.1,964.0] ||  -> equal(cross_product(u,v),identity_relation) member(unordered_pair(first(regular(cross_product(u,v))),singleton(second(regular(cross_product(u,v))))),regular(cross_product(u,v)))*.
% 299.99/300.68  209392[25:Res:208872.0,13362.0] || subclass(ordered_pair(u,ordinal_numbers),v)* well_ordering(omega,v) -> equal(integer_of(ordered_pair(unordered_pair(u,identity_relation),least(omega,ordered_pair(u,ordinal_numbers)))),identity_relation)**.
% 299.99/300.68  209806[8:SpR:481.0,206259.0] ||  -> subclass(symmetric_difference(power_class(intersection(complement(u),complement(v))),symmetric_difference(ordinal_numbers,image(element_relation,union(u,v)))),union(image(element_relation,union(u,v)),identity_relation))*.
% 299.99/300.68  209845[8:Rew:193234.0,209790.0] ||  -> subclass(symmetric_difference(complement(intersection(singleton(identity_relation),image(successor_relation,ordinal_numbers))),symmetric_difference(singleton(identity_relation),image(successor_relation,ordinal_numbers))),complement(symmetric_difference(singleton(identity_relation),image(successor_relation,ordinal_numbers))))*.
% 299.99/300.68  209875[24:Res:207863.1,13113.0] operation(u) || well_ordering(v,successor(u)) -> equal(segment(v,symmetric_difference(complement(u),ordinal_numbers),least(v,symmetric_difference(complement(u),ordinal_numbers))),identity_relation)**.
% 299.99/300.68  209871[24:SpR:481.0,207863.1] operation(image(element_relation,union(u,v))) ||  -> subclass(symmetric_difference(power_class(intersection(complement(u),complement(v))),ordinal_numbers),successor(image(element_relation,union(u,v))))*.
% 299.99/300.68  210300[8:Res:140864.1,40594.1] || member(singleton(symmetric_difference(ordinal_numbers,u)),complement(u))* member(symmetric_difference(ordinal_numbers,u),ordinal_numbers) -> member(singleton(singleton(singleton(symmetric_difference(ordinal_numbers,u)))),element_relation)*.
% 299.99/300.68  211523[16:MRR:211507.1,13039.0] || well_ordering(element_relation,image(choice,singleton(singleton(identity_relation))))* -> equal(image(choice,singleton(singleton(identity_relation))),ordinal_numbers) member(image(choice,singleton(singleton(identity_relation))),ordinal_numbers).
% 299.99/300.68  212408[7:SpL:13259.2,39296.0] || member(cross_product(u,v),ordinal_numbers) subclass(ordinal_numbers,complement(unordered_pair(w,apply(choice,cross_product(u,v)))))* -> equal(cross_product(u,v),identity_relation).
% 299.99/300.68  212407[7:SpL:13259.2,39499.0] || member(cross_product(u,v),ordinal_numbers) equal(complement(unordered_pair(w,apply(choice,cross_product(u,v)))),ordinal_numbers)** -> equal(cross_product(u,v),identity_relation).
% 299.99/300.68  212380[7:SpL:13259.2,39297.0] || member(cross_product(u,v),ordinal_numbers) subclass(ordinal_numbers,complement(unordered_pair(apply(choice,cross_product(u,v)),w)))* -> equal(cross_product(u,v),identity_relation).
% 299.99/300.68  212379[7:SpL:13259.2,39562.0] || member(cross_product(u,v),ordinal_numbers) equal(complement(unordered_pair(apply(choice,cross_product(u,v)),w)),ordinal_numbers)** -> equal(cross_product(u,v),identity_relation).
% 299.99/300.68  212364[7:SpR:13259.2,8642.1] || member(cross_product(u,v),ordinal_numbers) subclass(ordinal_numbers,w) -> equal(cross_product(u,v),identity_relation) member(apply(choice,cross_product(u,v)),w)*.
% 299.99/300.68  213463[8:SpR:145761.0,117380.1] operation(cross_product(u,singleton(v))) ||  -> equal(cross_product(cantor(segment(ordinal_numbers,u,v)),cantor(segment(ordinal_numbers,u,v))),segment(ordinal_numbers,u,v))**.
% 299.99/300.68  213497[8:Rew:145761.0,213485.2] operation(cross_product(u,singleton(v))) || member(ordered_pair(w,x),segment(ordinal_numbers,u,v))* -> member(w,cantor(segment(ordinal_numbers,u,v))).
% 299.99/300.68  213498[8:Rew:145761.0,213484.2] operation(cross_product(u,singleton(v))) || member(ordered_pair(w,x),segment(ordinal_numbers,u,v))* -> member(x,cantor(segment(ordinal_numbers,u,v))).
% 299.99/300.68  213634[7:Res:151877.0,13113.0] || well_ordering(u,complement(recursion_equation_functions(v)))* -> function(w) equal(segment(u,intersection(singleton(w),x),least(u,intersection(singleton(w),x))),identity_relation)**.
% 299.99/300.68  213656[7:Res:213622.0,13113.0] || well_ordering(u,complement(recursion_equation_functions(v)))* -> function(w) equal(segment(u,complement(complement(singleton(w))),least(u,complement(complement(singleton(w))))),identity_relation)**.
% 299.99/300.68  213690[7:Res:151512.0,13113.0] || well_ordering(u,complement(recursion_equation_functions(v)))* -> function(w) equal(segment(u,intersection(x,singleton(w)),least(u,intersection(x,singleton(w)))),identity_relation)**.
% 299.99/300.68  214271[25:SpR:208887.0,117380.1] operation(restrict(u,v,identity_relation)) ||  -> equal(cross_product(cantor(segment(u,v,ordinal_numbers)),cantor(segment(u,v,ordinal_numbers))),segment(u,v,ordinal_numbers))**.
% 299.99/300.68  214320[25:Rew:208887.0,214300.2] operation(restrict(u,v,identity_relation)) || member(ordered_pair(w,x),segment(u,v,ordinal_numbers))* -> member(w,cantor(segment(u,v,ordinal_numbers))).
% 299.99/300.68  214321[25:Rew:208887.0,214299.2] operation(restrict(u,v,identity_relation)) || member(ordered_pair(w,x),segment(u,v,ordinal_numbers))* -> member(x,cantor(segment(u,v,ordinal_numbers))).
% 299.99/300.68  214562[25:SpL:208985.1,8798.1] operation(u) || equal(sum_class(range_of(v)),u) member(ordered_pair(v,ordinal_numbers),cross_product(ordinal_numbers,ordinal_numbers))* -> member(ordered_pair(v,u),union_of_range_map)*.
% 299.99/300.68  214507[25:SpL:208985.1,8798.1] operation(u) || equal(sum_class(range_of(v)),ordinal_numbers) member(ordered_pair(v,u),cross_product(ordinal_numbers,ordinal_numbers))* -> member(ordered_pair(v,ordinal_numbers),union_of_range_map).
% 299.99/300.68  214927[7:Res:151501.1,13113.0] || member(u,v)* well_ordering(w,v)* -> equal(segment(w,intersection(x,singleton(u)),least(w,intersection(x,singleton(u)))),identity_relation)**.
% 299.99/300.68  214985[7:Res:151502.1,13113.0] || well_ordering(u,complement(v))* -> member(w,v)* equal(segment(u,intersection(x,singleton(w)),least(u,intersection(x,singleton(w)))),identity_relation)**.
% 299.99/300.68  215023[7:Res:151861.1,13113.0] || member(u,v)* well_ordering(w,v)* -> equal(segment(w,intersection(singleton(u),x),least(w,intersection(singleton(u),x))),identity_relation)**.
% 299.99/300.68  215057[7:Res:215011.1,13113.0] || member(u,v)* well_ordering(w,v)* -> equal(segment(w,complement(complement(singleton(u))),least(w,complement(complement(singleton(u))))),identity_relation)**.
% 299.99/300.68  215120[7:Res:151862.1,13113.0] || well_ordering(u,complement(v))* -> member(w,v)* equal(segment(u,intersection(singleton(w),x),least(u,intersection(singleton(w),x))),identity_relation)**.
% 299.99/300.68  215157[7:Res:215108.1,13113.0] || well_ordering(u,complement(v))* -> member(w,v)* equal(segment(u,complement(complement(singleton(w))),least(u,complement(complement(singleton(w))))),identity_relation)**.
% 299.99/300.68  215184[0:SpR:481.0,155157.1] || subclass(image(element_relation,union(u,v)),w) -> subclass(symmetric_difference(w,image(element_relation,union(u,v))),power_class(intersection(complement(u),complement(v))))*.
% 299.99/300.68  217867[20:Res:217827.0,13362.0] || subclass(inverse(identity_relation),u)* well_ordering(omega,u) -> equal(integer_of(ordered_pair(regular(complement(complement(symmetrization_of(identity_relation)))),least(omega,inverse(identity_relation)))),identity_relation)**.
% 299.99/300.68  217936[24:MRR:217935.3,217887.0] function(regular(complement(complement(symmetrization_of(identity_relation))))) || subclass(range_of(regular(complement(complement(symmetrization_of(identity_relation))))),identity_relation)* equal(cross_product(identity_relation,identity_relation),identity_relation) -> .
% 299.99/300.68  217955[8:Res:116148.1,17315.0] || section(u,recursion_equation_functions(v),w) -> equal(cantor(restrict(u,w,recursion_equation_functions(v))),identity_relation) function(regular(cantor(restrict(u,w,recursion_equation_functions(v)))))*.
% 299.99/300.68  218765[21:Res:218509.1,13362.0] || equal(rest_relation,domain_relation) subclass(rest_relation,u) well_ordering(omega,u)* -> equal(integer_of(ordered_pair(ordered_pair(omega,identity_relation),least(omega,rest_relation))),identity_relation)**.
% 299.99/300.68  219308[15:Res:215659.1,13362.0] || subclass(complement(u),identity_relation) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(range_of(identity_relation),least(omega,u))),identity_relation)**.
% 299.99/300.68  219629[8:Res:919.1,67561.0] ||  -> subclass(restrict(symmetric_difference(complement(u),ordinal_numbers),v,w),x) member(not_subclass_element(restrict(symmetric_difference(complement(u),ordinal_numbers),v,w),x),union(u,identity_relation))*.
% 299.99/300.68  219835[15:Res:217197.1,13362.0] || equal(complement(u),identity_relation) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(range_of(identity_relation),least(omega,u))),identity_relation)**.
% 299.99/300.68  220196[8:SpL:13259.2,217704.0] || member(cross_product(u,v),ordinal_numbers) equal(complement(complement(singleton(apply(choice,cross_product(u,v))))),identity_relation)** -> equal(cross_product(u,v),identity_relation).
% 299.99/300.68  220457[21:Res:196656.1,8798.1] || subclass(domain_relation,flip(cross_product(ordinal_numbers,ordinal_numbers))) equal(sum_class(range_of(ordered_pair(u,v))),identity_relation) -> member(ordered_pair(ordered_pair(u,v),identity_relation),union_of_range_map)*.
% 299.99/300.68  220559[21:Res:196657.1,8798.1] || subclass(domain_relation,rotate(cross_product(ordinal_numbers,ordinal_numbers))) equal(sum_class(range_of(ordered_pair(u,identity_relation))),v) -> member(ordered_pair(ordered_pair(u,identity_relation),v),union_of_range_map)*.
% 299.99/300.68  221130[7:Res:13236.2,19676.0] || well_ordering(u,symmetric_difference(v,inverse(v))) -> equal(symmetric_difference(v,inverse(v)),identity_relation) member(least(u,symmetric_difference(v,inverse(v))),symmetrization_of(v))*.
% 299.99/300.68  221129[7:Res:13236.2,19559.0] || well_ordering(u,symmetric_difference(v,singleton(v))) -> equal(symmetric_difference(v,singleton(v)),identity_relation) member(least(u,symmetric_difference(v,singleton(v))),successor(v))*.
% 299.99/300.68  221116[8:Res:13236.2,66086.1] || well_ordering(u,complement(compose(element_relation,ordinal_numbers))) member(least(u,complement(compose(element_relation,ordinal_numbers))),element_relation)* -> equal(complement(compose(element_relation,ordinal_numbers)),identity_relation).
% 299.99/300.68  221268[8:Res:215662.1,13362.0] || subclass(complement(u),identity_relation) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(singleton(w),least(omega,u))),identity_relation)**.
% 299.99/300.68  221525[8:Res:217198.1,13362.0] || equal(complement(u),identity_relation) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(singleton(w),least(omega,u))),identity_relation)**.
% 299.99/300.68  223079[7:SpL:189.0,13306.0] || member(regular(power_class(image(element_relation,power_class(u)))),image(element_relation,power_class(image(element_relation,complement(u)))))* -> equal(power_class(image(element_relation,power_class(u))),identity_relation).
% 299.99/300.68  223874[8:SpL:160927.0,490.0] || member(u,intersection(complement(v),union(w,symmetric_difference(ordinal_numbers,x))))* member(u,union(v,intersection(complement(w),union(x,identity_relation)))) -> .
% 299.99/300.68  223866[8:SpL:160927.0,490.0] || member(u,intersection(union(v,symmetric_difference(ordinal_numbers,w)),complement(x)))* member(u,union(intersection(complement(v),union(w,identity_relation)),x)) -> .
% 299.99/300.68  223865[8:SpL:160927.0,66637.0] || subclass(ordinal_numbers,intersection(complement(u),union(v,symmetric_difference(ordinal_numbers,w)))) member(omega,union(u,intersection(complement(v),union(w,identity_relation))))* -> .
% 299.99/300.68  223801[8:SpL:160927.0,66637.0] || subclass(ordinal_numbers,intersection(union(u,symmetric_difference(ordinal_numbers,v)),complement(w))) member(omega,union(intersection(complement(u),union(v,identity_relation)),w))* -> .
% 299.99/300.68  223755[8:SpR:160927.0,8835.1] || member(u,ordinal_numbers) -> member(u,image(element_relation,union(v,symmetric_difference(ordinal_numbers,w))))* member(u,power_class(intersection(complement(v),union(w,identity_relation)))).
% 299.99/300.68  223714[8:SpR:160927.0,19734.0] ||  -> subclass(symmetric_difference(union(u,symmetric_difference(ordinal_numbers,v)),complement(inverse(intersection(complement(u),union(v,identity_relation))))),symmetrization_of(intersection(complement(u),union(v,identity_relation))))*.
% 299.99/300.68  223713[8:SpR:160927.0,19733.0] ||  -> subclass(symmetric_difference(union(u,symmetric_difference(ordinal_numbers,v)),complement(singleton(intersection(complement(u),union(v,identity_relation))))),successor(intersection(complement(u),union(v,identity_relation))))*.
% 299.99/300.68  223929[8:Rew:223721.0,223736.0] ||  -> subclass(symmetric_difference(union(u,symmetric_difference(ordinal_numbers,v)),intersection(union(u,symmetric_difference(ordinal_numbers,v)),ordinal_numbers)),union(intersection(complement(u),union(v,identity_relation)),identity_relation))*.
% 299.99/300.68  223933[8:Rew:160927.0,223833.1] || member(not_subclass_element(union(u,symmetric_difference(ordinal_numbers,v)),w),intersection(complement(u),union(v,identity_relation)))* -> subclass(union(u,symmetric_difference(ordinal_numbers,v)),w).
% 299.99/300.68  223934[8:Rew:160927.0,223710.1] ||  -> member(regular(complement(union(u,symmetric_difference(ordinal_numbers,v)))),intersection(complement(u),union(v,identity_relation)))* equal(complement(union(u,symmetric_difference(ordinal_numbers,v))),identity_relation).
% 299.99/300.68  224193[8:SpL:160992.0,490.0] || member(u,intersection(complement(v),union(symmetric_difference(ordinal_numbers,w),x)))* member(u,union(v,intersection(union(w,identity_relation),complement(x)))) -> .
% 299.99/300.68  224185[8:SpL:160992.0,490.0] || member(u,intersection(union(symmetric_difference(ordinal_numbers,v),w),complement(x)))* member(u,union(intersection(union(v,identity_relation),complement(w)),x)) -> .
% 299.99/300.68  224184[8:SpL:160992.0,66637.0] || subclass(ordinal_numbers,intersection(complement(u),union(symmetric_difference(ordinal_numbers,v),w))) member(omega,union(u,intersection(union(v,identity_relation),complement(w))))* -> .
% 299.99/300.68  224119[8:SpL:160992.0,66637.0] || subclass(ordinal_numbers,intersection(union(symmetric_difference(ordinal_numbers,u),v),complement(w))) member(omega,union(intersection(union(u,identity_relation),complement(v)),w))* -> .
% 299.99/300.68  224072[8:SpR:160992.0,8835.1] || member(u,ordinal_numbers) -> member(u,image(element_relation,union(symmetric_difference(ordinal_numbers,v),w)))* member(u,power_class(intersection(union(v,identity_relation),complement(w)))).
% 299.99/300.68  224031[8:SpR:160992.0,19734.0] ||  -> subclass(symmetric_difference(union(symmetric_difference(ordinal_numbers,u),v),complement(inverse(intersection(union(u,identity_relation),complement(v))))),symmetrization_of(intersection(union(u,identity_relation),complement(v))))*.
% 299.99/300.68  224030[8:SpR:160992.0,19733.0] ||  -> subclass(symmetric_difference(union(symmetric_difference(ordinal_numbers,u),v),complement(singleton(intersection(union(u,identity_relation),complement(v))))),successor(intersection(union(u,identity_relation),complement(v))))*.
% 299.99/300.68  224244[8:Rew:224038.0,224053.0] ||  -> subclass(symmetric_difference(union(symmetric_difference(ordinal_numbers,u),v),intersection(union(symmetric_difference(ordinal_numbers,u),v),ordinal_numbers)),union(intersection(union(u,identity_relation),complement(v)),identity_relation))*.
% 299.99/300.68  224248[8:Rew:160992.0,224151.1] || member(not_subclass_element(union(symmetric_difference(ordinal_numbers,u),v),w),intersection(union(u,identity_relation),complement(v)))* -> subclass(union(symmetric_difference(ordinal_numbers,u),v),w).
% 299.99/300.68  224249[8:Rew:160992.0,224027.1] ||  -> member(regular(complement(union(symmetric_difference(ordinal_numbers,u),v))),intersection(union(u,identity_relation),complement(v)))* equal(complement(union(symmetric_difference(ordinal_numbers,u),v)),identity_relation).
% 299.99/300.68  224325[8:MRR:224287.3,218130.2] || member(regular(regular(intersection(u,v))),v)* member(regular(regular(intersection(u,v))),u)* -> equal(regular(intersection(u,v)),identity_relation).
% 299.99/300.68  224330[8:MRR:224300.0,60996.1] ||  -> member(regular(regular(image(element_relation,complement(u)))),power_class(u))* equal(regular(image(element_relation,complement(u))),identity_relation) equal(image(element_relation,complement(u)),identity_relation).
% 299.99/300.68  225437[7:Res:62.1,17312.1] || member(ordered_pair(u,regular(v)),compose(w,x)) subclass(v,complement(image(w,image(x,singleton(u)))))* -> equal(v,identity_relation).
% 299.99/300.68  225480[7:Obv:225400.2] || subclass(unordered_pair(u,v),complement(w))* member(v,w) -> equal(regular(unordered_pair(u,v)),u) equal(unordered_pair(u,v),identity_relation).
% 299.99/300.68  225481[7:Obv:225399.2] || subclass(unordered_pair(u,v),complement(w))* member(u,w) -> equal(regular(unordered_pair(u,v)),v) equal(unordered_pair(u,v),identity_relation).
% 299.99/300.68  226023[7:SpR:487.0,13578.1] ||  -> equal(symmetric_difference(image(element_relation,complement(u)),v),identity_relation) member(regular(symmetric_difference(image(element_relation,complement(u)),v)),complement(intersection(power_class(u),complement(v))))*.
% 299.99/300.68  226015[7:SpR:485.0,13578.1] ||  -> equal(symmetric_difference(u,image(element_relation,complement(v))),identity_relation) member(regular(symmetric_difference(u,image(element_relation,complement(v)))),complement(intersection(complement(u),power_class(v))))*.
% 299.99/300.68  226156[7:Res:9604.1,17321.0] || equal(sum_class(intersection(u,v)),intersection(u,v)) -> equal(sum_class(intersection(u,v)),identity_relation) member(regular(sum_class(intersection(u,v))),v)*.
% 299.99/300.68  226261[7:Res:9604.1,17322.0] || equal(sum_class(intersection(u,v)),intersection(u,v)) -> equal(sum_class(intersection(u,v)),identity_relation) member(regular(sum_class(intersection(u,v))),u)*.
% 299.99/300.68  226345[25:Res:226327.1,13362.0] || subclass(rest_relation,domain_relation) subclass(rest_relation,u) well_ordering(omega,u)* -> equal(integer_of(ordered_pair(ordered_pair(identity_relation,identity_relation),least(omega,rest_relation))),identity_relation)**.
% 299.99/300.68  227127[21:Res:196520.2,129.0] || member(u,ordinal_numbers)* equal(successor(u),identity_relation) subclass(successor_relation,v) well_ordering(w,v)* -> member(least(w,successor_relation),successor_relation)*.
% 299.99/300.68  227221[8:Res:217451.1,129.0] || equal(union(u,identity_relation),identity_relation) subclass(complement(u),v)* well_ordering(w,v)* -> member(least(w,complement(u)),complement(u))*.
% 299.99/300.68  228150[8:SpL:161356.2,219928.1] || member(u,ordinal_numbers) member(not_subclass_element(identity_relation,identity_relation),subset_relation) equal(singleton(range__dfg(v,u,ordinal_numbers)),identity_relation)** -> member(u,cantor(v)).
% 299.99/300.68  228912[8:Rew:13263.1,228911.2] || member(apply(choice,u),unordered_pair(v,u))* -> equal(regular(unordered_pair(v,u)),v) equal(u,identity_relation) equal(unordered_pair(v,u),identity_relation).
% 299.99/300.68  228914[8:Rew:13263.2,228913.2] || member(apply(choice,u),unordered_pair(u,v))* -> equal(regular(unordered_pair(u,v)),v) equal(u,identity_relation) equal(unordered_pair(u,v),identity_relation).
% 299.99/300.68  229031[7:Res:19563.1,129.0] || subclass(successor(u),v)* well_ordering(w,v)* -> equal(symmetric_difference(u,singleton(u)),identity_relation) member(least(w,successor(u)),successor(u))*.
% 299.99/300.68  229141[8:Res:67614.1,17387.0] || member(regular(intersection(complement(symmetric_difference(complement(u),ordinal_numbers)),v)),union(u,identity_relation))* -> equal(intersection(complement(symmetric_difference(complement(u),ordinal_numbers)),v),identity_relation).
% 299.99/300.68  229135[7:Res:3618.1,17387.0] || member(regular(intersection(complement(complement(intersection(u,v))),w)),symmetric_difference(u,v))* -> equal(intersection(complement(complement(intersection(u,v))),w),identity_relation).
% 299.99/300.68  229570[8:Res:67614.1,13571.0] || member(regular(intersection(u,complement(symmetric_difference(complement(v),ordinal_numbers)))),union(v,identity_relation))* -> equal(intersection(u,complement(symmetric_difference(complement(v),ordinal_numbers))),identity_relation).
% 299.99/300.68  229564[7:Res:3618.1,13571.0] || member(regular(intersection(u,complement(complement(intersection(v,w))))),symmetric_difference(v,w))* -> equal(intersection(u,complement(complement(intersection(v,w)))),identity_relation).
% 299.99/300.68  230148[7:Res:19679.1,129.0] || subclass(symmetrization_of(u),v)* well_ordering(w,v)* -> equal(symmetric_difference(u,inverse(u)),identity_relation) member(least(w,symmetrization_of(u)),symmetrization_of(u))*.
% 299.99/300.68  230482[8:MRR:230430.0,8655.0] || member(symmetric_difference(ordinal_numbers,u),ordinal_numbers) -> member(singleton(symmetric_difference(ordinal_numbers,u)),union(u,identity_relation))* member(singleton(singleton(singleton(symmetric_difference(ordinal_numbers,u)))),element_relation)*.
% 299.99/300.68  230638[8:Res:3618.1,18754.1] || member(unordered_pair(u,v),symmetric_difference(w,x))* subclass(ordinal_numbers,regular(complement(intersection(w,x)))) -> equal(complement(intersection(w,x)),identity_relation).
% 299.99/300.68  230703[8:MRR:230658.3,218143.2] || member(unordered_pair(u,v),cross_product(w,x))* member(unordered_pair(u,v),y)* subclass(ordinal_numbers,regular(restrict(y,w,x)))* -> .
% 299.99/300.68  230812[16:SpL:195257.0,1042.0] || member(not_subclass_element(power_class(image(element_relation,singleton(identity_relation))),u),image(element_relation,power_class(complement(singleton(identity_relation)))))* -> subclass(power_class(image(element_relation,singleton(identity_relation))),u).
% 299.99/300.68  230811[8:SpL:162038.0,1042.0] || member(not_subclass_element(power_class(image(element_relation,symmetrization_of(identity_relation))),u),image(element_relation,power_class(complement(inverse(identity_relation)))))* -> subclass(power_class(image(element_relation,symmetrization_of(identity_relation))),u).
% 299.99/300.68  231841[8:Rew:13263.1,231840.2] || member(not_subclass_element(u,v),unordered_pair(w,u))* -> equal(regular(unordered_pair(w,u)),w) subclass(u,v) equal(unordered_pair(w,u),identity_relation).
% 299.99/300.68  231843[8:Rew:13263.2,231842.2] || member(not_subclass_element(u,v),unordered_pair(u,w))* -> equal(regular(unordered_pair(u,w)),w) subclass(u,v) equal(unordered_pair(u,w),identity_relation).
% 299.99/300.68  231897[16:Res:231880.0,9665.1] inductive(regular(complement(singleton(identity_relation)))) || well_ordering(u,singleton(identity_relation)) -> member(least(u,regular(complement(singleton(identity_relation)))),regular(complement(singleton(identity_relation))))*.
% 299.99/300.68  231894[16:Res:231880.0,13070.0] || well_ordering(u,singleton(identity_relation)) -> equal(regular(complement(singleton(identity_relation))),identity_relation) member(least(u,regular(complement(singleton(identity_relation)))),regular(complement(singleton(identity_relation))))*.
% 299.99/300.68  232051[7:Res:139.1,17323.0] || member(restrict(u,v,w),ordinal_numbers) -> equal(sum_class(restrict(u,v,w)),identity_relation) member(regular(sum_class(restrict(u,v,w))),u)*.
% 299.99/300.68  232070[7:MRR:232058.2,13102.1] || connected(u,restrict(v,w,x)) -> well_ordering(u,restrict(v,w,x)) member(regular(not_well_ordering(u,restrict(v,w,x))),v)*.
% 299.99/300.68  233040[8:Res:155157.1,69182.0] || subclass(compose(element_relation,ordinal_numbers),u) member(regular(symmetric_difference(u,compose(element_relation,ordinal_numbers))),element_relation)* -> equal(symmetric_difference(u,compose(element_relation,ordinal_numbers)),identity_relation).
% 299.99/300.68  233117[8:SpL:13259.2,233014.0] || member(cross_product(u,v),ordinal_numbers) equal(complement(regular(singleton(apply(choice,cross_product(u,v))))),identity_relation)** -> equal(cross_product(u,v),identity_relation).
% 299.99/300.68  233201[16:Rew:195257.0,233184.1] || member(regular(image(element_relation,power_class(complement(singleton(identity_relation))))),power_class(image(element_relation,singleton(identity_relation))))* -> equal(image(element_relation,power_class(complement(singleton(identity_relation)))),identity_relation).
% 299.99/300.68  233202[8:Rew:162038.0,233183.1] || member(regular(image(element_relation,power_class(complement(inverse(identity_relation))))),power_class(image(element_relation,symmetrization_of(identity_relation))))* -> equal(image(element_relation,power_class(complement(inverse(identity_relation)))),identity_relation).
% 299.99/300.68  233359[8:Res:231881.0,8990.1] function(complement(singleton(cross_product(ordinal_numbers,ordinal_numbers)))) ||  -> equal(singleton(cross_product(ordinal_numbers,ordinal_numbers)),identity_relation) equal(complement(singleton(cross_product(ordinal_numbers,ordinal_numbers))),cross_product(ordinal_numbers,ordinal_numbers))**.
% 299.99/300.68  233451[14:Res:233378.0,129.0] || subclass(complement(singleton(singleton(identity_relation))),u)* well_ordering(v,u)* -> member(least(v,complement(singleton(singleton(identity_relation)))),complement(singleton(singleton(identity_relation))))*.
% 299.99/300.68  233448[14:Res:233378.0,13362.0] || subclass(complement(singleton(singleton(identity_relation))),u)* well_ordering(omega,u) -> equal(integer_of(ordered_pair(identity_relation,least(omega,complement(singleton(singleton(identity_relation)))))),identity_relation)**.
% 299.99/300.68  233583[21:MRR:233534.0,233534.3,13126.0,8667.0] || member(ordered_pair(u,v),cross_product(ordinal_numbers,ordinal_numbers)) member(ordered_pair(ordered_pair(v,u),identity_relation),w)* subclass(domain_relation,complement(flip(w))) -> .
% 299.99/300.68  233584[21:MRR:233533.0,233533.3,13126.0,8667.0] || member(ordered_pair(u,v),cross_product(ordinal_numbers,ordinal_numbers)) member(ordered_pair(ordered_pair(v,identity_relation),u),w)* subclass(domain_relation,complement(rotate(w))) -> .
% 299.99/300.68  233954[8:Res:8827.2,161200.0] || member(u,ordinal_numbers) subclass(rest_relation,image(element_relation,union(v,identity_relation))) member(ordered_pair(u,rest_of(u)),power_class(symmetric_difference(ordinal_numbers,v)))* -> .
% 299.99/300.68  233914[8:Res:51313.1,161200.0] || member(singleton(image(element_relation,union(u,identity_relation))),subset_relation) member(first(singleton(image(element_relation,union(u,identity_relation)))),power_class(symmetric_difference(ordinal_numbers,u)))* -> .
% 299.99/300.68  234166[16:Rew:195257.0,234156.2] || subclass(omega,image(element_relation,singleton(identity_relation))) -> equal(integer_of(not_subclass_element(power_class(complement(singleton(identity_relation))),u)),identity_relation)** subclass(power_class(complement(singleton(identity_relation))),u).
% 299.99/300.68  234167[8:Rew:162038.0,234155.2] || subclass(omega,image(element_relation,symmetrization_of(identity_relation))) -> equal(integer_of(not_subclass_element(power_class(complement(inverse(identity_relation))),u)),identity_relation)** subclass(power_class(complement(inverse(identity_relation))),u).
% 299.99/300.68  234382[16:Rew:195257.0,234342.2] || well_ordering(u,ordinal_numbers) member(least(u,power_class(complement(singleton(identity_relation)))),image(element_relation,singleton(identity_relation)))* -> equal(power_class(complement(singleton(identity_relation))),identity_relation).
% 299.99/300.68  234383[8:Rew:162038.0,234341.2] || well_ordering(u,ordinal_numbers) member(least(u,power_class(complement(inverse(identity_relation)))),image(element_relation,symmetrization_of(identity_relation)))* -> equal(power_class(complement(inverse(identity_relation))),identity_relation).
% 299.99/300.68  234631[8:SpL:13259.2,234115.0] || member(cross_product(u,v),ordinal_numbers) equal(complement(complement(singleton(apply(choice,cross_product(u,v))))),ordinal_numbers)** -> equal(cross_product(u,v),identity_relation).
% 299.99/300.68  234645[8:SpL:13259.2,234117.0] || member(cross_product(u,v),ordinal_numbers) subclass(ordinal_numbers,complement(complement(singleton(apply(choice,cross_product(u,v))))))* -> equal(cross_product(u,v),identity_relation).
% 299.99/300.68  234728[8:SpL:13259.2,232824.0] || member(cross_product(u,v),ordinal_numbers) subclass(ordinal_numbers,regular(unordered_pair(w,apply(choice,cross_product(u,v)))))* -> equal(cross_product(u,v),identity_relation).
% 299.99/300.68  234758[8:SpL:13259.2,233124.0] || member(cross_product(u,v),ordinal_numbers) subclass(ordinal_numbers,regular(unordered_pair(apply(choice,cross_product(u,v)),w)))* -> equal(cross_product(u,v),identity_relation).
% 299.99/300.68  234905[8:MRR:234822.0,61920.2] || member(complement(cantor(u)),ordinal_numbers) -> equal(apply(u,apply(choice,complement(cantor(u)))),sum_class(range_of(identity_relation)))** equal(complement(cantor(u)),identity_relation).
% 299.99/300.68  234915[8:SpL:13259.2,234736.0] || member(cross_product(u,v),ordinal_numbers) equal(regular(unordered_pair(w,apply(choice,cross_product(u,v)))),ordinal_numbers)** -> equal(cross_product(u,v),identity_relation).
% 299.99/300.68  234928[8:SpL:13259.2,234766.0] || member(cross_product(u,v),ordinal_numbers) equal(regular(unordered_pair(apply(choice,cross_product(u,v)),w)),ordinal_numbers)** -> equal(cross_product(u,v),identity_relation).
% 299.99/300.68  235031[7:SpL:234956.0,9470.1] || member(ordered_pair(u,v),compose(complement(cross_product(image(w,singleton(u)),ordinal_numbers)),w))* subclass(range_of(identity_relation),x)* -> member(v,x)*.
% 299.99/300.68  235026[7:SpL:234956.0,9470.1] || member(ordered_pair(u,v),compose(w,complement(cross_product(singleton(u),ordinal_numbers))))* subclass(image(w,range_of(identity_relation)),x)* -> member(v,x)*.
% 299.99/300.68  235119[16:Rew:195257.0,235074.1] ||  -> member(not_subclass_element(u,image(element_relation,power_class(complement(singleton(identity_relation))))),power_class(image(element_relation,singleton(identity_relation))))* subclass(u,image(element_relation,power_class(complement(singleton(identity_relation))))).
% 299.99/300.68  235120[8:Rew:162038.0,235073.1] ||  -> member(not_subclass_element(u,image(element_relation,power_class(complement(inverse(identity_relation))))),power_class(image(element_relation,symmetrization_of(identity_relation))))* subclass(u,image(element_relation,power_class(complement(inverse(identity_relation))))).
% 299.99/300.68  235281[8:Res:230445.1,13313.1] || member(apply(choice,complement(union(u,identity_relation))),u)* member(complement(union(u,identity_relation)),ordinal_numbers) -> equal(complement(union(u,identity_relation)),identity_relation).
% 299.99/300.68  235387[5:Res:28980.1,490.0] || subclass(rest_relation,flip(intersection(complement(u),complement(v)))) member(ordered_pair(ordered_pair(w,x),rest_of(ordered_pair(x,w))),union(u,v))* -> .
% 299.99/300.68  235515[5:Res:28979.1,490.0] || subclass(rest_relation,rotate(intersection(complement(u),complement(v)))) member(ordered_pair(ordered_pair(w,rest_of(ordered_pair(x,w))),x),union(u,v))* -> .
% 299.99/300.68  235723[18:Res:190510.1,36719.1] operation(u) || subclass(inverse(identity_relation),cantor(u))* -> equal(ordered_pair(first(regular(symmetrization_of(identity_relation))),second(regular(symmetrization_of(identity_relation)))),regular(symmetrization_of(identity_relation)))**.
% 299.99/300.68  235722[18:Res:194549.1,36719.1] operation(u) || subclass(symmetrization_of(identity_relation),cantor(u))* -> equal(ordered_pair(first(regular(symmetrization_of(identity_relation))),second(regular(symmetrization_of(identity_relation)))),regular(symmetrization_of(identity_relation)))**.
% 299.99/300.68  235695[5:Res:133837.1,36719.1] operation(u) || well_ordering(ordinal_numbers,complement(cantor(u)))* -> equal(ordered_pair(first(singleton(singleton(v))),second(singleton(singleton(v)))),singleton(singleton(v)))**.
% 299.99/300.68  235938[7:Res:69478.2,18535.2] || subclass(omega,symmetric_difference(u,v)) member(w,ordinal_numbers) subclass(ordinal_numbers,complement(union(u,v)))* -> equal(integer_of(power_class(w)),identity_relation)**.
% 299.99/300.68  235936[7:Res:69478.2,18571.2] || subclass(omega,symmetric_difference(u,v)) member(w,ordinal_numbers) subclass(ordinal_numbers,complement(union(u,v)))* -> equal(integer_of(sum_class(w)),identity_relation)**.
% 299.99/300.68  235934[7:Res:69478.2,19111.1] || subclass(omega,symmetric_difference(u,v)) subclass(w,complement(union(u,v)))* -> equal(integer_of(not_subclass_element(w,x)),identity_relation)** subclass(w,x).
% 299.99/300.68  236004[5:SpR:145758.0,39308.2] one_to_one(cross_product(u,ordinal_numbers)) || subclass(range_of(inverse(cross_product(u,ordinal_numbers))),v) -> maps(inverse(cross_product(u,ordinal_numbers)),image(ordinal_numbers,u),v)*.
% 299.99/300.68  236320[16:Rew:195257.0,236223.1] || member(not_subclass_element(intersection(u,power_class(complement(singleton(identity_relation)))),v),image(element_relation,singleton(identity_relation)))* -> subclass(intersection(u,power_class(complement(singleton(identity_relation)))),v).
% 299.99/300.68  236321[8:Rew:162038.0,236222.1] || member(not_subclass_element(intersection(u,power_class(complement(inverse(identity_relation)))),v),image(element_relation,symmetrization_of(identity_relation)))* -> subclass(intersection(u,power_class(complement(inverse(identity_relation)))),v).
% 299.99/300.68  236539[16:Rew:195257.0,236412.1] || member(not_subclass_element(intersection(power_class(complement(singleton(identity_relation))),u),v),image(element_relation,singleton(identity_relation)))* -> subclass(intersection(power_class(complement(singleton(identity_relation))),u),v).
% 299.99/300.68  236540[8:Rew:162038.0,236411.1] || member(not_subclass_element(intersection(power_class(complement(inverse(identity_relation))),u),v),image(element_relation,symmetrization_of(identity_relation)))* -> subclass(intersection(power_class(complement(inverse(identity_relation))),u),v).
% 299.99/300.68  236688[0:Obv:236677.1] || subclass(unordered_pair(u,v),omega) -> equal(not_subclass_element(unordered_pair(u,v),w),u)** subclass(unordered_pair(u,v),w) equal(integer_of(v),v).
% 299.99/300.68  236689[0:Obv:236676.1] || subclass(unordered_pair(u,v),omega) -> equal(not_subclass_element(unordered_pair(u,v),w),v)** subclass(unordered_pair(u,v),w) equal(integer_of(u),u).
% 299.99/300.68  236832[7:Res:17392.2,490.0] || subclass(u,intersection(complement(v),complement(w))) member(regular(intersection(u,x)),union(v,w))* -> equal(intersection(u,x),identity_relation).
% 299.99/300.68  236826[7:Res:17392.2,129.0] || subclass(u,v)* subclass(v,w)* well_ordering(x,w)* -> equal(intersection(u,y),identity_relation)** member(least(x,v),v)*.
% 299.99/300.68  236987[26:Res:225888.1,129.0] || equal(symmetric_difference(ordinal_numbers,u),omega) subclass(complement(u),v)* well_ordering(w,v)* -> member(least(w,complement(u)),complement(u))*.
% 299.99/300.68  237109[8:Res:13574.1,160772.0] || member(regular(intersection(u,intersection(v,symmetric_difference(ordinal_numbers,w)))),union(w,identity_relation))* -> equal(intersection(u,intersection(v,symmetric_difference(ordinal_numbers,w))),identity_relation).
% 299.99/300.68  237106[7:Res:13574.1,19676.0] ||  -> equal(intersection(u,intersection(v,symmetric_difference(w,inverse(w)))),identity_relation) member(regular(intersection(u,intersection(v,symmetric_difference(w,inverse(w))))),symmetrization_of(w))*.
% 299.99/300.68  237105[7:Res:13574.1,19559.0] ||  -> equal(intersection(u,intersection(v,symmetric_difference(w,singleton(w)))),identity_relation) member(regular(intersection(u,intersection(v,symmetric_difference(w,singleton(w))))),successor(w))*.
% 299.99/300.68  237100[7:Res:13574.1,18794.1] || member(regular(intersection(u,intersection(v,intersection(w,x)))),symmetric_difference(w,x))* -> equal(intersection(u,intersection(v,intersection(w,x))),identity_relation).
% 299.99/300.68  237092[8:Res:13574.1,66086.1] || member(regular(intersection(u,intersection(v,complement(compose(element_relation,ordinal_numbers))))),element_relation)* -> equal(intersection(u,intersection(v,complement(compose(element_relation,ordinal_numbers)))),identity_relation).
% 299.99/300.68  237760[8:Res:13573.1,160772.0] || member(regular(intersection(u,intersection(symmetric_difference(ordinal_numbers,v),w))),union(v,identity_relation))* -> equal(intersection(u,intersection(symmetric_difference(ordinal_numbers,v),w)),identity_relation).
% 299.99/300.68  237757[7:Res:13573.1,19676.0] ||  -> equal(intersection(u,intersection(symmetric_difference(v,inverse(v)),w)),identity_relation) member(regular(intersection(u,intersection(symmetric_difference(v,inverse(v)),w))),symmetrization_of(v))*.
% 299.99/300.68  237756[7:Res:13573.1,19559.0] ||  -> equal(intersection(u,intersection(symmetric_difference(v,singleton(v)),w)),identity_relation) member(regular(intersection(u,intersection(symmetric_difference(v,singleton(v)),w))),successor(v))*.
% 299.99/300.68  237751[7:Res:13573.1,18794.1] || member(regular(intersection(u,intersection(intersection(v,w),x))),symmetric_difference(v,w))* -> equal(intersection(u,intersection(intersection(v,w),x)),identity_relation).
% 299.99/300.68  237743[8:Res:13573.1,66086.1] || member(regular(intersection(u,intersection(complement(compose(element_relation,ordinal_numbers)),v))),element_relation)* -> equal(intersection(u,intersection(complement(compose(element_relation,ordinal_numbers)),v)),identity_relation).
% 299.99/300.68  238566[7:Res:13572.2,490.0] || subclass(u,intersection(complement(v),complement(w))) member(regular(intersection(x,u)),union(v,w))* -> equal(intersection(x,u),identity_relation).
% 299.99/300.68  238560[7:Res:13572.2,129.0] || subclass(u,v)* subclass(v,w)* well_ordering(x,w)* -> equal(intersection(y,u),identity_relation)** member(least(x,v),v)*.
% 299.99/300.68  239272[8:Res:17397.1,160772.0] || member(regular(intersection(intersection(symmetric_difference(ordinal_numbers,u),v),w)),union(u,identity_relation))* -> equal(intersection(intersection(symmetric_difference(ordinal_numbers,u),v),w),identity_relation).
% 299.99/300.68  239269[7:Res:17397.1,19676.0] ||  -> equal(intersection(intersection(symmetric_difference(u,inverse(u)),v),w),identity_relation) member(regular(intersection(intersection(symmetric_difference(u,inverse(u)),v),w)),symmetrization_of(u))*.
% 299.99/300.68  239268[7:Res:17397.1,19559.0] ||  -> equal(intersection(intersection(symmetric_difference(u,singleton(u)),v),w),identity_relation) member(regular(intersection(intersection(symmetric_difference(u,singleton(u)),v),w)),successor(u))*.
% 299.99/300.68  239263[7:Res:17397.1,18794.1] || member(regular(intersection(intersection(intersection(u,v),w),x)),symmetric_difference(u,v))* -> equal(intersection(intersection(intersection(u,v),w),x),identity_relation).
% 299.99/300.68  239255[8:Res:17397.1,66086.1] || member(regular(intersection(intersection(complement(compose(element_relation,ordinal_numbers)),u),v)),element_relation)* -> equal(intersection(intersection(complement(compose(element_relation,ordinal_numbers)),u),v),identity_relation).
% 299.99/300.68  240107[8:Res:17396.1,160772.0] || member(regular(intersection(intersection(u,symmetric_difference(ordinal_numbers,v)),w)),union(v,identity_relation))* -> equal(intersection(intersection(u,symmetric_difference(ordinal_numbers,v)),w),identity_relation).
% 299.99/300.68  240104[7:Res:17396.1,19676.0] ||  -> equal(intersection(intersection(u,symmetric_difference(v,inverse(v))),w),identity_relation) member(regular(intersection(intersection(u,symmetric_difference(v,inverse(v))),w)),symmetrization_of(v))*.
% 299.99/300.68  240103[7:Res:17396.1,19559.0] ||  -> equal(intersection(intersection(u,symmetric_difference(v,singleton(v))),w),identity_relation) member(regular(intersection(intersection(u,symmetric_difference(v,singleton(v))),w)),successor(v))*.
% 300.10/300.68  240098[7:Res:17396.1,18794.1] || member(regular(intersection(intersection(u,intersection(v,w)),x)),symmetric_difference(v,w))* -> equal(intersection(intersection(u,intersection(v,w)),x),identity_relation).
% 300.10/300.68  240090[8:Res:17396.1,66086.1] || member(regular(intersection(intersection(u,complement(compose(element_relation,ordinal_numbers))),v)),element_relation)* -> equal(intersection(intersection(u,complement(compose(element_relation,ordinal_numbers))),v),identity_relation).
% 300.10/300.68  48482[0:SpR:3594.0,19069.0] ||  -> subclass(symmetric_difference(complement(symmetric_difference(u,v)),union(complement(intersection(u,v)),union(u,v))),complement(symmetric_difference(complement(intersection(u,v)),union(u,v))))*.
% 300.10/300.68  50361[0:Res:295.0,9636.2] || member(u,v)* member(u,w)* well_ordering(x,intersection(w,v)) -> member(least(x,intersection(w,v)),intersection(w,v))*.
% 300.10/300.68  41061[0:SpL:3597.0,8559.2] || member(u,symmetrization_of(v)) member(u,complement(intersection(v,inverse(v))))* subclass(symmetric_difference(v,inverse(v)),w)* -> member(u,w)*.
% 300.10/300.68  19650[0:SpR:3597.0,163.0] ||  -> equal(intersection(complement(symmetric_difference(u,inverse(u))),union(complement(intersection(u,inverse(u))),symmetrization_of(u))),symmetric_difference(complement(intersection(u,inverse(u))),symmetrization_of(u)))**.
% 300.10/300.68  50244[0:Res:295.0,9660.2] || member(u,v)* member(w,x)* well_ordering(y,cross_product(x,v)) -> member(least(y,cross_product(x,v)),cross_product(x,v))*.
% 300.10/300.68  39639[2:Res:18946.0,9665.1] inductive(restrict(u,v,w)) || well_ordering(x,cross_product(v,w)) -> member(least(x,restrict(u,v,w)),restrict(u,v,w))*.
% 300.10/300.68  40887[0:SpR:3603.0,27.2] || member(u,union(v,cross_product(w,x))) member(u,complement(restrict(v,w,x))) -> member(u,symmetric_difference(v,cross_product(w,x)))*.
% 300.10/300.68  41004[0:SpR:3606.0,27.2] || member(u,union(cross_product(v,w),x)) member(u,complement(restrict(x,v,w))) -> member(u,symmetric_difference(cross_product(v,w),x))*.
% 300.10/300.68  49642[0:SpL:6355.1,18.0] || member(not_subclass_element(cross_product(u,v),w),cross_product(x,y))* -> subclass(cross_product(u,v),w) member(first(not_subclass_element(cross_product(u,v),w)),x).
% 300.10/300.68  49641[0:SpL:6355.1,19.0] || member(not_subclass_element(cross_product(u,v),w),cross_product(x,y))* -> subclass(cross_product(u,v),w) member(second(not_subclass_element(cross_product(u,v),w)),y).
% 300.10/300.68  47561[5:MRR:47514.0,41183.1] || member(not_subclass_element(u,intersection(v,complement(w))),v)* -> member(not_subclass_element(u,intersection(v,complement(w))),w)* subclass(u,intersection(v,complement(w))).
% 300.10/300.68  29149[0:Res:313.1,490.0] || member(not_subclass_element(intersection(intersection(complement(u),complement(v)),w),x),union(u,v))* -> subclass(intersection(intersection(complement(u),complement(v)),w),x).
% 300.10/300.68  29162[0:Res:303.1,490.0] || member(not_subclass_element(intersection(u,intersection(complement(v),complement(w))),x),union(v,w))* -> subclass(intersection(u,intersection(complement(v),complement(w))),x).
% 300.10/300.68  47002[5:Res:8666.0,9421.0] || member(u,v)* -> equal(ordered_pair(first(ordered_pair(u,unordered_pair(w,x))),second(ordered_pair(u,unordered_pair(w,x)))),ordered_pair(u,unordered_pair(w,x)))**.
% 300.10/300.68  46950[5:Res:8667.0,9421.0] || member(u,v)* -> equal(ordered_pair(first(ordered_pair(u,ordered_pair(w,x))),second(ordered_pair(u,ordered_pair(w,x)))),ordered_pair(u,ordered_pair(w,x)))**.
% 300.10/300.68  9867[5:Rew:963.0,9864.2] || equal(compose(u,singleton(v)),v) member(singleton(singleton(singleton(v))),cross_product(ordinal_numbers,ordinal_numbers))* -> member(singleton(singleton(singleton(v))),compose_class(u))*.
% 300.10/300.68  19532[0:SpR:3596.0,163.0] ||  -> equal(intersection(complement(symmetric_difference(u,singleton(u))),union(complement(intersection(u,singleton(u))),successor(u))),symmetric_difference(complement(intersection(u,singleton(u))),successor(u)))**.
% 300.10/300.68  39572[0:Res:6.1,3689.0] ||  -> subclass(ordered_pair(u,v),w) equal(not_subclass_element(ordered_pair(u,v),w),unordered_pair(u,singleton(v)))** equal(not_subclass_element(ordered_pair(u,v),w),singleton(u)).
% 300.10/300.68  44662[0:Res:10714.1,3729.1] || member(u,not_well_ordering(v,singleton(u)))* connected(v,singleton(u)) -> well_ordering(v,singleton(u)) equal(not_well_ordering(v,singleton(u)),singleton(u)).
% 300.10/300.68  39590[0:Res:2503.2,3689.0] || subclass(u,ordered_pair(v,w))* -> subclass(u,x) equal(not_subclass_element(u,x),unordered_pair(v,singleton(w)))* equal(not_subclass_element(u,x),singleton(v)).
% 300.10/300.68  41060[0:SpL:3596.0,8559.2] || member(u,successor(v)) member(u,complement(intersection(v,singleton(v))))* subclass(symmetric_difference(v,singleton(v)),w)* -> member(u,w)*.
% 300.10/300.68  69368[8:Res:69184.1,129.0] || member(u,element_relation)* subclass(compose(element_relation,ordinal_numbers),v)* well_ordering(w,v)* -> member(least(w,compose(element_relation,ordinal_numbers)),compose(element_relation,ordinal_numbers))*.
% 300.10/300.68  56503[5:Rew:126.0,56457.0] || member(restrict(u,v,singleton(w)),segment(u,v,w)) -> member(ordered_pair(restrict(u,v,singleton(w)),segment(u,v,w)),element_relation)*.
% 300.10/300.68  116270[8:Rew:116078.0,49640.2] || member(not_subclass_element(cross_product(u,v),w),rest_of(x)) -> subclass(cross_product(u,v),w) member(first(not_subclass_element(cross_product(u,v),w)),cantor(x))*.
% 300.10/300.68  116465[8:Rew:116078.0,50008.1] || member(u,subset_relation) member(first(u),cantor(v)) equal(restrict(v,first(u),ordinal_numbers),second(u))** -> member(u,rest_of(v)).
% 300.10/300.68  125722[5:Res:125717.0,9421.0] || member(u,v)* -> equal(ordered_pair(first(ordered_pair(u,least(element_relation,omega))),second(ordered_pair(u,least(element_relation,omega)))),ordered_pair(u,least(element_relation,omega)))**.
% 300.10/300.68  132370[5:Res:132293.0,9665.1] inductive(complement(successor(u))) || well_ordering(v,intersection(complement(u),complement(singleton(u)))) -> member(least(v,complement(successor(u))),complement(successor(u)))*.
% 300.10/300.68  132413[5:Res:132294.0,9665.1] inductive(complement(symmetrization_of(u))) || well_ordering(v,intersection(complement(u),complement(inverse(u)))) -> member(least(v,complement(symmetrization_of(u))),complement(symmetrization_of(u)))*.
% 300.10/300.68  134070[5:Res:133837.1,8554.1] || well_ordering(ordinal_numbers,complement(complement(intersection(u,v))))* member(singleton(singleton(w)),union(u,v)) -> member(singleton(singleton(w)),symmetric_difference(u,v))*.
% 300.10/300.68  140290[0:Res:133.2,19124.0] || connected(u,singleton(v)) -> well_ordering(u,singleton(v)) subclass(not_well_ordering(u,singleton(v)),w) equal(not_subclass_element(not_well_ordering(u,singleton(v)),w),v)**.
% 300.10/300.68  143022[8:Rew:141387.0,141693.1] inductive(symmetric_difference(sum_class(u),ordinal_numbers)) || well_ordering(v,symmetric_difference(ordinal_numbers,sum_class(u))) -> member(least(v,symmetric_difference(ordinal_numbers,sum_class(u))),complement(sum_class(u)))*.
% 300.10/300.68  141695[8:Rew:141387.0,118297.2] inductive(symmetric_difference(sum_class(u),ordinal_numbers)) || well_ordering(v,complement(sum_class(u))) -> member(least(v,symmetric_difference(ordinal_numbers,sum_class(u))),symmetric_difference(ordinal_numbers,sum_class(u)))*.
% 300.10/300.68  143026[8:Rew:141388.0,141865.1] inductive(symmetric_difference(inverse(u),ordinal_numbers)) || well_ordering(v,symmetric_difference(ordinal_numbers,inverse(u))) -> member(least(v,symmetric_difference(ordinal_numbers,inverse(u))),complement(inverse(u)))*.
% 300.10/300.68  141867[8:Rew:141388.0,118281.2] inductive(symmetric_difference(inverse(u),ordinal_numbers)) || well_ordering(v,complement(inverse(u))) -> member(least(v,symmetric_difference(ordinal_numbers,inverse(u))),symmetric_difference(ordinal_numbers,inverse(u)))*.
% 300.10/300.68  143035[8:Rew:141390.0,142292.1] inductive(symmetric_difference(cantor(u),ordinal_numbers)) || well_ordering(v,symmetric_difference(ordinal_numbers,cantor(u))) -> member(least(v,symmetric_difference(ordinal_numbers,cantor(u))),complement(cantor(u)))*.
% 300.10/300.68  142294[8:Rew:141390.0,118151.2] inductive(symmetric_difference(cantor(u),ordinal_numbers)) || well_ordering(v,complement(cantor(u))) -> member(least(v,symmetric_difference(ordinal_numbers,cantor(u))),symmetric_difference(ordinal_numbers,cantor(u)))*.
% 300.10/300.68  142295[8:Rew:141390.0,116657.2] inductive(symmetric_difference(domain_of(u),ordinal_numbers)) || well_ordering(v,complement(cantor(u))) -> member(least(v,symmetric_difference(ordinal_numbers,cantor(u))),symmetric_difference(ordinal_numbers,cantor(u)))*.
% 300.10/300.68  148868[8:Obv:148846.2] || subclass(unordered_pair(u,v),inverse(subset_relation))* member(v,subset_relation) -> equal(not_subclass_element(unordered_pair(u,v),w),u)** subclass(unordered_pair(u,v),w).
% 300.10/300.68  148869[8:Obv:148845.2] || subclass(unordered_pair(u,v),inverse(subset_relation))* member(u,subset_relation) -> equal(not_subclass_element(unordered_pair(u,v),w),v)** subclass(unordered_pair(u,v),w).
% 300.10/300.68  152255[0:Obv:152185.2] || subclass(unordered_pair(u,v),complement(w))* member(v,w) -> equal(not_subclass_element(unordered_pair(u,v),x),u)** subclass(unordered_pair(u,v),x).
% 300.10/300.68  152256[0:Obv:152184.2] || subclass(unordered_pair(u,v),complement(w))* member(u,w) -> equal(not_subclass_element(unordered_pair(u,v),x),v)** subclass(unordered_pair(u,v),x).
% 300.10/300.68  152918[5:Res:9604.1,19121.0] || equal(sum_class(intersection(u,v)),intersection(u,v)) -> subclass(sum_class(intersection(u,v)),w) member(not_subclass_element(sum_class(intersection(u,v)),w),u)*.
% 300.10/300.68  153042[5:Res:9604.1,19120.0] || equal(sum_class(intersection(u,v)),intersection(u,v)) -> subclass(sum_class(intersection(u,v)),w) member(not_subclass_element(sum_class(intersection(u,v)),w),v)*.
% 300.10/300.68  155196[0:SpR:154737.1,3603.0] || subclass(union(u,cross_product(v,w)),complement(restrict(u,v,w)))* -> equal(symmetric_difference(u,cross_product(v,w)),union(u,cross_product(v,w))).
% 300.10/300.68  155195[0:SpR:154737.1,3606.0] || subclass(union(cross_product(u,v),w),complement(restrict(w,u,v)))* -> equal(symmetric_difference(cross_product(u,v),w),union(cross_product(u,v),w)).
% 300.10/300.68  156968[8:Res:156922.1,131.3] || member(ordered_pair(u,least(complement(subset_relation),v)),inverse(subset_relation))* member(u,v) subclass(v,w)* well_ordering(complement(subset_relation),w)* -> .
% 300.10/300.68  132045[8:Res:116148.1,19115.0] || section(u,recursion_equation_functions(v),w) -> subclass(cantor(restrict(u,w,recursion_equation_functions(v))),x) function(not_subclass_element(cantor(restrict(u,w,recursion_equation_functions(v))),x))*.
% 300.10/300.68  116305[8:Rew:116078.0,36431.2] operation(restrict(u,v,singleton(w))) || member(ordered_pair(x,y),segment(u,v,w))* -> member(y,cantor(segment(u,v,w))).
% 300.10/300.68  116304[8:Rew:116078.0,36574.2] operation(restrict(u,v,singleton(w))) || member(ordered_pair(x,y),segment(u,v,w))* -> member(x,cantor(segment(u,v,w))).
% 300.10/300.68  116749[8:Rew:116078.0,94726.1] operation(u) || subclass(ordinal_numbers,complement(complement(cantor(u))))* -> equal(ordered_pair(first(ordered_pair(v,w)),second(ordered_pair(v,w))),ordered_pair(v,w))**.
% 300.10/300.68  116746[8:Rew:116078.0,96388.1] operation(u) || subclass(ordinal_numbers,complement(complement(cantor(u))))* -> equal(ordered_pair(first(unordered_pair(v,w)),second(unordered_pair(v,w))),unordered_pair(v,w))**.
% 300.10/300.68  117643[8:Rew:116078.0,116577.2,116078.0,116577.1] operation(u) || equal(compose(intersection(cantor(u),v),intersection(cantor(u),v)),intersection(cantor(u),v))** -> transitive(v,cantor(cantor(u))).
% 300.10/300.68  117642[8:Rew:116078.0,116576.2,116078.0,116576.1] operation(u) || subclass(compose(intersection(cantor(u),v),intersection(cantor(u),v)),intersection(cantor(u),v))* -> transitive(v,cantor(cantor(u))).
% 300.10/300.68  117641[8:Rew:116078.0,116575.2,116078.0,116575.1] operation(u) || transitive(v,cantor(cantor(u))) -> subclass(compose(intersection(cantor(u),v),intersection(cantor(u),v)),intersection(cantor(u),v))*.
% 300.10/300.68  115817[8:Res:66595.1,4392.1] operation(u) ||  -> subclass(cantor(u),v) equal(ordered_pair(first(not_subclass_element(cantor(u),v)),second(not_subclass_element(cantor(u),v))),not_subclass_element(cantor(u),v))**.
% 300.10/300.68  117640[8:Rew:116078.0,116543.3,116078.0,116543.2,116078.0,116543.2,116078.0,116543.1] operation(u) || member(v,cantor(cantor(u))) member(singleton(v),cantor(cantor(u))) -> member(singleton(singleton(singleton(v))),cantor(u))*.
% 300.10/300.68  64345[7:Res:13227.2,8554.1] || subclass(u,complement(intersection(v,w))) member(regular(u),union(v,w)) -> equal(u,identity_relation) member(regular(u),symmetric_difference(v,w))*.
% 300.10/300.68  81645[8:Res:67606.0,11.0] || subclass(complement(symmetric_difference(complement(u),ordinal_numbers)),symmetric_difference(union(u,identity_relation),ordinal_numbers))* -> equal(symmetric_difference(union(u,identity_relation),ordinal_numbers),complement(symmetric_difference(complement(u),ordinal_numbers))).
% 300.10/300.68  164946[8:Res:162025.0,9665.1] inductive(complement(union(u,identity_relation))) || well_ordering(v,symmetric_difference(ordinal_numbers,u)) -> member(least(v,complement(union(u,identity_relation))),complement(union(u,identity_relation)))*.
% 300.10/300.68  66993[8:Res:66340.0,9665.1] inductive(symmetric_difference(complement(u),ordinal_numbers)) || well_ordering(v,union(u,identity_relation)) -> member(least(v,symmetric_difference(complement(u),ordinal_numbers)),symmetric_difference(complement(u),ordinal_numbers))*.
% 300.10/300.68  68795[8:Rew:68757.0,66839.2] inductive(symmetric_difference(ordinal_numbers,complement(inverse(identity_relation)))) || well_ordering(u,symmetrization_of(identity_relation)) -> member(least(u,intersection(symmetrization_of(identity_relation),ordinal_numbers)),intersection(symmetrization_of(identity_relation),ordinal_numbers))*.
% 300.10/300.68  163164[8:Rew:162584.0,163157.3] || member(u,v) subclass(v,w)* well_ordering(symmetrization_of(identity_relation),w)* -> member(ordered_pair(u,least(symmetrization_of(identity_relation),v)),complement(inverse(identity_relation)))*.
% 300.10/300.68  66990[8:Res:66340.0,13070.0] || well_ordering(u,union(v,identity_relation)) -> equal(symmetric_difference(complement(v),ordinal_numbers),identity_relation) member(least(u,symmetric_difference(complement(v),ordinal_numbers)),symmetric_difference(complement(v),ordinal_numbers))*.
% 300.10/300.68  165309[8:Res:162025.0,13070.0] || well_ordering(u,symmetric_difference(ordinal_numbers,v)) -> equal(complement(union(v,identity_relation)),identity_relation) member(least(u,complement(union(v,identity_relation))),complement(union(v,identity_relation)))*.
% 300.10/300.68  62555[7:SpR:13100.0,49995.1] || member(not_subclass_element(restrict(u,v,singleton(w)),identity_relation),subset_relation) -> member(singleton(domain__dfg(u,v,w)),not_subclass_element(restrict(u,v,singleton(w)),identity_relation))*.
% 300.10/300.68  60995[7:Res:13072.1,9421.0] || member(u,v)* -> equal(w,identity_relation) equal(ordered_pair(first(ordered_pair(u,regular(w))),second(ordered_pair(u,regular(w)))),ordered_pair(u,regular(w)))**.
% 300.10/300.68  19445[7:Res:18946.0,13070.0] || well_ordering(u,cross_product(v,w)) -> equal(restrict(x,v,w),identity_relation) member(least(u,restrict(x,v,w)),restrict(x,v,w))*.
% 300.10/300.68  19821[7:Res:19734.0,13113.0] || well_ordering(u,symmetrization_of(v)) -> equal(segment(u,symmetric_difference(complement(v),complement(inverse(v))),least(u,symmetric_difference(complement(v),complement(inverse(v))))),identity_relation)**.
% 300.10/300.68  13582[7:Rew:13036.0,13018.0] ||  -> equal(intersection(u,unordered_pair(v,w)),identity_relation) equal(regular(intersection(u,unordered_pair(v,w))),w)** equal(regular(intersection(u,unordered_pair(v,w))),v)**.
% 300.10/300.68  17400[7:Res:13248.1,12.0] ||  -> equal(intersection(unordered_pair(u,v),w),identity_relation) equal(regular(intersection(unordered_pair(u,v),w)),v)** equal(regular(intersection(unordered_pair(u,v),w)),u)**.
% 300.10/300.68  19804[7:Res:19733.0,13113.0] || well_ordering(u,successor(v)) -> equal(segment(u,symmetric_difference(complement(v),complement(singleton(v))),least(u,symmetric_difference(complement(v),complement(singleton(v))))),identity_relation)**.
% 300.10/300.68  83292[7:Res:61019.0,12.0] ||  -> equal(complement(complement(unordered_pair(u,v))),identity_relation) equal(regular(complement(complement(unordered_pair(u,v)))),v)** equal(regular(complement(complement(unordered_pair(u,v)))),u)**.
% 300.10/300.68  165303[7:Res:132294.0,13070.0] || well_ordering(u,intersection(complement(v),complement(inverse(v)))) -> equal(complement(symmetrization_of(v)),identity_relation) member(least(u,complement(symmetrization_of(v))),complement(symmetrization_of(v)))*.
% 300.10/300.68  165302[7:Res:132293.0,13070.0] || well_ordering(u,intersection(complement(v),complement(singleton(v)))) -> equal(complement(successor(v)),identity_relation) member(least(u,complement(successor(v))),complement(successor(v)))*.
% 300.10/300.68  190507[18:Res:190499.0,9421.0] || member(u,v)* -> equal(ordered_pair(first(ordered_pair(u,regular(symmetrization_of(identity_relation)))),second(ordered_pair(u,regular(symmetrization_of(identity_relation))))),ordered_pair(u,regular(symmetrization_of(identity_relation))))**.
% 300.10/300.68  193201[8:Res:193179.0,129.0] || subclass(inverse(singleton(u)),v)* well_ordering(w,v)* -> asymmetric(singleton(u),x)* member(least(w,inverse(singleton(u))),inverse(singleton(u)))*.
% 300.10/300.68  132237[2:Res:39609.2,897.0] inductive(restrict(u,v,w)) || well_ordering(x,restrict(u,v,w)) -> member(least(x,restrict(u,v,w)),cross_product(v,w))*.
% 300.10/300.68  131205[5:Res:39607.2,12.0] inductive(unordered_pair(u,v)) || well_ordering(w,ordinal_numbers) -> equal(least(w,unordered_pair(u,v)),v)** equal(least(w,unordered_pair(u,v)),u)**.
% 300.10/300.68  131187[5:Res:39607.2,490.0] inductive(intersection(complement(u),complement(v))) || well_ordering(w,ordinal_numbers) member(least(w,intersection(complement(u),complement(v))),union(u,v))* -> .
% 300.10/300.68  18709[7:Res:13237.2,12.0] || well_ordering(u,ordinal_numbers) -> equal(unordered_pair(v,w),identity_relation) equal(least(u,unordered_pair(v,w)),w)** equal(least(u,unordered_pair(v,w)),v)**.
% 300.10/300.68  65407[7:Res:13237.2,490.0] || well_ordering(u,ordinal_numbers) member(least(u,intersection(complement(v),complement(w))),union(v,w))* -> equal(intersection(complement(v),complement(w)),identity_relation).
% 300.10/300.68  49229[5:Res:10.1,9639.1] || equal(u,unordered_pair(v,w))* member(w,ordinal_numbers) well_ordering(x,u)* -> member(least(x,unordered_pair(v,w)),unordered_pair(v,w))*.
% 300.10/300.68  49063[5:Res:10.1,9633.1] || equal(u,complement(v))* member(w,ordinal_numbers)* well_ordering(x,u)* -> member(w,v)* member(least(x,complement(v)),complement(v))*.
% 300.10/300.68  49299[5:Res:10.1,9640.1] || equal(u,unordered_pair(v,w))* member(v,ordinal_numbers) well_ordering(x,u)* -> member(least(x,unordered_pair(v,w)),unordered_pair(v,w))*.
% 300.10/300.68  130973[5:Res:9865.3,9876.0] || member(u,ordinal_numbers)* member(v,ordinal_numbers) equal(compose(w,v),u)* subclass(compose_class(w),x)* well_ordering(ordinal_numbers,x) -> .
% 300.10/300.68  163080[8:Res:162023.0,9633.1] || member(u,ordinal_numbers) well_ordering(v,complement(inverse(identity_relation))) -> member(u,symmetrization_of(identity_relation))* member(least(v,complement(symmetrization_of(identity_relation))),complement(symmetrization_of(identity_relation)))*.
% 300.10/300.68  46641[5:Res:9618.2,8651.0] || member(ordered_pair(u,v),cross_product(ordinal_numbers,ordinal_numbers))* subclass(composition_function,rest_of(w)) -> equal(restrict(w,u,ordinal_numbers),ordered_pair(v,compose(u,v)))*.
% 300.10/300.68  46629[8:Res:9618.2,14679.1] || member(ordered_pair(u,v),cross_product(ordinal_numbers,ordinal_numbers)) subclass(composition_function,inverse(subset_relation)) member(ordered_pair(u,ordered_pair(v,compose(u,v))),subset_relation)* -> .
% 300.10/300.68  46611[5:Res:9618.2,28.1] || member(ordered_pair(u,v),cross_product(ordinal_numbers,ordinal_numbers)) subclass(composition_function,complement(w)) member(ordered_pair(u,ordered_pair(v,compose(u,v))),w)* -> .
% 300.10/300.68  46622[5:Res:9618.2,26.0] || member(ordered_pair(u,v),cross_product(ordinal_numbers,ordinal_numbers)) subclass(composition_function,intersection(w,x))* -> member(ordered_pair(u,ordered_pair(v,compose(u,v))),x)*.
% 300.10/300.68  46623[5:Res:9618.2,25.0] || member(ordered_pair(u,v),cross_product(ordinal_numbers,ordinal_numbers)) subclass(composition_function,intersection(w,x))* -> member(ordered_pair(u,ordered_pair(v,compose(u,v))),w)*.
% 300.10/300.68  154335[5:Res:9618.2,151988.0] || member(ordered_pair(u,v),cross_product(ordinal_numbers,ordinal_numbers)) subclass(composition_function,complement(complement(w))) -> member(ordered_pair(u,ordered_pair(v,compose(u,v))),w)*.
% 300.10/300.68  167497[8:Res:9618.2,163154.0] || member(ordered_pair(u,v),cross_product(ordinal_numbers,ordinal_numbers)) subclass(composition_function,symmetrization_of(identity_relation)) -> member(ordered_pair(u,ordered_pair(v,compose(u,v))),inverse(identity_relation))*.
% 300.10/300.68  195636[16:Rew:195224.0,195306.1] inductive(symmetric_difference(ordinal_numbers,complement(singleton(identity_relation)))) || well_ordering(u,singleton(identity_relation)) -> member(least(u,intersection(singleton(identity_relation),ordinal_numbers)),intersection(singleton(identity_relation),ordinal_numbers))*.
% 300.10/300.68  195638[16:Rew:195224.0,195506.3] || member(u,v) subclass(v,w)* well_ordering(singleton(identity_relation),w)* -> member(ordered_pair(u,least(singleton(identity_relation),v)),complement(singleton(identity_relation)))*.
% 300.10/300.68  196075[18:Res:190510.1,8554.1] || subclass(inverse(identity_relation),complement(intersection(u,v))) member(regular(symmetrization_of(identity_relation)),union(u,v)) -> member(regular(symmetrization_of(identity_relation)),symmetric_difference(u,v))*.
% 300.10/300.68  197097[7:MRR:197094.3,13039.0] function(u) || well_ordering(v,cross_product(ordinal_numbers,ordinal_numbers)) subclass(singleton(least(v,u)),u) -> section(v,singleton(least(v,u)),u)*.
% 300.10/300.68  197289[7:SpR:33.0,13299.1] || asymmetric(cross_product(u,v),singleton(w)) -> equal(range__dfg(restrict(inverse(cross_product(u,v)),u,v),w,singleton(w)),second(not_subclass_element(identity_relation,identity_relation)))**.
% 300.10/300.68  197298[7:Rew:50855.1,197288.1] || member(singleton(u),subset_relation) asymmetric(v,u) -> equal(range__dfg(intersection(v,inverse(v)),first(singleton(u)),u),second(not_subclass_element(identity_relation,identity_relation)))**.
% 300.10/300.68  197810[8:SpL:117511.1,13301.0] operation(u) || equal(intersection(cantor(u),restrict(inverse(cross_product(v,w)),v,w)),identity_relation)** -> asymmetric(cross_product(v,w),cantor(cantor(u))).
% 300.10/300.68  197832[8:SpR:13302.1,117511.1] operation(u) || asymmetric(cross_product(v,w),cantor(cantor(u))) -> equal(intersection(cantor(u),restrict(inverse(cross_product(v,w)),v,w)),identity_relation)**.
% 300.10/300.68  198558[7:Res:13511.3,5.0] || member(u,ordinal_numbers) well_ordering(v,u) subclass(sum_class(u),w) -> equal(sum_class(u),identity_relation) member(least(v,sum_class(u)),w)*.
% 300.10/300.68  199099[18:Res:190510.1,13362.0] || subclass(inverse(identity_relation),u) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(regular(symmetrization_of(identity_relation)),least(omega,u))),identity_relation)**.
% 300.10/300.68  199076[8:Res:163152.1,13362.0] || subclass(ordinal_numbers,symmetrization_of(identity_relation)) subclass(inverse(identity_relation),u)* well_ordering(omega,u) -> equal(integer_of(ordered_pair(omega,least(omega,inverse(identity_relation)))),identity_relation)**.
% 300.10/300.68  199070[7:Res:964.0,13362.0] || subclass(ordered_pair(u,v),w)* well_ordering(omega,w) -> equal(integer_of(ordered_pair(unordered_pair(u,singleton(v)),least(omega,ordered_pair(u,v)))),identity_relation)**.
% 300.10/300.68  199050[7:Res:8702.1,13362.0] || member(u,ordinal_numbers) subclass(rest_relation,v) well_ordering(omega,v)* -> equal(integer_of(ordered_pair(ordered_pair(u,rest_of(u)),least(omega,rest_relation))),identity_relation)**.
% 300.10/300.68  199049[7:Res:133837.1,13362.0] || well_ordering(ordinal_numbers,complement(u)) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(singleton(singleton(w)),least(omega,u))),identity_relation)**.
% 300.10/300.68  199046[7:Res:9632.1,13362.0] || equal(complement(complement(u)),ordinal_numbers) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(singleton(w),least(omega,u))),identity_relation)**.
% 300.10/300.68  199006[7:Res:60219.0,13362.0] || subclass(u,v)* well_ordering(omega,v)* -> subclass(w,complement(u)) equal(integer_of(ordered_pair(not_subclass_element(w,complement(u)),least(omega,u))),identity_relation)**.
% 300.10/300.68  198977[7:Res:51313.1,13362.0] || member(singleton(u),subset_relation) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(first(singleton(u)),least(omega,u))),identity_relation)**.
% 300.10/300.68  198952[8:Res:156922.1,13362.0] || member(u,inverse(subset_relation)) subclass(complement(subset_relation),v)* well_ordering(omega,v) -> equal(integer_of(ordered_pair(u,least(omega,complement(subset_relation)))),identity_relation)**.
% 300.10/300.68  117636[8:Rew:116078.0,116418.4] operation(u) operation(v) || compatible(w,v,u) -> homomorphism(w,v,u) member(not_homomorphism2(w,v,u),cantor(cantor(v)))*.
% 300.10/300.68  117635[8:Rew:116078.0,116417.4] operation(u) operation(v) || compatible(w,v,u) -> homomorphism(w,v,u) member(not_homomorphism1(w,v,u),cantor(cantor(v)))*.
% 300.10/300.68  195694[7:Res:13225.3,12.0] || member(u,ordinal_numbers) subclass(u,unordered_pair(v,w))* -> equal(u,identity_relation) equal(apply(choice,u),w) equal(apply(choice,u),v).
% 300.10/300.68  195683[7:Res:13225.3,490.0] || member(u,ordinal_numbers) subclass(u,intersection(complement(v),complement(w))) member(apply(choice,u),union(v,w))* -> equal(u,identity_relation).
% 300.10/300.68  194674[7:Rew:30.0,194632.2,30.0,194632.0] || member(union(u,v),ordinal_numbers) member(apply(choice,union(u,v)),intersection(complement(u),complement(v)))* -> equal(union(u,v),identity_relation).
% 300.10/300.68  18826[7:Res:13069.2,897.0] || member(restrict(u,v,w),ordinal_numbers) -> equal(restrict(u,v,w),identity_relation) member(apply(choice,restrict(u,v,w)),cross_product(v,w))*.
% 300.10/300.68  197440[8:Rew:66293.0,197374.1,66293.0,197374.0] || member(symmetric_difference(complement(u),ordinal_numbers),ordinal_numbers) -> equal(symmetric_difference(complement(u),ordinal_numbers),identity_relation) member(apply(choice,symmetric_difference(complement(u),ordinal_numbers)),union(u,identity_relation))*.
% 300.10/300.68  197702[7:Res:13247.2,161.0] || member(intersection(u,omega),ordinal_numbers) -> equal(intersection(u,omega),identity_relation) equal(integer_of(apply(choice,intersection(u,omega))),apply(choice,intersection(u,omega)))**.
% 300.10/300.68  197703[7:Res:13247.2,8788.0] || member(intersection(u,recursion_equation_functions(v)),ordinal_numbers) -> equal(intersection(u,recursion_equation_functions(v)),identity_relation) subclass(apply(choice,intersection(u,recursion_equation_functions(v))),cross_product(ordinal_numbers,ordinal_numbers))*.
% 300.10/300.68  197413[7:Res:13246.2,161.0] || member(intersection(omega,u),ordinal_numbers) -> equal(intersection(omega,u),identity_relation) equal(integer_of(apply(choice,intersection(omega,u))),apply(choice,intersection(omega,u)))**.
% 300.10/300.68  197414[7:Res:13246.2,8788.0] || member(intersection(recursion_equation_functions(u),v),ordinal_numbers) -> equal(intersection(recursion_equation_functions(u),v),identity_relation) subclass(apply(choice,intersection(recursion_equation_functions(u),v)),cross_product(ordinal_numbers,ordinal_numbers))*.
% 300.10/300.68  152222[0:Res:62.1,19111.1] || member(ordered_pair(u,not_subclass_element(v,w)),compose(x,y))* subclass(v,complement(image(x,image(y,singleton(u))))) -> subclass(v,w).
% 300.10/300.68  146773[5:Res:62.1,18571.2] || member(ordered_pair(u,sum_class(v)),compose(w,x))* member(v,ordinal_numbers) subclass(ordinal_numbers,complement(image(w,image(x,singleton(u)))))* -> .
% 300.10/300.68  146843[5:Res:62.1,18535.2] || member(ordered_pair(u,power_class(v)),compose(w,x))* member(v,ordinal_numbers) subclass(ordinal_numbers,complement(image(w,image(x,singleton(u)))))* -> .
% 300.10/300.68  195401[16:Rew:195224.0,193399.0] || well_ordering(u,image(element_relation,singleton(identity_relation))) -> equal(segment(u,complement(power_class(complement(singleton(identity_relation)))),least(u,complement(power_class(complement(singleton(identity_relation)))))),identity_relation)**.
% 300.10/300.68  52618[5:Res:8642.1,9880.0] || subclass(ordinal_numbers,compose(u,v)) member(w,x)* subclass(x,y)* well_ordering(image(u,image(v,singleton(z))),y)* -> .
% 300.10/300.68  37618[5:SpR:72.0,9005.1] || member(restrict(element_relation,ordinal_numbers,image(u,singleton(v))),ordinal_numbers) -> member(ordered_pair(restrict(element_relation,ordinal_numbers,image(u,singleton(v))),apply(u,v)),domain_relation)*.
% 300.10/300.68  39334[5:Res:9006.3,490.0] function(u) || member(v,ordinal_numbers) subclass(ordinal_numbers,intersection(complement(w),complement(x))) member(image(u,v),union(w,x))* -> .
% 300.10/300.68  36244[0:SpR:481.0,483.0] ||  -> equal(union(u,intersection(complement(v),power_class(intersection(complement(w),complement(x))))),complement(intersection(complement(u),union(v,image(element_relation,union(w,x))))))**.
% 300.10/300.68  36854[5:SpL:481.0,8825.1] || member(u,ordinal_numbers) subclass(power_class(intersection(complement(v),complement(w))),x)* -> member(u,image(element_relation,union(v,w)))* member(u,x)*.
% 300.10/300.68  36192[0:SpR:481.0,482.0] ||  -> equal(union(intersection(complement(u),power_class(intersection(complement(v),complement(w)))),x),complement(intersection(union(u,image(element_relation,union(v,w))),complement(x))))**.
% 300.10/300.68  155387[0:SpL:481.0,941.1] || member(u,image(element_relation,power_class(image(element_relation,union(v,w))))) member(u,power_class(image(element_relation,power_class(intersection(complement(v),complement(w))))))* -> .
% 300.10/300.68  36256[0:SpR:481.0,483.0] ||  -> equal(union(u,intersection(power_class(intersection(complement(v),complement(w))),complement(x))),complement(intersection(complement(u),union(image(element_relation,union(v,w)),x))))**.
% 300.10/300.68  36204[0:SpR:481.0,482.0] ||  -> equal(union(intersection(power_class(intersection(complement(u),complement(v))),complement(w)),x),complement(intersection(union(image(element_relation,union(u,v)),w),complement(x))))**.
% 300.10/300.68  19516[0:Rew:481.0,19493.1] || member(not_subclass_element(power_class(intersection(complement(u),complement(v))),w),image(element_relation,union(u,v)))* -> subclass(power_class(intersection(complement(u),complement(v))),w).
% 300.10/300.68  83315[7:Rew:481.0,83274.1] ||  -> member(regular(complement(power_class(intersection(complement(u),complement(v))))),image(element_relation,union(u,v)))* equal(complement(power_class(intersection(complement(u),complement(v)))),identity_relation).
% 300.10/300.68  147760[0:SpL:189.0,1042.0] || member(not_subclass_element(power_class(image(element_relation,power_class(u))),v),image(element_relation,power_class(image(element_relation,complement(u)))))* -> subclass(power_class(image(element_relation,power_class(u))),v).
% 300.10/300.68  166711[7:Res:13210.1,941.1] || member(regular(intersection(u,power_class(image(element_relation,complement(v))))),image(element_relation,power_class(v)))* -> equal(intersection(u,power_class(image(element_relation,complement(v)))),identity_relation).
% 300.10/300.68  132515[5:Res:130711.0,11.0] || subclass(image(element_relation,power_class(u)),complement(power_class(image(element_relation,complement(u)))))* -> equal(complement(power_class(image(element_relation,complement(u)))),image(element_relation,power_class(u))).
% 300.10/300.68  166521[7:Res:13248.1,941.1] || member(regular(intersection(power_class(image(element_relation,complement(u))),v)),image(element_relation,power_class(u)))* -> equal(intersection(power_class(image(element_relation,complement(u))),v),identity_relation).
% 300.10/300.68  193457[8:Res:163093.0,13113.0] || well_ordering(u,image(element_relation,symmetrization_of(identity_relation))) -> equal(segment(u,complement(power_class(complement(inverse(identity_relation)))),least(u,complement(power_class(complement(inverse(identity_relation)))))),identity_relation)**.
% 300.10/300.68  153194[0:SpR:485.0,18204.1] ||  -> subclass(symmetric_difference(u,image(element_relation,complement(v))),w) member(not_subclass_element(symmetric_difference(u,image(element_relation,complement(v))),w),complement(intersection(complement(u),power_class(v))))*.
% 300.10/300.68  153205[0:SpR:487.0,18204.1] ||  -> subclass(symmetric_difference(image(element_relation,complement(u)),v),w) member(not_subclass_element(symmetric_difference(image(element_relation,complement(u)),v),w),complement(intersection(power_class(u),complement(v))))*.
% 300.10/300.68  132239[2:Res:39609.2,288.0] inductive(image(element_relation,complement(u))) || well_ordering(v,image(element_relation,complement(u))) member(least(v,image(element_relation,complement(u))),power_class(u))* -> .
% 300.10/300.68  18448[7:Res:13069.2,288.0] || member(image(element_relation,complement(u)),ordinal_numbers) member(apply(choice,image(element_relation,complement(u))),power_class(u))* -> equal(image(element_relation,complement(u)),identity_relation).
% 300.10/300.68  165439[15:Res:165431.0,9421.0] || member(u,v)* -> equal(ordered_pair(first(ordered_pair(u,sum_class(range_of(identity_relation)))),second(ordered_pair(u,sum_class(range_of(identity_relation))))),ordered_pair(u,sum_class(range_of(identity_relation))))**.
% 300.10/300.68  193453[8:Rew:161076.2,193447.4] inductive(singleton(u)) || member(u,ordinal_numbers) subclass(singleton(u),range_of(identity_relation))* -> member(u,cantor(successor_relation)) equal(range_of(identity_relation),singleton(u)).
% 300.10/300.68  37771[5:Rew:43.0,37756.2,8647.0,37756.2,43.0,37756.1] operation(flip(cross_product(u,ordinal_numbers))) || subclass(range_of(u),range_of(flip(cross_product(u,ordinal_numbers))))* -> equal(range_of(flip(cross_product(u,ordinal_numbers))),range_of(u)).
% 300.10/300.68  39312[5:SoR:8530.0,10858.2] single_valued_class(inverse(u)) || subclass(range_of(inverse(u)),v) equal(cross_product(ordinal_numbers,ordinal_numbers),inverse(u)) -> maps(inverse(u),range_of(u),v)*.
% 300.10/300.68  198334[5:Res:9837.3,5.0] || member(u,ordinal_numbers) member(v,ordinal_numbers) equal(sum_class(range_of(v)),u) subclass(union_of_range_map,w) -> member(ordered_pair(v,u),w)*.
% 300.10/300.68  142046[8:Rew:141389.0,116987.2] inductive(symmetric_difference(range_of(u),ordinal_numbers)) || well_ordering(v,complement(range_of(u))) -> member(least(v,symmetric_difference(ordinal_numbers,range_of(u))),symmetric_difference(ordinal_numbers,range_of(u)))*.
% 300.10/300.68  143030[8:Rew:141389.0,142044.1] inductive(symmetric_difference(range_of(u),ordinal_numbers)) || well_ordering(v,symmetric_difference(ordinal_numbers,range_of(u))) -> member(least(v,symmetric_difference(ordinal_numbers,range_of(u))),complement(range_of(u)))*.
% 300.10/300.68  197577[21:Rew:160429.0,197559.1] function(u) || subclass(range_of(u),identity_relation) equal(cantor(cantor(v)),cantor(u)) -> equal(w,identity_relation) compatible(u,v,regular(w))*.
% 300.10/300.68  197523[21:Rew:160429.0,197502.1] function(u) || subclass(range_of(u),identity_relation) equal(cantor(cantor(v)),cantor(u)) -> equal(singleton(w),identity_relation) compatible(u,v,w)*.
% 300.10/300.68  204157[8:Res:204134.1,131.3] || member(ordered_pair(u,least(symmetrization_of(identity_relation),v)),inverse(identity_relation))* member(u,v) subclass(v,w)* well_ordering(symmetrization_of(identity_relation),w)* -> .
% 300.10/300.68  204136[8:Res:204134.1,13362.0] || member(u,inverse(identity_relation)) subclass(symmetrization_of(identity_relation),v)* well_ordering(omega,v) -> equal(integer_of(ordered_pair(u,least(omega,symmetrization_of(identity_relation)))),identity_relation)**.
% 300.10/300.68  204169[18:Res:194549.1,13362.0] || subclass(symmetrization_of(identity_relation),u) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(regular(symmetrization_of(identity_relation)),least(omega,u))),identity_relation)**.
% 300.10/300.68  204166[18:Res:194549.1,8554.1] || subclass(symmetrization_of(identity_relation),complement(intersection(u,v))) member(regular(symmetrization_of(identity_relation)),union(u,v)) -> member(regular(symmetrization_of(identity_relation)),symmetric_difference(u,v))*.
% 300.10/300.68  204631[21:Res:196904.1,13362.0] || subclass(domain_relation,u) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(singleton(singleton(singleton(identity_relation))),least(omega,u))),identity_relation)**.
% 300.10/300.68  205171[15:Res:195033.1,13362.0] || equal(complement(complement(u)),ordinal_numbers) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(range_of(identity_relation),least(omega,u))),identity_relation)**.
% 300.10/300.68  18838[5:Res:18819.1,129.0] || member(u,subset_relation)* subclass(cross_product(ordinal_numbers,ordinal_numbers),v)* well_ordering(w,v)* -> member(least(w,cross_product(ordinal_numbers,ordinal_numbers)),cross_product(ordinal_numbers,ordinal_numbers))*.
% 300.10/300.68  167536[8:Rew:8637.0,167534.2] single_valued_class(image(successor_relation,cross_product(universal_class,universal_class))) || member(identity_relation,cross_product(ordinal_numbers,ordinal_numbers)) equal(image(successor_relation,cross_product(ordinal_numbers,ordinal_numbers)),cross_product(ordinal_numbers,ordinal_numbers))** -> .
% 300.10/300.68  167602[8:SoR:162899.0,10858.2] single_valued_class(image(successor_relation,cross_product(ordinal_numbers,ordinal_numbers))) || member(identity_relation,cross_product(ordinal_numbers,ordinal_numbers)) equal(image(successor_relation,cross_product(ordinal_numbers,ordinal_numbers)),cross_product(ordinal_numbers,ordinal_numbers))** -> .
% 300.10/300.68  205784[22:Res:205578.1,13362.0] || subclass(complement(u),v)* well_ordering(omega,v) -> member(singleton(identity_relation),u) equal(integer_of(ordered_pair(singleton(identity_relation),least(omega,complement(u)))),identity_relation)**.
% 300.10/300.68  206127[22:Res:205574.1,13362.0] || equal(u,singleton(singleton(identity_relation))) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(singleton(identity_relation),least(omega,u))),identity_relation)**.
% 300.10/300.68  206277[8:Rew:160491.0,206247.1] || member(u,union(complement(v),symmetric_difference(ordinal_numbers,v))) member(u,union(v,identity_relation)) -> member(u,symmetric_difference(complement(v),symmetric_difference(ordinal_numbers,v)))*.
% 300.10/300.68  207541[8:Res:192400.1,9665.1] inductive(symmetric_difference(u,ordinal_numbers)) || member(u,ordinals_with_null_class_as_identity) well_ordering(v,complement(u)) -> member(least(v,symmetric_difference(u,ordinal_numbers)),symmetric_difference(u,ordinal_numbers))*.
% 300.10/300.68  207538[8:Res:192400.1,13070.0] || member(u,ordinals_with_null_class_as_identity) well_ordering(v,complement(u)) -> equal(symmetric_difference(u,ordinal_numbers),identity_relation) member(least(v,symmetric_difference(u,ordinal_numbers)),symmetric_difference(u,ordinal_numbers))*.
% 300.10/300.68  208200[24:Res:207562.1,13362.0] operation(u) || subclass(ordered_pair(u,v),w)* well_ordering(omega,w) -> equal(integer_of(ordered_pair(identity_relation,least(omega,ordered_pair(u,v)))),identity_relation)**.
% 300.10/300.68  208363[24:Rew:207572.1,208345.3] operation(u) || equal(compose(v,identity_relation),u)* member(singleton(singleton(identity_relation)),cross_product(ordinal_numbers,ordinal_numbers))* -> member(singleton(singleton(identity_relation)),compose_class(v))*.
% 300.10/300.68  208331[24:SpL:207572.1,131.3] operation(least(u,v)) || member(identity_relation,v)* subclass(v,w)* well_ordering(u,w)* member(singleton(singleton(identity_relation)),u)* -> .
% 300.10/300.68  208499[7:SpL:13260.1,23.0] || member(regular(cross_product(u,v)),element_relation) -> equal(cross_product(u,v),identity_relation) member(first(regular(cross_product(u,v))),second(regular(cross_product(u,v))))*.
% 300.10/300.68  208960[25:SpL:208820.0,8803.0] || member(u,image(v,image(w,identity_relation))) member(ordered_pair(ordinal_numbers,u),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(ordinal_numbers,u),compose(v,w))*.
% 300.10/300.68  209488[8:Res:138.1,161646.1] || member(complement(complement(symmetrization_of(u))),ordinal_numbers)* connected(u,v)* -> equal(segment(element_relation,cross_product(v,v),least(element_relation,cross_product(v,v))),identity_relation)**.
% 300.10/300.68  209896[24:Res:207866.1,9665.1] operation(u) inductive(complement(successor(u))) || well_ordering(v,symmetric_difference(ordinal_numbers,u)) -> member(least(v,complement(successor(u))),complement(successor(u)))*.
% 300.10/300.68  209893[24:Res:207866.1,13070.0] operation(u) || well_ordering(v,symmetric_difference(ordinal_numbers,u)) -> equal(complement(successor(u)),identity_relation) member(least(v,complement(successor(u))),complement(successor(u)))*.
