TSTP Solution File: SET505-6 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET505-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 05:26:39 EDT 2022
% Result : Unsatisfiable 6.75s 6.92s
% Output : Refutation 6.88s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET505-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n026.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sat Jul 9 16:54:40 EDT 2022
% 0.12/0.33 % CPUTime :
% 6.75/6.92
% 6.75/6.92 SPASS V 3.9
% 6.75/6.92 SPASS beiseite: Proof found.
% 6.75/6.92 % SZS status Theorem
% 6.75/6.92 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.75/6.92 SPASS derived 18449 clauses, backtracked 1474 clauses, performed 6 splits and kept 8660 clauses.
% 6.75/6.92 SPASS allocated 92918 KBytes.
% 6.75/6.92 SPASS spent 0:00:06.57 on the problem.
% 6.75/6.92 0:00:00.04 for the input.
% 6.75/6.92 0:00:00.00 for the FLOTTER CNF translation.
% 6.75/6.92 0:00:00.19 for inferences.
% 6.75/6.92 0:00:00.30 for the backtracking.
% 6.75/6.92 0:00:05.91 for the reduction.
% 6.75/6.92
% 6.75/6.92
% 6.75/6.92 Here is a proof with depth 12, length 218 :
% 6.75/6.92 % SZS output start Refutation
% 6.75/6.92 1[0:Inp] || -> member(ordered_pair(universal_class,y__dfg),cross_product(universal_class,universal_class))*.
% 6.75/6.92 2[0:Inp] || member(u,v)*+ subclass(v,w)* -> member(u,w)*.
% 6.75/6.92 3[0:Inp] || -> subclass(u,v) member(not_subclass_element(u,v),u)*.
% 6.75/6.92 4[0:Inp] || member(not_subclass_element(u,v),v)* -> subclass(u,v).
% 6.75/6.92 5[0:Inp] || -> subclass(u,universal_class)*.
% 6.75/6.92 7[0:Inp] || equal(u,v) -> subclass(v,u)*.
% 6.75/6.92 8[0:Inp] || subclass(u,v)*+ subclass(v,u)* -> equal(v,u).
% 6.75/6.92 9[0:Inp] || member(u,unordered_pair(v,w))* -> equal(u,w) equal(u,v).
% 6.75/6.92 10[0:Inp] || member(u,universal_class) -> member(u,unordered_pair(u,v))*.
% 6.75/6.92 11[0:Inp] || member(u,universal_class) -> member(u,unordered_pair(v,u))*.
% 6.75/6.92 12[0:Inp] || -> member(unordered_pair(u,v),universal_class)*.
% 6.75/6.92 13[0:Inp] || -> equal(unordered_pair(u,u),singleton(u))**.
% 6.75/6.92 14[0:Inp] || -> equal(unordered_pair(singleton(u),unordered_pair(u,singleton(v))),ordered_pair(u,v))**.
% 6.75/6.92 15[0:Inp] || member(ordered_pair(u,v),cross_product(w,x))* -> member(u,w).
% 6.75/6.92 22[0:Inp] || member(u,intersection(v,w))* -> member(u,v).
% 6.75/6.92 23[0:Inp] || member(u,intersection(v,w))* -> member(u,w).
% 6.75/6.92 24[0:Inp] || member(u,v) member(u,w) -> member(u,intersection(w,v))*.
% 6.75/6.92 25[0:Inp] || member(u,v) member(u,complement(v))* -> .
% 6.75/6.92 26[0:Inp] || member(u,universal_class) -> member(u,v) member(u,complement(v))*.
% 6.75/6.92 27[0:Inp] || -> equal(complement(intersection(complement(u),complement(v))),union(u,v))**.
% 6.75/6.92 28[0:Inp] || -> equal(intersection(complement(intersection(u,v)),complement(intersection(complement(u),complement(v)))),symmetric_difference(u,v))**.
% 6.75/6.92 30[0:Inp] || -> equal(intersection(cross_product(u,v),w),restrict(w,u,v))**.
% 6.75/6.92 31[0:Inp] || member(u,domain_of(v)) equal(restrict(v,singleton(u),universal_class),null_class)** -> .
% 6.75/6.92 44[0:Inp] || -> equal(union(u,singleton(u)),successor(u))**.
