TSTP Solution File: NUM154-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM154-1 : 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 : Mon Jul 18 14:24:23 EDT 2022
% Result : Unsatisfiable 122.13s 122.31s
% Output : Refutation 125.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 27
% Syntax : Number of clauses : 108 ( 57 unt; 21 nHn; 108 RR)
% Number of literals : 172 ( 0 equ; 55 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 24 ( 24 usr; 8 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(successor(x__dfg),null_class),
file('NUM154-1.p',unknown),
[] ).
cnf(2,axiom,
( ~ member(u,v)
| ~ subclass(v,w)
| member(u,w) ),
file('NUM154-1.p',unknown),
[] ).
cnf(3,axiom,
( subclass(u,v)
| member(not_subclass_element(u,v),u) ),
file('NUM154-1.p',unknown),
[] ).
cnf(4,axiom,
( ~ member(not_subclass_element(u,v),v)
| subclass(u,v) ),
file('NUM154-1.p',unknown),
[] ).
cnf(5,axiom,
subclass(u,universal_class),
file('NUM154-1.p',unknown),
[] ).
cnf(7,axiom,
( ~ equal(u,v)
| subclass(v,u) ),
file('NUM154-1.p',unknown),
[] ).
cnf(8,axiom,
( ~ subclass(u,v)
| ~ subclass(v,u)
| equal(v,u) ),
file('NUM154-1.p',unknown),
[] ).
cnf(10,axiom,
( ~ member(u,universal_class)
| member(u,unordered_pair(u,v)) ),
file('NUM154-1.p',unknown),
[] ).
cnf(11,axiom,
( ~ member(u,universal_class)
| member(u,unordered_pair(v,u)) ),
file('NUM154-1.p',unknown),
[] ).
cnf(12,axiom,
member(unordered_pair(u,v),universal_class),
file('NUM154-1.p',unknown),
[] ).
cnf(13,axiom,
equal(unordered_pair(u,u),singleton(u)),
file('NUM154-1.p',unknown),
[] ).
cnf(14,axiom,
equal(unordered_pair(singleton(u),unordered_pair(u,singleton(v))),ordered_pair(u,v)),
file('NUM154-1.p',unknown),
[] ).
cnf(16,axiom,
( ~ member(ordered_pair(u,v),cross_product(w,x))
| member(v,x) ),
file('NUM154-1.p',unknown),
[] ).
cnf(18,axiom,
( ~ member(u,cross_product(v,w))
| equal(ordered_pair(first(u),second(u)),u) ),
file('NUM154-1.p',unknown),
[] ).
cnf(22,axiom,
( ~ member(u,intersection(v,w))
| member(u,v) ),
file('NUM154-1.p',unknown),
[] ).
cnf(23,axiom,
( ~ member(u,intersection(v,w))
| member(u,w) ),
file('NUM154-1.p',unknown),
[] ).
cnf(24,axiom,
( ~ member(u,v)
| ~ member(u,w)
| member(u,intersection(w,v)) ),
file('NUM154-1.p',unknown),
[] ).
cnf(25,axiom,
( ~ member(u,v)
| ~ member(u,complement(v)) ),
file('NUM154-1.p',unknown),
[] ).
cnf(26,axiom,
( ~ member(u,universal_class)
| member(u,v)
| member(u,complement(v)) ),
file('NUM154-1.p',unknown),
[] ).
cnf(27,axiom,
equal(complement(intersection(complement(u),complement(v))),union(u,v)),
file('NUM154-1.p',unknown),
[] ).
cnf(29,axiom,
equal(intersection(u,cross_product(v,w)),restrict(u,v,w)),
file('NUM154-1.p',unknown),
[] ).
cnf(31,axiom,
( ~ member(u,domain_of(v))
| ~ equal(restrict(v,singleton(u),universal_class),null_class) ),
file('NUM154-1.p',unknown),
[] ).
cnf(44,axiom,
equal(union(u,singleton(u)),successor(u)),
file('NUM154-1.p',unknown),
[] ).
cnf(63,axiom,
( ~ function(u)
| subclass(u,cross_product(universal_class,universal_class)) ),
file('NUM154-1.p',unknown),
[] ).