% 300.10/300.68  209884[24:SpR:161207.0,207866.1] operation(intersection(singleton(identity_relation),image(successor_relation,ordinal_numbers))) ||  -> subclass(complement(successor(intersection(singleton(identity_relation),image(successor_relation,ordinal_numbers)))),symmetric_difference(singleton(identity_relation),image(successor_relation,ordinal_numbers)))*.
% 300.10/300.68  210138[8:Res:208722.1,9665.1] inductive(symmetric_difference(u,ordinal_numbers)) || well_ordering(v,complement(u)) -> equal(singleton(u),identity_relation) member(least(v,symmetric_difference(u,ordinal_numbers)),symmetric_difference(u,ordinal_numbers))*.
% 300.10/300.68  210135[8:Res:208722.1,13070.0] || well_ordering(u,complement(v)) -> equal(singleton(v),identity_relation) equal(symmetric_difference(v,ordinal_numbers),identity_relation) member(least(u,symmetric_difference(v,ordinal_numbers)),symmetric_difference(v,ordinal_numbers))*.
% 300.10/300.68  210239[8:SpR:143170.0,161701.2] || section(ordinal_numbers,u,v) well_ordering(w,u) -> equal(segment(w,cantor(cross_product(v,u)),least(w,cantor(cross_product(v,u)))),identity_relation)**.
% 300.10/300.68  210433[14:Res:210404.0,129.0] || subclass(union(u,identity_relation),v)* well_ordering(w,v)* -> member(identity_relation,complement(u)) member(least(w,union(u,identity_relation)),union(u,identity_relation))*.
% 300.10/300.68  211322[8:Res:210606.1,9639.1] || equal(complement(u),ordinal_numbers) member(v,ordinal_numbers) well_ordering(w,complement(u))* -> member(least(w,unordered_pair(x,v)),unordered_pair(x,v))*.
% 300.10/300.68  211320[8:Res:210606.1,9640.1] || equal(complement(u),ordinal_numbers) member(v,ordinal_numbers) well_ordering(w,complement(u))* -> member(least(w,unordered_pair(v,x)),unordered_pair(v,x))*.
% 300.10/300.68  211556[8:Res:211438.1,9639.1] || equal(symmetrization_of(identity_relation),ordinal_numbers) member(u,ordinal_numbers) well_ordering(v,symmetrization_of(identity_relation)) -> member(least(v,unordered_pair(w,u)),unordered_pair(w,u))*.
% 300.10/300.68  211554[8:Res:211438.1,9640.1] || equal(symmetrization_of(identity_relation),ordinal_numbers) member(u,ordinal_numbers) well_ordering(v,symmetrization_of(identity_relation)) -> member(least(v,unordered_pair(u,w)),unordered_pair(u,w))*.
% 300.10/300.68  211640[8:Res:211441.1,9639.1] || equal(power_class(u),ordinal_numbers) member(v,ordinal_numbers) well_ordering(w,power_class(u))* -> member(least(w,unordered_pair(x,v)),unordered_pair(x,v))*.
% 300.10/300.68  211638[8:Res:211441.1,9640.1] || equal(power_class(u),ordinal_numbers) member(v,ordinal_numbers) well_ordering(w,power_class(u))* -> member(least(w,unordered_pair(v,x)),unordered_pair(v,x))*.
% 300.10/300.68  212410[7:SpL:13259.2,132438.0] || member(cross_product(u,v),ordinal_numbers) equal(w,apply(choice,cross_product(u,v)))* well_ordering(ordinal_numbers,w)* -> equal(cross_product(u,v),identity_relation).
% 300.10/300.68  212388[7:SpL:13259.2,130942.0] || member(cross_product(u,v),ordinal_numbers) subclass(apply(choice,cross_product(u,v)),w)* well_ordering(ordinal_numbers,w) -> equal(cross_product(u,v),identity_relation).
% 300.10/300.68  213499[8:Rew:145761.0,213486.2] operation(cross_product(u,singleton(v))) || subclass(segment(ordinal_numbers,u,v),complement(complement(symmetrization_of(w))))* -> connected(w,cantor(segment(ordinal_numbers,u,v))).
% 300.10/300.68  213500[8:Rew:145761.0,213466.1] operation(cross_product(u,singleton(v))) || connected(w,cantor(segment(ordinal_numbers,u,v))) -> subclass(segment(ordinal_numbers,u,v),complement(complement(symmetrization_of(w))))*.
% 300.10/300.68  214140[8:Rew:14756.0,214130.1,14756.0,214130.0] || member(ordered_pair(u,regular(range_of(identity_relation))),cross_product(ordinal_numbers,ordinal_numbers)) -> equal(range_of(identity_relation),identity_relation) member(ordered_pair(u,regular(range_of(identity_relation))),compose(identity_relation,v))*.
% 300.10/300.68  214145[8:MRR:214144.3,14676.0] || equal(compose_class(u),domain_relation) member(ordered_pair(v,regular(image(u,range_of(identity_relation)))),cross_product(ordinal_numbers,ordinal_numbers))* -> equal(image(u,range_of(identity_relation)),identity_relation).
% 300.10/300.68  214323[25:Rew:208887.0,214301.2] operation(restrict(u,v,identity_relation)) || subclass(segment(u,v,ordinal_numbers),complement(complement(symmetrization_of(w))))* -> connected(w,cantor(segment(u,v,ordinal_numbers))).
% 300.10/300.68  214324[25:Rew:208887.0,214274.1] operation(restrict(u,v,identity_relation)) || connected(w,cantor(segment(u,v,ordinal_numbers))) -> subclass(segment(u,v,ordinal_numbers),complement(complement(symmetrization_of(w))))*.
% 300.10/300.68  214592[25:SpL:208985.1,8802.1] operation(u) || equal(compose(v,w),u) member(ordered_pair(w,ordinal_numbers),cross_product(ordinal_numbers,ordinal_numbers))* -> member(ordered_pair(w,u),compose_class(v))*.
% 300.10/300.68  214573[25:SpL:208985.1,131.3] operation(least(u,v)) || member(w,v)* subclass(v,x)* well_ordering(u,x)* member(ordered_pair(w,ordinal_numbers),u)* -> .
% 300.10/300.68  214530[25:SpL:208985.1,8802.1] operation(u) || equal(compose(v,w),ordinal_numbers) member(ordered_pair(w,u),cross_product(ordinal_numbers,ordinal_numbers))* -> member(ordered_pair(w,ordinal_numbers),compose_class(v))*.
% 300.10/300.68  214481[25:SpR:208985.1,8865.1] operation(segment(u,v,w)) || member(restrict(u,v,singleton(w)),ordinal_numbers) -> member(ordered_pair(restrict(u,v,singleton(w)),ordinal_numbers),domain_relation)*.
% 300.10/300.68  215209[2:Res:155157.1,9665.1] inductive(symmetric_difference(u,v)) || subclass(v,u) well_ordering(w,complement(v)) -> member(least(w,symmetric_difference(u,v)),symmetric_difference(u,v))*.
% 300.10/300.68  215206[7:Res:155157.1,13070.0] || subclass(u,v) well_ordering(w,complement(u)) -> equal(symmetric_difference(v,u),identity_relation) member(least(w,symmetric_difference(v,u)),symmetric_difference(v,u))*.
% 300.10/300.68  217278[8:Rew:140603.0,216709.1] || equal(symmetric_difference(u,v),identity_relation) -> equal(symmetric_difference(complement(intersection(u,v)),union(u,v)),union(complement(intersection(u,v)),union(u,v)))**.
% 300.10/300.68  217934[21:Rew:160429.0,217927.1] function(u) || subclass(range_of(u),identity_relation) equal(cantor(cantor(v)),cantor(u)) -> compatible(u,v,regular(complement(complement(symmetrization_of(identity_relation)))))*.
% 300.10/300.68  218762[21:MRR:218761.3,13126.0] function(range_of(identity_relation)) function(u) || subclass(domain_relation,rest_relation) equal(compose(u,identity_relation),range_of(identity_relation)) -> member(range_of(identity_relation),recursion_equation_functions(u))*.
% 300.10/300.68  218835[21:MRR:218834.3,13126.0] function(range_of(identity_relation)) function(u) || subclass(rest_relation,domain_relation) equal(compose(u,identity_relation),range_of(identity_relation)) -> member(range_of(identity_relation),recursion_equation_functions(u))*.
% 300.10/300.68  218909[21:MRR:218908.3,13126.0] function(singleton(u)) function(v) || subclass(domain_relation,rest_relation) equal(compose(v,identity_relation),singleton(u)) -> member(singleton(u),recursion_equation_functions(v))*.
% 300.10/300.68  218976[21:MRR:218975.3,13126.0] function(singleton(u)) function(v) || subclass(rest_relation,domain_relation) equal(compose(v,identity_relation),singleton(u)) -> member(singleton(u),recursion_equation_functions(v))*.
% 300.10/300.68  220466[21:Res:196656.1,8802.1] || subclass(domain_relation,flip(cross_product(ordinal_numbers,ordinal_numbers))) equal(compose(u,ordered_pair(v,w)),identity_relation) -> member(ordered_pair(ordered_pair(v,w),identity_relation),compose_class(u))*.
% 300.10/300.68  220572[21:Res:196657.1,8802.1] || subclass(domain_relation,rotate(cross_product(ordinal_numbers,ordinal_numbers))) equal(compose(u,ordered_pair(v,identity_relation)),w) -> member(ordered_pair(ordered_pair(v,identity_relation),w),compose_class(u))*.
% 300.10/300.68  220743[8:Res:9618.2,219203.0] || member(ordered_pair(u,v),cross_product(ordinal_numbers,ordinal_numbers)) subclass(composition_function,rest_of(ordered_pair(u,ordered_pair(v,compose(u,v)))))* subclass(element_relation,identity_relation) -> .
% 300.10/300.68  221077[7:Obv:221073.3] || well_ordering(u,not_well_ordering(u,v)) connected(u,v) member(least(u,not_well_ordering(u,v)),not_well_ordering(u,v))* -> well_ordering(u,v).
% 300.10/300.68  221160[7:Res:13236.2,288.0] || well_ordering(u,image(element_relation,complement(v))) member(least(u,image(element_relation,complement(v))),power_class(v))* -> equal(image(element_relation,complement(v)),identity_relation).
% 300.10/300.68  221149[7:Res:13236.2,897.0] || well_ordering(u,restrict(v,w,x)) -> equal(restrict(v,w,x),identity_relation) member(least(u,restrict(v,w,x)),cross_product(w,x))*.
% 300.10/300.68  221132[8:Res:13236.2,67561.0] || well_ordering(u,symmetric_difference(complement(v),ordinal_numbers)) -> equal(symmetric_difference(complement(v),ordinal_numbers),identity_relation) member(least(u,symmetric_difference(complement(v),ordinal_numbers)),union(v,identity_relation))*.
% 300.10/300.68  221398[8:Res:39609.2,67561.0] inductive(symmetric_difference(complement(u),ordinal_numbers)) || well_ordering(v,symmetric_difference(complement(u),ordinal_numbers)) -> member(least(v,symmetric_difference(complement(u),ordinal_numbers)),union(u,identity_relation))*.
% 300.10/300.68  223558[21:Res:218825.1,13362.0] || subclass(rest_relation,domain_relation) subclass(rest_relation,u) well_ordering(omega,u)* -> equal(integer_of(ordered_pair(ordered_pair(range_of(identity_relation),identity_relation),least(omega,rest_relation))),identity_relation)**.
% 300.10/300.68  223868[8:SpL:160927.0,8825.1] || member(u,ordinal_numbers) subclass(union(v,symmetric_difference(ordinal_numbers,w)),x)* -> member(u,intersection(complement(v),union(w,identity_relation)))* member(u,x)*.
% 300.10/300.68  223767[8:SpR:160927.0,483.0] ||  -> equal(complement(intersection(complement(u),union(v,intersection(complement(w),union(x,identity_relation))))),union(u,intersection(complement(v),union(w,symmetric_difference(ordinal_numbers,x)))))**.
% 300.10/300.68  223751[8:SpR:160927.0,483.0] ||  -> equal(complement(intersection(complement(u),union(intersection(complement(v),union(w,identity_relation)),x))),union(u,intersection(union(v,symmetric_difference(ordinal_numbers,w)),complement(x))))**.
% 300.10/300.68  223747[8:SpR:160927.0,482.0] ||  -> equal(complement(intersection(union(u,intersection(complement(v),union(w,identity_relation))),complement(x))),union(intersection(complement(u),union(v,symmetric_difference(ordinal_numbers,w))),x))**.
% 300.10/300.68  223743[8:SpR:160927.0,155157.1] || subclass(intersection(complement(u),union(v,identity_relation)),w) -> subclass(symmetric_difference(w,intersection(complement(u),union(v,identity_relation))),union(u,symmetric_difference(ordinal_numbers,v)))*.
% 300.10/300.68  223724[24:SpR:160927.0,207863.1] operation(intersection(complement(u),union(v,identity_relation))) ||  -> subclass(symmetric_difference(union(u,symmetric_difference(ordinal_numbers,v)),ordinal_numbers),successor(intersection(complement(u),union(v,identity_relation))))*.
% 300.10/300.68  223718[8:SpR:160927.0,132294.0] ||  -> subclass(complement(symmetrization_of(intersection(complement(u),union(v,identity_relation)))),intersection(union(u,symmetric_difference(ordinal_numbers,v)),complement(inverse(intersection(complement(u),union(v,identity_relation))))))*.
% 300.10/300.68  223716[8:SpR:160927.0,132293.0] ||  -> subclass(complement(successor(intersection(complement(u),union(v,identity_relation)))),intersection(union(u,symmetric_difference(ordinal_numbers,v)),complement(singleton(intersection(complement(u),union(v,identity_relation))))))*.
% 300.10/300.68  223701[8:SpR:160927.0,482.0] ||  -> equal(complement(intersection(union(intersection(complement(u),union(v,identity_relation)),w),complement(x))),union(intersection(union(u,symmetric_difference(ordinal_numbers,v)),complement(w)),x))**.
% 300.10/300.68  223935[8:Rew:160927.0,223704.1] ||  -> member(not_subclass_element(complement(union(u,symmetric_difference(ordinal_numbers,v))),w),intersection(complement(u),union(v,identity_relation)))* subclass(complement(union(u,symmetric_difference(ordinal_numbers,v))),w).
% 300.10/300.68  224187[8:SpL:160992.0,8825.1] || member(u,ordinal_numbers) subclass(union(symmetric_difference(ordinal_numbers,v),w),x)* -> member(u,intersection(union(v,identity_relation),complement(w)))* member(u,x)*.
% 300.10/300.68  224085[8:SpR:160992.0,483.0] ||  -> equal(complement(intersection(complement(u),union(v,intersection(union(w,identity_relation),complement(x))))),union(u,intersection(complement(v),union(symmetric_difference(ordinal_numbers,w),x))))**.
% 300.10/300.68  224068[8:SpR:160992.0,483.0] ||  -> equal(complement(intersection(complement(u),union(intersection(union(v,identity_relation),complement(w)),x))),union(u,intersection(union(symmetric_difference(ordinal_numbers,v),w),complement(x))))**.
% 300.10/300.68  224064[8:SpR:160992.0,482.0] ||  -> equal(complement(intersection(union(u,intersection(union(v,identity_relation),complement(w))),complement(x))),union(intersection(complement(u),union(symmetric_difference(ordinal_numbers,v),w)),x))**.
% 300.10/300.68  224060[8:SpR:160992.0,155157.1] || subclass(intersection(union(u,identity_relation),complement(v)),w) -> subclass(symmetric_difference(w,intersection(union(u,identity_relation),complement(v))),union(symmetric_difference(ordinal_numbers,u),v))*.
% 300.10/300.68  224041[24:SpR:160992.0,207863.1] operation(intersection(union(u,identity_relation),complement(v))) ||  -> subclass(symmetric_difference(union(symmetric_difference(ordinal_numbers,u),v),ordinal_numbers),successor(intersection(union(u,identity_relation),complement(v))))*.
% 300.10/300.68  224035[8:SpR:160992.0,132294.0] ||  -> subclass(complement(symmetrization_of(intersection(union(u,identity_relation),complement(v)))),intersection(union(symmetric_difference(ordinal_numbers,u),v),complement(inverse(intersection(union(u,identity_relation),complement(v))))))*.
% 300.10/300.68  224033[8:SpR:160992.0,132293.0] ||  -> subclass(complement(successor(intersection(union(u,identity_relation),complement(v)))),intersection(union(symmetric_difference(ordinal_numbers,u),v),complement(singleton(intersection(union(u,identity_relation),complement(v))))))*.
% 300.10/300.68  224018[8:SpR:160992.0,482.0] ||  -> equal(complement(intersection(union(intersection(union(u,identity_relation),complement(v)),w),complement(x))),union(intersection(union(symmetric_difference(ordinal_numbers,u),v),complement(w)),x))**.
% 300.10/300.68  224250[8:Rew:160992.0,224021.1] ||  -> member(not_subclass_element(complement(union(symmetric_difference(ordinal_numbers,u),v)),w),intersection(union(u,identity_relation),complement(v)))* subclass(complement(union(symmetric_difference(ordinal_numbers,u),v)),w).
% 300.10/300.68  224722[21:Res:9618.2,194371.0] || member(ordered_pair(u,v),cross_product(ordinal_numbers,ordinal_numbers)) subclass(composition_function,cross_product(ordinal_numbers,ordinal_numbers)) member(ordered_pair(v,compose(u,v)),cantor(u))* -> .
% 300.10/300.68  225422[7:Res:8551.2,17312.1] || member(regular(u),cross_product(v,w)) member(regular(u),x) subclass(u,complement(restrict(x,v,w)))* -> equal(u,identity_relation).
% 300.10/300.68  226331[21:Res:218966.1,13362.0] || subclass(rest_relation,domain_relation) subclass(rest_relation,u) well_ordering(omega,u)* -> equal(integer_of(ordered_pair(ordered_pair(singleton(v),identity_relation),least(omega,rest_relation))),identity_relation)**.
% 300.10/300.68  226360[21:Res:226329.1,13362.0] || subclass(rest_relation,domain_relation) subclass(rest_relation,u) well_ordering(omega,u)* -> equal(integer_of(ordered_pair(singleton(singleton(singleton(identity_relation))),least(omega,rest_relation))),identity_relation)**.
% 300.10/300.68  226399[7:Res:13258.1,18791.0] ||  -> equal(restrict(symmetric_difference(complement(u),complement(v)),w,x),identity_relation) member(regular(restrict(symmetric_difference(complement(u),complement(v)),w,x)),union(u,v))*.
% 300.10/300.68  226801[7:Rew:189.0,226793.2] || subclass(omega,image(element_relation,power_class(u))) -> equal(integer_of(regular(power_class(image(element_relation,complement(u))))),identity_relation)** equal(power_class(image(element_relation,complement(u))),identity_relation).
% 300.10/300.68  227269[5:SpL:61728.2,18571.2] || member(u,ordinal_numbers) subclass(rest_relation,union_of_range_map) member(range_of(u),ordinal_numbers)* subclass(ordinal_numbers,complement(v)) member(rest_of(u),v)* -> .
% 300.10/300.68  228569[8:Res:228546.1,13362.0] || equal(complement(u),identity_relation) subclass(successor(u),v)* well_ordering(omega,v) -> equal(integer_of(ordered_pair(omega,least(omega,successor(u)))),identity_relation)**.
% 300.10/300.68  228601[8:Res:228547.1,13362.0] || equal(complement(u),identity_relation) subclass(successor(u),v)* well_ordering(omega,v) -> equal(integer_of(ordered_pair(identity_relation,least(omega,successor(u)))),identity_relation)**.
% 300.10/300.68  228668[8:Res:228646.1,13362.0] || equal(complement(u),identity_relation) subclass(symmetrization_of(u),v)* well_ordering(omega,v) -> equal(integer_of(ordered_pair(omega,least(omega,symmetrization_of(u)))),identity_relation)**.
% 300.10/300.68  228680[8:Res:228647.1,13362.0] || equal(complement(u),identity_relation) subclass(symmetrization_of(u),v)* well_ordering(omega,v) -> equal(integer_of(ordered_pair(identity_relation,least(omega,symmetrization_of(u)))),identity_relation)**.
% 300.10/300.68  228828[8:Res:228806.1,13362.0] || subclass(complement(u),identity_relation) subclass(successor(u),v)* well_ordering(omega,v) -> equal(integer_of(ordered_pair(omega,least(omega,successor(u)))),identity_relation)**.
% 300.10/300.68  228841[8:Res:228807.1,13362.0] || subclass(complement(u),identity_relation) subclass(successor(u),v)* well_ordering(omega,v) -> equal(integer_of(ordered_pair(identity_relation,least(omega,successor(u)))),identity_relation)**.
% 300.10/300.68  228965[8:Res:228945.1,13362.0] || subclass(complement(u),identity_relation) subclass(symmetrization_of(u),v)* well_ordering(omega,v) -> equal(integer_of(ordered_pair(omega,least(omega,symmetrization_of(u)))),identity_relation)**.
% 300.10/300.68  228978[8:Res:228946.1,13362.0] || subclass(complement(u),identity_relation) subclass(symmetrization_of(u),v)* well_ordering(omega,v) -> equal(integer_of(ordered_pair(identity_relation,least(omega,symmetrization_of(u)))),identity_relation)**.
% 300.10/300.68  229047[7:Rew:50855.1,229022.1] || member(singleton(u),subset_relation) -> equal(symmetric_difference(first(singleton(u)),u),identity_relation) member(regular(symmetric_difference(first(singleton(u)),u)),successor(first(singleton(u))))*.
% 300.10/300.68  230704[8:MRR:230643.0,8666.0] || subclass(ordinal_numbers,regular(intersection(complement(u),complement(v))))* -> member(unordered_pair(w,x),union(u,v))* equal(intersection(complement(u),complement(v)),identity_relation).
% 300.10/300.68  231845[8:MRR:231800.0,41183.1] ||  -> member(not_subclass_element(regular(image(element_relation,complement(u))),v),power_class(u))* subclass(regular(image(element_relation,complement(u))),v) equal(image(element_relation,complement(u)),identity_relation).
% 300.10/300.68  232054[7:Res:52.1,17323.0] inductive(restrict(u,v,w)) ||  -> equal(image(successor_relation,restrict(u,v,w)),identity_relation) member(regular(image(successor_relation,restrict(u,v,w))),u)*.
% 300.10/300.68  233025[8:Res:139.1,69182.0] || member(complement(compose(element_relation,ordinal_numbers)),ordinal_numbers) member(regular(sum_class(complement(compose(element_relation,ordinal_numbers)))),element_relation)* -> equal(sum_class(complement(compose(element_relation,ordinal_numbers))),identity_relation).
% 300.10/300.68  233059[8:MRR:233032.3,13102.1] || connected(u,complement(compose(element_relation,ordinal_numbers))) member(regular(not_well_ordering(u,complement(compose(element_relation,ordinal_numbers)))),element_relation)* -> well_ordering(u,complement(compose(element_relation,ordinal_numbers))).
% 300.10/300.68  233102[21:Res:196525.2,129.0] || member(u,ordinal_numbers) equal(sum_class(range_of(u)),identity_relation)** subclass(union_of_range_map,v) well_ordering(w,v)* -> member(least(w,union_of_range_map),union_of_range_map)*.
% 300.10/300.68  233361[8:Res:231881.0,9420.2] || member(u,v) member(w,x) -> equal(singleton(cross_product(x,v)),identity_relation) member(ordered_pair(w,u),complement(singleton(cross_product(x,v))))*.
% 300.10/300.68  233503[21:Res:27.2,196424.2] || member(ordered_pair(u,identity_relation),v)* member(ordered_pair(u,identity_relation),w)* member(u,ordinal_numbers) subclass(domain_relation,complement(intersection(w,v)))* -> .
% 300.10/300.68  233794[7:Res:61019.0,941.1] || member(regular(complement(complement(power_class(image(element_relation,complement(u)))))),image(element_relation,power_class(u)))* -> equal(complement(complement(power_class(image(element_relation,complement(u))))),identity_relation).
% 300.10/300.68  233768[8:SpL:160992.0,941.1] || member(u,image(element_relation,power_class(intersection(union(v,identity_relation),complement(w)))))* member(u,power_class(image(element_relation,union(symmetric_difference(ordinal_numbers,v),w)))) -> .
% 300.10/300.68  233767[8:SpL:160927.0,941.1] || member(u,image(element_relation,power_class(intersection(complement(v),union(w,identity_relation)))))* member(u,power_class(image(element_relation,union(v,symmetric_difference(ordinal_numbers,w))))) -> .
% 300.10/300.68  233930[8:Res:13210.1,161200.0] || member(regular(intersection(u,image(element_relation,union(v,identity_relation)))),power_class(symmetric_difference(ordinal_numbers,v)))* -> equal(intersection(u,image(element_relation,union(v,identity_relation))),identity_relation).
% 300.10/300.68  233917[8:Res:13248.1,161200.0] || member(regular(intersection(image(element_relation,union(u,identity_relation)),v)),power_class(symmetric_difference(ordinal_numbers,u)))* -> equal(intersection(image(element_relation,union(u,identity_relation)),v),identity_relation).
% 300.10/300.68  234353[8:Res:67614.1,18696.1] || member(least(u,complement(symmetric_difference(complement(v),ordinal_numbers))),union(v,identity_relation))* well_ordering(u,ordinal_numbers) -> equal(complement(symmetric_difference(complement(v),ordinal_numbers)),identity_relation).
% 300.10/300.68  234347[7:Res:3618.1,18696.1] || member(least(u,complement(complement(intersection(v,w)))),symmetric_difference(v,w))* well_ordering(u,ordinal_numbers) -> equal(complement(complement(intersection(v,w))),identity_relation).
% 300.10/300.68  234442[21:SpL:3594.0,196423.1] || member(u,ordinal_numbers) subclass(domain_relation,symmetric_difference(complement(intersection(v,w)),union(v,w)))* -> member(ordered_pair(u,identity_relation),complement(symmetric_difference(v,w)))*.
% 300.10/300.68  234571[8:Res:9618.2,233381.0] || member(ordered_pair(u,v),cross_product(ordinal_numbers,ordinal_numbers)) subclass(composition_function,singleton(omega)) -> equal(integer_of(ordered_pair(u,ordered_pair(v,compose(u,v)))),identity_relation)**.
% 300.10/300.68  235038[7:Rew:234956.0,235027.1] || member(ordered_pair(u,not_subclass_element(v,image(w,range_of(identity_relation)))),compose(w,complement(cross_product(singleton(u),ordinal_numbers))))* -> subclass(v,image(w,range_of(identity_relation))).
% 300.10/300.68  235192[8:Res:9618.2,234983.0] || member(ordered_pair(u,v),cross_product(ordinal_numbers,ordinal_numbers)) subclass(composition_function,cantor(complement(cross_product(singleton(ordered_pair(u,ordered_pair(v,compose(u,v)))),ordinal_numbers))))* -> .
% 300.10/300.68  235270[8:Res:230445.1,129.0] || member(u,v)* subclass(union(v,identity_relation),w)* well_ordering(x,w)* -> member(least(x,union(v,identity_relation)),union(v,identity_relation))*.
% 300.10/300.68  235431[5:Res:28980.1,941.1] || subclass(rest_relation,flip(power_class(image(element_relation,complement(u))))) member(ordered_pair(ordered_pair(v,w),rest_of(ordered_pair(w,v))),image(element_relation,power_class(u)))* -> .
% 300.10/300.68  235430[8:Res:28980.1,161200.0] || subclass(rest_relation,flip(image(element_relation,union(u,identity_relation)))) member(ordered_pair(ordered_pair(v,w),rest_of(ordered_pair(w,v))),power_class(symmetric_difference(ordinal_numbers,u)))* -> .
% 300.10/300.68  235422[5:Res:28980.1,161.0] || subclass(rest_relation,flip(omega)) -> equal(integer_of(ordered_pair(ordered_pair(u,v),rest_of(ordered_pair(v,u)))),ordered_pair(ordered_pair(u,v),rest_of(ordered_pair(v,u))))**.
% 300.10/300.68  235559[5:Res:28979.1,941.1] || subclass(rest_relation,rotate(power_class(image(element_relation,complement(u))))) member(ordered_pair(ordered_pair(v,rest_of(ordered_pair(w,v))),w),image(element_relation,power_class(u)))* -> .
% 300.10/300.68  235558[8:Res:28979.1,161200.0] || subclass(rest_relation,rotate(image(element_relation,union(u,identity_relation)))) member(ordered_pair(ordered_pair(v,rest_of(ordered_pair(w,v))),w),power_class(symmetric_difference(ordinal_numbers,u)))* -> .
% 300.10/300.68  235550[5:Res:28979.1,161.0] || subclass(rest_relation,rotate(omega)) -> equal(integer_of(ordered_pair(ordered_pair(u,rest_of(ordered_pair(v,u))),v)),ordered_pair(ordered_pair(u,rest_of(ordered_pair(v,u))),v))**.
% 300.10/300.68  235683[5:Res:126679.1,36719.1] operation(u) || subclass(omega,complement(complement(cantor(u))))* -> equal(ordered_pair(first(least(element_relation,omega)),second(least(element_relation,omega))),least(element_relation,omega))**.
% 300.10/300.68  235682[5:Res:127147.1,36719.1] operation(u) || subclass(ordinal_numbers,complement(complement(cantor(u))))* -> equal(ordered_pair(first(least(element_relation,omega)),second(least(element_relation,omega))),least(element_relation,omega))**.
% 300.10/300.68  235948[21:Res:69478.2,196424.2] || subclass(omega,symmetric_difference(u,v)) member(w,ordinal_numbers) subclass(domain_relation,complement(union(u,v)))* -> equal(integer_of(ordered_pair(w,identity_relation)),identity_relation)**.
% 300.10/300.68  235935[7:Res:69478.2,47534.0] || subclass(omega,symmetric_difference(u,v)) -> equal(integer_of(not_subclass_element(w,intersection(union(u,v),w))),identity_relation)** subclass(w,intersection(union(u,v),w)).
% 300.10/300.68  235905[7:SpR:482.0,69478.2] || subclass(omega,symmetric_difference(intersection(complement(u),complement(v)),w)) -> equal(integer_of(x),identity_relation) member(x,complement(intersection(union(u,v),complement(w))))*.
% 300.10/300.68  235896[7:SpR:483.0,69478.2] || subclass(omega,symmetric_difference(u,intersection(complement(v),complement(w)))) -> equal(integer_of(x),identity_relation) member(x,complement(intersection(complement(u),union(v,w))))*.
% 300.10/300.68  236253[8:Res:67614.1,18897.0] || member(not_subclass_element(intersection(u,complement(symmetric_difference(complement(v),ordinal_numbers))),w),union(v,identity_relation))* -> subclass(intersection(u,complement(symmetric_difference(complement(v),ordinal_numbers))),w).
% 300.10/300.68  236247[0:Res:3618.1,18897.0] || member(not_subclass_element(intersection(u,complement(complement(intersection(v,w)))),x),symmetric_difference(v,w))* -> subclass(intersection(u,complement(complement(intersection(v,w)))),x).
% 300.10/300.68  236457[8:Res:67614.1,19016.0] || member(not_subclass_element(intersection(complement(symmetric_difference(complement(u),ordinal_numbers)),v),w),union(u,identity_relation))* -> subclass(intersection(complement(symmetric_difference(complement(u),ordinal_numbers)),v),w).
% 300.10/300.68  236451[0:Res:3618.1,19016.0] || member(not_subclass_element(intersection(complement(complement(intersection(u,v))),w),x),symmetric_difference(u,v))* -> subclass(intersection(complement(complement(intersection(u,v))),w),x).
% 300.10/300.68  236607[5:SpL:481.0,36857.0] || equal(u,power_class(intersection(complement(v),complement(w))))* member(x,ordinal_numbers) -> member(x,image(element_relation,union(v,w)))* member(x,u)*.
% 300.10/300.68  236595[8:SpL:160992.0,36857.0] || equal(u,union(symmetric_difference(ordinal_numbers,v),w))* member(x,ordinal_numbers) -> member(x,intersection(union(v,identity_relation),complement(w)))* member(x,u)*.
% 300.10/300.68  236594[8:SpL:160927.0,36857.0] || equal(u,union(v,symmetric_difference(ordinal_numbers,w)))* member(x,ordinal_numbers) -> member(x,intersection(complement(v),union(w,identity_relation)))* member(x,u)*.
% 300.10/300.68  236876[7:Res:17392.2,941.1] || subclass(u,power_class(image(element_relation,complement(v)))) member(regular(intersection(u,w)),image(element_relation,power_class(v)))* -> equal(intersection(u,w),identity_relation).
% 300.10/300.68  236875[8:Res:17392.2,161200.0] || subclass(u,image(element_relation,union(v,identity_relation))) member(regular(intersection(u,w)),power_class(symmetric_difference(ordinal_numbers,v)))* -> equal(intersection(u,w),identity_relation).
% 300.10/300.68  236855[7:Res:17392.2,12.0] || subclass(u,unordered_pair(v,w))* -> equal(intersection(u,x),identity_relation) equal(regular(intersection(u,x)),w)* equal(regular(intersection(u,x)),v)*.
% 300.10/300.68  236936[7:Rew:3603.0,236773.1] || subclass(complement(restrict(u,v,w)),x) -> equal(symmetric_difference(u,cross_product(v,w)),identity_relation) member(regular(symmetric_difference(u,cross_product(v,w))),x)*.
% 300.10/300.68  236937[7:Rew:3606.0,236772.1] || subclass(complement(restrict(u,v,w)),x) -> equal(symmetric_difference(cross_product(v,w),u),identity_relation) member(regular(symmetric_difference(cross_product(v,w),u)),x)*.
% 300.10/300.68  237140[7:Res:13574.1,288.0] || member(regular(intersection(u,intersection(v,image(element_relation,complement(w))))),power_class(w))* -> equal(intersection(u,intersection(v,image(element_relation,complement(w)))),identity_relation).
% 300.10/300.68  237129[7:Res:13574.1,897.0] ||  -> equal(intersection(u,intersection(v,restrict(w,x,y))),identity_relation) member(regular(intersection(u,intersection(v,restrict(w,x,y)))),cross_product(x,y))*.
% 300.10/300.68  237108[8:Res:13574.1,67561.0] ||  -> equal(intersection(u,intersection(v,symmetric_difference(complement(w),ordinal_numbers))),identity_relation) member(regular(intersection(u,intersection(v,symmetric_difference(complement(w),ordinal_numbers)))),union(w,identity_relation))*.
% 300.10/300.68  237791[7:Res:13573.1,288.0] || member(regular(intersection(u,intersection(image(element_relation,complement(v)),w))),power_class(v))* -> equal(intersection(u,intersection(image(element_relation,complement(v)),w)),identity_relation).
% 300.10/300.68  237780[7:Res:13573.1,897.0] ||  -> equal(intersection(u,intersection(restrict(v,w,x),y)),identity_relation) member(regular(intersection(u,intersection(restrict(v,w,x),y))),cross_product(w,x))*.
% 300.10/300.68  237759[8:Res:13573.1,67561.0] ||  -> equal(intersection(u,intersection(symmetric_difference(complement(v),ordinal_numbers),w)),identity_relation) member(regular(intersection(u,intersection(symmetric_difference(complement(v),ordinal_numbers),w))),union(v,identity_relation))*.
% 300.10/300.68  237886[7:Rew:3603.0,237675.0] ||  -> equal(intersection(u,symmetric_difference(v,cross_product(w,x))),identity_relation) member(regular(intersection(u,symmetric_difference(v,cross_product(w,x)))),complement(restrict(v,w,x)))*.
% 300.10/300.68  237887[7:Rew:3606.0,237674.0] ||  -> equal(intersection(u,symmetric_difference(cross_product(v,w),x)),identity_relation) member(regular(intersection(u,symmetric_difference(cross_product(v,w),x))),complement(restrict(x,v,w)))*.
% 300.10/300.68  238610[7:Res:13572.2,941.1] || subclass(u,power_class(image(element_relation,complement(v)))) member(regular(intersection(w,u)),image(element_relation,power_class(v)))* -> equal(intersection(w,u),identity_relation).
% 300.10/300.68  238609[8:Res:13572.2,161200.0] || subclass(u,image(element_relation,union(v,identity_relation))) member(regular(intersection(w,u)),power_class(symmetric_difference(ordinal_numbers,v)))* -> equal(intersection(w,u),identity_relation).
% 300.10/300.68  238589[7:Res:13572.2,12.0] || subclass(u,unordered_pair(v,w))* -> equal(intersection(x,u),identity_relation) equal(regular(intersection(x,u)),w)* equal(regular(intersection(x,u)),v)*.
% 300.10/300.68  239303[7:Res:17397.1,288.0] || member(regular(intersection(intersection(image(element_relation,complement(u)),v),w)),power_class(u))* -> equal(intersection(intersection(image(element_relation,complement(u)),v),w),identity_relation).
% 300.10/300.68  239292[7:Res:17397.1,897.0] ||  -> equal(intersection(intersection(restrict(u,v,w),x),y),identity_relation) member(regular(intersection(intersection(restrict(u,v,w),x),y)),cross_product(v,w))*.
% 300.10/300.68  239271[8:Res:17397.1,67561.0] ||  -> equal(intersection(intersection(symmetric_difference(complement(u),ordinal_numbers),v),w),identity_relation) member(regular(intersection(intersection(symmetric_difference(complement(u),ordinal_numbers),v),w)),union(u,identity_relation))*.
% 300.10/300.68  239409[7:Rew:3603.0,239180.0] ||  -> equal(intersection(symmetric_difference(u,cross_product(v,w)),x),identity_relation) member(regular(intersection(symmetric_difference(u,cross_product(v,w)),x)),complement(restrict(u,v,w)))*.
% 300.10/300.68  239410[7:Rew:3606.0,239179.0] ||  -> equal(intersection(symmetric_difference(cross_product(u,v),w),x),identity_relation) member(regular(intersection(symmetric_difference(cross_product(u,v),w),x)),complement(restrict(w,u,v)))*.
% 300.10/300.68  240138[7:Res:17396.1,288.0] || member(regular(intersection(intersection(u,image(element_relation,complement(v))),w)),power_class(v))* -> equal(intersection(intersection(u,image(element_relation,complement(v))),w),identity_relation).
% 300.10/300.68  240127[7:Res:17396.1,897.0] ||  -> equal(intersection(intersection(u,restrict(v,w,x)),y),identity_relation) member(regular(intersection(intersection(u,restrict(v,w,x)),y)),cross_product(w,x))*.
% 300.10/300.68  240106[8:Res:17396.1,67561.0] ||  -> equal(intersection(intersection(u,symmetric_difference(complement(v),ordinal_numbers)),w),identity_relation) member(regular(intersection(intersection(u,symmetric_difference(complement(v),ordinal_numbers)),w)),union(v,identity_relation))*.
% 300.10/300.68  36169[0:SpR:482.0,163.0] ||  -> equal(intersection(complement(intersection(intersection(complement(u),complement(v)),w)),complement(intersection(union(u,v),complement(w)))),symmetric_difference(intersection(complement(u),complement(v)),w))**.
% 300.10/300.68  36221[0:SpR:483.0,163.0] ||  -> equal(intersection(complement(intersection(u,intersection(complement(v),complement(w)))),complement(intersection(complement(u),union(v,w)))),symmetric_difference(u,intersection(complement(v),complement(w))))**.
% 300.10/300.68  10866[5:Res:133.2,8787.1] single_valued_class(not_well_ordering(u,cross_product(ordinal_numbers,ordinal_numbers))) || connected(u,cross_product(ordinal_numbers,ordinal_numbers)) -> well_ordering(u,cross_product(ordinal_numbers,ordinal_numbers)) function(not_well_ordering(u,cross_product(ordinal_numbers,ordinal_numbers)))*.
% 300.10/300.68  12938[0:Res:27.2,290.0] || member(not_subclass_element(complement(intersection(u,v)),w),v)* member(not_subclass_element(complement(intersection(u,v)),w),u)* -> subclass(complement(intersection(u,v)),w).
% 300.10/300.68  47551[5:Rew:32.0,47521.2,32.0,47521.1,32.0,47521.0] || member(not_subclass_element(u,restrict(v,ordinal_numbers,ordinal_numbers)),subset_relation)* member(not_subclass_element(u,restrict(v,ordinal_numbers,ordinal_numbers)),v)* -> subclass(u,restrict(v,ordinal_numbers,ordinal_numbers)).
% 300.10/300.68  47566[0:Rew:3695.1,47565.1] || member(u,v) member(u,w) -> equal(not_subclass_element(unordered_pair(x,u),intersection(w,v)),x)** subclass(unordered_pair(x,u),intersection(w,v)).
% 300.10/300.68  47568[0:Rew:3695.2,47567.1] || member(u,v) member(u,w) -> equal(not_subclass_element(unordered_pair(u,x),intersection(w,v)),x)** subclass(unordered_pair(u,x),intersection(w,v)).
% 300.10/300.68  50971[5:MRR:50970.2,18819.1] || member(u,subset_relation) member(v,ordinal_numbers) member(ordered_pair(ordered_pair(second(u),first(u)),v),w)* -> member(ordered_pair(u,v),flip(w)).
% 300.10/300.68  50894[5:MRR:50893.2,18819.1] || member(u,subset_relation) member(v,ordinal_numbers) member(ordered_pair(ordered_pair(second(u),v),first(u)),w)* -> member(ordered_pair(u,v),rotate(w)).
% 300.10/300.68  50196[5:Res:50064.1,9421.0] || member(u,subset_relation) member(v,w)* -> equal(ordered_pair(first(ordered_pair(v,second(u))),second(ordered_pair(v,second(u)))),ordered_pair(v,second(u)))**.
% 300.10/300.68  50155[5:Res:50063.1,9421.0] || member(u,subset_relation) member(v,w)* -> equal(ordered_pair(first(ordered_pair(v,first(u))),second(ordered_pair(v,first(u)))),ordered_pair(v,first(u)))**.
% 300.10/300.68  45733[5:Res:9865.3,5.0] || member(u,ordinal_numbers) member(v,ordinal_numbers) equal(compose(w,v),u)* subclass(compose_class(w),x)* -> member(ordered_pair(v,u),x)*.
% 300.10/300.68  53016[5:Res:8667.0,9872.0] || member(ordered_pair(u,least(intersection(v,ordinal_numbers),w)),v)* member(u,w) subclass(w,x)* well_ordering(intersection(v,ordinal_numbers),x)* -> .
% 300.10/300.68  50869[5:Res:49995.1,3689.0] || member(ordered_pair(u,v),subset_relation) -> equal(singleton(first(ordered_pair(u,v))),unordered_pair(u,singleton(v)))** equal(singleton(first(ordered_pair(u,v))),singleton(u)).
% 300.10/300.68  9868[0:SpL:963.0,131.3] || member(singleton(least(u,v)),v)* subclass(v,w)* well_ordering(u,w)* member(singleton(singleton(singleton(least(u,v)))),u)* -> .
% 300.10/300.68  43735[5:Res:8978.2,8554.1] || member(u,ordinal_numbers) subclass(ordinal_numbers,complement(intersection(v,w))) member(sum_class(u),union(v,w)) -> member(sum_class(u),symmetric_difference(v,w))*.
% 300.10/300.68  47005[5:Res:8955.1,9421.0] || member(u,ordinal_numbers) member(v,w)* -> equal(ordered_pair(first(ordered_pair(v,sum_class(u))),second(ordered_pair(v,sum_class(u)))),ordered_pair(v,sum_class(u)))**.
% 300.10/300.68  69372[8:Res:69184.1,131.3] || member(ordered_pair(u,least(compose(element_relation,ordinal_numbers),v)),element_relation)* member(u,v) subclass(v,w)* well_ordering(compose(element_relation,ordinal_numbers),w)* -> .
% 300.10/300.68  94666[5:Res:39298.1,8554.1] || subclass(ordinal_numbers,complement(complement(complement(intersection(u,v)))))* member(ordered_pair(w,x),union(u,v)) -> member(ordered_pair(w,x),symmetric_difference(u,v))*.
% 300.10/300.68  96354[5:Res:40074.1,8554.1] || subclass(ordinal_numbers,complement(complement(complement(intersection(u,v)))))* member(unordered_pair(w,x),union(u,v)) -> member(unordered_pair(w,x),symmetric_difference(u,v))*.
% 300.10/300.68  116637[8:Rew:116078.0,10865.2] single_valued_class(domain_of(restrict(u,v,cross_product(ordinal_numbers,ordinal_numbers)))) || section(u,cross_product(ordinal_numbers,ordinal_numbers),v) -> function(cantor(restrict(u,v,cross_product(ordinal_numbers,ordinal_numbers))))*.
% 300.10/300.68  118994[8:Res:116148.1,8787.1] single_valued_class(cantor(restrict(u,v,cross_product(ordinal_numbers,ordinal_numbers)))) || section(u,cross_product(ordinal_numbers,ordinal_numbers),v) -> function(cantor(restrict(u,v,cross_product(ordinal_numbers,ordinal_numbers))))*.
% 300.10/300.68  127977[5:Res:126679.1,8554.1] || subclass(omega,complement(complement(complement(intersection(u,v)))))* member(least(element_relation,omega),union(u,v)) -> member(least(element_relation,omega),symmetric_difference(u,v)).
% 300.10/300.68  128311[5:Res:127147.1,8554.1] || subclass(ordinal_numbers,complement(complement(complement(intersection(u,v)))))* member(least(element_relation,omega),union(u,v)) -> member(least(element_relation,omega),symmetric_difference(u,v)).
% 300.10/300.68  131576[0:Res:2504.1,3689.0] || subclass(ordered_pair(u,v),ordered_pair(w,x))* -> equal(unordered_pair(u,singleton(v)),unordered_pair(w,singleton(x))) equal(unordered_pair(u,singleton(v)),singleton(w)).
% 300.10/300.68  131565[0:Res:2504.1,21.0] || subclass(ordered_pair(u,v),cross_product(w,x))* -> equal(ordered_pair(first(unordered_pair(u,singleton(v))),second(unordered_pair(u,singleton(v)))),unordered_pair(u,singleton(v)))**.
% 300.10/300.68  139830[5:MRR:139798.0,8667.0] || member(u,v) subclass(v,w)* well_ordering(union(x,y),w)* -> member(ordered_pair(u,least(union(x,y),v)),complement(y))*.
% 300.10/300.68  139913[5:MRR:139884.0,8667.0] || member(u,v) subclass(v,w)* well_ordering(union(x,y),w)* -> member(ordered_pair(u,least(union(x,y),v)),complement(x))*.
% 300.10/300.68  140472[0:Obv:140381.1] || member(u,v) -> equal(not_subclass_element(unordered_pair(w,u),intersection(v,unordered_pair(w,u))),w)** subclass(unordered_pair(w,u),intersection(v,unordered_pair(w,u))).
% 300.10/300.68  140473[0:Obv:140380.1] || member(u,v) -> equal(not_subclass_element(unordered_pair(u,w),intersection(v,unordered_pair(u,w))),w)** subclass(unordered_pair(u,w),intersection(v,unordered_pair(u,w))).
% 300.10/300.68  140862[8:Rew:140603.0,68978.0] || member(u,complement(v))* subclass(symmetric_difference(ordinal_numbers,v),w)* well_ordering(x,w)* -> member(least(x,symmetric_difference(ordinal_numbers,v)),symmetric_difference(ordinal_numbers,v))*.
% 300.10/300.68  146761[5:Res:8551.2,18571.2] || member(sum_class(u),cross_product(v,w))* member(sum_class(u),x)* member(u,ordinal_numbers) subclass(ordinal_numbers,complement(restrict(x,v,w)))* -> .
% 300.10/300.68  148979[5:Res:148963.1,9421.0] || member(u,ordinal_numbers) member(v,w)* -> equal(ordered_pair(first(ordered_pair(v,rest_of(u))),second(ordered_pair(v,rest_of(u)))),ordered_pair(v,rest_of(u)))**.
% 300.10/300.68  153355[0:Res:919.1,18791.0] ||  -> subclass(restrict(symmetric_difference(complement(u),complement(v)),w,x),y) member(not_subclass_element(restrict(symmetric_difference(complement(u),complement(v)),w,x),y),union(u,v))*.
% 300.10/300.68  155821[5:SpR:155653.0,3603.0] ||  -> equal(intersection(complement(subset_relation),union(complement(compose(complement(element_relation),inverse(element_relation))),cross_product(ordinal_numbers,ordinal_numbers))),symmetric_difference(complement(compose(complement(element_relation),inverse(element_relation))),cross_product(ordinal_numbers,ordinal_numbers)))**.
% 300.10/300.68  155820[5:SpR:155653.0,3606.0] ||  -> equal(intersection(complement(subset_relation),union(cross_product(ordinal_numbers,ordinal_numbers),complement(compose(complement(element_relation),inverse(element_relation))))),symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),complement(compose(complement(element_relation),inverse(element_relation)))))**.
% 300.10/300.68  156468[5:SpL:155665.0,8559.2] || member(u,union(subset_relation,cross_product(ordinal_numbers,ordinal_numbers)))* member(u,complement(subset_relation)) subclass(symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers)),v)* -> member(u,v)*.
% 300.10/300.68  156399[5:SpR:155665.0,163.0] ||  -> equal(intersection(complement(symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers))),union(complement(subset_relation),union(subset_relation,cross_product(ordinal_numbers,ordinal_numbers)))),symmetric_difference(complement(subset_relation),union(subset_relation,cross_product(ordinal_numbers,ordinal_numbers))))**.
% 300.10/300.68  156577[5:SpL:155666.0,8559.2] || member(u,union(cross_product(ordinal_numbers,ordinal_numbers),subset_relation))* member(u,complement(subset_relation)) subclass(symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation),v)* -> member(u,v)*.
% 300.10/300.68  156508[5:SpR:155666.0,163.0] ||  -> equal(intersection(complement(symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation)),union(complement(subset_relation),union(cross_product(ordinal_numbers,ordinal_numbers),subset_relation))),symmetric_difference(complement(subset_relation),union(cross_product(ordinal_numbers,ordinal_numbers),subset_relation)))**.
% 300.10/300.68  161668[8:Rew:160496.0,62164.2] || connected(u,v)* member(w,v)* well_ordering(x,complement(complement(symmetrization_of(u))))* -> member(least(x,cross_product(v,v)),cross_product(v,v))*.
% 300.10/300.68  117658[8:Rew:116078.0,116320.1] operation(restrict(element_relation,ordinal_numbers,u)) || member(v,cantor(sum_class(u))) member(w,cantor(sum_class(u))) -> member(ordered_pair(w,v),sum_class(u))*.
% 300.10/300.68  116881[8:Rew:116078.0,36744.1] operation(u) || subclass(v,cantor(u))* -> subclass(v,w) equal(ordered_pair(first(not_subclass_element(v,w)),second(not_subclass_element(v,w))),not_subclass_element(v,w))**.
% 300.10/300.68  117677[8:Rew:116078.0,116873.2,116078.0,116873.1] operation(u) || member(v,union(w,cantor(u))) member(v,complement(intersection(cantor(u),w)))* -> member(v,symmetric_difference(w,cantor(u))).
% 300.10/300.68  117676[8:Rew:116078.0,116867.2,116078.0,116867.1] operation(u) || member(v,union(cantor(u),w)) member(v,complement(intersection(w,cantor(u))))* -> member(v,symmetric_difference(cantor(u),w)).
% 300.10/300.68  117673[8:Rew:116078.0,116801.2] operation(u) || member(cantor(u),subset_relation) -> equal(ordered_pair(first(singleton(first(cantor(u)))),second(singleton(first(cantor(u))))),singleton(first(cantor(u))))**.
% 300.10/300.68  176980[8:Rew:116154.0,176969.2] operation(restrict(u,v,singleton(w))) || subclass(segment(u,v,w),complement(complement(symmetrization_of(x))))* -> connected(x,cantor(segment(u,v,w))).
% 300.10/300.68  177006[8:Res:161196.2,11.0] operation(u) || connected(v,cantor(cantor(u))) subclass(complement(complement(symmetrization_of(v))),cantor(u))* -> equal(complement(complement(symmetrization_of(v))),cantor(u)).
% 300.10/300.68  177013[8:Rew:116154.0,176999.1] operation(restrict(u,v,singleton(w))) || connected(x,cantor(segment(u,v,w))) -> subclass(segment(u,v,w),complement(complement(symmetrization_of(x))))*.
% 300.10/300.68  82266[8:Res:81336.1,8554.1] || subclass(domain_relation,complement(complement(complement(intersection(u,v)))))* member(ordered_pair(identity_relation,identity_relation),union(u,v)) -> member(ordered_pair(identity_relation,identity_relation),symmetric_difference(u,v)).
% 300.10/300.68  163288[5:Rew:61480.1,163285.1] || member(not_subclass_element(compose(u,inverse(u)),identity_relation),subset_relation) -> equal(ordered_pair(single_valued1(u),second(ordered_pair(single_valued1(u),single_valued2(u)))),ordered_pair(single_valued1(u),single_valued2(u)))**.
% 300.10/300.68  13665[7:Rew:13036.0,13485.2] || well_ordering(u,cross_product(ordinal_numbers,ordinal_numbers)) -> equal(recursion_equation_functions(v),identity_relation) equal(regular(recursion_equation_functions(v)),identity_relation) member(least(u,regular(recursion_equation_functions(v))),regular(recursion_equation_functions(v)))*.
% 300.10/300.68  64336[7:Rew:3594.0,64257.0] ||  -> equal(symmetric_difference(complement(intersection(u,v)),union(u,v)),identity_relation) member(regular(symmetric_difference(complement(intersection(u,v)),union(u,v))),complement(symmetric_difference(u,v)))*.
% 300.10/300.68  13432[7:Rew:13036.0,10949.4] || subclass(omega,u) member(v,w) subclass(w,x)* well_ordering(u,x)* -> equal(integer_of(ordered_pair(v,least(u,w))),identity_relation)**.
% 300.10/300.68  81643[8:Res:67606.0,13113.0] || well_ordering(u,complement(symmetric_difference(complement(v),ordinal_numbers))) -> equal(segment(u,symmetric_difference(union(v,identity_relation),ordinal_numbers),least(u,symmetric_difference(union(v,identity_relation),ordinal_numbers))),identity_relation)**.
% 300.10/300.68  188947[5:Rew:61480.1,188945.1] || member(not_subclass_element(compose(u,inverse(u)),identity_relation),subset_relation) -> equal(ordered_pair(first(ordered_pair(single_valued1(u),single_valued2(u))),single_valued2(u)),ordered_pair(single_valued1(u),single_valued2(u)))**.
% 300.10/300.68  46169[2:Res:9563.3,5.0] || connected(u,v) well_ordering(w,v) subclass(not_well_ordering(u,v),x) -> well_ordering(u,v) member(least(w,not_well_ordering(u,v)),x)*.
% 300.10/300.68  133497[5:Res:133486.1,9878.0] || well_ordering(cross_product(u,rest_relation),ordinal_numbers)* member(v,u)* member(v,rest_relation)* subclass(rest_relation,w) well_ordering(cross_product(u,rest_relation),w)* -> .
% 300.10/300.68  133518[5:Res:133495.1,9878.0] || well_ordering(cross_product(u,ordinal_numbers),ordinal_numbers)* member(v,u)* member(v,rest_relation)* subclass(rest_relation,w) well_ordering(cross_product(u,ordinal_numbers),w)* -> .
% 300.10/300.68  133504[5:Res:133488.1,9878.0] || well_ordering(cross_product(u,rest_relation),rest_relation)* member(v,u)* member(v,rest_relation)* subclass(rest_relation,w) well_ordering(cross_product(u,rest_relation),w)* -> .
% 300.10/300.68  133532[5:Res:133502.1,9878.0] || well_ordering(cross_product(u,ordinal_numbers),rest_relation)* member(v,u)* member(v,rest_relation)* subclass(rest_relation,w) well_ordering(cross_product(u,ordinal_numbers),w)* -> .
% 300.10/300.68  63700[8:SoR:9113.0,19277.2] single_valued_class(sum_class(cross_product(ordinal_numbers,ordinal_numbers))) || well_ordering(element_relation,cross_product(ordinal_numbers,ordinal_numbers))* equal(sum_class(cross_product(ordinal_numbers,ordinal_numbers)),identity_relation) -> member(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers).
% 300.10/300.68  63718[8:Rew:8637.0,63701.2] single_valued_class(sum_class(cross_product(universal_class,universal_class))) || well_ordering(element_relation,cross_product(ordinal_numbers,ordinal_numbers))* equal(sum_class(cross_product(ordinal_numbers,ordinal_numbers)),identity_relation) -> member(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers).
% 300.10/300.68  41121[5:MRR:40590.1,41096.1] || member(least(element_relation,u),ordinal_numbers)* member(v,least(element_relation,u))* member(v,u) subclass(u,w)* well_ordering(element_relation,w)* -> .
% 300.10/300.68  49065[5:Res:8665.1,9633.1] function(complement(u)) || member(v,ordinal_numbers)* well_ordering(w,cross_product(ordinal_numbers,ordinal_numbers)) -> member(v,u)* member(least(w,complement(u)),complement(u))*.
% 300.10/300.68  49231[5:Res:8665.1,9639.1] function(unordered_pair(u,v)) || member(v,ordinal_numbers) well_ordering(w,cross_product(ordinal_numbers,ordinal_numbers)) -> member(least(w,unordered_pair(u,v)),unordered_pair(u,v))*.
% 300.10/300.68  49301[5:Res:8665.1,9640.1] function(unordered_pair(u,v)) || member(u,ordinal_numbers) well_ordering(w,cross_product(ordinal_numbers,ordinal_numbers)) -> member(least(w,unordered_pair(u,v)),unordered_pair(u,v))*.
% 300.10/300.68  18847[5:Res:18819.1,131.3] || member(ordered_pair(u,least(cross_product(ordinal_numbers,ordinal_numbers),v)),subset_relation)* member(u,v) subclass(v,w)* well_ordering(cross_product(ordinal_numbers,ordinal_numbers),w)* -> .
% 300.10/300.68  51567[5:Res:51204.1,129.0] || member(singleton(u),subset_relation) subclass(singleton(singleton(u)),v)* well_ordering(w,v)* -> member(least(w,singleton(singleton(u))),singleton(singleton(u)))*.
% 300.10/300.68  63411[7:SpR:13584.1,9618.2] function(u) || member(ordered_pair(u,inverse(u)),cross_product(ordinal_numbers,ordinal_numbers)) subclass(composition_function,v) -> member(ordered_pair(u,ordered_pair(inverse(u),identity_relation)),v)*.
% 300.10/300.68  63462[7:SpR:13585.1,9618.2] single_valued_class(u) || member(ordered_pair(u,inverse(u)),cross_product(ordinal_numbers,ordinal_numbers)) subclass(composition_function,v) -> member(ordered_pair(u,ordered_pair(inverse(u),identity_relation)),v)*.
% 300.10/300.68  64608[8:SpR:18040.1,9618.2] || equal(compose_class(u),domain_relation) member(ordered_pair(u,identity_relation),cross_product(ordinal_numbers,ordinal_numbers)) subclass(composition_function,v) -> member(ordered_pair(u,ordered_pair(identity_relation,identity_relation)),v)*.
% 300.10/300.68  46614[5:Res:9618.2,8788.0] || member(ordered_pair(u,v),cross_product(ordinal_numbers,ordinal_numbers)) subclass(composition_function,recursion_equation_functions(w))* -> subclass(ordered_pair(u,ordered_pair(v,compose(u,v))),cross_product(ordinal_numbers,ordinal_numbers))*.
% 300.10/300.68  46626[5:Res:9618.2,898.0] || member(ordered_pair(u,v),cross_product(ordinal_numbers,ordinal_numbers)) subclass(composition_function,restrict(w,x,y))* -> member(ordered_pair(u,ordered_pair(v,compose(u,v))),w)*.
% 300.10/300.68  56419[5:Res:9618.2,56411.0] || member(ordered_pair(u,v),cross_product(ordinal_numbers,ordinal_numbers)) subclass(composition_function,rest_of(ordered_pair(u,ordered_pair(v,compose(u,v)))))* subclass(ordinal_numbers,complement(element_relation)) -> .
% 300.10/300.68  62153[8:Rew:15614.1,62141.2] || equal(rest_relation,domain_relation) member(identity_relation,recursion_equation_functions(u)) member(ordered_pair(u,identity_relation),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(u,ordered_pair(identity_relation,identity_relation)),composition_function)*.
% 300.10/300.68  194461[14:Res:165177.0,129.0] || subclass(symmetric_difference(ordinal_numbers,u),v)* well_ordering(w,v)* -> member(identity_relation,union(u,identity_relation)) member(least(w,symmetric_difference(ordinal_numbers,u)),symmetric_difference(ordinal_numbers,u))*.
% 300.10/300.68  194490[8:Res:163112.0,129.0] || subclass(complement(inverse(identity_relation)),u)* well_ordering(v,u)* -> subclass(singleton(w),symmetrization_of(identity_relation))* member(least(v,complement(inverse(identity_relation))),complement(inverse(identity_relation)))*.
% 300.10/300.68  194851[7:MRR:194849.2,13039.0] || well_ordering(u,cross_product(ordinal_numbers,ordinal_numbers)) subclass(singleton(least(u,compose_class(v))),compose_class(v)) -> section(u,singleton(least(u,compose_class(v))),compose_class(v))*.
% 300.10/300.68  194918[7:MRR:194916.2,13039.0] || well_ordering(u,cross_product(ordinal_numbers,ordinal_numbers)) subclass(singleton(least(u,rest_of(v))),rest_of(v)) -> section(u,singleton(least(u,rest_of(v))),rest_of(v))*.
% 300.10/300.68  195639[16:Rew:195224.0,195197.2] || subclass(complement(singleton(identity_relation)),u)* well_ordering(v,u)* -> subclass(singleton(w),singleton(identity_relation))* member(least(v,complement(singleton(identity_relation))),complement(singleton(identity_relation)))*.
% 300.10/300.68  196528[21:Rew:196372.1,196449.3] || member(u,ordinal_numbers) subclass(domain_relation,ordered_pair(v,w))* -> equal(ordered_pair(u,identity_relation),unordered_pair(v,singleton(w)))* equal(ordered_pair(u,identity_relation),singleton(v)).
% 300.10/300.68  196738[21:Rew:196550.0,196651.2] || subclass(domain_relation,cross_product(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers)) member(ordered_pair(ordered_pair(u,identity_relation),v),w) -> member(ordered_pair(ordered_pair(v,u),identity_relation),rotate(w))*.
% 300.10/300.68  196739[21:Rew:196550.0,196652.1] || subclass(domain_relation,cross_product(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers)) member(ordered_pair(ordered_pair(u,v),identity_relation),w) -> member(ordered_pair(ordered_pair(v,u),identity_relation),flip(w))*.
% 300.10/300.68  199086[14:Res:193906.1,13362.0] || equal(inverse(subset_relation),singleton(identity_relation)) subclass(complement(subset_relation),u)* well_ordering(omega,u) -> equal(integer_of(ordered_pair(identity_relation,least(omega,complement(subset_relation)))),identity_relation)**.
% 300.10/300.68  199085[18:Res:193924.1,13362.0] || equal(symmetrization_of(identity_relation),inverse(subset_relation)) subclass(complement(subset_relation),u)* well_ordering(omega,u) -> equal(integer_of(ordered_pair(identity_relation,least(omega,complement(subset_relation)))),identity_relation)**.
% 300.10/300.68  199084[18:Res:193927.1,13362.0] || equal(inverse(subset_relation),inverse(identity_relation)) subclass(complement(subset_relation),u)* well_ordering(omega,u) -> equal(integer_of(ordered_pair(identity_relation,least(omega,complement(subset_relation)))),identity_relation)**.
% 300.10/300.68  199074[8:Res:144409.1,13362.0] || equal(symmetric_difference(ordinal_numbers,u),ordinal_numbers) subclass(complement(u),v)* well_ordering(omega,v) -> equal(integer_of(ordered_pair(omega,least(omega,complement(u)))),identity_relation)**.
% 300.10/300.68  199056[7:Res:39298.1,13362.0] || subclass(ordinal_numbers,complement(complement(u))) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(ordered_pair(w,x),least(omega,u))),identity_relation)**.
% 300.10/300.68  199055[8:Res:117318.1,13362.0] || member(u,cantor(u)) subclass(element_relation,v) well_ordering(omega,v)* -> equal(integer_of(ordered_pair(ordered_pair(u,cantor(u)),least(omega,element_relation))),identity_relation)**.
% 300.10/300.68  199052[7:Res:41112.1,13362.0] || member(u,rest_of(u)) subclass(element_relation,v) well_ordering(omega,v)* -> equal(integer_of(ordered_pair(ordered_pair(u,rest_of(u)),least(omega,element_relation))),identity_relation)**.
% 300.10/300.68  199042[7:Res:967.0,13362.0] || subclass(singleton(singleton(singleton(u))),v)* well_ordering(omega,v) -> equal(integer_of(ordered_pair(singleton(singleton(u)),least(omega,singleton(singleton(singleton(u)))))),identity_relation)**.
% 300.10/300.68  199041[8:Res:163153.1,13362.0] || subclass(ordinal_numbers,symmetrization_of(identity_relation)) subclass(inverse(identity_relation),u)* well_ordering(omega,u) -> equal(integer_of(ordered_pair(singleton(v),least(omega,inverse(identity_relation)))),identity_relation)**.
% 300.10/300.68  199033[7:Res:126679.1,13362.0] || subclass(omega,complement(complement(u))) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(least(element_relation,omega),least(omega,u))),identity_relation)**.
% 300.10/300.68  199032[7:Res:127147.1,13362.0] || subclass(ordinal_numbers,complement(complement(u))) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(least(element_relation,omega),least(omega,u))),identity_relation)**.
% 300.10/300.68  199027[10:Res:80198.1,13362.0] || member(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers) subclass(ordinal_numbers,u) well_ordering(omega,u)* -> equal(integer_of(ordered_pair(least(element_relation,element_relation),least(omega,ordinal_numbers))),identity_relation)**.
% 300.10/300.68  199026[10:Res:76912.1,13362.0] || member(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers) subclass(element_relation,u) well_ordering(omega,u)* -> equal(integer_of(ordered_pair(least(element_relation,element_relation),least(omega,element_relation))),identity_relation)**.
% 300.10/300.68  199025[8:Res:80082.1,13362.0] || member(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers) subclass(ordinal_numbers,u) well_ordering(omega,u)* -> equal(integer_of(ordered_pair(least(element_relation,rest_relation),least(omega,ordinal_numbers))),identity_relation)**.
% 300.10/300.68  199024[8:Res:64007.1,13362.0] || member(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers) subclass(rest_relation,u) well_ordering(omega,u)* -> equal(integer_of(ordered_pair(least(element_relation,rest_relation),least(omega,rest_relation))),identity_relation)**.
% 300.10/300.68  199023[8:Res:17124.1,13362.0] || member(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers) subclass(domain_relation,u) well_ordering(omega,u)* -> equal(integer_of(ordered_pair(least(element_relation,domain_relation),least(omega,domain_relation))),identity_relation)**.
% 300.10/300.68  199012[7:Res:13227.2,13362.0] || subclass(u,v) subclass(v,w)* well_ordering(omega,w)* -> equal(u,identity_relation) equal(integer_of(ordered_pair(regular(u),least(omega,v))),identity_relation)**.
% 300.10/300.68  199011[7:Res:13210.1,13362.0] || subclass(u,v)* well_ordering(omega,v)* -> equal(intersection(w,u),identity_relation) equal(integer_of(ordered_pair(regular(intersection(w,u)),least(omega,u))),identity_relation)**.
% 300.10/300.68  198996[8:Res:41203.1,13362.0] || member(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers) subclass(ordinal_numbers,u) well_ordering(omega,u)* -> equal(integer_of(ordered_pair(least(element_relation,domain_relation),least(omega,ordinal_numbers))),identity_relation)**.
% 300.10/300.68  198979[7:Res:13248.1,13362.0] || subclass(u,v)* well_ordering(omega,v)* -> equal(intersection(u,w),identity_relation) equal(integer_of(ordered_pair(regular(intersection(u,w)),least(omega,u))),identity_relation)**.
% 300.10/300.68  198975[7:Res:40074.1,13362.0] || subclass(ordinal_numbers,complement(complement(u))) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(unordered_pair(w,x),least(omega,u))),identity_relation)**.
% 300.10/300.68  198969[7:Res:13125.2,13362.0] || subclass(omega,u) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(w),identity_relation) equal(integer_of(ordered_pair(w,least(omega,u))),identity_relation)**.
% 300.10/300.68  198964[8:Res:193179.0,13362.0] || subclass(inverse(singleton(u)),v)* well_ordering(omega,v) -> asymmetric(singleton(u),w)* equal(integer_of(ordered_pair(u,least(omega,inverse(singleton(u))))),identity_relation)**.
% 300.10/300.68  198963[7:Res:18819.1,13362.0] || member(u,subset_relation) subclass(cross_product(ordinal_numbers,ordinal_numbers),v)* well_ordering(omega,v) -> equal(integer_of(ordered_pair(u,least(omega,cross_product(ordinal_numbers,ordinal_numbers)))),identity_relation)**.
% 300.10/300.68  198962[8:Res:69184.1,13362.0] || member(u,element_relation) subclass(compose(element_relation,ordinal_numbers),v)* well_ordering(omega,v) -> equal(integer_of(ordered_pair(u,least(omega,compose(element_relation,ordinal_numbers)))),identity_relation)**.
% 300.10/300.68  198961[7:Res:8704.1,13362.0] || member(u,ordinal_numbers) subclass(unordered_pair(v,u),w)* well_ordering(omega,w) -> equal(integer_of(ordered_pair(u,least(omega,unordered_pair(v,u)))),identity_relation)**.
% 300.10/300.68  198960[7:Res:8703.1,13362.0] || member(u,ordinal_numbers) subclass(unordered_pair(u,v),w)* well_ordering(omega,w) -> equal(integer_of(ordered_pair(u,least(omega,unordered_pair(u,v)))),identity_relation)**.
% 300.10/300.68  199122[7:Res:13515.2,5.0] || well_ordering(u,cross_product(ordinal_numbers,ordinal_numbers)) subclass(compose(v,w),x) -> equal(compose(v,w),identity_relation) member(least(u,compose(v,w)),x)*.
% 300.10/300.68  28648[5:SpR:126.0,8826.2] || member(restrict(u,v,singleton(w)),ordinal_numbers) subclass(domain_relation,x) -> member(ordered_pair(restrict(u,v,singleton(w)),segment(u,v,w)),x)*.
% 300.10/300.68  197682[7:Res:13247.2,25.0] || member(intersection(u,intersection(v,w)),ordinal_numbers) -> equal(intersection(u,intersection(v,w)),identity_relation) member(apply(choice,intersection(u,intersection(v,w))),v)*.
% 300.10/300.68  197681[7:Res:13247.2,26.0] || member(intersection(u,intersection(v,w)),ordinal_numbers) -> equal(intersection(u,intersection(v,w)),identity_relation) member(apply(choice,intersection(u,intersection(v,w))),w)*.
% 300.10/300.68  197674[7:Res:13247.2,151988.0] || member(intersection(u,complement(complement(v))),ordinal_numbers) -> equal(intersection(u,complement(complement(v))),identity_relation) member(apply(choice,intersection(u,complement(complement(v)))),v)*.
% 300.10/300.68  197646[8:SpR:116209.1,13247.2] operation(u) || member(intersection(cantor(u),v),ordinal_numbers) -> equal(intersection(cantor(u),v),identity_relation) member(apply(choice,intersection(v,cantor(u))),v)*.
% 300.10/300.68  197394[7:Res:13246.2,25.0] || member(intersection(intersection(u,v),w),ordinal_numbers) -> equal(intersection(intersection(u,v),w),identity_relation) member(apply(choice,intersection(intersection(u,v),w)),u)*.
% 300.10/300.68  197393[7:Res:13246.2,26.0] || member(intersection(intersection(u,v),w),ordinal_numbers) -> equal(intersection(intersection(u,v),w),identity_relation) member(apply(choice,intersection(intersection(u,v),w)),v)*.
% 300.10/300.68  197376[8:SpR:116209.1,13246.2] operation(u) || member(intersection(v,cantor(u)),ordinal_numbers) -> equal(intersection(v,cantor(u)),identity_relation) member(apply(choice,intersection(cantor(u),v)),v)*.
% 300.10/300.68  197386[7:Res:13246.2,151988.0] || member(intersection(complement(complement(u)),v),ordinal_numbers) -> equal(intersection(complement(complement(u)),v),identity_relation) member(apply(choice,intersection(complement(complement(u)),v)),u)*.
% 300.10/300.68  144454[8:Rew:144397.0,142401.2] inductive(symmetric_difference(image(element_relation,complement(u)),ordinal_numbers)) || well_ordering(v,power_class(u)) -> member(least(v,intersection(power_class(u),ordinal_numbers)),intersection(power_class(u),ordinal_numbers))*.
% 300.10/300.68  43734[5:Res:8977.2,8554.1] || member(u,ordinal_numbers) subclass(ordinal_numbers,complement(intersection(v,w))) member(power_class(u),union(v,w)) -> member(power_class(u),symmetric_difference(v,w))*.
% 300.10/300.68  47006[5:Res:8956.1,9421.0] || member(u,ordinal_numbers) member(v,w)* -> equal(ordered_pair(first(ordered_pair(v,power_class(u))),second(ordered_pair(v,power_class(u)))),ordered_pair(v,power_class(u)))**.
% 300.10/300.68  146831[5:Res:8551.2,18535.2] || member(power_class(u),cross_product(v,w))* member(power_class(u),x)* member(u,ordinal_numbers) subclass(ordinal_numbers,complement(restrict(x,v,w)))* -> .
% 300.10/300.68  13318[7:Rew:13036.0,9472.1] || member(ordered_pair(u,regular(complement(image(v,image(w,singleton(u)))))),compose(v,w))* -> equal(complement(image(v,image(w,singleton(u)))),identity_relation).
% 300.10/300.68  163608[5:Res:143200.1,8803.0] || equal(image(u,image(v,singleton(w))),ordinal_numbers) member(ordered_pair(w,omega),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(w,omega),compose(u,v))*.
% 300.10/300.68  192204[7:Res:192149.1,8803.0] || equal(image(u,image(v,singleton(w))),ordinal_numbers) member(ordered_pair(w,identity_relation),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(w,identity_relation),compose(u,v))*.
% 300.10/300.68  10005[5:Res:8646.1,8803.0] || subclass(ordinal_numbers,image(u,image(v,singleton(w))))* member(ordered_pair(w,omega),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(w,omega),compose(u,v)).
% 300.10/300.68  13666[7:Rew:13036.0,13521.2] || subclass(ordinal_numbers,image(u,image(v,singleton(w))))* member(ordered_pair(w,identity_relation),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(w,identity_relation),compose(u,v)).
% 300.10/300.68  19714[0:Rew:72.0,19704.2] || member(image(u,singleton(v)),ordinal_numbers) subclass(image(u,singleton(v)),apply(u,v))* -> equal(image(u,singleton(v)),apply(u,v)).
% 300.10/300.68  155460[5:Res:9006.3,941.1] function(u) || member(v,ordinal_numbers) subclass(ordinal_numbers,power_class(image(element_relation,complement(w)))) member(image(u,v),image(element_relation,power_class(w)))* -> .
% 300.10/300.68  39512[5:SpR:481.0,8832.1] || member(u,ordinal_numbers) -> member(u,intersection(complement(v),power_class(intersection(complement(w),complement(x)))))* member(u,union(v,image(element_relation,union(w,x)))).
% 300.10/300.68  39525[5:SpR:481.0,8832.1] || member(u,ordinal_numbers) -> member(u,intersection(power_class(intersection(complement(v),complement(w))),complement(x)))* member(u,union(image(element_relation,union(v,w)),x)).
% 300.10/300.68  130701[5:Rew:481.0,130621.1] ||  -> member(not_subclass_element(complement(power_class(intersection(complement(u),complement(v)))),w),image(element_relation,union(u,v)))* subclass(complement(power_class(intersection(complement(u),complement(v)))),w).
% 300.10/300.68  159469[5:Rew:189.0,159429.1] ||  -> member(not_subclass_element(u,image(element_relation,power_class(image(element_relation,complement(v))))),power_class(image(element_relation,power_class(v))))* subclass(u,image(element_relation,power_class(image(element_relation,complement(v))))).
% 300.10/300.68  36323[0:SpR:189.0,3616.0] ||  -> equal(intersection(union(u,image(element_relation,power_class(v))),union(complement(u),power_class(image(element_relation,complement(v))))),symmetric_difference(complement(u),power_class(image(element_relation,complement(v)))))**.
% 300.10/300.68  155419[0:Res:303.1,941.1] || member(not_subclass_element(intersection(u,power_class(image(element_relation,complement(v)))),w),image(element_relation,power_class(v)))* -> subclass(intersection(u,power_class(image(element_relation,complement(v)))),w).
% 300.10/300.68  167346[7:Res:13237.2,941.1] || well_ordering(u,ordinal_numbers) member(least(u,power_class(image(element_relation,complement(v)))),image(element_relation,power_class(v)))* -> equal(power_class(image(element_relation,complement(v))),identity_relation).
% 300.10/300.68  36335[0:SpR:189.0,3616.0] ||  -> equal(intersection(union(image(element_relation,power_class(u)),v),union(power_class(image(element_relation,complement(u))),complement(v))),symmetric_difference(power_class(image(element_relation,complement(u))),complement(v)))**.
% 300.10/300.68  155398[0:Res:313.1,941.1] || member(not_subclass_element(intersection(power_class(image(element_relation,complement(u))),v),w),image(element_relation,power_class(u)))* -> subclass(intersection(power_class(image(element_relation,complement(u))),v),w).
% 300.10/300.68  155397[5:Res:41371.0,941.1] || member(not_subclass_element(complement(complement(power_class(image(element_relation,complement(u))))),v),image(element_relation,power_class(u)))* -> subclass(complement(complement(power_class(image(element_relation,complement(u))))),v).
% 300.10/300.68  155435[5:Res:39607.2,941.1] inductive(power_class(image(element_relation,complement(u)))) || well_ordering(v,ordinal_numbers) member(least(v,power_class(image(element_relation,complement(u)))),image(element_relation,power_class(u)))* -> .
% 300.10/300.68  46862[5:Rew:59.0,46855.3] || member(u,v) subclass(v,w)* well_ordering(power_class(x),w)* -> member(ordered_pair(u,least(power_class(x),v)),image(element_relation,complement(x)))*.
% 300.10/300.68  130759[5:Res:130710.0,9633.1] || member(u,ordinal_numbers) well_ordering(v,image(element_relation,complement(w))) -> member(u,power_class(w))* member(least(v,complement(power_class(w))),complement(power_class(w)))*.
% 300.10/300.68  156855[5:MRR:156829.0,8655.0] || member(image(element_relation,complement(u)),ordinal_numbers) -> member(singleton(image(element_relation,complement(u))),power_class(u))* member(singleton(singleton(singleton(image(element_relation,complement(u))))),element_relation)*.
% 300.10/300.68  145901[8:Rew:145758.0,145894.2] operation(cross_product(u,ordinal_numbers)) || subclass(cantor(cantor(cross_product(u,ordinal_numbers))),image(ordinal_numbers,u))* -> equal(cantor(cantor(cross_product(u,ordinal_numbers))),image(ordinal_numbers,u)).
% 300.10/300.68  61467[8:Rew:14756.0,61454.3] || member(ordered_pair(u,v),compose(identity_relation,w))* subclass(range_of(identity_relation),x)* well_ordering(y,x)* -> member(least(y,range_of(identity_relation)),range_of(identity_relation))*.
% 300.10/300.68  64619[8:MRR:64618.3,14676.0] || equal(compose_class(u),domain_relation) member(ordered_pair(v,not_subclass_element(image(u,range_of(identity_relation)),w)),cross_product(ordinal_numbers,ordinal_numbers))* -> subclass(image(u,range_of(identity_relation)),w).
% 300.10/300.68  199102[15:Res:167474.1,13362.0] || subclass(ordinal_numbers,symmetrization_of(identity_relation)) subclass(inverse(identity_relation),u)* well_ordering(omega,u) -> equal(integer_of(ordered_pair(range_of(identity_relation),least(omega,inverse(identity_relation)))),identity_relation)**.
% 300.10/300.68  46687[5:SpL:43.0,9747.0] || member(u,range_of(v))* subclass(rest_of(inverse(v)),w)* well_ordering(x,w)* -> member(least(x,rest_of(inverse(v))),rest_of(inverse(v)))*.
% 300.10/300.68  198782[21:Rew:160429.0,198769.2] function(u) function(v) || subclass(range_of(v),identity_relation) equal(cantor(cantor(w)),cantor(v)) -> compatible(v,w,apply(u,x))*.
% 300.10/300.68  198838[21:Rew:160429.0,198819.1] function(u) || subclass(range_of(u),identity_relation) equal(cantor(cantor(v)),cantor(u)) -> subclass(w,x) compatible(u,v,not_subclass_element(w,x))*.
% 300.10/300.68  198101[21:Rew:160429.0,198087.2] function(u) || member(v,ordinal_numbers) subclass(range_of(u),identity_relation) equal(cantor(cantor(w)),cantor(u)) -> compatible(u,w,power_class(v))*.
% 300.10/300.68  198056[21:Rew:160429.0,198042.2] function(u) || member(v,ordinal_numbers) subclass(range_of(u),identity_relation) equal(cantor(cantor(w)),cantor(u)) -> compatible(u,w,rest_of(v))*.
% 300.10/300.68  198011[21:Rew:160429.0,197997.2] function(u) || member(v,subset_relation) subclass(range_of(u),identity_relation) equal(cantor(cantor(w)),cantor(u)) -> compatible(u,w,second(v))*.
% 300.10/300.68  197962[21:Rew:160429.0,197948.2] function(u) || member(v,subset_relation) subclass(range_of(u),identity_relation) equal(cantor(cantor(w)),cantor(u)) -> compatible(u,w,first(v))*.
% 300.10/300.68  197916[21:Rew:160429.0,197902.2] function(u) || member(v,ordinal_numbers) subclass(range_of(u),identity_relation) equal(cantor(cantor(w)),cantor(u)) -> compatible(u,w,sum_class(v))*.
% 300.10/300.68  197496[21:SpL:196546.1,117602.1] function(u) || subclass(range_of(u),identity_relation) equal(cantor(cantor(v)),cantor(u)) -> equal(singleton(cantor(w)),identity_relation) compatible(u,v,w)*.
% 300.10/300.68  198940[8:Res:161565.3,5.0] operation(u) || well_ordering(v,cantor(cantor(u))) subclass(range_of(u),w) -> equal(range_of(u),identity_relation) member(least(v,range_of(u)),w)*.
% 300.10/300.68  204043[8:Res:192333.1,13362.0] || equal(symmetric_difference(ordinal_numbers,u),ordinal_numbers) subclass(complement(u),v)* well_ordering(omega,v) -> equal(integer_of(ordered_pair(identity_relation,least(omega,complement(u)))),identity_relation)**.
% 300.10/300.68  204628[21:Res:196904.1,8554.1] || subclass(domain_relation,complement(intersection(u,v))) member(singleton(singleton(singleton(identity_relation))),union(u,v)) -> member(singleton(singleton(singleton(identity_relation))),symmetric_difference(u,v))*.
% 300.10/300.68  208138[21:SpL:197474.0,9470.1] || member(ordered_pair(inverse(u),v),compose(w,x))* subclass(image(w,image(x,identity_relation)),y)* -> equal(range_of(u),identity_relation) member(v,y)*.
% 300.10/300.68  208396[24:SpR:207572.1,117604.3] operation(u) operation(v) || member(u,cantor(cantor(v)))* member(identity_relation,cantor(cantor(v))) -> member(singleton(singleton(identity_relation)),cantor(v))*.
% 300.10/300.68  208516[7:SpL:13260.1,49.0] || member(regular(cross_product(u,v)),successor_relation) -> equal(cross_product(u,v),identity_relation) equal(successor(first(regular(cross_product(u,v)))),second(regular(cross_product(u,v))))**.
% 300.10/300.68  208514[8:SpL:13260.1,116160.0] || member(regular(cross_product(u,v)),domain_relation) -> equal(cross_product(u,v),identity_relation) equal(cantor(first(regular(cross_product(u,v)))),second(regular(cross_product(u,v))))**.
% 300.10/300.68  208500[7:SpL:13260.1,149.0] || member(regular(cross_product(u,v)),rest_relation) -> equal(cross_product(u,v),identity_relation) equal(rest_of(first(regular(cross_product(u,v)))),second(regular(cross_product(u,v))))**.
% 300.10/300.68  208624[24:SpR:207572.1,9618.2] operation(compose(u,identity_relation)) || member(ordered_pair(u,identity_relation),cross_product(ordinal_numbers,ordinal_numbers)) subclass(composition_function,v) -> member(ordered_pair(u,singleton(singleton(identity_relation))),v)*.
% 300.10/300.68  209427[25:SpL:208885.0,141.1] || well_ordering(element_relation,image(u,identity_relation)) subclass(apply(u,ordinal_numbers),image(u,identity_relation))* -> equal(image(u,identity_relation),ordinal_numbers) member(image(u,identity_relation),ordinal_numbers).
% 300.10/300.68  209421[25:SpR:208885.0,13504.2] || member(image(u,identity_relation),ordinal_numbers) well_ordering(v,image(u,identity_relation)) -> equal(segment(v,apply(u,ordinal_numbers),least(v,apply(u,ordinal_numbers))),identity_relation)**.
% 300.10/300.68  209635[24:Rew:207558.1,209615.2] operation(u) || member(ordered_pair(u,not_subclass_element(v,image(w,image(x,identity_relation)))),compose(w,x))* -> subclass(v,image(w,image(x,identity_relation))).
% 300.10/300.68  209809[8:Res:206259.0,13113.0] || well_ordering(u,union(v,identity_relation)) -> equal(segment(u,symmetric_difference(complement(v),symmetric_difference(ordinal_numbers,v)),least(u,symmetric_difference(complement(v),symmetric_difference(ordinal_numbers,v)))),identity_relation)**.
% 300.10/300.68  210394[5:Res:9618.2,143186.0] || member(ordered_pair(u,v),cross_product(ordinal_numbers,ordinal_numbers)) subclass(composition_function,symmetric_difference(ordinal_numbers,w)) -> member(ordered_pair(u,ordered_pair(v,compose(u,v))),complement(w))*.
% 300.10/300.68  210430[14:Res:210404.0,13362.0] || subclass(union(u,identity_relation),v)* well_ordering(omega,v) -> member(identity_relation,complement(u)) equal(integer_of(ordered_pair(identity_relation,least(omega,union(u,identity_relation)))),identity_relation)**.
% 300.10/300.68  210503[5:Res:9618.2,143226.0] || member(ordered_pair(u,v),cross_product(ordinal_numbers,ordinal_numbers)) subclass(composition_function,symmetric_difference(ordinal_numbers,w)) member(ordered_pair(u,ordered_pair(v,compose(u,v))),w)* -> .
% 300.10/300.68  211324[8:Res:210606.1,9633.1] || equal(complement(u),ordinal_numbers) member(v,ordinal_numbers)* well_ordering(w,complement(u))* -> member(v,x)* member(least(w,complement(x)),complement(x))*.
% 300.10/300.68  211558[8:Res:211438.1,9633.1] || equal(symmetrization_of(identity_relation),ordinal_numbers) member(u,ordinal_numbers)* well_ordering(v,symmetrization_of(identity_relation)) -> member(u,w)* member(least(v,complement(w)),complement(w))*.
% 300.10/300.68  211642[8:Res:211441.1,9633.1] || equal(power_class(u),ordinal_numbers) member(v,ordinal_numbers)* well_ordering(w,power_class(u))* -> member(v,x)* member(least(w,complement(x)),complement(x))*.
% 300.10/300.68  212409[7:SpL:13259.2,8841.1] || member(cross_product(u,v),ordinal_numbers) subclass(ordinal_numbers,complement(w)) member(apply(choice,cross_product(u,v)),w)* -> equal(cross_product(u,v),identity_relation).
% 300.10/300.68  212363[7:SpR:13259.2,39298.1] || member(cross_product(u,v),ordinal_numbers) subclass(ordinal_numbers,complement(complement(w))) -> equal(cross_product(u,v),identity_relation) member(apply(choice,cross_product(u,v)),w)*.
% 300.10/300.68  212354[7:SpR:13259.2,962.0] || member(cross_product(u,v),ordinal_numbers) -> equal(cross_product(u,v),identity_relation) member(singleton(first(apply(choice,cross_product(u,v)))),apply(choice,cross_product(u,v)))*.
% 300.10/300.68  213469[8:SpR:145761.0,116203.2] function(cross_product(u,singleton(v))) || subclass(range_of(cross_product(u,singleton(v))),w) -> maps(cross_product(u,singleton(v)),segment(ordinal_numbers,u,v),w)*.
% 300.10/300.68  214250[24:SpR:13260.1,207615.1] operation(second(regular(cross_product(u,v)))) ||  -> equal(cross_product(u,v),identity_relation) member(unordered_pair(first(regular(cross_product(u,v))),identity_relation),regular(cross_product(u,v)))*.
% 300.10/300.68  214277[25:SpR:208887.0,116203.2] function(restrict(u,v,identity_relation)) || subclass(range_of(restrict(u,v,identity_relation)),w) -> maps(restrict(u,v,identity_relation),segment(u,v,ordinal_numbers),w)*.
% 300.10/300.68  214472[25:SpR:208985.1,117604.3] operation(u) operation(v) || member(u,cantor(cantor(v)))* member(w,cantor(cantor(v))) -> member(ordered_pair(w,ordinal_numbers),cantor(v))*.
% 300.10/300.68  214469[25:SpR:208985.1,9618.2] operation(compose(u,v)) || member(ordered_pair(u,v),cross_product(ordinal_numbers,ordinal_numbers)) subclass(composition_function,w) -> member(ordered_pair(u,ordered_pair(v,ordinal_numbers)),w)*.
% 300.10/300.68  214466[25:SpR:208985.1,13260.1] operation(second(regular(cross_product(u,v)))) ||  -> equal(cross_product(u,v),identity_relation) equal(ordered_pair(first(regular(cross_product(u,v))),ordinal_numbers),regular(cross_product(u,v)))**.
% 300.10/300.68  214428[25:SpR:208985.1,117604.3] operation(u) operation(v) || member(ordinal_numbers,cantor(cantor(v))) member(w,cantor(cantor(v))) -> member(ordered_pair(w,u),cantor(v))*.
% 300.10/300.68  217301[7:Res:13152.1,9665.1] inductive(regular(recursion_equation_functions(u))) || well_ordering(v,cross_product(ordinal_numbers,ordinal_numbers)) -> equal(recursion_equation_functions(u),identity_relation) member(least(v,regular(recursion_equation_functions(u))),regular(recursion_equation_functions(u)))*.
% 300.10/300.68  217469[8:EmS:13166.0,13166.1,10858.2,211494.1] single_valued_class(union(u,v)) || equal(union(u,v),cross_product(ordinal_numbers,ordinal_numbers))** equal(union(u,v),ordinal_numbers) -> member(identity_relation,cross_product(ordinal_numbers,ordinal_numbers))*.
% 300.10/300.68  217517[7:Res:61019.0,13362.0] || subclass(u,v)* well_ordering(omega,v)* -> equal(complement(complement(u)),identity_relation) equal(integer_of(ordered_pair(regular(complement(complement(u))),least(omega,u))),identity_relation)**.
% 300.10/300.68  217903[21:SpR:217890.0,116203.2] function(regular(complement(complement(symmetrization_of(identity_relation))))) || subclass(range_of(regular(complement(complement(symmetrization_of(identity_relation))))),u) -> maps(regular(complement(complement(symmetrization_of(identity_relation)))),identity_relation,u)*.
% 300.10/300.68  218267[8:Res:116127.5,217144.1] operation(u) operation(v) || compatible(w,v,u) subclass(cantor(v),x)* equal(identity_relation,x) -> homomorphism(w,v,u)*.
% 300.10/300.68  218519[21:Rew:218460.1,218468.2] || equal(rest_relation,domain_relation) member(omega,recursion_equation_functions(u)) member(ordered_pair(u,identity_relation),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(u,ordered_pair(identity_relation,omega)),composition_function)*.
% 300.10/300.68  219229[8:Res:116127.5,219073.1] operation(u) operation(v) || compatible(w,v,u) subclass(cantor(v),x)* subclass(x,identity_relation) -> homomorphism(w,v,u)*.
% 300.10/300.68  219456[7:Res:9461.1,13113.0] || well_ordering(u,cross_product(ordinal_numbers,ordinal_numbers)) -> subclass(recursion_equation_functions(v),w) equal(segment(u,not_subclass_element(recursion_equation_functions(v),w),least(u,not_subclass_element(recursion_equation_functions(v),w))),identity_relation)**.
