TSTP Solution File: SET071-7 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SET071-7 : 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 : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 15:36:16 EDT 2023
% Result : Unsatisfiable 0.23s 0.64s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 481
% Syntax : Number of formulae : 1875 ( 131 unt; 0 def)
% Number of atoms : 6334 ( 283 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 8907 (4448 ~;4071 |; 0 &)
% ( 388 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 397 ( 395 usr; 389 prp; 0-3 aty)
% Number of functors : 35 ( 35 usr; 10 con; 0-3 aty)
% Number of variables : 2378 (;2378 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4916,plain,
$false,
inference(avatar_sat_refutation,[],[f125,f130,f135,f140,f145,f149,f154,f158,f162,f166,f171,f175,f180,f185,f189,f193,f199,f204,f208,f213,f217,f221,f225,f229,f234,f242,f246,f250,f254,f258,f262,f266,f270,f274,f280,f290,f294,f304,f308,f312,f316,f320,f324,f328,f332,f336,f340,f344,f348,f352,f356,f380,f384,f388,f392,f400,f412,f426,f431,f436,f440,f447,f464,f471,f475,f479,f483,f487,f491,f495,f499,f503,f507,f532,f536,f562,f573,f579,f591,f600,f606,f611,f615,f636,f642,f654,f658,f662,f682,f688,f702,f708,f712,f716,f737,f741,f771,f775,f779,f783,f787,f794,f805,f814,f818,f823,f827,f831,f835,f847,f851,f863,f868,f872,f876,f880,f884,f901,f905,f909,f929,f933,f956,f964,f972,f976,f980,f984,f994,f998,f1007,f1026,f1038,f1051,f1060,f1077,f1086,f1090,f1116,f1135,f1153,f1157,f1161,f1165,f1169,f1183,f1220,f1225,f1230,f1253,f1264,f1268,f1295,f1301,f1306,f1326,f1330,f1335,f1340,f1344,f1353,f1357,f1362,f1375,f1397,f1409,f1425,f1432,f1439,f1443,f1452,f1459,f1463,f1470,f1478,f1482,f1487,f1491,f1495,f1506,f1513,f1524,f1531,f1551,f1560,f1604,f1605,f1606,f1607,f1608,f1609,f1610,f1611,f1612,f1613,f1614,f1615,f1616,f1617,f1618,f2015,f2019,f2021,f2024,f2027,f2030,f2033,f2035,f2037,f2040,f2043,f2049,f2052,f2055,f2057,f2059,f2062,f2064,f2068,f2071,f2074,f2077,f2079,f2081,f2084,f2088,f2091,f2094,f2096,f2098,f2100,f2103,f2107,f2110,f2113,f2115,f2117,f2120,f2123,f2126,f2129,f2131,f2133,f2136,f2140,f2143,f2146,f2149,f2152,f2155,f2159,f2162,f2166,f2168,f2171,f2175,f2178,f2181,f2183,f2185,f2187,f2190,f2194,f2197,f2200,f2202,f2205,f2208,f2211,f2214,f2216,f2224,f2227,f2230,f2233,f2236,f2239,f2243,f2246,f2250,f2253,f2256,f2261,f2263,f2266,f2270,f2272,f2274,f2276,f2278,f2280,f2282,f2284,f2286,f2288,f2290,f2292,f2294,f2296,f2298,f2300,f2302,f2304,f2306,f2308,f2310,f2319,f2401,f2420,f2428,f2446,f2456,f2468,f2472,f2481,f2489,f2500,f2507,f2511,f2527,f2535,f2542,f2548,f2552,f2556,f2560,f2597,f2603,f2613,f2623,f2628,f2648,f2652,f2656,f2685,f2698,f2712,f2719,f2743,f2751,f2757,f2762,f2781,f2789,f2793,f2798,f2802,f2806,f2833,f2843,f2848,f2873,f2881,f2886,f2893,f2897,f2901,f2913,f2917,f2921,f2934,f2952,f2967,f2980,f2988,f2994,f3016,f3021,f3051,f3058,f3072,f3076,f3094,f3099,f3108,f3119,f3124,f3130,f3134,f3138,f3144,f3148,f3152,f3176,f3195,f3221,f3318,f3360,f3414,f3446,f3479,f3487,f3495,f3548,f3556,f3572,f3576,f3592,f3601,f3605,f3609,f3613,f3617,f3627,f3632,f3658,f3689,f3696,f3703,f3711,f3719,f3732,f3736,f3769,f3773,f3781,f3787,f3791,f3796,f3803,f3807,f3839,f3847,f3860,f3868,f3878,f3882,f3886,f3890,f3898,f3903,f3907,f3928,f3935,f3939,f3945,f3955,f3965,f3969,f3973,f3982,f3986,f3990,f3994,f4018,f4025,f4030,f4034,f4038,f4056,f4060,f4064,f4068,f4078,f4082,f4086,f4099,f4127,f4131,f4139,f4153,f4179,f4183,f4211,f4219,f4228,f4254,f4268,f4285,f4289,f4293,f4299,f4303,f4307,f4352,f4367,f4383,f4387,f4402,f4411,f4415,f4419,f4423,f4440,f4482,f4490,f4512,f4516,f4540,f4550,f4567,f4571,f4591,f4721,f4725,f4817,f4826,f4871,f4902,f4915]) ).
fof(f4915,plain,
( ~ spl0_33
| spl0_87
| ~ spl0_190
| ~ spl0_388 ),
inference(avatar_contradiction_clause,[],[f4914]) ).
fof(f4914,plain,
( $false
| ~ spl0_33
| spl0_87
| ~ spl0_190
| ~ spl0_388 ),
inference(subsumption_resolution,[],[f4913,f653]) ).
fof(f653,plain,
( null_class != singleton(x)
| spl0_87 ),
inference(avatar_component_clause,[],[f651]) ).
fof(f651,plain,
( spl0_87
<=> null_class = singleton(x) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f4913,plain,
( null_class = singleton(x)
| ~ spl0_33
| ~ spl0_190
| ~ spl0_388 ),
inference(subsumption_resolution,[],[f4911,f1547]) ).
fof(f1547,plain,
( ! [X1] : ~ member(y,X1)
| ~ spl0_190 ),
inference(avatar_component_clause,[],[f1546]) ).
fof(f1546,plain,
( spl0_190
<=> ! [X1] : ~ member(y,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).
fof(f4911,plain,
( member(y,singleton(x))
| null_class = singleton(x)
| ~ spl0_33
| ~ spl0_388 ),
inference(superposition,[],[f269,f4901]) ).
fof(f4901,plain,
( y = regular(singleton(x))
| ~ spl0_388 ),
inference(avatar_component_clause,[],[f4899]) ).
fof(f4899,plain,
( spl0_388
<=> y = regular(singleton(x)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_388])]) ).
fof(f269,plain,
( ! [X0] :
( member(regular(X0),X0)
| null_class = X0 )
| ~ spl0_33 ),
inference(avatar_component_clause,[],[f268]) ).
fof(f268,plain,
( spl0_33
<=> ! [X0] :
( null_class = X0
| member(regular(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f4902,plain,
( spl0_388
| ~ spl0_33
| spl0_87
| ~ spl0_387 ),
inference(avatar_split_clause,[],[f4895,f4869,f651,f268,f4899]) ).
fof(f4869,plain,
( spl0_387
<=> ! [X0] :
( ~ member(X0,singleton(x))
| y = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_387])]) ).
fof(f4895,plain,
( y = regular(singleton(x))
| ~ spl0_33
| spl0_87
| ~ spl0_387 ),
inference(subsumption_resolution,[],[f4878,f653]) ).
fof(f4878,plain,
( y = regular(singleton(x))
| null_class = singleton(x)
| ~ spl0_33
| ~ spl0_387 ),
inference(resolution,[],[f4870,f269]) ).
fof(f4870,plain,
( ! [X0] :
( ~ member(X0,singleton(x))
| y = X0 )
| ~ spl0_387 ),
inference(avatar_component_clause,[],[f4869]) ).
fof(f4871,plain,
( spl0_387
| ~ spl0_96
| ~ spl0_385 ),
inference(avatar_split_clause,[],[f4866,f4815,f734,f4869]) ).
fof(f734,plain,
( spl0_96
<=> singleton(x) = singleton(y) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f4815,plain,
( spl0_385
<=> ! [X0,X1] :
( ~ member(X1,singleton(X0))
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_385])]) ).
fof(f4866,plain,
( ! [X0] :
( ~ member(X0,singleton(x))
| y = X0 )
| ~ spl0_96
| ~ spl0_385 ),
inference(superposition,[],[f4816,f736]) ).
fof(f736,plain,
( singleton(x) = singleton(y)
| ~ spl0_96 ),
inference(avatar_component_clause,[],[f734]) ).
fof(f4816,plain,
( ! [X0,X1] :
( ~ member(X1,singleton(X0))
| X0 = X1 )
| ~ spl0_385 ),
inference(avatar_component_clause,[],[f4815]) ).
fof(f4826,plain,
( spl0_386
| ~ spl0_23
| ~ spl0_142 ),
inference(avatar_split_clause,[],[f1241,f1114,f223,f4824]) ).
fof(f4824,plain,
( spl0_386
<=> ! [X11,X12] : subclass(singleton(singleton(X11)),ordered_pair(X11,X12)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_386])]) ).
fof(f223,plain,
( spl0_23
<=> ! [X0,X1] : subclass(singleton(X0),unordered_pair(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f1114,plain,
( spl0_142
<=> ! [X0,X1] : unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))) = ordered_pair(X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f1241,plain,
( ! [X11,X12] : subclass(singleton(singleton(X11)),ordered_pair(X11,X12))
| ~ spl0_23
| ~ spl0_142 ),
inference(superposition,[],[f224,f1115]) ).
fof(f1115,plain,
( ! [X0,X1] : unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))) = ordered_pair(X0,X1)
| ~ spl0_142 ),
inference(avatar_component_clause,[],[f1114]) ).
fof(f224,plain,
( ! [X0,X1] : subclass(singleton(X0),unordered_pair(X0,X1))
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f223]) ).
fof(f4817,plain,
( spl0_385
| ~ spl0_18
| ~ spl0_140 ),
inference(avatar_split_clause,[],[f1215,f1084,f202,f4815]) ).
fof(f202,plain,
( spl0_18
<=> ! [X0] : unordered_pair(X0,X0) = singleton(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f1084,plain,
( spl0_140
<=> ! [X2,X0,X1] :
( X1 = X2
| X0 = X2
| ~ member(X2,unordered_pair(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f1215,plain,
( ! [X0,X1] :
( ~ member(X1,singleton(X0))
| X0 = X1 )
| ~ spl0_18
| ~ spl0_140 ),
inference(duplicate_literal_removal,[],[f1208]) ).
fof(f1208,plain,
( ! [X0,X1] :
( ~ member(X1,singleton(X0))
| X0 = X1
| X0 = X1 )
| ~ spl0_18
| ~ spl0_140 ),
inference(superposition,[],[f1085,f203]) ).
fof(f203,plain,
( ! [X0] : unordered_pair(X0,X0) = singleton(X0)
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f202]) ).
fof(f1085,plain,
( ! [X2,X0,X1] :
( ~ member(X2,unordered_pair(X0,X1))
| X0 = X2
| X1 = X2 )
| ~ spl0_140 ),
inference(avatar_component_clause,[],[f1084]) ).
fof(f4725,plain,
( spl0_384
| ~ spl0_90
| ~ spl0_381 ),
inference(avatar_split_clause,[],[f4593,f4585,f680,f4723]) ).
fof(f4723,plain,
( spl0_384
<=> ! [X2] : subclass(omega,singleton(X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_384])]) ).
fof(f680,plain,
( spl0_90
<=> ! [X2] : subclass(singleton(x),singleton(X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f4585,plain,
( spl0_381
<=> omega = singleton(x) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_381])]) ).
fof(f4593,plain,
( ! [X2] : subclass(omega,singleton(X2))
| ~ spl0_90
| ~ spl0_381 ),
inference(backward_demodulation,[],[f681,f4587]) ).
fof(f4587,plain,
( omega = singleton(x)
| ~ spl0_381 ),
inference(avatar_component_clause,[],[f4585]) ).
fof(f681,plain,
( ! [X2] : subclass(singleton(x),singleton(X2))
| ~ spl0_90 ),
inference(avatar_component_clause,[],[f680]) ).
fof(f4721,plain,
( ~ spl0_383
| spl0_87
| ~ spl0_381 ),
inference(avatar_split_clause,[],[f4592,f4585,f651,f4718]) ).
fof(f4718,plain,
( spl0_383
<=> null_class = omega ),
introduced(avatar_definition,[new_symbols(naming,[spl0_383])]) ).
fof(f4592,plain,
( null_class != omega
| spl0_87
| ~ spl0_381 ),
inference(backward_demodulation,[],[f653,f4587]) ).
fof(f4591,plain,
( spl0_381
| spl0_382
| ~ spl0_75
| ~ spl0_202 ),
inference(avatar_split_clause,[],[f4526,f2487,f534,f4589,f4585]) ).
fof(f4589,plain,
( spl0_382
<=> ! [X8] :
( ~ subclass(universal_class,ordered_pair(x,X8))
| omega = singleton(singleton(X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_382])]) ).
fof(f534,plain,
( spl0_75
<=> ! [X13] :
( ~ subclass(universal_class,X13)
| member(omega,X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f2487,plain,
( spl0_202
<=> ! [X4,X3] :
( ~ member(X4,ordered_pair(x,X3))
| singleton(x) = X4
| singleton(singleton(X3)) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).
fof(f4526,plain,
( ! [X8] :
( ~ subclass(universal_class,ordered_pair(x,X8))
| omega = singleton(x)
| omega = singleton(singleton(X8)) )
| ~ spl0_75
| ~ spl0_202 ),
inference(resolution,[],[f535,f2488]) ).
fof(f2488,plain,
( ! [X3,X4] :
( ~ member(X4,ordered_pair(x,X3))
| singleton(x) = X4
| singleton(singleton(X3)) = X4 )
| ~ spl0_202 ),
inference(avatar_component_clause,[],[f2487]) ).
fof(f535,plain,
( ! [X13] :
( member(omega,X13)
| ~ subclass(universal_class,X13) )
| ~ spl0_75 ),
inference(avatar_component_clause,[],[f534]) ).
fof(f4571,plain,
( spl0_380
| ~ spl0_102
| ~ spl0_377 ),
inference(avatar_split_clause,[],[f4546,f4538,f785,f4569]) ).
fof(f4569,plain,
( spl0_380
<=> ! [X3,X4,X5,X2] : ~ subclass(ordered_pair(x,X2),restrict(intersection(complement(ordered_pair(x,X2)),X3),X4,X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_380])]) ).
fof(f785,plain,
( spl0_102
<=> ! [X5,X0,X1] : intersection(X5,cross_product(X0,X1)) = restrict(X5,X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f4538,plain,
( spl0_377
<=> ! [X2,X0,X1] : ~ subclass(ordered_pair(x,X0),intersection(intersection(complement(ordered_pair(x,X0)),X1),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_377])]) ).
fof(f4546,plain,
( ! [X2,X3,X4,X5] : ~ subclass(ordered_pair(x,X2),restrict(intersection(complement(ordered_pair(x,X2)),X3),X4,X5))
| ~ spl0_102
| ~ spl0_377 ),
inference(superposition,[],[f4539,f786]) ).
fof(f786,plain,
( ! [X0,X1,X5] : intersection(X5,cross_product(X0,X1)) = restrict(X5,X0,X1)
| ~ spl0_102 ),
inference(avatar_component_clause,[],[f785]) ).
fof(f4539,plain,
( ! [X2,X0,X1] : ~ subclass(ordered_pair(x,X0),intersection(intersection(complement(ordered_pair(x,X0)),X1),X2))
| ~ spl0_377 ),
inference(avatar_component_clause,[],[f4538]) ).
fof(f4567,plain,
( spl0_379
| ~ spl0_102
| ~ spl0_377 ),
inference(avatar_split_clause,[],[f4544,f4538,f785,f4565]) ).
fof(f4565,plain,
( spl0_379
<=> ! [X5,X4,X7,X6] : ~ subclass(ordered_pair(x,X4),intersection(restrict(complement(ordered_pair(x,X4)),X5,X6),X7)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_379])]) ).
fof(f4544,plain,
( ! [X6,X7,X4,X5] : ~ subclass(ordered_pair(x,X4),intersection(restrict(complement(ordered_pair(x,X4)),X5,X6),X7))
| ~ spl0_102
| ~ spl0_377 ),
inference(superposition,[],[f4539,f786]) ).
fof(f4550,plain,
( spl0_378
| ~ spl0_102
| ~ spl0_375 ),
inference(avatar_split_clause,[],[f4519,f4510,f785,f4548]) ).
fof(f4548,plain,
( spl0_378
<=> ! [X5,X4,X7,X6,X3] : ~ subclass(universal_class,restrict(restrict(complement(ordered_pair(x,X3)),X4,X5),X6,X7)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_378])]) ).
fof(f4510,plain,
( spl0_375
<=> ! [X6,X4,X5,X7] : ~ subclass(universal_class,intersection(restrict(complement(ordered_pair(x,X4)),X5,X6),X7)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_375])]) ).
fof(f4519,plain,
( ! [X3,X6,X7,X4,X5] : ~ subclass(universal_class,restrict(restrict(complement(ordered_pair(x,X3)),X4,X5),X6,X7))
| ~ spl0_102
| ~ spl0_375 ),
inference(superposition,[],[f4511,f786]) ).
fof(f4511,plain,
( ! [X6,X7,X4,X5] : ~ subclass(universal_class,intersection(restrict(complement(ordered_pair(x,X4)),X5,X6),X7))
| ~ spl0_375 ),
inference(avatar_component_clause,[],[f4510]) ).
fof(f4540,plain,
( spl0_377
| ~ spl0_8
| ~ spl0_373 ),
inference(avatar_split_clause,[],[f4483,f4480,f156,f4538]) ).
fof(f156,plain,
( spl0_8
<=> ! [X0] : subclass(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f4480,plain,
( spl0_373
<=> ! [X119,X118,X117,X116] :
( ~ subclass(X116,intersection(intersection(complement(ordered_pair(x,X117)),X118),X119))
| ~ subclass(ordered_pair(x,X117),X116) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_373])]) ).
fof(f4483,plain,
( ! [X2,X0,X1] : ~ subclass(ordered_pair(x,X0),intersection(intersection(complement(ordered_pair(x,X0)),X1),X2))
| ~ spl0_8
| ~ spl0_373 ),
inference(resolution,[],[f4481,f157]) ).
fof(f157,plain,
( ! [X0] : subclass(X0,X0)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f156]) ).
fof(f4481,plain,
( ! [X118,X119,X116,X117] :
( ~ subclass(ordered_pair(x,X117),X116)
| ~ subclass(X116,intersection(intersection(complement(ordered_pair(x,X117)),X118),X119)) )
| ~ spl0_373 ),
inference(avatar_component_clause,[],[f4480]) ).
fof(f4516,plain,
( spl0_376
| ~ spl0_102
| ~ spl0_374 ),
inference(avatar_split_clause,[],[f4496,f4488,f785,f4514]) ).
fof(f4514,plain,
( spl0_376
<=> ! [X4,X5,X2,X3] : ~ subclass(universal_class,restrict(intersection(complement(ordered_pair(x,X2)),X3),X4,X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_376])]) ).
fof(f4488,plain,
( spl0_374
<=> ! [X4,X5,X3] : ~ subclass(universal_class,intersection(intersection(complement(ordered_pair(x,X3)),X4),X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_374])]) ).
fof(f4496,plain,
( ! [X2,X3,X4,X5] : ~ subclass(universal_class,restrict(intersection(complement(ordered_pair(x,X2)),X3),X4,X5))
| ~ spl0_102
| ~ spl0_374 ),
inference(superposition,[],[f4489,f786]) ).
fof(f4489,plain,
( ! [X3,X4,X5] : ~ subclass(universal_class,intersection(intersection(complement(ordered_pair(x,X3)),X4),X5))
| ~ spl0_374 ),
inference(avatar_component_clause,[],[f4488]) ).
fof(f4512,plain,
( spl0_375
| ~ spl0_102
| ~ spl0_374 ),
inference(avatar_split_clause,[],[f4494,f4488,f785,f4510]) ).
fof(f4494,plain,
( ! [X6,X7,X4,X5] : ~ subclass(universal_class,intersection(restrict(complement(ordered_pair(x,X4)),X5,X6),X7))
| ~ spl0_102
| ~ spl0_374 ),
inference(superposition,[],[f4489,f786]) ).
fof(f4490,plain,
( spl0_374
| ~ spl0_6
| ~ spl0_373 ),
inference(avatar_split_clause,[],[f4484,f4480,f147,f4488]) ).
fof(f147,plain,
( spl0_6
<=> ! [X0] : subclass(X0,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f4484,plain,
( ! [X3,X4,X5] : ~ subclass(universal_class,intersection(intersection(complement(ordered_pair(x,X3)),X4),X5))
| ~ spl0_6
| ~ spl0_373 ),
inference(resolution,[],[f4481,f148]) ).
fof(f148,plain,
( ! [X0] : subclass(X0,universal_class)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f147]) ).
fof(f4482,plain,
( spl0_373
| ~ spl0_170
| ~ spl0_359 ),
inference(avatar_split_clause,[],[f4337,f4291,f1373,f4480]) ).
fof(f1373,plain,
( spl0_170
<=> ! [X2] : member(singleton(singleton(X2)),ordered_pair(x,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
fof(f4291,plain,
( spl0_359
<=> ! [X92,X88,X91,X90,X89] :
( ~ subclass(ordered_pair(x,X88),X89)
| ~ subclass(X89,intersection(intersection(complement(X90),X91),X92))
| ~ member(singleton(singleton(X88)),X90) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_359])]) ).
fof(f4337,plain,
( ! [X118,X119,X116,X117] :
( ~ subclass(X116,intersection(intersection(complement(ordered_pair(x,X117)),X118),X119))
| ~ subclass(ordered_pair(x,X117),X116) )
| ~ spl0_170
| ~ spl0_359 ),
inference(resolution,[],[f4292,f1374]) ).
fof(f1374,plain,
( ! [X2] : member(singleton(singleton(X2)),ordered_pair(x,X2))
| ~ spl0_170 ),
inference(avatar_component_clause,[],[f1373]) ).
fof(f4292,plain,
( ! [X90,X91,X88,X89,X92] :
( ~ member(singleton(singleton(X88)),X90)
| ~ subclass(X89,intersection(intersection(complement(X90),X91),X92))
| ~ subclass(ordered_pair(x,X88),X89) )
| ~ spl0_359 ),
inference(avatar_component_clause,[],[f4291]) ).
fof(f4440,plain,
( spl0_372
| ~ spl0_102
| ~ spl0_370 ),
inference(avatar_split_clause,[],[f4426,f4417,f785,f4438]) ).
fof(f4438,plain,
( spl0_372
<=> ! [X5,X4,X7,X6,X3] : ~ subclass(ordered_pair(x,X7),restrict(restrict(complement(universal_class),X3,X4),X5,X6)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_372])]) ).
fof(f4417,plain,
( spl0_370
<=> ! [X2,X5,X3,X4] : ~ subclass(ordered_pair(x,X4),intersection(restrict(complement(universal_class),X2,X3),X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_370])]) ).
fof(f4426,plain,
( ! [X3,X6,X7,X4,X5] : ~ subclass(ordered_pair(x,X7),restrict(restrict(complement(universal_class),X3,X4),X5,X6))
| ~ spl0_102
| ~ spl0_370 ),
inference(superposition,[],[f4418,f786]) ).
fof(f4418,plain,
( ! [X2,X3,X4,X5] : ~ subclass(ordered_pair(x,X4),intersection(restrict(complement(universal_class),X2,X3),X5))
| ~ spl0_370 ),
inference(avatar_component_clause,[],[f4417]) ).
fof(f4423,plain,
( spl0_371
| ~ spl0_102
| ~ spl0_367 ),
inference(avatar_split_clause,[],[f4407,f4400,f785,f4421]) ).
fof(f4421,plain,
( spl0_371
<=> ! [X4,X5,X2,X3] : ~ subclass(ordered_pair(x,X5),restrict(intersection(complement(universal_class),X2),X3,X4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_371])]) ).
fof(f4400,plain,
( spl0_367
<=> ! [X2,X0,X1] : ~ subclass(ordered_pair(x,X0),intersection(intersection(complement(universal_class),X1),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_367])]) ).
fof(f4407,plain,
( ! [X2,X3,X4,X5] : ~ subclass(ordered_pair(x,X5),restrict(intersection(complement(universal_class),X2),X3,X4))
| ~ spl0_102
| ~ spl0_367 ),
inference(superposition,[],[f4401,f786]) ).
fof(f4401,plain,
( ! [X2,X0,X1] : ~ subclass(ordered_pair(x,X0),intersection(intersection(complement(universal_class),X1),X2))
| ~ spl0_367 ),
inference(avatar_component_clause,[],[f4400]) ).
fof(f4419,plain,
( spl0_370
| ~ spl0_102
| ~ spl0_367 ),
inference(avatar_split_clause,[],[f4405,f4400,f785,f4417]) ).
fof(f4405,plain,
( ! [X2,X3,X4,X5] : ~ subclass(ordered_pair(x,X4),intersection(restrict(complement(universal_class),X2,X3),X5))
| ~ spl0_102
| ~ spl0_367 ),
inference(superposition,[],[f4401,f786]) ).
fof(f4415,plain,
( spl0_369
| ~ spl0_12
| ~ spl0_142 ),
inference(avatar_split_clause,[],[f1242,f1114,f173,f4413]) ).
fof(f4413,plain,
( spl0_369
<=> ! [X13,X14] : member(ordered_pair(X13,X14),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_369])]) ).
fof(f173,plain,
( spl0_12
<=> ! [X0,X1] : member(unordered_pair(X0,X1),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f1242,plain,
( ! [X14,X13] : member(ordered_pair(X13,X14),universal_class)
| ~ spl0_12
| ~ spl0_142 ),
inference(superposition,[],[f174,f1115]) ).
fof(f174,plain,
( ! [X0,X1] : member(unordered_pair(X0,X1),universal_class)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f173]) ).
fof(f4411,plain,
( spl0_368
| ~ spl0_102
| ~ spl0_365 ),
inference(avatar_split_clause,[],[f4389,f4381,f785,f4409]) ).
fof(f4409,plain,
( spl0_368
<=> ! [X4,X5,X2,X3] : ~ subclass(universal_class,restrict(restrict(complement(universal_class),X2,X3),X4,X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_368])]) ).
fof(f4381,plain,
( spl0_365
<=> ! [X2,X1,X3] : ~ subclass(universal_class,intersection(restrict(complement(universal_class),X1,X2),X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_365])]) ).
fof(f4389,plain,
( ! [X2,X3,X4,X5] : ~ subclass(universal_class,restrict(restrict(complement(universal_class),X2,X3),X4,X5))
| ~ spl0_102
| ~ spl0_365 ),
inference(superposition,[],[f4382,f786]) ).
fof(f4382,plain,
( ! [X2,X3,X1] : ~ subclass(universal_class,intersection(restrict(complement(universal_class),X1,X2),X3))
| ~ spl0_365 ),
inference(avatar_component_clause,[],[f4381]) ).
fof(f4402,plain,
( spl0_367
| ~ spl0_8
| ~ spl0_363 ),
inference(avatar_split_clause,[],[f4360,f4350,f156,f4400]) ).
fof(f4350,plain,
( spl0_363
<=> ! [X102,X105,X103,X104] :
( ~ subclass(X102,intersection(intersection(complement(universal_class),X103),X104))
| ~ subclass(ordered_pair(x,X105),X102) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_363])]) ).
fof(f4360,plain,
( ! [X2,X0,X1] : ~ subclass(ordered_pair(x,X0),intersection(intersection(complement(universal_class),X1),X2))
| ~ spl0_8
| ~ spl0_363 ),
inference(resolution,[],[f4351,f157]) ).
fof(f4351,plain,
( ! [X104,X102,X105,X103] :
( ~ subclass(ordered_pair(x,X105),X102)
| ~ subclass(X102,intersection(intersection(complement(universal_class),X103),X104)) )
| ~ spl0_363 ),
inference(avatar_component_clause,[],[f4350]) ).
fof(f4387,plain,
( spl0_366
| ~ spl0_102
| ~ spl0_364 ),
inference(avatar_split_clause,[],[f4371,f4365,f785,f4385]) ).
fof(f4385,plain,
( spl0_366
<=> ! [X2,X1,X3] : ~ subclass(universal_class,restrict(intersection(complement(universal_class),X1),X2,X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_366])]) ).
fof(f4365,plain,
( spl0_364
<=> ! [X4,X3] : ~ subclass(universal_class,intersection(intersection(complement(universal_class),X3),X4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_364])]) ).
fof(f4371,plain,
( ! [X2,X3,X1] : ~ subclass(universal_class,restrict(intersection(complement(universal_class),X1),X2,X3))
| ~ spl0_102
| ~ spl0_364 ),
inference(superposition,[],[f4366,f786]) ).
fof(f4366,plain,
( ! [X3,X4] : ~ subclass(universal_class,intersection(intersection(complement(universal_class),X3),X4))
| ~ spl0_364 ),
inference(avatar_component_clause,[],[f4365]) ).
fof(f4383,plain,
( spl0_365
| ~ spl0_102
| ~ spl0_364 ),
inference(avatar_split_clause,[],[f4369,f4365,f785,f4381]) ).
fof(f4369,plain,
( ! [X2,X3,X1] : ~ subclass(universal_class,intersection(restrict(complement(universal_class),X1,X2),X3))
| ~ spl0_102
| ~ spl0_364 ),
inference(superposition,[],[f4366,f786]) ).
fof(f4367,plain,
( spl0_364
| ~ spl0_6
| ~ spl0_363 ),
inference(avatar_split_clause,[],[f4361,f4350,f147,f4365]) ).
fof(f4361,plain,
( ! [X3,X4] : ~ subclass(universal_class,intersection(intersection(complement(universal_class),X3),X4))
| ~ spl0_6
| ~ spl0_363 ),
inference(resolution,[],[f4351,f148]) ).
fof(f4352,plain,
( spl0_363
| ~ spl0_25
| ~ spl0_359 ),
inference(avatar_split_clause,[],[f4334,f4291,f232,f4350]) ).
fof(f232,plain,
( spl0_25
<=> ! [X0] : member(singleton(X0),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f4334,plain,
( ! [X104,X102,X105,X103] :
( ~ subclass(X102,intersection(intersection(complement(universal_class),X103),X104))
| ~ subclass(ordered_pair(x,X105),X102) )
| ~ spl0_25
| ~ spl0_359 ),
inference(resolution,[],[f4292,f233]) ).
fof(f233,plain,
( ! [X0] : member(singleton(X0),universal_class)
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f232]) ).
fof(f4307,plain,
( spl0_362
| ~ spl0_26
| ~ spl0_269 ),
inference(avatar_split_clause,[],[f3826,f3150,f240,f4305]) ).
fof(f4305,plain,
( spl0_362
<=> ! [X94,X97,X95,X93,X96] :
( ~ subclass(ordered_pair(x,X93),X94)
| ~ subclass(X94,intersection(X95,intersection(complement(X96),X97)))
| ~ member(singleton(singleton(X93)),X96) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_362])]) ).
fof(f240,plain,
( spl0_26
<=> ! [X4,X0] :
( ~ member(X4,X0)
| ~ member(X4,complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f3150,plain,
( spl0_269
<=> ! [X35,X34,X36,X33,X32] :
( ~ subclass(X32,intersection(X33,intersection(X34,X35)))
| ~ subclass(ordered_pair(x,X36),X32)
| member(singleton(singleton(X36)),X34) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).
fof(f3826,plain,
( ! [X96,X94,X97,X95,X93] :
( ~ subclass(ordered_pair(x,X93),X94)
| ~ subclass(X94,intersection(X95,intersection(complement(X96),X97)))
| ~ member(singleton(singleton(X93)),X96) )
| ~ spl0_26
| ~ spl0_269 ),
inference(resolution,[],[f3151,f241]) ).
fof(f241,plain,
( ! [X0,X4] :
( ~ member(X4,complement(X0))
| ~ member(X4,X0) )
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f240]) ).
fof(f3151,plain,
( ! [X36,X34,X35,X32,X33] :
( member(singleton(singleton(X36)),X34)
| ~ subclass(ordered_pair(x,X36),X32)
| ~ subclass(X32,intersection(X33,intersection(X34,X35))) )
| ~ spl0_269 ),
inference(avatar_component_clause,[],[f3150]) ).
fof(f4303,plain,
( spl0_361
| ~ spl0_26
| ~ spl0_268 ),
inference(avatar_split_clause,[],[f3760,f3146,f240,f4301]) ).
fof(f4301,plain,
( spl0_361
<=> ! [X94,X97,X95,X93,X96] :
( ~ subclass(ordered_pair(x,X93),X94)
| ~ subclass(X94,intersection(X95,intersection(X96,complement(X97))))
| ~ member(singleton(singleton(X93)),X97) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_361])]) ).
fof(f3146,plain,
( spl0_268
<=> ! [X31,X29,X27,X28,X30] :
( ~ subclass(X27,intersection(X28,intersection(X29,X30)))
| ~ subclass(ordered_pair(x,X31),X27)
| member(singleton(singleton(X31)),X30) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).
fof(f3760,plain,
( ! [X96,X94,X97,X95,X93] :
( ~ subclass(ordered_pair(x,X93),X94)
| ~ subclass(X94,intersection(X95,intersection(X96,complement(X97))))
| ~ member(singleton(singleton(X93)),X97) )
| ~ spl0_26
| ~ spl0_268 ),
inference(resolution,[],[f3147,f241]) ).
fof(f3147,plain,
( ! [X31,X28,X29,X27,X30] :
( member(singleton(singleton(X31)),X30)
| ~ subclass(ordered_pair(x,X31),X27)
| ~ subclass(X27,intersection(X28,intersection(X29,X30))) )
| ~ spl0_268 ),
inference(avatar_component_clause,[],[f3146]) ).
fof(f4299,plain,
( spl0_360
| ~ spl0_26
| ~ spl0_267 ),
inference(avatar_split_clause,[],[f3649,f3142,f240,f4297]) ).
fof(f4297,plain,
( spl0_360
<=> ! [X92,X88,X91,X90,X89] :
( ~ subclass(X88,intersection(intersection(X89,complement(X90)),X91))
| ~ subclass(ordered_pair(x,X92),X88)
| ~ member(singleton(singleton(X92)),X90) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_360])]) ).
fof(f3142,plain,
( spl0_267
<=> ! [X9,X11,X10,X8,X7] :
( member(singleton(singleton(X7)),X8)
| ~ subclass(X9,intersection(intersection(X10,X8),X11))
| ~ subclass(ordered_pair(x,X7),X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).
fof(f3649,plain,
( ! [X90,X91,X88,X89,X92] :
( ~ subclass(X88,intersection(intersection(X89,complement(X90)),X91))
| ~ subclass(ordered_pair(x,X92),X88)
| ~ member(singleton(singleton(X92)),X90) )
| ~ spl0_26
| ~ spl0_267 ),
inference(resolution,[],[f3143,f241]) ).
fof(f3143,plain,
( ! [X10,X11,X8,X9,X7] :
( member(singleton(singleton(X7)),X8)
| ~ subclass(X9,intersection(intersection(X10,X8),X11))
| ~ subclass(ordered_pair(x,X7),X9) )
| ~ spl0_267 ),
inference(avatar_component_clause,[],[f3142]) ).
fof(f4293,plain,
( spl0_359
| ~ spl0_26
| ~ spl0_266 ),
inference(avatar_split_clause,[],[f3512,f3136,f240,f4291]) ).
fof(f3136,plain,
( spl0_266
<=> ! [X31,X29,X27,X28,X30] :
( ~ subclass(X27,intersection(intersection(X28,X29),X30))
| ~ subclass(ordered_pair(x,X31),X27)
| member(singleton(singleton(X31)),X28) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).
fof(f3512,plain,
( ! [X90,X91,X88,X89,X92] :
( ~ subclass(ordered_pair(x,X88),X89)
| ~ subclass(X89,intersection(intersection(complement(X90),X91),X92))
| ~ member(singleton(singleton(X88)),X90) )
| ~ spl0_26
| ~ spl0_266 ),
inference(resolution,[],[f3137,f241]) ).
fof(f3137,plain,
( ! [X31,X28,X29,X27,X30] :
( member(singleton(singleton(X31)),X28)
| ~ subclass(ordered_pair(x,X31),X27)
| ~ subclass(X27,intersection(intersection(X28,X29),X30)) )
| ~ spl0_266 ),
inference(avatar_component_clause,[],[f3136]) ).
fof(f4289,plain,
( spl0_358
| ~ spl0_188
| ~ spl0_265 ),
inference(avatar_split_clause,[],[f3460,f3132,f1522,f4287]) ).
fof(f4287,plain,
( spl0_358
<=> ! [X50,X51,X49] :
( ~ subclass(X49,complement(inverse(subset_relation)))
| ~ subclass(X50,X49)
| ~ subclass(ordered_pair(x,X51),X50)
| ~ subclass(ordered_pair(x,X51),identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_358])]) ).
fof(f1522,plain,
( spl0_188
<=> ! [X12] :
( ~ subclass(ordered_pair(x,X12),identity_relation)
| member(singleton(singleton(X12)),inverse(subset_relation)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).
fof(f3132,plain,
( spl0_265
<=> ! [X29,X27,X28,X30] :
( ~ subclass(ordered_pair(x,X27),X28)
| ~ subclass(X29,complement(X30))
| ~ subclass(X28,X29)
| ~ member(singleton(singleton(X27)),X30) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).
fof(f3460,plain,
( ! [X50,X51,X49] :
( ~ subclass(X49,complement(inverse(subset_relation)))
| ~ subclass(X50,X49)
| ~ subclass(ordered_pair(x,X51),X50)
| ~ subclass(ordered_pair(x,X51),identity_relation) )
| ~ spl0_188
| ~ spl0_265 ),
inference(resolution,[],[f3133,f1523]) ).
fof(f1523,plain,
( ! [X12] :
( member(singleton(singleton(X12)),inverse(subset_relation))
| ~ subclass(ordered_pair(x,X12),identity_relation) )
| ~ spl0_188 ),
inference(avatar_component_clause,[],[f1522]) ).
fof(f3133,plain,
( ! [X28,X29,X27,X30] :
( ~ member(singleton(singleton(X27)),X30)
| ~ subclass(X29,complement(X30))
| ~ subclass(X28,X29)
| ~ subclass(ordered_pair(x,X27),X28) )
| ~ spl0_265 ),
inference(avatar_component_clause,[],[f3132]) ).
fof(f4285,plain,
( spl0_357
| ~ spl0_198
| ~ spl0_206 ),
inference(avatar_split_clause,[],[f2530,f2525,f2454,f4283]) ).
fof(f4283,plain,
( spl0_357
<=> ! [X2,X3] :
( ~ subclass(ordered_pair(singleton(x),singleton(X2)),complement(ordered_pair(x,X3)))
| ~ subclass(ordered_pair(x,X3),singleton(ordered_pair(x,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_357])]) ).
fof(f2454,plain,
( spl0_198
<=> ! [X0,X1] :
( ~ subclass(X0,singleton(ordered_pair(x,X1)))
| subclass(X0,ordered_pair(singleton(x),singleton(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).
fof(f2525,plain,
( spl0_206
<=> ! [X8,X7] :
( ~ subclass(X7,complement(ordered_pair(x,X8)))
| ~ subclass(ordered_pair(x,X8),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).
fof(f2530,plain,
( ! [X2,X3] :
( ~ subclass(ordered_pair(singleton(x),singleton(X2)),complement(ordered_pair(x,X3)))
| ~ subclass(ordered_pair(x,X3),singleton(ordered_pair(x,X2))) )
| ~ spl0_198
| ~ spl0_206 ),
inference(resolution,[],[f2526,f2455]) ).
fof(f2455,plain,
( ! [X0,X1] :
( subclass(X0,ordered_pair(singleton(x),singleton(X1)))
| ~ subclass(X0,singleton(ordered_pair(x,X1))) )
| ~ spl0_198 ),
inference(avatar_component_clause,[],[f2454]) ).
fof(f2526,plain,
( ! [X8,X7] :
( ~ subclass(ordered_pair(x,X8),X7)
| ~ subclass(X7,complement(ordered_pair(x,X8))) )
| ~ spl0_206 ),
inference(avatar_component_clause,[],[f2525]) ).
fof(f4268,plain,
( spl0_356
| ~ spl0_25
| ~ spl0_265 ),
inference(avatar_split_clause,[],[f4259,f3132,f232,f4266]) ).
fof(f4266,plain,
( spl0_356
<=> ! [X9,X8,X10] :
( ~ subclass(X8,complement(universal_class))
| ~ subclass(X9,X8)
| ~ subclass(ordered_pair(x,X10),X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_356])]) ).
fof(f4259,plain,
( ! [X10,X8,X9] :
( ~ subclass(X8,complement(universal_class))
| ~ subclass(X9,X8)
| ~ subclass(ordered_pair(x,X10),X9) )
| ~ spl0_25
| ~ spl0_265 ),
inference(resolution,[],[f233,f3133]) ).
fof(f4254,plain,
( spl0_355
| ~ spl0_9
| ~ spl0_343 ),
inference(avatar_split_clause,[],[f4247,f4080,f160,f4252]) ).
fof(f4252,plain,
( spl0_355
<=> ! [X101,X98,X100,X99] :
( ~ subclass(ordered_pair(x,X98),X99)
| ~ subclass(X100,null_class)
| ~ subclass(X99,intersection(X101,X100)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_355])]) ).
fof(f160,plain,
( spl0_9
<=> ! [X4] : ~ member(X4,null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f4080,plain,
( spl0_343
<=> ! [X5,X9,X7,X6,X8] :
( ~ subclass(X5,intersection(X6,X7))
| ~ subclass(ordered_pair(x,X8),X5)
| ~ subclass(X7,X9)
| member(singleton(singleton(X8)),X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_343])]) ).
fof(f4247,plain,
( ! [X101,X98,X99,X100] :
( ~ subclass(ordered_pair(x,X98),X99)
| ~ subclass(X100,null_class)
| ~ subclass(X99,intersection(X101,X100)) )
| ~ spl0_9
| ~ spl0_343 ),
inference(resolution,[],[f4081,f161]) ).
fof(f161,plain,
( ! [X4] : ~ member(X4,null_class)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f160]) ).
fof(f4081,plain,
( ! [X8,X6,X9,X7,X5] :
( member(singleton(singleton(X8)),X9)
| ~ subclass(ordered_pair(x,X8),X5)
| ~ subclass(X7,X9)
| ~ subclass(X5,intersection(X6,X7)) )
| ~ spl0_343 ),
inference(avatar_component_clause,[],[f4080]) ).
fof(f4228,plain,
( spl0_354
| ~ spl0_198
| ~ spl0_353 ),
inference(avatar_split_clause,[],[f4222,f4217,f2454,f4226]) ).
fof(f4226,plain,
( spl0_354
<=> ! [X2,X3] :
( ~ subclass(ordered_pair(singleton(x),singleton(X2)),intersection(X3,null_class))
| ~ subclass(universal_class,singleton(ordered_pair(x,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_354])]) ).
fof(f4217,plain,
( spl0_353
<=> ! [X4,X3] :
( ~ subclass(X3,intersection(X4,null_class))
| ~ subclass(universal_class,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_353])]) ).
fof(f4222,plain,
( ! [X2,X3] :
( ~ subclass(ordered_pair(singleton(x),singleton(X2)),intersection(X3,null_class))
| ~ subclass(universal_class,singleton(ordered_pair(x,X2))) )
| ~ spl0_198
| ~ spl0_353 ),
inference(resolution,[],[f4218,f2455]) ).
fof(f4218,plain,
( ! [X3,X4] :
( ~ subclass(universal_class,X3)
| ~ subclass(X3,intersection(X4,null_class)) )
| ~ spl0_353 ),
inference(avatar_component_clause,[],[f4217]) ).
fof(f4219,plain,
( spl0_353
| ~ spl0_6
| ~ spl0_352 ),
inference(avatar_split_clause,[],[f4213,f4209,f147,f4217]) ).
fof(f4209,plain,
( spl0_352
<=> ! [X101,X98,X100,X99] :
( ~ subclass(ordered_pair(x,X98),X99)
| ~ subclass(X100,intersection(X101,null_class))
| ~ subclass(X99,X100) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_352])]) ).
fof(f4213,plain,
( ! [X3,X4] :
( ~ subclass(X3,intersection(X4,null_class))
| ~ subclass(universal_class,X3) )
| ~ spl0_6
| ~ spl0_352 ),
inference(resolution,[],[f4210,f148]) ).
fof(f4210,plain,
( ! [X101,X98,X99,X100] :
( ~ subclass(ordered_pair(x,X98),X99)
| ~ subclass(X100,intersection(X101,null_class))
| ~ subclass(X99,X100) )
| ~ spl0_352 ),
inference(avatar_component_clause,[],[f4209]) ).
fof(f4211,plain,
( spl0_352
| ~ spl0_9
| ~ spl0_342 ),
inference(avatar_split_clause,[],[f4203,f4076,f160,f4209]) ).
fof(f4076,plain,
( spl0_342
<=> ! [X13,X14,X12,X16,X15] :
( member(singleton(singleton(X12)),X13)
| ~ subclass(ordered_pair(x,X12),X14)
| ~ subclass(X15,intersection(X16,X13))
| ~ subclass(X14,X15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_342])]) ).
fof(f4203,plain,
( ! [X101,X98,X99,X100] :
( ~ subclass(ordered_pair(x,X98),X99)
| ~ subclass(X100,intersection(X101,null_class))
| ~ subclass(X99,X100) )
| ~ spl0_9
| ~ spl0_342 ),
inference(resolution,[],[f4077,f161]) ).
fof(f4077,plain,
( ! [X16,X14,X15,X12,X13] :
( member(singleton(singleton(X12)),X13)
| ~ subclass(ordered_pair(x,X12),X14)
| ~ subclass(X15,intersection(X16,X13))
| ~ subclass(X14,X15) )
| ~ spl0_342 ),
inference(avatar_component_clause,[],[f4076]) ).
fof(f4183,plain,
( spl0_351
| ~ spl0_9
| ~ spl0_341 ),
inference(avatar_split_clause,[],[f4172,f4066,f160,f4181]) ).
fof(f4181,plain,
( spl0_351
<=> ! [X101,X98,X100,X99] :
( ~ subclass(ordered_pair(x,X98),X99)
| ~ subclass(X100,null_class)
| ~ subclass(X99,intersection(X100,X101)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_351])]) ).
fof(f4066,plain,
( spl0_341
<=> ! [X5,X9,X7,X6,X8] :
( ~ subclass(X5,intersection(X6,X7))
| ~ subclass(ordered_pair(x,X8),X5)
| ~ subclass(X6,X9)
| member(singleton(singleton(X8)),X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_341])]) ).
fof(f4172,plain,
( ! [X101,X98,X99,X100] :
( ~ subclass(ordered_pair(x,X98),X99)
| ~ subclass(X100,null_class)
| ~ subclass(X99,intersection(X100,X101)) )
| ~ spl0_9
| ~ spl0_341 ),
inference(resolution,[],[f4067,f161]) ).
fof(f4067,plain,
( ! [X8,X6,X9,X7,X5] :
( member(singleton(singleton(X8)),X9)
| ~ subclass(ordered_pair(x,X8),X5)
| ~ subclass(X6,X9)
| ~ subclass(X5,intersection(X6,X7)) )
| ~ spl0_341 ),
inference(avatar_component_clause,[],[f4066]) ).
fof(f4179,plain,
spl0_350,
inference(avatar_split_clause,[],[f91,f4177]) ).
fof(f4177,plain,
( spl0_350
<=> ! [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_350])]) ).