cnf(67,axiom,
( equal(u,null_class)
| member(regular(u),u) ),
file('NUM154-1.p',unknown),
[] ).
cnf(77,axiom,
equal(complement(domain_of(intersection(u,identity_relation))),diagonalise(u)),
file('NUM154-1.p',unknown),
[] ).
cnf(148,axiom,
( ~ member(u,recursion_equation_functions(v))
| function(v) ),
file('NUM154-1.p',unknown),
[] ).
cnf(171,plain,
member(singleton(u),universal_class),
inference(spr,[status(thm),theory(equality)],[13,12]),
[iquote('0:SpR:13.0,12.0')] ).
cnf(178,plain,
( equal(recursion_equation_functions(u),null_class)
| function(u) ),
inference(res,[status(thm),theory(equality)],[67,148]),
[iquote('0:Res:67.1,148.0')] ).
cnf(179,plain,
( ~ member(u,null_class)
| function(v) ),
inference(rew,[status(thm),theory(equality)],[178,148]),
[iquote('0:Rew:178.0,148.0')] ).
cnf(213,plain,
( subclass(null_class,u)
| function(v) ),
inference(res,[status(thm),theory(equality)],[3,179]),
[iquote('0:Res:3.1,179.0')] ).
cnf(214,plain,
function(u),
inference(spt,[spt(split,[position(s1)])],[213]),
[iquote('1:Spt:213.1')] ).
cnf(215,plain,
subclass(u,cross_product(universal_class,universal_class)),
inference(mrr,[status(thm)],[63,214]),
[iquote('1:MRR:63.0,214.0')] ).
cnf(288,plain,
( ~ member(not_subclass_element(complement(u),v),u)
| subclass(complement(u),v) ),
inference(res,[status(thm),theory(equality)],[3,25]),
[iquote('0:Res:3.1,25.1')] ).
cnf(301,plain,
( subclass(intersection(u,v),w)
| member(not_subclass_element(intersection(u,v),w),v) ),
inference(res,[status(thm),theory(equality)],[3,23]),
[iquote('0:Res:3.1,23.0')] ).
cnf(319,plain,
( subclass(intersection(u,v),w)
| member(not_subclass_element(intersection(u,v),w),u) ),
inference(res,[status(thm),theory(equality)],[3,22]),
[iquote('0:Res:3.1,22.0')] ).
cnf(943,plain,
member(ordered_pair(u,v),universal_class),
inference(spr,[status(thm),theory(equality)],[14,12]),
[iquote('0:SpR:14.0,12.0')] ).
cnf(944,plain,
( ~ member(singleton(u),universal_class)
| member(singleton(u),ordered_pair(u,v)) ),
inference(spr,[status(thm),theory(equality)],[14,10]),
[iquote('0:SpR:14.0,10.1')] ).
cnf(945,plain,
( ~ member(unordered_pair(u,singleton(v)),universal_class)
| member(unordered_pair(u,singleton(v)),ordered_pair(u,v)) ),
inference(spr,[status(thm),theory(equality)],[14,11]),
[iquote('0:SpR:14.0,11.1')] ).
cnf(947,plain,
equal(unordered_pair(singleton(singleton(u)),singleton(singleton(u))),ordered_pair(singleton(u),u)),
inference(spr,[status(thm),theory(equality)],[13,14]),
[iquote('0:SpR:13.0,14.0')] ).
cnf(948,plain,
member(singleton(u),ordered_pair(u,v)),
inference(mrr,[status(thm)],[944,171]),
[iquote('0:MRR:944.0,171.0')] ).
cnf(949,plain,
equal(ordered_pair(singleton(u),u),singleton(singleton(singleton(u)))),
inference(rew,[status(thm),theory(equality)],[13,947]),
[iquote('0:Rew:13.0,947.0')] ).
cnf(950,plain,
member(unordered_pair(u,singleton(v)),ordered_pair(u,v)),
inference(mrr,[status(thm)],[945,12]),
[iquote('0:MRR:945.0,12.0')] ).