% 300.10/300.68  221175[8:MRR:221152.1,162891.0] || well_ordering(u,ordered_pair(v,w)) -> equal(least(u,ordered_pair(v,w)),unordered_pair(v,singleton(w)))** equal(least(u,ordered_pair(v,w)),singleton(v)).
% 300.10/300.68  222527[8:Res:217645.1,13362.0] || equal(complement(symmetrization_of(identity_relation)),identity_relation) subclass(inverse(identity_relation),u)* well_ordering(omega,u) -> equal(integer_of(ordered_pair(omega,least(omega,inverse(identity_relation)))),identity_relation)**.
% 300.10/300.68  223766[8:SpR:160927.0,8832.1] || member(u,ordinal_numbers) -> member(u,intersection(complement(v),union(w,symmetric_difference(ordinal_numbers,x))))* member(u,union(v,intersection(complement(w),union(x,identity_relation)))).
% 300.10/300.68  223750[8:SpR:160927.0,8832.1] || member(u,ordinal_numbers) -> member(u,intersection(union(v,symmetric_difference(ordinal_numbers,w)),complement(x)))* member(u,union(intersection(complement(v),union(w,identity_relation)),x)).
% 300.10/300.68  224084[8:SpR:160992.0,8832.1] || member(u,ordinal_numbers) -> member(u,intersection(complement(v),union(symmetric_difference(ordinal_numbers,w),x)))* member(u,union(v,intersection(union(w,identity_relation),complement(x)))).
% 300.10/300.68  224067[8:SpR:160992.0,8832.1] || member(u,ordinal_numbers) -> member(u,intersection(union(symmetric_difference(ordinal_numbers,v),w),complement(x)))* member(u,union(intersection(union(v,identity_relation),complement(w)),x)).
% 300.10/300.68  224283[8:Res:3618.1,18750.0] || member(regular(regular(complement(intersection(u,v)))),symmetric_difference(u,v))* -> equal(regular(complement(intersection(u,v))),identity_relation) equal(complement(intersection(u,v)),identity_relation).
% 300.10/300.68  224331[8:MRR:224306.2,218277.1] || member(ordered_pair(u,regular(regular(image(v,image(w,singleton(u)))))),compose(v,w))* -> equal(regular(image(v,image(w,singleton(u)))),identity_relation).
% 300.10/300.68  224784[26:Res:224684.1,8803.0] || subclass(omega,image(u,image(v,singleton(w))))* member(ordered_pair(w,identity_relation),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(w,identity_relation),compose(u,v)).
% 300.10/300.68  225916[26:Res:225794.1,8803.0] || equal(image(u,image(v,singleton(w))),omega) member(ordered_pair(w,identity_relation),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(w,identity_relation),compose(u,v))*.
% 300.10/300.68  226046[7:Res:13578.1,129.0] || subclass(union(u,v),w)* well_ordering(x,w)* -> equal(symmetric_difference(u,v),identity_relation) member(least(x,union(u,v)),union(u,v))*.
% 300.10/300.68  226395[7:Res:13258.1,490.0] || member(regular(restrict(intersection(complement(u),complement(v)),w,x)),union(u,v))* -> equal(restrict(intersection(complement(u),complement(v)),w,x),identity_relation).
% 300.10/300.68  227218[8:Res:217451.1,13362.0] || equal(union(u,identity_relation),identity_relation) subclass(complement(u),v)* well_ordering(omega,v) -> equal(integer_of(ordered_pair(identity_relation,least(omega,complement(u)))),identity_relation)**.
% 300.10/300.68  227295[5:Rew:61728.2,227270.4] || member(u,ordinal_numbers) subclass(rest_relation,union_of_range_map) member(range_of(u),ordinal_numbers) subclass(range_of(u),rest_of(u))* -> equal(range_of(u),rest_of(u)).
% 300.10/300.68  227337[7:SpR:192979.1,62.1] || member(ordered_pair(u,v),compose(w,regular(cross_product(singleton(u),ordinal_numbers))))* -> equal(cross_product(singleton(u),ordinal_numbers),identity_relation) member(v,image(w,range_of(identity_relation))).
% 300.10/300.68  227457[8:Res:217663.1,13362.0] || equal(union(u,identity_relation),identity_relation) subclass(complement(u),v)* well_ordering(omega,v) -> equal(integer_of(ordered_pair(omega,least(omega,complement(u)))),identity_relation)**.
% 300.10/300.68  228908[8:MRR:228878.3,218134.1] || member(apply(choice,regular(union(u,v))),ordinal_numbers) -> member(apply(choice,regular(union(u,v))),complement(v))* equal(regular(union(u,v)),identity_relation).
% 300.10/300.68  228909[8:MRR:228877.3,218133.1] || member(apply(choice,regular(union(u,v))),ordinal_numbers) -> member(apply(choice,regular(union(u,v))),complement(u))* equal(regular(union(u,v)),identity_relation).
% 300.10/300.68  228910[8:MRR:228873.3,218130.2] || member(apply(choice,regular(intersection(u,v))),v)* member(apply(choice,regular(intersection(u,v))),u)* -> equal(regular(intersection(u,v)),identity_relation).
% 300.10/300.68  229219[7:Rew:3594.0,229114.1] || member(regular(symmetric_difference(complement(intersection(u,v)),union(u,v))),symmetric_difference(u,v))* -> equal(symmetric_difference(complement(intersection(u,v)),union(u,v)),identity_relation).
% 300.10/300.68  231838[8:MRR:231786.3,218130.2] || member(not_subclass_element(regular(intersection(u,v)),w),v)* member(not_subclass_element(regular(intersection(u,v)),w),u)* -> subclass(regular(intersection(u,v)),w).
% 300.10/300.68  233028[8:Res:52.1,69182.0] inductive(complement(compose(element_relation,ordinal_numbers))) || member(regular(image(successor_relation,complement(compose(element_relation,ordinal_numbers)))),element_relation)* -> equal(image(successor_relation,complement(compose(element_relation,ordinal_numbers))),identity_relation).
% 300.10/300.68  233203[7:Rew:189.0,233185.1] || member(regular(image(element_relation,power_class(image(element_relation,complement(u))))),power_class(image(element_relation,power_class(u))))* -> equal(image(element_relation,power_class(image(element_relation,complement(u)))),identity_relation).
% 300.10/300.68  233551[21:Res:62.1,196424.2] || member(ordered_pair(u,ordered_pair(v,identity_relation)),compose(w,x))* member(v,ordinal_numbers) subclass(domain_relation,complement(image(w,image(x,singleton(u))))) -> .
% 300.10/300.68  233739[25:Res:233380.0,13362.0] || subclass(complement(singleton(ordered_pair(ordinal_numbers,u))),v)* well_ordering(omega,v) -> equal(integer_of(ordered_pair(identity_relation,least(omega,complement(singleton(ordered_pair(ordinal_numbers,u)))))),identity_relation)**.
% 300.10/300.68  233811[7:Res:13225.3,941.1] || member(u,ordinal_numbers) subclass(u,power_class(image(element_relation,complement(v)))) member(apply(choice,u),image(element_relation,power_class(v)))* -> equal(u,identity_relation).
% 300.10/300.68  233964[8:Res:9006.3,161200.0] function(u) || member(v,ordinal_numbers) subclass(ordinal_numbers,image(element_relation,union(w,identity_relation))) member(image(u,v),power_class(symmetric_difference(ordinal_numbers,w)))* -> .
% 300.10/300.68  233944[8:Res:39607.2,161200.0] inductive(image(element_relation,union(u,identity_relation))) || well_ordering(v,ordinal_numbers) member(least(v,image(element_relation,union(u,identity_relation))),power_class(symmetric_difference(ordinal_numbers,u)))* -> .
% 300.10/300.68  233936[8:Res:13237.2,161200.0] || well_ordering(u,ordinal_numbers) member(least(u,image(element_relation,union(v,identity_relation))),power_class(symmetric_difference(ordinal_numbers,v)))* -> equal(image(element_relation,union(v,identity_relation)),identity_relation).
% 300.10/300.68  233933[8:Res:13225.3,161200.0] || member(u,ordinal_numbers) subclass(u,image(element_relation,union(v,identity_relation))) member(apply(choice,u),power_class(symmetric_difference(ordinal_numbers,v)))* -> equal(u,identity_relation).
% 300.10/300.68  233928[8:Res:303.1,161200.0] || member(not_subclass_element(intersection(u,image(element_relation,union(v,identity_relation))),w),power_class(symmetric_difference(ordinal_numbers,v)))* -> subclass(intersection(u,image(element_relation,union(v,identity_relation))),w).
% 300.10/300.68  233911[8:Res:313.1,161200.0] || member(not_subclass_element(intersection(image(element_relation,union(u,identity_relation)),v),w),power_class(symmetric_difference(ordinal_numbers,u)))* -> subclass(intersection(image(element_relation,union(u,identity_relation)),v),w).
% 300.10/300.68  234168[7:Rew:189.0,234157.2] || subclass(omega,image(element_relation,power_class(u))) -> equal(integer_of(not_subclass_element(power_class(image(element_relation,complement(u))),v)),identity_relation)** subclass(power_class(image(element_relation,complement(u))),v).
% 300.10/300.68  234904[8:MRR:234823.3,234815.1] || member(apply(choice,regular(cantor(u))),ordinal_numbers) -> equal(apply(u,apply(choice,regular(cantor(u)))),sum_class(range_of(identity_relation)))** equal(regular(cantor(u)),identity_relation).
% 300.10/300.68  235297[8:Res:230445.1,131.3] || member(ordered_pair(u,least(union(v,identity_relation),w)),v)* member(u,w) subclass(w,x)* well_ordering(union(v,identity_relation),x)* -> .
% 300.10/300.68  235267[8:Res:230445.1,13362.0] || member(u,v) subclass(union(v,identity_relation),w)* well_ordering(omega,w) -> equal(integer_of(ordered_pair(u,least(omega,union(v,identity_relation)))),identity_relation)**.
% 300.10/300.68  235586[5:Res:28979.1,131.3] || subclass(rest_relation,rotate(u)) member(ordered_pair(v,rest_of(ordered_pair(least(u,w),v))),w)* subclass(w,x)* well_ordering(u,x)* -> .
% 300.10/300.68  235696[21:Res:196904.1,36719.1] operation(u) || subclass(domain_relation,cantor(u))* -> equal(ordered_pair(first(singleton(singleton(singleton(identity_relation)))),second(singleton(singleton(singleton(identity_relation))))),singleton(singleton(singleton(identity_relation))))**.
% 300.10/300.68  235959[7:Res:69478.2,13571.0] || subclass(omega,symmetric_difference(u,v)) -> equal(integer_of(regular(intersection(w,complement(union(u,v))))),identity_relation)** equal(intersection(w,complement(union(u,v))),identity_relation).
% 300.10/300.68  235958[7:Res:69478.2,17387.0] || subclass(omega,symmetric_difference(u,v)) -> equal(integer_of(regular(intersection(complement(union(u,v)),w))),identity_relation)** equal(intersection(complement(union(u,v)),w),identity_relation).
% 300.10/300.68  235927[8:Res:69478.2,18754.1] || subclass(omega,symmetric_difference(u,v)) subclass(ordinal_numbers,regular(union(u,v)))* -> equal(integer_of(unordered_pair(w,x)),identity_relation)** equal(union(u,v),identity_relation).
% 300.10/300.68  236118[5:Rew:50855.1,236081.1] || member(singleton(u),subset_relation) -> subclass(symmetric_difference(first(singleton(u)),u),v) member(not_subclass_element(symmetric_difference(first(singleton(u)),u),v),successor(first(singleton(u))))*.
% 300.10/300.68  236984[26:Res:225888.1,13362.0] || equal(symmetric_difference(ordinal_numbers,u),omega) subclass(complement(u),v)* well_ordering(omega,v) -> equal(integer_of(ordered_pair(identity_relation,least(omega,complement(u)))),identity_relation)**.
% 300.10/300.68  41088[0:SpL:3616.0,8559.2] || member(u,union(complement(v),complement(w)))* member(u,union(v,w)) subclass(symmetric_difference(complement(v),complement(w)),x)* -> member(u,x)*.
% 300.10/300.68  48638[0:Rew:3594.0,48485.0] ||  -> subclass(symmetric_difference(complement(intersection(u,v)),union(u,v)),w) member(not_subclass_element(symmetric_difference(complement(intersection(u,v)),union(u,v)),w),complement(symmetric_difference(u,v)))*.
% 300.10/300.68  43737[0:Res:2503.2,8554.1] || subclass(u,complement(intersection(v,w))) member(not_subclass_element(u,x),union(v,w)) -> subclass(u,x) member(not_subclass_element(u,x),symmetric_difference(v,w))*.
% 300.10/300.68  18911[0:Res:303.1,12.0] ||  -> subclass(intersection(u,unordered_pair(v,w)),x) equal(not_subclass_element(intersection(u,unordered_pair(v,w)),x),w)** equal(not_subclass_element(intersection(u,unordered_pair(v,w)),x),v)**.
% 300.10/300.68  19030[0:Res:313.1,12.0] ||  -> subclass(intersection(unordered_pair(u,v),w),x) equal(not_subclass_element(intersection(unordered_pair(u,v),w),x),v)** equal(not_subclass_element(intersection(unordered_pair(u,v),w),x),u)**.
% 300.10/300.68  49621[0:SpR:6355.1,964.0] ||  -> subclass(cross_product(u,v),w) member(unordered_pair(first(not_subclass_element(cross_product(u,v),w)),singleton(second(not_subclass_element(cross_product(u,v),w)))),not_subclass_element(cross_product(u,v),w))*.
% 300.10/300.68  50863[5:Res:49995.1,21.0] || member(cross_product(u,v),subset_relation) -> equal(ordered_pair(first(singleton(first(cross_product(u,v)))),second(singleton(first(cross_product(u,v))))),singleton(first(cross_product(u,v))))**.
% 300.10/300.68  51517[5:Res:51313.1,3689.0] || member(singleton(ordered_pair(u,v)),subset_relation)* -> equal(first(singleton(ordered_pair(u,v))),unordered_pair(u,singleton(v))) equal(first(singleton(ordered_pair(u,v))),singleton(u)).
% 300.10/300.68  130656[5:Res:41371.0,12.0] ||  -> subclass(complement(complement(unordered_pair(u,v))),w) equal(not_subclass_element(complement(complement(unordered_pair(u,v))),w),v)** equal(not_subclass_element(complement(complement(unordered_pair(u,v))),w),u)**.
% 300.10/300.68  132310[5:Res:130703.0,9665.1] inductive(complement(union(u,v))) || well_ordering(w,intersection(complement(u),complement(v))) -> member(least(w,complement(union(u,v))),complement(union(u,v)))*.
% 300.10/300.68  152205[0:Res:8551.2,19111.1] || member(not_subclass_element(u,v),cross_product(w,x))* member(not_subclass_element(u,v),y)* subclass(u,complement(restrict(y,w,x)))* -> subclass(u,v).
% 300.10/300.68  153351[0:Res:919.1,490.0] || member(not_subclass_element(restrict(intersection(complement(u),complement(v)),w,x),y),union(u,v))* -> subclass(restrict(intersection(complement(u),complement(v)),w,x),y).
% 300.10/300.68  155812[8:Rew:155653.0,155670.4,155653.0,155670.1] || member(ordinal_numbers,cantor(subset_relation)) equal(least(rest_of(subset_relation),u),subset_relation)** member(ordinal_numbers,u) subclass(u,v)* well_ordering(rest_of(subset_relation),v)* -> .
% 300.10/300.68  156484[5:Res:156404.0,9665.1] inductive(symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers))) || well_ordering(u,complement(subset_relation)) -> member(least(u,symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers))),symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers)))*.
% 300.10/300.68  156593[5:Res:156513.0,9665.1] inductive(symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation)) || well_ordering(u,complement(subset_relation)) -> member(least(u,symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation)),symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation))*.
% 300.10/300.68  156920[8:Res:156893.0,9636.2] || member(u,inverse(subset_relation))* member(u,v)* well_ordering(w,complement(subset_relation)) -> member(least(w,intersection(v,inverse(subset_relation))),intersection(v,inverse(subset_relation)))*.
% 300.10/300.68  156929[8:Res:156904.0,9665.1] inductive(restrict(inverse(subset_relation),u,v)) || well_ordering(w,complement(subset_relation)) -> member(least(w,restrict(inverse(subset_relation),u,v)),restrict(inverse(subset_relation),u,v))*.
% 300.10/300.68  156974[8:Res:156922.1,8562.0] || member(not_subclass_element(u,intersection(v,complement(subset_relation))),inverse(subset_relation))* member(not_subclass_element(u,intersection(v,complement(subset_relation))),v)* -> subclass(u,intersection(v,complement(subset_relation))).
% 300.10/300.68  157050[8:Res:157013.0,9636.2] || member(u,v)* member(u,inverse(subset_relation))* well_ordering(w,complement(subset_relation)) -> member(least(w,intersection(inverse(subset_relation),v)),intersection(inverse(subset_relation),v))*.
% 300.10/300.68  117707[8:Rew:116078.0,116843.2] operation(u) || member(singleton(cantor(u)),subset_relation) -> equal(ordered_pair(first(first(singleton(cantor(u)))),second(first(singleton(cantor(u))))),first(singleton(cantor(u))))**.
% 300.10/300.68  117695[8:Rew:116078.0,116542.3,116078.0,116542.2,116078.0,116542.2,116078.0,116542.1] operation(u) || member(v,cantor(cantor(u)))* member(w,cantor(cantor(u)))* subclass(cantor(u),x)* -> member(ordered_pair(w,v),x)*.
% 300.10/300.68  117696[8:Rew:116078.0,116555.4,116078.0,116555.3,116078.0,116555.2,116078.0,116555.2] operation(u) || member(v,subset_relation) member(second(v),cantor(cantor(u)))* member(first(v),cantor(cantor(u))) -> member(v,cantor(u)).
% 300.10/300.68  161735[8:Rew:69395.0,69786.2,160480.0,69786.2] inductive(symmetric_difference(intersection(u,ordinal_numbers),identity_relation)) || well_ordering(v,complement(symmetric_difference(u,ordinal_numbers))) -> member(least(v,complement(symmetric_difference(u,ordinal_numbers))),complement(symmetric_difference(u,ordinal_numbers)))*.
% 300.10/300.68  161688[8:Rew:116078.0,46417.4,116078.0,46417.2,116078.0,46417.1,116078.0,46417.1] operation(u) || member(v,cantor(cantor(u)))* subclass(cantor(u),w)* well_ordering(x,w)* -> member(least(x,cantor(u)),cantor(u))*.
% 300.10/300.68  161706[8:Rew:160491.0,140840.1] inductive(symmetric_difference(complement(intersection(ordinal_numbers,u)),ordinal_numbers)) || well_ordering(v,union(u,identity_relation)) -> member(least(v,symmetric_difference(complement(u),ordinal_numbers)),symmetric_difference(complement(u),ordinal_numbers))*.
% 300.10/300.68  13255[7:Rew:13036.0,13035.0] ||  -> equal(restrict(u,v,w),identity_relation) equal(ordered_pair(first(regular(restrict(u,v,w))),second(regular(restrict(u,v,w)))),regular(restrict(u,v,w)))**.
% 300.10/300.68  60990[7:Res:13072.1,8554.1] || member(regular(complement(intersection(u,v))),union(u,v)) -> equal(complement(intersection(u,v)),identity_relation) member(regular(complement(intersection(u,v))),symmetric_difference(u,v))*.
% 300.10/300.68  62114[8:Res:19172.1,9822.1] || equal(restrict(u,v,v),identity_relation) transitive(u,v) -> equal(compose(restrict(u,v,v),restrict(u,v,v)),restrict(u,v,v))**.
% 300.10/300.68  69521[7:Res:13125.2,8562.0] || subclass(omega,u) member(not_subclass_element(v,intersection(w,u)),w)* -> equal(integer_of(not_subclass_element(v,intersection(w,u))),identity_relation) subclass(v,intersection(w,u)).
% 300.10/300.68  19845[7:Res:3652.1,13113.0] || section(u,singleton(v),w) well_ordering(x,singleton(v)) -> equal(segment(x,segment(u,w,v),least(x,segment(u,w,v))),identity_relation)**.
% 300.10/300.68  161712[8:Rew:140613.0,67618.3] || member(u,v) subclass(v,w)* well_ordering(union(x,identity_relation),w)* -> member(ordered_pair(u,least(union(x,identity_relation),v)),symmetric_difference(ordinal_numbers,x))*.
% 300.10/300.68  165301[7:Res:130703.0,13070.0] || well_ordering(u,intersection(complement(v),complement(w))) -> equal(complement(union(v,w)),identity_relation) member(least(u,complement(union(v,w))),complement(union(v,w)))*.
% 300.10/300.68  165291[8:Res:156904.0,13070.0] || well_ordering(u,complement(subset_relation)) -> equal(restrict(inverse(subset_relation),v,w),identity_relation) member(least(u,restrict(inverse(subset_relation),v,w)),restrict(inverse(subset_relation),v,w))*.
% 300.10/300.68  165288[7:Res:156513.0,13070.0] || well_ordering(u,complement(subset_relation)) -> equal(symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation),identity_relation) member(least(u,symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation)),symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation))*.
% 300.10/300.68  165287[7:Res:156404.0,13070.0] || well_ordering(u,complement(subset_relation)) -> equal(symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers)),identity_relation) member(least(u,symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers))),symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers)))*.
% 300.10/300.68  132234[2:Res:39609.2,12.0] inductive(unordered_pair(u,v)) || well_ordering(w,unordered_pair(u,v)) -> equal(least(w,unordered_pair(u,v)),v)** equal(least(w,unordered_pair(u,v)),u)**.
% 300.10/300.68  42245[5:MRR:42240.1,41096.1] || member(least(successor_relation,u),ordinal_numbers)* equal(successor(v),least(successor_relation,u))* member(v,u)* subclass(u,w)* well_ordering(successor_relation,w)* -> .
% 300.10/300.68  148898[8:Res:148858.1,9633.1] || subclass(complement(u),inverse(subset_relation)) member(v,ordinal_numbers)* well_ordering(w,complement(subset_relation)) -> member(v,u)* member(least(w,complement(u)),complement(u))*.
% 300.10/300.68  148896[8:Res:148858.1,9639.1] || subclass(unordered_pair(u,v),inverse(subset_relation)) member(v,ordinal_numbers) well_ordering(w,complement(subset_relation)) -> member(least(w,unordered_pair(u,v)),unordered_pair(u,v))*.
% 300.10/300.68  134720[8:Res:116403.2,129.0] || member(u,ordinal_numbers)* subclass(rest_relation,rest_of(v)) subclass(cantor(v),w)* well_ordering(x,w)* -> member(least(x,cantor(v)),cantor(v))*.
% 300.10/300.68  148894[8:Res:148858.1,9640.1] || subclass(unordered_pair(u,v),inverse(subset_relation)) member(u,ordinal_numbers) well_ordering(w,complement(subset_relation)) -> member(least(w,unordered_pair(u,v)),unordered_pair(u,v))*.
% 300.10/300.68  153485[8:Res:153473.0,9633.1] || member(u,ordinal_numbers) well_ordering(v,complement(element_relation)) -> member(u,compose(element_relation,ordinal_numbers))* member(least(v,complement(compose(element_relation,ordinal_numbers))),complement(compose(element_relation,ordinal_numbers)))*.
% 300.10/300.68  157064[8:Res:157036.0,9633.1] || member(u,ordinal_numbers) well_ordering(v,complement(subset_relation)) -> member(u,complement(inverse(subset_relation)))* member(least(v,complement(complement(inverse(subset_relation)))),complement(complement(inverse(subset_relation))))*.
% 300.10/300.68  46618[5:Res:9618.2,129.0] || member(ordered_pair(u,v),cross_product(ordinal_numbers,ordinal_numbers))* subclass(composition_function,w) subclass(w,x)* well_ordering(y,x)* -> member(least(y,w),w)*.
% 300.10/300.68  46619[5:Res:9618.2,5.0] || member(ordered_pair(u,v),cross_product(ordinal_numbers,ordinal_numbers)) subclass(composition_function,w)* subclass(w,x)* -> member(ordered_pair(u,ordered_pair(v,compose(u,v))),x)*.
% 300.10/300.68  117697[8:Rew:116078.0,116601.3,116078.0,116601.2] operation(u) || member(ordered_pair(v,w),cross_product(ordinal_numbers,ordinal_numbers)) subclass(composition_function,cantor(u)) -> member(ordered_pair(w,compose(v,w)),cantor(cantor(u)))*.
% 300.10/300.68  46635[5:Res:9618.2,3617.0] || member(ordered_pair(u,v),cross_product(ordinal_numbers,ordinal_numbers)) subclass(composition_function,symmetric_difference(w,x)) -> member(ordered_pair(u,ordered_pair(v,compose(u,v))),union(w,x))*.
% 300.10/300.68  57178[5:Res:9618.2,19676.0] || member(ordered_pair(u,v),cross_product(ordinal_numbers,ordinal_numbers)) subclass(composition_function,symmetric_difference(w,inverse(w)))* -> member(ordered_pair(u,ordered_pair(v,compose(u,v))),symmetrization_of(w))*.
% 300.10/300.68  57111[5:Res:9618.2,19559.0] || member(ordered_pair(u,v),cross_product(ordinal_numbers,ordinal_numbers)) subclass(composition_function,symmetric_difference(w,singleton(w)))* -> member(ordered_pair(u,ordered_pair(v,compose(u,v))),successor(w))*.
% 300.10/300.68  69160[8:Res:9618.2,66086.1] || member(ordered_pair(u,v),cross_product(ordinal_numbers,ordinal_numbers)) subclass(composition_function,complement(compose(element_relation,ordinal_numbers))) member(ordered_pair(u,ordered_pair(v,compose(u,v))),element_relation)* -> .
% 300.10/300.68  194507[8:Res:163112.0,131.3] || member(u,v) subclass(v,w)* well_ordering(complement(inverse(identity_relation)),w)* -> subclass(singleton(ordered_pair(u,least(complement(inverse(identity_relation)),v))),symmetrization_of(identity_relation))*.
% 300.10/300.68  195643[16:Rew:195224.0,195216.3] || member(u,v) subclass(v,w)* well_ordering(complement(singleton(identity_relation)),w)* -> subclass(singleton(ordered_pair(u,least(complement(singleton(identity_relation)),v))),singleton(identity_relation))*.
% 300.10/300.68  196326[8:SpR:161356.2,161356.2] || member(u,ordinal_numbers) member(v,ordinal_numbers) -> member(u,cantor(w)) member(v,cantor(x)) equal(range__dfg(w,u,ordinal_numbers),range__dfg(x,v,ordinal_numbers))*.
% 300.10/300.68  196331[8:Rew:15663.0,196322.3] || member(u,ordinal_numbers) member(not_subclass_element(identity_relation,identity_relation),subset_relation) -> member(u,cantor(v)) equal(ordered_pair(single_valued3(identity_relation),range__dfg(v,u,ordinal_numbers)),not_subclass_element(identity_relation,identity_relation))**.
% 300.10/300.68  199096[14:Res:165177.0,13362.0] || subclass(symmetric_difference(ordinal_numbers,u),v)* well_ordering(omega,v) -> member(identity_relation,union(u,identity_relation)) equal(integer_of(ordered_pair(identity_relation,least(omega,symmetric_difference(ordinal_numbers,u)))),identity_relation)**.
% 300.10/300.68  199078[7:Res:2504.1,13362.0] || subclass(ordered_pair(u,v),w) subclass(w,x)* well_ordering(omega,x)* -> equal(integer_of(ordered_pair(unordered_pair(u,singleton(v)),least(omega,w))),identity_relation)**.
% 300.10/300.68  199017[7:Res:13237.2,13362.0] || well_ordering(u,ordinal_numbers) subclass(v,w)* well_ordering(omega,w)* -> equal(v,identity_relation) equal(integer_of(ordered_pair(least(u,v),least(omega,v))),identity_relation)**.
% 300.10/300.68  199009[7:Res:8978.2,13362.0] || member(u,ordinal_numbers) subclass(ordinal_numbers,v) subclass(v,w)* well_ordering(omega,w)* -> equal(integer_of(ordered_pair(sum_class(u),least(omega,v))),identity_relation)**.
% 300.10/300.68  199008[7:Res:303.1,13362.0] || subclass(u,v)* well_ordering(omega,v)* -> subclass(intersection(w,u),x) equal(integer_of(ordered_pair(not_subclass_element(intersection(w,u),x),least(omega,u))),identity_relation)**.
% 300.10/300.68  199007[7:Res:2503.2,13362.0] || subclass(u,v) subclass(v,w)* well_ordering(omega,w)* -> subclass(u,x) equal(integer_of(ordered_pair(not_subclass_element(u,x),least(omega,v))),identity_relation)**.
% 300.10/300.68  198974[7:Res:313.1,13362.0] || subclass(u,v)* well_ordering(omega,v)* -> subclass(intersection(u,w),x) equal(integer_of(ordered_pair(not_subclass_element(intersection(u,w),x),least(omega,u))),identity_relation)**.
% 300.10/300.68  198973[7:Res:41371.0,13362.0] || subclass(u,v)* well_ordering(omega,v)* -> subclass(complement(complement(u)),w) equal(integer_of(ordered_pair(not_subclass_element(complement(complement(u)),w),least(omega,u))),identity_relation)**.
% 300.10/300.68  198953[8:Res:163112.0,13362.0] || subclass(complement(inverse(identity_relation)),u)* well_ordering(omega,u) -> subclass(singleton(v),symmetrization_of(identity_relation)) equal(integer_of(ordered_pair(v,least(omega,complement(inverse(identity_relation))))),identity_relation)**.
% 300.10/300.68  198950[7:Res:8700.2,13362.0] || member(u,ordinal_numbers) subclass(complement(v),w)* well_ordering(omega,w) -> member(u,v) equal(integer_of(ordered_pair(u,least(omega,complement(v)))),identity_relation)**.
% 300.10/300.68  116474[8:Rew:116078.0,51471.3] operation(u) operation(v) || compatible(w,v,u) subclass(cantor(v),x)* subclass(ordinal_numbers,complement(x)) -> homomorphism(w,v,u)*.
% 300.10/300.68  46973[0:Res:62.1,9421.0] || member(ordered_pair(u,v),compose(w,x))* member(y,z)* -> equal(ordered_pair(first(ordered_pair(y,v)),second(ordered_pair(y,v))),ordered_pair(y,v))**.
% 300.10/300.68  198980[7:Res:13069.2,13362.0] || member(u,ordinal_numbers) subclass(u,v)* well_ordering(omega,v)* -> equal(u,identity_relation) equal(integer_of(ordered_pair(apply(choice,u),least(omega,u))),identity_relation)**.
% 300.10/300.68  197444[7:Rew:155665.0,197354.1,155665.0,197354.0] || member(symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers)),ordinal_numbers) -> equal(symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers)),identity_relation) member(apply(choice,symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers))),complement(subset_relation))*.
% 300.10/300.68  197443[7:Rew:155666.0,197355.1,155666.0,197355.0] || member(symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation),ordinal_numbers) -> equal(symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation),identity_relation) member(apply(choice,symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation)),complement(subset_relation))*.
% 300.10/300.68  197709[8:Res:13247.2,14681.0] || member(intersection(u,regular(v)),ordinal_numbers) member(apply(choice,intersection(u,regular(v))),v)* -> equal(intersection(u,regular(v)),identity_relation) equal(v,identity_relation).
% 300.10/300.68  197358[8:SpR:116209.1,13246.2] operation(u) || member(intersection(cantor(u),v),ordinal_numbers) -> equal(intersection(cantor(u),v),identity_relation) member(apply(choice,intersection(v,cantor(u))),cantor(u))*.
% 300.10/300.68  197420[8:Res:13246.2,14681.0] || member(intersection(regular(u),v),ordinal_numbers) member(apply(choice,intersection(regular(u),v)),u)* -> equal(intersection(regular(u),v),identity_relation) equal(u,identity_relation).
% 300.10/300.68  197664[8:SpR:116209.1,13247.2] operation(u) || member(intersection(v,cantor(u)),ordinal_numbers) -> equal(intersection(v,cantor(u)),identity_relation) member(apply(choice,intersection(cantor(u),v)),cantor(u))*.
% 300.10/300.68  199010[7:Res:8977.2,13362.0] || member(u,ordinal_numbers) subclass(ordinal_numbers,v) subclass(v,w)* well_ordering(omega,w)* -> equal(integer_of(ordered_pair(power_class(u),least(omega,v))),identity_relation)**.
% 300.10/300.68  12946[0:Res:62.1,290.0] || member(ordered_pair(u,not_subclass_element(complement(image(v,image(w,singleton(u)))),x)),compose(v,w))* -> subclass(complement(image(v,image(w,singleton(u)))),x).
% 300.10/300.68  195402[16:Rew:195224.0,194672.1] || member(power_class(complement(singleton(identity_relation))),ordinal_numbers) member(apply(choice,power_class(complement(singleton(identity_relation)))),image(element_relation,singleton(identity_relation)))* -> equal(power_class(complement(singleton(identity_relation))),identity_relation).
% 300.10/300.68  109521[5:Res:39298.1,9880.0] || subclass(ordinal_numbers,complement(complement(compose(u,v)))) member(w,x)* subclass(x,y)* well_ordering(image(u,image(v,singleton(z))),y)* -> .
% 300.10/300.68  190676[18:Res:190593.1,8803.0] || equal(image(u,image(v,singleton(w))),inverse(identity_relation)) member(ordered_pair(w,identity_relation),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(w,identity_relation),compose(u,v))*.
% 300.10/300.68  190567[18:Res:190442.1,8803.0] || equal(image(u,image(v,singleton(w))),symmetrization_of(identity_relation)) member(ordered_pair(w,identity_relation),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(w,identity_relation),compose(u,v))*.
% 300.10/300.68  165387[14:Res:165168.1,8803.0] || equal(image(u,image(v,singleton(w))),singleton(identity_relation)) member(ordered_pair(w,identity_relation),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(w,identity_relation),compose(u,v))*.
% 300.10/300.68  62105[8:Res:19172.1,8632.1] || equal(apply(u,v),identity_relation) well_ordering(element_relation,image(u,singleton(v)))* -> equal(image(u,singleton(v)),ordinal_numbers) member(image(u,singleton(v)),ordinal_numbers).
% 300.10/300.68  199001[7:Res:8976.2,13362.0] function(u) || member(v,ordinal_numbers) subclass(ordinal_numbers,w) well_ordering(omega,w)* -> equal(integer_of(ordered_pair(image(u,v),least(omega,ordinal_numbers))),identity_relation)**.
% 300.10/300.68  166852[5:SpR:19860.0,8859.1] || member(inverse(restrict(cross_product(u,ordinal_numbers),v,w)),ordinal_numbers) -> member(ordered_pair(inverse(restrict(cross_product(u,ordinal_numbers),v,w)),image(cross_product(v,w),u)),domain_relation)*.
% 300.10/300.68  133010[0:SpR:481.0,19485.0] ||  -> equal(power_class(intersection(power_class(intersection(complement(u),complement(v))),complement(singleton(image(element_relation,union(u,v)))))),complement(image(element_relation,successor(image(element_relation,union(u,v))))))**.
% 300.10/300.68  132756[0:SpR:481.0,19486.0] ||  -> equal(power_class(intersection(power_class(intersection(complement(u),complement(v))),complement(inverse(image(element_relation,union(u,v)))))),complement(image(element_relation,symmetrization_of(image(element_relation,union(u,v))))))**.
% 300.10/300.68  165157[7:Res:130711.0,13113.0] || well_ordering(u,image(element_relation,power_class(v))) -> equal(segment(u,complement(power_class(image(element_relation,complement(v)))),least(u,complement(power_class(image(element_relation,complement(v)))))),identity_relation)**.
% 300.10/300.68  194671[8:Rew:162038.0,194641.2,162038.0,194641.0] || member(power_class(complement(inverse(identity_relation))),ordinal_numbers) member(apply(choice,power_class(complement(inverse(identity_relation)))),image(element_relation,symmetrization_of(identity_relation)))* -> equal(power_class(complement(inverse(identity_relation))),identity_relation).
% 300.10/300.68  156828[5:Res:79577.0,40594.1] || member(image(element_relation,complement(u)),ordinal_numbers) -> subclass(singleton(singleton(image(element_relation,complement(u)))),power_class(u))* member(singleton(singleton(singleton(image(element_relation,complement(u))))),element_relation)*.
% 300.10/300.68  198538[8:SpR:145758.0,161460.2] operation(cross_product(u,ordinal_numbers)) || well_ordering(v,cantor(cantor(cross_product(u,ordinal_numbers)))) -> equal(segment(v,image(ordinal_numbers,u),least(v,image(ordinal_numbers,u))),identity_relation)**.
% 300.10/300.68  61469[8:Rew:14756.0,61445.1,14756.0,61445.0] || member(ordered_pair(u,not_subclass_element(range_of(identity_relation),v)),cross_product(ordinal_numbers,ordinal_numbers)) -> subclass(range_of(identity_relation),v) member(ordered_pair(u,not_subclass_element(range_of(identity_relation),v)),compose(identity_relation,w))*.
% 300.10/300.68  117689[8:Rew:116078.0,116334.2] one_to_one(u) || subclass(range_of(inverse(u)),cantor(range_of(u))) equal(cross_product(cantor(range_of(u)),cantor(range_of(u))),range_of(u))** -> operation(inverse(u)).
% 300.10/300.68  117688[8:Rew:116078.0,116324.2] operation(restrict(element_relation,ordinal_numbers,u)) || subclass(cantor(sum_class(u)),range_of(restrict(element_relation,ordinal_numbers,u)))* -> equal(range_of(restrict(element_relation,ordinal_numbers,u)),cantor(sum_class(u))).
% 300.10/300.68  145897[8:SpL:145758.0,117617.1] function(u) || subclass(range_of(u),cantor(image(ordinal_numbers,v))) equal(cantor(cantor(w)),cantor(u)) -> compatible(u,w,inverse(cross_product(v,ordinal_numbers)))*.
% 300.10/300.68  204159[8:Res:204134.1,8562.0] || member(not_subclass_element(u,intersection(v,symmetrization_of(identity_relation))),inverse(identity_relation))* member(not_subclass_element(u,intersection(v,symmetrization_of(identity_relation))),v)* -> subclass(u,intersection(v,symmetrization_of(identity_relation))).
% 300.10/300.68  204404[16:Res:195271.0,13362.0] || subclass(complement(singleton(identity_relation)),u)* well_ordering(omega,u) -> subclass(singleton(v),singleton(identity_relation)) equal(integer_of(ordered_pair(v,least(omega,complement(singleton(identity_relation))))),identity_relation)**.
% 300.10/300.68  204543[21:Rew:160429.0,204532.2] function(u) || well_ordering(v,ordinal_numbers) subclass(range_of(u),identity_relation) equal(cantor(cantor(w)),cantor(u)) -> compatible(u,w,least(v,ordinal_numbers))*.
% 300.10/300.68  204582[21:Rew:160429.0,204571.2] function(u) || well_ordering(v,rest_relation) subclass(range_of(u),identity_relation) equal(cantor(cantor(w)),cantor(u)) -> compatible(u,w,least(v,rest_relation))*.
% 300.10/300.68  204625[21:Rew:160429.0,204614.2] function(u) || well_ordering(v,ordinal_numbers) subclass(range_of(u),identity_relation) equal(cantor(cantor(w)),cantor(u)) -> compatible(u,w,least(v,rest_relation))*.
% 300.10/300.68  206521[7:Res:165794.1,13070.0] || well_ordering(u,omega) -> equal(integer_of(v),identity_relation) equal(intersection(w,singleton(v)),identity_relation) member(least(u,intersection(w,singleton(v))),intersection(w,singleton(v)))*.
% 300.10/300.68  206548[7:Res:165795.1,13070.0] || well_ordering(u,omega) -> equal(integer_of(v),identity_relation) equal(intersection(singleton(v),w),identity_relation) member(least(u,intersection(singleton(v),w)),intersection(singleton(v),w))*.
% 300.10/300.68  206563[7:Res:206540.1,13070.0] || well_ordering(u,omega) -> equal(integer_of(v),identity_relation) equal(complement(complement(singleton(v))),identity_relation) member(least(u,complement(complement(singleton(v)))),complement(complement(singleton(v))))*.
% 300.10/300.68  208218[7:Res:13333.3,5.0] inductive(u) || well_ordering(v,u) subclass(image(successor_relation,u),w) -> equal(image(successor_relation,u),identity_relation) member(least(v,image(successor_relation,u)),w)*.
% 300.10/300.68  208536[8:SpL:13260.1,117449.1] operation(u) || member(regular(cross_product(v,w)),cantor(u)) -> equal(cross_product(v,w),identity_relation) member(first(regular(cross_product(v,w))),cantor(cantor(u)))*.
% 300.10/300.68  208535[8:SpL:13260.1,117450.1] operation(u) || member(regular(cross_product(v,w)),cantor(u)) -> equal(cross_product(v,w),identity_relation) member(second(regular(cross_product(v,w))),cantor(cantor(u)))*.
% 300.10/300.68  208526[7:SpL:13260.1,157.0] || member(regular(cross_product(u,v)),union_of_range_map) -> equal(cross_product(u,v),identity_relation) equal(sum_class(range_of(first(regular(cross_product(u,v))))),second(regular(cross_product(u,v))))**.
% 300.10/300.68  209405[21:SpL:196546.1,117617.1] function(u) || subclass(range_of(u),identity_relation) equal(cantor(cantor(v)),cantor(u)) -> equal(singleton(range_of(w)),identity_relation) compatible(u,v,inverse(w))*.
% 300.10/300.68  209877[24:Res:207863.1,9665.1] operation(u) inductive(symmetric_difference(complement(u),ordinal_numbers)) || well_ordering(v,successor(u)) -> member(least(v,symmetric_difference(complement(u),ordinal_numbers)),symmetric_difference(complement(u),ordinal_numbers))*.
% 300.10/300.68  209874[24:Res:207863.1,13070.0] operation(u) || well_ordering(v,successor(u)) -> equal(symmetric_difference(complement(u),ordinal_numbers),identity_relation) member(least(v,symmetric_difference(complement(u),ordinal_numbers)),symmetric_difference(complement(u),ordinal_numbers))*.
% 300.10/300.68  210111[8:Res:138.1,161699.1] || member(complement(complement(symmetrization_of(u))),ordinal_numbers)* connected(u,v)* -> equal(cross_product(v,v),identity_relation) member(least(element_relation,cross_product(v,v)),cross_product(v,v))*.
% 300.10/300.68  210302[8:Res:140864.1,131.3] || member(ordered_pair(u,least(symmetric_difference(ordinal_numbers,v),w)),complement(v))* member(u,w) subclass(w,x)* well_ordering(symmetric_difference(ordinal_numbers,v),x)* -> .
% 300.10/300.68  210274[8:Res:140864.1,13362.0] || member(u,complement(v)) subclass(symmetric_difference(ordinal_numbers,v),w)* well_ordering(omega,w) -> equal(integer_of(ordered_pair(u,least(omega,symmetric_difference(ordinal_numbers,v)))),identity_relation)**.
% 300.10/300.68  210374[7:Res:13247.2,143186.0] || member(intersection(u,symmetric_difference(ordinal_numbers,v)),ordinal_numbers) -> equal(intersection(u,symmetric_difference(ordinal_numbers,v)),identity_relation) member(apply(choice,intersection(u,symmetric_difference(ordinal_numbers,v))),complement(v))*.
% 300.10/300.68  210365[7:Res:13246.2,143186.0] || member(intersection(symmetric_difference(ordinal_numbers,u),v),ordinal_numbers) -> equal(intersection(symmetric_difference(ordinal_numbers,u),v),identity_relation) member(apply(choice,intersection(symmetric_difference(ordinal_numbers,u),v)),complement(u))*.
% 300.10/300.68  210483[7:Res:13247.2,143226.0] || member(intersection(u,symmetric_difference(ordinal_numbers,v)),ordinal_numbers) member(apply(choice,intersection(u,symmetric_difference(ordinal_numbers,v))),v)* -> equal(intersection(u,symmetric_difference(ordinal_numbers,v)),identity_relation).
% 300.10/300.68  210474[7:Res:13246.2,143226.0] || member(intersection(symmetric_difference(ordinal_numbers,u),v),ordinal_numbers) member(apply(choice,intersection(symmetric_difference(ordinal_numbers,u),v)),u)* -> equal(intersection(symmetric_difference(ordinal_numbers,u),v),identity_relation).
% 300.10/300.68  212210[8:Rew:211586.1,212113.4] || equal(symmetrization_of(identity_relation),ordinal_numbers) member(u,v) subclass(v,w)* well_ordering(identity_relation,w)* -> member(ordered_pair(u,least(identity_relation,v)),symmetrization_of(identity_relation))*.
% 300.10/300.68  212297[8:Res:161774.3,41096.0] || section(u,v,w) well_ordering(x,v) -> equal(cantor(restrict(u,w,v)),identity_relation) member(least(x,cantor(restrict(u,w,v))),ordinal_numbers)*.
% 300.10/300.68  212752[8:Rew:211432.1,212653.4] || equal(complement(u),ordinal_numbers) member(v,w) subclass(w,x)* well_ordering(identity_relation,x)* -> member(ordered_pair(v,least(identity_relation,w)),complement(u))*.
% 300.10/300.68  212970[8:Rew:211670.1,212885.4] || equal(power_class(u),ordinal_numbers) member(v,w) subclass(w,x)* well_ordering(identity_relation,x)* -> member(ordered_pair(v,least(identity_relation,w)),power_class(u))*.
% 300.10/300.68  213465[8:SpR:145761.0,117511.1] operation(cross_product(u,singleton(v))) ||  -> equal(restrict(w,cantor(segment(ordinal_numbers,u,v)),cantor(segment(ordinal_numbers,u,v))),intersection(segment(ordinal_numbers,u,v),w))**.
% 300.10/300.68  213551[8:Res:116127.5,210517.1] operation(u) operation(v) || compatible(w,v,u) subclass(cantor(v),x)* equal(complement(x),ordinal_numbers) -> homomorphism(w,v,u)*.
% 300.10/300.68  213636[5:Res:151877.0,9665.1] inductive(intersection(singleton(u),v)) || well_ordering(w,complement(recursion_equation_functions(x)))* -> function(u) member(least(w,intersection(singleton(u),v)),intersection(singleton(u),v))*.
% 300.10/300.68  213633[7:Res:151877.0,13070.0] || well_ordering(u,complement(recursion_equation_functions(v)))* -> function(w) equal(intersection(singleton(w),x),identity_relation) member(least(u,intersection(singleton(w),x)),intersection(singleton(w),x))*.
% 300.10/300.68  213658[5:Res:213622.0,9665.1] inductive(complement(complement(singleton(u)))) || well_ordering(v,complement(recursion_equation_functions(w)))* -> function(u) member(least(v,complement(complement(singleton(u)))),complement(complement(singleton(u))))*.
% 300.10/300.68  213655[7:Res:213622.0,13070.0] || well_ordering(u,complement(recursion_equation_functions(v)))* -> function(w) equal(complement(complement(singleton(w))),identity_relation) member(least(u,complement(complement(singleton(w)))),complement(complement(singleton(w))))*.
% 300.10/300.68  213692[5:Res:151512.0,9665.1] inductive(intersection(u,singleton(v))) || well_ordering(w,complement(recursion_equation_functions(x)))* -> function(v) member(least(w,intersection(u,singleton(v))),intersection(u,singleton(v)))*.
% 300.10/300.68  213689[7:Res:151512.0,13070.0] || well_ordering(u,complement(recursion_equation_functions(v)))* -> function(w) equal(intersection(x,singleton(w)),identity_relation) member(least(u,intersection(x,singleton(w))),intersection(x,singleton(w)))*.
% 300.10/300.68  214254[24:Res:207615.1,13362.0] operation(u) || subclass(ordered_pair(v,u),w)* well_ordering(omega,w) -> equal(integer_of(ordered_pair(unordered_pair(v,identity_relation),least(omega,ordered_pair(v,u)))),identity_relation)**.
% 300.10/300.68  214273[25:SpR:208887.0,117511.1] operation(restrict(u,v,identity_relation)) ||  -> equal(restrict(w,cantor(segment(u,v,ordinal_numbers)),cantor(segment(u,v,ordinal_numbers))),intersection(segment(u,v,ordinal_numbers),w))**.
% 300.10/300.68  214458[25:SpR:208985.1,9617.2] operation(u) || member(u,recursion_equation_functions(v)) member(ordered_pair(v,rest_of(u)),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(v,ordered_pair(rest_of(u),ordinal_numbers)),composition_function)*.
% 300.10/300.68  214421[25:SpR:208985.1,9617.2] operation(u) || member(ordinal_numbers,recursion_equation_functions(v)) member(ordered_pair(v,rest_of(ordinal_numbers)),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(v,ordered_pair(rest_of(ordinal_numbers),u)),composition_function)*.
% 300.10/300.68  214682[7:Rew:155653.0,214665.1] || transitive(complement(compose(complement(element_relation),inverse(element_relation))),ordinal_numbers) well_ordering(u,subset_relation) -> equal(segment(u,compose(subset_relation,subset_relation),least(u,compose(subset_relation,subset_relation))),identity_relation)**.
% 300.10/300.68  214933[0:Res:151501.1,1301.1] || member(u,sum_class(intersection(v,singleton(u))))* member(intersection(v,singleton(u)),ordinal_numbers) -> equal(sum_class(intersection(v,singleton(u))),intersection(v,singleton(u))).
% 300.10/300.68  214929[2:Res:151501.1,9665.1] inductive(intersection(u,singleton(v))) || member(v,w)* well_ordering(x,w)* -> member(least(x,intersection(u,singleton(v))),intersection(u,singleton(v)))*.
% 300.10/300.68  214926[7:Res:151501.1,13070.0] || member(u,v)* well_ordering(w,v)* -> equal(intersection(x,singleton(u)),identity_relation) member(least(w,intersection(x,singleton(u))),intersection(x,singleton(u)))*.
% 300.10/300.68  214987[5:Res:151502.1,9665.1] inductive(intersection(u,singleton(v))) || well_ordering(w,complement(x))* -> member(v,x)* member(least(w,intersection(u,singleton(v))),intersection(u,singleton(v)))*.
% 300.10/300.68  214984[7:Res:151502.1,13070.0] || well_ordering(u,complement(v))* -> member(w,v)* equal(intersection(x,singleton(w)),identity_relation) member(least(u,intersection(x,singleton(w))),intersection(x,singleton(w)))*.
% 300.10/300.68  215029[0:Res:151861.1,1301.1] || member(u,sum_class(intersection(singleton(u),v)))* member(intersection(singleton(u),v),ordinal_numbers) -> equal(sum_class(intersection(singleton(u),v)),intersection(singleton(u),v)).
% 300.10/300.68  215025[2:Res:151861.1,9665.1] inductive(intersection(singleton(u),v)) || member(u,w)* well_ordering(x,w)* -> member(least(x,intersection(singleton(u),v)),intersection(singleton(u),v))*.
% 300.10/300.68  215022[7:Res:151861.1,13070.0] || member(u,v)* well_ordering(w,v)* -> equal(intersection(singleton(u),x),identity_relation) member(least(w,intersection(singleton(u),x)),intersection(singleton(u),x))*.
% 300.10/300.68  215063[5:Res:215011.1,1301.1] || member(u,sum_class(complement(complement(singleton(u)))))* member(complement(complement(singleton(u))),ordinal_numbers) -> equal(sum_class(complement(complement(singleton(u)))),complement(complement(singleton(u)))).
% 300.10/300.68  215059[5:Res:215011.1,9665.1] inductive(complement(complement(singleton(u)))) || member(u,v)* well_ordering(w,v)* -> member(least(w,complement(complement(singleton(u)))),complement(complement(singleton(u))))*.
% 300.10/300.68  215056[7:Res:215011.1,13070.0] || member(u,v)* well_ordering(w,v)* -> equal(complement(complement(singleton(u))),identity_relation) member(least(w,complement(complement(singleton(u)))),complement(complement(singleton(u))))*.
% 300.10/300.69  215122[5:Res:151862.1,9665.1] inductive(intersection(singleton(u),v)) || well_ordering(w,complement(x))* -> member(u,x)* member(least(w,intersection(singleton(u),v)),intersection(singleton(u),v))*.
% 300.10/300.69  215119[7:Res:151862.1,13070.0] || well_ordering(u,complement(v))* -> member(w,v)* equal(intersection(singleton(w),x),identity_relation) member(least(u,intersection(singleton(w),x)),intersection(singleton(w),x))*.
% 300.10/300.69  215159[5:Res:215108.1,9665.1] inductive(complement(complement(singleton(u)))) || well_ordering(v,complement(w))* -> member(u,w)* member(least(v,complement(complement(singleton(u)))),complement(complement(singleton(u))))*.
% 300.10/300.69  215156[7:Res:215108.1,13070.0] || well_ordering(u,complement(v))* -> member(w,v)* equal(complement(complement(singleton(w))),identity_relation) member(least(u,complement(complement(singleton(w)))),complement(complement(singleton(w))))*.
% 300.10/300.69  215905[15:MRR:215904.0,165460.0] || member(ordered_pair(u,apply(choice,range_of(identity_relation))),cross_product(ordinal_numbers,ordinal_numbers)) -> equal(range_of(identity_relation),identity_relation) member(ordered_pair(u,apply(choice,range_of(identity_relation))),compose(identity_relation,v))*.
% 300.10/300.69  217431[8:Res:216591.1,8803.0] || equal(complement(image(u,image(v,singleton(w)))),identity_relation)** member(ordered_pair(w,identity_relation),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(w,identity_relation),compose(u,v)).
% 300.10/300.69  217653[8:Res:216611.1,8803.0] || equal(complement(image(u,image(v,singleton(w)))),identity_relation)** member(ordered_pair(w,omega),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(w,omega),compose(u,v)).
% 300.10/300.69  218253[8:Res:10061.3,217144.1] || member(u,ordinal_numbers) member(ordered_pair(v,w),cross_product(ordinal_numbers,ordinal_numbers)) member(ordered_pair(ordered_pair(w,v),u),x)* equal(flip(x),identity_relation) -> .
% 300.10/300.69  218252[8:Res:10093.3,217144.1] || member(u,ordinal_numbers) member(ordered_pair(v,w),cross_product(ordinal_numbers,ordinal_numbers)) member(ordered_pair(ordered_pair(w,u),v),x)* equal(rotate(x),identity_relation) -> .
% 300.10/300.69  219214[8:Res:10061.3,219073.1] || member(u,ordinal_numbers) member(ordered_pair(v,w),cross_product(ordinal_numbers,ordinal_numbers)) member(ordered_pair(ordered_pair(w,v),u),x)* subclass(flip(x),identity_relation) -> .
% 300.10/300.69  219213[8:Res:10093.3,219073.1] || member(u,ordinal_numbers) member(ordered_pair(v,w),cross_product(ordinal_numbers,ordinal_numbers)) member(ordered_pair(ordered_pair(w,u),v),x)* subclass(rotate(x),identity_relation) -> .
% 300.10/300.69  220470[21:Res:196656.1,8821.1] || subclass(domain_relation,flip(cross_product(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers))) member(ordered_pair(ordered_pair(u,identity_relation),v),w) -> member(ordered_pair(ordered_pair(v,u),identity_relation),rotate(w))*.
% 300.10/300.69  220469[21:Res:196656.1,8820.1] || subclass(domain_relation,flip(cross_product(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers))) member(ordered_pair(ordered_pair(u,v),identity_relation),w) -> member(ordered_pair(ordered_pair(v,u),identity_relation),flip(w))*.
% 300.10/300.69  220430[21:Res:196656.1,3689.0] || subclass(domain_relation,flip(ordered_pair(u,v)))* -> equal(ordered_pair(ordered_pair(w,x),identity_relation),unordered_pair(u,singleton(v)))* equal(ordered_pair(ordered_pair(w,x),identity_relation),singleton(u)).
% 300.10/300.69  220394[21:Res:196656.1,13362.0] || subclass(domain_relation,flip(u)) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(ordered_pair(ordered_pair(w,x),identity_relation),least(omega,u))),identity_relation)**.
% 300.10/300.69  220385[21:SpR:13259.2,196656.1] || member(cross_product(u,v),ordinal_numbers) subclass(domain_relation,flip(w)) -> equal(cross_product(u,v),identity_relation) member(ordered_pair(apply(choice,cross_product(u,v)),identity_relation),w)*.
% 300.10/300.69  220576[21:Res:196657.1,8821.1] || subclass(domain_relation,rotate(cross_product(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers))) member(ordered_pair(ordered_pair(identity_relation,u),v),w) -> member(ordered_pair(ordered_pair(v,identity_relation),u),rotate(w))*.
% 300.10/300.69  220575[21:Res:196657.1,8820.1] || subclass(domain_relation,rotate(cross_product(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers))) member(ordered_pair(ordered_pair(identity_relation,u),v),w) -> member(ordered_pair(ordered_pair(u,identity_relation),v),flip(w))*.
% 300.10/300.69  220532[21:Res:196657.1,3689.0] || subclass(domain_relation,rotate(ordered_pair(u,v)))* -> equal(ordered_pair(ordered_pair(w,identity_relation),x),unordered_pair(u,singleton(v)))* equal(ordered_pair(ordered_pair(w,identity_relation),x),singleton(u)).
% 300.10/300.69  220496[21:Res:196657.1,13362.0] || subclass(domain_relation,rotate(u)) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(ordered_pair(ordered_pair(w,identity_relation),x),least(omega,u))),identity_relation)**.
% 300.10/300.69  220761[7:Res:39607.2,13362.0] inductive(u) || well_ordering(v,ordinal_numbers) subclass(u,w)* well_ordering(omega,w)* -> equal(integer_of(ordered_pair(least(v,u),least(omega,u))),identity_relation)**.
% 300.10/300.69  221146[7:Res:13236.2,12.0] || well_ordering(u,unordered_pair(v,w)) -> equal(unordered_pair(v,w),identity_relation) equal(least(u,unordered_pair(v,w)),w)** equal(least(u,unordered_pair(v,w)),v)**.
% 300.10/300.69  221118[7:Res:13236.2,13362.0] || well_ordering(u,v) subclass(v,w)* well_ordering(omega,w)* -> equal(v,identity_relation) equal(integer_of(ordered_pair(least(u,v),least(omega,v))),identity_relation)**.
% 300.10/300.69  221384[7:Res:39609.2,13362.0] inductive(u) || well_ordering(v,u) subclass(u,w)* well_ordering(omega,w)* -> equal(integer_of(ordered_pair(least(v,u),least(omega,u))),identity_relation)**.
% 300.10/300.69  223080[7:SpL:481.0,13306.0] || member(regular(power_class(image(element_relation,union(u,v)))),image(element_relation,power_class(intersection(complement(u),complement(v)))))* -> equal(power_class(image(element_relation,union(u,v))),identity_relation).
% 300.10/300.69  223873[8:SpL:160927.0,8554.1] || member(u,union(complement(v),union(w,identity_relation))) member(u,union(v,symmetric_difference(ordinal_numbers,w))) -> member(u,symmetric_difference(complement(v),union(w,identity_relation)))*.
% 300.10/300.69  224192[8:SpL:160992.0,8554.1] || member(u,union(union(v,identity_relation),complement(w))) member(u,union(symmetric_difference(ordinal_numbers,v),w)) -> member(u,symmetric_difference(union(v,identity_relation),complement(w)))*.
% 300.10/300.69  224531[10:SpL:223660.1,9470.1] || subclass(element_relation,identity_relation) member(ordered_pair(cross_product(ordinal_numbers,ordinal_numbers),u),compose(v,w))* subclass(image(v,image(w,identity_relation)),x)* -> member(u,x)*.
% 300.10/300.69  226017[7:SpR:482.0,13578.1] ||  -> equal(symmetric_difference(intersection(complement(u),complement(v)),w),identity_relation) member(regular(symmetric_difference(intersection(complement(u),complement(v)),w)),complement(intersection(union(u,v),complement(w))))*.
% 300.10/300.69  226008[7:SpR:483.0,13578.1] ||  -> equal(symmetric_difference(u,intersection(complement(v),complement(w))),identity_relation) member(regular(symmetric_difference(u,intersection(complement(v),complement(w)))),complement(intersection(complement(u),union(v,w))))*.
% 300.10/300.69  226804[8:Rew:160992.0,226782.2] || subclass(omega,intersection(union(u,identity_relation),complement(v)))* -> equal(integer_of(regular(union(symmetric_difference(ordinal_numbers,u),v))),identity_relation) equal(union(symmetric_difference(ordinal_numbers,u),v),identity_relation).
% 300.10/300.69  226805[8:Rew:160927.0,226781.2] || subclass(omega,intersection(complement(u),union(v,identity_relation)))* -> equal(integer_of(regular(union(u,symmetric_difference(ordinal_numbers,v)))),identity_relation) equal(union(u,symmetric_difference(ordinal_numbers,v)),identity_relation).
% 300.10/300.69  228244[8:Res:116148.1,17313.0] || section(u,recursion_equation_functions(v),w) -> equal(cantor(restrict(u,w,recursion_equation_functions(v))),identity_relation) subclass(regular(cantor(restrict(u,w,recursion_equation_functions(v)))),cross_product(ordinal_numbers,ordinal_numbers))*.
% 300.10/300.69  228869[8:Res:3618.1,61018.0] || member(apply(choice,regular(complement(intersection(u,v)))),symmetric_difference(u,v))* -> equal(regular(complement(intersection(u,v))),identity_relation) equal(complement(intersection(u,v)),identity_relation).
% 300.10/300.69  228915[8:MRR:228892.2,218277.1] || member(ordered_pair(u,apply(choice,regular(image(v,image(w,singleton(u)))))),compose(v,w))* -> equal(regular(image(v,image(w,singleton(u)))),identity_relation).
% 300.10/300.69  229215[8:Rew:160992.0,229088.1] || member(regular(intersection(union(symmetric_difference(ordinal_numbers,u),v),w)),intersection(union(u,identity_relation),complement(v)))* -> equal(intersection(union(symmetric_difference(ordinal_numbers,u),v),w),identity_relation).
% 300.10/300.69  229216[8:Rew:160927.0,229087.1] || member(regular(intersection(union(u,symmetric_difference(ordinal_numbers,v)),w)),intersection(complement(u),union(v,identity_relation)))* -> equal(intersection(union(u,symmetric_difference(ordinal_numbers,v)),w),identity_relation).
% 300.10/300.69  229802[8:Rew:160992.0,229531.1] || member(regular(intersection(u,union(symmetric_difference(ordinal_numbers,v),w))),intersection(union(v,identity_relation),complement(w)))* -> equal(intersection(u,union(symmetric_difference(ordinal_numbers,v),w)),identity_relation).
% 300.10/300.69  229803[8:Rew:160927.0,229530.1] || member(regular(intersection(u,union(v,symmetric_difference(ordinal_numbers,w)))),intersection(complement(v),union(w,identity_relation)))* -> equal(intersection(u,union(v,symmetric_difference(ordinal_numbers,w))),identity_relation).
% 300.10/300.69  230484[8:MRR:230432.0,8667.0] || member(u,v) subclass(v,w)* well_ordering(symmetric_difference(ordinal_numbers,x),w)* -> member(ordered_pair(u,least(symmetric_difference(ordinal_numbers,x),v)),union(x,identity_relation))*.
% 300.10/300.69  231246[7:SpR:3597.0,17447.1] ||  -> equal(symmetric_difference(complement(intersection(u,inverse(u))),symmetrization_of(u)),identity_relation) member(regular(symmetric_difference(complement(intersection(u,inverse(u))),symmetrization_of(u))),complement(symmetric_difference(u,inverse(u))))*.
% 300.10/300.69  231245[7:SpR:3596.0,17447.1] ||  -> equal(symmetric_difference(complement(intersection(u,singleton(u))),successor(u)),identity_relation) member(regular(symmetric_difference(complement(intersection(u,singleton(u))),successor(u))),complement(symmetric_difference(u,singleton(u))))*.
% 300.10/300.69  231782[8:Res:3618.1,18747.0] || member(not_subclass_element(regular(complement(intersection(u,v))),w),symmetric_difference(u,v))* -> subclass(regular(complement(intersection(u,v))),w) equal(complement(intersection(u,v)),identity_relation).
% 300.10/300.69  231844[8:MRR:231807.2,218277.1] || member(ordered_pair(u,not_subclass_element(regular(image(v,image(w,singleton(u)))),x)),compose(v,w))* -> subclass(regular(image(v,image(w,singleton(u)))),x).
% 300.10/300.69  233276[7:Res:17388.1,11.0] || subclass(cross_product(ordinal_numbers,ordinal_numbers),regular(intersection(recursion_equation_functions(u),v)))* -> equal(intersection(recursion_equation_functions(u),v),identity_relation) equal(regular(intersection(recursion_equation_functions(u),v)),cross_product(ordinal_numbers,ordinal_numbers)).
% 300.10/300.69  233429[7:Res:13566.1,11.0] || subclass(cross_product(ordinal_numbers,ordinal_numbers),regular(intersection(u,recursion_equation_functions(v))))* -> equal(intersection(u,recursion_equation_functions(v)),identity_relation) equal(regular(intersection(u,recursion_equation_functions(v))),cross_product(ordinal_numbers,ordinal_numbers)).
% 300.10/300.69  233472[8:Res:161057.2,31610.0] || well_ordering(u,ordinal_numbers) subclass(rest_relation,successor_relation) -> equal(recursion_equation_functions(v),identity_relation) equal(rest_of(cantor(least(u,recursion_equation_functions(v)))),successor(cantor(least(u,recursion_equation_functions(v)))))**.
% 300.10/300.69  233856[7:Res:13258.1,941.1] || member(regular(restrict(power_class(image(element_relation,complement(u))),v,w)),image(element_relation,power_class(u)))* -> equal(restrict(power_class(image(element_relation,complement(u))),v,w),identity_relation).
% 300.10/300.69  233887[22:Res:233384.0,129.0] || subclass(complement(singleton(singleton(singleton(identity_relation)))),u)* well_ordering(v,u)* -> member(least(v,complement(singleton(singleton(singleton(identity_relation))))),complement(singleton(singleton(singleton(identity_relation)))))*.
% 300.10/300.69  233884[22:Res:233384.0,13362.0] || subclass(complement(singleton(singleton(singleton(identity_relation)))),u)* well_ordering(omega,u) -> equal(integer_of(ordered_pair(singleton(identity_relation),least(omega,complement(singleton(singleton(singleton(identity_relation))))))),identity_relation)**.
% 300.10/300.69  233978[8:Res:13258.1,161200.0] || member(regular(restrict(image(element_relation,union(u,identity_relation)),v,w)),power_class(symmetric_difference(ordinal_numbers,u)))* -> equal(restrict(image(element_relation,union(u,identity_relation)),v,w),identity_relation).
% 300.10/300.69  234110[8:Res:233383.0,129.0] || subclass(complement(singleton(ordered_pair(u,v))),w)* well_ordering(x,w)* -> member(least(x,complement(singleton(ordered_pair(u,v)))),complement(singleton(ordered_pair(u,v))))*.
% 300.10/300.69  234107[8:Res:233383.0,13362.0] || subclass(complement(singleton(ordered_pair(u,v))),w)* well_ordering(omega,w) -> equal(integer_of(ordered_pair(singleton(u),least(omega,complement(singleton(ordered_pair(u,v)))))),identity_relation)**.
% 300.10/300.69  234906[8:MRR:234838.0,8667.0] || member(u,v) subclass(v,w)* well_ordering(cantor(x),w)* -> equal(apply(x,ordered_pair(u,least(cantor(x),v))),sum_class(range_of(identity_relation)))**.
% 300.10/300.69  234976[8:SpL:229238.0,116117.1] || member(u,cantor(complement(cross_product(u,ordinal_numbers))))* equal(identity_relation,v) subclass(rest_of(complement(cross_product(u,ordinal_numbers))),w)* -> member(ordered_pair(u,v),w)*.
% 300.10/300.69  235801[5:Res:133.2,19113.0] || connected(u,recursion_equation_functions(v)) -> well_ordering(u,recursion_equation_functions(v)) subclass(not_well_ordering(u,recursion_equation_functions(v)),w) subclass(not_subclass_element(not_well_ordering(u,recursion_equation_functions(v)),w),cross_product(ordinal_numbers,ordinal_numbers))*.
% 300.10/300.69  235957[8:Res:69478.2,18750.0] || subclass(omega,symmetric_difference(u,v)) -> equal(integer_of(regular(regular(union(u,v)))),identity_relation)** equal(regular(union(u,v)),identity_relation) equal(union(u,v),identity_relation).
% 300.10/300.69  235942[7:Res:69478.2,18696.1] || subclass(omega,symmetric_difference(u,v)) well_ordering(w,ordinal_numbers) -> equal(integer_of(least(w,complement(union(u,v)))),identity_relation)** equal(complement(union(u,v)),identity_relation).
% 300.10/300.69  236002[5:SpR:8649.0,39308.2] one_to_one(restrict(u,v,ordinal_numbers)) || subclass(range_of(inverse(restrict(u,v,ordinal_numbers))),w) -> maps(inverse(restrict(u,v,ordinal_numbers)),image(u,v),w)*.
% 300.10/300.69  236275[7:Res:69478.2,18897.0] || subclass(omega,symmetric_difference(u,v)) -> equal(integer_of(not_subclass_element(intersection(w,complement(union(u,v))),x)),identity_relation)** subclass(intersection(w,complement(union(u,v))),x).
% 300.10/300.69  236479[7:Res:69478.2,19016.0] || subclass(omega,symmetric_difference(u,v)) -> equal(integer_of(not_subclass_element(intersection(complement(union(u,v)),w),x)),identity_relation)** subclass(intersection(complement(union(u,v)),w),x).
% 300.10/300.69  236551[0:Rew:3594.0,236428.1] || member(not_subclass_element(symmetric_difference(complement(intersection(u,v)),union(u,v)),w),symmetric_difference(u,v))* -> subclass(symmetric_difference(complement(intersection(u,v)),union(u,v)),w).
% 300.10/300.69  237107[7:Res:13574.1,18791.0] ||  -> equal(intersection(u,intersection(v,symmetric_difference(complement(w),complement(x)))),identity_relation) member(regular(intersection(u,intersection(v,symmetric_difference(complement(w),complement(x))))),union(w,x))*.
% 300.10/300.69  237758[7:Res:13573.1,18791.0] ||  -> equal(intersection(u,intersection(symmetric_difference(complement(v),complement(w)),x)),identity_relation) member(regular(intersection(u,intersection(symmetric_difference(complement(v),complement(w)),x))),union(v,w))*.
% 300.10/300.69  239270[7:Res:17397.1,18791.0] ||  -> equal(intersection(intersection(symmetric_difference(complement(u),complement(v)),w),x),identity_relation) member(regular(intersection(intersection(symmetric_difference(complement(u),complement(v)),w),x)),union(u,v))*.
% 300.10/300.69  240105[7:Res:17396.1,18791.0] ||  -> equal(intersection(intersection(u,symmetric_difference(complement(v),complement(w))),x),identity_relation) member(regular(intersection(intersection(u,symmetric_difference(complement(v),complement(w))),x)),union(v,w))*.
% 300.10/300.69  36302[0:SpR:3616.0,163.0] ||  -> equal(intersection(complement(symmetric_difference(complement(u),complement(v))),union(union(u,v),union(complement(u),complement(v)))),symmetric_difference(union(u,v),union(complement(u),complement(v))))**.
% 300.10/300.69  39646[2:Res:19421.0,9665.1] inductive(symmetric_difference(complement(u),complement(v))) || well_ordering(w,union(u,v)) -> member(least(w,symmetric_difference(complement(u),complement(v))),symmetric_difference(complement(u),complement(v)))*.
% 300.10/300.69  69454[8:MRR:69453.0,41096.1] || member(u,complement(intersection(v,ordinal_numbers)))* subclass(symmetric_difference(v,ordinal_numbers),w)* well_ordering(x,w)* -> member(least(x,symmetric_difference(v,ordinal_numbers)),symmetric_difference(v,ordinal_numbers))*.
% 300.10/300.69  19870[0:SpR:916.0,122.1] || transitive(cross_product(u,v),w) -> subclass(compose(restrict(cross_product(w,w),u,v),restrict(cross_product(w,w),u,v)),restrict(cross_product(w,w),u,v))*.
% 300.10/300.69  19895[0:SpL:916.0,123.0] || subclass(compose(restrict(cross_product(u,u),v,w),restrict(cross_product(u,u),v,w)),restrict(cross_product(u,u),v,w))* -> transitive(cross_product(v,w),u).
% 300.10/300.69  44882[0:SpL:916.0,9777.0] || equal(compose(restrict(cross_product(u,u),v,w),restrict(cross_product(u,u),v,w)),restrict(cross_product(u,u),v,w))** -> transitive(cross_product(v,w),u).
% 300.10/300.69  47564[0:Rew:163.0,47481.2,163.0,47481.1] || member(not_subclass_element(u,symmetric_difference(v,w)),union(v,w)) member(not_subclass_element(u,symmetric_difference(v,w)),complement(intersection(v,w)))* -> subclass(u,symmetric_difference(v,w)).
% 300.10/300.69  39741[0:Res:8551.2,7.0] || member(not_subclass_element(u,restrict(v,w,x)),cross_product(w,x))* member(not_subclass_element(u,restrict(v,w,x)),v)* -> subclass(u,restrict(v,w,x)).
% 300.10/300.69  47016[5:Res:41183.1,9421.0] || member(u,v)* -> subclass(w,x) equal(ordered_pair(first(ordered_pair(u,not_subclass_element(w,x))),second(ordered_pair(u,not_subclass_element(w,x)))),ordered_pair(u,not_subclass_element(w,x)))**.
% 300.10/300.69  28947[5:Res:8827.2,21.0] || member(u,ordinal_numbers) subclass(rest_relation,cross_product(v,w))* -> equal(ordered_pair(first(ordered_pair(u,rest_of(u))),second(ordered_pair(u,rest_of(u)))),ordered_pair(u,rest_of(u)))**.
% 300.10/300.69  51511[5:Res:51313.1,21.0] || member(singleton(cross_product(u,v)),subset_relation) -> equal(ordered_pair(first(first(singleton(cross_product(u,v)))),second(first(singleton(cross_product(u,v))))),first(singleton(cross_product(u,v))))**.
% 300.10/300.69  46019[5:SpR:916.0,8865.1] || member(restrict(cross_product(u,v),w,singleton(x)),ordinal_numbers) -> member(ordered_pair(restrict(cross_product(w,singleton(x)),u,v),segment(cross_product(u,v),w,x)),domain_relation)*.
% 300.10/300.69  39592[5:Res:8827.2,3689.0] || member(u,ordinal_numbers) subclass(rest_relation,ordered_pair(v,w))* -> equal(ordered_pair(u,rest_of(u)),unordered_pair(v,singleton(w)))* equal(ordered_pair(u,rest_of(u)),singleton(v)).
% 300.10/300.69  49653[0:SpL:6355.1,23.0] || member(not_subclass_element(cross_product(u,v),w),element_relation) -> subclass(cross_product(u,v),w) member(first(not_subclass_element(cross_product(u,v),w)),second(not_subclass_element(cross_product(u,v),w)))*.
% 300.10/300.69  94722[5:Res:39298.1,8821.1] || subclass(ordinal_numbers,complement(complement(cross_product(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers))))* member(ordered_pair(ordered_pair(u,v),w),x) -> member(ordered_pair(ordered_pair(w,u),v),rotate(x))*.
% 300.10/300.69  94721[5:Res:39298.1,8820.1] || subclass(ordinal_numbers,complement(complement(cross_product(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers))))* member(ordered_pair(ordered_pair(u,v),w),x) -> member(ordered_pair(ordered_pair(v,u),w),flip(x))*.
% 300.10/300.69  96691[5:Res:60219.0,3689.0] ||  -> subclass(u,complement(ordered_pair(v,w))) equal(not_subclass_element(u,complement(ordered_pair(v,w))),unordered_pair(v,singleton(w)))** equal(not_subclass_element(u,complement(ordered_pair(v,w))),singleton(v)).
% 300.10/300.69  117724[8:Rew:116078.0,116619.1] || section(cross_product(u,v),w,x) subclass(w,cantor(restrict(cross_product(x,w),u,v)))* -> equal(cantor(restrict(cross_product(u,v),x,w)),w).
% 300.10/300.69  131532[0:Res:2504.1,8554.1] || subclass(ordered_pair(u,v),complement(intersection(w,x))) member(unordered_pair(u,singleton(v)),union(w,x)) -> member(unordered_pair(u,singleton(v)),symmetric_difference(w,x))*.
% 300.10/300.69  153197[0:SpR:482.0,18204.1] ||  -> subclass(symmetric_difference(intersection(complement(u),complement(v)),w),x) member(not_subclass_element(symmetric_difference(intersection(complement(u),complement(v)),w),x),complement(intersection(union(u,v),complement(w))))*.
% 300.10/300.69  153190[0:SpR:483.0,18204.1] ||  -> subclass(symmetric_difference(u,intersection(complement(v),complement(w))),x) member(not_subclass_element(symmetric_difference(u,intersection(complement(v),complement(w))),x),complement(intersection(complement(u),union(v,w))))*.
% 300.10/300.69  156476[5:Rew:155665.0,156470.1] || member(not_subclass_element(union(subset_relation,cross_product(ordinal_numbers,ordinal_numbers)),symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers))),complement(subset_relation))* -> subclass(union(subset_relation,cross_product(ordinal_numbers,ordinal_numbers)),symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers))).
% 300.10/300.69  156585[5:Rew:155666.0,156579.1] || member(not_subclass_element(union(cross_product(ordinal_numbers,ordinal_numbers),subset_relation),symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation)),complement(subset_relation))* -> subclass(union(cross_product(ordinal_numbers,ordinal_numbers),subset_relation),symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation)).
% 300.10/300.69  156814[5:Res:3618.1,40594.1] || member(singleton(complement(intersection(u,v))),symmetric_difference(u,v))* member(complement(intersection(u,v)),ordinal_numbers) -> member(singleton(singleton(singleton(complement(intersection(u,v))))),element_relation)*.
% 300.10/300.69  116306[8:Rew:116078.0,38129.1] operation(restrict(u,v,singleton(w))) ||  -> equal(restrict(x,cantor(segment(u,v,w)),cantor(segment(u,v,w))),intersection(segment(u,v,w),x))**.
% 300.10/300.69  116841[8:Rew:116078.0,96875.3] operation(u) inductive(symmetric_difference(ordinal_numbers,domain_of(u))) || well_ordering(v,complement(cantor(u))) -> member(least(v,symmetric_difference(ordinal_numbers,cantor(u))),symmetric_difference(ordinal_numbers,cantor(u)))*.
% 300.10/300.69  19765[7:Res:19421.0,13070.0] || well_ordering(u,union(v,w)) -> equal(symmetric_difference(complement(v),complement(w)),identity_relation) member(least(u,symmetric_difference(complement(v),complement(w))),symmetric_difference(complement(v),complement(w)))*.
% 300.10/300.69  66504[7:Res:13061.0,9878.0] || member(u,v)* member(u,w)* subclass(w,x)* well_ordering(cross_product(v,omega),x)* -> equal(integer_of(least(cross_product(v,omega),w)),identity_relation)**.
% 300.10/300.69  66707[7:Res:66492.1,9878.0] || member(u,v)* member(u,w)* subclass(w,x)* well_ordering(cross_product(v,ordinal_numbers),x)* -> equal(integer_of(least(cross_product(v,ordinal_numbers),w)),identity_relation)**.
% 300.10/300.69  61900[7:Res:18517.1,9878.0] || member(u,v)* member(u,w)* subclass(w,x)* well_ordering(cross_product(v,ordinal_numbers),x)* -> equal(singleton(least(cross_product(v,ordinal_numbers),w)),identity_relation)**.
% 300.10/300.69  190202[8:Res:161196.2,13113.0] operation(u) || connected(v,cantor(cantor(u)))* well_ordering(w,complement(complement(symmetrization_of(v))))* -> equal(segment(w,cantor(u),least(w,cantor(u))),identity_relation)**.
% 300.10/300.69  136681[2:Res:39609.2,18791.0] inductive(symmetric_difference(complement(u),complement(v))) || well_ordering(w,symmetric_difference(complement(u),complement(v))) -> member(least(w,symmetric_difference(complement(u),complement(v))),union(u,v))*.
% 300.10/300.69  40087[5:Rew:8637.0,40085.2] single_valued_class(sum_class(cross_product(universal_class,universal_class))) || well_ordering(element_relation,cross_product(ordinal_numbers,ordinal_numbers))* equal(sum_class(cross_product(ordinal_numbers,ordinal_numbers)),cross_product(ordinal_numbers,ordinal_numbers)) -> member(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers).
% 300.10/300.69  40043[5:SoR:9113.0,10858.2] single_valued_class(sum_class(cross_product(ordinal_numbers,ordinal_numbers))) || well_ordering(element_relation,cross_product(ordinal_numbers,ordinal_numbers))* equal(sum_class(cross_product(ordinal_numbers,ordinal_numbers)),cross_product(ordinal_numbers,ordinal_numbers)) -> member(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers).
% 300.10/300.69  42237[5:Res:9706.3,129.0] || member(u,ordinal_numbers)* member(v,ordinal_numbers)* equal(successor(v),u)* subclass(successor_relation,w) well_ordering(x,w)* -> member(least(x,successor_relation),successor_relation)*.
% 300.10/300.69  164948[8:Res:162025.0,9633.1] || member(u,ordinal_numbers) well_ordering(v,symmetric_difference(ordinal_numbers,w)) -> member(u,union(w,identity_relation))* member(least(v,complement(union(w,identity_relation))),complement(union(w,identity_relation)))*.
% 300.10/300.69  132375[5:Res:132293.0,9633.1] || member(u,ordinal_numbers) well_ordering(v,intersection(complement(w),complement(singleton(w)))) -> member(u,successor(w))* member(least(v,complement(successor(w))),complement(successor(w)))*.
% 300.10/300.69  132418[5:Res:132294.0,9633.1] || member(u,ordinal_numbers) well_ordering(v,intersection(complement(w),complement(inverse(w)))) -> member(u,symmetrization_of(w))* member(least(v,complement(symmetrization_of(w))),complement(symmetrization_of(w)))*.
% 300.10/300.69  50890[5:Res:10093.3,8841.1] || member(u,ordinal_numbers) member(ordered_pair(v,w),cross_product(ordinal_numbers,ordinal_numbers)) member(ordered_pair(ordered_pair(w,u),v),x)* subclass(ordinal_numbers,complement(rotate(x))) -> .
% 300.10/300.69  50967[5:Res:10061.3,8841.1] || member(u,ordinal_numbers) member(ordered_pair(v,w),cross_product(ordinal_numbers,ordinal_numbers)) member(ordered_pair(ordered_pair(w,v),u),x)* subclass(ordinal_numbers,complement(flip(x))) -> .
% 300.10/300.69  46608[5:SpR:154.1,9618.2] || member(u,recursion_equation_functions(v)) member(ordered_pair(v,rest_of(u)),cross_product(ordinal_numbers,ordinal_numbers)) subclass(composition_function,w) -> member(ordered_pair(v,ordered_pair(rest_of(u),u)),w)*.
% 300.10/300.69  131479[5:Res:9618.2,18794.1] || member(ordered_pair(u,v),cross_product(ordinal_numbers,ordinal_numbers)) subclass(composition_function,intersection(w,x)) member(ordered_pair(u,ordered_pair(v,compose(u,v))),symmetric_difference(w,x))* -> .
% 300.10/300.69  46625[5:Res:9618.2,897.0] || member(ordered_pair(u,v),cross_product(ordinal_numbers,ordinal_numbers)) subclass(composition_function,restrict(w,x,y))* -> member(ordered_pair(u,ordered_pair(v,compose(u,v))),cross_product(x,y))*.
% 300.10/300.69  65559[8:Res:9618.2,14681.0] || member(ordered_pair(u,v),cross_product(ordinal_numbers,ordinal_numbers)) subclass(composition_function,regular(w)) member(ordered_pair(u,ordered_pair(v,compose(u,v))),w)* -> equal(w,identity_relation).
% 300.10/300.69  196529[21:Rew:196372.1,196439.3] || member(u,ordinal_numbers) subclass(domain_relation,complement(intersection(v,w))) member(ordered_pair(u,identity_relation),union(v,w)) -> member(ordered_pair(u,identity_relation),symmetric_difference(v,w))*.
% 300.10/300.69  197260[7:MRR:197258.2,13039.0] || well_ordering(u,cross_product(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers)) subclass(singleton(least(u,rotate(v))),rotate(v)) -> section(u,singleton(least(u,rotate(v))),rotate(v))*.
% 300.10/300.69  197275[7:MRR:197273.2,13039.0] || well_ordering(u,cross_product(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers)) subclass(singleton(least(u,flip(v))),flip(v)) -> section(u,singleton(least(u,flip(v))),flip(v))*.
% 300.10/300.69  197760[7:MRR:197758.3,13039.0] || member(u,ordinal_numbers) well_ordering(v,u) subclass(singleton(least(v,sum_class(u))),sum_class(u)) -> section(v,singleton(least(v,sum_class(u))),sum_class(u))*.
% 300.10/300.69  199073[7:Res:8881.1,13362.0] || subclass(ordinal_numbers,symmetric_difference(u,v)) subclass(union(u,v),w)* well_ordering(omega,w) -> equal(integer_of(ordered_pair(omega,least(omega,union(u,v)))),identity_relation)**.
% 300.10/300.69  199072[7:Res:8892.1,13362.0] || equal(symmetric_difference(u,v),ordinal_numbers) subclass(union(u,v),w)* well_ordering(omega,w) -> equal(integer_of(ordered_pair(omega,least(omega,union(u,v)))),identity_relation)**.
% 300.10/300.69  199060[7:Res:41098.2,13362.0] || member(u,ordinal_numbers) member(v,u) subclass(element_relation,w) well_ordering(omega,w)* -> equal(integer_of(ordered_pair(ordered_pair(v,u),least(omega,element_relation))),identity_relation)**.
% 300.10/300.69  199054[21:Res:196416.2,13362.0] || member(u,ordinal_numbers) subclass(domain_relation,v) subclass(v,w)* well_ordering(omega,w)* -> equal(integer_of(ordered_pair(ordered_pair(u,identity_relation),least(omega,v))),identity_relation)**.
% 300.10/300.69  199039[7:Res:51204.1,13362.0] || member(singleton(u),subset_relation) subclass(singleton(singleton(u)),v)* well_ordering(omega,v) -> equal(integer_of(ordered_pair(singleton(u),least(omega,singleton(singleton(u))))),identity_relation)**.
% 300.10/300.69  116476[8:Rew:116078.0,51462.3] operation(u) operation(v) || compatible(w,v,u) subclass(cantor(v),subset_relation) -> homomorphism(w,v,u) member(not_homomorphism2(w,v,u),ordinal_numbers)*.
% 300.10/300.69  116475[8:Rew:116078.0,51461.3] operation(u) operation(v) || compatible(w,v,u) subclass(cantor(v),subset_relation) -> homomorphism(w,v,u) member(not_homomorphism1(w,v,u),ordinal_numbers)*.
% 300.10/300.69  47009[5:Res:18510.1,9421.0] function(u) || member(v,w)* -> equal(ordered_pair(first(ordered_pair(v,apply(u,x))),second(ordered_pair(v,apply(u,x)))),ordered_pair(v,apply(u,x)))**.
% 300.10/300.69  195695[7:Res:13225.3,21.0] || member(u,ordinal_numbers) subclass(u,cross_product(v,w))* -> equal(u,identity_relation) equal(ordered_pair(first(apply(choice,u)),second(apply(choice,u))),apply(choice,u))**.
% 300.10/300.69  163949[7:Res:13069.2,18791.0] || member(symmetric_difference(complement(u),complement(v)),ordinal_numbers) -> equal(symmetric_difference(complement(u),complement(v)),identity_relation) member(apply(choice,symmetric_difference(complement(u),complement(v))),union(u,v))*.
% 300.10/300.69  197684[7:Res:13247.2,3617.0] || member(intersection(u,symmetric_difference(v,w)),ordinal_numbers) -> equal(intersection(u,symmetric_difference(v,w)),identity_relation) member(apply(choice,intersection(u,symmetric_difference(v,w))),union(v,w))*.
% 300.10/300.69  197396[7:Res:13246.2,3617.0] || member(intersection(symmetric_difference(u,v),w),ordinal_numbers) -> equal(intersection(symmetric_difference(u,v),w),identity_relation) member(apply(choice,intersection(symmetric_difference(u,v),w)),union(u,v))*.
% 300.10/300.69  51266[5:SpL:50855.1,9470.1] || member(singleton(u),subset_relation) member(ordered_pair(first(singleton(u)),v),compose(w,x))* subclass(image(w,image(x,u)),y)* -> member(v,y)*.
% 300.10/300.69  165658[5:Res:143198.1,8803.0] || equal(image(u,image(v,singleton(w))),ordinal_numbers) member(ordered_pair(w,singleton(x)),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(w,singleton(x)),compose(u,v))*.
% 300.10/300.69  9996[5:Res:8645.1,8803.0] || subclass(ordinal_numbers,image(u,image(v,singleton(w)))) member(ordered_pair(w,singleton(x)),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(w,singleton(x)),compose(u,v))*.
% 300.10/300.69  62715[7:Res:284.1,13113.0] || member(image(u,singleton(v)),ordinal_numbers) well_ordering(w,image(u,singleton(v))) -> equal(segment(w,apply(u,v),least(w,apply(u,v))),identity_relation)**.
% 300.10/300.69  147761[0:SpL:481.0,1042.0] || member(not_subclass_element(power_class(image(element_relation,union(u,v))),w),image(element_relation,power_class(intersection(complement(u),complement(v)))))* -> subclass(power_class(image(element_relation,union(u,v))),w).
% 300.10/300.69  155462[0:Res:919.1,941.1] || member(not_subclass_element(restrict(power_class(image(element_relation,complement(u))),v,w),x),image(element_relation,power_class(u)))* -> subclass(restrict(power_class(image(element_relation,complement(u))),v,w),x).
% 300.10/300.69  29109[5:MRR:29094.0,8667.0] || member(u,v) subclass(v,w)* well_ordering(image(element_relation,complement(x)),w)* -> member(ordered_pair(u,least(image(element_relation,complement(x)),v)),power_class(x))*.
% 300.10/300.69  46631[5:Res:9618.2,288.0] || member(ordered_pair(u,v),cross_product(ordinal_numbers,ordinal_numbers)) subclass(composition_function,image(element_relation,complement(w))) member(ordered_pair(u,ordered_pair(v,compose(u,v))),power_class(w))* -> .
% 300.10/300.69  49067[5:Rew:59.0,49058.4] || member(u,ordinal_numbers) subclass(power_class(v),w)* well_ordering(x,w)* -> member(u,image(element_relation,complement(v)))* member(least(x,power_class(v)),power_class(v))*.
% 300.10/300.69  199097[14:Res:165178.0,13362.0] || subclass(image(element_relation,complement(u)),v)* well_ordering(omega,v) -> member(identity_relation,power_class(u)) equal(integer_of(ordered_pair(identity_relation,least(omega,image(element_relation,complement(u))))),identity_relation)**.
% 300.10/300.69  194694[14:Res:165178.0,129.0] || subclass(image(element_relation,complement(u)),v)* well_ordering(w,v)* -> member(identity_relation,power_class(u)) member(least(w,image(element_relation,complement(u))),image(element_relation,complement(u)))*.
% 300.10/300.69  40891[0:SpR:487.0,3603.0] ||  -> equal(intersection(complement(restrict(image(element_relation,complement(u)),v,w)),complement(intersection(power_class(u),complement(cross_product(v,w))))),symmetric_difference(image(element_relation,complement(u)),cross_product(v,w)))**.
% 300.10/300.69  41009[0:SpR:485.0,3606.0] ||  -> equal(intersection(complement(restrict(image(element_relation,complement(u)),v,w)),complement(intersection(complement(cross_product(v,w)),power_class(u)))),symmetric_difference(cross_product(v,w),image(element_relation,complement(u))))**.
% 300.10/300.69  61466[8:Rew:14756.0,61457.3] || member(ordered_pair(u,ordered_pair(v,least(range_of(identity_relation),w))),compose(identity_relation,x))* member(v,w) subclass(w,y)* well_ordering(range_of(identity_relation),y)* -> .
% 300.10/300.69  193454[8:MRR:193449.0,18.1] || member(u,image(v,range_of(identity_relation))) member(ordered_pair(w,u),cross_product(ordinal_numbers,ordinal_numbers)) -> member(w,cantor(x)) member(ordered_pair(w,u),compose(v,x))*.
% 300.10/300.69  165557[15:Res:165526.1,8803.0] || subclass(ordinal_numbers,image(u,image(v,singleton(w)))) member(ordered_pair(w,range_of(identity_relation)),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(w,range_of(identity_relation)),compose(u,v))*.
