TSTP Solution File: SET511-6 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET511-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n027.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 05:26:41 EDT 2022
% Result : Unsatisfiable 24.10s 24.30s
% Output : Refutation 24.49s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.14 % Problem : SET511-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.15/0.15 % Command : run_spass %d %s
% 0.15/0.37 % Computer : n027.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 600
% 0.15/0.37 % DateTime : Sun Jul 10 21:09:48 EDT 2022
% 0.15/0.37 % CPUTime :
% 24.10/24.30
% 24.10/24.30 SPASS V 3.9
% 24.10/24.30 SPASS beiseite: Proof found.
% 24.10/24.30 % SZS status Theorem
% 24.10/24.30 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 24.10/24.30 SPASS derived 32433 clauses, backtracked 1288 clauses, performed 12 splits and kept 14227 clauses.
% 24.10/24.30 SPASS allocated 109425 KBytes.
% 24.10/24.30 SPASS spent 0:0:23.86 on the problem.
% 24.10/24.30 0:00:00.04 for the input.
% 24.10/24.30 0:00:00.00 for the FLOTTER CNF translation.
% 24.10/24.30 0:00:00.43 for inferences.
% 24.10/24.30 0:00:01.18 for the backtracking.
% 24.10/24.30 0:0:21.79 for the reduction.
% 24.10/24.30
% 24.10/24.30
% 24.10/24.30 Here is a proof with depth 9, length 233 :
% 24.10/24.30 % SZS output start Refutation
% 24.10/24.30 1[0:Inp] || equal(unordered_pair(singleton(x__dfg),unordered_pair(x__dfg,null_class)),ordered_pair(x__dfg,universal_class))** -> .
% 24.10/24.30 2[0:Inp] || member(u,v)*+ subclass(v,w)* -> member(u,w)*.
% 24.10/24.30 3[0:Inp] || -> subclass(u,v) member(not_subclass_element(u,v),u)*.
% 24.10/24.30 4[0:Inp] || member(not_subclass_element(u,v),v)* -> subclass(u,v).
% 24.10/24.30 5[0:Inp] || -> subclass(u,universal_class)*.
% 24.10/24.30 7[0:Inp] || equal(u,v) -> subclass(v,u)*.
% 24.10/24.30 8[0:Inp] || subclass(u,v)*+ subclass(v,u)* -> equal(v,u).
% 24.10/24.30 9[0:Inp] || member(u,unordered_pair(v,w))* -> equal(u,w) equal(u,v).
% 24.10/24.30 10[0:Inp] || member(u,universal_class) -> member(u,unordered_pair(u,v))*.
% 24.10/24.30 11[0:Inp] || member(u,universal_class) -> member(u,unordered_pair(v,u))*.
% 24.10/24.30 12[0:Inp] || -> member(unordered_pair(u,v),universal_class)*.
% 24.10/24.30 13[0:Inp] || -> equal(unordered_pair(u,u),singleton(u))**.
% 24.10/24.30 14[0:Inp] || -> equal(unordered_pair(singleton(u),unordered_pair(u,singleton(v))),ordered_pair(u,v))**.
% 24.10/24.30 22[0:Inp] || member(u,intersection(v,w))* -> member(u,v).
% 24.10/24.30 23[0:Inp] || member(u,intersection(v,w))* -> member(u,w).
% 24.10/24.30 24[0:Inp] || member(u,v) member(u,w) -> member(u,intersection(w,v))*.
% 24.10/24.30 25[0:Inp] || member(u,v) member(u,complement(v))* -> .
% 24.10/24.30 26[0:Inp] || member(u,universal_class) -> member(u,v) member(u,complement(v))*.
% 24.10/24.30 27[0:Inp] || -> equal(complement(intersection(complement(u),complement(v))),union(u,v))**.
% 24.10/24.30 29[0:Inp] || -> equal(intersection(u,cross_product(v,w)),restrict(u,v,w))**.
% 24.10/24.30 31[0:Inp] || member(u,domain_of(v)) equal(restrict(v,singleton(u),universal_class),null_class)** -> .
% 24.10/24.30 44[0:Inp] || -> equal(union(u,singleton(u)),successor(u))**.
% 24.10/24.30 48[0:Inp] inductive(u) || -> member(null_class,u)*.
% 24.10/24.30 51[0:Inp] || -> inductive(omega)*.
% 24.10/24.30 54[0:Inp] || -> equal(domain_of(restrict(element_relation,universal_class,u)),sum_class(u))**.
% 24.10/24.30 67[0:Inp] || -> equal(u,null_class) member(regular(u),u)*.