cnf(984,plain,
( ~ member(not_subclass_element(u,complement(v)),universal_class)
| member(not_subclass_element(u,complement(v)),v)
| subclass(u,complement(v)) ),
inference(res,[status(thm),theory(equality)],[26,4]),
[iquote('0:Res:26.2,4.0')] ).
cnf(1026,plain,
( ~ member(not_subclass_element(complement(complement(u)),v),universal_class)
| member(not_subclass_element(complement(complement(u)),v),u)
| subclass(complement(complement(u)),v) ),
inference(res,[status(thm),theory(equality)],[26,288]),
[iquote('0:Res:26.2,288.0')] ).
cnf(1044,plain,
( ~ subclass(universal_class,u)
| equal(universal_class,u) ),
inference(res,[status(thm),theory(equality)],[5,8]),
[iquote('0:Res:5.0,8.0')] ).
cnf(1063,plain,
equal(cross_product(universal_class,universal_class),universal_class),
inference(res,[status(thm),theory(equality)],[215,1044]),
[iquote('1:Res:215.0,1044.0')] ).
cnf(2398,plain,
( ~ subclass(ordered_pair(u,v),w)
| member(unordered_pair(u,singleton(v)),w) ),
inference(res,[status(thm),theory(equality)],[950,2]),
[iquote('0:Res:950.0,2.0')] ).
cnf(2399,plain,
( ~ subclass(u,v)
| subclass(u,w)
| member(not_subclass_element(u,w),v) ),
inference(res,[status(thm),theory(equality)],[3,2]),
[iquote('0:Res:3.1,2.0')] ).
cnf(2420,plain,
( ~ member(ordered_pair(u,v),universal_class)
| member(v,universal_class) ),
inference(spl,[status(thm),theory(equality)],[1063,16]),
[iquote('1:SpL:1063.0,16.0')] ).
cnf(2422,plain,
member(u,universal_class),
inference(mrr,[status(thm)],[2420,943]),
[iquote('1:MRR:2420.0,943.0')] ).
cnf(4123,plain,
( ~ member(u,universal_class)
| equal(ordered_pair(first(u),second(u)),u) ),
inference(spl,[status(thm),theory(equality)],[1063,18]),
[iquote('1:SpL:1063.0,18.0')] ).
cnf(4133,plain,
equal(ordered_pair(first(u),second(u)),u),
inference(mrr,[status(thm)],[4123,2422]),
[iquote('1:MRR:4123.0,2422.0')] ).
cnf(4134,plain,
member(singleton(first(u)),u),
inference(spr,[status(thm),theory(equality)],[4133,948]),
[iquote('1:SpR:4133.0,948.0')] ).
cnf(4184,plain,
~ member(singleton(first(complement(u))),u),
inference(res,[status(thm),theory(equality)],[4134,25]),
[iquote('1:Res:4134.0,25.1')] ).
cnf(4195,plain,
$false,
inference(unc,[status(thm)],[4184,2422]),
[iquote('1:UnC:4184.0,2422.0')] ).
cnf(4196,plain,
subclass(null_class,u),
inference(spt,[spt(split,[position(s2)])],[213]),
[iquote('1:Spt:4195.0,213.0')] ).
cnf(4197,plain,
( ~ subclass(u,null_class)
| equal(u,null_class) ),
inference(res,[status(thm),theory(equality)],[4196,8]),
[iquote('1:Res:4196.0,8.0')] ).
cnf(8107,plain,
( ~ member(u,v)
| ~ member(u,w)
| ~ subclass(intersection(w,v),x)
| member(u,x) ),
inference(res,[status(thm),theory(equality)],[24,2]),
[iquote('0:Res:24.2,2.0')] ).
cnf(18358,plain,
( subclass(intersection(u,v),u)
| subclass(intersection(u,v),u) ),
inference(res,[status(thm),theory(equality)],[319,4]),
[iquote('0:Res:319.1,4.0')] ).
cnf(18363,plain,
subclass(intersection(u,v),u),
inference(obv,[status(thm),theory(equality)],[18358]),
[iquote('0:Obv:18358.0')] ).