% 300.10/300.69  117722[8:Rew:116078.0,116333.2] one_to_one(inverse(u)) || subclass(range_of(inverse(u)),cantor(range_of(u))) equal(cross_product(cantor(range_of(u)),cantor(range_of(u))),range_of(u))** -> operation(inverse(u)).
% 300.10/300.69  198340[5:MRR:198336.1,41096.1] || member(least(union_of_range_map,u),ordinal_numbers)* equal(sum_class(range_of(v)),least(union_of_range_map,u))* member(v,u)* subclass(u,w)* well_ordering(union_of_range_map,w)* -> .
% 300.10/300.69  145772[8:SpR:143170.0,117728.3] function(u) || subclass(range_of(u),cantor(segment(ordinal_numbers,v,w)))* equal(cantor(cantor(x)),cantor(u)) -> compatible(u,x,cross_product(v,singleton(w)))*.
% 300.10/300.69  117721[8:Rew:116078.0,116272.2,116078.0,116272.2,116078.0,116272.1] function(u) || subclass(range_of(u),cantor(image(v,w))) equal(cantor(cantor(x)),cantor(u)) -> compatible(u,x,inverse(restrict(v,w,ordinal_numbers)))*.
% 300.10/300.69  207836[24:SpL:207558.1,8803.0] operation(u) || member(v,image(w,image(x,identity_relation))) member(ordered_pair(u,v),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(u,v),compose(w,x))*.
% 300.10/300.69  208140[8:SpL:161076.2,9470.1] || member(u,ordinal_numbers) member(ordered_pair(u,v),compose(w,x))* subclass(image(w,range_of(identity_relation)),y)* -> member(u,cantor(x)) member(v,y)*.
% 300.10/300.69  208418[21:Res:198162.1,13362.0] || subclass(ordered_pair(inverse(u),v),w)* well_ordering(omega,w) -> equal(range_of(u),identity_relation) equal(integer_of(ordered_pair(identity_relation,least(omega,ordered_pair(inverse(u),v)))),identity_relation)**.
% 300.10/300.69  208509[7:SpL:13260.1,97.0] || member(regular(cross_product(u,v)),compose_class(w)) -> equal(cross_product(u,v),identity_relation) equal(compose(w,first(regular(cross_product(u,v)))),second(regular(cross_product(u,v))))**.
% 300.10/300.69  209437[25:Rew:208885.0,209422.2] || member(image(u,identity_relation),ordinal_numbers) well_ordering(v,image(u,identity_relation)) -> equal(apply(u,ordinal_numbers),identity_relation) member(least(v,apply(u,ordinal_numbers)),apply(u,ordinal_numbers))*.
% 300.10/300.69  209637[21:Rew:197474.0,209617.2] || member(ordered_pair(inverse(u),not_subclass_element(v,image(w,image(x,identity_relation)))),compose(w,x))* -> equal(range_of(u),identity_relation) subclass(v,image(w,image(x,identity_relation))).
% 300.10/300.69  209898[24:Res:207866.1,9633.1] operation(u) || member(v,ordinal_numbers) well_ordering(w,symmetric_difference(ordinal_numbers,u)) -> member(v,successor(u))* member(least(w,complement(successor(u))),complement(successor(u)))*.
% 300.10/300.69  209989[15:Res:209921.1,8803.0] || equal(image(u,image(v,singleton(w))),ordinal_numbers) member(ordered_pair(w,range_of(identity_relation)),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(w,range_of(identity_relation)),compose(u,v))*.
% 300.10/300.69  210765[25:SpR:208820.0,117728.3] function(u) || subclass(range_of(u),cantor(segment(v,w,ordinal_numbers)))* equal(cantor(cantor(x)),cantor(u)) -> compatible(u,x,restrict(v,w,identity_relation))*.
% 300.10/300.69  211084[8:Res:210572.1,9822.1] || equal(complement(restrict(u,v,v)),ordinal_numbers) transitive(u,v) -> equal(compose(restrict(u,v,v),restrict(u,v,v)),restrict(u,v,v))**.
% 300.10/300.69  211514[8:Res:210572.1,8632.1] || equal(complement(apply(u,v)),ordinal_numbers) well_ordering(element_relation,image(u,singleton(v)))* -> equal(image(u,singleton(v)),ordinal_numbers) member(image(u,singleton(v)),ordinal_numbers).
% 300.10/300.69  211608[8:Res:10093.3,210517.1] || member(u,ordinal_numbers) member(ordered_pair(v,w),cross_product(ordinal_numbers,ordinal_numbers)) member(ordered_pair(ordered_pair(w,u),v),x)* equal(complement(rotate(x)),ordinal_numbers) -> .
% 300.10/300.69  211981[8:Res:10061.3,210517.1] || member(u,ordinal_numbers) member(ordered_pair(v,w),cross_product(ordinal_numbers,ordinal_numbers)) member(ordered_pair(ordered_pair(w,v),u),x)* equal(complement(flip(x)),ordinal_numbers) -> .
% 300.10/300.69  212305[8:Rew:143170.0,212282.2] || section(ordinal_numbers,u,v) well_ordering(w,u) -> equal(cantor(cross_product(v,u)),identity_relation) member(least(w,cantor(cross_product(v,u))),cantor(cross_product(v,u)))*.
% 300.10/300.69  212357[24:SpR:13259.2,207562.1] operation(first(apply(choice,cross_product(u,v)))) || member(cross_product(u,v),ordinal_numbers) -> equal(cross_product(u,v),identity_relation) member(identity_relation,apply(choice,cross_product(u,v)))*.
% 300.10/300.69  214728[25:Res:116127.5,214614.1] operation(u) operation(v) operation(not_homomorphism2(w,v,u)) || compatible(w,v,u) subclass(cantor(v),subset_relation) -> homomorphism(w,v,u)*.
% 300.10/300.69  214777[25:Res:116127.5,214618.1] operation(u) operation(v) operation(not_homomorphism2(w,v,u)) || compatible(w,v,u) subclass(cantor(v),rest_relation) -> homomorphism(w,v,u)*.
% 300.10/300.69  214937[0:Res:151501.1,1300.1] inductive(intersection(u,singleton(v))) || member(v,image(successor_relation,intersection(u,singleton(v))))* -> equal(image(successor_relation,intersection(u,singleton(v))),intersection(u,singleton(v))).
% 300.10/300.69  215033[0:Res:151861.1,1300.1] inductive(intersection(singleton(u),v)) || member(u,image(successor_relation,intersection(singleton(u),v)))* -> equal(image(successor_relation,intersection(singleton(u),v)),intersection(singleton(u),v)).
% 300.10/300.69  215067[5:Res:215011.1,1300.1] inductive(complement(complement(singleton(u)))) || member(u,image(successor_relation,complement(complement(singleton(u)))))* -> equal(image(successor_relation,complement(complement(singleton(u)))),complement(complement(singleton(u)))).
% 300.10/300.69  218760[21:Rew:218397.1,218713.2] || subclass(domain_relation,rest_relation) member(range_of(identity_relation),recursion_equation_functions(u)) member(ordered_pair(u,identity_relation),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(u,ordered_pair(identity_relation,range_of(identity_relation))),composition_function)*.
% 300.10/300.69  218833[21:Rew:218573.1,218783.2] || subclass(rest_relation,domain_relation) member(range_of(identity_relation),recursion_equation_functions(u)) member(ordered_pair(u,identity_relation),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(u,ordered_pair(identity_relation,range_of(identity_relation))),composition_function)*.
% 300.10/300.69  218907[21:Rew:218384.1,218854.2] || subclass(domain_relation,rest_relation) member(singleton(u),recursion_equation_functions(v)) member(ordered_pair(v,identity_relation),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(v,ordered_pair(identity_relation,singleton(u))),composition_function)*.
% 300.10/300.69  218974[21:Rew:218560.1,218918.2] || subclass(rest_relation,domain_relation) member(singleton(u),recursion_equation_functions(v)) member(ordered_pair(v,identity_relation),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(v,ordered_pair(identity_relation,singleton(u))),composition_function)*.
% 300.10/300.69  219626[8:Res:9618.2,67561.0] || member(ordered_pair(u,v),cross_product(ordinal_numbers,ordinal_numbers)) subclass(composition_function,symmetric_difference(complement(w),ordinal_numbers)) -> member(ordered_pair(u,ordered_pair(v,compose(u,v))),union(w,identity_relation))*.
% 300.10/300.69  219807[8:Res:67614.1,40594.1] || member(singleton(symmetric_difference(complement(u),ordinal_numbers)),union(u,identity_relation))* member(symmetric_difference(complement(u),ordinal_numbers),ordinal_numbers) -> member(singleton(singleton(singleton(symmetric_difference(complement(u),ordinal_numbers)))),element_relation)*.
% 300.10/300.69  220064[8:Res:9618.2,160772.0] || member(ordered_pair(u,v),cross_product(ordinal_numbers,ordinal_numbers)) subclass(composition_function,symmetric_difference(ordinal_numbers,w)) member(ordered_pair(u,ordered_pair(v,compose(u,v))),union(w,identity_relation))* -> .
% 300.10/300.69  220423[21:Res:196656.1,21.0] || subclass(domain_relation,flip(cross_product(u,v)))* -> equal(ordered_pair(first(ordered_pair(ordered_pair(w,x),identity_relation)),second(ordered_pair(ordered_pair(w,x),identity_relation))),ordered_pair(ordered_pair(w,x),identity_relation))**.
% 300.10/300.69  220566[21:Res:196657.1,9880.0] || subclass(domain_relation,rotate(compose(u,v))) member(w,x)* subclass(x,y)* well_ordering(image(u,image(v,singleton(ordered_pair(z,identity_relation)))),y)* -> .
% 300.10/300.69  220525[21:Res:196657.1,21.0] || subclass(domain_relation,rotate(cross_product(u,v)))* -> equal(ordered_pair(first(ordered_pair(ordered_pair(w,identity_relation),x)),second(ordered_pair(ordered_pair(w,identity_relation),x))),ordered_pair(ordered_pair(w,identity_relation),x))**.
% 300.10/300.69  221131[7:Res:13236.2,18791.0] || well_ordering(u,symmetric_difference(complement(v),complement(w))) -> equal(symmetric_difference(complement(v),complement(w)),identity_relation) member(least(u,symmetric_difference(complement(v),complement(w))),union(v,w))*.
% 300.10/300.69  222660[21:MRR:222659.3,13126.0] function(sum_class(range_of(identity_relation))) function(u) || subclass(domain_relation,rest_relation) equal(compose(u,identity_relation),sum_class(range_of(identity_relation))) -> member(sum_class(range_of(identity_relation)),recursion_equation_functions(u))*.
% 300.10/300.69  223230[21:MRR:223229.3,13126.0] function(regular(symmetrization_of(identity_relation))) function(u) || subclass(domain_relation,rest_relation) equal(compose(u,identity_relation),regular(symmetrization_of(identity_relation))) -> member(regular(symmetrization_of(identity_relation)),recursion_equation_functions(u))*.
% 300.10/300.69  223290[21:MRR:223289.3,13126.0] function(least(element_relation,omega)) function(u) || subclass(domain_relation,rest_relation) equal(compose(u,identity_relation),least(element_relation,omega)) -> member(least(element_relation,omega),recursion_equation_functions(u))*.
% 300.10/300.69  223358[21:MRR:223357.3,13126.0] function(sum_class(range_of(identity_relation))) function(u) || subclass(rest_relation,domain_relation) equal(compose(u,identity_relation),sum_class(range_of(identity_relation))) -> member(sum_class(range_of(identity_relation)),recursion_equation_functions(u))*.
% 300.10/300.69  223424[21:MRR:223423.3,13126.0] function(regular(symmetrization_of(identity_relation))) function(u) || subclass(rest_relation,domain_relation) equal(compose(u,identity_relation),regular(symmetrization_of(identity_relation))) -> member(regular(symmetrization_of(identity_relation)),recursion_equation_functions(u))*.
% 300.10/300.69  223555[21:MRR:223554.3,13126.0] function(least(element_relation,omega)) function(u) || subclass(rest_relation,domain_relation) equal(compose(u,identity_relation),least(element_relation,omega)) -> member(least(element_relation,omega),recursion_equation_functions(u))*.
% 300.10/300.69  223858[8:SpL:160927.0,13306.0] || member(regular(power_class(intersection(complement(u),union(v,identity_relation)))),image(element_relation,union(u,symmetric_difference(ordinal_numbers,v))))* -> equal(power_class(intersection(complement(u),union(v,identity_relation))),identity_relation).
% 300.10/300.69  223752[8:SpR:160927.0,3616.0] ||  -> equal(intersection(union(u,intersection(complement(v),union(w,identity_relation))),union(complement(u),union(v,symmetric_difference(ordinal_numbers,w)))),symmetric_difference(complement(u),union(v,symmetric_difference(ordinal_numbers,w))))**.
% 300.10/300.69  223719[8:SpR:160927.0,19486.0] ||  -> equal(power_class(intersection(union(u,symmetric_difference(ordinal_numbers,v)),complement(inverse(intersection(complement(u),union(v,identity_relation)))))),complement(image(element_relation,symmetrization_of(intersection(complement(u),union(v,identity_relation))))))**.
% 300.10/300.69  223717[8:SpR:160927.0,19485.0] ||  -> equal(power_class(intersection(union(u,symmetric_difference(ordinal_numbers,v)),complement(singleton(intersection(complement(u),union(v,identity_relation)))))),complement(image(element_relation,successor(intersection(complement(u),union(v,identity_relation))))))**.
% 300.10/300.69  223712[8:SpR:160927.0,3616.0] ||  -> equal(intersection(union(intersection(complement(u),union(v,identity_relation)),w),union(union(u,symmetric_difference(ordinal_numbers,v)),complement(w))),symmetric_difference(union(u,symmetric_difference(ordinal_numbers,v)),complement(w)))**.
% 300.10/300.69  224177[8:SpL:160992.0,13306.0] || member(regular(power_class(intersection(union(u,identity_relation),complement(v)))),image(element_relation,union(symmetric_difference(ordinal_numbers,u),v)))* -> equal(power_class(intersection(union(u,identity_relation),complement(v))),identity_relation).
% 300.10/300.69  224069[8:SpR:160992.0,3616.0] ||  -> equal(intersection(union(u,intersection(union(v,identity_relation),complement(w))),union(complement(u),union(symmetric_difference(ordinal_numbers,v),w))),symmetric_difference(complement(u),union(symmetric_difference(ordinal_numbers,v),w)))**.
% 300.10/300.69  224036[8:SpR:160992.0,19486.0] ||  -> equal(power_class(intersection(union(symmetric_difference(ordinal_numbers,u),v),complement(inverse(intersection(union(u,identity_relation),complement(v)))))),complement(image(element_relation,symmetrization_of(intersection(union(u,identity_relation),complement(v))))))**.
% 300.10/300.69  224034[8:SpR:160992.0,19485.0] ||  -> equal(power_class(intersection(union(symmetric_difference(ordinal_numbers,u),v),complement(singleton(intersection(union(u,identity_relation),complement(v)))))),complement(image(element_relation,successor(intersection(union(u,identity_relation),complement(v))))))**.
% 300.10/300.69  224029[8:SpR:160992.0,3616.0] ||  -> equal(intersection(union(intersection(union(u,identity_relation),complement(v)),w),union(union(symmetric_difference(ordinal_numbers,u),v),complement(w))),symmetric_difference(union(symmetric_difference(ordinal_numbers,u),v),complement(w)))**.
% 300.10/300.69  224333[8:MRR:224288.0,60996.1] ||  -> member(regular(regular(intersection(complement(u),complement(v)))),union(u,v))* equal(regular(intersection(complement(u),complement(v))),identity_relation) equal(intersection(complement(u),complement(v)),identity_relation).
% 300.10/300.69  226165[8:Res:116148.1,17321.0] || section(u,intersection(v,w),x) -> equal(cantor(restrict(u,x,intersection(v,w))),identity_relation) member(regular(cantor(restrict(u,x,intersection(v,w)))),w)*.
% 300.10/300.69  226270[8:Res:116148.1,17322.0] || section(u,intersection(v,w),x) -> equal(cantor(restrict(u,x,intersection(v,w))),identity_relation) member(regular(cantor(restrict(u,x,intersection(v,w)))),v)*.
% 300.10/300.69  226414[7:Res:13258.1,12.0] ||  -> equal(restrict(unordered_pair(u,v),w,x),identity_relation) equal(regular(restrict(unordered_pair(u,v),w,x)),v)** equal(regular(restrict(unordered_pair(u,v),w,x)),u)**.
% 300.10/300.69  226386[7:Res:13258.1,13362.0] || subclass(u,v)* well_ordering(omega,v)* -> equal(restrict(u,w,x),identity_relation) equal(integer_of(ordered_pair(regular(restrict(u,w,x)),least(omega,u))),identity_relation)**.
% 300.10/300.69  226803[7:Rew:481.0,226794.2] || subclass(omega,image(element_relation,union(u,v))) -> equal(integer_of(regular(power_class(intersection(complement(u),complement(v))))),identity_relation)** equal(power_class(intersection(complement(u),complement(v))),identity_relation).
% 300.10/300.69  227254[5:SpR:61728.2,9005.1] || member(u,ordinal_numbers) subclass(rest_relation,union_of_range_map) member(restrict(element_relation,ordinal_numbers,range_of(u)),ordinal_numbers) -> member(ordered_pair(restrict(element_relation,ordinal_numbers,range_of(u)),rest_of(u)),domain_relation)*.
% 300.10/300.69  227342[7:SpR:192979.1,62.1] || member(ordered_pair(u,v),compose(regular(cross_product(image(w,singleton(u)),ordinal_numbers)),w))* -> equal(cross_product(image(w,singleton(u)),ordinal_numbers),identity_relation) member(v,range_of(identity_relation)).
% 300.10/300.69  227817[21:MRR:227816.3,13126.0] function(unordered_pair(u,v)) function(w) || subclass(domain_relation,rest_relation) equal(compose(w,identity_relation),unordered_pair(u,v)) -> member(unordered_pair(u,v),recursion_equation_functions(w))*.
% 300.10/300.69  227890[21:MRR:227889.3,13126.0] function(ordered_pair(u,v)) function(w) || subclass(domain_relation,rest_relation) equal(compose(w,identity_relation),ordered_pair(u,v)) -> member(ordered_pair(u,v),recursion_equation_functions(w))*.
% 300.10/300.69  227962[21:MRR:227961.3,13126.0] function(unordered_pair(u,v)) function(w) || subclass(rest_relation,domain_relation) equal(compose(w,identity_relation),unordered_pair(u,v)) -> member(unordered_pair(u,v),recursion_equation_functions(w))*.
% 300.10/300.69  228056[21:MRR:228055.3,13126.0] function(ordered_pair(u,v)) function(w) || subclass(rest_relation,domain_relation) equal(compose(w,identity_relation),ordered_pair(u,v)) -> member(ordered_pair(u,v),recursion_equation_functions(w))*.
% 300.10/300.69  229214[7:Rew:481.0,229100.1] || member(regular(intersection(power_class(intersection(complement(u),complement(v))),w)),image(element_relation,union(u,v)))* -> equal(intersection(power_class(intersection(complement(u),complement(v))),w),identity_relation).
% 300.10/300.69  229801[7:Rew:481.0,229543.1] || member(regular(intersection(u,power_class(intersection(complement(v),complement(w))))),image(element_relation,union(v,w)))* -> equal(intersection(u,power_class(intersection(complement(v),complement(w)))),identity_relation).
% 300.10/300.69  231251[7:SpR:155666.0,17447.1] ||  -> equal(symmetric_difference(complement(subset_relation),union(cross_product(ordinal_numbers,ordinal_numbers),subset_relation)),identity_relation) member(regular(symmetric_difference(complement(subset_relation),union(cross_product(ordinal_numbers,ordinal_numbers),subset_relation))),complement(symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation)))*.
% 300.10/300.69  231250[7:SpR:155665.0,17447.1] ||  -> equal(symmetric_difference(complement(subset_relation),union(subset_relation,cross_product(ordinal_numbers,ordinal_numbers))),identity_relation) member(regular(symmetric_difference(complement(subset_relation),union(subset_relation,cross_product(ordinal_numbers,ordinal_numbers)))),complement(symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers))))*.
% 300.10/300.69  232050[7:Res:9604.1,17323.0] || equal(sum_class(restrict(u,v,w)),restrict(u,v,w)) -> equal(sum_class(restrict(u,v,w)),identity_relation) member(regular(sum_class(restrict(u,v,w))),u)*.
% 300.10/300.69  233206[8:Rew:160992.0,233174.1] || member(regular(image(element_relation,union(symmetric_difference(ordinal_numbers,u),v))),power_class(intersection(union(u,identity_relation),complement(v))))* -> equal(image(element_relation,union(symmetric_difference(ordinal_numbers,u),v)),identity_relation).
% 300.10/300.69  233207[8:Rew:160927.0,233173.1] || member(regular(image(element_relation,union(u,symmetric_difference(ordinal_numbers,v)))),power_class(intersection(complement(u),union(v,identity_relation))))* -> equal(image(element_relation,union(u,symmetric_difference(ordinal_numbers,v))),identity_relation).
% 300.10/300.69  233321[8:Res:231881.0,9633.1] || member(u,ordinal_numbers)* well_ordering(v,complement(singleton(complement(w)))) -> equal(singleton(complement(w)),identity_relation) member(u,w)* member(least(v,complement(w)),complement(w))*.
% 300.10/300.69  233519[21:Res:8551.2,196424.2] || member(ordered_pair(u,identity_relation),cross_product(v,w))* member(ordered_pair(u,identity_relation),x)* member(u,ordinal_numbers) subclass(domain_relation,complement(restrict(x,v,w)))* -> .
% 300.10/300.69  233965[8:Res:919.1,161200.0] || member(not_subclass_element(restrict(image(element_relation,union(u,identity_relation)),v,w),x),power_class(symmetric_difference(ordinal_numbers,u)))* -> subclass(restrict(image(element_relation,union(u,identity_relation)),v,w),x).
% 300.10/300.69  234096[8:SpR:13259.2,233383.0] || member(cross_product(u,v),ordinal_numbers) -> equal(cross_product(u,v),identity_relation) member(singleton(first(apply(choice,cross_product(u,v)))),complement(singleton(apply(choice,cross_product(u,v)))))*.
% 300.10/300.69  234171[8:Rew:160992.0,234146.2] || subclass(omega,intersection(union(u,identity_relation),complement(v))) -> equal(integer_of(not_subclass_element(union(symmetric_difference(ordinal_numbers,u),v),w)),identity_relation)** subclass(union(symmetric_difference(ordinal_numbers,u),v),w).
% 300.10/300.69  234172[8:Rew:160927.0,234145.2] || subclass(omega,intersection(complement(u),union(v,identity_relation))) -> equal(integer_of(not_subclass_element(union(u,symmetric_difference(ordinal_numbers,v)),w)),identity_relation)** subclass(union(u,symmetric_difference(ordinal_numbers,v)),w).
% 300.10/300.69  234179[8:SpL:13259.2,234106.0] || member(cross_product(u,v),ordinal_numbers) member(singleton(first(apply(choice,cross_product(u,v)))),singleton(apply(choice,cross_product(u,v))))* -> equal(cross_product(u,v),identity_relation).
% 300.10/300.69  234389[8:Rew:160992.0,234332.2] || well_ordering(u,ordinal_numbers) member(least(u,union(symmetric_difference(ordinal_numbers,v),w)),intersection(union(v,identity_relation),complement(w)))* -> equal(union(symmetric_difference(ordinal_numbers,v),w),identity_relation).
% 300.10/300.69  234390[8:Rew:160927.0,234331.2] || well_ordering(u,ordinal_numbers) member(least(u,union(v,symmetric_difference(ordinal_numbers,w))),intersection(complement(v),union(w,identity_relation)))* -> equal(union(v,symmetric_difference(ordinal_numbers,w)),identity_relation).
% 300.10/300.69  235034[7:SpL:234956.0,8803.0] || member(u,range_of(identity_relation)) member(ordered_pair(v,u),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(v,u),compose(complement(cross_product(image(w,singleton(v)),ordinal_numbers)),w))*.
% 300.10/300.69  235029[7:SpL:234956.0,8803.0] || member(u,image(v,range_of(identity_relation))) member(ordered_pair(w,u),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(w,u),compose(v,complement(cross_product(singleton(w),ordinal_numbers))))*.
% 300.10/300.69  235125[8:Rew:160992.0,235064.1] ||  -> member(not_subclass_element(u,image(element_relation,union(symmetric_difference(ordinal_numbers,v),w))),power_class(intersection(union(v,identity_relation),complement(w))))* subclass(u,image(element_relation,union(symmetric_difference(ordinal_numbers,v),w))).
% 300.10/300.69  235126[8:Rew:160927.0,235063.1] ||  -> member(not_subclass_element(u,image(element_relation,union(v,symmetric_difference(ordinal_numbers,w)))),power_class(intersection(complement(v),union(w,identity_relation))))* subclass(u,image(element_relation,union(v,symmetric_difference(ordinal_numbers,w)))).
% 300.10/300.69  235453[5:Res:28980.1,8800.1] || subclass(rest_relation,flip(cross_product(ordinal_numbers,ordinal_numbers))) member(ordered_pair(u,v),rest_of(ordered_pair(v,u))) -> member(ordered_pair(ordered_pair(u,v),rest_of(ordered_pair(v,u))),element_relation)*.
% 300.10/300.69  235581[5:Res:28979.1,8800.1] || subclass(rest_relation,rotate(cross_product(ordinal_numbers,ordinal_numbers))) member(ordered_pair(u,rest_of(ordered_pair(v,u))),v) -> member(ordered_pair(ordered_pair(u,rest_of(ordered_pair(v,u))),v),element_relation)*.
% 300.10/300.69  235710[0:Res:2504.1,36719.1] operation(u) || subclass(ordered_pair(v,w),cantor(u))* -> equal(ordered_pair(first(unordered_pair(v,singleton(w))),second(unordered_pair(v,singleton(w)))),unordered_pair(v,singleton(w)))**.
% 300.10/300.69  235802[8:Res:116148.1,19113.0] || section(u,recursion_equation_functions(v),w) -> subclass(cantor(restrict(u,w,recursion_equation_functions(v))),x) subclass(not_subclass_element(cantor(restrict(u,w,recursion_equation_functions(v))),x),cross_product(ordinal_numbers,ordinal_numbers))*.
% 300.10/300.69  235952[8:Res:69478.2,18747.0] || subclass(omega,symmetric_difference(u,v)) -> equal(integer_of(not_subclass_element(regular(union(u,v)),w)),identity_relation)** subclass(regular(union(u,v)),w) equal(union(u,v),identity_relation).
% 300.10/300.69  235932[8:Res:69478.2,61018.0] || subclass(omega,symmetric_difference(u,v)) -> equal(integer_of(apply(choice,regular(union(u,v)))),identity_relation)** equal(regular(union(u,v)),identity_relation) equal(union(u,v),identity_relation).
% 300.10/300.69  236325[8:Rew:160992.0,236213.1] || member(not_subclass_element(intersection(u,union(symmetric_difference(ordinal_numbers,v),w)),x),intersection(union(v,identity_relation),complement(w)))* -> subclass(intersection(u,union(symmetric_difference(ordinal_numbers,v),w)),x).
% 300.10/300.69  236326[8:Rew:160927.0,236212.1] || member(not_subclass_element(intersection(u,union(v,symmetric_difference(ordinal_numbers,w))),x),intersection(complement(v),union(w,identity_relation)))* -> subclass(intersection(u,union(v,symmetric_difference(ordinal_numbers,w))),x).
% 300.10/300.69  236546[8:Rew:160992.0,236402.1] || member(not_subclass_element(intersection(union(symmetric_difference(ordinal_numbers,u),v),w),x),intersection(union(u,identity_relation),complement(v)))* -> subclass(intersection(union(symmetric_difference(ordinal_numbers,u),v),w),x).
% 300.10/300.69  236547[8:Rew:160927.0,236401.1] || member(not_subclass_element(intersection(union(u,symmetric_difference(ordinal_numbers,v)),w),x),intersection(complement(u),union(v,identity_relation)))* -> subclass(intersection(union(u,symmetric_difference(ordinal_numbers,v)),w),x).
% 300.10/300.69  237103[7:Res:13574.1,490.0] || member(regular(intersection(u,intersection(v,intersection(complement(w),complement(x))))),union(w,x))* -> equal(intersection(u,intersection(v,intersection(complement(w),complement(x)))),identity_relation).
% 300.10/300.69  237754[7:Res:13573.1,490.0] || member(regular(intersection(u,intersection(intersection(complement(v),complement(w)),x))),union(v,w))* -> equal(intersection(u,intersection(intersection(complement(v),complement(w)),x)),identity_relation).
% 300.10/300.69  239266[7:Res:17397.1,490.0] || member(regular(intersection(intersection(intersection(complement(u),complement(v)),w),x)),union(u,v))* -> equal(intersection(intersection(intersection(complement(u),complement(v)),w),x),identity_relation).
% 300.10/300.69  240101[7:Res:17396.1,490.0] || member(regular(intersection(intersection(u,intersection(complement(v),complement(w))),x)),union(v,w))* -> equal(intersection(intersection(u,intersection(complement(v),complement(w))),x),identity_relation).
% 300.10/300.69  48492[0:SpR:3594.0,3618.1] || member(u,symmetric_difference(complement(symmetric_difference(v,w)),union(complement(intersection(v,w)),union(v,w))))* -> member(u,complement(symmetric_difference(complement(intersection(v,w)),union(v,w)))).
% 300.10/300.69  50360[0:Res:10.1,9636.2] || equal(u,intersection(v,w))* member(x,w)* member(x,v)* well_ordering(y,u)* -> member(least(y,intersection(v,w)),intersection(v,w))*.
% 300.10/300.69  50243[0:Res:10.1,9660.2] || equal(u,cross_product(v,w))* member(x,w)* member(y,v)* well_ordering(z,u)* -> member(least(z,cross_product(v,w)),cross_product(v,w))*.
% 300.10/300.69  41063[0:SpL:3603.0,8559.2] || member(u,union(v,cross_product(w,x)))* member(u,complement(restrict(v,w,x))) subclass(symmetric_difference(v,cross_product(w,x)),y)* -> member(u,y)*.
% 300.10/300.69  41064[0:SpL:3606.0,8559.2] || member(u,union(cross_product(v,w),x))* member(u,complement(restrict(x,v,w))) subclass(symmetric_difference(cross_product(v,w),x),y)* -> member(u,y)*.
% 300.10/300.69  49650[0:SpL:6355.1,149.0] || member(not_subclass_element(cross_product(u,v),w),rest_relation) -> subclass(cross_product(u,v),w) equal(rest_of(first(not_subclass_element(cross_product(u,v),w))),second(not_subclass_element(cross_product(u,v),w)))**.
% 300.10/300.69  43718[0:Res:6.1,8554.1] || member(not_subclass_element(complement(intersection(u,v)),w),union(u,v)) -> subclass(complement(intersection(u,v)),w) member(not_subclass_element(complement(intersection(u,v)),w),symmetric_difference(u,v))*.
% 300.10/300.69  46868[5:Rew:30.0,46847.3] || member(u,v) subclass(v,w)* well_ordering(union(x,y),w)* -> member(ordered_pair(u,least(union(x,y),v)),intersection(complement(x),complement(y)))*.
% 300.10/300.69  69375[8:Res:69184.1,8562.0] || member(not_subclass_element(u,intersection(v,compose(element_relation,ordinal_numbers))),element_relation)* member(not_subclass_element(u,intersection(v,compose(element_relation,ordinal_numbers))),v)* -> subclass(u,intersection(v,compose(element_relation,ordinal_numbers))).
% 300.10/300.69  116329[8:Rew:116078.0,49638.2] || member(not_subclass_element(cross_product(u,v),w),domain_relation) -> subclass(cross_product(u,v),w) equal(cantor(first(not_subclass_element(cross_product(u,v),w))),second(not_subclass_element(cross_product(u,v),w)))**.
% 300.10/300.69  131394[0:SpL:3594.0,18794.1] || member(u,symmetric_difference(complement(symmetric_difference(v,w)),union(complement(intersection(v,w)),union(v,w))))* member(u,symmetric_difference(complement(intersection(v,w)),union(v,w))) -> .
% 300.10/300.69  139831[5:MRR:139802.0,41183.1] || member(not_subclass_element(u,intersection(v,union(w,x))),v)* -> member(not_subclass_element(u,intersection(v,union(w,x))),complement(x))* subclass(u,intersection(v,union(w,x))).
% 300.10/300.69  139914[5:MRR:139888.0,41183.1] || member(not_subclass_element(u,intersection(v,union(w,x))),v)* -> member(not_subclass_element(u,intersection(v,union(w,x))),complement(w))* subclass(u,intersection(v,union(w,x))).
% 300.10/300.69  140384[0:Res:27.2,47534.0] || member(not_subclass_element(u,intersection(intersection(v,w),u)),w)* member(not_subclass_element(u,intersection(intersection(v,w),u)),v)* -> subclass(u,intersection(intersection(v,w),u)).
% 300.10/300.69  140471[0:Rew:3616.0,140342.1] || member(not_subclass_element(union(complement(u),complement(v)),symmetric_difference(complement(u),complement(v))),union(u,v))* -> subclass(union(complement(u),complement(v)),symmetric_difference(complement(u),complement(v))).
% 300.10/300.69  145791[8:SpL:143170.0,116116.1] || member(u,cantor(ordinal_numbers))* equal(cross_product(u,ordinal_numbers),least(rest_of(ordinal_numbers),v))* member(u,v)* subclass(v,w)* well_ordering(rest_of(ordinal_numbers),w)* -> .
% 300.10/300.69  145800[5:Rew:143170.0,145785.2] || transitive(ordinal_numbers,u) subclass(cross_product(u,u),compose(cross_product(u,u),cross_product(u,u)))* -> equal(compose(cross_product(u,u),cross_product(u,u)),cross_product(u,u)).
% 300.10/300.69  152924[8:Res:116148.1,19121.0] || section(u,intersection(v,w),x) -> subclass(cantor(restrict(u,x,intersection(v,w))),y) member(not_subclass_element(cantor(restrict(u,x,intersection(v,w))),y),v)*.
% 300.10/300.69  152923[0:Res:133.2,19121.0] || connected(u,intersection(v,w)) -> well_ordering(u,intersection(v,w)) subclass(not_well_ordering(u,intersection(v,w)),x) member(not_subclass_element(not_well_ordering(u,intersection(v,w)),x),v)*.
% 300.10/300.69  153048[8:Res:116148.1,19120.0] || section(u,intersection(v,w),x) -> subclass(cantor(restrict(u,x,intersection(v,w))),y) member(not_subclass_element(cantor(restrict(u,x,intersection(v,w))),y),w)*.
% 300.10/300.69  153047[0:Res:133.2,19120.0] || connected(u,intersection(v,w)) -> well_ordering(u,intersection(v,w)) subclass(not_well_ordering(u,intersection(v,w)),x) member(not_subclass_element(not_well_ordering(u,intersection(v,w)),x),w)*.
% 300.10/300.69  49651[0:SpL:6355.1,49.0] || member(not_subclass_element(cross_product(u,v),w),successor_relation) -> subclass(cross_product(u,v),w) equal(successor(first(not_subclass_element(cross_product(u,v),w))),second(not_subclass_element(cross_product(u,v),w)))**.
% 300.10/300.69  161730[8:Rew:160496.0,69586.2,160498.0,69586.1] inductive(symmetric_difference(ordinal_numbers,union(identity_relation,u))) || well_ordering(v,complement(complement(complement(u)))) -> member(least(v,symmetric_difference(ordinal_numbers,complement(complement(u)))),symmetric_difference(ordinal_numbers,complement(complement(u))))*.
% 300.10/300.69  126569[5:Res:9461.1,9665.1] inductive(not_subclass_element(recursion_equation_functions(u),v)) || well_ordering(w,cross_product(ordinal_numbers,ordinal_numbers)) -> subclass(recursion_equation_functions(u),v) member(least(w,not_subclass_element(recursion_equation_functions(u),v)),not_subclass_element(recursion_equation_functions(u),v))*.
% 300.10/300.69  117737[8:Rew:116078.0,116755.2] operation(u) ||  -> subclass(v,complement(cantor(u))) equal(ordered_pair(first(not_subclass_element(v,complement(cantor(u)))),second(not_subclass_element(v,complement(cantor(u))))),not_subclass_element(v,complement(cantor(u))))**.
% 300.10/300.69  117733[8:Rew:116078.0,116580.3,116078.0,116580.1] operation(u) || member(not_subclass_element(cross_product(v,w),x),cantor(u)) -> subclass(cross_product(v,w),x) member(second(not_subclass_element(cross_product(v,w),x)),cantor(cantor(u)))*.
% 300.10/300.69  117732[8:Rew:116078.0,116579.3,116078.0,116579.1] operation(u) || member(not_subclass_element(cross_product(v,w),x),cantor(u)) -> subclass(cross_product(v,w),x) member(first(not_subclass_element(cross_product(v,w),x)),cantor(cantor(u)))*.
% 300.10/300.69  63736[7:Res:8551.2,13105.0] || member(regular(complement(restrict(u,v,w))),cross_product(v,w))* member(regular(complement(restrict(u,v,w))),u)* -> equal(complement(restrict(u,v,w)),identity_relation).
% 300.10/300.69  64306[7:Res:13248.1,3689.0] ||  -> equal(intersection(ordered_pair(u,v),w),identity_relation) equal(regular(intersection(ordered_pair(u,v),w)),unordered_pair(u,singleton(v)))** equal(regular(intersection(ordered_pair(u,v),w)),singleton(u)).
% 300.10/300.69  64217[7:Res:13210.1,3689.0] ||  -> equal(intersection(u,ordered_pair(v,w)),identity_relation) equal(regular(intersection(u,ordered_pair(v,w))),unordered_pair(v,singleton(w)))** equal(regular(intersection(u,ordered_pair(v,w))),singleton(v)).
% 300.10/300.69  190339[8:Res:161196.2,13070.0] operation(u) || connected(v,cantor(cantor(u)))* well_ordering(w,complement(complement(symmetrization_of(v))))* -> equal(cantor(u),identity_relation) member(least(w,cantor(u)),cantor(u))*.
% 300.10/300.69  132255[2:Res:39609.2,9878.0] inductive(u) || well_ordering(cross_product(v,u),u)* member(w,v)* member(w,u)* subclass(u,x) well_ordering(cross_product(v,u),x)* -> .
% 300.10/300.69  132214[2:Res:39609.2,490.0] inductive(intersection(complement(u),complement(v))) || well_ordering(w,intersection(complement(u),complement(v))) member(least(w,intersection(complement(u),complement(v))),union(u,v))* -> .
% 300.10/300.69  131226[5:Res:39607.2,9878.0] inductive(u) || well_ordering(cross_product(v,u),ordinal_numbers)* member(w,v)* member(w,u)* subclass(u,x) well_ordering(cross_product(v,u),x)* -> .
% 300.10/300.69  65424[7:Res:13237.2,9878.0] || well_ordering(cross_product(u,v),ordinal_numbers)* member(w,u)* member(w,v)* subclass(v,x) well_ordering(cross_product(u,v),x)* -> equal(v,identity_relation).
% 300.10/300.69  47010[5:Res:19525.1,9421.0] || well_ordering(u,ordinal_numbers) member(v,w)* -> equal(ordered_pair(first(ordered_pair(v,least(u,ordinal_numbers))),second(ordered_pair(v,least(u,ordinal_numbers)))),ordered_pair(v,least(u,ordinal_numbers)))**.
% 300.10/300.69  133493[5:Res:133486.1,9421.0] || well_ordering(u,ordinal_numbers) member(v,w)* -> equal(ordered_pair(first(ordered_pair(v,least(u,rest_relation))),second(ordered_pair(v,least(u,rest_relation)))),ordered_pair(v,least(u,rest_relation)))**.
% 300.10/300.69  133500[5:Res:133488.1,9421.0] || well_ordering(u,rest_relation) member(v,w)* -> equal(ordered_pair(first(ordered_pair(v,least(u,rest_relation))),second(ordered_pair(v,least(u,rest_relation)))),ordered_pair(v,least(u,rest_relation)))**.
% 300.10/300.69  139778[5:Res:39529.1,129.0] || member(u,ordinal_numbers) subclass(union(v,w),x)* well_ordering(y,x)* -> member(u,complement(w))* member(least(y,union(v,w)),union(v,w))*.
% 300.10/300.69  139864[5:Res:39530.1,129.0] || member(u,ordinal_numbers) subclass(union(v,w),x)* well_ordering(y,x)* -> member(u,complement(v))* member(least(y,union(v,w)),union(v,w))*.
% 300.10/300.69  136691[5:Res:9618.2,18791.0] || member(ordered_pair(u,v),cross_product(ordinal_numbers,ordinal_numbers)) subclass(composition_function,symmetric_difference(complement(w),complement(x))) -> member(ordered_pair(u,ordered_pair(v,compose(u,v))),union(w,x))*.
% 300.10/300.69  199081[7:Res:919.1,13362.0] || subclass(u,v)* well_ordering(omega,v)* -> subclass(restrict(u,w,x),y) equal(integer_of(ordered_pair(not_subclass_element(restrict(u,w,x),y),least(omega,u))),identity_relation)**.
% 300.10/300.69  199051[7:Res:8827.2,13362.0] || member(u,ordinal_numbers) subclass(rest_relation,v) subclass(v,w)* well_ordering(omega,w)* -> equal(integer_of(ordered_pair(ordered_pair(u,rest_of(u)),least(omega,v))),identity_relation)**.
% 300.10/300.69  198965[8:Res:116403.2,13362.0] || member(u,ordinal_numbers) subclass(rest_relation,rest_of(v)) subclass(cantor(v),w)* well_ordering(omega,w) -> equal(integer_of(ordered_pair(u,least(omega,cantor(v)))),identity_relation)**.
% 300.10/300.69  68560[8:Res:94.3,66290.0] operation(u) operation(v) || compatible(w,v,u) -> homomorphism(w,v,u) member(ordered_pair(not_homomorphism1(w,v,u),not_homomorphism2(w,v,u)),cantor(v))*.
% 300.10/300.69  83684[8:Res:83661.1,93.0] || equal(cantor(u),domain_relation) homomorphism(v,u,w)* -> equal(apply(w,ordered_pair(apply(v,identity_relation),apply(v,identity_relation))),apply(v,apply(u,ordered_pair(identity_relation,identity_relation))))*.
% 300.10/300.69  83207[8:Res:83183.1,93.0] || subclass(domain_relation,cantor(u)) homomorphism(v,u,w)* -> equal(apply(w,ordered_pair(apply(v,identity_relation),apply(v,identity_relation))),apply(v,apply(u,ordered_pair(identity_relation,identity_relation))))*.
% 300.10/300.69  116725[8:Rew:116078.0,10127.0] || subclass(ordinal_numbers,cantor(u)) homomorphism(v,u,w)* -> equal(apply(w,ordered_pair(apply(v,x),apply(v,y))),apply(v,apply(u,ordered_pair(x,y))))*.
% 300.10/300.69  195702[7:Res:13225.3,3689.0] || member(u,ordinal_numbers) subclass(u,ordered_pair(v,w))* -> equal(u,identity_relation) equal(apply(choice,u),unordered_pair(v,singleton(w))) equal(apply(choice,u),singleton(v)).
% 300.10/300.69  197699[7:Res:13247.2,898.0] || member(intersection(u,restrict(v,w,x)),ordinal_numbers) -> equal(intersection(u,restrict(v,w,x)),identity_relation) member(apply(choice,intersection(u,restrict(v,w,x))),v)*.
% 300.10/300.69  197680[7:Res:13247.2,18794.1] || member(intersection(u,intersection(v,w)),ordinal_numbers) member(apply(choice,intersection(u,intersection(v,w))),symmetric_difference(v,w))* -> equal(intersection(u,intersection(v,w)),identity_relation).
% 300.10/300.69  197410[7:Res:13246.2,898.0] || member(intersection(restrict(u,v,w),x),ordinal_numbers) -> equal(intersection(restrict(u,v,w),x),identity_relation) member(apply(choice,intersection(restrict(u,v,w),x)),u)*.
% 300.10/300.69  197392[7:Res:13246.2,18794.1] || member(intersection(intersection(u,v),w),ordinal_numbers) member(apply(choice,intersection(intersection(u,v),w)),symmetric_difference(u,v))* -> equal(intersection(intersection(u,v),w),identity_relation).
% 300.10/300.69  61925[7:Res:13069.2,490.0] || member(intersection(complement(u),complement(v)),ordinal_numbers) member(apply(choice,intersection(complement(u),complement(v))),union(u,v))* -> equal(intersection(complement(u),complement(v)),identity_relation).
% 300.10/300.69  194644[7:Res:3618.1,13313.1] || member(apply(choice,complement(complement(intersection(u,v)))),symmetric_difference(u,v))* member(complement(complement(intersection(u,v))),ordinal_numbers) -> equal(complement(complement(intersection(u,v))),identity_relation).
% 300.10/300.69  142393[8:Rew:141401.0,121694.2] inductive(symmetric_difference(apply(u,v),ordinal_numbers)) || well_ordering(w,complement(apply(u,v))) -> member(least(w,symmetric_difference(ordinal_numbers,apply(u,v))),symmetric_difference(ordinal_numbers,apply(u,v)))*.
% 300.10/300.69  54281[5:Res:8638.0,9664.1] || member(ordered_pair(u,v),compose(w,x))* well_ordering(y,ordinal_numbers) -> member(least(y,image(w,image(x,singleton(u)))),image(w,image(x,singleton(u))))*.
% 300.10/300.69  140420[0:Res:62.1,47534.0] || member(ordered_pair(u,not_subclass_element(v,intersection(image(w,image(x,singleton(u))),v))),compose(w,x))* -> subclass(v,intersection(image(w,image(x,singleton(u))),v)).
% 300.10/300.69  195400[16:Rew:195224.0,193401.1] inductive(complement(power_class(complement(singleton(identity_relation))))) || well_ordering(u,image(element_relation,singleton(identity_relation))) -> member(least(u,complement(power_class(complement(singleton(identity_relation))))),complement(power_class(complement(singleton(identity_relation)))))*.
% 300.10/300.69  195399[16:Rew:195224.0,193398.0] || well_ordering(u,image(element_relation,singleton(identity_relation))) -> equal(complement(power_class(complement(singleton(identity_relation)))),identity_relation) member(least(u,complement(power_class(complement(singleton(identity_relation))))),complement(power_class(complement(singleton(identity_relation)))))*.
% 300.10/300.69  69509[7:Res:13125.2,9471.0] || subclass(omega,compose(u,v)) -> equal(integer_of(ordered_pair(w,not_subclass_element(x,image(u,image(v,singleton(w)))))),identity_relation)** subclass(x,image(u,image(v,singleton(w)))).
% 300.10/300.69  142413[8:Rew:141402.0,121635.2] inductive(symmetric_difference(image(u,v),ordinal_numbers)) || well_ordering(w,complement(image(u,v))) -> member(least(w,symmetric_difference(ordinal_numbers,image(u,v))),symmetric_difference(ordinal_numbers,image(u,v)))*.
% 300.10/300.69  117729[8:Rew:116078.0,116533.2,116078.0,116533.2,116078.0,116533.1] operation(restrict(u,v,ordinal_numbers)) || subclass(cantor(cantor(restrict(u,v,ordinal_numbers))),image(u,v))* -> equal(cantor(cantor(restrict(u,v,ordinal_numbers))),image(u,v)).
% 300.10/300.69  198537[8:SpR:8649.0,161460.2] operation(restrict(u,v,ordinal_numbers)) || well_ordering(w,cantor(cantor(restrict(u,v,ordinal_numbers)))) -> equal(segment(w,image(u,v),least(w,image(u,v))),identity_relation)**.
% 300.10/300.69  36324[0:SpR:481.0,3616.0] ||  -> equal(intersection(union(u,image(element_relation,union(v,w))),union(complement(u),power_class(intersection(complement(v),complement(w))))),symmetric_difference(complement(u),power_class(intersection(complement(v),complement(w)))))**.
% 300.10/300.69  159472[5:Rew:481.0,159430.1] ||  -> member(not_subclass_element(u,image(element_relation,power_class(intersection(complement(v),complement(w))))),power_class(image(element_relation,union(v,w))))* subclass(u,image(element_relation,power_class(intersection(complement(v),complement(w))))).
% 300.10/300.69  36336[0:SpR:481.0,3616.0] ||  -> equal(intersection(union(image(element_relation,union(u,v)),w),union(power_class(intersection(complement(u),complement(v))),complement(w))),symmetric_difference(power_class(intersection(complement(u),complement(v))),complement(w)))**.
% 300.10/300.69  193456[8:Res:163093.0,13070.0] || well_ordering(u,image(element_relation,symmetrization_of(identity_relation))) -> equal(complement(power_class(complement(inverse(identity_relation)))),identity_relation) member(least(u,complement(power_class(complement(inverse(identity_relation))))),complement(power_class(complement(inverse(identity_relation)))))*.
% 300.10/300.69  193459[8:Res:163093.0,9665.1] inductive(complement(power_class(complement(inverse(identity_relation))))) || well_ordering(u,image(element_relation,symmetrization_of(identity_relation))) -> member(least(u,complement(power_class(complement(inverse(identity_relation))))),complement(power_class(complement(inverse(identity_relation)))))*.
% 300.10/300.69  96962[5:Res:79577.0,131.3] || member(u,v) subclass(v,w)* well_ordering(image(element_relation,complement(x)),w)* -> subclass(singleton(ordered_pair(u,least(image(element_relation,complement(x)),v))),power_class(x))*.
% 300.10/300.69  96948[5:Res:79577.0,129.0] || subclass(image(element_relation,complement(u)),v)* well_ordering(w,v)* -> subclass(singleton(x),power_class(u))* member(least(w,image(element_relation,complement(u))),image(element_relation,complement(u)))*.
% 300.10/300.69  198942[8:Rew:145758.0,198934.2] operation(cross_product(u,ordinal_numbers)) || well_ordering(v,cantor(cantor(cross_product(u,ordinal_numbers)))) -> equal(image(ordinal_numbers,u),identity_relation) member(least(v,image(ordinal_numbers,u)),image(ordinal_numbers,u))*.
% 300.10/300.69  198581[8:SpR:161076.2,13326.2] inductive(singleton(u)) || member(u,ordinal_numbers) well_ordering(v,singleton(u))* -> member(u,cantor(successor_relation)) equal(segment(v,range_of(identity_relation),least(v,range_of(identity_relation))),identity_relation)**.
% 300.10/300.69  198332[5:Res:9837.3,129.0] || member(u,ordinal_numbers)* member(v,ordinal_numbers) equal(sum_class(range_of(v)),u)* subclass(union_of_range_map,w) well_ordering(x,w)* -> member(least(x,union_of_range_map),union_of_range_map)*.
% 300.10/300.69  50461[0:SoR:8534.0,75.1] one_to_one(restrict(u,v,singleton(w))) || subclass(range_of(restrict(u,v,singleton(w))),x) -> maps(restrict(u,v,singleton(w)),segment(u,v,w),x)*.
% 300.10/300.69  50462[0:SoR:8534.0,82.1] operation(restrict(u,v,singleton(w))) || subclass(range_of(restrict(u,v,singleton(w))),x) -> maps(restrict(u,v,singleton(w)),segment(u,v,w),x)*.
% 300.10/300.69  198542[8:MRR:198540.3,13039.0] operation(u) || well_ordering(v,cantor(cantor(u))) subclass(singleton(least(v,range_of(u))),range_of(u)) -> section(v,singleton(least(v,range_of(u))),range_of(u))*.
% 300.10/300.69  208539[21:SpL:13260.1,194373.1] || member(first(regular(cross_product(u,v))),cantor(w)) member(ordered_pair(w,regular(cross_product(u,v))),cross_product(ordinal_numbers,cross_product(ordinal_numbers,ordinal_numbers)))* -> equal(cross_product(u,v),identity_relation).
% 300.10/300.69  208537[7:SpL:13260.1,100.0] || member(ordered_pair(u,regular(cross_product(v,w))),composition_function)* -> equal(cross_product(v,w),identity_relation) equal(compose(u,first(regular(cross_product(v,w)))),second(regular(cross_product(v,w)))).
% 300.10/300.69  208506[7:SpL:13260.1,8651.0] || member(regular(cross_product(u,v)),rest_of(w)) -> equal(cross_product(u,v),identity_relation) equal(restrict(w,first(regular(cross_product(u,v))),ordinal_numbers),second(regular(cross_product(u,v))))**.
% 300.10/300.69  209638[8:Rew:161076.2,209620.3] || member(u,ordinal_numbers) member(ordered_pair(u,not_subclass_element(v,image(w,range_of(identity_relation)))),compose(w,x))* -> member(u,cantor(x)) subclass(v,image(w,range_of(identity_relation))).
% 300.10/300.69  211395[8:Res:210606.1,9660.2] || equal(complement(u),ordinal_numbers) member(v,w)* member(x,y)* well_ordering(z,complement(u))* -> member(least(z,cross_product(y,w)),cross_product(y,w))*.
% 300.10/300.69  211379[8:Res:210606.1,9636.2] || equal(complement(u),ordinal_numbers) member(v,w)* member(v,x)* well_ordering(y,complement(u))* -> member(least(y,intersection(x,w)),intersection(x,w))*.
% 300.10/300.69  211524[24:Rew:207558.1,211501.4,207558.1,211501.3,207558.1,211501.1] operation(u) || well_ordering(element_relation,image(v,identity_relation)) subclass(apply(v,u),image(v,identity_relation))* -> equal(image(v,identity_relation),ordinal_numbers) member(image(v,identity_relation),ordinal_numbers).
% 300.10/300.69  211582[8:Res:211438.1,9660.2] || equal(symmetrization_of(identity_relation),ordinal_numbers) member(u,v)* member(w,x)* well_ordering(y,symmetrization_of(identity_relation)) -> member(least(y,cross_product(x,v)),cross_product(x,v))*.
% 300.10/300.69  211571[8:Res:211438.1,9636.2] || equal(symmetrization_of(identity_relation),ordinal_numbers) member(u,v)* member(u,w)* well_ordering(x,symmetrization_of(identity_relation)) -> member(least(x,intersection(w,v)),intersection(w,v))*.
% 300.10/300.69  211666[8:Res:211441.1,9660.2] || equal(power_class(u),ordinal_numbers) member(v,w)* member(x,y)* well_ordering(z,power_class(u))* -> member(least(z,cross_product(y,w)),cross_product(y,w))*.
% 300.10/300.69  211655[8:Res:211441.1,9636.2] || equal(power_class(u),ordinal_numbers) member(v,w)* member(v,x)* well_ordering(y,power_class(u))* -> member(least(y,intersection(x,w)),intersection(x,w))*.
% 300.10/300.69  214146[8:MRR:214121.3,14676.0] function(u) || member(ordered_pair(v,regular(image(u,image(inverse(u),singleton(v))))),cross_product(ordinal_numbers,ordinal_numbers))* -> equal(image(u,image(inverse(u),singleton(v))),identity_relation).
% 300.10/300.69  214147[8:MRR:214120.3,14676.0] single_valued_class(u) || member(ordered_pair(v,regular(image(u,image(inverse(u),singleton(v))))),cross_product(ordinal_numbers,ordinal_numbers))* -> equal(image(u,image(inverse(u),singleton(v))),identity_relation).
% 300.10/300.69  214249[24:SpR:6355.1,207615.1] operation(second(not_subclass_element(cross_product(u,v),w))) ||  -> subclass(cross_product(u,v),w) member(unordered_pair(first(not_subclass_element(cross_product(u,v),w)),identity_relation),not_subclass_element(cross_product(u,v),w))*.
% 300.10/300.69  214465[25:SpR:208985.1,6355.1] operation(second(not_subclass_element(cross_product(u,v),w))) ||  -> subclass(cross_product(u,v),w) equal(ordered_pair(first(not_subclass_element(cross_product(u,v),w)),ordinal_numbers),not_subclass_element(cross_product(u,v),w))**.
% 300.10/300.69  214766[25:SpL:13259.2,214618.1] operation(second(apply(choice,cross_product(u,v)))) || member(cross_product(u,v),ordinal_numbers) member(apply(choice,cross_product(u,v)),rest_relation)* -> equal(cross_product(u,v),identity_relation).
% 300.10/300.69  215846[7:Rew:155653.0,215817.2,155653.0,215817.1] || transitive(complement(compose(complement(element_relation),inverse(element_relation))),ordinal_numbers) well_ordering(u,subset_relation) -> equal(compose(subset_relation,subset_relation),identity_relation) member(least(u,compose(subset_relation,subset_relation)),compose(subset_relation,subset_relation))*.
% 300.10/300.69  219348[15:Res:215659.1,8803.0] || subclass(complement(image(u,image(v,singleton(w)))),identity_relation)* member(ordered_pair(w,range_of(identity_relation)),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(w,range_of(identity_relation)),compose(u,v)).
% 300.10/300.69  219455[7:Res:9461.1,13070.0] || well_ordering(u,cross_product(ordinal_numbers,ordinal_numbers)) -> subclass(recursion_equation_functions(v),w) equal(not_subclass_element(recursion_equation_functions(v),w),identity_relation) member(least(u,not_subclass_element(recursion_equation_functions(v),w)),not_subclass_element(recursion_equation_functions(v),w))*.
% 300.10/300.69  219797[8:Res:67614.1,13313.1] || member(apply(choice,complement(symmetric_difference(complement(u),ordinal_numbers))),union(u,identity_relation))* member(complement(symmetric_difference(complement(u),ordinal_numbers)),ordinal_numbers) -> equal(complement(symmetric_difference(complement(u),ordinal_numbers)),identity_relation).
% 300.10/300.69  219877[15:Res:217197.1,8803.0] || equal(complement(image(u,image(v,singleton(w)))),identity_relation) member(ordered_pair(w,range_of(identity_relation)),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(w,range_of(identity_relation)),compose(u,v))*.
% 300.10/300.69  220043[8:Res:13247.2,160772.0] || member(intersection(u,symmetric_difference(ordinal_numbers,v)),ordinal_numbers) member(apply(choice,intersection(u,symmetric_difference(ordinal_numbers,v))),union(v,identity_relation))* -> equal(intersection(u,symmetric_difference(ordinal_numbers,v)),identity_relation).
% 300.10/300.69  220034[8:Res:13246.2,160772.0] || member(intersection(symmetric_difference(ordinal_numbers,u),v),ordinal_numbers) member(apply(choice,intersection(symmetric_difference(ordinal_numbers,u),v)),union(u,identity_relation))* -> equal(intersection(symmetric_difference(ordinal_numbers,u),v),identity_relation).
% 300.10/300.69  220390[21:Res:196656.1,8554.1] || subclass(domain_relation,flip(complement(intersection(u,v)))) member(ordered_pair(ordered_pair(w,x),identity_relation),union(u,v)) -> member(ordered_pair(ordered_pair(w,x),identity_relation),symmetric_difference(u,v))*.
% 300.10/300.69  220492[21:Res:196657.1,8554.1] || subclass(domain_relation,rotate(complement(intersection(u,v)))) member(ordered_pair(ordered_pair(w,identity_relation),x),union(u,v)) -> member(ordered_pair(ordered_pair(w,identity_relation),x),symmetric_difference(u,v))*.
% 300.10/300.69  221173[7:Res:13236.2,9878.0] || well_ordering(cross_product(u,v),v)* member(w,u)* member(w,v)* subclass(v,x) well_ordering(cross_product(u,v),x)* -> equal(v,identity_relation).
% 300.10/300.69  221127[7:Res:13236.2,490.0] || well_ordering(u,intersection(complement(v),complement(w))) member(least(u,intersection(complement(v),complement(w))),union(v,w))* -> equal(intersection(complement(v),complement(w)),identity_relation).
% 300.10/300.69  221313[8:Res:215662.1,8803.0] || subclass(complement(image(u,image(v,singleton(w)))),identity_relation)* member(ordered_pair(w,singleton(x)),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(w,singleton(x)),compose(u,v))*.
% 300.10/300.69  221570[8:Res:217198.1,8803.0] || equal(complement(image(u,image(v,singleton(w)))),identity_relation) member(ordered_pair(w,singleton(x)),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(w,singleton(x)),compose(u,v))*.
% 300.10/300.69  223683[7:SpR:13260.1,13413.1] || subclass(omega,element_relation) -> equal(cross_product(u,v),identity_relation) equal(integer_of(regular(cross_product(u,v))),identity_relation) member(first(regular(cross_product(u,v))),second(regular(cross_product(u,v))))*.
% 300.10/300.69  224332[8:MRR:224297.3,218143.2] || member(regular(regular(restrict(u,v,w))),cross_product(v,w))* member(regular(regular(restrict(u,v,w))),u)* -> equal(regular(restrict(u,v,w)),identity_relation).
% 300.10/300.69  224621[10:Rew:223660.1,224532.2] || subclass(element_relation,identity_relation) member(ordered_pair(cross_product(ordinal_numbers,ordinal_numbers),not_subclass_element(u,image(v,image(w,identity_relation)))),compose(v,w))* -> subclass(u,image(v,image(w,identity_relation))).
% 300.10/300.69  224707[21:SpL:13260.1,194371.0] || member(regular(cross_product(u,v)),cross_product(ordinal_numbers,ordinal_numbers)) member(second(regular(cross_product(u,v))),cantor(first(regular(cross_product(u,v)))))* -> equal(cross_product(u,v),identity_relation).
% 300.10/300.69  227124[21:Res:196520.2,13362.0] || member(u,ordinal_numbers) equal(successor(u),identity_relation) subclass(successor_relation,v) well_ordering(omega,v)* -> equal(integer_of(ordered_pair(ordered_pair(u,identity_relation),least(omega,successor_relation))),identity_relation)**.
% 300.10/300.69  227267[5:SpL:61728.2,141.1] || member(u,ordinal_numbers) subclass(rest_relation,union_of_range_map) well_ordering(element_relation,range_of(u)) subclass(rest_of(u),range_of(u))* -> equal(range_of(u),ordinal_numbers) member(range_of(u),ordinal_numbers).
% 300.10/300.69  227265[5:SpR:19860.0,61728.2] || member(restrict(cross_product(u,ordinal_numbers),v,w),ordinal_numbers)* subclass(rest_relation,union_of_range_map) -> equal(rest_of(restrict(cross_product(u,ordinal_numbers),v,w)),sum_class(image(cross_product(v,w),u))).
% 300.10/300.69  230802[8:SpL:160992.0,1042.0] || member(not_subclass_element(power_class(intersection(union(u,identity_relation),complement(v))),w),image(element_relation,union(symmetric_difference(ordinal_numbers,u),v)))* -> subclass(power_class(intersection(union(u,identity_relation),complement(v))),w).
% 300.10/300.69  230801[8:SpL:160927.0,1042.0] || member(not_subclass_element(power_class(intersection(complement(u),union(v,identity_relation))),w),image(element_relation,union(u,symmetric_difference(ordinal_numbers,v))))* -> subclass(power_class(intersection(complement(u),union(v,identity_relation))),w).
% 300.10/300.69  231223[8:Rew:140603.0,231210.0,66036.0,231210.0,30.0,231210.0] ||  -> equal(symmetric_difference(union(inverse(identity_relation),symmetrization_of(identity_relation)),union(complement(inverse(identity_relation)),complement(symmetrization_of(identity_relation)))),union(union(inverse(identity_relation),symmetrization_of(identity_relation)),union(complement(inverse(identity_relation)),complement(symmetrization_of(identity_relation)))))**.
% 300.10/300.69  231325[7:Res:17447.1,129.0] || subclass(complement(intersection(u,v)),w)* well_ordering(x,w)* -> equal(symmetric_difference(u,v),identity_relation) member(least(x,complement(intersection(u,v))),complement(intersection(u,v)))*.
% 300.10/300.69  231847[8:MRR:231787.0,41183.1] ||  -> member(not_subclass_element(regular(intersection(complement(u),complement(v))),w),union(u,v))* subclass(regular(intersection(complement(u),complement(v))),w) equal(intersection(complement(u),complement(v)),identity_relation).
% 300.10/300.69  232062[7:Res:122.1,17323.0] || transitive(u,v) -> equal(compose(restrict(u,v,v),restrict(u,v,v)),identity_relation) member(regular(compose(restrict(u,v,v),restrict(u,v,v))),u)*.
% 300.10/300.69  233024[8:Res:9604.1,69182.0] || equal(sum_class(complement(compose(element_relation,ordinal_numbers))),complement(compose(element_relation,ordinal_numbers))) member(regular(sum_class(complement(compose(element_relation,ordinal_numbers)))),element_relation)* -> equal(sum_class(complement(compose(element_relation,ordinal_numbers))),identity_relation).
% 300.10/300.69  233205[7:Rew:481.0,233186.1] || member(regular(image(element_relation,power_class(intersection(complement(u),complement(v))))),power_class(image(element_relation,union(u,v))))* -> equal(image(element_relation,power_class(intersection(complement(u),complement(v)))),identity_relation).
% 300.10/300.69  233363[8:Res:231881.0,9470.1] || member(ordered_pair(u,v),compose(w,x)) -> equal(singleton(image(w,image(x,singleton(u)))),identity_relation) member(v,complement(singleton(image(w,image(x,singleton(u))))))*.
% 300.10/300.69  234170[7:Rew:481.0,234158.2] || subclass(omega,image(element_relation,union(u,v))) -> equal(integer_of(not_subclass_element(power_class(intersection(complement(u),complement(v))),w)),identity_relation)** subclass(power_class(intersection(complement(u),complement(v))),w).
% 300.10/300.69  234386[7:Rew:481.0,234344.2] || well_ordering(u,ordinal_numbers) member(least(u,power_class(intersection(complement(v),complement(w)))),image(element_relation,union(v,w)))* -> equal(power_class(intersection(complement(v),complement(w))),identity_relation).
% 300.10/300.69  234809[8:Res:193440.1,129.0] || member(u,ordinal_numbers) subclass(cantor(v),w)* well_ordering(x,w)* -> equal(apply(v,u),sum_class(range_of(identity_relation)))** member(least(x,cantor(v)),cantor(v))*.
% 300.10/300.69  234907[8:MRR:234843.0,41183.1] || member(not_subclass_element(u,intersection(v,cantor(w))),v)* -> equal(apply(w,not_subclass_element(u,intersection(v,cantor(w)))),sum_class(range_of(identity_relation)))** subclass(u,intersection(v,cantor(w))).
% 300.10/300.69  235300[8:Res:230445.1,8562.0] || member(not_subclass_element(u,intersection(v,union(w,identity_relation))),w)* member(not_subclass_element(u,intersection(v,union(w,identity_relation))),v)* -> subclass(u,intersection(v,union(w,identity_relation))).
% 300.10/300.69  235452[5:Res:28980.1,8799.1] || subclass(rest_relation,flip(cross_product(ordinal_numbers,ordinal_numbers))) equal(rest_of(ordered_pair(u,v)),successor(ordered_pair(v,u))) -> member(ordered_pair(ordered_pair(v,u),rest_of(ordered_pair(u,v))),successor_relation)*.
% 300.10/300.69  235410[5:Res:28980.1,12.0] || subclass(rest_relation,flip(unordered_pair(u,v)))* -> equal(ordered_pair(ordered_pair(w,x),rest_of(ordered_pair(x,w))),v)* equal(ordered_pair(ordered_pair(w,x),rest_of(ordered_pair(x,w))),u)*.
% 300.10/300.69  235580[5:Res:28979.1,8799.1] || subclass(rest_relation,rotate(cross_product(ordinal_numbers,ordinal_numbers))) equal(successor(ordered_pair(u,rest_of(ordered_pair(v,u)))),v) -> member(ordered_pair(ordered_pair(u,rest_of(ordered_pair(v,u))),v),successor_relation)*.
% 300.10/300.69  235538[5:Res:28979.1,12.0] || subclass(rest_relation,rotate(unordered_pair(u,v)))* -> equal(ordered_pair(ordered_pair(w,rest_of(ordered_pair(x,w))),x),v)* equal(ordered_pair(ordered_pair(w,rest_of(ordered_pair(x,w))),x),u)*.
% 300.10/300.69  235679[7:Res:13237.2,36719.1] operation(u) || well_ordering(v,ordinal_numbers) -> equal(cantor(u),identity_relation) equal(ordered_pair(first(least(v,cantor(u))),second(least(v,cantor(u)))),least(v,cantor(u)))**.
% 300.10/300.69  235945[7:Res:69478.2,40594.1] || subclass(omega,symmetric_difference(u,v)) member(union(u,v),ordinal_numbers) -> equal(integer_of(singleton(union(u,v))),identity_relation) member(singleton(singleton(singleton(union(u,v)))),element_relation)*.
% 300.10/300.69  236324[0:Rew:481.0,236225.1] || member(not_subclass_element(intersection(u,power_class(intersection(complement(v),complement(w)))),x),image(element_relation,union(v,w)))* -> subclass(intersection(u,power_class(intersection(complement(v),complement(w)))),x).
% 300.10/300.69  236545[0:Rew:481.0,236414.1] || member(not_subclass_element(intersection(power_class(intersection(complement(u),complement(v))),w),x),image(element_relation,union(u,v)))* -> subclass(intersection(power_class(intersection(complement(u),complement(v))),w),x).
% 300.10/300.69  236866[7:Res:17392.2,3689.0] || subclass(u,ordered_pair(v,w))* -> equal(intersection(u,x),identity_relation) equal(regular(intersection(u,x)),unordered_pair(v,singleton(w)))* equal(regular(intersection(u,x)),singleton(v)).
% 300.10/300.69  236856[7:Res:17392.2,21.0] || subclass(u,cross_product(v,w))* -> equal(intersection(u,x),identity_relation) equal(ordered_pair(first(regular(intersection(u,x))),second(regular(intersection(u,x)))),regular(intersection(u,x)))**.
% 300.10/300.69  237142[7:Res:13574.1,941.1] || member(regular(intersection(u,intersection(v,power_class(image(element_relation,complement(w)))))),image(element_relation,power_class(w)))* -> equal(intersection(u,intersection(v,power_class(image(element_relation,complement(w))))),identity_relation).
% 300.10/300.69  237141[8:Res:13574.1,161200.0] || member(regular(intersection(u,intersection(v,image(element_relation,union(w,identity_relation))))),power_class(symmetric_difference(ordinal_numbers,w)))* -> equal(intersection(u,intersection(v,image(element_relation,union(w,identity_relation)))),identity_relation).
% 300.10/300.69  237793[7:Res:13573.1,941.1] || member(regular(intersection(u,intersection(power_class(image(element_relation,complement(v))),w))),image(element_relation,power_class(v)))* -> equal(intersection(u,intersection(power_class(image(element_relation,complement(v))),w)),identity_relation).
% 300.10/300.69  237792[8:Res:13573.1,161200.0] || member(regular(intersection(u,intersection(image(element_relation,union(v,identity_relation)),w))),power_class(symmetric_difference(ordinal_numbers,v)))* -> equal(intersection(u,intersection(image(element_relation,union(v,identity_relation)),w)),identity_relation).
% 300.10/300.69  238600[7:Res:13572.2,3689.0] || subclass(u,ordered_pair(v,w))* -> equal(intersection(x,u),identity_relation) equal(regular(intersection(x,u)),unordered_pair(v,singleton(w)))* equal(regular(intersection(x,u)),singleton(v)).
% 300.10/300.69  238590[7:Res:13572.2,21.0] || subclass(u,cross_product(v,w))* -> equal(intersection(x,u),identity_relation) equal(ordered_pair(first(regular(intersection(x,u))),second(regular(intersection(x,u)))),regular(intersection(x,u)))**.
% 300.10/300.69  239305[7:Res:17397.1,941.1] || member(regular(intersection(intersection(power_class(image(element_relation,complement(u))),v),w)),image(element_relation,power_class(u)))* -> equal(intersection(intersection(power_class(image(element_relation,complement(u))),v),w),identity_relation).
% 300.10/300.69  239304[8:Res:17397.1,161200.0] || member(regular(intersection(intersection(image(element_relation,union(u,identity_relation)),v),w)),power_class(symmetric_difference(ordinal_numbers,u)))* -> equal(intersection(intersection(image(element_relation,union(u,identity_relation)),v),w),identity_relation).
% 300.10/300.69  240140[7:Res:17396.1,941.1] || member(regular(intersection(intersection(u,power_class(image(element_relation,complement(v)))),w)),image(element_relation,power_class(v)))* -> equal(intersection(intersection(u,power_class(image(element_relation,complement(v)))),w),identity_relation).
% 300.10/300.69  240139[8:Res:17396.1,161200.0] || member(regular(intersection(intersection(u,image(element_relation,union(v,identity_relation))),w)),power_class(symmetric_difference(ordinal_numbers,v)))* -> equal(intersection(intersection(u,image(element_relation,union(v,identity_relation))),w),identity_relation).
% 300.10/300.69  43680[0:SpL:163.0,8554.1] || member(u,union(complement(intersection(v,w)),union(v,w))) member(u,complement(symmetric_difference(v,w))) -> member(u,symmetric_difference(complement(intersection(v,w)),union(v,w)))*.
% 300.10/300.69  39648[2:Res:19734.0,9665.1] inductive(symmetric_difference(complement(u),complement(inverse(u)))) || well_ordering(v,symmetrization_of(u)) -> member(least(v,symmetric_difference(complement(u),complement(inverse(u)))),symmetric_difference(complement(u),complement(inverse(u))))*.
% 300.10/300.69  50364[5:Res:8665.1,9636.2] function(intersection(u,v)) || member(w,v)* member(w,u)* well_ordering(x,cross_product(ordinal_numbers,ordinal_numbers)) -> member(least(x,intersection(u,v)),intersection(u,v))*.
% 300.10/300.69  18945[0:Rew:32.0,18914.1,32.0,18914.0] ||  -> subclass(restrict(u,v,w),x) equal(ordered_pair(first(not_subclass_element(restrict(u,v,w),x)),second(not_subclass_element(restrict(u,v,w),x))),not_subclass_element(restrict(u,v,w),x))**.
% 300.10/300.69  53026[5:Res:8642.1,9872.0] || subclass(ordinal_numbers,u) member(ordered_pair(v,least(intersection(w,u),x)),w)* member(v,x) subclass(x,y)* well_ordering(intersection(w,u),y)* -> .
% 300.10/300.69  43739[5:Res:8827.2,8554.1] || member(u,ordinal_numbers) subclass(rest_relation,complement(intersection(v,w))) member(ordered_pair(u,rest_of(u)),union(v,w)) -> member(ordered_pair(u,rest_of(u)),symmetric_difference(v,w))*.
% 300.10/300.69  18798[0:Res:3618.1,131.3] || member(ordered_pair(u,least(complement(intersection(v,w)),x)),symmetric_difference(v,w))* member(u,x) subclass(x,y)* well_ordering(complement(intersection(v,w)),y)* -> .
% 300.10/300.69  50839[5:Res:49995.1,8554.1] || member(complement(intersection(u,v)),subset_relation) member(singleton(first(complement(intersection(u,v)))),union(u,v)) -> member(singleton(first(complement(intersection(u,v)))),symmetric_difference(u,v))*.
% 300.10/300.69  39647[2:Res:19733.0,9665.1] inductive(symmetric_difference(complement(u),complement(singleton(u)))) || well_ordering(v,successor(u)) -> member(least(v,symmetric_difference(complement(u),complement(singleton(u)))),symmetric_difference(complement(u),complement(singleton(u))))*.
% 300.10/300.69  39682[2:Res:3652.1,9665.1] inductive(segment(u,v,w)) || section(u,singleton(w),v) well_ordering(x,singleton(w)) -> member(least(x,segment(u,v,w)),segment(u,v,w))*.
% 300.10/300.69  79553[5:Res:60219.0,21.0] ||  -> subclass(u,complement(cross_product(v,w))) equal(ordered_pair(first(not_subclass_element(u,complement(cross_product(v,w)))),second(not_subclass_element(u,complement(cross_product(v,w))))),not_subclass_element(u,complement(cross_product(v,w))))**.
% 300.10/300.69  116314[8:Rew:116078.0,48743.0] || member(u,cantor(cross_product(v,w))) equal(restrict(cross_product(u,ordinal_numbers),v,w),x)* subclass(rest_of(cross_product(v,w)),y)* -> member(ordered_pair(u,x),y)*.
% 300.10/300.69  142494[8:Rew:141565.0,96860.2] inductive(symmetric_difference(complement(intersection(u,ordinal_numbers)),ordinal_numbers)) || well_ordering(v,complement(symmetric_difference(u,ordinal_numbers))) -> member(least(v,symmetric_difference(ordinal_numbers,symmetric_difference(u,ordinal_numbers))),symmetric_difference(ordinal_numbers,symmetric_difference(u,ordinal_numbers)))*.
% 300.10/300.69  153369[0:Res:919.1,12.0] ||  -> subclass(restrict(unordered_pair(u,v),w,x),y) equal(not_subclass_element(restrict(unordered_pair(u,v),w,x),y),v)** equal(not_subclass_element(restrict(unordered_pair(u,v),w,x),y),u)**.
% 300.10/300.69  155519[0:SpR:154945.0,3594.0] ||  -> equal(intersection(complement(symmetric_difference(u,intersection(u,v))),union(complement(intersection(u,v)),union(u,intersection(u,v)))),symmetric_difference(complement(intersection(u,v)),union(u,intersection(u,v))))**.
% 300.10/300.69  155938[0:SpR:155147.0,3594.0] ||  -> equal(intersection(complement(symmetric_difference(u,intersection(v,u))),union(complement(intersection(v,u)),union(u,intersection(v,u)))),symmetric_difference(complement(intersection(v,u)),union(u,intersection(v,u))))**.
% 300.10/300.69  156815[5:Res:27.2,40594.1] || member(singleton(intersection(u,v)),v)* member(singleton(intersection(u,v)),u)* member(intersection(u,v),ordinal_numbers) -> member(singleton(singleton(singleton(intersection(u,v)))),element_relation)*.
% 300.10/300.69  156856[5:MRR:156816.0,8655.0] || member(intersection(complement(u),complement(v)),ordinal_numbers) -> member(singleton(intersection(complement(u),complement(v))),union(u,v))* member(singleton(singleton(singleton(intersection(complement(u),complement(v))))),element_relation)*.
% 300.10/300.69  117749[8:Rew:116078.0,116870.3,116078.0,116870.2] operation(u) || member(not_subclass_element(v,intersection(w,cantor(u))),w)* member(not_subclass_element(v,intersection(cantor(u),w)),cantor(u))* -> subclass(v,intersection(cantor(u),w)).
% 300.10/300.69  117748[8:Rew:116078.0,116869.3,116078.0,116869.1] operation(u) || member(not_subclass_element(v,intersection(cantor(u),w)),cantor(u))* member(not_subclass_element(v,intersection(w,cantor(u))),w)* -> subclass(v,intersection(w,cantor(u))).
% 300.10/300.69  116866[8:Rew:116078.0,36746.2] operation(u) || member(v,ordinal_numbers) subclass(rest_relation,cantor(u))* -> equal(ordered_pair(first(ordered_pair(v,rest_of(v))),second(ordered_pair(v,rest_of(v)))),ordered_pair(v,rest_of(v)))**.
% 300.10/300.69  176974[8:Res:116148.1,161194.1] operation(restrict(u,v,complement(complement(symmetrization_of(w))))) || section(u,complement(complement(symmetrization_of(w))),v) -> connected(w,cantor(cantor(restrict(u,v,complement(complement(symmetrization_of(w)))))))*.
% 300.10/300.69  68913[8:MRR:68912.0,41096.1] || member(u,union(v,identity_relation))* subclass(symmetric_difference(complement(v),ordinal_numbers),w)* well_ordering(x,w)* -> member(least(x,symmetric_difference(complement(v),ordinal_numbers)),symmetric_difference(complement(v),ordinal_numbers))*.
% 300.10/300.69  81642[8:Res:67606.0,13070.0] || well_ordering(u,complement(symmetric_difference(complement(v),ordinal_numbers))) -> equal(symmetric_difference(union(v,identity_relation),ordinal_numbers),identity_relation) member(least(u,symmetric_difference(union(v,identity_relation),ordinal_numbers)),symmetric_difference(union(v,identity_relation),ordinal_numbers))*.
% 300.10/300.69  19822[7:Res:19734.0,13070.0] || well_ordering(u,symmetrization_of(v)) -> equal(symmetric_difference(complement(v),complement(inverse(v))),identity_relation) member(least(u,symmetric_difference(complement(v),complement(inverse(v)))),symmetric_difference(complement(v),complement(inverse(v))))*.
% 300.10/300.69  19846[7:Res:3652.1,13070.0] || section(u,singleton(v),w) well_ordering(x,singleton(v)) -> equal(segment(u,w,v),identity_relation) member(least(x,segment(u,w,v)),segment(u,w,v))*.
% 300.10/300.69  19805[7:Res:19733.0,13070.0] || well_ordering(u,successor(v)) -> equal(symmetric_difference(complement(v),complement(singleton(v))),identity_relation) member(least(u,symmetric_difference(complement(v),complement(singleton(v)))),symmetric_difference(complement(v),complement(singleton(v))))*.
% 300.10/300.69  18712[7:Res:13237.2,21.0] || well_ordering(u,ordinal_numbers) -> equal(cross_product(v,w),identity_relation) equal(ordered_pair(first(least(u,cross_product(v,w))),second(least(u,cross_product(v,w)))),least(u,cross_product(v,w)))**.
% 300.10/300.69  161772[8:Rew:140613.0,67619.3] || member(u,ordinal_numbers) subclass(union(v,identity_relation),w)* well_ordering(x,w)* -> member(u,symmetric_difference(ordinal_numbers,v))* member(least(x,union(v,identity_relation)),union(v,identity_relation))*.
% 300.10/300.69  132315[5:Res:130703.0,9633.1] || member(u,ordinal_numbers) well_ordering(v,intersection(complement(w),complement(x))) -> member(u,union(w,x))* member(least(v,complement(union(w,x))),complement(union(w,x)))*.
% 300.10/300.69  50246[5:Res:8665.1,9660.2] function(cross_product(u,v)) || member(w,v)* member(x,u)* well_ordering(y,cross_product(ordinal_numbers,ordinal_numbers)) -> member(least(y,cross_product(u,v)),cross_product(u,v))*.
% 300.10/300.69  46658[5:Res:9618.2,37.0] || member(ordered_pair(ordered_pair(u,v),w),cross_product(ordinal_numbers,ordinal_numbers)) subclass(composition_function,rotate(x)) -> member(ordered_pair(ordered_pair(v,ordered_pair(w,compose(ordered_pair(u,v),w))),u),x)*.
% 300.10/300.69  46657[5:Res:9618.2,40.0] || member(ordered_pair(ordered_pair(u,v),w),cross_product(ordinal_numbers,ordinal_numbers)) subclass(composition_function,flip(x)) -> member(ordered_pair(ordered_pair(v,u),ordered_pair(w,compose(ordered_pair(u,v),w))),x)*.
% 300.10/300.69  46624[5:Res:9618.2,490.0] || member(ordered_pair(u,v),cross_product(ordinal_numbers,ordinal_numbers)) subclass(composition_function,intersection(complement(w),complement(x))) member(ordered_pair(u,ordered_pair(v,compose(u,v))),union(w,x))* -> .
% 300.10/300.69  66811[5:Res:9618.2,161.0] || member(ordered_pair(u,v),cross_product(ordinal_numbers,ordinal_numbers)) subclass(composition_function,omega) -> equal(integer_of(ordered_pair(u,ordered_pair(v,compose(u,v)))),ordered_pair(u,ordered_pair(v,compose(u,v))))**.
% 300.10/300.69  194509[8:Res:163112.0,8562.0] || member(not_subclass_element(u,intersection(v,complement(inverse(identity_relation)))),v)* -> subclass(singleton(not_subclass_element(u,intersection(v,complement(inverse(identity_relation))))),symmetrization_of(identity_relation))* subclass(u,intersection(v,complement(inverse(identity_relation)))).
% 300.10/300.69  195646[16:Rew:195224.0,195218.1] || member(not_subclass_element(u,intersection(v,complement(singleton(identity_relation)))),v)* -> subclass(singleton(not_subclass_element(u,intersection(v,complement(singleton(identity_relation))))),singleton(identity_relation))* subclass(u,intersection(v,complement(singleton(identity_relation)))).
% 300.10/300.69  197098[7:Obv:197095.4] function(not_well_ordering(u,v)) || well_ordering(u,cross_product(ordinal_numbers,ordinal_numbers)) connected(u,v) member(least(u,not_well_ordering(u,v)),not_well_ordering(u,v))* -> well_ordering(u,v).
% 300.10/300.69  197321[7:MRR:197319.2,13039.0] || well_ordering(u,cross_product(ordinal_numbers,ordinal_numbers)) subclass(singleton(least(u,compose(v,w))),compose(v,w)) -> section(u,singleton(least(u,compose(v,w))),compose(v,w))*.
% 300.10/300.69  199071[7:Res:18211.1,13362.0] || subclass(ordinal_numbers,symmetric_difference(u,v)) subclass(union(u,v),w)* well_ordering(omega,w) -> equal(integer_of(ordered_pair(unordered_pair(x,y),least(omega,union(u,v)))),identity_relation)**.
% 300.10/300.69  198957[7:Res:39529.1,13362.0] || member(u,ordinal_numbers) subclass(union(v,w),x)* well_ordering(omega,x) -> member(u,complement(w)) equal(integer_of(ordered_pair(u,least(omega,union(v,w)))),identity_relation)**.
% 300.10/300.69  198956[7:Res:39530.1,13362.0] || member(u,ordinal_numbers) subclass(union(v,w),x)* well_ordering(omega,x) -> member(u,complement(v)) equal(integer_of(ordered_pair(u,least(omega,union(v,w)))),identity_relation)**.
% 300.10/300.69  198954[7:Res:27.2,13362.0] || member(u,v) member(u,w) subclass(intersection(w,v),x)* well_ordering(omega,x) -> equal(integer_of(ordered_pair(u,least(omega,intersection(w,v)))),identity_relation)**.
% 300.10/300.69  198951[7:Res:3618.1,13362.0] || member(u,symmetric_difference(v,w)) subclass(complement(intersection(v,w)),x)* well_ordering(omega,x) -> equal(integer_of(ordered_pair(u,least(omega,complement(intersection(v,w))))),identity_relation)**.
% 300.10/300.69  130974[8:Res:116127.5,9876.0] operation(u) operation(v) || compatible(w,v,u) subclass(cantor(v),x)* subclass(x,y)* well_ordering(ordinal_numbers,y)* -> homomorphism(w,v,u)*.
% 300.10/300.69  116478[8:Rew:116078.0,51455.3] operation(u) operation(v) || compatible(w,v,u) subclass(cantor(v),cross_product(x,y))* -> homomorphism(w,v,u) member(not_homomorphism1(w,v,u),x)*.
% 300.10/300.69  116477[8:Rew:116078.0,51454.3] operation(u) operation(v) || compatible(w,v,u) subclass(cantor(v),cross_product(x,y))* -> homomorphism(w,v,u) member(not_homomorphism2(w,v,u),y)*.
% 300.10/300.69  117741[8:Rew:116078.0,116278.3] operation(u) operation(v) || compatible(w,v,u) subclass(cantor(v),rest_of(x)) -> homomorphism(w,v,u) member(not_homomorphism1(w,v,u),cantor(x))*.
% 300.10/300.69  197451[7:Rew:3606.0,197352.1,3606.0,197352.0] || member(symmetric_difference(cross_product(u,v),w),ordinal_numbers) -> equal(symmetric_difference(cross_product(u,v),w),identity_relation) member(apply(choice,symmetric_difference(cross_product(u,v),w)),complement(restrict(w,u,v)))*.
% 300.10/300.69  197450[7:Rew:3603.0,197353.1,3603.0,197353.0] || member(symmetric_difference(u,cross_product(v,w)),ordinal_numbers) -> equal(symmetric_difference(u,cross_product(v,w)),identity_relation) member(apply(choice,symmetric_difference(u,cross_product(v,w))),complement(restrict(u,v,w)))*.
% 300.10/300.69  197685[7:Res:13247.2,19559.0] || member(intersection(u,symmetric_difference(v,singleton(v))),ordinal_numbers) -> equal(intersection(u,symmetric_difference(v,singleton(v))),identity_relation) member(apply(choice,intersection(u,symmetric_difference(v,singleton(v)))),successor(v))*.
% 300.10/300.69  197686[7:Res:13247.2,19676.0] || member(intersection(u,symmetric_difference(v,inverse(v))),ordinal_numbers) -> equal(intersection(u,symmetric_difference(v,inverse(v))),identity_relation) member(apply(choice,intersection(u,symmetric_difference(v,inverse(v)))),symmetrization_of(v))*.
% 300.10/300.69  197673[8:Res:13247.2,66086.1] || member(intersection(u,complement(compose(element_relation,ordinal_numbers))),ordinal_numbers) member(apply(choice,intersection(u,complement(compose(element_relation,ordinal_numbers)))),element_relation)* -> equal(intersection(u,complement(compose(element_relation,ordinal_numbers))),identity_relation).
% 300.10/300.69  197385[8:Res:13246.2,66086.1] || member(intersection(complement(compose(element_relation,ordinal_numbers)),u),ordinal_numbers) member(apply(choice,intersection(complement(compose(element_relation,ordinal_numbers)),u)),element_relation)* -> equal(intersection(complement(compose(element_relation,ordinal_numbers)),u),identity_relation).
% 300.10/300.69  197397[7:Res:13246.2,19559.0] || member(intersection(symmetric_difference(u,singleton(u)),v),ordinal_numbers) -> equal(intersection(symmetric_difference(u,singleton(u)),v),identity_relation) member(apply(choice,intersection(symmetric_difference(u,singleton(u)),v)),successor(u))*.
% 300.10/300.69  197398[7:Res:13246.2,19676.0] || member(intersection(symmetric_difference(u,inverse(u)),v),ordinal_numbers) -> equal(intersection(symmetric_difference(u,inverse(u)),v),identity_relation) member(apply(choice,intersection(symmetric_difference(u,inverse(u)),v)),symmetrization_of(u))*.
% 300.10/300.69  51344[5:Rew:50855.1,51267.2] || member(singleton(u),subset_relation) member(ordered_pair(first(singleton(u)),not_subclass_element(v,image(w,image(x,u)))),compose(w,x))* -> subclass(v,image(w,image(x,u))).
% 300.10/300.69  195397[16:Rew:195224.0,193393.3] || member(u,v) subclass(v,w)* well_ordering(power_class(complement(singleton(identity_relation))),w)* -> member(ordered_pair(u,least(power_class(complement(singleton(identity_relation))),v)),image(element_relation,singleton(identity_relation)))*.
% 300.10/300.69  49178[0:SpL:154.1,9471.0] || member(u,recursion_equation_functions(v)) member(ordered_pair(w,not_subclass_element(x,image(v,image(rest_of(u),singleton(w))))),u)* -> subclass(x,image(v,image(rest_of(u),singleton(w)))).
% 300.10/300.69  9995[5:Res:9632.1,8803.0] || equal(complement(complement(image(u,image(v,singleton(w))))),ordinal_numbers)** member(ordered_pair(w,singleton(x)),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(w,singleton(x)),compose(u,v))*.
% 300.10/300.69  147087[5:Res:143193.1,8803.0] || equal(image(u,image(v,singleton(w))),ordinal_numbers) member(ordered_pair(w,least(element_relation,omega)),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(w,least(element_relation,omega)),compose(u,v))*.
% 300.10/300.69  126006[5:Res:125731.1,8803.0] || subclass(ordinal_numbers,image(u,image(v,singleton(w)))) member(ordered_pair(w,least(element_relation,omega)),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(w,least(element_relation,omega)),compose(u,v))*.
% 300.10/300.69  10004[5:Res:8643.1,8803.0] || subclass(ordinal_numbers,image(u,image(v,singleton(w)))) member(ordered_pair(w,unordered_pair(x,y)),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(w,unordered_pair(x,y)),compose(u,v))*.
% 300.10/300.69  10003[5:Res:8642.1,8803.0] || subclass(ordinal_numbers,image(u,image(v,singleton(w)))) member(ordered_pair(w,ordered_pair(x,y)),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(w,ordered_pair(x,y)),compose(u,v))*.
% 300.10/300.69  191969[18:Res:190515.1,8803.0] || subclass(ordinal_numbers,image(u,image(v,singleton(w)))) member(ordered_pair(w,regular(symmetrization_of(identity_relation))),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(w,regular(symmetrization_of(identity_relation))),compose(u,v))*.
% 300.10/300.69  83896[7:Res:66696.2,8803.0] || subclass(ordinal_numbers,image(u,image(v,singleton(w))))* member(ordered_pair(w,x),cross_product(ordinal_numbers,ordinal_numbers)) -> equal(integer_of(x),identity_relation) member(ordered_pair(w,x),compose(u,v))*.