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.qYmJ0hwDFn/Vampire---4.8_12445',homomorphism6) ).
fof(f4153,plain,
( spl0_349
| ~ spl0_198
| ~ spl0_348 ),
inference(avatar_split_clause,[],[f4142,f4137,f2454,f4151]) ).
fof(f4151,plain,
( spl0_349
<=> ! [X2,X3] :
( ~ subclass(ordered_pair(singleton(x),singleton(X2)),intersection(null_class,X3))
| ~ subclass(universal_class,singleton(ordered_pair(x,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_349])]) ).
fof(f4137,plain,
( spl0_348
<=> ! [X4,X3] :
( ~ subclass(X3,intersection(null_class,X4))
| ~ subclass(universal_class,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_348])]) ).
fof(f4142,plain,
( ! [X2,X3] :
( ~ subclass(ordered_pair(singleton(x),singleton(X2)),intersection(null_class,X3))
| ~ subclass(universal_class,singleton(ordered_pair(x,X2))) )
| ~ spl0_198
| ~ spl0_348 ),
inference(resolution,[],[f4138,f2455]) ).
fof(f4138,plain,
( ! [X3,X4] :
( ~ subclass(universal_class,X3)
| ~ subclass(X3,intersection(null_class,X4)) )
| ~ spl0_348 ),
inference(avatar_component_clause,[],[f4137]) ).
fof(f4139,plain,
( spl0_348
| ~ spl0_6
| ~ spl0_347 ),
inference(avatar_split_clause,[],[f4133,f4129,f147,f4137]) ).
fof(f4129,plain,
( spl0_347
<=> ! [X101,X98,X100,X99] :
( ~ subclass(ordered_pair(x,X98),X99)
| ~ subclass(X100,intersection(null_class,X101))
| ~ subclass(X99,X100) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_347])]) ).
fof(f4133,plain,
( ! [X3,X4] :
( ~ subclass(X3,intersection(null_class,X4))
| ~ subclass(universal_class,X3) )
| ~ spl0_6
| ~ spl0_347 ),
inference(resolution,[],[f4130,f148]) ).
fof(f4130,plain,
( ! [X101,X98,X99,X100] :
( ~ subclass(ordered_pair(x,X98),X99)
| ~ subclass(X100,intersection(null_class,X101))
| ~ subclass(X99,X100) )
| ~ spl0_347 ),
inference(avatar_component_clause,[],[f4129]) ).
fof(f4131,plain,
( spl0_347
| ~ spl0_9
| ~ spl0_340 ),
inference(avatar_split_clause,[],[f4119,f4062,f160,f4129]) ).
fof(f4062,plain,
( spl0_340
<=> ! [X10,X11,X9,X8,X7] :
( member(singleton(singleton(X7)),X8)
| ~ subclass(ordered_pair(x,X7),X9)
| ~ subclass(X10,intersection(X8,X11))
| ~ subclass(X9,X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_340])]) ).
fof(f4119,plain,
( ! [X101,X98,X99,X100] :
( ~ subclass(ordered_pair(x,X98),X99)
| ~ subclass(X100,intersection(null_class,X101))
| ~ subclass(X99,X100) )
| ~ spl0_9
| ~ spl0_340 ),
inference(resolution,[],[f4063,f161]) ).
fof(f4063,plain,
( ! [X10,X11,X8,X9,X7] :
( member(singleton(singleton(X7)),X8)
| ~ subclass(ordered_pair(x,X7),X9)
| ~ subclass(X10,intersection(X8,X11))
| ~ subclass(X9,X10) )
| ~ spl0_340 ),
inference(avatar_component_clause,[],[f4062]) ).
fof(f4127,plain,
spl0_346,
inference(avatar_split_clause,[],[f89,f4125]) ).
fof(f4125,plain,
( spl0_346
<=> ! [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_346])]) ).
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.qYmJ0hwDFn/Vampire---4.8_12445',homomorphism4) ).
fof(f4099,plain,
( spl0_345
| ~ spl0_292
| ~ spl0_339 ),
inference(avatar_split_clause,[],[f4088,f4058,f3629,f4097]) ).
fof(f4097,plain,
( spl0_345
<=> ! [X0,X1] :
( ~ subclass(ordered_pair(x,X0),subset_relation)
| ~ subclass(cross_product(universal_class,universal_class),X1)
| member(singleton(singleton(X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_345])]) ).
fof(f3629,plain,
( spl0_292
<=> 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_292])]) ).
fof(f4058,plain,
( spl0_339
<=> ! [X5,X9,X7,X6,X8] :
( ~ subclass(ordered_pair(x,X5),restrict(X6,X7,X8))
| ~ subclass(cross_product(X7,X8),X9)
| member(singleton(singleton(X5)),X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_339])]) ).
fof(f4088,plain,
( ! [X0,X1] :
( ~ subclass(ordered_pair(x,X0),subset_relation)
| ~ subclass(cross_product(universal_class,universal_class),X1)
| member(singleton(singleton(X0)),X1) )
| ~ spl0_292
| ~ spl0_339 ),
inference(superposition,[],[f4059,f3631]) ).
fof(f3631,plain,
( subset_relation = restrict(restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class),universal_class,universal_class)
| ~ spl0_292 ),
inference(avatar_component_clause,[],[f3629]) ).
fof(f4059,plain,
( ! [X8,X6,X9,X7,X5] :
( ~ subclass(ordered_pair(x,X5),restrict(X6,X7,X8))
| ~ subclass(cross_product(X7,X8),X9)
| member(singleton(singleton(X5)),X9) )
| ~ spl0_339 ),
inference(avatar_component_clause,[],[f4058]) ).
fof(f4086,plain,
( spl0_344
| ~ spl0_199
| ~ spl0_292 ),
inference(avatar_split_clause,[],[f3713,f3629,f2466,f4084]) ).
fof(f4084,plain,
( spl0_344
<=> ! [X0] :
( ~ subclass(ordered_pair(x,X0),subset_relation)
| member(singleton(singleton(X0)),restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_344])]) ).
fof(f2466,plain,
( spl0_199
<=> ! [X9,X7,X6,X8] :
( ~ subclass(ordered_pair(x,X9),restrict(X8,X6,X7))
| member(singleton(singleton(X9)),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).
fof(f3713,plain,
( ! [X0] :
( ~ subclass(ordered_pair(x,X0),subset_relation)
| member(singleton(singleton(X0)),restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class)) )
| ~ spl0_199
| ~ spl0_292 ),
inference(superposition,[],[f2467,f3631]) ).
fof(f2467,plain,
( ! [X8,X6,X9,X7] :
( ~ subclass(ordered_pair(x,X9),restrict(X8,X6,X7))
| member(singleton(singleton(X9)),X8) )
| ~ spl0_199 ),
inference(avatar_component_clause,[],[f2466]) ).
fof(f4082,plain,
( spl0_343
| ~ spl0_65
| ~ spl0_228 ),
inference(avatar_split_clause,[],[f2766,f2760,f473,f4080]) ).
fof(f473,plain,
( spl0_65
<=> ! [X2,X0,X1] :
( ~ subclass(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f2760,plain,
( spl0_228
<=> ! [X18,X20,X17,X19] :
( member(singleton(singleton(X17)),X18)
| ~ subclass(X19,intersection(X20,X18))
| ~ subclass(ordered_pair(x,X17),X19) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).
fof(f2766,plain,
( ! [X8,X6,X9,X7,X5] :
( ~ subclass(X5,intersection(X6,X7))
| ~ subclass(ordered_pair(x,X8),X5)
| ~ subclass(X7,X9)
| member(singleton(singleton(X8)),X9) )
| ~ spl0_65
| ~ spl0_228 ),
inference(resolution,[],[f2761,f474]) ).
fof(f474,plain,
( ! [X2,X0,X1] :
( ~ member(X2,X0)
| ~ subclass(X0,X1)
| member(X2,X1) )
| ~ spl0_65 ),
inference(avatar_component_clause,[],[f473]) ).
fof(f2761,plain,
( ! [X18,X19,X17,X20] :
( member(singleton(singleton(X17)),X18)
| ~ subclass(X19,intersection(X20,X18))
| ~ subclass(ordered_pair(x,X17),X19) )
| ~ spl0_228 ),
inference(avatar_component_clause,[],[f2760]) ).
fof(f4078,plain,
( spl0_342
| ~ spl0_44
| ~ spl0_219 ),
inference(avatar_split_clause,[],[f2736,f2650,f326,f4076]) ).
fof(f326,plain,
( spl0_44
<=> ! [X4,X0,X1] :
( member(X4,X1)
| ~ member(X4,intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f2650,plain,
( spl0_219
<=> ! [X0,X3,X2,X1] :
( ~ subclass(X0,X1)
| ~ subclass(ordered_pair(x,X2),X0)
| ~ subclass(X1,X3)
| member(singleton(singleton(X2)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).
fof(f2736,plain,
( ! [X16,X14,X15,X12,X13] :
( member(singleton(singleton(X12)),X13)
| ~ subclass(ordered_pair(x,X12),X14)
| ~ subclass(X15,intersection(X16,X13))
| ~ subclass(X14,X15) )
| ~ spl0_44
| ~ spl0_219 ),
inference(resolution,[],[f327,f2651]) ).
fof(f2651,plain,
( ! [X2,X3,X0,X1] :
( member(singleton(singleton(X2)),X3)
| ~ subclass(ordered_pair(x,X2),X0)
| ~ subclass(X1,X3)
| ~ subclass(X0,X1) )
| ~ spl0_219 ),
inference(avatar_component_clause,[],[f2650]) ).
fof(f327,plain,
( ! [X0,X1,X4] :
( ~ member(X4,intersection(X0,X1))
| member(X4,X1) )
| ~ spl0_44 ),
inference(avatar_component_clause,[],[f326]) ).
fof(f4068,plain,
( spl0_341
| ~ spl0_65
| ~ spl0_224 ),
inference(avatar_split_clause,[],[f2721,f2717,f473,f4066]) ).
fof(f2717,plain,
( spl0_224
<=> ! [X13,X14,X12,X15] :
( member(singleton(singleton(X12)),X13)
| ~ subclass(X14,intersection(X13,X15))
| ~ subclass(ordered_pair(x,X12),X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).
fof(f2721,plain,
( ! [X8,X6,X9,X7,X5] :
( ~ subclass(X5,intersection(X6,X7))
| ~ subclass(ordered_pair(x,X8),X5)
| ~ subclass(X6,X9)
| member(singleton(singleton(X8)),X9) )
| ~ spl0_65
| ~ spl0_224 ),
inference(resolution,[],[f2718,f474]) ).
fof(f2718,plain,
( ! [X14,X15,X12,X13] :
( member(singleton(singleton(X12)),X13)
| ~ subclass(X14,intersection(X13,X15))
| ~ subclass(ordered_pair(x,X12),X14) )
| ~ spl0_224 ),
inference(avatar_component_clause,[],[f2717]) ).
fof(f4064,plain,
( spl0_340
| ~ spl0_43
| ~ spl0_219 ),
inference(avatar_split_clause,[],[f2705,f2650,f322,f4062]) ).
fof(f322,plain,
( spl0_43
<=> ! [X4,X0,X1] :
( member(X4,X0)
| ~ member(X4,intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f2705,plain,
( ! [X10,X11,X8,X9,X7] :
( member(singleton(singleton(X7)),X8)
| ~ subclass(ordered_pair(x,X7),X9)
| ~ subclass(X10,intersection(X8,X11))
| ~ subclass(X9,X10) )
| ~ spl0_43
| ~ spl0_219 ),
inference(resolution,[],[f323,f2651]) ).
fof(f323,plain,
( ! [X0,X1,X4] :
( ~ member(X4,intersection(X0,X1))
| member(X4,X0) )
| ~ spl0_43 ),
inference(avatar_component_clause,[],[f322]) ).
fof(f4060,plain,
( spl0_339
| ~ spl0_65
| ~ spl0_215 ),
inference(avatar_split_clause,[],[f2615,f2611,f473,f4058]) ).
fof(f2611,plain,
( spl0_215
<=> ! [X3,X4,X5,X2] :
( ~ subclass(ordered_pair(x,X5),restrict(X2,X3,X4))
| member(singleton(singleton(X5)),cross_product(X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).
fof(f2615,plain,
( ! [X8,X6,X9,X7,X5] :
( ~ subclass(ordered_pair(x,X5),restrict(X6,X7,X8))
| ~ subclass(cross_product(X7,X8),X9)
| member(singleton(singleton(X5)),X9) )
| ~ spl0_65
| ~ spl0_215 ),
inference(resolution,[],[f2612,f474]) ).
fof(f2612,plain,
( ! [X2,X3,X4,X5] :
( member(singleton(singleton(X5)),cross_product(X3,X4))
| ~ subclass(ordered_pair(x,X5),restrict(X2,X3,X4)) )
| ~ spl0_215 ),
inference(avatar_component_clause,[],[f2611]) ).
fof(f4056,plain,
spl0_338,
inference(avatar_split_clause,[],[f37,f4054]) ).
fof(f4054,plain,
( spl0_338
<=> ! [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_338])]) ).
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.qYmJ0hwDFn/Vampire---4.8_12445',flip3) ).
fof(f4038,plain,
spl0_337,
inference(avatar_split_clause,[],[f34,f4036]) ).
fof(f4036,plain,
( spl0_337
<=> ! [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_337])]) ).
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.qYmJ0hwDFn/Vampire---4.8_12445',rotate3) ).
fof(f4034,plain,
( spl0_336
| ~ spl0_48
| ~ spl0_333 ),
inference(avatar_split_clause,[],[f4021,f4016,f342,f4032]) ).
fof(f4032,plain,
( spl0_336
<=> ! [X4,X5] :
( ~ subclass(sum_class(X4),null_class)
| null_class = restrict(restrict(element_relation,universal_class,X4),singleton(singleton(singleton(X5))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_336])]) ).
fof(f342,plain,
( spl0_48
<=> ! [X0] : domain_of(restrict(element_relation,universal_class,X0)) = sum_class(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f4016,plain,
( spl0_333
<=> ! [X64,X65] :
( ~ subclass(domain_of(X64),null_class)
| null_class = restrict(X64,singleton(singleton(singleton(X65))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_333])]) ).
fof(f4021,plain,
( ! [X4,X5] :
( ~ subclass(sum_class(X4),null_class)
| null_class = restrict(restrict(element_relation,universal_class,X4),singleton(singleton(singleton(X5))),universal_class) )
| ~ spl0_48
| ~ spl0_333 ),
inference(superposition,[],[f4017,f343]) ).
fof(f343,plain,
( ! [X0] : domain_of(restrict(element_relation,universal_class,X0)) = sum_class(X0)
| ~ spl0_48 ),
inference(avatar_component_clause,[],[f342]) ).
fof(f4017,plain,
( ! [X65,X64] :
( ~ subclass(domain_of(X64),null_class)
| null_class = restrict(X64,singleton(singleton(singleton(X65))),universal_class) )
| ~ spl0_333 ),
inference(avatar_component_clause,[],[f4016]) ).
fof(f4030,plain,
( spl0_335
| ~ spl0_47
| ~ spl0_333 ),
inference(avatar_split_clause,[],[f4020,f4016,f338,f4028]) ).
fof(f4028,plain,
( spl0_335
<=> ! [X2,X3] :
( ~ subclass(inverse(X2),null_class)
| null_class = restrict(flip(cross_product(X2,universal_class)),singleton(singleton(singleton(X3))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_335])]) ).
fof(f338,plain,
( spl0_47
<=> ! [X1] : domain_of(flip(cross_product(X1,universal_class))) = inverse(X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f4020,plain,
( ! [X2,X3] :
( ~ subclass(inverse(X2),null_class)
| null_class = restrict(flip(cross_product(X2,universal_class)),singleton(singleton(singleton(X3))),universal_class) )
| ~ spl0_47
| ~ spl0_333 ),
inference(superposition,[],[f4017,f339]) ).
fof(f339,plain,
( ! [X1] : domain_of(flip(cross_product(X1,universal_class))) = inverse(X1)
| ~ spl0_47 ),
inference(avatar_component_clause,[],[f338]) ).
fof(f4025,plain,
( spl0_334
| ~ spl0_19
| ~ spl0_333 ),
inference(avatar_split_clause,[],[f4019,f4016,f206,f4023]) ).
fof(f4023,plain,
( spl0_334
<=> ! [X0,X1] :
( ~ subclass(range_of(X0),null_class)
| null_class = restrict(inverse(X0),singleton(singleton(singleton(X1))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_334])]) ).
fof(f206,plain,
( spl0_19
<=> ! [X4] : domain_of(inverse(X4)) = range_of(X4) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f4019,plain,
( ! [X0,X1] :
( ~ subclass(range_of(X0),null_class)
| null_class = restrict(inverse(X0),singleton(singleton(singleton(X1))),universal_class) )
| ~ spl0_19
| ~ spl0_333 ),
inference(superposition,[],[f4017,f207]) ).
fof(f207,plain,
( ! [X4] : domain_of(inverse(X4)) = range_of(X4)
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f206]) ).
fof(f4018,plain,
( spl0_333
| ~ spl0_9
| ~ spl0_329 ),
inference(avatar_split_clause,[],[f4012,f3980,f160,f4016]) ).
fof(f3980,plain,
( spl0_329
<=> ! [X16,X17,X15] :
( null_class = restrict(X15,singleton(singleton(singleton(X16))),universal_class)
| ~ subclass(domain_of(X15),X17)
| member(singleton(singleton(X16)),X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_329])]) ).
fof(f4012,plain,
( ! [X65,X64] :
( ~ subclass(domain_of(X64),null_class)
| null_class = restrict(X64,singleton(singleton(singleton(X65))),universal_class) )
| ~ spl0_9
| ~ spl0_329 ),
inference(resolution,[],[f3981,f161]) ).
fof(f3981,plain,
( ! [X16,X17,X15] :
( member(singleton(singleton(X16)),X17)
| ~ subclass(domain_of(X15),X17)
| null_class = restrict(X15,singleton(singleton(singleton(X16))),universal_class) )
| ~ spl0_329 ),
inference(avatar_component_clause,[],[f3980]) ).
fof(f3994,plain,
spl0_332,
inference(avatar_split_clause,[],[f90,f3992]) ).
fof(f3992,plain,
( spl0_332
<=> ! [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_332])]) ).
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.qYmJ0hwDFn/Vampire---4.8_12445',homomorphism5) ).
fof(f3990,plain,
( spl0_331
| ~ spl0_48
| ~ spl0_298 ),
inference(avatar_split_clause,[],[f3728,f3717,f342,f3988]) ).
fof(f3988,plain,
( spl0_331
<=> ! [X4,X5] :
( member(singleton(singleton(X5)),sum_class(X4))
| null_class = restrict(restrict(element_relation,universal_class,X4),singleton(singleton(singleton(X5))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_331])]) ).
fof(f3717,plain,
( spl0_298
<=> ! [X29,X28] :
( member(singleton(singleton(X28)),domain_of(X29))
| null_class = restrict(X29,singleton(singleton(singleton(X28))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).
fof(f3728,plain,
( ! [X4,X5] :
( member(singleton(singleton(X5)),sum_class(X4))
| null_class = restrict(restrict(element_relation,universal_class,X4),singleton(singleton(singleton(X5))),universal_class) )
| ~ spl0_48
| ~ spl0_298 ),
inference(superposition,[],[f3718,f343]) ).
fof(f3718,plain,
( ! [X28,X29] :
( member(singleton(singleton(X28)),domain_of(X29))
| null_class = restrict(X29,singleton(singleton(singleton(X28))),universal_class) )
| ~ spl0_298 ),
inference(avatar_component_clause,[],[f3717]) ).
fof(f3986,plain,
( spl0_330
| ~ spl0_47
| ~ spl0_298 ),
inference(avatar_split_clause,[],[f3727,f3717,f338,f3984]) ).
fof(f3984,plain,
( spl0_330
<=> ! [X2,X3] :
( member(singleton(singleton(X3)),inverse(X2))
| null_class = restrict(flip(cross_product(X2,universal_class)),singleton(singleton(singleton(X3))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_330])]) ).
fof(f3727,plain,
( ! [X2,X3] :
( member(singleton(singleton(X3)),inverse(X2))
| null_class = restrict(flip(cross_product(X2,universal_class)),singleton(singleton(singleton(X3))),universal_class) )
| ~ spl0_47
| ~ spl0_298 ),
inference(superposition,[],[f3718,f339]) ).
fof(f3982,plain,
( spl0_329
| ~ spl0_65
| ~ spl0_298 ),
inference(avatar_split_clause,[],[f3724,f3717,f473,f3980]) ).
fof(f3724,plain,
( ! [X16,X17,X15] :
( null_class = restrict(X15,singleton(singleton(singleton(X16))),universal_class)
| ~ subclass(domain_of(X15),X17)
| member(singleton(singleton(X16)),X17) )
| ~ spl0_65
| ~ spl0_298 ),
inference(resolution,[],[f3718,f474]) ).
fof(f3973,plain,
( spl0_328
| ~ spl0_27
| ~ spl0_324 ),
inference(avatar_split_clause,[],[f3957,f3953,f244,f3971]) ).
fof(f3971,plain,
( spl0_328
<=> ! [X2,X1] :
( ~ subclass(universal_class,successor(X1))
| ~ subclass(ordered_pair(x,X2),intersection(complement(X1),complement(singleton(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_328])]) ).
fof(f244,plain,
( spl0_27
<=> ! [X0] : union(X0,singleton(X0)) = successor(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f3953,plain,
( spl0_324
<=> ! [X2,X4,X3] :
( ~ subclass(universal_class,union(X2,X3))
| ~ subclass(ordered_pair(x,X4),intersection(complement(X2),complement(X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_324])]) ).
fof(f3957,plain,
( ! [X2,X1] :
( ~ subclass(universal_class,successor(X1))
| ~ subclass(ordered_pair(x,X2),intersection(complement(X1),complement(singleton(X1)))) )
| ~ spl0_27
| ~ spl0_324 ),
inference(superposition,[],[f3954,f245]) ).
fof(f245,plain,
( ! [X0] : union(X0,singleton(X0)) = successor(X0)
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f244]) ).
fof(f3954,plain,
( ! [X2,X3,X4] :
( ~ subclass(universal_class,union(X2,X3))
| ~ subclass(ordered_pair(x,X4),intersection(complement(X2),complement(X3))) )
| ~ spl0_324 ),
inference(avatar_component_clause,[],[f3953]) ).
fof(f3969,plain,
spl0_327,
inference(avatar_split_clause,[],[f59,f3967]) ).
fof(f3967,plain,
( spl0_327
<=> ! [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_327])]) ).
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.qYmJ0hwDFn/Vampire---4.8_12445',compose3) ).
fof(f3965,plain,
( spl0_325
| ~ spl0_326
| ~ spl0_98
| ~ spl0_324 ),
inference(avatar_split_clause,[],[f3956,f3953,f768,f3962,f3959]) ).
fof(f3959,plain,
( spl0_325
<=> ! [X0] : ~ subclass(ordered_pair(x,X0),intersection(complement(y),complement(singleton(x)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_325])]) ).
fof(f3962,plain,
( spl0_326
<=> subclass(universal_class,successor(y)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_326])]) ).
fof(f768,plain,
( spl0_98
<=> successor(y) = union(y,singleton(x)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f3956,plain,
( ! [X0] :
( ~ subclass(universal_class,successor(y))
| ~ subclass(ordered_pair(x,X0),intersection(complement(y),complement(singleton(x)))) )
| ~ spl0_98
| ~ spl0_324 ),
inference(superposition,[],[f3954,f770]) ).
fof(f770,plain,
( successor(y) = union(y,singleton(x))
| ~ spl0_98 ),
inference(avatar_component_clause,[],[f768]) ).
fof(f3955,plain,
( spl0_324
| ~ spl0_100
| ~ spl0_322 ),
inference(avatar_split_clause,[],[f3941,f3937,f777,f3953]) ).
fof(f777,plain,
( spl0_100
<=> ! [X0,X1] : complement(intersection(complement(X0),complement(X1))) = union(X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f3937,plain,
( spl0_322
<=> ! [X0,X1] :
( ~ subclass(universal_class,complement(X0))
| ~ subclass(ordered_pair(x,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_322])]) ).
fof(f3941,plain,
( ! [X2,X3,X4] :
( ~ subclass(universal_class,union(X2,X3))
| ~ subclass(ordered_pair(x,X4),intersection(complement(X2),complement(X3))) )
| ~ spl0_100
| ~ spl0_322 ),
inference(superposition,[],[f3938,f778]) ).
fof(f778,plain,
( ! [X0,X1] : complement(intersection(complement(X0),complement(X1))) = union(X0,X1)
| ~ spl0_100 ),
inference(avatar_component_clause,[],[f777]) ).
fof(f3938,plain,
( ! [X0,X1] :
( ~ subclass(universal_class,complement(X0))
| ~ subclass(ordered_pair(x,X1),X0) )
| ~ spl0_322 ),
inference(avatar_component_clause,[],[f3937]) ).
fof(f3945,plain,
( spl0_323
| ~ spl0_49
| ~ spl0_322 ),
inference(avatar_split_clause,[],[f3940,f3937,f346,f3943]) ).
fof(f3943,plain,
( spl0_323
<=> ! [X0,X1] :
( ~ subclass(universal_class,power_class(X0))
| ~ subclass(ordered_pair(x,X1),image(element_relation,complement(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_323])]) ).
fof(f346,plain,
( spl0_49
<=> ! [X0] : complement(image(element_relation,complement(X0))) = power_class(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f3940,plain,
( ! [X0,X1] :
( ~ subclass(universal_class,power_class(X0))
| ~ subclass(ordered_pair(x,X1),image(element_relation,complement(X0))) )
| ~ spl0_49
| ~ spl0_322 ),
inference(superposition,[],[f3938,f347]) ).
fof(f347,plain,
( ! [X0] : complement(image(element_relation,complement(X0))) = power_class(X0)
| ~ spl0_49 ),
inference(avatar_component_clause,[],[f346]) ).
fof(f3939,plain,
( spl0_322
| ~ spl0_8
| ~ spl0_320 ),
inference(avatar_split_clause,[],[f3929,f3926,f156,f3937]) ).
fof(f3926,plain,
( spl0_320
<=> ! [X4,X5,X3] :
( ~ subclass(universal_class,X3)
| ~ subclass(X3,complement(X4))
| ~ subclass(ordered_pair(x,X5),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_320])]) ).
fof(f3929,plain,
( ! [X0,X1] :
( ~ subclass(universal_class,complement(X0))
| ~ subclass(ordered_pair(x,X1),X0) )
| ~ spl0_8
| ~ spl0_320 ),
inference(resolution,[],[f3927,f157]) ).
fof(f3927,plain,
( ! [X3,X4,X5] :
( ~ subclass(universal_class,X3)
| ~ subclass(X3,complement(X4))
| ~ subclass(ordered_pair(x,X5),X4) )
| ~ spl0_320 ),
inference(avatar_component_clause,[],[f3926]) ).
fof(f3935,plain,
spl0_321,
inference(avatar_split_clause,[],[f81,f3933]) ).
fof(f3933,plain,
( spl0_321
<=> ! [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_321])]) ).
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.qYmJ0hwDFn/Vampire---4.8_12445',operation4) ).
fof(f3928,plain,
( spl0_320
| ~ spl0_6
| ~ spl0_316 ),
inference(avatar_split_clause,[],[f3922,f3888,f147,f3926]) ).
fof(f3888,plain,
( spl0_316
<=> ! [X24,X23,X25,X26] :
( ~ subclass(X23,complement(X24))
| ~ subclass(X25,X23)
| ~ subclass(ordered_pair(x,X26),X25)
| ~ subclass(ordered_pair(x,X26),X24) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).
fof(f3922,plain,
( ! [X3,X4,X5] :
( ~ subclass(universal_class,X3)
| ~ subclass(X3,complement(X4))
| ~ subclass(ordered_pair(x,X5),X4) )
| ~ spl0_6
| ~ spl0_316 ),
inference(resolution,[],[f3889,f148]) ).
fof(f3889,plain,
( ! [X26,X24,X25,X23] :
( ~ subclass(ordered_pair(x,X26),X25)
| ~ subclass(X25,X23)
| ~ subclass(X23,complement(X24))
| ~ subclass(ordered_pair(x,X26),X24) )
| ~ spl0_316 ),
inference(avatar_component_clause,[],[f3888]) ).
fof(f3907,plain,
spl0_319,
inference(avatar_split_clause,[],[f85,f3905]) ).
fof(f3905,plain,
( spl0_319
<=> ! [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_319])]) ).
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.qYmJ0hwDFn/Vampire---4.8_12445',compatible4) ).
fof(f3903,plain,
( spl0_318
| ~ spl0_186
| ~ spl0_265 ),
inference(avatar_split_clause,[],[f3461,f3132,f1504,f3901]) ).
fof(f3901,plain,
( spl0_318
<=> ! [X54,X52,X53] :
( ~ subclass(X52,complement(subset_relation))
| ~ subclass(X53,X52)
| ~ subclass(ordered_pair(x,X54),X53)
| ~ subclass(ordered_pair(x,X54),identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).
fof(f1504,plain,
( spl0_186
<=> ! [X12] :
( ~ subclass(ordered_pair(x,X12),identity_relation)
| member(singleton(singleton(X12)),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).
fof(f3461,plain,
( ! [X54,X52,X53] :
( ~ subclass(X52,complement(subset_relation))
| ~ subclass(X53,X52)
| ~ subclass(ordered_pair(x,X54),X53)
| ~ subclass(ordered_pair(x,X54),identity_relation) )
| ~ spl0_186
| ~ spl0_265 ),
inference(resolution,[],[f3133,f1505]) ).
fof(f1505,plain,
( ! [X12] :
( member(singleton(singleton(X12)),subset_relation)
| ~ subclass(ordered_pair(x,X12),identity_relation) )
| ~ spl0_186 ),
inference(avatar_component_clause,[],[f1504]) ).
fof(f3898,plain,
( spl0_317
| ~ spl0_155
| ~ spl0_190
| ~ spl0_307 ),
inference(avatar_split_clause,[],[f3894,f3801,f1546,f1262,f3896]) ).
fof(f3896,plain,
( spl0_317
<=> ! [X4,X5,X3] : ~ member(ordered_pair(X3,x),compose(X4,X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_317])]) ).
fof(f1262,plain,
( spl0_155
<=> ! [X0] : ordered_pair(X0,y) = ordered_pair(X0,x) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f3801,plain,
( spl0_307
<=> ! [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_307])]) ).
fof(f3894,plain,
( ! [X3,X4,X5] : ~ member(ordered_pair(X3,x),compose(X4,X5))
| ~ spl0_155
| ~ spl0_190
| ~ spl0_307 ),
inference(subsumption_resolution,[],[f3892,f1547]) ).
fof(f3892,plain,
( ! [X3,X4,X5] :
( ~ member(ordered_pair(X3,x),compose(X4,X5))
| member(y,image(X4,image(X5,singleton(X3)))) )
| ~ spl0_155
| ~ spl0_307 ),
inference(superposition,[],[f3802,f1263]) ).
fof(f1263,plain,
( ! [X0] : ordered_pair(X0,y) = ordered_pair(X0,x)
| ~ spl0_155 ),
inference(avatar_component_clause,[],[f1262]) ).
fof(f3802,plain,
( ! [X1,X7,X4,X5] :
( ~ member(ordered_pair(X1,X4),compose(X7,X5))
| member(X4,image(X7,image(X5,singleton(X1)))) )
| ~ spl0_307 ),
inference(avatar_component_clause,[],[f3801]) ).
fof(f3890,plain,
( spl0_316
| ~ spl0_172
| ~ spl0_265 ),
inference(avatar_split_clause,[],[f3454,f3132,f1407,f3888]) ).
fof(f1407,plain,
( spl0_172
<=> ! [X0,X1] :
( ~ subclass(ordered_pair(x,X0),X1)
| member(singleton(singleton(X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
fof(f3454,plain,
( ! [X26,X24,X25,X23] :
( ~ subclass(X23,complement(X24))
| ~ subclass(X25,X23)
| ~ subclass(ordered_pair(x,X26),X25)
| ~ subclass(ordered_pair(x,X26),X24) )
| ~ spl0_172
| ~ spl0_265 ),
inference(resolution,[],[f3133,f1408]) ).
fof(f1408,plain,
( ! [X0,X1] :
( member(singleton(singleton(X0)),X1)
| ~ subclass(ordered_pair(x,X0),X1) )
| ~ spl0_172 ),
inference(avatar_component_clause,[],[f1407]) ).
fof(f3886,plain,
( spl0_315
| ~ spl0_188
| ~ spl0_234 ),
inference(avatar_split_clause,[],[f2866,f2804,f1522,f3884]) ).
fof(f3884,plain,
( spl0_315
<=> ! [X38,X36,X37] :
( ~ subclass(ordered_pair(x,X36),X37)
| ~ subclass(X37,intersection(X38,complement(inverse(subset_relation))))
| ~ subclass(ordered_pair(x,X36),identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_315])]) ).
fof(f2804,plain,
( spl0_234
<=> ! [X38,X40,X39,X37] :
( ~ subclass(X37,intersection(X38,complement(X39)))
| ~ subclass(ordered_pair(x,X40),X37)
| ~ member(singleton(singleton(X40)),X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).
fof(f2866,plain,
( ! [X38,X36,X37] :
( ~ subclass(ordered_pair(x,X36),X37)
| ~ subclass(X37,intersection(X38,complement(inverse(subset_relation))))
| ~ subclass(ordered_pair(x,X36),identity_relation) )
| ~ spl0_188
| ~ spl0_234 ),
inference(resolution,[],[f2805,f1523]) ).
fof(f2805,plain,
( ! [X40,X38,X39,X37] :
( ~ member(singleton(singleton(X40)),X39)
| ~ subclass(ordered_pair(x,X40),X37)
| ~ subclass(X37,intersection(X38,complement(X39))) )
| ~ spl0_234 ),
inference(avatar_component_clause,[],[f2804]) ).
fof(f3882,plain,
( spl0_314
| ~ spl0_188
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2826,f2800,f1522,f3880]) ).
fof(f3880,plain,
( spl0_314
<=> ! [X38,X36,X37] :
( ~ subclass(ordered_pair(x,X36),X37)
| ~ subclass(X37,intersection(complement(inverse(subset_relation)),X38))
| ~ subclass(ordered_pair(x,X36),identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_314])]) ).
fof(f2800,plain,
( spl0_233
<=> ! [X35,X34,X33,X32] :
( ~ subclass(X32,intersection(complement(X33),X34))
| ~ subclass(ordered_pair(x,X35),X32)
| ~ member(singleton(singleton(X35)),X33) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).
fof(f2826,plain,
( ! [X38,X36,X37] :
( ~ subclass(ordered_pair(x,X36),X37)
| ~ subclass(X37,intersection(complement(inverse(subset_relation)),X38))
| ~ subclass(ordered_pair(x,X36),identity_relation) )
| ~ spl0_188
| ~ spl0_233 ),
inference(resolution,[],[f2801,f1523]) ).
fof(f2801,plain,
( ! [X34,X35,X32,X33] :
( ~ member(singleton(singleton(X35)),X33)
| ~ subclass(ordered_pair(x,X35),X32)
| ~ subclass(X32,intersection(complement(X33),X34)) )
| ~ spl0_233 ),
inference(avatar_component_clause,[],[f2800]) ).
fof(f3878,plain,
( spl0_313
| ~ spl0_198
| ~ spl0_229 ),
inference(avatar_split_clause,[],[f2784,f2779,f2454,f3876]) ).
fof(f3876,plain,
( spl0_313
<=> ! [X4,X5,X3] :
( ~ subclass(ordered_pair(singleton(x),singleton(X3)),intersection(X4,null_class))
| ~ subclass(ordered_pair(x,X5),singleton(ordered_pair(x,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_313])]) ).
fof(f2779,plain,
( spl0_229
<=> ! [X41,X43,X42] :
( ~ subclass(X41,intersection(X42,null_class))
| ~ subclass(ordered_pair(x,X43),X41) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).
fof(f2784,plain,
( ! [X3,X4,X5] :
( ~ subclass(ordered_pair(singleton(x),singleton(X3)),intersection(X4,null_class))
| ~ subclass(ordered_pair(x,X5),singleton(ordered_pair(x,X3))) )
| ~ spl0_198
| ~ spl0_229 ),
inference(resolution,[],[f2780,f2455]) ).
fof(f2780,plain,
( ! [X41,X42,X43] :
( ~ subclass(ordered_pair(x,X43),X41)
| ~ subclass(X41,intersection(X42,null_class)) )
| ~ spl0_229 ),
inference(avatar_component_clause,[],[f2779]) ).
fof(f3868,plain,
( spl0_312
| ~ spl0_198
| ~ spl0_225 ),
inference(avatar_split_clause,[],[f2746,f2741,f2454,f3866]) ).
fof(f3866,plain,
( spl0_312
<=> ! [X4,X5,X3] :
( ~ subclass(ordered_pair(singleton(x),singleton(X3)),intersection(null_class,X4))
| ~ subclass(ordered_pair(x,X5),singleton(ordered_pair(x,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).
fof(f2741,plain,
( spl0_225
<=> ! [X38,X36,X37] :
( ~ subclass(X36,intersection(null_class,X37))
| ~ subclass(ordered_pair(x,X38),X36) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).
fof(f2746,plain,
( ! [X3,X4,X5] :
( ~ subclass(ordered_pair(singleton(x),singleton(X3)),intersection(null_class,X4))
| ~ subclass(ordered_pair(x,X5),singleton(ordered_pair(x,X3))) )
| ~ spl0_198
| ~ spl0_225 ),
inference(resolution,[],[f2742,f2455]) ).
fof(f2742,plain,
( ! [X38,X36,X37] :
( ~ subclass(ordered_pair(x,X38),X36)
| ~ subclass(X36,intersection(null_class,X37)) )
| ~ spl0_225 ),
inference(avatar_component_clause,[],[f2741]) ).
fof(f3860,plain,
( spl0_311
| ~ spl0_8
| ~ spl0_309 ),
inference(avatar_split_clause,[],[f3840,f3837,f156,f3858]) ).
fof(f3858,plain,
( spl0_311
<=> ! [X2,X0,X1] : ~ subclass(ordered_pair(x,X0),intersection(X1,intersection(null_class,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_311])]) ).
fof(f3837,plain,
( spl0_309
<=> ! [X101,X98,X100,X99] :
( ~ subclass(ordered_pair(x,X98),X99)
| ~ subclass(X99,intersection(X100,intersection(null_class,X101))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).
fof(f3840,plain,
( ! [X2,X0,X1] : ~ subclass(ordered_pair(x,X0),intersection(X1,intersection(null_class,X2)))
| ~ spl0_8
| ~ spl0_309 ),
inference(resolution,[],[f3838,f157]) ).
fof(f3838,plain,
( ! [X101,X98,X99,X100] :
( ~ subclass(ordered_pair(x,X98),X99)
| ~ subclass(X99,intersection(X100,intersection(null_class,X101))) )
| ~ spl0_309 ),
inference(avatar_component_clause,[],[f3837]) ).
fof(f3847,plain,
( spl0_310
| ~ spl0_6
| ~ spl0_309 ),
inference(avatar_split_clause,[],[f3841,f3837,f147,f3845]) ).
fof(f3845,plain,
( spl0_310
<=> ! [X4,X3] : ~ subclass(universal_class,intersection(X3,intersection(null_class,X4))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).
fof(f3841,plain,
( ! [X3,X4] : ~ subclass(universal_class,intersection(X3,intersection(null_class,X4)))
| ~ spl0_6
| ~ spl0_309 ),
inference(resolution,[],[f3838,f148]) ).
fof(f3839,plain,
( spl0_309
| ~ spl0_9
| ~ spl0_269 ),
inference(avatar_split_clause,[],[f3827,f3150,f160,f3837]) ).
fof(f3827,plain,
( ! [X101,X98,X99,X100] :
( ~ subclass(ordered_pair(x,X98),X99)
| ~ subclass(X99,intersection(X100,intersection(null_class,X101))) )
| ~ spl0_9
| ~ spl0_269 ),
inference(resolution,[],[f3151,f161]) ).
fof(f3807,plain,
( spl0_308
| ~ spl0_104
| ~ spl0_306 ),
inference(avatar_split_clause,[],[f3798,f3794,f803,f3805]) ).
fof(f3805,plain,
( spl0_308
<=> ! [X2,X0,X1,X3] : ~ subclass(ordered_pair(x,X2),intersection(X3,restrict(null_class,X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).
fof(f803,plain,
( spl0_104
<=> ! [X5,X1,X0] : restrict(X5,X0,X1) = intersection(cross_product(X0,X1),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f3794,plain,
( spl0_306
<=> ! [X2,X0,X1] : ~ subclass(ordered_pair(x,X0),intersection(X1,intersection(X2,null_class))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).
fof(f3798,plain,
( ! [X2,X3,X0,X1] : ~ subclass(ordered_pair(x,X2),intersection(X3,restrict(null_class,X0,X1)))
| ~ spl0_104
| ~ spl0_306 ),
inference(superposition,[],[f3795,f804]) ).
fof(f804,plain,
( ! [X0,X1,X5] : restrict(X5,X0,X1) = intersection(cross_product(X0,X1),X5)
| ~ spl0_104 ),
inference(avatar_component_clause,[],[f803]) ).
fof(f3795,plain,
( ! [X2,X0,X1] : ~ subclass(ordered_pair(x,X0),intersection(X1,intersection(X2,null_class)))
| ~ spl0_306 ),
inference(avatar_component_clause,[],[f3794]) ).
fof(f3803,plain,
spl0_307,
inference(avatar_split_clause,[],[f58,f3801]) ).
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.qYmJ0hwDFn/Vampire---4.8_12445',compose2) ).
fof(f3796,plain,
( spl0_306
| ~ spl0_8
| ~ spl0_301 ),
inference(avatar_split_clause,[],[f3774,f3767,f156,f3794]) ).
fof(f3767,plain,
( spl0_301
<=> ! [X101,X98,X100,X99] :
( ~ subclass(ordered_pair(x,X98),X99)
| ~ subclass(X99,intersection(X100,intersection(X101,null_class))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).
fof(f3774,plain,
( ! [X2,X0,X1] : ~ subclass(ordered_pair(x,X0),intersection(X1,intersection(X2,null_class)))
| ~ spl0_8
| ~ spl0_301 ),
inference(resolution,[],[f3768,f157]) ).
fof(f3768,plain,
( ! [X101,X98,X99,X100] :
( ~ subclass(ordered_pair(x,X98),X99)
| ~ subclass(X99,intersection(X100,intersection(X101,null_class))) )
| ~ spl0_301 ),
inference(avatar_component_clause,[],[f3767]) ).
fof(f3791,plain,
( spl0_305
| ~ spl0_104
| ~ spl0_303 ),
inference(avatar_split_clause,[],[f3782,f3779,f803,f3789]) ).
fof(f3789,plain,
( spl0_305
<=> ! [X2,X0,X1] : ~ subclass(universal_class,intersection(X2,restrict(null_class,X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).
fof(f3779,plain,
( spl0_303
<=> ! [X4,X3] : ~ subclass(universal_class,intersection(X3,intersection(X4,null_class))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).
fof(f3782,plain,
( ! [X2,X0,X1] : ~ subclass(universal_class,intersection(X2,restrict(null_class,X0,X1)))
| ~ spl0_104
| ~ spl0_303 ),
inference(superposition,[],[f3780,f804]) ).
fof(f3780,plain,
( ! [X3,X4] : ~ subclass(universal_class,intersection(X3,intersection(X4,null_class)))
| ~ spl0_303 ),
inference(avatar_component_clause,[],[f3779]) ).
fof(f3787,plain,
spl0_304,
inference(avatar_split_clause,[],[f36,f3785]) ).
fof(f3785,plain,
( spl0_304
<=> ! [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_304])]) ).
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.qYmJ0hwDFn/Vampire---4.8_12445',flip2) ).
fof(f3781,plain,
( spl0_303
| ~ spl0_6
| ~ spl0_301 ),
inference(avatar_split_clause,[],[f3775,f3767,f147,f3779]) ).
fof(f3775,plain,
( ! [X3,X4] : ~ subclass(universal_class,intersection(X3,intersection(X4,null_class)))
| ~ spl0_6
| ~ spl0_301 ),
inference(resolution,[],[f3768,f148]) ).
fof(f3773,plain,
spl0_302,
inference(avatar_split_clause,[],[f33,f3771]) ).
fof(f3771,plain,
( spl0_302
<=> ! [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_302])]) ).
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.qYmJ0hwDFn/Vampire---4.8_12445',rotate2) ).
fof(f3769,plain,
( spl0_301
| ~ spl0_9
| ~ spl0_268 ),
inference(avatar_split_clause,[],[f3761,f3146,f160,f3767]) ).
fof(f3761,plain,
( ! [X101,X98,X99,X100] :
( ~ subclass(ordered_pair(x,X98),X99)
| ~ subclass(X99,intersection(X100,intersection(X101,null_class))) )
| ~ spl0_9
| ~ spl0_268 ),
inference(resolution,[],[f3147,f161]) ).
fof(f3736,plain,
( spl0_300
| ~ spl0_19
| ~ spl0_298 ),
inference(avatar_split_clause,[],[f3726,f3717,f206,f3734]) ).
fof(f3734,plain,
( spl0_300
<=> ! [X0,X1] :
( member(singleton(singleton(X1)),range_of(X0))
| null_class = restrict(inverse(X0),singleton(singleton(singleton(X1))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).
fof(f3726,plain,
( ! [X0,X1] :
( member(singleton(singleton(X1)),range_of(X0))
| null_class = restrict(inverse(X0),singleton(singleton(singleton(X1))),universal_class) )
| ~ spl0_19
| ~ spl0_298 ),
inference(superposition,[],[f3718,f207]) ).
fof(f3732,plain,
spl0_299,
inference(avatar_split_clause,[],[f20,f3730]) ).
fof(f3730,plain,
( spl0_299
<=> ! [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_299])]) ).