cnf(18387,plain,
subclass(restrict(u,v,w),u),
inference(spr,[status(thm),theory(equality)],[29,18363]),
[iquote('0:SpR:29.0,18363.0')] ).
cnf(18479,plain,
( subclass(intersection(u,v),v)
| subclass(intersection(u,v),v) ),
inference(res,[status(thm),theory(equality)],[301,4]),
[iquote('0:Res:301.1,4.0')] ).
cnf(18484,plain,
subclass(intersection(u,v),v),
inference(obv,[status(thm),theory(equality)],[18479]),
[iquote('0:Obv:18479.0')] ).
cnf(43399,plain,
( ~ subclass(u,universal_class)
| subclass(u,complement(v))
| member(not_subclass_element(u,complement(v)),v)
| subclass(u,complement(v)) ),
inference(res,[status(thm),theory(equality)],[2399,984]),
[iquote('0:Res:2399.2,984.0')] ).
cnf(43408,plain,
( ~ subclass(u,universal_class)
| member(not_subclass_element(u,complement(v)),v)
| subclass(u,complement(v)) ),
inference(obv,[status(thm),theory(equality)],[43399]),
[iquote('0:Obv:43399.1')] ).
cnf(43809,plain,
( ~ member(u,v)
| ~ member(u,w)
| member(u,universal_class) ),
inference(res,[status(thm),theory(equality)],[5,8107]),
[iquote('0:Res:5.0,8107.2')] ).
cnf(43816,plain,
( ~ member(u,v)
| member(u,universal_class) ),
inference(con,[status(thm)],[43809]),
[iquote('0:Con:43809.1')] ).
cnf(43903,plain,
( subclass(u,v)
| member(not_subclass_element(u,v),universal_class) ),
inference(res,[status(thm),theory(equality)],[3,43816]),
[iquote('0:Res:3.1,43816.0')] ).
cnf(44085,plain,
( member(not_subclass_element(complement(complement(u)),v),u)
| subclass(complement(complement(u)),v) ),
inference(mrr,[status(thm)],[1026,43903]),
[iquote('0:MRR:1026.0,43903.1')] ).
cnf(62254,plain,
( member(not_subclass_element(u,complement(v)),v)
| subclass(u,complement(v)) ),
inference(mrr,[status(thm)],[43408,5]),
[iquote('0:MRR:43408.0,5.0')] ).
cnf(122003,plain,
( subclass(complement(complement(u)),u)
| subclass(complement(complement(u)),u) ),
inference(res,[status(thm),theory(equality)],[44085,4]),
[iquote('0:Res:44085.0,4.0')] ).
cnf(122020,plain,
subclass(complement(complement(u)),u),
inference(obv,[status(thm),theory(equality)],[122003]),
[iquote('0:Obv:122003.0')] ).
cnf(122042,plain,
subclass(complement(union(u,v)),intersection(complement(u),complement(v))),
inference(spr,[status(thm),theory(equality)],[27,122020]),
[iquote('0:SpR:27.0,122020.0')] ).
cnf(137270,plain,
subclass(complement(successor(u)),intersection(complement(u),complement(singleton(u)))),
inference(spr,[status(thm),theory(equality)],[44,122042]),
[iquote('0:SpR:44.0,122042.0')] ).
cnf(146922,plain,
subclass(complement(null_class),intersection(complement(x__dfg),complement(singleton(x__dfg)))),
inference(spr,[status(thm),theory(equality)],[1,137270]),
[iquote('0:SpR:1.0,137270.0')] ).
cnf(150084,plain,
equal(intersection(null_class,u),null_class),
inference(res,[status(thm),theory(equality)],[18363,4197]),
[iquote('1:Res:18363.0,4197.0')] ).
cnf(150085,plain,
equal(restrict(null_class,u,v),null_class),
inference(res,[status(thm),theory(equality)],[18387,4197]),
[iquote('1:Res:18387.0,4197.0')] ).
cnf(150658,plain,
equal(complement(domain_of(null_class)),diagonalise(null_class)),
inference(spr,[status(thm),theory(equality)],[150084,77]),
[iquote('1:SpR:150084.0,77.0')] ).