% 24.10/24.30 68[0:Inp] || -> equal(u,null_class) equal(intersection(u,regular(u)),null_class)**.
% 24.10/24.30 69[0:Inp] || -> equal(sum_class(image(u,singleton(v))),apply(u,v))**.
% 24.10/24.30 71[0:Inp] || member(u,universal_class) -> equal(u,null_class) member(apply(choice,u),u)*.
% 24.10/24.30 76[0:Inp] || -> equal(intersection(inverse(subset_relation),subset_relation),identity_relation)**.
% 24.10/24.30 77[0:Inp] || -> equal(complement(domain_of(intersection(u,identity_relation))),diagonalise(u))**.
% 24.10/24.30 78[0:Inp] || -> equal(intersection(domain_of(u),diagonalise(compose(inverse(element_relation),u))),cantor(u))**.
% 24.10/24.30 128[0:SpR:13.0,12.0] || -> member(singleton(u),universal_class)*.
% 24.10/24.30 153[0:SpR:13.0,11.1] || member(u,universal_class) -> member(u,singleton(u))*.
% 24.10/24.30 158[0:Res:67.1,25.1] || member(regular(complement(u)),u)* -> equal(complement(u),null_class).
% 24.10/24.30 159[0:Res:3.1,25.1] || member(not_subclass_element(complement(u),v),u)* -> subclass(complement(u),v).
% 24.10/24.30 160[0:Res:3.1,4.0] || -> subclass(u,u)* subclass(u,u)*.
% 24.10/24.30 161[0:Obv:160.0] || -> subclass(u,u)*.
% 24.10/24.30 166[0:Res:67.1,23.0] || -> equal(intersection(u,v),null_class) member(regular(intersection(u,v)),v)*.
% 24.10/24.30 167[0:Res:3.1,23.0] || -> subclass(intersection(u,v),w) member(not_subclass_element(intersection(u,v),w),v)*.
% 24.10/24.30 170[0:SpL:68.1,22.0] || member(u,null_class)*+ -> equal(v,null_class) member(u,v)*.
% 24.10/24.30 173[0:Res:67.1,22.0] || -> equal(intersection(u,v),null_class) member(regular(intersection(u,v)),u)*.
% 24.10/24.30 174[0:Res:3.1,22.0] || -> subclass(intersection(u,v),w) member(not_subclass_element(intersection(u,v),w),u)*.
% 24.10/24.30 228[0:Res:3.1,170.0] || -> subclass(null_class,u) equal(v,null_class) member(not_subclass_element(null_class,u),v)*.
% 24.10/24.30 265[0:SpR:54.0,78.0] || -> equal(intersection(sum_class(u),diagonalise(compose(inverse(element_relation),restrict(element_relation,universal_class,u)))),cantor(restrict(element_relation,universal_class,u)))**.
% 24.10/24.30 280[0:SpR:14.0,10.1] || member(singleton(u),universal_class) -> member(singleton(u),ordered_pair(u,v))*.
% 24.10/24.30 283[0:SpR:13.0,14.0] || -> equal(unordered_pair(singleton(singleton(u)),singleton(singleton(u))),ordered_pair(singleton(u),u))**.
% 24.10/24.30 284[0:MRR:280.0,128.0] || -> member(singleton(u),ordered_pair(u,v))*.
% 24.10/24.30 285[0:Rew:13.0,283.0] || -> equal(ordered_pair(singleton(u),u),singleton(singleton(singleton(u))))**.
% 24.10/24.30 291[0:SpR:77.0,26.2] || member(u,universal_class) -> member(u,domain_of(intersection(v,identity_relation)))* member(u,diagonalise(v)).
% 24.10/24.30 293[0:Res:26.2,158.0] || member(regular(complement(complement(u))),universal_class)* -> member(regular(complement(complement(u))),u)* equal(complement(complement(u)),null_class).
% 24.10/24.30 295[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)).
% 24.10/24.30 297[0:SpR:285.0,284.0] || -> member(singleton(singleton(u)),singleton(singleton(singleton(u))))*.
% 24.10/24.30 331[0:Res:228.2,4.0] || -> subclass(null_class,u)* equal(u,null_class) subclass(null_class,u)*.
% 24.10/24.30 335[0:Obv:331.0] || -> equal(u,null_class) subclass(null_class,u)*.
% 24.10/24.30 336[0:MRR:335.0,7.0] || -> subclass(null_class,u)*.
% 24.10/24.30 345[0:Res:26.2,159.0] || member(not_subclass_element(complement(complement(u)),v),universal_class)* -> member(not_subclass_element(complement(complement(u)),v),u)* subclass(complement(complement(u)),v).