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.qYmJ0hwDFn/Vampire---4.8_12445',element_relation3) ).
fof(f3719,plain,
( spl0_298
| ~ spl0_6
| ~ spl0_172
| ~ spl0_286 ),
inference(avatar_split_clause,[],[f3685,f3599,f1407,f147,f3717]) ).
fof(f3599,plain,
( spl0_286
<=> ! [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_286])]) ).
fof(f3685,plain,
( ! [X28,X29] :
( member(singleton(singleton(X28)),domain_of(X29))
| null_class = restrict(X29,singleton(singleton(singleton(X28))),universal_class) )
| ~ spl0_6
| ~ spl0_172
| ~ spl0_286 ),
inference(subsumption_resolution,[],[f3678,f148]) ).
fof(f3678,plain,
( ! [X28,X29] :
( member(singleton(singleton(X28)),domain_of(X29))
| null_class = restrict(X29,singleton(singleton(singleton(X28))),universal_class)
| ~ subclass(ordered_pair(x,X28),universal_class) )
| ~ spl0_172
| ~ spl0_286 ),
inference(resolution,[],[f3600,f1408]) ).
fof(f3600,plain,
( ! [X0,X4] :
( ~ member(X4,universal_class)
| member(X4,domain_of(X0))
| restrict(X0,singleton(X4),universal_class) = null_class )
| ~ spl0_286 ),
inference(avatar_component_clause,[],[f3599]) ).
fof(f3711,plain,
( spl0_297
| ~ spl0_102
| ~ spl0_296 ),
inference(avatar_split_clause,[],[f3707,f3701,f785,f3709]) ).
fof(f3709,plain,
( spl0_297
<=> ! [X4,X5,X2,X3] : ~ subclass(ordered_pair(x,X5),restrict(intersection(X2,null_class),X3,X4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).
fof(f3701,plain,
( spl0_296
<=> ! [X2,X0,X1] : ~ subclass(ordered_pair(x,X0),intersection(intersection(X1,null_class),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).
fof(f3707,plain,
( ! [X2,X3,X4,X5] : ~ subclass(ordered_pair(x,X5),restrict(intersection(X2,null_class),X3,X4))
| ~ spl0_102
| ~ spl0_296 ),
inference(superposition,[],[f3702,f786]) ).
fof(f3702,plain,
( ! [X2,X0,X1] : ~ subclass(ordered_pair(x,X0),intersection(intersection(X1,null_class),X2))
| ~ spl0_296 ),
inference(avatar_component_clause,[],[f3701]) ).
fof(f3703,plain,
( spl0_296
| ~ spl0_8
| ~ spl0_293 ),
inference(avatar_split_clause,[],[f3659,f3656,f156,f3701]) ).
fof(f3656,plain,
( spl0_293
<=> ! [X93,X96,X94,X95] :
( ~ subclass(X93,intersection(intersection(X94,null_class),X95))
| ~ subclass(ordered_pair(x,X96),X93) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).
fof(f3659,plain,
( ! [X2,X0,X1] : ~ subclass(ordered_pair(x,X0),intersection(intersection(X1,null_class),X2))
| ~ spl0_8
| ~ spl0_293 ),
inference(resolution,[],[f3657,f157]) ).
fof(f3657,plain,
( ! [X96,X94,X95,X93] :
( ~ subclass(ordered_pair(x,X96),X93)
| ~ subclass(X93,intersection(intersection(X94,null_class),X95)) )
| ~ spl0_293 ),
inference(avatar_component_clause,[],[f3656]) ).
fof(f3696,plain,
( spl0_295
| ~ spl0_102
| ~ spl0_294 ),
inference(avatar_split_clause,[],[f3692,f3687,f785,f3694]) ).
fof(f3694,plain,
( spl0_295
<=> ! [X2,X1,X3] : ~ subclass(universal_class,restrict(intersection(X1,null_class),X2,X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).
fof(f3687,plain,
( spl0_294
<=> ! [X4,X3] : ~ subclass(universal_class,intersection(intersection(X3,null_class),X4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).
fof(f3692,plain,
( ! [X2,X3,X1] : ~ subclass(universal_class,restrict(intersection(X1,null_class),X2,X3))
| ~ spl0_102
| ~ spl0_294 ),
inference(superposition,[],[f3688,f786]) ).
fof(f3688,plain,
( ! [X3,X4] : ~ subclass(universal_class,intersection(intersection(X3,null_class),X4))
| ~ spl0_294 ),
inference(avatar_component_clause,[],[f3687]) ).
fof(f3689,plain,
( spl0_294
| ~ spl0_6
| ~ spl0_293 ),
inference(avatar_split_clause,[],[f3660,f3656,f147,f3687]) ).
fof(f3660,plain,
( ! [X3,X4] : ~ subclass(universal_class,intersection(intersection(X3,null_class),X4))
| ~ spl0_6
| ~ spl0_293 ),
inference(resolution,[],[f3657,f148]) ).
fof(f3658,plain,
( spl0_293
| ~ spl0_9
| ~ spl0_267 ),
inference(avatar_split_clause,[],[f3650,f3142,f160,f3656]) ).
fof(f3650,plain,
( ! [X96,X94,X95,X93] :
( ~ subclass(X93,intersection(intersection(X94,null_class),X95))
| ~ subclass(ordered_pair(x,X96),X93) )
| ~ spl0_9
| ~ spl0_267 ),
inference(resolution,[],[f3143,f161]) ).
fof(f3632,plain,
spl0_292,
inference(avatar_split_clause,[],[f120,f3629]) ).
fof(f120,plain,
subset_relation = restrict(restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class),universal_class,universal_class),
inference(forward_demodulation,[],[f119,f29]) ).
fof(f29,axiom,
! [X0,X1,X5] : restrict(X5,X0,X1) = intersection(cross_product(X0,X1),X5),
file('/export/starexec/sandbox2/tmp/tmp.qYmJ0hwDFn/Vampire---4.8_12445',restriction2) ).
fof(f119,plain,
subset_relation = restrict(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation)))),universal_class,universal_class),
inference(forward_demodulation,[],[f74,f29]) ).
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.qYmJ0hwDFn/Vampire---4.8_12445',subset_relation) ).
fof(f3627,plain,
( spl0_291
| ~ spl0_102
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f3620,f3607,f785,f3625]) ).
fof(f3625,plain,
( spl0_291
<=> ! [X5,X4,X7,X6,X3] : ~ subclass(ordered_pair(x,X7),restrict(restrict(null_class,X3,X4),X5,X6)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).
fof(f3607,plain,
( spl0_288
<=> ! [X2,X5,X3,X4] : ~ subclass(ordered_pair(x,X4),intersection(restrict(null_class,X2,X3),X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).
fof(f3620,plain,
( ! [X3,X6,X7,X4,X5] : ~ subclass(ordered_pair(x,X7),restrict(restrict(null_class,X3,X4),X5,X6))
| ~ spl0_102
| ~ spl0_288 ),
inference(superposition,[],[f3608,f786]) ).
fof(f3608,plain,
( ! [X2,X3,X4,X5] : ~ subclass(ordered_pair(x,X4),intersection(restrict(null_class,X2,X3),X5))
| ~ spl0_288 ),
inference(avatar_component_clause,[],[f3607]) ).
fof(f3617,plain,
spl0_290,
inference(avatar_split_clause,[],[f118,f3615]) ).
fof(f3615,plain,
( spl0_290
<=> ! [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_290])]) ).
fof(f118,plain,
! [X0] :
( member(ordered_pair(X0,successor(X0)),successor_relation)
| ~ member(ordered_pair(X0,successor(X0)),cross_product(universal_class,universal_class)) ),
inference(equality_resolution,[],[f46]) ).
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.qYmJ0hwDFn/Vampire---4.8_12445',successor_relation3) ).
fof(f3613,plain,
( spl0_289
| ~ spl0_102
| ~ spl0_285 ),
inference(avatar_split_clause,[],[f3597,f3590,f785,f3611]) ).
fof(f3611,plain,
( spl0_289
<=> ! [X4,X5,X2,X3] : ~ subclass(ordered_pair(x,X5),restrict(intersection(null_class,X2),X3,X4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).
fof(f3590,plain,
( spl0_285
<=> ! [X2,X0,X1] : ~ subclass(ordered_pair(x,X0),intersection(intersection(null_class,X1),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).
fof(f3597,plain,
( ! [X2,X3,X4,X5] : ~ subclass(ordered_pair(x,X5),restrict(intersection(null_class,X2),X3,X4))
| ~ spl0_102
| ~ spl0_285 ),
inference(superposition,[],[f3591,f786]) ).
fof(f3591,plain,
( ! [X2,X0,X1] : ~ subclass(ordered_pair(x,X0),intersection(intersection(null_class,X1),X2))
| ~ spl0_285 ),
inference(avatar_component_clause,[],[f3590]) ).
fof(f3609,plain,
( spl0_288
| ~ spl0_102
| ~ spl0_285 ),
inference(avatar_split_clause,[],[f3595,f3590,f785,f3607]) ).
fof(f3595,plain,
( ! [X2,X3,X4,X5] : ~ subclass(ordered_pair(x,X4),intersection(restrict(null_class,X2,X3),X5))
| ~ spl0_102
| ~ spl0_285 ),
inference(superposition,[],[f3591,f786]) ).
fof(f3605,plain,
( spl0_287
| ~ spl0_102
| ~ spl0_283 ),
inference(avatar_split_clause,[],[f3578,f3570,f785,f3603]) ).
fof(f3603,plain,
( spl0_287
<=> ! [X4,X5,X2,X3] : ~ subclass(universal_class,restrict(restrict(null_class,X2,X3),X4,X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).
fof(f3570,plain,
( spl0_283
<=> ! [X2,X1,X3] : ~ subclass(universal_class,intersection(restrict(null_class,X1,X2),X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).
fof(f3578,plain,
( ! [X2,X3,X4,X5] : ~ subclass(universal_class,restrict(restrict(null_class,X2,X3),X4,X5))
| ~ spl0_102
| ~ spl0_283 ),
inference(superposition,[],[f3571,f786]) ).
fof(f3571,plain,
( ! [X2,X3,X1] : ~ subclass(universal_class,intersection(restrict(null_class,X1,X2),X3))
| ~ spl0_283 ),
inference(avatar_component_clause,[],[f3570]) ).
fof(f3601,plain,
spl0_286,
inference(avatar_split_clause,[],[f31,f3599]) ).
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.qYmJ0hwDFn/Vampire---4.8_12445',domain2) ).
fof(f3592,plain,
( spl0_285
| ~ spl0_8
| ~ spl0_281 ),
inference(avatar_split_clause,[],[f3549,f3546,f156,f3590]) ).
fof(f3546,plain,
( spl0_281
<=> ! [X94,X95,X93,X96] :
( ~ subclass(ordered_pair(x,X93),X94)
| ~ subclass(X94,intersection(intersection(null_class,X95),X96)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).
fof(f3549,plain,
( ! [X2,X0,X1] : ~ subclass(ordered_pair(x,X0),intersection(intersection(null_class,X1),X2))
| ~ spl0_8
| ~ spl0_281 ),
inference(resolution,[],[f3547,f157]) ).
fof(f3547,plain,
( ! [X96,X94,X95,X93] :
( ~ subclass(ordered_pair(x,X93),X94)
| ~ subclass(X94,intersection(intersection(null_class,X95),X96)) )
| ~ spl0_281 ),
inference(avatar_component_clause,[],[f3546]) ).
fof(f3576,plain,
( spl0_284
| ~ spl0_102
| ~ spl0_282 ),
inference(avatar_split_clause,[],[f3568,f3554,f785,f3574]) ).
fof(f3574,plain,
( spl0_284
<=> ! [X2,X1,X3] : ~ subclass(universal_class,restrict(intersection(null_class,X1),X2,X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).
fof(f3554,plain,
( spl0_282
<=> ! [X4,X3] : ~ subclass(universal_class,intersection(intersection(null_class,X3),X4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).
fof(f3568,plain,
( ! [X2,X3,X1] : ~ subclass(universal_class,restrict(intersection(null_class,X1),X2,X3))
| ~ spl0_102
| ~ spl0_282 ),
inference(superposition,[],[f3555,f786]) ).
fof(f3555,plain,
( ! [X3,X4] : ~ subclass(universal_class,intersection(intersection(null_class,X3),X4))
| ~ spl0_282 ),
inference(avatar_component_clause,[],[f3554]) ).
fof(f3572,plain,
( spl0_283
| ~ spl0_102
| ~ spl0_282 ),
inference(avatar_split_clause,[],[f3566,f3554,f785,f3570]) ).
fof(f3566,plain,
( ! [X2,X3,X1] : ~ subclass(universal_class,intersection(restrict(null_class,X1,X2),X3))
| ~ spl0_102
| ~ spl0_282 ),
inference(superposition,[],[f3555,f786]) ).
fof(f3556,plain,
( spl0_282
| ~ spl0_6
| ~ spl0_281 ),
inference(avatar_split_clause,[],[f3550,f3546,f147,f3554]) ).
fof(f3550,plain,
( ! [X3,X4] : ~ subclass(universal_class,intersection(intersection(null_class,X3),X4))
| ~ spl0_6
| ~ spl0_281 ),
inference(resolution,[],[f3547,f148]) ).
fof(f3548,plain,
( spl0_281
| ~ spl0_9
| ~ spl0_266 ),
inference(avatar_split_clause,[],[f3513,f3136,f160,f3546]) ).
fof(f3513,plain,
( ! [X96,X94,X95,X93] :
( ~ subclass(ordered_pair(x,X93),X94)
| ~ subclass(X94,intersection(intersection(null_class,X95),X96)) )
| ~ spl0_9
| ~ spl0_266 ),
inference(resolution,[],[f3137,f161]) ).
fof(f3495,plain,
( spl0_280
| ~ spl0_198
| ~ spl0_279 ),
inference(avatar_split_clause,[],[f3491,f3485,f2454,f3493]) ).
fof(f3493,plain,
( spl0_280
<=> ! [X2,X3] :
( ~ subclass(ordered_pair(singleton(x),singleton(X2)),complement(ordered_pair(x,X3)))
| ~ subclass(universal_class,singleton(ordered_pair(x,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).
fof(f3485,plain,
( spl0_279
<=> ! [X2,X3] :
( ~ subclass(universal_class,X2)
| ~ subclass(X2,complement(ordered_pair(x,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).
fof(f3491,plain,
( ! [X2,X3] :
( ~ subclass(ordered_pair(singleton(x),singleton(X2)),complement(ordered_pair(x,X3)))
| ~ subclass(universal_class,singleton(ordered_pair(x,X2))) )
| ~ spl0_198
| ~ spl0_279 ),
inference(resolution,[],[f3486,f2455]) ).
fof(f3486,plain,
( ! [X2,X3] :
( ~ subclass(universal_class,X2)
| ~ subclass(X2,complement(ordered_pair(x,X3))) )
| ~ spl0_279 ),
inference(avatar_component_clause,[],[f3485]) ).
fof(f3487,plain,
( spl0_279
| ~ spl0_6
| ~ spl0_278 ),
inference(avatar_split_clause,[],[f3481,f3477,f147,f3485]) ).
fof(f3477,plain,
( spl0_278
<=> ! [X36,X37,X35] :
( ~ subclass(X35,complement(ordered_pair(x,X36)))
| ~ subclass(X37,X35)
| ~ subclass(ordered_pair(x,X36),X37) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).
fof(f3481,plain,
( ! [X2,X3] :
( ~ subclass(universal_class,X2)
| ~ subclass(X2,complement(ordered_pair(x,X3))) )
| ~ spl0_6
| ~ spl0_278 ),
inference(resolution,[],[f3478,f148]) ).
fof(f3478,plain,
( ! [X36,X37,X35] :
( ~ subclass(ordered_pair(x,X36),X37)
| ~ subclass(X37,X35)
| ~ subclass(X35,complement(ordered_pair(x,X36))) )
| ~ spl0_278 ),
inference(avatar_component_clause,[],[f3477]) ).
fof(f3479,plain,
( spl0_278
| ~ spl0_170
| ~ spl0_265 ),
inference(avatar_split_clause,[],[f3457,f3132,f1373,f3477]) ).
fof(f3457,plain,
( ! [X36,X37,X35] :
( ~ subclass(X35,complement(ordered_pair(x,X36)))
| ~ subclass(X37,X35)
| ~ subclass(ordered_pair(x,X36),X37) )
| ~ spl0_170
| ~ spl0_265 ),
inference(resolution,[],[f3133,f1374]) ).
fof(f3446,plain,
( spl0_277
| ~ spl0_6
| ~ spl0_264 ),
inference(avatar_split_clause,[],[f3440,f3128,f147,f3444]) ).
fof(f3444,plain,
( spl0_277
<=> ! [X4,X5,X3] :
( ~ subclass(ordered_pair(x,X3),X4)
| ~ subclass(universal_class,X5)
| ~ subclass(X4,complement(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).
fof(f3128,plain,
( spl0_264
<=> ! [X0,X3,X2,X1] :
( ~ subclass(X0,complement(X1))
| ~ subclass(ordered_pair(x,X2),X0)
| ~ subclass(X3,X1)
| ~ subclass(ordered_pair(x,X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).
fof(f3440,plain,
( ! [X3,X4,X5] :
( ~ subclass(ordered_pair(x,X3),X4)
| ~ subclass(universal_class,X5)
| ~ subclass(X4,complement(X5)) )
| ~ spl0_6
| ~ spl0_264 ),
inference(resolution,[],[f3129,f148]) ).
fof(f3129,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(ordered_pair(x,X2),X3)
| ~ subclass(ordered_pair(x,X2),X0)
| ~ subclass(X3,X1)
| ~ subclass(X0,complement(X1)) )
| ~ spl0_264 ),
inference(avatar_component_clause,[],[f3128]) ).
fof(f3414,plain,
( ~ spl0_276
| ~ spl0_198
| spl0_274 ),
inference(avatar_split_clause,[],[f3396,f3353,f2454,f3411]) ).
fof(f3411,plain,
( spl0_276
<=> subclass(universal_class,singleton(ordered_pair(x,x))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).
fof(f3353,plain,
( spl0_274
<=> subclass(universal_class,ordered_pair(singleton(x),singleton(x))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).
fof(f3396,plain,
( ~ subclass(universal_class,singleton(ordered_pair(x,x)))
| ~ spl0_198
| spl0_274 ),
inference(resolution,[],[f2455,f3355]) ).
fof(f3355,plain,
( ~ subclass(universal_class,ordered_pair(singleton(x),singleton(x)))
| spl0_274 ),
inference(avatar_component_clause,[],[f3353]) ).
fof(f3360,plain,
( ~ spl0_274
| spl0_275
| ~ spl0_96
| ~ spl0_155
| ~ spl0_271 ),
inference(avatar_split_clause,[],[f3320,f3189,f1262,f734,f3357,f3353]) ).
fof(f3357,plain,
( spl0_275
<=> null_class = ordered_pair(x,x) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).
fof(f3189,plain,
( spl0_271
<=> ! [X3] :
( null_class = ordered_pair(x,X3)
| ~ subclass(universal_class,ordered_pair(singleton(x),singleton(X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).
fof(f3320,plain,
( null_class = ordered_pair(x,x)
| ~ subclass(universal_class,ordered_pair(singleton(x),singleton(x)))
| ~ spl0_96
| ~ spl0_155
| ~ spl0_271 ),
inference(forward_demodulation,[],[f3216,f1263]) ).
fof(f3216,plain,
( ~ subclass(universal_class,ordered_pair(singleton(x),singleton(x)))
| null_class = ordered_pair(x,y)
| ~ spl0_96
| ~ spl0_271 ),
inference(superposition,[],[f3190,f736]) ).
fof(f3190,plain,
( ! [X3] :
( ~ subclass(universal_class,ordered_pair(singleton(x),singleton(X3)))
| null_class = ordered_pair(x,X3) )
| ~ spl0_271 ),
inference(avatar_component_clause,[],[f3189]) ).
fof(f3318,plain,
( ~ spl0_10
| spl0_87
| ~ spl0_103
| ~ spl0_272 ),
inference(avatar_contradiction_clause,[],[f3317]) ).
fof(f3317,plain,
( $false
| ~ spl0_10
| spl0_87
| ~ spl0_103
| ~ spl0_272 ),
inference(subsumption_resolution,[],[f3316,f653]) ).
fof(f3316,plain,
( null_class = singleton(x)
| ~ spl0_10
| ~ spl0_103
| ~ spl0_272 ),
inference(subsumption_resolution,[],[f3292,f165]) ).
fof(f165,plain,
( ! [X0] : subclass(null_class,X0)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f164]) ).
fof(f164,plain,
( spl0_10
<=> ! [X0] : subclass(null_class,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f3292,plain,
( ~ subclass(null_class,singleton(x))
| null_class = singleton(x)
| ~ spl0_103
| ~ spl0_272 ),
inference(superposition,[],[f793,f3194]) ).
fof(f3194,plain,
( null_class = singleton(singleton(x))
| ~ spl0_272 ),
inference(avatar_component_clause,[],[f3192]) ).
fof(f3192,plain,
( spl0_272
<=> null_class = singleton(singleton(x)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).
fof(f793,plain,
( ! [X2] :
( ~ subclass(singleton(X2),singleton(x))
| singleton(X2) = singleton(x) )
| ~ spl0_103 ),
inference(avatar_component_clause,[],[f792]) ).
fof(f792,plain,
( spl0_103
<=> ! [X2] :
( ~ subclass(singleton(X2),singleton(x))
| singleton(X2) = singleton(x) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f3221,plain,
( spl0_273
| ~ spl0_198
| ~ spl0_271 ),
inference(avatar_split_clause,[],[f3215,f3189,f2454,f3219]) ).
fof(f3219,plain,
( spl0_273
<=> ! [X0] :
( null_class = ordered_pair(x,X0)
| ~ subclass(universal_class,singleton(ordered_pair(x,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).
fof(f3215,plain,
( ! [X0] :
( null_class = ordered_pair(x,X0)
| ~ subclass(universal_class,singleton(ordered_pair(x,X0))) )
| ~ spl0_198
| ~ spl0_271 ),
inference(resolution,[],[f3190,f2455]) ).
fof(f3195,plain,
( spl0_271
| spl0_272
| ~ spl0_74
| ~ spl0_270 ),
inference(avatar_split_clause,[],[f3179,f3174,f530,f3192,f3189]) ).
fof(f530,plain,
( spl0_74
<=> ! [X12] :
( ~ subclass(universal_class,X12)
| member(null_class,X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f3174,plain,
( spl0_270
<=> ! [X14,X15] :
( ~ member(X15,ordered_pair(singleton(x),singleton(X14)))
| singleton(singleton(x)) = X15
| ordered_pair(x,X14) = X15 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).
fof(f3179,plain,
( ! [X3] :
( null_class = singleton(singleton(x))
| null_class = ordered_pair(x,X3)
| ~ subclass(universal_class,ordered_pair(singleton(x),singleton(X3))) )
| ~ spl0_74
| ~ spl0_270 ),
inference(resolution,[],[f3175,f531]) ).
fof(f531,plain,
( ! [X12] :
( member(null_class,X12)
| ~ subclass(universal_class,X12) )
| ~ spl0_74 ),
inference(avatar_component_clause,[],[f530]) ).
fof(f3175,plain,
( ! [X14,X15] :
( ~ member(X15,ordered_pair(singleton(x),singleton(X14)))
| singleton(singleton(x)) = X15
| ordered_pair(x,X14) = X15 )
| ~ spl0_270 ),
inference(avatar_component_clause,[],[f3174]) ).
fof(f3176,plain,
( spl0_270
| ~ spl0_140
| ~ spl0_194 ),
inference(avatar_split_clause,[],[f3169,f2399,f1084,f3174]) ).
fof(f2399,plain,
( spl0_194
<=> ! [X1] : ordered_pair(singleton(x),singleton(X1)) = unordered_pair(singleton(singleton(x)),ordered_pair(x,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).
fof(f3169,plain,
( ! [X14,X15] :
( ~ member(X15,ordered_pair(singleton(x),singleton(X14)))
| singleton(singleton(x)) = X15
| ordered_pair(x,X14) = X15 )
| ~ spl0_140
| ~ spl0_194 ),
inference(superposition,[],[f1085,f2400]) ).
fof(f2400,plain,
( ! [X1] : ordered_pair(singleton(x),singleton(X1)) = unordered_pair(singleton(singleton(x)),ordered_pair(x,X1))
| ~ spl0_194 ),
inference(avatar_component_clause,[],[f2399]) ).
fof(f3152,plain,
( spl0_269
| ~ spl0_43
| ~ spl0_228 ),
inference(avatar_split_clause,[],[f2772,f2760,f322,f3150]) ).
fof(f2772,plain,
( ! [X36,X34,X35,X32,X33] :
( ~ subclass(X32,intersection(X33,intersection(X34,X35)))
| ~ subclass(ordered_pair(x,X36),X32)
| member(singleton(singleton(X36)),X34) )
| ~ spl0_43
| ~ spl0_228 ),
inference(resolution,[],[f2761,f323]) ).
fof(f3148,plain,
( spl0_268
| ~ spl0_44
| ~ spl0_228 ),
inference(avatar_split_clause,[],[f2771,f2760,f326,f3146]) ).
fof(f2771,plain,
( ! [X31,X28,X29,X27,X30] :
( ~ subclass(X27,intersection(X28,intersection(X29,X30)))
| ~ subclass(ordered_pair(x,X31),X27)
| member(singleton(singleton(X31)),X30) )
| ~ spl0_44
| ~ spl0_228 ),
inference(resolution,[],[f2761,f327]) ).
fof(f3144,plain,
( spl0_267
| ~ spl0_44
| ~ spl0_224 ),
inference(avatar_split_clause,[],[f2735,f2717,f326,f3142]) ).
fof(f2735,plain,
( ! [X10,X11,X8,X9,X7] :
( member(singleton(singleton(X7)),X8)
| ~ subclass(X9,intersection(intersection(X10,X8),X11))
| ~ subclass(ordered_pair(x,X7),X9) )
| ~ spl0_44
| ~ spl0_224 ),
inference(resolution,[],[f327,f2718]) ).
fof(f3138,plain,
( spl0_266
| ~ spl0_43
| ~ spl0_224 ),
inference(avatar_split_clause,[],[f2726,f2717,f322,f3136]) ).
fof(f2726,plain,
( ! [X31,X28,X29,X27,X30] :
( ~ subclass(X27,intersection(intersection(X28,X29),X30))
| ~ subclass(ordered_pair(x,X31),X27)
| member(singleton(singleton(X31)),X28) )
| ~ spl0_43
| ~ spl0_224 ),
inference(resolution,[],[f2718,f323]) ).
fof(f3134,plain,
( spl0_265
| ~ spl0_26
| ~ spl0_219 ),
inference(avatar_split_clause,[],[f2677,f2650,f240,f3132]) ).
fof(f2677,plain,
( ! [X28,X29,X27,X30] :
( ~ subclass(ordered_pair(x,X27),X28)
| ~ subclass(X29,complement(X30))
| ~ subclass(X28,X29)
| ~ member(singleton(singleton(X27)),X30) )
| ~ spl0_26
| ~ spl0_219 ),
inference(resolution,[],[f2651,f241]) ).
fof(f3130,plain,
( spl0_264
| ~ spl0_195
| ~ spl0_205 ),
inference(avatar_split_clause,[],[f2517,f2509,f2418,f3128]) ).
fof(f2418,plain,
( spl0_195
<=> ! [X2,X0,X1] :
( ~ subclass(ordered_pair(x,X0),X1)
| ~ subclass(X1,X2)
| member(singleton(singleton(X0)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).
fof(f2509,plain,
( spl0_205
<=> ! [X2,X1,X3] :
( ~ member(singleton(singleton(X1)),X2)
| ~ subclass(X3,complement(X2))
| ~ subclass(ordered_pair(x,X1),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).
fof(f2517,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(X0,complement(X1))
| ~ subclass(ordered_pair(x,X2),X0)
| ~ subclass(X3,X1)
| ~ subclass(ordered_pair(x,X2),X3) )
| ~ spl0_195
| ~ spl0_205 ),
inference(resolution,[],[f2510,f2419]) ).
fof(f2419,plain,
( ! [X2,X0,X1] :
( member(singleton(singleton(X0)),X2)
| ~ subclass(X1,X2)
| ~ subclass(ordered_pair(x,X0),X1) )
| ~ spl0_195 ),
inference(avatar_component_clause,[],[f2418]) ).
fof(f2510,plain,
( ! [X2,X3,X1] :
( ~ member(singleton(singleton(X1)),X2)
| ~ subclass(X3,complement(X2))
| ~ subclass(ordered_pair(x,X1),X3) )
| ~ spl0_205 ),
inference(avatar_component_clause,[],[f2509]) ).
fof(f3124,plain,
( spl0_263
| ~ spl0_195
| ~ spl0_204 ),
inference(avatar_split_clause,[],[f2512,f2505,f2418,f3122]) ).
fof(f3122,plain,
( spl0_263
<=> ! [X2,X0,X1] :
( ~ subclass(ordered_pair(x,X0),power_class(X1))
| ~ subclass(X2,image(element_relation,complement(X1)))
| ~ subclass(ordered_pair(x,X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).
fof(f2505,plain,
( spl0_204
<=> ! [X0,X1] :
( ~ subclass(ordered_pair(x,X1),power_class(X0))
| ~ member(singleton(singleton(X1)),image(element_relation,complement(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).
fof(f2512,plain,
( ! [X2,X0,X1] :
( ~ subclass(ordered_pair(x,X0),power_class(X1))
| ~ subclass(X2,image(element_relation,complement(X1)))
| ~ subclass(ordered_pair(x,X0),X2) )
| ~ spl0_195
| ~ spl0_204 ),
inference(resolution,[],[f2506,f2419]) ).
fof(f2506,plain,
( ! [X0,X1] :
( ~ member(singleton(singleton(X1)),image(element_relation,complement(X0)))
| ~ subclass(ordered_pair(x,X1),power_class(X0)) )
| ~ spl0_204 ),
inference(avatar_component_clause,[],[f2505]) ).
fof(f3119,plain,
( spl0_262
| ~ spl0_102
| ~ spl0_237 ),
inference(avatar_split_clause,[],[f3063,f2846,f785,f3117]) ).
fof(f3117,plain,
( spl0_262
<=> ! [X18,X16,X17] : ~ subclass(ordered_pair(x,X16),restrict(complement(ordered_pair(x,X16)),X17,X18)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).
fof(f2846,plain,
( spl0_237
<=> ! [X0,X1] : ~ subclass(ordered_pair(x,X0),intersection(complement(ordered_pair(x,X0)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).
fof(f3063,plain,
( ! [X18,X16,X17] : ~ subclass(ordered_pair(x,X16),restrict(complement(ordered_pair(x,X16)),X17,X18))
| ~ spl0_102
| ~ spl0_237 ),
inference(superposition,[],[f2847,f786]) ).
fof(f2847,plain,
( ! [X0,X1] : ~ subclass(ordered_pair(x,X0),intersection(complement(ordered_pair(x,X0)),X1))
| ~ spl0_237 ),
inference(avatar_component_clause,[],[f2846]) ).
fof(f3108,plain,
( spl0_261
| ~ spl0_102
| ~ spl0_249 ),
inference(avatar_split_clause,[],[f3065,f2965,f785,f3106]) ).
fof(f3106,plain,
( spl0_261
<=> ! [X22,X24,X23] : ~ subclass(ordered_pair(x,X24),restrict(complement(universal_class),X22,X23)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).
fof(f2965,plain,
( spl0_249
<=> ! [X0,X1] : ~ subclass(ordered_pair(x,X0),intersection(complement(universal_class),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).
fof(f3065,plain,
( ! [X24,X22,X23] : ~ subclass(ordered_pair(x,X24),restrict(complement(universal_class),X22,X23))
| ~ spl0_102
| ~ spl0_249 ),
inference(superposition,[],[f2966,f786]) ).
fof(f2966,plain,
( ! [X0,X1] : ~ subclass(ordered_pair(x,X0),intersection(complement(universal_class),X1))
| ~ spl0_249 ),
inference(avatar_component_clause,[],[f2965]) ).
fof(f3099,plain,
( spl0_260
| ~ spl0_102
| ~ spl0_236 ),
inference(avatar_split_clause,[],[f3064,f2841,f785,f3097]) ).
fof(f3097,plain,
( spl0_260
<=> ! [X20,X21,X19] : ~ subclass(universal_class,restrict(complement(ordered_pair(x,X19)),X20,X21)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).
fof(f2841,plain,
( spl0_236
<=> ! [X2,X3] : ~ subclass(universal_class,intersection(complement(ordered_pair(x,X2)),X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).
fof(f3064,plain,
( ! [X21,X19,X20] : ~ subclass(universal_class,restrict(complement(ordered_pair(x,X19)),X20,X21))
| ~ spl0_102
| ~ spl0_236 ),
inference(superposition,[],[f2842,f786]) ).
fof(f2842,plain,
( ! [X2,X3] : ~ subclass(universal_class,intersection(complement(ordered_pair(x,X2)),X3))
| ~ spl0_236 ),
inference(avatar_component_clause,[],[f2841]) ).
fof(f3094,plain,
( spl0_259
| ~ spl0_102
| ~ spl0_227 ),
inference(avatar_split_clause,[],[f3067,f2755,f785,f3092]) ).
fof(f3092,plain,
( spl0_259
<=> ! [X29,X27,X28] : ~ subclass(ordered_pair(x,X29),restrict(null_class,X27,X28)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).
fof(f2755,plain,
( spl0_227
<=> ! [X0,X1] : ~ subclass(ordered_pair(x,X0),intersection(null_class,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).
fof(f3067,plain,
( ! [X28,X29,X27] : ~ subclass(ordered_pair(x,X29),restrict(null_class,X27,X28))
| ~ spl0_102
| ~ spl0_227 ),
inference(superposition,[],[f2756,f786]) ).
fof(f2756,plain,
( ! [X0,X1] : ~ subclass(ordered_pair(x,X0),intersection(null_class,X1))
| ~ spl0_227 ),
inference(avatar_component_clause,[],[f2755]) ).
fof(f3076,plain,
( spl0_258
| ~ spl0_102
| ~ spl0_248 ),
inference(avatar_split_clause,[],[f3066,f2950,f785,f3074]) ).
fof(f3074,plain,
( spl0_258
<=> ! [X25,X26] : ~ subclass(universal_class,restrict(complement(universal_class),X25,X26)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).
fof(f2950,plain,
( spl0_248
<=> ! [X2] : ~ subclass(universal_class,intersection(complement(universal_class),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).
fof(f3066,plain,
( ! [X26,X25] : ~ subclass(universal_class,restrict(complement(universal_class),X25,X26))
| ~ spl0_102
| ~ spl0_248 ),
inference(superposition,[],[f2951,f786]) ).
fof(f2951,plain,
( ! [X2] : ~ subclass(universal_class,intersection(complement(universal_class),X2))
| ~ spl0_248 ),
inference(avatar_component_clause,[],[f2950]) ).
fof(f3072,plain,
( spl0_257
| ~ spl0_102
| ~ spl0_226 ),
inference(avatar_split_clause,[],[f3068,f2749,f785,f3070]) ).
fof(f3070,plain,
( spl0_257
<=> ! [X30,X31] : ~ subclass(universal_class,restrict(null_class,X30,X31)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).
fof(f2749,plain,
( spl0_226
<=> ! [X2] : ~ subclass(universal_class,intersection(null_class,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).
fof(f3068,plain,
( ! [X31,X30] : ~ subclass(universal_class,restrict(null_class,X30,X31))
| ~ spl0_102
| ~ spl0_226 ),
inference(superposition,[],[f2750,f786]) ).
fof(f2750,plain,
( ! [X2] : ~ subclass(universal_class,intersection(null_class,X2))
| ~ spl0_226 ),
inference(avatar_component_clause,[],[f2749]) ).
fof(f3058,plain,
( spl0_256
| ~ spl0_96
| ~ spl0_255 ),
inference(avatar_split_clause,[],[f3053,f3049,f734,f3056]) ).
fof(f3056,plain,
( spl0_256
<=> ! [X0] :
( ~ subclass(ordered_pair(x,X0),singleton(x))
| y = singleton(singleton(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).
fof(f3049,plain,
( spl0_255
<=> ! [X0,X1] :
( ~ subclass(ordered_pair(x,X1),singleton(X0))
| singleton(singleton(X1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).
fof(f3053,plain,
( ! [X0] :
( ~ subclass(ordered_pair(x,X0),singleton(x))
| y = singleton(singleton(X0)) )
| ~ spl0_96
| ~ spl0_255 ),
inference(superposition,[],[f3050,f736]) ).
fof(f3050,plain,
( ! [X0,X1] :
( ~ subclass(ordered_pair(x,X1),singleton(X0))
| singleton(singleton(X1)) = X0 )
| ~ spl0_255 ),
inference(avatar_component_clause,[],[f3049]) ).
fof(f3051,plain,
( spl0_255
| ~ spl0_18
| ~ spl0_254 ),
inference(avatar_split_clause,[],[f3045,f3019,f202,f3049]) ).
fof(f3019,plain,
( spl0_254
<=> ! [X9,X11,X10] :
( ~ subclass(ordered_pair(x,X9),unordered_pair(X10,X11))
| singleton(singleton(X9)) = X10
| singleton(singleton(X9)) = X11 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).
fof(f3045,plain,
( ! [X0,X1] :
( ~ subclass(ordered_pair(x,X1),singleton(X0))
| singleton(singleton(X1)) = X0 )
| ~ spl0_18
| ~ spl0_254 ),
inference(duplicate_literal_removal,[],[f3036]) ).
fof(f3036,plain,
( ! [X0,X1] :
( ~ subclass(ordered_pair(x,X1),singleton(X0))
| singleton(singleton(X1)) = X0
| singleton(singleton(X1)) = X0 )
| ~ spl0_18
| ~ spl0_254 ),
inference(superposition,[],[f3020,f203]) ).
fof(f3020,plain,
( ! [X10,X11,X9] :
( ~ subclass(ordered_pair(x,X9),unordered_pair(X10,X11))
| singleton(singleton(X9)) = X10
| singleton(singleton(X9)) = X11 )
| ~ spl0_254 ),
inference(avatar_component_clause,[],[f3019]) ).
fof(f3021,plain,
( spl0_254
| ~ spl0_140
| ~ spl0_172 ),
inference(avatar_split_clause,[],[f1414,f1407,f1084,f3019]) ).
fof(f1414,plain,
( ! [X10,X11,X9] :
( ~ subclass(ordered_pair(x,X9),unordered_pair(X10,X11))
| singleton(singleton(X9)) = X10
| singleton(singleton(X9)) = X11 )
| ~ spl0_140
| ~ spl0_172 ),
inference(resolution,[],[f1408,f1085]) ).
fof(f3016,plain,
( spl0_253
| ~ spl0_66
| ~ spl0_223 ),
inference(avatar_split_clause,[],[f2714,f2710,f477,f3014]) ).
fof(f3014,plain,
( spl0_253
<=> ! [X2] :
( ~ subclass(ordered_pair(singleton(x),singleton(X2)),singleton(x))
| singleton(x) = ordered_pair(singleton(x),singleton(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).
fof(f477,plain,
( spl0_66
<=> ! [X0,X1] :
( ~ subclass(X0,X1)
| ~ subclass(X1,X0)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f2710,plain,
( spl0_223
<=> ! [X0] : subclass(singleton(x),ordered_pair(singleton(x),singleton(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).
fof(f2714,plain,
( ! [X2] :
( ~ subclass(ordered_pair(singleton(x),singleton(X2)),singleton(x))
| singleton(x) = ordered_pair(singleton(x),singleton(X2)) )
| ~ spl0_66
| ~ spl0_223 ),
inference(resolution,[],[f2711,f478]) ).
fof(f478,plain,
( ! [X0,X1] :
( ~ subclass(X1,X0)
| ~ subclass(X0,X1)
| X0 = X1 )
| ~ spl0_66 ),
inference(avatar_component_clause,[],[f477]) ).
fof(f2711,plain,
( ! [X0] : subclass(singleton(x),ordered_pair(singleton(x),singleton(X0)))
| ~ spl0_223 ),
inference(avatar_component_clause,[],[f2710]) ).
fof(f2994,plain,
( spl0_252
| ~ spl0_8
| ~ spl0_250 ),
inference(avatar_split_clause,[],[f2981,f2978,f156,f2992]) ).
fof(f2992,plain,
( spl0_252
<=> ! [X0,X1] : ~ subclass(ordered_pair(x,X0),intersection(X1,complement(universal_class))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).
fof(f2978,plain,
( spl0_250
<=> ! [X4,X5,X3] :
( ~ subclass(X3,intersection(X4,complement(universal_class)))
| ~ subclass(ordered_pair(x,X5),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).
fof(f2981,plain,
( ! [X0,X1] : ~ subclass(ordered_pair(x,X0),intersection(X1,complement(universal_class)))
| ~ spl0_8
| ~ spl0_250 ),
inference(resolution,[],[f2979,f157]) ).
fof(f2979,plain,
( ! [X3,X4,X5] :
( ~ subclass(ordered_pair(x,X5),X3)
| ~ subclass(X3,intersection(X4,complement(universal_class))) )
| ~ spl0_250 ),
inference(avatar_component_clause,[],[f2978]) ).
fof(f2988,plain,
( spl0_251
| ~ spl0_6
| ~ spl0_250 ),
inference(avatar_split_clause,[],[f2982,f2978,f147,f2986]) ).
fof(f2986,plain,
( spl0_251
<=> ! [X2] : ~ subclass(universal_class,intersection(X2,complement(universal_class))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).
fof(f2982,plain,
( ! [X2] : ~ subclass(universal_class,intersection(X2,complement(universal_class)))
| ~ spl0_6
| ~ spl0_250 ),
inference(resolution,[],[f2979,f148]) ).
fof(f2980,plain,
( spl0_250
| ~ spl0_6
| ~ spl0_245 ),
inference(avatar_split_clause,[],[f2972,f2915,f147,f2978]) ).
fof(f2915,plain,
( spl0_245
<=> ! [X24,X23,X25,X26] :
( ~ subclass(ordered_pair(x,X23),X24)
| ~ subclass(X24,intersection(X25,complement(X26)))
| ~ subclass(ordered_pair(x,X23),X26) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).
fof(f2972,plain,
( ! [X3,X4,X5] :
( ~ subclass(X3,intersection(X4,complement(universal_class)))
| ~ subclass(ordered_pair(x,X5),X3) )
| ~ spl0_6
| ~ spl0_245 ),
inference(resolution,[],[f2916,f148]) ).
fof(f2916,plain,
( ! [X26,X24,X25,X23] :
( ~ subclass(ordered_pair(x,X23),X26)
| ~ subclass(X24,intersection(X25,complement(X26)))
| ~ subclass(ordered_pair(x,X23),X24) )
| ~ spl0_245 ),
inference(avatar_component_clause,[],[f2915]) ).
fof(f2967,plain,
( spl0_249
| ~ spl0_8
| ~ spl0_247 ),
inference(avatar_split_clause,[],[f2945,f2932,f156,f2965]) ).
fof(f2932,plain,
( spl0_247
<=> ! [X4,X5,X3] :
( ~ subclass(X3,intersection(complement(universal_class),X4))
| ~ subclass(ordered_pair(x,X5),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).
fof(f2945,plain,
( ! [X0,X1] : ~ subclass(ordered_pair(x,X0),intersection(complement(universal_class),X1))
| ~ spl0_8
| ~ spl0_247 ),
inference(resolution,[],[f2933,f157]) ).
fof(f2933,plain,
( ! [X3,X4,X5] :
( ~ subclass(ordered_pair(x,X5),X3)
| ~ subclass(X3,intersection(complement(universal_class),X4)) )
| ~ spl0_247 ),
inference(avatar_component_clause,[],[f2932]) ).
fof(f2952,plain,
( spl0_248
| ~ spl0_6
| ~ spl0_247 ),
inference(avatar_split_clause,[],[f2946,f2932,f147,f2950]) ).
fof(f2946,plain,
( ! [X2] : ~ subclass(universal_class,intersection(complement(universal_class),X2))
| ~ spl0_6
| ~ spl0_247 ),
inference(resolution,[],[f2933,f148]) ).
fof(f2934,plain,
( spl0_247
| ~ spl0_6
| ~ spl0_243 ),
inference(avatar_split_clause,[],[f2928,f2899,f147,f2932]) ).
fof(f2899,plain,
( spl0_243
<=> ! [X24,X23,X25,X26] :
( ~ subclass(ordered_pair(x,X23),X24)
| ~ subclass(X24,intersection(complement(X25),X26))
| ~ subclass(ordered_pair(x,X23),X25) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).
fof(f2928,plain,
( ! [X3,X4,X5] :
( ~ subclass(X3,intersection(complement(universal_class),X4))
| ~ subclass(ordered_pair(x,X5),X3) )
| ~ spl0_6
| ~ spl0_243 ),
inference(resolution,[],[f2900,f148]) ).
fof(f2900,plain,
( ! [X26,X24,X25,X23] :
( ~ subclass(ordered_pair(x,X23),X25)
| ~ subclass(X24,intersection(complement(X25),X26))
| ~ subclass(ordered_pair(x,X23),X24) )
| ~ spl0_243 ),
inference(avatar_component_clause,[],[f2899]) ).
fof(f2921,plain,
( spl0_246
| ~ spl0_186
| ~ spl0_234 ),
inference(avatar_split_clause,[],[f2867,f2804,f1504,f2919]) ).
fof(f2919,plain,
( spl0_246
<=> ! [X41,X39,X40] :
( ~ subclass(ordered_pair(x,X39),X40)
| ~ subclass(X40,intersection(X41,complement(subset_relation)))
| ~ subclass(ordered_pair(x,X39),identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).
fof(f2867,plain,
( ! [X40,X41,X39] :
( ~ subclass(ordered_pair(x,X39),X40)
| ~ subclass(X40,intersection(X41,complement(subset_relation)))
| ~ subclass(ordered_pair(x,X39),identity_relation) )
| ~ spl0_186
| ~ spl0_234 ),
inference(resolution,[],[f2805,f1505]) ).