cnf(150811,plain,
( member(not_subclass_element(u,diagonalise(null_class)),domain_of(null_class))
| subclass(u,complement(domain_of(null_class))) ),
inference(spr,[status(thm),theory(equality)],[150658,62254]),
[iquote('1:SpR:150658.0,62254.0')] ).
cnf(150828,plain,
( member(not_subclass_element(u,diagonalise(null_class)),domain_of(null_class))
| subclass(u,diagonalise(null_class)) ),
inference(rew,[status(thm),theory(equality)],[150658,150811]),
[iquote('1:Rew:150658.0,150811.1')] ).
cnf(150858,plain,
( ~ member(u,domain_of(null_class))
| ~ equal(null_class,null_class) ),
inference(spl,[status(thm),theory(equality)],[150085,31]),
[iquote('1:SpL:150085.0,31.1')] ).
cnf(150860,plain,
~ member(u,domain_of(null_class)),
inference(obv,[status(thm),theory(equality)],[150858]),
[iquote('1:Obv:150858.1')] ).
cnf(150865,plain,
subclass(u,diagonalise(null_class)),
inference(mrr,[status(thm)],[150828,150860]),
[iquote('1:MRR:150828.0,150860.0')] ).
cnf(150891,plain,
equal(diagonalise(null_class),universal_class),
inference(res,[status(thm),theory(equality)],[150865,1044]),
[iquote('1:Res:150865.0,1044.0')] ).
cnf(150898,plain,
equal(complement(domain_of(null_class)),universal_class),
inference(rew,[status(thm),theory(equality)],[150891,150658]),
[iquote('1:Rew:150891.0,150658.0')] ).
cnf(151064,plain,
equal(domain_of(null_class),null_class),
inference(res,[status(thm),theory(equality)],[67,150860]),
[iquote('1:Res:67.1,150860.0')] ).
cnf(151073,plain,
~ subclass(ordered_pair(u,v),domain_of(null_class)),
inference(res,[status(thm),theory(equality)],[2398,150860]),
[iquote('1:Res:2398.1,150860.0')] ).
cnf(151076,plain,
equal(complement(null_class),universal_class),
inference(rew,[status(thm),theory(equality)],[151064,150898]),
[iquote('1:Rew:151064.0,150898.0')] ).
cnf(151106,plain,
~ subclass(ordered_pair(u,v),null_class),
inference(rew,[status(thm),theory(equality)],[151064,151073]),
[iquote('1:Rew:151064.0,151073.0')] ).
cnf(151251,plain,
subclass(universal_class,intersection(complement(x__dfg),complement(singleton(x__dfg)))),
inference(rew,[status(thm),theory(equality)],[151076,146922]),
[iquote('1:Rew:151076.0,146922.0')] ).
cnf(151623,plain,
~ equal(ordered_pair(u,v),null_class),
inference(res,[status(thm),theory(equality)],[7,151106]),
[iquote('1:Res:7.1,151106.0')] ).
cnf(152816,plain,
equal(intersection(complement(x__dfg),complement(singleton(x__dfg))),universal_class),
inference(res,[status(thm),theory(equality)],[151251,1044]),
[iquote('1:Res:151251.0,1044.0')] ).
cnf(152859,plain,
subclass(universal_class,complement(x__dfg)),
inference(spr,[status(thm),theory(equality)],[152816,18363]),
[iquote('1:SpR:152816.0,18363.0')] ).
cnf(152860,plain,
subclass(universal_class,complement(singleton(x__dfg))),
inference(spr,[status(thm),theory(equality)],[152816,18484]),
[iquote('1:SpR:152816.0,18484.0')] ).
cnf(152902,plain,
equal(complement(x__dfg),universal_class),
inference(res,[status(thm),theory(equality)],[152859,1044]),
[iquote('1:Res:152859.0,1044.0')] ).
cnf(152947,plain,
( ~ member(u,x__dfg)
| ~ member(u,universal_class) ),
inference(spl,[status(thm),theory(equality)],[152902,25]),
[iquote('1:SpL:152902.0,25.1')] ).
