TSTP Solution File: SET166-6 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET166-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% Computer : n013.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 : 300s
% DateTime : Fri Sep 1 22:28:11 EDT 2023
% Result : Unsatisfiable 0.16s 0.69s
% Output : Refutation 2.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 765
% Syntax : Number of formulae : 2114 ( 157 unt; 0 def)
% Number of atoms : 6776 ( 632 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 8445 (3783 ~;4011 |; 0 &)
% ( 651 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 663 ( 661 usr; 652 prp; 0-3 aty)
% Number of functors : 49 ( 49 usr; 15 con; 0-3 aty)
% Number of variables : 2582 (;2582 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8164,plain,
$false,
inference(avatar_sat_refutation,[],[f122,f127,f132,f137,f142,f146,f151,f155,f159,f163,f168,f173,f177,f181,f185,f190,f194,f198,f202,f207,f211,f215,f219,f223,f227,f233,f237,f241,f245,f249,f253,f257,f261,f265,f269,f274,f279,f284,f290,f294,f298,f302,f306,f310,f314,f318,f322,f326,f330,f334,f338,f342,f346,f350,f354,f358,f362,f366,f370,f390,f403,f407,f411,f415,f419,f423,f427,f431,f435,f440,f473,f487,f491,f495,f499,f503,f510,f514,f518,f522,f526,f530,f534,f544,f571,f576,f580,f584,f588,f592,f596,f600,f604,f621,f651,f655,f659,f666,f670,f690,f694,f698,f707,f711,f715,f725,f734,f738,f742,f746,f751,f764,f768,f775,f779,f792,f801,f806,f815,f819,f828,f832,f838,f847,f858,f863,f873,f877,f881,f885,f899,f903,f907,f911,f915,f943,f947,f951,f955,f959,f963,f1012,f1016,f1020,f1024,f1029,f1033,f1087,f1091,f1095,f1099,f1103,f1107,f1111,f1120,f1129,f1138,f1147,f1151,f1155,f1159,f1163,f1167,f1171,f1282,f1286,f1290,f1294,f1298,f1302,f1306,f1310,f1314,f1323,f1327,f1331,f1335,f1343,f1347,f1496,f1500,f1504,f1508,f1512,f1516,f1520,f1525,f1594,f1674,f1678,f1682,f1686,f1690,f1694,f1698,f1702,f1706,f1710,f1714,f1718,f1722,f1726,f1730,f1899,f1993,f1997,f2001,f2005,f2009,f2018,f2027,f2031,f2035,f2039,f2044,f2048,f2052,f2056,f2060,f2065,f2069,f2073,f2088,f2200,f2204,f2208,f2212,f2216,f2220,f2229,f2242,f2248,f2252,f2256,f2260,f2264,f2268,f2502,f2506,f2510,f2514,f2518,f2582,f2589,f2593,f2597,f2601,f2605,f2609,f2613,f2617,f2621,f2625,f2629,f2840,f2844,f2869,f2873,f2877,f2881,f2886,f2890,f2894,f3077,f3086,f3090,f3094,f3098,f3124,f3188,f3192,f3196,f3200,f3256,f3261,f3265,f3312,f3316,f3327,f3331,f3334,f3335,f3484,f3488,f3504,f3509,f3513,f3517,f3566,f3570,f3574,f3578,f3596,f3618,f3622,f3626,f3632,f3642,f3648,f3652,f3661,f3669,f3675,f3679,f3683,f3743,f3748,f3752,f3756,f3763,f3772,f3792,f3809,f3816,f3821,f3864,f3878,f3883,f3887,f3901,f3905,f3909,f3917,f3921,f3929,f3937,f3941,f3946,f3976,f3982,f3991,f3995,f3999,f4004,f4025,f4033,f4037,f4113,f4166,f4170,f4174,f4178,f4182,f4186,f4190,f4194,f4211,f4217,f4226,f4230,f4234,f4243,f4265,f4274,f4280,f4286,f4296,f4300,f4304,f4313,f4323,f4328,f4361,f4550,f4554,f4558,f4562,f4566,f4570,f4574,f4578,f4582,f4590,f4595,f4604,f4612,f4617,f4626,f4631,f4635,f4639,f4643,f4647,f4651,f4655,f4659,f4663,f4671,f4676,f4680,f4684,f4688,f4692,f4696,f4749,f4754,f4758,f4761,f5038,f5043,f5052,f5062,f5067,f5076,f5110,f5114,f5123,f5128,f5132,f5136,f5140,f5144,f5153,f5157,f5161,f5165,f5169,f5173,f5177,f5181,f5186,f5235,f5240,f5245,f5249,f5253,f5257,f5265,f5269,f5275,f5279,f5283,f5288,f5292,f5296,f5567,f5582,f5767,f5771,f5775,f5779,f5783,f5787,f5791,f5795,f5799,f5803,f5807,f5811,f5815,f5821,f5825,f5829,f5833,f5837,f5841,f5845,f5849,f5853,f5857,f5891,f5895,f5899,f5903,f5907,f5911,f5915,f5919,f5923,f5931,f5940,f5948,f5956,f5967,f5976,f5981,f5985,f5989,f5997,f6006,f6015,f6021,f6117,f6617,f6626,f6635,f6641,f6645,f6649,f6653,f6657,f6661,f6665,f6669,f6674,f6678,f6682,f6686,f6690,f6694,f6698,f6702,f6706,f6710,f6714,f6718,f6722,f6726,f6730,f6734,f6738,f6742,f6746,f6750,f6754,f6758,f6762,f6766,f6770,f6774,f6778,f6782,f6786,f6790,f6794,f6798,f6802,f6806,f6810,f6814,f6894,f7401,f7794,f7798,f7802,f7807,f7811,f7815,f7819,f7823,f7827,f7831,f7835,f7839,f7843,f7847,f7851,f7855,f7859,f7867,f7880,f7887,f7897,f7901,f7905,f7909,f7913,f7917,f7921,f7925,f7929,f7933,f7942,f7946,f7950,f7954,f7958,f7962,f7966,f7970,f7974,f7978,f7982,f7987,f7991,f7995,f7999,f8003,f8007,f8011,f8015,f8019,f8023,f8033,f8050,f8054,f8058,f8062,f8066,f8070,f8074,f8075,f8079,f8083,f8087,f8091,f8095,f8099,f8104,f8108,f8113,f8119,f8134,f8138,f8142,f8146,f8150,f8154,f8162,f8163]) ).
fof(f8163,plain,
( ~ spl0_84
| spl0_2
| ~ spl0_74
| spl0_604 ),
inference(avatar_split_clause,[],[f8024,f7939,f493,f124,f541]) ).
fof(f541,plain,
( spl0_84
<=> member(x,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f124,plain,
( spl0_2
<=> member(x,z) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f493,plain,
( spl0_74
<=> ! [X4,X0] :
( ~ member(X4,universal_class)
| member(X4,X0)
| member(X4,complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f7939,plain,
( spl0_604
<=> member(x,complement(z)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_604])]) ).
fof(f8024,plain,
( member(x,z)
| ~ member(x,universal_class)
| ~ spl0_74
| spl0_604 ),
inference(resolution,[],[f7941,f494]) ).
fof(f494,plain,
( ! [X0,X4] :
( member(X4,complement(X0))
| member(X4,X0)
| ~ member(X4,universal_class) )
| ~ spl0_74 ),
inference(avatar_component_clause,[],[f493]) ).
fof(f7941,plain,
( ~ member(x,complement(z))
| spl0_604 ),
inference(avatar_component_clause,[],[f7939]) ).
fof(f8162,plain,
( spl0_650
| ~ spl0_651
| ~ spl0_92
| ~ spl0_277 ),
inference(avatar_split_clause,[],[f3033,f2888,f598,f8159,f8156]) ).
fof(f8156,plain,
( spl0_650
<=> ! [X2,X3] :
( ~ member(ordered_pair(X2,X3),cross_product(universal_class,universal_class))
| member(X3,domain_of(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_650])]) ).
fof(f8159,plain,
( spl0_651
<=> subclass(composition_function,application_function) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_651])]) ).
fof(f598,plain,
( spl0_92
<=> ! [X4,X0,X1] :
( member(X1,domain_of(X0))
| ~ member(ordered_pair(X0,ordered_pair(X1,X4)),application_function) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f2888,plain,
( spl0_277
<=> ! [X2,X4,X3] :
( ~ member(ordered_pair(X2,X3),cross_product(universal_class,universal_class))
| ~ subclass(composition_function,X4)
| member(ordered_pair(X2,ordered_pair(X3,compose(X2,X3))),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).
fof(f3033,plain,
( ! [X2,X3] :
( ~ subclass(composition_function,application_function)
| ~ member(ordered_pair(X2,X3),cross_product(universal_class,universal_class))
| member(X3,domain_of(X2)) )
| ~ spl0_92
| ~ spl0_277 ),
inference(resolution,[],[f2889,f599]) ).
fof(f599,plain,
( ! [X0,X1,X4] :
( ~ member(ordered_pair(X0,ordered_pair(X1,X4)),application_function)
| member(X1,domain_of(X0)) )
| ~ spl0_92 ),
inference(avatar_component_clause,[],[f598]) ).
fof(f2889,plain,
( ! [X2,X3,X4] :
( member(ordered_pair(X2,ordered_pair(X3,compose(X2,X3))),X4)
| ~ subclass(composition_function,X4)
| ~ member(ordered_pair(X2,X3),cross_product(universal_class,universal_class)) )
| ~ spl0_277 ),
inference(avatar_component_clause,[],[f2888]) ).
fof(f8154,plain,
( spl0_649
| ~ spl0_20
| ~ spl0_273 ),
inference(avatar_split_clause,[],[f2941,f2871,f204,f8152]) ).
fof(f8152,plain,
( spl0_649
<=> ! [X34] :
( ~ member(not_subclass_element(X34,identity_relation),subset_relation)
| ~ member(not_subclass_element(X34,identity_relation),inverse(subset_relation))
| subclass(X34,identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_649])]) ).
fof(f204,plain,
( spl0_20
<=> identity_relation = intersection(inverse(subset_relation),subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f2871,plain,
( spl0_273
<=> ! [X11,X12,X10] :
( ~ member(not_subclass_element(X10,intersection(X11,X12)),X12)
| ~ member(not_subclass_element(X10,intersection(X11,X12)),X11)
| subclass(X10,intersection(X11,X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).
fof(f2941,plain,
( ! [X34] :
( ~ member(not_subclass_element(X34,identity_relation),subset_relation)
| ~ member(not_subclass_element(X34,identity_relation),inverse(subset_relation))
| subclass(X34,identity_relation) )
| ~ spl0_20
| ~ spl0_273 ),
inference(superposition,[],[f2872,f206]) ).
fof(f206,plain,
( identity_relation = intersection(inverse(subset_relation),subset_relation)
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f204]) ).
fof(f2872,plain,
( ! [X10,X11,X12] :
( ~ member(not_subclass_element(X10,intersection(X11,X12)),X12)
| ~ member(not_subclass_element(X10,intersection(X11,X12)),X11)
| subclass(X10,intersection(X11,X12)) )
| ~ spl0_273 ),
inference(avatar_component_clause,[],[f2871]) ).
fof(f8150,plain,
( spl0_648
| ~ spl0_259 ),
inference(avatar_split_clause,[],[f2649,f2587,f8148]) ).
fof(f8148,plain,
( spl0_648
<=> ! [X0,X1] :
( X0 != X1
| regular(unordered_pair(X0,X1)) = X1
| unordered_pair(X0,X1) = null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_648])]) ).
fof(f2587,plain,
( spl0_259
<=> ! [X9,X10] :
( regular(unordered_pair(X9,X10)) = X9
| regular(unordered_pair(X9,X10)) = X10
| null_class = unordered_pair(X9,X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).
fof(f2649,plain,
( ! [X0,X1] :
( X0 != X1
| regular(unordered_pair(X0,X1)) = X1
| unordered_pair(X0,X1) = null_class )
| ~ spl0_259 ),
inference(equality_factoring,[],[f2588]) ).
fof(f2588,plain,
( ! [X10,X9] :
( regular(unordered_pair(X9,X10)) = X10
| regular(unordered_pair(X9,X10)) = X9
| null_class = unordered_pair(X9,X10) )
| ~ spl0_259 ),
inference(avatar_component_clause,[],[f2587]) ).
fof(f8146,plain,
( spl0_647
| ~ spl0_259 ),
inference(avatar_split_clause,[],[f2648,f2587,f8144]) ).
fof(f8144,plain,
( spl0_647
<=> ! [X0,X1] :
( X0 != X1
| regular(unordered_pair(X0,X1)) = X0
| unordered_pair(X0,X1) = null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_647])]) ).
fof(f2648,plain,
( ! [X0,X1] :
( X0 != X1
| regular(unordered_pair(X0,X1)) = X0
| unordered_pair(X0,X1) = null_class )
| ~ spl0_259 ),
inference(equality_factoring,[],[f2588]) ).
fof(f8142,plain,
( spl0_646
| ~ spl0_188
| ~ spl0_255 ),
inference(avatar_split_clause,[],[f2537,f2508,f1494,f8140]) ).
fof(f8140,plain,
( spl0_646
<=> ! [X4,X3] :
( member(not_subclass_element(intersection(universal_class,X3),complement(X4)),X4)
| subclass(intersection(universal_class,X3),complement(X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_646])]) ).
fof(f1494,plain,
( spl0_188
<=> ! [X2,X0,X1] :
( member(not_subclass_element(intersection(X0,X1),X2),X0)
| subclass(intersection(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).
fof(f2508,plain,
( spl0_255
<=> ! [X6,X5] :
( member(not_subclass_element(X5,complement(X6)),X6)
| ~ member(not_subclass_element(X5,complement(X6)),universal_class)
| subclass(X5,complement(X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).
fof(f2537,plain,
( ! [X3,X4] :
( member(not_subclass_element(intersection(universal_class,X3),complement(X4)),X4)
| subclass(intersection(universal_class,X3),complement(X4)) )
| ~ spl0_188
| ~ spl0_255 ),
inference(duplicate_literal_removal,[],[f2521]) ).
fof(f2521,plain,
( ! [X3,X4] :
( member(not_subclass_element(intersection(universal_class,X3),complement(X4)),X4)
| subclass(intersection(universal_class,X3),complement(X4))
| subclass(intersection(universal_class,X3),complement(X4)) )
| ~ spl0_188
| ~ spl0_255 ),
inference(resolution,[],[f2509,f1495]) ).
fof(f1495,plain,
( ! [X2,X0,X1] :
( member(not_subclass_element(intersection(X0,X1),X2),X0)
| subclass(intersection(X0,X1),X2) )
| ~ spl0_188 ),
inference(avatar_component_clause,[],[f1494]) ).
fof(f2509,plain,
( ! [X6,X5] :
( ~ member(not_subclass_element(X5,complement(X6)),universal_class)
| member(not_subclass_element(X5,complement(X6)),X6)
| subclass(X5,complement(X6)) )
| ~ spl0_255 ),
inference(avatar_component_clause,[],[f2508]) ).
fof(f8138,plain,
( spl0_645
| ~ spl0_189
| ~ spl0_255 ),
inference(avatar_split_clause,[],[f2536,f2508,f1498,f8136]) ).
fof(f8136,plain,
( spl0_645
<=> ! [X6,X5] :
( member(not_subclass_element(intersection(X5,universal_class),complement(X6)),X6)
| subclass(intersection(X5,universal_class),complement(X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_645])]) ).
fof(f1498,plain,
( spl0_189
<=> ! [X2,X0,X1] :
( member(not_subclass_element(intersection(X0,X1),X2),X1)
| subclass(intersection(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).
fof(f2536,plain,
( ! [X6,X5] :
( member(not_subclass_element(intersection(X5,universal_class),complement(X6)),X6)
| subclass(intersection(X5,universal_class),complement(X6)) )
| ~ spl0_189
| ~ spl0_255 ),
inference(duplicate_literal_removal,[],[f2522]) ).
fof(f2522,plain,
( ! [X6,X5] :
( member(not_subclass_element(intersection(X5,universal_class),complement(X6)),X6)
| subclass(intersection(X5,universal_class),complement(X6))
| subclass(intersection(X5,universal_class),complement(X6)) )
| ~ spl0_189
| ~ spl0_255 ),
inference(resolution,[],[f2509,f1499]) ).
fof(f1499,plain,
( ! [X2,X0,X1] :
( member(not_subclass_element(intersection(X0,X1),X2),X1)
| subclass(intersection(X0,X1),X2) )
| ~ spl0_189 ),
inference(avatar_component_clause,[],[f1498]) ).
fof(f8134,plain,
( spl0_644
| ~ spl0_13
| ~ spl0_248 ),
inference(avatar_split_clause,[],[f2422,f2250,f175,f8132]) ).
fof(f8132,plain,
( spl0_644
<=> ! [X18] :
( member(null_class,cantor(X18))
| ~ member(null_class,domain_of(X18))
| ~ inductive(diagonalise(compose(inverse(element_relation),X18))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_644])]) ).
fof(f175,plain,
( spl0_13
<=> ! [X0] :
( ~ inductive(X0)
| member(null_class,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f2250,plain,
( spl0_248
<=> ! [X0,X1] :
( member(X1,cantor(X0))
| ~ member(X1,diagonalise(compose(inverse(element_relation),X0)))
| ~ member(X1,domain_of(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).
fof(f2422,plain,
( ! [X18] :
( member(null_class,cantor(X18))
| ~ member(null_class,domain_of(X18))
| ~ inductive(diagonalise(compose(inverse(element_relation),X18))) )
| ~ spl0_13
| ~ spl0_248 ),
inference(resolution,[],[f2251,f176]) ).
fof(f176,plain,
( ! [X0] :
( member(null_class,X0)
| ~ inductive(X0) )
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f175]) ).
fof(f2251,plain,
( ! [X0,X1] :
( ~ member(X1,diagonalise(compose(inverse(element_relation),X0)))
| member(X1,cantor(X0))
| ~ member(X1,domain_of(X0)) )
| ~ spl0_248 ),
inference(avatar_component_clause,[],[f2250]) ).
fof(f8119,plain,
( spl0_643
| ~ spl0_625
| ~ spl0_642 ),
inference(avatar_split_clause,[],[f8114,f8110,f8026,f8116]) ).
fof(f8116,plain,
( spl0_643
<=> complement(null_class) = union(identity_relation,intersection(complement(inverse(subset_relation)),complement(subset_relation))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_643])]) ).
fof(f8026,plain,
( spl0_625
<=> null_class = symmetric_difference(inverse(subset_relation),subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_625])]) ).
fof(f8110,plain,
( spl0_642
<=> complement(symmetric_difference(inverse(subset_relation),subset_relation)) = union(identity_relation,intersection(complement(inverse(subset_relation)),complement(subset_relation))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_642])]) ).
fof(f8114,plain,
( complement(null_class) = union(identity_relation,intersection(complement(inverse(subset_relation)),complement(subset_relation)))
| ~ spl0_625
| ~ spl0_642 ),
inference(forward_demodulation,[],[f8112,f8028]) ).
fof(f8028,plain,
( null_class = symmetric_difference(inverse(subset_relation),subset_relation)
| ~ spl0_625 ),
inference(avatar_component_clause,[],[f8026]) ).
fof(f8112,plain,
( complement(symmetric_difference(inverse(subset_relation),subset_relation)) = union(identity_relation,intersection(complement(inverse(subset_relation)),complement(subset_relation)))
| ~ spl0_642 ),
inference(avatar_component_clause,[],[f8110]) ).
fof(f8113,plain,
( spl0_642
| ~ spl0_195
| ~ spl0_240 ),
inference(avatar_split_clause,[],[f2330,f2214,f1522,f8110]) ).
fof(f1522,plain,
( spl0_195
<=> symmetric_difference(inverse(subset_relation),subset_relation) = intersection(complement(identity_relation),union(inverse(subset_relation),subset_relation)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).
fof(f2214,plain,
( spl0_240
<=> ! [X6,X4,X5] : union(X6,intersection(complement(X4),complement(X5))) = complement(intersection(complement(X6),union(X4,X5))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).
fof(f2330,plain,
( complement(symmetric_difference(inverse(subset_relation),subset_relation)) = union(identity_relation,intersection(complement(inverse(subset_relation)),complement(subset_relation)))
| ~ spl0_195
| ~ spl0_240 ),
inference(superposition,[],[f2215,f1524]) ).
fof(f1524,plain,
( symmetric_difference(inverse(subset_relation),subset_relation) = intersection(complement(identity_relation),union(inverse(subset_relation),subset_relation))
| ~ spl0_195 ),
inference(avatar_component_clause,[],[f1522]) ).
fof(f2215,plain,
( ! [X6,X4,X5] : union(X6,intersection(complement(X4),complement(X5))) = complement(intersection(complement(X6),union(X4,X5)))
| ~ spl0_240 ),
inference(avatar_component_clause,[],[f2214]) ).
fof(f8108,plain,
( spl0_641
| ~ spl0_99
| ~ spl0_240 ),
inference(avatar_split_clause,[],[f2329,f2214,f668,f8106]) ).
fof(f8106,plain,
( spl0_641
<=> ! [X0,X1] : complement(symmetric_difference(X0,X1)) = union(intersection(X0,X1),intersection(complement(X0),complement(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_641])]) ).
fof(f668,plain,
( spl0_99
<=> ! [X0,X1] : symmetric_difference(X0,X1) = intersection(complement(intersection(X0,X1)),union(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f2329,plain,
( ! [X0,X1] : complement(symmetric_difference(X0,X1)) = union(intersection(X0,X1),intersection(complement(X0),complement(X1)))
| ~ spl0_99
| ~ spl0_240 ),
inference(superposition,[],[f2215,f669]) ).
fof(f669,plain,
( ! [X0,X1] : symmetric_difference(X0,X1) = intersection(complement(intersection(X0,X1)),union(X0,X1))
| ~ spl0_99 ),
inference(avatar_component_clause,[],[f668]) ).
fof(f8104,plain,
( spl0_640
| ~ spl0_63
| ~ spl0_232 ),
inference(avatar_split_clause,[],[f2184,f2062,f409,f8101]) ).
fof(f8101,plain,
( spl0_640
<=> image(restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class),universal_class) = range_of(subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_640])]) ).
fof(f409,plain,
( spl0_63
<=> ! [X5,X0] : range_of(restrict(X5,X0,universal_class)) = image(X5,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f2062,plain,
( spl0_232
<=> subset_relation = restrict(restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class),universal_class,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).
fof(f2184,plain,
( image(restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class),universal_class) = range_of(subset_relation)
| ~ spl0_63
| ~ spl0_232 ),
inference(superposition,[],[f410,f2064]) ).
fof(f2064,plain,
( subset_relation = restrict(restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class),universal_class,universal_class)
| ~ spl0_232 ),
inference(avatar_component_clause,[],[f2062]) ).
fof(f410,plain,
( ! [X0,X5] : range_of(restrict(X5,X0,universal_class)) = image(X5,X0)
| ~ spl0_63 ),
inference(avatar_component_clause,[],[f409]) ).
fof(f8099,plain,
( spl0_639
| ~ spl0_132
| ~ spl0_228 ),
inference(avatar_split_clause,[],[f2144,f2046,f883,f8097]) ).
fof(f8097,plain,
( spl0_639
<=> ! [X50] :
( ~ member(X50,universal_class)
| ~ subclass(X50,singleton_relation)
| null_class = X50
| member(apply(choice,X50),element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_639])]) ).
fof(f883,plain,
( spl0_132
<=> ! [X0] :
( ~ member(X0,singleton_relation)
| member(X0,element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f2046,plain,
( spl0_228
<=> ! [X0,X1] :
( null_class = X0
| ~ member(X0,universal_class)
| ~ subclass(X0,X1)
| member(apply(choice,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).
fof(f2144,plain,
( ! [X50] :
( ~ member(X50,universal_class)
| ~ subclass(X50,singleton_relation)
| null_class = X50
| member(apply(choice,X50),element_relation) )
| ~ spl0_132
| ~ spl0_228 ),
inference(resolution,[],[f2047,f884]) ).
fof(f884,plain,
( ! [X0] :
( ~ member(X0,singleton_relation)
| member(X0,element_relation) )
| ~ spl0_132 ),
inference(avatar_component_clause,[],[f883]) ).
fof(f2047,plain,
( ! [X0,X1] :
( member(apply(choice,X0),X1)
| ~ member(X0,universal_class)
| ~ subclass(X0,X1)
| null_class = X0 )
| ~ spl0_228 ),
inference(avatar_component_clause,[],[f2046]) ).
fof(f8095,plain,
( spl0_638
| ~ spl0_60
| ~ spl0_228 ),
inference(avatar_split_clause,[],[f2141,f2046,f388,f8093]) ).
fof(f8093,plain,
( spl0_638
<=> ! [X45] :
( ~ member(X45,universal_class)
| ~ subclass(X45,identity_relation)
| null_class = X45
| member(apply(choice,X45),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_638])]) ).
fof(f388,plain,
( spl0_60
<=> ! [X0] :
( ~ member(X0,identity_relation)
| member(X0,subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f2141,plain,
( ! [X45] :
( ~ member(X45,universal_class)
| ~ subclass(X45,identity_relation)
| null_class = X45
| member(apply(choice,X45),subset_relation) )
| ~ spl0_60
| ~ spl0_228 ),
inference(resolution,[],[f2047,f389]) ).
fof(f389,plain,
( ! [X0] :
( ~ member(X0,identity_relation)
| member(X0,subset_relation) )
| ~ spl0_60 ),
inference(avatar_component_clause,[],[f388]) ).
fof(f8091,plain,
( spl0_637
| ~ spl0_88
| ~ spl0_224 ),
inference(avatar_split_clause,[],[f2095,f2029,f582,f8089]) ).
fof(f8089,plain,
( spl0_637
<=> ! [X1] :
( ~ member(X1,domain_of(regular(cross_product(singleton(X1),universal_class))))
| null_class = cross_product(singleton(X1),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_637])]) ).
fof(f582,plain,
( spl0_88
<=> ! [X4,X0] :
( ~ member(X4,domain_of(X0))
| restrict(X0,singleton(X4),universal_class) != null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f2029,plain,
( spl0_224
<=> ! [X4,X3] :
( null_class = restrict(regular(cross_product(X3,X4)),X3,X4)
| null_class = cross_product(X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).
fof(f2095,plain,
( ! [X1] :
( ~ member(X1,domain_of(regular(cross_product(singleton(X1),universal_class))))
| null_class = cross_product(singleton(X1),universal_class) )
| ~ spl0_88
| ~ spl0_224 ),
inference(trivial_inequality_removal,[],[f2090]) ).
fof(f2090,plain,
( ! [X1] :
( null_class != null_class
| ~ member(X1,domain_of(regular(cross_product(singleton(X1),universal_class))))
| null_class = cross_product(singleton(X1),universal_class) )
| ~ spl0_88
| ~ spl0_224 ),
inference(superposition,[],[f583,f2030]) ).
fof(f2030,plain,
( ! [X3,X4] :
( null_class = restrict(regular(cross_product(X3,X4)),X3,X4)
| null_class = cross_product(X3,X4) )
| ~ spl0_224 ),
inference(avatar_component_clause,[],[f2029]) ).
fof(f583,plain,
( ! [X0,X4] :
( restrict(X0,singleton(X4),universal_class) != null_class
| ~ member(X4,domain_of(X0)) )
| ~ spl0_88 ),
inference(avatar_component_clause,[],[f582]) ).
fof(f8087,plain,
( spl0_636
| ~ spl0_63
| ~ spl0_224 ),
inference(avatar_split_clause,[],[f2089,f2029,f409,f8085]) ).
fof(f8085,plain,
( spl0_636
<=> ! [X0] :
( image(regular(cross_product(X0,universal_class)),X0) = range_of(null_class)
| null_class = cross_product(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_636])]) ).
fof(f2089,plain,
( ! [X0] :
( image(regular(cross_product(X0,universal_class)),X0) = range_of(null_class)
| null_class = cross_product(X0,universal_class) )
| ~ spl0_63
| ~ spl0_224 ),
inference(superposition,[],[f410,f2030]) ).
fof(f8083,plain,
( spl0_635
| ~ spl0_172
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f1986,f1728,f1284,f8081]) ).
fof(f8081,plain,
( spl0_635
<=> ! [X10] :
( member(regular(symmetric_difference(X10,singleton(X10))),successor(X10))
| null_class = symmetric_difference(X10,singleton(X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_635])]) ).
fof(f1284,plain,
( spl0_172
<=> ! [X6,X5] :
( member(regular(intersection(X5,X6)),X6)
| null_class = intersection(X5,X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
fof(f1728,plain,
( spl0_212
<=> ! [X0] : symmetric_difference(X0,singleton(X0)) = intersection(complement(intersection(X0,singleton(X0))),successor(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).
fof(f1986,plain,
( ! [X10] :
( member(regular(symmetric_difference(X10,singleton(X10))),successor(X10))
| null_class = symmetric_difference(X10,singleton(X10)) )
| ~ spl0_172
| ~ spl0_212 ),
inference(superposition,[],[f1285,f1729]) ).
fof(f1729,plain,
( ! [X0] : symmetric_difference(X0,singleton(X0)) = intersection(complement(intersection(X0,singleton(X0))),successor(X0))
| ~ spl0_212 ),
inference(avatar_component_clause,[],[f1728]) ).
fof(f1285,plain,
( ! [X6,X5] :
( member(regular(intersection(X5,X6)),X6)
| null_class = intersection(X5,X6) )
| ~ spl0_172 ),
inference(avatar_component_clause,[],[f1284]) ).
fof(f8079,plain,
( spl0_634
| ~ spl0_27
| ~ spl0_208 ),
inference(avatar_split_clause,[],[f1920,f1712,f235,f8077]) ).
fof(f8077,plain,
( spl0_634
<=> ! [X29,X30,X31] :
( ~ function(X29)
| ~ subclass(universal_class,complement(X30))
| ~ member(X31,universal_class)
| ~ member(image(X29,X31),X30) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_634])]) ).
fof(f235,plain,
( spl0_27
<=> ! [X4,X0] :
( ~ member(X4,X0)
| ~ member(X4,complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f1712,plain,
( spl0_208
<=> ! [X2,X0,X1] :
( ~ member(X0,universal_class)
| ~ function(X1)
| ~ subclass(universal_class,X2)
| member(image(X1,X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).
fof(f1920,plain,
( ! [X31,X29,X30] :
( ~ function(X29)
| ~ subclass(universal_class,complement(X30))
| ~ member(X31,universal_class)
| ~ member(image(X29,X31),X30) )
| ~ spl0_27
| ~ spl0_208 ),
inference(resolution,[],[f1713,f236]) ).
fof(f236,plain,
( ! [X0,X4] :
( ~ member(X4,complement(X0))
| ~ member(X4,X0) )
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f235]) ).
fof(f1713,plain,
( ! [X2,X0,X1] :
( member(image(X1,X0),X2)
| ~ function(X1)
| ~ subclass(universal_class,X2)
| ~ member(X0,universal_class) )
| ~ spl0_208 ),
inference(avatar_component_clause,[],[f1712]) ).
fof(f8075,plain,
( ~ spl0_84
| spl0_1
| ~ spl0_74
| spl0_603 ),
inference(avatar_split_clause,[],[f7983,f7935,f493,f119,f541]) ).
fof(f119,plain,
( spl0_1
<=> member(x,y) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f7935,plain,
( spl0_603
<=> member(x,complement(y)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_603])]) ).
fof(f7983,plain,
( member(x,y)
| ~ member(x,universal_class)
| ~ spl0_74
| spl0_603 ),
inference(resolution,[],[f7937,f494]) ).
fof(f7937,plain,
( ~ member(x,complement(y))
| spl0_603 ),
inference(avatar_component_clause,[],[f7935]) ).
fof(f8074,plain,
( spl0_633
| ~ spl0_137
| ~ spl0_208 ),
inference(avatar_split_clause,[],[f1915,f1712,f913,f8072]) ).
fof(f8072,plain,
( spl0_633
<=> ! [X12,X11,X10] :
( ~ function(X10)
| ~ subclass(universal_class,singleton(X11))
| ~ member(X12,universal_class)
| image(X10,X12) = X11 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_633])]) ).
fof(f913,plain,
( spl0_137
<=> ! [X0,X1] :
( ~ member(X1,singleton(X0))
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f1915,plain,
( ! [X10,X11,X12] :
( ~ function(X10)
| ~ subclass(universal_class,singleton(X11))
| ~ member(X12,universal_class)
| image(X10,X12) = X11 )
| ~ spl0_137
| ~ spl0_208 ),
inference(resolution,[],[f1713,f914]) ).
fof(f914,plain,
( ! [X0,X1] :
( ~ member(X1,singleton(X0))
| X0 = X1 )
| ~ spl0_137 ),
inference(avatar_component_clause,[],[f913]) ).
fof(f8070,plain,
( spl0_632
| ~ spl0_52
| ~ spl0_206 ),
inference(avatar_split_clause,[],[f1876,f1704,f340,f8068]) ).
fof(f8068,plain,
( spl0_632
<=> ! [X6,X5] :
( ~ inductive(power_class(intersection(complement(X5),complement(X6))))
| ~ member(null_class,image(element_relation,union(X5,X6))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_632])]) ).
fof(f340,plain,
( spl0_52
<=> ! [X0] :
( ~ member(null_class,X0)
| ~ inductive(complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f1704,plain,
( spl0_206
<=> ! [X4,X3] : power_class(intersection(complement(X3),complement(X4))) = complement(image(element_relation,union(X3,X4))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).
fof(f1876,plain,
( ! [X6,X5] :
( ~ inductive(power_class(intersection(complement(X5),complement(X6))))
| ~ member(null_class,image(element_relation,union(X5,X6))) )
| ~ spl0_52
| ~ spl0_206 ),
inference(superposition,[],[f341,f1705]) ).
fof(f1705,plain,
( ! [X3,X4] : power_class(intersection(complement(X3),complement(X4))) = complement(image(element_relation,union(X3,X4)))
| ~ spl0_206 ),
inference(avatar_component_clause,[],[f1704]) ).
fof(f341,plain,
( ! [X0] :
( ~ inductive(complement(X0))
| ~ member(null_class,X0) )
| ~ spl0_52 ),
inference(avatar_component_clause,[],[f340]) ).
fof(f8066,plain,
( spl0_631
| ~ spl0_52
| ~ spl0_205 ),
inference(avatar_split_clause,[],[f1859,f1700,f340,f8064]) ).
fof(f8064,plain,
( spl0_631
<=> ! [X11,X10] :
( ~ inductive(union(X10,domain_of(intersection(X11,identity_relation))))
| ~ member(null_class,intersection(complement(X10),diagonalise(X11))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_631])]) ).
fof(f1700,plain,
( spl0_205
<=> ! [X2,X3] : union(X3,domain_of(intersection(X2,identity_relation))) = complement(intersection(complement(X3),diagonalise(X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).
fof(f1859,plain,
( ! [X10,X11] :
( ~ inductive(union(X10,domain_of(intersection(X11,identity_relation))))
| ~ member(null_class,intersection(complement(X10),diagonalise(X11))) )
| ~ spl0_52
| ~ spl0_205 ),
inference(superposition,[],[f341,f1701]) ).
fof(f1701,plain,
( ! [X2,X3] : union(X3,domain_of(intersection(X2,identity_relation))) = complement(intersection(complement(X3),diagonalise(X2)))
| ~ spl0_205 ),
inference(avatar_component_clause,[],[f1700]) ).
fof(f8062,plain,
( spl0_630
| ~ spl0_52
| ~ spl0_204 ),
inference(avatar_split_clause,[],[f1832,f1696,f340,f8060]) ).
fof(f8060,plain,
( spl0_630
<=> ! [X11,X10] :
( ~ inductive(union(X10,image(element_relation,complement(X11))))
| ~ member(null_class,intersection(complement(X10),power_class(X11))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_630])]) ).
fof(f1696,plain,
( spl0_204
<=> ! [X0,X1] : union(X1,image(element_relation,complement(X0))) = complement(intersection(complement(X1),power_class(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).
fof(f1832,plain,
( ! [X10,X11] :
( ~ inductive(union(X10,image(element_relation,complement(X11))))
| ~ member(null_class,intersection(complement(X10),power_class(X11))) )
| ~ spl0_52
| ~ spl0_204 ),
inference(superposition,[],[f341,f1697]) ).
fof(f1697,plain,
( ! [X0,X1] : union(X1,image(element_relation,complement(X0))) = complement(intersection(complement(X1),power_class(X0)))
| ~ spl0_204 ),
inference(avatar_component_clause,[],[f1696]) ).
fof(f8058,plain,
( spl0_629
| ~ spl0_52
| ~ spl0_203 ),
inference(avatar_split_clause,[],[f1807,f1692,f340,f8056]) ).
fof(f8056,plain,
( spl0_629
<=> ! [X11,X10] :
( ~ inductive(union(domain_of(intersection(X10,identity_relation)),X11))
| ~ member(null_class,intersection(diagonalise(X10),complement(X11))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_629])]) ).
fof(f1692,plain,
( spl0_203
<=> ! [X2,X3] : union(domain_of(intersection(X2,identity_relation)),X3) = complement(intersection(diagonalise(X2),complement(X3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).
fof(f1807,plain,
( ! [X10,X11] :
( ~ inductive(union(domain_of(intersection(X10,identity_relation)),X11))
| ~ member(null_class,intersection(diagonalise(X10),complement(X11))) )
| ~ spl0_52
| ~ spl0_203 ),
inference(superposition,[],[f341,f1693]) ).
fof(f1693,plain,
( ! [X2,X3] : union(domain_of(intersection(X2,identity_relation)),X3) = complement(intersection(diagonalise(X2),complement(X3)))
| ~ spl0_203 ),
inference(avatar_component_clause,[],[f1692]) ).
fof(f8054,plain,
( spl0_628
| ~ spl0_52
| ~ spl0_202 ),
inference(avatar_split_clause,[],[f1784,f1688,f340,f8052]) ).
fof(f8052,plain,
( spl0_628
<=> ! [X11,X10] :
( ~ inductive(union(image(element_relation,complement(X10)),X11))
| ~ member(null_class,intersection(power_class(X10),complement(X11))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_628])]) ).
fof(f1688,plain,
( spl0_202
<=> ! [X0,X1] : union(image(element_relation,complement(X0)),X1) = complement(intersection(power_class(X0),complement(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).
fof(f1784,plain,
( ! [X10,X11] :
( ~ inductive(union(image(element_relation,complement(X10)),X11))
| ~ member(null_class,intersection(power_class(X10),complement(X11))) )
| ~ spl0_52
| ~ spl0_202 ),
inference(superposition,[],[f341,f1689]) ).
fof(f1689,plain,
( ! [X0,X1] : union(image(element_relation,complement(X0)),X1) = complement(intersection(power_class(X0),complement(X1)))
| ~ spl0_202 ),
inference(avatar_component_clause,[],[f1688]) ).
fof(f8050,plain,
( spl0_627
| ~ spl0_33
| ~ spl0_199 ),
inference(avatar_split_clause,[],[f1736,f1676,f259,f8048]) ).
fof(f8048,plain,
( spl0_627
<=> ! [X4,X5] :
( ~ member(X4,universal_class)
| member(X4,X5)
| member(X4,cross_product(universal_class,universal_class))
| ~ function(complement(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_627])]) ).
fof(f259,plain,
( spl0_33
<=> ! [X8] :
( ~ function(X8)
| subclass(X8,cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f1676,plain,
( spl0_199
<=> ! [X2,X4,X3] :
( member(X2,X3)
| ~ member(X2,universal_class)
| ~ subclass(complement(X3),X4)
| member(X2,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).
fof(f1736,plain,
( ! [X4,X5] :
( ~ member(X4,universal_class)
| member(X4,X5)
| member(X4,cross_product(universal_class,universal_class))
| ~ function(complement(X5)) )
| ~ spl0_33
| ~ spl0_199 ),
inference(resolution,[],[f1677,f260]) ).
fof(f260,plain,
( ! [X8] :
( subclass(X8,cross_product(universal_class,universal_class))
| ~ function(X8) )
| ~ spl0_33 ),
inference(avatar_component_clause,[],[f259]) ).
fof(f1677,plain,
( ! [X2,X3,X4] :
( ~ subclass(complement(X3),X4)
| ~ member(X2,universal_class)
| member(X2,X3)
| member(X2,X4) )
| ~ spl0_199 ),
inference(avatar_component_clause,[],[f1676]) ).
fof(f8033,plain,
( spl0_625
| spl0_626
| ~ spl0_171
| ~ spl0_195 ),
inference(avatar_split_clause,[],[f1666,f1522,f1280,f8030,f8026]) ).
fof(f8030,plain,
( spl0_626
<=> member(regular(symmetric_difference(inverse(subset_relation),subset_relation)),complement(identity_relation)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_626])]) ).
fof(f1280,plain,
( spl0_171
<=> ! [X6,X5] :
( member(regular(intersection(X5,X6)),X5)
| null_class = intersection(X5,X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
fof(f1666,plain,
( member(regular(symmetric_difference(inverse(subset_relation),subset_relation)),complement(identity_relation))
| null_class = symmetric_difference(inverse(subset_relation),subset_relation)
| ~ spl0_171
| ~ spl0_195 ),
inference(superposition,[],[f1281,f1524]) ).
fof(f1281,plain,
( ! [X6,X5] :
( member(regular(intersection(X5,X6)),X5)
| null_class = intersection(X5,X6) )
| ~ spl0_171 ),
inference(avatar_component_clause,[],[f1280]) ).
fof(f8023,plain,
( spl0_624
| ~ spl0_138
| ~ spl0_194 ),
inference(avatar_split_clause,[],[f1638,f1518,f941,f8021]) ).
fof(f8021,plain,
( spl0_624
<=> ! [X18,X19,X20,X21] :
( ~ member(unordered_pair(X18,X19),union(X20,X21))
| ~ subclass(universal_class,intersection(complement(X20),complement(X21))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_624])]) ).
fof(f941,plain,
( spl0_138
<=> ! [X9,X11,X10] :
( ~ subclass(universal_class,X9)
| member(unordered_pair(X10,X11),X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f1518,plain,
( spl0_194
<=> ! [X9,X8,X7] :
( ~ member(X9,union(X7,X8))
| ~ member(X9,intersection(complement(X7),complement(X8))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).
fof(f1638,plain,
( ! [X21,X18,X19,X20] :
( ~ member(unordered_pair(X18,X19),union(X20,X21))
| ~ subclass(universal_class,intersection(complement(X20),complement(X21))) )
| ~ spl0_138
| ~ spl0_194 ),
inference(resolution,[],[f1519,f942]) ).
fof(f942,plain,
( ! [X10,X11,X9] :
( member(unordered_pair(X10,X11),X9)
| ~ subclass(universal_class,X9) )
| ~ spl0_138 ),
inference(avatar_component_clause,[],[f941]) ).
fof(f1519,plain,
( ! [X8,X9,X7] :
( ~ member(X9,intersection(complement(X7),complement(X8)))
| ~ member(X9,union(X7,X8)) )
| ~ spl0_194 ),
inference(avatar_component_clause,[],[f1518]) ).
fof(f8019,plain,
( spl0_623
| ~ spl0_141
| ~ spl0_193 ),
inference(avatar_split_clause,[],[f1628,f1514,f953,f8017]) ).
fof(f8017,plain,
( spl0_623
<=> ! [X70,X71] :
( ~ subclass(domain_relation,cantor(X70))
| ~ member(X71,universal_class)
| member(ordered_pair(X71,domain_of(X71)),domain_of(X70)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_623])]) ).
fof(f953,plain,
( spl0_141
<=> ! [X4,X5] :
( ~ member(X5,cantor(X4))
| member(X5,domain_of(X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f1514,plain,
( spl0_193
<=> ! [X2,X1] :
( ~ member(X1,universal_class)
| ~ subclass(domain_relation,X2)
| member(ordered_pair(X1,domain_of(X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).
fof(f1628,plain,
( ! [X70,X71] :
( ~ subclass(domain_relation,cantor(X70))
| ~ member(X71,universal_class)
| member(ordered_pair(X71,domain_of(X71)),domain_of(X70)) )
| ~ spl0_141
| ~ spl0_193 ),
inference(resolution,[],[f1515,f954]) ).
fof(f954,plain,
( ! [X4,X5] :
( ~ member(X5,cantor(X4))
| member(X5,domain_of(X4)) )
| ~ spl0_141 ),
inference(avatar_component_clause,[],[f953]) ).
fof(f1515,plain,
( ! [X2,X1] :
( member(ordered_pair(X1,domain_of(X1)),X2)
| ~ subclass(domain_relation,X2)
| ~ member(X1,universal_class) )
| ~ spl0_193 ),
inference(avatar_component_clause,[],[f1514]) ).
fof(f8015,plain,
( spl0_622
| ~ spl0_44
| ~ spl0_193 ),
inference(avatar_split_clause,[],[f1617,f1514,f308,f8013]) ).
fof(f8013,plain,
( spl0_622
<=> ! [X43,X44,X42] :
( ~ subclass(domain_relation,intersection(X42,X43))
| ~ member(X44,universal_class)
| member(ordered_pair(X44,domain_of(X44)),X42) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_622])]) ).
fof(f308,plain,
( spl0_44
<=> ! [X4,X0,X1] :
( member(X4,X0)
| ~ member(X4,intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f1617,plain,
( ! [X44,X42,X43] :
( ~ subclass(domain_relation,intersection(X42,X43))
| ~ member(X44,universal_class)
| member(ordered_pair(X44,domain_of(X44)),X42) )
| ~ spl0_44
| ~ spl0_193 ),
inference(resolution,[],[f1515,f309]) ).
fof(f309,plain,
( ! [X0,X1,X4] :
( ~ member(X4,intersection(X0,X1))
| member(X4,X0) )
| ~ spl0_44 ),
inference(avatar_component_clause,[],[f308]) ).
fof(f8011,plain,
( spl0_621
| ~ spl0_45
| ~ spl0_193 ),
inference(avatar_split_clause,[],[f1616,f1514,f312,f8009]) ).
fof(f8009,plain,
( spl0_621
<=> ! [X41,X39,X40] :
( ~ subclass(domain_relation,intersection(X39,X40))
| ~ member(X41,universal_class)
| member(ordered_pair(X41,domain_of(X41)),X40) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_621])]) ).
fof(f312,plain,
( spl0_45
<=> ! [X4,X0,X1] :
( member(X4,X1)
| ~ member(X4,intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f1616,plain,
( ! [X40,X41,X39] :
( ~ subclass(domain_relation,intersection(X39,X40))
| ~ member(X41,universal_class)
| member(ordered_pair(X41,domain_of(X41)),X40) )
| ~ spl0_45
| ~ spl0_193 ),
inference(resolution,[],[f1515,f313]) ).
fof(f313,plain,
( ! [X0,X1,X4] :
( ~ member(X4,intersection(X0,X1))
| member(X4,X1) )
| ~ spl0_45 ),
inference(avatar_component_clause,[],[f312]) ).
fof(f8007,plain,
( spl0_620
| ~ spl0_90
| ~ spl0_189 ),
inference(avatar_split_clause,[],[f1581,f1498,f590,f8005]) ).
fof(f8005,plain,
( spl0_620
<=> ! [X16,X15] :
( member(not_subclass_element(cantor(X15),X16),diagonalise(compose(inverse(element_relation),X15)))
| subclass(cantor(X15),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_620])]) ).
fof(f590,plain,
( spl0_90
<=> ! [X0] : intersection(domain_of(X0),diagonalise(compose(inverse(element_relation),X0))) = cantor(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f1581,plain,
( ! [X16,X15] :
( member(not_subclass_element(cantor(X15),X16),diagonalise(compose(inverse(element_relation),X15)))
| subclass(cantor(X15),X16) )
| ~ spl0_90
| ~ spl0_189 ),
inference(superposition,[],[f1499,f591]) ).
fof(f591,plain,
( ! [X0] : intersection(domain_of(X0),diagonalise(compose(inverse(element_relation),X0))) = cantor(X0)
| ~ spl0_90 ),
inference(avatar_component_clause,[],[f590]) ).
fof(f8003,plain,
( spl0_619
| ~ spl0_27
| ~ spl0_189 ),
inference(avatar_split_clause,[],[f1563,f1498,f235,f8001]) ).
fof(f8001,plain,
( spl0_619
<=> ! [X25,X27,X26] :
( subclass(intersection(X25,complement(X26)),X27)
| ~ member(not_subclass_element(intersection(X25,complement(X26)),X27),X26) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_619])]) ).
fof(f1563,plain,
( ! [X26,X27,X25] :
( subclass(intersection(X25,complement(X26)),X27)
| ~ member(not_subclass_element(intersection(X25,complement(X26)),X27),X26) )
| ~ spl0_27
| ~ spl0_189 ),
inference(resolution,[],[f1499,f236]) ).
fof(f7999,plain,
( spl0_618
| ~ spl0_137
| ~ spl0_189 ),
inference(avatar_split_clause,[],[f1559,f1498,f913,f7997]) ).
fof(f7997,plain,
( spl0_618
<=> ! [X11,X12,X10] :
( subclass(intersection(X10,singleton(X11)),X12)
| not_subclass_element(intersection(X10,singleton(X11)),X12) = X11 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_618])]) ).
fof(f1559,plain,
( ! [X10,X11,X12] :
( subclass(intersection(X10,singleton(X11)),X12)
| not_subclass_element(intersection(X10,singleton(X11)),X12) = X11 )
| ~ spl0_137
| ~ spl0_189 ),
inference(resolution,[],[f1499,f914]) ).
fof(f7995,plain,
( spl0_617
| ~ spl0_27
| ~ spl0_188 ),
inference(avatar_split_clause,[],[f1533,f1494,f235,f7993]) ).
fof(f7993,plain,
( spl0_617
<=> ! [X25,X27,X26] :
( subclass(intersection(complement(X25),X26),X27)
| ~ member(not_subclass_element(intersection(complement(X25),X26),X27),X25) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_617])]) ).
fof(f1533,plain,
( ! [X26,X27,X25] :
( subclass(intersection(complement(X25),X26),X27)
| ~ member(not_subclass_element(intersection(complement(X25),X26),X27),X25) )
| ~ spl0_27
| ~ spl0_188 ),
inference(resolution,[],[f1495,f236]) ).
fof(f7991,plain,
( spl0_616
| ~ spl0_137
| ~ spl0_188 ),
inference(avatar_split_clause,[],[f1529,f1494,f913,f7989]) ).
fof(f7989,plain,
( spl0_616
<=> ! [X11,X12,X10] :
( subclass(intersection(singleton(X10),X11),X12)
| not_subclass_element(intersection(singleton(X10),X11),X12) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_616])]) ).
fof(f1529,plain,
( ! [X10,X11,X12] :
( subclass(intersection(singleton(X10),X11),X12)
| not_subclass_element(intersection(singleton(X10),X11),X12) = X10 )
| ~ spl0_137
| ~ spl0_188 ),
inference(resolution,[],[f1495,f914]) ).
fof(f7987,plain,
( spl0_615
| ~ spl0_77
| ~ spl0_187 ),
inference(avatar_split_clause,[],[f1486,f1345,f508,f7985]) ).
fof(f7985,plain,
( spl0_615
<=> ! [X9,X7,X6,X8] :
( member(X9,complement(restrict(X8,X6,X7)))
| ~ member(X9,symmetric_difference(cross_product(X6,X7),X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_615])]) ).
fof(f508,plain,
( spl0_77
<=> ! [X5,X1,X0] : restrict(X5,X0,X1) = intersection(cross_product(X0,X1),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f1345,plain,
( spl0_187
<=> ! [X6,X7,X8] :
( ~ member(X8,symmetric_difference(X6,X7))
| member(X8,complement(intersection(X6,X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).
fof(f1486,plain,
( ! [X8,X6,X9,X7] :
( member(X9,complement(restrict(X8,X6,X7)))
| ~ member(X9,symmetric_difference(cross_product(X6,X7),X8)) )
| ~ spl0_77
| ~ spl0_187 ),
inference(superposition,[],[f1346,f509]) ).
fof(f509,plain,
( ! [X0,X1,X5] : restrict(X5,X0,X1) = intersection(cross_product(X0,X1),X5)
| ~ spl0_77 ),
inference(avatar_component_clause,[],[f508]) ).
fof(f1346,plain,
( ! [X8,X6,X7] :
( member(X8,complement(intersection(X6,X7)))
| ~ member(X8,symmetric_difference(X6,X7)) )
| ~ spl0_187 ),
inference(avatar_component_clause,[],[f1345]) ).
fof(f7982,plain,
( spl0_614
| ~ spl0_76
| ~ spl0_187 ),
inference(avatar_split_clause,[],[f1485,f1345,f501,f7980]) ).
fof(f7980,plain,
( spl0_614
<=> ! [X3,X4,X5,X2] :
( member(X5,complement(restrict(X2,X3,X4)))
| ~ member(X5,symmetric_difference(X2,cross_product(X3,X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_614])]) ).
fof(f501,plain,
( spl0_76
<=> ! [X5,X0,X1] : intersection(X5,cross_product(X0,X1)) = restrict(X5,X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f1485,plain,
( ! [X2,X3,X4,X5] :
( member(X5,complement(restrict(X2,X3,X4)))
| ~ member(X5,symmetric_difference(X2,cross_product(X3,X4))) )
| ~ spl0_76
| ~ spl0_187 ),
inference(superposition,[],[f1346,f502]) ).
fof(f502,plain,
( ! [X0,X1,X5] : intersection(X5,cross_product(X0,X1)) = restrict(X5,X0,X1)
| ~ spl0_76 ),
inference(avatar_component_clause,[],[f501]) ).
fof(f7978,plain,
( spl0_613
| ~ spl0_61
| ~ spl0_187 ),
inference(avatar_split_clause,[],[f1480,f1345,f401,f7976]) ).
fof(f7976,plain,
( spl0_613
<=> ! [X5,X4,X6,X3] :
( ~ member(X3,symmetric_difference(X4,X5))
| ~ subclass(complement(intersection(X4,X5)),X6)
| member(X3,X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_613])]) ).
fof(f401,plain,
( spl0_61
<=> ! [X2,X0,X1] :
( ~ subclass(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f1480,plain,
( ! [X3,X6,X4,X5] :
( ~ member(X3,symmetric_difference(X4,X5))
| ~ subclass(complement(intersection(X4,X5)),X6)
| member(X3,X6) )
| ~ spl0_61
| ~ spl0_187 ),
inference(resolution,[],[f1346,f402]) ).
fof(f402,plain,
( ! [X2,X0,X1] :
( ~ member(X2,X0)
| ~ subclass(X0,X1)
| member(X2,X1) )
| ~ spl0_61 ),
inference(avatar_component_clause,[],[f401]) ).
fof(f7974,plain,
( spl0_612
| ~ spl0_61
| ~ spl0_184 ),
inference(avatar_split_clause,[],[f1475,f1333,f401,f7972]) ).
fof(f7972,plain,
( spl0_612
<=> ! [X2,X0,X1] :
( ~ member(X0,cantor(X1))
| ~ subclass(diagonalise(compose(inverse(element_relation),X1)),X2)
| member(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_612])]) ).
fof(f1333,plain,
( spl0_184
<=> ! [X2,X3] :
( ~ member(X3,cantor(X2))
| member(X3,diagonalise(compose(inverse(element_relation),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).