fof(f2917,plain,
( spl0_245
| ~ spl0_172
| ~ spl0_234 ),
inference(avatar_split_clause,[],[f2863,f2804,f1407,f2915]) ).
fof(f2863,plain,
( ! [X26,X24,X25,X23] :
( ~ subclass(ordered_pair(x,X23),X24)
| ~ subclass(X24,intersection(X25,complement(X26)))
| ~ subclass(ordered_pair(x,X23),X26) )
| ~ spl0_172
| ~ spl0_234 ),
inference(resolution,[],[f2805,f1408]) ).
fof(f2913,plain,
( spl0_244
| ~ spl0_186
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2827,f2800,f1504,f2911]) ).
fof(f2911,plain,
( spl0_244
<=> ! [X41,X39,X40] :
( ~ subclass(ordered_pair(x,X39),X40)
| ~ subclass(X40,intersection(complement(subset_relation),X41))
| ~ subclass(ordered_pair(x,X39),identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).
fof(f2827,plain,
( ! [X40,X41,X39] :
( ~ subclass(ordered_pair(x,X39),X40)
| ~ subclass(X40,intersection(complement(subset_relation),X41))
| ~ subclass(ordered_pair(x,X39),identity_relation) )
| ~ spl0_186
| ~ spl0_233 ),
inference(resolution,[],[f2801,f1505]) ).
fof(f2901,plain,
( spl0_243
| ~ spl0_172
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2823,f2800,f1407,f2899]) ).
fof(f2823,plain,
( ! [X26,X24,X25,X23] :
( ~ subclass(ordered_pair(x,X23),X24)
| ~ subclass(X24,intersection(complement(X25),X26))
| ~ subclass(ordered_pair(x,X23),X25) )
| ~ spl0_172
| ~ spl0_233 ),
inference(resolution,[],[f2801,f1408]) ).
fof(f2897,plain,
( spl0_242
| ~ spl0_27
| ~ spl0_232 ),
inference(avatar_split_clause,[],[f2818,f2796,f244,f2895]) ).
fof(f2895,plain,
( spl0_242
<=> ! [X2,X1] :
( ~ subclass(ordered_pair(x,X2),successor(X1))
| ~ subclass(ordered_pair(x,X2),intersection(complement(X1),complement(singleton(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).
fof(f2796,plain,
( spl0_232
<=> ! [X6,X4,X5] :
( ~ subclass(ordered_pair(x,X4),union(X5,X6))
| ~ subclass(ordered_pair(x,X4),intersection(complement(X5),complement(X6))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).
fof(f2818,plain,
( ! [X2,X1] :
( ~ subclass(ordered_pair(x,X2),successor(X1))
| ~ subclass(ordered_pair(x,X2),intersection(complement(X1),complement(singleton(X1)))) )
| ~ spl0_27
| ~ spl0_232 ),
inference(superposition,[],[f2797,f245]) ).
fof(f2797,plain,
( ! [X6,X4,X5] :
( ~ subclass(ordered_pair(x,X4),union(X5,X6))
| ~ subclass(ordered_pair(x,X4),intersection(complement(X5),complement(X6))) )
| ~ spl0_232 ),
inference(avatar_component_clause,[],[f2796]) ).
fof(f2893,plain,
( spl0_241
| ~ spl0_98
| ~ spl0_232 ),
inference(avatar_split_clause,[],[f2817,f2796,f768,f2891]) ).
fof(f2891,plain,
( spl0_241
<=> ! [X0] :
( ~ subclass(ordered_pair(x,X0),successor(y))
| ~ subclass(ordered_pair(x,X0),intersection(complement(y),complement(singleton(x)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).
fof(f2817,plain,
( ! [X0] :
( ~ subclass(ordered_pair(x,X0),successor(y))
| ~ subclass(ordered_pair(x,X0),intersection(complement(y),complement(singleton(x)))) )
| ~ spl0_98
| ~ spl0_232 ),
inference(superposition,[],[f2797,f770]) ).
fof(f2886,plain,
( spl0_240
| ~ spl0_8
| ~ spl0_238 ),
inference(avatar_split_clause,[],[f2874,f2871,f156,f2884]) ).
fof(f2884,plain,
( spl0_240
<=> ! [X0,X1] : ~ subclass(ordered_pair(x,X0),intersection(X1,complement(ordered_pair(x,X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).
fof(f2871,plain,
( spl0_238
<=> ! [X29,X27,X28] :
( ~ subclass(ordered_pair(x,X27),X28)
| ~ subclass(X28,intersection(X29,complement(ordered_pair(x,X27)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).
fof(f2874,plain,
( ! [X0,X1] : ~ subclass(ordered_pair(x,X0),intersection(X1,complement(ordered_pair(x,X0))))
| ~ spl0_8
| ~ spl0_238 ),
inference(resolution,[],[f2872,f157]) ).
fof(f2872,plain,
( ! [X28,X29,X27] :
( ~ subclass(ordered_pair(x,X27),X28)
| ~ subclass(X28,intersection(X29,complement(ordered_pair(x,X27)))) )
| ~ spl0_238 ),
inference(avatar_component_clause,[],[f2871]) ).
fof(f2881,plain,
( spl0_239
| ~ spl0_6
| ~ spl0_238 ),
inference(avatar_split_clause,[],[f2875,f2871,f147,f2879]) ).
fof(f2879,plain,
( spl0_239
<=> ! [X2,X3] : ~ subclass(universal_class,intersection(X2,complement(ordered_pair(x,X3)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).
fof(f2875,plain,
( ! [X2,X3] : ~ subclass(universal_class,intersection(X2,complement(ordered_pair(x,X3))))
| ~ spl0_6
| ~ spl0_238 ),
inference(resolution,[],[f2872,f148]) ).
fof(f2873,plain,
( spl0_238
| ~ spl0_170
| ~ spl0_234 ),
inference(avatar_split_clause,[],[f2864,f2804,f1373,f2871]) ).
fof(f2864,plain,
( ! [X28,X29,X27] :
( ~ subclass(ordered_pair(x,X27),X28)
| ~ subclass(X28,intersection(X29,complement(ordered_pair(x,X27)))) )
| ~ spl0_170
| ~ spl0_234 ),
inference(resolution,[],[f2805,f1374]) ).
fof(f2848,plain,
( spl0_237
| ~ spl0_8
| ~ spl0_235 ),
inference(avatar_split_clause,[],[f2834,f2831,f156,f2846]) ).
fof(f2831,plain,
( spl0_235
<=> ! [X29,X27,X28] :
( ~ subclass(ordered_pair(x,X27),X28)
| ~ subclass(X28,intersection(complement(ordered_pair(x,X27)),X29)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).
fof(f2834,plain,
( ! [X0,X1] : ~ subclass(ordered_pair(x,X0),intersection(complement(ordered_pair(x,X0)),X1))
| ~ spl0_8
| ~ spl0_235 ),
inference(resolution,[],[f2832,f157]) ).
fof(f2832,plain,
( ! [X28,X29,X27] :
( ~ subclass(ordered_pair(x,X27),X28)
| ~ subclass(X28,intersection(complement(ordered_pair(x,X27)),X29)) )
| ~ spl0_235 ),
inference(avatar_component_clause,[],[f2831]) ).
fof(f2843,plain,
( spl0_236
| ~ spl0_6
| ~ spl0_235 ),
inference(avatar_split_clause,[],[f2835,f2831,f147,f2841]) ).
fof(f2835,plain,
( ! [X2,X3] : ~ subclass(universal_class,intersection(complement(ordered_pair(x,X2)),X3))
| ~ spl0_6
| ~ spl0_235 ),
inference(resolution,[],[f2832,f148]) ).
fof(f2833,plain,
( spl0_235
| ~ spl0_170
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2824,f2800,f1373,f2831]) ).
fof(f2824,plain,
( ! [X28,X29,X27] :
( ~ subclass(ordered_pair(x,X27),X28)
| ~ subclass(X28,intersection(complement(ordered_pair(x,X27)),X29)) )
| ~ spl0_170
| ~ spl0_233 ),
inference(resolution,[],[f2801,f1374]) ).
fof(f2806,plain,
( spl0_234
| ~ spl0_26
| ~ spl0_228 ),
inference(avatar_split_clause,[],[f2773,f2760,f240,f2804]) ).
fof(f2773,plain,
( ! [X40,X38,X39,X37] :
( ~ subclass(X37,intersection(X38,complement(X39)))
| ~ subclass(ordered_pair(x,X40),X37)
| ~ member(singleton(singleton(X40)),X39) )
| ~ spl0_26
| ~ spl0_228 ),
inference(resolution,[],[f2761,f241]) ).
fof(f2802,plain,
( spl0_233
| ~ spl0_26
| ~ spl0_224 ),
inference(avatar_split_clause,[],[f2727,f2717,f240,f2800]) ).
fof(f2727,plain,
( ! [X34,X35,X32,X33] :
( ~ subclass(X32,intersection(complement(X33),X34))
| ~ subclass(ordered_pair(x,X35),X32)
| ~ member(singleton(singleton(X35)),X33) )
| ~ spl0_26
| ~ spl0_224 ),
inference(resolution,[],[f2718,f241]) ).
fof(f2798,plain,
( spl0_232
| ~ spl0_172
| ~ spl0_218 ),
inference(avatar_split_clause,[],[f2668,f2646,f1407,f2796]) ).
fof(f2646,plain,
( spl0_218
<=> ! [X2,X4,X3] :
( ~ subclass(ordered_pair(x,X4),union(X2,X3))
| ~ member(singleton(singleton(X4)),intersection(complement(X2),complement(X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).
fof(f2668,plain,
( ! [X6,X4,X5] :
( ~ subclass(ordered_pair(x,X4),union(X5,X6))
| ~ subclass(ordered_pair(x,X4),intersection(complement(X5),complement(X6))) )
| ~ spl0_172
| ~ spl0_218 ),
inference(resolution,[],[f2647,f1408]) ).
fof(f2647,plain,
( ! [X2,X3,X4] :
( ~ member(singleton(singleton(X4)),intersection(complement(X2),complement(X3)))
| ~ subclass(ordered_pair(x,X4),union(X2,X3)) )
| ~ spl0_218 ),
inference(avatar_component_clause,[],[f2646]) ).
fof(f2793,plain,
( spl0_231
| ~ spl0_8
| ~ spl0_229 ),
inference(avatar_split_clause,[],[f2782,f2779,f156,f2791]) ).
fof(f2791,plain,
( spl0_231
<=> ! [X0,X1] : ~ subclass(ordered_pair(x,X0),intersection(X1,null_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).
fof(f2782,plain,
( ! [X0,X1] : ~ subclass(ordered_pair(x,X0),intersection(X1,null_class))
| ~ spl0_8
| ~ spl0_229 ),
inference(resolution,[],[f2780,f157]) ).
fof(f2789,plain,
( spl0_230
| ~ spl0_6
| ~ spl0_229 ),
inference(avatar_split_clause,[],[f2783,f2779,f147,f2787]) ).
fof(f2787,plain,
( spl0_230
<=> ! [X2] : ~ subclass(universal_class,intersection(X2,null_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).
fof(f2783,plain,
( ! [X2] : ~ subclass(universal_class,intersection(X2,null_class))
| ~ spl0_6
| ~ spl0_229 ),
inference(resolution,[],[f2780,f148]) ).
fof(f2781,plain,
( spl0_229
| ~ spl0_9
| ~ spl0_228 ),
inference(avatar_split_clause,[],[f2774,f2760,f160,f2779]) ).
fof(f2774,plain,
( ! [X41,X42,X43] :
( ~ subclass(X41,intersection(X42,null_class))
| ~ subclass(ordered_pair(x,X43),X41) )
| ~ spl0_9
| ~ spl0_228 ),
inference(resolution,[],[f2761,f161]) ).
fof(f2762,plain,
( spl0_228
| ~ spl0_44
| ~ spl0_195 ),
inference(avatar_split_clause,[],[f2737,f2418,f326,f2760]) ).
fof(f2737,plain,
( ! [X18,X19,X17,X20] :
( member(singleton(singleton(X17)),X18)
| ~ subclass(X19,intersection(X20,X18))
| ~ subclass(ordered_pair(x,X17),X19) )
| ~ spl0_44
| ~ spl0_195 ),
inference(resolution,[],[f327,f2419]) ).
fof(f2757,plain,
( spl0_227
| ~ spl0_8
| ~ spl0_225 ),
inference(avatar_split_clause,[],[f2744,f2741,f156,f2755]) ).
fof(f2744,plain,
( ! [X0,X1] : ~ subclass(ordered_pair(x,X0),intersection(null_class,X1))
| ~ spl0_8
| ~ spl0_225 ),
inference(resolution,[],[f2742,f157]) ).
fof(f2751,plain,
( spl0_226
| ~ spl0_6
| ~ spl0_225 ),
inference(avatar_split_clause,[],[f2745,f2741,f147,f2749]) ).
fof(f2745,plain,
( ! [X2] : ~ subclass(universal_class,intersection(null_class,X2))
| ~ spl0_6
| ~ spl0_225 ),
inference(resolution,[],[f2742,f148]) ).
fof(f2743,plain,
( spl0_225
| ~ spl0_9
| ~ spl0_224 ),
inference(avatar_split_clause,[],[f2728,f2717,f160,f2741]) ).
fof(f2728,plain,
( ! [X38,X36,X37] :
( ~ subclass(X36,intersection(null_class,X37))
| ~ subclass(ordered_pair(x,X38),X36) )
| ~ spl0_9
| ~ spl0_224 ),
inference(resolution,[],[f2718,f161]) ).
fof(f2719,plain,
( spl0_224
| ~ spl0_43
| ~ spl0_195 ),
inference(avatar_split_clause,[],[f2706,f2418,f322,f2717]) ).
fof(f2706,plain,
( ! [X14,X15,X12,X13] :
( member(singleton(singleton(X12)),X13)
| ~ subclass(X14,intersection(X13,X15))
| ~ subclass(ordered_pair(x,X12),X14) )
| ~ spl0_43
| ~ spl0_195 ),
inference(resolution,[],[f323,f2419]) ).
fof(f2712,plain,
( spl0_223
| ~ spl0_8
| ~ spl0_222 ),
inference(avatar_split_clause,[],[f2699,f2696,f156,f2710]) ).
fof(f2696,plain,
( spl0_222
<=> ! [X2,X3] :
( ~ subclass(X2,singleton(x))
| subclass(X2,ordered_pair(singleton(x),singleton(X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).
fof(f2699,plain,
( ! [X0] : subclass(singleton(x),ordered_pair(singleton(x),singleton(X0)))
| ~ spl0_8
| ~ spl0_222 ),
inference(resolution,[],[f2697,f157]) ).
fof(f2697,plain,
( ! [X2,X3] :
( ~ subclass(X2,singleton(x))
| subclass(X2,ordered_pair(singleton(x),singleton(X3))) )
| ~ spl0_222 ),
inference(avatar_component_clause,[],[f2696]) ).
fof(f2698,plain,
( spl0_222
| ~ spl0_90
| ~ spl0_220 ),
inference(avatar_split_clause,[],[f2691,f2654,f680,f2696]) ).
fof(f2654,plain,
( spl0_220
<=> ! [X2,X0,X1] :
( ~ subclass(X0,singleton(ordered_pair(x,X1)))
| ~ subclass(X2,X0)
| subclass(X2,ordered_pair(singleton(x),singleton(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).
fof(f2691,plain,
( ! [X2,X3] :
( ~ subclass(X2,singleton(x))
| subclass(X2,ordered_pair(singleton(x),singleton(X3))) )
| ~ spl0_90
| ~ spl0_220 ),
inference(resolution,[],[f2655,f681]) ).
fof(f2655,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,singleton(ordered_pair(x,X1)))
| ~ subclass(X2,X0)
| subclass(X2,ordered_pair(singleton(x),singleton(X1))) )
| ~ spl0_220 ),
inference(avatar_component_clause,[],[f2654]) ).
fof(f2685,plain,
( spl0_221
| ~ spl0_9
| ~ spl0_219 ),
inference(avatar_split_clause,[],[f2678,f2650,f160,f2683]) ).
fof(f2683,plain,
( spl0_221
<=> ! [X32,X33,X31] :
( ~ subclass(ordered_pair(x,X31),X32)
| ~ subclass(X33,null_class)
| ~ subclass(X32,X33) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).
fof(f2678,plain,
( ! [X31,X32,X33] :
( ~ subclass(ordered_pair(x,X31),X32)
| ~ subclass(X33,null_class)
| ~ subclass(X32,X33) )
| ~ spl0_9
| ~ spl0_219 ),
inference(resolution,[],[f2651,f161]) ).
fof(f2656,plain,
( spl0_220
| ~ spl0_71
| ~ spl0_198 ),
inference(avatar_split_clause,[],[f2460,f2454,f497,f2654]) ).
fof(f497,plain,
( spl0_71
<=> ! [X4,X0,X1] :
( ~ subclass(X0,X1)
| ~ subclass(X1,X4)
| subclass(X0,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f2460,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,singleton(ordered_pair(x,X1)))
| ~ subclass(X2,X0)
| subclass(X2,ordered_pair(singleton(x),singleton(X1))) )
| ~ spl0_71
| ~ spl0_198 ),
inference(resolution,[],[f2455,f498]) ).
fof(f498,plain,
( ! [X0,X1,X4] :
( ~ subclass(X1,X4)
| ~ subclass(X0,X1)
| subclass(X0,X4) )
| ~ spl0_71 ),
inference(avatar_component_clause,[],[f497]) ).
fof(f2652,plain,
( spl0_219
| ~ spl0_65
| ~ spl0_195 ),
inference(avatar_split_clause,[],[f2421,f2418,f473,f2650]) ).
fof(f2421,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(X0,X1)
| ~ subclass(ordered_pair(x,X2),X0)
| ~ subclass(X1,X3)
| member(singleton(singleton(X2)),X3) )
| ~ spl0_65
| ~ spl0_195 ),
inference(resolution,[],[f2419,f474]) ).
fof(f2648,plain,
( spl0_218
| ~ spl0_100
| ~ spl0_180 ),
inference(avatar_split_clause,[],[f1473,f1468,f777,f2646]) ).
fof(f1468,plain,
( spl0_180
<=> ! [X22,X21] :
( ~ subclass(ordered_pair(x,X21),complement(X22))
| ~ member(singleton(singleton(X21)),X22) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).
fof(f1473,plain,
( ! [X2,X3,X4] :
( ~ subclass(ordered_pair(x,X4),union(X2,X3))
| ~ member(singleton(singleton(X4)),intersection(complement(X2),complement(X3))) )
| ~ spl0_100
| ~ spl0_180 ),
inference(superposition,[],[f1469,f778]) ).
fof(f1469,plain,
( ! [X21,X22] :
( ~ subclass(ordered_pair(x,X21),complement(X22))
| ~ member(singleton(singleton(X21)),X22) )
| ~ spl0_180 ),
inference(avatar_component_clause,[],[f1468]) ).
fof(f2628,plain,
( spl0_217
| ~ spl0_66
| ~ spl0_171 ),
inference(avatar_split_clause,[],[f1399,f1395,f477,f2626]) ).
fof(f2626,plain,
( spl0_217
<=> ! [X2] :
( ~ subclass(ordered_pair(x,X2),singleton(singleton(singleton(X2))))
| ordered_pair(x,X2) = singleton(singleton(singleton(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).
fof(f1395,plain,
( spl0_171
<=> ! [X7] : subclass(singleton(singleton(singleton(X7))),ordered_pair(x,X7)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
fof(f1399,plain,
( ! [X2] :
( ~ subclass(ordered_pair(x,X2),singleton(singleton(singleton(X2))))
| ordered_pair(x,X2) = singleton(singleton(singleton(X2))) )
| ~ spl0_66
| ~ spl0_171 ),
inference(resolution,[],[f1396,f478]) ).
fof(f1396,plain,
( ! [X7] : subclass(singleton(singleton(singleton(X7))),ordered_pair(x,X7))
| ~ spl0_171 ),
inference(avatar_component_clause,[],[f1395]) ).
fof(f2623,plain,
( spl0_216
| ~ spl0_188
| ~ spl0_205 ),
inference(avatar_split_clause,[],[f2520,f2509,f1522,f2621]) ).
fof(f2621,plain,
( spl0_216
<=> ! [X9,X10] :
( ~ subclass(X9,complement(inverse(subset_relation)))
| ~ subclass(ordered_pair(x,X10),X9)
| ~ subclass(ordered_pair(x,X10),identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).
fof(f2520,plain,
( ! [X10,X9] :
( ~ subclass(X9,complement(inverse(subset_relation)))
| ~ subclass(ordered_pair(x,X10),X9)
| ~ subclass(ordered_pair(x,X10),identity_relation) )
| ~ spl0_188
| ~ spl0_205 ),
inference(resolution,[],[f2510,f1523]) ).
fof(f2613,plain,
( spl0_215
| ~ spl0_102
| ~ spl0_183 ),
inference(avatar_split_clause,[],[f1498,f1485,f785,f2611]) ).
fof(f1485,plain,
( spl0_183
<=> ! [X16,X17,X15] :
( ~ subclass(ordered_pair(x,X15),intersection(X16,X17))
| member(singleton(singleton(X15)),X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).
fof(f1498,plain,
( ! [X2,X3,X4,X5] :
( ~ subclass(ordered_pair(x,X5),restrict(X2,X3,X4))
| member(singleton(singleton(X5)),cross_product(X3,X4)) )
| ~ spl0_102
| ~ spl0_183 ),
inference(superposition,[],[f1486,f786]) ).
fof(f1486,plain,
( ! [X16,X17,X15] :
( ~ subclass(ordered_pair(x,X15),intersection(X16,X17))
| member(singleton(singleton(X15)),X17) )
| ~ spl0_183 ),
inference(avatar_component_clause,[],[f1485]) ).
fof(f2603,plain,
( spl0_214
| ~ spl0_8
| ~ spl0_213 ),
inference(avatar_split_clause,[],[f2598,f2595,f156,f2601]) ).
fof(f2601,plain,
( spl0_214
<=> ! [X0] : ~ subclass(ordered_pair(x,X0),complement(universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).
fof(f2595,plain,
( spl0_213
<=> ! [X2,X3] :
( ~ subclass(ordered_pair(x,X2),X3)
| ~ subclass(X3,complement(universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).
fof(f2598,plain,
( ! [X0] : ~ subclass(ordered_pair(x,X0),complement(universal_class))
| ~ spl0_8
| ~ spl0_213 ),
inference(resolution,[],[f2596,f157]) ).
fof(f2596,plain,
( ! [X2,X3] :
( ~ subclass(X3,complement(universal_class))
| ~ subclass(ordered_pair(x,X2),X3) )
| ~ spl0_213 ),
inference(avatar_component_clause,[],[f2595]) ).
fof(f2597,plain,
( spl0_213
| ~ spl0_6
| ~ spl0_211 ),
inference(avatar_split_clause,[],[f2569,f2554,f147,f2595]) ).
fof(f2554,plain,
( spl0_211
<=> ! [X6,X4,X5] :
( ~ subclass(X4,complement(X5))
| ~ subclass(ordered_pair(x,X6),X4)
| ~ subclass(ordered_pair(x,X6),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).
fof(f2569,plain,
( ! [X2,X3] :
( ~ subclass(ordered_pair(x,X2),X3)
| ~ subclass(X3,complement(universal_class)) )
| ~ spl0_6
| ~ spl0_211 ),
inference(resolution,[],[f2555,f148]) ).
fof(f2555,plain,
( ! [X6,X4,X5] :
( ~ subclass(ordered_pair(x,X6),X5)
| ~ subclass(ordered_pair(x,X6),X4)
| ~ subclass(X4,complement(X5)) )
| ~ spl0_211 ),
inference(avatar_component_clause,[],[f2554]) ).
fof(f2560,plain,
( spl0_212
| ~ spl0_186
| ~ spl0_205 ),
inference(avatar_split_clause,[],[f2521,f2509,f1504,f2558]) ).
fof(f2558,plain,
( spl0_212
<=> ! [X12,X11] :
( ~ subclass(X11,complement(subset_relation))
| ~ subclass(ordered_pair(x,X12),X11)
| ~ subclass(ordered_pair(x,X12),identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).
fof(f2521,plain,
( ! [X11,X12] :
( ~ subclass(X11,complement(subset_relation))
| ~ subclass(ordered_pair(x,X12),X11)
| ~ subclass(ordered_pair(x,X12),identity_relation) )
| ~ spl0_186
| ~ spl0_205 ),
inference(resolution,[],[f2510,f1505]) ).
fof(f2556,plain,
( spl0_211
| ~ spl0_172
| ~ spl0_205 ),
inference(avatar_split_clause,[],[f2518,f2509,f1407,f2554]) ).
fof(f2518,plain,
( ! [X6,X4,X5] :
( ~ subclass(X4,complement(X5))
| ~ subclass(ordered_pair(x,X6),X4)
| ~ subclass(ordered_pair(x,X6),X5) )
| ~ spl0_172
| ~ spl0_205 ),
inference(resolution,[],[f2510,f1408]) ).
fof(f2552,plain,
( spl0_210
| ~ spl0_172
| ~ spl0_204 ),
inference(avatar_split_clause,[],[f2513,f2505,f1407,f2550]) ).
fof(f2550,plain,
( spl0_210
<=> ! [X4,X3] :
( ~ subclass(ordered_pair(x,X3),power_class(X4))
| ~ subclass(ordered_pair(x,X3),image(element_relation,complement(X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).
fof(f2513,plain,
( ! [X3,X4] :
( ~ subclass(ordered_pair(x,X3),power_class(X4))
| ~ subclass(ordered_pair(x,X3),image(element_relation,complement(X4))) )
| ~ spl0_172
| ~ spl0_204 ),
inference(resolution,[],[f2506,f1408]) ).
fof(f2548,plain,
( spl0_209
| ~ spl0_65
| ~ spl0_188 ),
inference(avatar_split_clause,[],[f1525,f1522,f473,f2546]) ).
fof(f2546,plain,
( spl0_209
<=> ! [X0,X1] :
( ~ subclass(ordered_pair(x,X0),identity_relation)
| ~ subclass(inverse(subset_relation),X1)
| member(singleton(singleton(X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).
fof(f1525,plain,
( ! [X0,X1] :
( ~ subclass(ordered_pair(x,X0),identity_relation)
| ~ subclass(inverse(subset_relation),X1)
| member(singleton(singleton(X0)),X1) )
| ~ spl0_65
| ~ spl0_188 ),
inference(resolution,[],[f1523,f474]) ).
fof(f2542,plain,
( spl0_208
| ~ spl0_8
| ~ spl0_206 ),
inference(avatar_split_clause,[],[f2528,f2525,f156,f2540]) ).
fof(f2540,plain,
( spl0_208
<=> ! [X0] : ~ subclass(ordered_pair(x,X0),complement(ordered_pair(x,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).
fof(f2528,plain,
( ! [X0] : ~ subclass(ordered_pair(x,X0),complement(ordered_pair(x,X0)))
| ~ spl0_8
| ~ spl0_206 ),
inference(resolution,[],[f2526,f157]) ).
fof(f2535,plain,
( spl0_207
| ~ spl0_6
| ~ spl0_206 ),
inference(avatar_split_clause,[],[f2529,f2525,f147,f2533]) ).
fof(f2533,plain,
( spl0_207
<=> ! [X1] : ~ subclass(universal_class,complement(ordered_pair(x,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).
fof(f2529,plain,
( ! [X1] : ~ subclass(universal_class,complement(ordered_pair(x,X1)))
| ~ spl0_6
| ~ spl0_206 ),
inference(resolution,[],[f2526,f148]) ).
fof(f2527,plain,
( spl0_206
| ~ spl0_170
| ~ spl0_205 ),
inference(avatar_split_clause,[],[f2519,f2509,f1373,f2525]) ).
fof(f2519,plain,
( ! [X8,X7] :
( ~ subclass(X7,complement(ordered_pair(x,X8)))
| ~ subclass(ordered_pair(x,X8),X7) )
| ~ spl0_170
| ~ spl0_205 ),
inference(resolution,[],[f2510,f1374]) ).
fof(f2511,plain,
( spl0_205
| ~ spl0_26
| ~ spl0_195 ),
inference(avatar_split_clause,[],[f2458,f2418,f240,f2509]) ).
fof(f2458,plain,
( ! [X2,X3,X1] :
( ~ member(singleton(singleton(X1)),X2)
| ~ subclass(X3,complement(X2))
| ~ subclass(ordered_pair(x,X1),X3) )
| ~ spl0_26
| ~ spl0_195 ),
inference(resolution,[],[f241,f2419]) ).
fof(f2507,plain,
( spl0_204
| ~ spl0_49
| ~ spl0_180 ),
inference(avatar_split_clause,[],[f1472,f1468,f346,f2505]) ).
fof(f1472,plain,
( ! [X0,X1] :
( ~ subclass(ordered_pair(x,X1),power_class(X0))
| ~ member(singleton(singleton(X1)),image(element_relation,complement(X0))) )
| ~ spl0_49
| ~ spl0_180 ),
inference(superposition,[],[f1469,f347]) ).
fof(f2500,plain,
( spl0_203
| ~ spl0_74
| spl0_87
| ~ spl0_202 ),
inference(avatar_split_clause,[],[f2495,f2487,f651,f530,f2498]) ).
fof(f2498,plain,
( spl0_203
<=> ! [X1] :
( null_class = singleton(singleton(X1))
| ~ subclass(universal_class,ordered_pair(x,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).
fof(f2495,plain,
( ! [X1] :
( null_class = singleton(singleton(X1))
| ~ subclass(universal_class,ordered_pair(x,X1)) )
| ~ spl0_74
| spl0_87
| ~ spl0_202 ),
inference(subsumption_resolution,[],[f2491,f653]) ).
fof(f2491,plain,
( ! [X1] :
( null_class = singleton(x)
| null_class = singleton(singleton(X1))
| ~ subclass(universal_class,ordered_pair(x,X1)) )
| ~ spl0_74
| ~ spl0_202 ),
inference(resolution,[],[f2488,f531]) ).
fof(f2489,plain,
( spl0_202
| ~ spl0_140
| ~ spl0_169 ),
inference(avatar_split_clause,[],[f1367,f1360,f1084,f2487]) ).
fof(f1360,plain,
( spl0_169
<=> ! [X0] : unordered_pair(singleton(x),singleton(singleton(X0))) = ordered_pair(x,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
fof(f1367,plain,
( ! [X3,X4] :
( ~ member(X4,ordered_pair(x,X3))
| singleton(x) = X4
| singleton(singleton(X3)) = X4 )
| ~ spl0_140
| ~ spl0_169 ),
inference(superposition,[],[f1085,f1361]) ).
fof(f1361,plain,
( ! [X0] : unordered_pair(singleton(x),singleton(singleton(X0))) = ordered_pair(x,X0)
| ~ spl0_169 ),
inference(avatar_component_clause,[],[f1360]) ).
fof(f2481,plain,
( spl0_201
| ~ spl0_65
| ~ spl0_186 ),
inference(avatar_split_clause,[],[f1507,f1504,f473,f2479]) ).
fof(f2479,plain,
( spl0_201
<=> ! [X0,X1] :
( ~ subclass(ordered_pair(x,X0),identity_relation)
| ~ subclass(subset_relation,X1)
| member(singleton(singleton(X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).
fof(f1507,plain,
( ! [X0,X1] :
( ~ subclass(ordered_pair(x,X0),identity_relation)
| ~ subclass(subset_relation,X1)
| member(singleton(singleton(X0)),X1) )
| ~ spl0_65
| ~ spl0_186 ),
inference(resolution,[],[f1505,f474]) ).
fof(f2472,plain,
( spl0_200
| ~ spl0_77
| ~ spl0_198 ),
inference(avatar_split_clause,[],[f2462,f2454,f571,f2470]) ).
fof(f2470,plain,
( spl0_200
<=> ! [X5] :
( ~ subclass(universal_class,singleton(ordered_pair(x,X5)))
| universal_class = ordered_pair(singleton(x),singleton(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).
fof(f571,plain,
( spl0_77
<=> ! [X0] :
( ~ subclass(universal_class,X0)
| universal_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f2462,plain,
( ! [X5] :
( ~ subclass(universal_class,singleton(ordered_pair(x,X5)))
| universal_class = ordered_pair(singleton(x),singleton(X5)) )
| ~ spl0_77
| ~ spl0_198 ),
inference(resolution,[],[f2455,f572]) ).
fof(f572,plain,
( ! [X0] :
( ~ subclass(universal_class,X0)
| universal_class = X0 )
| ~ spl0_77 ),
inference(avatar_component_clause,[],[f571]) ).
fof(f2468,plain,
( spl0_199
| ~ spl0_104
| ~ spl0_183 ),
inference(avatar_split_clause,[],[f1499,f1485,f803,f2466]) ).
fof(f1499,plain,
( ! [X8,X6,X9,X7] :
( ~ subclass(ordered_pair(x,X9),restrict(X8,X6,X7))
| member(singleton(singleton(X9)),X8) )
| ~ spl0_104
| ~ spl0_183 ),
inference(superposition,[],[f1486,f804]) ).
fof(f2456,plain,
( spl0_198
| ~ spl0_71
| ~ spl0_197 ),
inference(avatar_split_clause,[],[f2447,f2444,f497,f2454]) ).
fof(f2444,plain,
( spl0_197
<=> ! [X4] : subclass(singleton(ordered_pair(x,X4)),ordered_pair(singleton(x),singleton(X4))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).
fof(f2447,plain,
( ! [X0,X1] :
( ~ subclass(X0,singleton(ordered_pair(x,X1)))
| subclass(X0,ordered_pair(singleton(x),singleton(X1))) )
| ~ spl0_71
| ~ spl0_197 ),
inference(resolution,[],[f2445,f498]) ).
fof(f2445,plain,
( ! [X4] : subclass(singleton(ordered_pair(x,X4)),ordered_pair(singleton(x),singleton(X4)))
| ~ spl0_197 ),
inference(avatar_component_clause,[],[f2444]) ).
fof(f2446,plain,
( spl0_197
| ~ spl0_24
| ~ spl0_194 ),
inference(avatar_split_clause,[],[f2438,f2399,f227,f2444]) ).
fof(f227,plain,
( spl0_24
<=> ! [X0,X1] : subclass(singleton(X1),unordered_pair(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f2438,plain,
( ! [X4] : subclass(singleton(ordered_pair(x,X4)),ordered_pair(singleton(x),singleton(X4)))
| ~ spl0_24
| ~ spl0_194 ),
inference(superposition,[],[f228,f2400]) ).
fof(f228,plain,
( ! [X0,X1] : subclass(singleton(X1),unordered_pair(X0,X1))
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f227]) ).
fof(f2428,plain,
( spl0_196
| ~ spl0_9
| ~ spl0_195 ),
inference(avatar_split_clause,[],[f2422,f2418,f160,f2426]) ).
fof(f2426,plain,
( spl0_196
<=> ! [X4,X5] :
( ~ subclass(X4,null_class)
| ~ subclass(ordered_pair(x,X5),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).
fof(f2422,plain,
( ! [X4,X5] :
( ~ subclass(X4,null_class)
| ~ subclass(ordered_pair(x,X5),X4) )
| ~ spl0_9
| ~ spl0_195 ),
inference(resolution,[],[f2419,f161]) ).
fof(f2420,plain,
( spl0_195
| ~ spl0_65
| ~ spl0_172 ),
inference(avatar_split_clause,[],[f1410,f1407,f473,f2418]) ).
fof(f1410,plain,
( ! [X2,X0,X1] :
( ~ subclass(ordered_pair(x,X0),X1)
| ~ subclass(X1,X2)
| member(singleton(singleton(X0)),X2) )
| ~ spl0_65
| ~ spl0_172 ),
inference(resolution,[],[f1408,f474]) ).
fof(f2401,plain,
( spl0_194
| ~ spl0_142
| ~ spl0_169 ),
inference(avatar_split_clause,[],[f1365,f1360,f1114,f2399]) ).
fof(f1365,plain,
( ! [X1] : ordered_pair(singleton(x),singleton(X1)) = unordered_pair(singleton(singleton(x)),ordered_pair(x,X1))
| ~ spl0_142
| ~ spl0_169 ),
inference(superposition,[],[f1115,f1361]) ).
fof(f2319,plain,
( spl0_193
| ~ spl0_158
| ~ spl0_190 ),
inference(avatar_split_clause,[],[f2311,f1546,f1299,f2317]) ).
fof(f2317,plain,
( spl0_193
<=> ! [X13] : ~ member(ordered_pair(x,X13),element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).
fof(f1299,plain,
( spl0_158
<=> ! [X13] :
( ~ member(ordered_pair(x,X13),element_relation)
| member(y,X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f2311,plain,
( ! [X13] : ~ member(ordered_pair(x,X13),element_relation)
| ~ spl0_158
| ~ spl0_190 ),
inference(subsumption_resolution,[],[f1300,f1547]) ).
fof(f1300,plain,
( ! [X13] :
( ~ member(ordered_pair(x,X13),element_relation)
| member(y,X13) )
| ~ spl0_158 ),
inference(avatar_component_clause,[],[f1299]) ).
fof(f2310,plain,
( ~ spl0_38
| ~ spl0_186
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2309]) ).
fof(f2309,plain,
( $false
| ~ spl0_38
| ~ spl0_186
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1603,f1562]) ).
fof(f1562,plain,
( ! [X0,X1] : subclass(X0,X1)
| ~ spl0_38
| ~ spl0_191 ),
inference(resolution,[],[f1550,f303]) ).
fof(f303,plain,
( ! [X0,X1] :
( member(not_subclass_element(X0,X1),X0)
| subclass(X0,X1) )
| ~ spl0_38 ),
inference(avatar_component_clause,[],[f302]) ).
fof(f302,plain,
( spl0_38
<=> ! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f1550,plain,
( ! [X2,X0] : ~ member(X0,X2)
| ~ spl0_191 ),
inference(avatar_component_clause,[],[f1549]) ).
fof(f1549,plain,
( spl0_191
<=> ! [X2,X0] : ~ member(X0,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).
fof(f1603,plain,
( ! [X40] : ~ subclass(ordered_pair(x,X40),identity_relation)
| ~ spl0_186
| ~ spl0_191 ),
inference(resolution,[],[f1550,f1505]) ).
fof(f2308,plain,
( ~ spl0_38
| ~ spl0_188
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2307]) ).
fof(f2307,plain,
( $false
| ~ spl0_38
| ~ spl0_188
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1600,f1562]) ).
fof(f1600,plain,
( ! [X38] : ~ subclass(ordered_pair(x,X38),identity_relation)
| ~ spl0_188
| ~ spl0_191 ),
inference(resolution,[],[f1550,f1523]) ).
fof(f2306,plain,
( ~ spl0_124
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2305]) ).
fof(f2305,plain,
( $false
| ~ spl0_124
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1598,f1550]) ).
fof(f1598,plain,
( ! [X36] : member(omega,X36)
| ~ spl0_124
| ~ spl0_191 ),
inference(resolution,[],[f1550,f932]) ).
fof(f932,plain,
( ! [X12] :
( member(omega,complement(X12))
| member(omega,X12) )
| ~ spl0_124 ),
inference(avatar_component_clause,[],[f931]) ).
fof(f931,plain,
( spl0_124
<=> ! [X12] :
( member(omega,X12)
| member(omega,complement(X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f2304,plain,
( ~ spl0_123
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2303]) ).
fof(f2303,plain,
( $false
| ~ spl0_123
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1597,f1550]) ).
fof(f1597,plain,
( ! [X35] : member(null_class,X35)
| ~ spl0_123
| ~ spl0_191 ),
inference(resolution,[],[f1550,f928]) ).
fof(f928,plain,
( ! [X11] :
( member(null_class,complement(X11))
| member(null_class,X11) )
| ~ spl0_123 ),
inference(avatar_component_clause,[],[f927]) ).
fof(f927,plain,
( spl0_123
<=> ! [X11] :
( member(null_class,X11)
| member(null_class,complement(X11)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f2302,plain,
( ~ spl0_38
| ~ spl0_172
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2301]) ).
fof(f2301,plain,
( $false
| ~ spl0_38
| ~ spl0_172
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1575,f1562]) ).
fof(f1575,plain,
( ! [X18,X19] : ~ subclass(ordered_pair(x,X18),X19)
| ~ spl0_172
| ~ spl0_191 ),
inference(resolution,[],[f1550,f1408]) ).
fof(f2300,plain,
( ~ spl0_38
| ~ spl0_75
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2299]) ).
fof(f2299,plain,
( $false
| ~ spl0_38
| ~ spl0_75
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1572,f1562]) ).
fof(f1572,plain,
( ! [X15] : ~ subclass(universal_class,X15)
| ~ spl0_75
| ~ spl0_191 ),
inference(resolution,[],[f1550,f535]) ).
fof(f2298,plain,
( ~ spl0_38
| ~ spl0_109
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2297]) ).
fof(f2297,plain,
( $false
| ~ spl0_38
| ~ spl0_109
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1571,f1562]) ).
fof(f1571,plain,
( ! [X14] : ~ subclass(singleton(omega),X14)
| ~ spl0_109
| ~ spl0_191 ),
inference(resolution,[],[f1550,f826]) ).
fof(f826,plain,
( ! [X33] :
( member(omega,X33)
| ~ subclass(singleton(omega),X33) )
| ~ spl0_109 ),
inference(avatar_component_clause,[],[f825]) ).
fof(f825,plain,
( spl0_109
<=> ! [X33] :
( ~ subclass(singleton(omega),X33)
| member(omega,X33) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f2296,plain,
( ~ spl0_38
| ~ spl0_121
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2295]) ).
fof(f2295,plain,
( $false
| ~ spl0_38
| ~ spl0_121
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1570,f1562]) ).
fof(f1570,plain,
( ! [X12,X13] : ~ subclass(unordered_pair(omega,X12),X13)
| ~ spl0_121
| ~ spl0_191 ),
inference(resolution,[],[f1550,f904]) ).
fof(f904,plain,
( ! [X21,X20] :
( member(omega,X21)
| ~ subclass(unordered_pair(omega,X20),X21) )
| ~ spl0_121 ),
inference(avatar_component_clause,[],[f903]) ).
fof(f903,plain,
( spl0_121
<=> ! [X20,X21] :
( ~ subclass(unordered_pair(omega,X20),X21)
| member(omega,X21) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f2294,plain,
( ~ spl0_38
| ~ spl0_126
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2293]) ).
fof(f2293,plain,
( $false
| ~ spl0_38
| ~ spl0_126
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1569,f1562]) ).
fof(f1569,plain,
( ! [X10,X11] : ~ subclass(unordered_pair(X10,omega),X11)
| ~ spl0_126
| ~ spl0_191 ),
inference(resolution,[],[f1550,f963]) ).
fof(f963,plain,
( ! [X31,X30] :
( member(omega,X31)
| ~ subclass(unordered_pair(X30,omega),X31) )
| ~ spl0_126 ),
inference(avatar_component_clause,[],[f962]) ).
fof(f962,plain,
( spl0_126
<=> ! [X30,X31] :
( ~ subclass(unordered_pair(X30,omega),X31)
| member(omega,X31) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f2292,plain,
( ~ spl0_38
| ~ spl0_74
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2291]) ).
fof(f2291,plain,
( $false
| ~ spl0_38
| ~ spl0_74
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1568,f1562]) ).
fof(f1568,plain,
( ! [X9] : ~ subclass(universal_class,X9)
| ~ spl0_74
| ~ spl0_191 ),
inference(resolution,[],[f1550,f531]) ).
fof(f2290,plain,
( ~ spl0_38
| ~ spl0_78
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2289]) ).
fof(f2289,plain,
( $false
| ~ spl0_38
| ~ spl0_78
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1567,f1562]) ).
fof(f1567,plain,
( ! [X8] : ~ subclass(omega,X8)
| ~ spl0_78
| ~ spl0_191 ),
inference(resolution,[],[f1550,f578]) ).
fof(f578,plain,
( ! [X38] :
( member(null_class,X38)
| ~ subclass(omega,X38) )
| ~ spl0_78 ),
inference(avatar_component_clause,[],[f577]) ).
fof(f577,plain,
( spl0_78
<=> ! [X38] :
( ~ subclass(omega,X38)
| member(null_class,X38) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f2288,plain,
( ~ spl0_38
| ~ spl0_108
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2287]) ).
fof(f2287,plain,
( $false
| ~ spl0_38
| ~ spl0_108
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1566,f1562]) ).
fof(f1566,plain,
( ! [X7] : ~ subclass(singleton(null_class),X7)
| ~ spl0_108
| ~ spl0_191 ),
inference(resolution,[],[f1550,f822]) ).
fof(f822,plain,
( ! [X32] :
( member(null_class,X32)
| ~ subclass(singleton(null_class),X32) )
| ~ spl0_108 ),
inference(avatar_component_clause,[],[f821]) ).
fof(f821,plain,
( spl0_108
<=> ! [X32] :
( ~ subclass(singleton(null_class),X32)
| member(null_class,X32) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f2286,plain,
( ~ spl0_38
| ~ spl0_120
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2285]) ).
fof(f2285,plain,
( $false
| ~ spl0_38
| ~ spl0_120
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1565,f1562]) ).
fof(f1565,plain,
( ! [X6,X5] : ~ subclass(unordered_pair(null_class,X5),X6)
| ~ spl0_120
| ~ spl0_191 ),
inference(resolution,[],[f1550,f900]) ).
fof(f900,plain,
( ! [X18,X19] :
( member(null_class,X19)
| ~ subclass(unordered_pair(null_class,X18),X19) )
| ~ spl0_120 ),
inference(avatar_component_clause,[],[f899]) ).
fof(f899,plain,
( spl0_120
<=> ! [X18,X19] :
( ~ subclass(unordered_pair(null_class,X18),X19)
| member(null_class,X19) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f2284,plain,
( ~ spl0_38
| ~ spl0_122
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2283]) ).
fof(f2283,plain,
( $false
| ~ spl0_38
| ~ spl0_122
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1564,f1562]) ).
fof(f1564,plain,
( ! [X3,X4] : ~ subclass(unordered_pair(X3,null_class),X4)
| ~ spl0_122
| ~ spl0_191 ),
inference(resolution,[],[f1550,f908]) ).
fof(f908,plain,
( ! [X28,X29] :
( member(null_class,X29)
| ~ subclass(unordered_pair(X28,null_class),X29) )
| ~ spl0_122 ),
inference(avatar_component_clause,[],[f907]) ).