cnf(152993,plain,
~ member(u,x__dfg),
inference(mrr,[status(thm)],[152947,43816]),
[iquote('1:MRR:152947.1,43816.1')] ).
cnf(153585,plain,
equal(complement(singleton(x__dfg)),universal_class),
inference(res,[status(thm),theory(equality)],[152860,1044]),
[iquote('1:Res:152860.0,1044.0')] ).
cnf(153654,plain,
( ~ member(u,singleton(x__dfg))
| ~ member(u,universal_class) ),
inference(spl,[status(thm),theory(equality)],[153585,25]),
[iquote('1:SpL:153585.0,25.1')] ).
cnf(153671,plain,
~ member(u,singleton(x__dfg)),
inference(mrr,[status(thm)],[153654,43816]),
[iquote('1:MRR:153654.1,43816.1')] ).
cnf(154424,plain,
equal(null_class,x__dfg),
inference(res,[status(thm),theory(equality)],[67,152993]),
[iquote('1:Res:67.1,152993.0')] ).
cnf(154450,plain,
( equal(u,x__dfg)
| member(regular(u),u) ),
inference(rew,[status(thm),theory(equality)],[154424,67]),
[iquote('1:Rew:154424.0,67.0')] ).
cnf(154463,plain,
~ equal(ordered_pair(u,v),x__dfg),
inference(rew,[status(thm),theory(equality)],[154424,151623]),
[iquote('1:Rew:154424.0,151623.0')] ).
cnf(155126,plain,
equal(singleton(x__dfg),x__dfg),
inference(res,[status(thm),theory(equality)],[154450,153671]),
[iquote('1:Res:154450.1,153671.0')] ).
cnf(155183,plain,
equal(ordered_pair(x__dfg,x__dfg),singleton(singleton(x__dfg))),
inference(spr,[status(thm),theory(equality)],[155126,949]),
[iquote('1:SpR:155126.0,949.0')] ).
cnf(155227,plain,
equal(ordered_pair(x__dfg,x__dfg),x__dfg),
inference(rew,[status(thm),theory(equality)],[155126,155183]),
[iquote('1:Rew:155126.0,155183.0,155126.0,155183.0')] ).
cnf(155228,plain,
$false,
inference(mrr,[status(thm)],[155227,154463]),
[iquote('1:MRR:155227.0,154463.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM154-1 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.06/0.13 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n027.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 : Tue Jul 5 22:11:27 EDT 2022
% 0.12/0.34 % CPUTime :
% 122.13/122.31
% 122.13/122.31 SPASS V 3.9
% 122.13/122.31 SPASS beiseite: Proof found.
% 122.13/122.31 % SZS status Theorem
% 122.13/122.31 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 122.13/122.31 SPASS derived 123304 clauses, backtracked 25843 clauses, performed 55 splits and kept 65848 clauses.
% 122.13/122.31 SPASS allocated 172029 KBytes.
% 122.13/122.31 SPASS spent 0:02:01.82 on the problem.
% 122.13/122.31 0:00:00.04 for the input.
% 122.13/122.31 0:00:00.00 for the FLOTTER CNF translation.
% 122.13/122.31 0:00:01.31 for inferences.
% 122.13/122.31 0:00:09.69 for the backtracking.
% 122.13/122.31 0:1:49.20 for the reduction.
% 122.13/122.31
% 122.13/122.31
% 122.13/122.31 Here is a proof with depth 12, length 108 :
% 122.13/122.31 % SZS output start Refutation
% See solution above
% 125.12/125.32 Formulae used in the proof : prove_corollary_5_to_successor_property1_1 subclass_members not_subclass_members1 not_subclass_members2 class_elements_are_sets equal_implies_subclass2 subclass_implies_equal unordered_pair2 unordered_pair3 unordered_pairs_in_universal singleton_set ordered_pair cartesian_product2 cartesian_product4 intersection1 intersection2 intersection3 complement1 complement2 union restriction1 domain1 successor function1 regularity1 diagonalisation recursion_equation_functions1
% 125.12/125.32
%------------------------------------------------------------------------------