fof(f1475,plain,
( ! [X2,X0,X1] :
( ~ member(X0,cantor(X1))
| ~ subclass(diagonalise(compose(inverse(element_relation),X1)),X2)
| member(X0,X2) )
| ~ spl0_61
| ~ spl0_184 ),
inference(resolution,[],[f1334,f402]) ).
fof(f1334,plain,
( ! [X2,X3] :
( member(X3,diagonalise(compose(inverse(element_relation),X2)))
| ~ member(X3,cantor(X2)) )
| ~ spl0_184 ),
inference(avatar_component_clause,[],[f1333]) ).
fof(f7970,plain,
( spl0_611
| ~ spl0_50
| ~ spl0_183 ),
inference(avatar_split_clause,[],[f1467,f1329,f332,f7968]) ).
fof(f7968,plain,
( spl0_611
<=> ! [X4,X3] : power_class(domain_of(restrict(identity_relation,X3,X4))) = complement(image(element_relation,diagonalise(cross_product(X3,X4)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_611])]) ).
fof(f332,plain,
( spl0_50
<=> ! [X0] : complement(image(element_relation,complement(X0))) = power_class(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f1329,plain,
( spl0_183
<=> ! [X13,X12] : diagonalise(cross_product(X12,X13)) = complement(domain_of(restrict(identity_relation,X12,X13))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).
fof(f1467,plain,
( ! [X3,X4] : power_class(domain_of(restrict(identity_relation,X3,X4))) = complement(image(element_relation,diagonalise(cross_product(X3,X4))))
| ~ spl0_50
| ~ spl0_183 ),
inference(superposition,[],[f333,f1330]) ).
fof(f1330,plain,
( ! [X12,X13] : diagonalise(cross_product(X12,X13)) = complement(domain_of(restrict(identity_relation,X12,X13)))
| ~ spl0_183 ),
inference(avatar_component_clause,[],[f1329]) ).
fof(f333,plain,
( ! [X0] : complement(image(element_relation,complement(X0))) = power_class(X0)
| ~ spl0_50 ),
inference(avatar_component_clause,[],[f332]) ).
fof(f7966,plain,
( spl0_610
| ~ spl0_61
| ~ spl0_179 ),
inference(avatar_split_clause,[],[f1453,f1312,f401,f7964]) ).
fof(f7964,plain,
( spl0_610
<=> ! [X2,X1] :
( ~ member(inverse(X1),universal_class)
| ~ subclass(domain_relation,X2)
| member(ordered_pair(inverse(X1),range_of(X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_610])]) ).
fof(f1312,plain,
( spl0_179
<=> ! [X0] :
( member(ordered_pair(inverse(X0),range_of(X0)),domain_relation)
| ~ member(inverse(X0),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).
fof(f1453,plain,
( ! [X2,X1] :
( ~ member(inverse(X1),universal_class)
| ~ subclass(domain_relation,X2)
| member(ordered_pair(inverse(X1),range_of(X1)),X2) )
| ~ spl0_61
| ~ spl0_179 ),
inference(resolution,[],[f1313,f402]) ).
fof(f1313,plain,
( ! [X0] :
( member(ordered_pair(inverse(X0),range_of(X0)),domain_relation)
| ~ member(inverse(X0),universal_class) )
| ~ spl0_179 ),
inference(avatar_component_clause,[],[f1312]) ).
fof(f7962,plain,
( spl0_609
| ~ spl0_145
| ~ spl0_177 ),
inference(avatar_split_clause,[],[f1441,f1304,f1014,f7960]) ).
fof(f7960,plain,
( spl0_609
<=> ! [X41,X40,X39] :
( ~ subclass(X39,null_class)
| subclass(X39,X40)
| member(not_subclass_element(X39,X40),X41)
| null_class = X41 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_609])]) ).
fof(f1014,plain,
( spl0_145
<=> ! [X2,X3] :
( ~ member(X3,null_class)
| member(X3,X2)
| null_class = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f1304,plain,
( spl0_177
<=> ! [X6,X7,X8] :
( ~ subclass(X6,X7)
| member(not_subclass_element(X6,X8),X7)
| subclass(X6,X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
fof(f1441,plain,
( ! [X40,X41,X39] :
( ~ subclass(X39,null_class)
| subclass(X39,X40)
| member(not_subclass_element(X39,X40),X41)
| null_class = X41 )
| ~ spl0_145
| ~ spl0_177 ),
inference(resolution,[],[f1305,f1015]) ).
fof(f1015,plain,
( ! [X2,X3] :
( ~ member(X3,null_class)
| member(X3,X2)
| null_class = X2 )
| ~ spl0_145 ),
inference(avatar_component_clause,[],[f1014]) ).
fof(f1305,plain,
( ! [X8,X6,X7] :
( member(not_subclass_element(X6,X8),X7)
| ~ subclass(X6,X7)
| subclass(X6,X8) )
| ~ spl0_177 ),
inference(avatar_component_clause,[],[f1304]) ).
fof(f7958,plain,
( spl0_608
| ~ spl0_146
| ~ spl0_177 ),
inference(avatar_split_clause,[],[f1440,f1304,f1018,f7956]) ).
fof(f7956,plain,
( spl0_608
<=> ! [X38,X37,X34,X36,X35] :
( ~ subclass(X34,restrict(X35,X36,X37))
| subclass(X34,X38)
| member(not_subclass_element(X34,X38),X35) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_608])]) ).
fof(f1018,plain,
( spl0_146
<=> ! [X5,X4,X7,X6] :
( ~ member(X7,restrict(X4,X5,X6))
| member(X7,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f1440,plain,
( ! [X38,X36,X37,X34,X35] :
( ~ subclass(X34,restrict(X35,X36,X37))
| subclass(X34,X38)
| member(not_subclass_element(X34,X38),X35) )
| ~ spl0_146
| ~ spl0_177 ),
inference(resolution,[],[f1305,f1019]) ).
fof(f1019,plain,
( ! [X6,X7,X4,X5] :
( ~ member(X7,restrict(X4,X5,X6))
| member(X7,X4) )
| ~ spl0_146 ),
inference(avatar_component_clause,[],[f1018]) ).
fof(f7954,plain,
( spl0_607
| ~ spl0_61
| ~ spl0_177 ),
inference(avatar_split_clause,[],[f1432,f1304,f401,f7952]) ).
fof(f7952,plain,
( spl0_607
<=> ! [X5,X4,X7,X6] :
( ~ subclass(X4,X5)
| subclass(X4,X6)
| ~ subclass(X5,X7)
| member(not_subclass_element(X4,X6),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_607])]) ).
fof(f1432,plain,
( ! [X6,X7,X4,X5] :
( ~ subclass(X4,X5)
| subclass(X4,X6)
| ~ subclass(X5,X7)
| member(not_subclass_element(X4,X6),X7) )
| ~ spl0_61
| ~ spl0_177 ),
inference(resolution,[],[f1305,f402]) ).
fof(f7950,plain,
( spl0_606
| ~ spl0_50
| ~ spl0_174 ),
inference(avatar_split_clause,[],[f1412,f1292,f332,f7948]) ).
fof(f7948,plain,
( spl0_606
<=> ! [X2] : power_class(image(element_relation,diagonalise(X2))) = complement(image(element_relation,power_class(domain_of(intersection(X2,identity_relation))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_606])]) ).
fof(f1292,plain,
( spl0_174
<=> ! [X0] : power_class(domain_of(intersection(X0,identity_relation))) = complement(image(element_relation,diagonalise(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).
fof(f1412,plain,
( ! [X2] : power_class(image(element_relation,diagonalise(X2))) = complement(image(element_relation,power_class(domain_of(intersection(X2,identity_relation)))))
| ~ spl0_50
| ~ spl0_174 ),
inference(superposition,[],[f333,f1293]) ).
fof(f1293,plain,
( ! [X0] : power_class(domain_of(intersection(X0,identity_relation))) = complement(image(element_relation,diagonalise(X0)))
| ~ spl0_174 ),
inference(avatar_component_clause,[],[f1292]) ).
fof(f7946,plain,
( spl0_605
| ~ spl0_50
| ~ spl0_173 ),
inference(avatar_split_clause,[],[f1403,f1288,f332,f7944]) ).
fof(f7944,plain,
( spl0_605
<=> ! [X2] : power_class(image(element_relation,power_class(X2))) = complement(image(element_relation,power_class(image(element_relation,complement(X2))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_605])]) ).
fof(f1288,plain,
( spl0_173
<=> ! [X0] : power_class(image(element_relation,complement(X0))) = complement(image(element_relation,power_class(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).
fof(f1403,plain,
( ! [X2] : power_class(image(element_relation,power_class(X2))) = complement(image(element_relation,power_class(image(element_relation,complement(X2)))))
| ~ spl0_50
| ~ spl0_173 ),
inference(superposition,[],[f333,f1289]) ).
fof(f1289,plain,
( ! [X0] : power_class(image(element_relation,complement(X0))) = complement(image(element_relation,power_class(X0)))
| ~ spl0_173 ),
inference(avatar_component_clause,[],[f1288]) ).
fof(f7942,plain,
( ~ spl0_603
| ~ spl0_604
| ~ spl0_3
| ~ spl0_558 ),
inference(avatar_split_clause,[],[f7586,f6776,f129,f7939,f7935]) ).
fof(f129,plain,
( spl0_3
<=> member(x,union(y,z)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f6776,plain,
( spl0_558
<=> ! [X2,X0,X1] :
( ~ member(X0,union(X1,X2))
| ~ member(X0,complement(X2))
| ~ member(X0,complement(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_558])]) ).
fof(f7586,plain,
( ~ member(x,complement(z))
| ~ member(x,complement(y))
| ~ spl0_3
| ~ spl0_558 ),
inference(resolution,[],[f6777,f131]) ).
fof(f131,plain,
( member(x,union(y,z))
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f129]) ).
fof(f6777,plain,
( ! [X2,X0,X1] :
( ~ member(X0,union(X1,X2))
| ~ member(X0,complement(X2))
| ~ member(X0,complement(X1)) )
| ~ spl0_558 ),
inference(avatar_component_clause,[],[f6776]) ).
fof(f7933,plain,
( spl0_602
| ~ spl0_141
| ~ spl0_172 ),
inference(avatar_split_clause,[],[f1390,f1284,f953,f7931]) ).
fof(f7931,plain,
( spl0_602
<=> ! [X38,X39] :
( null_class = intersection(X38,cantor(X39))
| member(regular(intersection(X38,cantor(X39))),domain_of(X39)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_602])]) ).
fof(f1390,plain,
( ! [X38,X39] :
( null_class = intersection(X38,cantor(X39))
| member(regular(intersection(X38,cantor(X39))),domain_of(X39)) )
| ~ spl0_141
| ~ spl0_172 ),
inference(resolution,[],[f1285,f954]) ).
fof(f7929,plain,
( spl0_601
| ~ spl0_145
| ~ spl0_172 ),
inference(avatar_split_clause,[],[f1384,f1284,f1014,f7927]) ).
fof(f7927,plain,
( spl0_601
<=> ! [X27,X26] :
( null_class = intersection(X26,null_class)
| member(regular(intersection(X26,null_class)),X27)
| null_class = X27 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_601])]) ).
fof(f1384,plain,
( ! [X26,X27] :
( null_class = intersection(X26,null_class)
| member(regular(intersection(X26,null_class)),X27)
| null_class = X27 )
| ~ spl0_145
| ~ spl0_172 ),
inference(resolution,[],[f1285,f1015]) ).
fof(f7925,plain,
( spl0_600
| ~ spl0_61
| ~ spl0_172 ),
inference(avatar_split_clause,[],[f1375,f1284,f401,f7923]) ).
fof(f7923,plain,
( spl0_600
<=> ! [X2,X0,X1] :
( intersection(X0,X1) = null_class
| ~ subclass(X1,X2)
| member(regular(intersection(X0,X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_600])]) ).
fof(f1375,plain,
( ! [X2,X0,X1] :
( intersection(X0,X1) = null_class
| ~ subclass(X1,X2)
| member(regular(intersection(X0,X1)),X2) )
| ~ spl0_61
| ~ spl0_172 ),
inference(resolution,[],[f1285,f402]) ).
fof(f7921,plain,
( spl0_599
| ~ spl0_99
| ~ spl0_171 ),
inference(avatar_split_clause,[],[f1370,f1280,f668,f7919]) ).
fof(f7919,plain,
( spl0_599
<=> ! [X8,X7] :
( member(regular(symmetric_difference(X7,X8)),complement(intersection(X7,X8)))
| null_class = symmetric_difference(X7,X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_599])]) ).
fof(f1370,plain,
( ! [X8,X7] :
( member(regular(symmetric_difference(X7,X8)),complement(intersection(X7,X8)))
| null_class = symmetric_difference(X7,X8) )
| ~ spl0_99
| ~ spl0_171 ),
inference(superposition,[],[f1281,f669]) ).
fof(f7917,plain,
( spl0_598
| ~ spl0_141
| ~ spl0_171 ),
inference(avatar_split_clause,[],[f1363,f1280,f953,f7915]) ).
fof(f7915,plain,
( spl0_598
<=> ! [X38,X39] :
( null_class = intersection(cantor(X38),X39)
| member(regular(intersection(cantor(X38),X39)),domain_of(X38)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_598])]) ).
fof(f1363,plain,
( ! [X38,X39] :
( null_class = intersection(cantor(X38),X39)
| member(regular(intersection(cantor(X38),X39)),domain_of(X38)) )
| ~ spl0_141
| ~ spl0_171 ),
inference(resolution,[],[f1281,f954]) ).
fof(f7913,plain,
( spl0_597
| ~ spl0_145
| ~ spl0_171 ),
inference(avatar_split_clause,[],[f1357,f1280,f1014,f7911]) ).
fof(f7911,plain,
( spl0_597
<=> ! [X27,X26] :
( null_class = intersection(null_class,X26)
| member(regular(intersection(null_class,X26)),X27)
| null_class = X27 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_597])]) ).
fof(f1357,plain,
( ! [X26,X27] :
( null_class = intersection(null_class,X26)
| member(regular(intersection(null_class,X26)),X27)
| null_class = X27 )
| ~ spl0_145
| ~ spl0_171 ),
inference(resolution,[],[f1281,f1015]) ).
fof(f7909,plain,
( spl0_596
| ~ spl0_61
| ~ spl0_171 ),
inference(avatar_split_clause,[],[f1348,f1280,f401,f7907]) ).
fof(f7907,plain,
( spl0_596
<=> ! [X2,X0,X1] :
( intersection(X0,X1) = null_class
| ~ subclass(X0,X2)
| member(regular(intersection(X0,X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_596])]) ).
fof(f1348,plain,
( ! [X2,X0,X1] :
( intersection(X0,X1) = null_class
| ~ subclass(X0,X2)
| member(regular(intersection(X0,X1)),X2) )
| ~ spl0_61
| ~ spl0_171 ),
inference(resolution,[],[f1281,f402]) ).
fof(f7905,plain,
( spl0_595
| ~ spl0_156
| ~ spl0_170 ),
inference(avatar_split_clause,[],[f1277,f1169,f1109,f7903]) ).
fof(f7903,plain,
( spl0_595
<=> ! [X18,X17,X19] :
( member(regular(X17),union(X18,X19))
| ~ subclass(X17,symmetric_difference(X18,X19))
| null_class = X17 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_595])]) ).
fof(f1109,plain,
( spl0_156
<=> ! [X22,X21] :
( ~ subclass(X21,X22)
| member(regular(X21),X22)
| null_class = X21 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f1169,plain,
( spl0_170
<=> ! [X4,X5,X3] :
( ~ member(X5,symmetric_difference(X3,X4))
| member(X5,union(X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
fof(f1277,plain,
( ! [X18,X19,X17] :
( member(regular(X17),union(X18,X19))
| ~ subclass(X17,symmetric_difference(X18,X19))
| null_class = X17 )
| ~ spl0_156
| ~ spl0_170 ),
inference(resolution,[],[f1170,f1110]) ).
fof(f1110,plain,
( ! [X21,X22] :
( member(regular(X21),X22)
| ~ subclass(X21,X22)
| null_class = X21 )
| ~ spl0_156 ),
inference(avatar_component_clause,[],[f1109]) ).
fof(f1170,plain,
( ! [X3,X4,X5] :
( ~ member(X5,symmetric_difference(X3,X4))
| member(X5,union(X3,X4)) )
| ~ spl0_170 ),
inference(avatar_component_clause,[],[f1169]) ).
fof(f7901,plain,
( spl0_594
| ~ spl0_155
| ~ spl0_170 ),
inference(avatar_split_clause,[],[f1275,f1169,f1105,f7899]) ).
fof(f7899,plain,
( spl0_594
<=> ! [X13,X12,X14] :
( member(power_class(X12),union(X13,X14))
| ~ subclass(universal_class,symmetric_difference(X13,X14))
| ~ member(X12,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_594])]) ).
fof(f1105,plain,
( spl0_155
<=> ! [X20,X19] :
( ~ subclass(universal_class,X19)
| member(power_class(X20),X19)
| ~ member(X20,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f1275,plain,
( ! [X14,X12,X13] :
( member(power_class(X12),union(X13,X14))
| ~ subclass(universal_class,symmetric_difference(X13,X14))
| ~ member(X12,universal_class) )
| ~ spl0_155
| ~ spl0_170 ),
inference(resolution,[],[f1170,f1106]) ).
fof(f1106,plain,
( ! [X19,X20] :
( member(power_class(X20),X19)
| ~ subclass(universal_class,X19)
| ~ member(X20,universal_class) )
| ~ spl0_155 ),
inference(avatar_component_clause,[],[f1105]) ).
fof(f7897,plain,
( spl0_593
| ~ spl0_154
| ~ spl0_170 ),
inference(avatar_split_clause,[],[f1274,f1169,f1101,f7895]) ).
fof(f7895,plain,
( spl0_593
<=> ! [X9,X11,X10] :
( member(sum_class(X9),union(X10,X11))
| ~ subclass(universal_class,symmetric_difference(X10,X11))
| ~ member(X9,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_593])]) ).
fof(f1101,plain,
( spl0_154
<=> ! [X18,X17] :
( ~ subclass(universal_class,X17)
| member(sum_class(X18),X17)
| ~ member(X18,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f1274,plain,
( ! [X10,X11,X9] :
( member(sum_class(X9),union(X10,X11))
| ~ subclass(universal_class,symmetric_difference(X10,X11))
| ~ member(X9,universal_class) )
| ~ spl0_154
| ~ spl0_170 ),
inference(resolution,[],[f1170,f1102]) ).
fof(f1102,plain,
( ! [X18,X17] :
( member(sum_class(X18),X17)
| ~ subclass(universal_class,X17)
| ~ member(X18,universal_class) )
| ~ spl0_154 ),
inference(avatar_component_clause,[],[f1101]) ).
fof(f7887,plain,
( spl0_592
| ~ spl0_39
| ~ spl0_170 ),
inference(avatar_split_clause,[],[f1271,f1169,f288,f7885]) ).
fof(f7885,plain,
( spl0_592
<=> ! [X2,X0,X1] :
( member(not_subclass_element(symmetric_difference(X0,X1),X2),union(X0,X1))
| subclass(symmetric_difference(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_592])]) ).
fof(f288,plain,
( spl0_39
<=> ! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f1271,plain,
( ! [X2,X0,X1] :
( member(not_subclass_element(symmetric_difference(X0,X1),X2),union(X0,X1))
| subclass(symmetric_difference(X0,X1),X2) )
| ~ spl0_39
| ~ spl0_170 ),
inference(resolution,[],[f1170,f289]) ).
fof(f289,plain,
( ! [X0,X1] :
( member(not_subclass_element(X0,X1),X0)
| subclass(X0,X1) )
| ~ spl0_39 ),
inference(avatar_component_clause,[],[f288]) ).
fof(f7880,plain,
( spl0_589
| spl0_590
| ~ spl0_591
| ~ spl0_34
| ~ spl0_169 ),
inference(avatar_split_clause,[],[f1268,f1165,f263,f7877,f7873,f7869]) ).
fof(f7869,plain,
( spl0_589
<=> null_class = inverse(subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_589])]) ).
fof(f7873,plain,
( spl0_590
<=> member(regular(inverse(subset_relation)),identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_590])]) ).
fof(f7877,plain,
( spl0_591
<=> member(regular(inverse(subset_relation)),subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_591])]) ).
fof(f263,plain,
( spl0_34
<=> ! [X0] :
( null_class = X0
| member(regular(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f1165,plain,
( spl0_169
<=> ! [X11] :
( member(X11,identity_relation)
| ~ member(X11,subset_relation)
| ~ member(X11,inverse(subset_relation)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
fof(f1268,plain,
( ~ member(regular(inverse(subset_relation)),subset_relation)
| member(regular(inverse(subset_relation)),identity_relation)
| null_class = inverse(subset_relation)
| ~ spl0_34
| ~ spl0_169 ),
inference(resolution,[],[f1166,f264]) ).
fof(f264,plain,
( ! [X0] :
( member(regular(X0),X0)
| null_class = X0 )
| ~ spl0_34 ),
inference(avatar_component_clause,[],[f263]) ).
fof(f1166,plain,
( ! [X11] :
( ~ member(X11,inverse(subset_relation))
| ~ member(X11,subset_relation)
| member(X11,identity_relation) )
| ~ spl0_169 ),
inference(avatar_component_clause,[],[f1165]) ).
fof(f7867,plain,
( ~ spl0_587
| spl0_588
| ~ spl0_138
| ~ spl0_169 ),
inference(avatar_split_clause,[],[f1264,f1165,f941,f7865,f7861]) ).
fof(f7861,plain,
( spl0_587
<=> subclass(universal_class,inverse(subset_relation)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_587])]) ).
fof(f7865,plain,
( spl0_588
<=> ! [X2,X3] :
( ~ member(unordered_pair(X2,X3),subset_relation)
| member(unordered_pair(X2,X3),identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_588])]) ).
fof(f1264,plain,
( ! [X2,X3] :
( ~ member(unordered_pair(X2,X3),subset_relation)
| member(unordered_pair(X2,X3),identity_relation)
| ~ subclass(universal_class,inverse(subset_relation)) )
| ~ spl0_138
| ~ spl0_169 ),
inference(resolution,[],[f1166,f942]) ).
fof(f7859,plain,
( spl0_586
| ~ spl0_86
| ~ spl0_167 ),
inference(avatar_split_clause,[],[f1258,f1157,f574,f7857]) ).
fof(f7857,plain,
( spl0_586
<=> ! [X2,X1] :
( ~ inductive(ordered_pair(X1,X2))
| null_class = unordered_pair(X1,singleton(X2))
| singleton(X1) = null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_586])]) ).
fof(f574,plain,
( spl0_86
<=> ! [X0,X1] : unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))) = ordered_pair(X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f1157,plain,
( spl0_167
<=> ! [X7,X8] :
( null_class = X7
| null_class = X8
| ~ inductive(unordered_pair(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
fof(f1258,plain,
( ! [X2,X1] :
( ~ inductive(ordered_pair(X1,X2))
| null_class = unordered_pair(X1,singleton(X2))
| singleton(X1) = null_class )
| ~ spl0_86
| ~ spl0_167 ),
inference(superposition,[],[f1158,f575]) ).
fof(f575,plain,
( ! [X0,X1] : unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))) = ordered_pair(X0,X1)
| ~ spl0_86 ),
inference(avatar_component_clause,[],[f574]) ).
fof(f1158,plain,
( ! [X8,X7] :
( ~ inductive(unordered_pair(X7,X8))
| null_class = X8
| null_class = X7 )
| ~ spl0_167 ),
inference(avatar_component_clause,[],[f1157]) ).
fof(f7855,plain,
( spl0_585
| ~ spl0_144
| ~ spl0_165 ),
inference(avatar_split_clause,[],[f1251,f1149,f1010,f7853]) ).
fof(f7853,plain,
( spl0_585
<=> ! [X7] :
( ~ member(regular(complement(regular(X7))),null_class)
| null_class = X7
| null_class = complement(regular(X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_585])]) ).
fof(f1010,plain,
( spl0_144
<=> ! [X0] :
( complement(X0) = null_class
| ~ member(regular(complement(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f1149,plain,
( spl0_165
<=> ! [X0,X1] :
( ~ member(X1,null_class)
| member(X1,regular(X0))
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
fof(f1251,plain,
( ! [X7] :
( ~ member(regular(complement(regular(X7))),null_class)
| null_class = X7
| null_class = complement(regular(X7)) )
| ~ spl0_144
| ~ spl0_165 ),
inference(resolution,[],[f1150,f1011]) ).
fof(f1011,plain,
( ! [X0] :
( ~ member(regular(complement(X0)),X0)
| complement(X0) = null_class )
| ~ spl0_144 ),
inference(avatar_component_clause,[],[f1010]) ).
fof(f1150,plain,
( ! [X0,X1] :
( member(X1,regular(X0))
| ~ member(X1,null_class)
| null_class = X0 )
| ~ spl0_165 ),
inference(avatar_component_clause,[],[f1149]) ).
fof(f7851,plain,
( spl0_584
| ~ spl0_151
| ~ spl0_156 ),
inference(avatar_split_clause,[],[f1243,f1109,f1089,f7849]) ).
fof(f7849,plain,
( spl0_584
<=> ! [X32,X33] :
( ~ subclass(X32,image(element_relation,complement(X33)))
| null_class = X32
| ~ member(regular(X32),power_class(X33)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_584])]) ).
fof(f1089,plain,
( spl0_151
<=> ! [X2,X1] :
( ~ member(X2,power_class(X1))
| ~ member(X2,image(element_relation,complement(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f1243,plain,
( ! [X32,X33] :
( ~ subclass(X32,image(element_relation,complement(X33)))
| null_class = X32
| ~ member(regular(X32),power_class(X33)) )
| ~ spl0_151
| ~ spl0_156 ),
inference(resolution,[],[f1110,f1090]) ).
fof(f1090,plain,
( ! [X2,X1] :
( ~ member(X2,image(element_relation,complement(X1)))
| ~ member(X2,power_class(X1)) )
| ~ spl0_151 ),
inference(avatar_component_clause,[],[f1089]) ).
fof(f7847,plain,
( spl0_583
| ~ spl0_334
| ~ spl0_568 ),
inference(avatar_split_clause,[],[f7803,f6892,f3899,f7845]) ).
fof(f7845,plain,
( spl0_583
<=> ! [X0,X1] : ~ subclass(universal_class,compose(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_583])]) ).
fof(f3899,plain,
( spl0_334
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,X0)
| member(ordered_pair(X1,X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_334])]) ).
fof(f6892,plain,
( spl0_568
<=> ! [X32,X33] : ~ member(ordered_pair(x,null_class),compose(X32,X33)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_568])]) ).
fof(f7803,plain,
( ! [X0,X1] : ~ subclass(universal_class,compose(X0,X1))
| ~ spl0_334
| ~ spl0_568 ),
inference(resolution,[],[f6893,f3900]) ).
fof(f3900,plain,
( ! [X2,X0,X1] :
( member(ordered_pair(X1,X2),X0)
| ~ subclass(universal_class,X0) )
| ~ spl0_334 ),
inference(avatar_component_clause,[],[f3899]) ).
fof(f6893,plain,
( ! [X32,X33] : ~ member(ordered_pair(x,null_class),compose(X32,X33))
| ~ spl0_568 ),
inference(avatar_component_clause,[],[f6892]) ).
fof(f7843,plain,
( spl0_582
| ~ spl0_152
| ~ spl0_156 ),
inference(avatar_split_clause,[],[f1241,f1109,f1093,f7841]) ).
fof(f7841,plain,
( spl0_582
<=> ! [X27,X26] :
( ~ subclass(X26,domain_of(intersection(X27,identity_relation)))
| null_class = X26
| ~ member(regular(X26),diagonalise(X27)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_582])]) ).
fof(f1093,plain,
( spl0_152
<=> ! [X2,X3] :
( ~ member(X3,diagonalise(X2))
| ~ member(X3,domain_of(intersection(X2,identity_relation))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f1241,plain,
( ! [X26,X27] :
( ~ subclass(X26,domain_of(intersection(X27,identity_relation)))
| null_class = X26
| ~ member(regular(X26),diagonalise(X27)) )
| ~ spl0_152
| ~ spl0_156 ),
inference(resolution,[],[f1110,f1094]) ).
fof(f1094,plain,
( ! [X2,X3] :
( ~ member(X3,domain_of(intersection(X2,identity_relation)))
| ~ member(X3,diagonalise(X2)) )
| ~ spl0_152 ),
inference(avatar_component_clause,[],[f1093]) ).
fof(f7839,plain,
( spl0_581
| ~ spl0_151
| ~ spl0_155 ),
inference(avatar_split_clause,[],[f1227,f1105,f1089,f7837]) ).
fof(f7837,plain,
( spl0_581
<=> ! [X32,X31] :
( ~ subclass(universal_class,image(element_relation,complement(X31)))
| ~ member(X32,universal_class)
| ~ member(power_class(X32),power_class(X31)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_581])]) ).
fof(f1227,plain,
( ! [X31,X32] :
( ~ subclass(universal_class,image(element_relation,complement(X31)))
| ~ member(X32,universal_class)
| ~ member(power_class(X32),power_class(X31)) )
| ~ spl0_151
| ~ spl0_155 ),
inference(resolution,[],[f1106,f1090]) ).
fof(f7835,plain,
( spl0_580
| ~ spl0_152
| ~ spl0_155 ),
inference(avatar_split_clause,[],[f1225,f1105,f1093,f7833]) ).
fof(f7833,plain,
( spl0_580
<=> ! [X25,X26] :
( ~ subclass(universal_class,domain_of(intersection(X25,identity_relation)))
| ~ member(X26,universal_class)
| ~ member(power_class(X26),diagonalise(X25)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_580])]) ).
fof(f1225,plain,
( ! [X26,X25] :
( ~ subclass(universal_class,domain_of(intersection(X25,identity_relation)))
| ~ member(X26,universal_class)
| ~ member(power_class(X26),diagonalise(X25)) )
| ~ spl0_152
| ~ spl0_155 ),
inference(resolution,[],[f1106,f1094]) ).
fof(f7831,plain,
( spl0_579
| ~ spl0_67
| ~ spl0_154 ),
inference(avatar_split_clause,[],[f1215,f1101,f425,f7829]) ).
fof(f7829,plain,
( spl0_579
<=> ! [X2,X0,X1] :
( member(apply(X0,X1),X2)
| ~ subclass(universal_class,X2)
| ~ member(image(X0,singleton(X1)),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_579])]) ).
fof(f425,plain,
( spl0_67
<=> ! [X1,X8] : sum_class(image(X8,singleton(X1))) = apply(X8,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f1215,plain,
( ! [X2,X0,X1] :
( member(apply(X0,X1),X2)
| ~ subclass(universal_class,X2)
| ~ member(image(X0,singleton(X1)),universal_class) )
| ~ spl0_67
| ~ spl0_154 ),
inference(superposition,[],[f1102,f426]) ).
fof(f426,plain,
( ! [X1,X8] : sum_class(image(X8,singleton(X1))) = apply(X8,X1)
| ~ spl0_67 ),
inference(avatar_component_clause,[],[f425]) ).
fof(f7827,plain,
( spl0_578
| ~ spl0_151
| ~ spl0_154 ),
inference(avatar_split_clause,[],[f1211,f1101,f1089,f7825]) ).
fof(f7825,plain,
( spl0_578
<=> ! [X32,X31] :
( ~ subclass(universal_class,image(element_relation,complement(X31)))
| ~ member(X32,universal_class)
| ~ member(sum_class(X32),power_class(X31)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_578])]) ).
fof(f1211,plain,
( ! [X31,X32] :
( ~ subclass(universal_class,image(element_relation,complement(X31)))
| ~ member(X32,universal_class)
| ~ member(sum_class(X32),power_class(X31)) )
| ~ spl0_151
| ~ spl0_154 ),
inference(resolution,[],[f1102,f1090]) ).
fof(f7823,plain,
( spl0_577
| ~ spl0_152
| ~ spl0_154 ),
inference(avatar_split_clause,[],[f1209,f1101,f1093,f7821]) ).
fof(f7821,plain,
( spl0_577
<=> ! [X25,X26] :
( ~ subclass(universal_class,domain_of(intersection(X25,identity_relation)))
| ~ member(X26,universal_class)
| ~ member(sum_class(X26),diagonalise(X25)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_577])]) ).
fof(f1209,plain,
( ! [X26,X25] :
( ~ subclass(universal_class,domain_of(intersection(X25,identity_relation)))
| ~ member(X26,universal_class)
| ~ member(sum_class(X26),diagonalise(X25)) )
| ~ spl0_152
| ~ spl0_154 ),
inference(resolution,[],[f1102,f1094]) ).
fof(f7819,plain,
( spl0_576
| ~ spl0_34
| ~ spl0_152 ),
inference(avatar_split_clause,[],[f1194,f1093,f263,f7817]) ).
fof(f7817,plain,
( spl0_576
<=> ! [X11] :
( ~ member(regular(domain_of(intersection(X11,identity_relation))),diagonalise(X11))
| null_class = domain_of(intersection(X11,identity_relation)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_576])]) ).
fof(f1194,plain,
( ! [X11] :
( ~ member(regular(domain_of(intersection(X11,identity_relation))),diagonalise(X11))
| null_class = domain_of(intersection(X11,identity_relation)) )
| ~ spl0_34
| ~ spl0_152 ),
inference(resolution,[],[f1094,f264]) ).
fof(f7815,plain,
( spl0_575
| ~ spl0_34
| ~ spl0_151 ),
inference(avatar_split_clause,[],[f1184,f1089,f263,f7813]) ).
fof(f7813,plain,
( spl0_575
<=> ! [X6] :
( ~ member(regular(image(element_relation,complement(X6))),power_class(X6))
| null_class = image(element_relation,complement(X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_575])]) ).
fof(f1184,plain,
( ! [X6] :
( ~ member(regular(image(element_relation,complement(X6))),power_class(X6))
| null_class = image(element_relation,complement(X6)) )
| ~ spl0_34
| ~ spl0_151 ),
inference(resolution,[],[f1090,f264]) ).
fof(f7811,plain,
( spl0_574
| ~ spl0_143
| ~ spl0_150 ),
inference(avatar_split_clause,[],[f1172,f1085,f961,f7809]) ).
fof(f7809,plain,
( spl0_574
<=> ! [X0] :
( subclass(complement(cross_product(universal_class,universal_class)),X0)
| ~ member(not_subclass_element(complement(cross_product(universal_class,universal_class)),X0),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_574])]) ).
fof(f961,plain,
( spl0_143
<=> ! [X2] :
( ~ member(X2,subset_relation)
| member(X2,cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f1085,plain,
( spl0_150
<=> ! [X0,X1] :
( subclass(complement(X0),X1)
| ~ member(not_subclass_element(complement(X0),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f1172,plain,
( ! [X0] :
( subclass(complement(cross_product(universal_class,universal_class)),X0)
| ~ member(not_subclass_element(complement(cross_product(universal_class,universal_class)),X0),subset_relation) )
| ~ spl0_143
| ~ spl0_150 ),
inference(resolution,[],[f1086,f962]) ).
fof(f962,plain,
( ! [X2] :
( member(X2,cross_product(universal_class,universal_class))
| ~ member(X2,subset_relation) )
| ~ spl0_143 ),
inference(avatar_component_clause,[],[f961]) ).
fof(f1086,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(complement(X0),X1),X0)
| subclass(complement(X0),X1) )
| ~ spl0_150 ),
inference(avatar_component_clause,[],[f1085]) ).
fof(f7807,plain,
( spl0_573
| ~ spl0_98
| ~ spl0_147 ),
inference(avatar_split_clause,[],[f1061,f1022,f664,f7805]) ).
fof(f7805,plain,
( spl0_573
<=> ! [X16,X15] :
( ~ member(ordered_pair(X16,singleton(singleton(singleton(X15)))),application_function)
| apply(X16,singleton(X15)) = X15 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_573])]) ).
fof(f664,plain,
( spl0_98
<=> ! [X4,X0,X1] :
( apply(X0,X1) = X4
| ~ member(ordered_pair(X0,ordered_pair(X1,X4)),application_function) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f1022,plain,
( spl0_147
<=> ! [X0] : ordered_pair(singleton(X0),X0) = singleton(singleton(singleton(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f1061,plain,
( ! [X16,X15] :
( ~ member(ordered_pair(X16,singleton(singleton(singleton(X15)))),application_function)
| apply(X16,singleton(X15)) = X15 )
| ~ spl0_98
| ~ spl0_147 ),
inference(superposition,[],[f665,f1023]) ).
fof(f1023,plain,
( ! [X0] : ordered_pair(singleton(X0),X0) = singleton(singleton(singleton(X0)))
| ~ spl0_147 ),
inference(avatar_component_clause,[],[f1022]) ).
fof(f665,plain,
( ! [X0,X1,X4] :
( ~ member(ordered_pair(X0,ordered_pair(X1,X4)),application_function)
| apply(X0,X1) = X4 )
| ~ spl0_98 ),
inference(avatar_component_clause,[],[f664]) ).
fof(f7802,plain,
( spl0_572
| ~ spl0_97
| ~ spl0_147 ),
inference(avatar_split_clause,[],[f1060,f1022,f657,f7800]) ).
fof(f7800,plain,
( spl0_572
<=> ! [X13,X14] :
( ~ member(ordered_pair(X14,singleton(singleton(singleton(X13)))),composition_function)
| compose(X14,singleton(X13)) = X13 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_572])]) ).
fof(f657,plain,
( spl0_97
<=> ! [X4,X0,X1] :
( compose(X0,X1) = X4
| ~ member(ordered_pair(X0,ordered_pair(X1,X4)),composition_function) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f1060,plain,
( ! [X14,X13] :
( ~ member(ordered_pair(X14,singleton(singleton(singleton(X13)))),composition_function)
| compose(X14,singleton(X13)) = X13 )
| ~ spl0_97
| ~ spl0_147 ),
inference(superposition,[],[f658,f1023]) ).
fof(f658,plain,
( ! [X0,X1,X4] :
( ~ member(ordered_pair(X0,ordered_pair(X1,X4)),composition_function)
| compose(X0,X1) = X4 )
| ~ spl0_97 ),
inference(avatar_component_clause,[],[f657]) ).
fof(f7798,plain,
( spl0_571
| ~ spl0_39
| ~ spl0_146 ),
inference(avatar_split_clause,[],[f1048,f1018,f288,f7796]) ).
fof(f7796,plain,
( spl0_571
<=> ! [X0,X3,X2,X1] :
( member(not_subclass_element(restrict(X0,X1,X2),X3),X0)
| subclass(restrict(X0,X1,X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_571])]) ).
fof(f1048,plain,
( ! [X2,X3,X0,X1] :
( member(not_subclass_element(restrict(X0,X1,X2),X3),X0)
| subclass(restrict(X0,X1,X2),X3) )
| ~ spl0_39
| ~ spl0_146 ),
inference(resolution,[],[f1019,f289]) ).
fof(f7794,plain,
( spl0_570
| ~ spl0_89
| ~ spl0_137 ),
inference(avatar_split_clause,[],[f939,f913,f586,f7792]) ).
fof(f7792,plain,
( spl0_570
<=> ! [X5] :
( apply(choice,singleton(X5)) = X5
| null_class = singleton(X5)
| ~ member(singleton(X5),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_570])]) ).
fof(f586,plain,
( spl0_89
<=> ! [X1] :
( ~ member(X1,universal_class)
| null_class = X1
| member(apply(choice,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f939,plain,
( ! [X5] :
( apply(choice,singleton(X5)) = X5
| null_class = singleton(X5)
| ~ member(singleton(X5),universal_class) )
| ~ spl0_89
| ~ spl0_137 ),
inference(resolution,[],[f914,f587]) ).
fof(f587,plain,
( ! [X1] :
( member(apply(choice,X1),X1)
| null_class = X1
| ~ member(X1,universal_class) )
| ~ spl0_89 ),
inference(avatar_component_clause,[],[f586]) ).
fof(f7401,plain,
( spl0_569
| ~ spl0_61
| ~ spl0_439 ),
inference(avatar_split_clause,[],[f7127,f5146,f401,f7399]) ).
fof(f7399,plain,
( spl0_569
<=> ! [X7] :
( ~ subclass(universal_class,X7)
| member(second(ordered_pair(x,null_class)),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_569])]) ).
fof(f5146,plain,
( spl0_439
<=> member(second(ordered_pair(x,null_class)),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_439])]) ).
fof(f7127,plain,
( ! [X7] :
( ~ subclass(universal_class,X7)
| member(second(ordered_pair(x,null_class)),X7) )
| ~ spl0_61
| ~ spl0_439 ),
inference(resolution,[],[f5148,f402]) ).
fof(f5148,plain,
( member(second(ordered_pair(x,null_class)),universal_class)
| ~ spl0_439 ),
inference(avatar_component_clause,[],[f5146]) ).
fof(f6894,plain,
( spl0_439
| spl0_568
| ~ spl0_290
| ~ spl0_419 ),
inference(avatar_split_clause,[],[f5106,f4694,f3258,f6892,f5146]) ).
fof(f3258,plain,
( spl0_290
<=> ordered_pair(x,null_class) = ordered_pair(first(ordered_pair(x,null_class)),second(ordered_pair(x,null_class))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).
fof(f4694,plain,
( spl0_419
<=> ! [X10,X7,X9,X8] :
( ~ member(ordered_pair(X7,X8),compose(X9,X10))
| member(X8,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_419])]) ).
fof(f5106,plain,
( ! [X32,X33] :
( ~ member(ordered_pair(x,null_class),compose(X32,X33))
| member(second(ordered_pair(x,null_class)),universal_class) )
| ~ spl0_290
| ~ spl0_419 ),
inference(superposition,[],[f4695,f3260]) ).
fof(f3260,plain,
( ordered_pair(x,null_class) = ordered_pair(first(ordered_pair(x,null_class)),second(ordered_pair(x,null_class)))
| ~ spl0_290 ),
inference(avatar_component_clause,[],[f3258]) ).
fof(f4695,plain,
( ! [X10,X8,X9,X7] :
( ~ member(ordered_pair(X7,X8),compose(X9,X10))
| member(X8,universal_class) )
| ~ spl0_419 ),
inference(avatar_component_clause,[],[f4694]) ).
fof(f6814,plain,
( spl0_567
| ~ spl0_134
| ~ spl0_265 ),
inference(avatar_split_clause,[],[f2805,f2611,f901,f6812]) ).
fof(f6812,plain,
( spl0_567
<=> ! [X22,X20,X21] :
( ~ inductive(symmetric_difference(cross_product(X21,X22),X20))
| member(null_class,complement(restrict(X20,X21,X22))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_567])]) ).
fof(f901,plain,
( spl0_134
<=> ! [X4,X3] :
( member(null_class,X3)
| ~ inductive(intersection(X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f2611,plain,
( spl0_265
<=> ! [X6,X4,X5] : symmetric_difference(cross_product(X4,X5),X6) = intersection(complement(restrict(X6,X4,X5)),union(cross_product(X4,X5),X6)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).
fof(f2805,plain,
( ! [X21,X22,X20] :
( ~ inductive(symmetric_difference(cross_product(X21,X22),X20))
| member(null_class,complement(restrict(X20,X21,X22))) )
| ~ spl0_134
| ~ spl0_265 ),
inference(superposition,[],[f902,f2612]) ).
fof(f2612,plain,
( ! [X6,X4,X5] : symmetric_difference(cross_product(X4,X5),X6) = intersection(complement(restrict(X6,X4,X5)),union(cross_product(X4,X5),X6))
| ~ spl0_265 ),
inference(avatar_component_clause,[],[f2611]) ).
fof(f902,plain,
( ! [X3,X4] :
( ~ inductive(intersection(X3,X4))
| member(null_class,X3) )
| ~ spl0_134 ),
inference(avatar_component_clause,[],[f901]) ).
fof(f6810,plain,
( spl0_566
| ~ spl0_134
| ~ spl0_264 ),
inference(avatar_split_clause,[],[f2784,f2607,f901,f6808]) ).
fof(f6808,plain,
( spl0_566
<=> ! [X20,X18,X19] :
( ~ inductive(symmetric_difference(X18,cross_product(X19,X20)))
| member(null_class,complement(restrict(X18,X19,X20))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_566])]) ).
fof(f2607,plain,
( spl0_264
<=> ! [X2,X1,X3] : symmetric_difference(X1,cross_product(X2,X3)) = intersection(complement(restrict(X1,X2,X3)),union(X1,cross_product(X2,X3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).
fof(f2784,plain,
( ! [X18,X19,X20] :
( ~ inductive(symmetric_difference(X18,cross_product(X19,X20)))
| member(null_class,complement(restrict(X18,X19,X20))) )
| ~ spl0_134
| ~ spl0_264 ),
inference(superposition,[],[f902,f2608]) ).
fof(f2608,plain,
( ! [X2,X3,X1] : symmetric_difference(X1,cross_product(X2,X3)) = intersection(complement(restrict(X1,X2,X3)),union(X1,cross_product(X2,X3)))
| ~ spl0_264 ),
inference(avatar_component_clause,[],[f2607]) ).
fof(f6806,plain,
( spl0_565
| ~ spl0_177
| ~ spl0_255 ),
inference(avatar_split_clause,[],[f2538,f2508,f1304,f6804]) ).
fof(f6804,plain,
( spl0_565
<=> ! [X2,X1] :
( member(not_subclass_element(X1,complement(X2)),X2)
| subclass(X1,complement(X2))
| ~ subclass(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_565])]) ).
fof(f2538,plain,
( ! [X2,X1] :
( member(not_subclass_element(X1,complement(X2)),X2)
| subclass(X1,complement(X2))
| ~ subclass(X1,universal_class) )
| ~ spl0_177
| ~ spl0_255 ),
inference(duplicate_literal_removal,[],[f2520]) ).
fof(f2520,plain,
( ! [X2,X1] :
( member(not_subclass_element(X1,complement(X2)),X2)
| subclass(X1,complement(X2))
| ~ subclass(X1,universal_class)
| subclass(X1,complement(X2)) )
| ~ spl0_177
| ~ spl0_255 ),
inference(resolution,[],[f2509,f1305]) ).
fof(f6802,plain,
( spl0_564
| ~ spl0_100
| ~ spl0_234 ),
inference(avatar_split_clause,[],[f2195,f2071,f688,f6800]) ).
fof(f6800,plain,
( spl0_564
<=> ! [X0] :
( member(ordered_pair(X0,successor(X0)),successor_relation)
| ~ member(successor(X0),universal_class)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_564])]) ).
fof(f688,plain,
( spl0_100
<=> ! [X0,X3,X2,X1] :
( ~ member(X2,X0)
| ~ member(X3,X1)
| member(ordered_pair(X2,X3),cross_product(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f2071,plain,
( spl0_234
<=> ! [X0] :
( member(ordered_pair(X0,successor(X0)),successor_relation)
| ~ member(ordered_pair(X0,successor(X0)),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).
fof(f2195,plain,
( ! [X0] :
( member(ordered_pair(X0,successor(X0)),successor_relation)
| ~ member(successor(X0),universal_class)
| ~ member(X0,universal_class) )
| ~ spl0_100
| ~ spl0_234 ),
inference(resolution,[],[f2072,f689]) ).
fof(f689,plain,
( ! [X2,X3,X0,X1] :
( member(ordered_pair(X2,X3),cross_product(X0,X1))
| ~ member(X3,X1)
| ~ member(X2,X0) )
| ~ spl0_100 ),
inference(avatar_component_clause,[],[f688]) ).
fof(f2072,plain,
( ! [X0] :
( ~ member(ordered_pair(X0,successor(X0)),cross_product(universal_class,universal_class))
| member(ordered_pair(X0,successor(X0)),successor_relation) )
| ~ spl0_234 ),
inference(avatar_component_clause,[],[f2071]) ).
fof(f6798,plain,
( spl0_563
| ~ spl0_73
| ~ spl0_290 ),
inference(avatar_split_clause,[],[f5081,f3258,f489,f6796]) ).
fof(f6796,plain,
( spl0_563
<=> ! [X2,X3] :
( ~ member(ordered_pair(x,null_class),cross_product(X2,X3))
| member(second(ordered_pair(x,null_class)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_563])]) ).
fof(f489,plain,
( spl0_73
<=> ! [X2,X0,X1,X3] :
( member(X3,X1)
| ~ member(ordered_pair(X2,X3),cross_product(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f5081,plain,
( ! [X2,X3] :
( ~ member(ordered_pair(x,null_class),cross_product(X2,X3))
| member(second(ordered_pair(x,null_class)),X3) )
| ~ spl0_73
| ~ spl0_290 ),
inference(superposition,[],[f490,f3260]) ).
fof(f490,plain,
( ! [X2,X3,X0,X1] :
( ~ member(ordered_pair(X2,X3),cross_product(X0,X1))
| member(X3,X1) )
| ~ spl0_73 ),
inference(avatar_component_clause,[],[f489]) ).
fof(f6794,plain,
( spl0_562
| ~ spl0_20
| ~ spl0_226 ),
inference(avatar_split_clause,[],[f2113,f2037,f204,f6792]) ).
fof(f6792,plain,
( spl0_562
<=> ! [X29,X30] :
( ~ subclass(identity_relation,X29)
| ~ member(X30,inverse(subset_relation))
| ~ member(X30,subset_relation)
| member(X30,X29) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_562])]) ).
fof(f2037,plain,
( spl0_226
<=> ! [X9,X7,X6,X8] :
( ~ member(X6,X7)
| ~ member(X6,X8)
| ~ subclass(intersection(X8,X7),X9)
| member(X6,X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).
fof(f2113,plain,
( ! [X29,X30] :
( ~ subclass(identity_relation,X29)
| ~ member(X30,inverse(subset_relation))
| ~ member(X30,subset_relation)
| member(X30,X29) )
| ~ spl0_20
| ~ spl0_226 ),
inference(superposition,[],[f2038,f206]) ).
fof(f2038,plain,
( ! [X8,X6,X9,X7] :
( ~ subclass(intersection(X8,X7),X9)
| ~ member(X6,X8)
| ~ member(X6,X7)
| member(X6,X9) )
| ~ spl0_226 ),
inference(avatar_component_clause,[],[f2037]) ).
fof(f6790,plain,
( spl0_561
| ~ spl0_188
| ~ spl0_211 ),
inference(avatar_split_clause,[],[f1976,f1724,f1494,f6788]) ).
fof(f6788,plain,
( spl0_561
<=> ! [X13,X14] :
( member(not_subclass_element(cantor(inverse(X13)),X14),range_of(X13))
| subclass(cantor(inverse(X13)),X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_561])]) ).
fof(f1724,plain,
( spl0_211
<=> ! [X0] : cantor(inverse(X0)) = intersection(range_of(X0),diagonalise(compose(inverse(element_relation),inverse(X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).
fof(f1976,plain,
( ! [X14,X13] :
( member(not_subclass_element(cantor(inverse(X13)),X14),range_of(X13))
| subclass(cantor(inverse(X13)),X14) )
| ~ spl0_188
| ~ spl0_211 ),
inference(superposition,[],[f1495,f1725]) ).
fof(f1725,plain,
( ! [X0] : cantor(inverse(X0)) = intersection(range_of(X0),diagonalise(compose(inverse(element_relation),inverse(X0))))
| ~ spl0_211 ),
inference(avatar_component_clause,[],[f1724]) ).
fof(f6786,plain,
( spl0_560
| ~ spl0_63
| ~ spl0_207 ),
inference(avatar_split_clause,[],[f1900,f1708,f409,f6784]) ).
fof(f6784,plain,
( spl0_560
<=> ! [X2,X0,X1] : image(cross_product(X0,X1),X2) = range_of(restrict(cross_product(X2,universal_class),X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_560])]) ).
fof(f1708,plain,
( spl0_207
<=> ! [X5,X7,X6,X8] : restrict(cross_product(X5,X6),X7,X8) = restrict(cross_product(X7,X8),X5,X6) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).
fof(f1900,plain,
( ! [X2,X0,X1] : image(cross_product(X0,X1),X2) = range_of(restrict(cross_product(X2,universal_class),X0,X1))
| ~ spl0_63
| ~ spl0_207 ),
inference(superposition,[],[f410,f1709]) ).
fof(f1709,plain,
( ! [X8,X6,X7,X5] : restrict(cross_product(X5,X6),X7,X8) = restrict(cross_product(X7,X8),X5,X6)
| ~ spl0_207 ),
inference(avatar_component_clause,[],[f1708]) ).
fof(f6782,plain,
( spl0_559
| ~ spl0_28
| ~ spl0_206 ),
inference(avatar_split_clause,[],[f1873,f1704,f239,f6780]) ).
fof(f6780,plain,
( spl0_559
<=> ! [X0] : power_class(intersection(complement(X0),complement(singleton(X0)))) = complement(image(element_relation,successor(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_559])]) ).
fof(f239,plain,
( spl0_28
<=> ! [X0] : union(X0,singleton(X0)) = successor(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f1873,plain,
( ! [X0] : power_class(intersection(complement(X0),complement(singleton(X0)))) = complement(image(element_relation,successor(X0)))
| ~ spl0_28
| ~ spl0_206 ),
inference(superposition,[],[f1705,f240]) ).
fof(f240,plain,
( ! [X0] : union(X0,singleton(X0)) = successor(X0)
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f239]) ).
fof(f6778,plain,
( spl0_558
| ~ spl0_87
| ~ spl0_194 ),
inference(avatar_split_clause,[],[f1633,f1518,f578,f6776]) ).
fof(f578,plain,
( spl0_87
<=> ! [X4,X0,X1] :
( ~ member(X4,X0)
| ~ member(X4,X1)
| member(X4,intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f1633,plain,
( ! [X2,X0,X1] :
( ~ member(X0,union(X1,X2))
| ~ member(X0,complement(X2))
| ~ member(X0,complement(X1)) )
| ~ spl0_87
| ~ spl0_194 ),
inference(resolution,[],[f1519,f579]) ).
fof(f579,plain,
( ! [X0,X1,X4] :
( member(X4,intersection(X0,X1))
| ~ member(X4,X1)
| ~ member(X4,X0) )
| ~ spl0_87 ),
inference(avatar_component_clause,[],[f578]) ).
fof(f6774,plain,
( spl0_557
| ~ spl0_27
| ~ spl0_193 ),
inference(avatar_split_clause,[],[f1618,f1514,f235,f6772]) ).
fof(f6772,plain,
( spl0_557
<=> ! [X45,X46] :
( ~ subclass(domain_relation,complement(X45))
| ~ member(X46,universal_class)
| ~ member(ordered_pair(X46,domain_of(X46)),X45) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_557])]) ).
fof(f1618,plain,
( ! [X46,X45] :
( ~ subclass(domain_relation,complement(X45))
| ~ member(X46,universal_class)
| ~ member(ordered_pair(X46,domain_of(X46)),X45) )
| ~ spl0_27
| ~ spl0_193 ),
inference(resolution,[],[f1515,f236]) ).
fof(f6770,plain,
( spl0_556
| ~ spl0_137
| ~ spl0_193 ),
inference(avatar_split_clause,[],[f1614,f1514,f913,f6768]) ).
fof(f6768,plain,
( spl0_556
<=> ! [X34,X35] :
( ~ subclass(domain_relation,singleton(X34))
| ~ member(X35,universal_class)
| ordered_pair(X35,domain_of(X35)) = X34 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_556])]) ).