% 24.10/24.30 358[0:Res:5.0,8.0] || subclass(universal_class,u)* -> equal(universal_class,u).
% 24.10/24.30 391[0:Res:128.0,2.0] || subclass(universal_class,u) -> member(singleton(v),u)*.
% 24.10/24.30 394[0:Res:48.1,2.0] inductive(u) || subclass(u,v)*+ -> member(null_class,v)*.
% 24.10/24.30 395[0:Res:67.1,2.0] || subclass(u,v) -> equal(u,null_class) member(regular(u),v)*.
% 24.10/24.30 396[0:Res:3.1,2.0] || subclass(u,v) -> subclass(u,w) member(not_subclass_element(u,w),v)*.
% 24.10/24.30 426[0:Res:391.1,25.1] || subclass(universal_class,complement(u)) member(singleton(v),u)* -> .
% 24.10/24.30 575[0:SpL:13.0,9.0] || member(u,singleton(v))* -> equal(u,v) equal(u,v).
% 24.10/24.30 586[0:Obv:575.1] || member(u,singleton(v))* -> equal(u,v).
% 24.10/24.30 591[0:Res:67.1,586.0] || -> equal(singleton(u),null_class) equal(regular(singleton(u)),u)**.
% 24.10/24.30 596[0:Res:71.2,586.0] || member(singleton(u),universal_class) -> equal(singleton(u),null_class) equal(apply(choice,singleton(u)),u)**.
% 24.10/24.30 599[0:MRR:596.0,128.0] || -> equal(singleton(u),null_class) equal(apply(choice,singleton(u)),u)**.
% 24.10/24.30 673[0:SpR:591.1,68.1] || -> equal(singleton(u),null_class) equal(singleton(u),null_class) equal(intersection(singleton(u),u),null_class)**.
% 24.10/24.30 678[0:Obv:673.0] || -> equal(singleton(u),null_class) equal(intersection(singleton(u),u),null_class)**.
% 24.10/24.30 838[0:SpR:68.1,24.2] || member(u,regular(v))* member(u,v) -> equal(v,null_class) member(u,null_class).
% 24.10/24.30 843[0:SpR:78.0,24.2] || member(u,diagonalise(compose(inverse(element_relation),v)))* member(u,domain_of(v)) -> member(u,cantor(v)).
% 24.10/24.30 847[0:Res:24.2,2.0] || member(u,v)* member(u,w)* subclass(intersection(w,v),x)*+ -> member(u,x)*.
% 24.10/24.30 850[0:Res:24.2,4.0] || member(not_subclass_element(u,intersection(v,w)),w)*+ member(not_subclass_element(u,intersection(v,w)),v)* -> subclass(u,intersection(v,w)).
% 24.10/24.30 877[0:Res:153.1,426.1] || member(singleton(u),universal_class) subclass(universal_class,complement(singleton(singleton(u))))* -> .
% 24.10/24.30 888[0:MRR:877.0,128.0] || subclass(universal_class,complement(singleton(singleton(u))))* -> .
% 24.10/24.30 934[0:SpR:678.1,77.0] || -> equal(singleton(identity_relation),null_class) equal(complement(domain_of(null_class)),diagonalise(singleton(identity_relation)))**.
% 24.10/24.30 1006[0:Res:5.0,394.1] inductive(u) || -> member(null_class,universal_class)*.
% 24.10/24.30 1027[0:EmS:1006.0,51.0] || -> member(null_class,universal_class)*.
% 24.10/24.30 1034[0:Res:1027.0,2.0] || subclass(universal_class,u) -> member(null_class,u)*.
% 24.10/24.30 1038[0:Res:1034.1,25.1] || subclass(universal_class,complement(u))* member(null_class,u) -> .
% 24.10/24.30 1061[0:Res:7.1,1038.0] || equal(complement(u),universal_class) member(null_class,u)* -> .
% 24.10/24.30 1067[0:Res:153.1,1061.1] || member(null_class,universal_class) equal(complement(singleton(null_class)),universal_class)** -> .
% 24.10/24.30 1078[0:MRR:1067.0,1027.0] || equal(complement(singleton(null_class)),universal_class)** -> .
% 24.10/24.30 1308[0:SpR:76.0,166.1] || -> equal(intersection(inverse(subset_relation),subset_relation),null_class)** member(regular(identity_relation),subset_relation).
% 24.10/24.30 1328[0:Rew:76.0,1308.0] || -> equal(identity_relation,null_class) member(regular(identity_relation),subset_relation)*.