% 300.10/300.69  125929[5:Res:125725.1,8803.0] || subclass(omega,image(u,image(v,singleton(w)))) member(ordered_pair(w,least(element_relation,omega)),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(w,least(element_relation,omega)),compose(u,v))*.
% 300.10/300.69  13416[7:Rew:13036.0,10927.2] || subclass(omega,image(u,image(v,singleton(w))))* member(ordered_pair(w,x),cross_product(ordinal_numbers,ordinal_numbers)) -> equal(integer_of(x),identity_relation) member(ordered_pair(w,x),compose(u,v))*.
% 300.10/300.69  16631[8:Res:15426.1,8803.0] || subclass(domain_relation,image(u,image(v,singleton(w)))) member(ordered_pair(w,ordered_pair(identity_relation,identity_relation)),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(w,ordered_pair(identity_relation,identity_relation)),compose(u,v))*.
% 300.10/300.69  147301[5:Res:143222.1,8803.0] || equal(image(u,image(v,singleton(w))),omega) member(ordered_pair(w,least(element_relation,omega)),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(w,least(element_relation,omega)),compose(u,v))*.
% 300.10/300.69  63423[8:MRR:63415.3,14676.0] function(u) || member(ordered_pair(v,not_subclass_element(image(u,image(inverse(u),singleton(v))),w)),cross_product(ordinal_numbers,ordinal_numbers))* -> subclass(image(u,image(inverse(u),singleton(v))),w).
% 300.10/300.69  63476[8:MRR:63467.3,14676.0] single_valued_class(u) || member(ordered_pair(v,not_subclass_element(image(u,image(inverse(u),singleton(v))),w)),cross_product(ordinal_numbers,ordinal_numbers))* -> subclass(image(u,image(inverse(u),singleton(v))),w).
% 300.10/300.69  39683[2:Res:284.1,9665.1] inductive(apply(u,v)) || member(image(u,singleton(v)),ordinal_numbers) well_ordering(w,image(u,singleton(v))) -> member(least(w,apply(u,v)),apply(u,v))*.
% 300.10/300.69  62822[7:Res:284.1,13070.0] || member(image(u,singleton(v)),ordinal_numbers) well_ordering(w,image(u,singleton(v))) -> equal(apply(u,v),identity_relation) member(least(w,apply(u,v)),apply(u,v))*.
% 300.10/300.69  50583[0:Res:10.1,8632.1] || equal(image(u,singleton(v)),apply(u,v)) well_ordering(element_relation,image(u,singleton(v)))* -> equal(image(u,singleton(v)),ordinal_numbers) member(image(u,singleton(v)),ordinal_numbers).
% 300.10/300.69  163960[7:Res:13069.2,941.1] || member(power_class(image(element_relation,complement(u))),ordinal_numbers) member(apply(choice,power_class(image(element_relation,complement(u)))),image(element_relation,power_class(u)))* -> equal(power_class(image(element_relation,complement(u))),identity_relation).
% 300.10/300.69  155434[2:Res:39609.2,941.1] inductive(power_class(image(element_relation,complement(u)))) || well_ordering(v,power_class(image(element_relation,complement(u)))) member(least(v,power_class(image(element_relation,complement(u)))),image(element_relation,power_class(u)))* -> .
% 300.10/300.69  193557[8:Rew:162038.0,193549.3] || member(u,v) subclass(v,w)* well_ordering(power_class(complement(inverse(identity_relation))),w)* -> member(ordered_pair(u,least(power_class(complement(inverse(identity_relation))),v)),image(element_relation,symmetrization_of(identity_relation)))*.
% 300.10/300.69  145893[8:SpL:145758.0,117602.1] function(cross_product(u,ordinal_numbers)) || subclass(image(ordinal_numbers,u),cantor(cantor(v)))* equal(cantor(cantor(w)),cantor(cross_product(u,ordinal_numbers))) -> compatible(cross_product(u,ordinal_numbers),w,v)*.
% 300.10/300.69  61725[0:SpL:6355.1,157.0] || member(not_subclass_element(cross_product(u,v),w),union_of_range_map) -> subclass(cross_product(u,v),w) equal(sum_class(range_of(first(not_subclass_element(cross_product(u,v),w)))),second(not_subclass_element(cross_product(u,v),w)))**.
% 300.10/300.69  191885[15:Res:165442.1,8803.0] || subclass(ordinal_numbers,image(u,image(v,singleton(w)))) member(ordered_pair(w,sum_class(range_of(identity_relation))),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(w,sum_class(range_of(identity_relation))),compose(u,v))*.
% 300.10/300.69  205209[15:Res:195033.1,8803.0] || equal(complement(complement(image(u,image(v,singleton(w))))),ordinal_numbers)** member(ordered_pair(w,range_of(identity_relation)),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(w,range_of(identity_relation)),compose(u,v)).
% 300.10/300.69  206165[22:Res:205574.1,8803.0] || equal(image(u,image(v,singleton(w))),singleton(singleton(identity_relation))) member(ordered_pair(w,singleton(identity_relation)),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(w,singleton(identity_relation)),compose(u,v))*.
% 300.10/300.69  206527[7:Res:165794.1,9636.2] || member(u,singleton(v))* member(u,w)* well_ordering(x,omega) -> equal(integer_of(v),identity_relation) member(least(x,intersection(w,singleton(v))),intersection(w,singleton(v)))*.
% 300.10/300.69  206554[7:Res:165795.1,9636.2] || member(u,v)* member(u,singleton(w))* well_ordering(x,omega) -> equal(integer_of(w),identity_relation) member(least(x,intersection(singleton(w),v)),intersection(singleton(w),v))*.
% 300.10/300.69  208221[8:Rew:161076.2,208212.4] inductive(singleton(u)) || member(u,ordinal_numbers) well_ordering(v,singleton(u))* -> member(u,cantor(successor_relation)) equal(range_of(identity_relation),identity_relation) member(least(v,range_of(identity_relation)),range_of(identity_relation))*.
% 300.10/300.69  209348[25:Rew:208840.0,209325.2] || member(ordered_pair(ordered_pair(ordinal_numbers,identity_relation),u),v) member(ordered_pair(singleton(singleton(identity_relation)),u),cross_product(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers))* -> member(ordered_pair(singleton(singleton(identity_relation)),u),flip(v))*.
% 300.10/300.69  209349[25:Rew:208840.0,209324.2] || member(ordered_pair(ordered_pair(ordinal_numbers,u),identity_relation),v) member(ordered_pair(singleton(singleton(identity_relation)),u),cross_product(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers))* -> member(ordered_pair(singleton(singleton(identity_relation)),u),rotate(v))*.
% 300.10/300.69  209542[7:Res:206540.1,9633.1] || member(u,ordinal_numbers) well_ordering(v,omega) -> equal(integer_of(w),identity_relation) member(u,complement(singleton(w)))* member(least(v,complement(complement(singleton(w)))),complement(complement(singleton(w))))*.
% 300.10/300.69  210304[8:Res:140864.1,8562.0] || member(not_subclass_element(u,intersection(v,symmetric_difference(ordinal_numbers,w))),complement(w))* member(not_subclass_element(u,intersection(v,symmetric_difference(ordinal_numbers,w))),v)* -> subclass(u,intersection(v,symmetric_difference(ordinal_numbers,w))).
% 300.10/300.69  211613[25:Rew:208840.0,211601.1] || member(u,ordinal_numbers) member(singleton(singleton(identity_relation)),cross_product(ordinal_numbers,ordinal_numbers)) member(ordered_pair(ordered_pair(ordinal_numbers,u),identity_relation),v) -> member(ordered_pair(singleton(singleton(identity_relation)),u),rotate(v))*.
% 300.10/300.69  211986[25:Rew:208840.0,211974.1] || member(u,ordinal_numbers) member(singleton(singleton(identity_relation)),cross_product(ordinal_numbers,ordinal_numbers)) member(ordered_pair(ordered_pair(ordinal_numbers,identity_relation),u),v) -> member(ordered_pair(singleton(singleton(identity_relation)),u),flip(v))*.
% 300.10/300.69  212411[7:SpL:13259.2,10702.0] || member(cross_product(u,v),ordinal_numbers) equal(w,apply(choice,cross_product(u,v))) -> equal(cross_product(u,v),identity_relation) member(singleton(first(apply(choice,cross_product(u,v)))),w)*.
% 300.10/300.69  212389[7:SpL:13259.2,2486.0] || member(cross_product(u,v),ordinal_numbers) subclass(apply(choice,cross_product(u,v)),w) -> equal(cross_product(u,v),identity_relation) member(singleton(first(apply(choice,cross_product(u,v)))),w)*.
% 300.10/300.69  212418[8:Rew:117380.1,212372.2,117380.1,212372.1] operation(u) || member(cantor(u),ordinal_numbers) -> equal(cantor(u),identity_relation) equal(ordered_pair(first(apply(choice,cantor(u))),second(apply(choice,cantor(u)))),apply(choice,cantor(u)))**.
% 300.10/300.69  213638[5:Res:151877.0,9636.2] || member(u,v)* member(u,singleton(w))* well_ordering(x,complement(recursion_equation_functions(y)))* -> function(w) member(least(x,intersection(singleton(w),v)),intersection(singleton(w),v))*.
% 300.10/300.69  213660[5:Res:213622.0,9633.1] || member(u,ordinal_numbers) well_ordering(v,complement(recursion_equation_functions(w)))* -> function(x) member(u,complement(singleton(x)))* member(least(v,complement(complement(singleton(x)))),complement(complement(singleton(x))))*.
% 300.10/300.69  213694[5:Res:151512.0,9636.2] || member(u,singleton(v))* member(u,w)* well_ordering(x,complement(recursion_equation_functions(y)))* -> function(v) member(least(x,intersection(w,singleton(v))),intersection(w,singleton(v)))*.
% 300.10/300.69  214938[0:Res:151501.1,9636.2] || member(u,v)* member(w,singleton(u))* member(w,x)* well_ordering(y,v)* -> member(least(y,intersection(x,singleton(u))),intersection(x,singleton(u)))*.
% 300.10/300.69  214990[5:Res:151502.1,9636.2] || member(u,singleton(v))* member(u,w)* well_ordering(x,complement(y))* -> member(v,y)* member(least(x,intersection(w,singleton(v))),intersection(w,singleton(v)))*.
% 300.10/300.69  215034[0:Res:151861.1,9636.2] || member(u,v)* member(w,x)* member(w,singleton(u))* well_ordering(y,v)* -> member(least(y,intersection(singleton(u),x)),intersection(singleton(u),x))*.
% 300.10/300.69  215068[5:Res:215011.1,9633.1] || member(u,v)* member(w,ordinal_numbers) well_ordering(x,v)* -> member(w,complement(singleton(u)))* member(least(x,complement(complement(singleton(u)))),complement(complement(singleton(u))))*.
% 300.10/300.69  215125[5:Res:151862.1,9636.2] || member(u,v)* member(u,singleton(w))* well_ordering(x,complement(y))* -> member(w,y)* member(least(x,intersection(singleton(w),v)),intersection(singleton(w),v))*.
% 300.10/300.69  215162[5:Res:215108.1,9633.1] || member(u,ordinal_numbers) well_ordering(v,complement(w))* -> member(x,w)* member(u,complement(singleton(x)))* member(least(v,complement(complement(singleton(x)))),complement(complement(singleton(x))))*.
% 300.10/300.69  218247[8:Res:13529.2,217144.1] || member(ordered_pair(u,regular(image(v,image(w,singleton(u))))),cross_product(ordinal_numbers,ordinal_numbers))* equal(compose(v,w),identity_relation) -> equal(image(v,image(w,singleton(u))),identity_relation).
% 300.10/300.69  219208[8:Res:13529.2,219073.1] || member(ordered_pair(u,regular(image(v,image(w,singleton(u))))),cross_product(ordinal_numbers,ordinal_numbers))* subclass(compose(v,w),identity_relation) -> equal(image(v,image(w,singleton(u))),identity_relation).
% 300.10/300.69  219809[8:Res:67614.1,131.3] || member(ordered_pair(u,least(symmetric_difference(complement(v),ordinal_numbers),w)),union(v,identity_relation))* member(u,w) subclass(w,x)* well_ordering(symmetric_difference(complement(v),ordinal_numbers),x)* -> .
% 300.10/300.69  219782[8:Res:67614.1,13362.0] || member(u,union(v,identity_relation)) subclass(symmetric_difference(complement(v),ordinal_numbers),w)* well_ordering(omega,w) -> equal(integer_of(ordered_pair(u,least(omega,symmetric_difference(complement(v),ordinal_numbers)))),identity_relation)**.
% 300.10/300.69  222658[21:Rew:218387.1,222604.2] || subclass(domain_relation,rest_relation) member(sum_class(range_of(identity_relation)),recursion_equation_functions(u)) member(ordered_pair(u,identity_relation),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(u,ordered_pair(identity_relation,sum_class(range_of(identity_relation)))),composition_function)*.
% 300.10/300.69  223228[21:Rew:218395.1,223176.2] || subclass(domain_relation,rest_relation) member(regular(symmetrization_of(identity_relation)),recursion_equation_functions(u)) member(ordered_pair(u,identity_relation),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(u,ordered_pair(identity_relation,regular(symmetrization_of(identity_relation)))),composition_function)*.
% 300.10/300.69  223288[21:Rew:218416.1,223239.2] || subclass(domain_relation,rest_relation) member(least(element_relation,omega),recursion_equation_functions(u)) member(ordered_pair(u,identity_relation),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(u,ordered_pair(identity_relation,least(element_relation,omega))),composition_function)*.
% 300.10/300.69  223356[21:Rew:218563.1,223299.2] || subclass(rest_relation,domain_relation) member(sum_class(range_of(identity_relation)),recursion_equation_functions(u)) member(ordered_pair(u,identity_relation),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(u,ordered_pair(identity_relation,sum_class(range_of(identity_relation)))),composition_function)*.
% 300.10/300.69  223422[21:Rew:218571.1,223367.2] || subclass(rest_relation,domain_relation) member(regular(symmetrization_of(identity_relation)),recursion_equation_functions(u)) member(ordered_pair(u,identity_relation),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(u,ordered_pair(identity_relation,regular(symmetrization_of(identity_relation)))),composition_function)*.
% 300.10/300.69  223553[21:Rew:218592.1,223501.2] || subclass(rest_relation,domain_relation) member(least(element_relation,omega),recursion_equation_functions(u)) member(ordered_pair(u,identity_relation),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(u,ordered_pair(identity_relation,least(element_relation,omega))),composition_function)*.
% 300.10/300.69  226043[7:Res:13578.1,13362.0] || subclass(union(u,v),w)* well_ordering(omega,w) -> equal(symmetric_difference(u,v),identity_relation) equal(integer_of(ordered_pair(regular(symmetric_difference(u,v)),least(omega,union(u,v)))),identity_relation)**.
% 300.10/300.69  227252[7:SpR:61728.2,13504.2] || member(u,ordinal_numbers) subclass(rest_relation,union_of_range_map) member(range_of(u),ordinal_numbers) well_ordering(v,range_of(u)) -> equal(segment(v,rest_of(u),least(v,rest_of(u))),identity_relation)**.
% 300.10/300.69  227349[7:SpL:192979.1,9470.1] || member(ordered_pair(u,v),compose(w,regular(cross_product(singleton(u),ordinal_numbers))))* subclass(image(w,range_of(identity_relation)),x)* -> equal(cross_product(singleton(u),ordinal_numbers),identity_relation) member(v,x)*.
% 300.10/300.69  227815[21:Rew:218383.1,227757.2] || subclass(domain_relation,rest_relation) member(unordered_pair(u,v),recursion_equation_functions(w)) member(ordered_pair(w,identity_relation),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(w,ordered_pair(identity_relation,unordered_pair(u,v))),composition_function)*.
% 300.10/300.69  227888[21:Rew:218385.1,227826.2] || subclass(domain_relation,rest_relation) member(ordered_pair(u,v),recursion_equation_functions(w)) member(ordered_pair(w,identity_relation),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(w,ordered_pair(identity_relation,ordered_pair(u,v))),composition_function)*.
% 300.10/300.69  227960[21:Rew:218559.1,227899.2] || subclass(rest_relation,domain_relation) member(unordered_pair(u,v),recursion_equation_functions(w)) member(ordered_pair(w,identity_relation),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(w,ordered_pair(identity_relation,unordered_pair(u,v))),composition_function)*.
% 300.10/300.69  227978[7:SpR:13260.1,13410.1] || subclass(omega,rest_relation) -> equal(cross_product(u,v),identity_relation) equal(integer_of(regular(cross_product(u,v))),identity_relation) equal(rest_of(first(regular(cross_product(u,v)))),second(regular(cross_product(u,v))))**.
% 300.10/300.69  228054[21:Rew:218561.1,227989.2] || subclass(rest_relation,domain_relation) member(ordered_pair(u,v),recursion_equation_functions(w)) member(ordered_pair(w,identity_relation),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(w,ordered_pair(identity_relation,ordered_pair(u,v))),composition_function)*.
% 300.10/300.69  228125[8:SpR:13260.1,160930.1] || subclass(omega,domain_relation) -> equal(cross_product(u,v),identity_relation) equal(integer_of(regular(cross_product(u,v))),identity_relation) equal(cantor(first(regular(cross_product(u,v)))),second(regular(cross_product(u,v))))**.
% 300.10/300.69  228190[7:SpR:13260.1,13412.1] || subclass(omega,successor_relation) -> equal(cross_product(u,v),identity_relation) equal(integer_of(regular(cross_product(u,v))),identity_relation) equal(successor(first(regular(cross_product(u,v)))),second(regular(cross_product(u,v))))**.
% 300.10/300.69  229028[7:Res:19563.1,13362.0] || subclass(successor(u),v)* well_ordering(omega,v) -> equal(symmetric_difference(u,singleton(u)),identity_relation) equal(integer_of(ordered_pair(regular(symmetric_difference(u,singleton(u))),least(omega,successor(u)))),identity_relation)**.
% 300.10/300.69  229159[7:Res:62.1,17387.0] || member(ordered_pair(u,regular(intersection(complement(image(v,image(w,singleton(u)))),x))),compose(v,w))* -> equal(intersection(complement(image(v,image(w,singleton(u)))),x),identity_relation).
% 300.10/300.69  229139[7:Res:27.2,17387.0] || member(regular(intersection(complement(intersection(u,v)),w)),v)* member(regular(intersection(complement(intersection(u,v)),w)),u)* -> equal(intersection(complement(intersection(u,v)),w),identity_relation).
% 300.10/300.69  229588[7:Res:62.1,13571.0] || member(ordered_pair(u,regular(intersection(v,complement(image(w,image(x,singleton(u))))))),compose(w,x))* -> equal(intersection(v,complement(image(w,image(x,singleton(u))))),identity_relation).
% 300.10/300.69  229568[7:Res:27.2,13571.0] || member(regular(intersection(u,complement(intersection(v,w)))),w)* member(regular(intersection(u,complement(intersection(v,w)))),v)* -> equal(intersection(u,complement(intersection(v,w))),identity_relation).
% 300.10/300.69  230145[7:Res:19679.1,13362.0] || subclass(symmetrization_of(u),v)* well_ordering(omega,v) -> equal(symmetric_difference(u,inverse(u)),identity_relation) equal(integer_of(ordered_pair(regular(symmetric_difference(u,inverse(u))),least(omega,symmetrization_of(u)))),identity_relation)**.
% 300.10/300.69  230401[8:Res:161066.1,129.0] || member(u,ordinal_numbers) subclass(symmetric_difference(ordinal_numbers,v),w)* well_ordering(x,w)* -> member(u,union(v,identity_relation))* member(least(x,symmetric_difference(ordinal_numbers,v)),symmetric_difference(ordinal_numbers,v))*.
% 300.10/300.69  230485[8:MRR:230434.0,41183.1] || member(not_subclass_element(u,intersection(v,symmetric_difference(ordinal_numbers,w))),v)* -> member(not_subclass_element(u,intersection(v,symmetric_difference(ordinal_numbers,w))),union(w,identity_relation))* subclass(u,intersection(v,symmetric_difference(ordinal_numbers,w))).
% 300.10/300.69  230747[7:SpL:18708.2,131.3] || well_ordering(u,ordinal_numbers) member(v,singleton(w)) subclass(singleton(w),x)* well_ordering(u,x)* member(ordered_pair(v,w),u)* -> equal(singleton(w),identity_relation).
% 300.10/300.69  231259[7:SpR:3616.0,17447.1] ||  -> equal(symmetric_difference(union(u,v),union(complement(u),complement(v))),identity_relation) member(regular(symmetric_difference(union(u,v),union(complement(u),complement(v)))),complement(symmetric_difference(complement(u),complement(v))))*.
% 300.10/300.69  233099[21:Res:196525.2,13362.0] || member(u,ordinal_numbers) equal(sum_class(range_of(u)),identity_relation) subclass(union_of_range_map,v) well_ordering(omega,v)* -> equal(integer_of(ordered_pair(ordered_pair(u,identity_relation),least(omega,union_of_range_map))),identity_relation)**.
% 300.10/300.69  233273[7:Res:17388.1,13113.0] || well_ordering(u,cross_product(ordinal_numbers,ordinal_numbers)) -> equal(intersection(recursion_equation_functions(v),w),identity_relation) equal(segment(u,regular(intersection(recursion_equation_functions(v),w)),least(u,regular(intersection(recursion_equation_functions(v),w)))),identity_relation)**.
% 300.10/300.69  233426[7:Res:13566.1,13113.0] || well_ordering(u,cross_product(ordinal_numbers,ordinal_numbers)) -> equal(intersection(v,recursion_equation_functions(w)),identity_relation) equal(segment(u,regular(intersection(v,recursion_equation_functions(w))),least(u,regular(intersection(v,recursion_equation_functions(w))))),identity_relation)**.
% 300.10/300.69  233463[8:Res:161057.2,13362.0] || well_ordering(u,ordinal_numbers) subclass(ordinal_numbers,v) well_ordering(omega,v)* -> equal(recursion_equation_functions(w),identity_relation) equal(integer_of(ordered_pair(cantor(least(u,recursion_equation_functions(w))),least(omega,ordinal_numbers))),identity_relation)**.
% 300.10/300.69  233813[7:Res:13236.2,941.1] || well_ordering(u,power_class(image(element_relation,complement(v)))) member(least(u,power_class(image(element_relation,complement(v)))),image(element_relation,power_class(v)))* -> equal(power_class(image(element_relation,complement(v))),identity_relation).
% 300.10/300.69  233943[8:Res:39609.2,161200.0] inductive(image(element_relation,union(u,identity_relation))) || well_ordering(v,image(element_relation,union(u,identity_relation))) member(least(v,image(element_relation,union(u,identity_relation))),power_class(symmetric_difference(ordinal_numbers,u)))* -> .
% 300.10/300.69  233935[8:Res:13236.2,161200.0] || well_ordering(u,image(element_relation,union(v,identity_relation))) member(least(u,image(element_relation,union(v,identity_relation))),power_class(symmetric_difference(ordinal_numbers,v)))* -> equal(image(element_relation,union(v,identity_relation)),identity_relation).
% 300.10/300.69  233924[8:Res:13069.2,161200.0] || member(image(element_relation,union(u,identity_relation)),ordinal_numbers) member(apply(choice,image(element_relation,union(u,identity_relation))),power_class(symmetric_difference(ordinal_numbers,u)))* -> equal(image(element_relation,union(u,identity_relation)),identity_relation).
% 300.10/300.69  234351[7:Res:27.2,18696.1] || member(least(u,complement(intersection(v,w))),w)* member(least(u,complement(intersection(v,w))),v)* well_ordering(u,ordinal_numbers) -> equal(complement(intersection(v,w)),identity_relation).
% 300.10/300.69  235451[5:Res:28980.1,8798.1] || subclass(rest_relation,flip(cross_product(ordinal_numbers,ordinal_numbers))) equal(sum_class(range_of(ordered_pair(u,v))),rest_of(ordered_pair(v,u))) -> member(ordered_pair(ordered_pair(u,v),rest_of(ordered_pair(v,u))),union_of_range_map)*.
% 300.10/300.69  235378[7:Res:28980.1,13362.0] || subclass(rest_relation,flip(u)) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(ordered_pair(ordered_pair(w,x),rest_of(ordered_pair(x,w))),least(omega,u))),identity_relation)**.
% 300.10/300.69  235579[5:Res:28979.1,8798.1] || subclass(rest_relation,rotate(cross_product(ordinal_numbers,ordinal_numbers))) equal(sum_class(range_of(ordered_pair(u,rest_of(ordered_pair(v,u))))),v) -> member(ordered_pair(ordered_pair(u,rest_of(ordered_pair(v,u))),v),union_of_range_map)*.
% 300.10/300.69  235506[7:Res:28979.1,13362.0] || subclass(rest_relation,rotate(u)) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(ordered_pair(ordered_pair(w,rest_of(ordered_pair(x,w))),x),least(omega,u))),identity_relation)**.
% 300.10/300.69  235706[21:Res:196656.1,36719.1] operation(u) || subclass(domain_relation,flip(cantor(u)))* -> equal(ordered_pair(first(ordered_pair(ordered_pair(v,w),identity_relation)),second(ordered_pair(ordered_pair(v,w),identity_relation))),ordered_pair(ordered_pair(v,w),identity_relation))**.
% 300.10/300.69  235702[21:Res:196657.1,36719.1] operation(u) || subclass(domain_relation,rotate(cantor(u)))* -> equal(ordered_pair(first(ordered_pair(ordered_pair(v,identity_relation),w)),second(ordered_pair(ordered_pair(v,identity_relation),w))),ordered_pair(ordered_pair(v,identity_relation),w))**.
% 300.10/300.69  235678[7:Res:13236.2,36719.1] operation(u) || well_ordering(v,cantor(u)) -> equal(cantor(u),identity_relation) equal(ordered_pair(first(least(v,cantor(u))),second(least(v,cantor(u)))),least(v,cantor(u)))**.
% 300.10/300.69  235676[7:Res:13225.3,36719.1] operation(u) || member(v,ordinal_numbers) subclass(v,cantor(u))* -> equal(v,identity_relation) equal(ordered_pair(first(apply(choice,v)),second(apply(choice,v))),apply(choice,v))**.
% 300.10/300.69  235673[7:Res:13210.1,36719.1] operation(u) ||  -> equal(intersection(v,cantor(u)),identity_relation) equal(ordered_pair(first(regular(intersection(v,cantor(u)))),second(regular(intersection(v,cantor(u))))),regular(intersection(v,cantor(u))))**.
% 300.10/300.69  235660[7:Res:13248.1,36719.1] operation(u) ||  -> equal(intersection(cantor(u),v),identity_relation) equal(ordered_pair(first(regular(intersection(cantor(u),v))),second(regular(intersection(cantor(u),v)))),regular(intersection(cantor(u),v)))**.
% 300.10/300.69  235659[7:Res:61019.0,36719.1] operation(u) ||  -> equal(complement(complement(cantor(u))),identity_relation) equal(ordered_pair(first(regular(complement(complement(cantor(u))))),second(regular(complement(complement(cantor(u)))))),regular(complement(complement(cantor(u)))))**.
% 300.10/300.69  235931[7:Res:69478.2,13313.1] || subclass(omega,symmetric_difference(u,v)) member(complement(union(u,v)),ordinal_numbers) -> equal(integer_of(apply(choice,complement(union(u,v)))),identity_relation)** equal(complement(union(u,v)),identity_relation).
% 300.10/300.69  236823[7:Res:17392.2,13362.0] || subclass(u,v) subclass(v,w)* well_ordering(omega,w)* -> equal(intersection(u,x),identity_relation) equal(integer_of(ordered_pair(regular(intersection(u,x)),least(omega,v))),identity_relation)**.
% 300.10/300.69  236938[7:Rew:3594.0,236771.1] || subclass(complement(symmetric_difference(u,v)),w) -> equal(symmetric_difference(complement(intersection(u,v)),union(u,v)),identity_relation) member(regular(symmetric_difference(complement(intersection(u,v)),union(u,v))),w)*.
% 300.10/300.69  237094[7:Res:13574.1,13362.0] || subclass(u,v)* well_ordering(omega,v)* -> equal(intersection(w,intersection(x,u)),identity_relation) equal(integer_of(ordered_pair(regular(intersection(w,intersection(x,u))),least(omega,u))),identity_relation)**.
% 300.10/300.69  237745[7:Res:13573.1,13362.0] || subclass(u,v)* well_ordering(omega,v)* -> equal(intersection(w,intersection(u,x)),identity_relation) equal(integer_of(ordered_pair(regular(intersection(w,intersection(u,x))),least(omega,u))),identity_relation)**.
% 300.10/300.69  237888[7:Rew:3594.0,237673.0] ||  -> equal(intersection(u,symmetric_difference(complement(intersection(v,w)),union(v,w))),identity_relation) member(regular(intersection(u,symmetric_difference(complement(intersection(v,w)),union(v,w)))),complement(symmetric_difference(v,w)))*.
% 300.10/300.69  238557[7:Res:13572.2,13362.0] || subclass(u,v) subclass(v,w)* well_ordering(omega,w)* -> equal(intersection(x,u),identity_relation) equal(integer_of(ordered_pair(regular(intersection(x,u)),least(omega,v))),identity_relation)**.
% 300.10/300.69  239257[7:Res:17397.1,13362.0] || subclass(u,v)* well_ordering(omega,v)* -> equal(intersection(intersection(u,w),x),identity_relation) equal(integer_of(ordered_pair(regular(intersection(intersection(u,w),x)),least(omega,u))),identity_relation)**.
% 300.10/300.69  239411[7:Rew:3594.0,239178.0] ||  -> equal(intersection(symmetric_difference(complement(intersection(u,v)),union(u,v)),w),identity_relation) member(regular(intersection(symmetric_difference(complement(intersection(u,v)),union(u,v)),w)),complement(symmetric_difference(u,v)))*.
% 300.10/300.69  240092[7:Res:17396.1,13362.0] || subclass(u,v)* well_ordering(omega,v)* -> equal(intersection(intersection(w,u),x),identity_relation) equal(integer_of(ordered_pair(regular(intersection(intersection(w,u),x)),least(omega,u))),identity_relation)**.
% 300.10/300.69  43682[0:SpL:3597.0,8554.1] || member(u,union(complement(intersection(v,inverse(v))),symmetrization_of(v))) member(u,complement(symmetric_difference(v,inverse(v)))) -> member(u,symmetric_difference(complement(intersection(v,inverse(v))),symmetrization_of(v)))*.
% 300.10/300.69  40889[0:SpR:482.0,3603.0] ||  -> equal(intersection(complement(restrict(intersection(complement(u),complement(v)),w,x)),complement(intersection(union(u,v),complement(cross_product(w,x))))),symmetric_difference(intersection(complement(u),complement(v)),cross_product(w,x)))**.
% 300.10/300.69  41010[0:SpR:483.0,3606.0] ||  -> equal(intersection(complement(restrict(intersection(complement(u),complement(v)),w,x)),complement(intersection(complement(cross_product(w,x)),union(u,v)))),symmetric_difference(cross_product(w,x),intersection(complement(u),complement(v))))**.
% 300.10/300.69  49643[0:SpL:6355.1,97.0] || member(not_subclass_element(cross_product(u,v),w),compose_class(x)) -> subclass(cross_product(u,v),w) equal(compose(x,first(not_subclass_element(cross_product(u,v),w))),second(not_subclass_element(cross_product(u,v),w)))**.
% 300.10/300.69  47569[0:Rew:3597.0,47483.2,3597.0,47483.1] || member(not_subclass_element(u,symmetric_difference(v,inverse(v))),symmetrization_of(v)) member(not_subclass_element(u,symmetric_difference(v,inverse(v))),complement(intersection(v,inverse(v))))* -> subclass(u,symmetric_difference(v,inverse(v))).
% 300.10/300.69  39742[0:Res:8551.2,290.0] || member(not_subclass_element(complement(restrict(u,v,w)),x),cross_product(v,w))* member(not_subclass_element(complement(restrict(u,v,w)),x),u)* -> subclass(complement(restrict(u,v,w)),x).
% 300.10/300.69  39558[5:MRR:39533.0,8667.0] || member(u,v) subclass(v,w)* well_ordering(intersection(complement(x),complement(y)),w)* -> member(ordered_pair(u,least(intersection(complement(x),complement(y)),v)),union(x,y))*.
% 300.10/300.69  51486[5:Res:51313.1,8554.1] || member(singleton(complement(intersection(u,v))),subset_relation) member(first(singleton(complement(intersection(u,v)))),union(u,v)) -> member(first(singleton(complement(intersection(u,v)))),symmetric_difference(u,v))*.
% 300.10/300.69  39575[0:Res:313.1,3689.0] ||  -> subclass(intersection(ordered_pair(u,v),w),x) equal(not_subclass_element(intersection(ordered_pair(u,v),w),x),unordered_pair(u,singleton(v)))** equal(not_subclass_element(intersection(ordered_pair(u,v),w),x),singleton(u)).
% 300.10/300.69  39589[0:Res:303.1,3689.0] ||  -> subclass(intersection(u,ordered_pair(v,w)),x) equal(not_subclass_element(intersection(u,ordered_pair(v,w)),x),unordered_pair(v,singleton(w)))** equal(not_subclass_element(intersection(u,ordered_pair(v,w)),x),singleton(v)).
% 300.10/300.69  43681[0:SpL:3596.0,8554.1] || member(u,union(complement(intersection(v,singleton(v))),successor(v))) member(u,complement(symmetric_difference(v,singleton(v)))) -> member(u,symmetric_difference(complement(intersection(v,singleton(v))),successor(v)))*.
% 300.10/300.69  47570[0:Rew:3596.0,47482.2,3596.0,47482.1] || member(not_subclass_element(u,symmetric_difference(v,singleton(v))),successor(v)) member(not_subclass_element(u,symmetric_difference(v,singleton(v))),complement(intersection(v,singleton(v))))* -> subclass(u,symmetric_difference(v,singleton(v))).
% 300.10/300.69  47012[8:Res:41203.1,9421.0] || member(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers) member(u,v)* -> equal(ordered_pair(first(ordered_pair(u,least(element_relation,domain_relation))),second(ordered_pair(u,least(element_relation,domain_relation)))),ordered_pair(u,least(element_relation,domain_relation)))**.
% 300.10/300.69  106601[10:Res:80198.1,9421.0] || member(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers) member(u,v)* -> equal(ordered_pair(first(ordered_pair(u,least(element_relation,element_relation))),second(ordered_pair(u,least(element_relation,element_relation)))),ordered_pair(u,least(element_relation,element_relation)))**.
% 300.10/300.69  106599[8:Res:80082.1,9421.0] || member(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers) member(u,v)* -> equal(ordered_pair(first(ordered_pair(u,least(element_relation,rest_relation))),second(ordered_pair(u,least(element_relation,rest_relation)))),ordered_pair(u,least(element_relation,rest_relation)))**.
% 300.10/300.69  116639[8:Rew:116078.0,39618.3] inductive(domain_of(restrict(u,v,w))) || section(u,w,v) well_ordering(x,w) -> member(least(x,cantor(restrict(u,v,w))),cantor(restrict(u,v,w)))*.
% 300.10/300.69  118986[8:Res:116148.1,9665.1] inductive(cantor(restrict(u,v,w))) || section(u,w,v) well_ordering(x,w) -> member(least(x,cantor(restrict(u,v,w))),cantor(restrict(u,v,w)))*.
% 300.10/300.69  130666[5:Res:41371.0,3689.0] ||  -> subclass(complement(complement(ordered_pair(u,v))),w) equal(not_subclass_element(complement(complement(ordered_pair(u,v))),w),unordered_pair(u,singleton(v)))** equal(not_subclass_element(complement(complement(ordered_pair(u,v))),w),singleton(u)).
% 300.10/300.69  140475[0:Rew:3603.0,140338.1] || member(not_subclass_element(union(u,cross_product(v,w)),symmetric_difference(u,cross_product(v,w))),complement(restrict(u,v,w)))* -> subclass(union(u,cross_product(v,w)),symmetric_difference(u,cross_product(v,w))).
% 300.10/300.69  140476[0:Rew:3606.0,140337.1] || member(not_subclass_element(union(cross_product(u,v),w),symmetric_difference(cross_product(u,v),w)),complement(restrict(w,u,v)))* -> subclass(union(cross_product(u,v),w),symmetric_difference(cross_product(u,v),w)).
% 300.10/300.69  148934[8:Res:148858.1,9660.2] || subclass(cross_product(u,v),inverse(subset_relation)) member(w,v)* member(x,u)* well_ordering(y,complement(subset_relation)) -> member(least(y,cross_product(u,v)),cross_product(u,v))*.
% 300.10/300.69  148919[8:Res:148858.1,9636.2] || subclass(intersection(u,v),inverse(subset_relation)) member(w,v)* member(w,u)* well_ordering(x,complement(subset_relation)) -> member(least(x,intersection(u,v)),intersection(u,v))*.
% 300.10/300.69  155852[8:SpL:155653.0,116117.1] || member(ordinal_numbers,cantor(complement(compose(complement(element_relation),inverse(element_relation)))))* equal(subset_relation,u) subclass(rest_of(complement(compose(complement(element_relation),inverse(element_relation)))),v)* -> member(ordered_pair(ordinal_numbers,u),v)*.
% 300.10/300.69  156962[8:Res:156922.1,9878.0] || member(least(cross_product(u,complement(subset_relation)),v),inverse(subset_relation))* member(w,u)* member(w,v)* subclass(v,x)* well_ordering(cross_product(u,complement(subset_relation)),x)* -> .
% 300.10/300.69  164723[8:SpL:13104.1,116117.1] || asymmetric(u,ordinal_numbers) member(ordinal_numbers,cantor(intersection(u,inverse(u))))* equal(identity_relation,v) subclass(rest_of(intersection(u,inverse(u))),w)* -> member(ordered_pair(ordinal_numbers,v),w)*.
% 300.10/300.69  83293[7:Res:61019.0,21.0] ||  -> equal(complement(complement(cross_product(u,v))),identity_relation) equal(ordered_pair(first(regular(complement(complement(cross_product(u,v))))),second(regular(complement(complement(cross_product(u,v)))))),regular(complement(complement(cross_product(u,v)))))**.
% 300.10/300.69  165029[8:SpL:161038.2,116117.1] || member(u,ordinal_numbers) member(singleton(u),cantor(v))* equal(identity_relation,w) subclass(rest_of(v),x)* -> member(u,cantor(v)) member(ordered_pair(singleton(u),w),x)*.
% 300.10/300.69  45741[5:MRR:45735.1,41096.1] || member(least(compose_class(u),v),ordinal_numbers)* equal(compose(u,w),least(compose_class(u),v))* member(w,v)* subclass(v,x)* well_ordering(compose_class(u),x)* -> .
% 300.10/300.69  130971[5:Res:10061.3,9876.0] || member(u,ordinal_numbers) member(ordered_pair(v,w),cross_product(ordinal_numbers,ordinal_numbers)) member(ordered_pair(ordered_pair(w,v),u),x)* subclass(flip(x),y)* well_ordering(ordinal_numbers,y) -> .
% 300.10/300.69  130970[5:Res:10093.3,9876.0] || member(u,ordinal_numbers) member(ordered_pair(v,w),cross_product(ordinal_numbers,ordinal_numbers)) member(ordered_pair(ordered_pair(w,u),v),x)* subclass(rotate(x),y)* well_ordering(ordinal_numbers,y) -> .
% 300.10/300.69  194379[21:MRR:194359.3,14676.0] || member(first(not_subclass_element(cross_product(u,v),w)),cantor(x)) member(ordered_pair(x,not_subclass_element(cross_product(u,v),w)),cross_product(ordinal_numbers,cross_product(ordinal_numbers,ordinal_numbers)))* -> subclass(cross_product(u,v),w).
% 300.10/300.69  197861[8:Rew:140603.0,197825.1,66036.0,197825.1] || asymmetric(cross_product(u,v),w) -> equal(symmetric_difference(restrict(inverse(cross_product(u,v)),u,v),cross_product(w,w)),union(restrict(inverse(cross_product(u,v)),u,v),cross_product(w,w)))**.
% 300.10/300.69  197862[8:Rew:140603.0,197824.1,66036.0,197824.1] || asymmetric(cross_product(u,v),w) -> equal(symmetric_difference(cross_product(w,w),restrict(inverse(cross_product(u,v)),u,v)),union(cross_product(w,w),restrict(inverse(cross_product(u,v)),u,v)))**.
% 300.10/300.69  199080[7:Res:18204.1,13362.0] || subclass(union(u,v),w)* well_ordering(omega,w) -> subclass(symmetric_difference(u,v),x) equal(integer_of(ordered_pair(not_subclass_element(symmetric_difference(u,v),x),least(omega,union(u,v)))),identity_relation)**.
% 300.10/300.69  199064[7:Res:9004.1,13362.0] || member(flip(cross_product(u,ordinal_numbers)),ordinal_numbers) subclass(domain_relation,v) well_ordering(omega,v)* -> equal(integer_of(ordered_pair(ordered_pair(flip(cross_product(u,ordinal_numbers)),inverse(u)),least(omega,domain_relation))),identity_relation)**.
% 300.10/300.69  116481[8:Rew:116078.0,51460.3] operation(u) operation(v) || compatible(w,v,u) subclass(cantor(v),element_relation) -> homomorphism(w,v,u) member(not_homomorphism1(w,v,u),not_homomorphism2(w,v,u))*.
% 300.10/300.69  199067[7:Res:9005.1,13362.0] || member(restrict(element_relation,ordinal_numbers,u),ordinal_numbers) subclass(domain_relation,v) well_ordering(omega,v)* -> equal(integer_of(ordered_pair(ordered_pair(restrict(element_relation,ordinal_numbers,u),sum_class(u)),least(omega,domain_relation))),identity_relation)**.
% 300.10/300.69  161773[8:Rew:116078.0,82309.0] || subclass(domain_relation,complement(complement(cantor(u)))) homomorphism(v,u,w)* -> equal(apply(w,ordered_pair(apply(v,identity_relation),apply(v,identity_relation))),apply(v,apply(u,ordered_pair(identity_relation,identity_relation))))*.
% 300.10/300.69  10124[0:Res:926.1,93.0] || member(ordered_pair(u,v),cantor(w)) homomorphism(x,w,y)* -> equal(apply(y,ordered_pair(apply(x,u),apply(x,v))),apply(x,apply(w,ordered_pair(u,v))))*.
% 300.10/300.69  116748[8:Rew:116078.0,94711.0] || subclass(ordinal_numbers,complement(complement(cantor(u)))) homomorphism(v,u,w)* -> equal(apply(w,ordered_pair(apply(v,x),apply(v,y))),apply(v,apply(u,ordered_pair(x,y))))*.
% 300.10/300.69  195672[7:Res:13225.3,8554.1] || member(u,ordinal_numbers) subclass(u,complement(intersection(v,w))) member(apply(choice,u),union(v,w)) -> equal(u,identity_relation) member(apply(choice,u),symmetric_difference(v,w))*.
% 300.10/300.69  199013[7:Res:13225.3,13362.0] || member(u,ordinal_numbers) subclass(u,v) subclass(v,w)* well_ordering(omega,w)* -> equal(u,identity_relation) equal(integer_of(ordered_pair(apply(choice,u),least(omega,v))),identity_relation)**.
% 300.10/300.69  197698[7:Res:13247.2,897.0] || member(intersection(u,restrict(v,w,x)),ordinal_numbers) -> equal(intersection(u,restrict(v,w,x)),identity_relation) member(apply(choice,intersection(u,restrict(v,w,x))),cross_product(w,x))*.
% 300.10/300.69  197409[7:Res:13246.2,897.0] || member(intersection(restrict(u,v,w),x),ordinal_numbers) -> equal(intersection(restrict(u,v,w),x),identity_relation) member(apply(choice,intersection(restrict(u,v,w),x)),cross_product(v,w))*.
% 300.10/300.69  17329[7:Res:13227.2,8803.0] || subclass(u,image(v,image(w,singleton(x)))) member(ordered_pair(x,regular(u)),cross_product(ordinal_numbers,ordinal_numbers)) -> equal(u,identity_relation) member(ordered_pair(x,regular(u)),compose(v,w))*.
% 300.10/300.69  198644[7:SpR:13262.1,284.1] || member(image(choice,singleton(unordered_pair(u,v))),ordinal_numbers)* -> equal(unordered_pair(u,v),identity_relation) equal(apply(choice,unordered_pair(u,v)),u) subclass(v,image(choice,singleton(unordered_pair(u,v))))*.
% 300.10/300.69  198652[7:SpR:13262.2,284.1] || member(image(choice,singleton(unordered_pair(u,v))),ordinal_numbers)* -> equal(unordered_pair(u,v),identity_relation) equal(apply(choice,unordered_pair(u,v)),v) subclass(u,image(choice,singleton(unordered_pair(u,v))))*.
% 300.10/300.69  134114[5:Res:133837.1,8803.0] || well_ordering(ordinal_numbers,complement(image(u,image(v,singleton(w)))))* member(ordered_pair(w,singleton(singleton(x))),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(w,singleton(singleton(x))),compose(u,v))*.
% 300.10/300.69  196111[18:Res:190510.1,8803.0] || subclass(inverse(identity_relation),image(u,image(v,singleton(w)))) member(ordered_pair(w,regular(symmetrization_of(identity_relation))),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(w,regular(symmetrization_of(identity_relation))),compose(u,v))*.
% 300.10/300.69  43746[5:Res:9006.3,8554.1] function(u) || member(v,ordinal_numbers) subclass(ordinal_numbers,complement(intersection(w,x))) member(image(u,v),union(w,x)) -> member(image(u,v),symmetric_difference(w,x))*.
% 300.10/300.69  199079[7:Res:9006.3,13362.0] function(u) || member(v,ordinal_numbers) subclass(ordinal_numbers,w) subclass(w,x)* well_ordering(omega,x)* -> equal(integer_of(ordered_pair(image(u,v),least(omega,w))),identity_relation)**.
% 300.10/300.69  198584[7:MRR:198582.3,13039.0] inductive(u) || well_ordering(v,u) subclass(singleton(least(v,image(successor_relation,u))),image(successor_relation,u)) -> section(v,singleton(least(v,image(successor_relation,u))),image(successor_relation,u))*.
% 300.10/300.69  155444[5:Res:9618.2,941.1] || member(ordered_pair(u,v),cross_product(ordinal_numbers,ordinal_numbers)) subclass(composition_function,power_class(image(element_relation,complement(w)))) member(ordered_pair(u,ordered_pair(v,compose(u,v))),image(element_relation,power_class(w)))* -> .
% 300.10/300.69  197706[7:Res:13247.2,288.0] || member(intersection(u,image(element_relation,complement(v))),ordinal_numbers) member(apply(choice,intersection(u,image(element_relation,complement(v)))),power_class(v))* -> equal(intersection(u,image(element_relation,complement(v))),identity_relation).
% 300.10/300.69  197417[7:Res:13246.2,288.0] || member(intersection(image(element_relation,complement(u)),v),ordinal_numbers) member(apply(choice,intersection(image(element_relation,complement(u)),v)),power_class(u))* -> equal(intersection(image(element_relation,complement(u)),v),identity_relation).
% 300.10/300.69  198944[8:Rew:8649.0,198933.2] operation(restrict(u,v,ordinal_numbers)) || well_ordering(w,cantor(cantor(restrict(u,v,ordinal_numbers)))) -> equal(image(u,v),identity_relation) member(least(w,image(u,v)),image(u,v))*.
% 300.10/300.69  14798[8:Rew:14769.0,14795.2,14769.0,14795.2] operation(u) operation(v) || equal(apply(u,ordered_pair(sum_class(range_of(identity_relation)),sum_class(range_of(identity_relation)))),sum_class(range_of(identity_relation)))** compatible(identity_relation,v,u) -> homomorphism(identity_relation,v,u)*.
% 300.10/300.69  51019[5:SoR:9962.0,75.1] one_to_one(flip(cross_product(u,ordinal_numbers))) || subclass(range_of(flip(cross_product(u,ordinal_numbers))),range_of(u))* equal(cross_product(range_of(u),range_of(u)),inverse(u)) -> operation(flip(cross_product(u,ordinal_numbers))).
% 300.10/300.69  63719[8:Rew:8637.0,63703.2] single_valued_class(flip(cross_product(u,universal_class))) || subclass(range_of(flip(cross_product(u,ordinal_numbers))),v) equal(flip(cross_product(u,ordinal_numbers)),identity_relation) -> maps(flip(cross_product(u,ordinal_numbers)),inverse(u),v)*.
% 300.10/300.69  63705[8:SoR:9087.0,19277.2] single_valued_class(flip(cross_product(u,ordinal_numbers))) || subclass(range_of(flip(cross_product(u,ordinal_numbers))),v) equal(flip(cross_product(u,ordinal_numbers)),identity_relation) -> maps(flip(cross_product(u,ordinal_numbers)),inverse(u),v)*.
% 300.10/300.69  145895[8:SpL:145758.0,117617.1] function(cross_product(u,ordinal_numbers)) || subclass(image(ordinal_numbers,u),cantor(range_of(v))) equal(cantor(cantor(w)),cantor(cross_product(u,ordinal_numbers))) -> compatible(cross_product(u,ordinal_numbers),w,inverse(v))*.
% 300.10/300.69  63698[8:SoR:9101.0,19277.2] single_valued_class(restrict(element_relation,ordinal_numbers,u)) || subclass(range_of(restrict(element_relation,ordinal_numbers,u)),v) equal(restrict(element_relation,ordinal_numbers,u),identity_relation) -> maps(restrict(element_relation,ordinal_numbers,u),sum_class(u),v)*.
% 300.10/300.69  63720[8:Rew:8637.0,63697.2] single_valued_class(restrict(element_relation,universal_class,u)) || subclass(range_of(restrict(element_relation,ordinal_numbers,u)),v) equal(restrict(element_relation,ordinal_numbers,u),identity_relation) -> maps(restrict(element_relation,ordinal_numbers,u),sum_class(u),v)*.
% 300.10/300.69  51396[5:Res:8642.1,10118.0] || subclass(ordinal_numbers,range_of(u)) homomorphism(v,inverse(u),w)* -> equal(apply(w,ordered_pair(apply(v,x),apply(v,y))),apply(v,apply(inverse(u),ordered_pair(x,y))))*.
% 300.10/300.69  63011[8:Res:15426.1,10118.0] || subclass(domain_relation,range_of(u)) homomorphism(v,inverse(u),w)* -> equal(apply(w,ordered_pair(apply(v,identity_relation),apply(v,identity_relation))),apply(v,apply(inverse(u),ordered_pair(identity_relation,identity_relation))))*.
% 300.10/300.69  198279[21:SpL:197474.0,8803.0] || member(u,image(v,image(w,identity_relation))) member(ordered_pair(inverse(x),u),cross_product(ordinal_numbers,ordinal_numbers)) -> equal(range_of(x),identity_relation) member(ordered_pair(inverse(x),u),compose(v,w))*.
% 300.10/300.69  204153[8:Res:204134.1,9878.0] || member(least(cross_product(u,symmetrization_of(identity_relation)),v),inverse(identity_relation))* member(w,u)* member(w,v)* subclass(v,x)* well_ordering(cross_product(u,symmetrization_of(identity_relation)),x)* -> .
% 300.10/300.69  204400[18:Res:194549.1,8803.0] || subclass(symmetrization_of(identity_relation),image(u,image(v,singleton(w)))) member(ordered_pair(w,regular(symmetrization_of(identity_relation))),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(w,regular(symmetrization_of(identity_relation))),compose(u,v))*.
% 300.10/300.69  206279[8:Rew:160491.0,206188.0] ||  -> equal(intersection(complement(symmetric_difference(complement(u),symmetric_difference(ordinal_numbers,u))),union(union(u,identity_relation),union(complement(u),symmetric_difference(ordinal_numbers,u)))),symmetric_difference(union(u,identity_relation),union(complement(u),symmetric_difference(ordinal_numbers,u))))**.
% 300.10/300.69  208482[7:SpR:13260.1,20.2] || member(second(regular(cross_product(u,v))),w) member(first(regular(cross_product(u,v))),x) -> equal(cross_product(u,v),identity_relation) member(regular(cross_product(u,v)),cross_product(x,w))*.
% 300.10/300.69  209811[8:Res:206259.0,9665.1] inductive(symmetric_difference(complement(u),symmetric_difference(ordinal_numbers,u))) || well_ordering(v,union(u,identity_relation)) -> member(least(v,symmetric_difference(complement(u),symmetric_difference(ordinal_numbers,u))),symmetric_difference(complement(u),symmetric_difference(ordinal_numbers,u)))*.
% 300.10/300.69  209808[8:Res:206259.0,13070.0] || well_ordering(u,union(v,identity_relation)) -> equal(symmetric_difference(complement(v),symmetric_difference(ordinal_numbers,v)),identity_relation) member(least(u,symmetric_difference(complement(v),symmetric_difference(ordinal_numbers,v))),symmetric_difference(complement(v),symmetric_difference(ordinal_numbers,v)))*.
% 300.10/300.69  210762[24:SpR:207558.1,117728.3] operation(u) function(v) || subclass(range_of(v),cantor(segment(w,x,u)))* equal(cantor(cantor(y)),cantor(v)) -> compatible(v,y,restrict(w,x,identity_relation))*.
% 300.10/300.69  212386[7:SpL:13259.2,18.0] || member(cross_product(u,v),ordinal_numbers) member(apply(choice,cross_product(u,v)),cross_product(w,x))* -> equal(cross_product(u,v),identity_relation) member(first(apply(choice,cross_product(u,v))),w).
% 300.10/300.69  212385[7:SpL:13259.2,19.0] || member(cross_product(u,v),ordinal_numbers) member(apply(choice,cross_product(u,v)),cross_product(w,x))* -> equal(cross_product(u,v),identity_relation) member(second(apply(choice,cross_product(u,v))),x).
% 300.10/300.69  212383[8:SpL:13259.2,116129.0] || member(cross_product(u,v),ordinal_numbers) member(apply(choice,cross_product(u,v)),rest_of(w)) -> equal(cross_product(u,v),identity_relation) member(first(apply(choice,cross_product(u,v))),cantor(w))*.
% 300.10/300.69  213501[8:Rew:145761.0,213481.2] operation(cross_product(u,singleton(v))) || subclass(cantor(segment(ordinal_numbers,u,v)),range_of(cross_product(u,singleton(v))))* -> equal(range_of(cross_product(u,singleton(v))),cantor(segment(ordinal_numbers,u,v))).
% 300.10/300.69  214139[7:Res:13529.2,8841.1] || member(ordered_pair(u,regular(image(v,image(w,singleton(u))))),cross_product(ordinal_numbers,ordinal_numbers))* subclass(ordinal_numbers,complement(compose(v,w))) -> equal(image(v,image(w,singleton(u))),identity_relation).
% 300.10/300.69  214138[8:Res:13529.2,210517.1] || member(ordered_pair(u,regular(image(v,image(w,singleton(u))))),cross_product(ordinal_numbers,ordinal_numbers))* equal(complement(compose(v,w)),ordinal_numbers) -> equal(image(v,image(w,singleton(u))),identity_relation).
% 300.10/300.69  214141[8:Rew:14756.0,214128.1,14756.0,214128.0] || member(ordered_pair(u,regular(image(v,range_of(identity_relation)))),cross_product(ordinal_numbers,ordinal_numbers)) -> equal(image(v,range_of(identity_relation)),identity_relation) member(ordered_pair(u,regular(image(v,range_of(identity_relation)))),compose(v,identity_relation))*.
% 300.10/300.69  214326[25:Rew:208887.0,214296.2] operation(restrict(u,v,identity_relation)) || subclass(cantor(segment(u,v,ordinal_numbers)),range_of(restrict(u,v,identity_relation)))* -> equal(range_of(restrict(u,v,identity_relation)),cantor(segment(u,v,ordinal_numbers))).
% 300.10/300.69  217869[20:Res:217827.0,9421.0] || member(u,v)* -> equal(ordered_pair(first(ordered_pair(u,regular(complement(complement(symmetrization_of(identity_relation)))))),second(ordered_pair(u,regular(complement(complement(symmetrization_of(identity_relation))))))),ordered_pair(u,regular(complement(complement(symmetrization_of(identity_relation))))))**.
% 300.10/300.69  218246[8:Res:9997.2,217144.1] || member(ordered_pair(u,not_subclass_element(image(v,image(w,singleton(u))),x)),cross_product(ordinal_numbers,ordinal_numbers))* equal(compose(v,w),identity_relation) -> subclass(image(v,image(w,singleton(u))),x).
% 300.10/300.69  219207[8:Res:9997.2,219073.1] || member(ordered_pair(u,not_subclass_element(image(v,image(w,singleton(u))),x)),cross_product(ordinal_numbers,ordinal_numbers))* subclass(compose(v,w),identity_relation) -> subclass(image(v,image(w,singleton(u))),x).
% 300.10/300.69  219605[8:Res:13247.2,67561.0] || member(intersection(u,symmetric_difference(complement(v),ordinal_numbers)),ordinal_numbers) -> equal(intersection(u,symmetric_difference(complement(v),ordinal_numbers)),identity_relation) member(apply(choice,intersection(u,symmetric_difference(complement(v),ordinal_numbers))),union(v,identity_relation))*.
% 300.10/300.69  219596[8:Res:13246.2,67561.0] || member(intersection(symmetric_difference(complement(u),ordinal_numbers),v),ordinal_numbers) -> equal(intersection(symmetric_difference(complement(u),ordinal_numbers),v),identity_relation) member(apply(choice,intersection(symmetric_difference(complement(u),ordinal_numbers),v)),union(u,identity_relation))*.
% 300.10/300.69  227296[7:Rew:61728.2,227253.4] || member(u,ordinal_numbers) subclass(rest_relation,union_of_range_map) member(range_of(u),ordinal_numbers) well_ordering(v,range_of(u)) -> equal(rest_of(u),identity_relation) member(least(v,rest_of(u)),rest_of(u))*.
% 300.10/300.69  227361[7:Rew:192979.1,227350.2] || member(ordered_pair(u,not_subclass_element(v,image(w,range_of(identity_relation)))),compose(w,regular(cross_product(singleton(u),ordinal_numbers))))* -> equal(cross_product(singleton(u),ordinal_numbers),identity_relation) subclass(v,image(w,range_of(identity_relation))).
% 300.10/300.69  227362[7:Rew:192979.1,227355.2] || member(ordered_pair(u,not_subclass_element(v,range_of(identity_relation))),compose(regular(cross_product(image(w,singleton(u)),ordinal_numbers)),w))* -> equal(cross_product(image(w,singleton(u)),ordinal_numbers),identity_relation) subclass(v,range_of(identity_relation)).
% 300.10/300.69  228916[8:MRR:228883.3,218143.2] || member(apply(choice,regular(restrict(u,v,w))),cross_product(v,w))* member(apply(choice,regular(restrict(u,v,w))),u)* -> equal(regular(restrict(u,v,w)),identity_relation).
% 300.10/300.69  230398[8:Res:161066.1,13362.0] || member(u,ordinal_numbers) subclass(symmetric_difference(ordinal_numbers,v),w)* well_ordering(omega,w) -> member(u,union(v,identity_relation)) equal(integer_of(ordered_pair(u,least(omega,symmetric_difference(ordinal_numbers,v)))),identity_relation)**.
% 300.10/300.69  231846[8:MRR:231797.3,218143.2] || member(not_subclass_element(regular(restrict(u,v,w)),x),cross_product(v,w))* member(not_subclass_element(regular(restrict(u,v,w)),x),u)* -> subclass(regular(restrict(u,v,w)),x).
% 300.10/300.69  232059[8:Res:116148.1,17323.0] || section(u,restrict(v,w,x),y) -> equal(cantor(restrict(u,y,restrict(v,w,x))),identity_relation) member(regular(cantor(restrict(u,y,restrict(v,w,x)))),v)*.
% 300.10/300.69  233725[7:SpR:13260.1,13409.1] || subclass(omega,union_of_range_map) -> equal(cross_product(u,v),identity_relation) equal(integer_of(regular(cross_product(u,v))),identity_relation) equal(sum_class(range_of(first(regular(cross_product(u,v))))),second(regular(cross_product(u,v))))**.
% 300.10/300.69  233962[8:Res:9618.2,161200.0] || member(ordered_pair(u,v),cross_product(ordinal_numbers,ordinal_numbers)) subclass(composition_function,image(element_relation,union(w,identity_relation))) member(ordered_pair(u,ordered_pair(v,compose(u,v))),power_class(symmetric_difference(ordinal_numbers,w)))* -> .
% 300.10/300.69  234368[7:Res:62.1,18696.1] || member(ordered_pair(u,least(v,complement(image(w,image(x,singleton(u)))))),compose(w,x))* well_ordering(v,ordinal_numbers) -> equal(complement(image(w,image(x,singleton(u)))),identity_relation).
% 300.10/300.69  234806[8:Res:193440.1,13362.0] || member(u,ordinal_numbers) subclass(cantor(v),w)* well_ordering(omega,w) -> equal(apply(v,u),sum_class(range_of(identity_relation))) equal(integer_of(ordered_pair(u,least(omega,cantor(v)))),identity_relation)**.
% 300.10/300.69  235046[7:Rew:234956.0,235019.1,234956.0,235019.0] || member(ordered_pair(u,regular(range_of(identity_relation))),cross_product(ordinal_numbers,ordinal_numbers)) -> equal(range_of(identity_relation),identity_relation) member(ordered_pair(u,regular(range_of(identity_relation))),compose(complement(cross_product(image(v,singleton(u)),ordinal_numbers)),v))*.
% 300.10/300.69  235083[7:Res:41368.0,13362.0] || subclass(power_class(u),v)* well_ordering(omega,v) -> subclass(w,image(element_relation,complement(u))) equal(integer_of(ordered_pair(not_subclass_element(w,image(element_relation,complement(u))),least(omega,power_class(u)))),identity_relation)**.
% 300.10/300.69  235460[5:Res:28980.1,8802.1] || subclass(rest_relation,flip(cross_product(ordinal_numbers,ordinal_numbers))) equal(compose(u,ordered_pair(v,w)),rest_of(ordered_pair(w,v))) -> member(ordered_pair(ordered_pair(v,w),rest_of(ordered_pair(w,v))),compose_class(u))*.
% 300.10/300.69  235369[7:SpR:13260.1,28980.1] || subclass(rest_relation,flip(u)) -> equal(cross_product(v,w),identity_relation) member(ordered_pair(regular(cross_product(v,w)),rest_of(ordered_pair(second(regular(cross_product(v,w))),first(regular(cross_product(v,w)))))),u)*.
% 300.10/300.69  235358[7:SpR:13260.1,28980.1] || subclass(rest_relation,flip(u)) -> equal(cross_product(v,w),identity_relation) member(ordered_pair(ordered_pair(second(regular(cross_product(v,w))),first(regular(cross_product(v,w)))),rest_of(regular(cross_product(v,w)))),u)*.
% 300.10/300.69  235592[5:Res:28979.1,8802.1] || subclass(rest_relation,rotate(cross_product(ordinal_numbers,ordinal_numbers))) equal(compose(u,ordered_pair(v,rest_of(ordered_pair(w,v)))),w) -> member(ordered_pair(ordered_pair(v,rest_of(ordered_pair(w,v))),w),compose_class(u))*.
% 300.10/300.69  235492[7:SpR:13260.1,28979.1] || subclass(rest_relation,rotate(u)) -> equal(cross_product(v,w),identity_relation) member(ordered_pair(ordered_pair(second(regular(cross_product(v,w))),rest_of(regular(cross_product(v,w)))),first(regular(cross_product(v,w)))),u)*.
% 300.10/300.69  236087[7:Res:19564.1,13362.0] || subclass(successor(u),v)* well_ordering(omega,v) -> subclass(symmetric_difference(u,singleton(u)),w) equal(integer_of(ordered_pair(not_subclass_element(symmetric_difference(u,singleton(u)),w),least(omega,successor(u)))),identity_relation)**.
% 300.10/300.69  236139[7:Res:19680.1,13362.0] || subclass(symmetrization_of(u),v)* well_ordering(omega,v) -> subclass(symmetric_difference(u,inverse(u)),w) equal(integer_of(ordered_pair(not_subclass_element(symmetric_difference(u,inverse(u)),w),least(omega,symmetrization_of(u)))),identity_relation)**.
% 300.10/300.69  236274[0:Res:62.1,18897.0] || member(ordered_pair(u,not_subclass_element(intersection(v,complement(image(w,image(x,singleton(u))))),y)),compose(w,x))* -> subclass(intersection(v,complement(image(w,image(x,singleton(u))))),y).
% 300.10/300.69  236478[0:Res:62.1,19016.0] || member(ordered_pair(u,not_subclass_element(intersection(complement(image(v,image(w,singleton(u)))),x),y)),compose(v,w))* -> subclass(intersection(complement(image(v,image(w,singleton(u)))),x),y).
% 300.10/300.69  236889[7:Res:17392.2,36719.1] operation(u) || subclass(v,cantor(u))* -> equal(intersection(v,w),identity_relation) equal(ordered_pair(first(regular(intersection(v,w))),second(regular(intersection(v,w)))),regular(intersection(v,w)))**.
% 300.10/300.69  236820[7:Res:17392.2,8554.1] || subclass(u,complement(intersection(v,w))) member(regular(intersection(u,x)),union(v,w)) -> equal(intersection(u,x),identity_relation) member(regular(intersection(u,x)),symmetric_difference(v,w))*.
% 300.10/300.69  237126[7:Res:13574.1,12.0] ||  -> equal(intersection(u,intersection(v,unordered_pair(w,x))),identity_relation) equal(regular(intersection(u,intersection(v,unordered_pair(w,x)))),x)** equal(regular(intersection(u,intersection(v,unordered_pair(w,x)))),w)**.
% 300.10/300.69  237777[7:Res:13573.1,12.0] ||  -> equal(intersection(u,intersection(unordered_pair(v,w),x)),identity_relation) equal(regular(intersection(u,intersection(unordered_pair(v,w),x))),w)** equal(regular(intersection(u,intersection(unordered_pair(v,w),x))),v)**.
% 300.10/300.69  238623[7:Res:13572.2,36719.1] operation(u) || subclass(v,cantor(u))* -> equal(intersection(w,v),identity_relation) equal(ordered_pair(first(regular(intersection(w,v))),second(regular(intersection(w,v)))),regular(intersection(w,v)))**.
% 300.10/300.69  238554[7:Res:13572.2,8554.1] || subclass(u,complement(intersection(v,w))) member(regular(intersection(x,u)),union(v,w)) -> equal(intersection(x,u),identity_relation) member(regular(intersection(x,u)),symmetric_difference(v,w))*.
% 300.10/300.69  239289[7:Res:17397.1,12.0] ||  -> equal(intersection(intersection(unordered_pair(u,v),w),x),identity_relation) equal(regular(intersection(intersection(unordered_pair(u,v),w),x)),v)** equal(regular(intersection(intersection(unordered_pair(u,v),w),x)),u)**.
% 300.10/300.69  240124[7:Res:17396.1,12.0] ||  -> equal(intersection(intersection(u,unordered_pair(v,w)),x),identity_relation) equal(regular(intersection(intersection(u,unordered_pair(v,w)),x)),w)** equal(regular(intersection(intersection(u,unordered_pair(v,w)),x)),v)**.
% 300.10/300.69  40877[0:SpR:3603.0,163.0] ||  -> equal(intersection(complement(symmetric_difference(u,cross_product(v,w))),union(complement(restrict(u,v,w)),union(u,cross_product(v,w)))),symmetric_difference(complement(restrict(u,v,w)),union(u,cross_product(v,w))))**.
% 300.10/300.69  40993[0:SpR:3606.0,163.0] ||  -> equal(intersection(complement(symmetric_difference(cross_product(u,v),w)),union(complement(restrict(w,u,v)),union(cross_product(u,v),w))),symmetric_difference(complement(restrict(w,u,v)),union(cross_product(u,v),w)))**.
% 300.10/300.69  46692[5:SpL:8647.0,9747.0] || member(u,inverse(v))* subclass(rest_of(flip(cross_product(v,ordinal_numbers))),w)* well_ordering(x,w)* -> member(least(x,rest_of(flip(cross_product(v,ordinal_numbers)))),rest_of(flip(cross_product(v,ordinal_numbers))))*.
% 300.10/300.69  49639[5:SpL:6355.1,8651.0] || member(not_subclass_element(cross_product(u,v),w),rest_of(x)) -> subclass(cross_product(u,v),w) equal(restrict(x,first(not_subclass_element(cross_product(u,v),w)),ordinal_numbers),second(not_subclass_element(cross_product(u,v),w)))**.
% 300.10/300.69  50079[5:Rew:18840.1,50051.3] || member(u,subset_relation) member(ordered_pair(ordered_pair(second(u),first(u)),v),w)* member(ordered_pair(u,v),cross_product(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers)) -> member(ordered_pair(u,v),flip(w)).
% 300.10/300.69  50080[5:Rew:18840.1,50050.3] || member(u,subset_relation) member(ordered_pair(ordered_pair(second(u),v),first(u)),w)* member(ordered_pair(u,v),cross_product(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers)) -> member(ordered_pair(u,v),rotate(w)).
% 300.10/300.69  28983[5:MRR:28974.0,8667.0] || subclass(rest_relation,cross_product(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers)) member(ordered_pair(ordered_pair(u,rest_of(ordered_pair(v,u))),v),w) -> member(ordered_pair(ordered_pair(v,u),rest_of(ordered_pair(v,u))),rotate(w))*.
% 300.10/300.69  28984[5:MRR:28973.0,8667.0] || subclass(rest_relation,cross_product(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers)) member(ordered_pair(ordered_pair(u,v),rest_of(ordered_pair(v,u))),w) -> member(ordered_pair(ordered_pair(v,u),rest_of(ordered_pair(v,u))),flip(w))*.
% 300.10/300.69  46691[5:SpL:8648.0,9747.0] || member(u,sum_class(v))* subclass(rest_of(restrict(element_relation,ordinal_numbers,v)),w)* well_ordering(x,w)* -> member(least(x,rest_of(restrict(element_relation,ordinal_numbers,v))),rest_of(restrict(element_relation,ordinal_numbers,v)))*.
% 300.10/300.69  69382[8:Res:69184.1,9878.0] || member(least(cross_product(u,compose(element_relation,ordinal_numbers)),v),element_relation)* member(w,u)* member(w,v)* subclass(v,x)* well_ordering(cross_product(u,compose(element_relation,ordinal_numbers)),x)* -> .
% 300.10/300.69  79538[5:Res:60219.0,8554.1] || member(not_subclass_element(u,complement(complement(intersection(v,w)))),union(v,w)) -> subclass(u,complement(complement(intersection(v,w)))) member(not_subclass_element(u,complement(complement(intersection(v,w)))),symmetric_difference(v,w))*.
% 300.10/300.69  109610[5:Res:39298.1,9872.0] || subclass(ordinal_numbers,complement(complement(u))) member(ordered_pair(v,least(intersection(w,u),x)),w)* member(v,x) subclass(x,y)* well_ordering(intersection(w,u),y)* -> .
% 300.10/300.69  156456[5:SpL:155665.0,8554.1] || member(u,union(complement(subset_relation),union(subset_relation,cross_product(ordinal_numbers,ordinal_numbers)))) member(u,complement(symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers)))) -> member(u,symmetric_difference(complement(subset_relation),union(subset_relation,cross_product(ordinal_numbers,ordinal_numbers))))*.
% 300.10/300.69  156565[5:SpL:155666.0,8554.1] || member(u,union(complement(subset_relation),union(cross_product(ordinal_numbers,ordinal_numbers),subset_relation))) member(u,complement(symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation))) -> member(u,symmetric_difference(complement(subset_relation),union(cross_product(ordinal_numbers,ordinal_numbers),subset_relation)))*.
% 300.10/300.69  116878[8:Rew:116078.0,48523.1] operation(u) ||  -> equal(intersection(complement(symmetric_difference(v,cantor(u))),union(complement(intersection(cantor(u),v)),union(v,cantor(u)))),symmetric_difference(complement(intersection(cantor(u),v)),union(v,cantor(u))))**.
% 300.10/300.69  116876[8:Rew:116078.0,48522.1] operation(u) ||  -> equal(intersection(complement(symmetric_difference(cantor(u),v)),union(complement(intersection(v,cantor(u))),union(cantor(u),v))),symmetric_difference(complement(intersection(v,cantor(u))),union(cantor(u),v)))**.
% 300.10/300.69  69530[7:Res:13125.2,9878.0] || subclass(omega,u) member(v,w)* member(v,x)* subclass(x,y)* well_ordering(cross_product(w,u),y)* -> equal(integer_of(least(cross_product(w,u),x)),identity_relation)**.
% 300.10/300.69  46168[2:Res:9563.3,129.0] || connected(u,v) well_ordering(w,v)* subclass(not_well_ordering(u,v),x)* well_ordering(y,x)* -> well_ordering(u,v) member(least(y,not_well_ordering(u,v)),not_well_ordering(u,v))*.
% 300.10/300.69  132207[2:Res:39609.2,9421.0] inductive(u) || well_ordering(v,u) member(w,x)* -> equal(ordered_pair(first(ordered_pair(w,least(v,u))),second(ordered_pair(w,least(v,u)))),ordered_pair(w,least(v,u)))**.
% 300.10/300.69  131181[5:Res:39607.2,9421.0] inductive(u) || well_ordering(v,ordinal_numbers) member(w,x)* -> equal(ordered_pair(first(ordered_pair(w,least(v,u))),second(ordered_pair(w,least(v,u)))),ordered_pair(w,least(v,u)))**.
% 300.10/300.69  65401[7:Res:13237.2,9421.0] || well_ordering(u,ordinal_numbers) member(v,w)* -> equal(x,identity_relation) equal(ordered_pair(first(ordered_pair(v,least(u,x))),second(ordered_pair(v,least(u,x)))),ordered_pair(v,least(u,x)))**.
% 300.10/300.69  45732[5:Res:9865.3,129.0] || member(u,ordinal_numbers)* member(v,ordinal_numbers) equal(compose(w,v),u)* subclass(compose_class(w),x)* well_ordering(y,x)* -> member(least(y,compose_class(w)),compose_class(w))*.
% 300.10/300.69  49072[5:Rew:30.0,49052.4] || member(u,ordinal_numbers) subclass(union(v,w),x)* well_ordering(y,x)* -> member(u,intersection(complement(v),complement(w)))* member(least(y,union(v,w)),union(v,w))*.
% 300.10/300.69  49975[5:Res:18819.1,9878.0] || member(least(cross_product(u,cross_product(ordinal_numbers,ordinal_numbers)),v),subset_relation)* member(w,u)* member(w,v)* subclass(v,x)* well_ordering(cross_product(u,cross_product(ordinal_numbers,ordinal_numbers)),x)* -> .
% 300.10/300.69  49668[0:SpL:6355.1,100.0] || member(ordered_pair(u,not_subclass_element(cross_product(v,w),x)),composition_function)* -> subclass(cross_product(v,w),x) equal(compose(u,first(not_subclass_element(cross_product(v,w),x))),second(not_subclass_element(cross_product(v,w),x))).
% 300.10/300.69  199059[7:Res:20.2,13362.0] || member(u,v) member(w,x) subclass(cross_product(x,v),y)* well_ordering(omega,y) -> equal(integer_of(ordered_pair(ordered_pair(w,u),least(omega,cross_product(x,v)))),identity_relation)**.
% 300.10/300.69  199053[7:Res:8801.1,13362.0] || member(ordered_pair(u,v),cross_product(ordinal_numbers,ordinal_numbers)) subclass(composition_function,w) well_ordering(omega,w)* -> equal(integer_of(ordered_pair(ordered_pair(u,ordered_pair(v,compose(u,v))),least(omega,composition_function))),identity_relation)**.
% 300.10/300.69  161784[8:Rew:116078.0,51459.3] operation(u) operation(v) || compatible(w,v,u) subclass(cantor(v),successor_relation) -> homomorphism(w,v,u) equal(successor(not_homomorphism1(w,v,u)),not_homomorphism2(w,v,u))**.
% 300.10/300.69  116482[8:Rew:116078.0,51458.3] operation(u) operation(v) || compatible(w,v,u) subclass(cantor(v),rest_relation) -> homomorphism(w,v,u) equal(rest_of(not_homomorphism1(w,v,u)),not_homomorphism2(w,v,u))**.
% 300.10/300.69  117759[8:Rew:116078.0,116264.3] operation(u) operation(v) || compatible(w,v,u) subclass(cantor(v),domain_relation) -> homomorphism(w,v,u) equal(cantor(not_homomorphism1(w,v,u)),not_homomorphism2(w,v,u))**.
% 300.10/300.69  61919[7:Res:13069.2,9421.0] || member(u,ordinal_numbers) member(v,w)* -> equal(u,identity_relation) equal(ordered_pair(first(ordered_pair(v,apply(choice,u))),second(ordered_pair(v,apply(choice,u)))),ordered_pair(v,apply(choice,u)))**.
% 300.10/300.69  18588[5:Res:8978.2,8803.0] || member(u,ordinal_numbers) subclass(ordinal_numbers,image(v,image(w,singleton(x)))) member(ordered_pair(x,sum_class(u)),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(x,sum_class(u)),compose(v,w))*.
% 300.10/300.69  18552[5:Res:8977.2,8803.0] || member(u,ordinal_numbers) subclass(ordinal_numbers,image(v,image(w,singleton(x)))) member(ordered_pair(x,power_class(u)),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(x,power_class(u)),compose(v,w))*.
% 300.10/300.69  54326[5:Res:9997.2,8841.1] || member(ordered_pair(u,not_subclass_element(image(v,image(w,singleton(u))),x)),cross_product(ordinal_numbers,ordinal_numbers))* subclass(ordinal_numbers,complement(compose(v,w))) -> subclass(image(v,image(w,singleton(u))),x).
% 300.10/300.69  49201[0:Obv:49188.1] || member(ordered_pair(u,v),compose(w,x)) -> equal(not_subclass_element(unordered_pair(y,v),image(w,image(x,singleton(u)))),y)** subclass(unordered_pair(y,v),image(w,image(x,singleton(u)))).
% 300.10/300.69  49202[0:Obv:49187.1] || member(ordered_pair(u,v),compose(w,x)) -> equal(not_subclass_element(unordered_pair(v,y),image(w,image(x,singleton(u)))),y)** subclass(unordered_pair(v,y),image(w,image(x,singleton(u)))).
% 300.10/300.69  82291[8:Res:81336.1,8803.0] || subclass(domain_relation,complement(complement(image(u,image(v,singleton(w))))))* member(ordered_pair(w,ordered_pair(identity_relation,identity_relation)),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(w,ordered_pair(identity_relation,identity_relation)),compose(u,v)).
% 300.10/300.69  128349[5:Res:127147.1,8803.0] || subclass(ordinal_numbers,complement(complement(image(u,image(v,singleton(w))))))* member(ordered_pair(w,least(element_relation,omega)),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(w,least(element_relation,omega)),compose(u,v)).
% 300.10/300.69  96382[5:Res:40074.1,8803.0] || subclass(ordinal_numbers,complement(complement(image(u,image(v,singleton(w))))))* member(ordered_pair(w,unordered_pair(x,y)),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(w,unordered_pair(x,y)),compose(u,v))*.
% 300.10/300.69  94694[5:Res:39298.1,8803.0] || subclass(ordinal_numbers,complement(complement(image(u,image(v,singleton(w))))))* member(ordered_pair(w,ordered_pair(x,y)),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(w,ordered_pair(x,y)),compose(u,v))*.
% 300.10/300.69  128014[5:Res:126679.1,8803.0] || subclass(omega,complement(complement(image(u,image(v,singleton(w))))))* member(ordered_pair(w,least(element_relation,omega)),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(w,least(element_relation,omega)),compose(u,v)).
% 300.10/300.69  47007[5:Res:8976.2,9421.0] function(u) || member(v,ordinal_numbers) member(w,x)* -> equal(ordered_pair(first(ordered_pair(w,image(u,v))),second(ordered_pair(w,image(u,v)))),ordered_pair(w,image(u,v)))**.
% 300.10/300.69  46867[5:Rew:189.0,46856.3] || member(u,v) subclass(v,w)* well_ordering(power_class(image(element_relation,complement(x))),w)* -> member(ordered_pair(u,least(power_class(image(element_relation,complement(x))),v)),image(element_relation,power_class(x)))*.
% 300.10/300.69  165304[7:Res:130711.0,13070.0] || well_ordering(u,image(element_relation,power_class(v))) -> equal(complement(power_class(image(element_relation,complement(v)))),identity_relation) member(least(u,complement(power_class(image(element_relation,complement(v))))),complement(power_class(image(element_relation,complement(v)))))*.
% 300.10/300.69  132511[5:Res:130711.0,9665.1] inductive(complement(power_class(image(element_relation,complement(u))))) || well_ordering(v,image(element_relation,power_class(u))) -> member(least(v,complement(power_class(image(element_relation,complement(u))))),complement(power_class(image(element_relation,complement(u)))))*.
% 300.10/300.69  47573[5:MRR:47522.0,41183.1] || member(not_subclass_element(u,intersection(v,image(element_relation,complement(w)))),v)* -> member(not_subclass_element(u,intersection(v,image(element_relation,complement(w)))),power_class(w))* subclass(u,intersection(v,image(element_relation,complement(w)))).
% 300.10/300.69  198968[7:Res:8835.1,13362.0] || member(u,ordinal_numbers) subclass(image(element_relation,complement(v)),w)* well_ordering(omega,w) -> member(u,power_class(v)) equal(integer_of(ordered_pair(u,least(omega,image(element_relation,complement(v))))),identity_relation)**.
% 300.10/300.69  29090[5:Res:8835.1,129.0] || member(u,ordinal_numbers) subclass(image(element_relation,complement(v)),w)* well_ordering(x,w)* -> member(u,power_class(v))* member(least(x,image(element_relation,complement(v))),image(element_relation,complement(v)))*.
% 300.10/300.69  61751[8:Rew:14769.0,61739.4,14769.0,61739.4] operation(u) || compatible(v,w,u) homomorphism(identity_relation,w,x)* -> homomorphism(v,w,u)* equal(apply(x,ordered_pair(sum_class(range_of(identity_relation)),sum_class(range_of(identity_relation)))),sum_class(range_of(identity_relation)))**.
% 300.10/300.69  61470[8:Rew:14756.0,61449.3] || member(ordered_pair(u,v),compose(w,identity_relation))* subclass(image(w,range_of(identity_relation)),x)* well_ordering(y,x)* -> member(least(y,image(w,range_of(identity_relation))),image(w,range_of(identity_relation)))*.
% 300.10/300.69  61468[8:Rew:14756.0,61452.3] || member(ordered_pair(u,ordered_pair(v,least(image(w,range_of(identity_relation)),x))),compose(w,identity_relation))* member(v,x) subclass(x,y)* well_ordering(image(w,range_of(identity_relation)),y)* -> .
% 300.10/300.69  139679[8:SpL:19860.0,117617.1] function(u) || subclass(range_of(u),cantor(image(cross_product(v,w),x))) equal(cantor(cantor(y)),cantor(u)) -> compatible(u,y,inverse(restrict(cross_product(x,ordinal_numbers),v,w)))*.
% 300.10/300.69  204669[21:Res:196904.1,8803.0] || subclass(domain_relation,image(u,image(v,singleton(w)))) member(ordered_pair(w,singleton(singleton(singleton(identity_relation)))),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(w,singleton(singleton(singleton(identity_relation)))),compose(u,v))*.
% 300.10/300.69  208513[7:SpL:13260.1,40.0] || member(ordered_pair(regular(cross_product(u,v)),w),flip(x)) -> equal(cross_product(u,v),identity_relation) member(ordered_pair(ordered_pair(second(regular(cross_product(u,v))),first(regular(cross_product(u,v)))),w),x)*.
% 300.10/300.69  208512[7:SpL:13260.1,37.0] || member(ordered_pair(regular(cross_product(u,v)),w),rotate(x)) -> equal(cross_product(u,v),identity_relation) member(ordered_pair(ordered_pair(second(regular(cross_product(u,v))),w),first(regular(cross_product(u,v)))),x)*.
% 300.10/300.69  209541[16:Res:195258.0,9633.1] || member(u,ordinal_numbers) well_ordering(v,image(element_relation,singleton(identity_relation))) -> member(u,power_class(complement(singleton(identity_relation))))* member(least(v,complement(power_class(complement(singleton(identity_relation))))),complement(power_class(complement(singleton(identity_relation)))))*.
% 300.10/300.69  209540[8:Res:163093.0,9633.1] || member(u,ordinal_numbers) well_ordering(v,image(element_relation,symmetrization_of(identity_relation))) -> member(u,power_class(complement(inverse(identity_relation))))* member(least(v,complement(power_class(complement(inverse(identity_relation))))),complement(power_class(complement(inverse(identity_relation)))))*.
% 300.10/300.69  213502[8:Rew:145761.0,213471.2,145761.0,213471.1] operation(cross_product(u,singleton(v))) || member(w,cantor(segment(ordinal_numbers,u,v))) member(x,cantor(segment(ordinal_numbers,u,v))) -> member(ordered_pair(x,w),segment(ordinal_numbers,u,v))*.
% 300.10/300.69  214071[5:Res:9618.2,152274.0] || member(ordered_pair(u,v),cross_product(ordinal_numbers,ordinal_numbers)) subclass(composition_function,complement(singleton(ordered_pair(u,ordered_pair(v,compose(u,v))))))* -> subclass(singleton(ordered_pair(u,ordered_pair(v,compose(u,v)))),w)*.
% 300.10/300.69  214327[25:Rew:208887.0,214279.2,208887.0,214279.1] operation(restrict(u,v,identity_relation)) || member(w,cantor(segment(u,v,ordinal_numbers))) member(x,cantor(segment(u,v,ordinal_numbers))) -> member(ordered_pair(x,w),segment(u,v,ordinal_numbers))*.
% 300.10/300.69  214676[7:Rew:143170.0,214663.1] || transitive(ordinal_numbers,u) well_ordering(v,cross_product(u,u)) -> equal(segment(v,compose(cross_product(u,u),cross_product(u,u)),least(v,compose(cross_product(u,u),cross_product(u,u)))),identity_relation)**.
% 300.10/300.69  214802[8:Res:9997.2,210517.1] || member(ordered_pair(u,not_subclass_element(image(v,image(w,singleton(u))),x)),cross_product(ordinal_numbers,ordinal_numbers))* equal(complement(compose(v,w)),ordinal_numbers) -> subclass(image(v,image(w,singleton(u))),x).
% 300.10/300.69  221147[7:Res:13236.2,21.0] || well_ordering(u,cross_product(v,w)) -> equal(cross_product(v,w),identity_relation) equal(ordered_pair(first(least(u,cross_product(v,w))),second(least(u,cross_product(v,w)))),least(u,cross_product(v,w)))**.
% 300.10/300.69  221120[7:Res:13236.2,9421.0] || well_ordering(u,v) member(w,x)* -> equal(v,identity_relation) equal(ordered_pair(first(ordered_pair(w,least(u,v))),second(ordered_pair(w,least(u,v)))),ordered_pair(w,least(u,v)))**.
% 300.10/300.69  223682[7:SpR:6355.1,13413.1] || subclass(omega,element_relation) -> subclass(cross_product(u,v),w) equal(integer_of(not_subclass_element(cross_product(u,v),w)),identity_relation) member(first(not_subclass_element(cross_product(u,v),w)),second(not_subclass_element(cross_product(u,v),w)))*.
% 300.10/300.69  223941[8:Rew:160927.0,223859.2,160927.0,223859.0] || member(union(u,symmetric_difference(ordinal_numbers,v)),ordinal_numbers) member(apply(choice,union(u,symmetric_difference(ordinal_numbers,v))),intersection(complement(u),union(v,identity_relation)))* -> equal(union(u,symmetric_difference(ordinal_numbers,v)),identity_relation).
% 300.10/300.69  224256[8:Rew:160992.0,224178.2,160992.0,224178.0] || member(union(symmetric_difference(ordinal_numbers,u),v),ordinal_numbers) member(apply(choice,union(symmetric_difference(ordinal_numbers,u),v)),intersection(union(u,identity_relation),complement(v)))* -> equal(union(symmetric_difference(ordinal_numbers,u),v),identity_relation).
% 300.10/300.69  224706[21:SpL:6355.1,194371.0] || member(not_subclass_element(cross_product(u,v),w),cross_product(ordinal_numbers,ordinal_numbers)) member(second(not_subclass_element(cross_product(u,v),w)),cantor(first(not_subclass_element(cross_product(u,v),w))))* -> subclass(cross_product(u,v),w).
% 300.10/300.69  226420[7:Res:13258.1,3689.0] ||  -> equal(restrict(ordered_pair(u,v),w,x),identity_relation) equal(regular(restrict(ordered_pair(u,v),w,x)),unordered_pair(u,singleton(v)))** equal(regular(restrict(ordered_pair(u,v),w,x)),singleton(u)).
% 300.10/300.69  227354[7:SpL:192979.1,9470.1] || member(ordered_pair(u,v),compose(regular(cross_product(image(w,singleton(u)),ordinal_numbers)),w))* subclass(range_of(identity_relation),x)* -> equal(cross_product(image(w,singleton(u)),ordinal_numbers),identity_relation) member(v,x)*.
% 300.10/300.69  230418[8:Res:161066.1,61018.0] || member(apply(choice,regular(symmetric_difference(ordinal_numbers,u))),ordinal_numbers) -> member(apply(choice,regular(symmetric_difference(ordinal_numbers,u))),union(u,identity_relation))* equal(regular(symmetric_difference(ordinal_numbers,u)),identity_relation) equal(symmetric_difference(ordinal_numbers,u),identity_relation).
% 300.10/300.69  231322[7:Res:17447.1,13362.0] || subclass(complement(intersection(u,v)),w)* well_ordering(omega,w) -> equal(symmetric_difference(u,v),identity_relation) equal(integer_of(ordered_pair(regular(symmetric_difference(u,v)),least(omega,complement(intersection(u,v))))),identity_relation)**.
% 300.10/300.69  233033[8:Res:116148.1,69182.0] || section(u,complement(compose(element_relation,ordinal_numbers)),v) member(regular(cantor(restrict(u,v,complement(compose(element_relation,ordinal_numbers))))),element_relation)* -> equal(cantor(restrict(u,v,complement(compose(element_relation,ordinal_numbers)))),identity_relation).
% 300.10/300.69  235047[7:Rew:234956.0,235030.3] || member(ordered_pair(u,v),compose(complement(cross_product(image(w,singleton(u)),ordinal_numbers)),w))* subclass(range_of(identity_relation),x)* well_ordering(y,x)* -> member(least(y,range_of(identity_relation)),range_of(identity_relation))*.
% 300.10/300.69  235291[8:Res:230445.1,9878.0] || member(least(cross_product(u,union(v,identity_relation)),w),v)* member(x,u)* member(x,w)* subclass(w,y)* well_ordering(cross_product(u,union(v,identity_relation)),y)* -> .
% 300.10/300.69  235947[7:Res:69478.2,131.3] || subclass(omega,symmetric_difference(u,v)) member(w,x) subclass(x,y)* well_ordering(union(u,v),y)* -> equal(integer_of(ordered_pair(w,least(union(u,v),x))),identity_relation)**.
% 300.10/300.69  235917[7:Res:69478.2,13362.0] || subclass(omega,symmetric_difference(u,v)) subclass(union(u,v),w)* well_ordering(omega,w) -> equal(integer_of(x),identity_relation) equal(integer_of(ordered_pair(x,least(omega,union(u,v)))),identity_relation)**.
% 300.10/300.69  236251[0:Res:27.2,18897.0] || member(not_subclass_element(intersection(u,complement(intersection(v,w))),x),w)* member(not_subclass_element(intersection(u,complement(intersection(v,w))),x),v)* -> subclass(intersection(u,complement(intersection(v,w))),x).
% 300.10/300.69  236455[0:Res:27.2,19016.0] || member(not_subclass_element(intersection(complement(intersection(u,v)),w),x),v)* member(not_subclass_element(intersection(complement(intersection(u,v)),w),x),u)* -> subclass(intersection(complement(intersection(u,v)),w),x).
% 300.10/300.69  50969[5:Rew:963.0,50956.1] || member(u,ordinal_numbers) member(singleton(singleton(singleton(v))),cross_product(ordinal_numbers,ordinal_numbers)) member(ordered_pair(ordered_pair(v,singleton(v)),u),w)* -> member(ordered_pair(singleton(singleton(singleton(v))),u),flip(w))*.
% 300.10/300.69  50892[5:Rew:963.0,50879.1] || member(u,ordinal_numbers) member(singleton(singleton(singleton(v))),cross_product(ordinal_numbers,ordinal_numbers)) member(ordered_pair(ordered_pair(v,u),singleton(v)),w)* -> member(ordered_pair(singleton(singleton(singleton(v))),u),rotate(w))*.
% 300.10/300.69  10063[5:Rew:963.0,10060.2] || member(ordered_pair(ordered_pair(u,singleton(u)),v),w)* member(ordered_pair(singleton(singleton(singleton(u))),v),cross_product(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers))* -> member(ordered_pair(singleton(singleton(singleton(u))),v),flip(w))*.