fof(f1614,plain,
( ! [X34,X35] :
( ~ subclass(domain_relation,singleton(X34))
| ~ member(X35,universal_class)
| ordered_pair(X35,domain_of(X35)) = X34 )
| ~ spl0_137
| ~ spl0_193 ),
inference(resolution,[],[f1515,f914]) ).
fof(f6766,plain,
( spl0_555
| ~ spl0_91
| ~ spl0_193 ),
inference(avatar_split_clause,[],[f1606,f1514,f594,f6764]) ).
fof(f6764,plain,
( spl0_555
<=> ! [X13,X14] :
( ~ subclass(domain_relation,compose_class(X13))
| ~ member(X14,universal_class)
| compose(X13,X14) = domain_of(X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_555])]) ).
fof(f594,plain,
( spl0_91
<=> ! [X4,X0,X1] :
( compose(X0,X1) = X4
| ~ member(ordered_pair(X1,X4),compose_class(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f1606,plain,
( ! [X14,X13] :
( ~ subclass(domain_relation,compose_class(X13))
| ~ member(X14,universal_class)
| compose(X13,X14) = domain_of(X14) )
| ~ spl0_91
| ~ spl0_193 ),
inference(resolution,[],[f1515,f595]) ).
fof(f595,plain,
( ! [X0,X1,X4] :
( ~ member(ordered_pair(X1,X4),compose_class(X0))
| compose(X0,X1) = X4 )
| ~ spl0_91 ),
inference(avatar_component_clause,[],[f594]) ).
fof(f6762,plain,
( spl0_554
| ~ spl0_70
| ~ spl0_187 ),
inference(avatar_split_clause,[],[f1488,f1345,f437,f6760]) ).
fof(f6760,plain,
( spl0_554
<=> ! [X11] :
( member(X11,complement(singleton_relation))
| ~ member(X11,symmetric_difference(complement(compose(element_relation,complement(identity_relation))),element_relation)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_554])]) ).
fof(f437,plain,
( spl0_70
<=> intersection(complement(compose(element_relation,complement(identity_relation))),element_relation) = singleton_relation ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f1488,plain,
( ! [X11] :
( member(X11,complement(singleton_relation))
| ~ member(X11,symmetric_difference(complement(compose(element_relation,complement(identity_relation))),element_relation)) )
| ~ spl0_70
| ~ spl0_187 ),
inference(superposition,[],[f1346,f439]) ).
fof(f439,plain,
( intersection(complement(compose(element_relation,complement(identity_relation))),element_relation) = singleton_relation
| ~ spl0_70 ),
inference(avatar_component_clause,[],[f437]) ).
fof(f6758,plain,
( spl0_553
| ~ spl0_66
| ~ spl0_187 ),
inference(avatar_split_clause,[],[f1484,f1345,f421,f6756]) ).
fof(f6756,plain,
( spl0_553
<=> ! [X0,X1] :
( member(X1,complement(null_class))
| ~ member(X1,symmetric_difference(X0,regular(X0)))
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_553])]) ).
fof(f421,plain,
( spl0_66
<=> ! [X0] :
( null_class = X0
| null_class = intersection(X0,regular(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f1484,plain,
( ! [X0,X1] :
( member(X1,complement(null_class))
| ~ member(X1,symmetric_difference(X0,regular(X0)))
| null_class = X0 )
| ~ spl0_66
| ~ spl0_187 ),
inference(superposition,[],[f1346,f422]) ).
fof(f422,plain,
( ! [X0] :
( null_class = intersection(X0,regular(X0))
| null_class = X0 )
| ~ spl0_66 ),
inference(avatar_component_clause,[],[f421]) ).
fof(f6754,plain,
( spl0_552
| ~ spl0_72
| ~ spl0_290 ),
inference(avatar_split_clause,[],[f5080,f3258,f485,f6752]) ).
fof(f6752,plain,
( spl0_552
<=> ! [X0,X1] :
( ~ member(ordered_pair(x,null_class),cross_product(X0,X1))
| member(first(ordered_pair(x,null_class)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_552])]) ).
fof(f485,plain,
( spl0_72
<=> ! [X0,X3,X2,X1] :
( member(X2,X0)
| ~ member(ordered_pair(X2,X3),cross_product(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f5080,plain,
( ! [X0,X1] :
( ~ member(ordered_pair(x,null_class),cross_product(X0,X1))
| member(first(ordered_pair(x,null_class)),X0) )
| ~ spl0_72
| ~ spl0_290 ),
inference(superposition,[],[f486,f3260]) ).
fof(f486,plain,
( ! [X2,X3,X0,X1] :
( ~ member(ordered_pair(X2,X3),cross_product(X0,X1))
| member(X2,X0) )
| ~ spl0_72 ),
inference(avatar_component_clause,[],[f485]) ).
fof(f6750,plain,
( spl0_551
| ~ spl0_138
| ~ spl0_182 ),
inference(avatar_split_clause,[],[f1457,f1325,f941,f6748]) ).
fof(f6748,plain,
( spl0_551
<=> ! [X10,X11,X13,X12,X9] :
( member(unordered_pair(X9,X10),cross_product(X11,X12))
| ~ subclass(universal_class,restrict(X13,X11,X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_551])]) ).
fof(f1325,plain,
( spl0_182
<=> ! [X0,X3,X2,X1] :
( ~ member(X3,restrict(X0,X1,X2))
| member(X3,cross_product(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).
fof(f1457,plain,
( ! [X10,X11,X9,X12,X13] :
( member(unordered_pair(X9,X10),cross_product(X11,X12))
| ~ subclass(universal_class,restrict(X13,X11,X12)) )
| ~ spl0_138
| ~ spl0_182 ),
inference(resolution,[],[f1326,f942]) ).
fof(f1326,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X3,restrict(X0,X1,X2))
| member(X3,cross_product(X1,X2)) )
| ~ spl0_182 ),
inference(avatar_component_clause,[],[f1325]) ).
fof(f6746,plain,
( spl0_550
| ~ spl0_141
| ~ spl0_177 ),
inference(avatar_split_clause,[],[f1447,f1304,f953,f6744]) ).
fof(f6744,plain,
( spl0_550
<=> ! [X57,X59,X58] :
( ~ subclass(X57,cantor(X58))
| subclass(X57,X59)
| member(not_subclass_element(X57,X59),domain_of(X58)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_550])]) ).
fof(f1447,plain,
( ! [X58,X59,X57] :
( ~ subclass(X57,cantor(X58))
| subclass(X57,X59)
| member(not_subclass_element(X57,X59),domain_of(X58)) )
| ~ spl0_141
| ~ spl0_177 ),
inference(resolution,[],[f1305,f954]) ).
fof(f6742,plain,
( spl0_549
| ~ spl0_44
| ~ spl0_177 ),
inference(avatar_split_clause,[],[f1437,f1304,f308,f6740]) ).
fof(f6740,plain,
( spl0_549
<=> ! [X24,X23,X25,X26] :
( ~ subclass(X23,intersection(X24,X25))
| subclass(X23,X26)
| member(not_subclass_element(X23,X26),X24) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_549])]) ).
fof(f1437,plain,
( ! [X26,X24,X25,X23] :
( ~ subclass(X23,intersection(X24,X25))
| subclass(X23,X26)
| member(not_subclass_element(X23,X26),X24) )
| ~ spl0_44
| ~ spl0_177 ),
inference(resolution,[],[f1305,f309]) ).
fof(f6738,plain,
( spl0_548
| ~ spl0_45
| ~ spl0_177 ),
inference(avatar_split_clause,[],[f1436,f1304,f312,f6736]) ).
fof(f6736,plain,
( spl0_548
<=> ! [X19,X20,X21,X22] :
( ~ subclass(X19,intersection(X20,X21))
| subclass(X19,X22)
| member(not_subclass_element(X19,X22),X21) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_548])]) ).
fof(f1436,plain,
( ! [X21,X19,X22,X20] :
( ~ subclass(X19,intersection(X20,X21))
| subclass(X19,X22)
| member(not_subclass_element(X19,X22),X21) )
| ~ spl0_45
| ~ spl0_177 ),
inference(resolution,[],[f1305,f313]) ).
fof(f6734,plain,
( spl0_547
| ~ spl0_90
| ~ spl0_172 ),
inference(avatar_split_clause,[],[f1398,f1284,f590,f6732]) ).
fof(f6732,plain,
( spl0_547
<=> ! [X9] :
( member(regular(cantor(X9)),diagonalise(compose(inverse(element_relation),X9)))
| null_class = cantor(X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_547])]) ).
fof(f1398,plain,
( ! [X9] :
( member(regular(cantor(X9)),diagonalise(compose(inverse(element_relation),X9)))
| null_class = cantor(X9) )
| ~ spl0_90
| ~ spl0_172 ),
inference(superposition,[],[f1285,f591]) ).
fof(f6730,plain,
( spl0_546
| ~ spl0_27
| ~ spl0_172 ),
inference(avatar_split_clause,[],[f1381,f1284,f235,f6728]) ).
fof(f6728,plain,
( spl0_546
<=> ! [X18,X17] :
( null_class = intersection(X17,complement(X18))
| ~ member(regular(intersection(X17,complement(X18))),X18) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_546])]) ).
fof(f1381,plain,
( ! [X18,X17] :
( null_class = intersection(X17,complement(X18))
| ~ member(regular(intersection(X17,complement(X18))),X18) )
| ~ spl0_27
| ~ spl0_172 ),
inference(resolution,[],[f1285,f236]) ).
fof(f6726,plain,
( spl0_545
| ~ spl0_137
| ~ spl0_172 ),
inference(avatar_split_clause,[],[f1377,f1284,f913,f6724]) ).
fof(f6724,plain,
( spl0_545
<=> ! [X6,X7] :
( null_class = intersection(X6,singleton(X7))
| regular(intersection(X6,singleton(X7))) = X7 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_545])]) ).
fof(f1377,plain,
( ! [X6,X7] :
( null_class = intersection(X6,singleton(X7))
| regular(intersection(X6,singleton(X7))) = X7 )
| ~ spl0_137
| ~ spl0_172 ),
inference(resolution,[],[f1285,f914]) ).
fof(f6722,plain,
( spl0_544
| ~ spl0_27
| ~ spl0_171 ),
inference(avatar_split_clause,[],[f1354,f1280,f235,f6720]) ).
fof(f6720,plain,
( spl0_544
<=> ! [X18,X17] :
( null_class = intersection(complement(X17),X18)
| ~ member(regular(intersection(complement(X17),X18)),X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_544])]) ).
fof(f1354,plain,
( ! [X18,X17] :
( null_class = intersection(complement(X17),X18)
| ~ member(regular(intersection(complement(X17),X18)),X17) )
| ~ spl0_27
| ~ spl0_171 ),
inference(resolution,[],[f1281,f236]) ).
fof(f6718,plain,
( spl0_543
| ~ spl0_137
| ~ spl0_171 ),
inference(avatar_split_clause,[],[f1350,f1280,f913,f6716]) ).
fof(f6716,plain,
( spl0_543
<=> ! [X6,X7] :
( null_class = intersection(singleton(X6),X7)
| regular(intersection(singleton(X6),X7)) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_543])]) ).
fof(f1350,plain,
( ! [X6,X7] :
( null_class = intersection(singleton(X6),X7)
| regular(intersection(singleton(X6),X7)) = X6 )
| ~ spl0_137
| ~ spl0_171 ),
inference(resolution,[],[f1281,f914]) ).
fof(f6714,plain,
( spl0_542
| ~ spl0_34
| ~ spl0_170 ),
inference(avatar_split_clause,[],[f1276,f1169,f263,f6712]) ).
fof(f6712,plain,
( spl0_542
<=> ! [X16,X15] :
( member(regular(symmetric_difference(X15,X16)),union(X15,X16))
| null_class = symmetric_difference(X15,X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_542])]) ).
fof(f1276,plain,
( ! [X16,X15] :
( member(regular(symmetric_difference(X15,X16)),union(X15,X16))
| null_class = symmetric_difference(X15,X16) )
| ~ spl0_34
| ~ spl0_170 ),
inference(resolution,[],[f1170,f264]) ).
fof(f6710,plain,
( spl0_541
| ~ spl0_61
| ~ spl0_168 ),
inference(avatar_split_clause,[],[f1260,f1161,f401,f6708]) ).
fof(f6708,plain,
( spl0_541
<=> ! [X2,X0,X1] :
( ~ member(singleton(X0),universal_class)
| ~ subclass(ordered_pair(X0,X1),X2)
| member(singleton(X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_541])]) ).
fof(f1161,plain,
( spl0_168
<=> ! [X6,X5] :
( member(singleton(X5),ordered_pair(X5,X6))
| ~ member(singleton(X5),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
fof(f1260,plain,
( ! [X2,X0,X1] :
( ~ member(singleton(X0),universal_class)
| ~ subclass(ordered_pair(X0,X1),X2)
| member(singleton(X0),X2) )
| ~ spl0_61
| ~ spl0_168 ),
inference(resolution,[],[f1162,f402]) ).
fof(f1162,plain,
( ! [X6,X5] :
( member(singleton(X5),ordered_pair(X5,X6))
| ~ member(singleton(X5),universal_class) )
| ~ spl0_168 ),
inference(avatar_component_clause,[],[f1161]) ).
fof(f6706,plain,
( spl0_540
| ~ spl0_61
| ~ spl0_166 ),
inference(avatar_split_clause,[],[f1253,f1153,f401,f6704]) ).
fof(f6704,plain,
( spl0_540
<=> ! [X2,X1] :
( ~ member(X1,singleton_relation)
| ~ subclass(complement(compose(element_relation,complement(identity_relation))),X2)
| member(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_540])]) ).
fof(f1153,plain,
( spl0_166
<=> ! [X1] :
( ~ member(X1,singleton_relation)
| member(X1,complement(compose(element_relation,complement(identity_relation)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
fof(f1253,plain,
( ! [X2,X1] :
( ~ member(X1,singleton_relation)
| ~ subclass(complement(compose(element_relation,complement(identity_relation))),X2)
| member(X1,X2) )
| ~ spl0_61
| ~ spl0_166 ),
inference(resolution,[],[f1154,f402]) ).
fof(f1154,plain,
( ! [X1] :
( member(X1,complement(compose(element_relation,complement(identity_relation))))
| ~ member(X1,singleton_relation) )
| ~ spl0_166 ),
inference(avatar_component_clause,[],[f1153]) ).
fof(f6702,plain,
( spl0_539
| ~ spl0_40
| ~ spl0_165 ),
inference(avatar_split_clause,[],[f1249,f1149,f292,f6700]) ).
fof(f6700,plain,
( spl0_539
<=> ! [X4,X3] :
( ~ member(not_subclass_element(X3,regular(X4)),null_class)
| null_class = X4
| subclass(X3,regular(X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_539])]) ).
fof(f292,plain,
( spl0_40
<=> ! [X0,X1] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f1249,plain,
( ! [X3,X4] :
( ~ member(not_subclass_element(X3,regular(X4)),null_class)
| null_class = X4
| subclass(X3,regular(X4)) )
| ~ spl0_40
| ~ spl0_165 ),
inference(resolution,[],[f1150,f293]) ).
fof(f293,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(X0,X1),X1)
| subclass(X0,X1) )
| ~ spl0_40 ),
inference(avatar_component_clause,[],[f292]) ).
fof(f6698,plain,
( spl0_538
| ~ spl0_61
| ~ spl0_165 ),
inference(avatar_split_clause,[],[f1248,f1149,f401,f6696]) ).
fof(f6696,plain,
( spl0_538
<=> ! [X2,X0,X1] :
( ~ member(X0,null_class)
| null_class = X1
| ~ subclass(regular(X1),X2)
| member(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_538])]) ).
fof(f1248,plain,
( ! [X2,X0,X1] :
( ~ member(X0,null_class)
| null_class = X1
| ~ subclass(regular(X1),X2)
| member(X0,X2) )
| ~ spl0_61
| ~ spl0_165 ),
inference(resolution,[],[f1150,f402]) ).
fof(f6694,plain,
( spl0_537
| ~ spl0_146
| ~ spl0_156 ),
inference(avatar_split_clause,[],[f1239,f1109,f1018,f6692]) ).
fof(f6692,plain,
( spl0_537
<=> ! [X20,X21,X23,X22] :
( ~ subclass(X20,restrict(X21,X22,X23))
| null_class = X20
| member(regular(X20),X21) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_537])]) ).
fof(f1239,plain,
( ! [X21,X22,X23,X20] :
( ~ subclass(X20,restrict(X21,X22,X23))
| null_class = X20
| member(regular(X20),X21) )
| ~ spl0_146
| ~ spl0_156 ),
inference(resolution,[],[f1110,f1019]) ).
fof(f6690,plain,
( spl0_536
| ~ spl0_61
| ~ spl0_156 ),
inference(avatar_split_clause,[],[f1232,f1109,f401,f6688]) ).
fof(f6688,plain,
( spl0_536
<=> ! [X2,X1,X3] :
( ~ subclass(X1,X2)
| null_class = X1
| ~ subclass(X2,X3)
| member(regular(X1),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_536])]) ).
fof(f1232,plain,
( ! [X2,X3,X1] :
( ~ subclass(X1,X2)
| null_class = X1
| ~ subclass(X2,X3)
| member(regular(X1),X3) )
| ~ spl0_61
| ~ spl0_156 ),
inference(resolution,[],[f1110,f402]) ).
fof(f6686,plain,
( spl0_535
| ~ spl0_146
| ~ spl0_155 ),
inference(avatar_split_clause,[],[f1223,f1105,f1018,f6684]) ).
fof(f6684,plain,
( spl0_535
<=> ! [X19,X20,X21,X22] :
( ~ subclass(universal_class,restrict(X19,X20,X21))
| ~ member(X22,universal_class)
| member(power_class(X22),X19) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_535])]) ).
fof(f1223,plain,
( ! [X21,X19,X22,X20] :
( ~ subclass(universal_class,restrict(X19,X20,X21))
| ~ member(X22,universal_class)
| member(power_class(X22),X19) )
| ~ spl0_146
| ~ spl0_155 ),
inference(resolution,[],[f1106,f1019]) ).
fof(f6682,plain,
( spl0_534
| ~ spl0_61
| ~ spl0_155 ),
inference(avatar_split_clause,[],[f1216,f1105,f401,f6680]) ).
fof(f6680,plain,
( spl0_534
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,X0)
| ~ member(X1,universal_class)
| ~ subclass(X0,X2)
| member(power_class(X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_534])]) ).
fof(f1216,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,X0)
| ~ member(X1,universal_class)
| ~ subclass(X0,X2)
| member(power_class(X1),X2) )
| ~ spl0_61
| ~ spl0_155 ),
inference(resolution,[],[f1106,f402]) ).
fof(f6678,plain,
( spl0_533
| ~ spl0_146
| ~ spl0_154 ),
inference(avatar_split_clause,[],[f1207,f1101,f1018,f6676]) ).
fof(f6676,plain,
( spl0_533
<=> ! [X19,X20,X21,X22] :
( ~ subclass(universal_class,restrict(X19,X20,X21))
| ~ member(X22,universal_class)
| member(sum_class(X22),X19) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_533])]) ).
fof(f1207,plain,
( ! [X21,X19,X22,X20] :
( ~ subclass(universal_class,restrict(X19,X20,X21))
| ~ member(X22,universal_class)
| member(sum_class(X22),X19) )
| ~ spl0_146
| ~ spl0_154 ),
inference(resolution,[],[f1102,f1019]) ).
fof(f6674,plain,
( spl0_532
| ~ spl0_61
| ~ spl0_154 ),
inference(avatar_split_clause,[],[f1200,f1101,f401,f6672]) ).
fof(f6672,plain,
( spl0_532
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,X0)
| ~ member(X1,universal_class)
| ~ subclass(X0,X2)
| member(sum_class(X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_532])]) ).
fof(f1200,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,X0)
| ~ member(X1,universal_class)
| ~ subclass(X0,X2)
| member(sum_class(X1),X2) )
| ~ spl0_61
| ~ spl0_154 ),
inference(resolution,[],[f1102,f402]) ).
fof(f6669,plain,
( spl0_531
| ~ spl0_77
| ~ spl0_152 ),
inference(avatar_split_clause,[],[f1196,f1093,f508,f6667]) ).
fof(f6667,plain,
( spl0_531
<=> ! [X2,X0,X1] :
( ~ member(X2,domain_of(restrict(identity_relation,X0,X1)))
| ~ member(X2,diagonalise(cross_product(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_531])]) ).
fof(f1196,plain,
( ! [X2,X0,X1] :
( ~ member(X2,domain_of(restrict(identity_relation,X0,X1)))
| ~ member(X2,diagonalise(cross_product(X0,X1))) )
| ~ spl0_77
| ~ spl0_152 ),
inference(superposition,[],[f1094,f509]) ).
fof(f6665,plain,
( spl0_530
| ~ spl0_55
| ~ spl0_151 ),
inference(avatar_split_clause,[],[f1187,f1089,f352,f6663]) ).
fof(f6663,plain,
( spl0_530
<=> ! [X2,X3] :
( ~ member(X3,image(element_relation,diagonalise(X2)))
| ~ member(X3,power_class(domain_of(intersection(X2,identity_relation)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_530])]) ).
fof(f352,plain,
( spl0_55
<=> ! [X5] : complement(domain_of(intersection(X5,identity_relation))) = diagonalise(X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f1187,plain,
( ! [X2,X3] :
( ~ member(X3,image(element_relation,diagonalise(X2)))
| ~ member(X3,power_class(domain_of(intersection(X2,identity_relation)))) )
| ~ spl0_55
| ~ spl0_151 ),
inference(superposition,[],[f1090,f353]) ).
fof(f353,plain,
( ! [X5] : complement(domain_of(intersection(X5,identity_relation))) = diagonalise(X5)
| ~ spl0_55 ),
inference(avatar_component_clause,[],[f352]) ).
fof(f6661,plain,
( spl0_529
| ~ spl0_50
| ~ spl0_151 ),
inference(avatar_split_clause,[],[f1186,f1089,f332,f6659]) ).
fof(f6659,plain,
( spl0_529
<=> ! [X0,X1] :
( ~ member(X1,image(element_relation,power_class(X0)))
| ~ member(X1,power_class(image(element_relation,complement(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_529])]) ).
fof(f1186,plain,
( ! [X0,X1] :
( ~ member(X1,image(element_relation,power_class(X0)))
| ~ member(X1,power_class(image(element_relation,complement(X0)))) )
| ~ spl0_50
| ~ spl0_151 ),
inference(superposition,[],[f1090,f333]) ).
fof(f6657,plain,
( spl0_528
| ~ spl0_55
| ~ spl0_150 ),
inference(avatar_split_clause,[],[f1179,f1085,f352,f6655]) ).
fof(f6655,plain,
( spl0_528
<=> ! [X2,X3] :
( ~ member(not_subclass_element(diagonalise(X2),X3),domain_of(intersection(X2,identity_relation)))
| subclass(diagonalise(X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_528])]) ).
fof(f1179,plain,
( ! [X2,X3] :
( ~ member(not_subclass_element(diagonalise(X2),X3),domain_of(intersection(X2,identity_relation)))
| subclass(diagonalise(X2),X3) )
| ~ spl0_55
| ~ spl0_150 ),
inference(superposition,[],[f1086,f353]) ).
fof(f6653,plain,
( spl0_527
| ~ spl0_50
| ~ spl0_150 ),
inference(avatar_split_clause,[],[f1178,f1085,f332,f6651]) ).
fof(f6651,plain,
( spl0_527
<=> ! [X0,X1] :
( ~ member(not_subclass_element(power_class(X0),X1),image(element_relation,complement(X0)))
| subclass(power_class(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_527])]) ).
fof(f1178,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(power_class(X0),X1),image(element_relation,complement(X0)))
| subclass(power_class(X0),X1) )
| ~ spl0_50
| ~ spl0_150 ),
inference(superposition,[],[f1086,f333]) ).
fof(f6649,plain,
( spl0_526
| ~ spl0_92
| ~ spl0_147 ),
inference(avatar_split_clause,[],[f1059,f1022,f598,f6647]) ).
fof(f6647,plain,
( spl0_526
<=> ! [X12,X11] :
( ~ member(ordered_pair(X12,singleton(singleton(singleton(X11)))),application_function)
| member(singleton(X11),domain_of(X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_526])]) ).
fof(f1059,plain,
( ! [X11,X12] :
( ~ member(ordered_pair(X12,singleton(singleton(singleton(X11)))),application_function)
| member(singleton(X11),domain_of(X12)) )
| ~ spl0_92
| ~ spl0_147 ),
inference(superposition,[],[f599,f1023]) ).
fof(f6645,plain,
( spl0_525
| ~ spl0_91
| ~ spl0_147 ),
inference(avatar_split_clause,[],[f1058,f1022,f594,f6643]) ).
fof(f6643,plain,
( spl0_525
<=> ! [X9,X10] :
( ~ member(singleton(singleton(singleton(X9))),compose_class(X10))
| compose(X10,singleton(X9)) = X9 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_525])]) ).
fof(f1058,plain,
( ! [X10,X9] :
( ~ member(singleton(singleton(singleton(X9))),compose_class(X10))
| compose(X10,singleton(X9)) = X9 )
| ~ spl0_91
| ~ spl0_147 ),
inference(superposition,[],[f595,f1023]) ).
fof(f6641,plain,
( spl0_524
| ~ spl0_34
| ~ spl0_146 ),
inference(avatar_split_clause,[],[f1051,f1018,f263,f6639]) ).
fof(f6639,plain,
( spl0_524
<=> ! [X13,X12,X14] :
( member(regular(restrict(X12,X13,X14)),X12)
| null_class = restrict(X12,X13,X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_524])]) ).
fof(f1051,plain,
( ! [X14,X12,X13] :
( member(regular(restrict(X12,X13,X14)),X12)
| null_class = restrict(X12,X13,X14) )
| ~ spl0_34
| ~ spl0_146 ),
inference(resolution,[],[f1019,f264]) ).
fof(f6635,plain,
( spl0_522
| ~ spl0_523
| ~ spl0_345
| ~ spl0_422 ),
inference(avatar_split_clause,[],[f6477,f5040,f3974,f6632,f6628]) ).
fof(f6628,plain,
( spl0_522
<=> member(second(ordered_pair(x,x)),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_522])]) ).
fof(f6632,plain,
( spl0_523
<=> member(ordered_pair(x,x),subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_523])]) ).
fof(f3974,plain,
( spl0_345
<=> ! [X6,X7] :
( ~ member(ordered_pair(X6,X7),subset_relation)
| member(X7,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_345])]) ).
fof(f5040,plain,
( spl0_422
<=> ordered_pair(x,x) = ordered_pair(first(ordered_pair(x,x)),second(ordered_pair(x,x))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_422])]) ).
fof(f6477,plain,
( ~ member(ordered_pair(x,x),subset_relation)
| member(second(ordered_pair(x,x)),universal_class)
| ~ spl0_345
| ~ spl0_422 ),
inference(superposition,[],[f3975,f5042]) ).
fof(f5042,plain,
( ordered_pair(x,x) = ordered_pair(first(ordered_pair(x,x)),second(ordered_pair(x,x)))
| ~ spl0_422 ),
inference(avatar_component_clause,[],[f5040]) ).
fof(f3975,plain,
( ! [X6,X7] :
( ~ member(ordered_pair(X6,X7),subset_relation)
| member(X7,universal_class) )
| ~ spl0_345 ),
inference(avatar_component_clause,[],[f3974]) ).
fof(f6626,plain,
( ~ spl0_520
| spl0_521
| ~ spl0_143
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1034,f1010,f961,f6623,f6619]) ).
fof(f6619,plain,
( spl0_520
<=> member(regular(complement(cross_product(universal_class,universal_class))),subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_520])]) ).
fof(f6623,plain,
( spl0_521
<=> null_class = complement(cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_521])]) ).
fof(f1034,plain,
( null_class = complement(cross_product(universal_class,universal_class))
| ~ member(regular(complement(cross_product(universal_class,universal_class))),subset_relation)
| ~ spl0_143
| ~ spl0_144 ),
inference(resolution,[],[f1011,f962]) ).
fof(f6617,plain,
( spl0_519
| ~ spl0_108
| ~ spl0_143 ),
inference(avatar_split_clause,[],[f1005,f961,f732,f6615]) ).
fof(f6615,plain,
( spl0_519
<=> ! [X4,X5] :
( ~ member(ordered_pair(X4,X5),subset_relation)
| member(ordered_pair(X4,X5),element_relation)
| ~ member(X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_519])]) ).
fof(f732,plain,
( spl0_108
<=> ! [X0,X1] :
( ~ member(X0,X1)
| member(ordered_pair(X0,X1),element_relation)
| ~ member(ordered_pair(X0,X1),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f1005,plain,
( ! [X4,X5] :
( ~ member(ordered_pair(X4,X5),subset_relation)
| member(ordered_pair(X4,X5),element_relation)
| ~ member(X4,X5) )
| ~ spl0_108
| ~ spl0_143 ),
inference(resolution,[],[f962,f733]) ).
fof(f733,plain,
( ! [X0,X1] :
( ~ member(ordered_pair(X0,X1),cross_product(universal_class,universal_class))
| member(ordered_pair(X0,X1),element_relation)
| ~ member(X0,X1) )
| ~ spl0_108 ),
inference(avatar_component_clause,[],[f732]) ).
fof(f6117,plain,
( ~ spl0_518
| ~ spl0_13
| spl0_515 ),
inference(avatar_split_clause,[],[f6016,f6008,f175,f6114]) ).
fof(f6114,plain,
( spl0_518
<=> inductive(complement(singleton_relation)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_518])]) ).
fof(f6008,plain,
( spl0_515
<=> member(null_class,complement(singleton_relation)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_515])]) ).
fof(f6016,plain,
( ~ inductive(complement(singleton_relation))
| ~ spl0_13
| spl0_515 ),
inference(resolution,[],[f6009,f176]) ).
fof(f6009,plain,
( ~ member(null_class,complement(singleton_relation))
| spl0_515 ),
inference(avatar_component_clause,[],[f6008]) ).
fof(f6021,plain,
( spl0_517
| ~ spl0_39
| ~ spl0_273 ),
inference(avatar_split_clause,[],[f2948,f2871,f288,f6019]) ).
fof(f6019,plain,
( spl0_517
<=> ! [X0,X1] :
( ~ member(not_subclass_element(X0,intersection(X1,X0)),X1)
| subclass(X0,intersection(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_517])]) ).
fof(f2948,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(X0,intersection(X1,X0)),X1)
| subclass(X0,intersection(X1,X0)) )
| ~ spl0_39
| ~ spl0_273 ),
inference(duplicate_literal_removal,[],[f2905]) ).
fof(f2905,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(X0,intersection(X1,X0)),X1)
| subclass(X0,intersection(X1,X0))
| subclass(X0,intersection(X1,X0)) )
| ~ spl0_39
| ~ spl0_273 ),
inference(resolution,[],[f2872,f289]) ).
fof(f6015,plain,
( spl0_515
| ~ spl0_516
| ~ spl0_134
| ~ spl0_270 ),
inference(avatar_split_clause,[],[f2850,f2837,f901,f6012,f6008]) ).
fof(f6012,plain,
( spl0_516
<=> inductive(symmetric_difference(complement(compose(element_relation,complement(identity_relation))),element_relation)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_516])]) ).
fof(f2837,plain,
( spl0_270
<=> symmetric_difference(complement(compose(element_relation,complement(identity_relation))),element_relation) = intersection(complement(singleton_relation),union(complement(compose(element_relation,complement(identity_relation))),element_relation)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).
fof(f2850,plain,
( ~ inductive(symmetric_difference(complement(compose(element_relation,complement(identity_relation))),element_relation))
| member(null_class,complement(singleton_relation))
| ~ spl0_134
| ~ spl0_270 ),
inference(superposition,[],[f902,f2839]) ).
fof(f2839,plain,
( symmetric_difference(complement(compose(element_relation,complement(identity_relation))),element_relation) = intersection(complement(singleton_relation),union(complement(compose(element_relation,complement(identity_relation))),element_relation))
| ~ spl0_270 ),
inference(avatar_component_clause,[],[f2837]) ).
fof(f6006,plain,
( spl0_514
| ~ spl0_56
| ~ spl0_252 ),
inference(avatar_split_clause,[],[f2491,f2266,f356,f6004]) ).
fof(f6004,plain,
( spl0_514
<=> ! [X0] :
( ~ function(domain_of(X0))
| compatible(domain_of(X0),X0,domain_of(X0))
| ~ operation(domain_of(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_514])]) ).
fof(f356,plain,
( spl0_56
<=> ! [X8] :
( ~ operation(X8)
| subclass(range_of(X8),domain_of(domain_of(X8))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f2266,plain,
( spl0_252
<=> ! [X0,X1] :
( compatible(domain_of(X0),X0,X1)
| ~ function(domain_of(X0))
| ~ subclass(range_of(domain_of(X0)),domain_of(domain_of(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).
fof(f2491,plain,
( ! [X0] :
( ~ function(domain_of(X0))
| compatible(domain_of(X0),X0,domain_of(X0))
| ~ operation(domain_of(X0)) )
| ~ spl0_56
| ~ spl0_252 ),
inference(resolution,[],[f2267,f357]) ).
fof(f357,plain,
( ! [X8] :
( subclass(range_of(X8),domain_of(domain_of(X8)))
| ~ operation(X8) )
| ~ spl0_56 ),
inference(avatar_component_clause,[],[f356]) ).
fof(f2267,plain,
( ! [X0,X1] :
( ~ subclass(range_of(domain_of(X0)),domain_of(domain_of(X1)))
| ~ function(domain_of(X0))
| compatible(domain_of(X0),X0,X1) )
| ~ spl0_252 ),
inference(avatar_component_clause,[],[f2266]) ).
fof(f5997,plain,
( spl0_512
| spl0_513
| ~ spl0_134
| ~ spl0_249 ),
inference(avatar_split_clause,[],[f2437,f2254,f901,f5995,f5991]) ).
fof(f5991,plain,
( spl0_512
<=> member(null_class,complement(null_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_512])]) ).
fof(f5995,plain,
( spl0_513
<=> ! [X8] :
( ~ inductive(symmetric_difference(X8,regular(X8)))
| null_class = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_513])]) ).
fof(f2254,plain,
( spl0_249
<=> ! [X0] :
( symmetric_difference(X0,regular(X0)) = intersection(complement(null_class),union(X0,regular(X0)))
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).
fof(f2437,plain,
( ! [X8] :
( ~ inductive(symmetric_difference(X8,regular(X8)))
| member(null_class,complement(null_class))
| null_class = X8 )
| ~ spl0_134
| ~ spl0_249 ),
inference(superposition,[],[f902,f2255]) ).
fof(f2255,plain,
( ! [X0] :
( symmetric_difference(X0,regular(X0)) = intersection(complement(null_class),union(X0,regular(X0)))
| null_class = X0 )
| ~ spl0_249 ),
inference(avatar_component_clause,[],[f2254]) ).
fof(f5989,plain,
( spl0_511
| ~ spl0_44
| ~ spl0_241 ),
inference(avatar_split_clause,[],[f2354,f2218,f308,f5987]) ).
fof(f5987,plain,
( spl0_511
<=> ! [X6,X8,X7] :
( member(X6,union(X7,X8))
| ~ member(X6,universal_class)
| member(X6,complement(X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_511])]) ).
fof(f2218,plain,
( spl0_241
<=> ! [X2,X0,X1] :
( member(X2,union(X0,X1))
| member(X2,intersection(complement(X0),complement(X1)))
| ~ member(X2,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).
fof(f2354,plain,
( ! [X8,X6,X7] :
( member(X6,union(X7,X8))
| ~ member(X6,universal_class)
| member(X6,complement(X7)) )
| ~ spl0_44
| ~ spl0_241 ),
inference(resolution,[],[f2219,f309]) ).
fof(f2219,plain,
( ! [X2,X0,X1] :
( member(X2,intersection(complement(X0),complement(X1)))
| member(X2,union(X0,X1))
| ~ member(X2,universal_class) )
| ~ spl0_241 ),
inference(avatar_component_clause,[],[f2218]) ).
fof(f5985,plain,
( spl0_510
| ~ spl0_45
| ~ spl0_241 ),
inference(avatar_split_clause,[],[f2353,f2218,f312,f5983]) ).
fof(f5983,plain,
( spl0_510
<=> ! [X4,X5,X3] :
( member(X3,union(X4,X5))
| ~ member(X3,universal_class)
| member(X3,complement(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_510])]) ).
fof(f2353,plain,
( ! [X3,X4,X5] :
( member(X3,union(X4,X5))
| ~ member(X3,universal_class)
| member(X3,complement(X5)) )
| ~ spl0_45
| ~ spl0_241 ),
inference(resolution,[],[f2219,f313]) ).
fof(f5981,plain,
( spl0_509
| ~ spl0_143
| ~ spl0_234 ),
inference(avatar_split_clause,[],[f2196,f2071,f961,f5979]) ).
fof(f5979,plain,
( spl0_509
<=> ! [X1] :
( member(ordered_pair(X1,successor(X1)),successor_relation)
| ~ member(ordered_pair(X1,successor(X1)),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_509])]) ).
fof(f2196,plain,
( ! [X1] :
( member(ordered_pair(X1,successor(X1)),successor_relation)
| ~ member(ordered_pair(X1,successor(X1)),subset_relation) )
| ~ spl0_143
| ~ spl0_234 ),
inference(resolution,[],[f2072,f962]) ).
fof(f5976,plain,
( ~ spl0_507
| spl0_508
| ~ spl0_63
| ~ spl0_215 ),
inference(avatar_split_clause,[],[f2076,f1991,f409,f5973,f5969]) ).
fof(f5969,plain,
( spl0_507
<=> operation(restrict(element_relation,universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_507])]) ).
fof(f5973,plain,
( spl0_508
<=> subclass(image(element_relation,universal_class),domain_of(sum_class(universal_class))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_508])]) ).
fof(f1991,plain,
( spl0_215
<=> ! [X2] :
( subclass(range_of(restrict(element_relation,universal_class,X2)),domain_of(sum_class(X2)))
| ~ operation(restrict(element_relation,universal_class,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).
fof(f2076,plain,
( subclass(image(element_relation,universal_class),domain_of(sum_class(universal_class)))
| ~ operation(restrict(element_relation,universal_class,universal_class))
| ~ spl0_63
| ~ spl0_215 ),
inference(superposition,[],[f1992,f410]) ).
fof(f1992,plain,
( ! [X2] :
( subclass(range_of(restrict(element_relation,universal_class,X2)),domain_of(sum_class(X2)))
| ~ operation(restrict(element_relation,universal_class,X2)) )
| ~ spl0_215 ),
inference(avatar_component_clause,[],[f1991]) ).
fof(f5967,plain,
( spl0_506
| ~ spl0_171
| ~ spl0_211 ),
inference(avatar_split_clause,[],[f1973,f1724,f1280,f5965]) ).
fof(f5965,plain,
( spl0_506
<=> ! [X9] :
( member(regular(cantor(inverse(X9))),range_of(X9))
| null_class = cantor(inverse(X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_506])]) ).
fof(f1973,plain,
( ! [X9] :
( member(regular(cantor(inverse(X9))),range_of(X9))
| null_class = cantor(inverse(X9)) )
| ~ spl0_171
| ~ spl0_211 ),
inference(superposition,[],[f1281,f1725]) ).
fof(f5956,plain,
( spl0_504
| spl0_505
| ~ spl0_13
| ~ spl0_209 ),
inference(avatar_split_clause,[],[f1939,f1716,f175,f5953,f5950]) ).
fof(f5950,plain,
( spl0_504
<=> ! [X18] :
( ~ member(null_class,X18)
| ~ inductive(regular(X18))
| null_class = X18 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_504])]) ).
fof(f5953,plain,
( spl0_505
<=> member(null_class,null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_505])]) ).
fof(f1716,plain,
( spl0_209
<=> ! [X0,X1] :
( member(X1,null_class)
| ~ member(X1,regular(X0))
| ~ member(X1,X0)
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).
fof(f1939,plain,
( ! [X18] :
( member(null_class,null_class)
| ~ member(null_class,X18)
| null_class = X18
| ~ inductive(regular(X18)) )
| ~ spl0_13
| ~ spl0_209 ),
inference(resolution,[],[f1717,f176]) ).
fof(f1717,plain,
( ! [X0,X1] :
( ~ member(X1,regular(X0))
| member(X1,null_class)
| ~ member(X1,X0)
| null_class = X0 )
| ~ spl0_209 ),
inference(avatar_component_clause,[],[f1716]) ).
fof(f5948,plain,
( spl0_502
| ~ spl0_503
| ~ spl0_132
| ~ spl0_193 ),
inference(avatar_split_clause,[],[f1629,f1514,f883,f5945,f5942]) ).
fof(f5942,plain,
( spl0_502
<=> ! [X72] :
( ~ member(X72,universal_class)
| member(ordered_pair(X72,domain_of(X72)),element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_502])]) ).
fof(f5945,plain,
( spl0_503
<=> subclass(domain_relation,singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_503])]) ).
fof(f1629,plain,
( ! [X72] :
( ~ subclass(domain_relation,singleton_relation)
| ~ member(X72,universal_class)
| member(ordered_pair(X72,domain_of(X72)),element_relation) )
| ~ spl0_132
| ~ spl0_193 ),
inference(resolution,[],[f1515,f884]) ).
fof(f5940,plain,
( spl0_500
| ~ spl0_501
| ~ spl0_314
| ~ spl0_345 ),
inference(avatar_split_clause,[],[f5885,f3974,f3658,f5937,f5933]) ).
fof(f5933,plain,
( spl0_500
<=> member(second(ordered_pair(x,omega)),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_500])]) ).
fof(f5937,plain,
( spl0_501
<=> member(ordered_pair(x,omega),subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_501])]) ).
fof(f3658,plain,
( spl0_314
<=> ordered_pair(x,omega) = ordered_pair(first(ordered_pair(x,omega)),second(ordered_pair(x,omega))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_314])]) ).
fof(f5885,plain,
( ~ member(ordered_pair(x,omega),subset_relation)
| member(second(ordered_pair(x,omega)),universal_class)
| ~ spl0_314
| ~ spl0_345 ),
inference(superposition,[],[f3975,f3660]) ).
fof(f3660,plain,
( ordered_pair(x,omega) = ordered_pair(first(ordered_pair(x,omega)),second(ordered_pair(x,omega)))
| ~ spl0_314 ),
inference(avatar_component_clause,[],[f3658]) ).
fof(f5931,plain,
( spl0_498
| ~ spl0_499
| ~ spl0_60
| ~ spl0_193 ),
inference(avatar_split_clause,[],[f1627,f1514,f388,f5928,f5925]) ).
fof(f5925,plain,
( spl0_498
<=> ! [X69] :
( ~ member(X69,universal_class)
| member(ordered_pair(X69,domain_of(X69)),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_498])]) ).
fof(f5928,plain,
( spl0_499
<=> subclass(domain_relation,identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_499])]) ).
fof(f1627,plain,
( ! [X69] :
( ~ subclass(domain_relation,identity_relation)
| ~ member(X69,universal_class)
| member(ordered_pair(X69,domain_of(X69)),subset_relation) )
| ~ spl0_60
| ~ spl0_193 ),
inference(resolution,[],[f1515,f389]) ).
fof(f5923,plain,
( spl0_497
| ~ spl0_73
| ~ spl0_193 ),
inference(avatar_split_clause,[],[f1600,f1514,f489,f5921]) ).
fof(f5921,plain,
( spl0_497
<=> ! [X2,X0,X1] :
( ~ subclass(domain_relation,cross_product(X0,X1))
| ~ member(X2,universal_class)
| member(domain_of(X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_497])]) ).
fof(f1600,plain,
( ! [X2,X0,X1] :
( ~ subclass(domain_relation,cross_product(X0,X1))
| ~ member(X2,universal_class)
| member(domain_of(X2),X1) )
| ~ spl0_73
| ~ spl0_193 ),
inference(resolution,[],[f1515,f490]) ).
fof(f5919,plain,
( spl0_496
| ~ spl0_132
| ~ spl0_189 ),
inference(avatar_split_clause,[],[f1574,f1498,f883,f5917]) ).
fof(f5917,plain,
( spl0_496
<=> ! [X64,X63] :
( subclass(intersection(X63,singleton_relation),X64)
| member(not_subclass_element(intersection(X63,singleton_relation),X64),element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_496])]) ).
fof(f1574,plain,
( ! [X63,X64] :
( subclass(intersection(X63,singleton_relation),X64)
| member(not_subclass_element(intersection(X63,singleton_relation),X64),element_relation) )
| ~ spl0_132
| ~ spl0_189 ),
inference(resolution,[],[f1499,f884]) ).
fof(f5915,plain,
( spl0_495
| ~ spl0_60
| ~ spl0_189 ),
inference(avatar_split_clause,[],[f1572,f1498,f388,f5913]) ).
fof(f5913,plain,
( spl0_495
<=> ! [X59,X58] :
( subclass(intersection(X58,identity_relation),X59)
| member(not_subclass_element(intersection(X58,identity_relation),X59),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_495])]) ).
fof(f1572,plain,
( ! [X58,X59] :
( subclass(intersection(X58,identity_relation),X59)
| member(not_subclass_element(intersection(X58,identity_relation),X59),subset_relation) )
| ~ spl0_60
| ~ spl0_189 ),
inference(resolution,[],[f1499,f389]) ).
fof(f5911,plain,
( spl0_494
| ~ spl0_70
| ~ spl0_188 ),
inference(avatar_split_clause,[],[f1549,f1494,f437,f5909]) ).
fof(f5909,plain,
( spl0_494
<=> ! [X11] :
( member(not_subclass_element(singleton_relation,X11),complement(compose(element_relation,complement(identity_relation))))
| subclass(singleton_relation,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_494])]) ).
fof(f1549,plain,
( ! [X11] :
( member(not_subclass_element(singleton_relation,X11),complement(compose(element_relation,complement(identity_relation))))
| subclass(singleton_relation,X11) )
| ~ spl0_70
| ~ spl0_188 ),
inference(superposition,[],[f1495,f439]) ).
fof(f5907,plain,
( spl0_493
| ~ spl0_132
| ~ spl0_188 ),
inference(avatar_split_clause,[],[f1544,f1494,f883,f5905]) ).
fof(f5905,plain,
( spl0_493
<=> ! [X64,X63] :
( subclass(intersection(singleton_relation,X63),X64)
| member(not_subclass_element(intersection(singleton_relation,X63),X64),element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_493])]) ).
fof(f1544,plain,
( ! [X63,X64] :
( subclass(intersection(singleton_relation,X63),X64)
| member(not_subclass_element(intersection(singleton_relation,X63),X64),element_relation) )
| ~ spl0_132
| ~ spl0_188 ),
inference(resolution,[],[f1495,f884]) ).
fof(f5903,plain,
( spl0_492
| ~ spl0_60
| ~ spl0_188 ),
inference(avatar_split_clause,[],[f1542,f1494,f388,f5901]) ).
fof(f5901,plain,
( spl0_492
<=> ! [X59,X58] :
( subclass(intersection(identity_relation,X58),X59)
| member(not_subclass_element(intersection(identity_relation,X58),X59),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_492])]) ).
fof(f1542,plain,
( ! [X58,X59] :
( subclass(intersection(identity_relation,X58),X59)
| member(not_subclass_element(intersection(identity_relation,X58),X59),subset_relation) )
| ~ spl0_60
| ~ spl0_188 ),
inference(resolution,[],[f1495,f389]) ).
fof(f5899,plain,
( spl0_491
| ~ spl0_75
| ~ spl0_187 ),
inference(avatar_split_clause,[],[f1492,f1345,f497,f5897]) ).
fof(f5897,plain,
( spl0_491
<=> ! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,symmetric_difference(complement(X0),complement(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_491])]) ).
fof(f497,plain,
( spl0_75
<=> ! [X0,X1] : complement(intersection(complement(X0),complement(X1))) = union(X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f1492,plain,
( ! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,symmetric_difference(complement(X0),complement(X1))) )
| ~ spl0_75
| ~ spl0_187 ),
inference(superposition,[],[f1346,f498]) ).
fof(f498,plain,
( ! [X0,X1] : complement(intersection(complement(X0),complement(X1))) = union(X0,X1)
| ~ spl0_75 ),
inference(avatar_component_clause,[],[f497]) ).
fof(f5895,plain,
( spl0_490
| ~ spl0_52
| ~ spl0_183 ),
inference(avatar_split_clause,[],[f1468,f1329,f340,f5893]) ).
fof(f5893,plain,
( spl0_490
<=> ! [X6,X5] :
( ~ inductive(diagonalise(cross_product(X5,X6)))
| ~ member(null_class,domain_of(restrict(identity_relation,X5,X6))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_490])]) ).
fof(f1468,plain,
( ! [X6,X5] :
( ~ inductive(diagonalise(cross_product(X5,X6)))
| ~ member(null_class,domain_of(restrict(identity_relation,X5,X6))) )
| ~ spl0_52
| ~ spl0_183 ),
inference(superposition,[],[f341,f1330]) ).
fof(f5891,plain,
( spl0_489
| ~ spl0_27
| ~ spl0_177 ),
inference(avatar_split_clause,[],[f1438,f1304,f235,f5889]) ).
fof(f5889,plain,
( spl0_489
<=> ! [X29,X27,X28] :
( ~ subclass(X27,complement(X28))
| subclass(X27,X29)
| ~ member(not_subclass_element(X27,X29),X28) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_489])]) ).
fof(f1438,plain,
( ! [X28,X29,X27] :
( ~ subclass(X27,complement(X28))
| subclass(X27,X29)
| ~ member(not_subclass_element(X27,X29),X28) )
| ~ spl0_27
| ~ spl0_177 ),
inference(resolution,[],[f1305,f236]) ).
fof(f5857,plain,
( spl0_488
| ~ spl0_137
| ~ spl0_177 ),
inference(avatar_split_clause,[],[f1434,f1304,f913,f5855]) ).
fof(f5855,plain,
( spl0_488
<=> ! [X13,X12,X14] :
( ~ subclass(X12,singleton(X13))
| subclass(X12,X14)
| not_subclass_element(X12,X14) = X13 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_488])]) ).
fof(f1434,plain,
( ! [X14,X12,X13] :
( ~ subclass(X12,singleton(X13))
| subclass(X12,X14)
| not_subclass_element(X12,X14) = X13 )
| ~ spl0_137
| ~ spl0_177 ),
inference(resolution,[],[f1305,f914]) ).
fof(f5853,plain,
( spl0_487
| ~ spl0_33
| ~ spl0_176 ),
inference(avatar_split_clause,[],[f1427,f1300,f259,f5851]) ).
fof(f5851,plain,
( spl0_487
<=> ! [X4,X3] :
( member(X3,cross_product(universal_class,universal_class))
| ~ member(X3,universal_class)
| ~ function(unordered_pair(X4,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_487])]) ).
fof(f1300,plain,
( spl0_176
<=> ! [X4,X5,X3] :
( ~ subclass(unordered_pair(X3,X4),X5)
| member(X4,X5)
| ~ member(X4,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).
fof(f1427,plain,
( ! [X3,X4] :
( member(X3,cross_product(universal_class,universal_class))
| ~ member(X3,universal_class)
| ~ function(unordered_pair(X4,X3)) )
| ~ spl0_33
| ~ spl0_176 ),
inference(resolution,[],[f1301,f260]) ).
fof(f1301,plain,
( ! [X3,X4,X5] :
( ~ subclass(unordered_pair(X3,X4),X5)
| member(X4,X5)
| ~ member(X4,universal_class) )
| ~ spl0_176 ),
inference(avatar_component_clause,[],[f1300]) ).
fof(f5849,plain,
( spl0_486
| ~ spl0_33
| ~ spl0_175 ),
inference(avatar_split_clause,[],[f1422,f1296,f259,f5847]) ).
fof(f5847,plain,
( spl0_486
<=> ! [X4,X3] :
( member(X3,cross_product(universal_class,universal_class))
| ~ member(X3,universal_class)
| ~ function(unordered_pair(X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_486])]) ).
fof(f1296,plain,
( spl0_175
<=> ! [X2,X0,X1] :
( ~ subclass(unordered_pair(X0,X1),X2)
| member(X0,X2)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).
fof(f1422,plain,
( ! [X3,X4] :
( member(X3,cross_product(universal_class,universal_class))
| ~ member(X3,universal_class)
| ~ function(unordered_pair(X3,X4)) )
| ~ spl0_33
| ~ spl0_175 ),
inference(resolution,[],[f1297,f260]) ).
fof(f1297,plain,
( ! [X2,X0,X1] :
( ~ subclass(unordered_pair(X0,X1),X2)
| member(X0,X2)
| ~ member(X0,universal_class) )
| ~ spl0_175 ),
inference(avatar_component_clause,[],[f1296]) ).
fof(f5845,plain,
( spl0_485
| ~ spl0_52
| ~ spl0_174 ),
inference(avatar_split_clause,[],[f1413,f1292,f340,f5843]) ).
fof(f5843,plain,
( spl0_485
<=> ! [X3] :
( ~ inductive(power_class(domain_of(intersection(X3,identity_relation))))
| ~ member(null_class,image(element_relation,diagonalise(X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_485])]) ).
fof(f1413,plain,
( ! [X3] :
( ~ inductive(power_class(domain_of(intersection(X3,identity_relation))))
| ~ member(null_class,image(element_relation,diagonalise(X3))) )
| ~ spl0_52
| ~ spl0_174 ),
inference(superposition,[],[f341,f1293]) ).
fof(f5841,plain,
( spl0_484
| ~ spl0_52
| ~ spl0_173 ),
inference(avatar_split_clause,[],[f1404,f1288,f340,f5839]) ).
fof(f5839,plain,
( spl0_484
<=> ! [X3] :
( ~ inductive(power_class(image(element_relation,complement(X3))))
| ~ member(null_class,image(element_relation,power_class(X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_484])]) ).
fof(f1404,plain,
( ! [X3] :
( ~ inductive(power_class(image(element_relation,complement(X3))))
| ~ member(null_class,image(element_relation,power_class(X3))) )
| ~ spl0_52
| ~ spl0_173 ),
inference(superposition,[],[f341,f1289]) ).
fof(f5837,plain,
( spl0_483
| ~ spl0_138
| ~ spl0_170 ),
inference(avatar_split_clause,[],[f1272,f1169,f941,f5835]) ).
fof(f5835,plain,
( spl0_483
<=> ! [X5,X4,X6,X3] :
( member(unordered_pair(X3,X4),union(X5,X6))
| ~ subclass(universal_class,symmetric_difference(X5,X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_483])]) ).
fof(f1272,plain,
( ! [X3,X6,X4,X5] :
( member(unordered_pair(X3,X4),union(X5,X6))
| ~ subclass(universal_class,symmetric_difference(X5,X6)) )
| ~ spl0_138
| ~ spl0_170 ),
inference(resolution,[],[f1170,f942]) ).
fof(f5833,plain,
( spl0_482
| ~ spl0_141
| ~ spl0_156 ),
inference(avatar_split_clause,[],[f1245,f1109,f953,f5831]) ).
fof(f5831,plain,
( spl0_482
<=> ! [X36,X35] :
( ~ subclass(X35,cantor(X36))
| null_class = X35
| member(regular(X35),domain_of(X36)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_482])]) ).