% 6.75/6.92 48[0:Inp] inductive(u) || -> member(null_class,u)*.
% 6.75/6.92 51[0:Inp] || -> inductive(omega)*.
% 6.75/6.92 67[0:Inp] || -> equal(u,null_class) member(regular(u),u)*.
% 6.75/6.92 68[0:Inp] || -> equal(u,null_class) equal(intersection(u,regular(u)),null_class)**.
% 6.75/6.92 71[0:Inp] || member(u,universal_class) -> equal(u,null_class) member(apply(choice,u),u)*.
% 6.75/6.92 76[0:Inp] || -> equal(intersection(inverse(subset_relation),subset_relation),identity_relation)**.
% 6.75/6.92 77[0:Inp] || -> equal(complement(domain_of(intersection(u,identity_relation))),diagonalise(u))**.
% 6.75/6.92 114[0:Rew:27.0,28.0] || -> equal(intersection(complement(intersection(u,v)),union(u,v)),symmetric_difference(u,v))**.
% 6.75/6.92 118[0:Res:1.0,15.0] || -> member(universal_class,universal_class)*.
% 6.75/6.92 133[0:SpR:13.0,12.0] || -> member(singleton(u),universal_class)*.
% 6.75/6.92 158[0:SpR:13.0,11.1] || member(u,universal_class) -> member(u,singleton(u))*.
% 6.75/6.92 164[0:Res:67.1,25.1] || member(regular(complement(u)),u)* -> equal(complement(u),null_class).
% 6.75/6.92 172[0:Res:67.1,23.0] || -> equal(intersection(u,v),null_class) member(regular(intersection(u,v)),v)*.
% 6.75/6.92 173[0:Res:3.1,23.0] || -> subclass(intersection(u,v),w) member(not_subclass_element(intersection(u,v),w),v)*.
% 6.75/6.92 179[0:Res:67.1,22.0] || -> equal(intersection(u,v),null_class) member(regular(intersection(u,v)),u)*.
% 6.75/6.92 180[0:Res:3.1,22.0] || -> subclass(intersection(u,v),w) member(not_subclass_element(intersection(u,v),w),u)*.
% 6.75/6.92 260[0:SpR:14.0,10.1] || member(singleton(u),universal_class) -> member(singleton(u),ordered_pair(u,v))*.
% 6.75/6.92 263[0:SpR:13.0,14.0] || -> equal(unordered_pair(singleton(singleton(u)),singleton(singleton(u))),ordered_pair(singleton(u),u))**.
% 6.75/6.92 264[0:MRR:260.0,133.0] || -> member(singleton(u),ordered_pair(u,v))*.
% 6.75/6.92 265[0:Rew:13.0,263.0] || -> equal(ordered_pair(singleton(u),u),singleton(singleton(singleton(u))))**.
% 6.75/6.92 269[0:SpR:265.0,264.0] || -> member(singleton(singleton(u)),singleton(singleton(singleton(u))))*.
% 6.75/6.92 277[0:SpR:77.0,26.2] || member(u,universal_class) -> member(u,domain_of(intersection(v,identity_relation)))* member(u,diagonalise(v)).
% 6.75/6.92 281[0:Res:26.2,4.0] || member(not_subclass_element(u,complement(v)),universal_class)*+ -> member(not_subclass_element(u,complement(v)),v)* subclass(u,complement(v)).
% 6.75/6.92 324[0:Res:5.0,8.0] || subclass(universal_class,u)* -> equal(universal_class,u).
% 6.75/6.92 354[0:Res:118.0,2.0] || subclass(universal_class,u)* -> member(universal_class,u).
% 6.75/6.92 359[0:Res:48.1,2.0] inductive(u) || subclass(u,v)* -> member(null_class,v).
% 6.75/6.92 360[0:Res:67.1,2.0] || subclass(u,v) -> equal(u,null_class) member(regular(u),v)*.
% 6.75/6.92 361[0:Res:3.1,2.0] || subclass(u,v) -> subclass(u,w) member(not_subclass_element(u,w),v)*.
% 6.75/6.92 394[0:Res:7.1,354.0] || equal(u,universal_class) -> member(universal_class,u)*.