fof(f907,plain,
( spl0_122
<=> ! [X29,X28] :
( ~ subclass(unordered_pair(X28,null_class),X29)
| member(null_class,X29) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f2282,plain,
( ~ spl0_51
| spl0_105
| ~ spl0_181
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2281]) ).
fof(f2281,plain,
( $false
| ~ spl0_51
| spl0_105
| ~ spl0_181
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f2007,f2017]) ).
fof(f2017,plain,
( ! [X0,X1] : X0 = X1
| ~ spl0_51
| ~ spl0_181
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f2016,f1550]) ).
fof(f2016,plain,
( ! [X0,X1] :
( X0 = X1
| member(not_subclass_element(X1,X0),X1) )
| ~ spl0_51
| ~ spl0_181
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1622,f1550]) ).
fof(f1622,plain,
( ! [X0,X1] :
( member(null_class,X0)
| X0 = X1
| member(not_subclass_element(X1,X0),X1) )
| ~ spl0_51
| ~ spl0_181
| ~ spl0_191 ),
inference(backward_demodulation,[],[f1477,f1563]) ).
fof(f1563,plain,
( ! [X2] : null_class = X2
| ~ spl0_51
| ~ spl0_191 ),
inference(resolution,[],[f1550,f355]) ).
fof(f355,plain,
( ! [X4] :
( member(not_subclass_element(X4,null_class),X4)
| null_class = X4 )
| ~ spl0_51 ),
inference(avatar_component_clause,[],[f354]) ).
fof(f354,plain,
( spl0_51
<=> ! [X4] :
( null_class = X4
| member(not_subclass_element(X4,null_class),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f1477,plain,
( ! [X0,X1] :
( member(not_subclass_element(X1,X0),X1)
| member(not_subclass_element(X0,X1),X0)
| X0 = X1 )
| ~ spl0_181 ),
inference(avatar_component_clause,[],[f1476]) ).
fof(f1476,plain,
( spl0_181
<=> ! [X0,X1] :
( X0 = X1
| member(not_subclass_element(X1,X0),X1)
| member(not_subclass_element(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).
fof(f2007,plain,
( universal_class != null_class
| ~ spl0_51
| spl0_105
| ~ spl0_191 ),
inference(backward_demodulation,[],[f808,f1563]) ).
fof(f808,plain,
( universal_class != subset_relation
| spl0_105 ),
inference(avatar_component_clause,[],[f807]) ).
fof(f807,plain,
( spl0_105
<=> universal_class = subset_relation ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f2280,plain,
( ~ spl0_38
| ~ spl0_51
| spl0_81
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2279]) ).
fof(f2279,plain,
( $false
| ~ spl0_38
| ~ spl0_51
| spl0_81
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1993,f1562]) ).
fof(f1993,plain,
( ~ subclass(subset_relation,null_class)
| ~ spl0_51
| spl0_81
| ~ spl0_191 ),
inference(backward_demodulation,[],[f599,f1563]) ).
fof(f599,plain,
( ~ subclass(subset_relation,identity_relation)
| spl0_81 ),
inference(avatar_component_clause,[],[f597]) ).
fof(f597,plain,
( spl0_81
<=> subclass(subset_relation,identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f2278,plain,
( ~ spl0_51
| spl0_80
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2277]) ).
fof(f2277,plain,
( $false
| ~ spl0_51
| spl0_80
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1992,f1563]) ).
fof(f1992,plain,
( null_class != subset_relation
| ~ spl0_51
| spl0_80
| ~ spl0_191 ),
inference(backward_demodulation,[],[f594,f1563]) ).
fof(f594,plain,
( identity_relation != subset_relation
| spl0_80 ),
inference(avatar_component_clause,[],[f593]) ).
fof(f593,plain,
( spl0_80
<=> identity_relation = subset_relation ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f2276,plain,
( ~ spl0_10
| ~ spl0_51
| spl0_152
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2275]) ).
fof(f2275,plain,
( $false
| ~ spl0_10
| ~ spl0_51
| spl0_152
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1984,f165]) ).
fof(f1984,plain,
( ~ subclass(null_class,subset_relation)
| ~ spl0_51
| spl0_152
| ~ spl0_191 ),
inference(backward_demodulation,[],[f1224,f1563]) ).
fof(f1224,plain,
( ~ subclass(omega,subset_relation)
| spl0_152 ),
inference(avatar_component_clause,[],[f1222]) ).
fof(f1222,plain,
( spl0_152
<=> subclass(omega,subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f2274,plain,
( ~ spl0_10
| ~ spl0_51
| spl0_150
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2273]) ).
fof(f2273,plain,
( $false
| ~ spl0_10
| ~ spl0_51
| spl0_150
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1983,f165]) ).
fof(f1983,plain,
( ~ subclass(null_class,identity_relation)
| ~ spl0_51
| spl0_150
| ~ spl0_191 ),
inference(backward_demodulation,[],[f1182,f1563]) ).
fof(f1182,plain,
( ~ subclass(omega,identity_relation)
| spl0_150 ),
inference(avatar_component_clause,[],[f1180]) ).
fof(f1180,plain,
( spl0_150
<=> subclass(omega,identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f2272,plain,
( ~ spl0_10
| ~ spl0_51
| spl0_79
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2271]) ).
fof(f2271,plain,
( $false
| ~ spl0_10
| ~ spl0_51
| spl0_79
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1982,f165]) ).
fof(f1982,plain,
( ~ subclass(null_class,null_class)
| ~ spl0_51
| spl0_79
| ~ spl0_191 ),
inference(backward_demodulation,[],[f590,f1563]) ).
fof(f590,plain,
( ~ subclass(omega,null_class)
| spl0_79 ),
inference(avatar_component_clause,[],[f588]) ).
fof(f588,plain,
( spl0_79
<=> subclass(omega,null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f2270,plain,
( ~ spl0_10
| ~ spl0_38
| ~ spl0_51
| ~ spl0_65
| ~ spl0_78
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2269]) ).
fof(f2269,plain,
( $false
| ~ spl0_10
| ~ spl0_38
| ~ spl0_51
| ~ spl0_65
| ~ spl0_78
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f2268,f1550]) ).
fof(f2268,plain,
( ! [X1] : member(null_class,X1)
| ~ spl0_10
| ~ spl0_38
| ~ spl0_51
| ~ spl0_65
| ~ spl0_78
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f2267,f1562]) ).
fof(f2267,plain,
( ! [X0,X1] :
( ~ subclass(X0,X1)
| member(null_class,X1) )
| ~ spl0_10
| ~ spl0_51
| ~ spl0_65
| ~ spl0_78
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1981,f165]) ).
fof(f1981,plain,
( ! [X0,X1] :
( ~ subclass(null_class,X0)
| ~ subclass(X0,X1)
| member(null_class,X1) )
| ~ spl0_51
| ~ spl0_65
| ~ spl0_78
| ~ spl0_191 ),
inference(backward_demodulation,[],[f580,f1563]) ).
fof(f580,plain,
( ! [X0,X1] :
( ~ subclass(omega,X0)
| ~ subclass(X0,X1)
| member(null_class,X1) )
| ~ spl0_65
| ~ spl0_78 ),
inference(resolution,[],[f578,f474]) ).
fof(f2266,plain,
( ~ spl0_10
| ~ spl0_51
| ~ spl0_78
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2265]) ).
fof(f2265,plain,
( $false
| ~ spl0_10
| ~ spl0_51
| ~ spl0_78
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f2264,f1550]) ).
fof(f2264,plain,
( ! [X38] : member(null_class,X38)
| ~ spl0_10
| ~ spl0_51
| ~ spl0_78
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1980,f165]) ).
fof(f1980,plain,
( ! [X38] :
( ~ subclass(null_class,X38)
| member(null_class,X38) )
| ~ spl0_51
| ~ spl0_78
| ~ spl0_191 ),
inference(backward_demodulation,[],[f578,f1563]) ).
fof(f2263,plain,
( ~ spl0_9
| ~ spl0_17
| ~ spl0_51
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2262]) ).
fof(f2262,plain,
( $false
| ~ spl0_9
| ~ spl0_17
| ~ spl0_51
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1977,f161]) ).
fof(f1977,plain,
( member(null_class,null_class)
| ~ spl0_17
| ~ spl0_51
| ~ spl0_191 ),
inference(backward_demodulation,[],[f198,f1563]) ).
fof(f198,plain,
( member(null_class,omega)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f196]) ).
fof(f196,plain,
( spl0_17
<=> member(null_class,omega) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f2261,plain,
( ~ spl0_51
| spl0_166
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2260]) ).
fof(f2260,plain,
( $false
| ~ spl0_51
| spl0_166
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1972,f1563]) ).
fof(f1972,plain,
( null_class != y
| ~ spl0_51
| spl0_166
| ~ spl0_191 ),
inference(backward_demodulation,[],[f1347,f1563]) ).
fof(f1347,plain,
( y != successor(y)
| spl0_166 ),
inference(avatar_component_clause,[],[f1346]) ).
fof(f1346,plain,
( spl0_166
<=> y = successor(y) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
fof(f2256,plain,
( ~ spl0_38
| ~ spl0_51
| ~ spl0_104
| ~ spl0_146
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2255]) ).
fof(f2255,plain,
( $false
| ~ spl0_38
| ~ spl0_51
| ~ spl0_104
| ~ spl0_146
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f2254,f1550]) ).
fof(f2254,plain,
( ! [X6] : member(null_class,X6)
| ~ spl0_38
| ~ spl0_51
| ~ spl0_104
| ~ spl0_146
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1950,f1562]) ).
fof(f1950,plain,
( ! [X6] :
( ~ subclass(omega,null_class)
| member(null_class,X6) )
| ~ spl0_51
| ~ spl0_104
| ~ spl0_146
| ~ spl0_191 ),
inference(backward_demodulation,[],[f1172,f1563]) ).
fof(f1172,plain,
( ! [X6,X4,X5] :
( ~ subclass(omega,restrict(X6,X4,X5))
| member(null_class,X6) )
| ~ spl0_104
| ~ spl0_146 ),
inference(superposition,[],[f1160,f804]) ).
fof(f1160,plain,
( ! [X4,X5] :
( ~ subclass(omega,intersection(X4,X5))
| member(null_class,X5) )
| ~ spl0_146 ),
inference(avatar_component_clause,[],[f1159]) ).
fof(f1159,plain,
( spl0_146
<=> ! [X4,X5] :
( ~ subclass(omega,intersection(X4,X5))
| member(null_class,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f2253,plain,
( ~ spl0_49
| ~ spl0_51
| ~ spl0_124
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2252]) ).
fof(f2252,plain,
( $false
| ~ spl0_49
| ~ spl0_51
| ~ spl0_124
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f2251,f1550]) ).
fof(f2251,plain,
( ! [X0] : member(omega,power_class(X0))
| ~ spl0_49
| ~ spl0_51
| ~ spl0_124
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1941,f1550]) ).
fof(f1941,plain,
( ! [X0] :
( member(omega,image(element_relation,null_class))
| member(omega,power_class(X0)) )
| ~ spl0_49
| ~ spl0_51
| ~ spl0_124
| ~ spl0_191 ),
inference(backward_demodulation,[],[f939,f1563]) ).
fof(f939,plain,
( ! [X0] :
( member(omega,power_class(X0))
| member(omega,image(element_relation,complement(X0))) )
| ~ spl0_49
| ~ spl0_124 ),
inference(superposition,[],[f932,f347]) ).
fof(f2250,plain,
( ~ spl0_10
| ~ spl0_51
| ~ spl0_65
| ~ spl0_124
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2249]) ).
fof(f2249,plain,
( $false
| ~ spl0_10
| ~ spl0_51
| ~ spl0_65
| ~ spl0_124
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f2248,f1550]) ).
fof(f2248,plain,
( ! [X2] : member(omega,X2)
| ~ spl0_10
| ~ spl0_51
| ~ spl0_65
| ~ spl0_124
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f2247,f1550]) ).
fof(f2247,plain,
( ! [X2,X1] :
( member(omega,X1)
| member(omega,X2) )
| ~ spl0_10
| ~ spl0_51
| ~ spl0_65
| ~ spl0_124
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1940,f165]) ).
fof(f1940,plain,
( ! [X2,X1] :
( ~ subclass(null_class,X2)
| member(omega,X1)
| member(omega,X2) )
| ~ spl0_51
| ~ spl0_65
| ~ spl0_124
| ~ spl0_191 ),
inference(backward_demodulation,[],[f938,f1563]) ).
fof(f938,plain,
( ! [X2,X1] :
( member(omega,X1)
| ~ subclass(complement(X1),X2)
| member(omega,X2) )
| ~ spl0_65
| ~ spl0_124 ),
inference(resolution,[],[f932,f474]) ).
fof(f2246,plain,
( ~ spl0_49
| ~ spl0_51
| ~ spl0_123
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2245]) ).
fof(f2245,plain,
( $false
| ~ spl0_49
| ~ spl0_51
| ~ spl0_123
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f2244,f1550]) ).
fof(f2244,plain,
( ! [X0] : member(null_class,power_class(X0))
| ~ spl0_49
| ~ spl0_51
| ~ spl0_123
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1939,f1550]) ).
fof(f1939,plain,
( ! [X0] :
( member(null_class,image(element_relation,null_class))
| member(null_class,power_class(X0)) )
| ~ spl0_49
| ~ spl0_51
| ~ spl0_123
| ~ spl0_191 ),
inference(backward_demodulation,[],[f936,f1563]) ).
fof(f936,plain,
( ! [X0] :
( member(null_class,power_class(X0))
| member(null_class,image(element_relation,complement(X0))) )
| ~ spl0_49
| ~ spl0_123 ),
inference(superposition,[],[f928,f347]) ).
fof(f2243,plain,
( ~ spl0_10
| ~ spl0_51
| ~ spl0_65
| ~ spl0_123
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2242]) ).
fof(f2242,plain,
( $false
| ~ spl0_10
| ~ spl0_51
| ~ spl0_65
| ~ spl0_123
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f2241,f1550]) ).
fof(f2241,plain,
( ! [X2] : member(null_class,X2)
| ~ spl0_10
| ~ spl0_51
| ~ spl0_65
| ~ spl0_123
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f2240,f1550]) ).
fof(f2240,plain,
( ! [X2,X1] :
( member(null_class,X1)
| member(null_class,X2) )
| ~ spl0_10
| ~ spl0_51
| ~ spl0_65
| ~ spl0_123
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1938,f165]) ).
fof(f1938,plain,
( ! [X2,X1] :
( ~ subclass(null_class,X2)
| member(null_class,X1)
| member(null_class,X2) )
| ~ spl0_51
| ~ spl0_65
| ~ spl0_123
| ~ spl0_191 ),
inference(backward_demodulation,[],[f935,f1563]) ).
fof(f935,plain,
( ! [X2,X1] :
( member(null_class,X1)
| ~ subclass(complement(X1),X2)
| member(null_class,X2) )
| ~ spl0_65
| ~ spl0_123 ),
inference(resolution,[],[f928,f474]) ).
fof(f2239,plain,
( ~ spl0_9
| ~ spl0_51
| ~ spl0_124
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2238]) ).
fof(f2238,plain,
( $false
| ~ spl0_9
| ~ spl0_51
| ~ spl0_124
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f2237,f1550]) ).
fof(f2237,plain,
( ! [X12] : member(omega,X12)
| ~ spl0_9
| ~ spl0_51
| ~ spl0_124
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1937,f161]) ).
fof(f1937,plain,
( ! [X12] :
( member(omega,null_class)
| member(omega,X12) )
| ~ spl0_51
| ~ spl0_124
| ~ spl0_191 ),
inference(backward_demodulation,[],[f932,f1563]) ).
fof(f2236,plain,
( ~ spl0_9
| ~ spl0_51
| ~ spl0_123
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2235]) ).
fof(f2235,plain,
( $false
| ~ spl0_9
| ~ spl0_51
| ~ spl0_123
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f2234,f1550]) ).
fof(f2234,plain,
( ! [X11] : member(null_class,X11)
| ~ spl0_9
| ~ spl0_51
| ~ spl0_123
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1936,f161]) ).
fof(f1936,plain,
( ! [X11] :
( member(null_class,null_class)
| member(null_class,X11) )
| ~ spl0_51
| ~ spl0_123
| ~ spl0_191 ),
inference(backward_demodulation,[],[f928,f1563]) ).
fof(f2233,plain,
( ~ spl0_9
| ~ spl0_51
| ~ spl0_100
| ~ spl0_124
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2232]) ).
fof(f2232,plain,
( $false
| ~ spl0_9
| ~ spl0_51
| ~ spl0_100
| ~ spl0_124
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f2231,f1550]) ).
fof(f2231,plain,
( ! [X16,X15] : member(omega,union(X15,X16))
| ~ spl0_9
| ~ spl0_51
| ~ spl0_100
| ~ spl0_124
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1918,f161]) ).
fof(f1918,plain,
( ! [X16,X15] :
( member(omega,null_class)
| member(omega,union(X15,X16)) )
| ~ spl0_51
| ~ spl0_100
| ~ spl0_124
| ~ spl0_191 ),
inference(backward_demodulation,[],[f952,f1563]) ).
fof(f952,plain,
( ! [X16,X15] :
( member(omega,union(X15,X16))
| member(omega,intersection(complement(X15),complement(X16))) )
| ~ spl0_100
| ~ spl0_124 ),
inference(superposition,[],[f932,f778]) ).
fof(f2230,plain,
( ~ spl0_9
| ~ spl0_51
| ~ spl0_100
| ~ spl0_123
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2229]) ).
fof(f2229,plain,
( $false
| ~ spl0_9
| ~ spl0_51
| ~ spl0_100
| ~ spl0_123
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f2228,f1550]) ).
fof(f2228,plain,
( ! [X14,X13] : member(null_class,union(X13,X14))
| ~ spl0_9
| ~ spl0_51
| ~ spl0_100
| ~ spl0_123
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1917,f161]) ).
fof(f1917,plain,
( ! [X14,X13] :
( member(null_class,null_class)
| member(null_class,union(X13,X14)) )
| ~ spl0_51
| ~ spl0_100
| ~ spl0_123
| ~ spl0_191 ),
inference(backward_demodulation,[],[f951,f1563]) ).
fof(f951,plain,
( ! [X14,X13] :
( member(null_class,union(X13,X14))
| member(null_class,intersection(complement(X13),complement(X14))) )
| ~ spl0_100
| ~ spl0_123 ),
inference(superposition,[],[f928,f778]) ).
fof(f2227,plain,
( ~ spl0_38
| ~ spl0_51
| ~ spl0_147
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2226]) ).
fof(f2226,plain,
( $false
| ~ spl0_38
| ~ spl0_51
| ~ spl0_147
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f2225,f1550]) ).
fof(f2225,plain,
( ! [X6] : member(null_class,X6)
| ~ spl0_38
| ~ spl0_51
| ~ spl0_147
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1905,f1562]) ).
fof(f1905,plain,
( ! [X6] :
( ~ subclass(omega,null_class)
| member(null_class,X6) )
| ~ spl0_51
| ~ spl0_147
| ~ spl0_191 ),
inference(backward_demodulation,[],[f1164,f1563]) ).
fof(f1164,plain,
( ! [X6,X7] :
( ~ subclass(omega,intersection(X6,X7))
| member(null_class,X6) )
| ~ spl0_147 ),
inference(avatar_component_clause,[],[f1163]) ).
fof(f1163,plain,
( spl0_147
<=> ! [X6,X7] :
( ~ subclass(omega,intersection(X6,X7))
| member(null_class,X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f2224,plain,
( ~ spl0_38
| ~ spl0_51
| ~ spl0_146
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2223]) ).
fof(f2223,plain,
( $false
| ~ spl0_38
| ~ spl0_51
| ~ spl0_146
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f2222,f1550]) ).
fof(f2222,plain,
( ! [X5] : member(null_class,X5)
| ~ spl0_38
| ~ spl0_51
| ~ spl0_146
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1904,f1562]) ).
fof(f1904,plain,
( ! [X5] :
( ~ subclass(omega,null_class)
| member(null_class,X5) )
| ~ spl0_51
| ~ spl0_146
| ~ spl0_191 ),
inference(backward_demodulation,[],[f1160,f1563]) ).
fof(f2216,plain,
( ~ spl0_51
| spl0_133
| ~ spl0_181
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2215]) ).
fof(f2215,plain,
( $false
| ~ spl0_51
| spl0_133
| ~ spl0_181
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1891,f2017]) ).
fof(f1891,plain,
( universal_class != null_class
| ~ spl0_51
| spl0_133
| ~ spl0_191 ),
inference(backward_demodulation,[],[f1001,f1563]) ).
fof(f1001,plain,
( universal_class != cross_product(universal_class,universal_class)
| spl0_133 ),
inference(avatar_component_clause,[],[f1000]) ).
fof(f1000,plain,
( spl0_133
<=> universal_class = cross_product(universal_class,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f2214,plain,
( ~ spl0_9
| ~ spl0_38
| ~ spl0_51
| ~ spl0_102
| ~ spl0_146
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2213]) ).
fof(f2213,plain,
( $false
| ~ spl0_9
| ~ spl0_38
| ~ spl0_51
| ~ spl0_102
| ~ spl0_146
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f2212,f1562]) ).
fof(f2212,plain,
( ! [X2,X3,X1] : ~ subclass(omega,restrict(X1,X2,X3))
| ~ spl0_9
| ~ spl0_51
| ~ spl0_102
| ~ spl0_146
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1865,f161]) ).
fof(f1865,plain,
( ! [X2,X3,X1] :
( member(null_class,null_class)
| ~ subclass(omega,restrict(X1,X2,X3)) )
| ~ spl0_51
| ~ spl0_102
| ~ spl0_146
| ~ spl0_191 ),
inference(backward_demodulation,[],[f1171,f1563]) ).
fof(f1171,plain,
( ! [X2,X3,X1] :
( ~ subclass(omega,restrict(X1,X2,X3))
| member(null_class,cross_product(X2,X3)) )
| ~ spl0_102
| ~ spl0_146 ),
inference(superposition,[],[f1160,f786]) ).
fof(f2211,plain,
( ~ spl0_9
| ~ spl0_38
| ~ spl0_51
| ~ spl0_102
| ~ spl0_129
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2210]) ).
fof(f2210,plain,
( $false
| ~ spl0_9
| ~ spl0_38
| ~ spl0_51
| ~ spl0_102
| ~ spl0_129
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f2209,f1562]) ).
fof(f2209,plain,
( ! [X2,X3,X1] : ~ subclass(universal_class,restrict(X1,X2,X3))
| ~ spl0_9
| ~ spl0_51
| ~ spl0_102
| ~ spl0_129
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1864,f161]) ).
fof(f1864,plain,
( ! [X2,X3,X1] :
( member(omega,null_class)
| ~ subclass(universal_class,restrict(X1,X2,X3)) )
| ~ spl0_51
| ~ spl0_102
| ~ spl0_129
| ~ spl0_191 ),
inference(backward_demodulation,[],[f1128,f1563]) ).
fof(f1128,plain,
( ! [X2,X3,X1] :
( ~ subclass(universal_class,restrict(X1,X2,X3))
| member(omega,cross_product(X2,X3)) )
| ~ spl0_102
| ~ spl0_129 ),
inference(superposition,[],[f979,f786]) ).
fof(f979,plain,
( ! [X4,X5] :
( ~ subclass(universal_class,intersection(X4,X5))
| member(omega,X5) )
| ~ spl0_129 ),
inference(avatar_component_clause,[],[f978]) ).
fof(f978,plain,
( spl0_129
<=> ! [X4,X5] :
( ~ subclass(universal_class,intersection(X4,X5))
| member(omega,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f2208,plain,
( ~ spl0_9
| ~ spl0_38
| ~ spl0_51
| ~ spl0_102
| ~ spl0_127
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2207]) ).
fof(f2207,plain,
( $false
| ~ spl0_9
| ~ spl0_38
| ~ spl0_51
| ~ spl0_102
| ~ spl0_127
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f2206,f1562]) ).
fof(f2206,plain,
( ! [X2,X3,X1] : ~ subclass(universal_class,restrict(X1,X2,X3))
| ~ spl0_9
| ~ spl0_51
| ~ spl0_102
| ~ spl0_127
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1863,f161]) ).
fof(f1863,plain,
( ! [X2,X3,X1] :
( member(null_class,null_class)
| ~ subclass(universal_class,restrict(X1,X2,X3)) )
| ~ spl0_51
| ~ spl0_102
| ~ spl0_127
| ~ spl0_191 ),
inference(backward_demodulation,[],[f1118,f1563]) ).
fof(f1118,plain,
( ! [X2,X3,X1] :
( ~ subclass(universal_class,restrict(X1,X2,X3))
| member(null_class,cross_product(X2,X3)) )
| ~ spl0_102
| ~ spl0_127 ),
inference(superposition,[],[f971,f786]) ).
fof(f971,plain,
( ! [X4,X5] :
( ~ subclass(universal_class,intersection(X4,X5))
| member(null_class,X5) )
| ~ spl0_127 ),
inference(avatar_component_clause,[],[f970]) ).
fof(f970,plain,
( spl0_127
<=> ! [X4,X5] :
( ~ subclass(universal_class,intersection(X4,X5))
| member(null_class,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f2205,plain,
( ~ spl0_10
| ~ spl0_51
| ~ spl0_173
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2204]) ).
fof(f2204,plain,
( $false
| ~ spl0_10
| ~ spl0_51
| ~ spl0_173
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1854,f165]) ).
fof(f1854,plain,
( ~ subclass(null_class,null_class)
| ~ spl0_51
| ~ spl0_173
| ~ spl0_191 ),
inference(backward_demodulation,[],[f1424,f1563]) ).
fof(f1424,plain,
( ! [X23] : ~ subclass(ordered_pair(x,X23),null_class)
| ~ spl0_173 ),
inference(avatar_component_clause,[],[f1423]) ).
fof(f1423,plain,
( spl0_173
<=> ! [X23] : ~ subclass(ordered_pair(x,X23),null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).
fof(f2202,plain,
( ~ spl0_10
| ~ spl0_51
| spl0_114
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2201]) ).
fof(f2201,plain,
( $false
| ~ spl0_10
| ~ spl0_51
| spl0_114
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1810,f165]) ).
fof(f1810,plain,
( ~ subclass(null_class,null_class)
| ~ spl0_51
| spl0_114
| ~ spl0_191 ),
inference(backward_demodulation,[],[f862,f1563]) ).
fof(f862,plain,
( ~ subclass(singleton(omega),null_class)
| spl0_114 ),
inference(avatar_component_clause,[],[f860]) ).
fof(f860,plain,
( spl0_114
<=> subclass(singleton(omega),null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f2200,plain,
( ~ spl0_10
| ~ spl0_43
| ~ spl0_51
| ~ spl0_109
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2199]) ).
fof(f2199,plain,
( $false
| ~ spl0_10
| ~ spl0_43
| ~ spl0_51
| ~ spl0_109
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f2198,f1550]) ).
fof(f2198,plain,
( ! [X6] : member(omega,X6)
| ~ spl0_10
| ~ spl0_43
| ~ spl0_51
| ~ spl0_109
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1808,f165]) ).
fof(f1808,plain,
( ! [X6,X7] :
( ~ subclass(null_class,intersection(X6,X7))
| member(omega,X6) )
| ~ spl0_43
| ~ spl0_51
| ~ spl0_109
| ~ spl0_191 ),
inference(backward_demodulation,[],[f856,f1563]) ).
fof(f856,plain,
( ! [X6,X7] :
( ~ subclass(singleton(omega),intersection(X6,X7))
| member(omega,X6) )
| ~ spl0_43
| ~ spl0_109 ),
inference(resolution,[],[f826,f323]) ).
fof(f2197,plain,
( ~ spl0_10
| ~ spl0_44
| ~ spl0_51
| ~ spl0_109
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2196]) ).
fof(f2196,plain,
( $false
| ~ spl0_10
| ~ spl0_44
| ~ spl0_51
| ~ spl0_109
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f2195,f1550]) ).
fof(f2195,plain,
( ! [X5] : member(omega,X5)
| ~ spl0_10
| ~ spl0_44
| ~ spl0_51
| ~ spl0_109
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1807,f165]) ).
fof(f1807,plain,
( ! [X4,X5] :
( ~ subclass(null_class,intersection(X4,X5))
| member(omega,X5) )
| ~ spl0_44
| ~ spl0_51
| ~ spl0_109
| ~ spl0_191 ),
inference(backward_demodulation,[],[f855,f1563]) ).
fof(f855,plain,
( ! [X4,X5] :
( ~ subclass(singleton(omega),intersection(X4,X5))
| member(omega,X5) )
| ~ spl0_44
| ~ spl0_109 ),
inference(resolution,[],[f826,f327]) ).
fof(f2194,plain,
( ~ spl0_10
| ~ spl0_38
| ~ spl0_51
| ~ spl0_65
| ~ spl0_109
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2193]) ).
fof(f2193,plain,
( $false
| ~ spl0_10
| ~ spl0_38
| ~ spl0_51
| ~ spl0_65
| ~ spl0_109
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f2192,f1550]) ).
fof(f2192,plain,
( ! [X1] : member(omega,X1)
| ~ spl0_10
| ~ spl0_38
| ~ spl0_51
| ~ spl0_65
| ~ spl0_109
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f2191,f1562]) ).
fof(f2191,plain,
( ! [X0,X1] :
( ~ subclass(X0,X1)
| member(omega,X1) )
| ~ spl0_10
| ~ spl0_51
| ~ spl0_65
| ~ spl0_109
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1806,f165]) ).
fof(f1806,plain,
( ! [X0,X1] :
( ~ subclass(null_class,X0)
| ~ subclass(X0,X1)
| member(omega,X1) )
| ~ spl0_51
| ~ spl0_65
| ~ spl0_109
| ~ spl0_191 ),
inference(backward_demodulation,[],[f852,f1563]) ).
fof(f852,plain,
( ! [X0,X1] :
( ~ subclass(singleton(omega),X0)
| ~ subclass(X0,X1)
| member(omega,X1) )
| ~ spl0_65
| ~ spl0_109 ),
inference(resolution,[],[f826,f474]) ).
fof(f2190,plain,
( ~ spl0_10
| ~ spl0_51
| ~ spl0_109
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2189]) ).
fof(f2189,plain,
( $false
| ~ spl0_10
| ~ spl0_51
| ~ spl0_109
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f2188,f1550]) ).
fof(f2188,plain,
( ! [X33] : member(omega,X33)
| ~ spl0_10
| ~ spl0_51
| ~ spl0_109
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1805,f165]) ).
fof(f1805,plain,
( ! [X33] :
( ~ subclass(null_class,X33)
| member(omega,X33) )
| ~ spl0_51
| ~ spl0_109
| ~ spl0_191 ),
inference(backward_demodulation,[],[f826,f1563]) ).
fof(f2187,plain,
( ~ spl0_9
| ~ spl0_51
| ~ spl0_57
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2186]) ).
fof(f2186,plain,
( $false
| ~ spl0_9
| ~ spl0_51
| ~ spl0_57
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1804,f161]) ).
fof(f1804,plain,
( member(omega,null_class)
| ~ spl0_51
| ~ spl0_57
| ~ spl0_191 ),
inference(backward_demodulation,[],[f411,f1563]) ).
fof(f411,plain,
( member(omega,singleton(omega))
| ~ spl0_57 ),
inference(avatar_component_clause,[],[f409]) ).
fof(f409,plain,
( spl0_57
<=> member(omega,singleton(omega)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f2185,plain,
( ~ spl0_10
| ~ spl0_51
| ~ spl0_108
| spl0_149
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2184]) ).
fof(f2184,plain,
( $false
| ~ spl0_10
| ~ spl0_51
| ~ spl0_108
| spl0_149
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1802,f165]) ).
fof(f1802,plain,
( ~ subclass(null_class,subset_relation)
| ~ spl0_51
| ~ spl0_108
| spl0_149
| ~ spl0_191 ),
inference(backward_demodulation,[],[f1187,f1563]) ).
fof(f1187,plain,
( ~ subclass(singleton(null_class),subset_relation)
| ~ spl0_108
| spl0_149 ),
inference(resolution,[],[f1177,f822]) ).
fof(f1177,plain,
( ~ member(null_class,subset_relation)
| spl0_149 ),
inference(avatar_component_clause,[],[f1176]) ).
fof(f1176,plain,
( spl0_149
<=> member(null_class,subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f2183,plain,
( ~ spl0_10
| ~ spl0_51
| spl0_112
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2182]) ).
fof(f2182,plain,
( $false
| ~ spl0_10
| ~ spl0_51
| spl0_112
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1799,f165]) ).
fof(f1799,plain,
( ~ subclass(null_class,null_class)
| ~ spl0_51
| spl0_112
| ~ spl0_191 ),
inference(backward_demodulation,[],[f846,f1563]) ).
fof(f846,plain,
( ~ subclass(singleton(null_class),null_class)
| spl0_112 ),
inference(avatar_component_clause,[],[f844]) ).
fof(f844,plain,
( spl0_112
<=> subclass(singleton(null_class),null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f2181,plain,
( ~ spl0_10
| ~ spl0_43
| ~ spl0_51
| ~ spl0_108
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2180]) ).
fof(f2180,plain,
( $false
| ~ spl0_10
| ~ spl0_43
| ~ spl0_51
| ~ spl0_108
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f2179,f1550]) ).
fof(f2179,plain,
( ! [X6] : member(null_class,X6)
| ~ spl0_10
| ~ spl0_43
| ~ spl0_51
| ~ spl0_108
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1797,f165]) ).
fof(f1797,plain,
( ! [X6,X7] :
( ~ subclass(null_class,intersection(X6,X7))
| member(null_class,X6) )
| ~ spl0_43
| ~ spl0_51
| ~ spl0_108
| ~ spl0_191 ),
inference(backward_demodulation,[],[f840,f1563]) ).
fof(f840,plain,
( ! [X6,X7] :
( ~ subclass(singleton(null_class),intersection(X6,X7))
| member(null_class,X6) )
| ~ spl0_43
| ~ spl0_108 ),
inference(resolution,[],[f822,f323]) ).
fof(f2178,plain,
( ~ spl0_10
| ~ spl0_44
| ~ spl0_51
| ~ spl0_108
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2177]) ).
fof(f2177,plain,
( $false
| ~ spl0_10
| ~ spl0_44
| ~ spl0_51
| ~ spl0_108
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f2176,f1550]) ).
fof(f2176,plain,
( ! [X5] : member(null_class,X5)
| ~ spl0_10
| ~ spl0_44
| ~ spl0_51
| ~ spl0_108
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1796,f165]) ).
fof(f1796,plain,
( ! [X4,X5] :
( ~ subclass(null_class,intersection(X4,X5))
| member(null_class,X5) )
| ~ spl0_44
| ~ spl0_51
| ~ spl0_108
| ~ spl0_191 ),
inference(backward_demodulation,[],[f839,f1563]) ).
fof(f839,plain,
( ! [X4,X5] :
( ~ subclass(singleton(null_class),intersection(X4,X5))
| member(null_class,X5) )
| ~ spl0_44
| ~ spl0_108 ),
inference(resolution,[],[f822,f327]) ).
fof(f2175,plain,
( ~ spl0_10
| ~ spl0_38
| ~ spl0_51
| ~ spl0_65
| ~ spl0_108
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2174]) ).
fof(f2174,plain,
( $false
| ~ spl0_10
| ~ spl0_38
| ~ spl0_51
| ~ spl0_65
| ~ spl0_108
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f2173,f1550]) ).
fof(f2173,plain,
( ! [X1] : member(null_class,X1)
| ~ spl0_10
| ~ spl0_38
| ~ spl0_51
| ~ spl0_65
| ~ spl0_108
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f2172,f1562]) ).
fof(f2172,plain,
( ! [X0,X1] :
( ~ subclass(X0,X1)
| member(null_class,X1) )
| ~ spl0_10
| ~ spl0_51
| ~ spl0_65
| ~ spl0_108
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1795,f165]) ).
fof(f1795,plain,
( ! [X0,X1] :
( ~ subclass(null_class,X0)
| ~ subclass(X0,X1)
| member(null_class,X1) )
| ~ spl0_51
| ~ spl0_65
| ~ spl0_108
| ~ spl0_191 ),
inference(backward_demodulation,[],[f836,f1563]) ).
fof(f836,plain,
( ! [X0,X1] :
( ~ subclass(singleton(null_class),X0)
| ~ subclass(X0,X1)
| member(null_class,X1) )
| ~ spl0_65
| ~ spl0_108 ),
inference(resolution,[],[f822,f474]) ).
fof(f2171,plain,
( ~ spl0_10
| ~ spl0_51
| ~ spl0_108
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2170]) ).
fof(f2170,plain,
( $false
| ~ spl0_10
| ~ spl0_51
| ~ spl0_108
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f2169,f1550]) ).
fof(f2169,plain,
( ! [X32] : member(null_class,X32)
| ~ spl0_10
| ~ spl0_51
| ~ spl0_108
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1794,f165]) ).
fof(f1794,plain,
( ! [X32] :
( ~ subclass(null_class,X32)
| member(null_class,X32) )
| ~ spl0_51
| ~ spl0_108
| ~ spl0_191 ),
inference(backward_demodulation,[],[f822,f1563]) ).
fof(f2168,plain,
( ~ spl0_9
| ~ spl0_51
| ~ spl0_56
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2167]) ).
fof(f2167,plain,
( $false
| ~ spl0_9
| ~ spl0_51
| ~ spl0_56
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1793,f161]) ).
fof(f1793,plain,
( member(null_class,null_class)
| ~ spl0_51
| ~ spl0_56
| ~ spl0_191 ),
inference(backward_demodulation,[],[f399,f1563]) ).
fof(f399,plain,
( member(null_class,singleton(null_class))
| ~ spl0_56 ),
inference(avatar_component_clause,[],[f397]) ).
fof(f397,plain,
( spl0_56
<=> member(null_class,singleton(null_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f2166,plain,
( ~ spl0_38
| ~ spl0_51
| ~ spl0_65
| ~ spl0_188
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2165]) ).
fof(f2165,plain,
( $false
| ~ spl0_38
| ~ spl0_51
| ~ spl0_65
| ~ spl0_188
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f2164,f1562]) ).
fof(f2164,plain,
( ! [X1] : ~ subclass(inverse(subset_relation),X1)
| ~ spl0_38
| ~ spl0_51
| ~ spl0_65
| ~ spl0_188
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f2163,f1562]) ).
fof(f2163,plain,
( ! [X0,X1] :
( ~ subclass(ordered_pair(x,X0),identity_relation)
| ~ subclass(inverse(subset_relation),X1) )
| ~ spl0_51
| ~ spl0_65
| ~ spl0_188
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1792,f1550]) ).
fof(f1792,plain,
( ! [X0,X1] :
( member(singleton(null_class),X1)
| ~ subclass(ordered_pair(x,X0),identity_relation)
| ~ subclass(inverse(subset_relation),X1) )
| ~ spl0_51
| ~ spl0_65
| ~ spl0_188
| ~ spl0_191 ),
inference(backward_demodulation,[],[f1525,f1563]) ).
fof(f2162,plain,
( ~ spl0_38
| ~ spl0_51
| ~ spl0_188
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2161]) ).
fof(f2161,plain,
( $false
| ~ spl0_38
| ~ spl0_51
| ~ spl0_188
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f2160,f1562]) ).
fof(f2160,plain,
( ! [X12] : ~ subclass(ordered_pair(x,X12),identity_relation)
| ~ spl0_51
| ~ spl0_188
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1791,f1550]) ).
fof(f1791,plain,
( ! [X12] :
( member(singleton(null_class),inverse(subset_relation))
| ~ subclass(ordered_pair(x,X12),identity_relation) )
| ~ spl0_51
| ~ spl0_188
| ~ spl0_191 ),
inference(backward_demodulation,[],[f1523,f1563]) ).
fof(f2159,plain,
( ~ spl0_38
| ~ spl0_51
| ~ spl0_65
| ~ spl0_186
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2158]) ).
fof(f2158,plain,
( $false
| ~ spl0_38
| ~ spl0_51
| ~ spl0_65
| ~ spl0_186
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f2157,f1562]) ).
fof(f2157,plain,
( ! [X1] : ~ subclass(subset_relation,X1)
| ~ spl0_38
| ~ spl0_51
| ~ spl0_65
| ~ spl0_186
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f2156,f1562]) ).
fof(f2156,plain,
( ! [X0,X1] :
( ~ subclass(ordered_pair(x,X0),identity_relation)
| ~ subclass(subset_relation,X1) )
| ~ spl0_51
| ~ spl0_65
| ~ spl0_186
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1790,f1550]) ).
fof(f1790,plain,
( ! [X0,X1] :
( member(singleton(null_class),X1)
| ~ subclass(ordered_pair(x,X0),identity_relation)
| ~ subclass(subset_relation,X1) )
| ~ spl0_51
| ~ spl0_65
| ~ spl0_186
| ~ spl0_191 ),
inference(backward_demodulation,[],[f1507,f1563]) ).
fof(f2155,plain,
( ~ spl0_38
| ~ spl0_51
| ~ spl0_186
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2154]) ).
fof(f2154,plain,
( $false
| ~ spl0_38
| ~ spl0_51
| ~ spl0_186
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f2153,f1562]) ).
fof(f2153,plain,
( ! [X12] : ~ subclass(ordered_pair(x,X12),identity_relation)
| ~ spl0_51
| ~ spl0_186
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1789,f1550]) ).
fof(f1789,plain,
( ! [X12] :
( member(singleton(null_class),subset_relation)
| ~ subclass(ordered_pair(x,X12),identity_relation) )
| ~ spl0_51
| ~ spl0_186
| ~ spl0_191 ),
inference(backward_demodulation,[],[f1505,f1563]) ).
fof(f2152,plain,
( ~ spl0_38
| ~ spl0_51
| ~ spl0_104
| ~ spl0_183
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2151]) ).
fof(f2151,plain,
( $false
| ~ spl0_38
| ~ spl0_51
| ~ spl0_104
| ~ spl0_183
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f2150,f1562]) ).
fof(f2150,plain,
( ! [X8,X6,X9,X7] : ~ subclass(ordered_pair(x,X9),restrict(X8,X6,X7))
| ~ spl0_51
| ~ spl0_104
| ~ spl0_183
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1788,f1550]) ).
fof(f1788,plain,
( ! [X8,X6,X9,X7] :
( member(singleton(null_class),X8)
| ~ subclass(ordered_pair(x,X9),restrict(X8,X6,X7)) )
| ~ spl0_51
| ~ spl0_104
| ~ spl0_183
| ~ spl0_191 ),
inference(backward_demodulation,[],[f1499,f1563]) ).
fof(f2149,plain,
( ~ spl0_38
| ~ spl0_51
| ~ spl0_102
| ~ spl0_183
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2148]) ).
fof(f2148,plain,
( $false
| ~ spl0_38
| ~ spl0_51
| ~ spl0_102
| ~ spl0_183
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f2147,f1562]) ).
fof(f2147,plain,
( ! [X2,X3,X4,X5] : ~ subclass(ordered_pair(x,X5),restrict(X2,X3,X4))
| ~ spl0_51
| ~ spl0_102
| ~ spl0_183
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1787,f1550]) ).
fof(f1787,plain,
( ! [X2,X3,X4,X5] :
( member(singleton(null_class),cross_product(X3,X4))
| ~ subclass(ordered_pair(x,X5),restrict(X2,X3,X4)) )
| ~ spl0_51
| ~ spl0_102
| ~ spl0_183
| ~ spl0_191 ),
inference(backward_demodulation,[],[f1498,f1563]) ).
fof(f2146,plain,
( ~ spl0_38
| ~ spl0_51
| ~ spl0_184
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2145]) ).
fof(f2145,plain,
( $false
| ~ spl0_38
| ~ spl0_51
| ~ spl0_184
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f2144,f1562]) ).
fof(f2144,plain,
( ! [X18,X19,X20] : ~ subclass(ordered_pair(x,X18),intersection(X19,X20))
| ~ spl0_51
| ~ spl0_184
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1786,f1550]) ).
fof(f1786,plain,
( ! [X18,X19,X20] :
( member(singleton(null_class),X19)
| ~ subclass(ordered_pair(x,X18),intersection(X19,X20)) )
| ~ spl0_51
| ~ spl0_184
| ~ spl0_191 ),
inference(backward_demodulation,[],[f1490,f1563]) ).
fof(f1490,plain,
( ! [X18,X19,X20] :
( ~ subclass(ordered_pair(x,X18),intersection(X19,X20))
| member(singleton(singleton(X18)),X19) )
| ~ spl0_184 ),
inference(avatar_component_clause,[],[f1489]) ).
fof(f1489,plain,
( spl0_184
<=> ! [X20,X18,X19] :
( ~ subclass(ordered_pair(x,X18),intersection(X19,X20))
| member(singleton(singleton(X18)),X19) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).
fof(f2143,plain,
( ~ spl0_38
| ~ spl0_51
| ~ spl0_183
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2142]) ).
fof(f2142,plain,
( $false
| ~ spl0_38
| ~ spl0_51
| ~ spl0_183
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f2141,f1562]) ).
fof(f2141,plain,
( ! [X16,X17,X15] : ~ subclass(ordered_pair(x,X15),intersection(X16,X17))
| ~ spl0_51
| ~ spl0_183
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1785,f1550]) ).
fof(f1785,plain,
( ! [X16,X17,X15] :
( member(singleton(null_class),X17)
| ~ subclass(ordered_pair(x,X15),intersection(X16,X17)) )
| ~ spl0_51
| ~ spl0_183
| ~ spl0_191 ),
inference(backward_demodulation,[],[f1486,f1563]) ).
fof(f2140,plain,
( ~ spl0_38
| ~ spl0_51
| ~ spl0_65
| ~ spl0_172
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2139]) ).
fof(f2139,plain,
( $false
| ~ spl0_38
| ~ spl0_51
| ~ spl0_65
| ~ spl0_172
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f2138,f1562]) ).
fof(f2138,plain,
( ! [X2,X1] : ~ subclass(X1,X2)
| ~ spl0_38
| ~ spl0_51
| ~ spl0_65
| ~ spl0_172
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f2137,f1562]) ).
fof(f2137,plain,
( ! [X2,X0,X1] :
( ~ subclass(ordered_pair(x,X0),X1)
| ~ subclass(X1,X2) )
| ~ spl0_51
| ~ spl0_65
| ~ spl0_172
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1779,f1550]) ).
fof(f1779,plain,
( ! [X2,X0,X1] :
( member(singleton(null_class),X2)
| ~ subclass(ordered_pair(x,X0),X1)
| ~ subclass(X1,X2) )
| ~ spl0_51
| ~ spl0_65
| ~ spl0_172
| ~ spl0_191 ),
inference(backward_demodulation,[],[f1410,f1563]) ).