fof(f1245,plain,
( ! [X36,X35] :
( ~ subclass(X35,cantor(X36))
| null_class = X35
| member(regular(X35),domain_of(X36)) )
| ~ spl0_141
| ~ spl0_156 ),
inference(resolution,[],[f1110,f954]) ).
fof(f5829,plain,
( spl0_481
| ~ spl0_44
| ~ spl0_156 ),
inference(avatar_split_clause,[],[f1237,f1109,f308,f5827]) ).
fof(f5827,plain,
( spl0_481
<=> ! [X16,X17,X15] :
( ~ subclass(X15,intersection(X16,X17))
| null_class = X15
| member(regular(X15),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_481])]) ).
fof(f1237,plain,
( ! [X16,X17,X15] :
( ~ subclass(X15,intersection(X16,X17))
| null_class = X15
| member(regular(X15),X16) )
| ~ spl0_44
| ~ spl0_156 ),
inference(resolution,[],[f1110,f309]) ).
fof(f5825,plain,
( spl0_480
| ~ spl0_45
| ~ spl0_156 ),
inference(avatar_split_clause,[],[f1236,f1109,f312,f5823]) ).
fof(f5823,plain,
( spl0_480
<=> ! [X13,X12,X14] :
( ~ subclass(X12,intersection(X13,X14))
| null_class = X12
| member(regular(X12),X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_480])]) ).
fof(f1236,plain,
( ! [X14,X12,X13] :
( ~ subclass(X12,intersection(X13,X14))
| null_class = X12
| member(regular(X12),X14) )
| ~ spl0_45
| ~ spl0_156 ),
inference(resolution,[],[f1110,f313]) ).
fof(f5821,plain,
( spl0_479
| ~ spl0_141
| ~ spl0_155 ),
inference(avatar_split_clause,[],[f1229,f1105,f953,f5819]) ).
fof(f5819,plain,
( spl0_479
<=> ! [X34,X35] :
( ~ subclass(universal_class,cantor(X34))
| ~ member(X35,universal_class)
| member(power_class(X35),domain_of(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_479])]) ).
fof(f1229,plain,
( ! [X34,X35] :
( ~ subclass(universal_class,cantor(X34))
| ~ member(X35,universal_class)
| member(power_class(X35),domain_of(X34)) )
| ~ spl0_141
| ~ spl0_155 ),
inference(resolution,[],[f1106,f954]) ).
fof(f5815,plain,
( spl0_478
| ~ spl0_44
| ~ spl0_155 ),
inference(avatar_split_clause,[],[f1221,f1105,f308,f5813]) ).
fof(f5813,plain,
( spl0_478
<=> ! [X16,X14,X15] :
( ~ subclass(universal_class,intersection(X14,X15))
| ~ member(X16,universal_class)
| member(power_class(X16),X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_478])]) ).
fof(f1221,plain,
( ! [X16,X14,X15] :
( ~ subclass(universal_class,intersection(X14,X15))
| ~ member(X16,universal_class)
| member(power_class(X16),X14) )
| ~ spl0_44
| ~ spl0_155 ),
inference(resolution,[],[f1106,f309]) ).
fof(f5811,plain,
( spl0_477
| ~ spl0_45
| ~ spl0_155 ),
inference(avatar_split_clause,[],[f1220,f1105,f312,f5809]) ).
fof(f5809,plain,
( spl0_477
<=> ! [X11,X12,X13] :
( ~ subclass(universal_class,intersection(X11,X12))
| ~ member(X13,universal_class)
| member(power_class(X13),X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_477])]) ).
fof(f1220,plain,
( ! [X11,X12,X13] :
( ~ subclass(universal_class,intersection(X11,X12))
| ~ member(X13,universal_class)
| member(power_class(X13),X12) )
| ~ spl0_45
| ~ spl0_155 ),
inference(resolution,[],[f1106,f313]) ).
fof(f5807,plain,
( spl0_476
| ~ spl0_141
| ~ spl0_154 ),
inference(avatar_split_clause,[],[f1213,f1101,f953,f5805]) ).
fof(f5805,plain,
( spl0_476
<=> ! [X34,X35] :
( ~ subclass(universal_class,cantor(X34))
| ~ member(X35,universal_class)
| member(sum_class(X35),domain_of(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_476])]) ).
fof(f1213,plain,
( ! [X34,X35] :
( ~ subclass(universal_class,cantor(X34))
| ~ member(X35,universal_class)
| member(sum_class(X35),domain_of(X34)) )
| ~ spl0_141
| ~ spl0_154 ),
inference(resolution,[],[f1102,f954]) ).
fof(f5803,plain,
( spl0_475
| ~ spl0_44
| ~ spl0_154 ),
inference(avatar_split_clause,[],[f1205,f1101,f308,f5801]) ).
fof(f5801,plain,
( spl0_475
<=> ! [X16,X14,X15] :
( ~ subclass(universal_class,intersection(X14,X15))
| ~ member(X16,universal_class)
| member(sum_class(X16),X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_475])]) ).
fof(f1205,plain,
( ! [X16,X14,X15] :
( ~ subclass(universal_class,intersection(X14,X15))
| ~ member(X16,universal_class)
| member(sum_class(X16),X14) )
| ~ spl0_44
| ~ spl0_154 ),
inference(resolution,[],[f1102,f309]) ).
fof(f5799,plain,
( spl0_474
| ~ spl0_45
| ~ spl0_154 ),
inference(avatar_split_clause,[],[f1204,f1101,f312,f5797]) ).
fof(f5797,plain,
( spl0_474
<=> ! [X11,X12,X13] :
( ~ subclass(universal_class,intersection(X11,X12))
| ~ member(X13,universal_class)
| member(sum_class(X13),X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_474])]) ).
fof(f1204,plain,
( ! [X11,X12,X13] :
( ~ subclass(universal_class,intersection(X11,X12))
| ~ member(X13,universal_class)
| member(sum_class(X13),X12) )
| ~ spl0_45
| ~ spl0_154 ),
inference(resolution,[],[f1102,f313]) ).
fof(f5795,plain,
( spl0_473
| ~ spl0_139
| ~ spl0_153 ),
inference(avatar_split_clause,[],[f1197,f1097,f945,f5793]) ).
fof(f5793,plain,
( spl0_473
<=> ! [X0] :
( ~ operation(inverse(X0))
| member(null_class,domain_of(range_of(X0)))
| ~ inductive(range_of(inverse(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_473])]) ).
fof(f945,plain,
( spl0_139
<=> ! [X14,X15] :
( ~ subclass(X14,X15)
| member(null_class,X15)
| ~ inductive(X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f1097,plain,
( spl0_153
<=> ! [X0] :
( subclass(range_of(inverse(X0)),domain_of(range_of(X0)))
| ~ operation(inverse(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f1197,plain,
( ! [X0] :
( ~ operation(inverse(X0))
| member(null_class,domain_of(range_of(X0)))
| ~ inductive(range_of(inverse(X0))) )
| ~ spl0_139
| ~ spl0_153 ),
inference(resolution,[],[f1098,f946]) ).
fof(f946,plain,
( ! [X14,X15] :
( ~ subclass(X14,X15)
| member(null_class,X15)
| ~ inductive(X14) )
| ~ spl0_139 ),
inference(avatar_component_clause,[],[f945]) ).
fof(f1098,plain,
( ! [X0] :
( subclass(range_of(inverse(X0)),domain_of(range_of(X0)))
| ~ operation(inverse(X0)) )
| ~ spl0_153 ),
inference(avatar_component_clause,[],[f1097]) ).
fof(f5791,plain,
( spl0_472
| ~ spl0_138
| ~ spl0_152 ),
inference(avatar_split_clause,[],[f1191,f1093,f941,f5789]) ).
fof(f5789,plain,
( spl0_472
<=> ! [X6,X4,X5] :
( ~ member(unordered_pair(X4,X5),diagonalise(X6))
| ~ subclass(universal_class,domain_of(intersection(X6,identity_relation))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_472])]) ).
fof(f1191,plain,
( ! [X6,X4,X5] :
( ~ member(unordered_pair(X4,X5),diagonalise(X6))
| ~ subclass(universal_class,domain_of(intersection(X6,identity_relation))) )
| ~ spl0_138
| ~ spl0_152 ),
inference(resolution,[],[f1094,f942]) ).
fof(f5787,plain,
( spl0_471
| ~ spl0_138
| ~ spl0_151 ),
inference(avatar_split_clause,[],[f1182,f1089,f941,f5785]) ).
fof(f5785,plain,
( spl0_471
<=> ! [X4,X2,X3] :
( ~ member(unordered_pair(X2,X3),power_class(X4))
| ~ subclass(universal_class,image(element_relation,complement(X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_471])]) ).
fof(f1182,plain,
( ! [X2,X3,X4] :
( ~ member(unordered_pair(X2,X3),power_class(X4))
| ~ subclass(universal_class,image(element_relation,complement(X4))) )
| ~ spl0_138
| ~ spl0_151 ),
inference(resolution,[],[f1090,f942]) ).
fof(f5783,plain,
( spl0_470
| ~ spl0_135
| ~ spl0_150 ),
inference(avatar_split_clause,[],[f1176,f1085,f905,f5781]) ).
fof(f5781,plain,
( spl0_470
<=> ! [X8] :
( subclass(complement(inverse(subset_relation)),X8)
| ~ member(not_subclass_element(complement(inverse(subset_relation)),X8),identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_470])]) ).
fof(f905,plain,
( spl0_135
<=> ! [X0] :
( ~ member(X0,identity_relation)
| member(X0,inverse(subset_relation)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f1176,plain,
( ! [X8] :
( subclass(complement(inverse(subset_relation)),X8)
| ~ member(not_subclass_element(complement(inverse(subset_relation)),X8),identity_relation) )
| ~ spl0_135
| ~ spl0_150 ),
inference(resolution,[],[f1086,f906]) ).
fof(f906,plain,
( ! [X0] :
( member(X0,inverse(subset_relation))
| ~ member(X0,identity_relation) )
| ~ spl0_135 ),
inference(avatar_component_clause,[],[f905]) ).
fof(f5779,plain,
( spl0_469
| ~ spl0_72
| ~ spl0_147 ),
inference(avatar_split_clause,[],[f1056,f1022,f485,f5777]) ).
fof(f5777,plain,
( spl0_469
<=> ! [X4,X5,X3] :
( ~ member(singleton(singleton(singleton(X3))),cross_product(X4,X5))
| member(singleton(X3),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_469])]) ).
fof(f1056,plain,
( ! [X3,X4,X5] :
( ~ member(singleton(singleton(singleton(X3))),cross_product(X4,X5))
| member(singleton(X3),X4) )
| ~ spl0_72
| ~ spl0_147 ),
inference(superposition,[],[f486,f1023]) ).
fof(f5775,plain,
( spl0_468
| ~ spl0_55
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1041,f1010,f352,f5773]) ).
fof(f5773,plain,
( spl0_468
<=> ! [X1] :
( ~ member(regular(diagonalise(X1)),domain_of(intersection(X1,identity_relation)))
| null_class = diagonalise(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_468])]) ).
fof(f1041,plain,
( ! [X1] :
( ~ member(regular(diagonalise(X1)),domain_of(intersection(X1,identity_relation)))
| null_class = diagonalise(X1) )
| ~ spl0_55
| ~ spl0_144 ),
inference(superposition,[],[f1011,f353]) ).
fof(f5771,plain,
( spl0_467
| ~ spl0_50
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1040,f1010,f332,f5769]) ).
fof(f5769,plain,
( spl0_467
<=> ! [X0] :
( ~ member(regular(power_class(X0)),image(element_relation,complement(X0)))
| null_class = power_class(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_467])]) ).
fof(f1040,plain,
( ! [X0] :
( ~ member(regular(power_class(X0)),image(element_relation,complement(X0)))
| null_class = power_class(X0) )
| ~ spl0_50
| ~ spl0_144 ),
inference(superposition,[],[f1011,f333]) ).
fof(f5767,plain,
( spl0_466
| ~ spl0_40
| ~ spl0_143 ),
inference(avatar_split_clause,[],[f1004,f961,f292,f5765]) ).
fof(f5765,plain,
( spl0_466
<=> ! [X3] :
( ~ member(not_subclass_element(X3,cross_product(universal_class,universal_class)),subset_relation)
| subclass(X3,cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_466])]) ).
fof(f1004,plain,
( ! [X3] :
( ~ member(not_subclass_element(X3,cross_product(universal_class,universal_class)),subset_relation)
| subclass(X3,cross_product(universal_class,universal_class)) )
| ~ spl0_40
| ~ spl0_143 ),
inference(resolution,[],[f962,f293]) ).
fof(f5582,plain,
( spl0_465
| ~ spl0_326
| ~ spl0_449 ),
inference(avatar_split_clause,[],[f5236,f5233,f3785,f5580]) ).
fof(f5580,plain,
( spl0_465
<=> ! [X37] :
( singleton_relation = intersection(X37,identity_relation)
| member(regular(intersection(X37,identity_relation)),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_465])]) ).
fof(f3785,plain,
( spl0_326
<=> null_class = singleton_relation ),
introduced(avatar_definition,[new_symbols(naming,[spl0_326])]) ).
fof(f5233,plain,
( spl0_449
<=> ! [X37] :
( null_class = intersection(X37,identity_relation)
| member(regular(intersection(X37,identity_relation)),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_449])]) ).
fof(f5236,plain,
( ! [X37] :
( singleton_relation = intersection(X37,identity_relation)
| member(regular(intersection(X37,identity_relation)),subset_relation) )
| ~ spl0_326
| ~ spl0_449 ),
inference(forward_demodulation,[],[f5234,f3787]) ).
fof(f3787,plain,
( null_class = singleton_relation
| ~ spl0_326 ),
inference(avatar_component_clause,[],[f3785]) ).
fof(f5234,plain,
( ! [X37] :
( member(regular(intersection(X37,identity_relation)),subset_relation)
| null_class = intersection(X37,identity_relation) )
| ~ spl0_449 ),
inference(avatar_component_clause,[],[f5233]) ).
fof(f5567,plain,
( ~ spl0_464
| ~ spl0_326
| spl0_440 ),
inference(avatar_split_clause,[],[f5228,f5150,f3785,f5564]) ).
fof(f5564,plain,
( spl0_464
<=> member(ordered_pair(x,singleton_relation),subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_464])]) ).
fof(f5150,plain,
( spl0_440
<=> member(ordered_pair(x,null_class),subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_440])]) ).
fof(f5228,plain,
( ~ member(ordered_pair(x,singleton_relation),subset_relation)
| ~ spl0_326
| spl0_440 ),
inference(superposition,[],[f5152,f3787]) ).
fof(f5152,plain,
( ~ member(ordered_pair(x,null_class),subset_relation)
| spl0_440 ),
inference(avatar_component_clause,[],[f5150]) ).
fof(f5296,plain,
( spl0_463
| ~ spl0_128
| ~ spl0_284 ),
inference(avatar_split_clause,[],[f3218,f3122,f861,f5294]) ).
fof(f5294,plain,
( spl0_463
<=> ! [X57,X56] :
( member(regular(cross_product(X56,X57)),universal_class)
| null_class = cross_product(X56,X57) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_463])]) ).
fof(f861,plain,
( spl0_128
<=> ! [X8,X7] : member(ordered_pair(X7,X8),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f3122,plain,
( spl0_284
<=> ! [X6,X5] :
( regular(cross_product(X5,X6)) = ordered_pair(first(regular(cross_product(X5,X6))),second(regular(cross_product(X5,X6))))
| null_class = cross_product(X5,X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).
fof(f3218,plain,
( ! [X56,X57] :
( member(regular(cross_product(X56,X57)),universal_class)
| null_class = cross_product(X56,X57) )
| ~ spl0_128
| ~ spl0_284 ),
inference(superposition,[],[f862,f3123]) ).
fof(f3123,plain,
( ! [X6,X5] :
( regular(cross_product(X5,X6)) = ordered_pair(first(regular(cross_product(X5,X6))),second(regular(cross_product(X5,X6))))
| null_class = cross_product(X5,X6) )
| ~ spl0_284 ),
inference(avatar_component_clause,[],[f3122]) ).
fof(f862,plain,
( ! [X8,X7] : member(ordered_pair(X7,X8),universal_class)
| ~ spl0_128 ),
inference(avatar_component_clause,[],[f861]) ).
fof(f5292,plain,
( spl0_462
| ~ spl0_44
| ~ spl0_263 ),
inference(avatar_split_clause,[],[f2760,f2603,f308,f5290]) ).
fof(f5290,plain,
( spl0_462
<=> ! [X0,X1] :
( ~ member(X1,cantor(restrict(element_relation,universal_class,X0)))
| member(X1,sum_class(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_462])]) ).
fof(f2603,plain,
( spl0_263
<=> ! [X2] : cantor(restrict(element_relation,universal_class,X2)) = intersection(sum_class(X2),diagonalise(compose(inverse(element_relation),restrict(element_relation,universal_class,X2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).
fof(f2760,plain,
( ! [X0,X1] :
( ~ member(X1,cantor(restrict(element_relation,universal_class,X0)))
| member(X1,sum_class(X0)) )
| ~ spl0_44
| ~ spl0_263 ),
inference(superposition,[],[f309,f2604]) ).
fof(f2604,plain,
( ! [X2] : cantor(restrict(element_relation,universal_class,X2)) = intersection(sum_class(X2),diagonalise(compose(inverse(element_relation),restrict(element_relation,universal_class,X2))))
| ~ spl0_263 ),
inference(avatar_component_clause,[],[f2603]) ).
fof(f5288,plain,
( spl0_461
| ~ spl0_44
| ~ spl0_262 ),
inference(avatar_split_clause,[],[f2744,f2599,f308,f5286]) ).
fof(f5286,plain,
( spl0_461
<=> ! [X0,X1] :
( ~ member(X1,cantor(flip(cross_product(X0,universal_class))))
| member(X1,inverse(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_461])]) ).
fof(f2599,plain,
( spl0_262
<=> ! [X1] : cantor(flip(cross_product(X1,universal_class))) = intersection(inverse(X1),diagonalise(compose(inverse(element_relation),flip(cross_product(X1,universal_class))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).
fof(f2744,plain,
( ! [X0,X1] :
( ~ member(X1,cantor(flip(cross_product(X0,universal_class))))
| member(X1,inverse(X0)) )
| ~ spl0_44
| ~ spl0_262 ),
inference(superposition,[],[f309,f2600]) ).
fof(f2600,plain,
( ! [X1] : cantor(flip(cross_product(X1,universal_class))) = intersection(inverse(X1),diagonalise(compose(inverse(element_relation),flip(cross_product(X1,universal_class)))))
| ~ spl0_262 ),
inference(avatar_component_clause,[],[f2599]) ).
fof(f5283,plain,
( spl0_460
| ~ spl0_134
| ~ spl0_250 ),
inference(avatar_split_clause,[],[f2476,f2258,f901,f5281]) ).
fof(f5281,plain,
( spl0_460
<=> ! [X11,X12] :
( ~ inductive(symmetric_difference(complement(X11),complement(X12)))
| member(null_class,union(X11,X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_460])]) ).
fof(f2258,plain,
( spl0_250
<=> ! [X0,X1] : symmetric_difference(complement(X0),complement(X1)) = intersection(union(X0,X1),union(complement(X0),complement(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).
fof(f2476,plain,
( ! [X11,X12] :
( ~ inductive(symmetric_difference(complement(X11),complement(X12)))
| member(null_class,union(X11,X12)) )
| ~ spl0_134
| ~ spl0_250 ),
inference(superposition,[],[f902,f2259]) ).
fof(f2259,plain,
( ! [X0,X1] : symmetric_difference(complement(X0),complement(X1)) = intersection(union(X0,X1),union(complement(X0),complement(X1)))
| ~ spl0_250 ),
inference(avatar_component_clause,[],[f2258]) ).
fof(f5279,plain,
( spl0_459
| ~ spl0_146
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2189,f2067,f1018,f5277]) ).
fof(f5277,plain,
( spl0_459
<=> ! [X1] :
( ~ member(X1,subset_relation)
| member(X1,complement(compose(complement(element_relation),inverse(element_relation)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_459])]) ).
fof(f2067,plain,
( spl0_233
<=> ! [X1] :
( ~ member(X1,subset_relation)
| member(X1,restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).
fof(f2189,plain,
( ! [X1] :
( ~ member(X1,subset_relation)
| member(X1,complement(compose(complement(element_relation),inverse(element_relation)))) )
| ~ spl0_146
| ~ spl0_233 ),
inference(resolution,[],[f2068,f1019]) ).
fof(f2068,plain,
( ! [X1] :
( member(X1,restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class))
| ~ member(X1,subset_relation) )
| ~ spl0_233 ),
inference(avatar_component_clause,[],[f2067]) ).
fof(f5275,plain,
( ~ spl0_458
| ~ spl0_334
| spl0_440 ),
inference(avatar_split_clause,[],[f5227,f5150,f3899,f5272]) ).
fof(f5272,plain,
( spl0_458
<=> subclass(universal_class,subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_458])]) ).
fof(f5227,plain,
( ~ subclass(universal_class,subset_relation)
| ~ spl0_334
| spl0_440 ),
inference(resolution,[],[f5152,f3900]) ).
fof(f5269,plain,
( spl0_457
| ~ spl0_13
| ~ spl0_194 ),
inference(avatar_split_clause,[],[f1640,f1518,f175,f5267]) ).
fof(f5267,plain,
( spl0_457
<=> ! [X25,X26] :
( ~ member(null_class,union(X25,X26))
| ~ inductive(intersection(complement(X25),complement(X26))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_457])]) ).
fof(f1640,plain,
( ! [X26,X25] :
( ~ member(null_class,union(X25,X26))
| ~ inductive(intersection(complement(X25),complement(X26))) )
| ~ spl0_13
| ~ spl0_194 ),
inference(resolution,[],[f1519,f176]) ).
fof(f5265,plain,
( spl0_455
| ~ spl0_456
| ~ spl0_65
| ~ spl0_193 ),
inference(avatar_split_clause,[],[f1605,f1514,f417,f5262,f5259]) ).
fof(f5259,plain,
( spl0_455
<=> ! [X12] :
( ~ member(X12,universal_class)
| domain_of(X12) = successor(X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_455])]) ).
fof(f5262,plain,
( spl0_456
<=> subclass(domain_relation,successor_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_456])]) ).
fof(f417,plain,
( spl0_65
<=> ! [X0,X1] :
( successor(X0) = X1
| ~ member(ordered_pair(X0,X1),successor_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f1605,plain,
( ! [X12] :
( ~ subclass(domain_relation,successor_relation)
| ~ member(X12,universal_class)
| domain_of(X12) = successor(X12) )
| ~ spl0_65
| ~ spl0_193 ),
inference(resolution,[],[f1515,f418]) ).
fof(f418,plain,
( ! [X0,X1] :
( ~ member(ordered_pair(X0,X1),successor_relation)
| successor(X0) = X1 )
| ~ spl0_65 ),
inference(avatar_component_clause,[],[f417]) ).
fof(f5257,plain,
( spl0_454
| ~ spl0_72
| ~ spl0_193 ),
inference(avatar_split_clause,[],[f1601,f1514,f485,f5255]) ).
fof(f5255,plain,
( spl0_454
<=> ! [X4,X5,X3] :
( ~ subclass(domain_relation,cross_product(X3,X4))
| ~ member(X5,universal_class)
| member(X5,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_454])]) ).
fof(f1601,plain,
( ! [X3,X4,X5] :
( ~ subclass(domain_relation,cross_product(X3,X4))
| ~ member(X5,universal_class)
| member(X5,X3) )
| ~ spl0_72
| ~ spl0_193 ),
inference(resolution,[],[f1515,f486]) ).
fof(f5253,plain,
( spl0_453
| ~ spl0_79
| ~ spl0_178 ),
inference(avatar_split_clause,[],[f1451,f1308,f516,f5251]) ).
fof(f5251,plain,
( spl0_453
<=> ! [X0,X1] :
( member(apply(X0,X1),universal_class)
| ~ member(singleton(X1),universal_class)
| ~ function(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_453])]) ).
fof(f516,plain,
( spl0_79
<=> ! [X0,X8] :
( ~ function(X8)
| ~ member(X0,universal_class)
| member(image(X8,X0),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f1308,plain,
( spl0_178
<=> ! [X0,X1] :
( member(apply(X0,X1),universal_class)
| ~ member(image(X0,singleton(X1)),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).
fof(f1451,plain,
( ! [X0,X1] :
( member(apply(X0,X1),universal_class)
| ~ member(singleton(X1),universal_class)
| ~ function(X0) )
| ~ spl0_79
| ~ spl0_178 ),
inference(resolution,[],[f1309,f517]) ).
fof(f517,plain,
( ! [X0,X8] :
( member(image(X8,X0),universal_class)
| ~ member(X0,universal_class)
| ~ function(X8) )
| ~ spl0_79 ),
inference(avatar_component_clause,[],[f516]) ).
fof(f1309,plain,
( ! [X0,X1] :
( ~ member(image(X0,singleton(X1)),universal_class)
| member(apply(X0,X1),universal_class) )
| ~ spl0_178 ),
inference(avatar_component_clause,[],[f1308]) ).
fof(f5249,plain,
( spl0_452
| ~ spl0_132
| ~ spl0_177 ),
inference(avatar_split_clause,[],[f1448,f1304,f883,f5247]) ).
fof(f5247,plain,
( spl0_452
<=> ! [X61,X60] :
( ~ subclass(X60,singleton_relation)
| subclass(X60,X61)
| member(not_subclass_element(X60,X61),element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_452])]) ).
fof(f1448,plain,
( ! [X60,X61] :
( ~ subclass(X60,singleton_relation)
| subclass(X60,X61)
| member(not_subclass_element(X60,X61),element_relation) )
| ~ spl0_132
| ~ spl0_177 ),
inference(resolution,[],[f1305,f884]) ).
fof(f5245,plain,
( spl0_451
| ~ spl0_60
| ~ spl0_177 ),
inference(avatar_split_clause,[],[f1446,f1304,f388,f5243]) ).
fof(f5243,plain,
( spl0_451
<=> ! [X55,X56] :
( ~ subclass(X55,identity_relation)
| subclass(X55,X56)
| member(not_subclass_element(X55,X56),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_451])]) ).
fof(f1446,plain,
( ! [X56,X55] :
( ~ subclass(X55,identity_relation)
| subclass(X55,X56)
| member(not_subclass_element(X55,X56),subset_relation) )
| ~ spl0_60
| ~ spl0_177 ),
inference(resolution,[],[f1305,f389]) ).
fof(f5240,plain,
( spl0_450
| ~ spl0_132
| ~ spl0_172 ),
inference(avatar_split_clause,[],[f1391,f1284,f883,f5238]) ).
fof(f5238,plain,
( spl0_450
<=> ! [X40] :
( null_class = intersection(X40,singleton_relation)
| member(regular(intersection(X40,singleton_relation)),element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_450])]) ).
fof(f1391,plain,
( ! [X40] :
( null_class = intersection(X40,singleton_relation)
| member(regular(intersection(X40,singleton_relation)),element_relation) )
| ~ spl0_132
| ~ spl0_172 ),
inference(resolution,[],[f1285,f884]) ).
fof(f5235,plain,
( spl0_449
| ~ spl0_60
| ~ spl0_172 ),
inference(avatar_split_clause,[],[f1389,f1284,f388,f5233]) ).
fof(f1389,plain,
( ! [X37] :
( null_class = intersection(X37,identity_relation)
| member(regular(intersection(X37,identity_relation)),subset_relation) )
| ~ spl0_60
| ~ spl0_172 ),
inference(resolution,[],[f1285,f389]) ).
fof(f5186,plain,
( spl0_326
| spl0_448
| ~ spl0_70
| ~ spl0_171 ),
inference(avatar_split_clause,[],[f1369,f1280,f437,f5183,f3785]) ).
fof(f5183,plain,
( spl0_448
<=> member(regular(singleton_relation),complement(compose(element_relation,complement(identity_relation)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_448])]) ).
fof(f1369,plain,
( member(regular(singleton_relation),complement(compose(element_relation,complement(identity_relation))))
| null_class = singleton_relation
| ~ spl0_70
| ~ spl0_171 ),
inference(superposition,[],[f1281,f439]) ).
fof(f5181,plain,
( spl0_447
| ~ spl0_132
| ~ spl0_171 ),
inference(avatar_split_clause,[],[f1364,f1280,f883,f5179]) ).
fof(f5179,plain,
( spl0_447
<=> ! [X40] :
( null_class = intersection(singleton_relation,X40)
| member(regular(intersection(singleton_relation,X40)),element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_447])]) ).
fof(f1364,plain,
( ! [X40] :
( null_class = intersection(singleton_relation,X40)
| member(regular(intersection(singleton_relation,X40)),element_relation) )
| ~ spl0_132
| ~ spl0_171 ),
inference(resolution,[],[f1281,f884]) ).
fof(f5177,plain,
( spl0_446
| ~ spl0_60
| ~ spl0_171 ),
inference(avatar_split_clause,[],[f1362,f1280,f388,f5175]) ).
fof(f5175,plain,
( spl0_446
<=> ! [X37] :
( null_class = intersection(identity_relation,X37)
| member(regular(intersection(identity_relation,X37)),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_446])]) ).
fof(f1362,plain,
( ! [X37] :
( null_class = intersection(identity_relation,X37)
| member(regular(intersection(identity_relation,X37)),subset_relation) )
| ~ spl0_60
| ~ spl0_171 ),
inference(resolution,[],[f1281,f389]) ).
fof(f5173,plain,
( spl0_445
| ~ spl0_27
| ~ spl0_156 ),
inference(avatar_split_clause,[],[f1238,f1109,f235,f5171]) ).
fof(f5171,plain,
( spl0_445
<=> ! [X18,X19] :
( ~ subclass(X18,complement(X19))
| null_class = X18
| ~ member(regular(X18),X19) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_445])]) ).
fof(f1238,plain,
( ! [X18,X19] :
( ~ subclass(X18,complement(X19))
| null_class = X18
| ~ member(regular(X18),X19) )
| ~ spl0_27
| ~ spl0_156 ),
inference(resolution,[],[f1110,f236]) ).
fof(f5169,plain,
( spl0_444
| ~ spl0_137
| ~ spl0_156 ),
inference(avatar_split_clause,[],[f1234,f1109,f913,f5167]) ).
fof(f5167,plain,
( spl0_444
<=> ! [X8,X7] :
( ~ subclass(X7,singleton(X8))
| null_class = X7
| regular(X7) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_444])]) ).
fof(f1234,plain,
( ! [X8,X7] :
( ~ subclass(X7,singleton(X8))
| null_class = X7
| regular(X7) = X8 )
| ~ spl0_137
| ~ spl0_156 ),
inference(resolution,[],[f1110,f914]) ).
fof(f5165,plain,
( spl0_443
| ~ spl0_27
| ~ spl0_155 ),
inference(avatar_split_clause,[],[f1222,f1105,f235,f5163]) ).
fof(f5163,plain,
( spl0_443
<=> ! [X18,X17] :
( ~ subclass(universal_class,complement(X17))
| ~ member(X18,universal_class)
| ~ member(power_class(X18),X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_443])]) ).
fof(f1222,plain,
( ! [X18,X17] :
( ~ subclass(universal_class,complement(X17))
| ~ member(X18,universal_class)
| ~ member(power_class(X18),X17) )
| ~ spl0_27
| ~ spl0_155 ),
inference(resolution,[],[f1106,f236]) ).
fof(f5161,plain,
( spl0_442
| ~ spl0_137
| ~ spl0_155 ),
inference(avatar_split_clause,[],[f1218,f1105,f913,f5159]) ).
fof(f5159,plain,
( spl0_442
<=> ! [X6,X7] :
( ~ subclass(universal_class,singleton(X6))
| ~ member(X7,universal_class)
| power_class(X7) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_442])]) ).
fof(f1218,plain,
( ! [X6,X7] :
( ~ subclass(universal_class,singleton(X6))
| ~ member(X7,universal_class)
| power_class(X7) = X6 )
| ~ spl0_137
| ~ spl0_155 ),
inference(resolution,[],[f1106,f914]) ).
fof(f5157,plain,
( spl0_441
| ~ spl0_27
| ~ spl0_154 ),
inference(avatar_split_clause,[],[f1206,f1101,f235,f5155]) ).
fof(f5155,plain,
( spl0_441
<=> ! [X18,X17] :
( ~ subclass(universal_class,complement(X17))
| ~ member(X18,universal_class)
| ~ member(sum_class(X18),X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_441])]) ).
fof(f1206,plain,
( ! [X18,X17] :
( ~ subclass(universal_class,complement(X17))
| ~ member(X18,universal_class)
| ~ member(sum_class(X18),X17) )
| ~ spl0_27
| ~ spl0_154 ),
inference(resolution,[],[f1102,f236]) ).
fof(f5153,plain,
( spl0_439
| ~ spl0_440
| ~ spl0_290
| ~ spl0_345 ),
inference(avatar_split_clause,[],[f5104,f3974,f3258,f5150,f5146]) ).
fof(f5104,plain,
( ~ member(ordered_pair(x,null_class),subset_relation)
| member(second(ordered_pair(x,null_class)),universal_class)
| ~ spl0_290
| ~ spl0_345 ),
inference(superposition,[],[f3975,f3260]) ).
fof(f5144,plain,
( spl0_438
| ~ spl0_137
| ~ spl0_154 ),
inference(avatar_split_clause,[],[f1202,f1101,f913,f5142]) ).
fof(f5142,plain,
( spl0_438
<=> ! [X6,X7] :
( ~ subclass(universal_class,singleton(X6))
| ~ member(X7,universal_class)
| sum_class(X7) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_438])]) ).
fof(f1202,plain,
( ! [X6,X7] :
( ~ subclass(universal_class,singleton(X6))
| ~ member(X7,universal_class)
| sum_class(X7) = X6 )
| ~ spl0_137
| ~ spl0_154 ),
inference(resolution,[],[f1102,f914]) ).
fof(f5140,plain,
( spl0_437
| ~ spl0_73
| ~ spl0_147 ),
inference(avatar_split_clause,[],[f1057,f1022,f489,f5138]) ).
fof(f5138,plain,
( spl0_437
<=> ! [X6,X8,X7] :
( ~ member(singleton(singleton(singleton(X6))),cross_product(X7,X8))
| member(X6,X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_437])]) ).
fof(f1057,plain,
( ! [X8,X6,X7] :
( ~ member(singleton(singleton(singleton(X6))),cross_product(X7,X8))
| member(X6,X8) )
| ~ spl0_73
| ~ spl0_147 ),
inference(superposition,[],[f490,f1023]) ).
fof(f5136,plain,
( spl0_436
| ~ spl0_68
| ~ spl0_147 ),
inference(avatar_split_clause,[],[f1055,f1022,f429,f5134]) ).
fof(f5134,plain,
( spl0_436
<=> ! [X2] :
( ~ member(singleton(singleton(singleton(X2))),domain_relation)
| domain_of(singleton(X2)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_436])]) ).
fof(f429,plain,
( spl0_68
<=> ! [X0,X1] :
( domain_of(X0) = X1
| ~ member(ordered_pair(X0,X1),domain_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f1055,plain,
( ! [X2] :
( ~ member(singleton(singleton(singleton(X2))),domain_relation)
| domain_of(singleton(X2)) = X2 )
| ~ spl0_68
| ~ spl0_147 ),
inference(superposition,[],[f430,f1023]) ).
fof(f430,plain,
( ! [X0,X1] :
( ~ member(ordered_pair(X0,X1),domain_relation)
| domain_of(X0) = X1 )
| ~ spl0_68 ),
inference(avatar_component_clause,[],[f429]) ).
fof(f5132,plain,
( spl0_435
| ~ spl0_65
| ~ spl0_147 ),
inference(avatar_split_clause,[],[f1054,f1022,f417,f5130]) ).
fof(f5130,plain,
( spl0_435
<=> ! [X1] :
( ~ member(singleton(singleton(singleton(X1))),successor_relation)
| successor(singleton(X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_435])]) ).
fof(f1054,plain,
( ! [X1] :
( ~ member(singleton(singleton(singleton(X1))),successor_relation)
| successor(singleton(X1)) = X1 )
| ~ spl0_65
| ~ spl0_147 ),
inference(superposition,[],[f418,f1023]) ).
fof(f5128,plain,
( spl0_434
| ~ spl0_138
| ~ spl0_146 ),
inference(avatar_split_clause,[],[f1049,f1018,f941,f5126]) ).
fof(f5126,plain,
( spl0_434
<=> ! [X5,X4,X7,X6,X8] :
( member(unordered_pair(X4,X5),X6)
| ~ subclass(universal_class,restrict(X6,X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_434])]) ).
fof(f1049,plain,
( ! [X8,X6,X7,X4,X5] :
( member(unordered_pair(X4,X5),X6)
| ~ subclass(universal_class,restrict(X6,X7,X8)) )
| ~ spl0_138
| ~ spl0_146 ),
inference(resolution,[],[f1019,f942]) ).
fof(f5123,plain,
( ~ spl0_432
| spl0_433
| ~ spl0_135
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1038,f1010,f905,f5120,f5116]) ).
fof(f5116,plain,
( spl0_432
<=> member(regular(complement(inverse(subset_relation))),identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_432])]) ).
fof(f5120,plain,
( spl0_433
<=> null_class = complement(inverse(subset_relation)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_433])]) ).
fof(f1038,plain,
( null_class = complement(inverse(subset_relation))
| ~ member(regular(complement(inverse(subset_relation))),identity_relation)
| ~ spl0_135
| ~ spl0_144 ),
inference(resolution,[],[f1011,f906]) ).
fof(f5114,plain,
( spl0_431
| ~ spl0_61
| ~ spl0_143 ),
inference(avatar_split_clause,[],[f1003,f961,f401,f5112]) ).
fof(f5112,plain,
( spl0_431
<=> ! [X2,X1] :
( ~ member(X1,subset_relation)
| ~ subclass(cross_product(universal_class,universal_class),X2)
| member(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_431])]) ).
fof(f1003,plain,
( ! [X2,X1] :
( ~ member(X1,subset_relation)
| ~ subclass(cross_product(universal_class,universal_class),X2)
| member(X1,X2) )
| ~ spl0_61
| ~ spl0_143 ),
inference(resolution,[],[f962,f402]) ).
fof(f5110,plain,
( spl0_430
| ~ spl0_39
| ~ spl0_141 ),
inference(avatar_split_clause,[],[f997,f953,f288,f5108]) ).
fof(f5108,plain,
( spl0_430
<=> ! [X0,X1] :
( member(not_subclass_element(cantor(X0),X1),domain_of(X0))
| subclass(cantor(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_430])]) ).
fof(f997,plain,
( ! [X0,X1] :
( member(not_subclass_element(cantor(X0),X1),domain_of(X0))
| subclass(cantor(X0),X1) )
| ~ spl0_39
| ~ spl0_141 ),
inference(resolution,[],[f954,f289]) ).
fof(f5076,plain,
( ~ spl0_4
| ~ spl0_428
| spl0_429
| ~ spl0_29
| ~ spl0_140 ),
inference(avatar_split_clause,[],[f994,f949,f243,f5073,f5069,f134]) ).
fof(f134,plain,
( spl0_4
<=> inductive(omega) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f5069,plain,
( spl0_428
<=> inductive(image(successor_relation,omega)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_428])]) ).
fof(f5073,plain,
( spl0_429
<=> omega = image(successor_relation,omega) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_429])]) ).
fof(f243,plain,
( spl0_29
<=> ! [X0] :
( ~ inductive(X0)
| subclass(image(successor_relation,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f949,plain,
( spl0_140
<=> ! [X7] :
( ~ subclass(X7,omega)
| omega = X7
| ~ inductive(X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f994,plain,
( omega = image(successor_relation,omega)
| ~ inductive(image(successor_relation,omega))
| ~ inductive(omega)
| ~ spl0_29
| ~ spl0_140 ),
inference(resolution,[],[f950,f244]) ).
fof(f244,plain,
( ! [X0] :
( subclass(image(successor_relation,X0),X0)
| ~ inductive(X0) )
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f243]) ).
fof(f950,plain,
( ! [X7] :
( ~ subclass(X7,omega)
| omega = X7
| ~ inductive(X7) )
| ~ spl0_140 ),
inference(avatar_component_clause,[],[f949]) ).
fof(f5067,plain,
( spl0_427
| ~ spl0_61
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f964,f941,f401,f5065]) ).
fof(f5065,plain,
( spl0_427
<=> ! [X2,X0,X1,X3] :
( ~ subclass(universal_class,X0)
| ~ subclass(X0,X1)
| member(unordered_pair(X2,X3),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_427])]) ).
fof(f964,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(universal_class,X0)
| ~ subclass(X0,X1)
| member(unordered_pair(X2,X3),X1) )
| ~ spl0_61
| ~ spl0_138 ),
inference(resolution,[],[f942,f402]) ).
fof(f5062,plain,
( ~ spl0_425
| spl0_326
| spl0_426
| ~ spl0_89
| ~ spl0_132 ),
inference(avatar_split_clause,[],[f895,f883,f586,f5059,f3785,f5055]) ).
fof(f5055,plain,
( spl0_425
<=> member(singleton_relation,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_425])]) ).
fof(f5059,plain,
( spl0_426
<=> member(apply(choice,singleton_relation),element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_426])]) ).
fof(f895,plain,
( member(apply(choice,singleton_relation),element_relation)
| null_class = singleton_relation
| ~ member(singleton_relation,universal_class)
| ~ spl0_89
| ~ spl0_132 ),
inference(resolution,[],[f884,f587]) ).
fof(f5052,plain,
( ~ spl0_423
| spl0_324
| spl0_424
| ~ spl0_60
| ~ spl0_89 ),
inference(avatar_split_clause,[],[f868,f586,f388,f5049,f3765,f5045]) ).
fof(f5045,plain,
( spl0_423
<=> member(identity_relation,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_423])]) ).
fof(f3765,plain,
( spl0_324
<=> null_class = identity_relation ),
introduced(avatar_definition,[new_symbols(naming,[spl0_324])]) ).
fof(f5049,plain,
( spl0_424
<=> member(apply(choice,identity_relation),subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_424])]) ).
fof(f868,plain,
( member(apply(choice,identity_relation),subset_relation)
| null_class = identity_relation
| ~ member(identity_relation,universal_class)
| ~ spl0_60
| ~ spl0_89 ),
inference(resolution,[],[f389,f587]) ).
fof(f5043,plain,
( spl0_422
| ~ spl0_3
| ~ spl0_279 ),
inference(avatar_split_clause,[],[f3183,f3075,f129,f5040]) ).
fof(f3075,plain,
( spl0_279
<=> ! [X221,X222] :
( ~ member(X221,X222)
| ordered_pair(x,X221) = ordered_pair(first(ordered_pair(x,X221)),second(ordered_pair(x,X221))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).
fof(f3183,plain,
( ordered_pair(x,x) = ordered_pair(first(ordered_pair(x,x)),second(ordered_pair(x,x)))
| ~ spl0_3
| ~ spl0_279 ),
inference(resolution,[],[f3076,f131]) ).
fof(f3076,plain,
( ! [X222,X221] :
( ~ member(X221,X222)
| ordered_pair(x,X221) = ordered_pair(first(ordered_pair(x,X221)),second(ordered_pair(x,X221))) )
| ~ spl0_279 ),
inference(avatar_component_clause,[],[f3075]) ).
fof(f5038,plain,
( spl0_421
| ~ spl0_52
| ~ spl0_75 ),
inference(avatar_split_clause,[],[f553,f497,f340,f5036]) ).
fof(f5036,plain,
( spl0_421
<=> ! [X6,X5] :
( ~ inductive(union(X5,X6))
| ~ member(null_class,intersection(complement(X5),complement(X6))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_421])]) ).
fof(f553,plain,
( ! [X6,X5] :
( ~ inductive(union(X5,X6))
| ~ member(null_class,intersection(complement(X5),complement(X6))) )
| ~ spl0_52
| ~ spl0_75 ),
inference(superposition,[],[f341,f498]) ).
fof(f4761,plain,
( ~ spl0_214
| ~ spl0_143
| spl0_246 ),
inference(avatar_split_clause,[],[f4330,f2239,f961,f1896]) ).
fof(f1896,plain,
( spl0_214
<=> member(null_class,subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).
fof(f2239,plain,
( spl0_246
<=> member(null_class,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).
fof(f4330,plain,
( ~ member(null_class,subset_relation)
| ~ spl0_143
| spl0_246 ),
inference(resolution,[],[f2241,f962]) ).
fof(f2241,plain,
( ~ member(null_class,cross_product(universal_class,universal_class))
| spl0_246 ),
inference(avatar_component_clause,[],[f2239]) ).
fof(f4758,plain,
( spl0_420
| ~ spl0_73
| ~ spl0_186 ),
inference(avatar_split_clause,[],[f3951,f1340,f489,f4756]) ).
fof(f4756,plain,
( spl0_420
<=> ! [X2,X3] :
( ~ member(null_class,cross_product(X2,X3))
| member(second(null_class),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_420])]) ).
fof(f1340,plain,
( spl0_186
<=> null_class = ordered_pair(first(null_class),second(null_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).
fof(f3951,plain,
( ! [X2,X3] :
( ~ member(null_class,cross_product(X2,X3))
| member(second(null_class),X3) )
| ~ spl0_73
| ~ spl0_186 ),
inference(superposition,[],[f490,f1342]) ).
fof(f1342,plain,
( null_class = ordered_pair(first(null_class),second(null_class))
| ~ spl0_186 ),
inference(avatar_component_clause,[],[f1340]) ).
fof(f4754,plain,
( ~ spl0_214
| ~ spl0_143
| spl0_246 ),
inference(avatar_split_clause,[],[f4330,f2239,f961,f1896]) ).
fof(f4749,plain,
( spl0_214
| ~ spl0_60
| ~ spl0_400 ),
inference(avatar_split_clause,[],[f4618,f4609,f388,f1896]) ).
fof(f4609,plain,
( spl0_400
<=> member(null_class,identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_400])]) ).
fof(f4618,plain,
( member(null_class,subset_relation)
| ~ spl0_60
| ~ spl0_400 ),
inference(resolution,[],[f4611,f389]) ).
fof(f4611,plain,
( member(null_class,identity_relation)
| ~ spl0_400 ),
inference(avatar_component_clause,[],[f4609]) ).
fof(f4696,plain,
( spl0_419
| ~ spl0_6
| ~ spl0_271 ),
inference(avatar_split_clause,[],[f2863,f2842,f144,f4694]) ).
fof(f144,plain,
( spl0_6
<=> ! [X0] : subclass(X0,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f2842,plain,
( spl0_271
<=> ! [X4,X0,X3,X2,X1] :
( ~ member(ordered_pair(X0,X1),compose(X2,X3))
| ~ subclass(image(X2,image(X3,singleton(X0))),X4)
| member(X1,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).
fof(f2863,plain,
( ! [X10,X8,X9,X7] :
( ~ member(ordered_pair(X7,X8),compose(X9,X10))
| member(X8,universal_class) )
| ~ spl0_6
| ~ spl0_271 ),
inference(resolution,[],[f2843,f145]) ).
fof(f145,plain,
( ! [X0] : subclass(X0,universal_class)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f144]) ).
fof(f2843,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ subclass(image(X2,image(X3,singleton(X0))),X4)
| ~ member(ordered_pair(X0,X1),compose(X2,X3))
| member(X1,X4) )
| ~ spl0_271 ),
inference(avatar_component_clause,[],[f2842]) ).
fof(f4692,plain,
( spl0_418
| ~ spl0_134
| ~ spl0_263 ),
inference(avatar_split_clause,[],[f2764,f2603,f901,f4690]) ).
fof(f4690,plain,
( spl0_418
<=> ! [X7] :
( ~ inductive(cantor(restrict(element_relation,universal_class,X7)))
| member(null_class,sum_class(X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_418])]) ).
fof(f2764,plain,
( ! [X7] :
( ~ inductive(cantor(restrict(element_relation,universal_class,X7)))
| member(null_class,sum_class(X7)) )
| ~ spl0_134
| ~ spl0_263 ),
inference(superposition,[],[f902,f2604]) ).
fof(f4688,plain,
( spl0_417
| ~ spl0_134
| ~ spl0_262 ),
inference(avatar_split_clause,[],[f2748,f2599,f901,f4686]) ).
fof(f4686,plain,
( spl0_417
<=> ! [X7] :
( ~ inductive(cantor(flip(cross_product(X7,universal_class))))
| member(null_class,inverse(X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_417])]) ).
fof(f2748,plain,
( ! [X7] :
( ~ inductive(cantor(flip(cross_product(X7,universal_class))))
| member(null_class,inverse(X7)) )
| ~ spl0_134
| ~ spl0_262 ),
inference(superposition,[],[f902,f2600]) ).
fof(f4684,plain,
( spl0_416
| ~ spl0_39
| ~ spl0_255 ),
inference(avatar_split_clause,[],[f2539,f2508,f288,f4682]) ).
fof(f4682,plain,
( spl0_416
<=> ! [X0] :
( member(not_subclass_element(universal_class,complement(X0)),X0)
| subclass(universal_class,complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_416])]) ).
fof(f2539,plain,
( ! [X0] :
( member(not_subclass_element(universal_class,complement(X0)),X0)
| subclass(universal_class,complement(X0)) )
| ~ spl0_39
| ~ spl0_255 ),
inference(duplicate_literal_removal,[],[f2519]) ).
fof(f2519,plain,
( ! [X0] :
( member(not_subclass_element(universal_class,complement(X0)),X0)
| subclass(universal_class,complement(X0))
| subclass(universal_class,complement(X0)) )
| ~ spl0_39
| ~ spl0_255 ),
inference(resolution,[],[f2509,f289]) ).
fof(f4680,plain,
( spl0_415
| ~ spl0_45
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f1980,f1728,f312,f4678]) ).
fof(f4678,plain,
( spl0_415
<=> ! [X2,X3] :
( ~ member(X3,symmetric_difference(X2,singleton(X2)))
| member(X3,successor(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_415])]) ).
fof(f1980,plain,
( ! [X2,X3] :
( ~ member(X3,symmetric_difference(X2,singleton(X2)))
| member(X3,successor(X2)) )
| ~ spl0_45
| ~ spl0_212 ),
inference(superposition,[],[f313,f1729]) ).
fof(f4676,plain,
( ~ spl0_414
| ~ spl0_6
| ~ spl0_10
| ~ spl0_350
| ~ spl0_362 ),
inference(avatar_split_clause,[],[f4400,f4188,f3997,f161,f144,f4673]) ).
fof(f4673,plain,
( spl0_414
<=> subclass(universal_class,null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_414])]) ).
fof(f161,plain,
( spl0_10
<=> ! [X0,X1] : member(unordered_pair(X0,X1),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f3997,plain,
( spl0_350
<=> ! [X0] :
( ~ subclass(complement(X0),X0)
| complement(X0) = null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_350])]) ).
fof(f4188,plain,
( spl0_362
<=> ! [X24,X25,X23] :
( ~ subclass(universal_class,complement(X23))
| ~ member(unordered_pair(X24,X25),X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_362])]) ).
fof(f4400,plain,
( ~ subclass(universal_class,null_class)
| ~ spl0_6
| ~ spl0_10
| ~ spl0_350
| ~ spl0_362 ),
inference(forward_demodulation,[],[f4374,f4132]) ).
fof(f4132,plain,
( null_class = complement(universal_class)
| ~ spl0_6
| ~ spl0_350 ),
inference(resolution,[],[f3998,f145]) ).
fof(f3998,plain,
( ! [X0] :
( ~ subclass(complement(X0),X0)
| complement(X0) = null_class )
| ~ spl0_350 ),
inference(avatar_component_clause,[],[f3997]) ).
fof(f4374,plain,
( ~ subclass(universal_class,complement(universal_class))
| ~ spl0_10
| ~ spl0_362 ),
inference(resolution,[],[f4189,f162]) ).
fof(f162,plain,
( ! [X0,X1] : member(unordered_pair(X0,X1),universal_class)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f161]) ).
fof(f4189,plain,
( ! [X24,X25,X23] :
( ~ member(unordered_pair(X24,X25),X23)
| ~ subclass(universal_class,complement(X23)) )
| ~ spl0_362 ),
inference(avatar_component_clause,[],[f4188]) ).
fof(f4671,plain,
( spl0_412
| ~ spl0_413
| ~ spl0_43
| ~ spl0_193 ),
inference(avatar_split_clause,[],[f1603,f1514,f304,f4668,f4665]) ).
fof(f4665,plain,
( spl0_412
<=> ! [X7] :
( ~ member(X7,universal_class)
| member(X7,domain_of(X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_412])]) ).
fof(f4668,plain,
( spl0_413
<=> subclass(domain_relation,element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_413])]) ).
fof(f304,plain,
( spl0_43
<=> ! [X0,X1] :
( member(X0,X1)
| ~ member(ordered_pair(X0,X1),element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f1603,plain,
( ! [X7] :
( ~ subclass(domain_relation,element_relation)
| ~ member(X7,universal_class)
| member(X7,domain_of(X7)) )
| ~ spl0_43
| ~ spl0_193 ),
inference(resolution,[],[f1515,f305]) ).
fof(f305,plain,
( ! [X0,X1] :
( ~ member(ordered_pair(X0,X1),element_relation)
| member(X0,X1) )
| ~ spl0_43 ),
inference(avatar_component_clause,[],[f304]) ).
fof(f4663,plain,
( spl0_411
| ~ spl0_112
| ~ spl0_188 ),
inference(avatar_split_clause,[],[f1548,f1494,f748,f4661]) ).
fof(f4661,plain,
( spl0_411
<=> ! [X10] :
( member(not_subclass_element(subset_relation,X10),cross_product(universal_class,universal_class))
| subclass(subset_relation,X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_411])]) ).
fof(f748,plain,
( spl0_112
<=> subset_relation = intersection(cross_product(universal_class,universal_class),restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f1548,plain,
( ! [X10] :
( member(not_subclass_element(subset_relation,X10),cross_product(universal_class,universal_class))
| subclass(subset_relation,X10) )
| ~ spl0_112
| ~ spl0_188 ),
inference(superposition,[],[f1495,f750]) ).
fof(f750,plain,
( subset_relation = intersection(cross_product(universal_class,universal_class),restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class))
| ~ spl0_112 ),
inference(avatar_component_clause,[],[f748]) ).
fof(f4659,plain,
( spl0_410
| ~ spl0_20
| ~ spl0_187 ),
inference(avatar_split_clause,[],[f1491,f1345,f204,f4657]) ).
fof(f4657,plain,
( spl0_410
<=> ! [X17] :
( member(X17,complement(identity_relation))
| ~ member(X17,symmetric_difference(inverse(subset_relation),subset_relation)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_410])]) ).
fof(f1491,plain,
( ! [X17] :
( member(X17,complement(identity_relation))
| ~ member(X17,symmetric_difference(inverse(subset_relation),subset_relation)) )
| ~ spl0_20
| ~ spl0_187 ),
inference(superposition,[],[f1346,f206]) ).
fof(f4655,plain,
( spl0_409
| ~ spl0_27
| ~ spl0_187 ),
inference(avatar_split_clause,[],[f1479,f1345,f235,f4653]) ).