% 6.75/6.92 419[0:Res:394.1,25.1] || equal(complement(u),universal_class) member(universal_class,u)* -> .
% 6.75/6.92 510[0:Res:158.1,419.1] || member(universal_class,universal_class) equal(complement(singleton(universal_class)),universal_class)** -> .
% 6.75/6.92 517[0:MRR:510.0,118.0] || equal(complement(singleton(universal_class)),universal_class)** -> .
% 6.75/6.92 536[0:SpL:13.0,9.0] || member(u,singleton(v))* -> equal(u,v) equal(u,v).
% 6.75/6.92 549[0:Obv:536.1] || member(u,singleton(v))* -> equal(u,v).
% 6.75/6.92 552[0:Res:67.1,549.0] || -> equal(singleton(u),null_class) equal(regular(singleton(u)),u)**.
% 6.75/6.92 553[0:Res:3.1,549.0] || -> subclass(singleton(u),v) equal(not_subclass_element(singleton(u),v),u)**.
% 6.75/6.92 557[0:Res:71.2,549.0] || member(singleton(u),universal_class) -> equal(singleton(u),null_class) equal(apply(choice,singleton(u)),u)**.
% 6.75/6.92 562[0:MRR:557.0,133.0] || -> equal(singleton(u),null_class) equal(apply(choice,singleton(u)),u)**.
% 6.75/6.92 664[0:SpR:552.1,67.1] || -> equal(singleton(u),null_class) equal(singleton(u),null_class) member(u,singleton(u))*.
% 6.75/6.92 665[0:SpR:552.1,68.1] || -> equal(singleton(u),null_class) equal(singleton(u),null_class) equal(intersection(singleton(u),u),null_class)**.
% 6.75/6.92 667[0:Obv:664.0] || -> equal(singleton(u),null_class) member(u,singleton(u))*.
% 6.75/6.92 668[0:Obv:665.0] || -> equal(singleton(u),null_class) equal(intersection(singleton(u),u),null_class)**.
% 6.75/6.92 1078[0:Res:24.2,2.0] || member(u,v)* member(u,w)* subclass(intersection(w,v),x)*+ -> member(u,x)*.
% 6.75/6.92 2227[0:SpR:668.1,77.0] || -> equal(singleton(identity_relation),null_class) equal(complement(domain_of(null_class)),diagonalise(singleton(identity_relation)))**.
% 6.75/6.92 2230[0:SpR:668.1,24.2] || member(u,v) member(u,singleton(v))* -> equal(singleton(v),null_class) member(u,null_class).
% 6.75/6.92 2299[0:Res:5.0,359.1] inductive(u) || -> member(null_class,universal_class)*.
% 6.75/6.92 2324[0:EmS:2299.0,51.0] || -> member(null_class,universal_class)*.
% 6.75/6.92 2520[0:SpR:76.0,172.1] || -> equal(intersection(inverse(subset_relation),subset_relation),null_class)** member(regular(identity_relation),subset_relation).
% 6.75/6.92 2540[0:Rew:76.0,2520.0] || -> equal(identity_relation,null_class) member(regular(identity_relation),subset_relation)*.
% 6.75/6.92 2546[1:Spt:2540.0] || -> equal(identity_relation,null_class)**.
% 6.75/6.92 2548[1:Rew:2546.0,77.0] || -> equal(complement(domain_of(intersection(u,null_class))),diagonalise(u))**.
% 6.75/6.92 2610[1:Rew:2546.0,277.1] || member(u,universal_class) -> member(u,domain_of(intersection(v,null_class)))* member(u,diagonalise(v)).
% 6.75/6.92 2644[1:Rew:2546.0,2227.0] || -> equal(singleton(null_class),null_class) equal(complement(domain_of(null_class)),diagonalise(singleton(identity_relation)))**.
% 6.75/6.92 2665[1:Rew:2546.0,2644.1] || -> equal(singleton(null_class),null_class) equal(complement(domain_of(null_class)),diagonalise(singleton(null_class)))**.
% 6.75/6.92 3187[0:SpR:553.1,3.1] || -> subclass(singleton(u),v)* subclass(singleton(u),v)* member(u,singleton(u))*.