% 300.10/300.69  10095[5:Rew:963.0,10092.2] || member(ordered_pair(ordered_pair(u,v),singleton(u)),w)* member(ordered_pair(singleton(singleton(singleton(u))),v),cross_product(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers))* -> member(ordered_pair(singleton(singleton(singleton(u))),v),rotate(w))*.
% 300.10/300.69  134788[8:MRR:134748.0,8667.0] || subclass(rest_relation,rest_of(u)) member(ordered_pair(v,least(intersection(w,cantor(u)),x)),w)* member(v,x) subclass(x,y)* well_ordering(intersection(w,cantor(u)),y)* -> .
% 300.10/300.69  155194[0:SpR:154737.1,3594.0] || subclass(union(complement(intersection(u,v)),union(u,v)),complement(symmetric_difference(u,v)))* -> equal(symmetric_difference(complement(intersection(u,v)),union(u,v)),union(complement(intersection(u,v)),union(u,v))).
% 300.10/300.69  117767[8:Rew:116078.0,116303.2] operation(restrict(u,v,singleton(w))) || member(x,cantor(segment(u,v,w))) member(y,cantor(segment(u,v,w))) -> member(ordered_pair(y,x),segment(u,v,w))*.
% 300.10/300.69  117773[8:Rew:116078.0,116823.2] operation(u) ||  -> subclass(intersection(cantor(u),v),w) equal(ordered_pair(first(not_subclass_element(intersection(cantor(u),v),w)),second(not_subclass_element(intersection(cantor(u),v),w))),not_subclass_element(intersection(cantor(u),v),w))**.
% 300.10/300.69  117772[8:Rew:116078.0,116811.1] operation(u) ||  -> subclass(intersection(v,cantor(u)),w) equal(ordered_pair(first(not_subclass_element(intersection(v,cantor(u)),w)),second(not_subclass_element(intersection(v,cantor(u)),w))),not_subclass_element(intersection(v,cantor(u)),w))**.
% 300.10/300.69  117771[8:Rew:116078.0,116566.3,116078.0,116566.3,116078.0,116566.2,116078.0,116566.2,116078.0,116566.2,116078.0,116566.1,116078.0,116566.1] operation(u) || section(v,cantor(cantor(u)),cantor(cantor(u))) subclass(cantor(cantor(u)),cantor(intersection(cantor(u),v)))* -> equal(cantor(intersection(cantor(u),v)),cantor(cantor(u))).
% 300.10/300.69  117770[8:Rew:116078.0,116552.5,116078.0,116552.2,116078.0,116552.1,116078.0,116552.1] operation(u) || member(least(cantor(u),v),cantor(cantor(u)))* member(w,cantor(cantor(u)))* member(w,v)* subclass(v,x)* well_ordering(cantor(u),x)* -> .
% 300.10/300.69  62553[7:SpR:13100.0,18840.1] || member(not_subclass_element(restrict(u,v,singleton(w)),identity_relation),subset_relation) -> equal(ordered_pair(domain__dfg(u,v,w),second(not_subclass_element(restrict(u,v,singleton(w)),identity_relation))),not_subclass_element(restrict(u,v,singleton(w)),identity_relation))**.
% 300.10/300.69  62523[7:SpR:13101.0,18840.1] || member(not_subclass_element(restrict(u,singleton(v),w),identity_relation),subset_relation) -> equal(ordered_pair(first(not_subclass_element(restrict(u,singleton(v),w),identity_relation)),range__dfg(u,v,w)),not_subclass_element(restrict(u,singleton(v),w),identity_relation))**.
% 300.10/300.69  64281[7:Res:13248.1,8554.1] || member(regular(intersection(complement(intersection(u,v)),w)),union(u,v)) -> equal(intersection(complement(intersection(u,v)),w),identity_relation) member(regular(intersection(complement(intersection(u,v)),w)),symmetric_difference(u,v))*.
% 300.10/300.69  64192[7:Res:13210.1,8554.1] || member(regular(intersection(u,complement(intersection(v,w)))),union(v,w)) -> equal(intersection(u,complement(intersection(v,w))),identity_relation) member(regular(intersection(u,complement(intersection(v,w)))),symmetric_difference(v,w))*.
% 300.10/300.69  83276[7:Res:61019.0,8554.1] || member(regular(complement(complement(complement(intersection(u,v))))),union(u,v)) -> equal(complement(complement(complement(intersection(u,v)))),identity_relation) member(regular(complement(complement(complement(intersection(u,v))))),symmetric_difference(u,v))*.
% 300.10/300.69  131174[5:Res:39607.2,8554.1] inductive(complement(intersection(u,v))) || well_ordering(w,ordinal_numbers) member(least(w,complement(intersection(u,v))),union(u,v)) -> member(least(w,complement(intersection(u,v))),symmetric_difference(u,v))*.
% 300.10/300.69  65396[7:Res:13237.2,8554.1] || well_ordering(u,ordinal_numbers) member(least(u,complement(intersection(v,w))),union(v,w)) -> equal(complement(intersection(v,w)),identity_relation) member(least(u,complement(intersection(v,w))),symmetric_difference(v,w))*.
% 300.10/300.69  46654[5:Res:9618.2,8800.1] || member(ordered_pair(u,v),cross_product(ordinal_numbers,ordinal_numbers)) subclass(composition_function,cross_product(ordinal_numbers,ordinal_numbers)) member(u,ordered_pair(v,compose(u,v))) -> member(ordered_pair(u,ordered_pair(v,compose(u,v))),element_relation)*.
% 300.10/300.69  48250[5:SpR:963.0,9617.2] || member(u,recursion_equation_functions(singleton(ordered_pair(rest_of(u),u)))) member(ordered_pair(singleton(ordered_pair(rest_of(u),u)),rest_of(u)),cross_product(ordinal_numbers,ordinal_numbers))* -> member(singleton(singleton(singleton(ordered_pair(rest_of(u),u)))),composition_function).
% 300.10/300.69  194503[8:Res:163112.0,9878.0] || member(u,v)* member(u,w)* subclass(w,x)* well_ordering(cross_product(v,complement(inverse(identity_relation))),x)* -> subclass(singleton(least(cross_product(v,complement(inverse(identity_relation))),w)),symmetrization_of(identity_relation))*.
% 300.10/300.69  195647[16:Rew:195224.0,195212.4] || member(u,v)* member(u,w)* subclass(w,x)* well_ordering(cross_product(v,complement(singleton(identity_relation))),x)* -> subclass(singleton(least(cross_product(v,complement(singleton(identity_relation))),w)),singleton(identity_relation))*.
% 300.10/300.69  199062[7:Res:9706.3,13362.0] || member(u,ordinal_numbers) member(v,ordinal_numbers) equal(successor(v),u) subclass(successor_relation,w) well_ordering(omega,w)* -> equal(integer_of(ordered_pair(ordered_pair(v,u),least(omega,successor_relation))),identity_relation)**.
% 300.10/300.69  199022[7:Res:13500.2,13362.0] || well_ordering(u,cross_product(ordinal_numbers,ordinal_numbers)) subclass(rest_of(v),w)* well_ordering(omega,w) -> equal(rest_of(v),identity_relation) equal(integer_of(ordered_pair(least(u,rest_of(v)),least(omega,rest_of(v)))),identity_relation)**.
% 300.10/300.69  199021[7:Res:13501.2,13362.0] || well_ordering(u,cross_product(ordinal_numbers,ordinal_numbers)) subclass(compose_class(v),w)* well_ordering(omega,w) -> equal(compose_class(v),identity_relation) equal(integer_of(ordered_pair(least(u,compose_class(v)),least(omega,compose_class(v)))),identity_relation)**.
% 300.10/300.69  116529[8:Rew:116078.0,51423.3] operation(u) operation(v) || compatible(w,v,u) subclass(cantor(v),recursion_equation_functions(x))* -> homomorphism(w,v,u) function(ordered_pair(not_homomorphism1(w,v,u),not_homomorphism2(w,v,u)))*.
% 300.10/300.69  46711[5:Res:94.3,9747.0] operation(u) operation(v) || compatible(w,v,u) subclass(rest_of(v),x)* well_ordering(y,x)* -> homomorphism(w,v,u)* member(least(y,rest_of(v)),rest_of(v))*.
% 300.10/300.69  196459[21:Rew:196372.1,161812.3] || member(u,ordinal_numbers) subclass(domain_relation,cantor(v)) homomorphism(w,v,x)* -> equal(apply(x,ordered_pair(apply(w,u),apply(w,identity_relation))),apply(w,apply(v,ordered_pair(u,identity_relation))))*.
% 300.10/300.69  116395[8:Rew:116078.0,50081.1] || member(u,subset_relation) member(u,cantor(v)) homomorphism(w,v,x)* -> equal(apply(x,ordered_pair(apply(w,first(u)),apply(w,second(u)))),apply(w,apply(v,u)))*.
% 300.10/300.69  199014[7:Res:13247.2,13362.0] || member(intersection(u,v),ordinal_numbers) subclass(v,w)* well_ordering(omega,w)* -> equal(intersection(u,v),identity_relation) equal(integer_of(ordered_pair(apply(choice,intersection(u,v)),least(omega,v))),identity_relation)**.
% 300.10/300.69  198981[7:Res:13246.2,13362.0] || member(intersection(u,v),ordinal_numbers) subclass(u,w)* well_ordering(omega,w)* -> equal(intersection(u,v),identity_relation) equal(integer_of(ordered_pair(apply(choice,intersection(u,v)),least(omega,u))),identity_relation)**.
% 300.10/300.69  194647[7:Res:27.2,13313.1] || member(apply(choice,complement(intersection(u,v))),v)* member(apply(choice,complement(intersection(u,v))),u)* member(complement(intersection(u,v)),ordinal_numbers) -> equal(complement(intersection(u,v)),identity_relation).
% 300.10/300.69  19129[5:Res:2503.2,8803.0] || subclass(u,image(v,image(w,singleton(x)))) member(ordered_pair(x,not_subclass_element(u,y)),cross_product(ordinal_numbers,ordinal_numbers)) -> subclass(u,y) member(ordered_pair(x,not_subclass_element(u,y)),compose(v,w))*.
% 300.10/300.69  117765[8:Rew:116078.0,116276.2,116078.0,116276.2,116078.0,116276.1,116078.0,116276.1] one_to_one(restrict(u,v,ordinal_numbers)) || subclass(image(u,v),cantor(cantor(w))) equal(cantor(cantor(x)),cantor(restrict(u,v,ordinal_numbers))) -> compatible(restrict(u,v,ordinal_numbers),x,w)*.
% 300.10/300.69  117766[8:Rew:116078.0,116277.2,116078.0,116277.2,116078.0,116277.1,116078.0,116277.1] operation(restrict(u,v,ordinal_numbers)) || subclass(image(u,v),cantor(cantor(w))) equal(cantor(cantor(x)),cantor(restrict(u,v,ordinal_numbers))) -> compatible(restrict(u,v,ordinal_numbers),x,w)*.
% 300.10/300.69  106811[5:Res:79577.0,8562.0] || member(not_subclass_element(u,intersection(v,image(element_relation,complement(w)))),v)* -> subclass(singleton(not_subclass_element(u,intersection(v,image(element_relation,complement(w))))),power_class(w))* subclass(u,intersection(v,image(element_relation,complement(w)))).
% 300.10/300.69  61471[8:Rew:14756.0,61443.1,14756.0,61443.0] || member(ordered_pair(u,not_subclass_element(image(v,range_of(identity_relation)),w)),cross_product(ordinal_numbers,ordinal_numbers)) -> subclass(image(v,range_of(identity_relation)),w) member(ordered_pair(u,not_subclass_element(image(v,range_of(identity_relation)),w)),compose(v,identity_relation))*.
% 300.10/300.69  47707[5:SoR:9087.0,10858.2] single_valued_class(flip(cross_product(u,ordinal_numbers))) || subclass(range_of(flip(cross_product(u,ordinal_numbers))),v) equal(flip(cross_product(u,ordinal_numbers)),cross_product(ordinal_numbers,ordinal_numbers)) -> maps(flip(cross_product(u,ordinal_numbers)),inverse(u),v)*.
% 300.10/300.69  47645[5:Rew:8637.0,47643.2] single_valued_class(flip(cross_product(u,universal_class))) || subclass(range_of(flip(cross_product(u,ordinal_numbers))),v) equal(flip(cross_product(u,ordinal_numbers)),cross_product(ordinal_numbers,ordinal_numbers)) -> maps(flip(cross_product(u,ordinal_numbers)),inverse(u),v)*.
% 300.10/300.69  47900[5:SoR:9101.0,10858.2] single_valued_class(restrict(element_relation,ordinal_numbers,u)) || subclass(range_of(restrict(element_relation,ordinal_numbers,u)),v) equal(restrict(element_relation,ordinal_numbers,u),cross_product(ordinal_numbers,ordinal_numbers)) -> maps(restrict(element_relation,ordinal_numbers,u),sum_class(u),v)*.
% 300.10/300.69  47887[5:Rew:8637.0,47885.2] single_valued_class(restrict(element_relation,universal_class,u)) || subclass(range_of(restrict(element_relation,ordinal_numbers,u)),v) equal(restrict(element_relation,ordinal_numbers,u),cross_product(ordinal_numbers,ordinal_numbers)) -> maps(restrict(element_relation,ordinal_numbers,u),sum_class(u),v)*.
% 300.10/300.69  109134[5:Res:39298.1,10118.0] || subclass(ordinal_numbers,complement(complement(range_of(u)))) homomorphism(v,inverse(u),w)* -> equal(apply(w,ordered_pair(apply(v,x),apply(v,y))),apply(v,apply(inverse(u),ordered_pair(x,y))))*.
% 300.10/300.69  117764[8:Rew:116078.0,116263.2,116078.0,116263.2,116078.0,116263.1] function(u) || subclass(range_of(u),cantor(segment(cross_product(v,w),x,y))) equal(cantor(cantor(z)),cantor(u)) -> compatible(u,z,restrict(cross_product(x,singleton(y)),v,w))*.
% 300.10/300.69  208364[24:Rew:207572.1,208335.3] operation(u) || member(ordered_pair(ordered_pair(u,identity_relation),v),w)* member(ordered_pair(singleton(singleton(identity_relation)),v),cross_product(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers))* -> member(ordered_pair(singleton(singleton(identity_relation)),v),flip(w))*.
% 300.10/300.69  208365[24:Rew:207572.1,208334.3] operation(u) || member(ordered_pair(ordered_pair(u,v),identity_relation),w)* member(ordered_pair(singleton(singleton(identity_relation)),v),cross_product(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers))* -> member(ordered_pair(singleton(singleton(identity_relation)),v),rotate(w))*.
% 300.10/300.69  208483[7:SpR:13260.1,41098.2] || member(second(regular(cross_product(u,v))),ordinal_numbers) member(first(regular(cross_product(u,v))),second(regular(cross_product(u,v))))* -> equal(cross_product(u,v),identity_relation) member(regular(cross_product(u,v)),element_relation).
% 300.10/300.69  210243[8:SpR:916.0,161701.2] || section(cross_product(u,v),w,x) well_ordering(y,w) -> equal(segment(y,cantor(restrict(cross_product(x,w),u,v)),least(y,cantor(restrict(cross_product(x,w),u,v)))),identity_relation)**.
% 300.10/300.69  210296[8:Res:140864.1,9878.0] || member(least(cross_product(u,symmetric_difference(ordinal_numbers,v)),w),complement(v))* member(x,u)* member(x,w)* subclass(w,y)* well_ordering(cross_product(u,symmetric_difference(ordinal_numbers,v)),y)* -> .
% 300.10/300.69  210446[8:SoR:117719.0,19277.2] single_valued_class(inverse(u)) || subclass(range_of(inverse(u)),cantor(range_of(u))) equal(cross_product(cantor(range_of(u)),cantor(range_of(u))),range_of(u))** equal(inverse(u),identity_relation) -> operation(inverse(u)).
% 300.10/300.69  211614[24:Rew:207572.1,211597.2] operation(u) || member(v,ordinal_numbers) member(singleton(singleton(identity_relation)),cross_product(ordinal_numbers,ordinal_numbers)) member(ordered_pair(ordered_pair(u,v),identity_relation),w)* -> member(ordered_pair(singleton(singleton(identity_relation)),v),rotate(w))*.
% 300.10/300.69  211987[24:Rew:207572.1,211970.2] operation(u) || member(v,ordinal_numbers) member(singleton(singleton(identity_relation)),cross_product(ordinal_numbers,ordinal_numbers)) member(ordered_pair(ordered_pair(u,identity_relation),v),w)* -> member(ordered_pair(singleton(singleton(identity_relation)),v),flip(w))*.
% 300.10/300.69  212355[7:SpR:13259.2,964.0] || member(cross_product(u,v),ordinal_numbers) -> equal(cross_product(u,v),identity_relation) member(unordered_pair(first(apply(choice,cross_product(u,v))),singleton(second(apply(choice,cross_product(u,v))))),apply(choice,cross_product(u,v)))*.
% 300.10/300.69  213424[25:Rew:208840.0,213416.2] || member(singleton(singleton(identity_relation)),range_of(u)) homomorphism(v,inverse(u),w)* -> equal(apply(w,ordered_pair(apply(v,identity_relation),apply(v,ordinal_numbers))),apply(v,apply(inverse(u),singleton(singleton(identity_relation)))))*.
% 300.10/300.69  213569[8:Res:116127.5,157.0] operation(u) operation(v) || compatible(w,v,u) subclass(cantor(v),union_of_range_map) -> homomorphism(w,v,u) equal(sum_class(range_of(not_homomorphism1(w,v,u))),not_homomorphism2(w,v,u))**.
% 300.10/300.69  214599[25:SpL:208985.1,8821.1] operation(u) || member(ordered_pair(ordered_pair(v,u),w),x) member(ordered_pair(ordered_pair(w,v),ordinal_numbers),cross_product(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers))* -> member(ordered_pair(ordered_pair(w,v),u),rotate(x))*.
% 300.10/300.69  214595[25:SpL:208985.1,8820.1] operation(u) || member(ordered_pair(ordered_pair(v,w),u),x) member(ordered_pair(ordered_pair(w,v),ordinal_numbers),cross_product(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers))* -> member(ordered_pair(ordered_pair(w,v),u),flip(x))*.
% 300.10/300.69  214578[25:SpL:208985.1,8820.1] operation(u) || member(ordered_pair(ordered_pair(u,v),w),x) member(ordered_pair(ordered_pair(v,ordinal_numbers),w),cross_product(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers))* -> member(ordered_pair(ordered_pair(v,u),w),flip(x))*.
% 300.10/300.69  214577[25:SpL:208985.1,8821.1] operation(u) || member(ordered_pair(ordered_pair(u,v),w),x) member(ordered_pair(ordered_pair(w,ordinal_numbers),v),cross_product(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers))* -> member(ordered_pair(ordered_pair(w,u),v),rotate(x))*.
% 300.10/300.69  214535[25:SpL:208985.1,8821.1] operation(u) || member(ordered_pair(ordered_pair(v,ordinal_numbers),w),x) member(ordered_pair(ordered_pair(w,v),u),cross_product(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers))* -> member(ordered_pair(ordered_pair(w,v),ordinal_numbers),rotate(x))*.
% 300.10/300.69  214533[25:SpL:208985.1,8820.1] operation(u) || member(ordered_pair(ordered_pair(v,w),ordinal_numbers),x) member(ordered_pair(ordered_pair(w,v),u),cross_product(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers))* -> member(ordered_pair(ordered_pair(w,v),ordinal_numbers),flip(x))*.
% 300.10/300.69  214516[25:SpL:208985.1,8820.1] operation(u) || member(ordered_pair(ordered_pair(ordinal_numbers,v),w),x) member(ordered_pair(ordered_pair(v,u),w),cross_product(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers))* -> member(ordered_pair(ordered_pair(v,ordinal_numbers),w),flip(x))*.
% 300.10/300.69  214515[25:SpL:208985.1,8821.1] operation(u) || member(ordered_pair(ordered_pair(ordinal_numbers,v),w),x) member(ordered_pair(ordered_pair(w,u),v),cross_product(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers))* -> member(ordered_pair(ordered_pair(w,ordinal_numbers),v),rotate(x))*.
% 300.10/300.69  214462[25:SpR:208985.1,10061.3] operation(u) || member(v,ordinal_numbers) member(ordered_pair(w,u),cross_product(ordinal_numbers,ordinal_numbers)) member(ordered_pair(ordered_pair(u,w),v),x)* -> member(ordered_pair(ordered_pair(w,ordinal_numbers),v),flip(x))*.
% 300.10/300.69  214461[25:SpR:208985.1,10093.3] operation(u) || member(v,ordinal_numbers) member(ordered_pair(w,u),cross_product(ordinal_numbers,ordinal_numbers)) member(ordered_pair(ordered_pair(u,v),w),x)* -> member(ordered_pair(ordered_pair(w,ordinal_numbers),v),rotate(x))*.
% 300.10/300.69  214425[25:SpR:208985.1,10061.3] operation(u) || member(v,ordinal_numbers) member(ordered_pair(w,ordinal_numbers),cross_product(ordinal_numbers,ordinal_numbers)) member(ordered_pair(ordered_pair(ordinal_numbers,w),v),x) -> member(ordered_pair(ordered_pair(w,u),v),flip(x))*.
% 300.10/300.69  214424[25:SpR:208985.1,10093.3] operation(u) || member(v,ordinal_numbers) member(ordered_pair(w,ordinal_numbers),cross_product(ordinal_numbers,ordinal_numbers)) member(ordered_pair(ordered_pair(ordinal_numbers,v),w),x) -> member(ordered_pair(ordered_pair(w,u),v),rotate(x))*.
% 300.10/300.69  215910[8:MRR:215909.4,14676.0] || equal(compose_class(u),domain_relation) member(image(u,range_of(identity_relation)),ordinal_numbers) member(ordered_pair(v,apply(choice,image(u,range_of(identity_relation)))),cross_product(ordinal_numbers,ordinal_numbers))* -> equal(image(u,range_of(identity_relation)),identity_relation).
% 300.10/300.69  224553[10:SpL:223660.1,8803.0] || subclass(element_relation,identity_relation) member(u,image(v,image(w,identity_relation))) member(ordered_pair(cross_product(ordinal_numbers,ordinal_numbers),u),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(cross_product(ordinal_numbers,ordinal_numbers),u),compose(v,w))*.
% 300.10/300.69  227977[7:SpR:6355.1,13410.1] || subclass(omega,rest_relation) -> subclass(cross_product(u,v),w) equal(integer_of(not_subclass_element(cross_product(u,v),w)),identity_relation) equal(rest_of(first(not_subclass_element(cross_product(u,v),w))),second(not_subclass_element(cross_product(u,v),w)))**.
% 300.10/300.69  228124[8:SpR:6355.1,160930.1] || subclass(omega,domain_relation) -> subclass(cross_product(u,v),w) equal(integer_of(not_subclass_element(cross_product(u,v),w)),identity_relation) equal(cantor(first(not_subclass_element(cross_product(u,v),w))),second(not_subclass_element(cross_product(u,v),w)))**.
% 300.10/300.69  228189[7:SpR:6355.1,13412.1] || subclass(omega,successor_relation) -> subclass(cross_product(u,v),w) equal(integer_of(not_subclass_element(cross_product(u,v),w)),identity_relation) equal(successor(first(not_subclass_element(cross_product(u,v),w))),second(not_subclass_element(cross_product(u,v),w)))**.
% 300.10/300.69  233360[8:Res:231881.0,9660.2] || member(u,v)* member(w,x)* well_ordering(y,complement(singleton(cross_product(x,v)))) -> equal(singleton(cross_product(x,v)),identity_relation) member(least(y,cross_product(x,v)),cross_product(x,v))*.
% 300.10/300.69  233346[8:Res:231881.0,9636.2] || member(u,v)* member(u,w)* well_ordering(x,complement(singleton(intersection(w,v)))) -> equal(singleton(intersection(w,v)),identity_relation) member(least(x,intersection(w,v)),intersection(w,v))*.
% 300.10/300.69  235048[7:Rew:234956.0,235020.1,234956.0,235020.0] || member(ordered_pair(u,not_subclass_element(range_of(identity_relation),v)),cross_product(ordinal_numbers,ordinal_numbers)) -> subclass(range_of(identity_relation),v) member(ordered_pair(u,not_subclass_element(range_of(identity_relation),v)),compose(complement(cross_product(image(w,singleton(u)),ordinal_numbers)),w))*.
% 300.10/300.69  235051[15:MRR:235050.0,165460.0] || member(ordered_pair(u,apply(choice,range_of(identity_relation))),cross_product(ordinal_numbers,ordinal_numbers)) -> equal(range_of(identity_relation),identity_relation) member(ordered_pair(u,apply(choice,range_of(identity_relation))),compose(complement(cross_product(image(v,singleton(u)),ordinal_numbers)),v))*.
% 300.10/300.69  235464[5:Res:28980.1,8821.1] || subclass(rest_relation,flip(cross_product(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers))) member(ordered_pair(ordered_pair(u,rest_of(ordered_pair(u,v))),v),w) -> member(ordered_pair(ordered_pair(v,u),rest_of(ordered_pair(u,v))),rotate(w))*.
% 300.10/300.69  235463[5:Res:28980.1,8820.1] || subclass(rest_relation,flip(cross_product(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers))) member(ordered_pair(ordered_pair(u,v),rest_of(ordered_pair(u,v))),w) -> member(ordered_pair(ordered_pair(v,u),rest_of(ordered_pair(u,v))),flip(w))*.
% 300.10/300.69  235421[5:Res:28980.1,3689.0] || subclass(rest_relation,flip(ordered_pair(u,v)))* -> equal(ordered_pair(ordered_pair(w,x),rest_of(ordered_pair(x,w))),unordered_pair(u,singleton(v)))* equal(ordered_pair(ordered_pair(w,x),rest_of(ordered_pair(x,w))),singleton(u)).
% 300.10/300.69  235596[5:Res:28979.1,8821.1] || subclass(rest_relation,rotate(cross_product(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers))) member(ordered_pair(ordered_pair(rest_of(ordered_pair(u,v)),u),v),w) -> member(ordered_pair(ordered_pair(v,rest_of(ordered_pair(u,v))),u),rotate(w))*.
% 300.10/300.69  235595[5:Res:28979.1,8820.1] || subclass(rest_relation,rotate(cross_product(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers))) member(ordered_pair(ordered_pair(rest_of(ordered_pair(u,v)),v),u),w) -> member(ordered_pair(ordered_pair(v,rest_of(ordered_pair(u,v))),u),flip(w))*.
% 300.10/300.69  235549[5:Res:28979.1,3689.0] || subclass(rest_relation,rotate(ordered_pair(u,v)))* -> equal(ordered_pair(ordered_pair(w,rest_of(ordered_pair(x,w))),x),unordered_pair(u,singleton(v)))* equal(ordered_pair(ordered_pair(w,rest_of(ordered_pair(x,w))),x),singleton(u)).
% 300.10/300.69  235653[5:Res:41371.0,36719.1] operation(u) ||  -> subclass(complement(complement(cantor(u))),v) equal(ordered_pair(first(not_subclass_element(complement(complement(cantor(u))),v)),second(not_subclass_element(complement(complement(cantor(u))),v))),not_subclass_element(complement(complement(cantor(u))),v))**.
% 300.10/300.69  43709[0:SpL:3616.0,8554.1] || member(u,union(union(v,w),union(complement(v),complement(w)))) member(u,complement(symmetric_difference(complement(v),complement(w)))) -> member(u,symmetric_difference(union(v,w),union(complement(v),complement(w))))*.
% 300.10/300.69  48578[0:SpL:3594.0,8559.2] || member(u,union(complement(intersection(v,w)),union(v,w)))* member(u,complement(symmetric_difference(v,w))) subclass(symmetric_difference(complement(intersection(v,w)),union(v,w)),x)* -> member(u,x)*.
% 300.10/300.69  50399[0:Rew:163.0,50326.4] || member(u,union(v,w)) member(u,complement(intersection(v,w)))* subclass(symmetric_difference(v,w),x)* well_ordering(y,x)* -> member(least(y,symmetric_difference(v,w)),symmetric_difference(v,w))*.
% 300.10/300.69  39735[0:Res:8551.2,129.0] || member(u,cross_product(v,w))* member(u,x)* subclass(restrict(x,v,w),y)* well_ordering(z,y)* -> member(least(z,restrict(x,v,w)),restrict(x,v,w))*.
% 300.10/300.69  49627[0:SpR:6355.1,20.2] || member(second(not_subclass_element(cross_product(u,v),w)),x) member(first(not_subclass_element(cross_product(u,v),w)),y) -> subclass(cross_product(u,v),w) member(not_subclass_element(cross_product(u,v),w),cross_product(y,x))*.
% 300.10/300.69  47515[0:Res:3618.1,8562.0] || member(not_subclass_element(u,intersection(v,complement(intersection(w,x)))),symmetric_difference(w,x))* member(not_subclass_element(u,intersection(v,complement(intersection(w,x)))),v)* -> subclass(u,intersection(v,complement(intersection(w,x)))).
% 300.10/300.69  130657[5:Res:41371.0,21.0] ||  -> subclass(complement(complement(cross_product(u,v))),w) equal(ordered_pair(first(not_subclass_element(complement(complement(cross_product(u,v))),w)),second(not_subclass_element(complement(complement(cross_product(u,v))),w))),not_subclass_element(complement(complement(cross_product(u,v))),w))**.
% 300.10/300.69  140405[0:Res:8551.2,47534.0] || member(not_subclass_element(u,intersection(restrict(v,w,x),u)),cross_product(w,x))* member(not_subclass_element(u,intersection(restrict(v,w,x),u)),v)* -> subclass(u,intersection(restrict(v,w,x),u)).
% 300.10/300.69  153379[0:Res:919.1,3689.0] ||  -> subclass(restrict(ordered_pair(u,v),w,x),y) equal(not_subclass_element(restrict(ordered_pair(u,v),w,x),y),unordered_pair(u,singleton(v)))** equal(not_subclass_element(restrict(ordered_pair(u,v),w,x),y),singleton(u)).
% 300.10/300.69  156479[5:Rew:155665.0,156457.2,155665.0,156457.1] || member(not_subclass_element(u,symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers))),union(subset_relation,cross_product(ordinal_numbers,ordinal_numbers)))* member(not_subclass_element(u,symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers))),complement(subset_relation)) -> subclass(u,symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers))).
% 300.10/300.69  156588[5:Rew:155666.0,156566.2,155666.0,156566.1] || member(not_subclass_element(u,symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation)),union(cross_product(ordinal_numbers,ordinal_numbers),subset_relation))* member(not_subclass_element(u,symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation)),complement(subset_relation)) -> subclass(u,symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation)).
% 300.10/300.69  50887[5:Res:10093.3,5.0] || member(u,ordinal_numbers) member(ordered_pair(v,w),cross_product(ordinal_numbers,ordinal_numbers)) member(ordered_pair(ordered_pair(w,u),v),x)* subclass(rotate(x),y)* -> member(ordered_pair(ordered_pair(v,w),u),y)*.
% 300.10/300.69  50964[5:Res:10061.3,5.0] || member(u,ordinal_numbers) member(ordered_pair(v,w),cross_product(ordinal_numbers,ordinal_numbers)) member(ordered_pair(ordered_pair(w,v),u),x)* subclass(flip(x),y)* -> member(ordered_pair(ordered_pair(v,w),u),y)*.
% 300.10/300.69  46653[5:Res:9618.2,8799.1] || member(ordered_pair(u,v),cross_product(ordinal_numbers,ordinal_numbers)) subclass(composition_function,cross_product(ordinal_numbers,ordinal_numbers)) equal(ordered_pair(v,compose(u,v)),successor(u)) -> member(ordered_pair(u,ordered_pair(v,compose(u,v))),successor_relation)*.
% 300.10/300.69  46628[5:Res:9618.2,12.0] || member(ordered_pair(u,v),cross_product(ordinal_numbers,ordinal_numbers)) subclass(composition_function,unordered_pair(w,x))* -> equal(ordered_pair(u,ordered_pair(v,compose(u,v))),x)* equal(ordered_pair(u,ordered_pair(v,compose(u,v))),w)*.
% 300.10/300.69  199058[8:Res:116123.2,13362.0] || member(u,cantor(v)) equal(restrict(v,u,ordinal_numbers),w) subclass(rest_of(v),x)* well_ordering(omega,x) -> equal(integer_of(ordered_pair(ordered_pair(u,w),least(omega,rest_of(v)))),identity_relation)**.
% 300.10/300.69  198966[7:Res:8551.2,13362.0] || member(u,cross_product(v,w)) member(u,x) subclass(restrict(x,v,w),y)* well_ordering(omega,y) -> equal(integer_of(ordered_pair(u,least(omega,restrict(x,v,w)))),identity_relation)**.
% 300.10/300.69  117780[8:Rew:116078.0,116352.6,116078.0,116352.4,116078.0,116352.4] operation(u) operation(v) operation(w) || compatible(x,v,u) subclass(cantor(v),cantor(w)) -> homomorphism(x,v,u) member(not_homomorphism1(x,v,u),cantor(cantor(w)))*.
% 300.10/300.69  117781[8:Rew:116078.0,116353.6,116078.0,116353.4,116078.0,116353.4] operation(u) operation(v) operation(w) || compatible(x,v,u) subclass(cantor(v),cantor(w)) -> homomorphism(x,v,u) member(not_homomorphism2(x,v,u),cantor(cantor(w)))*.
% 300.10/300.69  116484[8:Rew:116078.0,51456.3] operation(u) operation(v) || compatible(w,v,u) subclass(cantor(v),compose_class(x)) -> homomorphism(w,v,u) equal(compose(x,not_homomorphism1(w,v,u)),not_homomorphism2(w,v,u))**.
% 300.10/300.69  116483[8:Rew:116078.0,51435.3] operation(u) operation(v) || compatible(w,v,u) subclass(cantor(v),singleton(x))* -> homomorphism(w,v,u) equal(ordered_pair(not_homomorphism1(w,v,u),not_homomorphism2(w,v,u)),x)*.
% 300.10/300.69  116485[8:Rew:116078.0,10128.0] || member(singleton(singleton(singleton(u))),cantor(v)) homomorphism(w,v,x)* -> equal(apply(x,ordered_pair(apply(w,singleton(u)),apply(w,u))),apply(w,apply(v,singleton(singleton(singleton(u))))))*.
% 300.10/300.69  197687[7:Res:13247.2,18791.0] || member(intersection(u,symmetric_difference(complement(v),complement(w))),ordinal_numbers) -> equal(intersection(u,symmetric_difference(complement(v),complement(w))),identity_relation) member(apply(choice,intersection(u,symmetric_difference(complement(v),complement(w)))),union(v,w))*.
% 300.10/300.69  197399[7:Res:13246.2,18791.0] || member(intersection(symmetric_difference(complement(u),complement(v)),w),ordinal_numbers) -> equal(intersection(symmetric_difference(complement(u),complement(v)),w),identity_relation) member(apply(choice,intersection(symmetric_difference(complement(u),complement(v)),w)),union(u,v))*.
% 300.10/300.69  131572[5:Res:2504.1,8803.0] || subclass(ordered_pair(u,v),image(w,image(x,singleton(y)))) member(ordered_pair(y,unordered_pair(u,singleton(v))),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(y,unordered_pair(u,singleton(v))),compose(w,x))*.
% 300.10/300.69  51297[5:SpL:50855.1,8803.0] || member(singleton(u),subset_relation) member(v,image(w,image(x,u))) member(ordered_pair(first(singleton(u)),v),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(first(singleton(u)),v),compose(w,x))*.
% 300.10/300.69  196530[21:Rew:196372.1,196452.3] || member(u,ordinal_numbers) subclass(domain_relation,image(v,image(w,singleton(x)))) member(ordered_pair(x,ordered_pair(u,identity_relation)),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(x,ordered_pair(u,identity_relation)),compose(v,w))*.
% 300.10/300.69  54285[0:Res:295.0,9664.1] || member(ordered_pair(u,v),compose(w,x))* well_ordering(y,image(w,image(x,singleton(u)))) -> member(least(y,image(w,image(x,singleton(u)))),image(w,image(x,singleton(u))))*.
% 300.10/300.69  194677[7:Rew:481.0,194639.2,481.0,194639.0] || member(power_class(intersection(complement(u),complement(v))),ordinal_numbers) member(apply(choice,power_class(intersection(complement(u),complement(v)))),image(element_relation,union(u,v)))* -> equal(power_class(intersection(complement(u),complement(v))),identity_relation).
% 300.10/300.69  69371[8:Res:69184.1,9880.0] || member(ordered_pair(u,ordered_pair(v,least(image(element_relation,image(ordinal_numbers,singleton(u))),w))),element_relation)* member(v,w) subclass(w,x)* well_ordering(image(element_relation,image(ordinal_numbers,singleton(u))),x)* -> .
% 300.10/300.69  117777[8:Rew:116078.0,116275.2,116078.0,116275.2,116078.0,116275.1] function(restrict(u,v,ordinal_numbers)) || subclass(image(u,v),cantor(range_of(w))) equal(cantor(cantor(x)),cantor(restrict(u,v,ordinal_numbers))) -> compatible(restrict(u,v,ordinal_numbers),x,inverse(w))*.
% 300.10/300.69  199063[7:Res:9837.3,13362.0] || member(u,ordinal_numbers) member(v,ordinal_numbers) equal(sum_class(range_of(v)),u) subclass(union_of_range_map,w) well_ordering(omega,w)* -> equal(integer_of(ordered_pair(ordered_pair(v,u),least(omega,union_of_range_map))),identity_relation)**.
% 300.10/300.69  117779[8:Rew:116078.0,116319.2] one_to_one(restrict(element_relation,ordinal_numbers,u)) || subclass(range_of(restrict(element_relation,ordinal_numbers,u)),cantor(sum_class(u)))* equal(cross_product(cantor(sum_class(u)),cantor(sum_class(u))),sum_class(u)) -> operation(restrict(element_relation,ordinal_numbers,u)).
% 300.10/300.69  117778[8:Rew:116078.0,116307.2] operation(restrict(u,v,singleton(w))) || subclass(cantor(segment(u,v,w)),range_of(restrict(u,v,singleton(w))))* -> equal(range_of(restrict(u,v,singleton(w))),cantor(segment(u,v,w))).
% 300.10/300.69  208542[7:Rew:13260.1,208522.3] || member(first(regular(cross_product(u,v))),second(regular(cross_product(u,v))))* member(regular(cross_product(u,v)),cross_product(ordinal_numbers,ordinal_numbers)) -> equal(cross_product(u,v),identity_relation) member(regular(cross_product(u,v)),element_relation).
% 300.10/300.69  209548[16:Rew:195257.0,209521.4] || member(u,ordinal_numbers) subclass(power_class(complement(singleton(identity_relation))),v)* well_ordering(w,v)* -> member(u,image(element_relation,singleton(identity_relation)))* member(least(w,power_class(complement(singleton(identity_relation)))),power_class(complement(singleton(identity_relation))))*.
% 300.10/300.69  209549[8:Rew:162038.0,209520.4] || member(u,ordinal_numbers) subclass(power_class(complement(inverse(identity_relation))),v)* well_ordering(w,v)* -> member(u,image(element_relation,symmetrization_of(identity_relation)))* member(least(w,power_class(complement(inverse(identity_relation)))),power_class(complement(inverse(identity_relation))))*.
% 300.10/300.69  212377[7:SpL:13259.2,23.0] || member(cross_product(u,v),ordinal_numbers) member(apply(choice,cross_product(u,v)),element_relation) -> equal(cross_product(u,v),identity_relation) member(first(apply(choice,cross_product(u,v))),second(apply(choice,cross_product(u,v))))*.
% 300.10/300.69  214026[25:Rew:208820.0,214013.3] || member(ordered_pair(ordinal_numbers,ordered_pair(u,least(image(v,image(w,identity_relation)),x))),compose(v,w))* member(u,x) subclass(x,y)* well_ordering(image(v,image(w,identity_relation)),y)* -> .
% 300.10/300.69  214133[7:Res:13529.2,9876.0] || member(ordered_pair(u,regular(image(v,image(w,singleton(u))))),cross_product(ordinal_numbers,ordinal_numbers))* subclass(compose(v,w),x)* well_ordering(ordinal_numbers,x) -> equal(image(v,image(w,singleton(u))),identity_relation).
% 300.10/300.69  214142[25:Rew:208820.0,214127.1,208820.0,214127.0] || member(ordered_pair(ordinal_numbers,regular(image(u,image(v,identity_relation)))),cross_product(ordinal_numbers,ordinal_numbers)) -> equal(image(u,image(v,identity_relation)),identity_relation) member(ordered_pair(ordinal_numbers,regular(image(u,image(v,identity_relation)))),compose(u,v))*.
% 300.10/300.69  214942[8:Res:151501.1,117594.1] || member(u,cantor(restrict(v,w,intersection(x,singleton(u)))))* section(v,intersection(x,singleton(u)),w) -> equal(cantor(restrict(v,w,intersection(x,singleton(u)))),intersection(x,singleton(u))).
% 300.10/300.69  215038[8:Res:151861.1,117594.1] || member(u,cantor(restrict(v,w,intersection(singleton(u),x))))* section(v,intersection(singleton(u),x),w) -> equal(cantor(restrict(v,w,intersection(singleton(u),x))),intersection(singleton(u),x)).
% 300.10/300.69  215072[8:Res:215011.1,117594.1] || member(u,cantor(restrict(v,w,complement(complement(singleton(u))))))* section(v,complement(complement(singleton(u))),w) -> equal(cantor(restrict(v,w,complement(complement(singleton(u))))),complement(complement(singleton(u)))).
% 300.10/300.69  219811[8:Res:67614.1,8562.0] || member(not_subclass_element(u,intersection(v,symmetric_difference(complement(w),ordinal_numbers))),union(w,identity_relation))* member(not_subclass_element(u,intersection(v,symmetric_difference(complement(w),ordinal_numbers))),v)* -> subclass(u,intersection(v,symmetric_difference(complement(w),ordinal_numbers))).
% 300.10/300.69  223940[8:Rew:160927.0,223876.3] || member(u,v) subclass(v,w)* well_ordering(union(x,symmetric_difference(ordinal_numbers,y)),w)* -> member(ordered_pair(u,least(union(x,symmetric_difference(ordinal_numbers,y)),v)),intersection(complement(x),union(y,identity_relation)))*.
% 300.10/300.69  224255[8:Rew:160992.0,224195.3] || member(u,v) subclass(v,w)* well_ordering(union(symmetric_difference(ordinal_numbers,x),y),w)* -> member(ordered_pair(u,least(union(symmetric_difference(ordinal_numbers,x),y),v)),intersection(union(x,identity_relation),complement(y)))*.
% 300.10/300.69  227352[7:SpL:192979.1,8803.0] || member(u,image(v,range_of(identity_relation))) member(ordered_pair(w,u),cross_product(ordinal_numbers,ordinal_numbers)) -> equal(cross_product(singleton(w),ordinal_numbers),identity_relation) member(ordered_pair(w,u),compose(v,regular(cross_product(singleton(w),ordinal_numbers))))*.
% 300.10/300.69  231249[7:SpR:3603.0,17447.1] ||  -> equal(symmetric_difference(complement(restrict(u,v,w)),union(u,cross_product(v,w))),identity_relation) member(regular(symmetric_difference(complement(restrict(u,v,w)),union(u,cross_product(v,w)))),complement(symmetric_difference(u,cross_product(v,w))))*.
% 300.10/300.69  231248[7:SpR:3606.0,17447.1] ||  -> equal(symmetric_difference(complement(restrict(u,v,w)),union(cross_product(v,w),u)),identity_relation) member(regular(symmetric_difference(complement(restrict(u,v,w)),union(cross_product(v,w),u))),complement(symmetric_difference(cross_product(v,w),u)))*.
% 300.10/300.69  233275[7:Res:17388.1,9665.1] inductive(regular(intersection(recursion_equation_functions(u),v))) || well_ordering(w,cross_product(ordinal_numbers,ordinal_numbers)) -> equal(intersection(recursion_equation_functions(u),v),identity_relation) member(least(w,regular(intersection(recursion_equation_functions(u),v))),regular(intersection(recursion_equation_functions(u),v)))*.
% 300.10/300.69  233272[7:Res:17388.1,13070.0] || well_ordering(u,cross_product(ordinal_numbers,ordinal_numbers)) -> equal(intersection(recursion_equation_functions(v),w),identity_relation) equal(regular(intersection(recursion_equation_functions(v),w)),identity_relation) member(least(u,regular(intersection(recursion_equation_functions(v),w))),regular(intersection(recursion_equation_functions(v),w)))*.
% 300.10/300.69  233428[7:Res:13566.1,9665.1] inductive(regular(intersection(u,recursion_equation_functions(v)))) || well_ordering(w,cross_product(ordinal_numbers,ordinal_numbers)) -> equal(intersection(u,recursion_equation_functions(v)),identity_relation) member(least(w,regular(intersection(u,recursion_equation_functions(v)))),regular(intersection(u,recursion_equation_functions(v))))*.
% 300.10/300.69  233425[7:Res:13566.1,13070.0] || well_ordering(u,cross_product(ordinal_numbers,ordinal_numbers)) -> equal(intersection(v,recursion_equation_functions(w)),identity_relation) equal(regular(intersection(v,recursion_equation_functions(w))),identity_relation) member(least(u,regular(intersection(v,recursion_equation_functions(w)))),regular(intersection(v,recursion_equation_functions(w))))*.
% 300.10/300.69  233724[7:SpR:6355.1,13409.1] || subclass(omega,union_of_range_map) -> subclass(cross_product(u,v),w) equal(integer_of(not_subclass_element(cross_product(u,v),w)),identity_relation) equal(sum_class(range_of(first(not_subclass_element(cross_product(u,v),w)))),second(not_subclass_element(cross_product(u,v),w)))**.
% 300.10/300.69  235041[7:Rew:234956.0,235033.3] || member(ordered_pair(u,ordered_pair(v,least(range_of(identity_relation),w))),compose(complement(cross_product(image(x,singleton(u)),ordinal_numbers)),x))* member(v,w) subclass(w,y)* well_ordering(range_of(identity_relation),y)* -> .
% 300.10/300.69  235368[5:SpR:6355.1,28980.1] || subclass(rest_relation,flip(u)) -> subclass(cross_product(v,w),x) member(ordered_pair(not_subclass_element(cross_product(v,w),x),rest_of(ordered_pair(second(not_subclass_element(cross_product(v,w),x)),first(not_subclass_element(cross_product(v,w),x))))),u)*.
% 300.10/300.69  235357[5:SpR:6355.1,28980.1] || subclass(rest_relation,flip(u)) -> subclass(cross_product(v,w),x) member(ordered_pair(ordered_pair(second(not_subclass_element(cross_product(v,w),x)),first(not_subclass_element(cross_product(v,w),x))),rest_of(not_subclass_element(cross_product(v,w),x))),u)*.
% 300.10/300.69  235491[5:SpR:6355.1,28979.1] || subclass(rest_relation,rotate(u)) -> subclass(cross_product(v,w),x) member(ordered_pair(ordered_pair(second(not_subclass_element(cross_product(v,w),x)),rest_of(not_subclass_element(cross_product(v,w),x))),first(not_subclass_element(cross_product(v,w),x))),u)*.
% 300.10/300.69  47574[0:Rew:3616.0,47510.2,3616.0,47510.1] || member(not_subclass_element(u,symmetric_difference(complement(v),complement(w))),union(complement(v),complement(w)))* member(not_subclass_element(u,symmetric_difference(complement(v),complement(w))),union(v,w)) -> subclass(u,symmetric_difference(complement(v),complement(w))).
% 300.10/300.69  43720[0:Res:313.1,8554.1] || member(not_subclass_element(intersection(complement(intersection(u,v)),w),x),union(u,v)) -> subclass(intersection(complement(intersection(u,v)),w),x) member(not_subclass_element(intersection(complement(intersection(u,v)),w),x),symmetric_difference(u,v))*.
% 300.10/300.69  43736[0:Res:303.1,8554.1] || member(not_subclass_element(intersection(u,complement(intersection(v,w))),x),union(v,w)) -> subclass(intersection(u,complement(intersection(v,w))),x) member(not_subclass_element(intersection(u,complement(intersection(v,w))),x),symmetric_difference(v,w))*.
% 300.10/300.69  49644[0:SpL:6355.1,40.0] || member(ordered_pair(not_subclass_element(cross_product(u,v),w),x),flip(y)) -> subclass(cross_product(u,v),w) member(ordered_pair(ordered_pair(second(not_subclass_element(cross_product(u,v),w)),first(not_subclass_element(cross_product(u,v),w))),x),y)*.
% 300.10/300.69  49645[0:SpL:6355.1,37.0] || member(ordered_pair(not_subclass_element(cross_product(u,v),w),x),rotate(y)) -> subclass(cross_product(u,v),w) member(ordered_pair(ordered_pair(second(not_subclass_element(cross_product(u,v),w)),x),first(not_subclass_element(cross_product(u,v),w))),y)*.
% 300.10/300.69  130626[5:Res:41371.0,8554.1] || member(not_subclass_element(complement(complement(complement(intersection(u,v)))),w),union(u,v)) -> subclass(complement(complement(complement(intersection(u,v)))),w) member(not_subclass_element(complement(complement(complement(intersection(u,v)))),w),symmetric_difference(u,v))*.
% 300.10/300.69  161807[8:Rew:116078.0,51353.6,116078.0,51353.3,116078.0,51353.2,116078.0,51353.2,116078.0,51353.2] operation(u) operation(v) || equal(cantor(cantor(v)),cantor(u)) subclass(cantor(v),w)* well_ordering(x,w)* -> homomorphism(u,v,u)* member(least(x,cantor(v)),cantor(v))*.
% 300.10/300.69  134736[8:Res:116403.2,9878.0] || member(least(cross_product(u,cantor(v)),w),ordinal_numbers)* subclass(rest_relation,rest_of(v)) member(x,u)* member(x,w)* subclass(w,y)* well_ordering(cross_product(u,cantor(v)),y)* -> .
% 300.10/300.69  199036[7:Res:13511.3,13362.0] || member(u,ordinal_numbers) well_ordering(v,u) subclass(sum_class(u),w)* well_ordering(omega,w) -> equal(sum_class(u),identity_relation) equal(integer_of(ordered_pair(least(v,sum_class(u)),least(omega,sum_class(u)))),identity_relation)**.
% 300.10/300.69  198955[7:Res:8832.1,13362.0] || member(u,ordinal_numbers) subclass(intersection(complement(v),complement(w)),x)* well_ordering(omega,x) -> member(u,union(v,w)) equal(integer_of(ordered_pair(u,least(omega,intersection(complement(v),complement(w))))),identity_relation)**.
% 300.10/300.69  154340[8:Res:116127.5,151988.0] operation(u) operation(v) || compatible(w,v,u) subclass(cantor(v),complement(complement(x))) -> homomorphism(w,v,u) member(ordered_pair(not_homomorphism1(w,v,u),not_homomorphism2(w,v,u)),x)*.
% 300.10/300.69  116489[8:Rew:116078.0,51443.3] operation(u) operation(v) || compatible(w,v,u) subclass(cantor(v),inverse(subset_relation)) member(ordered_pair(not_homomorphism1(w,v,u),not_homomorphism2(w,v,u)),subset_relation)* -> homomorphism(w,v,u).
% 300.10/300.69  116488[8:Rew:116078.0,51431.3] operation(u) operation(v) || compatible(w,v,u) subclass(cantor(v),intersection(x,y))* -> homomorphism(w,v,u) member(ordered_pair(not_homomorphism1(w,v,u),not_homomorphism2(w,v,u)),x)*.
% 300.10/300.69  116487[8:Rew:116078.0,51430.3] operation(u) operation(v) || compatible(w,v,u) subclass(cantor(v),intersection(x,y))* -> homomorphism(w,v,u) member(ordered_pair(not_homomorphism1(w,v,u),not_homomorphism2(w,v,u)),y)*.
% 300.10/300.69  116486[8:Rew:116078.0,51418.3] operation(u) operation(v) || compatible(w,v,u) subclass(cantor(v),complement(x)) member(ordered_pair(not_homomorphism1(w,v,u),not_homomorphism2(w,v,u)),x)* -> homomorphism(w,v,u).
% 300.10/300.69  116479[8:Rew:116078.0,51452.3] operation(u) operation(v) || compatible(w,v,u) subclass(cantor(v),rest_of(x)) -> homomorphism(w,v,u) equal(restrict(x,not_homomorphism1(w,v,u),ordinal_numbers),not_homomorphism2(w,v,u))**.
% 300.10/300.69  116473[8:Rew:116078.0,51426.3] operation(u) operation(v) || compatible(w,v,u) subclass(cantor(v),x)* subclass(x,y)* well_ordering(z,y)* -> homomorphism(w,v,u)* member(least(z,x),x)*.
% 300.10/300.69  199157[7:Res:8865.1,13362.0] || member(restrict(u,v,singleton(w)),ordinal_numbers) subclass(domain_relation,x) well_ordering(omega,x)* -> equal(integer_of(ordered_pair(ordered_pair(restrict(u,v,singleton(w)),segment(u,v,w)),least(omega,domain_relation))),identity_relation)**.
% 300.10/300.69  116467[8:Rew:116078.0,28964.1] || member(u,ordinal_numbers) subclass(rest_relation,cantor(v)) homomorphism(w,v,x)* -> equal(apply(x,ordered_pair(apply(w,u),apply(w,rest_of(u)))),apply(w,apply(v,ordered_pair(u,rest_of(u)))))*.
% 300.10/300.69  161808[8:Rew:116078.0,13433.0] || subclass(omega,cantor(u)) homomorphism(v,u,w)* -> equal(integer_of(ordered_pair(x,y)),identity_relation) equal(apply(w,ordered_pair(apply(v,x),apply(v,y))),apply(v,apply(u,ordered_pair(x,y))))*.
% 300.10/300.69  197695[7:Res:13247.2,12.0] || member(intersection(u,unordered_pair(v,w)),ordinal_numbers) -> equal(intersection(u,unordered_pair(v,w)),identity_relation) equal(apply(choice,intersection(u,unordered_pair(v,w))),w)** equal(apply(choice,intersection(u,unordered_pair(v,w))),v)**.
% 300.10/300.69  197683[7:Res:13247.2,490.0] || member(intersection(u,intersection(complement(v),complement(w))),ordinal_numbers) member(apply(choice,intersection(u,intersection(complement(v),complement(w)))),union(v,w))* -> equal(intersection(u,intersection(complement(v),complement(w))),identity_relation).
% 300.10/300.69  197406[7:Res:13246.2,12.0] || member(intersection(unordered_pair(u,v),w),ordinal_numbers) -> equal(intersection(unordered_pair(u,v),w),identity_relation) equal(apply(choice,intersection(unordered_pair(u,v),w)),v)** equal(apply(choice,intersection(unordered_pair(u,v),w)),u)**.
% 300.10/300.69  197395[7:Res:13246.2,490.0] || member(intersection(intersection(complement(u),complement(v)),w),ordinal_numbers) member(apply(choice,intersection(intersection(complement(u),complement(v)),w)),union(u,v))* -> equal(intersection(intersection(complement(u),complement(v)),w),identity_relation).
% 300.10/300.69  130962[5:Res:9997.2,9876.0] || member(ordered_pair(u,not_subclass_element(image(v,image(w,singleton(u))),x)),cross_product(ordinal_numbers,ordinal_numbers))* subclass(compose(v,w),y)* well_ordering(ordinal_numbers,y) -> subclass(image(v,image(w,singleton(u))),x).
% 300.10/300.69  46869[5:Rew:481.0,46857.3] || member(u,v) subclass(v,w)* well_ordering(power_class(intersection(complement(x),complement(y))),w)* -> member(ordered_pair(u,least(power_class(intersection(complement(x),complement(y))),v)),image(element_relation,union(x,y)))*.
% 300.10/300.69  132516[5:Res:130711.0,9633.1] || member(u,ordinal_numbers) well_ordering(v,image(element_relation,power_class(w))) -> member(u,power_class(image(element_relation,complement(w))))* member(least(v,complement(power_class(image(element_relation,complement(w))))),complement(power_class(image(element_relation,complement(w)))))*.
% 300.10/300.69  108165[5:Res:79577.0,9878.0] || member(u,v)* member(u,w)* subclass(w,x)* well_ordering(cross_product(v,image(element_relation,complement(y))),x)* -> subclass(singleton(least(cross_product(v,image(element_relation,complement(y))),w)),power_class(y))*.
% 300.10/300.69  117783[8:Rew:116078.0,116332.2] single_valued_class(inverse(u)) || subclass(range_of(inverse(u)),cantor(range_of(u))) equal(cross_product(cantor(range_of(u)),cantor(range_of(u))),range_of(u))** equal(cross_product(ordinal_numbers,ordinal_numbers),inverse(u)) -> operation(inverse(u)).
% 300.10/300.69  51404[5:Rew:18840.1,51391.3] || member(u,subset_relation) member(u,range_of(v)) homomorphism(w,inverse(v),x)* -> equal(apply(x,ordered_pair(apply(w,first(u)),apply(w,second(u)))),apply(w,apply(inverse(v),u)))*.
% 300.10/300.69  62884[5:Res:9618.2,8798.1] || member(ordered_pair(u,v),cross_product(ordinal_numbers,ordinal_numbers)) subclass(composition_function,cross_product(ordinal_numbers,ordinal_numbers)) equal(ordered_pair(v,compose(u,v)),sum_class(range_of(u))) -> member(ordered_pair(u,ordered_pair(v,compose(u,v))),union_of_range_map)*.
% 300.10/300.69  208366[24:Rew:207572.1,208332.2] operation(least(intersection(u,v),w)) || member(singleton(singleton(identity_relation)),v) member(singleton(singleton(identity_relation)),u) member(identity_relation,w)* subclass(w,x)* well_ordering(intersection(u,v),x)* -> .
% 300.10/300.69  208543[7:Rew:13260.1,208521.3] || equal(successor(first(regular(cross_product(u,v)))),second(regular(cross_product(u,v)))) member(regular(cross_product(u,v)),cross_product(ordinal_numbers,ordinal_numbers))* -> equal(cross_product(u,v),identity_relation) member(regular(cross_product(u,v)),successor_relation).
% 300.10/300.69  209858[7:MRR:209855.3,13039.0] || connected(u,v) well_ordering(w,v) subclass(singleton(least(w,not_well_ordering(u,v))),not_well_ordering(u,v)) -> well_ordering(u,v) section(w,singleton(least(w,not_well_ordering(u,v))),not_well_ordering(u,v))*.
% 300.10/300.69  212298[8:Res:161774.3,5.0] || section(u,v,w) well_ordering(x,v) subclass(cantor(restrict(u,w,v)),y) -> equal(cantor(restrict(u,w,v)),identity_relation) member(least(x,cantor(restrict(u,w,v))),y)*.
% 300.10/300.69  212414[8:SpL:13259.2,117449.1] operation(u) || member(cross_product(v,w),ordinal_numbers) member(apply(choice,cross_product(v,w)),cantor(u)) -> equal(cross_product(v,w),identity_relation) member(first(apply(choice,cross_product(v,w))),cantor(cantor(u)))*.
% 300.10/300.69  212413[8:SpL:13259.2,117450.1] operation(u) || member(cross_product(v,w),ordinal_numbers) member(apply(choice,cross_product(v,w)),cantor(u)) -> equal(cross_product(v,w),identity_relation) member(second(apply(choice,cross_product(v,w))),cantor(cantor(u)))*.
% 300.10/300.69  212394[7:SpL:13259.2,49.0] || member(cross_product(u,v),ordinal_numbers) member(apply(choice,cross_product(u,v)),successor_relation) -> equal(cross_product(u,v),identity_relation) equal(successor(first(apply(choice,cross_product(u,v)))),second(apply(choice,cross_product(u,v))))**.
% 300.10/300.69  212392[8:SpL:13259.2,116160.0] || member(cross_product(u,v),ordinal_numbers) member(apply(choice,cross_product(u,v)),domain_relation) -> equal(cross_product(u,v),identity_relation) equal(cantor(first(apply(choice,cross_product(u,v)))),second(apply(choice,cross_product(u,v))))**.
% 300.10/300.69  212378[7:SpL:13259.2,149.0] || member(cross_product(u,v),ordinal_numbers) member(apply(choice,cross_product(u,v)),rest_relation) -> equal(cross_product(u,v),identity_relation) equal(rest_of(first(apply(choice,cross_product(u,v)))),second(apply(choice,cross_product(u,v))))**.
% 300.10/300.69  213419[21:Res:196416.2,10118.0] || member(u,ordinal_numbers) subclass(domain_relation,range_of(v)) homomorphism(w,inverse(v),x)* -> equal(apply(x,ordered_pair(apply(w,u),apply(w,identity_relation))),apply(w,apply(inverse(v),ordered_pair(u,identity_relation))))*.
% 300.10/300.69  213541[8:Res:116127.5,163154.0] operation(u) operation(v) || compatible(w,v,u) subclass(cantor(v),symmetrization_of(identity_relation)) -> homomorphism(w,v,u) member(ordered_pair(not_homomorphism1(w,v,u),not_homomorphism2(w,v,u)),inverse(identity_relation))*.
% 300.10/300.69  214149[8:MRR:214148.0,18.1] || member(ordered_pair(u,regular(image(v,range_of(identity_relation)))),cross_product(ordinal_numbers,ordinal_numbers)) -> member(u,cantor(w)) equal(image(v,range_of(identity_relation)),identity_relation) member(ordered_pair(u,regular(image(v,range_of(identity_relation)))),compose(v,w))*.
% 300.10/300.69  214251[24:SpR:13259.2,207615.1] operation(second(apply(choice,cross_product(u,v)))) || member(cross_product(u,v),ordinal_numbers) -> equal(cross_product(u,v),identity_relation) member(unordered_pair(first(apply(choice,cross_product(u,v))),identity_relation),apply(choice,cross_product(u,v)))*.
% 300.10/300.69  214467[25:SpR:208985.1,13259.2] operation(second(apply(choice,cross_product(u,v)))) || member(cross_product(u,v),ordinal_numbers) -> equal(cross_product(u,v),identity_relation) equal(ordered_pair(first(apply(choice,cross_product(u,v))),ordinal_numbers),apply(choice,cross_product(u,v)))**.
% 300.10/300.69  214623[25:Rew:208985.1,214574.2] operation(least(intersection(u,v),w)) || member(ordered_pair(x,ordinal_numbers),v)* member(ordered_pair(x,ordinal_numbers),u)* member(x,w)* subclass(w,y)* well_ordering(intersection(u,v),y)* -> .
% 300.10/300.69  214752[8:Res:211441.1,9664.1] || equal(power_class(u),ordinal_numbers) member(ordered_pair(v,w),compose(x,y))* well_ordering(z,power_class(u))* -> member(least(z,image(x,image(y,singleton(v)))),image(x,image(y,singleton(v))))*.
% 300.10/300.69  214751[8:Res:210606.1,9664.1] || equal(complement(u),ordinal_numbers) member(ordered_pair(v,w),compose(x,y))* well_ordering(z,complement(u))* -> member(least(z,image(x,image(y,singleton(v)))),image(x,image(y,singleton(v))))*.
% 300.10/300.69  214746[8:Res:211438.1,9664.1] || equal(symmetrization_of(identity_relation),ordinal_numbers) member(ordered_pair(u,v),compose(w,x))* well_ordering(y,symmetrization_of(identity_relation)) -> member(least(y,image(w,image(x,singleton(u)))),image(w,image(x,singleton(u))))*.
% 300.10/300.69  214755[25:Rew:208820.0,214737.3] || member(ordered_pair(ordinal_numbers,u),compose(v,w))* subclass(image(v,image(w,identity_relation)),x)* well_ordering(y,x)* -> member(least(y,image(v,image(w,identity_relation))),image(v,image(w,identity_relation)))*.
% 300.10/300.69  214941[0:Res:151501.1,3729.1] || member(u,not_well_ordering(v,intersection(w,singleton(u))))* connected(v,intersection(w,singleton(u))) -> well_ordering(v,intersection(w,singleton(u))) equal(not_well_ordering(v,intersection(w,singleton(u))),intersection(w,singleton(u))).
% 300.10/300.69  215037[0:Res:151861.1,3729.1] || member(u,not_well_ordering(v,intersection(singleton(u),w)))* connected(v,intersection(singleton(u),w)) -> well_ordering(v,intersection(singleton(u),w)) equal(not_well_ordering(v,intersection(singleton(u),w)),intersection(singleton(u),w)).
% 300.10/300.69  215071[5:Res:215011.1,3729.1] || member(u,not_well_ordering(v,complement(complement(singleton(u)))))* connected(v,complement(complement(singleton(u)))) -> well_ordering(v,complement(complement(singleton(u)))) equal(not_well_ordering(v,complement(complement(singleton(u)))),complement(complement(singleton(u)))).
% 300.10/300.69  220437[21:Res:196656.1,8803.0] || subclass(domain_relation,flip(image(u,image(v,singleton(w))))) member(ordered_pair(w,ordered_pair(ordered_pair(x,y),identity_relation)),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(w,ordered_pair(ordered_pair(x,y),identity_relation)),compose(u,v))*.
% 300.10/300.69  220586[21:Res:196657.1,9872.0] || subclass(domain_relation,rotate(u)) member(ordered_pair(ordered_pair(v,identity_relation),least(intersection(w,u),x)),w)* member(ordered_pair(v,identity_relation),x) subclass(x,y)* well_ordering(intersection(w,u),y)* -> .
% 300.10/300.69  220539[21:Res:196657.1,8803.0] || subclass(domain_relation,rotate(image(u,image(v,singleton(w))))) member(ordered_pair(w,ordered_pair(ordered_pair(x,identity_relation),y)),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(w,ordered_pair(ordered_pair(x,identity_relation),y)),compose(u,v))*.
% 300.10/300.69  220742[8:Res:116127.5,219203.0] operation(u) operation(v) || compatible(w,v,u) subclass(cantor(v),rest_of(ordered_pair(not_homomorphism1(w,v,u),not_homomorphism2(w,v,u))))* subclass(element_relation,identity_relation) -> homomorphism(w,v,u).
% 300.10/300.69  223764[8:SpR:160927.0,3594.0] ||  -> equal(intersection(complement(symmetric_difference(complement(u),union(v,identity_relation))),union(union(u,symmetric_difference(ordinal_numbers,v)),union(complement(u),union(v,identity_relation)))),symmetric_difference(union(u,symmetric_difference(ordinal_numbers,v)),union(complement(u),union(v,identity_relation))))**.
% 300.10/300.69  224081[8:SpR:160992.0,3594.0] ||  -> equal(intersection(complement(symmetric_difference(union(u,identity_relation),complement(v))),union(union(symmetric_difference(ordinal_numbers,u),v),union(union(u,identity_relation),complement(v)))),symmetric_difference(union(symmetric_difference(ordinal_numbers,u),v),union(union(u,identity_relation),complement(v))))**.
% 300.10/300.69  224721[21:Res:116127.5,194371.0] operation(u) operation(v) || compatible(w,v,u) subclass(cantor(v),cross_product(ordinal_numbers,ordinal_numbers)) member(not_homomorphism2(w,v,u),cantor(not_homomorphism1(w,v,u)))* -> homomorphism(w,v,u).
% 300.10/300.69  228886[8:Res:8835.1,61018.0] || member(apply(choice,regular(image(element_relation,complement(u)))),ordinal_numbers) -> member(apply(choice,regular(image(element_relation,complement(u)))),power_class(u))* equal(regular(image(element_relation,complement(u))),identity_relation) equal(image(element_relation,complement(u)),identity_relation).
% 300.10/300.69  229149[7:Res:8551.2,17387.0] || member(regular(intersection(complement(restrict(u,v,w)),x)),cross_product(v,w))* member(regular(intersection(complement(restrict(u,v,w)),x)),u)* -> equal(intersection(complement(restrict(u,v,w)),x),identity_relation).
% 300.10/300.69  229578[7:Res:8551.2,13571.0] || member(regular(intersection(u,complement(restrict(v,w,x)))),cross_product(w,x))* member(regular(intersection(u,complement(restrict(v,w,x)))),v)* -> equal(intersection(u,complement(restrict(v,w,x))),identity_relation).
% 300.10/300.69  234361[7:Res:8551.2,18696.1] || member(least(u,complement(restrict(v,w,x))),cross_product(w,x))* member(least(u,complement(restrict(v,w,x))),v)* well_ordering(u,ordinal_numbers) -> equal(complement(restrict(v,w,x)),identity_relation).
% 300.10/300.69  234570[8:Res:116127.5,233381.0] operation(u) operation(v) || compatible(w,v,u) subclass(cantor(v),singleton(omega)) -> homomorphism(w,v,u) equal(integer_of(ordered_pair(not_homomorphism1(w,v,u),not_homomorphism2(w,v,u))),identity_relation)**.
% 300.10/300.69  235043[7:Rew:234956.0,235015.1,234956.0,235015.0] || member(ordered_pair(u,regular(image(v,range_of(identity_relation)))),cross_product(ordinal_numbers,ordinal_numbers)) -> equal(image(v,range_of(identity_relation)),identity_relation) member(ordered_pair(u,regular(image(v,range_of(identity_relation)))),compose(v,complement(cross_product(singleton(u),ordinal_numbers))))*.
% 300.10/300.69  235191[8:Res:116127.5,234983.0] operation(u) operation(v) || compatible(w,v,u) subclass(cantor(v),cantor(complement(cross_product(singleton(ordered_pair(not_homomorphism1(w,v,u),not_homomorphism2(w,v,u))),ordinal_numbers))))* -> homomorphism(w,v,u).
% 300.10/300.69  235188[8:Res:117604.3,234983.0] operation(complement(cross_product(singleton(ordered_pair(u,v)),ordinal_numbers))) || member(v,cantor(cantor(complement(cross_product(singleton(ordered_pair(u,v)),ordinal_numbers)))))* member(u,cantor(cantor(complement(cross_product(singleton(ordered_pair(u,v)),ordinal_numbers)))))* -> .
% 300.10/300.69  235375[5:Res:28980.1,8554.1] || subclass(rest_relation,flip(complement(intersection(u,v)))) member(ordered_pair(ordered_pair(w,x),rest_of(ordered_pair(x,w))),union(u,v)) -> member(ordered_pair(ordered_pair(w,x),rest_of(ordered_pair(x,w))),symmetric_difference(u,v))*.
% 300.10/300.69  235503[5:Res:28979.1,8554.1] || subclass(rest_relation,rotate(complement(intersection(u,v)))) member(ordered_pair(ordered_pair(w,rest_of(ordered_pair(x,w))),x),union(u,v)) -> member(ordered_pair(ordered_pair(w,rest_of(ordered_pair(x,w))),x),symmetric_difference(u,v))*.
% 300.10/300.69  235950[7:Res:69478.2,8562.0] || subclass(omega,symmetric_difference(u,v)) member(not_subclass_element(w,intersection(x,union(u,v))),x)* -> equal(integer_of(not_subclass_element(w,intersection(x,union(u,v)))),identity_relation) subclass(w,intersection(x,union(u,v))).
% 300.10/300.69  236003[5:SpR:19860.0,39308.2] one_to_one(restrict(cross_product(u,ordinal_numbers),v,w)) || subclass(range_of(inverse(restrict(cross_product(u,ordinal_numbers),v,w))),x) -> maps(inverse(restrict(cross_product(u,ordinal_numbers),v,w)),image(cross_product(v,w),u),x)*.
% 300.10/300.69  237132[7:Res:13574.1,3689.0] ||  -> equal(intersection(u,intersection(v,ordered_pair(w,x))),identity_relation) equal(regular(intersection(u,intersection(v,ordered_pair(w,x)))),unordered_pair(w,singleton(x)))** equal(regular(intersection(u,intersection(v,ordered_pair(w,x)))),singleton(w)).
% 300.10/300.69  237234[7:Rew:32.0,237127.1,32.0,237127.0] ||  -> equal(intersection(u,restrict(v,w,x)),identity_relation) equal(ordered_pair(first(regular(intersection(u,restrict(v,w,x)))),second(regular(intersection(u,restrict(v,w,x))))),regular(intersection(u,restrict(v,w,x))))**.
% 300.10/300.69  237783[7:Res:13573.1,3689.0] ||  -> equal(intersection(u,intersection(ordered_pair(v,w),x)),identity_relation) equal(regular(intersection(u,intersection(ordered_pair(v,w),x))),unordered_pair(v,singleton(w)))** equal(regular(intersection(u,intersection(ordered_pair(v,w),x))),singleton(v)).
% 300.10/300.69  239295[7:Res:17397.1,3689.0] ||  -> equal(intersection(intersection(ordered_pair(u,v),w),x),identity_relation) equal(regular(intersection(intersection(ordered_pair(u,v),w),x)),unordered_pair(u,singleton(v)))** equal(regular(intersection(intersection(ordered_pair(u,v),w),x)),singleton(u)).
% 300.10/300.69  239412[7:Rew:33.0,239290.1,33.0,239290.0] ||  -> equal(intersection(restrict(u,v,w),x),identity_relation) equal(ordered_pair(first(regular(intersection(restrict(u,v,w),x))),second(regular(intersection(restrict(u,v,w),x)))),regular(intersection(restrict(u,v,w),x)))**.
% 300.10/300.69  240130[7:Res:17396.1,3689.0] ||  -> equal(intersection(intersection(u,ordered_pair(v,w)),x),identity_relation) equal(regular(intersection(intersection(u,ordered_pair(v,w)),x)),unordered_pair(v,singleton(w)))** equal(regular(intersection(intersection(u,ordered_pair(v,w)),x)),singleton(v)).
% 300.10/300.69  49969[0:Res:3618.1,9878.0] || member(least(cross_product(u,complement(intersection(v,w))),x),symmetric_difference(v,w))* member(y,u)* member(y,x)* subclass(x,z)* well_ordering(cross_product(u,complement(intersection(v,w))),z)* -> .
% 300.10/300.69  47575[5:MRR:47519.0,41183.1] || member(not_subclass_element(u,intersection(v,intersection(complement(w),complement(x)))),v)* -> member(not_subclass_element(u,intersection(v,intersection(complement(w),complement(x)))),union(w,x))* subclass(u,intersection(v,intersection(complement(w),complement(x)))).
% 300.10/300.69  117794[8:Rew:116078.0,116809.5,116078.0,116809.3] operation(u) || member(v,cantor(u))* member(v,w)* subclass(intersection(cantor(u),w),x)* well_ordering(y,x)* -> member(least(y,intersection(w,cantor(u))),intersection(w,cantor(u)))*.
% 300.10/300.69  117793[8:Rew:116078.0,116808.5,116078.0,116808.3] operation(u) || member(v,w)* member(v,cantor(u))* subclass(intersection(w,cantor(u)),x)* well_ordering(y,x)* -> member(least(y,intersection(cantor(u),w)),intersection(cantor(u),w))*.
% 300.10/300.69  66505[7:Res:13061.0,9872.0] || member(ordered_pair(u,least(intersection(v,omega),w)),v)* member(u,w) subclass(w,x)* well_ordering(intersection(v,omega),x)* -> equal(integer_of(ordered_pair(u,least(intersection(v,omega),w))),identity_relation).
% 300.10/300.69  132200[2:Res:39609.2,8554.1] inductive(complement(intersection(u,v))) || well_ordering(w,complement(intersection(u,v))) member(least(w,complement(intersection(u,v))),union(u,v)) -> member(least(w,complement(intersection(u,v))),symmetric_difference(u,v))*.
% 300.10/300.69  39527[5:Res:8832.1,129.0] || member(u,ordinal_numbers) subclass(intersection(complement(v),complement(w)),x)* well_ordering(y,x)* -> member(u,union(v,w))* member(least(y,intersection(complement(v),complement(w))),intersection(complement(v),complement(w)))*.
% 300.10/300.69  46663[5:Res:9618.2,8802.1] || member(ordered_pair(u,v),cross_product(ordinal_numbers,ordinal_numbers)) subclass(composition_function,cross_product(ordinal_numbers,ordinal_numbers)) equal(compose(w,u),ordered_pair(v,compose(u,v))) -> member(ordered_pair(u,ordered_pair(v,compose(u,v))),compose_class(w))*.
% 300.10/300.69  196221[7:Res:13501.2,9878.0] || well_ordering(cross_product(u,compose_class(v)),cross_product(ordinal_numbers,ordinal_numbers))* member(w,u)* member(w,compose_class(v))* subclass(compose_class(v),x) well_ordering(cross_product(u,compose_class(v)),x)* -> equal(compose_class(v),identity_relation).
% 300.10/300.69  196282[7:Res:13500.2,9878.0] || well_ordering(cross_product(u,rest_of(v)),cross_product(ordinal_numbers,ordinal_numbers))* member(w,u)* member(w,rest_of(v))* subclass(rest_of(v),x) well_ordering(cross_product(u,rest_of(v)),x)* -> equal(rest_of(v),identity_relation).
% 300.10/300.69  199061[7:Res:9865.3,13362.0] || member(u,ordinal_numbers) member(v,ordinal_numbers) equal(compose(w,v),u) subclass(compose_class(w),x)* well_ordering(omega,x) -> equal(integer_of(ordered_pair(ordered_pair(v,u),least(omega,compose_class(w)))),identity_relation)**.
% 300.10/300.69  116528[8:Rew:116078.0,51421.3] operation(u) operation(v) || compatible(w,v,u) subclass(cantor(v),recursion_equation_functions(x))* -> homomorphism(w,v,u) subclass(ordered_pair(not_homomorphism1(w,v,u),not_homomorphism2(w,v,u)),cross_product(ordinal_numbers,ordinal_numbers))*.
% 300.10/300.69  116493[8:Rew:116078.0,56421.3] operation(u) operation(v) || compatible(w,v,u) subclass(cantor(v),rest_of(ordered_pair(not_homomorphism1(w,v,u),not_homomorphism2(w,v,u))))* subclass(ordinal_numbers,complement(element_relation)) -> homomorphism(w,v,u).
% 300.10/300.69  116492[8:Rew:116078.0,51434.3] operation(u) operation(v) || compatible(w,v,u) subclass(cantor(v),restrict(x,y,z))* -> homomorphism(w,v,u) member(ordered_pair(not_homomorphism1(w,v,u),not_homomorphism2(w,v,u)),x)*.
% 300.10/300.69  156827[5:Res:8551.2,40594.1] || member(singleton(restrict(u,v,w)),cross_product(v,w))* member(singleton(restrict(u,v,w)),u)* member(restrict(u,v,w),ordinal_numbers) -> member(singleton(singleton(singleton(restrict(u,v,w)))),element_relation)*.
% 300.10/300.69  117789[8:Rew:116078.0,116419.1,116078.0,116419.1,116078.0,116419.0] || member(u,cantor(cantor(v))) member(w,cantor(cantor(v))) homomorphism(x,v,y)* -> equal(apply(y,ordered_pair(apply(x,w),apply(x,u))),apply(x,apply(v,ordered_pair(w,u))))*.
% 300.10/300.69  61914[7:Res:13069.2,8554.1] || member(complement(intersection(u,v)),ordinal_numbers) member(apply(choice,complement(intersection(u,v))),union(u,v)) -> equal(complement(intersection(u,v)),identity_relation) member(apply(choice,complement(intersection(u,v))),symmetric_difference(u,v))*.
% 300.10/300.69  28948[5:Res:8827.2,8803.0] || member(u,ordinal_numbers) subclass(rest_relation,image(v,image(w,singleton(x)))) member(ordered_pair(x,ordered_pair(u,rest_of(u))),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(x,ordered_pair(u,rest_of(u))),compose(v,w))*.
% 300.10/300.69  156843[5:Res:62.1,40594.1] || member(ordered_pair(u,singleton(image(v,image(w,singleton(u))))),compose(v,w))* member(image(v,image(w,singleton(u))),ordinal_numbers) -> member(singleton(singleton(singleton(image(v,image(w,singleton(u)))))),element_relation).
% 300.10/300.69  199077[7:Res:62.1,13362.0] || member(ordered_pair(u,v),compose(w,x)) subclass(image(w,image(x,singleton(u))),y)* well_ordering(omega,y) -> equal(integer_of(ordered_pair(v,least(omega,image(w,image(x,singleton(u)))))),identity_relation)**.
% 300.10/300.69  65621[7:SpL:13096.1,8632.1] || well_ordering(element_relation,image(choice,singleton(singleton(u))))* subclass(u,image(choice,singleton(singleton(u))))* -> equal(singleton(u),identity_relation) equal(image(choice,singleton(singleton(u))),ordinal_numbers) member(image(choice,singleton(singleton(u))),ordinal_numbers).
% 300.10/300.69  61738[8:SpR:14769.0,10130.4] operation(u) || compatible(v,w,u) homomorphism(x,w,identity_relation) -> homomorphism(v,w,u) equal(apply(x,apply(w,ordered_pair(not_homomorphism1(v,w,u),not_homomorphism2(v,w,u)))),sum_class(range_of(identity_relation)))**.
% 300.10/300.69  51403[0:Rew:963.0,51389.2] || member(singleton(singleton(singleton(u))),range_of(v)) homomorphism(w,inverse(v),x)* -> equal(apply(x,ordered_pair(apply(w,singleton(u)),apply(w,u))),apply(w,apply(inverse(v),singleton(singleton(singleton(u))))))*.
% 300.10/300.69  199037[8:Res:161565.3,13362.0] operation(u) || well_ordering(v,cantor(cantor(u))) subclass(range_of(u),w)* well_ordering(omega,w) -> equal(range_of(u),identity_relation) equal(integer_of(ordered_pair(least(v,range_of(u)),least(omega,range_of(u)))),identity_relation)**.
% 300.10/300.69  208534[7:SpL:13260.1,3689.0] || member(u,regular(cross_product(v,w)))* -> equal(cross_product(v,w),identity_relation) equal(u,unordered_pair(first(regular(cross_product(v,w))),singleton(second(regular(cross_product(v,w))))))* equal(u,singleton(first(regular(cross_product(v,w))))).
% 300.10/300.69  208544[7:Rew:13260.1,208520.3] || equal(sum_class(range_of(first(regular(cross_product(u,v))))),second(regular(cross_product(u,v)))) member(regular(cross_product(u,v)),cross_product(ordinal_numbers,ordinal_numbers))* -> equal(cross_product(u,v),identity_relation) member(regular(cross_product(u,v)),union_of_range_map).
% 300.10/300.69  208630[7:Res:9618.2,13362.0] || member(ordered_pair(u,v),cross_product(ordinal_numbers,ordinal_numbers)) subclass(composition_function,w) subclass(w,x)* well_ordering(omega,x)* -> equal(integer_of(ordered_pair(ordered_pair(u,ordered_pair(v,compose(u,v))),least(omega,w))),identity_relation)**.
% 300.10/300.69  210244[8:SpR:117511.1,161701.2] operation(u) || section(v,cantor(cantor(u)),cantor(cantor(u))) well_ordering(w,cantor(cantor(u))) -> equal(segment(w,cantor(intersection(cantor(u),v)),least(w,cantor(intersection(cantor(u),v)))),identity_relation)**.
% 300.10/300.69  212404[7:SpL:13259.2,157.0] || member(cross_product(u,v),ordinal_numbers) member(apply(choice,cross_product(u,v)),union_of_range_map) -> equal(cross_product(u,v),identity_relation) equal(sum_class(range_of(first(apply(choice,cross_product(u,v))))),second(apply(choice,cross_product(u,v))))**.
% 300.10/300.69  213425[24:Rew:207572.1,213411.3] operation(u) || member(singleton(singleton(identity_relation)),range_of(v)) homomorphism(w,inverse(v),x)* -> equal(apply(x,ordered_pair(apply(w,identity_relation),apply(w,u))),apply(w,apply(inverse(v),singleton(singleton(identity_relation)))))*.
% 300.10/300.69  213523[8:Res:116127.5,143186.0] operation(u) operation(v) || compatible(w,v,u) subclass(cantor(v),symmetric_difference(ordinal_numbers,x)) -> homomorphism(w,v,u) member(ordered_pair(not_homomorphism1(w,v,u),not_homomorphism2(w,v,u)),complement(x))*.
% 300.10/300.69  213522[8:Res:116127.5,143226.0] operation(u) operation(v) || compatible(w,v,u) subclass(cantor(v),symmetric_difference(ordinal_numbers,x)) member(ordered_pair(not_homomorphism1(w,v,u),not_homomorphism2(w,v,u)),x)* -> homomorphism(w,v,u).
% 300.10/300.69  214569[25:SpL:208985.1,10118.0] operation(u) || member(ordered_pair(v,ordinal_numbers),range_of(w)) homomorphism(x,inverse(w),y)* -> equal(apply(y,ordered_pair(apply(x,v),apply(x,u))),apply(x,apply(inverse(w),ordered_pair(v,u))))*.
% 300.10/300.69  214514[25:SpL:208985.1,10118.0] operation(u) || member(ordered_pair(v,u),range_of(w))* homomorphism(x,inverse(w),y)* -> equal(apply(y,ordered_pair(apply(x,v),apply(x,ordinal_numbers))),apply(x,apply(inverse(w),ordered_pair(v,ordinal_numbers))))*.
% 300.10/300.69  214479[25:SpR:208985.1,116127.5] operation(not_homomorphism2(u,v,w)) operation(w) operation(v) || compatible(u,v,w) subclass(cantor(v),x) -> homomorphism(u,v,w) member(ordered_pair(not_homomorphism1(u,v,w),ordinal_numbers),x)*.
% 300.10/300.69  214807[25:Rew:208820.0,214790.1,208820.0,214790.0] || member(ordered_pair(ordinal_numbers,not_subclass_element(image(u,image(v,identity_relation)),w)),cross_product(ordinal_numbers,ordinal_numbers)) -> subclass(image(u,image(v,identity_relation)),w) member(ordered_pair(ordinal_numbers,not_subclass_element(image(u,image(v,identity_relation)),w)),compose(u,v))*.
% 300.10/300.69  219804[8:Res:67614.1,9878.0] || member(least(cross_product(u,symmetric_difference(complement(v),ordinal_numbers)),w),union(v,identity_relation))* member(x,u)* member(x,w)* subclass(w,y)* well_ordering(cross_product(u,symmetric_difference(complement(v),ordinal_numbers)),y)* -> .
% 300.10/300.69  220471[21:Res:196656.1,10118.0] || subclass(domain_relation,flip(range_of(u))) homomorphism(v,inverse(u),w)* -> equal(apply(w,ordered_pair(apply(v,ordered_pair(x,y)),apply(v,identity_relation))),apply(v,apply(inverse(u),ordered_pair(ordered_pair(x,y),identity_relation))))*.
% 300.10/300.69  220577[21:Res:196657.1,10118.0] || subclass(domain_relation,rotate(range_of(u))) homomorphism(v,inverse(u),w)* -> equal(apply(w,ordered_pair(apply(v,ordered_pair(x,identity_relation)),apply(v,y))),apply(v,apply(inverse(u),ordered_pair(ordered_pair(x,identity_relation),y))))*.
% 300.10/300.69  221115[7:Res:13236.2,8554.1] || well_ordering(u,complement(intersection(v,w))) member(least(u,complement(intersection(v,w))),union(v,w)) -> equal(complement(intersection(v,w)),identity_relation) member(least(u,complement(intersection(v,w))),symmetric_difference(v,w))*.
% 300.10/300.69  226383[7:Res:13258.1,8554.1] || member(regular(restrict(complement(intersection(u,v)),w,x)),union(u,v)) -> equal(restrict(complement(intersection(u,v)),w,x),identity_relation) member(regular(restrict(complement(intersection(u,v)),w,x)),symmetric_difference(u,v))*.
% 300.10/300.69  227357[7:SpL:192979.1,8803.0] || member(u,range_of(identity_relation)) member(ordered_pair(v,u),cross_product(ordinal_numbers,ordinal_numbers)) -> equal(cross_product(image(w,singleton(v)),ordinal_numbers),identity_relation) member(ordered_pair(v,u),compose(regular(cross_product(image(w,singleton(v)),ordinal_numbers)),w))*.
% 300.10/300.69  230748[7:SpL:18708.2,9878.0] || well_ordering(cross_product(u,v),ordinal_numbers)* member(w,v)* member(x,u)* member(x,singleton(w))* subclass(singleton(w),y)* well_ordering(cross_product(u,v),y)* -> equal(singleton(w),identity_relation).
% 300.10/300.69  233812[7:Res:13247.2,941.1] || member(intersection(u,power_class(image(element_relation,complement(v)))),ordinal_numbers) member(apply(choice,intersection(u,power_class(image(element_relation,complement(v))))),image(element_relation,power_class(v)))* -> equal(intersection(u,power_class(image(element_relation,complement(v)))),identity_relation).
% 300.10/300.69  233803[7:Res:13246.2,941.1] || member(intersection(power_class(image(element_relation,complement(u))),v),ordinal_numbers) member(apply(choice,intersection(power_class(image(element_relation,complement(u))),v)),image(element_relation,power_class(u)))* -> equal(intersection(power_class(image(element_relation,complement(u))),v),identity_relation).
% 300.10/300.69  233934[8:Res:13247.2,161200.0] || member(intersection(u,image(element_relation,union(v,identity_relation))),ordinal_numbers) member(apply(choice,intersection(u,image(element_relation,union(v,identity_relation)))),power_class(symmetric_difference(ordinal_numbers,v)))* -> equal(intersection(u,image(element_relation,union(v,identity_relation))),identity_relation).
% 300.10/300.69  233925[8:Res:13246.2,161200.0] || member(intersection(image(element_relation,union(u,identity_relation)),v),ordinal_numbers) member(apply(choice,intersection(image(element_relation,union(u,identity_relation)),v)),power_class(symmetric_difference(ordinal_numbers,u)))* -> equal(intersection(image(element_relation,union(u,identity_relation)),v),identity_relation).
% 300.10/300.69  234977[8:SpL:229238.0,116116.1] || member(u,cantor(complement(cross_product(u,ordinal_numbers))))* equal(least(rest_of(complement(cross_product(u,ordinal_numbers))),v),identity_relation)** member(u,v) subclass(v,w)* well_ordering(rest_of(complement(cross_product(u,ordinal_numbers))),w)* -> .
% 300.10/300.69  235040[7:Rew:234956.0,235028.3] || member(ordered_pair(u,ordered_pair(v,least(image(w,range_of(identity_relation)),x))),compose(w,complement(cross_product(singleton(u),ordinal_numbers))))* member(v,x) subclass(x,y)* well_ordering(image(w,range_of(identity_relation)),y)* -> .
% 300.10/300.69  235044[7:Rew:234956.0,235025.3] || member(ordered_pair(u,v),compose(w,complement(cross_product(singleton(u),ordinal_numbers))))* subclass(image(w,range_of(identity_relation)),x)* well_ordering(y,x)* -> member(least(y,image(w,range_of(identity_relation))),image(w,range_of(identity_relation)))*.
% 300.10/300.69  50400[0:Rew:3597.0,50328.4] || member(u,symmetrization_of(v)) member(u,complement(intersection(v,inverse(v))))* subclass(symmetric_difference(v,inverse(v)),w)* well_ordering(x,w)* -> member(least(x,symmetric_difference(v,inverse(v))),symmetric_difference(v,inverse(v)))*.
% 300.10/300.69  47576[0:Rew:3606.0,47486.2,3606.0,47486.1] || member(not_subclass_element(u,symmetric_difference(cross_product(v,w),x)),union(cross_product(v,w),x))* member(not_subclass_element(u,symmetric_difference(cross_product(v,w),x)),complement(restrict(x,v,w))) -> subclass(u,symmetric_difference(cross_product(v,w),x)).
% 300.10/300.69  47577[0:Rew:3603.0,47485.2,3603.0,47485.1] || member(not_subclass_element(u,symmetric_difference(v,cross_product(w,x))),union(v,cross_product(w,x)))* member(not_subclass_element(u,symmetric_difference(v,cross_product(w,x))),complement(restrict(v,w,x))) -> subclass(u,symmetric_difference(v,cross_product(w,x))).
% 300.10/300.69  46690[5:SpL:126.0,9747.0] || member(u,segment(v,w,x))* subclass(rest_of(restrict(v,w,singleton(x))),y)* well_ordering(z,y)* -> member(least(z,rest_of(restrict(v,w,singleton(x)))),rest_of(restrict(v,w,singleton(x))))*.
% 300.10/300.69  50401[0:Rew:3596.0,50327.4] || member(u,successor(v)) member(u,complement(intersection(v,singleton(v))))* subclass(symmetric_difference(v,singleton(v)),w)* well_ordering(x,w)* -> member(least(x,symmetric_difference(v,singleton(v))),symmetric_difference(v,singleton(v)))*.