fof(f4653,plain,
( spl0_409
<=> ! [X2,X0,X1] :
( ~ member(X0,symmetric_difference(X1,X2))
| ~ member(X0,intersection(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_409])]) ).
fof(f1479,plain,
( ! [X2,X0,X1] :
( ~ member(X0,symmetric_difference(X1,X2))
| ~ member(X0,intersection(X1,X2)) )
| ~ spl0_27
| ~ spl0_187 ),
inference(resolution,[],[f1346,f236]) ).
fof(f4651,plain,
( spl0_408
| ~ spl0_132
| ~ spl0_156 ),
inference(avatar_split_clause,[],[f1246,f1109,f883,f4649]) ).
fof(f4649,plain,
( spl0_408
<=> ! [X37] :
( ~ subclass(X37,singleton_relation)
| null_class = X37
| member(regular(X37),element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_408])]) ).
fof(f1246,plain,
( ! [X37] :
( ~ subclass(X37,singleton_relation)
| null_class = X37
| member(regular(X37),element_relation) )
| ~ spl0_132
| ~ spl0_156 ),
inference(resolution,[],[f1110,f884]) ).
fof(f4647,plain,
( spl0_407
| ~ spl0_60
| ~ spl0_156 ),
inference(avatar_split_clause,[],[f1244,f1109,f388,f4645]) ).
fof(f4645,plain,
( spl0_407
<=> ! [X34] :
( ~ subclass(X34,identity_relation)
| null_class = X34
| member(regular(X34),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_407])]) ).
fof(f1244,plain,
( ! [X34] :
( ~ subclass(X34,identity_relation)
| null_class = X34
| member(regular(X34),subset_relation) )
| ~ spl0_60
| ~ spl0_156 ),
inference(resolution,[],[f1110,f389]) ).
fof(f4643,plain,
( spl0_406
| ~ spl0_43
| ~ spl0_147 ),
inference(avatar_split_clause,[],[f1053,f1022,f304,f4641]) ).
fof(f4641,plain,
( spl0_406
<=> ! [X0] :
( ~ member(singleton(singleton(singleton(X0))),element_relation)
| member(singleton(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_406])]) ).
fof(f1053,plain,
( ! [X0] :
( ~ member(singleton(singleton(singleton(X0))),element_relation)
| member(singleton(X0),X0) )
| ~ spl0_43
| ~ spl0_147 ),
inference(superposition,[],[f305,f1023]) ).
fof(f4639,plain,
( spl0_405
| ~ spl0_95
| ~ spl0_143 ),
inference(avatar_split_clause,[],[f1002,f961,f649,f4637]) ).
fof(f4637,plain,
( spl0_405
<=> ! [X0] :
( ~ member(X0,subset_relation)
| ordered_pair(first(X0),second(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_405])]) ).
fof(f649,plain,
( spl0_95
<=> ! [X4,X0,X1] :
( ~ member(X4,cross_product(X0,X1))
| ordered_pair(first(X4),second(X4)) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f1002,plain,
( ! [X0] :
( ~ member(X0,subset_relation)
| ordered_pair(first(X0),second(X0)) = X0 )
| ~ spl0_95
| ~ spl0_143 ),
inference(resolution,[],[f962,f650]) ).
fof(f650,plain,
( ! [X0,X1,X4] :
( ~ member(X4,cross_product(X0,X1))
| ordered_pair(first(X4),second(X4)) = X4 )
| ~ spl0_95 ),
inference(avatar_component_clause,[],[f649]) ).
fof(f4635,plain,
( spl0_404
| ~ spl0_34
| ~ spl0_141 ),
inference(avatar_split_clause,[],[f1000,f953,f263,f4633]) ).
fof(f4633,plain,
( spl0_404
<=> ! [X6] :
( member(regular(cantor(X6)),domain_of(X6))
| null_class = cantor(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_404])]) ).
fof(f1000,plain,
( ! [X6] :
( member(regular(cantor(X6)),domain_of(X6))
| null_class = cantor(X6) )
| ~ spl0_34
| ~ spl0_141 ),
inference(resolution,[],[f954,f264]) ).
fof(f4631,plain,
( ~ spl0_403
| ~ spl0_13
| spl0_373 ),
inference(avatar_split_clause,[],[f4287,f4267,f175,f4628]) ).
fof(f4628,plain,
( spl0_403
<=> inductive(complement(identity_relation)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_403])]) ).
fof(f4267,plain,
( spl0_373
<=> member(null_class,complement(identity_relation)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_373])]) ).
fof(f4287,plain,
( ~ inductive(complement(identity_relation))
| ~ spl0_13
| spl0_373 ),
inference(resolution,[],[f4268,f176]) ).
fof(f4268,plain,
( ~ member(null_class,complement(identity_relation))
| spl0_373 ),
inference(avatar_component_clause,[],[f4267]) ).
fof(f4626,plain,
( spl0_402
| ~ spl0_138
| ~ spl0_141 ),
inference(avatar_split_clause,[],[f998,f953,f941,f4624]) ).
fof(f4624,plain,
( spl0_402
<=> ! [X4,X2,X3] :
( member(unordered_pair(X2,X3),domain_of(X4))
| ~ subclass(universal_class,cantor(X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_402])]) ).
fof(f998,plain,
( ! [X2,X3,X4] :
( member(unordered_pair(X2,X3),domain_of(X4))
| ~ subclass(universal_class,cantor(X4)) )
| ~ spl0_138
| ~ spl0_141 ),
inference(resolution,[],[f954,f942]) ).
fof(f4617,plain,
( spl0_401
| spl0_400
| ~ spl0_51
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f988,f945,f336,f4609,f4615]) ).
fof(f4615,plain,
( spl0_401
<=> ! [X11] :
( ~ inductive(compose(X11,inverse(X11)))
| ~ single_valued_class(X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_401])]) ).
fof(f336,plain,
( spl0_51
<=> ! [X0] :
( ~ single_valued_class(X0)
| subclass(compose(X0,inverse(X0)),identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f988,plain,
( ! [X11] :
( member(null_class,identity_relation)
| ~ inductive(compose(X11,inverse(X11)))
| ~ single_valued_class(X11) )
| ~ spl0_51
| ~ spl0_139 ),
inference(resolution,[],[f946,f337]) ).
fof(f337,plain,
( ! [X0] :
( subclass(compose(X0,inverse(X0)),identity_relation)
| ~ single_valued_class(X0) )
| ~ spl0_51 ),
inference(avatar_component_clause,[],[f336]) ).
fof(f4612,plain,
( spl0_399
| spl0_400
| ~ spl0_54
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f987,f945,f348,f4609,f4606]) ).
fof(f4606,plain,
( spl0_399
<=> ! [X10] :
( ~ inductive(compose(X10,inverse(X10)))
| ~ function(X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_399])]) ).
fof(f348,plain,
( spl0_54
<=> ! [X8] :
( ~ function(X8)
| subclass(compose(X8,inverse(X8)),identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f987,plain,
( ! [X10] :
( member(null_class,identity_relation)
| ~ inductive(compose(X10,inverse(X10)))
| ~ function(X10) )
| ~ spl0_54
| ~ spl0_139 ),
inference(resolution,[],[f946,f349]) ).
fof(f349,plain,
( ! [X8] :
( subclass(compose(X8,inverse(X8)),identity_relation)
| ~ function(X8) )
| ~ spl0_54 ),
inference(avatar_component_clause,[],[f348]) ).
fof(f4604,plain,
( spl0_398
| ~ spl0_56
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f982,f945,f356,f4602]) ).
fof(f4602,plain,
( spl0_398
<=> ! [X5] :
( member(null_class,domain_of(domain_of(X5)))
| ~ inductive(range_of(X5))
| ~ operation(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_398])]) ).
fof(f982,plain,
( ! [X5] :
( member(null_class,domain_of(domain_of(X5)))
| ~ inductive(range_of(X5))
| ~ operation(X5) )
| ~ spl0_56
| ~ spl0_139 ),
inference(resolution,[],[f946,f357]) ).
fof(f4595,plain,
( spl0_397
| spl0_396
| ~ spl0_47
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f981,f945,f320,f4587,f4593]) ).
fof(f4593,plain,
( spl0_397
<=> ! [X4] : ~ inductive(flip(X4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_397])]) ).
fof(f4587,plain,
( spl0_396
<=> member(null_class,cross_product(cross_product(universal_class,universal_class),universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_396])]) ).
fof(f320,plain,
( spl0_47
<=> ! [X0] : subclass(flip(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f981,plain,
( ! [X4] :
( member(null_class,cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ inductive(flip(X4)) )
| ~ spl0_47
| ~ spl0_139 ),
inference(resolution,[],[f946,f321]) ).
fof(f321,plain,
( ! [X0] : subclass(flip(X0),cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ spl0_47 ),
inference(avatar_component_clause,[],[f320]) ).
fof(f4590,plain,
( spl0_395
| spl0_396
| ~ spl0_46
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f980,f945,f316,f4587,f4584]) ).
fof(f4584,plain,
( spl0_395
<=> ! [X3] : ~ inductive(rotate(X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_395])]) ).
fof(f316,plain,
( spl0_46
<=> ! [X0] : subclass(rotate(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f980,plain,
( ! [X3] :
( member(null_class,cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ inductive(rotate(X3)) )
| ~ spl0_46
| ~ spl0_139 ),
inference(resolution,[],[f946,f317]) ).
fof(f317,plain,
( ! [X0] : subclass(rotate(X0),cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ spl0_46 ),
inference(avatar_component_clause,[],[f316]) ).
fof(f4582,plain,
( spl0_394
| ~ spl0_44
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f969,f941,f308,f4580]) ).
fof(f4580,plain,
( spl0_394
<=> ! [X22,X20,X21,X19] :
( ~ subclass(universal_class,intersection(X19,X20))
| member(unordered_pair(X21,X22),X19) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_394])]) ).
fof(f969,plain,
( ! [X21,X19,X22,X20] :
( ~ subclass(universal_class,intersection(X19,X20))
| member(unordered_pair(X21,X22),X19) )
| ~ spl0_44
| ~ spl0_138 ),
inference(resolution,[],[f942,f309]) ).
fof(f4578,plain,
( spl0_393
| ~ spl0_45
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f968,f941,f312,f4576]) ).
fof(f4576,plain,
( spl0_393
<=> ! [X18,X16,X17,X15] :
( ~ subclass(universal_class,intersection(X15,X16))
| member(unordered_pair(X17,X18),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_393])]) ).
fof(f968,plain,
( ! [X18,X16,X17,X15] :
( ~ subclass(universal_class,intersection(X15,X16))
| member(unordered_pair(X17,X18),X16) )
| ~ spl0_45
| ~ spl0_138 ),
inference(resolution,[],[f942,f313]) ).
fof(f4574,plain,
( spl0_392
| ~ spl0_39
| ~ spl0_137 ),
inference(avatar_split_clause,[],[f936,f913,f288,f4572]) ).
fof(f4572,plain,
( spl0_392
<=> ! [X2,X1] :
( not_subclass_element(singleton(X1),X2) = X1
| subclass(singleton(X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_392])]) ).
fof(f936,plain,
( ! [X2,X1] :
( not_subclass_element(singleton(X1),X2) = X1
| subclass(singleton(X1),X2) )
| ~ spl0_39
| ~ spl0_137 ),
inference(resolution,[],[f914,f289]) ).
fof(f4570,plain,
( spl0_391
| ~ spl0_90
| ~ spl0_136 ),
inference(avatar_split_clause,[],[f933,f909,f590,f4568]) ).
fof(f4568,plain,
( spl0_391
<=> ! [X9] :
( ~ inductive(cantor(X9))
| member(null_class,diagonalise(compose(inverse(element_relation),X9))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_391])]) ).
fof(f909,plain,
( spl0_136
<=> ! [X4,X3] :
( member(null_class,X3)
| ~ inductive(intersection(X4,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f933,plain,
( ! [X9] :
( ~ inductive(cantor(X9))
| member(null_class,diagonalise(compose(inverse(element_relation),X9))) )
| ~ spl0_90
| ~ spl0_136 ),
inference(superposition,[],[f910,f591]) ).
fof(f910,plain,
( ! [X3,X4] :
( ~ inductive(intersection(X4,X3))
| member(null_class,X3) )
| ~ spl0_136 ),
inference(avatar_component_clause,[],[f909]) ).
fof(f4566,plain,
( spl0_390
| ~ spl0_40
| ~ spl0_135 ),
inference(avatar_split_clause,[],[f926,f905,f292,f4564]) ).
fof(f4564,plain,
( spl0_390
<=> ! [X2] :
( ~ member(not_subclass_element(X2,inverse(subset_relation)),identity_relation)
| subclass(X2,inverse(subset_relation)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_390])]) ).
fof(f926,plain,
( ! [X2] :
( ~ member(not_subclass_element(X2,inverse(subset_relation)),identity_relation)
| subclass(X2,inverse(subset_relation)) )
| ~ spl0_40
| ~ spl0_135 ),
inference(resolution,[],[f906,f293]) ).
fof(f4562,plain,
( spl0_389
| ~ spl0_61
| ~ spl0_135 ),
inference(avatar_split_clause,[],[f925,f905,f401,f4560]) ).
fof(f4560,plain,
( spl0_389
<=> ! [X0,X1] :
( ~ member(X0,identity_relation)
| ~ subclass(inverse(subset_relation),X1)
| member(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_389])]) ).
fof(f925,plain,
( ! [X0,X1] :
( ~ member(X0,identity_relation)
| ~ subclass(inverse(subset_relation),X1)
| member(X0,X1) )
| ~ spl0_61
| ~ spl0_135 ),
inference(resolution,[],[f906,f402]) ).
fof(f4558,plain,
( spl0_388
| ~ spl0_99
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f922,f901,f668,f4556]) ).
fof(f4556,plain,
( spl0_388
<=> ! [X8,X7] :
( ~ inductive(symmetric_difference(X7,X8))
| member(null_class,complement(intersection(X7,X8))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_388])]) ).
fof(f922,plain,
( ! [X8,X7] :
( ~ inductive(symmetric_difference(X7,X8))
| member(null_class,complement(intersection(X7,X8))) )
| ~ spl0_99
| ~ spl0_134 ),
inference(superposition,[],[f902,f669]) ).
fof(f4554,plain,
( spl0_387
| ~ spl0_77
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f919,f901,f508,f4552]) ).
fof(f4552,plain,
( spl0_387
<=> ! [X6,X4,X5] :
( ~ inductive(restrict(X6,X4,X5))
| member(null_class,cross_product(X4,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_387])]) ).
fof(f919,plain,
( ! [X6,X4,X5] :
( ~ inductive(restrict(X6,X4,X5))
| member(null_class,cross_product(X4,X5)) )
| ~ spl0_77
| ~ spl0_134 ),
inference(superposition,[],[f902,f509]) ).
fof(f4550,plain,
( spl0_386
| ~ spl0_61
| ~ spl0_133 ),
inference(avatar_split_clause,[],[f916,f897,f401,f4548]) ).
fof(f4548,plain,
( spl0_386
<=> ! [X0,X1] :
( ~ member(X0,universal_class)
| ~ subclass(singleton(X0),X1)
| member(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_386])]) ).
fof(f897,plain,
( spl0_133
<=> ! [X0] :
( member(X0,singleton(X0))
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f916,plain,
( ! [X0,X1] :
( ~ member(X0,universal_class)
| ~ subclass(singleton(X0),X1)
| member(X0,X1) )
| ~ spl0_61
| ~ spl0_133 ),
inference(resolution,[],[f898,f402]) ).
fof(f898,plain,
( ! [X0] :
( member(X0,singleton(X0))
| ~ member(X0,universal_class) )
| ~ spl0_133 ),
inference(avatar_component_clause,[],[f897]) ).
fof(f4361,plain,
( ~ spl0_385
| ~ spl0_5
| ~ spl0_363 ),
inference(avatar_split_clause,[],[f4331,f4192,f139,f4358]) ).
fof(f4358,plain,
( spl0_385
<=> inductive(choice) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_385])]) ).
fof(f139,plain,
( spl0_5
<=> function(choice) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f4192,plain,
( spl0_363
<=> ! [X2] :
( ~ inductive(X2)
| ~ function(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_363])]) ).
fof(f4331,plain,
( ~ inductive(choice)
| ~ spl0_5
| ~ spl0_363 ),
inference(resolution,[],[f4193,f141]) ).
fof(f141,plain,
( function(choice)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f139]) ).
fof(f4193,plain,
( ! [X2] :
( ~ function(X2)
| ~ inductive(X2) )
| ~ spl0_363 ),
inference(avatar_component_clause,[],[f4192]) ).
fof(f4328,plain,
( spl0_384
| ~ spl0_72
| ~ spl0_186 ),
inference(avatar_split_clause,[],[f3950,f1340,f485,f4326]) ).
fof(f4326,plain,
( spl0_384
<=> ! [X0,X1] :
( ~ member(null_class,cross_product(X0,X1))
| member(first(null_class),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_384])]) ).
fof(f3950,plain,
( ! [X0,X1] :
( ~ member(null_class,cross_product(X0,X1))
| member(first(null_class),X0) )
| ~ spl0_72
| ~ spl0_186 ),
inference(superposition,[],[f486,f1342]) ).
fof(f4323,plain,
( spl0_382
| ~ spl0_383
| ~ spl0_68
| ~ spl0_186 ),
inference(avatar_split_clause,[],[f3949,f1340,f429,f4320,f4316]) ).
fof(f4316,plain,
( spl0_382
<=> second(null_class) = domain_of(first(null_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_382])]) ).
fof(f4320,plain,
( spl0_383
<=> member(null_class,domain_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_383])]) ).
fof(f3949,plain,
( ~ member(null_class,domain_relation)
| second(null_class) = domain_of(first(null_class))
| ~ spl0_68
| ~ spl0_186 ),
inference(superposition,[],[f430,f1342]) ).
fof(f4313,plain,
( spl0_380
| ~ spl0_381
| ~ spl0_65
| ~ spl0_186 ),
inference(avatar_split_clause,[],[f3948,f1340,f417,f4310,f4306]) ).
fof(f4306,plain,
( spl0_380
<=> second(null_class) = successor(first(null_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_380])]) ).
fof(f4310,plain,
( spl0_381
<=> member(null_class,successor_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_381])]) ).
fof(f3948,plain,
( ~ member(null_class,successor_relation)
| second(null_class) = successor(first(null_class))
| ~ spl0_65
| ~ spl0_186 ),
inference(superposition,[],[f418,f1342]) ).
fof(f4304,plain,
( spl0_379
| ~ spl0_6
| ~ spl0_226 ),
inference(avatar_split_clause,[],[f2101,f2037,f144,f4302]) ).
fof(f4302,plain,
( spl0_379
<=> ! [X2,X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,X2)
| member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_379])]) ).
fof(f2101,plain,
( ! [X2,X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,X2)
| member(X0,universal_class) )
| ~ spl0_6
| ~ spl0_226 ),
inference(resolution,[],[f2038,f145]) ).
fof(f4300,plain,
( spl0_378
| ~ spl0_136
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f1984,f1728,f909,f4298]) ).
fof(f4298,plain,
( spl0_378
<=> ! [X8] :
( ~ inductive(symmetric_difference(X8,singleton(X8)))
| member(null_class,successor(X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_378])]) ).
fof(f1984,plain,
( ! [X8] :
( ~ inductive(symmetric_difference(X8,singleton(X8)))
| member(null_class,successor(X8)) )
| ~ spl0_136
| ~ spl0_212 ),
inference(superposition,[],[f910,f1729]) ).
fof(f4296,plain,
( spl0_377
| ~ spl0_44
| ~ spl0_211 ),
inference(avatar_split_clause,[],[f1967,f1724,f308,f4294]) ).
fof(f4294,plain,
( spl0_377
<=> ! [X0,X1] :
( ~ member(X1,cantor(inverse(X0)))
| member(X1,range_of(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_377])]) ).
fof(f1967,plain,
( ! [X0,X1] :
( ~ member(X1,cantor(inverse(X0)))
| member(X1,range_of(X0)) )
| ~ spl0_44
| ~ spl0_211 ),
inference(superposition,[],[f309,f1725]) ).
fof(f4286,plain,
( spl0_376
| ~ spl0_127
| ~ spl0_370 ),
inference(avatar_split_clause,[],[f4247,f4236,f855,f4283]) ).
fof(f4283,plain,
( spl0_376
<=> member(subset_relation,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_376])]) ).
fof(f855,plain,
( spl0_127
<=> member(null_class,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f4236,plain,
( spl0_370
<=> null_class = subset_relation ),
introduced(avatar_definition,[new_symbols(naming,[spl0_370])]) ).
fof(f4247,plain,
( member(subset_relation,universal_class)
| ~ spl0_127
| ~ spl0_370 ),
inference(superposition,[],[f856,f4238]) ).
fof(f4238,plain,
( null_class = subset_relation
| ~ spl0_370 ),
inference(avatar_component_clause,[],[f4236]) ).
fof(f856,plain,
( member(null_class,universal_class)
| ~ spl0_127 ),
inference(avatar_component_clause,[],[f855]) ).
fof(f4280,plain,
( ~ spl0_375
| ~ spl0_370
| spl0_373 ),
inference(avatar_split_clause,[],[f4275,f4267,f4236,f4277]) ).
fof(f4277,plain,
( spl0_375
<=> member(subset_relation,complement(identity_relation)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_375])]) ).
fof(f4275,plain,
( ~ member(subset_relation,complement(identity_relation))
| ~ spl0_370
| spl0_373 ),
inference(forward_demodulation,[],[f4268,f4238]) ).
fof(f4274,plain,
( spl0_373
| ~ spl0_374
| ~ spl0_134
| ~ spl0_195 ),
inference(avatar_split_clause,[],[f1664,f1522,f901,f4271,f4267]) ).
fof(f4271,plain,
( spl0_374
<=> inductive(symmetric_difference(inverse(subset_relation),subset_relation)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_374])]) ).
fof(f1664,plain,
( ~ inductive(symmetric_difference(inverse(subset_relation),subset_relation))
| member(null_class,complement(identity_relation))
| ~ spl0_134
| ~ spl0_195 ),
inference(superposition,[],[f902,f1524]) ).
fof(f4265,plain,
( spl0_372
| ~ spl0_20
| ~ spl0_188 ),
inference(avatar_split_clause,[],[f1552,f1494,f204,f4263]) ).
fof(f4263,plain,
( spl0_372
<=> ! [X17] :
( member(not_subclass_element(identity_relation,X17),inverse(subset_relation))
| subclass(identity_relation,X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_372])]) ).
fof(f1552,plain,
( ! [X17] :
( member(not_subclass_element(identity_relation,X17),inverse(subset_relation))
| subclass(identity_relation,X17) )
| ~ spl0_20
| ~ spl0_188 ),
inference(superposition,[],[f1495,f206]) ).
fof(f4243,plain,
( spl0_370
| spl0_371
| ~ spl0_112
| ~ spl0_171 ),
inference(avatar_split_clause,[],[f1368,f1280,f748,f4240,f4236]) ).
fof(f4240,plain,
( spl0_371
<=> member(regular(subset_relation),cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_371])]) ).
fof(f1368,plain,
( member(regular(subset_relation),cross_product(universal_class,universal_class))
| null_class = subset_relation
| ~ spl0_112
| ~ spl0_171 ),
inference(superposition,[],[f1281,f750]) ).
fof(f4234,plain,
( spl0_369
| ~ spl0_27
| ~ spl0_166 ),
inference(avatar_split_clause,[],[f1252,f1153,f235,f4232]) ).
fof(f4232,plain,
( spl0_369
<=> ! [X0] :
( ~ member(X0,singleton_relation)
| ~ member(X0,compose(element_relation,complement(identity_relation))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_369])]) ).
fof(f1252,plain,
( ! [X0] :
( ~ member(X0,singleton_relation)
| ~ member(X0,compose(element_relation,complement(identity_relation))) )
| ~ spl0_27
| ~ spl0_166 ),
inference(resolution,[],[f1154,f236]) ).
fof(f4230,plain,
( spl0_368
| ~ spl0_13
| ~ spl0_152 ),
inference(avatar_split_clause,[],[f1193,f1093,f175,f4228]) ).
fof(f4228,plain,
( spl0_368
<=> ! [X10] :
( ~ member(null_class,diagonalise(X10))
| ~ inductive(domain_of(intersection(X10,identity_relation))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_368])]) ).
fof(f1193,plain,
( ! [X10] :
( ~ member(null_class,diagonalise(X10))
| ~ inductive(domain_of(intersection(X10,identity_relation))) )
| ~ spl0_13
| ~ spl0_152 ),
inference(resolution,[],[f1094,f176]) ).
fof(f4226,plain,
( spl0_367
| ~ spl0_13
| ~ spl0_151 ),
inference(avatar_split_clause,[],[f1183,f1089,f175,f4224]) ).
fof(f4224,plain,
( spl0_367
<=> ! [X5] :
( ~ member(null_class,power_class(X5))
| ~ inductive(image(element_relation,complement(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_367])]) ).
fof(f1183,plain,
( ! [X5] :
( ~ member(null_class,power_class(X5))
| ~ inductive(image(element_relation,complement(X5))) )
| ~ spl0_13
| ~ spl0_151 ),
inference(resolution,[],[f1090,f176]) ).
fof(f4217,plain,
( ~ spl0_366
| spl0_365
| ~ spl0_37
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f992,f945,f276,f4208,f4214]) ).
fof(f4214,plain,
( spl0_366
<=> inductive(application_function) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_366])]) ).
fof(f4208,plain,
( spl0_365
<=> member(null_class,cross_product(universal_class,cross_product(universal_class,universal_class))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_365])]) ).
fof(f276,plain,
( spl0_37
<=> subclass(application_function,cross_product(universal_class,cross_product(universal_class,universal_class))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f992,plain,
( member(null_class,cross_product(universal_class,cross_product(universal_class,universal_class)))
| ~ inductive(application_function)
| ~ spl0_37
| ~ spl0_139 ),
inference(resolution,[],[f946,f278]) ).
fof(f278,plain,
( subclass(application_function,cross_product(universal_class,cross_product(universal_class,universal_class)))
| ~ spl0_37 ),
inference(avatar_component_clause,[],[f276]) ).
fof(f4211,plain,
( ~ spl0_364
| spl0_365
| ~ spl0_36
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f990,f945,f271,f4208,f4204]) ).
fof(f4204,plain,
( spl0_364
<=> inductive(composition_function) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_364])]) ).
fof(f271,plain,
( spl0_36
<=> subclass(composition_function,cross_product(universal_class,cross_product(universal_class,universal_class))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f990,plain,
( member(null_class,cross_product(universal_class,cross_product(universal_class,universal_class)))
| ~ inductive(composition_function)
| ~ spl0_36
| ~ spl0_139 ),
inference(resolution,[],[f946,f273]) ).
fof(f273,plain,
( subclass(composition_function,cross_product(universal_class,cross_product(universal_class,universal_class)))
| ~ spl0_36 ),
inference(avatar_component_clause,[],[f271]) ).
fof(f4194,plain,
( spl0_363
| spl0_246
| ~ spl0_33
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f978,f945,f259,f2239,f4192]) ).
fof(f978,plain,
( ! [X2] :
( member(null_class,cross_product(universal_class,universal_class))
| ~ inductive(X2)
| ~ function(X2) )
| ~ spl0_33
| ~ spl0_139 ),
inference(resolution,[],[f946,f260]) ).
fof(f4190,plain,
( spl0_362
| ~ spl0_27
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f970,f941,f235,f4188]) ).
fof(f970,plain,
( ! [X24,X25,X23] :
( ~ subclass(universal_class,complement(X23))
| ~ member(unordered_pair(X24,X25),X23) )
| ~ spl0_27
| ~ spl0_138 ),
inference(resolution,[],[f942,f236]) ).
fof(f4186,plain,
( spl0_361
| ~ spl0_137
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f966,f941,f913,f4184]) ).
fof(f4184,plain,
( spl0_361
<=> ! [X9,X8,X10] :
( ~ subclass(universal_class,singleton(X8))
| unordered_pair(X9,X10) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_361])]) ).
fof(f966,plain,
( ! [X10,X8,X9] :
( ~ subclass(universal_class,singleton(X8))
| unordered_pair(X9,X10) = X8 )
| ~ spl0_137
| ~ spl0_138 ),
inference(resolution,[],[f942,f914]) ).
fof(f4182,plain,
( spl0_360
| ~ spl0_6
| ~ spl0_350
| ~ spl0_353 ),
inference(avatar_split_clause,[],[f4162,f4031,f3997,f144,f4180]) ).
fof(f4180,plain,
( spl0_360
<=> ! [X0] : subclass(null_class,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_360])]) ).
fof(f4031,plain,
( spl0_353
<=> ! [X2,X3] :
( ~ subclass(complement(X2),X2)
| subclass(complement(X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_353])]) ).
fof(f4162,plain,
( ! [X0] : subclass(null_class,X0)
| ~ spl0_6
| ~ spl0_350
| ~ spl0_353 ),
inference(forward_demodulation,[],[f4147,f4132]) ).
fof(f4147,plain,
( ! [X0] : subclass(complement(universal_class),X0)
| ~ spl0_6
| ~ spl0_353 ),
inference(resolution,[],[f4032,f145]) ).
fof(f4032,plain,
( ! [X2,X3] :
( ~ subclass(complement(X2),X2)
| subclass(complement(X2),X3) )
| ~ spl0_353 ),
inference(avatar_component_clause,[],[f4031]) ).
fof(f4178,plain,
( spl0_359
| ~ spl0_34
| ~ spl0_137 ),
inference(avatar_split_clause,[],[f938,f913,f263,f4176]) ).
fof(f4176,plain,
( spl0_359
<=> ! [X4] :
( regular(singleton(X4)) = X4
| singleton(X4) = null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_359])]) ).
fof(f938,plain,
( ! [X4] :
( regular(singleton(X4)) = X4
| singleton(X4) = null_class )
| ~ spl0_34
| ~ spl0_137 ),
inference(resolution,[],[f914,f264]) ).
fof(f4174,plain,
( spl0_358
| ~ spl0_99
| ~ spl0_136 ),
inference(avatar_split_clause,[],[f932,f909,f668,f4172]) ).
fof(f4172,plain,
( spl0_358
<=> ! [X8,X7] :
( ~ inductive(symmetric_difference(X7,X8))
| member(null_class,union(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_358])]) ).
fof(f932,plain,
( ! [X8,X7] :
( ~ inductive(symmetric_difference(X7,X8))
| member(null_class,union(X7,X8)) )
| ~ spl0_99
| ~ spl0_136 ),
inference(superposition,[],[f910,f669]) ).
fof(f4170,plain,
( spl0_357
| ~ spl0_52
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f394,f352,f340,f4168]) ).
fof(f4168,plain,
( spl0_357
<=> ! [X1] :
( ~ inductive(diagonalise(X1))
| ~ member(null_class,domain_of(intersection(X1,identity_relation))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_357])]) ).
fof(f394,plain,
( ! [X1] :
( ~ inductive(diagonalise(X1))
| ~ member(null_class,domain_of(intersection(X1,identity_relation))) )
| ~ spl0_52
| ~ spl0_55 ),
inference(superposition,[],[f341,f353]) ).
fof(f4166,plain,
( spl0_356
| ~ spl0_50
| ~ spl0_52 ),
inference(avatar_split_clause,[],[f385,f340,f332,f4164]) ).
fof(f4164,plain,
( spl0_356
<=> ! [X0] :
( ~ inductive(power_class(X0))
| ~ member(null_class,image(element_relation,complement(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_356])]) ).
fof(f385,plain,
( ! [X0] :
( ~ inductive(power_class(X0))
| ~ member(null_class,image(element_relation,complement(X0))) )
| ~ spl0_50
| ~ spl0_52 ),
inference(superposition,[],[f341,f333]) ).
fof(f4113,plain,
( spl0_355
| ~ spl0_61
| ~ spl0_246 ),
inference(avatar_split_clause,[],[f3945,f2239,f401,f4111]) ).
fof(f4111,plain,
( spl0_355
<=> ! [X2] :
( ~ subclass(cross_product(universal_class,universal_class),X2)
| member(null_class,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_355])]) ).
fof(f3945,plain,
( ! [X2] :
( ~ subclass(cross_product(universal_class,universal_class),X2)
| member(null_class,X2) )
| ~ spl0_61
| ~ spl0_246 ),
inference(resolution,[],[f2240,f402]) ).
fof(f2240,plain,
( member(null_class,cross_product(universal_class,universal_class))
| ~ spl0_246 ),
inference(avatar_component_clause,[],[f2239]) ).
fof(f4037,plain,
( spl0_354
| ~ spl0_134
| ~ spl0_211 ),
inference(avatar_split_clause,[],[f1971,f1724,f901,f4035]) ).
fof(f4035,plain,
( spl0_354
<=> ! [X7] :
( ~ inductive(cantor(inverse(X7)))
| member(null_class,range_of(X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_354])]) ).
fof(f1971,plain,
( ! [X7] :
( ~ inductive(cantor(inverse(X7)))
| member(null_class,range_of(X7)) )
| ~ spl0_134
| ~ spl0_211 ),
inference(superposition,[],[f902,f1725]) ).
fof(f4033,plain,
( spl0_353
| ~ spl0_150
| ~ spl0_177 ),
inference(avatar_split_clause,[],[f1449,f1304,f1085,f4031]) ).
fof(f1449,plain,
( ! [X2,X3] :
( ~ subclass(complement(X2),X2)
| subclass(complement(X2),X3) )
| ~ spl0_150
| ~ spl0_177 ),
inference(duplicate_literal_removal,[],[f1431]) ).
fof(f1431,plain,
( ! [X2,X3] :
( ~ subclass(complement(X2),X2)
| subclass(complement(X2),X3)
| subclass(complement(X2),X3) )
| ~ spl0_150
| ~ spl0_177 ),
inference(resolution,[],[f1305,f1086]) ).
fof(f4025,plain,
( spl0_352
| ~ spl0_324
| ~ spl0_328 ),
inference(avatar_split_clause,[],[f3810,f3807,f3765,f4023]) ).
fof(f4023,plain,
( spl0_352
<=> ! [X9] :
( member(identity_relation,domain_of(X9))
| ~ inductive(cantor(X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_352])]) ).
fof(f3807,plain,
( spl0_328
<=> ! [X9] :
( ~ inductive(cantor(X9))
| member(null_class,domain_of(X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_328])]) ).
fof(f3810,plain,
( ! [X9] :
( member(identity_relation,domain_of(X9))
| ~ inductive(cantor(X9)) )
| ~ spl0_324
| ~ spl0_328 ),
inference(forward_demodulation,[],[f3808,f3767]) ).
fof(f3767,plain,
( null_class = identity_relation
| ~ spl0_324 ),
inference(avatar_component_clause,[],[f3765]) ).
fof(f3808,plain,
( ! [X9] :
( member(null_class,domain_of(X9))
| ~ inductive(cantor(X9)) )
| ~ spl0_328 ),
inference(avatar_component_clause,[],[f3807]) ).
fof(f4004,plain,
( spl0_324
| spl0_351
| ~ spl0_20
| ~ spl0_171 ),
inference(avatar_split_clause,[],[f1372,f1280,f204,f4001,f3765]) ).
fof(f4001,plain,
( spl0_351
<=> member(regular(identity_relation),inverse(subset_relation)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_351])]) ).
fof(f1372,plain,
( member(regular(identity_relation),inverse(subset_relation))
| null_class = identity_relation
| ~ spl0_20
| ~ spl0_171 ),
inference(superposition,[],[f1281,f206]) ).
fof(f3999,plain,
( spl0_350
| ~ spl0_144
| ~ spl0_156 ),
inference(avatar_split_clause,[],[f1247,f1109,f1010,f3997]) ).
fof(f1247,plain,
( ! [X0] :
( ~ subclass(complement(X0),X0)
| complement(X0) = null_class )
| ~ spl0_144
| ~ spl0_156 ),
inference(duplicate_literal_removal,[],[f1231]) ).
fof(f1231,plain,
( ! [X0] :
( ~ subclass(complement(X0),X0)
| complement(X0) = null_class
| complement(X0) = null_class )
| ~ spl0_144
| ~ spl0_156 ),
inference(resolution,[],[f1110,f1011]) ).
fof(f3995,plain,
( spl0_349
| ~ spl0_32
| ~ spl0_149 ),
inference(avatar_split_clause,[],[f1081,f1031,f255,f3993]) ).
fof(f3993,plain,
( spl0_349
<=> ! [X2,X1] :
( function(compose(X1,X2))
| ~ single_valued_class(compose(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_349])]) ).
fof(f255,plain,
( spl0_32
<=> ! [X5,X7] : subclass(compose(X7,X5),cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f1031,plain,
( spl0_149
<=> ! [X1] :
( ~ subclass(X1,cross_product(universal_class,universal_class))
| function(X1)
| ~ single_valued_class(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f1081,plain,
( ! [X2,X1] :
( function(compose(X1,X2))
| ~ single_valued_class(compose(X1,X2)) )
| ~ spl0_32
| ~ spl0_149 ),
inference(resolution,[],[f1032,f256]) ).
fof(f256,plain,
( ! [X7,X5] : subclass(compose(X7,X5),cross_product(universal_class,universal_class))
| ~ spl0_32 ),
inference(avatar_component_clause,[],[f255]) ).
fof(f1032,plain,
( ! [X1] :
( ~ subclass(X1,cross_product(universal_class,universal_class))
| function(X1)
| ~ single_valued_class(X1) )
| ~ spl0_149 ),
inference(avatar_component_clause,[],[f1031]) ).
fof(f3991,plain,
( ~ spl0_347
| spl0_348
| ~ spl0_26
| ~ spl0_149 ),
inference(avatar_split_clause,[],[f1076,f1031,f231,f3988,f3984]) ).
fof(f3984,plain,
( spl0_347
<=> single_valued_class(cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_347])]) ).
fof(f3988,plain,
( spl0_348
<=> function(cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_348])]) ).
fof(f231,plain,
( spl0_26
<=> ! [X0] : subclass(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f1076,plain,
( function(cross_product(universal_class,universal_class))
| ~ single_valued_class(cross_product(universal_class,universal_class))
| ~ spl0_26
| ~ spl0_149 ),
inference(resolution,[],[f1032,f232]) ).
fof(f232,plain,
( ! [X0] : subclass(X0,X0)
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f231]) ).
fof(f3982,plain,
( spl0_346
| ~ spl0_72
| ~ spl0_143 ),
inference(avatar_split_clause,[],[f1007,f961,f485,f3980]) ).
fof(f3980,plain,
( spl0_346
<=> ! [X9,X8] :
( ~ member(ordered_pair(X8,X9),subset_relation)
| member(X8,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_346])]) ).
fof(f1007,plain,
( ! [X8,X9] :
( ~ member(ordered_pair(X8,X9),subset_relation)
| member(X8,universal_class) )
| ~ spl0_72
| ~ spl0_143 ),
inference(resolution,[],[f962,f486]) ).
fof(f3976,plain,
( spl0_345
| ~ spl0_73
| ~ spl0_143 ),
inference(avatar_split_clause,[],[f1006,f961,f489,f3974]) ).
fof(f1006,plain,
( ! [X6,X7] :
( ~ member(ordered_pair(X6,X7),subset_relation)
| member(X7,universal_class) )
| ~ spl0_73
| ~ spl0_143 ),
inference(resolution,[],[f962,f490]) ).
fof(f3946,plain,
( spl0_186
| ~ spl0_95
| ~ spl0_246 ),
inference(avatar_split_clause,[],[f3942,f2239,f649,f1340]) ).
fof(f3942,plain,
( null_class = ordered_pair(first(null_class),second(null_class))
| ~ spl0_95
| ~ spl0_246 ),
inference(resolution,[],[f2240,f650]) ).
fof(f3941,plain,
( spl0_344
| spl0_246
| ~ spl0_24
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f989,f945,f221,f2239,f3939]) ).
fof(f3939,plain,
( spl0_344
<=> ! [X12] : ~ inductive(compose_class(X12)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_344])]) ).
fof(f221,plain,
( spl0_24
<=> ! [X0] : subclass(compose_class(X0),cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f989,plain,
( ! [X12] :
( member(null_class,cross_product(universal_class,universal_class))
| ~ inductive(compose_class(X12)) )
| ~ spl0_24
| ~ spl0_139 ),
inference(resolution,[],[f946,f222]) ).
fof(f222,plain,
( ! [X0] : subclass(compose_class(X0),cross_product(universal_class,universal_class))
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f221]) ).
fof(f3937,plain,
( spl0_342
| ~ spl0_343
| ~ spl0_132
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f973,f941,f883,f3934,f3931]) ).
fof(f3931,plain,
( spl0_342
<=> ! [X34,X33] : member(unordered_pair(X33,X34),element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_342])]) ).
fof(f3934,plain,
( spl0_343
<=> subclass(universal_class,singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_343])]) ).
fof(f973,plain,
( ! [X34,X33] :
( ~ subclass(universal_class,singleton_relation)
| member(unordered_pair(X33,X34),element_relation) )
| ~ spl0_132
| ~ spl0_138 ),
inference(resolution,[],[f942,f884]) ).
fof(f3929,plain,
( spl0_340
| ~ spl0_341
| ~ spl0_60
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f972,f941,f388,f3926,f3923]) ).
fof(f3923,plain,
( spl0_340
<=> ! [X32,X31] : member(unordered_pair(X31,X32),subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_340])]) ).
fof(f3926,plain,
( spl0_341
<=> subclass(universal_class,identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_341])]) ).
fof(f972,plain,
( ! [X31,X32] :
( ~ subclass(universal_class,identity_relation)
| member(unordered_pair(X31,X32),subset_relation) )
| ~ spl0_60
| ~ spl0_138 ),
inference(resolution,[],[f942,f389]) ).
fof(f3921,plain,
( spl0_339
| ~ spl0_76
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f918,f901,f501,f3919]) ).
fof(f3919,plain,
( spl0_339
<=> ! [X2,X1,X3] :
( ~ inductive(restrict(X1,X2,X3))
| member(null_class,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_339])]) ).
fof(f918,plain,
( ! [X2,X3,X1] :
( ~ inductive(restrict(X1,X2,X3))
| member(null_class,X1) )
| ~ spl0_76
| ~ spl0_134 ),
inference(superposition,[],[f902,f502]) ).
fof(f3917,plain,
( spl0_337
| ~ spl0_338
| ~ spl0_66
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f917,f901,f421,f3914,f3911]) ).
fof(f3911,plain,
( spl0_337
<=> ! [X0] :
( member(null_class,X0)
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_337])]) ).
fof(f3914,plain,
( spl0_338
<=> inductive(null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_338])]) ).
fof(f917,plain,
( ! [X0] :
( ~ inductive(null_class)
| member(null_class,X0)
| null_class = X0 )
| ~ spl0_66
| ~ spl0_134 ),
inference(superposition,[],[f902,f422]) ).
fof(f3909,plain,
( spl0_336
| ~ spl0_39
| ~ spl0_132 ),
inference(avatar_split_clause,[],[f892,f883,f288,f3907]) ).
fof(f3907,plain,
( spl0_336
<=> ! [X0] :
( member(not_subclass_element(singleton_relation,X0),element_relation)
| subclass(singleton_relation,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_336])]) ).
fof(f892,plain,
( ! [X0] :
( member(not_subclass_element(singleton_relation,X0),element_relation)
| subclass(singleton_relation,X0) )
| ~ spl0_39
| ~ spl0_132 ),
inference(resolution,[],[f884,f289]) ).
fof(f3905,plain,
( spl0_335
| ~ spl0_39
| ~ spl0_60 ),
inference(avatar_split_clause,[],[f865,f388,f288,f3903]) ).
fof(f3903,plain,
( spl0_335
<=> ! [X0] :
( member(not_subclass_element(identity_relation,X0),subset_relation)
| subclass(identity_relation,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_335])]) ).
fof(f865,plain,
( ! [X0] :
( member(not_subclass_element(identity_relation,X0),subset_relation)
| subclass(identity_relation,X0) )
| ~ spl0_39
| ~ spl0_60 ),
inference(resolution,[],[f389,f289]) ).
fof(f3901,plain,
( spl0_334
| ~ spl0_61
| ~ spl0_128 ),
inference(avatar_split_clause,[],[f864,f861,f401,f3899]) ).
fof(f864,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,X0)
| member(ordered_pair(X1,X2),X0) )
| ~ spl0_61
| ~ spl0_128 ),
inference(resolution,[],[f862,f402]) ).
fof(f3887,plain,
( spl0_331
| ~ spl0_326
| ~ spl0_328 ),
inference(avatar_split_clause,[],[f3869,f3807,f3785,f3862]) ).
fof(f3862,plain,
( spl0_331
<=> ! [X9] :
( member(singleton_relation,domain_of(X9))
| ~ inductive(cantor(X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_331])]) ).
fof(f3869,plain,
( ! [X9] :
( member(singleton_relation,domain_of(X9))
| ~ inductive(cantor(X9)) )
| ~ spl0_326
| ~ spl0_328 ),
inference(forward_demodulation,[],[f3808,f3787]) ).
fof(f3883,plain,
( spl0_333
| ~ spl0_20
| ~ spl0_318 ),
inference(avatar_split_clause,[],[f3734,f3681,f204,f3880]) ).
fof(f3880,plain,
( spl0_333
<=> subclass(identity_relation,subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_333])]) ).
fof(f3681,plain,
( spl0_318
<=> ! [X0,X1] : subclass(intersection(X0,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).
fof(f3734,plain,
( subclass(identity_relation,subset_relation)
| ~ spl0_20
| ~ spl0_318 ),
inference(superposition,[],[f3682,f206]) ).
fof(f3682,plain,
( ! [X0,X1] : subclass(intersection(X0,X1),X1)
| ~ spl0_318 ),
inference(avatar_component_clause,[],[f3681]) ).
fof(f3878,plain,
( ~ spl0_332
| spl0_324
| ~ spl0_326 ),
inference(avatar_split_clause,[],[f3873,f3785,f3765,f3875]) ).
fof(f3875,plain,
( spl0_332
<=> identity_relation = singleton_relation ),
introduced(avatar_definition,[new_symbols(naming,[spl0_332])]) ).
fof(f3873,plain,
( identity_relation != singleton_relation
| spl0_324
| ~ spl0_326 ),
inference(forward_demodulation,[],[f3766,f3787]) ).
fof(f3766,plain,
( null_class != identity_relation
| spl0_324 ),
inference(avatar_component_clause,[],[f3765]) ).
fof(f3864,plain,
( spl0_331
| ~ spl0_324
| ~ spl0_326
| ~ spl0_328 ),
inference(avatar_split_clause,[],[f3811,f3807,f3785,f3765,f3862]) ).
fof(f3811,plain,
( ! [X9] :
( member(singleton_relation,domain_of(X9))
| ~ inductive(cantor(X9)) )
| ~ spl0_324
| ~ spl0_326
| ~ spl0_328 ),
inference(forward_demodulation,[],[f3810,f3793]) ).
fof(f3793,plain,
( identity_relation = singleton_relation
| ~ spl0_324
| ~ spl0_326 ),
inference(superposition,[],[f3787,f3767]) ).
fof(f3821,plain,
( ~ spl0_330
| spl0_246
| ~ spl0_16
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f991,f945,f187,f2239,f3818]) ).
fof(f3818,plain,
( spl0_330
<=> inductive(domain_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_330])]) ).
fof(f187,plain,
( spl0_16
<=> subclass(domain_relation,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f991,plain,
( member(null_class,cross_product(universal_class,universal_class))
| ~ inductive(domain_relation)
| ~ spl0_16
| ~ spl0_139 ),
inference(resolution,[],[f946,f189]) ).
fof(f189,plain,
( subclass(domain_relation,cross_product(universal_class,universal_class))
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f187]) ).
fof(f3816,plain,
( ~ spl0_329
| spl0_246
| ~ spl0_12
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f984,f945,f170,f2239,f3813]) ).
fof(f3813,plain,
( spl0_329
<=> inductive(successor_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_329])]) ).
fof(f170,plain,
( spl0_12
<=> subclass(successor_relation,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f984,plain,
( member(null_class,cross_product(universal_class,universal_class))
| ~ inductive(successor_relation)
| ~ spl0_12
| ~ spl0_139 ),
inference(resolution,[],[f946,f172]) ).
fof(f172,plain,
( subclass(successor_relation,cross_product(universal_class,universal_class))
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f170]) ).
fof(f3809,plain,
( spl0_328
| ~ spl0_90
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f923,f901,f590,f3807]) ).
fof(f923,plain,
( ! [X9] :
( ~ inductive(cantor(X9))
| member(null_class,domain_of(X9)) )
| ~ spl0_90
| ~ spl0_134 ),
inference(superposition,[],[f902,f591]) ).
fof(f3792,plain,
( spl0_326
| spl0_327
| ~ spl0_34
| ~ spl0_132 ),
inference(avatar_split_clause,[],[f894,f883,f263,f3789,f3785]) ).
fof(f3789,plain,
( spl0_327
<=> member(regular(singleton_relation),element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_327])]) ).
fof(f894,plain,
( member(regular(singleton_relation),element_relation)
| null_class = singleton_relation
| ~ spl0_34
| ~ spl0_132 ),
inference(resolution,[],[f884,f264]) ).
fof(f3772,plain,
( spl0_324
| spl0_325
| ~ spl0_34
| ~ spl0_60 ),
inference(avatar_split_clause,[],[f867,f388,f263,f3769,f3765]) ).
fof(f3769,plain,
( spl0_325
<=> member(regular(identity_relation),subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_325])]) ).
fof(f867,plain,
( member(regular(identity_relation),subset_relation)
| null_class = identity_relation
| ~ spl0_34
| ~ spl0_60 ),
inference(resolution,[],[f389,f264]) ).
fof(f3763,plain,
( spl0_323
| ~ spl0_38
| ~ spl0_61 ),
inference(avatar_split_clause,[],[f445,f401,f282,f3761]) ).
fof(f3761,plain,
( spl0_323
<=> ! [X13,X12] :
( ~ subclass(universal_class,X12)
| member(singleton(X13),X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_323])]) ).
fof(f282,plain,
( spl0_38
<=> ! [X0] : member(singleton(X0),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f445,plain,
( ! [X12,X13] :
( ~ subclass(universal_class,X12)
| member(singleton(X13),X12) )
| ~ spl0_38
| ~ spl0_61 ),
inference(resolution,[],[f402,f283]) ).
fof(f283,plain,
( ! [X0] : member(singleton(X0),universal_class)
| ~ spl0_38 ),
inference(avatar_component_clause,[],[f282]) ).
fof(f3756,plain,
( spl0_322
| ~ spl0_61
| ~ spl0_127 ),
inference(avatar_split_clause,[],[f2882,f855,f401,f3754]) ).
fof(f3754,plain,
( spl0_322
<=> ! [X0] :
( ~ subclass(universal_class,X0)
| member(null_class,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_322])]) ).
fof(f2882,plain,
( ! [X0] :
( ~ subclass(universal_class,X0)
| member(null_class,X0) )
| ~ spl0_61
| ~ spl0_127 ),
inference(resolution,[],[f856,f402]) ).
fof(f3752,plain,
( spl0_321
| ~ spl0_24
| ~ spl0_149 ),
inference(avatar_split_clause,[],[f1082,f1031,f221,f3750]) ).
fof(f3750,plain,
( spl0_321
<=> ! [X3] :
( function(compose_class(X3))
| ~ single_valued_class(compose_class(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_321])]) ).
fof(f1082,plain,
( ! [X3] :
( function(compose_class(X3))
| ~ single_valued_class(compose_class(X3)) )
| ~ spl0_24
| ~ spl0_149 ),
inference(resolution,[],[f1032,f222]) ).
fof(f3748,plain,
( spl0_320
| ~ spl0_70
| ~ spl0_318 ),
inference(avatar_split_clause,[],[f3721,f3681,f437,f3745]) ).
fof(f3745,plain,
( spl0_320
<=> subclass(singleton_relation,element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_320])]) ).
fof(f3721,plain,
( subclass(singleton_relation,element_relation)
| ~ spl0_70
| ~ spl0_318 ),
inference(superposition,[],[f3682,f439]) ).
fof(f3743,plain,
( spl0_319
| ~ spl0_13
| ~ spl0_137 ),
inference(avatar_split_clause,[],[f937,f913,f175,f3741]) ).
fof(f3741,plain,
( spl0_319
<=> ! [X3] :
( null_class = X3
| ~ inductive(singleton(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_319])]) ).
fof(f937,plain,
( ! [X3] :
( null_class = X3
| ~ inductive(singleton(X3)) )
| ~ spl0_13
| ~ spl0_137 ),
inference(resolution,[],[f914,f176]) ).
fof(f3683,plain,
( spl0_318
| ~ spl0_40
| ~ spl0_189 ),
inference(avatar_split_clause,[],[f1583,f1498,f292,f3681]) ).
fof(f1583,plain,
( ! [X0,X1] : subclass(intersection(X0,X1),X1)
| ~ spl0_40
| ~ spl0_189 ),
inference(duplicate_literal_removal,[],[f1556]) ).
fof(f1556,plain,
( ! [X0,X1] :
( subclass(intersection(X0,X1),X1)
| subclass(intersection(X0,X1),X1) )
| ~ spl0_40
| ~ spl0_189 ),
inference(resolution,[],[f1499,f293]) ).
fof(f3679,plain,
( spl0_317
| ~ spl0_40
| ~ spl0_188 ),
inference(avatar_split_clause,[],[f1553,f1494,f292,f3677]) ).
fof(f3677,plain,
( spl0_317
<=> ! [X0,X1] : subclass(intersection(X0,X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_317])]) ).
fof(f1553,plain,
( ! [X0,X1] : subclass(intersection(X0,X1),X0)
| ~ spl0_40
| ~ spl0_188 ),
inference(duplicate_literal_removal,[],[f1526]) ).
fof(f1526,plain,
( ! [X0,X1] :
( subclass(intersection(X0,X1),X0)
| subclass(intersection(X0,X1),X0) )
| ~ spl0_40
| ~ spl0_188 ),
inference(resolution,[],[f1495,f293]) ).
fof(f3675,plain,
( spl0_316
| ~ spl0_120
| ~ spl0_124 ),
inference(avatar_split_clause,[],[f839,f836,f813,f3673]) ).
fof(f3673,plain,
( spl0_316
<=> ! [X4,X0,X3,X2,X1] :
( ~ homomorphism(X0,X1,X2)
| apply(X2,ordered_pair(apply(X0,not_homomorphism1(X3,X1,X4)),apply(X0,not_homomorphism2(X3,X1,X4)))) = apply(X0,apply(X1,ordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism2(X3,X1,X4))))
| ~ operation(X4)
| ~ compatible(X3,X1,X4)
| homomorphism(X3,X1,X4)
| ~ operation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).
fof(f813,plain,
( spl0_120
<=> ! [X9,X11,X10] :
( ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11)
| member(ordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism2(X9,X10,X11)),domain_of(X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f836,plain,
( spl0_124
<=> ! [X10,X11,X0,X9,X1] :
( ~ homomorphism(X9,X10,X11)
| ~ member(ordered_pair(X0,X1),domain_of(X10))
| apply(X11,ordered_pair(apply(X9,X0),apply(X9,X1))) = apply(X9,apply(X10,ordered_pair(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f839,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ homomorphism(X0,X1,X2)
| apply(X2,ordered_pair(apply(X0,not_homomorphism1(X3,X1,X4)),apply(X0,not_homomorphism2(X3,X1,X4)))) = apply(X0,apply(X1,ordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism2(X3,X1,X4))))
| ~ operation(X4)
| ~ compatible(X3,X1,X4)
| homomorphism(X3,X1,X4)
| ~ operation(X1) )
| ~ spl0_120
| ~ spl0_124 ),
inference(resolution,[],[f837,f814]) ).
