TSTP Solution File: SEU133+2 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU133+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n011.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 : Sun May 5 09:27:18 EDT 2024
% Result : Theorem 2.02s 0.67s
% Output : Refutation 2.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 547
% Syntax : Number of formulae : 1820 ( 117 unt; 0 def)
% Number of atoms : 6062 ( 436 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 7526 (3284 ~;3571 |; 131 &)
% ( 513 <=>; 26 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 500 ( 498 usr; 492 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 5 con; 0-3 aty)
% Number of variables : 3195 (3158 !; 37 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10710,plain,
$false,
inference(avatar_sat_refutation,[],[f209,f214,f219,f224,f228,f232,f236,f240,f244,f248,f252,f256,f260,f264,f268,f272,f276,f287,f291,f297,f304,f308,f312,f316,f320,f324,f328,f353,f358,f362,f366,f370,f374,f411,f415,f419,f423,f428,f432,f437,f469,f473,f477,f490,f495,f500,f504,f508,f525,f529,f533,f543,f547,f551,f555,f559,f580,f584,f588,f631,f635,f639,f643,f647,f651,f659,f665,f669,f696,f700,f704,f708,f716,f741,f745,f749,f753,f757,f761,f765,f818,f822,f826,f830,f878,f882,f886,f890,f920,f924,f928,f932,f936,f940,f959,f998,f1002,f1006,f1036,f1040,f1044,f1062,f1066,f1070,f1075,f1100,f1104,f1108,f1112,f1116,f1193,f1197,f1201,f1205,f1209,f1213,f1217,f1221,f1225,f1229,f1233,f1237,f1241,f1245,f1249,f1253,f1389,f1422,f1426,f1430,f1434,f1438,f1442,f1446,f1450,f1569,f1573,f1577,f1640,f1644,f1648,f1652,f1656,f1660,f1693,f1762,f1766,f1770,f1774,f1778,f1782,f1786,f1790,f1794,f1798,f1802,f1806,f1810,f1868,f1980,f2007,f2011,f2015,f2096,f2100,f2183,f2187,f2191,f2195,f2199,f2203,f2306,f2310,f2314,f2318,f2322,f2326,f2330,f2334,f2574,f2578,f2582,f2586,f2590,f2594,f2598,f2602,f2606,f2610,f2614,f2618,f2802,f2806,f2810,f2814,f2818,f2920,f2924,f2973,f2977,f2981,f2985,f2989,f2993,f2997,f3001,f3005,f3009,f3013,f3017,f3021,f3025,f3107,f3269,f3273,f3277,f3281,f3285,f3289,f3293,f3297,f3301,f3525,f3529,f3533,f3537,f3660,f3664,f3668,f3672,f3676,f3680,f3684,f3873,f3983,f3987,f3991,f3995,f3999,f4003,f4007,f4011,f4015,f4019,f4067,f4071,f4075,f4079,f4083,f4087,f4091,f4095,f4099,f4103,f4107,f4111,f4115,f4119,f4123,f4127,f4344,f4472,f4486,f4490,f4494,f4498,f4502,f4506,f4510,f4514,f4518,f4522,f4526,f4530,f4534,f4538,f4542,f4546,f4550,f4554,f4558,f4562,f4566,f4570,f4574,f4578,f4582,f4586,f4590,f4594,f4598,f4602,f4606,f4610,f4773,f5173,f5262,f5266,f5270,f5274,f5278,f5282,f5286,f5342,f5346,f5350,f5355,f5359,f5363,f5367,f5371,f5375,f5379,f5383,f5387,f5391,f5395,f5399,f5403,f5407,f5411,f5415,f5919,f5923,f5927,f5931,f5935,f5939,f5943,f5963,f5967,f5971,f5975,f5979,f5983,f5988,f6021,f6025,f6045,f6049,f6053,f6057,f6061,f6065,f6069,f6073,f6077,f6081,f6100,f6104,f6581,f6860,f6864,f6868,f6872,f6876,f6880,f6884,f6888,f6892,f6896,f6900,f6904,f6908,f6912,f6916,f6920,f6924,f6928,f6932,f6936,f6940,f6967,f7047,f7051,f7055,f7059,f7063,f7067,f7071,f7075,f7079,f7083,f7087,f7091,f7095,f7099,f7103,f7107,f7111,f7115,f7119,f7123,f7127,f7131,f7135,f7139,f7143,f7147,f7151,f7155,f7159,f7163,f7167,f7171,f7175,f7179,f7183,f7187,f7191,f7195,f7199,f7203,f7207,f7211,f8320,f8324,f8328,f8332,f8336,f8464,f8468,f8472,f8476,f8480,f8484,f8488,f8492,f8497,f8501,f8505,f8509,f8513,f8517,f8521,f8525,f8529,f8533,f8537,f8541,f8545,f8549,f8553,f8557,f8561,f8565,f8569,f8573,f8577,f8581,f8585,f8589,f8593,f8597,f8601,f8605,f8609,f8613,f8769,f9121,f9786,f10126,f10130,f10134,f10181,f10185,f10189,f10193,f10197,f10201,f10205,f10209,f10213,f10217,f10259,f10263,f10267,f10271,f10275,f10279,f10283,f10287,f10291,f10295,f10299,f10303,f10307,f10311,f10315,f10319,f10470,f10696]) ).