% 6.75/6.92 3191[0:Obv:3187.0] || -> subclass(singleton(u),v)* member(u,singleton(u))*.
% 6.75/6.92 3192[0:Rew:667.0,3191.0] || -> subclass(null_class,u)* member(v,singleton(v))*.
% 6.75/6.92 3195[2:Spt:3192.0] || -> subclass(null_class,u)*.
% 6.75/6.92 3201[2:Res:3195.0,8.0] || subclass(u,null_class)* -> equal(u,null_class).
% 6.75/6.92 3407[0:Res:360.2,164.0] || subclass(complement(u),u)* -> equal(complement(u),null_class) equal(complement(u),null_class).
% 6.75/6.92 3422[0:Obv:3407.1] || subclass(complement(u),u)* -> equal(complement(u),null_class).
% 6.75/6.92 3431[0:Res:5.0,3422.0] || -> equal(complement(universal_class),null_class)**.
% 6.75/6.92 3442[0:SpR:3431.0,27.0] || -> equal(complement(intersection(null_class,complement(u))),union(universal_class,u))**.
% 6.75/6.92 3444[0:SpR:3431.0,27.0] || -> equal(complement(intersection(complement(u),null_class)),union(u,universal_class))**.
% 6.75/6.92 3456[0:SpL:3431.0,25.1] || member(u,universal_class) member(u,null_class)* -> .
% 6.75/6.92 3504[0:Res:179.1,3456.1] || member(regular(intersection(null_class,u)),universal_class)* -> equal(intersection(null_class,u),null_class).
% 6.75/6.92 3515[0:Res:172.1,3456.1] || member(regular(intersection(u,null_class)),universal_class)* -> equal(intersection(u,null_class),null_class).
% 6.75/6.92 3674[3:Spt:2665.0] || -> equal(singleton(null_class),null_class)**.
% 6.75/6.92 3682[3:SpR:3674.0,269.0] || -> member(singleton(null_class),singleton(singleton(null_class)))*.
% 6.75/6.92 3720[3:Rew:3674.0,3682.0,3674.0,3682.0] || -> member(null_class,null_class)*.
% 6.75/6.92 3731[3:Res:3720.0,3456.1] || member(null_class,universal_class)* -> .
% 6.75/6.92 3735[3:MRR:3731.0,2324.0] || -> .
% 6.75/6.92 3745[3:Spt:3735.0,2665.0,3674.0] || equal(singleton(null_class),null_class)** -> .
% 6.75/6.92 3746[3:Spt:3735.0,2665.1] || -> equal(complement(domain_of(null_class)),diagonalise(singleton(null_class)))**.
% 6.75/6.92 4314[0:Res:173.1,4.0] || -> subclass(intersection(u,v),v)* subclass(intersection(u,v),v)*.
% 6.75/6.92 4316[0:Obv:4314.0] || -> subclass(intersection(u,v),v)*.
% 6.75/6.92 4347[2:Res:4316.0,3201.0] || -> equal(intersection(u,null_class),null_class)**.
% 6.75/6.92 4352[2:Rew:4347.0,3444.0] || -> equal(union(u,universal_class),complement(null_class))**.
% 6.75/6.92 4353[2:Rew:4347.0,2548.0] || -> equal(complement(domain_of(null_class)),diagonalise(u))*.
% 6.75/6.92 4397[2:Rew:4347.0,2610.1] || member(u,universal_class) -> member(u,domain_of(null_class))* member(u,diagonalise(v))*.
% 6.75/6.92 4463[3:Rew:3746.0,4353.0] || -> equal(diagonalise(singleton(null_class)),diagonalise(u))*.
% 6.75/6.92 4552[2:SpR:4347.0,114.0] || -> equal(intersection(complement(null_class),union(u,null_class)),symmetric_difference(u,null_class))**.
% 6.75/6.92 4559[2:SpR:4347.0,30.0] || -> equal(restrict(null_class,u,v),null_class)**.
% 6.75/6.92 4575[2:SpL:4347.0,22.0] || member(u,null_class)* -> member(u,v)*.
% 6.75/6.92 4593[2:MRR:3456.0,4575.1] || member(u,null_class)* -> .
% 6.75/6.92 4626[2:Res:179.1,4593.0] || -> equal(intersection(null_class,u),null_class)**.