fof(f814,plain,
( ! [X10,X11,X9] :
( member(ordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism2(X9,X10,X11)),domain_of(X10))
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11)
| ~ operation(X10) )
| ~ spl0_120 ),
inference(avatar_component_clause,[],[f813]) ).
fof(f837,plain,
( ! [X10,X0,X11,X1,X9] :
( ~ member(ordered_pair(X0,X1),domain_of(X10))
| ~ homomorphism(X9,X10,X11)
| apply(X11,ordered_pair(apply(X9,X0),apply(X9,X1))) = apply(X9,apply(X10,ordered_pair(X0,X1))) )
| ~ spl0_124 ),
inference(avatar_component_clause,[],[f836]) ).
fof(f3669,plain,
( spl0_315
| ~ spl0_89
| ~ spl0_118 ),
inference(avatar_split_clause,[],[f811,f799,f586,f3667]) ).
fof(f3667,plain,
( spl0_315
<=> ! [X16,X14,X15] :
( member(ordered_pair(X14,apply(choice,image(X15,image(X16,singleton(X14))))),compose(X15,X16))
| ~ member(ordered_pair(X14,apply(choice,image(X15,image(X16,singleton(X14))))),cross_product(universal_class,universal_class))
| null_class = image(X15,image(X16,singleton(X14)))
| ~ member(image(X15,image(X16,singleton(X14))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_315])]) ).
fof(f799,plain,
( spl0_118
<=> ! [X4,X7,X5,X1] :
( ~ member(ordered_pair(X1,X4),cross_product(universal_class,universal_class))
| member(ordered_pair(X1,X4),compose(X7,X5))
| ~ member(X4,image(X7,image(X5,singleton(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f811,plain,
( ! [X16,X14,X15] :
( member(ordered_pair(X14,apply(choice,image(X15,image(X16,singleton(X14))))),compose(X15,X16))
| ~ member(ordered_pair(X14,apply(choice,image(X15,image(X16,singleton(X14))))),cross_product(universal_class,universal_class))
| null_class = image(X15,image(X16,singleton(X14)))
| ~ member(image(X15,image(X16,singleton(X14))),universal_class) )
| ~ spl0_89
| ~ spl0_118 ),
inference(resolution,[],[f800,f587]) ).
fof(f800,plain,
( ! [X1,X7,X4,X5] :
( ~ member(X4,image(X7,image(X5,singleton(X1))))
| member(ordered_pair(X1,X4),compose(X7,X5))
| ~ member(ordered_pair(X1,X4),cross_product(universal_class,universal_class)) )
| ~ spl0_118 ),
inference(avatar_component_clause,[],[f799]) ).
fof(f3661,plain,
( spl0_314
| ~ spl0_7
| ~ spl0_279 ),
inference(avatar_split_clause,[],[f3170,f3075,f148,f3658]) ).
fof(f148,plain,
( spl0_7
<=> member(omega,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f3170,plain,
( ordered_pair(x,omega) = ordered_pair(first(ordered_pair(x,omega)),second(ordered_pair(x,omega)))
| ~ spl0_7
| ~ spl0_279 ),
inference(resolution,[],[f3076,f150]) ).
fof(f150,plain,
( member(omega,universal_class)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f148]) ).
fof(f3652,plain,
( spl0_313
| ~ spl0_49
| ~ spl0_120 ),
inference(avatar_split_clause,[],[f823,f813,f328,f3650]) ).
fof(f3650,plain,
( spl0_313
<=> ! [X6,X8,X7] :
( member(ordered_pair(not_homomorphism1(X7,restrict(element_relation,universal_class,X6),X8),not_homomorphism2(X7,restrict(element_relation,universal_class,X6),X8)),sum_class(X6))
| ~ operation(X8)
| ~ compatible(X7,restrict(element_relation,universal_class,X6),X8)
| homomorphism(X7,restrict(element_relation,universal_class,X6),X8)
| ~ operation(restrict(element_relation,universal_class,X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_313])]) ).
fof(f328,plain,
( spl0_49
<=> ! [X0] : domain_of(restrict(element_relation,universal_class,X0)) = sum_class(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f823,plain,
( ! [X8,X6,X7] :
( member(ordered_pair(not_homomorphism1(X7,restrict(element_relation,universal_class,X6),X8),not_homomorphism2(X7,restrict(element_relation,universal_class,X6),X8)),sum_class(X6))
| ~ operation(X8)
| ~ compatible(X7,restrict(element_relation,universal_class,X6),X8)
| homomorphism(X7,restrict(element_relation,universal_class,X6),X8)
| ~ operation(restrict(element_relation,universal_class,X6)) )
| ~ spl0_49
| ~ spl0_120 ),
inference(superposition,[],[f814,f329]) ).
fof(f329,plain,
( ! [X0] : domain_of(restrict(element_relation,universal_class,X0)) = sum_class(X0)
| ~ spl0_49 ),
inference(avatar_component_clause,[],[f328]) ).
fof(f3648,plain,
( spl0_312
| ~ spl0_48
| ~ spl0_120 ),
inference(avatar_split_clause,[],[f822,f813,f324,f3646]) ).
fof(f3646,plain,
( spl0_312
<=> ! [X4,X5,X3] :
( member(ordered_pair(not_homomorphism1(X4,flip(cross_product(X3,universal_class)),X5),not_homomorphism2(X4,flip(cross_product(X3,universal_class)),X5)),inverse(X3))
| ~ operation(X5)
| ~ compatible(X4,flip(cross_product(X3,universal_class)),X5)
| homomorphism(X4,flip(cross_product(X3,universal_class)),X5)
| ~ operation(flip(cross_product(X3,universal_class))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).
fof(f324,plain,
( spl0_48
<=> ! [X1] : domain_of(flip(cross_product(X1,universal_class))) = inverse(X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f822,plain,
( ! [X3,X4,X5] :
( member(ordered_pair(not_homomorphism1(X4,flip(cross_product(X3,universal_class)),X5),not_homomorphism2(X4,flip(cross_product(X3,universal_class)),X5)),inverse(X3))
| ~ operation(X5)
| ~ compatible(X4,flip(cross_product(X3,universal_class)),X5)
| homomorphism(X4,flip(cross_product(X3,universal_class)),X5)
| ~ operation(flip(cross_product(X3,universal_class))) )
| ~ spl0_48
| ~ spl0_120 ),
inference(superposition,[],[f814,f325]) ).
fof(f325,plain,
( ! [X1] : domain_of(flip(cross_product(X1,universal_class))) = inverse(X1)
| ~ spl0_48 ),
inference(avatar_component_clause,[],[f324]) ).
fof(f3642,plain,
( spl0_311
| ~ spl0_39
| ~ spl0_118 ),
inference(avatar_split_clause,[],[f808,f799,f288,f3640]) ).
fof(f3640,plain,
( spl0_311
<=> ! [X5,X4,X7,X6] :
( member(ordered_pair(X4,not_subclass_element(image(X5,image(X6,singleton(X4))),X7)),compose(X5,X6))
| ~ member(ordered_pair(X4,not_subclass_element(image(X5,image(X6,singleton(X4))),X7)),cross_product(universal_class,universal_class))
| subclass(image(X5,image(X6,singleton(X4))),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_311])]) ).
fof(f808,plain,
( ! [X6,X7,X4,X5] :
( member(ordered_pair(X4,not_subclass_element(image(X5,image(X6,singleton(X4))),X7)),compose(X5,X6))
| ~ member(ordered_pair(X4,not_subclass_element(image(X5,image(X6,singleton(X4))),X7)),cross_product(universal_class,universal_class))
| subclass(image(X5,image(X6,singleton(X4))),X7) )
| ~ spl0_39
| ~ spl0_118 ),
inference(resolution,[],[f800,f289]) ).
fof(f3632,plain,
( spl0_310
| ~ spl0_107
| ~ spl0_124 ),
inference(avatar_split_clause,[],[f840,f836,f723,f3630]) ).
fof(f3630,plain,
( spl0_310
<=> ! [X5,X9,X7,X6,X8] :
( ~ homomorphism(X5,X6,X7)
| apply(X7,ordered_pair(apply(X5,X8),apply(X5,X9))) = apply(X5,apply(X6,ordered_pair(X8,X9)))
| ~ member(ordered_pair(X8,X9),universal_class)
| null_class = restrict(X6,singleton(ordered_pair(X8,X9)),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).
fof(f723,plain,
( spl0_107
<=> ! [X4,X0] :
( ~ member(X4,universal_class)
| member(X4,domain_of(X0))
| restrict(X0,singleton(X4),universal_class) = null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f840,plain,
( ! [X8,X6,X9,X7,X5] :
( ~ homomorphism(X5,X6,X7)
| apply(X7,ordered_pair(apply(X5,X8),apply(X5,X9))) = apply(X5,apply(X6,ordered_pair(X8,X9)))
| ~ member(ordered_pair(X8,X9),universal_class)
| null_class = restrict(X6,singleton(ordered_pair(X8,X9)),universal_class) )
| ~ spl0_107
| ~ spl0_124 ),
inference(resolution,[],[f837,f724]) ).
fof(f724,plain,
( ! [X0,X4] :
( member(X4,domain_of(X0))
| ~ member(X4,universal_class)
| restrict(X0,singleton(X4),universal_class) = null_class )
| ~ spl0_107 ),
inference(avatar_component_clause,[],[f723]) ).
fof(f3626,plain,
( spl0_309
| ~ spl0_34
| ~ spl0_118 ),
inference(avatar_split_clause,[],[f810,f799,f263,f3624]) ).
fof(f3624,plain,
( spl0_309
<=> ! [X13,X12,X11] :
( member(ordered_pair(X11,regular(image(X12,image(X13,singleton(X11))))),compose(X12,X13))
| ~ member(ordered_pair(X11,regular(image(X12,image(X13,singleton(X11))))),cross_product(universal_class,universal_class))
| null_class = image(X12,image(X13,singleton(X11))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).
fof(f810,plain,
( ! [X11,X12,X13] :
( member(ordered_pair(X11,regular(image(X12,image(X13,singleton(X11))))),compose(X12,X13))
| ~ member(ordered_pair(X11,regular(image(X12,image(X13,singleton(X11))))),cross_product(universal_class,universal_class))
| null_class = image(X12,image(X13,singleton(X11))) )
| ~ spl0_34
| ~ spl0_118 ),
inference(resolution,[],[f800,f264]) ).
fof(f3622,plain,
( spl0_308
| ~ spl0_49
| ~ spl0_124 ),
inference(avatar_split_clause,[],[f843,f836,f328,f3620]) ).
fof(f3620,plain,
( spl0_308
<=> ! [X10,X11,X14,X13,X12] :
( ~ member(ordered_pair(X11,X12),sum_class(X10))
| ~ homomorphism(X13,restrict(element_relation,universal_class,X10),X14)
| apply(X14,ordered_pair(apply(X13,X11),apply(X13,X12))) = apply(X13,apply(restrict(element_relation,universal_class,X10),ordered_pair(X11,X12))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).
fof(f843,plain,
( ! [X10,X11,X14,X12,X13] :
( ~ member(ordered_pair(X11,X12),sum_class(X10))
| ~ homomorphism(X13,restrict(element_relation,universal_class,X10),X14)
| apply(X14,ordered_pair(apply(X13,X11),apply(X13,X12))) = apply(X13,apply(restrict(element_relation,universal_class,X10),ordered_pair(X11,X12))) )
| ~ spl0_49
| ~ spl0_124 ),
inference(superposition,[],[f837,f329]) ).
fof(f3618,plain,
( spl0_307
| ~ spl0_48
| ~ spl0_124 ),
inference(avatar_split_clause,[],[f842,f836,f324,f3616]) ).
fof(f3616,plain,
( spl0_307
<=> ! [X5,X9,X7,X6,X8] :
( ~ member(ordered_pair(X6,X7),inverse(X5))
| ~ homomorphism(X8,flip(cross_product(X5,universal_class)),X9)
| apply(X9,ordered_pair(apply(X8,X6),apply(X8,X7))) = apply(X8,apply(flip(cross_product(X5,universal_class)),ordered_pair(X6,X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_307])]) ).
fof(f842,plain,
( ! [X8,X6,X9,X7,X5] :
( ~ member(ordered_pair(X6,X7),inverse(X5))
| ~ homomorphism(X8,flip(cross_product(X5,universal_class)),X9)
| apply(X9,ordered_pair(apply(X8,X6),apply(X8,X7))) = apply(X8,apply(flip(cross_product(X5,universal_class)),ordered_pair(X6,X7))) )
| ~ spl0_48
| ~ spl0_124 ),
inference(superposition,[],[f837,f325]) ).
fof(f3596,plain,
( spl0_306
| ~ spl0_99
| ~ spl0_112 ),
inference(avatar_split_clause,[],[f757,f748,f668,f3593]) ).
fof(f3593,plain,
( spl0_306
<=> symmetric_difference(cross_product(universal_class,universal_class),restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class)) = intersection(complement(subset_relation),union(cross_product(universal_class,universal_class),restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).
fof(f757,plain,
( symmetric_difference(cross_product(universal_class,universal_class),restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class)) = intersection(complement(subset_relation),union(cross_product(universal_class,universal_class),restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class)))
| ~ spl0_99
| ~ spl0_112 ),
inference(superposition,[],[f669,f750]) ).
fof(f3578,plain,
( spl0_305
| ~ spl0_19
| ~ spl0_124 ),
inference(avatar_split_clause,[],[f841,f836,f200,f3576]) ).
fof(f3576,plain,
( spl0_305
<=> ! [X4,X0,X3,X2,X1] :
( ~ member(ordered_pair(X1,X2),range_of(X0))
| ~ homomorphism(X3,inverse(X0),X4)
| apply(X4,ordered_pair(apply(X3,X1),apply(X3,X2))) = apply(X3,apply(inverse(X0),ordered_pair(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).
fof(f200,plain,
( spl0_19
<=> ! [X4] : domain_of(inverse(X4)) = range_of(X4) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f841,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ member(ordered_pair(X1,X2),range_of(X0))
| ~ homomorphism(X3,inverse(X0),X4)
| apply(X4,ordered_pair(apply(X3,X1),apply(X3,X2))) = apply(X3,apply(inverse(X0),ordered_pair(X1,X2))) )
| ~ spl0_19
| ~ spl0_124 ),
inference(superposition,[],[f837,f201]) ).
fof(f201,plain,
( ! [X4] : domain_of(inverse(X4)) = range_of(X4)
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f200]) ).
fof(f3574,plain,
( spl0_304
| ~ spl0_19
| ~ spl0_120 ),
inference(avatar_split_clause,[],[f821,f813,f200,f3572]) ).
fof(f3572,plain,
( spl0_304
<=> ! [X2,X0,X1] :
( member(ordered_pair(not_homomorphism1(X1,inverse(X0),X2),not_homomorphism2(X1,inverse(X0),X2)),range_of(X0))
| ~ operation(X2)
| ~ compatible(X1,inverse(X0),X2)
| homomorphism(X1,inverse(X0),X2)
| ~ operation(inverse(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_304])]) ).
fof(f821,plain,
( ! [X2,X0,X1] :
( member(ordered_pair(not_homomorphism1(X1,inverse(X0),X2),not_homomorphism2(X1,inverse(X0),X2)),range_of(X0))
| ~ operation(X2)
| ~ compatible(X1,inverse(X0),X2)
| homomorphism(X1,inverse(X0),X2)
| ~ operation(inverse(X0)) )
| ~ spl0_19
| ~ spl0_120 ),
inference(superposition,[],[f814,f201]) ).
fof(f3570,plain,
( spl0_303
| ~ spl0_49
| ~ spl0_117 ),
inference(avatar_split_clause,[],[f795,f790,f328,f3568]) ).
fof(f3568,plain,
( spl0_303
<=> ! [X2] :
( sum_class(X2) != cross_product(domain_of(sum_class(X2)),domain_of(sum_class(X2)))
| operation(restrict(element_relation,universal_class,X2))
| ~ subclass(range_of(restrict(element_relation,universal_class,X2)),domain_of(sum_class(X2)))
| ~ function(restrict(element_relation,universal_class,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).
fof(f790,plain,
( spl0_117
<=> ! [X8] :
( ~ function(X8)
| operation(X8)
| ~ subclass(range_of(X8),domain_of(domain_of(X8)))
| domain_of(X8) != cross_product(domain_of(domain_of(X8)),domain_of(domain_of(X8))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f795,plain,
( ! [X2] :
( sum_class(X2) != cross_product(domain_of(sum_class(X2)),domain_of(sum_class(X2)))
| operation(restrict(element_relation,universal_class,X2))
| ~ subclass(range_of(restrict(element_relation,universal_class,X2)),domain_of(sum_class(X2)))
| ~ function(restrict(element_relation,universal_class,X2)) )
| ~ spl0_49
| ~ spl0_117 ),
inference(superposition,[],[f791,f329]) ).
fof(f791,plain,
( ! [X8] :
( domain_of(X8) != cross_product(domain_of(domain_of(X8)),domain_of(domain_of(X8)))
| operation(X8)
| ~ subclass(range_of(X8),domain_of(domain_of(X8)))
| ~ function(X8) )
| ~ spl0_117 ),
inference(avatar_component_clause,[],[f790]) ).
fof(f3566,plain,
( spl0_302
| ~ spl0_89
| ~ spl0_95 ),
inference(avatar_split_clause,[],[f674,f649,f586,f3564]) ).
fof(f3564,plain,
( spl0_302
<=> ! [X8,X7] :
( apply(choice,cross_product(X7,X8)) = ordered_pair(first(apply(choice,cross_product(X7,X8))),second(apply(choice,cross_product(X7,X8))))
| null_class = cross_product(X7,X8)
| ~ member(cross_product(X7,X8),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).
fof(f674,plain,
( ! [X8,X7] :
( apply(choice,cross_product(X7,X8)) = ordered_pair(first(apply(choice,cross_product(X7,X8))),second(apply(choice,cross_product(X7,X8))))
| null_class = cross_product(X7,X8)
| ~ member(cross_product(X7,X8),universal_class) )
| ~ spl0_89
| ~ spl0_95 ),
inference(resolution,[],[f650,f587]) ).
fof(f3517,plain,
( spl0_301
| ~ spl0_61
| ~ spl0_120 ),
inference(avatar_split_clause,[],[f820,f813,f401,f3515]) ).
fof(f3515,plain,
( spl0_301
<=> ! [X0,X3,X2,X1] :
( ~ operation(X0)
| ~ compatible(X1,X2,X0)
| homomorphism(X1,X2,X0)
| ~ operation(X2)
| ~ subclass(domain_of(X2),X3)
| member(ordered_pair(not_homomorphism1(X1,X2,X0),not_homomorphism2(X1,X2,X0)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).
fof(f820,plain,
( ! [X2,X3,X0,X1] :
( ~ operation(X0)
| ~ compatible(X1,X2,X0)
| homomorphism(X1,X2,X0)
| ~ operation(X2)
| ~ subclass(domain_of(X2),X3)
| member(ordered_pair(not_homomorphism1(X1,X2,X0),not_homomorphism2(X1,X2,X0)),X3) )
| ~ spl0_61
| ~ spl0_120 ),
inference(resolution,[],[f814,f402]) ).
fof(f3513,plain,
( spl0_300
| ~ spl0_49
| ~ spl0_115 ),
inference(avatar_split_clause,[],[f785,f773,f328,f3511]) ).
fof(f3511,plain,
( spl0_300
<=> ! [X6,X7,X8] :
( sum_class(X6) != domain_of(domain_of(X7))
| compatible(restrict(element_relation,universal_class,X6),X7,X8)
| ~ function(restrict(element_relation,universal_class,X6))
| ~ subclass(range_of(restrict(element_relation,universal_class,X6)),domain_of(domain_of(X8))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).
fof(f773,plain,
( spl0_115
<=> ! [X9,X11,X10] :
( ~ function(X9)
| compatible(X9,X10,X11)
| domain_of(domain_of(X10)) != domain_of(X9)
| ~ subclass(range_of(X9),domain_of(domain_of(X11))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f785,plain,
( ! [X8,X6,X7] :
( sum_class(X6) != domain_of(domain_of(X7))
| compatible(restrict(element_relation,universal_class,X6),X7,X8)
| ~ function(restrict(element_relation,universal_class,X6))
| ~ subclass(range_of(restrict(element_relation,universal_class,X6)),domain_of(domain_of(X8))) )
| ~ spl0_49
| ~ spl0_115 ),
inference(superposition,[],[f774,f329]) ).
fof(f774,plain,
( ! [X10,X11,X9] :
( domain_of(domain_of(X10)) != domain_of(X9)
| compatible(X9,X10,X11)
| ~ function(X9)
| ~ subclass(range_of(X9),domain_of(domain_of(X11))) )
| ~ spl0_115 ),
inference(avatar_component_clause,[],[f773]) ).
fof(f3509,plain,
( spl0_299
| ~ spl0_48
| ~ spl0_115 ),
inference(avatar_split_clause,[],[f784,f773,f324,f3507]) ).
fof(f3507,plain,
( spl0_299
<=> ! [X4,X5,X3] :
( inverse(X3) != domain_of(domain_of(X4))
| compatible(flip(cross_product(X3,universal_class)),X4,X5)
| ~ function(flip(cross_product(X3,universal_class)))
| ~ subclass(range_of(flip(cross_product(X3,universal_class))),domain_of(domain_of(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_299])]) ).
fof(f784,plain,
( ! [X3,X4,X5] :
( inverse(X3) != domain_of(domain_of(X4))
| compatible(flip(cross_product(X3,universal_class)),X4,X5)
| ~ function(flip(cross_product(X3,universal_class)))
| ~ subclass(range_of(flip(cross_product(X3,universal_class))),domain_of(domain_of(X5))) )
| ~ spl0_48
| ~ spl0_115 ),
inference(superposition,[],[f774,f325]) ).
fof(f3504,plain,
( spl0_298
| ~ spl0_19
| ~ spl0_48
| ~ spl0_117 ),
inference(avatar_split_clause,[],[f797,f790,f324,f200,f3502]) ).
fof(f3502,plain,
( spl0_298
<=> ! [X1] :
( ~ subclass(range_of(flip(cross_product(X1,universal_class))),range_of(X1))
| inverse(X1) != cross_product(range_of(X1),range_of(X1))
| operation(flip(cross_product(X1,universal_class)))
| ~ function(flip(cross_product(X1,universal_class))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).
fof(f797,plain,
( ! [X1] :
( ~ subclass(range_of(flip(cross_product(X1,universal_class))),range_of(X1))
| inverse(X1) != cross_product(range_of(X1),range_of(X1))
| operation(flip(cross_product(X1,universal_class)))
| ~ function(flip(cross_product(X1,universal_class))) )
| ~ spl0_19
| ~ spl0_48
| ~ spl0_117 ),
inference(forward_demodulation,[],[f796,f201]) ).
fof(f796,plain,
( ! [X1] :
( inverse(X1) != cross_product(range_of(X1),range_of(X1))
| operation(flip(cross_product(X1,universal_class)))
| ~ subclass(range_of(flip(cross_product(X1,universal_class))),domain_of(inverse(X1)))
| ~ function(flip(cross_product(X1,universal_class))) )
| ~ spl0_19
| ~ spl0_48
| ~ spl0_117 ),
inference(forward_demodulation,[],[f794,f201]) ).
fof(f794,plain,
( ! [X1] :
( inverse(X1) != cross_product(domain_of(inverse(X1)),domain_of(inverse(X1)))
| operation(flip(cross_product(X1,universal_class)))
| ~ subclass(range_of(flip(cross_product(X1,universal_class))),domain_of(inverse(X1)))
| ~ function(flip(cross_product(X1,universal_class))) )
| ~ spl0_48
| ~ spl0_117 ),
inference(superposition,[],[f791,f325]) ).
fof(f3488,plain,
( spl0_297
| ~ spl0_100
| ~ spl0_123 ),
inference(avatar_split_clause,[],[f834,f830,f688,f3486]) ).
fof(f3486,plain,
( spl0_297
<=> ! [X0,X3,X2,X1] :
( member(ordered_pair(ordered_pair(X0,X1),X2),flip(X3))
| ~ member(ordered_pair(ordered_pair(X1,X0),X2),X3)
| ~ member(X2,universal_class)
| ~ member(ordered_pair(X0,X1),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).
fof(f830,plain,
( spl0_123
<=> ! [X3,X0,X6,X2] :
( ~ member(ordered_pair(ordered_pair(X3,X2),X6),X0)
| member(ordered_pair(ordered_pair(X2,X3),X6),flip(X0))
| ~ member(ordered_pair(ordered_pair(X2,X3),X6),cross_product(cross_product(universal_class,universal_class),universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f834,plain,
( ! [X2,X3,X0,X1] :
( member(ordered_pair(ordered_pair(X0,X1),X2),flip(X3))
| ~ member(ordered_pair(ordered_pair(X1,X0),X2),X3)
| ~ member(X2,universal_class)
| ~ member(ordered_pair(X0,X1),cross_product(universal_class,universal_class)) )
| ~ spl0_100
| ~ spl0_123 ),
inference(resolution,[],[f831,f689]) ).
fof(f831,plain,
( ! [X2,X3,X0,X6] :
( ~ member(ordered_pair(ordered_pair(X2,X3),X6),cross_product(cross_product(universal_class,universal_class),universal_class))
| member(ordered_pair(ordered_pair(X2,X3),X6),flip(X0))
| ~ member(ordered_pair(ordered_pair(X3,X2),X6),X0) )
| ~ spl0_123 ),
inference(avatar_component_clause,[],[f830]) ).
fof(f3484,plain,
( spl0_296
| ~ spl0_100
| ~ spl0_122 ),
inference(avatar_split_clause,[],[f833,f826,f688,f3482]) ).
fof(f3482,plain,
( spl0_296
<=> ! [X0,X3,X2,X1] :
( member(ordered_pair(ordered_pair(X0,X1),X2),rotate(X3))
| ~ member(ordered_pair(ordered_pair(X1,X2),X0),X3)
| ~ member(X2,universal_class)
| ~ member(ordered_pair(X0,X1),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).
fof(f826,plain,
( spl0_122
<=> ! [X3,X0,X6,X2] :
( ~ member(ordered_pair(ordered_pair(X3,X6),X2),X0)
| member(ordered_pair(ordered_pair(X2,X3),X6),rotate(X0))
| ~ member(ordered_pair(ordered_pair(X2,X3),X6),cross_product(cross_product(universal_class,universal_class),universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f833,plain,
( ! [X2,X3,X0,X1] :
( member(ordered_pair(ordered_pair(X0,X1),X2),rotate(X3))
| ~ member(ordered_pair(ordered_pair(X1,X2),X0),X3)
| ~ member(X2,universal_class)
| ~ member(ordered_pair(X0,X1),cross_product(universal_class,universal_class)) )
| ~ spl0_100
| ~ spl0_122 ),
inference(resolution,[],[f827,f689]) ).
fof(f827,plain,
( ! [X2,X3,X0,X6] :
( ~ member(ordered_pair(ordered_pair(X2,X3),X6),cross_product(cross_product(universal_class,universal_class),universal_class))
| member(ordered_pair(ordered_pair(X2,X3),X6),rotate(X0))
| ~ member(ordered_pair(ordered_pair(X3,X6),X2),X0) )
| ~ spl0_122 ),
inference(avatar_component_clause,[],[f826]) ).
fof(f3335,plain,
( ~ spl0_4
| ~ spl0_275 ),
inference(avatar_contradiction_clause,[],[f3332]) ).
fof(f3332,plain,
( $false
| ~ spl0_4
| ~ spl0_275 ),
inference(resolution,[],[f2880,f136]) ).
fof(f136,plain,
( inductive(omega)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f134]) ).
fof(f2880,plain,
( ! [X0] : ~ inductive(X0)
| ~ spl0_275 ),
inference(avatar_component_clause,[],[f2879]) ).
fof(f2879,plain,
( spl0_275
<=> ! [X0] : ~ inductive(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).
fof(f3334,plain,
( ~ spl0_126
| ~ spl0_275 ),
inference(avatar_contradiction_clause,[],[f3333]) ).
fof(f3333,plain,
( $false
| ~ spl0_126
| ~ spl0_275 ),
inference(resolution,[],[f2880,f853]) ).
fof(f853,plain,
( inductive(universal_class)
| ~ spl0_126 ),
inference(avatar_component_clause,[],[f851]) ).
fof(f851,plain,
( spl0_126
<=> inductive(universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f3331,plain,
( spl0_295
| ~ spl0_39
| ~ spl0_95 ),
inference(avatar_split_clause,[],[f671,f649,f288,f3329]) ).
fof(f3329,plain,
( spl0_295
<=> ! [X2,X0,X1] :
( not_subclass_element(cross_product(X0,X1),X2) = ordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),second(not_subclass_element(cross_product(X0,X1),X2)))
| subclass(cross_product(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).
fof(f671,plain,
( ! [X2,X0,X1] :
( not_subclass_element(cross_product(X0,X1),X2) = ordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),second(not_subclass_element(cross_product(X0,X1),X2)))
| subclass(cross_product(X0,X1),X2) )
| ~ spl0_39
| ~ spl0_95 ),
inference(resolution,[],[f650,f289]) ).
fof(f3327,plain,
( spl0_294
| ~ spl0_85
| ~ spl0_89 ),
inference(avatar_split_clause,[],[f632,f586,f569,f3325]) ).
fof(f3325,plain,
( spl0_294
<=> ! [X2,X3] :
( null_class = unordered_pair(X2,X3)
| ~ member(unordered_pair(X2,X3),universal_class)
| apply(choice,unordered_pair(X2,X3)) = X2
| apply(choice,unordered_pair(X2,X3)) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).
fof(f569,plain,
( spl0_85
<=> ! [X2,X0,X1] :
( X1 = X2
| X0 = X2
| ~ member(X2,unordered_pair(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f632,plain,
( ! [X2,X3] :
( null_class = unordered_pair(X2,X3)
| ~ member(unordered_pair(X2,X3),universal_class)
| apply(choice,unordered_pair(X2,X3)) = X2
| apply(choice,unordered_pair(X2,X3)) = X3 )
| ~ spl0_85
| ~ spl0_89 ),
inference(resolution,[],[f587,f570]) ).
fof(f570,plain,
( ! [X2,X0,X1] :
( ~ member(X2,unordered_pair(X0,X1))
| X0 = X2
| X1 = X2 )
| ~ spl0_85 ),
inference(avatar_component_clause,[],[f569]) ).
fof(f3316,plain,
( spl0_293
| ~ spl0_100
| ~ spl0_121 ),
inference(avatar_split_clause,[],[f824,f817,f688,f3314]) ).
fof(f3314,plain,
( spl0_293
<=> ! [X2,X0,X1] :
( member(ordered_pair(X0,ordered_pair(X1,apply(X0,X1))),application_function)
| ~ member(X1,domain_of(X0))
| ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class))
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).
fof(f817,plain,
( spl0_121
<=> ! [X4,X0,X1] :
( ~ member(X1,domain_of(X0))
| member(ordered_pair(X0,ordered_pair(X1,apply(X0,X1))),application_function)
| ~ member(ordered_pair(X0,ordered_pair(X1,X4)),cross_product(universal_class,cross_product(universal_class,universal_class))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f824,plain,
( ! [X2,X0,X1] :
( member(ordered_pair(X0,ordered_pair(X1,apply(X0,X1))),application_function)
| ~ member(X1,domain_of(X0))
| ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class))
| ~ member(X0,universal_class) )
| ~ spl0_100
| ~ spl0_121 ),
inference(resolution,[],[f818,f689]) ).
fof(f818,plain,
( ! [X0,X1,X4] :
( ~ member(ordered_pair(X0,ordered_pair(X1,X4)),cross_product(universal_class,cross_product(universal_class,universal_class)))
| member(ordered_pair(X0,ordered_pair(X1,apply(X0,X1))),application_function)
| ~ member(X1,domain_of(X0)) )
| ~ spl0_121 ),
inference(avatar_component_clause,[],[f817]) ).
fof(f3312,plain,
( spl0_292
| ~ spl0_19
| ~ spl0_117 ),
inference(avatar_split_clause,[],[f793,f790,f200,f3310]) ).
fof(f3310,plain,
( spl0_292
<=> ! [X0] :
( range_of(X0) != cross_product(domain_of(range_of(X0)),domain_of(range_of(X0)))
| operation(inverse(X0))
| ~ subclass(range_of(inverse(X0)),domain_of(range_of(X0)))
| ~ function(inverse(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).
fof(f793,plain,
( ! [X0] :
( range_of(X0) != cross_product(domain_of(range_of(X0)),domain_of(range_of(X0)))
| operation(inverse(X0))
| ~ subclass(range_of(inverse(X0)),domain_of(range_of(X0)))
| ~ function(inverse(X0)) )
| ~ spl0_19
| ~ spl0_117 ),
inference(superposition,[],[f791,f201]) ).
fof(f3265,plain,
( spl0_291
| ~ spl0_40
| ~ spl0_111 ),
inference(avatar_split_clause,[],[f754,f744,f292,f3263]) ).
fof(f3263,plain,
( spl0_291
<=> ! [X5,X7,X6,X8] :
( ~ member(ordered_pair(X5,not_subclass_element(X6,image(X7,image(X8,singleton(X5))))),compose(X7,X8))
| subclass(X6,image(X7,image(X8,singleton(X5)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).
fof(f744,plain,
( spl0_111
<=> ! [X4,X7,X5,X1] :
( ~ member(ordered_pair(X1,X4),compose(X7,X5))
| member(X4,image(X7,image(X5,singleton(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f754,plain,
( ! [X8,X6,X7,X5] :
( ~ member(ordered_pair(X5,not_subclass_element(X6,image(X7,image(X8,singleton(X5))))),compose(X7,X8))
| subclass(X6,image(X7,image(X8,singleton(X5)))) )
| ~ spl0_40
| ~ spl0_111 ),
inference(resolution,[],[f745,f293]) ).
fof(f745,plain,
( ! [X1,X7,X4,X5] :
( member(X4,image(X7,image(X5,singleton(X1))))
| ~ member(ordered_pair(X1,X4),compose(X7,X5)) )
| ~ spl0_111 ),
inference(avatar_component_clause,[],[f744]) ).
fof(f3261,plain,
( spl0_290
| ~ spl0_127
| ~ spl0_279 ),
inference(avatar_split_clause,[],[f3167,f3075,f855,f3258]) ).
fof(f3167,plain,
( ordered_pair(x,null_class) = ordered_pair(first(ordered_pair(x,null_class)),second(ordered_pair(x,null_class)))
| ~ spl0_127
| ~ spl0_279 ),
inference(resolution,[],[f3076,f856]) ).
fof(f3256,plain,
( spl0_289
| ~ spl0_99 ),
inference(avatar_split_clause,[],[f679,f668,f3254]) ).
fof(f3254,plain,
( spl0_289
<=> ! [X8,X7] : symmetric_difference(complement(intersection(X7,X8)),union(X7,X8)) = intersection(complement(symmetric_difference(X7,X8)),union(complement(intersection(X7,X8)),union(X7,X8))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).
fof(f679,plain,
( ! [X8,X7] : symmetric_difference(complement(intersection(X7,X8)),union(X7,X8)) = intersection(complement(symmetric_difference(X7,X8)),union(complement(intersection(X7,X8)),union(X7,X8)))
| ~ spl0_99 ),
inference(superposition,[],[f669,f669]) ).
fof(f3200,plain,
( spl0_288
| ~ spl0_13
| ~ spl0_118 ),
inference(avatar_split_clause,[],[f809,f799,f175,f3198]) ).
fof(f3198,plain,
( spl0_288
<=> ! [X9,X8,X10] :
( member(ordered_pair(X8,null_class),compose(X9,X10))
| ~ member(ordered_pair(X8,null_class),cross_product(universal_class,universal_class))
| ~ inductive(image(X9,image(X10,singleton(X8)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).
fof(f809,plain,
( ! [X10,X8,X9] :
( member(ordered_pair(X8,null_class),compose(X9,X10))
| ~ member(ordered_pair(X8,null_class),cross_product(universal_class,universal_class))
| ~ inductive(image(X9,image(X10,singleton(X8)))) )
| ~ spl0_13
| ~ spl0_118 ),
inference(resolution,[],[f800,f176]) ).
fof(f3196,plain,
( spl0_287
| ~ spl0_19
| ~ spl0_115 ),
inference(avatar_split_clause,[],[f783,f773,f200,f3194]) ).
fof(f3194,plain,
( spl0_287
<=> ! [X2,X0,X1] :
( range_of(X0) != domain_of(domain_of(X1))
| compatible(inverse(X0),X1,X2)
| ~ function(inverse(X0))
| ~ subclass(range_of(inverse(X0)),domain_of(domain_of(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).
fof(f783,plain,
( ! [X2,X0,X1] :
( range_of(X0) != domain_of(domain_of(X1))
| compatible(inverse(X0),X1,X2)
| ~ function(inverse(X0))
| ~ subclass(range_of(inverse(X0)),domain_of(domain_of(X2))) )
| ~ spl0_19
| ~ spl0_115 ),
inference(superposition,[],[f774,f201]) ).
fof(f3192,plain,
( spl0_286
| ~ spl0_49
| ~ spl0_115 ),
inference(avatar_split_clause,[],[f782,f773,f328,f3190]) ).
fof(f3190,plain,
( spl0_286
<=> ! [X6,X7,X8] :
( domain_of(X7) != domain_of(sum_class(X6))
| compatible(X7,restrict(element_relation,universal_class,X6),X8)
| ~ function(X7)
| ~ subclass(range_of(X7),domain_of(domain_of(X8))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).
fof(f782,plain,
( ! [X8,X6,X7] :
( domain_of(X7) != domain_of(sum_class(X6))
| compatible(X7,restrict(element_relation,universal_class,X6),X8)
| ~ function(X7)
| ~ subclass(range_of(X7),domain_of(domain_of(X8))) )
| ~ spl0_49
| ~ spl0_115 ),
inference(superposition,[],[f774,f329]) ).
fof(f3188,plain,
( spl0_285
| ~ spl0_90
| ~ spl0_99 ),
inference(avatar_split_clause,[],[f680,f668,f590,f3186]) ).
fof(f3186,plain,
( spl0_285
<=> ! [X9] : symmetric_difference(domain_of(X9),diagonalise(compose(inverse(element_relation),X9))) = intersection(complement(cantor(X9)),union(domain_of(X9),diagonalise(compose(inverse(element_relation),X9)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).
fof(f680,plain,
( ! [X9] : symmetric_difference(domain_of(X9),diagonalise(compose(inverse(element_relation),X9))) = intersection(complement(cantor(X9)),union(domain_of(X9),diagonalise(compose(inverse(element_relation),X9))))
| ~ spl0_90
| ~ spl0_99 ),
inference(superposition,[],[f669,f591]) ).
fof(f3124,plain,
( spl0_284
| ~ spl0_34
| ~ spl0_95 ),
inference(avatar_split_clause,[],[f673,f649,f263,f3122]) ).
fof(f673,plain,
( ! [X6,X5] :
( regular(cross_product(X5,X6)) = ordered_pair(first(regular(cross_product(X5,X6))),second(regular(cross_product(X5,X6))))
| null_class = cross_product(X5,X6) )
| ~ spl0_34
| ~ spl0_95 ),
inference(resolution,[],[f650,f264]) ).
fof(f3098,plain,
( spl0_283
| ~ spl0_19
| ~ spl0_48
| ~ spl0_115 ),
inference(avatar_split_clause,[],[f787,f773,f324,f200,f3096]) ).
fof(f3096,plain,
( spl0_283
<=> ! [X4,X5,X3] :
( domain_of(X4) != range_of(X3)
| compatible(X4,flip(cross_product(X3,universal_class)),X5)
| ~ function(X4)
| ~ subclass(range_of(X4),domain_of(domain_of(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).
fof(f787,plain,
( ! [X3,X4,X5] :
( domain_of(X4) != range_of(X3)
| compatible(X4,flip(cross_product(X3,universal_class)),X5)
| ~ function(X4)
| ~ subclass(range_of(X4),domain_of(domain_of(X5))) )
| ~ spl0_19
| ~ spl0_48
| ~ spl0_115 ),
inference(forward_demodulation,[],[f781,f201]) ).
fof(f781,plain,
( ! [X3,X4,X5] :
( domain_of(X4) != domain_of(inverse(X3))
| compatible(X4,flip(cross_product(X3,universal_class)),X5)
| ~ function(X4)
| ~ subclass(range_of(X4),domain_of(domain_of(X5))) )
| ~ spl0_48
| ~ spl0_115 ),
inference(superposition,[],[f774,f325]) ).
fof(f3094,plain,
( spl0_282
| ~ spl0_40
| ~ spl0_107 ),
inference(avatar_split_clause,[],[f727,f723,f292,f3092]) ).
fof(f3092,plain,
( spl0_282
<=> ! [X4,X3] :
( ~ member(not_subclass_element(X3,domain_of(X4)),universal_class)
| null_class = restrict(X4,singleton(not_subclass_element(X3,domain_of(X4))),universal_class)
| subclass(X3,domain_of(X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).
fof(f727,plain,
( ! [X3,X4] :
( ~ member(not_subclass_element(X3,domain_of(X4)),universal_class)
| null_class = restrict(X4,singleton(not_subclass_element(X3,domain_of(X4))),universal_class)
| subclass(X3,domain_of(X4)) )
| ~ spl0_40
| ~ spl0_107 ),
inference(resolution,[],[f724,f293]) ).
fof(f3090,plain,
( spl0_281
| ~ spl0_49
| ~ spl0_93 ),
inference(avatar_split_clause,[],[f647,f602,f328,f3088]) ).
fof(f3088,plain,
( spl0_281
<=> ! [X4,X5] :
( maps(restrict(element_relation,universal_class,X4),sum_class(X4),X5)
| ~ subclass(range_of(restrict(element_relation,universal_class,X4)),X5)
| ~ function(restrict(element_relation,universal_class,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).
fof(f602,plain,
( spl0_93
<=> ! [X1,X8] :
( ~ function(X8)
| ~ subclass(range_of(X8),X1)
| maps(X8,domain_of(X8),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f647,plain,
( ! [X4,X5] :
( maps(restrict(element_relation,universal_class,X4),sum_class(X4),X5)
| ~ subclass(range_of(restrict(element_relation,universal_class,X4)),X5)
| ~ function(restrict(element_relation,universal_class,X4)) )
| ~ spl0_49
| ~ spl0_93 ),
inference(superposition,[],[f603,f329]) ).
fof(f603,plain,
( ! [X1,X8] :
( maps(X8,domain_of(X8),X1)
| ~ subclass(range_of(X8),X1)
| ~ function(X8) )
| ~ spl0_93 ),
inference(avatar_component_clause,[],[f602]) ).
fof(f3086,plain,
( spl0_280
| ~ spl0_48
| ~ spl0_93 ),
inference(avatar_split_clause,[],[f646,f602,f324,f3084]) ).
fof(f3084,plain,
( spl0_280
<=> ! [X2,X3] :
( maps(flip(cross_product(X2,universal_class)),inverse(X2),X3)
| ~ subclass(range_of(flip(cross_product(X2,universal_class))),X3)
| ~ function(flip(cross_product(X2,universal_class))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).
fof(f646,plain,
( ! [X2,X3] :
( maps(flip(cross_product(X2,universal_class)),inverse(X2),X3)
| ~ subclass(range_of(flip(cross_product(X2,universal_class))),X3)
| ~ function(flip(cross_product(X2,universal_class))) )
| ~ spl0_48
| ~ spl0_93 ),
inference(superposition,[],[f603,f325]) ).
fof(f3077,plain,
( spl0_279
| ~ spl0_3
| ~ spl0_274 ),
inference(avatar_split_clause,[],[f3009,f2875,f129,f3075]) ).
fof(f2875,plain,
( spl0_274
<=> ! [X10,X11,X9,X8] :
( ~ member(X8,X9)
| ~ member(X10,X11)
| ordered_pair(X10,X8) = ordered_pair(first(ordered_pair(X10,X8)),second(ordered_pair(X10,X8))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).
fof(f3009,plain,
( ! [X222,X221] :
( ~ member(X221,X222)
| ordered_pair(x,X221) = ordered_pair(first(ordered_pair(x,X221)),second(ordered_pair(x,X221))) )
| ~ spl0_3
| ~ spl0_274 ),
inference(resolution,[],[f2876,f131]) ).
fof(f2876,plain,
( ! [X10,X11,X8,X9] :
( ~ member(X10,X11)
| ~ member(X8,X9)
| ordered_pair(X10,X8) = ordered_pair(first(ordered_pair(X10,X8)),second(ordered_pair(X10,X8))) )
| ~ spl0_274 ),
inference(avatar_component_clause,[],[f2875]) ).
fof(f2894,plain,
( spl0_278
| ~ spl0_19
| ~ spl0_115 ),
inference(avatar_split_clause,[],[f780,f773,f200,f2892]) ).
fof(f2892,plain,
( spl0_278
<=> ! [X2,X0,X1] :
( domain_of(X1) != domain_of(range_of(X0))
| compatible(X1,inverse(X0),X2)
| ~ function(X1)
| ~ subclass(range_of(X1),domain_of(domain_of(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).
fof(f780,plain,
( ! [X2,X0,X1] :
( domain_of(X1) != domain_of(range_of(X0))
| compatible(X1,inverse(X0),X2)
| ~ function(X1)
| ~ subclass(range_of(X1),domain_of(domain_of(X2))) )
| ~ spl0_19
| ~ spl0_115 ),
inference(superposition,[],[f774,f201]) ).
fof(f2890,plain,
( spl0_277
| ~ spl0_61
| ~ spl0_114 ),
inference(avatar_split_clause,[],[f771,f766,f401,f2888]) ).
fof(f766,plain,
( spl0_114
<=> ! [X0,X1] :
( ~ member(ordered_pair(X0,X1),cross_product(universal_class,universal_class))
| member(ordered_pair(X0,ordered_pair(X1,compose(X0,X1))),composition_function) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f771,plain,
( ! [X2,X3,X4] :
( ~ member(ordered_pair(X2,X3),cross_product(universal_class,universal_class))
| ~ subclass(composition_function,X4)
| member(ordered_pair(X2,ordered_pair(X3,compose(X2,X3))),X4) )
| ~ spl0_61
| ~ spl0_114 ),
inference(resolution,[],[f767,f402]) ).
fof(f767,plain,
( ! [X0,X1] :
( member(ordered_pair(X0,ordered_pair(X1,compose(X0,X1))),composition_function)
| ~ member(ordered_pair(X0,X1),cross_product(universal_class,universal_class)) )
| ~ spl0_114 ),
inference(avatar_component_clause,[],[f766]) ).
fof(f2886,plain,
( spl0_276
| ~ spl0_87
| ~ spl0_112 ),
inference(avatar_split_clause,[],[f758,f748,f578,f2884]) ).
fof(f2884,plain,
( spl0_276
<=> ! [X0] :
( member(X0,subset_relation)
| ~ member(X0,restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class))
| ~ member(X0,cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).
fof(f758,plain,
( ! [X0] :
( member(X0,subset_relation)
| ~ member(X0,restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class))
| ~ member(X0,cross_product(universal_class,universal_class)) )
| ~ spl0_87
| ~ spl0_112 ),
inference(superposition,[],[f579,f750]) ).
fof(f2881,plain,
( spl0_275
| spl0_127
| ~ spl0_6
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f976,f945,f144,f855,f2879]) ).
fof(f976,plain,
( ! [X0] :
( member(null_class,universal_class)
| ~ inductive(X0) )
| ~ spl0_6
| ~ spl0_139 ),
inference(resolution,[],[f946,f145]) ).
fof(f2877,plain,
( spl0_274
| ~ spl0_95
| ~ spl0_100 ),
inference(avatar_split_clause,[],[f718,f688,f649,f2875]) ).
fof(f718,plain,
( ! [X10,X11,X8,X9] :
( ~ member(X8,X9)
| ~ member(X10,X11)
| ordered_pair(X10,X8) = ordered_pair(first(ordered_pair(X10,X8)),second(ordered_pair(X10,X8))) )
| ~ spl0_95
| ~ spl0_100 ),
inference(resolution,[],[f689,f650]) ).
fof(f2873,plain,
( spl0_273
| ~ spl0_40
| ~ spl0_87 ),
inference(avatar_split_clause,[],[f625,f578,f292,f2871]) ).
fof(f625,plain,
( ! [X10,X11,X12] :
( ~ member(not_subclass_element(X10,intersection(X11,X12)),X12)
| ~ member(not_subclass_element(X10,intersection(X11,X12)),X11)
| subclass(X10,intersection(X11,X12)) )
| ~ spl0_40
| ~ spl0_87 ),
inference(resolution,[],[f579,f293]) ).
fof(f2869,plain,
( spl0_272
| ~ spl0_39
| ~ spl0_85 ),
inference(avatar_split_clause,[],[f607,f569,f288,f2867]) ).
fof(f2867,plain,
( spl0_272
<=> ! [X6,X4,X5] :
( not_subclass_element(unordered_pair(X4,X5),X6) = X4
| not_subclass_element(unordered_pair(X4,X5),X6) = X5
| subclass(unordered_pair(X4,X5),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).
fof(f607,plain,
( ! [X6,X4,X5] :
( not_subclass_element(unordered_pair(X4,X5),X6) = X4
| not_subclass_element(unordered_pair(X4,X5),X6) = X5
| subclass(unordered_pair(X4,X5),X6) )
| ~ spl0_39
| ~ spl0_85 ),
inference(resolution,[],[f570,f289]) ).
fof(f2844,plain,
( spl0_271
| ~ spl0_61
| ~ spl0_111 ),
inference(avatar_split_clause,[],[f753,f744,f401,f2842]) ).
fof(f753,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ member(ordered_pair(X0,X1),compose(X2,X3))
| ~ subclass(image(X2,image(X3,singleton(X0))),X4)
| member(X1,X4) )
| ~ spl0_61
| ~ spl0_111 ),
inference(resolution,[],[f745,f402]) ).
fof(f2840,plain,
( spl0_270
| ~ spl0_70
| ~ spl0_99 ),
inference(avatar_split_clause,[],[f678,f668,f437,f2837]) ).
fof(f678,plain,
( symmetric_difference(complement(compose(element_relation,complement(identity_relation))),element_relation) = intersection(complement(singleton_relation),union(complement(compose(element_relation,complement(identity_relation))),element_relation))
| ~ spl0_70
| ~ spl0_99 ),
inference(superposition,[],[f669,f439]) ).
fof(f2629,plain,
( spl0_269
| ~ spl0_116 ),
inference(avatar_split_clause,[],[f788,f777,f2627]) ).
fof(f2627,plain,
( spl0_269
<=> ! [X0,X1] :
( member(ordered_pair(X0,compose(X1,X0)),compose_class(X1))
| ~ member(ordered_pair(X0,compose(X1,X0)),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).
fof(f777,plain,
( spl0_116
<=> ! [X4,X0,X1] :
( compose(X0,X1) != X4
| member(ordered_pair(X1,X4),compose_class(X0))
| ~ member(ordered_pair(X1,X4),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f788,plain,
( ! [X0,X1] :
( member(ordered_pair(X0,compose(X1,X0)),compose_class(X1))
| ~ member(ordered_pair(X0,compose(X1,X0)),cross_product(universal_class,universal_class)) )
| ~ spl0_116 ),
inference(equality_resolution,[],[f778]) ).
fof(f778,plain,
( ! [X0,X1,X4] :
( compose(X0,X1) != X4
| member(ordered_pair(X1,X4),compose_class(X0))
| ~ member(ordered_pair(X1,X4),cross_product(universal_class,universal_class)) )
| ~ spl0_116 ),
inference(avatar_component_clause,[],[f777]) ).
fof(f2625,plain,
( spl0_268
| ~ spl0_49
| ~ spl0_107 ),
inference(avatar_split_clause,[],[f730,f723,f328,f2623]) ).
fof(f2623,plain,
( spl0_268
<=> ! [X4,X5] :
( member(X5,sum_class(X4))
| ~ member(X5,universal_class)
| null_class = restrict(restrict(element_relation,universal_class,X4),singleton(X5),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).
fof(f730,plain,
( ! [X4,X5] :
( member(X5,sum_class(X4))
| ~ member(X5,universal_class)
| null_class = restrict(restrict(element_relation,universal_class,X4),singleton(X5),universal_class) )
| ~ spl0_49
| ~ spl0_107 ),
inference(superposition,[],[f724,f329]) ).
fof(f2621,plain,
( spl0_267
| ~ spl0_48
| ~ spl0_107 ),
inference(avatar_split_clause,[],[f729,f723,f324,f2619]) ).
fof(f2619,plain,
( spl0_267
<=> ! [X2,X3] :
( member(X3,inverse(X2))
| ~ member(X3,universal_class)
| null_class = restrict(flip(cross_product(X2,universal_class)),singleton(X3),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).
fof(f729,plain,
( ! [X2,X3] :
( member(X3,inverse(X2))
| ~ member(X3,universal_class)
| null_class = restrict(flip(cross_product(X2,universal_class)),singleton(X3),universal_class) )
| ~ spl0_48
| ~ spl0_107 ),
inference(superposition,[],[f724,f325]) ).
fof(f2617,plain,
( spl0_266
| ~ spl0_61
| ~ spl0_107 ),
inference(avatar_split_clause,[],[f726,f723,f401,f2615]) ).
fof(f2615,plain,
( spl0_266
<=> ! [X2,X0,X1] :
( ~ member(X0,universal_class)
| null_class = restrict(X1,singleton(X0),universal_class)
| ~ subclass(domain_of(X1),X2)
| member(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).
fof(f726,plain,
( ! [X2,X0,X1] :
( ~ member(X0,universal_class)
| null_class = restrict(X1,singleton(X0),universal_class)
| ~ subclass(domain_of(X1),X2)
| member(X0,X2) )
| ~ spl0_61
| ~ spl0_107 ),
inference(resolution,[],[f724,f402]) ).
fof(f2613,plain,
( spl0_265
| ~ spl0_77
| ~ spl0_99 ),
inference(avatar_split_clause,[],[f677,f668,f508,f2611]) ).
fof(f677,plain,
( ! [X6,X4,X5] : symmetric_difference(cross_product(X4,X5),X6) = intersection(complement(restrict(X6,X4,X5)),union(cross_product(X4,X5),X6))
| ~ spl0_77
| ~ spl0_99 ),
inference(superposition,[],[f669,f509]) ).
fof(f2609,plain,
( spl0_264
| ~ spl0_76
| ~ spl0_99 ),
inference(avatar_split_clause,[],[f676,f668,f501,f2607]) ).
fof(f676,plain,
( ! [X2,X3,X1] : symmetric_difference(X1,cross_product(X2,X3)) = intersection(complement(restrict(X1,X2,X3)),union(X1,cross_product(X2,X3)))
| ~ spl0_76
| ~ spl0_99 ),
inference(superposition,[],[f669,f502]) ).
fof(f2605,plain,
( spl0_263
| ~ spl0_49
| ~ spl0_90 ),
inference(avatar_split_clause,[],[f638,f590,f328,f2603]) ).