fof(f10696,plain,
( spl15_1
| ~ spl15_491 ),
inference(avatar_contradiction_clause,[],[f10619]) ).
fof(f10619,plain,
( $false
| spl15_1
| ~ spl15_491 ),
inference(resolution,[],[f10469,f208]) ).
fof(f208,plain,
( ~ subset(set_difference(sK3,sK4),sK3)
| spl15_1 ),
inference(avatar_component_clause,[],[f206]) ).
fof(f206,plain,
( spl15_1
<=> subset(set_difference(sK3,sK4),sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_1])]) ).
fof(f10469,plain,
( ! [X0,X1] : subset(set_difference(X0,X1),X0)
| ~ spl15_491 ),
inference(avatar_component_clause,[],[f10468]) ).
fof(f10468,plain,
( spl15_491
<=> ! [X0,X1] : subset(set_difference(X0,X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_491])]) ).
fof(f10470,plain,
( spl15_491
| ~ spl15_47
| ~ spl15_462 ),
inference(avatar_split_clause,[],[f10354,f10124,f502,f10468]) ).
fof(f502,plain,
( spl15_47
<=> ! [X0,X1] :
( subset(X0,X1)
| ~ in(sK9(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_47])]) ).
fof(f10124,plain,
( spl15_462
<=> ! [X2,X0,X1] :
( in(sK9(set_difference(X0,X1),X2),X0)
| subset(set_difference(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_462])]) ).
fof(f10354,plain,
( ! [X0,X1] : subset(set_difference(X0,X1),X0)
| ~ spl15_47
| ~ spl15_462 ),
inference(duplicate_literal_removal,[],[f10320]) ).
fof(f10320,plain,
( ! [X0,X1] :
( subset(set_difference(X0,X1),X0)
| subset(set_difference(X0,X1),X0) )
| ~ spl15_47
| ~ spl15_462 ),
inference(resolution,[],[f10125,f503]) ).
fof(f503,plain,
( ! [X0,X1] :
( ~ in(sK9(X0,X1),X1)
| subset(X0,X1) )
| ~ spl15_47 ),
inference(avatar_component_clause,[],[f502]) ).
fof(f10125,plain,
( ! [X2,X0,X1] :
( in(sK9(set_difference(X0,X1),X2),X0)
| subset(set_difference(X0,X1),X2) )
| ~ spl15_462 ),
inference(avatar_component_clause,[],[f10124]) ).
fof(f10319,plain,
( spl15_490
| ~ spl15_17
| ~ spl15_212 ),
inference(avatar_split_clause,[],[f3246,f3023,f274,f10317]) ).
fof(f10317,plain,
( spl15_490
<=> ! [X0,X1] :
( in(sK11(sK14,X0,X1),X1)
| sP1(sK14,X0,X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_490])]) ).
fof(f274,plain,
( spl15_17
<=> ! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_17])]) ).
fof(f3023,plain,
( spl15_212
<=> ! [X0,X1] :
( sP1(sK14,X0,X1)
| in(sK11(sK14,X0,X1),X0)
| in(sK11(sK14,X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_212])]) ).
fof(f3246,plain,
( ! [X0,X1] :
( in(sK11(sK14,X0,X1),X1)
| sP1(sK14,X0,X1)
| ~ empty(X0) )
| ~ spl15_17
| ~ spl15_212 ),
inference(resolution,[],[f3024,f275]) ).
fof(f275,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) )
| ~ spl15_17 ),
inference(avatar_component_clause,[],[f274]) ).
fof(f3024,plain,
( ! [X0,X1] :
( in(sK11(sK14,X0,X1),X1)
| in(sK11(sK14,X0,X1),X0)
| sP1(sK14,X0,X1) )
| ~ spl15_212 ),
inference(avatar_component_clause,[],[f3023]) ).
fof(f10315,plain,
( spl15_489
| ~ spl15_17
| ~ spl15_212 ),
inference(avatar_split_clause,[],[f3230,f3023,f274,f10313]) ).
fof(f10313,plain,
( spl15_489
<=> ! [X0,X1] :
( in(sK11(sK14,X0,X1),X0)
| sP1(sK14,X0,X1)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_489])]) ).