% 6.75/6.92 4644[2:Rew:4626.0,3442.0] || -> equal(union(universal_class,u),complement(null_class))**.
% 6.75/6.92 4675[3:SpR:4463.0,4463.0] || -> equal(diagonalise(u),diagonalise(v))*.
% 6.75/6.92 4709[2:SpR:4352.0,114.0] || -> equal(intersection(complement(intersection(u,universal_class)),complement(null_class)),symmetric_difference(u,universal_class))**.
% 6.75/6.92 4750[2:SpR:4644.0,44.0] || -> equal(complement(null_class),successor(universal_class))**.
% 6.75/6.92 4759[2:Rew:4750.0,4644.0] || -> equal(union(universal_class,u),successor(universal_class))**.
% 6.75/6.92 4782[2:Rew:4750.0,4552.0] || -> equal(intersection(successor(universal_class),union(u,null_class)),symmetric_difference(u,null_class))**.
% 6.75/6.92 4784[2:Rew:4750.0,4709.0] || -> equal(intersection(complement(intersection(u,universal_class)),successor(universal_class)),symmetric_difference(u,universal_class))**.
% 6.75/6.92 4849[2:SpL:4559.0,31.1] || member(u,domain_of(null_class))* equal(null_class,null_class) -> .
% 6.75/6.92 4850[2:Obv:4849.1] || member(u,domain_of(null_class))* -> .
% 6.75/6.92 4851[2:MRR:4397.1,4850.0] || member(u,universal_class) -> member(u,diagonalise(v))*.
% 6.75/6.92 4856[2:Res:67.1,4850.0] || -> equal(domain_of(null_class),null_class)**.
% 6.75/6.92 4884[3:Rew:4856.0,3746.0] || -> equal(diagonalise(singleton(null_class)),complement(null_class))**.
% 6.75/6.92 4947[3:Rew:4750.0,4884.0] || -> equal(diagonalise(singleton(null_class)),successor(universal_class))**.
% 6.75/6.92 5068[2:Res:4851.1,4.0] || member(not_subclass_element(u,diagonalise(v)),universal_class)* -> subclass(u,diagonalise(v)).
% 6.75/6.92 5069[3:SpR:4947.0,4675.0] || -> equal(diagonalise(u),successor(universal_class))**.
% 6.75/6.92 5088[3:Rew:5069.0,5068.0] || member(not_subclass_element(u,successor(universal_class)),universal_class)* -> subclass(u,diagonalise(v))*.
% 6.75/6.92 5112[3:Rew:5069.0,5088.1] || member(not_subclass_element(u,successor(universal_class)),universal_class)* -> subclass(u,successor(universal_class)).
% 6.75/6.92 5487[0:Res:180.1,4.0] || -> subclass(intersection(u,v),u)* subclass(intersection(u,v),u)*.
% 6.75/6.92 5491[0:Obv:5487.0] || -> subclass(intersection(u,v),u)*.
% 6.75/6.92 5509[0:SpR:114.0,5491.0] || -> subclass(symmetric_difference(u,v),complement(intersection(u,v)))*.
% 6.75/6.92 6237[2:SpR:4759.0,4782.0] || -> equal(intersection(successor(universal_class),successor(universal_class)),symmetric_difference(universal_class,null_class))**.
% 6.75/6.92 6265[2:SpR:6237.0,24.2] || member(u,successor(universal_class)) member(u,successor(universal_class)) -> member(u,symmetric_difference(universal_class,null_class))*.
% 6.75/6.92 6285[2:Obv:6265.0] || member(u,successor(universal_class)) -> member(u,symmetric_difference(universal_class,null_class))*.
% 6.75/6.92 6720[2:Res:6285.1,4.0] || member(not_subclass_element(u,symmetric_difference(universal_class,null_class)),successor(universal_class))* -> subclass(u,symmetric_difference(universal_class,null_class)).
% 6.75/6.92 7680[2:SpR:668.1,4784.0] || -> equal(singleton(universal_class),null_class) equal(intersection(complement(null_class),successor(universal_class)),symmetric_difference(singleton(universal_class),universal_class))**.