% 300.10/300.69  49628[5:SpR:6355.1,41098.2] || member(second(not_subclass_element(cross_product(u,v),w)),ordinal_numbers) member(first(not_subclass_element(cross_product(u,v),w)),second(not_subclass_element(cross_product(u,v),w)))* -> subclass(cross_product(u,v),w) member(not_subclass_element(cross_product(u,v),w),element_relation).
% 300.10/300.69  177007[8:Res:161196.2,116155.1] operation(restrict(u,v,complement(complement(symmetrization_of(w))))) || connected(w,cantor(cantor(restrict(u,v,complement(complement(symmetrization_of(w)))))))* subclass(complement(complement(symmetrization_of(w))),v) -> section(u,complement(complement(symmetrization_of(w))),v).
% 300.10/300.69  165030[8:SpL:161038.2,116116.1] || member(u,ordinal_numbers) member(singleton(u),cantor(v))* equal(least(rest_of(v),w),identity_relation)** member(singleton(u),w)* subclass(w,x)* well_ordering(rest_of(v),x)* -> member(u,cantor(v)).
% 300.10/300.69  199117[7:Res:13515.2,13362.0] || well_ordering(u,cross_product(ordinal_numbers,ordinal_numbers)) subclass(compose(v,w),x)* well_ordering(omega,x) -> equal(compose(v,w),identity_relation) equal(integer_of(ordered_pair(least(u,compose(v,w)),least(omega,compose(v,w)))),identity_relation)**.
% 300.10/300.69  116526[8:Rew:116078.0,109282.3] operation(u) operation(v) || compatible(w,v,u) subclass(cantor(v),complement(compose(element_relation,ordinal_numbers))) member(ordered_pair(not_homomorphism1(w,v,u),not_homomorphism2(w,v,u)),element_relation)* -> homomorphism(w,v,u).
% 300.10/300.69  116496[8:Rew:116078.0,51447.3] operation(u) operation(v) || compatible(w,v,u) subclass(cantor(v),symmetric_difference(x,y)) -> homomorphism(w,v,u) member(ordered_pair(not_homomorphism1(w,v,u),not_homomorphism2(w,v,u)),union(x,y))*.
% 300.10/300.69  116495[8:Rew:116078.0,57112.3] operation(u) operation(v) || compatible(w,v,u) subclass(cantor(v),symmetric_difference(x,singleton(x)))* -> homomorphism(w,v,u) member(ordered_pair(not_homomorphism1(w,v,u),not_homomorphism2(w,v,u)),successor(x))*.
% 300.10/300.69  116494[8:Rew:116078.0,57179.3] operation(u) operation(v) || compatible(w,v,u) subclass(cantor(v),symmetric_difference(x,inverse(x)))* -> homomorphism(w,v,u) member(ordered_pair(not_homomorphism1(w,v,u),not_homomorphism2(w,v,u)),symmetrization_of(x))*.
% 300.10/300.69  116472[8:Rew:116078.0,51427.3] operation(u) operation(v) || compatible(w,v,u) subclass(cantor(v),x)* subclass(x,y)* -> homomorphism(w,v,u) member(ordered_pair(not_homomorphism1(w,v,u),not_homomorphism2(w,v,u)),y)*.
% 300.10/300.69  54927[5:SpR:10130.4,18510.1] operation(u) function(v) || compatible(w,x,u) homomorphism(y,x,v)* -> homomorphism(w,x,u) member(apply(y,apply(x,ordered_pair(not_homomorphism1(w,x,u),not_homomorphism2(w,x,u)))),ordinal_numbers)*.
% 300.10/300.69  197449[7:Rew:33.0,197407.2,33.0,197407.1,33.0,197407.0] || member(restrict(u,v,w),ordinal_numbers) -> equal(restrict(u,v,w),identity_relation) equal(ordered_pair(first(apply(choice,restrict(u,v,w))),second(apply(choice,restrict(u,v,w)))),apply(choice,restrict(u,v,w)))**.
% 300.10/300.69  39344[5:Res:9006.3,8803.0] function(u) || member(v,ordinal_numbers) subclass(ordinal_numbers,image(w,image(x,singleton(y)))) member(ordered_pair(y,image(u,v)),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(y,image(u,v)),compose(w,x))*.
% 300.10/300.69  195708[7:Res:13225.3,8803.0] || member(u,ordinal_numbers) subclass(u,image(v,image(w,singleton(x)))) member(ordered_pair(x,apply(choice,u)),cross_product(ordinal_numbers,ordinal_numbers)) -> equal(u,identity_relation) member(ordered_pair(x,apply(choice,u)),compose(v,w))*.
% 300.10/300.69  194661[7:Res:62.1,13313.1] || member(ordered_pair(u,apply(choice,complement(image(v,image(w,singleton(u)))))),compose(v,w))* member(complement(image(v,image(w,singleton(u)))),ordinal_numbers) -> equal(complement(image(v,image(w,singleton(u)))),identity_relation).
% 300.10/300.69  49071[5:Rew:189.0,49059.4] || member(u,ordinal_numbers) subclass(power_class(image(element_relation,complement(v))),w)* well_ordering(x,w)* -> member(u,image(element_relation,power_class(v)))* member(least(x,power_class(image(element_relation,complement(v)))),power_class(image(element_relation,complement(v))))*.
% 300.10/300.69  51400[5:Res:8827.2,10118.0] || member(u,ordinal_numbers) subclass(rest_relation,range_of(v)) homomorphism(w,inverse(v),x)* -> equal(apply(x,ordered_pair(apply(w,u),apply(w,rest_of(u)))),apply(w,apply(inverse(v),ordered_pair(u,rest_of(u)))))*.
% 300.10/300.69  63696[8:SoR:8534.0,19277.2] single_valued_class(restrict(u,v,singleton(w))) || subclass(range_of(restrict(u,v,singleton(w))),x) equal(restrict(u,v,singleton(w)),identity_relation) -> maps(restrict(u,v,singleton(w)),segment(u,v,w),x)*.
% 300.10/300.69  69504[7:Res:13125.2,10118.0] || subclass(omega,range_of(u)) homomorphism(v,inverse(u),w)* -> equal(integer_of(ordered_pair(x,y)),identity_relation) equal(apply(w,ordered_pair(apply(v,x),apply(v,y))),apply(v,apply(inverse(u),ordered_pair(x,y))))*.
% 300.10/300.69  208177[7:Res:9563.3,13362.0] || connected(u,v) well_ordering(w,v) subclass(not_well_ordering(u,v),x)* well_ordering(omega,x) -> well_ordering(u,v) equal(integer_of(ordered_pair(least(w,not_well_ordering(u,v)),least(omega,not_well_ordering(u,v)))),identity_relation)**.
% 300.10/300.69  208399[8:Res:117604.3,13362.0] operation(u) || member(v,cantor(cantor(u))) member(w,cantor(cantor(u))) subclass(cantor(u),x)* well_ordering(omega,x) -> equal(integer_of(ordered_pair(ordered_pair(w,v),least(omega,cantor(u)))),identity_relation)**.
% 300.10/300.69  208492[8:SpR:13260.1,117604.3] operation(u) || member(second(regular(cross_product(v,w))),cantor(cantor(u)))* member(first(regular(cross_product(v,w))),cantor(cantor(u))) -> equal(cross_product(v,w),identity_relation) member(regular(cross_product(v,w)),cantor(u)).
% 300.10/300.69  208545[7:Rew:13260.1,208538.3] || equal(compose(u,first(regular(cross_product(v,w)))),second(regular(cross_product(v,w))))** member(regular(cross_product(v,w)),cross_product(ordinal_numbers,ordinal_numbers))* -> equal(cross_product(v,w),identity_relation) member(regular(cross_product(v,w)),compose_class(u)).
% 300.10/300.69  209379[7:Res:9617.2,13362.0] || member(u,recursion_equation_functions(v)) member(ordered_pair(v,rest_of(u)),cross_product(ordinal_numbers,ordinal_numbers)) subclass(composition_function,w) well_ordering(omega,w)* -> equal(integer_of(ordered_pair(ordered_pair(v,ordered_pair(rest_of(u),u)),least(omega,composition_function))),identity_relation)**.
% 300.10/300.69  212417[21:SpL:13259.2,194373.1] || member(cross_product(u,v),ordinal_numbers) member(first(apply(choice,cross_product(u,v))),cantor(w)) member(ordered_pair(w,apply(choice,cross_product(u,v))),cross_product(ordinal_numbers,cross_product(ordinal_numbers,ordinal_numbers)))* -> equal(cross_product(u,v),identity_relation).
% 300.10/300.69  212387[7:SpL:13259.2,97.0] || member(cross_product(u,v),ordinal_numbers) member(apply(choice,cross_product(u,v)),compose_class(w)) -> equal(cross_product(u,v),identity_relation) equal(compose(w,first(apply(choice,cross_product(u,v)))),second(apply(choice,cross_product(u,v))))**.
% 300.10/300.69  214027[24:Rew:207558.1,214010.4] operation(u) || member(ordered_pair(u,ordered_pair(v,least(image(w,image(x,identity_relation)),y))),compose(w,x))* member(v,y) subclass(y,z)* well_ordering(image(w,image(x,identity_relation)),z)* -> .
% 300.10/300.69  214143[24:Rew:207558.1,214124.2,207558.1,214124.1] operation(u) || member(ordered_pair(u,regular(image(v,image(w,identity_relation)))),cross_product(ordinal_numbers,ordinal_numbers)) -> equal(image(v,image(w,identity_relation)),identity_relation) member(ordered_pair(u,regular(image(v,image(w,identity_relation)))),compose(v,w))*.
% 300.10/300.69  214811[8:MRR:214810.0,18.1] || member(ordered_pair(u,not_subclass_element(image(v,range_of(identity_relation)),w)),cross_product(ordinal_numbers,ordinal_numbers)) -> member(u,cantor(x)) subclass(image(v,range_of(identity_relation)),w) member(ordered_pair(u,not_subclass_element(image(v,range_of(identity_relation)),w)),compose(v,x))*.
% 300.10/300.69  215826[7:Res:13361.3,41096.0] || transitive(u,v) well_ordering(w,restrict(u,v,v)) -> equal(compose(restrict(u,v,v),restrict(u,v,v)),identity_relation) member(least(w,compose(restrict(u,v,v),restrict(u,v,v))),ordinal_numbers)*.
% 300.10/300.69  226308[8:SpR:19860.0,161460.2] operation(restrict(cross_product(u,ordinal_numbers),v,w)) || well_ordering(x,cantor(cantor(restrict(cross_product(u,ordinal_numbers),v,w)))) -> equal(segment(x,image(cross_product(v,w),u),least(x,image(cross_product(v,w),u))),identity_relation)**.
% 300.10/300.69  235045[7:Rew:234956.0,235016.1,234956.0,235016.0] || member(ordered_pair(u,not_subclass_element(image(v,range_of(identity_relation)),w)),cross_product(ordinal_numbers,ordinal_numbers)) -> subclass(image(v,range_of(identity_relation)),w) member(ordered_pair(u,not_subclass_element(image(v,range_of(identity_relation)),w)),compose(v,complement(cross_product(singleton(u),ordinal_numbers))))*.
% 300.10/300.69  235411[5:Res:28980.1,21.0] || subclass(rest_relation,flip(cross_product(u,v)))* -> equal(ordered_pair(first(ordered_pair(ordered_pair(w,x),rest_of(ordered_pair(x,w)))),second(ordered_pair(ordered_pair(w,x),rest_of(ordered_pair(x,w))))),ordered_pair(ordered_pair(w,x),rest_of(ordered_pair(x,w))))**.
% 300.10/300.69  235539[5:Res:28979.1,21.0] || subclass(rest_relation,rotate(cross_product(u,v)))* -> equal(ordered_pair(first(ordered_pair(ordered_pair(w,rest_of(ordered_pair(x,w))),x)),second(ordered_pair(ordered_pair(w,rest_of(ordered_pair(x,w))),x))),ordered_pair(ordered_pair(w,rest_of(ordered_pair(x,w))),x))**.
% 300.10/300.69  236263[0:Res:8551.2,18897.0] || member(not_subclass_element(intersection(u,complement(restrict(v,w,x))),y),cross_product(w,x))* member(not_subclass_element(intersection(u,complement(restrict(v,w,x))),y),v)* -> subclass(intersection(u,complement(restrict(v,w,x))),y).
% 300.10/300.69  236467[0:Res:8551.2,19016.0] || member(not_subclass_element(intersection(complement(restrict(u,v,w)),x),y),cross_product(v,w))* member(not_subclass_element(intersection(complement(restrict(u,v,w)),x),y),u)* -> subclass(intersection(complement(restrict(u,v,w)),x),y).
% 300.10/300.69  236873[7:Res:17392.2,8803.0] || subclass(u,image(v,image(w,singleton(x)))) member(ordered_pair(x,regular(intersection(u,y))),cross_product(ordinal_numbers,ordinal_numbers)) -> equal(intersection(u,y),identity_relation) member(ordered_pair(x,regular(intersection(u,y))),compose(v,w))*.
% 300.10/300.69  238607[7:Res:13572.2,8803.0] || subclass(u,image(v,image(w,singleton(x)))) member(ordered_pair(x,regular(intersection(y,u))),cross_product(ordinal_numbers,ordinal_numbers)) -> equal(intersection(y,u),identity_relation) member(ordered_pair(x,regular(intersection(y,u))),compose(v,w))*.
% 300.10/300.69  43684[0:SpL:3603.0,8554.1] || member(u,union(complement(restrict(v,w,x)),union(v,cross_product(w,x)))) member(u,complement(symmetric_difference(v,cross_product(w,x)))) -> member(u,symmetric_difference(complement(restrict(v,w,x)),union(v,cross_product(w,x))))*.
% 300.10/300.69  43685[0:SpL:3606.0,8554.1] || member(u,union(complement(restrict(v,w,x)),union(cross_product(w,x),v))) member(u,complement(symmetric_difference(cross_product(w,x),v))) -> member(u,symmetric_difference(complement(restrict(v,w,x)),union(cross_product(w,x),v)))*.
% 300.10/300.69  53054[5:MRR:53004.0,41096.1] || member(ordered_pair(u,least(intersection(v,complement(w)),x)),v)* member(u,x) subclass(x,y)* well_ordering(intersection(v,complement(w)),y)* -> member(ordered_pair(u,least(intersection(v,complement(w)),x)),w)*.
% 300.10/300.69  49680[5:Rew:6355.1,49658.3] || member(first(not_subclass_element(cross_product(u,v),w)),second(not_subclass_element(cross_product(u,v),w)))* member(not_subclass_element(cross_product(u,v),w),cross_product(ordinal_numbers,ordinal_numbers)) -> subclass(cross_product(u,v),w) member(not_subclass_element(cross_product(u,v),w),element_relation).
% 300.10/300.69  116313[8:Rew:116078.0,50992.0] || member(u,cantor(cross_product(v,w))) equal(restrict(cross_product(u,ordinal_numbers),v,w),least(rest_of(cross_product(v,w)),x))* member(u,x)* subclass(x,y)* well_ordering(rest_of(cross_product(v,w)),y)* -> .
% 300.10/300.69  153337[0:Res:919.1,8554.1] || member(not_subclass_element(restrict(complement(intersection(u,v)),w,x),y),union(u,v)) -> subclass(restrict(complement(intersection(u,v)),w,x),y) member(not_subclass_element(restrict(complement(intersection(u,v)),w,x),y),symmetric_difference(u,v))*.
% 300.10/300.69  49968[5:Res:8700.2,9878.0] || member(least(cross_product(u,complement(v)),w),ordinal_numbers)* member(x,u)* member(x,w)* subclass(w,y)* well_ordering(cross_product(u,complement(v)),y)* -> member(least(cross_product(u,complement(v)),w),v)*.
% 300.10/300.69  50886[5:Res:10093.3,129.0] || member(u,ordinal_numbers) member(ordered_pair(v,w),cross_product(ordinal_numbers,ordinal_numbers)) member(ordered_pair(ordered_pair(w,u),v),x)* subclass(rotate(x),y)* well_ordering(z,y)* -> member(least(z,rotate(x)),rotate(x))*.
% 300.10/300.69  50963[5:Res:10061.3,129.0] || member(u,ordinal_numbers) member(ordered_pair(v,w),cross_product(ordinal_numbers,ordinal_numbers)) member(ordered_pair(ordered_pair(w,v),u),x)* subclass(flip(x),y)* well_ordering(z,y)* -> member(least(z,flip(x)),flip(x))*.
% 300.10/300.69  46638[5:Res:9618.2,3689.0] || member(ordered_pair(u,v),cross_product(ordinal_numbers,ordinal_numbers)) subclass(composition_function,ordered_pair(w,x))* -> equal(ordered_pair(u,ordered_pair(v,compose(u,v))),unordered_pair(w,singleton(x)))* equal(ordered_pair(u,ordered_pair(v,compose(u,v))),singleton(w)).
% 300.10/300.69  196217[7:Res:13501.2,9421.0] || well_ordering(u,cross_product(ordinal_numbers,ordinal_numbers)) member(v,w)* -> equal(compose_class(x),identity_relation) equal(ordered_pair(first(ordered_pair(v,least(u,compose_class(x)))),second(ordered_pair(v,least(u,compose_class(x))))),ordered_pair(v,least(u,compose_class(x))))**.
% 300.10/300.69  196278[7:Res:13500.2,9421.0] || well_ordering(u,cross_product(ordinal_numbers,ordinal_numbers)) member(v,w)* -> equal(rest_of(x),identity_relation) equal(ordered_pair(first(ordered_pair(v,least(u,rest_of(x)))),second(ordered_pair(v,least(u,rest_of(x))))),ordered_pair(v,least(u,rest_of(x))))**.
% 300.10/300.69  198559[7:Res:13511.3,9878.0] || member(u,ordinal_numbers) well_ordering(cross_product(v,sum_class(u)),u)* member(w,v)* member(w,sum_class(u))* subclass(sum_class(u),x) well_ordering(cross_product(v,sum_class(u)),x)* -> equal(sum_class(u),identity_relation).
% 300.10/300.69  131484[8:Res:116127.5,18794.1] operation(u) operation(v) || compatible(w,v,u) subclass(cantor(v),intersection(x,y)) member(ordered_pair(not_homomorphism1(w,v,u),not_homomorphism2(w,v,u)),symmetric_difference(x,y))* -> homomorphism(w,v,u).
% 300.10/300.69  116491[8:Rew:116078.0,51433.3] operation(u) operation(v) || compatible(w,v,u) subclass(cantor(v),restrict(x,y,z))* -> homomorphism(w,v,u) member(ordered_pair(not_homomorphism1(w,v,u),not_homomorphism2(w,v,u)),cross_product(y,z))*.
% 300.10/300.69  197452[7:Rew:3594.0,197351.1,3594.0,197351.0] || member(symmetric_difference(complement(intersection(u,v)),union(u,v)),ordinal_numbers) -> equal(symmetric_difference(complement(intersection(u,v)),union(u,v)),identity_relation) member(apply(choice,symmetric_difference(complement(intersection(u,v)),union(u,v))),complement(symmetric_difference(u,v)))*.
% 300.10/300.69  54284[0:Res:10.1,9664.1] || equal(u,image(v,image(w,singleton(x))))* member(ordered_pair(x,y),compose(v,w))* well_ordering(z,u)* -> member(least(z,image(v,image(w,singleton(x)))),image(v,image(w,singleton(x))))*.
% 300.10/300.69  61135[0:Res:52.1,9664.1] inductive(image(u,singleton(v))) || member(ordered_pair(v,w),compose(successor_relation,u))* well_ordering(x,image(u,singleton(v))) -> member(least(x,image(successor_relation,image(u,singleton(v)))),image(successor_relation,image(u,singleton(v))))*.
% 300.10/300.69  116497[8:Rew:116078.0,51445.3] operation(u) operation(v) || compatible(w,v,u) subclass(cantor(v),image(element_relation,complement(x))) member(ordered_pair(not_homomorphism1(w,v,u),not_homomorphism2(w,v,u)),power_class(x))* -> homomorphism(w,v,u).
% 300.10/300.69  145898[5:SpL:145758.0,10118.0] || member(ordered_pair(u,v),image(ordinal_numbers,w)) homomorphism(x,inverse(cross_product(w,ordinal_numbers)),y)* -> equal(apply(y,ordered_pair(apply(x,u),apply(x,v))),apply(x,apply(inverse(cross_product(w,ordinal_numbers)),ordered_pair(u,v))))*.
% 300.10/300.69  63704[8:SoR:9962.0,19277.2] single_valued_class(flip(cross_product(u,ordinal_numbers))) || subclass(range_of(flip(cross_product(u,ordinal_numbers))),range_of(u))* equal(cross_product(range_of(u),range_of(u)),inverse(u)) equal(flip(cross_product(u,ordinal_numbers)),identity_relation) -> operation(flip(cross_product(u,ordinal_numbers))).
% 300.10/300.69  208213[7:Res:13333.3,13362.0] inductive(u) || well_ordering(v,u) subclass(image(successor_relation,u),w)* well_ordering(omega,w) -> equal(image(successor_relation,u),identity_relation) equal(integer_of(ordered_pair(least(v,image(successor_relation,u)),least(omega,image(successor_relation,u)))),identity_relation)**.
% 300.10/300.69  208489[8:SpR:13260.1,116123.2] || member(first(regular(cross_product(u,v))),cantor(w)) equal(restrict(w,first(regular(cross_product(u,v))),ordinal_numbers),second(regular(cross_product(u,v))))** -> equal(cross_product(u,v),identity_relation) member(regular(cross_product(u,v)),rest_of(w)).
% 300.10/300.69  212415[7:SpL:13259.2,100.0] || member(cross_product(u,v),ordinal_numbers) member(ordered_pair(w,apply(choice,cross_product(u,v))),composition_function)* -> equal(cross_product(u,v),identity_relation) equal(compose(w,first(apply(choice,cross_product(u,v)))),second(apply(choice,cross_product(u,v)))).
% 300.10/300.69  212384[7:SpL:13259.2,8651.0] || member(cross_product(u,v),ordinal_numbers) member(apply(choice,cross_product(u,v)),rest_of(w)) -> equal(cross_product(u,v),identity_relation) equal(restrict(w,first(apply(choice,cross_product(u,v))),ordinal_numbers),second(apply(choice,cross_product(u,v))))**.
% 300.10/300.69  213548[8:Res:116127.5,14681.0] operation(u) operation(v) || compatible(w,v,u) subclass(cantor(v),regular(x)) member(ordered_pair(not_homomorphism1(w,v,u),not_homomorphism2(w,v,u)),x)* -> homomorphism(w,v,u) equal(x,identity_relation).
% 300.10/300.69  214756[24:Rew:207558.1,214734.4] operation(u) || member(ordered_pair(u,v),compose(w,x))* subclass(image(w,image(x,identity_relation)),y)* well_ordering(z,y)* -> member(least(z,image(w,image(x,identity_relation))),image(w,image(x,identity_relation)))*.
% 300.10/300.69  215834[7:Rew:143170.0,215815.2,143170.0,215815.1] || transitive(ordinal_numbers,u) well_ordering(v,cross_product(u,u)) -> equal(compose(cross_product(u,u),cross_product(u,u)),identity_relation) member(least(v,compose(cross_product(u,u),cross_product(u,u))),compose(cross_product(u,u),cross_product(u,u)))*.
% 300.10/300.69  215936[21:SpR:10130.4,196564.1] operation(u) function(v) || compatible(w,x,u) homomorphism(y,x,v)* -> homomorphism(w,x,u) equal(cantor(apply(y,apply(x,ordered_pair(not_homomorphism1(w,x,u),not_homomorphism2(w,x,u))))),identity_relation)**.
% 300.10/300.69  219625[8:Res:116127.5,67561.0] operation(u) operation(v) || compatible(w,v,u) subclass(cantor(v),symmetric_difference(complement(x),ordinal_numbers)) -> homomorphism(w,v,u) member(ordered_pair(not_homomorphism1(w,v,u),not_homomorphism2(w,v,u)),union(x,identity_relation))*.
% 300.10/300.69  220063[8:Res:116127.5,160772.0] operation(u) operation(v) || compatible(w,v,u) subclass(cantor(v),symmetric_difference(ordinal_numbers,x)) member(ordered_pair(not_homomorphism1(w,v,u),not_homomorphism2(w,v,u)),union(x,identity_relation))* -> homomorphism(w,v,u).
% 300.10/300.69  223684[7:SpR:13259.2,13413.1] || member(cross_product(u,v),ordinal_numbers) subclass(omega,element_relation) -> equal(cross_product(u,v),identity_relation) equal(integer_of(apply(choice,cross_product(u,v))),identity_relation) member(first(apply(choice,cross_product(u,v))),second(apply(choice,cross_product(u,v))))*.
% 300.10/300.69  224708[21:SpL:13259.2,194371.0] || member(cross_product(u,v),ordinal_numbers) member(apply(choice,cross_product(u,v)),cross_product(ordinal_numbers,ordinal_numbers)) member(second(apply(choice,cross_product(u,v))),cantor(first(apply(choice,cross_product(u,v)))))* -> equal(cross_product(u,v),identity_relation).
% 300.10/300.69  230749[8:SpL:18708.2,116116.1] || well_ordering(rest_of(u),ordinal_numbers) member(v,cantor(u)) equal(restrict(u,v,ordinal_numbers),w)* member(v,singleton(w))* subclass(singleton(w),x)* well_ordering(rest_of(u),x)* -> equal(singleton(w),identity_relation).
% 300.10/300.69  235941[7:Res:69478.2,9878.0] || subclass(omega,symmetric_difference(u,v)) member(w,x)* member(w,y)* subclass(y,z)* well_ordering(cross_product(x,union(u,v)),z)* -> equal(integer_of(least(cross_product(x,union(u,v)),y)),identity_relation)**.
% 300.10/300.69  237155[7:Res:13574.1,36719.1] operation(u) ||  -> equal(intersection(v,intersection(w,cantor(u))),identity_relation) equal(ordered_pair(first(regular(intersection(v,intersection(w,cantor(u))))),second(regular(intersection(v,intersection(w,cantor(u)))))),regular(intersection(v,intersection(w,cantor(u)))))**.
% 300.10/300.69  237806[7:Res:13573.1,36719.1] operation(u) ||  -> equal(intersection(v,intersection(cantor(u),w)),identity_relation) equal(ordered_pair(first(regular(intersection(v,intersection(cantor(u),w)))),second(regular(intersection(v,intersection(cantor(u),w))))),regular(intersection(v,intersection(cantor(u),w))))**.
% 300.10/300.69  239318[7:Res:17397.1,36719.1] operation(u) ||  -> equal(intersection(intersection(cantor(u),v),w),identity_relation) equal(ordered_pair(first(regular(intersection(intersection(cantor(u),v),w))),second(regular(intersection(intersection(cantor(u),v),w)))),regular(intersection(intersection(cantor(u),v),w)))**.
% 300.10/300.69  240153[7:Res:17396.1,36719.1] operation(u) ||  -> equal(intersection(intersection(v,cantor(u)),w),identity_relation) equal(ordered_pair(first(regular(intersection(intersection(v,cantor(u)),w))),second(regular(intersection(intersection(v,cantor(u)),w)))),regular(intersection(intersection(v,cantor(u)),w)))**.
% 300.10/300.69  48516[0:SpR:163.0,3594.0] ||  -> equal(intersection(complement(symmetric_difference(complement(intersection(u,v)),union(u,v))),union(complement(symmetric_difference(u,v)),union(complement(intersection(u,v)),union(u,v)))),symmetric_difference(complement(symmetric_difference(u,v)),union(complement(intersection(u,v)),union(u,v))))**.
% 300.10/300.69  47518[0:Res:27.2,8562.0] || member(not_subclass_element(u,intersection(v,intersection(w,x))),x)* member(not_subclass_element(u,intersection(v,intersection(w,x))),w)* member(not_subclass_element(u,intersection(v,intersection(w,x))),v)* -> subclass(u,intersection(v,intersection(w,x))).
% 300.10/300.69  49681[5:Rew:6355.1,49657.3] || equal(successor(first(not_subclass_element(cross_product(u,v),w))),second(not_subclass_element(cross_product(u,v),w))) member(not_subclass_element(cross_product(u,v),w),cross_product(ordinal_numbers,ordinal_numbers))* -> subclass(cross_product(u,v),w) member(not_subclass_element(cross_product(u,v),w),successor_relation).
% 300.10/300.69  53039[5:Rew:32.0,53011.4,32.0,53011.1,32.0,53011.0] || member(ordered_pair(u,least(restrict(v,ordinal_numbers,ordinal_numbers),w)),subset_relation)* member(ordered_pair(u,least(restrict(v,ordinal_numbers,ordinal_numbers),w)),v)* member(u,w) subclass(w,x)* well_ordering(restrict(v,ordinal_numbers,ordinal_numbers),x)* -> .
% 300.10/300.69  197850[8:SpL:13302.1,116117.1] || asymmetric(cross_product(u,v),ordinal_numbers) member(ordinal_numbers,cantor(restrict(inverse(cross_product(u,v)),u,v)))* equal(identity_relation,w) subclass(rest_of(restrict(inverse(cross_product(u,v)),u,v)),x)* -> member(ordered_pair(ordinal_numbers,w),x)*.
% 300.10/300.69  136696[8:Res:116127.5,18791.0] operation(u) operation(v) || compatible(w,v,u) subclass(cantor(v),symmetric_difference(complement(x),complement(y))) -> homomorphism(w,v,u) member(ordered_pair(not_homomorphism1(w,v,u),not_homomorphism2(w,v,u)),union(x,y))*.
% 300.10/300.69  63012[8:Res:15426.1,10120.0] || subclass(domain_relation,segment(u,v,w)) homomorphism(x,restrict(u,v,singleton(w)),y)* -> equal(apply(y,ordered_pair(apply(x,identity_relation),apply(x,identity_relation))),apply(x,apply(restrict(u,v,singleton(w)),ordered_pair(identity_relation,identity_relation))))*.
% 300.10/300.69  54469[5:Res:8642.1,10120.0] || subclass(ordinal_numbers,segment(u,v,w)) homomorphism(x,restrict(u,v,singleton(w)),y)* -> equal(apply(y,ordered_pair(apply(x,z),apply(x,x1))),apply(x,apply(restrict(u,v,singleton(w)),ordered_pair(z,x1))))*.
% 300.10/300.69  54937[5:SpR:10130.4,18510.1] operation(u) function(v) || compatible(w,x,u) homomorphism(v,x,y) -> homomorphism(w,x,u) member(apply(y,ordered_pair(apply(v,not_homomorphism1(w,x,u)),apply(v,not_homomorphism2(w,x,u)))),ordinal_numbers)*.
% 300.10/300.69  197701[7:Res:13247.2,3689.0] || member(intersection(u,ordered_pair(v,w)),ordinal_numbers) -> equal(intersection(u,ordered_pair(v,w)),identity_relation) equal(apply(choice,intersection(u,ordered_pair(v,w))),unordered_pair(v,singleton(w)))** equal(apply(choice,intersection(u,ordered_pair(v,w))),singleton(v)).
% 300.10/300.69  197412[7:Res:13246.2,3689.0] || member(intersection(ordered_pair(u,v),w),ordinal_numbers) -> equal(intersection(ordered_pair(u,v),w),identity_relation) equal(apply(choice,intersection(ordered_pair(u,v),w)),unordered_pair(u,singleton(v)))** equal(apply(choice,intersection(ordered_pair(u,v),w)),singleton(u)).
% 300.10/300.69  194654[7:Res:8551.2,13313.1] || member(apply(choice,complement(restrict(u,v,w))),cross_product(v,w))* member(apply(choice,complement(restrict(u,v,w))),u)* member(complement(restrict(u,v,w)),ordinal_numbers) -> equal(complement(restrict(u,v,w)),identity_relation).
% 300.10/300.69  54286[5:Res:8665.1,9664.1] function(image(u,image(v,singleton(w)))) || member(ordered_pair(w,x),compose(u,v))* well_ordering(y,cross_product(ordinal_numbers,ordinal_numbers)) -> member(least(y,image(u,image(v,singleton(w)))),image(u,image(v,singleton(w))))*.
% 300.10/300.69  139690[8:Rew:19860.0,139676.2] operation(restrict(cross_product(u,ordinal_numbers),v,w)) || subclass(cantor(cantor(restrict(cross_product(u,ordinal_numbers),v,w))),image(cross_product(v,w),u))* -> equal(cantor(cantor(restrict(cross_product(u,ordinal_numbers),v,w))),image(cross_product(v,w),u)).
% 300.10/300.69  48499[0:SpR:485.0,3594.0] ||  -> equal(intersection(complement(symmetric_difference(u,image(element_relation,complement(v)))),union(complement(intersection(u,image(element_relation,complement(v)))),complement(intersection(complement(u),power_class(v))))),symmetric_difference(complement(intersection(u,image(element_relation,complement(v)))),complement(intersection(complement(u),power_class(v)))))**.
% 300.10/300.69  48511[0:SpR:487.0,3594.0] ||  -> equal(intersection(complement(symmetric_difference(image(element_relation,complement(u)),v)),union(complement(intersection(image(element_relation,complement(u)),v)),complement(intersection(power_class(u),complement(v))))),symmetric_difference(complement(intersection(image(element_relation,complement(u)),v)),complement(intersection(power_class(u),complement(v)))))**.
% 300.10/300.69  50464[5:SoR:8534.0,10858.2] single_valued_class(restrict(u,v,singleton(w))) || subclass(range_of(restrict(u,v,singleton(w))),x) equal(restrict(u,v,singleton(w)),cross_product(ordinal_numbers,ordinal_numbers)) -> maps(restrict(u,v,singleton(w)),segment(u,v,w),x)*.
% 300.10/300.69  198941[8:Res:161565.3,9878.0] operation(u) || well_ordering(cross_product(v,range_of(u)),cantor(cantor(u)))* member(w,v)* member(w,range_of(u))* subclass(range_of(u),x) well_ordering(cross_product(v,range_of(u)),x)* -> equal(range_of(u),identity_relation).
% 300.10/300.69  212286[8:SpR:916.0,161774.3] || section(cross_product(u,v),w,x) well_ordering(y,w) -> equal(cantor(restrict(cross_product(u,v),x,w)),identity_relation) member(least(y,cantor(restrict(cross_product(x,w),u,v))),cantor(restrict(cross_product(x,w),u,v)))*.
% 300.10/300.69  214018[24:SpL:207572.1,9880.0] operation(least(image(u,image(v,singleton(w))),x)) || member(ordered_pair(w,singleton(singleton(identity_relation))),compose(u,v))* member(identity_relation,x)* subclass(x,y)* well_ordering(image(u,image(v,singleton(w))),y)* -> .
% 300.10/300.69  214028[21:Rew:197474.0,214012.3] || member(ordered_pair(inverse(u),ordered_pair(v,least(image(w,image(x,identity_relation)),y))),compose(w,x))* member(v,y) subclass(y,z)* well_ordering(image(w,image(x,identity_relation)),z)* -> equal(range_of(u),identity_relation).
% 300.10/300.69  214598[25:SpL:208985.1,9880.0] operation(least(image(u,image(v,singleton(w))),x)) || member(ordered_pair(w,ordered_pair(y,ordinal_numbers)),compose(u,v))* member(y,x)* subclass(x,z)* well_ordering(image(u,image(v,singleton(w))),z)* -> .
% 300.10/300.69  214808[24:Rew:207558.1,214787.2,207558.1,214787.1] operation(u) || member(ordered_pair(u,not_subclass_element(image(v,image(w,identity_relation)),x)),cross_product(ordinal_numbers,ordinal_numbers)) -> subclass(image(v,image(w,identity_relation)),x) member(ordered_pair(u,not_subclass_element(image(v,image(w,identity_relation)),x)),compose(v,w))*.
% 300.10/300.69  215967[21:SpL:10130.4,198470.1] operation(u) function(v) || compatible(w,x,u) homomorphism(y,x,v)* equal(rest_of(apply(y,apply(x,ordered_pair(not_homomorphism1(w,x,u),not_homomorphism2(w,x,u))))),rest_relation)** -> homomorphism(w,x,u).
% 300.10/300.69  223942[8:Rew:160927.0,223867.4] || member(u,ordinal_numbers) subclass(union(v,symmetric_difference(ordinal_numbers,w)),x)* well_ordering(y,x)* -> member(u,intersection(complement(v),union(w,identity_relation)))* member(least(y,union(v,symmetric_difference(ordinal_numbers,w))),union(v,symmetric_difference(ordinal_numbers,w)))*.
% 300.10/300.69  224257[8:Rew:160992.0,224186.4] || member(u,ordinal_numbers) subclass(union(symmetric_difference(ordinal_numbers,v),w),x)* well_ordering(y,x)* -> member(u,intersection(union(v,identity_relation),complement(w)))* member(least(y,union(symmetric_difference(ordinal_numbers,v),w)),union(symmetric_difference(ordinal_numbers,v),w))*.
% 300.10/300.69  227369[7:Rew:192979.1,227343.2,192979.1,227343.0] || member(ordered_pair(u,regular(range_of(identity_relation))),cross_product(ordinal_numbers,ordinal_numbers)) -> equal(cross_product(image(v,singleton(u)),ordinal_numbers),identity_relation) equal(range_of(identity_relation),identity_relation) member(ordered_pair(u,regular(range_of(identity_relation))),compose(regular(cross_product(image(v,singleton(u)),ordinal_numbers)),v))*.
% 300.10/300.69  227979[7:SpR:13259.2,13410.1] || member(cross_product(u,v),ordinal_numbers) subclass(omega,rest_relation) -> equal(cross_product(u,v),identity_relation) equal(integer_of(apply(choice,cross_product(u,v))),identity_relation) equal(rest_of(first(apply(choice,cross_product(u,v)))),second(apply(choice,cross_product(u,v))))**.
% 300.10/300.69  228126[8:SpR:13259.2,160930.1] || member(cross_product(u,v),ordinal_numbers) subclass(omega,domain_relation) -> equal(cross_product(u,v),identity_relation) equal(integer_of(apply(choice,cross_product(u,v))),identity_relation) equal(cantor(first(apply(choice,cross_product(u,v)))),second(apply(choice,cross_product(u,v))))**.
% 300.10/300.69  228191[7:SpR:13259.2,13412.1] || member(cross_product(u,v),ordinal_numbers) subclass(omega,successor_relation) -> equal(cross_product(u,v),identity_relation) equal(integer_of(apply(choice,cross_product(u,v))),identity_relation) equal(successor(first(apply(choice,cross_product(u,v)))),second(apply(choice,cross_product(u,v))))**.
% 300.10/300.69  233465[8:Res:161057.2,9421.0] || well_ordering(u,ordinal_numbers) member(v,w)* -> equal(recursion_equation_functions(x),identity_relation) equal(ordered_pair(first(ordered_pair(v,cantor(least(u,recursion_equation_functions(x))))),second(ordered_pair(v,cantor(least(u,recursion_equation_functions(x)))))),ordered_pair(v,cantor(least(u,recursion_equation_functions(x)))))**.
% 300.10/300.69  235708[5:Res:28980.1,36719.1] operation(u) || subclass(rest_relation,flip(cantor(u)))* -> equal(ordered_pair(first(ordered_pair(ordered_pair(v,w),rest_of(ordered_pair(w,v)))),second(ordered_pair(ordered_pair(v,w),rest_of(ordered_pair(w,v))))),ordered_pair(ordered_pair(v,w),rest_of(ordered_pair(w,v))))**.
% 300.10/300.69  235703[5:Res:28979.1,36719.1] operation(u) || subclass(rest_relation,rotate(cantor(u)))* -> equal(ordered_pair(first(ordered_pair(ordered_pair(v,rest_of(ordered_pair(w,v))),w)),second(ordered_pair(ordered_pair(v,rest_of(ordered_pair(w,v))),w))),ordered_pair(ordered_pair(v,rest_of(ordered_pair(w,v))),w))**.
% 300.10/300.69  237091[7:Res:13574.1,8554.1] || member(regular(intersection(u,intersection(v,complement(intersection(w,x))))),union(w,x)) -> equal(intersection(u,intersection(v,complement(intersection(w,x)))),identity_relation) member(regular(intersection(u,intersection(v,complement(intersection(w,x))))),symmetric_difference(w,x))*.
% 300.10/300.69  237742[7:Res:13573.1,8554.1] || member(regular(intersection(u,intersection(complement(intersection(v,w)),x))),union(v,w)) -> equal(intersection(u,intersection(complement(intersection(v,w)),x)),identity_relation) member(regular(intersection(u,intersection(complement(intersection(v,w)),x))),symmetric_difference(v,w))*.
% 300.10/300.69  239254[7:Res:17397.1,8554.1] || member(regular(intersection(intersection(complement(intersection(u,v)),w),x)),union(u,v)) -> equal(intersection(intersection(complement(intersection(u,v)),w),x),identity_relation) member(regular(intersection(intersection(complement(intersection(u,v)),w),x)),symmetric_difference(u,v))*.
% 300.10/300.69  240089[7:Res:17396.1,8554.1] || member(regular(intersection(intersection(u,complement(intersection(v,w))),x)),union(v,w)) -> equal(intersection(intersection(u,complement(intersection(v,w))),x),identity_relation) member(regular(intersection(intersection(u,complement(intersection(v,w))),x)),symmetric_difference(v,w))*.
% 300.10/300.69  49676[0:SpL:6355.1,3689.0] || member(u,not_subclass_element(cross_product(v,w),x))* -> subclass(cross_product(v,w),x) equal(u,unordered_pair(first(not_subclass_element(cross_product(v,w),x)),singleton(second(not_subclass_element(cross_product(v,w),x)))))* equal(u,singleton(first(not_subclass_element(cross_product(v,w),x)))).
% 300.10/300.69  156480[5:Rew:155665.0,156467.4] || member(u,union(subset_relation,cross_product(ordinal_numbers,ordinal_numbers)))* member(u,complement(subset_relation)) subclass(symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers)),v)* well_ordering(w,v)* -> member(least(w,symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers))),symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers)))*.
% 300.10/300.69  156589[5:Rew:155666.0,156576.4] || member(u,union(cross_product(ordinal_numbers,ordinal_numbers),subset_relation))* member(u,complement(subset_relation)) subclass(symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation),v)* well_ordering(w,v)* -> member(least(w,symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation)),symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation))*.
% 300.10/300.69  156975[8:Res:156922.1,9872.0] || member(ordered_pair(u,least(intersection(v,complement(subset_relation)),w)),inverse(subset_relation))* member(ordered_pair(u,least(intersection(v,complement(subset_relation)),w)),v)* member(u,w) subclass(w,x)* well_ordering(intersection(v,complement(subset_relation)),x)* -> .
% 300.10/300.69  117804[8:Rew:116078.0,116574.3,116078.0,116574.2,116078.0,116574.1] operation(u) || transitive(v,cantor(cantor(u))) subclass(intersection(cantor(u),v),compose(intersection(cantor(u),v),intersection(cantor(u),v)))* -> equal(compose(intersection(cantor(u),v),intersection(cantor(u),v)),intersection(cantor(u),v)).
% 300.10/300.69  117805[8:Rew:116078.0,116578.4,116078.0,116578.2,116078.0,116578.1,116078.0,116578.1] operation(u) || member(second(not_subclass_element(cross_product(v,w),x)),cantor(cantor(u)))* member(first(not_subclass_element(cross_product(v,w),x)),cantor(cantor(u))) -> subclass(cross_product(v,w),x) member(not_subclass_element(cross_product(v,w),x),cantor(u)).
% 300.10/300.69  69531[7:Res:13125.2,9872.0] || subclass(omega,u) member(ordered_pair(v,least(intersection(w,u),x)),w)* member(v,x) subclass(x,y)* well_ordering(intersection(w,u),y)* -> equal(integer_of(ordered_pair(v,least(intersection(w,u),x))),identity_relation).
% 300.10/300.69  164724[8:SpL:13104.1,116116.1] || asymmetric(u,ordinal_numbers) member(ordinal_numbers,cantor(intersection(u,inverse(u)))) equal(least(rest_of(intersection(u,inverse(u))),v),identity_relation)** member(ordinal_numbers,v) subclass(v,w)* well_ordering(rest_of(intersection(u,inverse(u))),w)* -> .
% 300.10/300.69  46612[5:Res:9618.2,8554.1] || member(ordered_pair(u,v),cross_product(ordinal_numbers,ordinal_numbers)) subclass(composition_function,complement(intersection(w,x))) member(ordered_pair(u,ordered_pair(v,compose(u,v))),union(w,x)) -> member(ordered_pair(u,ordered_pair(v,compose(u,v))),symmetric_difference(w,x))*.
% 300.10/300.69  198555[7:Res:13511.3,9421.0] || member(u,ordinal_numbers) well_ordering(v,u) member(w,x)* -> equal(sum_class(u),identity_relation) equal(ordered_pair(first(ordered_pair(w,least(v,sum_class(u)))),second(ordered_pair(w,least(v,sum_class(u))))),ordered_pair(w,least(v,sum_class(u))))**.
% 300.10/300.69  116498[8:Rew:116078.0,51432.3] operation(u) operation(v) || compatible(w,v,u) subclass(cantor(v),intersection(complement(x),complement(y))) member(ordered_pair(not_homomorphism1(w,v,u),not_homomorphism2(w,v,u)),union(x,y))* -> homomorphism(w,v,u).
% 300.10/300.69  51388[5:SpL:8649.0,10118.0] || member(ordered_pair(u,v),image(w,x)) homomorphism(y,inverse(restrict(w,x,ordinal_numbers)),z)* -> equal(apply(z,ordered_pair(apply(y,u),apply(y,v))),apply(y,apply(inverse(restrict(w,x,ordinal_numbers)),ordered_pair(u,v))))*.
% 300.10/300.69  69493[7:Res:13125.2,9880.0] || subclass(omega,compose(u,v)) member(w,x) subclass(x,y)* well_ordering(image(u,image(v,singleton(z))),y)* -> equal(integer_of(ordered_pair(z,ordered_pair(w,least(image(u,image(v,singleton(z))),x)))),identity_relation)**.
% 300.10/300.69  148936[8:Res:148858.1,9664.1] || subclass(image(u,image(v,singleton(w))),inverse(subset_relation)) member(ordered_pair(w,x),compose(u,v))* well_ordering(y,complement(subset_relation)) -> member(least(y,image(u,image(v,singleton(w)))),image(u,image(v,singleton(w))))*.
% 300.10/300.69  50865[5:Res:49995.1,8803.0] || member(image(u,image(v,singleton(w))),subset_relation) member(ordered_pair(w,singleton(first(image(u,image(v,singleton(w)))))),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(w,singleton(first(image(u,image(v,singleton(w)))))),compose(u,v))*.
% 300.10/300.69  62892[5:Rew:6355.1,62882.3] || equal(sum_class(range_of(first(not_subclass_element(cross_product(u,v),w)))),second(not_subclass_element(cross_product(u,v),w))) member(not_subclass_element(cross_product(u,v),w),cross_product(ordinal_numbers,ordinal_numbers))* -> subclass(cross_product(u,v),w) member(not_subclass_element(cross_product(u,v),w),union_of_range_map).
% 300.10/300.69  51022[5:SoR:9962.0,10858.2] single_valued_class(flip(cross_product(u,ordinal_numbers))) || subclass(range_of(flip(cross_product(u,ordinal_numbers))),range_of(u))* equal(cross_product(range_of(u),range_of(u)),inverse(u)) equal(flip(cross_product(u,ordinal_numbers)),cross_product(ordinal_numbers,ordinal_numbers)) -> operation(flip(cross_product(u,ordinal_numbers))).
% 300.10/300.69  204160[8:Res:204134.1,9872.0] || member(ordered_pair(u,least(intersection(v,symmetrization_of(identity_relation)),w)),inverse(identity_relation))* member(ordered_pair(u,least(intersection(v,symmetrization_of(identity_relation)),w)),v)* member(u,w) subclass(w,x)* well_ordering(intersection(v,symmetrization_of(identity_relation)),x)* -> .
% 300.10/300.69  212319[8:Rew:117511.1,212287.3] operation(u) || section(v,cantor(cantor(u)),cantor(cantor(u))) well_ordering(w,cantor(cantor(u))) -> equal(cantor(intersection(cantor(u),v)),identity_relation) member(least(w,cantor(intersection(cantor(u),v))),cantor(intersection(cantor(u),v)))*.
% 300.10/300.69  212358[7:SpR:13259.2,20.2] || member(cross_product(u,v),ordinal_numbers) member(second(apply(choice,cross_product(u,v))),w) member(first(apply(choice,cross_product(u,v))),x) -> equal(cross_product(u,v),identity_relation) member(apply(choice,cross_product(u,v)),cross_product(x,w))*.
% 300.10/300.69  212756[8:SoR:117762.0,19277.2] single_valued_class(restrict(u,v,ordinal_numbers)) || subclass(image(u,v),cantor(cantor(w))) equal(cantor(cantor(x)),cantor(restrict(u,v,ordinal_numbers))) equal(restrict(u,v,ordinal_numbers),identity_relation) -> compatible(restrict(u,v,ordinal_numbers),x,w)*.
% 300.10/300.69  214029[8:Rew:161076.2,214015.4] || member(u,ordinal_numbers) member(ordered_pair(u,ordered_pair(v,least(image(w,range_of(identity_relation)),x))),compose(w,y))* member(v,x) subclass(x,z)* well_ordering(image(w,range_of(identity_relation)),z)* -> member(u,cantor(y)).
% 300.10/300.69  214150[21:Rew:197474.0,214126.2,197474.0,214126.0] || member(ordered_pair(inverse(u),regular(image(v,image(w,identity_relation)))),cross_product(ordinal_numbers,ordinal_numbers)) -> equal(range_of(u),identity_relation) equal(image(v,image(w,identity_relation)),identity_relation) member(ordered_pair(inverse(u),regular(image(v,image(w,identity_relation)))),compose(v,w))*.
% 300.10/300.69  214757[8:Rew:161076.2,214739.5] || member(u,ordinal_numbers) member(ordered_pair(u,v),compose(w,x))* subclass(image(w,range_of(identity_relation)),y)* well_ordering(z,y)* -> member(u,cantor(x)) member(least(z,image(w,range_of(identity_relation))),image(w,range_of(identity_relation)))*.
% 300.10/300.69  214758[21:Rew:197474.0,214736.4] || member(ordered_pair(inverse(u),v),compose(w,x))* subclass(image(w,image(x,identity_relation)),y)* well_ordering(z,y)* -> equal(range_of(u),identity_relation) member(least(z,image(w,image(x,identity_relation))),image(w,image(x,identity_relation)))*.
% 300.10/300.69  215906[8:Rew:14756.0,215890.2,14756.0,215890.1,14756.0,215890.0] || member(image(u,range_of(identity_relation)),ordinal_numbers) member(ordered_pair(v,apply(choice,image(u,range_of(identity_relation)))),cross_product(ordinal_numbers,ordinal_numbers)) -> equal(image(u,range_of(identity_relation)),identity_relation) member(ordered_pair(v,apply(choice,image(u,range_of(identity_relation)))),compose(u,identity_relation))*.
% 300.10/300.69  215911[8:MRR:215883.4,14676.0] function(u) || member(image(u,image(inverse(u),singleton(v))),ordinal_numbers) member(ordered_pair(v,apply(choice,image(u,image(inverse(u),singleton(v))))),cross_product(ordinal_numbers,ordinal_numbers))* -> equal(image(u,image(inverse(u),singleton(v))),identity_relation).
% 300.10/300.69  215912[8:MRR:215882.4,14676.0] single_valued_class(u) || member(image(u,image(inverse(u),singleton(v))),ordinal_numbers) member(ordered_pair(v,apply(choice,image(u,image(inverse(u),singleton(v))))),cross_product(ordinal_numbers,ordinal_numbers))* -> equal(image(u,image(inverse(u),singleton(v))),identity_relation).
% 300.10/300.69  215948[21:SpR:10130.4,196564.1] operation(u) function(v) || compatible(w,x,u) homomorphism(v,x,y) -> homomorphism(w,x,u) equal(cantor(apply(y,ordered_pair(apply(v,not_homomorphism1(w,x,u)),apply(v,not_homomorphism2(w,x,u))))),identity_relation)**.
% 300.10/300.69  218268[8:Res:13530.3,217144.1] || member(image(u,image(v,singleton(w))),ordinal_numbers) member(ordered_pair(w,apply(choice,image(u,image(v,singleton(w))))),cross_product(ordinal_numbers,ordinal_numbers))* equal(compose(u,v),identity_relation) -> equal(image(u,image(v,singleton(w))),identity_relation).
% 300.10/300.69  219230[8:Res:13530.3,219073.1] || member(image(u,image(v,singleton(w))),ordinal_numbers) member(ordered_pair(w,apply(choice,image(u,image(v,singleton(w))))),cross_product(ordinal_numbers,ordinal_numbers))* subclass(compose(u,v),identity_relation) -> equal(image(u,image(v,singleton(w))),identity_relation).
% 300.10/300.69  224625[10:Rew:223660.1,224533.4] || subclass(element_relation,identity_relation) member(ordered_pair(cross_product(ordinal_numbers,ordinal_numbers),ordered_pair(u,least(image(v,image(w,identity_relation)),x))),compose(v,w))* member(u,x) subclass(x,y)* well_ordering(image(v,image(w,identity_relation)),y)* -> .
% 300.10/300.69  227370[7:Rew:192979.1,227353.4] || member(ordered_pair(u,v),compose(regular(cross_product(image(w,singleton(u)),ordinal_numbers)),w))* subclass(range_of(identity_relation),x)* well_ordering(y,x)* -> equal(cross_product(image(w,singleton(u)),ordinal_numbers),identity_relation) member(least(y,range_of(identity_relation)),range_of(identity_relation))*.
% 300.10/300.69  228874[8:Res:8832.1,61018.0] || member(apply(choice,regular(intersection(complement(u),complement(v)))),ordinal_numbers) -> member(apply(choice,regular(intersection(complement(u),complement(v)))),union(u,v))* equal(regular(intersection(complement(u),complement(v))),identity_relation) equal(intersection(complement(u),complement(v)),identity_relation).
% 300.10/300.69  230758[7:Rew:18708.2,230750.2] || well_ordering(intersection(u,v),ordinal_numbers)* member(ordered_pair(w,x),v)* member(ordered_pair(w,x),u)* member(w,singleton(x)) subclass(singleton(x),y)* well_ordering(intersection(u,v),y)* -> equal(singleton(x),identity_relation).
% 300.10/300.69  233726[7:SpR:13259.2,13409.1] || member(cross_product(u,v),ordinal_numbers) subclass(omega,union_of_range_map) -> equal(cross_product(u,v),identity_relation) equal(integer_of(apply(choice,cross_product(u,v))),identity_relation) equal(sum_class(range_of(first(apply(choice,cross_product(u,v))))),second(apply(choice,cross_product(u,v))))**.
% 300.10/300.69  235370[7:SpR:13259.2,28980.1] || member(cross_product(u,v),ordinal_numbers) subclass(rest_relation,flip(w)) -> equal(cross_product(u,v),identity_relation) member(ordered_pair(apply(choice,cross_product(u,v)),rest_of(ordered_pair(second(apply(choice,cross_product(u,v))),first(apply(choice,cross_product(u,v)))))),w)*.
% 300.10/300.69  235359[7:SpR:13259.2,28980.1] || member(cross_product(u,v),ordinal_numbers) subclass(rest_relation,flip(w)) -> equal(cross_product(u,v),identity_relation) member(ordered_pair(ordered_pair(second(apply(choice,cross_product(u,v))),first(apply(choice,cross_product(u,v)))),rest_of(apply(choice,cross_product(u,v)))),w)*.
% 300.10/300.69  235493[7:SpR:13259.2,28979.1] || member(cross_product(u,v),ordinal_numbers) subclass(rest_relation,rotate(w)) -> equal(cross_product(u,v),identity_relation) member(ordered_pair(ordered_pair(second(apply(choice,cross_product(u,v))),rest_of(apply(choice,cross_product(u,v)))),first(apply(choice,cross_product(u,v)))),w)*.
% 300.10/300.69  235677[7:Res:13247.2,36719.1] operation(u) || member(intersection(v,cantor(u)),ordinal_numbers) -> equal(intersection(v,cantor(u)),identity_relation) equal(ordered_pair(first(apply(choice,intersection(v,cantor(u)))),second(apply(choice,intersection(v,cantor(u))))),apply(choice,intersection(v,cantor(u))))**.
% 300.10/300.69  235668[7:Res:13246.2,36719.1] operation(u) || member(intersection(cantor(u),v),ordinal_numbers) -> equal(intersection(cantor(u),v),identity_relation) equal(ordered_pair(first(apply(choice,intersection(cantor(u),v))),second(apply(choice,intersection(cantor(u),v)))),apply(choice,intersection(cantor(u),v)))**.
% 300.10/300.69  50404[0:Rew:3616.0,50357.4] || member(u,union(complement(v),complement(w)))* member(u,union(v,w)) subclass(symmetric_difference(complement(v),complement(w)),x)* well_ordering(y,x)* -> member(least(y,symmetric_difference(complement(v),complement(w))),symmetric_difference(complement(v),complement(w)))*.
% 300.10/300.69  48518[0:SpR:3597.0,3594.0] ||  -> equal(intersection(complement(symmetric_difference(complement(intersection(u,inverse(u))),symmetrization_of(u))),union(complement(symmetric_difference(u,inverse(u))),union(complement(intersection(u,inverse(u))),symmetrization_of(u)))),symmetric_difference(complement(symmetric_difference(u,inverse(u))),union(complement(intersection(u,inverse(u))),symmetrization_of(u))))**.
% 300.10/300.69  49682[5:Rew:6355.1,49673.3] || equal(compose(u,first(not_subclass_element(cross_product(v,w),x))),second(not_subclass_element(cross_product(v,w),x)))** member(not_subclass_element(cross_product(v,w),x),cross_product(ordinal_numbers,ordinal_numbers))* -> subclass(cross_product(v,w),x) member(not_subclass_element(cross_product(v,w),x),compose_class(u)).
% 300.10/300.69  53049[0:Rew:32.0,53018.5,32.0,53018.2,32.0,53018.0] || member(least(restrict(u,v,w),x),w)* member(y,v) member(ordered_pair(y,least(restrict(u,v,w),x)),u)* member(y,x) subclass(x,z)* well_ordering(restrict(u,v,w),z)* -> .
% 300.10/300.69  39740[0:Res:8551.2,131.3] || member(ordered_pair(u,least(restrict(v,w,x),y)),cross_product(w,x))* member(ordered_pair(u,least(restrict(v,w,x),y)),v)* member(u,y) subclass(y,z)* well_ordering(restrict(v,w,x),z)* -> .
% 300.10/300.69  53057[0:Rew:163.0,52970.4,163.0,52970.1] || member(ordered_pair(u,least(symmetric_difference(v,w),x)),union(v,w)) member(ordered_pair(u,least(symmetric_difference(v,w),x)),complement(intersection(v,w)))* member(u,x) subclass(x,y)* well_ordering(symmetric_difference(v,w),y)* -> .
% 300.10/300.69  48517[0:SpR:3596.0,3594.0] ||  -> equal(intersection(complement(symmetric_difference(complement(intersection(u,singleton(u))),successor(u))),union(complement(symmetric_difference(u,singleton(u))),union(complement(intersection(u,singleton(u))),successor(u)))),symmetric_difference(complement(symmetric_difference(u,singleton(u))),union(complement(intersection(u,singleton(u))),successor(u))))**.
% 300.10/300.69  49988[2:Res:9563.3,9878.0] || connected(u,v) well_ordering(cross_product(w,not_well_ordering(u,v)),v)* member(x,w)* member(x,not_well_ordering(u,v))* subclass(not_well_ordering(u,v),y) well_ordering(cross_product(w,not_well_ordering(u,v)),y)* -> well_ordering(u,v).
% 300.10/300.69  46630[5:Res:9618.2,21.0] || member(ordered_pair(u,v),cross_product(ordinal_numbers,ordinal_numbers)) subclass(composition_function,cross_product(w,x))* -> equal(ordered_pair(first(ordered_pair(u,ordered_pair(v,compose(u,v)))),second(ordered_pair(u,ordered_pair(v,compose(u,v))))),ordered_pair(u,ordered_pair(v,compose(u,v))))**.
% 300.10/300.69  199123[7:Res:13515.2,9878.0] || well_ordering(cross_product(u,compose(v,w)),cross_product(ordinal_numbers,ordinal_numbers))* member(x,u)* member(x,compose(v,w))* subclass(compose(v,w),y) well_ordering(cross_product(u,compose(v,w)),y)* -> equal(compose(v,w),identity_relation).
% 300.10/300.69  110025[5:Res:39298.1,10120.0] || subclass(ordinal_numbers,complement(complement(segment(u,v,w)))) homomorphism(x,restrict(u,v,singleton(w)),y)* -> equal(apply(y,ordered_pair(apply(x,z),apply(x,x1))),apply(x,apply(restrict(u,v,singleton(w)),ordered_pair(z,x1))))*.
% 300.10/300.69  52628[5:Rew:50855.1,52610.4] || member(singleton(u),subset_relation) member(ordered_pair(first(singleton(u)),ordered_pair(v,least(image(w,image(x,u)),y))),compose(w,x))* member(v,y) subclass(y,z)* well_ordering(image(w,image(x,u)),z)* -> .
% 300.10/300.69  52603[0:SpL:154.1,9880.0] || member(u,recursion_equation_functions(v)) member(ordered_pair(w,ordered_pair(x,least(image(v,image(rest_of(u),singleton(w))),y))),u)* member(x,y) subclass(y,z)* well_ordering(image(v,image(rest_of(u),singleton(w))),z)* -> .
% 300.10/300.69  51513[5:Res:51313.1,8803.0] || member(singleton(image(u,image(v,singleton(w)))),subset_relation) member(ordered_pair(w,first(singleton(image(u,image(v,singleton(w)))))),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(w,first(singleton(image(u,image(v,singleton(w)))))),compose(u,v))*.
% 300.10/300.69  139675[8:SpL:19860.0,117602.1] function(restrict(cross_product(u,ordinal_numbers),v,w)) || subclass(image(cross_product(v,w),u),cantor(cantor(x))) equal(cantor(cantor(y)),cantor(restrict(cross_product(u,ordinal_numbers),v,w))) -> compatible(restrict(cross_product(u,ordinal_numbers),v,w),y,x)*.
% 300.10/300.69  49073[5:Rew:481.0,49060.4] || member(u,ordinal_numbers) subclass(power_class(intersection(complement(v),complement(w))),x)* well_ordering(y,x)* -> member(u,image(element_relation,union(v,w)))* member(least(y,power_class(intersection(complement(v),complement(w)))),power_class(intersection(complement(v),complement(w))))*.
% 300.10/300.69  155450[8:Res:116127.5,941.1] operation(u) operation(v) || compatible(w,v,u) subclass(cantor(v),power_class(image(element_relation,complement(x)))) member(ordered_pair(not_homomorphism1(w,v,u),not_homomorphism2(w,v,u)),image(element_relation,power_class(x)))* -> homomorphism(w,v,u).
% 300.10/300.69  198937[8:Res:161565.3,9421.0] operation(u) || well_ordering(v,cantor(cantor(u))) member(w,x)* -> equal(range_of(u),identity_relation) equal(ordered_pair(first(ordered_pair(w,least(v,range_of(u)))),second(ordered_pair(w,least(v,range_of(u))))),ordered_pair(w,least(v,range_of(u))))**.
% 300.10/300.69  210260[8:MRR:210250.3,13039.0] || section(u,v,w) well_ordering(x,v) subclass(singleton(least(x,cantor(restrict(u,w,v)))),cantor(restrict(u,w,v))) -> section(x,singleton(least(x,cantor(restrict(u,w,v)))),cantor(restrict(u,w,v)))*.
% 300.10/300.69  212391[7:SpL:13259.2,40.0] || member(cross_product(u,v),ordinal_numbers) member(ordered_pair(apply(choice,cross_product(u,v)),w),flip(x)) -> equal(cross_product(u,v),identity_relation) member(ordered_pair(ordered_pair(second(apply(choice,cross_product(u,v))),first(apply(choice,cross_product(u,v)))),w),x)*.
% 300.10/300.69  212390[7:SpL:13259.2,37.0] || member(cross_product(u,v),ordinal_numbers) member(ordered_pair(apply(choice,cross_product(u,v)),w),rotate(x)) -> equal(cross_product(u,v),identity_relation) member(ordered_pair(ordered_pair(second(apply(choice,cross_product(u,v))),w),first(apply(choice,cross_product(u,v)))),x)*.
% 300.10/300.69  213670[8:SoR:117776.0,19277.2] single_valued_class(restrict(element_relation,ordinal_numbers,u)) || subclass(range_of(restrict(element_relation,ordinal_numbers,u)),cantor(sum_class(u)))* equal(cross_product(cantor(sum_class(u)),cantor(sum_class(u))),sum_class(u)) equal(restrict(element_relation,ordinal_numbers,u),identity_relation) -> operation(restrict(element_relation,ordinal_numbers,u)).
% 300.10/300.69  214137[7:Res:13529.2,5.0] || member(ordered_pair(u,regular(image(v,image(w,singleton(u))))),cross_product(ordinal_numbers,ordinal_numbers))* subclass(compose(v,w),x) -> equal(image(v,image(w,singleton(u))),identity_relation) member(ordered_pair(u,regular(image(v,image(w,singleton(u))))),x)*.
% 300.10/300.69  214901[25:Rew:208840.0,214892.2] || member(singleton(singleton(identity_relation)),segment(u,v,w)) homomorphism(x,restrict(u,v,singleton(w)),y)* -> equal(apply(y,ordered_pair(apply(x,identity_relation),apply(x,ordinal_numbers))),apply(x,apply(restrict(u,v,singleton(w)),singleton(singleton(identity_relation)))))*.
% 300.10/300.69  215903[7:Res:13530.3,8841.1] || member(image(u,image(v,singleton(w))),ordinal_numbers) member(ordered_pair(w,apply(choice,image(u,image(v,singleton(w))))),cross_product(ordinal_numbers,ordinal_numbers))* subclass(ordinal_numbers,complement(compose(u,v))) -> equal(image(u,image(v,singleton(w))),identity_relation).
% 300.10/300.69  215902[8:Res:13530.3,210517.1] || member(image(u,image(v,singleton(w))),ordinal_numbers) member(ordered_pair(w,apply(choice,image(u,image(v,singleton(w))))),cross_product(ordinal_numbers,ordinal_numbers))* equal(complement(compose(u,v)),ordinal_numbers) -> equal(image(u,image(v,singleton(w))),identity_relation).
% 300.10/300.69  215972[21:SpL:10130.4,198470.1] operation(u) function(v) || compatible(w,x,u) homomorphism(v,x,y) equal(rest_of(apply(y,ordered_pair(apply(v,not_homomorphism1(w,x,u)),apply(v,not_homomorphism2(w,x,u))))),rest_relation)** -> homomorphism(w,x,u).
% 300.10/300.69  224626[10:Rew:223660.1,224530.4] || subclass(element_relation,identity_relation) member(ordered_pair(cross_product(ordinal_numbers,ordinal_numbers),u),compose(v,w))* subclass(image(v,image(w,identity_relation)),x)* well_ordering(y,x)* -> member(least(y,image(v,image(w,identity_relation))),image(v,image(w,identity_relation)))*.
% 300.10/300.69  226323[8:Rew:19860.0,226309.2] operation(restrict(cross_product(u,ordinal_numbers),v,w)) || well_ordering(x,cantor(cantor(restrict(cross_product(u,ordinal_numbers),v,w)))) -> equal(image(cross_product(v,w),u),identity_relation) member(least(x,image(cross_product(v,w),u)),image(cross_product(v,w),u))*.
% 300.10/300.69  227366[7:Rew:192979.1,227339.2,192979.1,227339.0] || member(ordered_pair(u,regular(image(v,range_of(identity_relation)))),cross_product(ordinal_numbers,ordinal_numbers)) -> equal(cross_product(singleton(u),ordinal_numbers),identity_relation) equal(image(v,range_of(identity_relation)),identity_relation) member(ordered_pair(u,regular(image(v,range_of(identity_relation)))),compose(v,regular(cross_product(singleton(u),ordinal_numbers))))*.
% 300.10/300.69  227371[7:Rew:192979.1,227344.2,192979.1,227344.0] || member(ordered_pair(u,not_subclass_element(range_of(identity_relation),v)),cross_product(ordinal_numbers,ordinal_numbers)) -> equal(cross_product(image(w,singleton(u)),ordinal_numbers),identity_relation) subclass(range_of(identity_relation),v) member(ordered_pair(u,not_subclass_element(range_of(identity_relation),v)),compose(regular(cross_product(image(w,singleton(u)),ordinal_numbers)),w))*.
% 300.10/300.69  227374[15:MRR:227373.0,165460.0] || member(ordered_pair(u,apply(choice,range_of(identity_relation))),cross_product(ordinal_numbers,ordinal_numbers)) -> equal(cross_product(image(v,singleton(u)),ordinal_numbers),identity_relation) equal(range_of(identity_relation),identity_relation) member(ordered_pair(u,apply(choice,range_of(identity_relation))),compose(regular(cross_product(image(v,singleton(u)),ordinal_numbers)),v))*.
% 300.10/300.69  231247[7:SpR:3594.0,17447.1] ||  -> equal(symmetric_difference(complement(symmetric_difference(u,v)),union(complement(intersection(u,v)),union(u,v))),identity_relation) member(regular(symmetric_difference(complement(symmetric_difference(u,v)),union(complement(intersection(u,v)),union(u,v)))),complement(symmetric_difference(complement(intersection(u,v)),union(u,v))))*.
% 300.10/300.69  233961[8:Res:116127.5,161200.0] operation(u) operation(v) || compatible(w,v,u) subclass(cantor(v),image(element_relation,union(x,identity_relation))) member(ordered_pair(not_homomorphism1(w,v,u),not_homomorphism2(w,v,u)),power_class(symmetric_difference(ordinal_numbers,x)))* -> homomorphism(w,v,u).
% 300.10/300.69  235428[5:Res:28980.1,8803.0] || subclass(rest_relation,flip(image(u,image(v,singleton(w))))) member(ordered_pair(w,ordered_pair(ordered_pair(x,y),rest_of(ordered_pair(y,x)))),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(w,ordered_pair(ordered_pair(x,y),rest_of(ordered_pair(y,x)))),compose(u,v))*.
% 300.10/300.69  235556[5:Res:28979.1,8803.0] || subclass(rest_relation,rotate(image(u,image(v,singleton(w))))) member(ordered_pair(w,ordered_pair(ordered_pair(x,rest_of(ordered_pair(y,x))),y)),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(w,ordered_pair(ordered_pair(x,rest_of(ordered_pair(y,x))),y)),compose(u,v))*.
% 300.10/300.69  49972[0:Res:27.2,9878.0] || member(least(cross_product(u,intersection(v,w)),x),w)* member(least(cross_product(u,intersection(v,w)),x),v)* member(y,u)* member(y,x)* subclass(x,z)* well_ordering(cross_product(u,intersection(v,w)),z)* -> .
% 300.10/300.69  69383[8:Res:69184.1,9872.0] || member(ordered_pair(u,least(intersection(v,compose(element_relation,ordinal_numbers)),w)),element_relation)* member(ordered_pair(u,least(intersection(v,compose(element_relation,ordinal_numbers)),w)),v)* member(u,w) subclass(w,x)* well_ordering(intersection(v,compose(element_relation,ordinal_numbers)),x)* -> .
% 300.10/300.69  116269[8:Rew:116078.0,49633.0] || member(first(not_subclass_element(cross_product(u,v),w)),cantor(x)) equal(restrict(x,first(not_subclass_element(cross_product(u,v),w)),ordinal_numbers),second(not_subclass_element(cross_product(u,v),w)))** -> subclass(cross_product(u,v),w) member(not_subclass_element(cross_product(u,v),w),rest_of(x)).
% 300.10/300.69  139832[5:MRR:139803.0,8667.0] || member(ordered_pair(u,least(intersection(v,union(w,x)),y)),v)* member(u,y) subclass(y,z)* well_ordering(intersection(v,union(w,x)),z)* -> member(ordered_pair(u,least(intersection(v,union(w,x)),y)),complement(x))*.
% 300.10/300.69  139915[5:MRR:139889.0,8667.0] || member(ordered_pair(u,least(intersection(v,union(w,x)),y)),v)* member(u,y) subclass(y,z)* well_ordering(intersection(v,union(w,x)),z)* -> member(ordered_pair(u,least(intersection(v,union(w,x)),y)),complement(w))*.
% 300.10/300.69  140477[0:Rew:3594.0,140336.1] || member(not_subclass_element(union(complement(intersection(u,v)),union(u,v)),symmetric_difference(complement(intersection(u,v)),union(u,v))),complement(symmetric_difference(u,v)))* -> subclass(union(complement(intersection(u,v)),union(u,v)),symmetric_difference(complement(intersection(u,v)),union(u,v))).
% 300.10/300.69  155853[8:SpL:155653.0,116116.1] || member(ordinal_numbers,cantor(complement(compose(complement(element_relation),inverse(element_relation))))) equal(least(rest_of(complement(compose(complement(element_relation),inverse(element_relation)))),u),subset_relation)** member(ordinal_numbers,u) subclass(u,v)* well_ordering(rest_of(complement(compose(complement(element_relation),inverse(element_relation)))),v)* -> .
% 300.10/300.70  47001[2:Res:9563.3,9421.0] || connected(u,v) well_ordering(w,v) member(x,y)* -> well_ordering(u,v) equal(ordered_pair(first(ordered_pair(x,least(w,not_well_ordering(u,v)))),second(ordered_pair(x,least(w,not_well_ordering(u,v))))),ordered_pair(x,least(w,not_well_ordering(u,v))))**.
% 300.10/300.70  139793[5:Res:39529.1,9878.0] || member(least(cross_product(u,union(v,w)),x),ordinal_numbers) member(y,u)* member(y,x)* subclass(x,z)* well_ordering(cross_product(u,union(v,w)),z)* -> member(least(cross_product(u,union(v,w)),x),complement(w))*.
% 300.10/300.70  139879[5:Res:39530.1,9878.0] || member(least(cross_product(u,union(v,w)),x),ordinal_numbers) member(y,u)* member(y,x)* subclass(x,z)* well_ordering(cross_product(u,union(v,w)),z)* -> member(least(cross_product(u,union(v,w)),x),complement(v))*.
% 300.10/300.70  53020[5:Res:41098.2,9872.0] || member(least(intersection(u,element_relation),v),ordinal_numbers) member(w,least(intersection(u,element_relation),v)) member(ordered_pair(w,least(intersection(u,element_relation),v)),u)* member(w,v) subclass(v,x)* well_ordering(intersection(u,element_relation),x)* -> .
% 300.10/300.70  199119[7:Res:13515.2,9421.0] || well_ordering(u,cross_product(ordinal_numbers,ordinal_numbers)) member(v,w)* -> equal(compose(x,y),identity_relation) equal(ordered_pair(first(ordered_pair(v,least(u,compose(x,y)))),second(ordered_pair(v,least(u,compose(x,y))))),ordered_pair(v,least(u,compose(x,y))))**.
% 300.10/300.70  116530[8:Rew:116078.0,113751.3] operation(u) operation(v) || compatible(w,v,u) subclass(cantor(v),omega) -> homomorphism(w,v,u) equal(integer_of(ordered_pair(not_homomorphism1(w,v,u),not_homomorphism2(w,v,u))),ordered_pair(not_homomorphism1(w,v,u),not_homomorphism2(w,v,u)))**.
% 300.10/300.70  54294[5:Rew:50855.1,54276.4] || member(singleton(u),subset_relation) member(ordered_pair(first(singleton(u)),v),compose(w,x))* subclass(image(w,image(x,u)),y)* well_ordering(z,y)* -> member(least(z,image(w,image(x,u))),image(w,image(x,u)))*.
% 300.10/300.70  47526[0:Res:62.1,8562.0] || member(ordered_pair(u,not_subclass_element(v,intersection(w,image(x,image(y,singleton(u)))))),compose(x,y))* member(not_subclass_element(v,intersection(w,image(x,image(y,singleton(u))))),w)* -> subclass(v,intersection(w,image(x,image(y,singleton(u))))).
% 300.10/300.70  80754[5:Res:60219.0,8803.0] || member(ordered_pair(u,not_subclass_element(v,complement(image(w,image(x,singleton(u)))))),cross_product(ordinal_numbers,ordinal_numbers)) -> subclass(v,complement(image(w,image(x,singleton(u))))) member(ordered_pair(u,not_subclass_element(v,complement(image(w,image(x,singleton(u)))))),compose(w,x))*.
% 300.10/300.70  49980[0:Res:62.1,9878.0] || member(ordered_pair(u,least(cross_product(v,image(w,image(x,singleton(u)))),y)),compose(w,x))* member(z,v)* member(z,y)* subclass(y,x1)* well_ordering(cross_product(v,image(w,image(x,singleton(u)))),x1)* -> .
% 300.10/300.70  50577[0:SpL:159.0,8632.1] || well_ordering(element_relation,image(recursion(u,successor_relation,union_of_range_map),singleton(v))) subclass(ordinal_add(u,v),image(recursion(u,successor_relation,union_of_range_map),singleton(v)))* -> equal(image(recursion(u,successor_relation,union_of_range_map),singleton(v)),ordinal_numbers) member(image(recursion(u,successor_relation,union_of_range_map),singleton(v)),ordinal_numbers).
% 300.10/300.70  117811[8:Rew:116078.0,116274.2,116078.0,116274.2,116078.0,116274.1,116078.0,116274.1] single_valued_class(restrict(u,v,ordinal_numbers)) || subclass(image(u,v),cantor(cantor(w))) equal(cantor(cantor(x)),cantor(restrict(u,v,ordinal_numbers))) equal(restrict(u,v,ordinal_numbers),cross_product(ordinal_numbers,ordinal_numbers)) -> compatible(restrict(u,v,ordinal_numbers),x,w)*.
% 300.10/300.70  139677[8:SpL:19860.0,117617.1] function(restrict(cross_product(u,ordinal_numbers),v,w)) || subclass(image(cross_product(v,w),u),cantor(range_of(x))) equal(cantor(cantor(y)),cantor(restrict(cross_product(u,ordinal_numbers),v,w))) -> compatible(restrict(cross_product(u,ordinal_numbers),v,w),y,inverse(x))*.
% 300.10/300.70  208220[7:Res:13333.3,9878.0] inductive(u) || well_ordering(cross_product(v,image(successor_relation,u)),u)* member(w,v)* member(w,image(successor_relation,u))* subclass(image(successor_relation,u),x) well_ordering(cross_product(v,image(successor_relation,u)),x)* -> equal(image(successor_relation,u),identity_relation).
% 300.10/300.70  208485[7:SpR:13260.1,9706.3] || member(second(regular(cross_product(u,v))),ordinal_numbers)* member(first(regular(cross_product(u,v))),ordinal_numbers) equal(successor(first(regular(cross_product(u,v)))),second(regular(cross_product(u,v)))) -> equal(cross_product(u,v),identity_relation) member(regular(cross_product(u,v)),successor_relation).
% 300.10/300.70  213503[8:Rew:145761.0,213482.1] function(cross_product(u,singleton(v))) || subclass(range_of(cross_product(u,singleton(v))),cantor(segment(ordinal_numbers,u,v))) equal(cross_product(cantor(segment(ordinal_numbers,u,v)),cantor(segment(ordinal_numbers,u,v))),segment(ordinal_numbers,u,v))** -> operation(cross_product(u,singleton(v))).
% 300.10/300.70  214328[25:Rew:208887.0,214297.1] function(restrict(u,v,identity_relation)) || subclass(range_of(restrict(u,v,identity_relation)),cantor(segment(u,v,ordinal_numbers))) equal(cross_product(cantor(segment(u,v,ordinal_numbers)),cantor(segment(u,v,ordinal_numbers))),segment(u,v,ordinal_numbers))** -> operation(restrict(u,v,identity_relation)).
% 300.10/300.70  214708[8:Rew:117511.1,214667.2] operation(u) || transitive(v,cantor(cantor(u))) well_ordering(w,intersection(cantor(u),v)) -> equal(segment(w,compose(intersection(cantor(u),v),intersection(cantor(u),v)),least(w,compose(intersection(cantor(u),v),intersection(cantor(u),v)))),identity_relation)**.
% 300.10/300.70  214812[21:Rew:197474.0,214789.2,197474.0,214789.0] || member(ordered_pair(inverse(u),not_subclass_element(image(v,image(w,identity_relation)),x)),cross_product(ordinal_numbers,ordinal_numbers)) -> equal(range_of(u),identity_relation) subclass(image(v,image(w,identity_relation)),x) member(ordered_pair(inverse(u),not_subclass_element(image(v,image(w,identity_relation)),x)),compose(v,w))*.
% 300.10/300.70  224627[10:Rew:223660.1,224427.2,223660.1,224427.1] || subclass(element_relation,identity_relation) member(ordered_pair(cross_product(ordinal_numbers,ordinal_numbers),regular(image(u,image(v,identity_relation)))),cross_product(ordinal_numbers,ordinal_numbers)) -> equal(image(u,image(v,identity_relation)),identity_relation) member(ordered_pair(cross_product(ordinal_numbers,ordinal_numbers),regular(image(u,image(v,identity_relation)))),compose(u,v))*.
% 300.10/300.70  227363[7:Rew:192979.1,227351.3] || member(ordered_pair(u,ordered_pair(v,least(image(w,range_of(identity_relation)),x))),compose(w,regular(cross_product(singleton(u),ordinal_numbers))))* member(v,x) subclass(x,y)* well_ordering(image(w,range_of(identity_relation)),y)* -> equal(cross_product(singleton(u),ordinal_numbers),identity_relation).
% 300.10/300.70  227365[7:Rew:192979.1,227356.3] || member(ordered_pair(u,ordered_pair(v,least(range_of(identity_relation),w))),compose(regular(cross_product(image(x,singleton(u)),ordinal_numbers)),x))* member(v,w) subclass(w,y)* well_ordering(range_of(identity_relation),y)* -> equal(cross_product(image(x,singleton(u)),ordinal_numbers),identity_relation).
% 300.10/300.70  227367[7:Rew:192979.1,227348.4] || member(ordered_pair(u,v),compose(w,regular(cross_product(singleton(u),ordinal_numbers))))* subclass(image(w,range_of(identity_relation)),x)* well_ordering(y,x)* -> equal(cross_product(singleton(u),ordinal_numbers),identity_relation) member(least(y,image(w,range_of(identity_relation))),image(w,range_of(identity_relation)))*.
% 300.10/300.70  234832[8:Res:193440.1,9878.0] || member(least(cross_product(u,cantor(v)),w),ordinal_numbers) member(x,u)* member(x,w)* subclass(w,y)* well_ordering(cross_product(u,cantor(v)),y)* -> equal(apply(v,least(cross_product(u,cantor(v)),w)),sum_class(range_of(identity_relation)))**.
% 300.10/300.70  234908[8:MRR:234844.0,8667.0] || member(ordered_pair(u,least(intersection(v,cantor(w)),x)),v)* member(u,x) subclass(x,y)* well_ordering(intersection(v,cantor(w)),y)* -> equal(apply(w,ordered_pair(u,least(intersection(v,cantor(w)),x))),sum_class(range_of(identity_relation)))**.
% 300.10/300.70  235301[8:Res:230445.1,9872.0] || member(ordered_pair(u,least(intersection(v,union(w,identity_relation)),x)),w)* member(ordered_pair(u,least(intersection(v,union(w,identity_relation)),x)),v)* member(u,x) subclass(x,y)* well_ordering(intersection(v,union(w,identity_relation)),y)* -> .
% 300.10/300.70  235465[5:Res:28980.1,10118.0] || subclass(rest_relation,flip(range_of(u))) homomorphism(v,inverse(u),w)* -> equal(apply(w,ordered_pair(apply(v,ordered_pair(x,y)),apply(v,rest_of(ordered_pair(y,x))))),apply(v,apply(inverse(u),ordered_pair(ordered_pair(x,y),rest_of(ordered_pair(y,x))))))*.
% 300.10/300.70  235597[5:Res:28979.1,10118.0] || subclass(rest_relation,rotate(range_of(u))) homomorphism(v,inverse(u),w)* -> equal(apply(w,ordered_pair(apply(v,ordered_pair(x,rest_of(ordered_pair(y,x)))),apply(v,y))),apply(v,apply(inverse(u),ordered_pair(ordered_pair(x,rest_of(ordered_pair(y,x))),y))))*.
% 300.10/300.70  50408[0:Rew:3603.0,50330.4] || member(u,union(v,cross_product(w,x)))* member(u,complement(restrict(v,w,x))) subclass(symmetric_difference(v,cross_product(w,x)),y)* well_ordering(z,y)* -> member(least(z,symmetric_difference(v,cross_product(w,x))),symmetric_difference(v,cross_product(w,x)))*.
% 300.10/300.70  50407[0:Rew:3606.0,50331.4] || member(u,union(cross_product(v,w),x))* member(u,complement(restrict(x,v,w))) subclass(symmetric_difference(cross_product(v,w),x),y)* well_ordering(z,y)* -> member(least(z,symmetric_difference(cross_product(v,w),x)),symmetric_difference(cross_product(v,w),x))*.
% 300.10/300.70  53053[0:Rew:963.0,53002.1] || member(singleton(singleton(singleton(least(intersection(u,v),w)))),v)* member(singleton(singleton(singleton(least(intersection(u,v),w)))),u)* member(singleton(least(intersection(u,v),w)),w)* subclass(w,x)* well_ordering(intersection(u,v),x)* -> .
% 300.10/300.70  156401[5:SpR:155665.0,3594.0] ||  -> equal(intersection(complement(symmetric_difference(complement(subset_relation),union(subset_relation,cross_product(ordinal_numbers,ordinal_numbers)))),union(complement(symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers))),union(complement(subset_relation),union(subset_relation,cross_product(ordinal_numbers,ordinal_numbers))))),symmetric_difference(complement(symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers))),union(complement(subset_relation),union(subset_relation,cross_product(ordinal_numbers,ordinal_numbers)))))**.
% 300.10/300.70  156510[5:SpR:155666.0,3594.0] ||  -> equal(intersection(complement(symmetric_difference(complement(subset_relation),union(cross_product(ordinal_numbers,ordinal_numbers),subset_relation))),union(complement(symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation)),union(complement(subset_relation),union(cross_product(ordinal_numbers,ordinal_numbers),subset_relation)))),symmetric_difference(complement(symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation)),union(complement(subset_relation),union(cross_product(ordinal_numbers,ordinal_numbers),subset_relation))))**.
% 300.10/300.70  117818[8:Rew:116078.0,116871.5,116078.0,116871.2] operation(u) || member(ordered_pair(v,least(intersection(w,cantor(u)),x)),w)* member(ordered_pair(v,least(intersection(cantor(u),w),x)),cantor(u))* member(v,x) subclass(x,y)* well_ordering(intersection(cantor(u),w),y)* -> .
% 300.10/300.70  117819[8:Rew:116078.0,116872.5,116078.0,116872.1] operation(u) || member(ordered_pair(v,least(intersection(cantor(u),w),x)),cantor(u))* member(ordered_pair(v,least(intersection(w,cantor(u)),x)),w)* member(v,x) subclass(x,y)* well_ordering(intersection(w,cantor(u)),y)* -> .
% 300.10/300.70  53052[5:MRR:53021.1,41096.1] || member(least(intersection(u,successor_relation),v),ordinal_numbers) equal(successor(w),least(intersection(u,successor_relation),v)) member(ordered_pair(w,least(intersection(u,successor_relation),v)),u)* member(w,v) subclass(v,x)* well_ordering(intersection(u,successor_relation),x)* -> .
% 300.10/300.70  50888[5:Res:10093.3,131.3] || member(least(rotate(u),v),ordinal_numbers) member(ordered_pair(w,x),cross_product(ordinal_numbers,ordinal_numbers)) member(ordered_pair(ordered_pair(x,least(rotate(u),v)),w),u)* member(ordered_pair(w,x),v) subclass(v,y)* well_ordering(rotate(u),y)* -> .
% 300.10/300.70  50965[5:Res:10061.3,131.3] || member(least(flip(u),v),ordinal_numbers) member(ordered_pair(w,x),cross_product(ordinal_numbers,ordinal_numbers)) member(ordered_pair(ordered_pair(x,w),least(flip(u),v)),u)* member(ordered_pair(w,x),v) subclass(v,y)* well_ordering(flip(u),y)* -> .
% 300.10/300.70  116909[8:Rew:116078.0,46664.2] operation(u) || member(ordered_pair(v,w),cross_product(ordinal_numbers,ordinal_numbers)) subclass(composition_function,cantor(u))* -> equal(ordered_pair(first(ordered_pair(v,ordered_pair(w,compose(v,w)))),second(ordered_pair(v,ordered_pair(w,compose(v,w))))),ordered_pair(v,ordered_pair(w,compose(v,w))))**.
% 300.10/300.70  194510[8:Res:163112.0,9872.0] || member(ordered_pair(u,least(intersection(v,complement(inverse(identity_relation))),w)),v)* member(u,w) subclass(w,x)* well_ordering(intersection(v,complement(inverse(identity_relation))),x)* -> subclass(singleton(ordered_pair(u,least(intersection(v,complement(inverse(identity_relation))),w))),symmetrization_of(identity_relation))*.
% 300.10/300.70  195648[16:Rew:195224.0,195219.4] || member(ordered_pair(u,least(intersection(v,complement(singleton(identity_relation))),w)),v)* member(u,w) subclass(w,x)* well_ordering(intersection(v,complement(singleton(identity_relation))),x)* -> subclass(singleton(ordered_pair(u,least(intersection(v,complement(singleton(identity_relation))),w))),singleton(identity_relation))*.
% 300.10/300.70  54478[5:Rew:18840.1,54463.3] || member(u,subset_relation) member(u,segment(v,w,x)) homomorphism(y,restrict(v,w,singleton(x)),z)* -> equal(apply(z,ordered_pair(apply(y,first(u)),apply(y,second(u)))),apply(y,apply(restrict(v,w,singleton(x)),u)))*.
% 300.10/300.70  83299[7:Res:61019.0,8803.0] || member(ordered_pair(u,regular(complement(complement(image(v,image(w,singleton(u))))))),cross_product(ordinal_numbers,ordinal_numbers)) -> equal(complement(complement(image(v,image(w,singleton(u))))),identity_relation) member(ordered_pair(u,regular(complement(complement(image(v,image(w,singleton(u))))))),compose(v,w))*.
% 300.10/300.70  54324[5:Res:9997.2,5.0] || member(ordered_pair(u,not_subclass_element(image(v,image(w,singleton(u))),x)),cross_product(ordinal_numbers,ordinal_numbers))* subclass(compose(v,w),y) -> subclass(image(v,image(w,singleton(u))),x) member(ordered_pair(u,not_subclass_element(image(v,image(w,singleton(u))),x)),y)*.
% 300.10/300.70  17404[7:Res:13248.1,8803.0] || member(ordered_pair(u,regular(intersection(image(v,image(w,singleton(u))),x))),cross_product(ordinal_numbers,ordinal_numbers)) -> equal(intersection(image(v,image(w,singleton(u))),x),identity_relation) member(ordered_pair(u,regular(intersection(image(v,image(w,singleton(u))),x))),compose(v,w))*.
% 300.10/300.70  13583[7:Rew:13036.0,13028.1] || member(ordered_pair(u,regular(intersection(v,image(w,image(x,singleton(u)))))),cross_product(ordinal_numbers,ordinal_numbers)) -> equal(intersection(v,image(w,image(x,singleton(u)))),identity_relation) member(ordered_pair(u,regular(intersection(v,image(w,image(x,singleton(u)))))),compose(w,x))*.
% 300.10/300.70  131211[5:Res:39607.2,8803.0] inductive(image(u,image(v,singleton(w)))) || well_ordering(x,ordinal_numbers) member(ordered_pair(w,least(x,image(u,image(v,singleton(w))))),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(w,least(x,image(u,image(v,singleton(w))))),compose(u,v))*.
% 300.10/300.70  18713[7:Res:13237.2,8803.0] || well_ordering(u,ordinal_numbers) member(ordered_pair(v,least(u,image(w,image(x,singleton(v))))),cross_product(ordinal_numbers,ordinal_numbers)) -> equal(image(w,image(x,singleton(v))),identity_relation) member(ordered_pair(v,least(u,image(w,image(x,singleton(v))))),compose(w,x))*.
% 300.10/300.70  117815[8:Rew:116078.0,116318.2] single_valued_class(restrict(element_relation,ordinal_numbers,u)) || subclass(range_of(restrict(element_relation,ordinal_numbers,u)),cantor(sum_class(u)))* equal(cross_product(cantor(sum_class(u)),cantor(sum_class(u))),sum_class(u)) equal(restrict(element_relation,ordinal_numbers,u),cross_product(ordinal_numbers,ordinal_numbers)) -> operation(restrict(element_relation,ordinal_numbers,u)).