fof(f3230,plain,
( ! [X0,X1] :
( in(sK11(sK14,X0,X1),X0)
| sP1(sK14,X0,X1)
| ~ empty(X1) )
| ~ spl15_17
| ~ spl15_212 ),
inference(resolution,[],[f3024,f275]) ).
fof(f10311,plain,
( spl15_488
| ~ spl15_17
| ~ spl15_211 ),
inference(avatar_split_clause,[],[f3207,f3019,f274,f10309]) ).
fof(f10309,plain,
( spl15_488
<=> ! [X0,X1] :
( in(sK11(X0,sK14,X1),X1)
| sP1(X0,sK14,X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_488])]) ).
fof(f3019,plain,
( spl15_211
<=> ! [X0,X1] :
( sP1(X0,sK14,X1)
| in(sK11(X0,sK14,X1),X0)
| in(sK11(X0,sK14,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_211])]) ).
fof(f3207,plain,
( ! [X0,X1] :
( in(sK11(X0,sK14,X1),X1)
| sP1(X0,sK14,X1)
| ~ empty(X0) )
| ~ spl15_17
| ~ spl15_211 ),
inference(resolution,[],[f3020,f275]) ).
fof(f3020,plain,
( ! [X0,X1] :
( in(sK11(X0,sK14,X1),X1)
| in(sK11(X0,sK14,X1),X0)
| sP1(X0,sK14,X1) )
| ~ spl15_211 ),
inference(avatar_component_clause,[],[f3019]) ).
fof(f10307,plain,
( spl15_487
| ~ spl15_17
| ~ spl15_211 ),
inference(avatar_split_clause,[],[f3191,f3019,f274,f10305]) ).
fof(f10305,plain,
( spl15_487
<=> ! [X0,X1] :
( in(sK11(X0,sK14,X1),X0)
| sP1(X0,sK14,X1)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_487])]) ).
fof(f3191,plain,
( ! [X0,X1] :
( in(sK11(X0,sK14,X1),X0)
| sP1(X0,sK14,X1)
| ~ empty(X1) )
| ~ spl15_17
| ~ spl15_211 ),
inference(resolution,[],[f3020,f275]) ).
fof(f10303,plain,
( spl15_486
| ~ spl15_17
| ~ spl15_209 ),
inference(avatar_split_clause,[],[f3166,f3011,f274,f10301]) ).
fof(f10301,plain,
( spl15_486
<=> ! [X0,X1] :
( in(sK11(X0,X1,sK14),X1)
| sP1(X0,X1,sK14)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_486])]) ).
fof(f3011,plain,
( spl15_209
<=> ! [X0,X1] :
( sP1(X0,X1,sK14)
| in(sK11(X0,X1,sK14),X0)
| in(sK11(X0,X1,sK14),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_209])]) ).
fof(f3166,plain,
( ! [X0,X1] :
( in(sK11(X0,X1,sK14),X1)
| sP1(X0,X1,sK14)
| ~ empty(X0) )
| ~ spl15_17
| ~ spl15_209 ),
inference(resolution,[],[f3012,f275]) ).
fof(f3012,plain,
( ! [X0,X1] :
( in(sK11(X0,X1,sK14),X1)
| in(sK11(X0,X1,sK14),X0)
| sP1(X0,X1,sK14) )
| ~ spl15_209 ),
inference(avatar_component_clause,[],[f3011]) ).
fof(f10299,plain,
( spl15_485
| ~ spl15_93
| ~ spl15_275 ),
inference(avatar_split_clause,[],[f4876,f4532,f934,f10297]) ).
fof(f10297,plain,
( spl15_485
<=> ! [X2,X0,X1] :
( disjoint(X0,X1)
| ~ empty(set_union2(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_485])]) ).
fof(f934,plain,
( spl15_93
<=> ! [X0,X1] :
( disjoint(X0,X1)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_93])]) ).
fof(f4532,plain,
( spl15_275
<=> ! [X2,X0,X1] :
( disjoint(X0,X2)
| ~ disjoint(X0,set_union2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_275])]) ).
fof(f4876,plain,
( ! [X2,X0,X1] :
( disjoint(X0,X1)
| ~ empty(set_union2(X0,X2)) )
| ~ spl15_93
| ~ spl15_275 ),
inference(resolution,[],[f4533,f935]) ).
fof(f935,plain,
( ! [X0,X1] :
( disjoint(X0,X1)
| ~ empty(X1) )
| ~ spl15_93 ),
inference(avatar_component_clause,[],[f934]) ).
fof(f4533,plain,
( ! [X2,X0,X1] :
( ~ disjoint(X0,set_union2(X0,X1))
| disjoint(X0,X2) )
| ~ spl15_275 ),
inference(avatar_component_clause,[],[f4532]) ).