fof(f2136,plain,
( ~ spl0_38
| ~ spl0_51
| ~ spl0_172
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2135]) ).
fof(f2135,plain,
( $false
| ~ spl0_38
| ~ spl0_51
| ~ spl0_172
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f2134,f1562]) ).
fof(f2134,plain,
( ! [X0,X1] : ~ subclass(ordered_pair(x,X0),X1)
| ~ spl0_51
| ~ spl0_172
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1778,f1550]) ).
fof(f1778,plain,
( ! [X0,X1] :
( member(singleton(null_class),X1)
| ~ subclass(ordered_pair(x,X0),X1) )
| ~ spl0_51
| ~ spl0_172
| ~ spl0_191 ),
inference(backward_demodulation,[],[f1408,f1563]) ).
fof(f2133,plain,
( ~ spl0_51
| ~ spl0_170
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2132]) ).
fof(f2132,plain,
( $false
| ~ spl0_51
| ~ spl0_170
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1775,f1550]) ).
fof(f1775,plain,
( ! [X2] : member(singleton(null_class),ordered_pair(x,X2))
| ~ spl0_51
| ~ spl0_170
| ~ spl0_191 ),
inference(backward_demodulation,[],[f1374,f1563]) ).
fof(f2131,plain,
( ~ spl0_51
| ~ spl0_60
| ~ spl0_142
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2130]) ).
fof(f2130,plain,
( $false
| ~ spl0_51
| ~ spl0_60
| ~ spl0_142
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1771,f1550]) ).
fof(f1771,plain,
( ! [X0,X1] : member(null_class,ordered_pair(X0,X1))
| ~ spl0_51
| ~ spl0_60
| ~ spl0_142
| ~ spl0_191 ),
inference(backward_demodulation,[],[f1238,f1563]) ).
fof(f1238,plain,
( ! [X0,X1] : member(singleton(X0),ordered_pair(X0,X1))
| ~ spl0_60
| ~ spl0_142 ),
inference(superposition,[],[f435,f1115]) ).
fof(f435,plain,
( ! [X3,X4] : member(singleton(X3),unordered_pair(singleton(X3),X4))
| ~ spl0_60 ),
inference(avatar_component_clause,[],[f434]) ).
fof(f434,plain,
( spl0_60
<=> ! [X4,X3] : member(singleton(X3),unordered_pair(singleton(X3),X4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f2129,plain,
( ~ spl0_38
| ~ spl0_51
| ~ spl0_82
| ~ spl0_132
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2128]) ).
fof(f2128,plain,
( $false
| ~ spl0_38
| ~ spl0_51
| ~ spl0_82
| ~ spl0_132
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f2127,f1562]) ).
fof(f2127,plain,
( ~ subclass(universal_class,choice)
| ~ spl0_51
| ~ spl0_82
| ~ spl0_132
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1768,f1550]) ).
fof(f1768,plain,
( member(null_class,cross_product(universal_class,universal_class))
| ~ subclass(universal_class,choice)
| ~ spl0_51
| ~ spl0_82
| ~ spl0_132
| ~ spl0_191 ),
inference(backward_demodulation,[],[f1146,f1563]) ).
fof(f1146,plain,
( ! [X5] :
( ~ subclass(universal_class,choice)
| member(singleton(X5),cross_product(universal_class,universal_class)) )
| ~ spl0_82
| ~ spl0_132 ),
inference(resolution,[],[f997,f605]) ).
fof(f605,plain,
( ! [X10,X11] :
( ~ subclass(universal_class,X10)
| member(singleton(X11),X10) )
| ~ spl0_82 ),
inference(avatar_component_clause,[],[f604]) ).
fof(f604,plain,
( spl0_82
<=> ! [X11,X10] :
( ~ subclass(universal_class,X10)
| member(singleton(X11),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f997,plain,
( ! [X25] :
( subclass(X25,cross_product(universal_class,universal_class))
| ~ subclass(X25,choice) )
| ~ spl0_132 ),
inference(avatar_component_clause,[],[f996]) ).
fof(f996,plain,
( spl0_132
<=> ! [X25] :
( ~ subclass(X25,choice)
| subclass(X25,cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f2126,plain,
( ~ spl0_25
| ~ spl0_51
| ~ spl0_97
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2125]) ).
fof(f2125,plain,
( $false
| ~ spl0_25
| ~ spl0_51
| ~ spl0_97
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f2124,f1550]) ).
fof(f2124,plain,
( ! [X10,X9] : member(singleton(X9),complement(X10))
| ~ spl0_25
| ~ spl0_51
| ~ spl0_97
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1767,f1550]) ).
fof(f1767,plain,
( ! [X10,X9] :
( member(null_class,X10)
| member(singleton(X9),complement(X10)) )
| ~ spl0_25
| ~ spl0_51
| ~ spl0_97
| ~ spl0_191 ),
inference(backward_demodulation,[],[f913,f1563]) ).
fof(f913,plain,
( ! [X10,X9] :
( member(singleton(X9),X10)
| member(singleton(X9),complement(X10)) )
| ~ spl0_25
| ~ spl0_97 ),
inference(resolution,[],[f740,f233]) ).
fof(f740,plain,
( ! [X0,X4] :
( ~ member(X4,universal_class)
| member(X4,X0)
| member(X4,complement(X0)) )
| ~ spl0_97 ),
inference(avatar_component_clause,[],[f739]) ).
fof(f739,plain,
( spl0_97
<=> ! [X4,X0] :
( ~ member(X4,universal_class)
| member(X4,X0)
| member(X4,complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f2123,plain,
( ~ spl0_38
| ~ spl0_51
| ~ spl0_82
| ~ spl0_119
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2122]) ).
fof(f2122,plain,
( $false
| ~ spl0_38
| ~ spl0_51
| ~ spl0_82
| ~ spl0_119
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f2121,f1562]) ).
fof(f2121,plain,
( ~ subclass(universal_class,successor_relation)
| ~ spl0_51
| ~ spl0_82
| ~ spl0_119
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1766,f1550]) ).
fof(f1766,plain,
( member(null_class,cross_product(universal_class,universal_class))
| ~ subclass(universal_class,successor_relation)
| ~ spl0_51
| ~ spl0_82
| ~ spl0_119
| ~ spl0_191 ),
inference(backward_demodulation,[],[f896,f1563]) ).
fof(f896,plain,
( ! [X5] :
( ~ subclass(universal_class,successor_relation)
| member(singleton(X5),cross_product(universal_class,universal_class)) )
| ~ spl0_82
| ~ spl0_119 ),
inference(resolution,[],[f883,f605]) ).
fof(f883,plain,
( ! [X18] :
( subclass(X18,cross_product(universal_class,universal_class))
| ~ subclass(X18,successor_relation) )
| ~ spl0_119 ),
inference(avatar_component_clause,[],[f882]) ).
fof(f882,plain,
( spl0_119
<=> ! [X18] :
( ~ subclass(X18,successor_relation)
| subclass(X18,cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f2120,plain,
( ~ spl0_38
| ~ spl0_51
| ~ spl0_62
| ~ spl0_65
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2119]) ).
fof(f2119,plain,
( $false
| ~ spl0_38
| ~ spl0_51
| ~ spl0_62
| ~ spl0_65
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f2118,f1550]) ).
fof(f2118,plain,
( ! [X34,X35] : member(singleton(X34),X35)
| ~ spl0_38
| ~ spl0_51
| ~ spl0_62
| ~ spl0_65
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1759,f1562]) ).
fof(f1759,plain,
( ! [X34,X35] :
( ~ subclass(singleton(null_class),X35)
| member(singleton(X34),X35) )
| ~ spl0_51
| ~ spl0_62
| ~ spl0_65
| ~ spl0_191 ),
inference(backward_demodulation,[],[f525,f1563]) ).
fof(f525,plain,
( ! [X34,X35] :
( ~ subclass(singleton(singleton(X34)),X35)
| member(singleton(X34),X35) )
| ~ spl0_62
| ~ spl0_65 ),
inference(resolution,[],[f474,f446]) ).
fof(f446,plain,
( ! [X0] : member(singleton(X0),singleton(singleton(X0)))
| ~ spl0_62 ),
inference(avatar_component_clause,[],[f445]) ).
fof(f445,plain,
( spl0_62
<=> ! [X0] : member(singleton(X0),singleton(singleton(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f2117,plain,
( ~ spl0_51
| ~ spl0_62
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2116]) ).
fof(f2116,plain,
( $false
| ~ spl0_51
| ~ spl0_62
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1757,f1550]) ).
fof(f1757,plain,
( member(null_class,singleton(null_class))
| ~ spl0_51
| ~ spl0_62
| ~ spl0_191 ),
inference(backward_demodulation,[],[f446,f1563]) ).
fof(f2115,plain,
( ~ spl0_10
| ~ spl0_51
| ~ spl0_139
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2114]) ).
fof(f2114,plain,
( $false
| ~ spl0_10
| ~ spl0_51
| ~ spl0_139
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1744,f165]) ).
fof(f1744,plain,
( ~ subclass(null_class,null_class)
| ~ spl0_51
| ~ spl0_139
| ~ spl0_191 ),
inference(backward_demodulation,[],[f1076,f1563]) ).
fof(f1076,plain,
( ! [X17] : ~ subclass(unordered_pair(omega,X17),null_class)
| ~ spl0_139 ),
inference(avatar_component_clause,[],[f1075]) ).
fof(f1075,plain,
( spl0_139
<=> ! [X17] : ~ subclass(unordered_pair(omega,X17),null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f2113,plain,
( ~ spl0_10
| ~ spl0_43
| ~ spl0_51
| ~ spl0_121
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2112]) ).
fof(f2112,plain,
( $false
| ~ spl0_10
| ~ spl0_43
| ~ spl0_51
| ~ spl0_121
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f2111,f1550]) ).
fof(f2111,plain,
( ! [X13] : member(omega,X13)
| ~ spl0_10
| ~ spl0_43
| ~ spl0_51
| ~ spl0_121
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1742,f165]) ).
fof(f1742,plain,
( ! [X14,X13] :
( ~ subclass(null_class,intersection(X13,X14))
| member(omega,X13) )
| ~ spl0_43
| ~ spl0_51
| ~ spl0_121
| ~ spl0_191 ),
inference(backward_demodulation,[],[f1071,f1563]) ).
fof(f1071,plain,
( ! [X14,X12,X13] :
( ~ subclass(unordered_pair(omega,X12),intersection(X13,X14))
| member(omega,X13) )
| ~ spl0_43
| ~ spl0_121 ),
inference(resolution,[],[f904,f323]) ).
fof(f2110,plain,
( ~ spl0_10
| ~ spl0_44
| ~ spl0_51
| ~ spl0_121
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2109]) ).
fof(f2109,plain,
( $false
| ~ spl0_10
| ~ spl0_44
| ~ spl0_51
| ~ spl0_121
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f2108,f1550]) ).
fof(f2108,plain,
( ! [X11] : member(omega,X11)
| ~ spl0_10
| ~ spl0_44
| ~ spl0_51
| ~ spl0_121
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1741,f165]) ).
fof(f1741,plain,
( ! [X10,X11] :
( ~ subclass(null_class,intersection(X10,X11))
| member(omega,X11) )
| ~ spl0_44
| ~ spl0_51
| ~ spl0_121
| ~ spl0_191 ),
inference(backward_demodulation,[],[f1070,f1563]) ).
fof(f1070,plain,
( ! [X10,X11,X9] :
( ~ subclass(unordered_pair(omega,X9),intersection(X10,X11))
| member(omega,X11) )
| ~ spl0_44
| ~ spl0_121 ),
inference(resolution,[],[f904,f327]) ).
fof(f2107,plain,
( ~ spl0_10
| ~ spl0_38
| ~ spl0_51
| ~ spl0_65
| ~ spl0_121
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2106]) ).
fof(f2106,plain,
( $false
| ~ spl0_10
| ~ spl0_38
| ~ spl0_51
| ~ spl0_65
| ~ spl0_121
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f2105,f1550]) ).
fof(f2105,plain,
( ! [X2] : member(omega,X2)
| ~ spl0_10
| ~ spl0_38
| ~ spl0_51
| ~ spl0_65
| ~ spl0_121
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f2104,f1562]) ).
fof(f2104,plain,
( ! [X2,X1] :
( ~ subclass(X1,X2)
| member(omega,X2) )
| ~ spl0_10
| ~ spl0_51
| ~ spl0_65
| ~ spl0_121
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1740,f165]) ).
fof(f1740,plain,
( ! [X2,X1] :
( ~ subclass(null_class,X1)
| ~ subclass(X1,X2)
| member(omega,X2) )
| ~ spl0_51
| ~ spl0_65
| ~ spl0_121
| ~ spl0_191 ),
inference(backward_demodulation,[],[f1066,f1563]) ).
fof(f1066,plain,
( ! [X2,X0,X1] :
( ~ subclass(unordered_pair(omega,X0),X1)
| ~ subclass(X1,X2)
| member(omega,X2) )
| ~ spl0_65
| ~ spl0_121 ),
inference(resolution,[],[f904,f474]) ).
fof(f2103,plain,
( ~ spl0_10
| ~ spl0_51
| ~ spl0_121
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2102]) ).
fof(f2102,plain,
( $false
| ~ spl0_10
| ~ spl0_51
| ~ spl0_121
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f2101,f1550]) ).
fof(f2101,plain,
( ! [X21] : member(omega,X21)
| ~ spl0_10
| ~ spl0_51
| ~ spl0_121
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1739,f165]) ).
fof(f1739,plain,
( ! [X21] :
( ~ subclass(null_class,X21)
| member(omega,X21) )
| ~ spl0_51
| ~ spl0_121
| ~ spl0_191 ),
inference(backward_demodulation,[],[f904,f1563]) ).
fof(f2100,plain,
( ~ spl0_9
| ~ spl0_51
| ~ spl0_53
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2099]) ).
fof(f2099,plain,
( $false
| ~ spl0_9
| ~ spl0_51
| ~ spl0_53
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1738,f161]) ).
fof(f1738,plain,
( member(omega,null_class)
| ~ spl0_51
| ~ spl0_53
| ~ spl0_191 ),
inference(backward_demodulation,[],[f383,f1563]) ).
fof(f383,plain,
( ! [X6] : member(omega,unordered_pair(omega,X6))
| ~ spl0_53 ),
inference(avatar_component_clause,[],[f382]) ).
fof(f382,plain,
( spl0_53
<=> ! [X6] : member(omega,unordered_pair(omega,X6)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f2098,plain,
( ~ spl0_10
| ~ spl0_51
| ~ spl0_120
| spl0_149
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2097]) ).
fof(f2097,plain,
( $false
| ~ spl0_10
| ~ spl0_51
| ~ spl0_120
| spl0_149
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1735,f165]) ).
fof(f1735,plain,
( ~ subclass(null_class,subset_relation)
| ~ spl0_51
| ~ spl0_120
| spl0_149
| ~ spl0_191 ),
inference(backward_demodulation,[],[f1186,f1563]) ).
fof(f1186,plain,
( ! [X1] : ~ subclass(unordered_pair(null_class,X1),subset_relation)
| ~ spl0_120
| spl0_149 ),
inference(resolution,[],[f1177,f900]) ).
fof(f2096,plain,
( ~ spl0_10
| ~ spl0_51
| ~ spl0_137
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2095]) ).
fof(f2095,plain,
( $false
| ~ spl0_10
| ~ spl0_51
| ~ spl0_137
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1734,f165]) ).
fof(f1734,plain,
( ~ subclass(null_class,null_class)
| ~ spl0_51
| ~ spl0_137
| ~ spl0_191 ),
inference(backward_demodulation,[],[f1050,f1563]) ).
fof(f1050,plain,
( ! [X19] : ~ subclass(unordered_pair(null_class,X19),null_class)
| ~ spl0_137 ),
inference(avatar_component_clause,[],[f1049]) ).
fof(f1049,plain,
( spl0_137
<=> ! [X19] : ~ subclass(unordered_pair(null_class,X19),null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f2094,plain,
( ~ spl0_10
| ~ spl0_43
| ~ spl0_51
| ~ spl0_120
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2093]) ).
fof(f2093,plain,
( $false
| ~ spl0_10
| ~ spl0_43
| ~ spl0_51
| ~ spl0_120
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f2092,f1550]) ).
fof(f2092,plain,
( ! [X15] : member(null_class,X15)
| ~ spl0_10
| ~ spl0_43
| ~ spl0_51
| ~ spl0_120
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1732,f165]) ).
fof(f1732,plain,
( ! [X16,X15] :
( ~ subclass(null_class,intersection(X15,X16))
| member(null_class,X15) )
| ~ spl0_43
| ~ spl0_51
| ~ spl0_120
| ~ spl0_191 ),
inference(backward_demodulation,[],[f1045,f1563]) ).
fof(f1045,plain,
( ! [X16,X14,X15] :
( ~ subclass(unordered_pair(null_class,X14),intersection(X15,X16))
| member(null_class,X15) )
| ~ spl0_43
| ~ spl0_120 ),
inference(resolution,[],[f900,f323]) ).
fof(f2091,plain,
( ~ spl0_10
| ~ spl0_44
| ~ spl0_51
| ~ spl0_120
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2090]) ).
fof(f2090,plain,
( $false
| ~ spl0_10
| ~ spl0_44
| ~ spl0_51
| ~ spl0_120
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f2089,f1550]) ).
fof(f2089,plain,
( ! [X13] : member(null_class,X13)
| ~ spl0_10
| ~ spl0_44
| ~ spl0_51
| ~ spl0_120
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1731,f165]) ).
fof(f1731,plain,
( ! [X12,X13] :
( ~ subclass(null_class,intersection(X12,X13))
| member(null_class,X13) )
| ~ spl0_44
| ~ spl0_51
| ~ spl0_120
| ~ spl0_191 ),
inference(backward_demodulation,[],[f1044,f1563]) ).
fof(f1044,plain,
( ! [X11,X12,X13] :
( ~ subclass(unordered_pair(null_class,X11),intersection(X12,X13))
| member(null_class,X13) )
| ~ spl0_44
| ~ spl0_120 ),
inference(resolution,[],[f900,f327]) ).
fof(f2088,plain,
( ~ spl0_10
| ~ spl0_38
| ~ spl0_51
| ~ spl0_65
| ~ spl0_120
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2087]) ).
fof(f2087,plain,
( $false
| ~ spl0_10
| ~ spl0_38
| ~ spl0_51
| ~ spl0_65
| ~ spl0_120
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f2086,f1550]) ).
fof(f2086,plain,
( ! [X4] : member(null_class,X4)
| ~ spl0_10
| ~ spl0_38
| ~ spl0_51
| ~ spl0_65
| ~ spl0_120
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f2085,f1562]) ).
fof(f2085,plain,
( ! [X3,X4] :
( ~ subclass(X3,X4)
| member(null_class,X4) )
| ~ spl0_10
| ~ spl0_51
| ~ spl0_65
| ~ spl0_120
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1730,f165]) ).
fof(f1730,plain,
( ! [X3,X4] :
( ~ subclass(null_class,X3)
| ~ subclass(X3,X4)
| member(null_class,X4) )
| ~ spl0_51
| ~ spl0_65
| ~ spl0_120
| ~ spl0_191 ),
inference(backward_demodulation,[],[f1040,f1563]) ).
fof(f1040,plain,
( ! [X2,X3,X4] :
( ~ subclass(unordered_pair(null_class,X2),X3)
| ~ subclass(X3,X4)
| member(null_class,X4) )
| ~ spl0_65
| ~ spl0_120 ),
inference(resolution,[],[f900,f474]) ).
fof(f2084,plain,
( ~ spl0_10
| ~ spl0_51
| ~ spl0_120
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2083]) ).
fof(f2083,plain,
( $false
| ~ spl0_10
| ~ spl0_51
| ~ spl0_120
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f2082,f1550]) ).
fof(f2082,plain,
( ! [X19] : member(null_class,X19)
| ~ spl0_10
| ~ spl0_51
| ~ spl0_120
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1727,f165]) ).
fof(f1727,plain,
( ! [X19] :
( ~ subclass(null_class,X19)
| member(null_class,X19) )
| ~ spl0_51
| ~ spl0_120
| ~ spl0_191 ),
inference(backward_demodulation,[],[f900,f1563]) ).
fof(f2081,plain,
( ~ spl0_9
| ~ spl0_51
| ~ spl0_52
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2080]) ).
fof(f2080,plain,
( $false
| ~ spl0_9
| ~ spl0_51
| ~ spl0_52
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1726,f161]) ).
fof(f1726,plain,
( member(null_class,null_class)
| ~ spl0_51
| ~ spl0_52
| ~ spl0_191 ),
inference(backward_demodulation,[],[f379,f1563]) ).
fof(f379,plain,
( ! [X5] : member(null_class,unordered_pair(null_class,X5))
| ~ spl0_52 ),
inference(avatar_component_clause,[],[f378]) ).
fof(f378,plain,
( spl0_52
<=> ! [X5] : member(null_class,unordered_pair(null_class,X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f2079,plain,
( ~ spl0_9
| ~ spl0_51
| ~ spl0_60
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2078]) ).
fof(f2078,plain,
( $false
| ~ spl0_9
| ~ spl0_51
| ~ spl0_60
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1723,f161]) ).
fof(f1723,plain,
( ! [X3] : member(singleton(X3),null_class)
| ~ spl0_51
| ~ spl0_60
| ~ spl0_191 ),
inference(backward_demodulation,[],[f435,f1563]) ).
fof(f2077,plain,
( ~ spl0_10
| ~ spl0_51
| ~ spl0_60
| ~ spl0_65
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2076]) ).
fof(f2076,plain,
( $false
| ~ spl0_10
| ~ spl0_51
| ~ spl0_60
| ~ spl0_65
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f2075,f1550]) ).
fof(f2075,plain,
( ! [X24,X22] : member(singleton(X22),X24)
| ~ spl0_10
| ~ spl0_51
| ~ spl0_60
| ~ spl0_65
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1722,f165]) ).
fof(f1722,plain,
( ! [X24,X22] :
( ~ subclass(null_class,X24)
| member(singleton(X22),X24) )
| ~ spl0_51
| ~ spl0_60
| ~ spl0_65
| ~ spl0_191 ),
inference(backward_demodulation,[],[f519,f1563]) ).
fof(f519,plain,
( ! [X24,X22,X23] :
( ~ subclass(unordered_pair(singleton(X22),X23),X24)
| member(singleton(X22),X24) )
| ~ spl0_60
| ~ spl0_65 ),
inference(resolution,[],[f474,f435]) ).
fof(f2074,plain,
( ~ spl0_10
| ~ spl0_43
| ~ spl0_51
| ~ spl0_126
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2073]) ).
fof(f2073,plain,
( $false
| ~ spl0_10
| ~ spl0_43
| ~ spl0_51
| ~ spl0_126
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f2072,f1550]) ).
fof(f2072,plain,
( ! [X13] : member(omega,X13)
| ~ spl0_10
| ~ spl0_43
| ~ spl0_51
| ~ spl0_126
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1712,f165]) ).
fof(f1712,plain,
( ! [X14,X13] :
( ~ subclass(null_class,intersection(X13,X14))
| member(omega,X13) )
| ~ spl0_43
| ~ spl0_51
| ~ spl0_126
| ~ spl0_191 ),
inference(backward_demodulation,[],[f1110,f1563]) ).
fof(f1110,plain,
( ! [X14,X12,X13] :
( ~ subclass(unordered_pair(X12,omega),intersection(X13,X14))
| member(omega,X13) )
| ~ spl0_43
| ~ spl0_126 ),
inference(resolution,[],[f963,f323]) ).
fof(f2071,plain,
( ~ spl0_10
| ~ spl0_44
| ~ spl0_51
| ~ spl0_126
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2070]) ).
fof(f2070,plain,
( $false
| ~ spl0_10
| ~ spl0_44
| ~ spl0_51
| ~ spl0_126
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f2069,f1550]) ).
fof(f2069,plain,
( ! [X11] : member(omega,X11)
| ~ spl0_10
| ~ spl0_44
| ~ spl0_51
| ~ spl0_126
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1711,f165]) ).
fof(f1711,plain,
( ! [X10,X11] :
( ~ subclass(null_class,intersection(X10,X11))
| member(omega,X11) )
| ~ spl0_44
| ~ spl0_51
| ~ spl0_126
| ~ spl0_191 ),
inference(backward_demodulation,[],[f1109,f1563]) ).
fof(f1109,plain,
( ! [X10,X11,X9] :
( ~ subclass(unordered_pair(X9,omega),intersection(X10,X11))
| member(omega,X11) )
| ~ spl0_44
| ~ spl0_126 ),
inference(resolution,[],[f963,f327]) ).
fof(f2068,plain,
( ~ spl0_10
| ~ spl0_38
| ~ spl0_51
| ~ spl0_65
| ~ spl0_126
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2067]) ).
fof(f2067,plain,
( $false
| ~ spl0_10
| ~ spl0_38
| ~ spl0_51
| ~ spl0_65
| ~ spl0_126
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f2066,f1550]) ).
fof(f2066,plain,
( ! [X2] : member(omega,X2)
| ~ spl0_10
| ~ spl0_38
| ~ spl0_51
| ~ spl0_65
| ~ spl0_126
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f2065,f1562]) ).
fof(f2065,plain,
( ! [X2,X1] :
( ~ subclass(X1,X2)
| member(omega,X2) )
| ~ spl0_10
| ~ spl0_51
| ~ spl0_65
| ~ spl0_126
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1710,f165]) ).
fof(f1710,plain,
( ! [X2,X1] :
( ~ subclass(null_class,X1)
| ~ subclass(X1,X2)
| member(omega,X2) )
| ~ spl0_51
| ~ spl0_65
| ~ spl0_126
| ~ spl0_191 ),
inference(backward_demodulation,[],[f1105,f1563]) ).
fof(f1105,plain,
( ! [X2,X0,X1] :
( ~ subclass(unordered_pair(X0,omega),X1)
| ~ subclass(X1,X2)
| member(omega,X2) )
| ~ spl0_65
| ~ spl0_126 ),
inference(resolution,[],[f963,f474]) ).
fof(f2064,plain,
( ~ spl0_10
| ~ spl0_51
| ~ spl0_141
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2063]) ).
fof(f2063,plain,
( $false
| ~ spl0_10
| ~ spl0_51
| ~ spl0_141
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1709,f165]) ).
fof(f1709,plain,
( ~ subclass(null_class,null_class)
| ~ spl0_51
| ~ spl0_141
| ~ spl0_191 ),
inference(backward_demodulation,[],[f1089,f1563]) ).
fof(f1089,plain,
( ! [X0] : ~ subclass(unordered_pair(X0,omega),null_class)
| ~ spl0_141 ),
inference(avatar_component_clause,[],[f1088]) ).
fof(f1088,plain,
( spl0_141
<=> ! [X0] : ~ subclass(unordered_pair(X0,omega),null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f2062,plain,
( ~ spl0_10
| ~ spl0_51
| ~ spl0_126
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2061]) ).
fof(f2061,plain,
( $false
| ~ spl0_10
| ~ spl0_51
| ~ spl0_126
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f2060,f1550]) ).
fof(f2060,plain,
( ! [X31] : member(omega,X31)
| ~ spl0_10
| ~ spl0_51
| ~ spl0_126
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1708,f165]) ).
fof(f1708,plain,
( ! [X31] :
( ~ subclass(null_class,X31)
| member(omega,X31) )
| ~ spl0_51
| ~ spl0_126
| ~ spl0_191 ),
inference(backward_demodulation,[],[f963,f1563]) ).
fof(f2059,plain,
( ~ spl0_9
| ~ spl0_51
| ~ spl0_55
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2058]) ).
fof(f2058,plain,
( $false
| ~ spl0_9
| ~ spl0_51
| ~ spl0_55
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1707,f161]) ).
fof(f1707,plain,
( member(omega,null_class)
| ~ spl0_51
| ~ spl0_55
| ~ spl0_191 ),
inference(backward_demodulation,[],[f391,f1563]) ).
fof(f391,plain,
( ! [X6] : member(omega,unordered_pair(X6,omega))
| ~ spl0_55 ),
inference(avatar_component_clause,[],[f390]) ).
fof(f390,plain,
( spl0_55
<=> ! [X6] : member(omega,unordered_pair(X6,omega)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f2057,plain,
( ~ spl0_10
| ~ spl0_51
| ~ spl0_122
| spl0_149
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2056]) ).
fof(f2056,plain,
( $false
| ~ spl0_10
| ~ spl0_51
| ~ spl0_122
| spl0_149
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1704,f165]) ).
fof(f1704,plain,
( ~ subclass(null_class,subset_relation)
| ~ spl0_51
| ~ spl0_122
| spl0_149
| ~ spl0_191 ),
inference(backward_demodulation,[],[f1185,f1563]) ).
fof(f1185,plain,
( ! [X0] : ~ subclass(unordered_pair(X0,null_class),subset_relation)
| ~ spl0_122
| spl0_149 ),
inference(resolution,[],[f1177,f908]) ).
fof(f2055,plain,
( ~ spl0_10
| ~ spl0_43
| ~ spl0_51
| ~ spl0_122
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2054]) ).
fof(f2054,plain,
( $false
| ~ spl0_10
| ~ spl0_43
| ~ spl0_51
| ~ spl0_122
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f2053,f1550]) ).
fof(f2053,plain,
( ! [X15] : member(null_class,X15)
| ~ spl0_10
| ~ spl0_43
| ~ spl0_51
| ~ spl0_122
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1702,f165]) ).
fof(f1702,plain,
( ! [X16,X15] :
( ~ subclass(null_class,intersection(X15,X16))
| member(null_class,X15) )
| ~ spl0_43
| ~ spl0_51
| ~ spl0_122
| ~ spl0_191 ),
inference(backward_demodulation,[],[f1102,f1563]) ).
fof(f1102,plain,
( ! [X16,X14,X15] :
( ~ subclass(unordered_pair(X14,null_class),intersection(X15,X16))
| member(null_class,X15) )
| ~ spl0_43
| ~ spl0_122 ),
inference(resolution,[],[f908,f323]) ).
fof(f2052,plain,
( ~ spl0_10
| ~ spl0_44
| ~ spl0_51
| ~ spl0_122
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2051]) ).
fof(f2051,plain,
( $false
| ~ spl0_10
| ~ spl0_44
| ~ spl0_51
| ~ spl0_122
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f2050,f1550]) ).
fof(f2050,plain,
( ! [X13] : member(null_class,X13)
| ~ spl0_10
| ~ spl0_44
| ~ spl0_51
| ~ spl0_122
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1701,f165]) ).
fof(f1701,plain,
( ! [X12,X13] :
( ~ subclass(null_class,intersection(X12,X13))
| member(null_class,X13) )
| ~ spl0_44
| ~ spl0_51
| ~ spl0_122
| ~ spl0_191 ),
inference(backward_demodulation,[],[f1101,f1563]) ).
fof(f1101,plain,
( ! [X11,X12,X13] :
( ~ subclass(unordered_pair(X11,null_class),intersection(X12,X13))
| member(null_class,X13) )
| ~ spl0_44
| ~ spl0_122 ),
inference(resolution,[],[f908,f327]) ).
fof(f2049,plain,
( ~ spl0_10
| ~ spl0_38
| ~ spl0_51
| ~ spl0_65
| ~ spl0_122
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2048]) ).
fof(f2048,plain,
( $false
| ~ spl0_10
| ~ spl0_38
| ~ spl0_51
| ~ spl0_65
| ~ spl0_122
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f2047,f1550]) ).
fof(f2047,plain,
( ! [X4] : member(null_class,X4)
| ~ spl0_10
| ~ spl0_38
| ~ spl0_51
| ~ spl0_65
| ~ spl0_122
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f2046,f1562]) ).
fof(f2046,plain,
( ! [X3,X4] :
( ~ subclass(X3,X4)
| member(null_class,X4) )
| ~ spl0_10
| ~ spl0_51
| ~ spl0_65
| ~ spl0_122
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1700,f165]) ).
fof(f1700,plain,
( ! [X3,X4] :
( ~ subclass(null_class,X3)
| ~ subclass(X3,X4)
| member(null_class,X4) )
| ~ spl0_51
| ~ spl0_65
| ~ spl0_122
| ~ spl0_191 ),
inference(backward_demodulation,[],[f1097,f1563]) ).
fof(f1097,plain,
( ! [X2,X3,X4] :
( ~ subclass(unordered_pair(X2,null_class),X3)
| ~ subclass(X3,X4)
| member(null_class,X4) )
| ~ spl0_65
| ~ spl0_122 ),
inference(resolution,[],[f908,f474]) ).
fof(f2043,plain,
( ~ spl0_10
| ~ spl0_51
| ~ spl0_138
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2042]) ).
fof(f2042,plain,
( $false
| ~ spl0_10
| ~ spl0_51
| ~ spl0_138
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1698,f165]) ).
fof(f1698,plain,
( ~ subclass(null_class,null_class)
| ~ spl0_51
| ~ spl0_138
| ~ spl0_191 ),
inference(backward_demodulation,[],[f1059,f1563]) ).
fof(f1059,plain,
( ! [X0] : ~ subclass(unordered_pair(X0,null_class),null_class)
| ~ spl0_138 ),
inference(avatar_component_clause,[],[f1058]) ).
fof(f1058,plain,
( spl0_138
<=> ! [X0] : ~ subclass(unordered_pair(X0,null_class),null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f2040,plain,
( ~ spl0_10
| ~ spl0_51
| ~ spl0_122
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2039]) ).
fof(f2039,plain,
( $false
| ~ spl0_10
| ~ spl0_51
| ~ spl0_122
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f2038,f1550]) ).
fof(f2038,plain,
( ! [X29] : member(null_class,X29)
| ~ spl0_10
| ~ spl0_51
| ~ spl0_122
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1696,f165]) ).
fof(f1696,plain,
( ! [X29] :
( ~ subclass(null_class,X29)
| member(null_class,X29) )
| ~ spl0_51
| ~ spl0_122
| ~ spl0_191 ),
inference(backward_demodulation,[],[f908,f1563]) ).
fof(f2037,plain,
( ~ spl0_9
| ~ spl0_51
| ~ spl0_54
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2036]) ).
fof(f2036,plain,
( $false
| ~ spl0_9
| ~ spl0_51
| ~ spl0_54
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1695,f161]) ).
fof(f1695,plain,
( member(null_class,null_class)
| ~ spl0_51
| ~ spl0_54
| ~ spl0_191 ),
inference(backward_demodulation,[],[f387,f1563]) ).
fof(f387,plain,
( ! [X5] : member(null_class,unordered_pair(X5,null_class))
| ~ spl0_54 ),
inference(avatar_component_clause,[],[f386]) ).
fof(f386,plain,
( spl0_54
<=> ! [X5] : member(null_class,unordered_pair(X5,null_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f2035,plain,
( ~ spl0_9
| ~ spl0_51
| ~ spl0_61
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2034]) ).
fof(f2034,plain,
( $false
| ~ spl0_9
| ~ spl0_51
| ~ spl0_61
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1694,f161]) ).
fof(f1694,plain,
( ! [X3] : member(singleton(X3),null_class)
| ~ spl0_51
| ~ spl0_61
| ~ spl0_191 ),
inference(backward_demodulation,[],[f439,f1563]) ).
fof(f439,plain,
( ! [X3,X4] : member(singleton(X3),unordered_pair(X4,singleton(X3)))
| ~ spl0_61 ),
inference(avatar_component_clause,[],[f438]) ).
fof(f438,plain,
( spl0_61
<=> ! [X4,X3] : member(singleton(X3),unordered_pair(X4,singleton(X3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f2033,plain,
( ~ spl0_10
| ~ spl0_51
| ~ spl0_61
| ~ spl0_65
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2032]) ).
fof(f2032,plain,
( $false
| ~ spl0_10
| ~ spl0_51
| ~ spl0_61
| ~ spl0_65
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f2031,f1550]) ).
fof(f2031,plain,
( ! [X26,X27] : member(singleton(X26),X27)
| ~ spl0_10
| ~ spl0_51
| ~ spl0_61
| ~ spl0_65
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1693,f165]) ).
fof(f1693,plain,
( ! [X26,X27] :
( ~ subclass(null_class,X27)
| member(singleton(X26),X27) )
| ~ spl0_51
| ~ spl0_61
| ~ spl0_65
| ~ spl0_191 ),
inference(backward_demodulation,[],[f520,f1563]) ).
fof(f520,plain,
( ! [X26,X27,X25] :
( ~ subclass(unordered_pair(X25,singleton(X26)),X27)
| member(singleton(X26),X27) )
| ~ spl0_61
| ~ spl0_65 ),
inference(resolution,[],[f474,f439]) ).
fof(f2030,plain,
( ~ spl0_38
| ~ spl0_51
| ~ spl0_117
| ~ spl0_132
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2029]) ).
fof(f2029,plain,
( $false
| ~ spl0_38
| ~ spl0_51
| ~ spl0_117
| ~ spl0_132
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f2028,f1562]) ).
fof(f2028,plain,
( ~ subclass(universal_class,choice)
| ~ spl0_51
| ~ spl0_117
| ~ spl0_132
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1674,f1550]) ).
fof(f1674,plain,
( member(null_class,cross_product(universal_class,universal_class))
| ~ subclass(universal_class,choice)
| ~ spl0_51
| ~ spl0_117
| ~ spl0_132
| ~ spl0_191 ),
inference(backward_demodulation,[],[f1145,f1563]) ).
fof(f1145,plain,
( ! [X3,X4] :
( ~ subclass(universal_class,choice)
| member(unordered_pair(X3,X4),cross_product(universal_class,universal_class)) )
| ~ spl0_117
| ~ spl0_132 ),
inference(resolution,[],[f997,f875]) ).
fof(f875,plain,
( ! [X8,X9,X7] :
( ~ subclass(universal_class,X7)
| member(unordered_pair(X8,X9),X7) )
| ~ spl0_117 ),
inference(avatar_component_clause,[],[f874]) ).
fof(f874,plain,
( spl0_117
<=> ! [X9,X7,X8] :
( ~ subclass(universal_class,X7)
| member(unordered_pair(X8,X9),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f2027,plain,
( ~ spl0_12
| ~ spl0_51
| ~ spl0_97
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2026]) ).
fof(f2026,plain,
( $false
| ~ spl0_12
| ~ spl0_51
| ~ spl0_97
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f2025,f1550]) ).
fof(f2025,plain,
( ! [X8,X6,X7] : member(unordered_pair(X6,X7),complement(X8))
| ~ spl0_12
| ~ spl0_51
| ~ spl0_97
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1672,f1550]) ).
fof(f1672,plain,
( ! [X8,X6,X7] :
( member(null_class,X8)
| member(unordered_pair(X6,X7),complement(X8)) )
| ~ spl0_12
| ~ spl0_51
| ~ spl0_97
| ~ spl0_191 ),
inference(backward_demodulation,[],[f912,f1563]) ).
fof(f912,plain,
( ! [X8,X6,X7] :
( member(unordered_pair(X6,X7),X8)
| member(unordered_pair(X6,X7),complement(X8)) )
| ~ spl0_12
| ~ spl0_97 ),
inference(resolution,[],[f740,f174]) ).
fof(f2024,plain,
( ~ spl0_38
| ~ spl0_51
| ~ spl0_117
| ~ spl0_119
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2023]) ).
fof(f2023,plain,
( $false
| ~ spl0_38
| ~ spl0_51
| ~ spl0_117
| ~ spl0_119
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f2022,f1562]) ).
fof(f2022,plain,
( ~ subclass(universal_class,successor_relation)
| ~ spl0_51
| ~ spl0_117
| ~ spl0_119
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1669,f1550]) ).
fof(f1669,plain,
( member(null_class,cross_product(universal_class,universal_class))
| ~ subclass(universal_class,successor_relation)
| ~ spl0_51
| ~ spl0_117
| ~ spl0_119
| ~ spl0_191 ),
inference(backward_demodulation,[],[f895,f1563]) ).
fof(f895,plain,
( ! [X3,X4] :
( ~ subclass(universal_class,successor_relation)
| member(unordered_pair(X3,X4),cross_product(universal_class,universal_class)) )
| ~ spl0_117
| ~ spl0_119 ),
inference(resolution,[],[f883,f875]) ).
fof(f2021,plain,
( ~ spl0_12
| ~ spl0_41
| ~ spl0_51
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2020]) ).
fof(f2020,plain,
( $false
| ~ spl0_12
| ~ spl0_41
| ~ spl0_51
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1654,f1550]) ).
fof(f1654,plain,
( ! [X2] : member(null_class,unordered_pair(X2,null_class))
| ~ spl0_12
| ~ spl0_41
| ~ spl0_51
| ~ spl0_191 ),
inference(backward_demodulation,[],[f369,f1563]) ).
fof(f369,plain,
( ! [X2,X0,X1] : member(unordered_pair(X0,X1),unordered_pair(X2,unordered_pair(X0,X1)))
| ~ spl0_12
| ~ spl0_41 ),
inference(resolution,[],[f315,f174]) ).
fof(f315,plain,
( ! [X0,X1] :
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X0,X1)) )
| ~ spl0_41 ),
inference(avatar_component_clause,[],[f314]) ).
fof(f314,plain,
( spl0_41
<=> ! [X0,X1] :
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f2019,plain,
( ~ spl0_12
| ~ spl0_40
| ~ spl0_51
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2018]) ).
fof(f2018,plain,
( $false
| ~ spl0_12
| ~ spl0_40
| ~ spl0_51
| ~ spl0_191 ),
inference(subsumption_resolution,[],[f1653,f1550]) ).
fof(f1653,plain,
( ! [X2] : member(null_class,unordered_pair(null_class,X2))
| ~ spl0_12
| ~ spl0_40
| ~ spl0_51
| ~ spl0_191 ),
inference(backward_demodulation,[],[f361,f1563]) ).
fof(f361,plain,
( ! [X2,X0,X1] : member(unordered_pair(X0,X1),unordered_pair(unordered_pair(X0,X1),X2))
| ~ spl0_12
| ~ spl0_40 ),
inference(resolution,[],[f311,f174]) ).
fof(f311,plain,
( ! [X0,X1] :
( ~ member(X0,universal_class)
| member(X0,unordered_pair(X0,X1)) )
| ~ spl0_40 ),
inference(avatar_component_clause,[],[f310]) ).
fof(f310,plain,
( spl0_40
<=> ! [X0,X1] :
( ~ member(X0,universal_class)
| member(X0,unordered_pair(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f2015,plain,
( ~ spl0_51
| spl0_87
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f2014]) ).
fof(f2014,plain,
( $false
| ~ spl0_51
| spl0_87
| ~ spl0_191 ),
inference(trivial_inequality_removal,[],[f1812]) ).
fof(f1812,plain,
( null_class != null_class
| ~ spl0_51
| spl0_87
| ~ spl0_191 ),
inference(backward_demodulation,[],[f653,f1563]) ).
fof(f1618,plain,
( ~ spl0_12
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f1578]) ).
fof(f1578,plain,
( $false
| ~ spl0_12
| ~ spl0_191 ),
inference(resolution,[],[f1550,f174]) ).
fof(f1617,plain,
( ~ spl0_25
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f1579]) ).
fof(f1579,plain,
( $false
| ~ spl0_25
| ~ spl0_191 ),
inference(resolution,[],[f1550,f233]) ).
fof(f1616,plain,
( ~ spl0_11
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f1580]) ).
fof(f1580,plain,
( $false
| ~ spl0_11
| ~ spl0_191 ),
inference(resolution,[],[f1550,f170]) ).
fof(f170,plain,
( member(null_class,universal_class)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f168]) ).
fof(f168,plain,
( spl0_11
<=> member(null_class,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f1615,plain,
( ~ spl0_7
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f1582]) ).
fof(f1582,plain,
( $false
| ~ spl0_7
| ~ spl0_191 ),
inference(resolution,[],[f1550,f153]) ).
fof(f153,plain,
( member(omega,universal_class)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f151]) ).
fof(f151,plain,
( spl0_7
<=> member(omega,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f1614,plain,
( ~ spl0_52
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f1585]) ).
fof(f1585,plain,
( $false
| ~ spl0_52
| ~ spl0_191 ),
inference(resolution,[],[f1550,f379]) ).
fof(f1613,plain,
( ~ spl0_53
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f1586]) ).
fof(f1586,plain,
( $false
| ~ spl0_53
| ~ spl0_191 ),
inference(resolution,[],[f1550,f383]) ).
fof(f1612,plain,
( ~ spl0_60
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f1587]) ).
fof(f1587,plain,
( $false
| ~ spl0_60
| ~ spl0_191 ),
inference(resolution,[],[f1550,f435]) ).
fof(f1611,plain,
( ~ spl0_61
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f1588]) ).
fof(f1588,plain,
( $false
| ~ spl0_61
| ~ spl0_191 ),
inference(resolution,[],[f1550,f439]) ).
fof(f1610,plain,
( ~ spl0_54
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f1589]) ).
fof(f1589,plain,
( $false
| ~ spl0_54
| ~ spl0_191 ),
inference(resolution,[],[f1550,f387]) ).
fof(f1609,plain,
( ~ spl0_55
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f1590]) ).
fof(f1590,plain,
( $false
| ~ spl0_55
| ~ spl0_191 ),
inference(resolution,[],[f1550,f391]) ).
fof(f1608,plain,
( ~ spl0_56
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f1591]) ).
fof(f1591,plain,
( $false
| ~ spl0_56
| ~ spl0_191 ),
inference(resolution,[],[f1550,f399]) ).
fof(f1607,plain,
( ~ spl0_57
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f1592]) ).
fof(f1592,plain,
( $false
| ~ spl0_57
| ~ spl0_191 ),
inference(resolution,[],[f1550,f411]) ).
fof(f1606,plain,
( ~ spl0_62
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f1593]) ).
fof(f1593,plain,
( $false
| ~ spl0_62
| ~ spl0_191 ),
inference(resolution,[],[f1550,f446]) ).
fof(f1605,plain,
( ~ spl0_170
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f1594]) ).
fof(f1594,plain,
( $false
| ~ spl0_170
| ~ spl0_191 ),
inference(resolution,[],[f1550,f1374]) ).
fof(f1604,plain,
( ~ spl0_17
| ~ spl0_191 ),
inference(avatar_contradiction_clause,[],[f1601]) ).
fof(f1601,plain,
( $false
| ~ spl0_17
| ~ spl0_191 ),
inference(resolution,[],[f1550,f198]) ).
fof(f1560,plain,
( spl0_192
| spl0_191
| ~ spl0_156
| ~ spl0_176 ),
inference(avatar_split_clause,[],[f1538,f1441,f1266,f1549,f1558]) ).