% 6.75/6.92 7698[2:Rew:6237.0,7680.1,4750.0,7680.1] || -> equal(singleton(universal_class),null_class) equal(symmetric_difference(singleton(universal_class),universal_class),symmetric_difference(universal_class,null_class))**.
% 6.75/6.92 7864[3:Res:361.2,5112.0] || subclass(u,universal_class) -> subclass(u,successor(universal_class))* subclass(u,successor(universal_class))*.
% 6.75/6.92 7868[3:Obv:7864.1] || subclass(u,universal_class) -> subclass(u,successor(universal_class))*.
% 6.75/6.92 7869[3:MRR:7868.0,5.0] || -> subclass(u,successor(universal_class))*.
% 6.75/6.92 7881[3:Res:7869.0,324.0] || -> equal(successor(universal_class),universal_class)**.
% 6.75/6.92 7895[3:Rew:7881.0,4750.0] || -> equal(complement(null_class),universal_class)**.
% 6.75/6.92 8267[3:Rew:7881.0,6720.0] || member(not_subclass_element(u,symmetric_difference(universal_class,null_class)),universal_class)* -> subclass(u,symmetric_difference(universal_class,null_class)).
% 6.75/6.92 10055[0:Res:361.2,281.0] || subclass(u,universal_class) -> subclass(u,complement(v)) member(not_subclass_element(u,complement(v)),v)* subclass(u,complement(v)).
% 6.75/6.92 10060[0:Obv:10055.1] || subclass(u,universal_class) -> member(not_subclass_element(u,complement(v)),v)* subclass(u,complement(v)).
% 6.75/6.92 10061[0:MRR:10060.0,5.0] || -> member(not_subclass_element(u,complement(v)),v)* subclass(u,complement(v)).
% 6.75/6.92 10506[0:Res:5.0,1078.2] || member(u,v)* member(u,w)* -> member(u,universal_class)*.
% 6.75/6.92 10516[0:Con:10506.1] || member(u,v)*+ -> member(u,universal_class)*.
% 6.75/6.92 10568[0:Res:67.1,10516.0] || -> equal(u,null_class) member(regular(u),universal_class)*.
% 6.75/6.92 10570[0:Res:3.1,10516.0] || -> subclass(u,v) member(not_subclass_element(u,v),universal_class)*.
% 6.75/6.92 10706[3:MRR:8267.0,10570.1] || -> subclass(u,symmetric_difference(universal_class,null_class))*.
% 6.75/6.92 10928[3:Res:10706.0,324.0] || -> equal(symmetric_difference(universal_class,null_class),universal_class)**.
% 6.75/6.92 10944[3:Rew:10928.0,7698.1] || -> equal(singleton(universal_class),null_class) equal(symmetric_difference(singleton(universal_class),universal_class),universal_class)**.
% 6.75/6.92 11578[4:Spt:10944.0] || -> equal(singleton(universal_class),null_class)**.
% 6.75/6.92 11579[4:Rew:11578.0,517.0] || equal(complement(null_class),universal_class)** -> .
% 6.75/6.92 11583[4:Rew:7895.0,11579.0] || equal(universal_class,universal_class)* -> .
% 6.75/6.92 11584[4:Obv:11583.0] || -> .
% 6.75/6.92 11585[4:Spt:11584.0,10944.0,11578.0] || equal(singleton(universal_class),null_class)** -> .
% 6.75/6.92 11586[4:Spt:11584.0,10944.1] || -> equal(symmetric_difference(singleton(universal_class),universal_class),universal_class)**.
% 6.75/6.92 11588[4:SpR:11586.0,5509.0] || -> subclass(universal_class,complement(intersection(singleton(universal_class),universal_class)))*.
% 6.75/6.92 11603[4:Res:11588.0,324.0] || -> equal(complement(intersection(singleton(universal_class),universal_class)),universal_class)**.
% 6.75/6.92 11654[4:SpL:11603.0,25.1] || member(u,intersection(singleton(universal_class),universal_class))* member(u,universal_class) -> .
% 6.88/7.05 11673[4:MRR:11654.1,23.1] || member(u,intersection(singleton(universal_class),universal_class))* -> .
% 6.88/7.05 11724[4:Res:24.2,11673.0] || member(u,universal_class) member(u,singleton(universal_class))* -> .