% 24.10/24.30 1334[1:Spt:1328.0] || -> equal(identity_relation,null_class)**.
% 24.10/24.30 1336[1:Rew:1334.0,77.0] || -> equal(complement(domain_of(intersection(u,null_class))),diagonalise(u))**.
% 24.10/24.30 1403[1:Rew:1334.0,291.1] || member(u,universal_class) -> member(u,domain_of(intersection(v,null_class)))* member(u,diagonalise(v)).
% 24.10/24.30 1464[1:Rew:1334.0,934.0] || -> equal(singleton(null_class),null_class) equal(complement(domain_of(null_class)),diagonalise(singleton(identity_relation)))**.
% 24.10/24.30 1469[1:Rew:1334.0,1464.1] || -> equal(singleton(null_class),null_class) equal(complement(domain_of(null_class)),diagonalise(singleton(null_class)))**.
% 24.10/24.30 1678[2:Spt:1469.0] || -> equal(singleton(null_class),null_class)**.
% 24.10/24.30 1687[2:SpR:1678.0,297.0] || -> member(singleton(null_class),singleton(singleton(null_class)))*.
% 24.10/24.30 1731[2:Rew:1678.0,1687.0,1678.0,1687.0] || -> member(null_class,null_class)*.
% 24.10/24.30 1758[2:Res:1731.0,2.0] || subclass(null_class,u) -> member(null_class,u)*.
% 24.10/24.30 1761[2:MRR:1758.0,336.0] || -> member(null_class,u)*.
% 24.10/24.30 1777[2:Res:1761.0,9.0] || -> equal(null_class,u)* equal(null_class,v)*.
% 24.10/24.30 1791[2:Con:1777.1] || -> equal(null_class,u)*.
% 24.10/24.30 1792[2:AED:1.0,1791.0] || -> .
% 24.10/24.30 1793[2:Spt:1792.0,1469.0,1678.0] || equal(singleton(null_class),null_class)** -> .
% 24.10/24.30 1794[2:Spt:1792.0,1469.1] || -> equal(complement(domain_of(null_class)),diagonalise(singleton(null_class)))**.
% 24.10/24.30 1979[0:Res:395.2,158.0] || subclass(complement(u),u)* -> equal(complement(u),null_class) equal(complement(u),null_class).
% 24.10/24.30 1981[0:Res:395.2,586.0] || subclass(u,singleton(v))* -> equal(u,null_class) equal(regular(u),v).
% 24.10/24.30 1983[0:Res:395.2,25.1] || subclass(u,complement(v)) member(regular(u),v)* -> equal(u,null_class).
% 24.10/24.30 1994[0:Obv:1979.1] || subclass(complement(u),u)* -> equal(complement(u),null_class).
% 24.10/24.30 2117[0:Res:5.0,1994.0] || -> equal(complement(universal_class),null_class)**.
% 24.10/24.30 2130[0:SpR:2117.0,27.0] || -> equal(complement(intersection(null_class,complement(u))),union(universal_class,u))**.
% 24.10/24.30 2144[0:SpL:2117.0,25.1] || member(u,universal_class)* member(u,null_class) -> .
% 24.10/24.30 2189[0:Res:395.2,2144.0] || subclass(u,universal_class) member(regular(u),null_class)* -> equal(u,null_class).
% 24.10/24.30 2194[0:MRR:2189.0,5.0] || member(regular(u),null_class)* -> equal(u,null_class).
% 24.10/24.30 2211[0:Res:173.1,2194.0] || -> equal(intersection(null_class,u),null_class)** equal(intersection(null_class,u),null_class)**.
% 24.10/24.30 2212[0:Res:166.1,2194.0] || -> equal(intersection(u,null_class),null_class)** equal(intersection(u,null_class),null_class)**.
% 24.10/24.30 2214[0:Obv:2211.0] || -> equal(intersection(null_class,u),null_class)**.
% 24.10/24.30 2215[0:Rew:2214.0,2130.0] || -> equal(union(universal_class,u),complement(null_class))**.
% 24.10/24.30 2216[0:Obv:2212.0] || -> equal(intersection(u,null_class),null_class)**.
% 24.10/24.30 2217[1:Rew:2216.0,1336.0] || -> equal(complement(domain_of(null_class)),diagonalise(u))*.
% 24.10/24.30 2222[1:Rew:2216.0,1403.1] || member(u,universal_class) -> member(u,domain_of(null_class))* member(u,diagonalise(v))*.
% 24.10/24.30 2250[2:Rew:1794.0,2217.0] || -> equal(diagonalise(singleton(null_class)),diagonalise(u))*.