fof(f638,plain,
( ! [X2] : cantor(restrict(element_relation,universal_class,X2)) = intersection(sum_class(X2),diagonalise(compose(inverse(element_relation),restrict(element_relation,universal_class,X2))))
| ~ spl0_49
| ~ spl0_90 ),
inference(superposition,[],[f591,f329]) ).
fof(f2601,plain,
( spl0_262
| ~ spl0_48
| ~ spl0_90 ),
inference(avatar_split_clause,[],[f637,f590,f324,f2599]) ).
fof(f637,plain,
( ! [X1] : cantor(flip(cross_product(X1,universal_class))) = intersection(inverse(X1),diagonalise(compose(inverse(element_relation),flip(cross_product(X1,universal_class)))))
| ~ spl0_48
| ~ spl0_90 ),
inference(superposition,[],[f591,f325]) ).
fof(f2597,plain,
( spl0_261
| ~ spl0_44
| ~ spl0_89 ),
inference(avatar_split_clause,[],[f634,f586,f308,f2595]) ).
fof(f2595,plain,
( spl0_261
<=> ! [X6,X7] :
( null_class = intersection(X6,X7)
| ~ member(intersection(X6,X7),universal_class)
| member(apply(choice,intersection(X6,X7)),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).
fof(f634,plain,
( ! [X6,X7] :
( null_class = intersection(X6,X7)
| ~ member(intersection(X6,X7),universal_class)
| member(apply(choice,intersection(X6,X7)),X6) )
| ~ spl0_44
| ~ spl0_89 ),
inference(resolution,[],[f587,f309]) ).
fof(f2593,plain,
( spl0_260
| ~ spl0_45
| ~ spl0_89 ),
inference(avatar_split_clause,[],[f633,f586,f312,f2591]) ).
fof(f2591,plain,
( spl0_260
<=> ! [X4,X5] :
( null_class = intersection(X4,X5)
| ~ member(intersection(X4,X5),universal_class)
| member(apply(choice,intersection(X4,X5)),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).
fof(f633,plain,
( ! [X4,X5] :
( null_class = intersection(X4,X5)
| ~ member(intersection(X4,X5),universal_class)
| member(apply(choice,intersection(X4,X5)),X5) )
| ~ spl0_45
| ~ spl0_89 ),
inference(resolution,[],[f587,f313]) ).
fof(f2589,plain,
( spl0_259
| ~ spl0_34
| ~ spl0_85 ),
inference(avatar_split_clause,[],[f609,f569,f263,f2587]) ).
fof(f609,plain,
( ! [X10,X9] :
( regular(unordered_pair(X9,X10)) = X9
| regular(unordered_pair(X9,X10)) = X10
| null_class = unordered_pair(X9,X10) )
| ~ spl0_34
| ~ spl0_85 ),
inference(resolution,[],[f570,f264]) ).
fof(f2582,plain,
( ~ spl0_258
| ~ spl0_13
| spl0_243 ),
inference(avatar_split_clause,[],[f2490,f2226,f175,f2579]) ).
fof(f2579,plain,
( spl0_258
<=> inductive(element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).
fof(f2226,plain,
( spl0_243
<=> member(null_class,element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).
fof(f2490,plain,
( ~ inductive(element_relation)
| ~ spl0_13
| spl0_243 ),
inference(resolution,[],[f2227,f176]) ).
fof(f2227,plain,
( ~ member(null_class,element_relation)
| spl0_243 ),
inference(avatar_component_clause,[],[f2226]) ).
fof(f2518,plain,
( spl0_257
| ~ spl0_61
| ~ spl0_100 ),
inference(avatar_split_clause,[],[f719,f688,f401,f2516]) ).
fof(f2516,plain,
( spl0_257
<=> ! [X16,X13,X14,X12,X15] :
( ~ member(X12,X13)
| ~ member(X14,X15)
| ~ subclass(cross_product(X15,X13),X16)
| member(ordered_pair(X14,X12),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).
fof(f719,plain,
( ! [X16,X14,X15,X12,X13] :
( ~ member(X12,X13)
| ~ member(X14,X15)
| ~ subclass(cross_product(X15,X13),X16)
| member(ordered_pair(X14,X12),X16) )
| ~ spl0_61
| ~ spl0_100 ),
inference(resolution,[],[f689,f402]) ).
fof(f2514,plain,
( spl0_256
| ~ spl0_87
| ~ spl0_99 ),
inference(avatar_split_clause,[],[f684,f668,f578,f2512]) ).
fof(f2512,plain,
( spl0_256
<=> ! [X2,X0,X1] :
( member(X2,symmetric_difference(X0,X1))
| ~ member(X2,union(X0,X1))
| ~ member(X2,complement(intersection(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).
fof(f684,plain,
( ! [X2,X0,X1] :
( member(X2,symmetric_difference(X0,X1))
| ~ member(X2,union(X0,X1))
| ~ member(X2,complement(intersection(X0,X1))) )
| ~ spl0_87
| ~ spl0_99 ),
inference(superposition,[],[f579,f669]) ).
fof(f2510,plain,
( spl0_255
| ~ spl0_40
| ~ spl0_74 ),
inference(avatar_split_clause,[],[f537,f493,f292,f2508]) ).
fof(f537,plain,
( ! [X6,X5] :
( member(not_subclass_element(X5,complement(X6)),X6)
| ~ member(not_subclass_element(X5,complement(X6)),universal_class)
| subclass(X5,complement(X6)) )
| ~ spl0_40
| ~ spl0_74 ),
inference(resolution,[],[f494,f293]) ).
fof(f2506,plain,
( spl0_254
| ~ spl0_47
| ~ spl0_62 ),
inference(avatar_split_clause,[],[f457,f405,f320,f2504]) ).
fof(f2504,plain,
( spl0_254
<=> ! [X4] :
( ~ subclass(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X4))
| cross_product(cross_product(universal_class,universal_class),universal_class) = flip(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).
fof(f405,plain,
( spl0_62
<=> ! [X0,X1] :
( ~ subclass(X0,X1)
| ~ subclass(X1,X0)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f457,plain,
( ! [X4] :
( ~ subclass(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X4))
| cross_product(cross_product(universal_class,universal_class),universal_class) = flip(X4) )
| ~ spl0_47
| ~ spl0_62 ),
inference(resolution,[],[f406,f321]) ).
fof(f406,plain,
( ! [X0,X1] :
( ~ subclass(X1,X0)
| ~ subclass(X0,X1)
| X0 = X1 )
| ~ spl0_62 ),
inference(avatar_component_clause,[],[f405]) ).
fof(f2502,plain,
( spl0_253
| ~ spl0_46
| ~ spl0_62 ),
inference(avatar_split_clause,[],[f456,f405,f316,f2500]) ).
fof(f2500,plain,
( spl0_253
<=> ! [X3] :
( ~ subclass(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X3))
| cross_product(cross_product(universal_class,universal_class),universal_class) = rotate(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).
fof(f456,plain,
( ! [X3] :
( ~ subclass(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X3))
| cross_product(cross_product(universal_class,universal_class),universal_class) = rotate(X3) )
| ~ spl0_46
| ~ spl0_62 ),
inference(resolution,[],[f406,f317]) ).
fof(f2268,plain,
( spl0_252
| ~ spl0_115 ),
inference(avatar_split_clause,[],[f786,f773,f2266]) ).
fof(f786,plain,
( ! [X0,X1] :
( compatible(domain_of(X0),X0,X1)
| ~ function(domain_of(X0))
| ~ subclass(range_of(domain_of(X0)),domain_of(domain_of(X1))) )
| ~ spl0_115 ),
inference(equality_resolution,[],[f774]) ).
fof(f2264,plain,
( spl0_251
| ~ spl0_19
| ~ spl0_107 ),
inference(avatar_split_clause,[],[f728,f723,f200,f2262]) ).
fof(f2262,plain,
( spl0_251
<=> ! [X0,X1] :
( member(X1,range_of(X0))
| ~ member(X1,universal_class)
| null_class = restrict(inverse(X0),singleton(X1),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).
fof(f728,plain,
( ! [X0,X1] :
( member(X1,range_of(X0))
| ~ member(X1,universal_class)
| null_class = restrict(inverse(X0),singleton(X1),universal_class) )
| ~ spl0_19
| ~ spl0_107 ),
inference(superposition,[],[f724,f201]) ).
fof(f2260,plain,
( spl0_250
| ~ spl0_75
| ~ spl0_99 ),
inference(avatar_split_clause,[],[f682,f668,f497,f2258]) ).
fof(f682,plain,
( ! [X0,X1] : symmetric_difference(complement(X0),complement(X1)) = intersection(union(X0,X1),union(complement(X0),complement(X1)))
| ~ spl0_75
| ~ spl0_99 ),
inference(superposition,[],[f669,f498]) ).
fof(f2256,plain,
( spl0_249
| ~ spl0_66
| ~ spl0_99 ),
inference(avatar_split_clause,[],[f675,f668,f421,f2254]) ).
fof(f675,plain,
( ! [X0] :
( symmetric_difference(X0,regular(X0)) = intersection(complement(null_class),union(X0,regular(X0)))
| null_class = X0 )
| ~ spl0_66
| ~ spl0_99 ),
inference(superposition,[],[f669,f422]) ).
fof(f2252,plain,
( spl0_248
| ~ spl0_87
| ~ spl0_90 ),
inference(avatar_split_clause,[],[f639,f590,f578,f2250]) ).
fof(f639,plain,
( ! [X0,X1] :
( member(X1,cantor(X0))
| ~ member(X1,diagonalise(compose(inverse(element_relation),X0)))
| ~ member(X1,domain_of(X0)) )
| ~ spl0_87
| ~ spl0_90 ),
inference(superposition,[],[f579,f591]) ).
fof(f2248,plain,
( spl0_247
| ~ spl0_85
| ~ spl0_86 ),
inference(avatar_split_clause,[],[f613,f574,f569,f2246]) ).
fof(f2246,plain,
( spl0_247
<=> ! [X2,X0,X1] :
( ~ member(X2,ordered_pair(X0,X1))
| singleton(X0) = X2
| unordered_pair(X0,singleton(X1)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).
fof(f613,plain,
( ! [X2,X0,X1] :
( ~ member(X2,ordered_pair(X0,X1))
| singleton(X0) = X2
| unordered_pair(X0,singleton(X1)) = X2 )
| ~ spl0_85
| ~ spl0_86 ),
inference(superposition,[],[f570,f575]) ).
fof(f2242,plain,
( ~ spl0_244
| spl0_245
| ~ spl0_246
| ~ spl0_33
| ~ spl0_78 ),
inference(avatar_split_clause,[],[f566,f512,f259,f2239,f2235,f2231]) ).
fof(f2231,plain,
( spl0_244
<=> function(image(successor_relation,cross_product(universal_class,universal_class))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).
fof(f2235,plain,
( spl0_245
<=> inductive(cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).
fof(f512,plain,
( spl0_78
<=> ! [X0] :
( inductive(X0)
| ~ member(null_class,X0)
| ~ subclass(image(successor_relation,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f566,plain,
( ~ member(null_class,cross_product(universal_class,universal_class))
| inductive(cross_product(universal_class,universal_class))
| ~ function(image(successor_relation,cross_product(universal_class,universal_class)))
| ~ spl0_33
| ~ spl0_78 ),
inference(resolution,[],[f513,f260]) ).
fof(f513,plain,
( ! [X0] :
( ~ subclass(image(successor_relation,X0),X0)
| ~ member(null_class,X0)
| inductive(X0) )
| ~ spl0_78 ),
inference(avatar_component_clause,[],[f512]) ).
fof(f2229,plain,
( ~ spl0_242
| spl0_243
| ~ spl0_13
| ~ spl0_132 ),
inference(avatar_split_clause,[],[f893,f883,f175,f2226,f2222]) ).
fof(f2222,plain,
( spl0_242
<=> inductive(singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).
fof(f893,plain,
( member(null_class,element_relation)
| ~ inductive(singleton_relation)
| ~ spl0_13
| ~ spl0_132 ),
inference(resolution,[],[f884,f176]) ).
fof(f2220,plain,
( spl0_241
| ~ spl0_74
| ~ spl0_75 ),
inference(avatar_split_clause,[],[f551,f497,f493,f2218]) ).
fof(f551,plain,
( ! [X2,X0,X1] :
( member(X2,union(X0,X1))
| member(X2,intersection(complement(X0),complement(X1)))
| ~ member(X2,universal_class) )
| ~ spl0_74
| ~ spl0_75 ),
inference(superposition,[],[f494,f498]) ).
fof(f2216,plain,
( spl0_240
| ~ spl0_75 ),
inference(avatar_split_clause,[],[f550,f497,f2214]) ).
fof(f550,plain,
( ! [X6,X4,X5] : union(X6,intersection(complement(X4),complement(X5))) = complement(intersection(complement(X6),union(X4,X5)))
| ~ spl0_75 ),
inference(superposition,[],[f498,f498]) ).
fof(f2212,plain,
( spl0_239
| ~ spl0_75 ),
inference(avatar_split_clause,[],[f547,f497,f2210]) ).
fof(f2210,plain,
( spl0_239
<=> ! [X6,X4,X5] : union(intersection(complement(X4),complement(X5)),X6) = complement(intersection(union(X4,X5),complement(X6))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).
fof(f547,plain,
( ! [X6,X4,X5] : union(intersection(complement(X4),complement(X5)),X6) = complement(intersection(union(X4,X5),complement(X6)))
| ~ spl0_75 ),
inference(superposition,[],[f498,f498]) ).
fof(f2208,plain,
( spl0_238
| ~ spl0_49
| ~ spl0_69 ),
inference(avatar_split_clause,[],[f481,f433,f328,f2206]) ).
fof(f2206,plain,
( spl0_238
<=> ! [X2] :
( member(ordered_pair(restrict(element_relation,universal_class,X2),sum_class(X2)),domain_relation)
| ~ member(restrict(element_relation,universal_class,X2),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).
fof(f433,plain,
( spl0_69
<=> ! [X0] :
( ~ member(X0,universal_class)
| member(ordered_pair(X0,domain_of(X0)),domain_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f481,plain,
( ! [X2] :
( member(ordered_pair(restrict(element_relation,universal_class,X2),sum_class(X2)),domain_relation)
| ~ member(restrict(element_relation,universal_class,X2),universal_class) )
| ~ spl0_49
| ~ spl0_69 ),
inference(superposition,[],[f434,f329]) ).
fof(f434,plain,
( ! [X0] :
( member(ordered_pair(X0,domain_of(X0)),domain_relation)
| ~ member(X0,universal_class) )
| ~ spl0_69 ),
inference(avatar_component_clause,[],[f433]) ).
fof(f2204,plain,
( spl0_237
| ~ spl0_48
| ~ spl0_69 ),
inference(avatar_split_clause,[],[f480,f433,f324,f2202]) ).
fof(f2202,plain,
( spl0_237
<=> ! [X1] :
( member(ordered_pair(flip(cross_product(X1,universal_class)),inverse(X1)),domain_relation)
| ~ member(flip(cross_product(X1,universal_class)),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).
fof(f480,plain,
( ! [X1] :
( member(ordered_pair(flip(cross_product(X1,universal_class)),inverse(X1)),domain_relation)
| ~ member(flip(cross_product(X1,universal_class)),universal_class) )
| ~ spl0_48
| ~ spl0_69 ),
inference(superposition,[],[f434,f325]) ).
fof(f2200,plain,
( spl0_236
| ~ spl0_56
| ~ spl0_63 ),
inference(avatar_split_clause,[],[f469,f409,f356,f2198]) ).
fof(f2198,plain,
( spl0_236
<=> ! [X0,X1] :
( subclass(image(X0,X1),domain_of(domain_of(restrict(X0,X1,universal_class))))
| ~ operation(restrict(X0,X1,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).
fof(f469,plain,
( ! [X0,X1] :
( subclass(image(X0,X1),domain_of(domain_of(restrict(X0,X1,universal_class))))
| ~ operation(restrict(X0,X1,universal_class)) )
| ~ spl0_56
| ~ spl0_63 ),
inference(superposition,[],[f357,f410]) ).
fof(f2088,plain,
( ~ spl0_235
| ~ spl0_13
| spl0_214 ),
inference(avatar_split_clause,[],[f2040,f1896,f175,f2085]) ).
fof(f2085,plain,
( spl0_235
<=> inductive(subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).
fof(f2040,plain,
( ~ inductive(subset_relation)
| ~ spl0_13
| spl0_214 ),
inference(resolution,[],[f1897,f176]) ).
fof(f1897,plain,
( ~ member(null_class,subset_relation)
| spl0_214 ),
inference(avatar_component_clause,[],[f1896]) ).
fof(f2073,plain,
( spl0_234
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f769,f762,f2071]) ).
fof(f762,plain,
( spl0_113
<=> ! [X0,X1] :
( successor(X0) != X1
| member(ordered_pair(X0,X1),successor_relation)
| ~ member(ordered_pair(X0,X1),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f769,plain,
( ! [X0] :
( member(ordered_pair(X0,successor(X0)),successor_relation)
| ~ member(ordered_pair(X0,successor(X0)),cross_product(universal_class,universal_class)) )
| ~ spl0_113 ),
inference(equality_resolution,[],[f763]) ).
fof(f763,plain,
( ! [X0,X1] :
( successor(X0) != X1
| member(ordered_pair(X0,X1),successor_relation)
| ~ member(ordered_pair(X0,X1),cross_product(universal_class,universal_class)) )
| ~ spl0_113 ),
inference(avatar_component_clause,[],[f762]) ).
fof(f2069,plain,
( spl0_233
| ~ spl0_45
| ~ spl0_112 ),
inference(avatar_split_clause,[],[f759,f748,f312,f2067]) ).
fof(f759,plain,
( ! [X1] :
( ~ member(X1,subset_relation)
| member(X1,restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class)) )
| ~ spl0_45
| ~ spl0_112 ),
inference(superposition,[],[f313,f750]) ).
fof(f2065,plain,
( spl0_232
| ~ spl0_77
| ~ spl0_112 ),
inference(avatar_split_clause,[],[f755,f748,f508,f2062]) ).
fof(f755,plain,
( subset_relation = restrict(restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class),universal_class,universal_class)
| ~ spl0_77
| ~ spl0_112 ),
inference(superposition,[],[f750,f509]) ).
fof(f2060,plain,
( spl0_231
| ~ spl0_100
| ~ spl0_108 ),
inference(avatar_split_clause,[],[f752,f732,f688,f2058]) ).
fof(f2058,plain,
( spl0_231
<=> ! [X0,X1] :
( member(ordered_pair(X0,X1),element_relation)
| ~ member(X0,X1)
| ~ member(X1,universal_class)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).
fof(f752,plain,
( ! [X0,X1] :
( member(ordered_pair(X0,X1),element_relation)
| ~ member(X0,X1)
| ~ member(X1,universal_class)
| ~ member(X0,universal_class) )
| ~ spl0_100
| ~ spl0_108 ),
inference(resolution,[],[f733,f689]) ).
fof(f2056,plain,
( spl0_230
| ~ spl0_19
| ~ spl0_93 ),
inference(avatar_split_clause,[],[f645,f602,f200,f2054]) ).
fof(f2054,plain,
( spl0_230
<=> ! [X0,X1] :
( maps(inverse(X0),range_of(X0),X1)
| ~ subclass(range_of(inverse(X0)),X1)
| ~ function(inverse(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).
fof(f645,plain,
( ! [X0,X1] :
( maps(inverse(X0),range_of(X0),X1)
| ~ subclass(range_of(inverse(X0)),X1)
| ~ function(inverse(X0)) )
| ~ spl0_19
| ~ spl0_93 ),
inference(superposition,[],[f603,f201]) ).
fof(f2052,plain,
( spl0_229
| ~ spl0_27
| ~ spl0_89 ),
inference(avatar_split_clause,[],[f635,f586,f235,f2050]) ).
fof(f2050,plain,
( spl0_229
<=> ! [X8] :
( null_class = complement(X8)
| ~ member(complement(X8),universal_class)
| ~ member(apply(choice,complement(X8)),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).
fof(f635,plain,
( ! [X8] :
( null_class = complement(X8)
| ~ member(complement(X8),universal_class)
| ~ member(apply(choice,complement(X8)),X8) )
| ~ spl0_27
| ~ spl0_89 ),
inference(resolution,[],[f587,f236]) ).
fof(f2048,plain,
( spl0_228
| ~ spl0_61
| ~ spl0_89 ),
inference(avatar_split_clause,[],[f631,f586,f401,f2046]) ).
fof(f631,plain,
( ! [X0,X1] :
( null_class = X0
| ~ member(X0,universal_class)
| ~ subclass(X0,X1)
| member(apply(choice,X0),X1) )
| ~ spl0_61
| ~ spl0_89 ),
inference(resolution,[],[f587,f402]) ).
fof(f2044,plain,
( spl0_227
| ~ spl0_76
| ~ spl0_87 ),
inference(avatar_split_clause,[],[f627,f578,f501,f2042]) ).
fof(f2042,plain,
( spl0_227
<=> ! [X3,X4,X5,X2] :
( member(X5,restrict(X2,X3,X4))
| ~ member(X5,cross_product(X3,X4))
| ~ member(X5,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).
fof(f627,plain,
( ! [X2,X3,X4,X5] :
( member(X5,restrict(X2,X3,X4))
| ~ member(X5,cross_product(X3,X4))
| ~ member(X5,X2) )
| ~ spl0_76
| ~ spl0_87 ),
inference(superposition,[],[f579,f502]) ).
fof(f2039,plain,
( spl0_226
| ~ spl0_61
| ~ spl0_87 ),
inference(avatar_split_clause,[],[f624,f578,f401,f2037]) ).
fof(f624,plain,
( ! [X8,X6,X9,X7] :
( ~ member(X6,X7)
| ~ member(X6,X8)
| ~ subclass(intersection(X8,X7),X9)
| member(X6,X9) )
| ~ spl0_61
| ~ spl0_87 ),
inference(resolution,[],[f579,f402]) ).
fof(f2035,plain,
( spl0_225
| ~ spl0_42
| ~ spl0_86 ),
inference(avatar_split_clause,[],[f614,f574,f300,f2033]) ).
fof(f2033,plain,
( spl0_225
<=> ! [X4,X3] :
( member(unordered_pair(X3,singleton(X4)),ordered_pair(X3,X4))
| ~ member(unordered_pair(X3,singleton(X4)),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).
fof(f300,plain,
( spl0_42
<=> ! [X0,X1] :
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f614,plain,
( ! [X3,X4] :
( member(unordered_pair(X3,singleton(X4)),ordered_pair(X3,X4))
| ~ member(unordered_pair(X3,singleton(X4)),universal_class) )
| ~ spl0_42
| ~ spl0_86 ),
inference(superposition,[],[f301,f575]) ).
fof(f301,plain,
( ! [X0,X1] :
( member(X1,unordered_pair(X0,X1))
| ~ member(X1,universal_class) )
| ~ spl0_42 ),
inference(avatar_component_clause,[],[f300]) ).
fof(f2031,plain,
( spl0_224
| ~ spl0_66
| ~ spl0_77 ),
inference(avatar_split_clause,[],[f557,f508,f421,f2029]) ).
fof(f557,plain,
( ! [X3,X4] :
( null_class = restrict(regular(cross_product(X3,X4)),X3,X4)
| null_class = cross_product(X3,X4) )
| ~ spl0_66
| ~ spl0_77 ),
inference(superposition,[],[f509,f422]) ).
fof(f2027,plain,
( spl0_222
| ~ spl0_223
| ~ spl0_37
| ~ spl0_62 ),
inference(avatar_split_clause,[],[f468,f405,f276,f2024,f2020]) ).
fof(f2020,plain,
( spl0_222
<=> cross_product(universal_class,cross_product(universal_class,universal_class)) = application_function ),
introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).
fof(f2024,plain,
( spl0_223
<=> subclass(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).
fof(f468,plain,
( ~ subclass(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function)
| cross_product(universal_class,cross_product(universal_class,universal_class)) = application_function
| ~ spl0_37
| ~ spl0_62 ),
inference(resolution,[],[f406,f278]) ).
fof(f2018,plain,
( spl0_220
| ~ spl0_221
| ~ spl0_36
| ~ spl0_62 ),
inference(avatar_split_clause,[],[f466,f405,f271,f2015,f2011]) ).
fof(f2011,plain,
( spl0_220
<=> composition_function = cross_product(universal_class,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).
fof(f2015,plain,
( spl0_221
<=> subclass(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).
fof(f466,plain,
( ~ subclass(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function)
| composition_function = cross_product(universal_class,cross_product(universal_class,universal_class))
| ~ spl0_36
| ~ spl0_62 ),
inference(resolution,[],[f406,f273]) ).
fof(f2009,plain,
( spl0_219
| ~ spl0_51
| ~ spl0_62 ),
inference(avatar_split_clause,[],[f464,f405,f336,f2007]) ).
fof(f2007,plain,
( spl0_219
<=> ! [X11] :
( ~ subclass(identity_relation,compose(X11,inverse(X11)))
| identity_relation = compose(X11,inverse(X11))
| ~ single_valued_class(X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).
fof(f464,plain,
( ! [X11] :
( ~ subclass(identity_relation,compose(X11,inverse(X11)))
| identity_relation = compose(X11,inverse(X11))
| ~ single_valued_class(X11) )
| ~ spl0_51
| ~ spl0_62 ),
inference(resolution,[],[f406,f337]) ).
fof(f2005,plain,
( spl0_218
| ~ spl0_54
| ~ spl0_62 ),
inference(avatar_split_clause,[],[f463,f405,f348,f2003]) ).
fof(f2003,plain,
( spl0_218
<=> ! [X10] :
( ~ subclass(identity_relation,compose(X10,inverse(X10)))
| identity_relation = compose(X10,inverse(X10))
| ~ function(X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).
fof(f463,plain,
( ! [X10] :
( ~ subclass(identity_relation,compose(X10,inverse(X10)))
| identity_relation = compose(X10,inverse(X10))
| ~ function(X10) )
| ~ spl0_54
| ~ spl0_62 ),
inference(resolution,[],[f406,f349]) ).
fof(f2001,plain,
( spl0_217
| ~ spl0_32
| ~ spl0_62 ),
inference(avatar_split_clause,[],[f462,f405,f255,f1999]) ).
fof(f1999,plain,
( spl0_217
<=> ! [X9,X8] :
( ~ subclass(cross_product(universal_class,universal_class),compose(X8,X9))
| cross_product(universal_class,universal_class) = compose(X8,X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).
fof(f462,plain,
( ! [X8,X9] :
( ~ subclass(cross_product(universal_class,universal_class),compose(X8,X9))
| cross_product(universal_class,universal_class) = compose(X8,X9) )
| ~ spl0_32
| ~ spl0_62 ),
inference(resolution,[],[f406,f256]) ).
fof(f1997,plain,
( spl0_216
| ~ spl0_56
| ~ spl0_62 ),
inference(avatar_split_clause,[],[f458,f405,f356,f1995]) ).
fof(f1995,plain,
( spl0_216
<=> ! [X5] :
( ~ subclass(domain_of(domain_of(X5)),range_of(X5))
| domain_of(domain_of(X5)) = range_of(X5)
| ~ operation(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).
fof(f458,plain,
( ! [X5] :
( ~ subclass(domain_of(domain_of(X5)),range_of(X5))
| domain_of(domain_of(X5)) = range_of(X5)
| ~ operation(X5) )
| ~ spl0_56
| ~ spl0_62 ),
inference(resolution,[],[f406,f357]) ).
fof(f1993,plain,
( spl0_215
| ~ spl0_49
| ~ spl0_56 ),
inference(avatar_split_clause,[],[f398,f356,f328,f1991]) ).
fof(f398,plain,
( ! [X2] :
( subclass(range_of(restrict(element_relation,universal_class,X2)),domain_of(sum_class(X2)))
| ~ operation(restrict(element_relation,universal_class,X2)) )
| ~ spl0_49
| ~ spl0_56 ),
inference(superposition,[],[f357,f329]) ).
fof(f1899,plain,
( ~ spl0_213
| spl0_214
| ~ spl0_13
| ~ spl0_60 ),
inference(avatar_split_clause,[],[f866,f388,f175,f1896,f1892]) ).
fof(f1892,plain,
( spl0_213
<=> inductive(identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).
fof(f866,plain,
( member(null_class,subset_relation)
| ~ inductive(identity_relation)
| ~ spl0_13
| ~ spl0_60 ),
inference(resolution,[],[f389,f176]) ).
fof(f1730,plain,
( spl0_212
| ~ spl0_28
| ~ spl0_99 ),
inference(avatar_split_clause,[],[f683,f668,f239,f1728]) ).
fof(f683,plain,
( ! [X0] : symmetric_difference(X0,singleton(X0)) = intersection(complement(intersection(X0,singleton(X0))),successor(X0))
| ~ spl0_28
| ~ spl0_99 ),
inference(superposition,[],[f669,f240]) ).
fof(f1726,plain,
( spl0_211
| ~ spl0_19
| ~ spl0_90 ),
inference(avatar_split_clause,[],[f636,f590,f200,f1724]) ).
fof(f636,plain,
( ! [X0] : cantor(inverse(X0)) = intersection(range_of(X0),diagonalise(compose(inverse(element_relation),inverse(X0))))
| ~ spl0_19
| ~ spl0_90 ),
inference(superposition,[],[f591,f201]) ).
fof(f1722,plain,
( spl0_210
| ~ spl0_70
| ~ spl0_87 ),
inference(avatar_split_clause,[],[f629,f578,f437,f1720]) ).
fof(f1720,plain,
( spl0_210
<=> ! [X10] :
( member(X10,singleton_relation)
| ~ member(X10,element_relation)
| ~ member(X10,complement(compose(element_relation,complement(identity_relation)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).
fof(f629,plain,
( ! [X10] :
( member(X10,singleton_relation)
| ~ member(X10,element_relation)
| ~ member(X10,complement(compose(element_relation,complement(identity_relation)))) )
| ~ spl0_70
| ~ spl0_87 ),
inference(superposition,[],[f579,f439]) ).
fof(f1718,plain,
( spl0_209
| ~ spl0_66
| ~ spl0_87 ),
inference(avatar_split_clause,[],[f626,f578,f421,f1716]) ).
fof(f626,plain,
( ! [X0,X1] :
( member(X1,null_class)
| ~ member(X1,regular(X0))
| ~ member(X1,X0)
| null_class = X0 )
| ~ spl0_66
| ~ spl0_87 ),
inference(superposition,[],[f579,f422]) ).
fof(f1714,plain,
( spl0_208
| ~ spl0_61
| ~ spl0_79 ),
inference(avatar_split_clause,[],[f567,f516,f401,f1712]) ).
fof(f567,plain,
( ! [X2,X0,X1] :
( ~ member(X0,universal_class)
| ~ function(X1)
| ~ subclass(universal_class,X2)
| member(image(X1,X0),X2) )
| ~ spl0_61
| ~ spl0_79 ),
inference(resolution,[],[f517,f402]) ).
fof(f1710,plain,
( spl0_207
| ~ spl0_76
| ~ spl0_77 ),
inference(avatar_split_clause,[],[f558,f508,f501,f1708]) ).
fof(f558,plain,
( ! [X8,X6,X7,X5] : restrict(cross_product(X5,X6),X7,X8) = restrict(cross_product(X7,X8),X5,X6)
| ~ spl0_76
| ~ spl0_77 ),
inference(superposition,[],[f509,f502]) ).
fof(f1706,plain,
( spl0_206
| ~ spl0_50
| ~ spl0_75 ),
inference(avatar_split_clause,[],[f552,f497,f332,f1704]) ).
fof(f552,plain,
( ! [X3,X4] : power_class(intersection(complement(X3),complement(X4))) = complement(image(element_relation,union(X3,X4)))
| ~ spl0_50
| ~ spl0_75 ),
inference(superposition,[],[f333,f498]) ).
fof(f1702,plain,
( spl0_205
| ~ spl0_55
| ~ spl0_75 ),
inference(avatar_split_clause,[],[f549,f497,f352,f1700]) ).
fof(f549,plain,
( ! [X2,X3] : union(X3,domain_of(intersection(X2,identity_relation))) = complement(intersection(complement(X3),diagonalise(X2)))
| ~ spl0_55
| ~ spl0_75 ),
inference(superposition,[],[f498,f353]) ).
fof(f1698,plain,
( spl0_204
| ~ spl0_50
| ~ spl0_75 ),
inference(avatar_split_clause,[],[f548,f497,f332,f1696]) ).
fof(f548,plain,
( ! [X0,X1] : union(X1,image(element_relation,complement(X0))) = complement(intersection(complement(X1),power_class(X0)))
| ~ spl0_50
| ~ spl0_75 ),
inference(superposition,[],[f498,f333]) ).
fof(f1694,plain,
( spl0_203
| ~ spl0_55
| ~ spl0_75 ),
inference(avatar_split_clause,[],[f546,f497,f352,f1692]) ).
fof(f546,plain,
( ! [X2,X3] : union(domain_of(intersection(X2,identity_relation)),X3) = complement(intersection(diagonalise(X2),complement(X3)))
| ~ spl0_55
| ~ spl0_75 ),
inference(superposition,[],[f498,f353]) ).
fof(f1690,plain,
( spl0_202
| ~ spl0_50
| ~ spl0_75 ),
inference(avatar_split_clause,[],[f545,f497,f332,f1688]) ).
fof(f545,plain,
( ! [X0,X1] : union(image(element_relation,complement(X0)),X1) = complement(intersection(power_class(X0),complement(X1)))
| ~ spl0_50
| ~ spl0_75 ),
inference(superposition,[],[f498,f333]) ).
fof(f1686,plain,
( spl0_201
| ~ spl0_55
| ~ spl0_74 ),
inference(avatar_split_clause,[],[f539,f493,f352,f1684]) ).
fof(f1684,plain,
( spl0_201
<=> ! [X2,X3] :
( member(X3,diagonalise(X2))
| member(X3,domain_of(intersection(X2,identity_relation)))
| ~ member(X3,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).
fof(f539,plain,
( ! [X2,X3] :
( member(X3,diagonalise(X2))
| member(X3,domain_of(intersection(X2,identity_relation)))
| ~ member(X3,universal_class) )
| ~ spl0_55
| ~ spl0_74 ),
inference(superposition,[],[f494,f353]) ).
fof(f1682,plain,
( spl0_200
| ~ spl0_50
| ~ spl0_74 ),
inference(avatar_split_clause,[],[f538,f493,f332,f1680]) ).
fof(f1680,plain,
( spl0_200
<=> ! [X0,X1] :
( member(X1,power_class(X0))
| member(X1,image(element_relation,complement(X0)))
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).
fof(f538,plain,
( ! [X0,X1] :
( member(X1,power_class(X0))
| member(X1,image(element_relation,complement(X0)))
| ~ member(X1,universal_class) )
| ~ spl0_50
| ~ spl0_74 ),
inference(superposition,[],[f494,f333]) ).
fof(f1678,plain,
( spl0_199
| ~ spl0_61
| ~ spl0_74 ),
inference(avatar_split_clause,[],[f536,f493,f401,f1676]) ).
fof(f536,plain,
( ! [X2,X3,X4] :
( member(X2,X3)
| ~ member(X2,universal_class)
| ~ subclass(complement(X3),X4)
| member(X2,X4) )
| ~ spl0_61
| ~ spl0_74 ),
inference(resolution,[],[f494,f402]) ).
fof(f1674,plain,
( spl0_198
| ~ spl0_19
| ~ spl0_48
| ~ spl0_56 ),
inference(avatar_split_clause,[],[f399,f356,f324,f200,f1672]) ).
fof(f1672,plain,
( spl0_198
<=> ! [X1] :
( subclass(range_of(flip(cross_product(X1,universal_class))),range_of(X1))
| ~ operation(flip(cross_product(X1,universal_class))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).
fof(f399,plain,
( ! [X1] :
( subclass(range_of(flip(cross_product(X1,universal_class))),range_of(X1))
| ~ operation(flip(cross_product(X1,universal_class))) )
| ~ spl0_19
| ~ spl0_48
| ~ spl0_56 ),
inference(forward_demodulation,[],[f397,f201]) ).
fof(f397,plain,
( ! [X1] :
( subclass(range_of(flip(cross_product(X1,universal_class))),domain_of(inverse(X1)))
| ~ operation(flip(cross_product(X1,universal_class))) )
| ~ spl0_48
| ~ spl0_56 ),
inference(superposition,[],[f357,f325]) ).
fof(f1594,plain,
( ~ spl0_196
| spl0_197
| ~ spl0_16
| ~ spl0_149 ),
inference(avatar_split_clause,[],[f1083,f1031,f187,f1591,f1587]) ).
fof(f1587,plain,
( spl0_196
<=> single_valued_class(domain_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).
fof(f1591,plain,
( spl0_197
<=> function(domain_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).
fof(f1083,plain,
( function(domain_relation)
| ~ single_valued_class(domain_relation)
| ~ spl0_16
| ~ spl0_149 ),
inference(resolution,[],[f1032,f189]) ).
fof(f1525,plain,
( spl0_195
| ~ spl0_20
| ~ spl0_99 ),
inference(avatar_split_clause,[],[f681,f668,f204,f1522]) ).
fof(f681,plain,
( symmetric_difference(inverse(subset_relation),subset_relation) = intersection(complement(identity_relation),union(inverse(subset_relation),subset_relation))
| ~ spl0_20
| ~ spl0_99 ),
inference(superposition,[],[f669,f206]) ).
fof(f1520,plain,
( spl0_194
| ~ spl0_27
| ~ spl0_75 ),
inference(avatar_split_clause,[],[f554,f497,f235,f1518]) ).
fof(f554,plain,
( ! [X8,X9,X7] :
( ~ member(X9,union(X7,X8))
| ~ member(X9,intersection(complement(X7),complement(X8))) )
| ~ spl0_27
| ~ spl0_75 ),
inference(superposition,[],[f236,f498]) ).
fof(f1516,plain,
( spl0_193
| ~ spl0_61
| ~ spl0_69 ),
inference(avatar_split_clause,[],[f478,f433,f401,f1514]) ).
fof(f478,plain,
( ! [X2,X1] :
( ~ member(X1,universal_class)
| ~ subclass(domain_relation,X2)
| member(ordered_pair(X1,domain_of(X1)),X2) )
| ~ spl0_61
| ~ spl0_69 ),
inference(resolution,[],[f434,f402]) ).
fof(f1512,plain,
( spl0_192
| ~ spl0_24
| ~ spl0_62 ),
inference(avatar_split_clause,[],[f465,f405,f221,f1510]) ).
fof(f1510,plain,
( spl0_192
<=> ! [X12] :
( ~ subclass(cross_product(universal_class,universal_class),compose_class(X12))
| cross_product(universal_class,universal_class) = compose_class(X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).
fof(f465,plain,
( ! [X12] :
( ~ subclass(cross_product(universal_class,universal_class),compose_class(X12))
| cross_product(universal_class,universal_class) = compose_class(X12) )
| ~ spl0_24
| ~ spl0_62 ),
inference(resolution,[],[f406,f222]) ).
fof(f1508,plain,
( spl0_191
| ~ spl0_29
| ~ spl0_62 ),
inference(avatar_split_clause,[],[f459,f405,f243,f1506]) ).
fof(f1506,plain,
( spl0_191
<=> ! [X6] :
( ~ subclass(X6,image(successor_relation,X6))
| image(successor_relation,X6) = X6
| ~ inductive(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).
fof(f459,plain,
( ! [X6] :
( ~ subclass(X6,image(successor_relation,X6))
| image(successor_relation,X6) = X6
| ~ inductive(X6) )
| ~ spl0_29
| ~ spl0_62 ),
inference(resolution,[],[f406,f244]) ).
fof(f1504,plain,
( spl0_190
| ~ spl0_33
| ~ spl0_62 ),
inference(avatar_split_clause,[],[f454,f405,f259,f1502]) ).
fof(f1502,plain,
( spl0_190
<=> ! [X2] :
( ~ subclass(cross_product(universal_class,universal_class),X2)
| cross_product(universal_class,universal_class) = X2
| ~ function(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).
fof(f454,plain,
( ! [X2] :
( ~ subclass(cross_product(universal_class,universal_class),X2)
| cross_product(universal_class,universal_class) = X2
| ~ function(X2) )
| ~ spl0_33
| ~ spl0_62 ),
inference(resolution,[],[f406,f260]) ).
fof(f1500,plain,
( spl0_189
| ~ spl0_39
| ~ spl0_45 ),
inference(avatar_split_clause,[],[f380,f312,f288,f1498]) ).
fof(f380,plain,
( ! [X2,X0,X1] :
( member(not_subclass_element(intersection(X0,X1),X2),X1)
| subclass(intersection(X0,X1),X2) )
| ~ spl0_39
| ~ spl0_45 ),
inference(resolution,[],[f313,f289]) ).
fof(f1496,plain,
( spl0_188
| ~ spl0_39
| ~ spl0_44 ),
inference(avatar_split_clause,[],[f376,f308,f288,f1494]) ).
fof(f376,plain,
( ! [X2,X0,X1] :
( member(not_subclass_element(intersection(X0,X1),X2),X0)
| subclass(intersection(X0,X1),X2) )
| ~ spl0_39
| ~ spl0_44 ),
inference(resolution,[],[f309,f289]) ).
fof(f1347,plain,
( spl0_187
| ~ spl0_44
| ~ spl0_99 ),
inference(avatar_split_clause,[],[f686,f668,f308,f1345]) ).
fof(f686,plain,
( ! [X8,X6,X7] :
( ~ member(X8,symmetric_difference(X6,X7))
| member(X8,complement(intersection(X6,X7))) )
| ~ spl0_44
| ~ spl0_99 ),
inference(superposition,[],[f309,f669]) ).
fof(f1343,plain,
( spl0_185
| spl0_186
| ~ spl0_13
| ~ spl0_95 ),
inference(avatar_split_clause,[],[f672,f649,f175,f1340,f1337]) ).
fof(f1337,plain,
( spl0_185
<=> ! [X4,X3] : ~ inductive(cross_product(X3,X4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).
fof(f672,plain,
( ! [X3,X4] :
( null_class = ordered_pair(first(null_class),second(null_class))
| ~ inductive(cross_product(X3,X4)) )
| ~ spl0_13
| ~ spl0_95 ),
inference(resolution,[],[f650,f176]) ).
fof(f1335,plain,
( spl0_184
| ~ spl0_45
| ~ spl0_90 ),
inference(avatar_split_clause,[],[f640,f590,f312,f1333]) ).
fof(f640,plain,
( ! [X2,X3] :
( ~ member(X3,cantor(X2))
| member(X3,diagonalise(compose(inverse(element_relation),X2))) )
| ~ spl0_45
| ~ spl0_90 ),
inference(superposition,[],[f313,f591]) ).
fof(f1331,plain,
( spl0_183
| ~ spl0_55
| ~ spl0_77 ),
inference(avatar_split_clause,[],[f562,f508,f352,f1329]) ).
fof(f562,plain,
( ! [X12,X13] : diagonalise(cross_product(X12,X13)) = complement(domain_of(restrict(identity_relation,X12,X13)))
| ~ spl0_55
| ~ spl0_77 ),
inference(superposition,[],[f353,f509]) ).
fof(f1327,plain,
( spl0_182
| ~ spl0_45
| ~ spl0_76 ),
inference(avatar_split_clause,[],[f555,f501,f312,f1325]) ).
fof(f555,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X3,restrict(X0,X1,X2))
| member(X3,cross_product(X1,X2)) )
| ~ spl0_45
| ~ spl0_76 ),
inference(superposition,[],[f313,f502]) ).
fof(f1323,plain,
( ~ spl0_180
| spl0_181
| ~ spl0_12
| ~ spl0_149 ),
inference(avatar_split_clause,[],[f1079,f1031,f170,f1320,f1316]) ).
fof(f1316,plain,
( spl0_180
<=> single_valued_class(successor_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).
fof(f1320,plain,
( spl0_181
<=> function(successor_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).
fof(f1079,plain,
( function(successor_relation)
| ~ single_valued_class(successor_relation)
| ~ spl0_12
| ~ spl0_149 ),
inference(resolution,[],[f1032,f172]) ).
fof(f1314,plain,
( spl0_179
| ~ spl0_19
| ~ spl0_69 ),
inference(avatar_split_clause,[],[f479,f433,f200,f1312]) ).
fof(f479,plain,
( ! [X0] :
( member(ordered_pair(inverse(X0),range_of(X0)),domain_relation)
| ~ member(inverse(X0),universal_class) )
| ~ spl0_19
| ~ spl0_69 ),
inference(superposition,[],[f434,f201]) ).
fof(f1310,plain,
( spl0_178
| ~ spl0_30
| ~ spl0_67 ),
inference(avatar_split_clause,[],[f476,f425,f247,f1308]) ).
fof(f247,plain,
( spl0_30
<=> ! [X0] :
( ~ member(X0,universal_class)
| member(sum_class(X0),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f476,plain,
( ! [X0,X1] :
( member(apply(X0,X1),universal_class)
| ~ member(image(X0,singleton(X1)),universal_class) )
| ~ spl0_30
| ~ spl0_67 ),
inference(superposition,[],[f248,f426]) ).
fof(f248,plain,
( ! [X0] :
( member(sum_class(X0),universal_class)
| ~ member(X0,universal_class) )
| ~ spl0_30 ),
inference(avatar_component_clause,[],[f247]) ).
fof(f1306,plain,
( spl0_177
| ~ spl0_39
| ~ spl0_61 ),
inference(avatar_split_clause,[],[f443,f401,f288,f1304]) ).
fof(f443,plain,
( ! [X8,X6,X7] :
( ~ subclass(X6,X7)
| member(not_subclass_element(X6,X8),X7)
| subclass(X6,X8) )
| ~ spl0_39
| ~ spl0_61 ),
inference(resolution,[],[f402,f289]) ).
fof(f1302,plain,
( spl0_176
| ~ spl0_42
| ~ spl0_61 ),
inference(avatar_split_clause,[],[f442,f401,f300,f1300]) ).
fof(f442,plain,
( ! [X3,X4,X5] :
( ~ subclass(unordered_pair(X3,X4),X5)
| member(X4,X5)
| ~ member(X4,universal_class) )
| ~ spl0_42
| ~ spl0_61 ),
inference(resolution,[],[f402,f301]) ).
fof(f1298,plain,
( spl0_175
| ~ spl0_41
| ~ spl0_61 ),
inference(avatar_split_clause,[],[f441,f401,f296,f1296]) ).
fof(f296,plain,
( spl0_41
<=> ! [X0,X1] :
( ~ member(X0,universal_class)
| member(X0,unordered_pair(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f441,plain,
( ! [X2,X0,X1] :
( ~ subclass(unordered_pair(X0,X1),X2)
| member(X0,X2)
| ~ member(X0,universal_class) )
| ~ spl0_41
| ~ spl0_61 ),
inference(resolution,[],[f402,f297]) ).
fof(f297,plain,
( ! [X0,X1] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) )
| ~ spl0_41 ),
inference(avatar_component_clause,[],[f296]) ).
fof(f1294,plain,
( spl0_174
| ~ spl0_50
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f393,f352,f332,f1292]) ).
fof(f393,plain,
( ! [X0] : power_class(domain_of(intersection(X0,identity_relation))) = complement(image(element_relation,diagonalise(X0)))
| ~ spl0_50
| ~ spl0_55 ),
inference(superposition,[],[f333,f353]) ).
fof(f1290,plain,
( spl0_173
| ~ spl0_50 ),
inference(avatar_split_clause,[],[f384,f332,f1288]) ).
fof(f384,plain,
( ! [X0] : power_class(image(element_relation,complement(X0))) = complement(image(element_relation,power_class(X0)))
| ~ spl0_50 ),
inference(superposition,[],[f333,f333]) ).
fof(f1286,plain,
( spl0_172
| ~ spl0_34
| ~ spl0_45 ),
inference(avatar_split_clause,[],[f382,f312,f263,f1284]) ).
fof(f382,plain,
( ! [X6,X5] :
( member(regular(intersection(X5,X6)),X6)
| null_class = intersection(X5,X6) )
| ~ spl0_34
| ~ spl0_45 ),
inference(resolution,[],[f313,f264]) ).
fof(f1282,plain,
( spl0_171
| ~ spl0_34
| ~ spl0_44 ),
inference(avatar_split_clause,[],[f378,f308,f263,f1280]) ).
fof(f378,plain,
( ! [X6,X5] :
( member(regular(intersection(X5,X6)),X5)
| null_class = intersection(X5,X6) )
| ~ spl0_34
| ~ spl0_44 ),
inference(resolution,[],[f309,f264]) ).
fof(f1171,plain,
( spl0_170
| ~ spl0_45
| ~ spl0_99 ),
inference(avatar_split_clause,[],[f685,f668,f312,f1169]) ).
fof(f685,plain,
( ! [X3,X4,X5] :
( ~ member(X5,symmetric_difference(X3,X4))
| member(X5,union(X3,X4)) )
| ~ spl0_45
| ~ spl0_99 ),
inference(superposition,[],[f313,f669]) ).
fof(f1167,plain,
( spl0_169
| ~ spl0_20
| ~ spl0_87 ),
inference(avatar_split_clause,[],[f630,f578,f204,f1165]) ).
fof(f630,plain,
( ! [X11] :
( member(X11,identity_relation)
| ~ member(X11,subset_relation)
| ~ member(X11,inverse(subset_relation)) )
| ~ spl0_20
| ~ spl0_87 ),
inference(superposition,[],[f579,f206]) ).
fof(f1163,plain,
( spl0_168
| ~ spl0_41
| ~ spl0_86 ),
inference(avatar_split_clause,[],[f615,f574,f296,f1161]) ).
fof(f615,plain,
( ! [X6,X5] :
( member(singleton(X5),ordered_pair(X5,X6))
| ~ member(singleton(X5),universal_class) )
| ~ spl0_41
| ~ spl0_86 ),
inference(superposition,[],[f297,f575]) ).
fof(f1159,plain,
( spl0_167
| ~ spl0_13
| ~ spl0_85 ),
inference(avatar_split_clause,[],[f608,f569,f175,f1157]) ).
fof(f608,plain,
( ! [X8,X7] :
( null_class = X7
| null_class = X8
| ~ inductive(unordered_pair(X7,X8)) )
| ~ spl0_13
| ~ spl0_85 ),
inference(resolution,[],[f570,f176]) ).
fof(f1155,plain,
( spl0_166
| ~ spl0_44
| ~ spl0_70 ),
inference(avatar_split_clause,[],[f483,f437,f308,f1153]) ).
fof(f483,plain,
( ! [X1] :
( ~ member(X1,singleton_relation)
| member(X1,complement(compose(element_relation,complement(identity_relation)))) )
| ~ spl0_44
| ~ spl0_70 ),
inference(superposition,[],[f309,f439]) ).
fof(f1151,plain,
( spl0_165
| ~ spl0_45
| ~ spl0_66 ),
inference(avatar_split_clause,[],[f474,f421,f312,f1149]) ).
fof(f474,plain,
( ! [X0,X1] :
( ~ member(X1,null_class)
| member(X1,regular(X0))
| null_class = X0 )
| ~ spl0_45
| ~ spl0_66 ),
inference(superposition,[],[f313,f422]) ).
fof(f1147,plain,
( ~ spl0_163
| spl0_164
| ~ spl0_11
| ~ spl0_149 ),
inference(avatar_split_clause,[],[f1077,f1031,f165,f1144,f1140]) ).
fof(f1140,plain,
( spl0_163
<=> single_valued_class(element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
fof(f1144,plain,
( spl0_164
<=> function(element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
fof(f165,plain,
( spl0_11
<=> subclass(element_relation,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f1077,plain,
( function(element_relation)
| ~ single_valued_class(element_relation)
| ~ spl0_11
| ~ spl0_149 ),
inference(resolution,[],[f1032,f167]) ).
fof(f167,plain,
( subclass(element_relation,cross_product(universal_class,universal_class))
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f165]) ).
fof(f1138,plain,
( spl0_161
| ~ spl0_162
| ~ spl0_16
| ~ spl0_62 ),
inference(avatar_split_clause,[],[f467,f405,f187,f1135,f1131]) ).
fof(f1131,plain,
( spl0_161
<=> cross_product(universal_class,universal_class) = domain_relation ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
fof(f1135,plain,
( spl0_162
<=> subclass(cross_product(universal_class,universal_class),domain_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
fof(f467,plain,
( ~ subclass(cross_product(universal_class,universal_class),domain_relation)
| cross_product(universal_class,universal_class) = domain_relation
| ~ spl0_16
| ~ spl0_62 ),
inference(resolution,[],[f406,f189]) ).
fof(f1129,plain,
( spl0_159
| ~ spl0_160
| ~ spl0_12
| ~ spl0_62 ),
inference(avatar_split_clause,[],[f460,f405,f170,f1126,f1122]) ).
fof(f1122,plain,
( spl0_159
<=> cross_product(universal_class,universal_class) = successor_relation ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f1126,plain,
( spl0_160
<=> subclass(cross_product(universal_class,universal_class),successor_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
fof(f460,plain,
( ~ subclass(cross_product(universal_class,universal_class),successor_relation)
| cross_product(universal_class,universal_class) = successor_relation
| ~ spl0_12
| ~ spl0_62 ),
inference(resolution,[],[f406,f172]) ).
fof(f1120,plain,
( spl0_157
| ~ spl0_158
| ~ spl0_11
| ~ spl0_62 ),
inference(avatar_split_clause,[],[f455,f405,f165,f1117,f1113]) ).
fof(f1113,plain,
( spl0_157
<=> element_relation = cross_product(universal_class,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f1117,plain,
( spl0_158
<=> subclass(cross_product(universal_class,universal_class),element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f455,plain,
( ~ subclass(cross_product(universal_class,universal_class),element_relation)
| element_relation = cross_product(universal_class,universal_class)
| ~ spl0_11
| ~ spl0_62 ),
inference(resolution,[],[f406,f167]) ).
fof(f1111,plain,
( spl0_156
| ~ spl0_34
| ~ spl0_61 ),
inference(avatar_split_clause,[],[f450,f401,f263,f1109]) ).
fof(f450,plain,
( ! [X21,X22] :
( ~ subclass(X21,X22)
| member(regular(X21),X22)
| null_class = X21 )
| ~ spl0_34
| ~ spl0_61 ),
inference(resolution,[],[f402,f264]) ).
fof(f1107,plain,
( spl0_155
| ~ spl0_31
| ~ spl0_61 ),
inference(avatar_split_clause,[],[f449,f401,f251,f1105]) ).
fof(f251,plain,
( spl0_31
<=> ! [X2] :
( ~ member(X2,universal_class)
| member(power_class(X2),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f449,plain,
( ! [X19,X20] :
( ~ subclass(universal_class,X19)
| member(power_class(X20),X19)
| ~ member(X20,universal_class) )
| ~ spl0_31
| ~ spl0_61 ),
inference(resolution,[],[f402,f252]) ).
fof(f252,plain,
( ! [X2] :
( member(power_class(X2),universal_class)
| ~ member(X2,universal_class) )
| ~ spl0_31 ),
inference(avatar_component_clause,[],[f251]) ).
fof(f1103,plain,
( spl0_154
| ~ spl0_30
| ~ spl0_61 ),
inference(avatar_split_clause,[],[f448,f401,f247,f1101]) ).