fof(f1558,plain,
( spl0_192
<=> ! [X26] : ~ member(x,X26) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).
fof(f1266,plain,
( spl0_156
<=> ! [X4,X5,X3] : ~ member(ordered_pair(x,X3),cross_product(X4,X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f1441,plain,
( spl0_176
<=> ! [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_176])]) ).
fof(f1538,plain,
( ! [X26,X24,X25] :
( ~ member(X24,X25)
| ~ member(x,X26) )
| ~ spl0_156
| ~ spl0_176 ),
inference(resolution,[],[f1442,f1267]) ).
fof(f1267,plain,
( ! [X3,X4,X5] : ~ member(ordered_pair(x,X3),cross_product(X4,X5))
| ~ spl0_156 ),
inference(avatar_component_clause,[],[f1266]) ).
fof(f1442,plain,
( ! [X2,X3,X0,X1] :
( member(ordered_pair(X2,X3),cross_product(X0,X1))
| ~ member(X3,X1)
| ~ member(X2,X0) )
| ~ spl0_176 ),
inference(avatar_component_clause,[],[f1441]) ).
fof(f1551,plain,
( spl0_190
| spl0_191
| ~ spl0_154
| ~ spl0_156
| ~ spl0_176 ),
inference(avatar_split_clause,[],[f1544,f1441,f1266,f1251,f1549,f1546]) ).
fof(f1251,plain,
( spl0_154
<=> ! [X5] : ordered_pair(x,X5) = ordered_pair(y,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f1544,plain,
( ! [X2,X0,X1] :
( ~ member(X0,X2)
| ~ member(y,X1) )
| ~ spl0_154
| ~ spl0_156
| ~ spl0_176 ),
inference(subsumption_resolution,[],[f1542,f1267]) ).
fof(f1542,plain,
( ! [X2,X0,X1] :
( member(ordered_pair(x,X0),cross_product(X1,X2))
| ~ member(X0,X2)
| ~ member(y,X1) )
| ~ spl0_154
| ~ spl0_176 ),
inference(superposition,[],[f1442,f1252]) ).
fof(f1252,plain,
( ! [X5] : ordered_pair(x,X5) = ordered_pair(y,X5)
| ~ spl0_154 ),
inference(avatar_component_clause,[],[f1251]) ).
fof(f1531,plain,
( spl0_189
| ~ spl0_66
| ~ spl0_177 ),
inference(avatar_split_clause,[],[f1454,f1450,f477,f1529]) ).
fof(f1529,plain,
( spl0_189
<=> ! [X2] :
( ~ subclass(ordered_pair(x,X2),singleton(x))
| singleton(x) = ordered_pair(x,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).
fof(f1450,plain,
( spl0_177
<=> ! [X1] : subclass(singleton(x),ordered_pair(x,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
fof(f1454,plain,
( ! [X2] :
( ~ subclass(ordered_pair(x,X2),singleton(x))
| singleton(x) = ordered_pair(x,X2) )
| ~ spl0_66
| ~ spl0_177 ),
inference(resolution,[],[f1451,f478]) ).
fof(f1451,plain,
( ! [X1] : subclass(singleton(x),ordered_pair(x,X1))
| ~ spl0_177 ),
inference(avatar_component_clause,[],[f1450]) ).
fof(f1524,plain,
( spl0_188
| ~ spl0_20
| ~ spl0_184 ),
inference(avatar_split_clause,[],[f1519,f1489,f210,f1522]) ).
fof(f210,plain,
( spl0_20
<=> identity_relation = intersection(inverse(subset_relation),subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f1519,plain,
( ! [X12] :
( ~ subclass(ordered_pair(x,X12),identity_relation)
| member(singleton(singleton(X12)),inverse(subset_relation)) )
| ~ spl0_20
| ~ spl0_184 ),
inference(superposition,[],[f1490,f212]) ).
fof(f212,plain,
( identity_relation = intersection(inverse(subset_relation),subset_relation)
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f210]) ).
fof(f1513,plain,
spl0_187,
inference(avatar_split_clause,[],[f101,f1511]) ).
fof(f1511,plain,
( spl0_187
<=> ! [X0,X1] :
( X0 = X1
| ~ member(not_subclass_element(X1,X0),X0)
| ~ member(not_subclass_element(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).
fof(f101,axiom,
! [X0,X1] :
( X0 = X1
| ~ member(not_subclass_element(X1,X0),X0)
| ~ member(not_subclass_element(X0,X1),X1) ),
file('/export/starexec/sandbox2/tmp/tmp.qYmJ0hwDFn/Vampire---4.8_12445',equality4) ).
fof(f1506,plain,
( spl0_186
| ~ spl0_20
| ~ spl0_183 ),
inference(avatar_split_clause,[],[f1501,f1485,f210,f1504]) ).
fof(f1501,plain,
( ! [X12] :
( ~ subclass(ordered_pair(x,X12),identity_relation)
| member(singleton(singleton(X12)),subset_relation) )
| ~ spl0_20
| ~ spl0_183 ),
inference(superposition,[],[f1486,f212]) ).
fof(f1495,plain,
spl0_185,
inference(avatar_split_clause,[],[f99,f1493]) ).
fof(f1493,plain,
( spl0_185
<=> ! [X0,X1] :
( X0 = X1
| ~ member(not_subclass_element(X0,X1),X1)
| member(not_subclass_element(X1,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).
fof(f99,axiom,
! [X0,X1] :
( X0 = X1
| ~ member(not_subclass_element(X0,X1),X1)
| member(not_subclass_element(X1,X0),X1) ),
file('/export/starexec/sandbox2/tmp/tmp.qYmJ0hwDFn/Vampire---4.8_12445',equality2) ).
fof(f1491,plain,
( spl0_184
| ~ spl0_43
| ~ spl0_172 ),
inference(avatar_split_clause,[],[f1417,f1407,f322,f1489]) ).
fof(f1417,plain,
( ! [X18,X19,X20] :
( ~ subclass(ordered_pair(x,X18),intersection(X19,X20))
| member(singleton(singleton(X18)),X19) )
| ~ spl0_43
| ~ spl0_172 ),
inference(resolution,[],[f1408,f323]) ).
fof(f1487,plain,
( spl0_183
| ~ spl0_44
| ~ spl0_172 ),
inference(avatar_split_clause,[],[f1416,f1407,f326,f1485]) ).
fof(f1416,plain,
( ! [X16,X17,X15] :
( ~ subclass(ordered_pair(x,X15),intersection(X16,X17))
| member(singleton(singleton(X15)),X17) )
| ~ spl0_44
| ~ spl0_172 ),
inference(resolution,[],[f1408,f327]) ).
fof(f1482,plain,
( spl0_182
| ~ spl0_19
| ~ spl0_174 ),
inference(avatar_split_clause,[],[f1433,f1430,f206,f1480]) ).
fof(f1480,plain,
( spl0_182
<=> ! [X0] :
( ~ member(y,range_of(X0))
| null_class != restrict(inverse(X0),singleton(x),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).
fof(f1430,plain,
( spl0_174
<=> ! [X0] :
( null_class != restrict(X0,singleton(x),universal_class)
| ~ member(y,domain_of(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).
fof(f1433,plain,
( ! [X0] :
( ~ member(y,range_of(X0))
| null_class != restrict(inverse(X0),singleton(x),universal_class) )
| ~ spl0_19
| ~ spl0_174 ),
inference(superposition,[],[f1431,f207]) ).
fof(f1431,plain,
( ! [X0] :
( ~ member(y,domain_of(X0))
| null_class != restrict(X0,singleton(x),universal_class) )
| ~ spl0_174 ),
inference(avatar_component_clause,[],[f1430]) ).
fof(f1478,plain,
spl0_181,
inference(avatar_split_clause,[],[f98,f1476]) ).
fof(f98,axiom,
! [X0,X1] :
( X0 = X1
| member(not_subclass_element(X1,X0),X1)
| member(not_subclass_element(X0,X1),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.qYmJ0hwDFn/Vampire---4.8_12445',equality1) ).
fof(f1470,plain,
( spl0_180
| ~ spl0_26
| ~ spl0_172 ),
inference(avatar_split_clause,[],[f1418,f1407,f240,f1468]) ).
fof(f1418,plain,
( ! [X21,X22] :
( ~ subclass(ordered_pair(x,X21),complement(X22))
| ~ member(singleton(singleton(X21)),X22) )
| ~ spl0_26
| ~ spl0_172 ),
inference(resolution,[],[f1408,f241]) ).
fof(f1463,plain,
spl0_179,
inference(avatar_split_clause,[],[f64,f1461]) ).
fof(f1461,plain,
( spl0_179
<=> ! [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_179])]) ).
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.qYmJ0hwDFn/Vampire---4.8_12445',function3) ).
fof(f1459,plain,
( spl0_178
| ~ spl0_71
| ~ spl0_177 ),
inference(avatar_split_clause,[],[f1453,f1450,f497,f1457]) ).
fof(f1457,plain,
( spl0_178
<=> ! [X0,X1] :
( ~ subclass(X0,singleton(x))
| subclass(X0,ordered_pair(x,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).
fof(f1453,plain,
( ! [X0,X1] :
( ~ subclass(X0,singleton(x))
| subclass(X0,ordered_pair(x,X1)) )
| ~ spl0_71
| ~ spl0_177 ),
inference(resolution,[],[f1451,f498]) ).
fof(f1452,plain,
( spl0_177
| ~ spl0_90
| ~ spl0_175 ),
inference(avatar_split_clause,[],[f1445,f1437,f680,f1450]) ).
fof(f1437,plain,
( spl0_175
<=> ! [X0,X1] :
( ~ subclass(X0,singleton(singleton(singleton(X1))))
| subclass(X0,ordered_pair(x,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).
fof(f1445,plain,
( ! [X1] : subclass(singleton(x),ordered_pair(x,X1))
| ~ spl0_90
| ~ spl0_175 ),
inference(resolution,[],[f1438,f681]) ).
fof(f1438,plain,
( ! [X0,X1] :
( ~ subclass(X0,singleton(singleton(singleton(X1))))
| subclass(X0,ordered_pair(x,X1)) )
| ~ spl0_175 ),
inference(avatar_component_clause,[],[f1437]) ).
fof(f1443,plain,
spl0_176,
inference(avatar_split_clause,[],[f16,f1441]) ).
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.qYmJ0hwDFn/Vampire---4.8_12445',cartesian_product3) ).
fof(f1439,plain,
( spl0_175
| ~ spl0_71
| ~ spl0_171 ),
inference(avatar_split_clause,[],[f1398,f1395,f497,f1437]) ).
fof(f1398,plain,
( ! [X0,X1] :
( ~ subclass(X0,singleton(singleton(singleton(X1))))
| subclass(X0,ordered_pair(x,X1)) )
| ~ spl0_71
| ~ spl0_171 ),
inference(resolution,[],[f1396,f498]) ).
fof(f1432,plain,
( spl0_174
| ~ spl0_96
| ~ spl0_145 ),
inference(avatar_split_clause,[],[f1296,f1155,f734,f1430]) ).
fof(f1155,plain,
( spl0_145
<=> ! [X4,X0] :
( ~ member(X4,domain_of(X0))
| restrict(X0,singleton(X4),universal_class) != null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f1296,plain,
( ! [X0] :
( null_class != restrict(X0,singleton(x),universal_class)
| ~ member(y,domain_of(X0)) )
| ~ spl0_96
| ~ spl0_145 ),
inference(superposition,[],[f1156,f736]) ).
fof(f1156,plain,
( ! [X0,X4] :
( restrict(X0,singleton(X4),universal_class) != null_class
| ~ member(X4,domain_of(X0)) )
| ~ spl0_145 ),
inference(avatar_component_clause,[],[f1155]) ).
fof(f1425,plain,
( spl0_173
| ~ spl0_9
| ~ spl0_172 ),
inference(avatar_split_clause,[],[f1419,f1407,f160,f1423]) ).
fof(f1419,plain,
( ! [X23] : ~ subclass(ordered_pair(x,X23),null_class)
| ~ spl0_9
| ~ spl0_172 ),
inference(resolution,[],[f1408,f161]) ).
fof(f1409,plain,
( spl0_172
| ~ spl0_65
| ~ spl0_170 ),
inference(avatar_split_clause,[],[f1389,f1373,f473,f1407]) ).
fof(f1389,plain,
( ! [X0,X1] :
( ~ subclass(ordered_pair(x,X0),X1)
| member(singleton(singleton(X0)),X1) )
| ~ spl0_65
| ~ spl0_170 ),
inference(resolution,[],[f1374,f474]) ).
fof(f1397,plain,
( spl0_171
| ~ spl0_24
| ~ spl0_169 ),
inference(avatar_split_clause,[],[f1368,f1360,f227,f1395]) ).
fof(f1368,plain,
( ! [X7] : subclass(singleton(singleton(singleton(X7))),ordered_pair(x,X7))
| ~ spl0_24
| ~ spl0_169 ),
inference(superposition,[],[f228,f1361]) ).
fof(f1375,plain,
( spl0_170
| ~ spl0_61
| ~ spl0_169 ),
inference(avatar_split_clause,[],[f1366,f1360,f438,f1373]) ).
fof(f1366,plain,
( ! [X2] : member(singleton(singleton(X2)),ordered_pair(x,X2))
| ~ spl0_61
| ~ spl0_169 ),
inference(superposition,[],[f439,f1361]) ).
fof(f1362,plain,
( spl0_169
| ~ spl0_93
| ~ spl0_95
| ~ spl0_96
| ~ spl0_142 ),
inference(avatar_split_clause,[],[f1247,f1114,f734,f714,f706,f1360]) ).
fof(f706,plain,
( spl0_93
<=> ! [X0] : singleton(X0) = unordered_pair(x,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f714,plain,
( spl0_95
<=> ! [X1] : singleton(X1) = unordered_pair(y,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f1247,plain,
( ! [X0] : unordered_pair(singleton(x),singleton(singleton(X0))) = ordered_pair(x,X0)
| ~ spl0_93
| ~ spl0_95
| ~ spl0_96
| ~ spl0_142 ),
inference(backward_demodulation,[],[f1243,f1246]) ).
fof(f1246,plain,
( ! [X5] : ordered_pair(x,X5) = ordered_pair(y,X5)
| ~ spl0_93
| ~ spl0_95
| ~ spl0_96
| ~ spl0_142 ),
inference(forward_demodulation,[],[f1236,f1243]) ).
fof(f1236,plain,
( ! [X5] : ordered_pair(x,X5) = unordered_pair(singleton(x),singleton(singleton(X5)))
| ~ spl0_93
| ~ spl0_142 ),
inference(superposition,[],[f1115,f707]) ).
fof(f707,plain,
( ! [X0] : singleton(X0) = unordered_pair(x,X0)
| ~ spl0_93 ),
inference(avatar_component_clause,[],[f706]) ).
fof(f1243,plain,
( ! [X0] : ordered_pair(y,X0) = unordered_pair(singleton(x),singleton(singleton(X0)))
| ~ spl0_95
| ~ spl0_96
| ~ spl0_142 ),
inference(forward_demodulation,[],[f1231,f715]) ).
fof(f715,plain,
( ! [X1] : singleton(X1) = unordered_pair(y,X1)
| ~ spl0_95 ),
inference(avatar_component_clause,[],[f714]) ).
fof(f1231,plain,
( ! [X0] : ordered_pair(y,X0) = unordered_pair(singleton(x),unordered_pair(y,singleton(X0)))
| ~ spl0_96
| ~ spl0_142 ),
inference(superposition,[],[f1115,f736]) ).
fof(f1357,plain,
spl0_168,
inference(avatar_split_clause,[],[f93,f1355]) ).
fof(f1355,plain,
( spl0_168
<=> ! [X0,X3,X2,X1] :
( member(X1,unordered_pair(X0,X1))
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
fof(f93,axiom,
! [X2,X3,X0,X1] :
( member(X1,unordered_pair(X0,X1))
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
file('/export/starexec/sandbox2/tmp/tmp.qYmJ0hwDFn/Vampire---4.8_12445',corollary_2_to_unordered_pair) ).
fof(f1353,plain,
( spl0_166
| ~ spl0_167
| ~ spl0_155
| ~ spl0_163 ),
inference(avatar_split_clause,[],[f1336,f1333,f1262,f1350,f1346]) ).
fof(f1350,plain,
( spl0_167
<=> member(ordered_pair(x,x),successor_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
fof(f1333,plain,
( spl0_163
<=> ! [X12] :
( ~ member(ordered_pair(x,X12),successor_relation)
| successor(y) = X12 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
fof(f1336,plain,
( ~ member(ordered_pair(x,x),successor_relation)
| y = successor(y)
| ~ spl0_155
| ~ spl0_163 ),
inference(superposition,[],[f1334,f1263]) ).
fof(f1334,plain,
( ! [X12] :
( ~ member(ordered_pair(x,X12),successor_relation)
| successor(y) = X12 )
| ~ spl0_163 ),
inference(avatar_component_clause,[],[f1333]) ).
fof(f1344,plain,
spl0_165,
inference(avatar_split_clause,[],[f92,f1342]) ).
fof(f1342,plain,
( spl0_165
<=> ! [X0,X3,X2,X1] :
( member(X0,unordered_pair(X0,X1))
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
fof(f92,axiom,
! [X2,X3,X0,X1] :
( member(X0,unordered_pair(X0,X1))
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
file('/export/starexec/sandbox2/tmp/tmp.qYmJ0hwDFn/Vampire---4.8_12445',corollary_1_to_unordered_pair) ).
fof(f1340,plain,
( spl0_164
| ~ spl0_68
| ~ spl0_155 ),
inference(avatar_split_clause,[],[f1285,f1262,f485,f1338]) ).
fof(f1338,plain,
( spl0_164
<=> ! [X12] :
( ~ member(ordered_pair(X12,x),successor_relation)
| y = successor(X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
fof(f485,plain,
( spl0_68
<=> ! [X0,X1] :
( successor(X0) = X1
| ~ member(ordered_pair(X0,X1),successor_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f1285,plain,
( ! [X12] :
( ~ member(ordered_pair(X12,x),successor_relation)
| y = successor(X12) )
| ~ spl0_68
| ~ spl0_155 ),
inference(superposition,[],[f486,f1263]) ).
fof(f486,plain,
( ! [X0,X1] :
( ~ member(ordered_pair(X0,X1),successor_relation)
| successor(X0) = X1 )
| ~ spl0_68 ),
inference(avatar_component_clause,[],[f485]) ).
fof(f1335,plain,
( spl0_163
| ~ spl0_68
| ~ spl0_154 ),
inference(avatar_split_clause,[],[f1258,f1251,f485,f1333]) ).
fof(f1258,plain,
( ! [X12] :
( ~ member(ordered_pair(x,X12),successor_relation)
| successor(y) = X12 )
| ~ spl0_68
| ~ spl0_154 ),
inference(superposition,[],[f486,f1252]) ).
fof(f1330,plain,
spl0_162,
inference(avatar_split_clause,[],[f17,f1328]) ).
fof(f1328,plain,
( spl0_162
<=> ! [X4,X0,X1] :
( ~ member(X4,cross_product(X0,X1))
| ordered_pair(first(X4),second(X4)) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
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.qYmJ0hwDFn/Vampire---4.8_12445',cartesian_product4) ).
fof(f1326,plain,
( spl0_160
| ~ spl0_161
| ~ spl0_155
| ~ spl0_158 ),
inference(avatar_split_clause,[],[f1302,f1299,f1262,f1323,f1319]) ).
fof(f1319,plain,
( spl0_160
<=> member(y,y) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
fof(f1323,plain,
( spl0_161
<=> member(ordered_pair(x,x),element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
fof(f1302,plain,
( ~ member(ordered_pair(x,x),element_relation)
| member(y,y)
| ~ spl0_155
| ~ spl0_158 ),
inference(superposition,[],[f1300,f1263]) ).
fof(f1306,plain,
( spl0_159
| ~ spl0_42
| ~ spl0_155 ),
inference(avatar_split_clause,[],[f1286,f1262,f318,f1304]) ).
fof(f1304,plain,
( spl0_159
<=> ! [X13] :
( ~ member(ordered_pair(X13,x),element_relation)
| member(X13,y) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f318,plain,
( spl0_42
<=> ! [X0,X1] :
( member(X0,X1)
| ~ member(ordered_pair(X0,X1),element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f1286,plain,
( ! [X13] :
( ~ member(ordered_pair(X13,x),element_relation)
| member(X13,y) )
| ~ spl0_42
| ~ spl0_155 ),
inference(superposition,[],[f319,f1263]) ).
fof(f319,plain,
( ! [X0,X1] :
( ~ member(ordered_pair(X0,X1),element_relation)
| member(X0,X1) )
| ~ spl0_42 ),
inference(avatar_component_clause,[],[f318]) ).
fof(f1301,plain,
( spl0_158
| ~ spl0_42
| ~ spl0_154 ),
inference(avatar_split_clause,[],[f1259,f1251,f318,f1299]) ).
fof(f1259,plain,
( ! [X13] :
( ~ member(ordered_pair(x,X13),element_relation)
| member(y,X13) )
| ~ spl0_42
| ~ spl0_154 ),
inference(superposition,[],[f319,f1252]) ).
fof(f1295,plain,
( spl0_157
| spl0_2
| ~ spl0_115
| ~ spl0_155 ),
inference(avatar_split_clause,[],[f1289,f1262,f866,f127,f1293]) ).
fof(f1293,plain,
( spl0_157
<=> ! [X2,X0,X1] : ~ member(ordered_pair(X0,x),cross_product(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f127,plain,
( spl0_2
<=> member(y,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f866,plain,
( spl0_115
<=> ! [X2,X0,X1,X3] :
( member(X3,universal_class)
| ~ member(ordered_pair(X2,X3),cross_product(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f1289,plain,
( ! [X2,X0,X1] : ~ member(ordered_pair(X0,x),cross_product(X1,X2))
| spl0_2
| ~ spl0_115
| ~ spl0_155 ),
inference(subsumption_resolution,[],[f1281,f129]) ).
fof(f129,plain,
( ~ member(y,universal_class)
| spl0_2 ),
inference(avatar_component_clause,[],[f127]) ).
fof(f1281,plain,
( ! [X2,X0,X1] :
( ~ member(ordered_pair(X0,x),cross_product(X1,X2))
| member(y,universal_class) )
| ~ spl0_115
| ~ spl0_155 ),
inference(superposition,[],[f867,f1263]) ).
fof(f867,plain,
( ! [X2,X3,X0,X1] :
( ~ member(ordered_pair(X2,X3),cross_product(X0,X1))
| member(X3,universal_class) )
| ~ spl0_115 ),
inference(avatar_component_clause,[],[f866]) ).
fof(f1268,plain,
( spl0_156
| spl0_2
| ~ spl0_113
| ~ spl0_154 ),
inference(avatar_split_clause,[],[f1260,f1251,f849,f127,f1266]) ).
fof(f849,plain,
( spl0_113
<=> ! [X0,X3,X2,X1] :
( member(X2,universal_class)
| ~ member(ordered_pair(X2,X3),cross_product(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f1260,plain,
( ! [X3,X4,X5] : ~ member(ordered_pair(x,X3),cross_product(X4,X5))
| spl0_2
| ~ spl0_113
| ~ spl0_154 ),
inference(subsumption_resolution,[],[f1255,f129]) ).
fof(f1255,plain,
( ! [X3,X4,X5] :
( ~ member(ordered_pair(x,X3),cross_product(X4,X5))
| member(y,universal_class) )
| ~ spl0_113
| ~ spl0_154 ),
inference(superposition,[],[f850,f1252]) ).
fof(f850,plain,
( ! [X2,X3,X0,X1] :
( ~ member(ordered_pair(X2,X3),cross_product(X0,X1))
| member(X2,universal_class) )
| ~ spl0_113 ),
inference(avatar_component_clause,[],[f849]) ).
fof(f1264,plain,
( spl0_155
| ~ spl0_96
| ~ spl0_142 ),
inference(avatar_split_clause,[],[f1244,f1114,f734,f1262]) ).
fof(f1244,plain,
( ! [X0] : ordered_pair(X0,y) = ordered_pair(X0,x)
| ~ spl0_96
| ~ spl0_142 ),
inference(forward_demodulation,[],[f1232,f1115]) ).
fof(f1232,plain,
( ! [X0] : ordered_pair(X0,y) = unordered_pair(singleton(X0),unordered_pair(X0,singleton(x)))
| ~ spl0_96
| ~ spl0_142 ),
inference(superposition,[],[f1115,f736]) ).
fof(f1253,plain,
( spl0_154
| ~ spl0_93
| ~ spl0_95
| ~ spl0_96
| ~ spl0_142 ),
inference(avatar_split_clause,[],[f1246,f1114,f734,f714,f706,f1251]) ).
fof(f1230,plain,
( ~ spl0_153
| ~ spl0_74
| spl0_149 ),
inference(avatar_split_clause,[],[f1189,f1176,f530,f1227]) ).
fof(f1227,plain,
( spl0_153
<=> subclass(universal_class,subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f1189,plain,
( ~ subclass(universal_class,subset_relation)
| ~ spl0_74
| spl0_149 ),
inference(resolution,[],[f1177,f531]) ).
fof(f1225,plain,
( ~ spl0_152
| ~ spl0_78
| spl0_149 ),
inference(avatar_split_clause,[],[f1188,f1176,f577,f1222]) ).
fof(f1188,plain,
( ~ subclass(omega,subset_relation)
| ~ spl0_78
| spl0_149 ),
inference(resolution,[],[f1177,f578]) ).
fof(f1220,plain,
( ~ spl0_151
| ~ spl0_58
| spl0_149 ),
inference(avatar_split_clause,[],[f1184,f1176,f424,f1217]) ).
fof(f1217,plain,
( spl0_151
<=> member(null_class,identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f424,plain,
( spl0_58
<=> ! [X0] :
( ~ member(X0,identity_relation)
| member(X0,subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f1184,plain,
( ~ member(null_class,identity_relation)
| ~ spl0_58
| spl0_149 ),
inference(resolution,[],[f1177,f425]) ).
fof(f425,plain,
( ! [X0] :
( member(X0,subset_relation)
| ~ member(X0,identity_relation) )
| ~ spl0_58 ),
inference(avatar_component_clause,[],[f424]) ).
fof(f1183,plain,
( spl0_149
| ~ spl0_150
| ~ spl0_20
| ~ spl0_146 ),
inference(avatar_split_clause,[],[f1174,f1159,f210,f1180,f1176]) ).
fof(f1174,plain,
( ~ subclass(omega,identity_relation)
| member(null_class,subset_relation)
| ~ spl0_20
| ~ spl0_146 ),
inference(superposition,[],[f1160,f212]) ).
fof(f1169,plain,
spl0_148,
inference(avatar_split_clause,[],[f70,f1167]) ).
fof(f1167,plain,
( spl0_148
<=> ! [X1] :
( ~ member(X1,universal_class)
| null_class = X1
| member(apply(choice,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f70,axiom,
! [X1] :
( ~ member(X1,universal_class)
| null_class = X1
| member(apply(choice,X1),X1) ),
file('/export/starexec/sandbox2/tmp/tmp.qYmJ0hwDFn/Vampire---4.8_12445',choice2) ).
fof(f1165,plain,
( spl0_147
| ~ spl0_43
| ~ spl0_78 ),
inference(avatar_split_clause,[],[f584,f577,f322,f1163]) ).
fof(f584,plain,
( ! [X6,X7] :
( ~ subclass(omega,intersection(X6,X7))
| member(null_class,X6) )
| ~ spl0_43
| ~ spl0_78 ),
inference(resolution,[],[f578,f323]) ).
fof(f1161,plain,
( spl0_146
| ~ spl0_44
| ~ spl0_78 ),
inference(avatar_split_clause,[],[f583,f577,f326,f1159]) ).
fof(f583,plain,
( ! [X4,X5] :
( ~ subclass(omega,intersection(X4,X5))
| member(null_class,X5) )
| ~ spl0_44
| ~ spl0_78 ),
inference(resolution,[],[f578,f327]) ).
fof(f1157,plain,
spl0_145,
inference(avatar_split_clause,[],[f30,f1155]) ).
fof(f30,axiom,
! [X0,X4] :
( ~ member(X4,domain_of(X0))
| restrict(X0,singleton(X4),universal_class) != null_class ),
file('/export/starexec/sandbox2/tmp/tmp.qYmJ0hwDFn/Vampire---4.8_12445',domain1) ).
fof(f1153,plain,
( ~ spl0_144
| ~ spl0_77
| ~ spl0_132
| spl0_133 ),
inference(avatar_split_clause,[],[f1148,f1000,f996,f571,f1150]) ).
fof(f1150,plain,
( spl0_144
<=> subclass(universal_class,choice) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f1148,plain,
( ~ subclass(universal_class,choice)
| ~ spl0_77
| ~ spl0_132
| spl0_133 ),
inference(subsumption_resolution,[],[f1147,f1001]) ).
fof(f1147,plain,
( ~ subclass(universal_class,choice)
| universal_class = cross_product(universal_class,universal_class)
| ~ spl0_77
| ~ spl0_132 ),
inference(resolution,[],[f997,f572]) ).
fof(f1135,plain,
spl0_143,
inference(avatar_split_clause,[],[f23,f1133]) ).
fof(f1133,plain,
( spl0_143
<=> ! [X4,X0,X1] :
( ~ member(X4,X0)
| ~ member(X4,X1)
| member(X4,intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f23,axiom,
! [X0,X1,X4] :
( ~ member(X4,X0)
| ~ member(X4,X1)
| member(X4,intersection(X0,X1)) ),
file('/export/starexec/sandbox2/tmp/tmp.qYmJ0hwDFn/Vampire---4.8_12445',intersection3) ).
fof(f1116,plain,
spl0_142,
inference(avatar_split_clause,[],[f13,f1114]) ).
fof(f13,axiom,
! [X0,X1] : unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))) = ordered_pair(X0,X1),
file('/export/starexec/sandbox2/tmp/tmp.qYmJ0hwDFn/Vampire---4.8_12445',ordered_pair) ).
fof(f1090,plain,
( spl0_141
| ~ spl0_34
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1079,f1075,f272,f1088]) ).
fof(f272,plain,
( spl0_34
<=> ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f1079,plain,
( ! [X0] : ~ subclass(unordered_pair(X0,omega),null_class)
| ~ spl0_34
| ~ spl0_139 ),
inference(superposition,[],[f1076,f273]) ).
fof(f273,plain,
( ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0)
| ~ spl0_34 ),
inference(avatar_component_clause,[],[f272]) ).
fof(f1086,plain,
spl0_140,
inference(avatar_split_clause,[],[f8,f1084]) ).
fof(f8,axiom,
! [X2,X0,X1] :
( X1 = X2
| X0 = X2
| ~ member(X2,unordered_pair(X0,X1)) ),
file('/export/starexec/sandbox2/tmp/tmp.qYmJ0hwDFn/Vampire---4.8_12445',unordered_pair_member) ).
fof(f1077,plain,
( spl0_139
| ~ spl0_9
| ~ spl0_121 ),
inference(avatar_split_clause,[],[f1073,f903,f160,f1075]) ).
fof(f1073,plain,
( ! [X17] : ~ subclass(unordered_pair(omega,X17),null_class)
| ~ spl0_9
| ~ spl0_121 ),
inference(resolution,[],[f904,f161]) ).
fof(f1060,plain,
( spl0_138
| ~ spl0_34
| ~ spl0_137 ),
inference(avatar_split_clause,[],[f1053,f1049,f272,f1058]) ).
fof(f1053,plain,
( ! [X0] : ~ subclass(unordered_pair(X0,null_class),null_class)
| ~ spl0_34
| ~ spl0_137 ),
inference(superposition,[],[f1050,f273]) ).
fof(f1051,plain,
( spl0_137
| ~ spl0_9
| ~ spl0_120 ),
inference(avatar_split_clause,[],[f1047,f899,f160,f1049]) ).
fof(f1047,plain,
( ! [X19] : ~ subclass(unordered_pair(null_class,X19),null_class)
| ~ spl0_9
| ~ spl0_120 ),
inference(resolution,[],[f900,f161]) ).
fof(f1038,plain,
( spl0_133
| ~ spl0_136
| ~ spl0_77
| ~ spl0_119 ),
inference(avatar_split_clause,[],[f897,f882,f571,f1035,f1000]) ).
fof(f1035,plain,
( spl0_136
<=> subclass(universal_class,successor_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f897,plain,
( ~ subclass(universal_class,successor_relation)
| universal_class = cross_product(universal_class,universal_class)
| ~ spl0_77
| ~ spl0_119 ),
inference(resolution,[],[f883,f572]) ).
fof(f1026,plain,
( spl0_135
| ~ spl0_6
| ~ spl0_11
| ~ spl0_107 ),
inference(avatar_split_clause,[],[f1021,f816,f168,f147,f1023]) ).
fof(f1023,plain,
( spl0_135
<=> inductive(universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f816,plain,
( spl0_107
<=> ! [X0] :
( inductive(X0)
| ~ member(null_class,X0)
| ~ subclass(image(successor_relation,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f1021,plain,
( inductive(universal_class)
| ~ spl0_6
| ~ spl0_11
| ~ spl0_107 ),
inference(subsumption_resolution,[],[f1011,f148]) ).
fof(f1011,plain,
( inductive(universal_class)
| ~ subclass(image(successor_relation,universal_class),universal_class)
| ~ spl0_11
| ~ spl0_107 ),
inference(resolution,[],[f817,f170]) ).
fof(f817,plain,
( ! [X0] :
( ~ member(null_class,X0)
| inductive(X0)
| ~ subclass(image(successor_relation,X0),X0) )
| ~ spl0_107 ),
inference(avatar_component_clause,[],[f816]) ).
fof(f1007,plain,
( spl0_133
| ~ spl0_134
| ~ spl0_77
| ~ spl0_118 ),
inference(avatar_split_clause,[],[f892,f878,f571,f1004,f1000]) ).
fof(f1004,plain,
( spl0_134
<=> subclass(universal_class,element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f878,plain,
( spl0_118
<=> ! [X10] :
( ~ subclass(X10,element_relation)
| subclass(X10,cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f892,plain,
( ~ subclass(universal_class,element_relation)
| universal_class = cross_product(universal_class,universal_class)
| ~ spl0_77
| ~ spl0_118 ),
inference(resolution,[],[f879,f572]) ).
fof(f879,plain,
( ! [X10] :
( subclass(X10,cross_product(universal_class,universal_class))
| ~ subclass(X10,element_relation) )
| ~ spl0_118 ),
inference(avatar_component_clause,[],[f878]) ).
fof(f998,plain,
( spl0_132
| ~ spl0_36
| ~ spl0_71 ),
inference(avatar_split_clause,[],[f632,f497,f287,f996]) ).
fof(f287,plain,
( spl0_36
<=> subclass(choice,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f632,plain,
( ! [X25] :
( ~ subclass(X25,choice)
| subclass(X25,cross_product(universal_class,universal_class)) )
| ~ spl0_36
| ~ spl0_71 ),
inference(resolution,[],[f498,f289]) ).
fof(f289,plain,
( subclass(choice,cross_product(universal_class,universal_class))
| ~ spl0_36 ),
inference(avatar_component_clause,[],[f287]) ).
fof(f994,plain,
( spl0_131
| ~ spl0_35
| ~ spl0_71 ),
inference(avatar_split_clause,[],[f627,f497,f277,f992]) ).
fof(f992,plain,
( spl0_131
<=> ! [X17] :
( ~ subclass(X17,image(successor_relation,omega))
| subclass(X17,omega) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f277,plain,
( spl0_35
<=> subclass(image(successor_relation,omega),omega) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f627,plain,
( ! [X17] :
( ~ subclass(X17,image(successor_relation,omega))
| subclass(X17,omega) )
| ~ spl0_35
| ~ spl0_71 ),
inference(resolution,[],[f498,f279]) ).
fof(f279,plain,
( subclass(image(successor_relation,omega),omega)
| ~ spl0_35 ),
inference(avatar_component_clause,[],[f277]) ).
fof(f984,plain,
( spl0_130
| ~ spl0_43
| ~ spl0_75 ),
inference(avatar_split_clause,[],[f567,f534,f322,f982]) ).
fof(f982,plain,
( spl0_130
<=> ! [X6,X7] :
( ~ subclass(universal_class,intersection(X6,X7))
| member(omega,X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f567,plain,
( ! [X6,X7] :
( ~ subclass(universal_class,intersection(X6,X7))
| member(omega,X6) )
| ~ spl0_43
| ~ spl0_75 ),
inference(resolution,[],[f535,f323]) ).
fof(f980,plain,
( spl0_129
| ~ spl0_44
| ~ spl0_75 ),
inference(avatar_split_clause,[],[f566,f534,f326,f978]) ).
fof(f566,plain,
( ! [X4,X5] :
( ~ subclass(universal_class,intersection(X4,X5))
| member(omega,X5) )
| ~ spl0_44
| ~ spl0_75 ),
inference(resolution,[],[f535,f327]) ).
fof(f976,plain,
( spl0_128
| ~ spl0_43
| ~ spl0_74 ),
inference(avatar_split_clause,[],[f555,f530,f322,f974]) ).
fof(f974,plain,
( spl0_128
<=> ! [X6,X7] :
( ~ subclass(universal_class,intersection(X6,X7))
| member(null_class,X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f555,plain,
( ! [X6,X7] :
( ~ subclass(universal_class,intersection(X6,X7))
| member(null_class,X6) )
| ~ spl0_43
| ~ spl0_74 ),
inference(resolution,[],[f531,f323]) ).
fof(f972,plain,
( spl0_127
| ~ spl0_44
| ~ spl0_74 ),
inference(avatar_split_clause,[],[f554,f530,f326,f970]) ).
fof(f554,plain,
( ! [X4,X5] :
( ~ subclass(universal_class,intersection(X4,X5))
| member(null_class,X5) )
| ~ spl0_44
| ~ spl0_74 ),
inference(resolution,[],[f531,f327]) ).
fof(f964,plain,
( spl0_126
| ~ spl0_55
| ~ spl0_65 ),
inference(avatar_split_clause,[],[f522,f473,f390,f962]) ).
fof(f522,plain,
( ! [X31,X30] :
( ~ subclass(unordered_pair(X30,omega),X31)
| member(omega,X31) )
| ~ spl0_55
| ~ spl0_65 ),
inference(resolution,[],[f474,f391]) ).
fof(f956,plain,
( spl0_125
| ~ spl0_37
| ~ spl0_100 ),
inference(avatar_split_clause,[],[f944,f777,f292,f954]) ).
fof(f954,plain,
( spl0_125
<=> ! [X0] : union(complement(X0),X0) = complement(null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f292,plain,
( spl0_37
<=> ! [X0] : null_class = intersection(complement(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f944,plain,
( ! [X0] : union(complement(X0),X0) = complement(null_class)
| ~ spl0_37
| ~ spl0_100 ),
inference(superposition,[],[f778,f293]) ).
fof(f293,plain,
( ! [X0] : null_class = intersection(complement(X0),X0)
| ~ spl0_37 ),
inference(avatar_component_clause,[],[f292]) ).
fof(f933,plain,
( spl0_124
| ~ spl0_7
| ~ spl0_97 ),
inference(avatar_split_clause,[],[f915,f739,f151,f931]) ).
fof(f915,plain,
( ! [X12] :
( member(omega,X12)
| member(omega,complement(X12)) )
| ~ spl0_7
| ~ spl0_97 ),
inference(resolution,[],[f740,f153]) ).
fof(f929,plain,
( spl0_123
| ~ spl0_11
| ~ spl0_97 ),
inference(avatar_split_clause,[],[f914,f739,f168,f927]) ).
fof(f914,plain,
( ! [X11] :
( member(null_class,X11)
| member(null_class,complement(X11)) )
| ~ spl0_11
| ~ spl0_97 ),
inference(resolution,[],[f740,f170]) ).
fof(f909,plain,
( spl0_122
| ~ spl0_54
| ~ spl0_65 ),
inference(avatar_split_clause,[],[f521,f473,f386,f907]) ).
fof(f521,plain,
( ! [X28,X29] :
( ~ subclass(unordered_pair(X28,null_class),X29)
| member(null_class,X29) )
| ~ spl0_54
| ~ spl0_65 ),
inference(resolution,[],[f474,f387]) ).
fof(f905,plain,
( spl0_121
| ~ spl0_53
| ~ spl0_65 ),
inference(avatar_split_clause,[],[f518,f473,f382,f903]) ).
fof(f518,plain,
( ! [X21,X20] :
( ~ subclass(unordered_pair(omega,X20),X21)
| member(omega,X21) )
| ~ spl0_53
| ~ spl0_65 ),
inference(resolution,[],[f474,f383]) ).
fof(f901,plain,
( spl0_120
| ~ spl0_52
| ~ spl0_65 ),
inference(avatar_split_clause,[],[f517,f473,f378,f899]) ).
fof(f517,plain,
( ! [X18,X19] :
( ~ subclass(unordered_pair(null_class,X18),X19)
| member(null_class,X19) )
| ~ spl0_52
| ~ spl0_65 ),
inference(resolution,[],[f474,f379]) ).
fof(f884,plain,
( spl0_119
| ~ spl0_14
| ~ spl0_71 ),
inference(avatar_split_clause,[],[f628,f497,f182,f882]) ).
fof(f182,plain,
( spl0_14
<=> subclass(successor_relation,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f628,plain,
( ! [X18] :
( ~ subclass(X18,successor_relation)
| subclass(X18,cross_product(universal_class,universal_class)) )
| ~ spl0_14
| ~ spl0_71 ),
inference(resolution,[],[f498,f184]) ).
fof(f184,plain,
( subclass(successor_relation,cross_product(universal_class,universal_class))
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f182]) ).
fof(f880,plain,
( spl0_118
| ~ spl0_13
| ~ spl0_71 ),
inference(avatar_split_clause,[],[f623,f497,f177,f878]) ).
fof(f177,plain,
( spl0_13
<=> subclass(element_relation,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f623,plain,
( ! [X10] :
( ~ subclass(X10,element_relation)
| subclass(X10,cross_product(universal_class,universal_class)) )
| ~ spl0_13
| ~ spl0_71 ),
inference(resolution,[],[f498,f179]) ).
fof(f179,plain,
( subclass(element_relation,cross_product(universal_class,universal_class))
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f177]) ).
fof(f876,plain,
( spl0_117
| ~ spl0_12
| ~ spl0_65 ),
inference(avatar_split_clause,[],[f511,f473,f173,f874]) ).
fof(f511,plain,
( ! [X8,X9,X7] :
( ~ subclass(universal_class,X7)
| member(unordered_pair(X8,X9),X7) )
| ~ spl0_12
| ~ spl0_65 ),
inference(resolution,[],[f474,f174]) ).
fof(f872,plain,
( spl0_116
| ~ spl0_106
| ~ spl0_82
| ~ spl0_86 ),
inference(avatar_split_clause,[],[f800,f640,f604,f811,f870]) ).
fof(f870,plain,
( spl0_116
<=> ! [X3] : member(singleton(X3),subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f811,plain,
( spl0_106
<=> subclass(universal_class,identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f640,plain,
( spl0_86
<=> ! [X24] :
( ~ subclass(X24,identity_relation)
| subclass(X24,subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f800,plain,
( ! [X3] :
( ~ subclass(universal_class,identity_relation)
| member(singleton(X3),subset_relation) )
| ~ spl0_82
| ~ spl0_86 ),
inference(resolution,[],[f641,f605]) ).
fof(f641,plain,
( ! [X24] :
( subclass(X24,subset_relation)
| ~ subclass(X24,identity_relation) )
| ~ spl0_86 ),
inference(avatar_component_clause,[],[f640]) ).
fof(f868,plain,
spl0_115,
inference(avatar_split_clause,[],[f95,f866]) ).
fof(f95,axiom,
! [X2,X3,X0,X1] :
( member(X3,universal_class)
| ~ member(ordered_pair(X2,X3),cross_product(X0,X1)) ),
file('/export/starexec/sandbox2/tmp/tmp.qYmJ0hwDFn/Vampire---4.8_12445',corollary_2_to_cartesian_product) ).
fof(f863,plain,
( ~ spl0_114
| ~ spl0_9
| ~ spl0_109 ),
inference(avatar_split_clause,[],[f858,f825,f160,f860]) ).
fof(f858,plain,
( ~ subclass(singleton(omega),null_class)
| ~ spl0_9
| ~ spl0_109 ),
inference(resolution,[],[f826,f161]) ).
fof(f851,plain,
spl0_113,
inference(avatar_split_clause,[],[f94,f849]) ).
fof(f94,axiom,
! [X2,X3,X0,X1] :
( member(X2,universal_class)
| ~ member(ordered_pair(X2,X3),cross_product(X0,X1)) ),
file('/export/starexec/sandbox2/tmp/tmp.qYmJ0hwDFn/Vampire---4.8_12445',corollary_1_to_cartesian_product) ).
fof(f847,plain,
( ~ spl0_112
| ~ spl0_9
| ~ spl0_108 ),
inference(avatar_split_clause,[],[f842,f821,f160,f844]) ).
fof(f842,plain,
( ~ subclass(singleton(null_class),null_class)
| ~ spl0_9
| ~ spl0_108 ),
inference(resolution,[],[f822,f161]) ).
fof(f835,plain,
spl0_111,
inference(avatar_split_clause,[],[f65,f833]) ).
fof(f833,plain,
( spl0_111
<=> ! [X0,X8] :
( ~ function(X8)
| ~ member(X0,universal_class)
| member(image(X8,X0),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f65,axiom,
! [X0,X8] :
( ~ function(X8)
| ~ member(X0,universal_class)
| member(image(X8,X0),universal_class) ),
file('/export/starexec/sandbox2/tmp/tmp.qYmJ0hwDFn/Vampire---4.8_12445',replacement) ).
fof(f831,plain,
( spl0_110
| ~ spl0_26
| ~ spl0_78 ),
inference(avatar_split_clause,[],[f585,f577,f240,f829]) ).
fof(f829,plain,
( spl0_110
<=> ! [X8] :
( ~ subclass(omega,complement(X8))
| ~ member(null_class,X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f585,plain,
( ! [X8] :
( ~ subclass(omega,complement(X8))
| ~ member(null_class,X8) )
| ~ spl0_26
| ~ spl0_78 ),
inference(resolution,[],[f578,f241]) ).
fof(f827,plain,
( spl0_109
| ~ spl0_57
| ~ spl0_65 ),
inference(avatar_split_clause,[],[f524,f473,f409,f825]) ).
fof(f524,plain,
( ! [X33] :
( ~ subclass(singleton(omega),X33)
| member(omega,X33) )
| ~ spl0_57
| ~ spl0_65 ),
inference(resolution,[],[f474,f411]) ).