% 24.10/24.30 2252[2:Rew:2250.0,78.0] || -> equal(intersection(domain_of(u),diagonalise(singleton(null_class))),cantor(u))**.
% 24.10/24.30 2276[2:Rew:2250.0,265.0] || -> equal(intersection(sum_class(u),diagonalise(singleton(null_class))),cantor(restrict(element_relation,universal_class,u)))**.
% 24.10/24.30 2278[2:Rew:2250.0,843.0] || member(u,diagonalise(singleton(null_class)))* member(u,domain_of(v))* -> member(u,cantor(v)).
% 24.10/24.30 2288[2:SpR:2250.0,2250.0] || -> equal(diagonalise(u),diagonalise(v))*.
% 24.10/24.30 2296[0:SpR:2214.0,29.0] || -> equal(restrict(null_class,u,v),null_class)**.
% 24.10/24.30 2312[0:SpL:2214.0,23.0] || member(u,null_class)* -> member(u,v)*.
% 24.10/24.30 2326[0:MRR:2144.0,2312.1] || member(u,null_class)* -> .
% 24.10/24.30 2328[0:MRR:838.3,2326.0] || member(u,regular(v))* member(u,v) -> equal(v,null_class).
% 24.10/24.30 2375[2:SpR:2288.0,2252.0] || -> equal(intersection(domain_of(u),diagonalise(v)),cantor(u))**.
% 24.10/24.30 2396[0:SpR:2215.0,44.0] || -> equal(complement(null_class),successor(universal_class))**.
% 24.10/24.30 2422[0:SpR:2396.0,27.0] || -> equal(complement(intersection(successor(universal_class),complement(u))),union(null_class,u))**.
% 24.10/24.30 2473[0:SpL:2296.0,31.1] || member(u,domain_of(null_class))* equal(null_class,null_class) -> .
% 24.10/24.30 2474[0:Obv:2473.1] || member(u,domain_of(null_class))* -> .
% 24.10/24.30 2475[1:MRR:2222.1,2474.0] || member(u,universal_class) -> member(u,diagonalise(v))*.
% 24.10/24.30 2479[0:Res:67.1,2474.0] || -> equal(domain_of(null_class),null_class)**.
% 24.10/24.30 2499[2:Rew:2479.0,1794.0] || -> equal(diagonalise(singleton(null_class)),complement(null_class))**.
% 24.10/24.30 2528[2:Rew:2396.0,2499.0] || -> equal(diagonalise(singleton(null_class)),successor(universal_class))**.
% 24.10/24.30 2529[2:Rew:2528.0,2278.0] || member(u,successor(universal_class)) member(u,domain_of(v))* -> member(u,cantor(v)).
% 24.10/24.30 2542[2:Rew:2528.0,2276.0] || -> equal(intersection(sum_class(u),successor(universal_class)),cantor(restrict(element_relation,universal_class,u)))**.
% 24.10/24.30 2605[1:Res:2475.1,4.0] || member(not_subclass_element(u,diagonalise(v)),universal_class)* -> subclass(u,diagonalise(v)).
% 24.10/24.30 2631[2:SpR:2528.0,2288.0] || -> equal(diagonalise(u),successor(universal_class))**.
% 24.10/24.30 2639[2:Rew:2631.0,2375.0] || -> equal(intersection(domain_of(u),successor(universal_class)),cantor(u))**.
% 24.10/24.30 2646[2:Rew:2631.0,2605.0] || member(not_subclass_element(u,successor(universal_class)),universal_class)* -> subclass(u,diagonalise(v))*.
% 24.10/24.30 2667[2:Rew:2631.0,2646.1] || member(not_subclass_element(u,successor(universal_class)),universal_class)* -> subclass(u,successor(universal_class)).
% 24.10/24.30 3118[0:Res:3.1,2328.0] || member(not_subclass_element(regular(u),v),u)* -> subclass(regular(u),v) equal(u,null_class).
% 24.10/24.30 3206[0:Res:167.1,4.0] || -> subclass(intersection(u,v),v)* subclass(intersection(u,v),v)*.
% 24.10/24.30 3210[0:Obv:3206.0] || -> subclass(intersection(u,v),v)*.
% 24.10/24.30 3295[0:Res:174.1,4.0] || -> subclass(intersection(u,v),u)* subclass(intersection(u,v),u)*.
% 24.10/24.30 3299[0:Obv:3295.0] || -> subclass(intersection(u,v),u)*.
% 24.10/24.30 3324[2:SpR:2639.0,3299.0] || -> subclass(cantor(u),domain_of(u))*.