% 6.88/7.05 11767[4:MRR:11724.0,10516.1] || member(u,singleton(universal_class))* -> .
% 6.88/7.05 11784[4:Res:71.2,11767.0] || member(singleton(universal_class),universal_class)* -> equal(singleton(universal_class),null_class).
% 6.88/7.05 11812[4:MRR:11784.0,11784.1,133.0,11585.0] || -> .
% 6.88/7.05 11813[2:Spt:11812.0,3192.1] || -> member(u,singleton(u))*.
% 6.88/7.05 11814[0:MRR:3456.0,10516.1] || member(u,null_class)* -> .
% 6.88/7.05 11817[0:MRR:3515.0,10568.1] || -> equal(intersection(u,null_class),null_class)**.
% 6.88/7.05 11820[0:Rew:11817.0,3444.0] || -> equal(union(u,universal_class),complement(null_class))**.
% 6.88/7.05 11874[0:MRR:3504.0,10568.1] || -> equal(intersection(null_class,u),null_class)**.
% 6.88/7.05 11877[0:Rew:11874.0,3442.0] || -> equal(union(universal_class,u),complement(null_class))**.
% 6.88/7.05 11996[0:MRR:2230.3,11814.0] || member(u,v) member(u,singleton(v))* -> equal(singleton(v),null_class).
% 6.88/7.05 12044[2:Res:11813.0,10516.0] || -> member(u,universal_class)*.
% 6.88/7.05 12045[2:Res:11813.0,2.0] || subclass(singleton(u),v)* -> member(u,v).
% 6.88/7.05 12050[2:MRR:71.0,12044.0] || -> equal(u,null_class) member(apply(choice,u),u)*.
% 6.88/7.05 12367[0:Res:10061.0,11814.0] || -> subclass(u,complement(null_class))*.
% 6.88/7.05 12369[0:Res:361.2,11814.0] || subclass(u,null_class)*+ -> subclass(u,v)*.
% 6.88/7.05 12380[0:Res:12367.0,324.0] || -> equal(complement(null_class),universal_class)**.
% 6.88/7.05 12403[0:Rew:12380.0,11820.0] || -> equal(union(u,universal_class),universal_class)**.
% 6.88/7.05 12408[0:Rew:12380.0,11877.0] || -> equal(union(universal_class,u),universal_class)**.
% 6.88/7.05 12492[0:SpR:11817.0,114.0] || -> equal(intersection(complement(null_class),union(u,null_class)),symmetric_difference(u,null_class))**.
% 6.88/7.05 12538[0:Rew:12380.0,12492.0] || -> equal(intersection(universal_class,union(u,null_class)),symmetric_difference(u,null_class))**.
% 6.88/7.05 12617[0:SpR:12403.0,114.0] || -> equal(intersection(complement(intersection(u,universal_class)),universal_class),symmetric_difference(u,universal_class))**.
% 6.88/7.05 13232[0:Res:7.1,12369.0] || equal(null_class,u) -> subclass(u,v)*.
% 6.88/7.05 13737[2:Res:13232.1,12045.0] || equal(singleton(u),null_class) -> member(u,v)*.
% 6.88/7.05 13782[2:Res:13737.1,11814.0] || equal(singleton(u),null_class)** -> .
% 6.88/7.05 13791[2:MRR:562.0,13782.0] || -> equal(apply(choice,singleton(u)),u)**.
% 6.88/7.05 13795[2:MRR:11996.2,13782.0] || member(u,v) member(u,singleton(v))* -> .
% 6.88/7.05 14322[0:SpR:12408.0,12538.0] || -> equal(intersection(universal_class,universal_class),symmetric_difference(universal_class,null_class))**.
% 6.88/7.05 14391[0:SpR:14322.0,24.2] || member(u,universal_class) member(u,universal_class) -> member(u,symmetric_difference(universal_class,null_class))*.
% 6.88/7.05 14404[0:Obv:14391.0] || member(u,universal_class) -> member(u,symmetric_difference(universal_class,null_class))*.
% 6.88/7.05 17352[2:Res:12050.1,13795.1] || member(apply(choice,singleton(u)),u)* -> equal(singleton(u),null_class).