% 300.10/300.70  208215[7:Res:13333.3,9421.0] inductive(u) || well_ordering(v,u) member(w,x)* -> equal(image(successor_relation,u),identity_relation) equal(ordered_pair(first(ordered_pair(w,least(v,image(successor_relation,u)))),second(ordered_pair(w,least(v,image(successor_relation,u))))),ordered_pair(w,least(v,image(successor_relation,u))))**.
% 300.10/300.70  208486[7:SpR:13260.1,9837.3] || member(second(regular(cross_product(u,v))),ordinal_numbers) member(first(regular(cross_product(u,v))),ordinal_numbers) equal(sum_class(range_of(first(regular(cross_product(u,v))))),second(regular(cross_product(u,v))))** -> equal(cross_product(u,v),identity_relation) member(regular(cross_product(u,v)),union_of_range_map).
% 300.10/300.70  210305[8:Res:140864.1,9872.0] || member(ordered_pair(u,least(intersection(v,symmetric_difference(ordinal_numbers,w)),x)),complement(w))* member(ordered_pair(u,least(intersection(v,symmetric_difference(ordinal_numbers,w)),x)),v)* member(u,x) subclass(x,y)* well_ordering(intersection(v,symmetric_difference(ordinal_numbers,w)),y)* -> .
% 300.10/300.70  212359[7:SpR:13259.2,41098.2] || member(cross_product(u,v),ordinal_numbers) member(second(apply(choice,cross_product(u,v))),ordinal_numbers) member(first(apply(choice,cross_product(u,v))),second(apply(choice,cross_product(u,v))))* -> equal(cross_product(u,v),identity_relation) member(apply(choice,cross_product(u,v)),element_relation).
% 300.10/300.70  214135[7:Res:13529.2,129.0] || member(ordered_pair(u,regular(image(v,image(w,singleton(u))))),cross_product(ordinal_numbers,ordinal_numbers))* subclass(compose(v,w),x)* well_ordering(y,x)* -> equal(image(v,image(w,singleton(u))),identity_relation) member(least(y,compose(v,w)),compose(v,w))*.
% 300.10/300.70  214123[7:SpR:154.1,13529.2] || member(u,recursion_equation_functions(v)) member(ordered_pair(w,regular(image(v,image(rest_of(u),singleton(w))))),cross_product(ordinal_numbers,ordinal_numbers))* -> equal(image(v,image(rest_of(u),singleton(w))),identity_relation) member(ordered_pair(w,regular(image(v,image(rest_of(u),singleton(w))))),u)*.
% 300.10/300.70  214151[7:Rew:50855.1,214125.2,50855.1,214125.1] || member(singleton(u),subset_relation) member(ordered_pair(first(singleton(u)),regular(image(v,image(w,u)))),cross_product(ordinal_numbers,ordinal_numbers)) -> equal(image(v,image(w,u)),identity_relation) member(ordered_pair(first(singleton(u)),regular(image(v,image(w,u)))),compose(v,w))*.
% 300.10/300.70  214895[21:Res:196416.2,10120.0] || member(u,ordinal_numbers) subclass(domain_relation,segment(v,w,x)) homomorphism(y,restrict(v,w,singleton(x)),z)* -> equal(apply(z,ordered_pair(apply(y,u),apply(y,identity_relation))),apply(y,apply(restrict(v,w,singleton(x)),ordered_pair(u,identity_relation))))*.
% 300.10/300.70  227368[7:Rew:192979.1,227340.2,192979.1,227340.0] || member(ordered_pair(u,not_subclass_element(image(v,range_of(identity_relation)),w)),cross_product(ordinal_numbers,ordinal_numbers)) -> equal(cross_product(singleton(u),ordinal_numbers),identity_relation) subclass(image(v,range_of(identity_relation)),w) member(ordered_pair(u,not_subclass_element(image(v,range_of(identity_relation)),w)),compose(v,regular(cross_product(singleton(u),ordinal_numbers))))*.
% 300.10/300.70  230427[8:Res:161066.1,9878.0] || member(least(cross_product(u,symmetric_difference(ordinal_numbers,v)),w),ordinal_numbers) member(x,u)* member(x,w)* subclass(w,y)* well_ordering(cross_product(u,symmetric_difference(ordinal_numbers,v)),y)* -> member(least(cross_product(u,symmetric_difference(ordinal_numbers,v)),w),union(v,identity_relation))*.
% 300.10/300.70  230486[8:MRR:230435.0,8667.0] || member(ordered_pair(u,least(intersection(v,symmetric_difference(ordinal_numbers,w)),x)),v)* member(u,x) subclass(x,y)* well_ordering(intersection(v,symmetric_difference(ordinal_numbers,w)),y)* -> member(ordered_pair(u,least(intersection(v,symmetric_difference(ordinal_numbers,w)),x)),union(w,identity_relation))*.
% 300.10/300.70  48501[0:SpR:482.0,3594.0] ||  -> equal(intersection(complement(symmetric_difference(intersection(complement(u),complement(v)),w)),union(complement(intersection(intersection(complement(u),complement(v)),w)),complement(intersection(union(u,v),complement(w))))),symmetric_difference(complement(intersection(intersection(complement(u),complement(v)),w)),complement(intersection(union(u,v),complement(w)))))**.
% 300.10/300.70  48500[0:SpR:483.0,3594.0] ||  -> equal(intersection(complement(symmetric_difference(u,intersection(complement(v),complement(w)))),union(complement(intersection(u,intersection(complement(v),complement(w)))),complement(intersection(complement(u),union(v,w))))),symmetric_difference(complement(intersection(u,intersection(complement(v),complement(w)))),complement(intersection(complement(u),union(v,w)))))**.
% 300.10/300.70  53059[0:Rew:3597.0,52972.4,3597.0,52972.1] || member(ordered_pair(u,least(symmetric_difference(v,inverse(v)),w)),symmetrization_of(v)) member(ordered_pair(u,least(symmetric_difference(v,inverse(v)),w)),complement(intersection(v,inverse(v))))* member(u,w) subclass(w,x)* well_ordering(symmetric_difference(v,inverse(v)),x)* -> .
% 300.10/300.70  53060[0:Rew:3596.0,52971.4,3596.0,52971.1] || member(ordered_pair(u,least(symmetric_difference(v,singleton(v)),w)),successor(v)) member(ordered_pair(u,least(symmetric_difference(v,singleton(v)),w)),complement(intersection(v,singleton(v))))* member(u,w) subclass(w,x)* well_ordering(symmetric_difference(v,singleton(v)),x)* -> .
% 300.10/300.70  54477[0:Rew:963.0,54461.2] || member(singleton(singleton(singleton(u))),segment(v,w,x)) homomorphism(y,restrict(v,w,singleton(x)),z)* -> equal(apply(z,ordered_pair(apply(y,singleton(u)),apply(y,u))),apply(y,apply(restrict(v,w,singleton(x)),singleton(singleton(singleton(u))))))*.
% 300.10/300.70  197672[7:Res:13247.2,8554.1] || member(intersection(u,complement(intersection(v,w))),ordinal_numbers) member(apply(choice,intersection(u,complement(intersection(v,w)))),union(v,w)) -> equal(intersection(u,complement(intersection(v,w))),identity_relation) member(apply(choice,intersection(u,complement(intersection(v,w)))),symmetric_difference(v,w))*.
% 300.10/300.70  197384[7:Res:13246.2,8554.1] || member(intersection(complement(intersection(u,v)),w),ordinal_numbers) member(apply(choice,intersection(complement(intersection(u,v)),w)),union(u,v)) -> equal(intersection(complement(intersection(u,v)),w),identity_relation) member(apply(choice,intersection(complement(intersection(u,v)),w)),symmetric_difference(u,v))*.
% 300.10/300.70  54323[5:Res:9997.2,129.0] || member(ordered_pair(u,not_subclass_element(image(v,image(w,singleton(u))),x)),cross_product(ordinal_numbers,ordinal_numbers))* subclass(compose(v,w),y)* well_ordering(z,y)* -> subclass(image(v,image(w,singleton(u))),x) member(least(z,compose(v,w)),compose(v,w))*.
% 300.10/300.70  198341[5:MRR:198338.1,41096.1] || member(least(intersection(u,union_of_range_map),v),ordinal_numbers) equal(sum_class(range_of(w)),least(intersection(u,union_of_range_map),v)) member(ordered_pair(w,least(intersection(u,union_of_range_map),v)),u)* member(w,v) subclass(v,x)* well_ordering(intersection(u,union_of_range_map),x)* -> .
% 300.10/300.70  208484[7:SpR:13260.1,9865.3] || member(second(regular(cross_product(u,v))),ordinal_numbers) member(first(regular(cross_product(u,v))),ordinal_numbers) equal(compose(w,first(regular(cross_product(u,v)))),second(regular(cross_product(u,v))))** -> equal(cross_product(u,v),identity_relation) member(regular(cross_product(u,v)),compose_class(w)).
% 300.10/300.70  211602[7:Res:10093.3,13362.0] || member(u,ordinal_numbers) member(ordered_pair(v,w),cross_product(ordinal_numbers,ordinal_numbers)) member(ordered_pair(ordered_pair(w,u),v),x) subclass(rotate(x),y)* well_ordering(omega,y) -> equal(integer_of(ordered_pair(ordered_pair(ordered_pair(v,w),u),least(omega,rotate(x)))),identity_relation)**.
% 300.10/300.70  211975[7:Res:10061.3,13362.0] || member(u,ordinal_numbers) member(ordered_pair(v,w),cross_product(ordinal_numbers,ordinal_numbers)) member(ordered_pair(ordered_pair(w,v),u),x) subclass(flip(x),y)* well_ordering(omega,y) -> equal(integer_of(ordered_pair(ordered_pair(ordered_pair(v,w),u),least(omega,flip(x)))),identity_relation)**.
% 300.10/300.70  212420[7:Rew:13259.2,212400.4] || member(cross_product(u,v),ordinal_numbers) member(first(apply(choice,cross_product(u,v))),second(apply(choice,cross_product(u,v))))* member(apply(choice,cross_product(u,v)),cross_product(ordinal_numbers,ordinal_numbers)) -> equal(cross_product(u,v),identity_relation) member(apply(choice,cross_product(u,v)),element_relation).
% 300.10/300.70  214069[8:Res:116127.5,152274.0] operation(u) operation(v) || compatible(w,v,u) subclass(cantor(v),complement(singleton(ordered_pair(not_homomorphism1(w,v,u),not_homomorphism2(w,v,u)))))* -> homomorphism(w,v,u) subclass(singleton(ordered_pair(not_homomorphism1(w,v,u),not_homomorphism2(w,v,u))),x)*.
% 300.10/300.70  214891[25:SpL:208985.1,10120.0] operation(u) || member(ordered_pair(v,u),segment(w,x,y))* homomorphism(z,restrict(w,x,singleton(y)),x1)* -> equal(apply(x1,ordered_pair(apply(z,v),apply(z,ordinal_numbers))),apply(z,apply(restrict(w,x,singleton(y)),ordered_pair(v,ordinal_numbers))))*.
% 300.10/300.70  214903[24:Rew:207572.1,214886.3] operation(u) || member(singleton(singleton(identity_relation)),segment(v,w,x)) homomorphism(y,restrict(v,w,singleton(x)),z)* -> equal(apply(z,ordered_pair(apply(y,identity_relation),apply(y,u))),apply(y,apply(restrict(v,w,singleton(x)),singleton(singleton(identity_relation)))))*.
% 300.10/300.70  214885[25:SpL:208985.1,10120.0] operation(u) || member(ordered_pair(v,ordinal_numbers),segment(w,x,y)) homomorphism(z,restrict(w,x,singleton(y)),x1)* -> equal(apply(x1,ordered_pair(apply(z,v),apply(z,u))),apply(z,apply(restrict(w,x,singleton(y)),ordered_pair(v,u))))*.
% 300.10/300.70  215897[7:Res:13530.3,9876.0] || member(image(u,image(v,singleton(w))),ordinal_numbers) member(ordered_pair(w,apply(choice,image(u,image(v,singleton(w))))),cross_product(ordinal_numbers,ordinal_numbers))* subclass(compose(u,v),x)* well_ordering(ordinal_numbers,x) -> equal(image(u,image(v,singleton(w))),identity_relation).
% 300.10/300.70  215907[25:Rew:208820.0,215889.2,208820.0,215889.1,208820.0,215889.0] || member(image(u,image(v,identity_relation)),ordinal_numbers) member(ordered_pair(ordinal_numbers,apply(choice,image(u,image(v,identity_relation)))),cross_product(ordinal_numbers,ordinal_numbers)) -> equal(image(u,image(v,identity_relation)),identity_relation) member(ordered_pair(ordinal_numbers,apply(choice,image(u,image(v,identity_relation)))),compose(u,v))*.
% 300.10/300.70  215914[8:MRR:215913.0,18.1] || member(image(u,range_of(identity_relation)),ordinal_numbers) member(ordered_pair(v,apply(choice,image(u,range_of(identity_relation)))),cross_product(ordinal_numbers,ordinal_numbers)) -> member(v,cantor(w)) equal(image(u,range_of(identity_relation)),identity_relation) member(ordered_pair(v,apply(choice,image(u,range_of(identity_relation)))),compose(u,w))*.
% 300.10/300.70  220472[21:Res:196656.1,10120.0] || subclass(domain_relation,flip(segment(u,v,w))) homomorphism(x,restrict(u,v,singleton(w)),y)* -> equal(apply(y,ordered_pair(apply(x,ordered_pair(z,x1)),apply(x,identity_relation))),apply(x,apply(restrict(u,v,singleton(w)),ordered_pair(ordered_pair(z,x1),identity_relation))))*.
% 300.10/300.70  220578[21:Res:196657.1,10120.0] || subclass(domain_relation,rotate(segment(u,v,w))) homomorphism(x,restrict(u,v,singleton(w)),y)* -> equal(apply(y,ordered_pair(apply(x,ordered_pair(z,identity_relation)),apply(x,x1))),apply(x,apply(restrict(u,v,singleton(w)),ordered_pair(ordered_pair(z,identity_relation),x1))))*.
% 300.10/300.70  224628[10:Rew:223660.1,224428.2,223660.1,224428.1] || subclass(element_relation,identity_relation) member(ordered_pair(cross_product(ordinal_numbers,ordinal_numbers),not_subclass_element(image(u,image(v,identity_relation)),w)),cross_product(ordinal_numbers,ordinal_numbers)) -> subclass(image(u,image(v,identity_relation)),w) member(ordered_pair(cross_product(ordinal_numbers,ordinal_numbers),not_subclass_element(image(u,image(v,identity_relation)),w)),compose(u,v))*.
% 300.10/300.70  230751[7:SpL:18708.2,9880.0] || well_ordering(image(u,image(v,singleton(w))),ordinal_numbers) member(ordered_pair(w,ordered_pair(x,y)),compose(u,v))* member(x,singleton(y)) subclass(singleton(y),z)* well_ordering(image(u,image(v,singleton(w))),z)* -> equal(singleton(y),identity_relation).
% 300.10/300.70  235049[7:Rew:234956.0,235017.2,234956.0,235017.1,234956.0,235017.0] || member(image(u,range_of(identity_relation)),ordinal_numbers) member(ordered_pair(v,apply(choice,image(u,range_of(identity_relation)))),cross_product(ordinal_numbers,ordinal_numbers)) -> equal(image(u,range_of(identity_relation)),identity_relation) member(ordered_pair(v,apply(choice,image(u,range_of(identity_relation)))),compose(u,complement(cross_product(singleton(v),ordinal_numbers))))*.
% 300.10/300.70  48576[0:SpL:3594.0,8554.1] || member(u,union(complement(symmetric_difference(v,w)),union(complement(intersection(v,w)),union(v,w)))) member(u,complement(symmetric_difference(complement(intersection(v,w)),union(v,w)))) -> member(u,symmetric_difference(complement(symmetric_difference(v,w)),union(complement(intersection(v,w)),union(v,w))))*.
% 300.10/300.70  39624[2:Res:122.1,9665.1] inductive(compose(restrict(u,v,v),restrict(u,v,v))) || transitive(u,v) well_ordering(w,restrict(u,v,v)) -> member(least(w,compose(restrict(u,v,v),restrict(u,v,v))),compose(restrict(u,v,v),restrict(u,v,v)))*.
% 300.10/300.70  47520[0:Res:8551.2,8562.0] || member(not_subclass_element(u,intersection(v,restrict(w,x,y))),cross_product(x,y))* member(not_subclass_element(u,intersection(v,restrict(w,x,y))),w)* member(not_subclass_element(u,intersection(v,restrict(w,x,y))),v)* -> subclass(u,intersection(v,restrict(w,x,y))).
% 300.10/300.70  116394[8:Rew:116078.0,53017.0] || member(u,cantor(v)) equal(restrict(v,u,ordinal_numbers),least(intersection(w,rest_of(v)),x)) member(ordered_pair(u,least(intersection(w,rest_of(v)),x)),w)* member(u,x) subclass(x,y)* well_ordering(intersection(w,rest_of(v)),y)* -> .
% 300.10/300.70  116502[8:Rew:116078.0,51465.3] operation(u) operation(v) || compatible(w,v,u) subclass(cantor(v),cross_product(ordinal_numbers,ordinal_numbers)) member(not_homomorphism1(w,v,u),not_homomorphism2(w,v,u)) -> homomorphism(w,v,u) member(ordered_pair(not_homomorphism1(w,v,u),not_homomorphism2(w,v,u)),element_relation)*.
% 300.10/300.70  54474[5:Res:8827.2,10120.0] || member(u,ordinal_numbers) subclass(rest_relation,segment(v,w,x)) homomorphism(y,restrict(v,w,singleton(x)),z)* -> equal(apply(z,ordered_pair(apply(y,u),apply(y,rest_of(u)))),apply(y,apply(restrict(v,w,singleton(x)),ordered_pair(u,rest_of(u)))))*.
% 300.10/300.70  116366[8:Rew:116078.0,46646.1] || member(ordered_pair(u,v),cross_product(ordinal_numbers,ordinal_numbers)) subclass(composition_function,cantor(w)) homomorphism(x,w,y)* -> equal(apply(y,ordered_pair(apply(x,u),apply(x,ordered_pair(v,compose(u,v))))),apply(x,apply(w,ordered_pair(u,ordered_pair(v,compose(u,v))))))*.
% 300.10/300.70  69505[7:Res:13125.2,10120.0] || subclass(omega,segment(u,v,w)) homomorphism(x,restrict(u,v,singleton(w)),y)* -> equal(integer_of(ordered_pair(z,x1)),identity_relation) equal(apply(y,ordered_pair(apply(x,z),apply(x,x1))),apply(x,apply(restrict(u,v,singleton(w)),ordered_pair(z,x1))))*.
% 300.10/300.70  54340[5:Rew:50855.1,54316.2,50855.1,54316.1] || member(singleton(u),subset_relation) member(ordered_pair(first(singleton(u)),not_subclass_element(image(v,image(w,u)),x)),cross_product(ordinal_numbers,ordinal_numbers)) -> subclass(image(v,image(w,u)),x) member(ordered_pair(first(singleton(u)),not_subclass_element(image(v,image(w,u)),x)),compose(v,w))*.
% 300.10/300.70  130662[5:Res:41371.0,8803.0] || member(ordered_pair(u,not_subclass_element(complement(complement(image(v,image(w,singleton(u))))),x)),cross_product(ordinal_numbers,ordinal_numbers)) -> subclass(complement(complement(image(v,image(w,singleton(u))))),x) member(ordered_pair(u,not_subclass_element(complement(complement(image(v,image(w,singleton(u))))),x)),compose(v,w))*.
% 300.10/300.70  52614[0:SpL:963.0,9880.0] || member(ordered_pair(u,singleton(singleton(singleton(least(image(v,image(w,singleton(u))),x))))),compose(v,w))* member(singleton(least(image(v,image(w,singleton(u))),x)),x)* subclass(x,y)* well_ordering(image(v,image(w,singleton(u))),y)* -> .
% 300.10/300.70  19034[5:Res:313.1,8803.0] || member(ordered_pair(u,not_subclass_element(intersection(image(v,image(w,singleton(u))),x),y)),cross_product(ordinal_numbers,ordinal_numbers)) -> subclass(intersection(image(v,image(w,singleton(u))),x),y) member(ordered_pair(u,not_subclass_element(intersection(image(v,image(w,singleton(u))),x),y)),compose(v,w))*.
% 300.10/300.70  18915[5:Res:303.1,8803.0] || member(ordered_pair(u,not_subclass_element(intersection(v,image(w,image(x,singleton(u)))),y)),cross_product(ordinal_numbers,ordinal_numbers)) -> subclass(intersection(v,image(w,image(x,singleton(u)))),y) member(ordered_pair(u,not_subclass_element(intersection(v,image(w,image(x,singleton(u)))),y)),compose(w,x))*.
% 300.10/300.70  54309[5:SpR:154.1,9997.2] || member(u,recursion_equation_functions(v)) member(ordered_pair(w,not_subclass_element(image(v,image(rest_of(u),singleton(w))),x)),cross_product(ordinal_numbers,ordinal_numbers))* -> subclass(image(v,image(rest_of(u),singleton(w))),x) member(ordered_pair(w,not_subclass_element(image(v,image(rest_of(u),singleton(w))),x)),u)*.
% 300.10/300.70  53064[5:MRR:53012.0,41096.1] || member(ordered_pair(u,least(intersection(v,image(element_relation,complement(w))),x)),v)* member(u,x) subclass(x,y)* well_ordering(intersection(v,image(element_relation,complement(w))),y)* -> member(ordered_pair(u,least(intersection(v,image(element_relation,complement(w))),x)),power_class(w))*.
% 300.10/300.70  49976[5:Res:8835.1,9878.0] || member(least(cross_product(u,image(element_relation,complement(v))),w),ordinal_numbers) member(x,u)* member(x,w)* subclass(w,y)* well_ordering(cross_product(u,image(element_relation,complement(v))),y)* -> member(least(cross_product(u,image(element_relation,complement(v))),w),power_class(v))*.
% 300.10/300.70  117823[8:Rew:116078.0,116302.2] one_to_one(restrict(u,v,singleton(w))) || subclass(range_of(restrict(u,v,singleton(w))),cantor(segment(u,v,w)))* equal(cross_product(cantor(segment(u,v,w)),cantor(segment(u,v,w))),segment(u,v,w)) -> operation(restrict(u,v,singleton(w))).
% 300.10/300.70  161824[8:Rew:116078.0,51349.8,116078.0,51349.5,116078.0,51349.4,116078.0,51349.4,116078.0,51349.4,116078.0,51349.3,116078.0,51349.3] function(u) operation(v) operation(w) || equal(cantor(cantor(v)),range_of(u)) equal(cantor(cantor(w)),cantor(u)) subclass(cantor(w),x)* well_ordering(y,x)* -> homomorphism(u,w,v)* member(least(y,cantor(w)),cantor(w))*.
% 300.10/300.70  208546[7:Rew:13260.1,208528.3] || member(ordered_pair(ordered_pair(second(regular(cross_product(u,v))),first(regular(cross_product(u,v)))),w),x)* member(ordered_pair(regular(cross_product(u,v)),w),cross_product(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers)) -> equal(cross_product(u,v),identity_relation) member(ordered_pair(regular(cross_product(u,v)),w),flip(x)).
% 300.10/300.70  208547[7:Rew:13260.1,208527.3] || member(ordered_pair(ordered_pair(second(regular(cross_product(u,v))),w),first(regular(cross_product(u,v)))),x)* member(ordered_pair(regular(cross_product(u,v)),w),cross_product(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers)) -> equal(cross_product(u,v),identity_relation) member(ordered_pair(regular(cross_product(u,v)),w),rotate(x)).
% 300.10/300.70  211616[7:Rew:13260.1,211600.1] || member(u,ordinal_numbers) member(regular(cross_product(v,w)),cross_product(ordinal_numbers,ordinal_numbers)) member(ordered_pair(ordered_pair(second(regular(cross_product(v,w))),u),first(regular(cross_product(v,w)))),x)* -> equal(cross_product(v,w),identity_relation) member(ordered_pair(regular(cross_product(v,w)),u),rotate(x)).
% 300.10/300.70  211989[7:Rew:13260.1,211973.1] || member(u,ordinal_numbers) member(regular(cross_product(v,w)),cross_product(ordinal_numbers,ordinal_numbers)) member(ordered_pair(ordered_pair(second(regular(cross_product(v,w))),first(regular(cross_product(v,w)))),u),x)* -> equal(cross_product(v,w),identity_relation) member(ordered_pair(regular(cross_product(v,w)),u),flip(x)).
% 300.10/300.70  212421[7:Rew:13259.2,212399.4] || member(cross_product(u,v),ordinal_numbers) equal(successor(first(apply(choice,cross_product(u,v)))),second(apply(choice,cross_product(u,v)))) member(apply(choice,cross_product(u,v)),cross_product(ordinal_numbers,ordinal_numbers))* -> equal(cross_product(u,v),identity_relation) member(apply(choice,cross_product(u,v)),successor_relation).
% 300.10/300.70  233362[8:Res:231881.0,9664.1] || member(ordered_pair(u,v),compose(w,x))* well_ordering(y,complement(singleton(image(w,image(x,singleton(u)))))) -> equal(singleton(image(w,image(x,singleton(u)))),identity_relation) member(least(y,image(w,image(x,singleton(u)))),image(w,image(x,singleton(u))))*.
% 300.10/300.70  48545[0:SpR:3616.0,3594.0] ||  -> equal(intersection(complement(symmetric_difference(union(u,v),union(complement(u),complement(v)))),union(complement(symmetric_difference(complement(u),complement(v))),union(union(u,v),union(complement(u),complement(v))))),symmetric_difference(complement(symmetric_difference(complement(u),complement(v))),union(union(u,v),union(complement(u),complement(v)))))**.
% 300.10/300.70  161826[8:Rew:116078.0,51464.3] operation(u) operation(v) || compatible(w,v,u) subclass(cantor(v),cross_product(ordinal_numbers,ordinal_numbers)) equal(successor(not_homomorphism1(w,v,u)),not_homomorphism2(w,v,u)) -> homomorphism(w,v,u) member(ordered_pair(not_homomorphism1(w,v,u),not_homomorphism2(w,v,u)),successor_relation)*.
% 300.10/300.70  116503[8:Rew:116078.0,51436.3] operation(u) operation(v) || compatible(w,v,u) subclass(cantor(v),unordered_pair(x,y))* -> homomorphism(w,v,u) equal(ordered_pair(not_homomorphism1(w,v,u),not_homomorphism2(w,v,u)),y)* equal(ordered_pair(not_homomorphism1(w,v,u),not_homomorphism2(w,v,u)),x)*.
% 300.10/300.70  162897[8:MRR:61943.4,162891.0] operation(u) || compatible(v,w,u) homomorphism(x,w,choice) -> homomorphism(v,w,u) member(apply(x,apply(w,ordered_pair(not_homomorphism1(v,w,u),not_homomorphism2(v,w,u)))),ordered_pair(apply(x,not_homomorphism1(v,w,u)),apply(x,not_homomorphism2(v,w,u))))*.
% 300.10/300.70  139681[5:SpL:19860.0,10118.0] || member(ordered_pair(u,v),image(cross_product(w,x),y)) homomorphism(z,inverse(restrict(cross_product(y,ordinal_numbers),w,x)),x1)* -> equal(apply(x1,ordered_pair(apply(z,u),apply(z,v))),apply(z,apply(inverse(restrict(cross_product(y,ordinal_numbers),w,x)),ordered_pair(u,v))))*.
% 300.10/300.70  46634[5:Res:9618.2,8803.0] || member(ordered_pair(u,v),cross_product(ordinal_numbers,ordinal_numbers)) subclass(composition_function,image(w,image(x,singleton(y)))) member(ordered_pair(y,ordered_pair(u,ordered_pair(v,compose(u,v)))),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(y,ordered_pair(u,ordered_pair(v,compose(u,v)))),compose(w,x))*.
% 300.10/300.70  109605[5:Res:79577.0,9872.0] || member(ordered_pair(u,least(intersection(v,image(element_relation,complement(w))),x)),v)* member(u,x) subclass(x,y)* well_ordering(intersection(v,image(element_relation,complement(w))),y)* -> subclass(singleton(ordered_pair(u,least(intersection(v,image(element_relation,complement(w))),x))),power_class(w))*.
% 300.10/300.70  212412[7:SpL:13259.2,3689.0] || member(cross_product(u,v),ordinal_numbers) member(w,apply(choice,cross_product(u,v)))* -> equal(cross_product(u,v),identity_relation) equal(w,unordered_pair(first(apply(choice,cross_product(u,v))),singleton(second(apply(choice,cross_product(u,v))))))* equal(w,singleton(first(apply(choice,cross_product(u,v))))).
% 300.10/300.70  212370[8:SpR:13259.2,117604.3] operation(u) || member(cross_product(v,w),ordinal_numbers) member(second(apply(choice,cross_product(v,w))),cantor(cantor(u)))* member(first(apply(choice,cross_product(v,w))),cantor(cantor(u))) -> equal(cross_product(v,w),identity_relation) member(apply(choice,cross_product(v,w)),cantor(u)).
% 300.10/300.70  212422[7:Rew:13259.2,212398.4] || member(cross_product(u,v),ordinal_numbers) equal(sum_class(range_of(first(apply(choice,cross_product(u,v))))),second(apply(choice,cross_product(u,v)))) member(apply(choice,cross_product(u,v)),cross_product(ordinal_numbers,ordinal_numbers))* -> equal(cross_product(u,v),identity_relation) member(apply(choice,cross_product(u,v)),union_of_range_map).
% 300.10/300.70  213508[8:Res:116127.5,13362.0] operation(u) operation(v) || compatible(w,v,u) subclass(cantor(v),x) subclass(x,y)* well_ordering(omega,y)* -> homomorphism(w,v,u) equal(integer_of(ordered_pair(ordered_pair(not_homomorphism1(w,v,u),not_homomorphism2(w,v,u)),least(omega,x))),identity_relation)**.
% 300.10/300.70  214402[25:Rew:208985.1,214397.3] operation(not_homomorphism2(element_relation,u,v)) operation(v) operation(u) || equal(apply(element_relation,apply(u,ordered_pair(not_homomorphism1(element_relation,u,v),ordinal_numbers))),apply(v,ordered_pair(apply(element_relation,not_homomorphism1(element_relation,u,v)),sum_class(ordinal_numbers))))* compatible(element_relation,u,v) -> homomorphism(element_relation,u,v).
% 300.10/300.70  226427[7:Res:13258.1,8803.0] || member(ordered_pair(u,regular(restrict(image(v,image(w,singleton(u))),x,y))),cross_product(ordinal_numbers,ordinal_numbers)) -> equal(restrict(image(v,image(w,singleton(u))),x,y),identity_relation) member(ordered_pair(u,regular(restrict(image(v,image(w,singleton(u))),x,y))),compose(v,w))*.
% 300.10/300.70  49974[0:Res:8551.2,9878.0] || member(least(cross_product(u,restrict(v,w,x)),y),cross_product(w,x))* member(least(cross_product(u,restrict(v,w,x)),y),v)* member(z,u)* member(z,y)* subclass(y,x1)* well_ordering(cross_product(u,restrict(v,w,x)),x1)* -> .
% 300.10/300.70  53005[0:Res:3618.1,9872.0] || member(ordered_pair(u,least(intersection(v,complement(intersection(w,x))),y)),symmetric_difference(w,x))* member(ordered_pair(u,least(intersection(v,complement(intersection(w,x))),y)),v)* member(u,y) subclass(y,z)* well_ordering(intersection(v,complement(intersection(w,x))),z)* -> .
% 300.10/300.70  156481[5:Rew:155665.0,156462.4,155665.0,156462.1] || member(ordered_pair(u,least(symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers)),v)),union(subset_relation,cross_product(ordinal_numbers,ordinal_numbers)))* member(ordered_pair(u,least(symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers)),v)),complement(subset_relation)) member(u,v) subclass(v,w)* well_ordering(symmetric_difference(subset_relation,cross_product(ordinal_numbers,ordinal_numbers)),w)* -> .
% 300.10/300.70  156590[5:Rew:155666.0,156571.4,155666.0,156571.1] || member(ordered_pair(u,least(symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation),v)),union(cross_product(ordinal_numbers,ordinal_numbers),subset_relation))* member(ordered_pair(u,least(symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation),v)),complement(subset_relation)) member(u,v) subclass(v,w)* well_ordering(symmetric_difference(cross_product(ordinal_numbers,ordinal_numbers),subset_relation),w)* -> .
% 300.10/300.70  49629[5:SpR:6355.1,9706.3] || member(second(not_subclass_element(cross_product(u,v),w)),ordinal_numbers)* member(first(not_subclass_element(cross_product(u,v),w)),ordinal_numbers) equal(successor(first(not_subclass_element(cross_product(u,v),w))),second(not_subclass_element(cross_product(u,v),w))) -> subclass(cross_product(u,v),w) member(not_subclass_element(cross_product(u,v),w),successor_relation).
% 300.10/300.70  51395[5:Res:9618.2,10118.0] || member(ordered_pair(u,v),cross_product(ordinal_numbers,ordinal_numbers)) subclass(composition_function,range_of(w)) homomorphism(x,inverse(w),y)* -> equal(apply(y,ordered_pair(apply(x,u),apply(x,ordered_pair(v,compose(u,v))))),apply(x,apply(inverse(w),ordered_pair(u,ordered_pair(v,compose(u,v))))))*.
% 300.10/300.70  212423[7:Rew:13259.2,212416.4] || member(cross_product(u,v),ordinal_numbers) equal(compose(w,first(apply(choice,cross_product(u,v)))),second(apply(choice,cross_product(u,v))))** member(apply(choice,cross_product(u,v)),cross_product(ordinal_numbers,ordinal_numbers))* -> equal(cross_product(u,v),identity_relation) member(apply(choice,cross_product(u,v)),compose_class(w)).
% 300.10/300.70  213564[8:Res:116127.5,8798.1] operation(u) operation(v) || compatible(w,v,u) subclass(cantor(v),cross_product(ordinal_numbers,ordinal_numbers)) equal(sum_class(range_of(not_homomorphism1(w,v,u))),not_homomorphism2(w,v,u)) -> homomorphism(w,v,u) member(ordered_pair(not_homomorphism1(w,v,u),not_homomorphism2(w,v,u)),union_of_range_map)*.
% 300.10/300.70  214382[25:Rew:208985.1,214374.3] operation(not_homomorphism2(u,v,w)) operation(w) operation(v) || equal(apply(u,apply(v,ordered_pair(not_homomorphism1(u,v,w),ordinal_numbers))),apply(w,ordered_pair(apply(u,not_homomorphism1(u,v,w)),apply(u,ordinal_numbers))))* compatible(u,v,w) -> homomorphism(u,v,w).
% 300.10/300.70  215908[24:Rew:207558.1,215886.3,207558.1,215886.2,207558.1,215886.1] operation(u) || member(image(v,image(w,identity_relation)),ordinal_numbers) member(ordered_pair(u,apply(choice,image(v,image(w,identity_relation)))),cross_product(ordinal_numbers,ordinal_numbers)) -> equal(image(v,image(w,identity_relation)),identity_relation) member(ordered_pair(u,apply(choice,image(v,image(w,identity_relation)))),compose(v,w))*.
% 300.10/300.70  215978[25:Rew:208985.1,215955.5] operation(not_homomorphism2(u,v,w)) operation(w) || compatible(u,v,w) homomorphism(element_relation,v,x) -> homomorphism(u,v,w) equal(apply(x,ordered_pair(apply(element_relation,not_homomorphism1(u,v,w)),sum_class(ordinal_numbers))),apply(element_relation,apply(v,ordered_pair(not_homomorphism1(u,v,w),ordinal_numbers))))*.
% 300.10/300.70  219812[8:Res:67614.1,9872.0] || member(ordered_pair(u,least(intersection(v,symmetric_difference(complement(w),ordinal_numbers)),x)),union(w,identity_relation))* member(ordered_pair(u,least(intersection(v,symmetric_difference(complement(w),ordinal_numbers)),x)),v)* member(u,x) subclass(x,y)* well_ordering(intersection(v,symmetric_difference(complement(w),ordinal_numbers)),y)* -> .
% 300.10/300.70  48668[0:Rew:3594.0,48577.2,3594.0,48577.1] || member(not_subclass_element(u,symmetric_difference(complement(intersection(v,w)),union(v,w))),union(complement(intersection(v,w)),union(v,w)))* member(not_subclass_element(u,symmetric_difference(complement(intersection(v,w)),union(v,w))),complement(symmetric_difference(v,w))) -> subclass(u,symmetric_difference(complement(intersection(v,w)),union(v,w))).
% 300.10/300.70  53063[0:Rew:3616.0,53001.4,3616.0,53001.1] || member(ordered_pair(u,least(symmetric_difference(complement(v),complement(w)),x)),union(complement(v),complement(w)))* member(ordered_pair(u,least(symmetric_difference(complement(v),complement(w)),x)),union(v,w)) member(u,x) subclass(x,y)* well_ordering(symmetric_difference(complement(v),complement(w)),y)* -> .
% 300.10/300.70  117827[8:Rew:116078.0,116581.6,116078.0,116581.3,116078.0,116581.2,116078.0,116581.2,116078.0,116581.1] operation(u) || member(least(intersection(v,cantor(u)),w),cantor(cantor(u)))* member(x,cantor(cantor(u))) member(ordered_pair(x,least(intersection(v,cantor(u)),w)),v)* member(x,w) subclass(w,y)* well_ordering(intersection(v,cantor(u)),y)* -> .
% 300.10/300.70  53058[5:MRR:53022.1,41096.1] || member(least(intersection(u,compose_class(v)),w),ordinal_numbers) equal(compose(v,x),least(intersection(u,compose_class(v)),w)) member(ordered_pair(x,least(intersection(u,compose_class(v)),w)),u)* member(x,w) subclass(w,y)* well_ordering(intersection(u,compose_class(v)),y)* -> .
% 300.10/300.70  46659[5:Res:9618.2,8820.1] || member(ordered_pair(ordered_pair(u,v),w),cross_product(ordinal_numbers,ordinal_numbers)) subclass(composition_function,cross_product(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers)) member(ordered_pair(ordered_pair(v,u),ordered_pair(w,compose(ordered_pair(u,v),w))),x) -> member(ordered_pair(ordered_pair(u,v),ordered_pair(w,compose(ordered_pair(u,v),w))),flip(x))*.
% 300.10/300.70  46660[5:Res:9618.2,8821.1] || member(ordered_pair(ordered_pair(u,v),w),cross_product(ordinal_numbers,ordinal_numbers)) subclass(composition_function,cross_product(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers)) member(ordered_pair(ordered_pair(v,ordered_pair(w,compose(ordered_pair(u,v),w))),u),x) -> member(ordered_pair(ordered_pair(u,v),ordered_pair(w,compose(ordered_pair(u,v),w))),rotate(x))*.
% 300.10/300.70  116501[8:Rew:116078.0,51469.3] operation(u) operation(v) || compatible(w,v,u) subclass(cantor(v),cross_product(ordinal_numbers,ordinal_numbers)) equal(compose(x,not_homomorphism1(w,v,u)),not_homomorphism2(w,v,u)) -> homomorphism(w,v,u) member(ordered_pair(not_homomorphism1(w,v,u),not_homomorphism2(w,v,u)),compose_class(x))*.
% 300.10/300.70  36755[0:Obv:36724.1] operation(u) operation(v) || compatible(w,v,u) -> homomorphism(w,v,u) equal(ordered_pair(first(ordered_pair(not_homomorphism1(w,v,u),not_homomorphism2(w,v,u))),second(ordered_pair(not_homomorphism1(w,v,u),not_homomorphism2(w,v,u)))),ordered_pair(not_homomorphism1(w,v,u),not_homomorphism2(w,v,u)))**.
% 300.10/300.70  153375[5:Res:919.1,8803.0] || member(ordered_pair(u,not_subclass_element(restrict(image(v,image(w,singleton(u))),x,y),z)),cross_product(ordinal_numbers,ordinal_numbers)) -> subclass(restrict(image(v,image(w,singleton(u))),x,y),z) member(ordered_pair(u,not_subclass_element(restrict(image(v,image(w,singleton(u))),x,y),z)),compose(v,w))*.
% 300.10/300.70  132240[5:Res:39609.2,8803.0] inductive(image(u,image(v,singleton(w)))) || well_ordering(x,image(u,image(v,singleton(w)))) member(ordered_pair(w,least(x,image(u,image(v,singleton(w))))),cross_product(ordinal_numbers,ordinal_numbers)) -> member(ordered_pair(w,least(x,image(u,image(v,singleton(w))))),compose(u,v))*.
% 300.10/300.70  198329[5:SpR:6355.1,9837.3] || member(second(not_subclass_element(cross_product(u,v),w)),ordinal_numbers) member(first(not_subclass_element(cross_product(u,v),w)),ordinal_numbers) equal(sum_class(range_of(first(not_subclass_element(cross_product(u,v),w)))),second(not_subclass_element(cross_product(u,v),w)))** -> subclass(cross_product(u,v),w) member(not_subclass_element(cross_product(u,v),w),union_of_range_map).
% 300.10/300.70  211510[7:SpL:13262.1,8632.1] || well_ordering(element_relation,image(choice,singleton(unordered_pair(u,v))))* subclass(v,image(choice,singleton(unordered_pair(u,v))))* -> equal(unordered_pair(u,v),identity_relation) equal(apply(choice,unordered_pair(u,v)),u) equal(image(choice,singleton(unordered_pair(u,v))),ordinal_numbers) member(image(choice,singleton(unordered_pair(u,v))),ordinal_numbers).
% 300.10/300.70  211509[7:SpL:13262.2,8632.1] || well_ordering(element_relation,image(choice,singleton(unordered_pair(u,v))))* subclass(u,image(choice,singleton(unordered_pair(u,v))))* -> equal(unordered_pair(u,v),identity_relation) equal(apply(choice,unordered_pair(u,v)),v) equal(image(choice,singleton(unordered_pair(u,v))),ordinal_numbers) member(image(choice,singleton(unordered_pair(u,v))),ordinal_numbers).
% 300.10/300.70  212293[8:Res:161774.3,13362.0] || section(u,v,w) well_ordering(x,v) subclass(cantor(restrict(u,w,v)),y)* well_ordering(omega,y) -> equal(cantor(restrict(u,w,v)),identity_relation) equal(integer_of(ordered_pair(least(x,cantor(restrict(u,w,v))),least(omega,cantor(restrict(u,w,v))))),identity_relation)**.
% 300.10/300.70  212367[8:SpR:13259.2,116123.2] || member(cross_product(u,v),ordinal_numbers) member(first(apply(choice,cross_product(u,v))),cantor(w)) equal(restrict(w,first(apply(choice,cross_product(u,v))),ordinal_numbers),second(apply(choice,cross_product(u,v))))** -> equal(cross_product(u,v),identity_relation) member(apply(choice,cross_product(u,v)),rest_of(w)).
% 300.10/300.70  213428[7:Rew:13260.1,213414.3] || member(regular(cross_product(u,v)),range_of(w)) homomorphism(x,inverse(w),y)* -> equal(cross_product(u,v),identity_relation) equal(apply(y,ordered_pair(apply(x,first(regular(cross_product(u,v)))),apply(x,second(regular(cross_product(u,v)))))),apply(x,apply(inverse(w),regular(cross_product(u,v)))))*.
% 300.10/300.70  215979[25:Rew:208972.1,215962.5] operation(not_homomorphism2(u,v,w)) operation(w) || compatible(u,v,w) homomorphism(x,v,y) -> homomorphism(u,v,w) equal(apply(y,ordered_pair(apply(x,not_homomorphism1(u,v,w)),apply(x,ordinal_numbers))),apply(x,apply(v,ordered_pair(not_homomorphism1(u,v,w),ordinal_numbers))))*.
% 300.10/300.70  221159[7:Res:13236.2,8803.0] || well_ordering(u,image(v,image(w,singleton(x)))) member(ordered_pair(x,least(u,image(v,image(w,singleton(x))))),cross_product(ordinal_numbers,ordinal_numbers)) -> equal(image(v,image(w,singleton(x))),identity_relation) member(ordered_pair(x,least(u,image(v,image(w,singleton(x))))),compose(v,w))*.
% 300.10/300.70  235951[7:Res:69478.2,9872.0] || subclass(omega,symmetric_difference(u,v)) member(ordered_pair(w,least(intersection(x,union(u,v)),y)),x)* member(w,y) subclass(y,z)* well_ordering(intersection(x,union(u,v)),z)* -> equal(integer_of(ordered_pair(w,least(intersection(x,union(u,v)),y))),identity_relation).
% 300.10/300.70  51930[0:SpL:916.0,9822.1] || transitive(cross_product(u,v),w) subclass(restrict(cross_product(w,w),u,v),compose(restrict(cross_product(w,w),u,v),restrict(cross_product(w,w),u,v)))* -> equal(compose(restrict(cross_product(u,v),w,w),restrict(cross_product(u,v),w,w)),restrict(cross_product(u,v),w,w)).
% 300.10/300.70  49683[5:Rew:6355.1,49667.3] || member(ordered_pair(ordered_pair(second(not_subclass_element(cross_product(u,v),w)),first(not_subclass_element(cross_product(u,v),w))),x),y)* member(ordered_pair(not_subclass_element(cross_product(u,v),w),x),cross_product(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers)) -> subclass(cross_product(u,v),w) member(ordered_pair(not_subclass_element(cross_product(u,v),w),x),flip(y)).
% 300.10/300.70  49684[5:Rew:6355.1,49666.3] || member(ordered_pair(ordered_pair(second(not_subclass_element(cross_product(u,v),w)),x),first(not_subclass_element(cross_product(u,v),w))),y)* member(ordered_pair(not_subclass_element(cross_product(u,v),w),x),cross_product(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers)) -> subclass(cross_product(u,v),w) member(ordered_pair(not_subclass_element(cross_product(u,v),w),x),rotate(y)).
% 300.10/300.70  50973[5:Rew:6355.1,50960.1] || member(u,ordinal_numbers) member(not_subclass_element(cross_product(v,w),x),cross_product(ordinal_numbers,ordinal_numbers)) member(ordered_pair(ordered_pair(second(not_subclass_element(cross_product(v,w),x)),first(not_subclass_element(cross_product(v,w),x))),u),y)* -> subclass(cross_product(v,w),x) member(ordered_pair(not_subclass_element(cross_product(v,w),x),u),flip(y)).
% 300.10/300.70  50896[5:Rew:6355.1,50883.1] || member(u,ordinal_numbers) member(not_subclass_element(cross_product(v,w),x),cross_product(ordinal_numbers,ordinal_numbers)) member(ordered_pair(ordered_pair(second(not_subclass_element(cross_product(v,w),x)),u),first(not_subclass_element(cross_product(v,w),x))),y)* -> subclass(cross_product(v,w),x) member(ordered_pair(not_subclass_element(cross_product(v,w),x),u),rotate(y)).
% 300.10/300.70  53067[5:MRR:53009.0,41096.1] || member(ordered_pair(u,least(intersection(v,intersection(complement(w),complement(x))),y)),v)* member(u,y) subclass(y,z)* well_ordering(intersection(v,intersection(complement(w),complement(x))),z)* -> member(ordered_pair(u,least(intersection(v,intersection(complement(w),complement(x))),y)),union(w,x))*.
% 300.10/300.70  49630[5:SpR:6355.1,9865.3] || member(second(not_subclass_element(cross_product(u,v),w)),ordinal_numbers) member(first(not_subclass_element(cross_product(u,v),w)),ordinal_numbers) equal(compose(x,first(not_subclass_element(cross_product(u,v),w))),second(not_subclass_element(cross_product(u,v),w)))** -> subclass(cross_product(u,v),w) member(not_subclass_element(cross_product(u,v),w),compose_class(x)).
% 300.10/300.70  49973[5:Res:8832.1,9878.0] || member(least(cross_product(u,intersection(complement(v),complement(w))),x),ordinal_numbers) member(y,u)* member(y,x)* subclass(x,z)* well_ordering(cross_product(u,intersection(complement(v),complement(w))),z)* -> member(least(cross_product(u,intersection(complement(v),complement(w))),x),union(v,w))*.
% 300.10/300.70  214398[25:SpL:214339.1,95.2] operation(not_homomorphism1(element_relation,u,v)) operation(v) operation(u) || equal(apply(element_relation,apply(u,ordered_pair(not_homomorphism1(element_relation,u,v),not_homomorphism2(element_relation,u,v)))),apply(v,ordered_pair(sum_class(ordinal_numbers),apply(element_relation,not_homomorphism2(element_relation,u,v)))))** compatible(element_relation,u,v) -> homomorphism(element_relation,u,v).
% 300.10/300.70  214396[25:SpL:214339.1,95.2] operation(apply(u,ordered_pair(not_homomorphism1(element_relation,u,v),not_homomorphism2(element_relation,u,v)))) operation(v) operation(u) || equal(apply(v,ordered_pair(apply(element_relation,not_homomorphism1(element_relation,u,v)),apply(element_relation,not_homomorphism2(element_relation,u,v)))),sum_class(ordinal_numbers))** compatible(element_relation,u,v) -> homomorphism(element_relation,u,v).
% 300.10/300.70  214666[7:SpR:916.0,13360.2] || transitive(cross_product(u,v),w) well_ordering(x,restrict(cross_product(u,v),w,w)) -> equal(segment(x,compose(restrict(cross_product(w,w),u,v),restrict(cross_product(w,w),u,v)),least(x,compose(restrict(cross_product(w,w),u,v),restrict(cross_product(w,w),u,v)))),identity_relation)**.
% 300.10/300.70  215827[7:Res:13361.3,5.0] || transitive(u,v) well_ordering(w,restrict(u,v,v)) subclass(compose(restrict(u,v,v),restrict(u,v,v)),x) -> equal(compose(restrict(u,v,v),restrict(u,v,v)),identity_relation) member(least(w,compose(restrict(u,v,v),restrict(u,v,v))),x)*.
% 300.10/300.70  235604[5:Res:28979.1,9872.0] || subclass(rest_relation,rotate(u)) member(ordered_pair(ordered_pair(v,rest_of(ordered_pair(least(intersection(w,u),x),v))),least(intersection(w,u),x)),w)* member(ordered_pair(v,rest_of(ordered_pair(least(intersection(w,u),x),v))),x) subclass(x,y)* well_ordering(intersection(w,u),y)* -> .
% 300.10/300.70  235686[8:Res:161774.3,36719.1] operation(restrict(u,v,w)) || section(u,w,v) well_ordering(x,w) -> equal(cantor(restrict(u,v,w)),identity_relation) equal(ordered_pair(first(least(x,cantor(restrict(u,v,w)))),second(least(x,cantor(restrict(u,v,w))))),least(x,cantor(restrict(u,v,w))))**.
% 300.10/300.70  237139[7:Res:13574.1,8803.0] || member(ordered_pair(u,regular(intersection(v,intersection(w,image(x,image(y,singleton(u))))))),cross_product(ordinal_numbers,ordinal_numbers)) -> equal(intersection(v,intersection(w,image(x,image(y,singleton(u))))),identity_relation) member(ordered_pair(u,regular(intersection(v,intersection(w,image(x,image(y,singleton(u))))))),compose(x,y))*.
% 300.10/300.70  237790[7:Res:13573.1,8803.0] || member(ordered_pair(u,regular(intersection(v,intersection(image(w,image(x,singleton(u))),y)))),cross_product(ordinal_numbers,ordinal_numbers)) -> equal(intersection(v,intersection(image(w,image(x,singleton(u))),y)),identity_relation) member(ordered_pair(u,regular(intersection(v,intersection(image(w,image(x,singleton(u))),y)))),compose(w,x))*.
% 300.10/300.70  239302[7:Res:17397.1,8803.0] || member(ordered_pair(u,regular(intersection(intersection(image(v,image(w,singleton(u))),x),y))),cross_product(ordinal_numbers,ordinal_numbers)) -> equal(intersection(intersection(image(v,image(w,singleton(u))),x),y),identity_relation) member(ordered_pair(u,regular(intersection(intersection(image(v,image(w,singleton(u))),x),y))),compose(v,w))*.
% 300.10/300.70  240137[7:Res:17396.1,8803.0] || member(ordered_pair(u,regular(intersection(intersection(v,image(w,image(x,singleton(u)))),y))),cross_product(ordinal_numbers,ordinal_numbers)) -> equal(intersection(intersection(v,image(w,image(x,singleton(u)))),y),identity_relation) member(ordered_pair(u,regular(intersection(intersection(v,image(w,image(x,singleton(u)))),y))),compose(w,x))*.
% 300.10/300.70  53066[0:Rew:3603.0,52974.4,3603.0,52974.1] || member(ordered_pair(u,least(symmetric_difference(v,cross_product(w,x)),y)),union(v,cross_product(w,x)))* member(ordered_pair(u,least(symmetric_difference(v,cross_product(w,x)),y)),complement(restrict(v,w,x))) member(u,y) subclass(y,z)* well_ordering(symmetric_difference(v,cross_product(w,x)),z)* -> .
% 300.10/300.70  53065[0:Rew:3606.0,52975.4,3606.0,52975.1] || member(ordered_pair(u,least(symmetric_difference(cross_product(v,w),x),y)),union(cross_product(v,w),x))* member(ordered_pair(u,least(symmetric_difference(cross_product(v,w),x),y)),complement(restrict(x,v,w))) member(u,y) subclass(y,z)* well_ordering(symmetric_difference(cross_product(v,w),x),z)* -> .
% 300.10/300.70  116504[8:Rew:116078.0,51450.3] operation(u) operation(v) || compatible(w,v,u) subclass(cantor(v),ordered_pair(x,y))* -> homomorphism(w,v,u) equal(ordered_pair(not_homomorphism1(w,v,u),not_homomorphism2(w,v,u)),unordered_pair(x,singleton(y)))* equal(ordered_pair(not_homomorphism1(w,v,u),not_homomorphism2(w,v,u)),singleton(x)).
% 300.10/300.70  116279[8:Rew:116078.0,49685.0] || member(not_subclass_element(cross_product(u,v),w),cantor(x)) homomorphism(y,x,z)* -> subclass(cross_product(u,v),w) equal(apply(z,ordered_pair(apply(y,first(not_subclass_element(cross_product(u,v),w))),apply(y,second(not_subclass_element(cross_product(u,v),w))))),apply(y,apply(x,not_subclass_element(cross_product(u,v),w))))*.
% 300.10/300.70  161827[8:Rew:116078.0,51350.8,116078.0,51350.5,116078.0,51350.4,116078.0,51350.4,116078.0,51350.4] function(u) operation(flip(cross_product(v,ordinal_numbers))) operation(w) || subclass(range_of(u),range_of(v)) equal(cantor(cantor(w)),cantor(u)) subclass(cantor(w),x)* well_ordering(y,x)* -> homomorphism(u,w,flip(cross_product(v,ordinal_numbers)))* member(least(y,cantor(w)),cantor(w))*.
% 300.10/300.70  214375[25:SpL:208972.1,95.2] operation(not_homomorphism1(u,v,w)) operation(w) operation(v) || equal(apply(u,apply(v,ordered_pair(not_homomorphism1(u,v,w),not_homomorphism2(u,v,w)))),apply(w,ordered_pair(apply(u,ordinal_numbers),apply(u,not_homomorphism2(u,v,w)))))** compatible(u,v,w) -> homomorphism(u,v,w).
% 300.10/300.70  214373[25:SpL:208972.1,95.2] operation(apply(u,ordered_pair(not_homomorphism1(v,u,w),not_homomorphism2(v,u,w)))) operation(w) operation(u) || equal(apply(w,ordered_pair(apply(v,not_homomorphism1(v,u,w)),apply(v,not_homomorphism2(v,u,w)))),apply(v,ordinal_numbers))** compatible(v,u,w) -> homomorphism(v,u,w).
% 300.10/300.70  214608[25:SpL:208985.1,95.2] operation(apply(u,not_homomorphism2(u,v,w))) operation(w) operation(v) || equal(apply(u,apply(v,ordered_pair(not_homomorphism1(u,v,w),not_homomorphism2(u,v,w)))),apply(w,ordered_pair(apply(u,not_homomorphism1(u,v,w)),ordinal_numbers)))** compatible(u,v,w) -> homomorphism(u,v,w).
% 300.10/300.70  215850[8:Rew:117511.1,215819.3,117511.1,215819.2] operation(u) || transitive(v,cantor(cantor(u))) well_ordering(w,intersection(cantor(u),v)) -> equal(compose(intersection(cantor(u),v),intersection(cantor(u),v)),identity_relation) member(least(w,compose(intersection(cantor(u),v),intersection(cantor(u),v))),compose(intersection(cantor(u),v),intersection(cantor(u),v)))*.
% 300.10/300.70  215915[21:Rew:197474.0,215888.3,197474.0,215888.1,197474.0,215888.0] || member(image(u,image(v,identity_relation)),ordinal_numbers) member(ordered_pair(inverse(w),apply(choice,image(u,image(v,identity_relation)))),cross_product(ordinal_numbers,ordinal_numbers)) -> equal(range_of(w),identity_relation) equal(image(u,image(v,identity_relation)),identity_relation) member(ordered_pair(inverse(w),apply(choice,image(u,image(v,identity_relation)))),compose(u,v))*.
% 300.10/300.70  215959[25:SpR:214339.1,10130.4] operation(not_homomorphism1(u,v,w)) operation(w) || compatible(u,v,w) homomorphism(element_relation,v,x) -> homomorphism(u,v,w) equal(apply(x,ordered_pair(sum_class(ordinal_numbers),apply(element_relation,not_homomorphism2(u,v,w)))),apply(element_relation,apply(v,ordered_pair(not_homomorphism1(u,v,w),not_homomorphism2(u,v,w)))))*.
% 300.10/300.70  215987[8:MRR:215932.3,215932.6,8667.0,162891.0] operation(u) || compatible(v,w,u) homomorphism(x,w,choice) subclass(ordered_pair(apply(x,not_homomorphism1(v,w,u)),apply(x,not_homomorphism2(v,w,u))),y)* -> homomorphism(v,w,u) member(apply(x,apply(w,ordered_pair(not_homomorphism1(v,w,u),not_homomorphism2(v,w,u)))),y)*.
% 300.10/300.70  227372[7:Rew:192979.1,227341.3,192979.1,227341.1,192979.1,227341.0] || member(image(u,range_of(identity_relation)),ordinal_numbers) member(ordered_pair(v,apply(choice,image(u,range_of(identity_relation)))),cross_product(ordinal_numbers,ordinal_numbers)) -> equal(cross_product(singleton(v),ordinal_numbers),identity_relation) equal(image(u,range_of(identity_relation)),identity_relation) member(ordered_pair(v,apply(choice,image(u,range_of(identity_relation)))),compose(u,regular(cross_product(singleton(v),ordinal_numbers))))*.
% 300.10/300.70  235466[5:Res:28980.1,10120.0] || subclass(rest_relation,flip(segment(u,v,w))) homomorphism(x,restrict(u,v,singleton(w)),y)* -> equal(apply(y,ordered_pair(apply(x,ordered_pair(z,x1)),apply(x,rest_of(ordered_pair(x1,z))))),apply(x,apply(restrict(u,v,singleton(w)),ordered_pair(ordered_pair(z,x1),rest_of(ordered_pair(x1,z))))))*.
% 300.10/300.70  235598[5:Res:28979.1,10120.0] || subclass(rest_relation,rotate(segment(u,v,w))) homomorphism(x,restrict(u,v,singleton(w)),y)* -> equal(apply(y,ordered_pair(apply(x,ordered_pair(z,rest_of(ordered_pair(x1,z)))),apply(x,x1))),apply(x,apply(restrict(u,v,singleton(w)),ordered_pair(ordered_pair(z,rest_of(ordered_pair(x1,z))),x1))))*.
% 300.10/300.70  197851[8:SpL:13302.1,116116.1] || asymmetric(cross_product(u,v),ordinal_numbers) member(ordinal_numbers,cantor(restrict(inverse(cross_product(u,v)),u,v))) equal(least(rest_of(restrict(inverse(cross_product(u,v)),u,v)),w),identity_relation)** member(ordinal_numbers,w) subclass(w,x)* well_ordering(rest_of(restrict(inverse(cross_product(u,v)),u,v)),x)* -> .
% 300.10/300.70  61541[7:SpR:10130.4,13099.0] operation(u) || compatible(v,w,u) homomorphism(add_relation,w,x) -> homomorphism(v,w,u) equal(recursion(identity_relation,apply(x,ordered_pair(apply(add_relation,not_homomorphism1(v,w,u)),apply(add_relation,not_homomorphism2(v,w,u)))),union_of_range_map),ordinal_multiply(apply(w,ordered_pair(not_homomorphism1(v,w,u),not_homomorphism2(v,w,u))),y))*.
% 300.10/300.70  54963[0:Rew:159.0,54949.4,159.0,54949.4] operation(u) || compatible(v,w,u) homomorphism(recursion(x,successor_relation,union_of_range_map),w,y) -> homomorphism(v,w,u) equal(apply(y,ordered_pair(ordinal_add(x,not_homomorphism1(v,w,u)),ordinal_add(x,not_homomorphism2(v,w,u)))),ordinal_add(x,apply(w,ordered_pair(not_homomorphism1(v,w,u),not_homomorphism2(v,w,u)))))*.
% 300.10/300.70  54931[0:SpR:10130.4,159.0] operation(u) || compatible(v,w,u) homomorphism(x,w,recursion(y,successor_relation,union_of_range_map)) -> homomorphism(v,w,u) equal(apply(x,apply(w,ordered_pair(not_homomorphism1(v,w,u),not_homomorphism2(v,w,u)))),ordinal_add(y,ordered_pair(apply(x,not_homomorphism1(v,w,u)),apply(x,not_homomorphism2(v,w,u)))))*.
% 300.10/300.70  61540[7:SpR:10130.4,13099.0] operation(u) || compatible(v,w,u) homomorphism(x,w,add_relation) -> homomorphism(v,w,u) equal(recursion(identity_relation,apply(x,apply(w,ordered_pair(not_homomorphism1(v,w,u),not_homomorphism2(v,w,u)))),union_of_range_map),ordinal_multiply(ordered_pair(apply(x,not_homomorphism1(v,w,u)),apply(x,not_homomorphism2(v,w,u))),y))*.
% 300.10/300.70  54967[0:MRR:54966.1,90.1] operation(u) || homomorphism(v,w,x) equal(apply(u,ordered_pair(apply(v,not_homomorphism1(v,w,u)),apply(v,not_homomorphism2(v,w,u)))),apply(x,ordered_pair(apply(v,not_homomorphism1(v,w,u)),apply(v,not_homomorphism2(v,w,u)))))* compatible(v,w,u) -> homomorphism(v,w,u).
% 300.10/300.70  161829[8:Rew:116078.0,51351.8,116078.0,51351.5,116078.0,51351.4,116078.0,51351.4,116078.0,51351.4,116078.0,51351.3] function(u) operation(restrict(element_relation,ordinal_numbers,v)) operation(w) || subclass(range_of(u),cantor(sum_class(v))) equal(cantor(cantor(w)),cantor(u)) subclass(cantor(w),x)* well_ordering(y,x)* -> homomorphism(u,w,restrict(element_relation,ordinal_numbers,v))* member(least(y,cantor(w)),cantor(w))*.
% 300.10/300.70  215961[25:SpR:208985.1,10130.4] operation(apply(u,not_homomorphism2(v,w,x))) operation(x) || compatible(v,w,x) homomorphism(u,w,y) -> homomorphism(v,w,x) equal(apply(y,ordered_pair(apply(u,not_homomorphism1(v,w,x)),ordinal_numbers)),apply(u,apply(w,ordered_pair(not_homomorphism1(v,w,x),not_homomorphism2(v,w,x)))))*.
% 300.10/300.70  215958[25:SpR:208972.1,10130.4] operation(not_homomorphism1(u,v,w)) operation(w) || compatible(u,v,w) homomorphism(x,v,y) -> homomorphism(u,v,w) equal(apply(y,ordered_pair(apply(x,ordinal_numbers),apply(x,not_homomorphism2(u,v,w)))),apply(x,apply(v,ordered_pair(not_homomorphism1(u,v,w),not_homomorphism2(u,v,w)))))*.
% 300.10/300.70  215945[25:SpR:10130.4,208972.1] operation(u) operation(apply(v,ordered_pair(not_homomorphism1(w,v,u),not_homomorphism2(w,v,u)))) || compatible(w,v,u) homomorphism(x,v,y) -> homomorphism(w,v,u) equal(apply(y,ordered_pair(apply(x,not_homomorphism1(w,v,u)),apply(x,not_homomorphism2(w,v,u)))),apply(x,ordinal_numbers))**.
% 300.10/300.70  48520[0:SpR:3603.0,3594.0] ||  -> equal(intersection(complement(symmetric_difference(complement(restrict(u,v,w)),union(u,cross_product(v,w)))),union(complement(symmetric_difference(u,cross_product(v,w))),union(complement(restrict(u,v,w)),union(u,cross_product(v,w))))),symmetric_difference(complement(symmetric_difference(u,cross_product(v,w))),union(complement(restrict(u,v,w)),union(u,cross_product(v,w)))))**.
% 300.10/300.70  48521[0:SpR:3606.0,3594.0] ||  -> equal(intersection(complement(symmetric_difference(complement(restrict(u,v,w)),union(cross_product(v,w),u))),union(complement(symmetric_difference(cross_product(v,w),u)),union(complement(restrict(u,v,w)),union(cross_product(v,w),u)))),symmetric_difference(complement(symmetric_difference(cross_product(v,w),u)),union(complement(restrict(u,v,w)),union(cross_product(v,w),u))))**.
% 300.10/300.70  116505[8:Rew:116078.0,51419.3] operation(u) operation(v) || compatible(w,v,u) subclass(cantor(v),complement(intersection(x,y))) member(ordered_pair(not_homomorphism1(w,v,u),not_homomorphism2(w,v,u)),union(x,y)) -> homomorphism(w,v,u) member(ordered_pair(not_homomorphism1(w,v,u),not_homomorphism2(w,v,u)),symmetric_difference(x,y))*.
% 300.10/300.70  51406[0:Rew:6355.1,51393.3] || member(not_subclass_element(cross_product(u,v),w),range_of(x)) homomorphism(y,inverse(x),z)* -> subclass(cross_product(u,v),w) equal(apply(z,ordered_pair(apply(y,first(not_subclass_element(cross_product(u,v),w))),apply(y,second(not_subclass_element(cross_product(u,v),w))))),apply(y,apply(inverse(x),not_subclass_element(cross_product(u,v),w))))*.
% 300.10/300.70  208219[7:Res:13333.3,8803.0] inductive(image(u,singleton(v))) || well_ordering(w,image(u,singleton(v))) member(ordered_pair(v,least(w,image(successor_relation,image(u,singleton(v))))),cross_product(ordinal_numbers,ordinal_numbers)) -> equal(image(successor_relation,image(u,singleton(v))),identity_relation) member(ordered_pair(v,least(w,image(successor_relation,image(u,singleton(v))))),compose(successor_relation,u))*.
% 300.10/300.70  214132[7:Res:13529.2,13362.0] || member(ordered_pair(u,regular(image(v,image(w,singleton(u))))),cross_product(ordinal_numbers,ordinal_numbers)) subclass(compose(v,w),x)* well_ordering(omega,x) -> equal(image(v,image(w,singleton(u))),identity_relation) equal(integer_of(ordered_pair(ordered_pair(u,regular(image(v,image(w,singleton(u))))),least(omega,compose(v,w)))),identity_relation)**.
% 300.10/300.70  215901[7:Res:13530.3,5.0] || member(image(u,image(v,singleton(w))),ordinal_numbers) member(ordered_pair(w,apply(choice,image(u,image(v,singleton(w))))),cross_product(ordinal_numbers,ordinal_numbers))* subclass(compose(u,v),x) -> equal(image(u,image(v,singleton(w))),identity_relation) member(ordered_pair(w,apply(choice,image(u,image(v,singleton(w))))),x)*.
% 300.10/300.70  224629[10:Rew:223660.1,224455.3,223660.1,224455.2,223660.1,224455.1] || subclass(element_relation,identity_relation) member(image(u,image(v,identity_relation)),ordinal_numbers) member(ordered_pair(cross_product(ordinal_numbers,ordinal_numbers),apply(choice,image(u,image(v,identity_relation)))),cross_product(ordinal_numbers,ordinal_numbers)) -> equal(image(u,image(v,identity_relation)),identity_relation) member(ordered_pair(cross_product(ordinal_numbers,ordinal_numbers),apply(choice,image(u,image(v,identity_relation)))),compose(u,v))*.
% 300.10/300.70  212295[8:Res:161774.3,9421.0] || section(u,v,w) well_ordering(x,v) member(y,z)* -> equal(cantor(restrict(u,w,v)),identity_relation) equal(ordered_pair(first(ordered_pair(y,least(x,cantor(restrict(u,w,v))))),second(ordered_pair(y,least(x,cantor(restrict(u,w,v)))))),ordered_pair(y,least(x,cantor(restrict(u,w,v)))))**.
% 300.10/300.70  212361[7:SpR:13259.2,9706.3] || member(cross_product(u,v),ordinal_numbers) member(second(apply(choice,cross_product(u,v))),ordinal_numbers)* member(first(apply(choice,cross_product(u,v))),ordinal_numbers) equal(successor(first(apply(choice,cross_product(u,v)))),second(apply(choice,cross_product(u,v)))) -> equal(cross_product(u,v),identity_relation) member(apply(choice,cross_product(u,v)),successor_relation).
% 300.10/300.70  215764[8:SoR:117822.0,19277.2] single_valued_class(restrict(u,v,singleton(w))) || subclass(range_of(restrict(u,v,singleton(w))),cantor(segment(u,v,w)))* equal(cross_product(cantor(segment(u,v,w)),cantor(segment(u,v,w))),segment(u,v,w)) equal(restrict(u,v,singleton(w)),identity_relation) -> operation(restrict(u,v,singleton(w))).
% 300.10/300.70  215899[7:Res:13530.3,129.0] || member(image(u,image(v,singleton(w))),ordinal_numbers) member(ordered_pair(w,apply(choice,image(u,image(v,singleton(w))))),cross_product(ordinal_numbers,ordinal_numbers))* subclass(compose(u,v),x)* well_ordering(y,x)* -> equal(image(u,image(v,singleton(w))),identity_relation) member(least(y,compose(u,v)),compose(u,v))*.
% 300.10/300.70  215916[7:Rew:50855.1,215887.3,50855.1,215887.2,50855.1,215887.1] || member(singleton(u),subset_relation) member(image(v,image(w,u)),ordinal_numbers) member(ordered_pair(first(singleton(u)),apply(choice,image(v,image(w,u)))),cross_product(ordinal_numbers,ordinal_numbers)) -> equal(image(v,image(w,u)),identity_relation) member(ordered_pair(first(singleton(u)),apply(choice,image(v,image(w,u)))),compose(v,w))*.
% 300.10/300.70  50409[0:Rew:3594.0,50332.4] || member(u,union(complement(intersection(v,w)),union(v,w)))* member(u,complement(symmetric_difference(v,w))) subclass(symmetric_difference(complement(intersection(v,w)),union(v,w)),x)* well_ordering(y,x)* -> member(least(y,symmetric_difference(complement(intersection(v,w)),union(v,w))),symmetric_difference(complement(intersection(v,w)),union(v,w)))*.
% 300.10/300.70  53008[0:Res:27.2,9872.0] || member(ordered_pair(u,least(intersection(v,intersection(w,x)),y)),x)* member(ordered_pair(u,least(intersection(v,intersection(w,x)),y)),w)* member(ordered_pair(u,least(intersection(v,intersection(w,x)),y)),v)* member(u,y) subclass(y,z)* well_ordering(intersection(v,intersection(w,x)),z)* -> .
% 300.10/300.70  212300[8:Res:161774.3,9878.0] || section(u,v,w) well_ordering(cross_product(x,cantor(restrict(u,w,v))),v)* member(y,x)* member(y,cantor(restrict(u,w,v)))* subclass(cantor(restrict(u,w,v)),z) well_ordering(cross_product(x,cantor(restrict(u,w,v))),z)* -> equal(cantor(restrict(u,w,v)),identity_relation).
% 300.10/300.70  212362[7:SpR:13259.2,9837.3] || member(cross_product(u,v),ordinal_numbers) member(second(apply(choice,cross_product(u,v))),ordinal_numbers) member(first(apply(choice,cross_product(u,v))),ordinal_numbers) equal(sum_class(range_of(first(apply(choice,cross_product(u,v))))),second(apply(choice,cross_product(u,v))))** -> equal(cross_product(u,v),identity_relation) member(apply(choice,cross_product(u,v)),union_of_range_map).
% 300.10/300.70  214796[7:Res:9997.2,13362.0] || member(ordered_pair(u,not_subclass_element(image(v,image(w,singleton(u))),x)),cross_product(ordinal_numbers,ordinal_numbers)) subclass(compose(v,w),y)* well_ordering(omega,y) -> subclass(image(v,image(w,singleton(u))),x) equal(integer_of(ordered_pair(ordered_pair(u,not_subclass_element(image(v,image(w,singleton(u))),x)),least(omega,compose(v,w)))),identity_relation)**.
% 300.10/300.70  54467[5:Res:9618.2,10120.0] || member(ordered_pair(u,v),cross_product(ordinal_numbers,ordinal_numbers)) subclass(composition_function,segment(w,x,y)) homomorphism(z,restrict(w,x,singleton(y)),x1)* -> equal(apply(x1,ordered_pair(apply(z,u),apply(z,ordered_pair(v,compose(u,v))))),apply(z,apply(restrict(w,x,singleton(y)),ordered_pair(u,ordered_pair(v,compose(u,v))))))*.
% 300.10/300.70  54968[0:Obv:54946.6] operation(u) || homomorphism(v,w,x) compatible(y,w,u) homomorphism(v,w,z) -> homomorphism(y,w,u) equal(apply(z,ordered_pair(apply(v,not_homomorphism1(y,w,u)),apply(v,not_homomorphism2(y,w,u)))),apply(x,ordered_pair(apply(v,not_homomorphism1(y,w,u)),apply(v,not_homomorphism2(y,w,u)))))*.
% 300.10/300.70  53025[0:Res:62.1,9872.0] || member(ordered_pair(u,ordered_pair(v,least(intersection(w,image(x,image(y,singleton(u)))),z))),compose(x,y))* member(ordered_pair(v,least(intersection(w,image(x,image(y,singleton(u)))),z)),w)* member(v,z) subclass(z,x1)* well_ordering(intersection(w,image(x,image(y,singleton(u)))),x1)* -> .
% 300.10/300.70  117839[8:Rew:116078.0,116301.2] single_valued_class(restrict(u,v,singleton(w))) || subclass(range_of(restrict(u,v,singleton(w))),cantor(segment(u,v,w)))* equal(cross_product(cantor(segment(u,v,w)),cantor(segment(u,v,w))),segment(u,v,w)) equal(restrict(u,v,singleton(w)),cross_product(ordinal_numbers,ordinal_numbers)) -> operation(restrict(u,v,singleton(w))).
% 300.10/300.70  161830[8:Rew:116078.0,51352.8,116078.0,51352.5,116078.0,51352.4,116078.0,51352.4,116078.0,51352.4,116078.0,51352.3] function(u) operation(restrict(v,w,singleton(x))) operation(y) || subclass(range_of(u),cantor(segment(v,w,x))) equal(cantor(cantor(y)),cantor(u)) subclass(cantor(y),z)* well_ordering(x1,z)* -> homomorphism(u,y,restrict(v,w,singleton(x)))* member(least(x1,cantor(y)),cantor(y))*.
% 300.10/300.70  212360[7:SpR:13259.2,9865.3] || member(cross_product(u,v),ordinal_numbers) member(second(apply(choice,cross_product(u,v))),ordinal_numbers) member(first(apply(choice,cross_product(u,v))),ordinal_numbers) equal(compose(w,first(apply(choice,cross_product(u,v)))),second(apply(choice,cross_product(u,v))))** -> equal(cross_product(u,v),identity_relation) member(apply(choice,cross_product(u,v)),compose_class(w)).
% 300.10/300.70  212424[7:Rew:13259.2,212406.4] || member(cross_product(u,v),ordinal_numbers) member(ordered_pair(ordered_pair(second(apply(choice,cross_product(u,v))),first(apply(choice,cross_product(u,v)))),w),x)* member(ordered_pair(apply(choice,cross_product(u,v)),w),cross_product(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers)) -> equal(cross_product(u,v),identity_relation) member(ordered_pair(apply(choice,cross_product(u,v)),w),flip(x)).
% 300.10/300.70  212425[7:Rew:13259.2,212405.4] || member(cross_product(u,v),ordinal_numbers) member(ordered_pair(ordered_pair(second(apply(choice,cross_product(u,v))),w),first(apply(choice,cross_product(u,v)))),x)* member(ordered_pair(apply(choice,cross_product(u,v)),w),cross_product(cross_product(ordinal_numbers,ordinal_numbers),ordinal_numbers)) -> equal(cross_product(u,v),identity_relation) member(ordered_pair(apply(choice,cross_product(u,v)),w),rotate(x)).
% 300.10/300.70  212426[7:Rew:13259.2,212366.2] || member(cross_product(u,v),ordinal_numbers) member(w,ordinal_numbers) member(apply(choice,cross_product(u,v)),cross_product(ordinal_numbers,ordinal_numbers)) member(ordered_pair(ordered_pair(second(apply(choice,cross_product(u,v))),first(apply(choice,cross_product(u,v)))),w),x)* -> equal(cross_product(u,v),identity_relation) member(ordered_pair(apply(choice,cross_product(u,v)),w),flip(x)).
% 300.10/300.70  212427[7:Rew:13259.2,212365.2] || member(cross_product(u,v),ordinal_numbers) member(w,ordinal_numbers) member(apply(choice,cross_product(u,v)),cross_product(ordinal_numbers,ordinal_numbers)) member(ordered_pair(ordered_pair(second(apply(choice,cross_product(u,v))),w),first(apply(choice,cross_product(u,v)))),x)* -> equal(cross_product(u,v),identity_relation) member(ordered_pair(apply(choice,cross_product(u,v)),w),rotate(x)).
% 300.10/300.70  215885[7:SpR:154.1,13530.3] || member(u,recursion_equation_functions(v)) member(image(v,image(rest_of(u),singleton(w))),ordinal_numbers) member(ordered_pair(w,apply(choice,image(v,image(rest_of(u),singleton(w))))),cross_product(ordinal_numbers,ordinal_numbers))* -> equal(image(v,image(rest_of(u),singleton(w))),identity_relation) member(ordered_pair(w,apply(choice,image(v,image(rest_of(u),singleton(w))))),u)*.
% 300.10/300.70  197707[7:Res:13247.2,8803.0] || member(intersection(u,image(v,image(w,singleton(x)))),ordinal_numbers) member(ordered_pair(x,apply(choice,intersection(u,image(v,image(w,singleton(x)))))),cross_product(ordinal_numbers,ordinal_numbers)) -> equal(intersection(u,image(v,image(w,singleton(x)))),identity_relation) member(ordered_pair(x,apply(choice,intersection(u,image(v,image(w,singleton(x)))))),compose(v,w))*.
% 300.10/300.70  197418[7:Res:13246.2,8803.0] || member(intersection(image(u,image(v,singleton(w))),x),ordinal_numbers) member(ordered_pair(w,apply(choice,intersection(image(u,image(v,singleton(w))),x))),cross_product(ordinal_numbers,ordinal_numbers)) -> equal(intersection(image(u,image(v,singleton(w))),x),identity_relation) member(ordered_pair(w,apply(choice,intersection(image(u,image(v,singleton(w))),x))),compose(u,v))*.
% 300.10/300.70  214906[7:Rew:13260.1,214889.3] || member(regular(cross_product(u,v)),segment(w,x,y)) homomorphism(z,restrict(w,x,singleton(y)),x1)* -> equal(cross_product(u,v),identity_relation) equal(apply(x1,ordered_pair(apply(z,first(regular(cross_product(u,v)))),apply(z,second(regular(cross_product(u,v)))))),apply(z,apply(restrict(w,x,singleton(y)),regular(cross_product(u,v)))))*.
% 300.10/300.70  117840[8:Rew:116078.0,116281.3] operation(u) operation(v) || compatible(w,v,u) subclass(cantor(v),cantor(x)) homomorphism(y,x,z)* -> homomorphism(w,v,u) equal(apply(z,ordered_pair(apply(y,not_homomorphism1(w,v,u)),apply(y,not_homomorphism2(w,v,u)))),apply(y,apply(x,ordered_pair(not_homomorphism1(w,v,u),not_homomorphism2(w,v,u)))))*.
% 300.10/300.70  116520[8:Rew:116078.0,51446.3] operation(u) operation(v) || compatible(w,v,u) subclass(cantor(v),image(x,image(y,singleton(z)))) member(ordered_pair(z,ordered_pair(not_homomorphism1(w,v,u),not_homomorphism2(w,v,u))),cross_product(ordinal_numbers,ordinal_numbers)) -> homomorphism(w,v,u) member(ordered_pair(z,ordered_pair(not_homomorphism1(w,v,u),not_homomorphism2(w,v,u))),compose(x,y))*.
% 300.10/300.70  213430[7:Rew:13259.2,213415.4] || member(cross_product(u,v),ordinal_numbers) member(apply(choice,cross_product(u,v)),range_of(w)) homomorphism(x,inverse(w),y)* -> equal(cross_product(u,v),identity_relation) equal(apply(y,ordered_pair(apply(x,first(apply(choice,cross_product(u,v)))),apply(x,second(apply(choice,cross_product(u,v)))))),apply(x,apply(inverse(w),apply(choice,cross_product(u,v)))))*.
% 300.10/300.70  116506[8:Rew:116078.0,51463.3] operation(u) operation(v) || compatible(w,v,u) subclass(cantor(v),range_of(x)) homomorphism(y,inverse(x),z)* -> homomorphism(w,v,u) equal(apply(z,ordered_pair(apply(y,not_homomorphism1(w,v,u)),apply(y,not_homomorphism2(w,v,u)))),apply(y,apply(inverse(x),ordered_pair(not_homomorphism1(w,v,u),not_homomorphism2(w,v,u)))))*.
% 300.10/300.70  214712[7:MRR:214670.3,13039.0] || transitive(u,v) well_ordering(w,restrict(u,v,v)) subclass(singleton(least(w,compose(restrict(u,v,v),restrict(u,v,v)))),compose(restrict(u,v,v),restrict(u,v,v))) -> section(w,singleton(least(w,compose(restrict(u,v,v),restrict(u,v,v)))),compose(restrict(u,v,v),restrict(u,v,v)))*.
% 300.10/300.70  53010[0:Res:8551.2,9872.0] || member(ordered_pair(u,least(intersection(v,restrict(w,x,y)),z)),cross_product(x,y))* member(ordered_pair(u,least(intersection(v,restrict(w,x,y)),z)),w)* member(ordered_pair(u,least(intersection(v,restrict(w,x,y)),z)),v)* member(u,z) subclass(z,x1)* well_ordering(intersection(v,restrict(w,x,y)),x1)* -> .
% 300.10/300.70  54480[0:Rew:6355.1,54465.3] || member(not_subclass_element(cross_product(u,v),w),segment(x,y,z)) homomorphism(x1,restrict(x,y,singleton(z)),x2)* -> subclass(cross_product(u,v),w) equal(apply(x2,ordered_pair(apply(x1,first(not_subclass_element(cross_product(u,v),w))),apply(x1,second(not_subclass_element(cross_product(u,v),w))))),apply(x1,apply(restrict(x,y,singleton(z)),not_subclass_element(cross_product(u,v),w))))*.
% 300.10/300.70  53068[0:Rew:3594.0,52976.4,3594.0,52976.1] || member(ordered_pair(u,least(symmetric_difference(complement(intersection(v,w)),union(v,w)),x)),union(complement(intersection(v,w)),union(v,w)))* member(ordered_pair(u,least(symmetric_difference(complement(intersection(v,w)),union(v,w)),x)),complement(symmetric_difference(v,w))) member(u,x) subclass(x,y)* well_ordering(symmetric_difference(complement(intersection(v,w)),union(v,w)),y)* -> .
% 300.10/300.70  215818[7:SpR:916.0,13361.3] || transitive(cross_product(u,v),w) well_ordering(x,restrict(cross_product(u,v),w,w)) -> equal(compose(restrict(cross_product(u,v),w,w),restrict(cross_product(u,v),w,w)),identity_relation) member(least(x,compose(restrict(cross_product(w,w),u,v),restrict(cross_product(w,w),u,v))),compose(restrict(cross_product(w,w),u,v),restrict(cross_product(w,w),u,v)))*.
% 300.10/300.70  53024[5:Res:10061.3,9872.0] || member(least(intersection(u,flip(v)),w),ordinal_numbers) member(ordered_pair(x,y),cross_product(ordinal_numbers,ordinal_numbers)) member(ordered_pair(ordered_pair(y,x),least(intersection(u,flip(v)),w)),v)* member(ordered_pair(ordered_pair(x,y),least(intersection(u,flip(v)),w)),u)* member(ordered_pair(x,y),w) subclass(w,z)* well_ordering(intersection(u,flip(v)),z)* -> .
% 300.10/300.70  53023[5:Res:10093.3,9872.0] || member(least(intersection(u,rotate(v)),w),ordinal_numbers) member(ordered_pair(x,y),cross_product(ordinal_numbers,ordinal_numbers)) member(ordered_pair(ordered_pair(y,least(intersection(u,rotate(v)),w)),x),v)* member(ordered_pair(ordered_pair(x,y),least(intersection(u,rotate(v)),w)),u)* member(ordered_pair(x,y),w) subclass(w,z)* well_ordering(intersection(u,rotate(v)),z)* -> .
% 300.10/300.70  216053[25:Rew:214376.1,216048.3] operation(not_homomorphism2(recursion(u,successor_relation,union_of_range_map),v,w)) operation(w) operation(v) || equal(apply(w,ordered_pair(ordinal_add(u,not_homomorphism1(recursion(u,successor_relation,union_of_range_map),v,w)),ordinal_add(u,ordinal_numbers))),ordinal_add(u,apply(v,ordered_pair(not_homomorphism1(recursion(u,successor_relation,union_of_range_map),v,w),ordinal_numbers))))* compatible(recursion(u,successor_relation,union_of_range_map),v,w) -> homomorphism(recursion(u,successor_relation,union_of_range_map),v,w).
% 300.10/300.70  215896[7:Res:13530.3,13362.0] || member(image(u,image(v,singleton(w))),ordinal_numbers) member(ordered_pair(w,apply(choice,image(u,image(v,singleton(w))))),cross_product(ordinal_numbers,ordinal_numbers)) subclass(compose(u,v),x)* well_ordering(omega,x) -> equal(image(u,image(v,singleton(w))),identity_relation) equal(integer_of(ordered_pair(ordered_pair(w,apply(choice,image(u,image(v,singleton(w))))),least(omega,compose(u,v)))),identity_relation)**.
% 300.10/300.70  48483[0:SpR:3594.0,3594.0] ||  -> equal(intersection(complement(symmetric_difference(complement(symmetric_difference(u,v)),union(complement(intersection(u,v)),union(u,v)))),union(complement(symmetric_difference(complement(intersection(u,v)),union(u,v))),union(complement(symmetric_difference(u,v)),union(complement(intersection(u,v)),union(u,v))))),symmetric_difference(complement(symmetric_difference(complement(intersection(u,v)),union(u,v))),union(complement(symmetric_difference(u,v)),union(complement(intersection(u,v)),union(u,v)))))**.
% 300.10/300.70  54938[0:SpR:10130.4,284.1] operation(u) || compatible(v,w,u) homomorphism(x,w,y) member(image(x,singleton(apply(w,ordered_pair(not_homomorphism1(v,w,u),not_homomorphism2(v,w,u))))),ordinal_numbers) -> homomorphism(v,w,u) subclass(apply(y,ordered_pair(apply(x,not_homomorphism1(v,w,u)),apply(x,not_homomorphism2(v,w,u)))),image(x,singleton(apply(w,ordered_pair(not_homomorphism1(v,w,u),not_homomorphism2(v,w,u))))))*.
% 300.10/300.70  214908[7:Rew:13259.2,214890.4] || member(cross_product(u,v),ordinal_numbers) member(apply(choice,cross_product(u,v)),segment(w,x,y)) homomorphism(z,restrict(w,x,singleton(y)),x1)* -> equal(cross_product(u,v),identity_relation) equal(apply(x1,ordered_pair(apply(z,first(apply(choice,cross_product(u,v)))),apply(z,second(apply(choice,cross_product(u,v)))))),apply(z,apply(restrict(w,x,singleton(y)),apply(choice,cross_product(u,v)))))*.
% 300.10/300.70  215822[7:Res:13361.3,13362.0] || transitive(u,v) well_ordering(w,restrict(u,v,v)) subclass(compose(restrict(u,v,v),restrict(u,v,v)),x)* well_ordering(omega,x) -> equal(compose(restrict(u,v,v),restrict(u,v,v)),identity_relation) equal(integer_of(ordered_pair(least(w,compose(restrict(u,v,v),restrict(u,v,v))),least(omega,compose(restrict(u,v,v),restrict(u,v,v))))),identity_relation)**.
% 300.10/300.70  116507[8:Rew:116078.0,54468.3] operation(u) operation(v) || compatible(w,v,u) subclass(cantor(v),segment(x,y,z)) homomorphism(x1,restrict(x,y,singleton(z)),x2)* -> homomorphism(w,v,u) equal(apply(x2,ordered_pair(apply(x1,not_homomorphism1(w,v,u)),apply(x1,not_homomorphism2(w,v,u)))),apply(x1,apply(restrict(x,y,singleton(z)),ordered_pair(not_homomorphism1(w,v,u),not_homomorphism2(w,v,u)))))*.
% 300.10/300.70  54928[0:SpR:10130.4,284.1] operation(u) || compatible(v,w,u) homomorphism(x,w,y) member(image(y,singleton(ordered_pair(apply(x,not_homomorphism1(v,w,u)),apply(x,not_homomorphism2(v,w,u))))),ordinal_numbers) -> homomorphism(v,w,u) subclass(apply(x,apply(w,ordered_pair(not_homomorphism1(v,w,u),not_homomorphism2(v,w,u)))),image(y,singleton(ordered_pair(apply(x,not_homomorphism1(v,w,u)),apply(x,not_homomorphism2(v,w,u))))))*.
% 300.10/300.70  216052[25:SpL:214376.1,10145.2] operation(apply(u,ordered_pair(not_homomorphism1(recursion(v,successor_relation,union_of_range_map),u,w),not_homomorphism2(recursion(v,successor_relation,union_of_range_map),u,w)))) operation(w) operation(u) || equal(apply(w,ordered_pair(ordinal_add(v,not_homomorphism1(recursion(v,successor_relation,union_of_range_map),u,w)),ordinal_add(v,not_homomorphism2(recursion(v,successor_relation,union_of_range_map),u,w)))),ordinal_add(v,ordinal_numbers))** compatible(recursion(v,successor_relation,union_of_range_map),u,w) -> homomorphism(recursion(v,successor_relation,union_of_range_map),u,w).
% 300.10/300.70  216043[25:SpL:208985.1,10145.2] operation(ordinal_add(u,not_homomorphism2(recursion(u,successor_relation,union_of_range_map),v,w))) operation(w) operation(v) || equal(ordinal_add(u,apply(v,ordered_pair(not_homomorphism1(recursion(u,successor_relation,union_of_range_map),v,w),not_homomorphism2(recursion(u,successor_relation,union_of_range_map),v,w)))),apply(w,ordered_pair(ordinal_add(u,not_homomorphism1(recursion(u,successor_relation,union_of_range_map),v,w)),ordinal_numbers)))** compatible(recursion(u,successor_relation,union_of_range_map),v,w) -> homomorphism(recursion(u,successor_relation,union_of_range_map),v,w).
% 300.10/300.70  216042[25:SpL:214376.1,10145.2] operation(not_homomorphism1(recursion(u,successor_relation,union_of_range_map),v,w)) operation(w) operation(v) || equal(ordinal_add(u,apply(v,ordered_pair(not_homomorphism1(recursion(u,successor_relation,union_of_range_map),v,w),not_homomorphism2(recursion(u,successor_relation,union_of_range_map),v,w)))),apply(w,ordered_pair(ordinal_add(u,ordinal_numbers),ordinal_add(u,not_homomorphism2(recursion(u,successor_relation,union_of_range_map),v,w)))))** compatible(recursion(u,successor_relation,union_of_range_map),v,w) -> homomorphism(recursion(u,successor_relation,union_of_range_map),v,w).
% 300.10/300.70  54951[0:SpR:159.0,10130.4] operation(u) || compatible(v,recursion(w,successor_relation,union_of_range_map),u) homomorphism(x,recursion(w,successor_relation,union_of_range_map),y) -> homomorphism(v,recursion(w,successor_relation,union_of_range_map),u) equal(apply(y,ordered_pair(apply(x,not_homomorphism1(v,recursion(w,successor_relation,union_of_range_map),u)),apply(x,not_homomorCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------