% 24.10/24.30 3341[2:Res:3324.0,8.0] || subclass(domain_of(u),cantor(u))* -> equal(domain_of(u),cantor(u)).
% 24.10/24.30 4339[2:Res:3.1,2529.1] || member(not_subclass_element(domain_of(u),v),successor(universal_class)) -> subclass(domain_of(u),v) member(not_subclass_element(domain_of(u),v),cantor(u))*.
% 24.10/24.30 5579[2:Res:396.2,2667.0] || subclass(u,universal_class) -> subclass(u,successor(universal_class))* subclass(u,successor(universal_class))*.
% 24.10/24.30 5583[2:Obv:5579.1] || subclass(u,universal_class) -> subclass(u,successor(universal_class))*.
% 24.10/24.30 5584[2:MRR:5583.0,5.0] || -> subclass(u,successor(universal_class))*.
% 24.10/24.30 5590[2:Res:5584.0,358.0] || -> equal(successor(universal_class),universal_class)**.
% 24.10/24.30 5597[2:Rew:5590.0,2396.0] || -> equal(complement(null_class),universal_class)**.
% 24.10/24.30 5636[2:Rew:5590.0,2542.0] || -> equal(cantor(restrict(element_relation,universal_class,u)),intersection(sum_class(u),universal_class))**.
% 24.10/24.30 5978[2:Rew:5590.0,4339.0] || member(not_subclass_element(domain_of(u),v),universal_class) -> subclass(domain_of(u),v) member(not_subclass_element(domain_of(u),v),cantor(u))*.
% 24.10/24.30 7975[0:Res:396.2,295.0] || subclass(u,universal_class) -> subclass(u,complement(v)) member(not_subclass_element(u,complement(v)),v)* subclass(u,complement(v)).
% 24.10/24.30 7980[0:Obv:7975.1] || subclass(u,universal_class) -> member(not_subclass_element(u,complement(v)),v)* subclass(u,complement(v)).
% 24.10/24.30 7981[0:MRR:7980.0,5.0] || -> member(not_subclass_element(u,complement(v)),v)* subclass(u,complement(v)).
% 24.10/24.30 8029[0:Res:7981.0,2326.0] || -> subclass(u,complement(null_class))*.
% 24.10/24.30 8350[0:Res:5.0,847.2] || member(u,v)* member(u,w)* -> member(u,universal_class)*.
% 24.10/24.30 8360[0:Con:8350.1] || member(u,v)*+ -> member(u,universal_class)*.
% 24.10/24.30 8410[0:Res:67.1,8360.0] || -> equal(u,null_class) member(regular(u),universal_class)*.
% 24.10/24.30 8412[0:Res:3.1,8360.0] || -> subclass(u,v) member(not_subclass_element(u,v),universal_class)*.
% 24.49/24.67 8485[0:MRR:293.0,8410.1] || -> member(regular(complement(complement(u))),u)* equal(complement(complement(u)),null_class).
% 24.49/24.67 8527[0:MRR:345.0,8412.1] || -> member(not_subclass_element(complement(complement(u)),v),u)* subclass(complement(complement(u)),v).
% 24.49/24.67 8528[2:MRR:5978.0,8412.1] || -> subclass(domain_of(u),v) member(not_subclass_element(domain_of(u),v),cantor(u))*.
% 24.49/24.67 10946[0:Res:3.1,850.0] || member(not_subclass_element(u,intersection(v,u)),v)* -> subclass(u,intersection(v,u)) subclass(u,intersection(v,u)).
% 24.49/24.67 10962[0:Obv:10946.1] || member(not_subclass_element(u,intersection(v,u)),v)* -> subclass(u,intersection(v,u)).
% 24.49/24.67 13818[2:Res:8528.1,4.0] || -> subclass(domain_of(u),cantor(u))* subclass(domain_of(u),cantor(u))*.
% 24.49/24.67 13822[2:Obv:13818.0] || -> subclass(domain_of(u),cantor(u))*.
% 24.49/24.67 13823[2:MRR:3341.0,13822.0] || -> equal(domain_of(u),cantor(u))**.
% 24.49/24.67 13910[2:Rew:13823.0,54.0] || -> equal(cantor(restrict(element_relation,universal_class,u)),sum_class(u))**.
% 24.49/24.67 14442[2:Rew:5636.0,13910.0] || -> equal(intersection(sum_class(u),universal_class),sum_class(u))**.
% 24.49/24.67 15003[2:SpR:69.0,14442.0] || -> equal(intersection(apply(u,v),universal_class),apply(u,v))**.