fof(f448,plain,
( ! [X18,X17] :
( ~ subclass(universal_class,X17)
| member(sum_class(X18),X17)
| ~ member(X18,universal_class) )
| ~ spl0_30
| ~ spl0_61 ),
inference(resolution,[],[f402,f248]) ).
fof(f1099,plain,
( spl0_153
| ~ spl0_19
| ~ spl0_56 ),
inference(avatar_split_clause,[],[f396,f356,f200,f1097]) ).
fof(f396,plain,
( ! [X0] :
( subclass(range_of(inverse(X0)),domain_of(range_of(X0)))
| ~ operation(inverse(X0)) )
| ~ spl0_19
| ~ spl0_56 ),
inference(superposition,[],[f357,f201]) ).
fof(f1095,plain,
( spl0_152
| ~ spl0_27
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f395,f352,f235,f1093]) ).
fof(f395,plain,
( ! [X2,X3] :
( ~ member(X3,diagonalise(X2))
| ~ member(X3,domain_of(intersection(X2,identity_relation))) )
| ~ spl0_27
| ~ spl0_55 ),
inference(superposition,[],[f236,f353]) ).
fof(f1091,plain,
( spl0_151
| ~ spl0_27
| ~ spl0_50 ),
inference(avatar_split_clause,[],[f386,f332,f235,f1089]) ).
fof(f386,plain,
( ! [X2,X1] :
( ~ member(X2,power_class(X1))
| ~ member(X2,image(element_relation,complement(X1))) )
| ~ spl0_27
| ~ spl0_50 ),
inference(superposition,[],[f236,f333]) ).
fof(f1087,plain,
( spl0_150
| ~ spl0_27
| ~ spl0_39 ),
inference(avatar_split_clause,[],[f371,f288,f235,f1085]) ).
fof(f371,plain,
( ! [X0,X1] :
( subclass(complement(X0),X1)
| ~ member(not_subclass_element(complement(X0),X1),X0) )
| ~ spl0_27
| ~ spl0_39 ),
inference(resolution,[],[f289,f236]) ).
fof(f1033,plain,
( spl0_149
| ~ spl0_51
| ~ spl0_105 ),
inference(avatar_split_clause,[],[f721,f709,f336,f1031]) ).
fof(f709,plain,
( spl0_105
<=> ! [X8] :
( function(X8)
| ~ subclass(X8,cross_product(universal_class,universal_class))
| ~ subclass(compose(X8,inverse(X8)),identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f721,plain,
( ! [X1] :
( ~ subclass(X1,cross_product(universal_class,universal_class))
| function(X1)
| ~ single_valued_class(X1) )
| ~ spl0_51
| ~ spl0_105 ),
inference(resolution,[],[f710,f337]) ).
fof(f710,plain,
( ! [X8] :
( ~ subclass(compose(X8,inverse(X8)),identity_relation)
| ~ subclass(X8,cross_product(universal_class,universal_class))
| function(X8) )
| ~ spl0_105 ),
inference(avatar_component_clause,[],[f709]) ).
fof(f1029,plain,
( ~ spl0_148
| spl0_104
| ~ spl0_143 ),
inference(avatar_split_clause,[],[f1008,f961,f704,f1026]) ).
fof(f1026,plain,
( spl0_148
<=> member(x,subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f704,plain,
( spl0_104
<=> member(x,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f1008,plain,
( ~ member(x,subset_relation)
| spl0_104
| ~ spl0_143 ),
inference(resolution,[],[f962,f705]) ).
fof(f705,plain,
( ~ member(x,cross_product(universal_class,universal_class))
| spl0_104 ),
inference(avatar_component_clause,[],[f704]) ).
fof(f1024,plain,
( spl0_147
| ~ spl0_18
| ~ spl0_86 ),
inference(avatar_split_clause,[],[f617,f574,f196,f1022]) ).
fof(f196,plain,
( spl0_18
<=> ! [X0] : unordered_pair(X0,X0) = singleton(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f617,plain,
( ! [X0] : ordered_pair(singleton(X0),X0) = singleton(singleton(singleton(X0)))
| ~ spl0_18
| ~ spl0_86 ),
inference(forward_demodulation,[],[f612,f197]) ).
fof(f197,plain,
( ! [X0] : unordered_pair(X0,X0) = singleton(X0)
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f196]) ).
fof(f612,plain,
( ! [X0] : ordered_pair(singleton(X0),X0) = unordered_pair(singleton(singleton(X0)),singleton(singleton(X0)))
| ~ spl0_18
| ~ spl0_86 ),
inference(superposition,[],[f575,f197]) ).
fof(f1020,plain,
( spl0_146
| ~ spl0_44
| ~ spl0_76 ),
inference(avatar_split_clause,[],[f556,f501,f308,f1018]) ).
fof(f556,plain,
( ! [X6,X7,X4,X5] :
( ~ member(X7,restrict(X4,X5,X6))
| member(X7,X4) )
| ~ spl0_44
| ~ spl0_76 ),
inference(superposition,[],[f309,f502]) ).
fof(f1016,plain,
( spl0_145
| ~ spl0_44
| ~ spl0_66 ),
inference(avatar_split_clause,[],[f475,f421,f308,f1014]) ).
fof(f475,plain,
( ! [X2,X3] :
( ~ member(X3,null_class)
| member(X3,X2)
| null_class = X2 )
| ~ spl0_44
| ~ spl0_66 ),
inference(superposition,[],[f309,f422]) ).
fof(f1012,plain,
( spl0_144
| ~ spl0_27
| ~ spl0_34 ),
inference(avatar_split_clause,[],[f285,f263,f235,f1010]) ).
fof(f285,plain,
( ! [X0] :
( complement(X0) = null_class
| ~ member(regular(complement(X0)),X0) )
| ~ spl0_27
| ~ spl0_34 ),
inference(resolution,[],[f264,f236]) ).
fof(f963,plain,
( spl0_143
| ~ spl0_44
| ~ spl0_112 ),
inference(avatar_split_clause,[],[f760,f748,f308,f961]) ).
fof(f760,plain,
( ! [X2] :
( ~ member(X2,subset_relation)
| member(X2,cross_product(universal_class,universal_class)) )
| ~ spl0_44
| ~ spl0_112 ),
inference(superposition,[],[f309,f750]) ).
fof(f959,plain,
( spl0_142
| ~ spl0_15
| ~ spl0_64 ),
inference(avatar_split_clause,[],[f849,f413,f183,f957]) ).
fof(f957,plain,
( spl0_142
<=> ! [X0] :
( single_valued_class(inverse(X0))
| ~ one_to_one(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f183,plain,
( spl0_15
<=> ! [X8] :
( ~ one_to_one(X8)
| function(inverse(X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f413,plain,
( spl0_64
<=> ! [X0] :
( ~ function(X0)
| single_valued_class(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f849,plain,
( ! [X0] :
( single_valued_class(inverse(X0))
| ~ one_to_one(X0) )
| ~ spl0_15
| ~ spl0_64 ),
inference(resolution,[],[f414,f184]) ).
fof(f184,plain,
( ! [X8] :
( function(inverse(X8))
| ~ one_to_one(X8) )
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f183]) ).
fof(f414,plain,
( ! [X0] :
( ~ function(X0)
| single_valued_class(X0) )
| ~ spl0_64 ),
inference(avatar_component_clause,[],[f413]) ).
fof(f955,plain,
( spl0_141
| ~ spl0_44
| ~ spl0_90 ),
inference(avatar_split_clause,[],[f641,f590,f308,f953]) ).
fof(f641,plain,
( ! [X4,X5] :
( ~ member(X5,cantor(X4))
| member(X5,domain_of(X4)) )
| ~ spl0_44
| ~ spl0_90 ),
inference(superposition,[],[f309,f591]) ).
fof(f951,plain,
( spl0_140
| ~ spl0_14
| ~ spl0_62 ),
inference(avatar_split_clause,[],[f461,f405,f179,f949]) ).
fof(f179,plain,
( spl0_14
<=> ! [X1] :
( ~ inductive(X1)
| subclass(omega,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f461,plain,
( ! [X7] :
( ~ subclass(X7,omega)
| omega = X7
| ~ inductive(X7) )
| ~ spl0_14
| ~ spl0_62 ),
inference(resolution,[],[f406,f180]) ).
fof(f180,plain,
( ! [X1] :
( subclass(omega,X1)
| ~ inductive(X1) )
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f179]) ).
fof(f947,plain,
( spl0_139
| ~ spl0_13
| ~ spl0_61 ),
inference(avatar_split_clause,[],[f446,f401,f175,f945]) ).
fof(f446,plain,
( ! [X14,X15] :
( ~ subclass(X14,X15)
| member(null_class,X15)
| ~ inductive(X14) )
| ~ spl0_13
| ~ spl0_61 ),
inference(resolution,[],[f402,f176]) ).
fof(f943,plain,
( spl0_138
| ~ spl0_10
| ~ spl0_61 ),
inference(avatar_split_clause,[],[f444,f401,f161,f941]) ).
fof(f444,plain,
( ! [X10,X11,X9] :
( ~ subclass(universal_class,X9)
| member(unordered_pair(X10,X11),X9) )
| ~ spl0_10
| ~ spl0_61 ),
inference(resolution,[],[f402,f162]) ).
fof(f915,plain,
( spl0_137
| ~ spl0_18
| ~ spl0_85 ),
inference(avatar_split_clause,[],[f611,f569,f196,f913]) ).
fof(f611,plain,
( ! [X0,X1] :
( ~ member(X1,singleton(X0))
| X0 = X1 )
| ~ spl0_18
| ~ spl0_85 ),
inference(duplicate_literal_removal,[],[f610]) ).
fof(f610,plain,
( ! [X0,X1] :
( ~ member(X1,singleton(X0))
| X0 = X1
| X0 = X1 )
| ~ spl0_18
| ~ spl0_85 ),
inference(superposition,[],[f570,f197]) ).
fof(f911,plain,
( spl0_136
| ~ spl0_13
| ~ spl0_45 ),
inference(avatar_split_clause,[],[f381,f312,f175,f909]) ).
fof(f381,plain,
( ! [X3,X4] :
( member(null_class,X3)
| ~ inductive(intersection(X4,X3)) )
| ~ spl0_13
| ~ spl0_45 ),
inference(resolution,[],[f313,f176]) ).
fof(f907,plain,
( spl0_135
| ~ spl0_20
| ~ spl0_44 ),
inference(avatar_split_clause,[],[f379,f308,f204,f905]) ).
fof(f379,plain,
( ! [X0] :
( ~ member(X0,identity_relation)
| member(X0,inverse(subset_relation)) )
| ~ spl0_20
| ~ spl0_44 ),
inference(superposition,[],[f309,f206]) ).
fof(f903,plain,
( spl0_134
| ~ spl0_13
| ~ spl0_44 ),
inference(avatar_split_clause,[],[f377,f308,f175,f901]) ).
fof(f377,plain,
( ! [X3,X4] :
( member(null_class,X3)
| ~ inductive(intersection(X3,X4)) )
| ~ spl0_13
| ~ spl0_44 ),
inference(resolution,[],[f309,f176]) ).
fof(f899,plain,
( spl0_133
| ~ spl0_18
| ~ spl0_41 ),
inference(avatar_split_clause,[],[f374,f296,f196,f897]) ).
fof(f374,plain,
( ! [X0] :
( member(X0,singleton(X0))
| ~ member(X0,universal_class) )
| ~ spl0_18
| ~ spl0_41 ),
inference(superposition,[],[f297,f197]) ).
fof(f885,plain,
( spl0_132
| ~ spl0_45
| ~ spl0_70 ),
inference(avatar_split_clause,[],[f482,f437,f312,f883]) ).
fof(f482,plain,
( ! [X0] :
( ~ member(X0,singleton_relation)
| member(X0,element_relation) )
| ~ spl0_45
| ~ spl0_70 ),
inference(superposition,[],[f313,f439]) ).
fof(f881,plain,
( spl0_131
| ~ spl0_6
| ~ spl0_62 ),
inference(avatar_split_clause,[],[f452,f405,f144,f879]) ).
fof(f879,plain,
( spl0_131
<=> ! [X0] :
( ~ subclass(universal_class,X0)
| universal_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f452,plain,
( ! [X0] :
( ~ subclass(universal_class,X0)
| universal_class = X0 )
| ~ spl0_6
| ~ spl0_62 ),
inference(resolution,[],[f406,f145]) ).
fof(f877,plain,
( spl0_130
| ~ spl0_7
| ~ spl0_61 ),
inference(avatar_split_clause,[],[f447,f401,f148,f875]) ).
fof(f875,plain,
( spl0_130
<=> ! [X16] :
( ~ subclass(universal_class,X16)
| member(omega,X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f447,plain,
( ! [X16] :
( ~ subclass(universal_class,X16)
| member(omega,X16) )
| ~ spl0_7
| ~ spl0_61 ),
inference(resolution,[],[f402,f150]) ).
fof(f873,plain,
( spl0_129
| ~ spl0_5
| ~ spl0_64 ),
inference(avatar_split_clause,[],[f848,f413,f139,f870]) ).
fof(f870,plain,
( spl0_129
<=> single_valued_class(choice) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f848,plain,
( single_valued_class(choice)
| ~ spl0_5
| ~ spl0_64 ),
inference(resolution,[],[f414,f141]) ).
fof(f863,plain,
( spl0_128
| ~ spl0_10
| ~ spl0_86 ),
inference(avatar_split_clause,[],[f616,f574,f161,f861]) ).
fof(f616,plain,
( ! [X8,X7] : member(ordered_pair(X7,X8),universal_class)
| ~ spl0_10
| ~ spl0_86 ),
inference(superposition,[],[f162,f575]) ).
fof(f858,plain,
( spl0_126
| ~ spl0_127
| ~ spl0_6
| ~ spl0_78 ),
inference(avatar_split_clause,[],[f565,f512,f144,f855,f851]) ).
fof(f565,plain,
( ~ member(null_class,universal_class)
| inductive(universal_class)
| ~ spl0_6
| ~ spl0_78 ),
inference(resolution,[],[f513,f145]) ).
fof(f847,plain,
spl0_125,
inference(avatar_split_clause,[],[f91,f845]) ).
fof(f845,plain,
( spl0_125
<=> ! [X9,X11,X10] :
( ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11)
| apply(X11,ordered_pair(apply(X9,not_homomorphism1(X9,X10,X11)),apply(X9,not_homomorphism2(X9,X10,X11)))) != apply(X9,apply(X10,ordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism2(X9,X10,X11)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f91,axiom,
! [X10,X11,X9] :
( ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11)
| apply(X11,ordered_pair(apply(X9,not_homomorphism1(X9,X10,X11)),apply(X9,not_homomorphism2(X9,X10,X11)))) != apply(X9,apply(X10,ordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism2(X9,X10,X11)))) ),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',homomorphism6) ).
fof(f838,plain,
spl0_124,
inference(avatar_split_clause,[],[f89,f836]) ).
fof(f89,axiom,
! [X10,X0,X11,X1,X9] :
( ~ homomorphism(X9,X10,X11)
| ~ member(ordered_pair(X0,X1),domain_of(X10))
| apply(X11,ordered_pair(apply(X9,X0),apply(X9,X1))) = apply(X9,apply(X10,ordered_pair(X0,X1))) ),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',homomorphism4) ).
fof(f832,plain,
spl0_123,
inference(avatar_split_clause,[],[f37,f830]) ).
fof(f37,axiom,
! [X2,X3,X0,X6] :
( ~ member(ordered_pair(ordered_pair(X3,X2),X6),X0)
| member(ordered_pair(ordered_pair(X2,X3),X6),flip(X0))
| ~ member(ordered_pair(ordered_pair(X2,X3),X6),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',flip3) ).
fof(f828,plain,
spl0_122,
inference(avatar_split_clause,[],[f34,f826]) ).
fof(f34,axiom,
! [X2,X3,X0,X6] :
( ~ member(ordered_pair(ordered_pair(X3,X6),X2),X0)
| member(ordered_pair(ordered_pair(X2,X3),X6),rotate(X0))
| ~ member(ordered_pair(ordered_pair(X2,X3),X6),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',rotate3) ).
fof(f819,plain,
spl0_121,
inference(avatar_split_clause,[],[f108,f817]) ).
fof(f108,axiom,
! [X0,X1,X4] :
( ~ member(X1,domain_of(X0))
| member(ordered_pair(X0,ordered_pair(X1,apply(X0,X1))),application_function)
| ~ member(ordered_pair(X0,ordered_pair(X1,X4)),cross_product(universal_class,cross_product(universal_class,universal_class))) ),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',application_function_defn4) ).
fof(f815,plain,
spl0_120,
inference(avatar_split_clause,[],[f90,f813]) ).
fof(f90,axiom,
! [X10,X11,X9] :
( ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11)
| member(ordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism2(X9,X10,X11)),domain_of(X10)) ),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',homomorphism5) ).
fof(f806,plain,
( ~ spl0_119
| spl0_104
| ~ spl0_33
| ~ spl0_71 ),
inference(avatar_split_clause,[],[f506,f471,f259,f704,f803]) ).
fof(f803,plain,
( spl0_119
<=> function(union(y,z)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f471,plain,
( spl0_71
<=> ! [X23] :
( ~ subclass(union(y,z),X23)
| member(x,X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f506,plain,
( member(x,cross_product(universal_class,universal_class))
| ~ function(union(y,z))
| ~ spl0_33
| ~ spl0_71 ),
inference(resolution,[],[f472,f260]) ).
fof(f472,plain,
( ! [X23] :
( ~ subclass(union(y,z),X23)
| member(x,X23) )
| ~ spl0_71 ),
inference(avatar_component_clause,[],[f471]) ).
fof(f801,plain,
spl0_118,
inference(avatar_split_clause,[],[f59,f799]) ).
fof(f59,axiom,
! [X1,X7,X4,X5] :
( ~ member(ordered_pair(X1,X4),cross_product(universal_class,universal_class))
| member(ordered_pair(X1,X4),compose(X7,X5))
| ~ member(X4,image(X7,image(X5,singleton(X1)))) ),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',compose3) ).
fof(f792,plain,
spl0_117,
inference(avatar_split_clause,[],[f81,f790]) ).
fof(f81,axiom,
! [X8] :
( ~ function(X8)
| operation(X8)
| ~ subclass(range_of(X8),domain_of(domain_of(X8)))
| domain_of(X8) != cross_product(domain_of(domain_of(X8)),domain_of(domain_of(X8))) ),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',operation4) ).
fof(f779,plain,
spl0_116,
inference(avatar_split_clause,[],[f94,f777]) ).
fof(f94,axiom,
! [X0,X1,X4] :
( compose(X0,X1) != X4
| member(ordered_pair(X1,X4),compose_class(X0))
| ~ member(ordered_pair(X1,X4),cross_product(universal_class,universal_class)) ),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',compose_class_definition3) ).
fof(f775,plain,
spl0_115,
inference(avatar_split_clause,[],[f85,f773]) ).
fof(f85,axiom,
! [X10,X11,X9] :
( ~ function(X9)
| compatible(X9,X10,X11)
| domain_of(domain_of(X10)) != domain_of(X9)
| ~ subclass(range_of(X9),domain_of(domain_of(X11))) ),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',compatible4) ).
fof(f768,plain,
spl0_114,
inference(avatar_split_clause,[],[f97,f766]) ).
fof(f97,axiom,
! [X0,X1] :
( ~ member(ordered_pair(X0,X1),cross_product(universal_class,universal_class))
| member(ordered_pair(X0,ordered_pair(X1,compose(X0,X1))),composition_function) ),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',definition_of_composition_function3) ).
fof(f764,plain,
spl0_113,
inference(avatar_split_clause,[],[f46,f762]) ).
fof(f46,axiom,
! [X0,X1] :
( successor(X0) != X1
| member(ordered_pair(X0,X1),successor_relation)
| ~ member(ordered_pair(X0,X1),cross_product(universal_class,universal_class)) ),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',successor_relation3) ).
fof(f751,plain,
spl0_112,
inference(avatar_split_clause,[],[f117,f748]) ).
fof(f117,plain,
subset_relation = intersection(cross_product(universal_class,universal_class),restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class)),
inference(forward_demodulation,[],[f74,f29]) ).
fof(f29,axiom,
! [X0,X1,X5] : restrict(X5,X0,X1) = intersection(cross_product(X0,X1),X5),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',restriction2) ).
fof(f74,axiom,
intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation))))) = subset_relation,
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',subset_relation) ).
fof(f746,plain,
spl0_111,
inference(avatar_split_clause,[],[f58,f744]) ).
fof(f58,axiom,
! [X1,X7,X4,X5] :
( ~ member(ordered_pair(X1,X4),compose(X7,X5))
| member(X4,image(X7,image(X5,singleton(X1)))) ),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',compose2) ).
fof(f742,plain,
spl0_110,
inference(avatar_split_clause,[],[f36,f740]) ).
fof(f740,plain,
( spl0_110
<=> ! [X3,X0,X6,X2] :
( member(ordered_pair(ordered_pair(X3,X2),X6),X0)
| ~ member(ordered_pair(ordered_pair(X2,X3),X6),flip(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f36,axiom,
! [X2,X3,X0,X6] :
( member(ordered_pair(ordered_pair(X3,X2),X6),X0)
| ~ member(ordered_pair(ordered_pair(X2,X3),X6),flip(X0)) ),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',flip2) ).
fof(f738,plain,
spl0_109,
inference(avatar_split_clause,[],[f33,f736]) ).
fof(f736,plain,
( spl0_109
<=> ! [X3,X0,X6,X2] :
( member(ordered_pair(ordered_pair(X3,X6),X2),X0)
| ~ member(ordered_pair(ordered_pair(X2,X3),X6),rotate(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f33,axiom,
! [X2,X3,X0,X6] :
( member(ordered_pair(ordered_pair(X3,X6),X2),X0)
| ~ member(ordered_pair(ordered_pair(X2,X3),X6),rotate(X0)) ),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',rotate2) ).
fof(f734,plain,
spl0_108,
inference(avatar_split_clause,[],[f20,f732]) ).
fof(f20,axiom,
! [X0,X1] :
( ~ member(X0,X1)
| member(ordered_pair(X0,X1),element_relation)
| ~ member(ordered_pair(X0,X1),cross_product(universal_class,universal_class)) ),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',element_relation3) ).
fof(f725,plain,
spl0_107,
inference(avatar_split_clause,[],[f31,f723]) ).
fof(f31,axiom,
! [X0,X4] :
( ~ member(X4,universal_class)
| member(X4,domain_of(X0))
| restrict(X0,singleton(X4),universal_class) = null_class ),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',domain2) ).
fof(f715,plain,
spl0_106,
inference(avatar_split_clause,[],[f103,f713]) ).
fof(f713,plain,
( spl0_106
<=> ! [X0] : domain(X0,image(inverse(X0),singleton(single_valued1(X0))),single_valued2(X0)) = single_valued3(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f103,axiom,
! [X0] : domain(X0,image(inverse(X0),singleton(single_valued1(X0))),single_valued2(X0)) = single_valued3(X0),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',single_valued_term_defn3) ).
fof(f711,plain,
spl0_105,
inference(avatar_split_clause,[],[f64,f709]) ).
fof(f64,axiom,
! [X8] :
( function(X8)
| ~ subclass(X8,cross_product(universal_class,universal_class))
| ~ subclass(compose(X8,inverse(X8)),identity_relation) ),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',function3) ).
fof(f707,plain,
( ~ spl0_103
| spl0_104
| ~ spl0_33
| ~ spl0_94 ),
inference(avatar_split_clause,[],[f662,f619,f259,f704,f700]) ).
fof(f700,plain,
( spl0_103
<=> function(universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f619,plain,
( spl0_94
<=> ! [X0] :
( ~ subclass(universal_class,X0)
| member(x,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f662,plain,
( member(x,cross_product(universal_class,universal_class))
| ~ function(universal_class)
| ~ spl0_33
| ~ spl0_94 ),
inference(resolution,[],[f620,f260]) ).
fof(f620,plain,
( ! [X0] :
( ~ subclass(universal_class,X0)
| member(x,X0) )
| ~ spl0_94 ),
inference(avatar_component_clause,[],[f619]) ).
fof(f698,plain,
spl0_102,
inference(avatar_split_clause,[],[f41,f696]) ).
fof(f696,plain,
( spl0_102
<=> ! [X4,X0,X1] : second(not_subclass_element(restrict(X4,singleton(X0),X1),null_class)) = range(X4,X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f41,axiom,
! [X0,X1,X4] : second(not_subclass_element(restrict(X4,singleton(X0),X1),null_class)) = range(X4,X0,X1),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',range) ).
fof(f694,plain,
spl0_101,
inference(avatar_split_clause,[],[f40,f692]) ).
fof(f692,plain,
( spl0_101
<=> ! [X4,X0,X1] : first(not_subclass_element(restrict(X4,X0,singleton(X1)),null_class)) = domain(X4,X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f40,axiom,
! [X0,X1,X4] : first(not_subclass_element(restrict(X4,X0,singleton(X1)),null_class)) = domain(X4,X0,X1),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',domain) ).
fof(f690,plain,
spl0_100,
inference(avatar_split_clause,[],[f16,f688]) ).
fof(f16,axiom,
! [X2,X3,X0,X1] :
( ~ member(X2,X0)
| ~ member(X3,X1)
| member(ordered_pair(X2,X3),cross_product(X0,X1)) ),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',cartesian_product3) ).
fof(f670,plain,
spl0_99,
inference(avatar_split_clause,[],[f116,f668]) ).
fof(f116,plain,
! [X0,X1] : symmetric_difference(X0,X1) = intersection(complement(intersection(X0,X1)),union(X0,X1)),
inference(forward_demodulation,[],[f27,f26]) ).
fof(f26,axiom,
! [X0,X1] : complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',union) ).
fof(f27,axiom,
! [X0,X1] : intersection(complement(intersection(X0,X1)),complement(intersection(complement(X0),complement(X1)))) = symmetric_difference(X0,X1),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',symmetric_difference) ).
fof(f666,plain,
spl0_98,
inference(avatar_split_clause,[],[f107,f664]) ).
fof(f107,axiom,
! [X0,X1,X4] :
( apply(X0,X1) = X4
| ~ member(ordered_pair(X0,ordered_pair(X1,X4)),application_function) ),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',application_function_defn3) ).
fof(f659,plain,
spl0_97,
inference(avatar_split_clause,[],[f96,f657]) ).
fof(f96,axiom,
! [X0,X1,X4] :
( compose(X0,X1) = X4
| ~ member(ordered_pair(X0,ordered_pair(X1,X4)),composition_function) ),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',definition_of_composition_function2) ).
fof(f655,plain,
spl0_96,
inference(avatar_split_clause,[],[f79,f653]) ).
fof(f653,plain,
( spl0_96
<=> ! [X8] :
( ~ operation(X8)
| domain_of(X8) = cross_product(domain_of(domain_of(X8)),domain_of(domain_of(X8))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f79,axiom,
! [X8] :
( ~ operation(X8)
| domain_of(X8) = cross_product(domain_of(domain_of(X8)),domain_of(domain_of(X8))) ),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',operation2) ).
fof(f651,plain,
spl0_95,
inference(avatar_split_clause,[],[f17,f649]) ).
fof(f17,axiom,
! [X0,X1,X4] :
( ~ member(X4,cross_product(X0,X1))
| ordered_pair(first(X4),second(X4)) = X4 ),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',cartesian_product4) ).
fof(f621,plain,
( spl0_94
| ~ spl0_61
| ~ spl0_84 ),
inference(avatar_split_clause,[],[f572,f541,f401,f619]) ).
fof(f572,plain,
( ! [X0] :
( ~ subclass(universal_class,X0)
| member(x,X0) )
| ~ spl0_61
| ~ spl0_84 ),
inference(resolution,[],[f543,f402]) ).
fof(f543,plain,
( member(x,universal_class)
| ~ spl0_84 ),
inference(avatar_component_clause,[],[f541]) ).
fof(f604,plain,
spl0_93,
inference(avatar_split_clause,[],[f112,f602]) ).
fof(f112,axiom,
! [X1,X8] :
( ~ function(X8)
| ~ subclass(range_of(X8),X1)
| maps(X8,domain_of(X8),X1) ),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',maps4) ).
fof(f600,plain,
spl0_92,
inference(avatar_split_clause,[],[f106,f598]) ).
fof(f106,axiom,
! [X0,X1,X4] :
( member(X1,domain_of(X0))
| ~ member(ordered_pair(X0,ordered_pair(X1,X4)),application_function) ),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',application_function_defn2) ).
fof(f596,plain,
spl0_91,
inference(avatar_split_clause,[],[f93,f594]) ).
fof(f93,axiom,
! [X0,X1,X4] :
( compose(X0,X1) = X4
| ~ member(ordered_pair(X1,X4),compose_class(X0)) ),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',compose_class_definition2) ).
fof(f592,plain,
spl0_90,
inference(avatar_split_clause,[],[f77,f590]) ).
fof(f77,axiom,
! [X0] : intersection(domain_of(X0),diagonalise(compose(inverse(element_relation),X0))) = cantor(X0),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',cantor_class) ).
fof(f588,plain,
spl0_89,
inference(avatar_split_clause,[],[f70,f586]) ).
fof(f70,axiom,
! [X1] :
( ~ member(X1,universal_class)
| null_class = X1
| member(apply(choice,X1),X1) ),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',choice2) ).
fof(f584,plain,
spl0_88,
inference(avatar_split_clause,[],[f30,f582]) ).
fof(f30,axiom,
! [X0,X4] :
( ~ member(X4,domain_of(X0))
| restrict(X0,singleton(X4),universal_class) != null_class ),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',domain1) ).
fof(f580,plain,
spl0_87,
inference(avatar_split_clause,[],[f23,f578]) ).
fof(f23,axiom,
! [X0,X1,X4] :
( ~ member(X4,X0)
| ~ member(X4,X1)
| member(X4,intersection(X0,X1)) ),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',intersection3) ).
fof(f576,plain,
spl0_86,
inference(avatar_split_clause,[],[f13,f574]) ).
fof(f13,axiom,
! [X0,X1] : unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))) = ordered_pair(X0,X1),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',ordered_pair) ).
fof(f571,plain,
spl0_85,
inference(avatar_split_clause,[],[f8,f569]) ).
fof(f8,axiom,
! [X2,X0,X1] :
( X1 = X2
| X0 = X2
| ~ member(X2,unordered_pair(X0,X1)) ),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',unordered_pair_member) ).
fof(f544,plain,
( spl0_84
| ~ spl0_6
| ~ spl0_71 ),
inference(avatar_split_clause,[],[f504,f471,f144,f541]) ).
fof(f504,plain,
( member(x,universal_class)
| ~ spl0_6
| ~ spl0_71 ),
inference(resolution,[],[f472,f145]) ).
fof(f534,plain,
spl0_83,
inference(avatar_split_clause,[],[f102,f532]) ).
fof(f532,plain,
( spl0_83
<=> ! [X0] : second(not_subclass_element(compose(X0,inverse(X0)),identity_relation)) = single_valued2(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f102,axiom,
! [X0] : second(not_subclass_element(compose(X0,inverse(X0)),identity_relation)) = single_valued2(X0),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',single_valued_term_defn2) ).
fof(f530,plain,
spl0_82,
inference(avatar_split_clause,[],[f101,f528]) ).
fof(f528,plain,
( spl0_82
<=> ! [X0] : first(not_subclass_element(compose(X0,inverse(X0)),identity_relation)) = single_valued1(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f101,axiom,
! [X0] : first(not_subclass_element(compose(X0,inverse(X0)),identity_relation)) = single_valued1(X0),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',single_valued_term_defn1) ).
fof(f526,plain,
spl0_81,
inference(avatar_split_clause,[],[f84,f524]) ).
fof(f524,plain,
( spl0_81
<=> ! [X9,X11,X10] :
( ~ compatible(X9,X10,X11)
| subclass(range_of(X9),domain_of(domain_of(X11))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f84,axiom,
! [X10,X11,X9] :
( ~ compatible(X9,X10,X11)
| subclass(range_of(X9),domain_of(domain_of(X11))) ),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',compatible3) ).
fof(f522,plain,
spl0_80,
inference(avatar_split_clause,[],[f83,f520]) ).
fof(f520,plain,
( spl0_80
<=> ! [X9,X11,X10] :
( ~ compatible(X9,X10,X11)
| domain_of(domain_of(X10)) = domain_of(X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f83,axiom,
! [X10,X11,X9] :
( ~ compatible(X9,X10,X11)
| domain_of(domain_of(X10)) = domain_of(X9) ),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',compatible2) ).
fof(f518,plain,
spl0_79,
inference(avatar_split_clause,[],[f65,f516]) ).
fof(f65,axiom,
! [X0,X8] :
( ~ function(X8)
| ~ member(X0,universal_class)
| member(image(X8,X0),universal_class) ),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',replacement) ).
fof(f514,plain,
spl0_78,
inference(avatar_split_clause,[],[f49,f512]) ).
fof(f49,axiom,
! [X0] :
( inductive(X0)
| ~ member(null_class,X0)
| ~ subclass(image(successor_relation,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',inductive3) ).
fof(f510,plain,
spl0_77,
inference(avatar_split_clause,[],[f29,f508]) ).
fof(f503,plain,
spl0_76,
inference(avatar_split_clause,[],[f28,f501]) ).
fof(f28,axiom,
! [X0,X1,X5] : intersection(X5,cross_product(X0,X1)) = restrict(X5,X0,X1),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',restriction1) ).
fof(f499,plain,
spl0_75,
inference(avatar_split_clause,[],[f26,f497]) ).
fof(f495,plain,
spl0_74,
inference(avatar_split_clause,[],[f25,f493]) ).
fof(f25,axiom,
! [X0,X4] :
( ~ member(X4,universal_class)
| member(X4,X0)
| member(X4,complement(X0)) ),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',complement2) ).
fof(f491,plain,
spl0_73,
inference(avatar_split_clause,[],[f15,f489]) ).
fof(f15,axiom,
! [X2,X3,X0,X1] :
( member(X3,X1)
| ~ member(ordered_pair(X2,X3),cross_product(X0,X1)) ),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',cartesian_product2) ).
fof(f487,plain,
spl0_72,
inference(avatar_split_clause,[],[f14,f485]) ).
fof(f14,axiom,
! [X2,X3,X0,X1] :
( member(X2,X0)
| ~ member(ordered_pair(X2,X3),cross_product(X0,X1)) ),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',cartesian_product1) ).
fof(f473,plain,
( spl0_71
| ~ spl0_3
| ~ spl0_61 ),
inference(avatar_split_clause,[],[f451,f401,f129,f471]) ).
fof(f451,plain,
( ! [X23] :
( ~ subclass(union(y,z),X23)
| member(x,X23) )
| ~ spl0_3
| ~ spl0_61 ),
inference(resolution,[],[f402,f131]) ).
fof(f440,plain,
spl0_70,
inference(avatar_split_clause,[],[f104,f437]) ).
fof(f104,axiom,
intersection(complement(compose(element_relation,complement(identity_relation))),element_relation) = singleton_relation,
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',compose_can_define_singleton) ).
fof(f435,plain,
spl0_69,
inference(avatar_split_clause,[],[f100,f433]) ).
fof(f100,axiom,
! [X0] :
( ~ member(X0,universal_class)
| member(ordered_pair(X0,domain_of(X0)),domain_relation) ),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',definition_of_domain_relation3) ).
fof(f431,plain,
spl0_68,
inference(avatar_split_clause,[],[f99,f429]) ).
fof(f99,axiom,
! [X0,X1] :
( domain_of(X0) = X1
| ~ member(ordered_pair(X0,X1),domain_relation) ),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',definition_of_domain_relation2) ).
fof(f427,plain,
spl0_67,
inference(avatar_split_clause,[],[f68,f425]) ).
fof(f68,axiom,
! [X1,X8] : sum_class(image(X8,singleton(X1))) = apply(X8,X1),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',apply) ).
fof(f423,plain,
spl0_66,
inference(avatar_split_clause,[],[f67,f421]) ).
fof(f67,axiom,
! [X0] :
( null_class = X0
| null_class = intersection(X0,regular(X0)) ),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',regularity2) ).
fof(f419,plain,
spl0_65,
inference(avatar_split_clause,[],[f45,f417]) ).
fof(f45,axiom,
! [X0,X1] :
( successor(X0) = X1
| ~ member(ordered_pair(X0,X1),successor_relation) ),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',successor_relation2) ).
fof(f415,plain,
( spl0_64
| ~ spl0_53
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f392,f348,f344,f413]) ).
fof(f344,plain,
( spl0_53
<=> ! [X0] :
( single_valued_class(X0)
| ~ subclass(compose(X0,inverse(X0)),identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f392,plain,
( ! [X0] :
( ~ function(X0)
| single_valued_class(X0) )
| ~ spl0_53
| ~ spl0_54 ),
inference(resolution,[],[f349,f345]) ).
fof(f345,plain,
( ! [X0] :
( ~ subclass(compose(X0,inverse(X0)),identity_relation)
| single_valued_class(X0) )
| ~ spl0_53 ),
inference(avatar_component_clause,[],[f344]) ).
fof(f411,plain,
spl0_63,
inference(avatar_split_clause,[],[f42,f409]) ).
fof(f42,axiom,
! [X0,X5] : range_of(restrict(X5,X0,universal_class)) = image(X5,X0),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',image) ).
fof(f407,plain,
spl0_62,
inference(avatar_split_clause,[],[f7,f405]) ).
fof(f7,axiom,
! [X0,X1] :
( ~ subclass(X0,X1)
| ~ subclass(X1,X0)
| X0 = X1 ),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',subclass_implies_equal) ).
fof(f403,plain,
spl0_61,
inference(avatar_split_clause,[],[f1,f401]) ).
fof(f1,axiom,
! [X2,X0,X1] :
( ~ subclass(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',subclass_members) ).
fof(f390,plain,
( spl0_60
| ~ spl0_20
| ~ spl0_45 ),
inference(avatar_split_clause,[],[f383,f312,f204,f388]) ).
fof(f383,plain,
( ! [X0] :
( ~ member(X0,identity_relation)
| member(X0,subset_relation) )
| ~ spl0_20
| ~ spl0_45 ),
inference(superposition,[],[f313,f206]) ).
fof(f370,plain,
spl0_59,
inference(avatar_split_clause,[],[f111,f368]) ).
fof(f368,plain,
( spl0_59
<=> ! [X0,X1,X8] :
( ~ maps(X8,X0,X1)
| subclass(range_of(X8),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f111,axiom,
! [X0,X1,X8] :
( ~ maps(X8,X0,X1)
| subclass(range_of(X8),X1) ),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',maps3) ).
fof(f366,plain,
spl0_58,
inference(avatar_split_clause,[],[f110,f364]) ).
fof(f364,plain,
( spl0_58
<=> ! [X0,X1,X8] :
( ~ maps(X8,X0,X1)
| domain_of(X8) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f110,axiom,
! [X0,X1,X8] :
( ~ maps(X8,X0,X1)
| domain_of(X8) = X0 ),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',maps2) ).
fof(f362,plain,
spl0_57,
inference(avatar_split_clause,[],[f88,f360]) ).
fof(f360,plain,
( spl0_57
<=> ! [X9,X11,X10] :
( ~ homomorphism(X9,X10,X11)
| compatible(X9,X10,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f88,axiom,
! [X10,X11,X9] :
( ~ homomorphism(X9,X10,X11)
| compatible(X9,X10,X11) ),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',homomorphism3) ).
fof(f358,plain,
spl0_56,
inference(avatar_split_clause,[],[f80,f356]) ).
fof(f80,axiom,
! [X8] :
( ~ operation(X8)
| subclass(range_of(X8),domain_of(domain_of(X8))) ),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',operation3) ).
fof(f354,plain,
spl0_55,
inference(avatar_split_clause,[],[f76,f352]) ).
fof(f76,axiom,
! [X5] : complement(domain_of(intersection(X5,identity_relation))) = diagonalise(X5),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',diagonalisation) ).
fof(f350,plain,
spl0_54,
inference(avatar_split_clause,[],[f63,f348]) ).
fof(f63,axiom,
! [X8] :
( ~ function(X8)
| subclass(compose(X8,inverse(X8)),identity_relation) ),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',function2) ).
fof(f346,plain,
spl0_53,
inference(avatar_split_clause,[],[f61,f344]) ).
fof(f61,axiom,
! [X0] :
( single_valued_class(X0)
| ~ subclass(compose(X0,inverse(X0)),identity_relation) ),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',single_valued_class2) ).
fof(f342,plain,
( spl0_52
| ~ spl0_13
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f280,f235,f175,f340]) ).
fof(f280,plain,
( ! [X0] :
( ~ member(null_class,X0)
| ~ inductive(complement(X0)) )
| ~ spl0_13
| ~ spl0_27 ),
inference(resolution,[],[f236,f176]) ).
fof(f338,plain,
spl0_51,
inference(avatar_split_clause,[],[f60,f336]) ).
fof(f60,axiom,
! [X0] :
( ~ single_valued_class(X0)
| subclass(compose(X0,inverse(X0)),identity_relation) ),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',single_valued_class1) ).
fof(f334,plain,
spl0_50,
inference(avatar_split_clause,[],[f55,f332]) ).
fof(f55,axiom,
! [X0] : complement(image(element_relation,complement(X0))) = power_class(X0),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',power_class_definition) ).
fof(f330,plain,
spl0_49,
inference(avatar_split_clause,[],[f53,f328]) ).
fof(f53,axiom,
! [X0] : domain_of(restrict(element_relation,universal_class,X0)) = sum_class(X0),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',sum_class_definition) ).
fof(f326,plain,
spl0_48,
inference(avatar_split_clause,[],[f38,f324]) ).
fof(f38,axiom,
! [X1] : domain_of(flip(cross_product(X1,universal_class))) = inverse(X1),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',inverse) ).
fof(f322,plain,
spl0_47,
inference(avatar_split_clause,[],[f35,f320]) ).
fof(f35,axiom,
! [X0] : subclass(flip(X0),cross_product(cross_product(universal_class,universal_class),universal_class)),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',flip1) ).
fof(f318,plain,
spl0_46,
inference(avatar_split_clause,[],[f32,f316]) ).
fof(f32,axiom,
! [X0] : subclass(rotate(X0),cross_product(cross_product(universal_class,universal_class),universal_class)),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',rotate1) ).
fof(f314,plain,
spl0_45,
inference(avatar_split_clause,[],[f22,f312]) ).
fof(f22,axiom,
! [X0,X1,X4] :
( member(X4,X1)
| ~ member(X4,intersection(X0,X1)) ),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',intersection2) ).
fof(f310,plain,
spl0_44,
inference(avatar_split_clause,[],[f21,f308]) ).
fof(f21,axiom,
! [X0,X1,X4] :
( member(X4,X0)
| ~ member(X4,intersection(X0,X1)) ),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',intersection1) ).
fof(f306,plain,
spl0_43,
inference(avatar_split_clause,[],[f19,f304]) ).
fof(f19,axiom,
! [X0,X1] :
( member(X0,X1)
| ~ member(ordered_pair(X0,X1),element_relation) ),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',element_relation2) ).
fof(f302,plain,
spl0_42,
inference(avatar_split_clause,[],[f10,f300]) ).
fof(f10,axiom,
! [X0,X1] :
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X0,X1)) ),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',unordered_pair3) ).
fof(f298,plain,
spl0_41,
inference(avatar_split_clause,[],[f9,f296]) ).
fof(f9,axiom,
! [X0,X1] :
( ~ member(X0,universal_class)
| member(X0,unordered_pair(X0,X1)) ),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',unordered_pair2) ).
fof(f294,plain,
spl0_40,
inference(avatar_split_clause,[],[f3,f292]) ).
fof(f3,axiom,
! [X0,X1] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',not_subclass_members2) ).
fof(f290,plain,
spl0_39,
inference(avatar_split_clause,[],[f2,f288]) ).
fof(f2,axiom,
! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',not_subclass_members1) ).
fof(f284,plain,
( spl0_38
| ~ spl0_10
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f229,f196,f161,f282]) ).
fof(f229,plain,
( ! [X0] : member(singleton(X0),universal_class)
| ~ spl0_10
| ~ spl0_18 ),
inference(superposition,[],[f162,f197]) ).
fof(f279,plain,
spl0_37,
inference(avatar_split_clause,[],[f105,f276]) ).
fof(f105,axiom,
subclass(application_function,cross_product(universal_class,cross_product(universal_class,universal_class))),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',application_function_defn1) ).
fof(f274,plain,
spl0_36,
inference(avatar_split_clause,[],[f95,f271]) ).
fof(f95,axiom,
subclass(composition_function,cross_product(universal_class,cross_product(universal_class,universal_class))),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',definition_of_composition_function1) ).
fof(f269,plain,
spl0_35,
inference(avatar_split_clause,[],[f73,f267]) ).
fof(f267,plain,
( spl0_35
<=> ! [X8] :
( ~ function(X8)
| one_to_one(X8)
| ~ function(inverse(X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f73,axiom,
! [X8] :
( ~ function(X8)
| one_to_one(X8)
| ~ function(inverse(X8)) ),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',one_to_one3) ).
fof(f265,plain,
spl0_34,
inference(avatar_split_clause,[],[f66,f263]) ).
fof(f66,axiom,
! [X0] :
( null_class = X0
| member(regular(X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',regularity1) ).
fof(f261,plain,
spl0_33,
inference(avatar_split_clause,[],[f62,f259]) ).
fof(f62,axiom,
! [X8] :
( ~ function(X8)
| subclass(X8,cross_product(universal_class,universal_class)) ),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',function1) ).
fof(f257,plain,
spl0_32,
inference(avatar_split_clause,[],[f57,f255]) ).
fof(f57,axiom,
! [X7,X5] : subclass(compose(X7,X5),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',compose1) ).
fof(f253,plain,
spl0_31,
inference(avatar_split_clause,[],[f56,f251]) ).
fof(f56,axiom,
! [X2] :
( ~ member(X2,universal_class)
| member(power_class(X2),universal_class) ),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',power_class2) ).
fof(f249,plain,
spl0_30,
inference(avatar_split_clause,[],[f54,f247]) ).
fof(f54,axiom,
! [X0] :
( ~ member(X0,universal_class)
| member(sum_class(X0),universal_class) ),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',sum_class2) ).
fof(f245,plain,
spl0_29,
inference(avatar_split_clause,[],[f48,f243]) ).
fof(f48,axiom,
! [X0] :
( ~ inductive(X0)
| subclass(image(successor_relation,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',inductive2) ).
fof(f241,plain,
spl0_28,
inference(avatar_split_clause,[],[f43,f239]) ).
fof(f43,axiom,
! [X0] : union(X0,singleton(X0)) = successor(X0),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',successor) ).
fof(f237,plain,
spl0_27,
inference(avatar_split_clause,[],[f24,f235]) ).
fof(f24,axiom,
! [X0,X4] :
( ~ member(X4,X0)
| ~ member(X4,complement(X0)) ),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',complement1) ).
fof(f233,plain,
( spl0_26
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f228,f192,f231]) ).
fof(f192,plain,
( spl0_17
<=> ! [X0,X1] :
( X0 != X1
| subclass(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f228,plain,
( ! [X0] : subclass(X0,X0)
| ~ spl0_17 ),
inference(equality_resolution,[],[f193]) ).
fof(f193,plain,
( ! [X0,X1] :
( X0 != X1
| subclass(X1,X0) )
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f192]) ).
fof(f227,plain,
spl0_25,
inference(avatar_split_clause,[],[f109,f225]) ).
fof(f225,plain,
( spl0_25
<=> ! [X0,X1,X8] :
( function(X8)
| ~ maps(X8,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f109,axiom,
! [X0,X1,X8] :
( function(X8)
| ~ maps(X8,X0,X1) ),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',maps1) ).
fof(f223,plain,
spl0_24,
inference(avatar_split_clause,[],[f92,f221]) ).
fof(f92,axiom,
! [X0] : subclass(compose_class(X0),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',compose_class_definition1) ).
fof(f219,plain,
spl0_23,
inference(avatar_split_clause,[],[f87,f217]) ).
fof(f217,plain,
( spl0_23
<=> ! [X9,X11,X10] :
( operation(X11)
| ~ homomorphism(X9,X10,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f87,axiom,
! [X10,X11,X9] :
( operation(X11)
| ~ homomorphism(X9,X10,X11) ),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',homomorphism2) ).
fof(f215,plain,
spl0_22,
inference(avatar_split_clause,[],[f86,f213]) ).
fof(f213,plain,
( spl0_22
<=> ! [X9,X11,X10] :
( operation(X10)
| ~ homomorphism(X9,X10,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f86,axiom,
! [X10,X11,X9] :
( operation(X10)
| ~ homomorphism(X9,X10,X11) ),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',homomorphism1) ).
fof(f211,plain,
spl0_21,
inference(avatar_split_clause,[],[f82,f209]) ).
fof(f209,plain,
( spl0_21
<=> ! [X9,X11,X10] :
( function(X9)
| ~ compatible(X9,X10,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f82,axiom,
! [X10,X11,X9] :
( function(X9)
| ~ compatible(X9,X10,X11) ),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',compatible1) ).
fof(f207,plain,
spl0_20,
inference(avatar_split_clause,[],[f75,f204]) ).
fof(f75,axiom,
identity_relation = intersection(inverse(subset_relation),subset_relation),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',identity_relation) ).
fof(f202,plain,
spl0_19,
inference(avatar_split_clause,[],[f39,f200]) ).
fof(f39,axiom,
! [X4] : domain_of(inverse(X4)) = range_of(X4),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',range_of) ).
fof(f198,plain,
spl0_18,
inference(avatar_split_clause,[],[f12,f196]) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',singleton_set) ).
fof(f194,plain,
spl0_17,
inference(avatar_split_clause,[],[f6,f192]) ).
fof(f6,axiom,
! [X0,X1] :
( X0 != X1
| subclass(X1,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',equal_implies_subclass2) ).
fof(f190,plain,
spl0_16,
inference(avatar_split_clause,[],[f98,f187]) ).
fof(f98,axiom,
subclass(domain_relation,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',definition_of_domain_relation1) ).
fof(f185,plain,
spl0_15,
inference(avatar_split_clause,[],[f72,f183]) ).
fof(f72,axiom,
! [X8] :
( ~ one_to_one(X8)
| function(inverse(X8)) ),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',one_to_one2) ).
fof(f181,plain,
spl0_14,
inference(avatar_split_clause,[],[f51,f179]) ).
fof(f51,axiom,
! [X1] :
( ~ inductive(X1)
| subclass(omega,X1) ),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',omega_is_inductive2) ).
fof(f177,plain,
spl0_13,
inference(avatar_split_clause,[],[f47,f175]) ).
fof(f47,axiom,
! [X0] :
( ~ inductive(X0)
| member(null_class,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',inductive1) ).
fof(f173,plain,
spl0_12,
inference(avatar_split_clause,[],[f44,f170]) ).
fof(f44,axiom,
subclass(successor_relation,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',successor_relation1) ).
fof(f168,plain,
spl0_11,
inference(avatar_split_clause,[],[f18,f165]) ).
fof(f18,axiom,
subclass(element_relation,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',element_relation1) ).
fof(f163,plain,
spl0_10,
inference(avatar_split_clause,[],[f11,f161]) ).
fof(f11,axiom,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',unordered_pairs_in_universal) ).
fof(f159,plain,
spl0_9,
inference(avatar_split_clause,[],[f78,f157]) ).
fof(f157,plain,
( spl0_9
<=> ! [X8] :
( ~ operation(X8)
| function(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f78,axiom,
! [X8] :
( ~ operation(X8)
| function(X8) ),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',operation1) ).
fof(f155,plain,
spl0_8,
inference(avatar_split_clause,[],[f71,f153]) ).
fof(f153,plain,
( spl0_8
<=> ! [X8] :
( ~ one_to_one(X8)
| function(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f71,axiom,
! [X8] :
( ~ one_to_one(X8)
| function(X8) ),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',one_to_one1) ).
fof(f151,plain,
spl0_7,
inference(avatar_split_clause,[],[f52,f148]) ).
fof(f52,axiom,
member(omega,universal_class),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',omega_in_universal) ).
fof(f146,plain,
spl0_6,
inference(avatar_split_clause,[],[f4,f144]) ).
fof(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',class_elements_are_sets) ).
fof(f142,plain,
spl0_5,
inference(avatar_split_clause,[],[f69,f139]) ).
fof(f69,axiom,
function(choice),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',choice1) ).
fof(f137,plain,
spl0_4,
inference(avatar_split_clause,[],[f50,f134]) ).
fof(f50,axiom,
inductive(omega),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',omega_is_inductive1) ).
fof(f132,plain,
spl0_3,
inference(avatar_split_clause,[],[f113,f129]) ).
fof(f113,axiom,
member(x,union(y,z)),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',prove_members_of_union1_1) ).
fof(f127,plain,
~ spl0_2,
inference(avatar_split_clause,[],[f115,f124]) ).
fof(f115,axiom,
~ member(x,z),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',prove_members_of_union1_3) ).
fof(f122,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f114,f119]) ).
fof(f114,axiom,
~ member(x,y),
file('/export/starexec/sandbox2/tmp/tmp.wbUAoy1ELV/Vampire---4.8_23777',prove_members_of_union1_2) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.12 % Problem : SET166-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.05/0.14 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.11/0.33 % Computer : n013.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Wed Aug 30 15:45:31 EDT 2023
% 0.11/0.34 % CPUTime :
% 0.11/0.39 % (23883)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.40 % (23884)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on Vampire---4 for (846ds/0Mi)
% 0.16/0.40 % (23887)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on Vampire---4 for (533ds/0Mi)
% 0.16/0.40 % (23885)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on Vampire---4 for (793ds/0Mi)
% 0.16/0.40 % (23886)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on Vampire---4 for (569ds/0Mi)
% 0.16/0.40 % (23888)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on Vampire---4 for (531ds/0Mi)
% 0.16/0.40 % (23889)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on Vampire---4 for (522ds/0Mi)
% 0.16/0.40 % (23890)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on Vampire---4 for (497ds/0Mi)
% 0.16/0.40 TRYING [1]
% 0.16/0.41 TRYING [2]
% 0.16/0.42 TRYING [1]
% 0.16/0.42 TRYING [3]
% 0.16/0.42 TRYING [2]
% 0.16/0.48 TRYING [4]
% 0.16/0.49 TRYING [3]
% 0.16/0.64 TRYING [5]
% 0.16/0.66 TRYING [4]
% 0.16/0.68 % (23888)First to succeed.
% 0.16/0.69 % (23888)Refutation found. Thanks to Tanya!
% 0.16/0.69 % SZS status Unsatisfiable for Vampire---4
% 0.16/0.69 % SZS output start Proof for Vampire---4
% See solution above
% 2.17/0.70 % (23888)------------------------------
% 2.17/0.70 % (23888)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 2.17/0.70 % (23888)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 2.17/0.70 % (23888)Termination reason: Refutation
% 2.17/0.70
% 2.17/0.70 % (23888)Memory used [KB]: 14328
% 2.17/0.70 % (23888)Time elapsed: 0.293 s
% 2.17/0.70 % (23888)------------------------------
% 2.17/0.70 % (23888)------------------------------
% 2.17/0.70 % (23883)Success in time 0.352 s
% 2.17/0.70 % Vampire---4.8 exiting
%------------------------------------------------------------------------------