fof(f823,plain,
( spl0_108
| ~ spl0_56
| ~ spl0_65 ),
inference(avatar_split_clause,[],[f523,f473,f397,f821]) ).
fof(f523,plain,
( ! [X32] :
( ~ subclass(singleton(null_class),X32)
| member(null_class,X32) )
| ~ spl0_56
| ~ spl0_65 ),
inference(resolution,[],[f474,f399]) ).
fof(f818,plain,
spl0_107,
inference(avatar_split_clause,[],[f49,f816]) ).
fof(f49,axiom,
! [X0] :
( inductive(X0)
| ~ member(null_class,X0)
| ~ subclass(image(successor_relation,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.qYmJ0hwDFn/Vampire---4.8_12445',inductive3) ).
fof(f814,plain,
( spl0_105
| ~ spl0_106
| ~ spl0_77
| ~ spl0_86 ),
inference(avatar_split_clause,[],[f801,f640,f571,f811,f807]) ).
fof(f801,plain,
( ~ subclass(universal_class,identity_relation)
| universal_class = subset_relation
| ~ spl0_77
| ~ spl0_86 ),
inference(resolution,[],[f641,f572]) ).
fof(f805,plain,
spl0_104,
inference(avatar_split_clause,[],[f29,f803]) ).
fof(f794,plain,
( spl0_103
| ~ spl0_66
| ~ spl0_90 ),
inference(avatar_split_clause,[],[f684,f680,f477,f792]) ).
fof(f684,plain,
( ! [X2] :
( ~ subclass(singleton(X2),singleton(x))
| singleton(X2) = singleton(x) )
| ~ spl0_66
| ~ spl0_90 ),
inference(resolution,[],[f681,f478]) ).
fof(f787,plain,
spl0_102,
inference(avatar_split_clause,[],[f28,f785]) ).
fof(f28,axiom,
! [X0,X1,X5] : intersection(X5,cross_product(X0,X1)) = restrict(X5,X0,X1),
file('/export/starexec/sandbox2/tmp/tmp.qYmJ0hwDFn/Vampire---4.8_12445',restriction1) ).
fof(f783,plain,
( spl0_101
| ~ spl0_71
| ~ spl0_90 ),
inference(avatar_split_clause,[],[f683,f680,f497,f781]) ).
fof(f781,plain,
( spl0_101
<=> ! [X0,X1] :
( ~ subclass(X0,singleton(x))
| subclass(X0,singleton(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f683,plain,
( ! [X0,X1] :
( ~ subclass(X0,singleton(x))
| subclass(X0,singleton(X1)) )
| ~ spl0_71
| ~ spl0_90 ),
inference(resolution,[],[f681,f498]) ).
fof(f779,plain,
spl0_100,
inference(avatar_split_clause,[],[f26,f777]) ).
fof(f26,axiom,
! [X0,X1] : complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
file('/export/starexec/sandbox2/tmp/tmp.qYmJ0hwDFn/Vampire---4.8_12445',union) ).
fof(f775,plain,
( spl0_99
| ~ spl0_70
| ~ spl0_96 ),
inference(avatar_split_clause,[],[f753,f734,f493,f773]) ).
fof(f773,plain,
( spl0_99
<=> ! [X4] : apply(X4,y) = apply(X4,x) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f493,plain,
( spl0_70
<=> ! [X1,X8] : sum_class(image(X8,singleton(X1))) = apply(X8,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f753,plain,
( ! [X4] : apply(X4,y) = apply(X4,x)
| ~ spl0_70
| ~ spl0_96 ),
inference(forward_demodulation,[],[f749,f494]) ).
fof(f494,plain,
( ! [X1,X8] : sum_class(image(X8,singleton(X1))) = apply(X8,X1)
| ~ spl0_70 ),
inference(avatar_component_clause,[],[f493]) ).
fof(f749,plain,
( ! [X4] : apply(X4,y) = sum_class(image(X4,singleton(x)))
| ~ spl0_70
| ~ spl0_96 ),
inference(superposition,[],[f494,f736]) ).
fof(f771,plain,
( spl0_98
| ~ spl0_27
| ~ spl0_96 ),
inference(avatar_split_clause,[],[f745,f734,f244,f768]) ).
fof(f745,plain,
( successor(y) = union(y,singleton(x))
| ~ spl0_27
| ~ spl0_96 ),
inference(superposition,[],[f245,f736]) ).
fof(f741,plain,
spl0_97,
inference(avatar_split_clause,[],[f25,f739]) ).
fof(f25,axiom,
! [X0,X4] :
( ~ member(X4,universal_class)
| member(X4,X0)
| member(X4,complement(X0)) ),
file('/export/starexec/sandbox2/tmp/tmp.qYmJ0hwDFn/Vampire---4.8_12445',complement2) ).
fof(f737,plain,
( spl0_96
| ~ spl0_89
| ~ spl0_93 ),
inference(avatar_split_clause,[],[f719,f706,f660,f734]) ).
fof(f660,plain,
( spl0_89
<=> ! [X1] : singleton(X1) = unordered_pair(X1,y) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f719,plain,
( singleton(x) = singleton(y)
| ~ spl0_89
| ~ spl0_93 ),
inference(superposition,[],[f707,f661]) ).
fof(f661,plain,
( ! [X1] : singleton(X1) = unordered_pair(X1,y)
| ~ spl0_89 ),
inference(avatar_component_clause,[],[f660]) ).
fof(f716,plain,
( spl0_95
| spl0_2
| ~ spl0_73 ),
inference(avatar_split_clause,[],[f664,f505,f127,f714]) ).
fof(f505,plain,
( spl0_73
<=> ! [X0,X1] :
( member(X0,universal_class)
| unordered_pair(X0,X1) = singleton(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f664,plain,
( ! [X1] : singleton(X1) = unordered_pair(y,X1)
| spl0_2
| ~ spl0_73 ),
inference(resolution,[],[f506,f129]) ).
fof(f506,plain,
( ! [X0,X1] :
( member(X0,universal_class)
| unordered_pair(X0,X1) = singleton(X1) )
| ~ spl0_73 ),
inference(avatar_component_clause,[],[f505]) ).
fof(f712,plain,
spl0_94,
inference(avatar_split_clause,[],[f15,f710]) ).
fof(f710,plain,
( spl0_94
<=> ! [X2,X0,X1,X3] :
( member(X3,X1)
| ~ member(ordered_pair(X2,X3),cross_product(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
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.qYmJ0hwDFn/Vampire---4.8_12445',cartesian_product2) ).
fof(f708,plain,
( spl0_93
| spl0_1
| ~ spl0_73 ),
inference(avatar_split_clause,[],[f663,f505,f122,f706]) ).
fof(f122,plain,
( spl0_1
<=> member(x,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f663,plain,
( ! [X0] : singleton(X0) = unordered_pair(x,X0)
| spl0_1
| ~ spl0_73 ),
inference(resolution,[],[f506,f124]) ).
fof(f124,plain,
( ~ member(x,universal_class)
| spl0_1 ),
inference(avatar_component_clause,[],[f122]) ).
fof(f702,plain,
( spl0_92
| ~ spl0_24
| ~ spl0_89 ),
inference(avatar_split_clause,[],[f693,f660,f227,f700]) ).
fof(f700,plain,
( spl0_92
<=> ! [X2] : subclass(singleton(y),singleton(X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f693,plain,
( ! [X2] : subclass(singleton(y),singleton(X2))
| ~ spl0_24
| ~ spl0_89 ),
inference(superposition,[],[f228,f661]) ).
fof(f688,plain,
spl0_91,
inference(avatar_split_clause,[],[f14,f686]) ).
fof(f686,plain,
( spl0_91
<=> ! [X0,X3,X2,X1] :
( member(X2,X0)
| ~ member(ordered_pair(X2,X3),cross_product(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
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.qYmJ0hwDFn/Vampire---4.8_12445',cartesian_product1) ).
fof(f682,plain,
( spl0_90
| ~ spl0_24
| ~ spl0_88 ),
inference(avatar_split_clause,[],[f673,f656,f227,f680]) ).
fof(f656,plain,
( spl0_88
<=> ! [X0] : singleton(X0) = unordered_pair(X0,x) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f673,plain,
( ! [X2] : subclass(singleton(x),singleton(X2))
| ~ spl0_24
| ~ spl0_88 ),
inference(superposition,[],[f228,f657]) ).
fof(f657,plain,
( ! [X0] : singleton(X0) = unordered_pair(X0,x)
| ~ spl0_88 ),
inference(avatar_component_clause,[],[f656]) ).
fof(f662,plain,
( spl0_89
| spl0_2
| ~ spl0_72 ),
inference(avatar_split_clause,[],[f644,f501,f127,f660]) ).
fof(f501,plain,
( spl0_72
<=> ! [X0,X1] :
( member(X1,universal_class)
| unordered_pair(X0,X1) = singleton(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f644,plain,
( ! [X1] : singleton(X1) = unordered_pair(X1,y)
| spl0_2
| ~ spl0_72 ),
inference(resolution,[],[f502,f129]) ).
fof(f502,plain,
( ! [X0,X1] :
( member(X1,universal_class)
| unordered_pair(X0,X1) = singleton(X0) )
| ~ spl0_72 ),
inference(avatar_component_clause,[],[f501]) ).
fof(f658,plain,
( spl0_88
| spl0_1
| ~ spl0_72 ),
inference(avatar_split_clause,[],[f643,f501,f122,f656]) ).
fof(f643,plain,
( ! [X0] : singleton(X0) = unordered_pair(X0,x)
| spl0_1
| ~ spl0_72 ),
inference(resolution,[],[f502,f124]) ).
fof(f654,plain,
( ~ spl0_87
| spl0_2
| spl0_3
| ~ spl0_72 ),
inference(avatar_split_clause,[],[f649,f501,f132,f127,f651]) ).
fof(f132,plain,
( spl0_3
<=> null_class = unordered_pair(x,y) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f649,plain,
( null_class != singleton(x)
| spl0_2
| spl0_3
| ~ spl0_72 ),
inference(backward_demodulation,[],[f134,f644]) ).
fof(f134,plain,
( null_class != unordered_pair(x,y)
| spl0_3 ),
inference(avatar_component_clause,[],[f132]) ).
fof(f642,plain,
( spl0_86
| ~ spl0_64
| ~ spl0_71 ),
inference(avatar_split_clause,[],[f631,f497,f468,f640]) ).
fof(f468,plain,
( spl0_64
<=> subclass(identity_relation,subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f631,plain,
( ! [X24] :
( ~ subclass(X24,identity_relation)
| subclass(X24,subset_relation) )
| ~ spl0_64
| ~ spl0_71 ),
inference(resolution,[],[f498,f470]) ).
fof(f470,plain,
( subclass(identity_relation,subset_relation)
| ~ spl0_64 ),
inference(avatar_component_clause,[],[f468]) ).
fof(f636,plain,
( spl0_85
| ~ spl0_10
| ~ spl0_71 ),
inference(avatar_split_clause,[],[f624,f497,f164,f634]) ).
fof(f634,plain,
( spl0_85
<=> ! [X12,X11] :
( ~ subclass(X11,null_class)
| subclass(X11,X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f624,plain,
( ! [X11,X12] :
( ~ subclass(X11,null_class)
| subclass(X11,X12) )
| ~ spl0_10
| ~ spl0_71 ),
inference(resolution,[],[f498,f165]) ).
fof(f615,plain,
( spl0_84
| ~ spl0_26
| ~ spl0_75 ),
inference(avatar_split_clause,[],[f568,f534,f240,f613]) ).
fof(f613,plain,
( spl0_84
<=> ! [X8] :
( ~ subclass(universal_class,complement(X8))
| ~ member(omega,X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f568,plain,
( ! [X8] :
( ~ subclass(universal_class,complement(X8))
| ~ member(omega,X8) )
| ~ spl0_26
| ~ spl0_75 ),
inference(resolution,[],[f535,f241]) ).
fof(f611,plain,
( spl0_83
| ~ spl0_26
| ~ spl0_74 ),
inference(avatar_split_clause,[],[f556,f530,f240,f609]) ).
fof(f609,plain,
( spl0_83
<=> ! [X8] :
( ~ subclass(universal_class,complement(X8))
| ~ member(null_class,X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f556,plain,
( ! [X8] :
( ~ subclass(universal_class,complement(X8))
| ~ member(null_class,X8) )
| ~ spl0_26
| ~ spl0_74 ),
inference(resolution,[],[f531,f241]) ).
fof(f606,plain,
( spl0_82
| ~ spl0_25
| ~ spl0_65 ),
inference(avatar_split_clause,[],[f512,f473,f232,f604]) ).
fof(f512,plain,
( ! [X10,X11] :
( ~ subclass(universal_class,X10)
| member(singleton(X11),X10) )
| ~ spl0_25
| ~ spl0_65 ),
inference(resolution,[],[f474,f233]) ).
fof(f600,plain,
( spl0_80
| ~ spl0_81
| ~ spl0_64
| ~ spl0_66 ),
inference(avatar_split_clause,[],[f549,f477,f468,f597,f593]) ).
fof(f549,plain,
( ~ subclass(subset_relation,identity_relation)
| identity_relation = subset_relation
| ~ spl0_64
| ~ spl0_66 ),
inference(resolution,[],[f478,f470]) ).
fof(f591,plain,
( ~ spl0_79
| ~ spl0_9
| ~ spl0_78 ),
inference(avatar_split_clause,[],[f586,f577,f160,f588]) ).
fof(f586,plain,
( ~ subclass(omega,null_class)
| ~ spl0_9
| ~ spl0_78 ),
inference(resolution,[],[f578,f161]) ).
fof(f579,plain,
( spl0_78
| ~ spl0_17
| ~ spl0_65 ),
inference(avatar_split_clause,[],[f527,f473,f196,f577]) ).
fof(f527,plain,
( ! [X38] :
( ~ subclass(omega,X38)
| member(null_class,X38) )
| ~ spl0_17
| ~ spl0_65 ),
inference(resolution,[],[f474,f198]) ).
fof(f573,plain,
( spl0_77
| ~ spl0_6
| ~ spl0_66 ),
inference(avatar_split_clause,[],[f537,f477,f147,f571]) ).
fof(f537,plain,
( ! [X0] :
( ~ subclass(universal_class,X0)
| universal_class = X0 )
| ~ spl0_6
| ~ spl0_66 ),
inference(resolution,[],[f478,f148]) ).
fof(f562,plain,
( ~ spl0_76
| ~ spl0_9
| ~ spl0_74 ),
inference(avatar_split_clause,[],[f557,f530,f160,f559]) ).
fof(f559,plain,
( spl0_76
<=> subclass(universal_class,null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f557,plain,
( ~ subclass(universal_class,null_class)
| ~ spl0_9
| ~ spl0_74 ),
inference(resolution,[],[f531,f161]) ).
fof(f536,plain,
( spl0_75
| ~ spl0_7
| ~ spl0_65 ),
inference(avatar_split_clause,[],[f514,f473,f151,f534]) ).
fof(f514,plain,
( ! [X13] :
( ~ subclass(universal_class,X13)
| member(omega,X13) )
| ~ spl0_7
| ~ spl0_65 ),
inference(resolution,[],[f474,f153]) ).
fof(f532,plain,
( spl0_74
| ~ spl0_11
| ~ spl0_65 ),
inference(avatar_split_clause,[],[f513,f473,f168,f530]) ).
fof(f513,plain,
( ! [X12] :
( ~ subclass(universal_class,X12)
| member(null_class,X12) )
| ~ spl0_11
| ~ spl0_65 ),
inference(resolution,[],[f474,f170]) ).
fof(f507,plain,
spl0_73,
inference(avatar_split_clause,[],[f112,f505]) ).
fof(f112,axiom,
! [X0,X1] :
( member(X0,universal_class)
| unordered_pair(X0,X1) = singleton(X1) ),
file('/export/starexec/sandbox2/tmp/tmp.qYmJ0hwDFn/Vampire---4.8_12445',unordered_pair_equals_singleton2) ).
fof(f503,plain,
spl0_72,
inference(avatar_split_clause,[],[f111,f501]) ).
fof(f111,axiom,
! [X0,X1] :
( member(X1,universal_class)
| unordered_pair(X0,X1) = singleton(X0) ),
file('/export/starexec/sandbox2/tmp/tmp.qYmJ0hwDFn/Vampire---4.8_12445',unordered_pair_equals_singleton1) ).
fof(f499,plain,
spl0_71,
inference(avatar_split_clause,[],[f97,f497]) ).
fof(f97,axiom,
! [X0,X1,X4] :
( ~ subclass(X0,X1)
| ~ subclass(X1,X4)
| subclass(X0,X4) ),
file('/export/starexec/sandbox2/tmp/tmp.qYmJ0hwDFn/Vampire---4.8_12445',transitivity_of_subclass) ).
fof(f495,plain,
spl0_70,
inference(avatar_split_clause,[],[f68,f493]) ).
fof(f68,axiom,
! [X1,X8] : sum_class(image(X8,singleton(X1))) = apply(X8,X1),
file('/export/starexec/sandbox2/tmp/tmp.qYmJ0hwDFn/Vampire---4.8_12445',apply) ).
fof(f491,plain,
spl0_69,
inference(avatar_split_clause,[],[f67,f489]) ).
fof(f489,plain,
( spl0_69
<=> ! [X0] :
( null_class = X0
| null_class = intersection(X0,regular(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f67,axiom,
! [X0] :
( null_class = X0
| null_class = intersection(X0,regular(X0)) ),
file('/export/starexec/sandbox2/tmp/tmp.qYmJ0hwDFn/Vampire---4.8_12445',regularity2) ).
fof(f487,plain,
spl0_68,
inference(avatar_split_clause,[],[f45,f485]) ).
fof(f45,axiom,
! [X0,X1] :
( successor(X0) = X1
| ~ member(ordered_pair(X0,X1),successor_relation) ),
file('/export/starexec/sandbox2/tmp/tmp.qYmJ0hwDFn/Vampire---4.8_12445',successor_relation2) ).
fof(f483,plain,
spl0_67,
inference(avatar_split_clause,[],[f42,f481]) ).
fof(f481,plain,
( spl0_67
<=> ! [X5,X0] : range_of(restrict(X5,X0,universal_class)) = image(X5,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f42,axiom,
! [X0,X5] : range_of(restrict(X5,X0,universal_class)) = image(X5,X0),
file('/export/starexec/sandbox2/tmp/tmp.qYmJ0hwDFn/Vampire---4.8_12445',image) ).
fof(f479,plain,
spl0_66,
inference(avatar_split_clause,[],[f7,f477]) ).
fof(f7,axiom,
! [X0,X1] :
( ~ subclass(X0,X1)
| ~ subclass(X1,X0)
| X0 = X1 ),
file('/export/starexec/sandbox2/tmp/tmp.qYmJ0hwDFn/Vampire---4.8_12445',subclass_implies_equal) ).
fof(f475,plain,
spl0_65,
inference(avatar_split_clause,[],[f1,f473]) ).
fof(f1,axiom,
! [X2,X0,X1] :
( ~ subclass(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
file('/export/starexec/sandbox2/tmp/tmp.qYmJ0hwDFn/Vampire---4.8_12445',subclass_members) ).
fof(f471,plain,
( spl0_64
| ~ spl0_38
| ~ spl0_63 ),
inference(avatar_split_clause,[],[f466,f462,f302,f468]) ).
fof(f462,plain,
( spl0_63
<=> ! [X0] :
( ~ member(not_subclass_element(X0,subset_relation),identity_relation)
| subclass(X0,subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f466,plain,
( subclass(identity_relation,subset_relation)
| ~ spl0_38
| ~ spl0_63 ),
inference(duplicate_literal_removal,[],[f465]) ).
fof(f465,plain,
( subclass(identity_relation,subset_relation)
| subclass(identity_relation,subset_relation)
| ~ spl0_38
| ~ spl0_63 ),
inference(resolution,[],[f463,f303]) ).
fof(f463,plain,
( ! [X0] :
( ~ member(not_subclass_element(X0,subset_relation),identity_relation)
| subclass(X0,subset_relation) )
| ~ spl0_63 ),
inference(avatar_component_clause,[],[f462]) ).
fof(f464,plain,
( spl0_63
| ~ spl0_39
| ~ spl0_58 ),
inference(avatar_split_clause,[],[f427,f424,f306,f462]) ).
fof(f306,plain,
( spl0_39
<=> ! [X0,X1] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f427,plain,
( ! [X0] :
( ~ member(not_subclass_element(X0,subset_relation),identity_relation)
| subclass(X0,subset_relation) )
| ~ spl0_39
| ~ spl0_58 ),
inference(resolution,[],[f425,f307]) ).
fof(f307,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(X0,X1),X1)
| subclass(X0,X1) )
| ~ spl0_39 ),
inference(avatar_component_clause,[],[f306]) ).
fof(f447,plain,
( spl0_62
| ~ spl0_18
| ~ spl0_60 ),
inference(avatar_split_clause,[],[f441,f434,f202,f445]) ).
fof(f441,plain,
( ! [X0] : member(singleton(X0),singleton(singleton(X0)))
| ~ spl0_18
| ~ spl0_60 ),
inference(superposition,[],[f435,f203]) ).
fof(f440,plain,
( spl0_61
| ~ spl0_25
| ~ spl0_41 ),
inference(avatar_split_clause,[],[f370,f314,f232,f438]) ).
fof(f370,plain,
( ! [X3,X4] : member(singleton(X3),unordered_pair(X4,singleton(X3)))
| ~ spl0_25
| ~ spl0_41 ),
inference(resolution,[],[f315,f233]) ).
fof(f436,plain,
( spl0_60
| ~ spl0_25
| ~ spl0_40 ),
inference(avatar_split_clause,[],[f362,f310,f232,f434]) ).
fof(f362,plain,
( ! [X3,X4] : member(singleton(X3),unordered_pair(singleton(X3),X4))
| ~ spl0_25
| ~ spl0_40 ),
inference(resolution,[],[f311,f233]) ).
fof(f431,plain,
( spl0_59
| ~ spl0_20
| ~ spl0_43 ),
inference(avatar_split_clause,[],[f403,f322,f210,f429]) ).
fof(f429,plain,
( spl0_59
<=> ! [X0] :
( ~ member(X0,identity_relation)
| member(X0,inverse(subset_relation)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f403,plain,
( ! [X0] :
( ~ member(X0,identity_relation)
| member(X0,inverse(subset_relation)) )
| ~ spl0_20
| ~ spl0_43 ),
inference(superposition,[],[f323,f212]) ).
fof(f426,plain,
( spl0_58
| ~ spl0_20
| ~ spl0_44 ),
inference(avatar_split_clause,[],[f415,f326,f210,f424]) ).
fof(f415,plain,
( ! [X0] :
( ~ member(X0,identity_relation)
| member(X0,subset_relation) )
| ~ spl0_20
| ~ spl0_44 ),
inference(superposition,[],[f327,f212]) ).
fof(f412,plain,
( spl0_57
| ~ spl0_18
| ~ spl0_53 ),
inference(avatar_split_clause,[],[f405,f382,f202,f409]) ).
fof(f405,plain,
( member(omega,singleton(omega))
| ~ spl0_18
| ~ spl0_53 ),
inference(superposition,[],[f383,f203]) ).
fof(f400,plain,
( spl0_56
| ~ spl0_18
| ~ spl0_52 ),
inference(avatar_split_clause,[],[f393,f378,f202,f397]) ).
fof(f393,plain,
( member(null_class,singleton(null_class))
| ~ spl0_18
| ~ spl0_52 ),
inference(superposition,[],[f379,f203]) ).
fof(f392,plain,
( spl0_55
| ~ spl0_7
| ~ spl0_41 ),
inference(avatar_split_clause,[],[f372,f314,f151,f390]) ).
fof(f372,plain,
( ! [X6] : member(omega,unordered_pair(X6,omega))
| ~ spl0_7
| ~ spl0_41 ),
inference(resolution,[],[f315,f153]) ).
fof(f388,plain,
( spl0_54
| ~ spl0_11
| ~ spl0_41 ),
inference(avatar_split_clause,[],[f371,f314,f168,f386]) ).
fof(f371,plain,
( ! [X5] : member(null_class,unordered_pair(X5,null_class))
| ~ spl0_11
| ~ spl0_41 ),
inference(resolution,[],[f315,f170]) ).
fof(f384,plain,
( spl0_53
| ~ spl0_7
| ~ spl0_40 ),
inference(avatar_split_clause,[],[f364,f310,f151,f382]) ).
fof(f364,plain,
( ! [X6] : member(omega,unordered_pair(omega,X6))
| ~ spl0_7
| ~ spl0_40 ),
inference(resolution,[],[f311,f153]) ).
fof(f380,plain,
( spl0_52
| ~ spl0_11
| ~ spl0_40 ),
inference(avatar_split_clause,[],[f363,f310,f168,f378]) ).
fof(f363,plain,
( ! [X5] : member(null_class,unordered_pair(null_class,X5))
| ~ spl0_11
| ~ spl0_40 ),
inference(resolution,[],[f311,f170]) ).
fof(f356,plain,
spl0_51,
inference(avatar_split_clause,[],[f106,f354]) ).
fof(f106,axiom,
! [X4] :
( null_class = X4
| member(not_subclass_element(X4,null_class),X4) ),
file('/export/starexec/sandbox2/tmp/tmp.qYmJ0hwDFn/Vampire---4.8_12445',null_class_is_unique) ).
fof(f352,plain,
spl0_50,
inference(avatar_split_clause,[],[f63,f350]) ).
fof(f350,plain,
( spl0_50
<=> ! [X8] :
( ~ function(X8)
| subclass(compose(X8,inverse(X8)),identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f63,axiom,
! [X8] :
( ~ function(X8)
| subclass(compose(X8,inverse(X8)),identity_relation) ),
file('/export/starexec/sandbox2/tmp/tmp.qYmJ0hwDFn/Vampire---4.8_12445',function2) ).
fof(f348,plain,
spl0_49,
inference(avatar_split_clause,[],[f55,f346]) ).
fof(f55,axiom,
! [X0] : complement(image(element_relation,complement(X0))) = power_class(X0),
file('/export/starexec/sandbox2/tmp/tmp.qYmJ0hwDFn/Vampire---4.8_12445',power_class_definition) ).
fof(f344,plain,
spl0_48,
inference(avatar_split_clause,[],[f53,f342]) ).
fof(f53,axiom,
! [X0] : domain_of(restrict(element_relation,universal_class,X0)) = sum_class(X0),
file('/export/starexec/sandbox2/tmp/tmp.qYmJ0hwDFn/Vampire---4.8_12445',sum_class_definition) ).
fof(f340,plain,
spl0_47,
inference(avatar_split_clause,[],[f38,f338]) ).
fof(f38,axiom,
! [X1] : domain_of(flip(cross_product(X1,universal_class))) = inverse(X1),
file('/export/starexec/sandbox2/tmp/tmp.qYmJ0hwDFn/Vampire---4.8_12445',inverse) ).
fof(f336,plain,
spl0_46,
inference(avatar_split_clause,[],[f35,f334]) ).
fof(f334,plain,
( spl0_46
<=> ! [X0] : subclass(flip(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f35,axiom,
! [X0] : subclass(flip(X0),cross_product(cross_product(universal_class,universal_class),universal_class)),
file('/export/starexec/sandbox2/tmp/tmp.qYmJ0hwDFn/Vampire---4.8_12445',flip1) ).
fof(f332,plain,
spl0_45,
inference(avatar_split_clause,[],[f32,f330]) ).
fof(f330,plain,
( spl0_45
<=> ! [X0] : subclass(rotate(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f32,axiom,
! [X0] : subclass(rotate(X0),cross_product(cross_product(universal_class,universal_class),universal_class)),
file('/export/starexec/sandbox2/tmp/tmp.qYmJ0hwDFn/Vampire---4.8_12445',rotate1) ).
fof(f328,plain,
spl0_44,
inference(avatar_split_clause,[],[f22,f326]) ).
fof(f22,axiom,
! [X0,X1,X4] :
( member(X4,X1)
| ~ member(X4,intersection(X0,X1)) ),
file('/export/starexec/sandbox2/tmp/tmp.qYmJ0hwDFn/Vampire---4.8_12445',intersection2) ).
fof(f324,plain,
spl0_43,
inference(avatar_split_clause,[],[f21,f322]) ).
fof(f21,axiom,
! [X0,X1,X4] :
( member(X4,X0)
| ~ member(X4,intersection(X0,X1)) ),
file('/export/starexec/sandbox2/tmp/tmp.qYmJ0hwDFn/Vampire---4.8_12445',intersection1) ).
fof(f320,plain,
spl0_42,
inference(avatar_split_clause,[],[f19,f318]) ).
fof(f19,axiom,
! [X0,X1] :
( member(X0,X1)
| ~ member(ordered_pair(X0,X1),element_relation) ),
file('/export/starexec/sandbox2/tmp/tmp.qYmJ0hwDFn/Vampire---4.8_12445',element_relation2) ).
fof(f316,plain,
spl0_41,
inference(avatar_split_clause,[],[f10,f314]) ).
fof(f10,axiom,
! [X0,X1] :
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X0,X1)) ),
file('/export/starexec/sandbox2/tmp/tmp.qYmJ0hwDFn/Vampire---4.8_12445',unordered_pair3) ).
fof(f312,plain,
spl0_40,
inference(avatar_split_clause,[],[f9,f310]) ).
fof(f9,axiom,
! [X0,X1] :
( ~ member(X0,universal_class)
| member(X0,unordered_pair(X0,X1)) ),
file('/export/starexec/sandbox2/tmp/tmp.qYmJ0hwDFn/Vampire---4.8_12445',unordered_pair2) ).
fof(f308,plain,
spl0_39,
inference(avatar_split_clause,[],[f3,f306]) ).
fof(f3,axiom,
! [X0,X1] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
file('/export/starexec/sandbox2/tmp/tmp.qYmJ0hwDFn/Vampire---4.8_12445',not_subclass_members2) ).
fof(f304,plain,
spl0_38,
inference(avatar_split_clause,[],[f2,f302]) ).
fof(f2,axiom,
! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.qYmJ0hwDFn/Vampire---4.8_12445',not_subclass_members1) ).
fof(f294,plain,
( spl0_37
| ~ spl0_21
| ~ spl0_33 ),
inference(avatar_split_clause,[],[f282,f268,f215,f292]) ).
fof(f215,plain,
( spl0_21
<=> ! [X0,X1] : ~ member(X1,intersection(complement(X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f282,plain,
( ! [X0] : null_class = intersection(complement(X0),X0)
| ~ spl0_21
| ~ spl0_33 ),
inference(resolution,[],[f269,f216]) ).
fof(f216,plain,
( ! [X0,X1] : ~ member(X1,intersection(complement(X0),X0))
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f215]) ).
fof(f290,plain,
( spl0_36
| ~ spl0_5
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f281,f264,f142,f287]) ).
fof(f142,plain,
( spl0_5
<=> function(choice) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f264,plain,
( spl0_32
<=> ! [X8] :
( ~ function(X8)
| subclass(X8,cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f281,plain,
( subclass(choice,cross_product(universal_class,universal_class))
| ~ spl0_5
| ~ spl0_32 ),
inference(resolution,[],[f265,f144]) ).
fof(f144,plain,
( function(choice)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f142]) ).
fof(f265,plain,
( ! [X8] :
( ~ function(X8)
| subclass(X8,cross_product(universal_class,universal_class)) )
| ~ spl0_32 ),
inference(avatar_component_clause,[],[f264]) ).
fof(f280,plain,
( spl0_35
| ~ spl0_4
| ~ spl0_28 ),
inference(avatar_split_clause,[],[f275,f248,f137,f277]) ).
fof(f137,plain,
( spl0_4
<=> inductive(omega) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f248,plain,
( spl0_28
<=> ! [X0] :
( ~ inductive(X0)
| subclass(image(successor_relation,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f275,plain,
( subclass(image(successor_relation,omega),omega)
| ~ spl0_4
| ~ spl0_28 ),
inference(resolution,[],[f249,f139]) ).
fof(f139,plain,
( inductive(omega)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f137]) ).
fof(f249,plain,
( ! [X0] :
( ~ inductive(X0)
| subclass(image(successor_relation,X0),X0) )
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f248]) ).
fof(f274,plain,
spl0_34,
inference(avatar_split_clause,[],[f108,f272]) ).
fof(f108,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/tmp/tmp.qYmJ0hwDFn/Vampire---4.8_12445',commutativity_of_unordered_pair) ).
fof(f270,plain,
spl0_33,
inference(avatar_split_clause,[],[f66,f268]) ).
fof(f66,axiom,
! [X0] :
( null_class = X0
| member(regular(X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.qYmJ0hwDFn/Vampire---4.8_12445',regularity1) ).
fof(f266,plain,
spl0_32,
inference(avatar_split_clause,[],[f62,f264]) ).
fof(f62,axiom,
! [X8] :
( ~ function(X8)
| subclass(X8,cross_product(universal_class,universal_class)) ),
file('/export/starexec/sandbox2/tmp/tmp.qYmJ0hwDFn/Vampire---4.8_12445',function1) ).
fof(f262,plain,
spl0_31,
inference(avatar_split_clause,[],[f57,f260]) ).
fof(f260,plain,
( spl0_31
<=> ! [X5,X7] : subclass(compose(X7,X5),cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f57,axiom,
! [X7,X5] : subclass(compose(X7,X5),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/tmp/tmp.qYmJ0hwDFn/Vampire---4.8_12445',compose1) ).
fof(f258,plain,
spl0_30,
inference(avatar_split_clause,[],[f56,f256]) ).
fof(f256,plain,
( spl0_30
<=> ! [X2] :
( ~ member(X2,universal_class)
| member(power_class(X2),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f56,axiom,
! [X2] :
( ~ member(X2,universal_class)
| member(power_class(X2),universal_class) ),
file('/export/starexec/sandbox2/tmp/tmp.qYmJ0hwDFn/Vampire---4.8_12445',power_class2) ).
fof(f254,plain,
spl0_29,
inference(avatar_split_clause,[],[f54,f252]) ).
fof(f252,plain,
( spl0_29
<=> ! [X0] :
( ~ member(X0,universal_class)
| member(sum_class(X0),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f54,axiom,
! [X0] :
( ~ member(X0,universal_class)
| member(sum_class(X0),universal_class) ),
file('/export/starexec/sandbox2/tmp/tmp.qYmJ0hwDFn/Vampire---4.8_12445',sum_class2) ).
fof(f250,plain,
spl0_28,
inference(avatar_split_clause,[],[f48,f248]) ).
fof(f48,axiom,
! [X0] :
( ~ inductive(X0)
| subclass(image(successor_relation,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.qYmJ0hwDFn/Vampire---4.8_12445',inductive2) ).
fof(f246,plain,
spl0_27,
inference(avatar_split_clause,[],[f43,f244]) ).
fof(f43,axiom,
! [X0] : union(X0,singleton(X0)) = successor(X0),
file('/export/starexec/sandbox2/tmp/tmp.qYmJ0hwDFn/Vampire---4.8_12445',successor) ).
fof(f242,plain,
spl0_26,
inference(avatar_split_clause,[],[f24,f240]) ).
fof(f24,axiom,
! [X0,X4] :
( ~ member(X4,X0)
| ~ member(X4,complement(X0)) ),
file('/export/starexec/sandbox2/tmp/tmp.qYmJ0hwDFn/Vampire---4.8_12445',complement1) ).
fof(f234,plain,
( spl0_25
| ~ spl0_12
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f230,f202,f173,f232]) ).
fof(f230,plain,
( ! [X0] : member(singleton(X0),universal_class)
| ~ spl0_12
| ~ spl0_18 ),
inference(superposition,[],[f174,f203]) ).
fof(f229,plain,
spl0_24,
inference(avatar_split_clause,[],[f110,f227]) ).
fof(f110,axiom,
! [X0,X1] : subclass(singleton(X1),unordered_pair(X0,X1)),
file('/export/starexec/sandbox2/tmp/tmp.qYmJ0hwDFn/Vampire---4.8_12445',singleton_in_unordered_pair2) ).
fof(f225,plain,
spl0_23,
inference(avatar_split_clause,[],[f109,f223]) ).
fof(f109,axiom,
! [X0,X1] : subclass(singleton(X0),unordered_pair(X0,X1)),
file('/export/starexec/sandbox2/tmp/tmp.qYmJ0hwDFn/Vampire---4.8_12445',singleton_in_unordered_pair1) ).
fof(f221,plain,
spl0_22,
inference(avatar_split_clause,[],[f105,f219]) ).
fof(f219,plain,
( spl0_22
<=> ! [X0] :
( ~ subclass(X0,null_class)
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f105,axiom,
! [X0] :
( ~ subclass(X0,null_class)
| null_class = X0 ),
file('/export/starexec/sandbox2/tmp/tmp.qYmJ0hwDFn/Vampire---4.8_12445',corollary_of_null_class_is_subclass) ).
fof(f217,plain,
spl0_21,
inference(avatar_split_clause,[],[f102,f215]) ).
fof(f102,axiom,
! [X0,X1] : ~ member(X1,intersection(complement(X0),X0)),
file('/export/starexec/sandbox2/tmp/tmp.qYmJ0hwDFn/Vampire---4.8_12445',special_classes_lemma) ).
fof(f213,plain,
spl0_20,
inference(avatar_split_clause,[],[f75,f210]) ).
fof(f75,axiom,
identity_relation = intersection(inverse(subset_relation),subset_relation),
file('/export/starexec/sandbox2/tmp/tmp.qYmJ0hwDFn/Vampire---4.8_12445',identity_relation) ).
fof(f208,plain,
spl0_19,
inference(avatar_split_clause,[],[f39,f206]) ).
fof(f39,axiom,
! [X4] : domain_of(inverse(X4)) = range_of(X4),
file('/export/starexec/sandbox2/tmp/tmp.qYmJ0hwDFn/Vampire---4.8_12445',range_of) ).
fof(f204,plain,
spl0_18,
inference(avatar_split_clause,[],[f12,f202]) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox2/tmp/tmp.qYmJ0hwDFn/Vampire---4.8_12445',singleton_set) ).
fof(f199,plain,
( spl0_17
| ~ spl0_4
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f194,f187,f137,f196]) ).
fof(f187,plain,
( spl0_15
<=> ! [X0] :
( ~ inductive(X0)
| member(null_class,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f194,plain,
( member(null_class,omega)
| ~ spl0_4
| ~ spl0_15 ),
inference(resolution,[],[f188,f139]) ).
fof(f188,plain,
( ! [X0] :
( ~ inductive(X0)
| member(null_class,X0) )
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f187]) ).
fof(f193,plain,
spl0_16,
inference(avatar_split_clause,[],[f51,f191]) ).
fof(f191,plain,
( spl0_16
<=> ! [X1] :
( ~ inductive(X1)
| subclass(omega,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f51,axiom,
! [X1] :
( ~ inductive(X1)
| subclass(omega,X1) ),
file('/export/starexec/sandbox2/tmp/tmp.qYmJ0hwDFn/Vampire---4.8_12445',omega_is_inductive2) ).
fof(f189,plain,
spl0_15,
inference(avatar_split_clause,[],[f47,f187]) ).
fof(f47,axiom,
! [X0] :
( ~ inductive(X0)
| member(null_class,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.qYmJ0hwDFn/Vampire---4.8_12445',inductive1) ).
fof(f185,plain,
spl0_14,
inference(avatar_split_clause,[],[f44,f182]) ).
fof(f44,axiom,
subclass(successor_relation,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/tmp/tmp.qYmJ0hwDFn/Vampire---4.8_12445',successor_relation1) ).
fof(f180,plain,
spl0_13,
inference(avatar_split_clause,[],[f18,f177]) ).
fof(f18,axiom,
subclass(element_relation,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/tmp/tmp.qYmJ0hwDFn/Vampire---4.8_12445',element_relation1) ).
fof(f175,plain,
spl0_12,
inference(avatar_split_clause,[],[f11,f173]) ).
fof(f11,axiom,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
file('/export/starexec/sandbox2/tmp/tmp.qYmJ0hwDFn/Vampire---4.8_12445',unordered_pairs_in_universal) ).
fof(f171,plain,
spl0_11,
inference(avatar_split_clause,[],[f107,f168]) ).
fof(f107,axiom,
member(null_class,universal_class),
file('/export/starexec/sandbox2/tmp/tmp.qYmJ0hwDFn/Vampire---4.8_12445',null_class_is_a_set) ).
fof(f166,plain,
spl0_10,
inference(avatar_split_clause,[],[f104,f164]) ).
fof(f104,axiom,
! [X0] : subclass(null_class,X0),
file('/export/starexec/sandbox2/tmp/tmp.qYmJ0hwDFn/Vampire---4.8_12445',null_class_is_subclass) ).
fof(f162,plain,
spl0_9,
inference(avatar_split_clause,[],[f103,f160]) ).
fof(f103,axiom,
! [X4] : ~ member(X4,null_class),
file('/export/starexec/sandbox2/tmp/tmp.qYmJ0hwDFn/Vampire---4.8_12445',existence_of_null_class) ).
fof(f158,plain,
spl0_8,
inference(avatar_split_clause,[],[f96,f156]) ).
fof(f96,axiom,
! [X0] : subclass(X0,X0),
file('/export/starexec/sandbox2/tmp/tmp.qYmJ0hwDFn/Vampire---4.8_12445',subclass_is_reflexive) ).
fof(f154,plain,
spl0_7,
inference(avatar_split_clause,[],[f52,f151]) ).
fof(f52,axiom,
member(omega,universal_class),
file('/export/starexec/sandbox2/tmp/tmp.qYmJ0hwDFn/Vampire---4.8_12445',omega_in_universal) ).
fof(f149,plain,
spl0_6,
inference(avatar_split_clause,[],[f4,f147]) ).
fof(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox2/tmp/tmp.qYmJ0hwDFn/Vampire---4.8_12445',class_elements_are_sets) ).
fof(f145,plain,
spl0_5,
inference(avatar_split_clause,[],[f69,f142]) ).
fof(f69,axiom,
function(choice),
file('/export/starexec/sandbox2/tmp/tmp.qYmJ0hwDFn/Vampire---4.8_12445',choice1) ).
fof(f140,plain,
spl0_4,
inference(avatar_split_clause,[],[f50,f137]) ).
fof(f50,axiom,
inductive(omega),
file('/export/starexec/sandbox2/tmp/tmp.qYmJ0hwDFn/Vampire---4.8_12445',omega_is_inductive1) ).
fof(f135,plain,
~ spl0_3,
inference(avatar_split_clause,[],[f113,f132]) ).
fof(f113,axiom,
null_class != unordered_pair(x,y),
file('/export/starexec/sandbox2/tmp/tmp.qYmJ0hwDFn/Vampire---4.8_12445',prove_null_unordered_pair_1) ).
fof(f130,plain,
~ spl0_2,
inference(avatar_split_clause,[],[f115,f127]) ).
fof(f115,axiom,
~ member(y,universal_class),
file('/export/starexec/sandbox2/tmp/tmp.qYmJ0hwDFn/Vampire---4.8_12445',prove_null_unordered_pair_3) ).
fof(f125,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f114,f122]) ).
fof(f114,axiom,
~ member(x,universal_class),
file('/export/starexec/sandbox2/tmp/tmp.qYmJ0hwDFn/Vampire---4.8_12445',prove_null_unordered_pair_2) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : SET071-7 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.13/0.15 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.15/0.36 % Computer : n027.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Sat Aug 26 10:06:50 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.15/0.37 This is a CNF_UNS_RFO_SEQ_NHN problem
% 0.15/0.37 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/tmp/tmp.qYmJ0hwDFn/Vampire---4.8_12445
% 0.15/0.37 % (12552)Running in auto input_syntax mode. Trying TPTP
% 0.23/0.41 % (12554)ott+3_2:7_add=large:amm=off:anc=all:bce=on:drc=off:fsd=off:fde=unused:gs=on:irw=on:lcm=predicate:lma=on:msp=off:nwc=10.0:sac=on_598 on Vampire---4 for (598ds/0Mi)
% 0.23/0.43 % (12553)lrs+1010_20_av=off:bd=off:bs=on:bsr=on:bce=on:flr=on:fde=none:gsp=on:nwc=3.0:tgt=ground:urr=ec_only:stl=125_1192 on Vampire---4 for (1192ds/0Mi)
% 0.23/0.43 % (12556)lrs+2_5:4_anc=none:br=off:fde=unused:gsp=on:nm=32:nwc=1.3:sims=off:sos=all:urr=on:stl=62_558 on Vampire---4 for (558ds/0Mi)
% 0.23/0.43 % (12557)lrs-1010_20_afr=on:anc=all_dependent:bs=on:bsr=on:cond=on:er=known:fde=none:nm=4:nwc=1.3:sims=off:sp=frequency:urr=on:stl=62_533 on Vampire---4 for (533ds/0Mi)
% 0.23/0.43 % (12558)lrs-1010_2_av=off:bce=on:cond=on:er=filter:fde=unused:lcm=predicate:nm=2:nwc=3.0:sims=off:sp=frequency:urr=on:stl=188_520 on Vampire---4 for (520ds/0Mi)
% 0.23/0.43 % (12559)ott+1010_1_aac=none:bce=on:ep=RS:fsd=off:nm=4:nwc=2.0:nicw=on:sas=z3:sims=off_453 on Vampire---4 for (453ds/0Mi)
% 0.23/0.43 % (12555)lrs+11_10:1_bs=unit_only:drc=off:fsd=off:fde=none:gs=on:msp=off:nm=16:nwc=2.0:nicw=on:sos=all:sac=on:sp=reverse_frequency:stl=62_575 on Vampire---4 for (575ds/0Mi)
% 0.23/0.62 % (12554)First to succeed.
% 0.23/0.64 % (12558)Also succeeded, but the first one will report.
% 0.23/0.64 % (12554)Refutation found. Thanks to Tanya!
% 0.23/0.64 % SZS status Unsatisfiable for Vampire---4
% 0.23/0.64 % SZS output start Proof for Vampire---4
% See solution above
% 0.23/0.65 % (12554)------------------------------
% 0.23/0.65 % (12554)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.23/0.65 % (12554)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.23/0.65 % (12554)Termination reason: Refutation
% 0.23/0.65
% 0.23/0.65 % (12554)Memory used [KB]: 13560
% 0.23/0.65 % (12554)Time elapsed: 0.230 s
% 0.23/0.65 % (12554)------------------------------
% 0.23/0.65 % (12554)------------------------------
% 0.23/0.65 % (12552)Success in time 0.281 s
% 0.23/0.65 % Vampire---4.8 exiting
%------------------------------------------------------------------------------