% 24.49/24.67 15309[2:SpR:599.1,15003.0] || -> equal(singleton(u),null_class) equal(intersection(u,universal_class),u)**.
% 24.49/24.67 15372[2:SpR:15309.1,678.1] || -> equal(singleton(singleton(universal_class)),null_class)** equal(singleton(universal_class),null_class) equal(singleton(universal_class),null_class).
% 24.49/24.67 15420[2:Obv:15372.1] || -> equal(singleton(singleton(universal_class)),null_class)** equal(singleton(universal_class),null_class).
% 24.49/24.67 15498[2:SpL:15420.0,888.0] || subclass(universal_class,complement(null_class))* -> equal(singleton(universal_class),null_class).
% 24.49/24.67 15501[2:Rew:5597.0,15498.0] || subclass(universal_class,universal_class)* -> equal(singleton(universal_class),null_class).
% 24.49/24.67 15502[2:MRR:15501.0,161.0] || -> equal(singleton(universal_class),null_class)**.
% 24.49/24.67 15526[2:SpR:15502.0,14.0] || -> equal(unordered_pair(singleton(u),unordered_pair(u,null_class)),ordered_pair(u,universal_class))**.
% 24.49/24.67 15580[2:UnC:15526.0,1.0] || -> .
% 24.49/24.67 15594[1:Spt:15580.0,1328.0,1334.0] || equal(identity_relation,null_class)** -> .
% 24.49/24.67 15595[1:Spt:15580.0,1328.1] || -> member(regular(identity_relation),subset_relation)*.
% 24.49/24.67 15596[0:Rew:2396.0,8029.0] || -> subclass(u,successor(universal_class))*.
% 24.49/24.67 15650[0:Res:15596.0,358.0] || -> equal(successor(universal_class),universal_class)**.
% 24.49/24.67 15673[0:Rew:15650.0,2422.0] || -> equal(complement(intersection(universal_class,complement(u))),union(null_class,u))**.
% 24.49/24.67 15711[0:Rew:15650.0,2396.0] || -> equal(complement(null_class),universal_class)**.
% 24.49/24.67 23945[0:Res:8527.0,4.0] || -> subclass(complement(complement(u)),u)* subclass(complement(complement(u)),u)*.
% 24.49/24.67 23951[0:Obv:23945.0] || -> subclass(complement(complement(u)),u)*.
% 24.49/24.67 23995[0:SpR:15673.0,23951.0] || -> subclass(complement(union(null_class,u)),intersection(universal_class,complement(u)))*.
% 24.49/24.67 24473[0:SpR:44.0,23995.0] || -> subclass(complement(successor(null_class)),intersection(universal_class,complement(singleton(null_class))))*.
% 24.49/24.67 24492[0:Res:24473.0,8.0] || subclass(intersection(universal_class,complement(singleton(null_class))),complement(successor(null_class)))* -> equal(intersection(universal_class,complement(singleton(null_class))),complement(successor(null_class))).
% 24.49/24.67 25903[0:Res:67.1,1983.1] || subclass(u,complement(u))* -> equal(u,null_class) equal(u,null_class).
% 24.49/24.67 25950[0:Obv:25903.1] || subclass(u,complement(u))* -> equal(u,null_class).
% 24.49/24.67 27965[0:Res:8412.1,10962.0] || -> subclass(u,intersection(universal_class,u))* subclass(u,intersection(universal_class,u))*.
% 24.49/24.67 27991[0:Obv:27965.0] || -> subclass(u,intersection(universal_class,u))*.
% 24.49/24.67 28137[0:Res:27991.0,8.0] || subclass(intersection(universal_class,u),u)* -> equal(intersection(universal_class,u),u).
% 24.49/24.67 28193[0:MRR:28137.0,3210.0] || -> equal(intersection(universal_class,u),u)**.
% 24.49/24.67 28199[0:Rew:28193.0,15673.0] || -> equal(complement(complement(u)),union(null_class,u))**.
% 24.49/24.67 28282[0:Rew:28193.0,24492.0] || subclass(complement(singleton(null_class)),complement(successor(null_class)))* -> equal(intersection(universal_class,complement(singleton(null_class))),complement(successor(null_class))).
% 24.49/24.67 28495[0:Rew:28199.0,8485.0] || -> member(regular(union(null_class,u)),u)* equal(complement(complement(u)),null_class).
% 24.49/24.67 28501[0:Rew:28199.0,23951.0] || -> subclass(union(null_class,u),u)*.
% 24.49/24.67 28880[0:Rew:28199.0,28495.1] || -> member(regular(union(null_class,u)),u)* equal(union(null_class,u),null_class).