% 6.88/7.05 17373[2:Rew:13791.0,17352.0] || member(u,u)* -> equal(singleton(u),null_class).
% 6.88/7.05 17374[2:MRR:17373.1,13782.0] || member(u,u)* -> .
% 6.88/7.05 17375[2:UnC:17374.0,12044.0] || -> .
% 6.88/7.05 17383[1:Spt:17375.0,2540.0,2546.0] || equal(identity_relation,null_class)** -> .
% 6.88/7.05 17384[1:Spt:17375.0,2540.1] || -> member(regular(identity_relation),subset_relation)*.
% 6.88/7.05 18479[0:Res:14404.1,4.0] || member(not_subclass_element(u,symmetric_difference(universal_class,null_class)),universal_class)* -> subclass(u,symmetric_difference(universal_class,null_class)).
% 6.88/7.05 18486[0:MRR:18479.0,10570.1] || -> subclass(u,symmetric_difference(universal_class,null_class))*.
% 6.88/7.05 18648[0:Res:18486.0,324.0] || -> equal(symmetric_difference(universal_class,null_class),universal_class)**.
% 6.88/7.05 18654[0:Rew:18648.0,14322.0] || -> equal(intersection(universal_class,universal_class),universal_class)**.
% 6.88/7.05 22516[0:SpR:668.1,12617.0] || -> equal(singleton(universal_class),null_class) equal(intersection(complement(null_class),universal_class),symmetric_difference(singleton(universal_class),universal_class))**.
% 6.88/7.05 22537[0:Rew:18654.0,22516.1,12380.0,22516.1] || -> equal(singleton(universal_class),null_class) equal(symmetric_difference(singleton(universal_class),universal_class),universal_class)**.
% 6.88/7.05 22549[2:Spt:22537.0] || -> equal(singleton(universal_class),null_class)**.
% 6.88/7.05 22551[2:Rew:22549.0,517.0] || equal(complement(null_class),universal_class)** -> .
% 6.88/7.05 22554[2:Rew:12380.0,22551.0] || equal(universal_class,universal_class)* -> .
% 6.88/7.05 22555[2:Obv:22554.0] || -> .
% 6.88/7.05 22556[2:Spt:22555.0,22537.0,22549.0] || equal(singleton(universal_class),null_class)** -> .
% 6.88/7.05 22557[2:Spt:22555.0,22537.1] || -> equal(symmetric_difference(singleton(universal_class),universal_class),universal_class)**.
% 6.88/7.05 22559[2:SpR:22557.0,5509.0] || -> subclass(universal_class,complement(intersection(singleton(universal_class),universal_class)))*.
% 6.88/7.05 22578[2:Res:22559.0,324.0] || -> equal(complement(intersection(singleton(universal_class),universal_class)),universal_class)**.
% 6.88/7.05 22652[2:SpL:22578.0,25.1] || member(u,intersection(singleton(universal_class),universal_class))* member(u,universal_class) -> .
% 6.88/7.05 22673[2:MRR:22652.1,10516.1] || member(u,intersection(singleton(universal_class),universal_class))* -> .
% 6.88/7.05 22780[2:Res:24.2,22673.0] || member(u,universal_class) member(u,singleton(universal_class))* -> .
% 6.88/7.05 22835[2:MRR:22780.0,10516.1] || member(u,singleton(universal_class))* -> .
% 6.88/7.05 22862[2:Res:71.2,22835.0] || member(singleton(universal_class),universal_class)* -> equal(singleton(universal_class),null_class).
% 6.88/7.05 22894[2:MRR:22862.0,22862.1,133.0,22556.0] || -> .
% 6.88/7.05 % SZS output end Refutation
% 6.88/7.05 Formulae used in the proof : prove_corollary_2_to_universal_class_not_set_1 subclass_members not_subclass_members1 not_subclass_members2 class_elements_are_sets equal_implies_subclass2 subclass_implies_equal unordered_pair_member unordered_pair2 unordered_pair3 unordered_pairs_in_universal singleton_set ordered_pair cartesian_product1 intersection1 intersection2 intersection3 complement1 complement2 union symmetric_difference restriction2 domain1 successor inductive1 omega_is_inductive1 regularity1 regularity2 choice2 identity_relation diagonalisation
% 6.88/7.05
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