% 24.49/24.67 29117[0:Rew:28193.0,28282.1] || subclass(complement(singleton(null_class)),complement(successor(null_class)))* -> equal(complement(successor(null_class)),complement(singleton(null_class))).
% 24.49/24.67 29364[0:SpR:44.0,28501.0] || -> subclass(successor(null_class),singleton(null_class))*.
% 24.49/24.67 29383[0:Res:29364.0,1981.0] || -> equal(successor(null_class),null_class) equal(regular(successor(null_class)),null_class)**.
% 24.49/24.67 29621[0:SpR:44.0,28880.0] || -> member(regular(successor(null_class)),singleton(null_class))* equal(union(null_class,singleton(null_class)),null_class).
% 24.49/24.67 29661[0:Rew:44.0,29621.1] || -> member(regular(successor(null_class)),singleton(null_class))* equal(successor(null_class),null_class).
% 24.49/24.67 29662[0:Rew:29383.1,29661.0] || -> member(null_class,singleton(null_class))* equal(successor(null_class),null_class).
% 24.49/24.67 30740[2:Spt:29662.1] || -> equal(successor(null_class),null_class)**.
% 24.49/24.67 30753[2:Rew:30740.0,29117.0] || subclass(complement(singleton(null_class)),complement(null_class))* -> equal(complement(successor(null_class)),complement(singleton(null_class))).
% 24.49/24.67 30775[2:Rew:15711.0,30753.0] || subclass(complement(singleton(null_class)),universal_class)* -> equal(complement(successor(null_class)),complement(singleton(null_class))).
% 24.49/24.67 30776[2:Rew:30740.0,30775.1] || subclass(complement(singleton(null_class)),universal_class)* -> equal(complement(singleton(null_class)),complement(null_class)).
% 24.49/24.67 30777[2:Rew:15711.0,30776.1] || subclass(complement(singleton(null_class)),universal_class)* -> equal(complement(singleton(null_class)),universal_class).
% 24.49/24.67 30778[2:MRR:30777.0,30777.1,5.0,1078.0] || -> .
% 24.49/24.67 30783[2:Spt:30778.0,29662.1,30740.0] || equal(successor(null_class),null_class)** -> .
% 24.49/24.67 30784[2:Spt:30778.0,29662.0] || -> member(null_class,singleton(null_class))*.
% 24.49/24.67 34996[0:Res:7981.0,3118.0] || -> subclass(regular(u),complement(u))* subclass(regular(u),complement(u))* equal(u,null_class).
% 24.49/24.67 35006[0:Obv:34996.0] || -> subclass(regular(u),complement(u))* equal(u,null_class).
% 24.49/24.67 35051[0:SpR:591.1,35006.0] || -> equal(singleton(u),null_class) subclass(u,complement(singleton(u)))* equal(singleton(u),null_class).
% 24.49/24.67 35063[0:Obv:35051.0] || -> subclass(u,complement(singleton(u)))* equal(singleton(u),null_class).
% 24.49/24.67 41868[0:Res:35063.0,358.0] || -> equal(singleton(universal_class),null_class) equal(complement(singleton(universal_class)),universal_class)**.
% 24.49/24.67 41911[3:Spt:41868.0] || -> equal(singleton(universal_class),null_class)**.
% 24.49/24.67 41949[3:SpR:41911.0,14.0] || -> equal(unordered_pair(singleton(u),unordered_pair(u,null_class)),ordered_pair(u,universal_class))**.
% 24.49/24.67 42037[3:UnC:41949.0,1.0] || -> .
% 24.49/24.67 42067[3:Spt:42037.0,41868.0,41911.0] || equal(singleton(universal_class),null_class)** -> .
% 24.49/24.67 42068[3:Spt:42037.0,41868.1] || -> equal(complement(singleton(universal_class)),universal_class)**.
% 24.49/24.67 42179[3:SpL:42068.0,25950.0] || subclass(singleton(universal_class),universal_class)* -> equal(singleton(universal_class),null_class).
% 24.49/24.67 42238[3:MRR:42179.0,5.0] || -> equal(singleton(universal_class),null_class)**.
% 24.49/24.67 42239[3:MRR:42238.0,42067.0] || -> .
% 24.49/24.67 % SZS output end Refutation
% 24.49/24.67 Formulae used in the proof : prove_corollary_1_to_property_1_of_ordered_pair_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 intersection1 intersection2 intersection3 complement1 complement2 union restriction1 domain1 successor inductive1 omega_is_inductive1 sum_class_definition regularity1 regularity2 apply choice2 identity_relation diagonalisation cantor_class
% 24.49/24.67
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