fof(f10295,plain,
( spl15_484
| ~ spl15_17
| ~ spl15_209 ),
inference(avatar_split_clause,[],[f3150,f3011,f274,f10293]) ).
fof(f10293,plain,
( spl15_484
<=> ! [X0,X1] :
( in(sK11(X0,X1,sK14),X0)
| sP1(X0,X1,sK14)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_484])]) ).
fof(f3150,plain,
( ! [X0,X1] :
( in(sK11(X0,X1,sK14),X0)
| sP1(X0,X1,sK14)
| ~ empty(X1) )
| ~ spl15_17
| ~ spl15_209 ),
inference(resolution,[],[f3012,f275]) ).
fof(f10291,plain,
( spl15_483
| ~ spl15_17
| ~ spl15_208 ),
inference(avatar_split_clause,[],[f3127,f3007,f274,f10289]) ).
fof(f10289,plain,
( spl15_483
<=> ! [X0,X1] :
( in(sK11(X0,X0,X1),X1)
| sP1(X0,X0,X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_483])]) ).
fof(f3007,plain,
( spl15_208
<=> ! [X4,X5] :
( in(sK11(X4,X4,X5),X5)
| in(sK11(X4,X4,X5),X4)
| sP1(X4,X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_208])]) ).
fof(f3127,plain,
( ! [X0,X1] :
( in(sK11(X0,X0,X1),X1)
| sP1(X0,X0,X1)
| ~ empty(X0) )
| ~ spl15_17
| ~ spl15_208 ),
inference(resolution,[],[f3008,f275]) ).
fof(f3008,plain,
( ! [X4,X5] :
( in(sK11(X4,X4,X5),X5)
| in(sK11(X4,X4,X5),X4)
| sP1(X4,X4,X5) )
| ~ spl15_208 ),
inference(avatar_component_clause,[],[f3007]) ).
fof(f10287,plain,
( spl15_482
| ~ spl15_17
| ~ spl15_208 ),
inference(avatar_split_clause,[],[f3111,f3007,f274,f10285]) ).
fof(f10285,plain,
( spl15_482
<=> ! [X0,X1] :
( in(sK11(X0,X0,X1),X0)
| sP1(X0,X0,X1)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_482])]) ).
fof(f3111,plain,
( ! [X0,X1] :
( in(sK11(X0,X0,X1),X0)
| sP1(X0,X0,X1)
| ~ empty(X1) )
| ~ spl15_17
| ~ spl15_208 ),
inference(resolution,[],[f3008,f275]) ).
fof(f10283,plain,
( spl15_481
| ~ spl15_17
| ~ spl15_207 ),
inference(avatar_split_clause,[],[f3084,f3003,f274,f10281]) ).
fof(f10281,plain,
( spl15_481
<=> ! [X0,X1] :
( in(sK11(X0,X1,X0),X1)
| sP1(X0,X1,X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_481])]) ).
fof(f3003,plain,
( spl15_207
<=> ! [X2,X3] :
( in(sK11(X2,X3,X2),X2)
| in(sK11(X2,X3,X2),X3)
| sP1(X2,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_207])]) ).
fof(f3084,plain,
( ! [X0,X1] :
( in(sK11(X0,X1,X0),X1)
| sP1(X0,X1,X0)
| ~ empty(X0) )
| ~ spl15_17
| ~ spl15_207 ),
inference(resolution,[],[f3004,f275]) ).
fof(f3004,plain,
( ! [X2,X3] :
( in(sK11(X2,X3,X2),X3)
| in(sK11(X2,X3,X2),X2)
| sP1(X2,X3,X2) )
| ~ spl15_207 ),
inference(avatar_component_clause,[],[f3003]) ).
fof(f10279,plain,
( spl15_480
| ~ spl15_17
| ~ spl15_207 ),
inference(avatar_split_clause,[],[f3068,f3003,f274,f10277]) ).
fof(f10277,plain,
( spl15_480
<=> ! [X0,X1] :
( in(sK11(X0,X1,X0),X0)
| sP1(X0,X1,X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_480])]) ).
fof(f3068,plain,
( ! [X0,X1] :
( in(sK11(X0,X1,X0),X0)
| sP1(X0,X1,X0)
| ~ empty(X1) )
| ~ spl15_17
| ~ spl15_207 ),
inference(resolution,[],[f3004,f275]) ).
fof(f10275,plain,
( spl15_479
| ~ spl15_17
| ~ spl15_206 ),
inference(avatar_split_clause,[],[f3045,f2999,f274,f10273]) ).
fof(f10273,plain,
( spl15_479
<=> ! [X0,X1] :
( in(sK11(X0,X1,X1),X1)
| sP1(X0,X1,X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_479])]) ).
fof(f2999,plain,
( spl15_206
<=> ! [X0,X1] :
( in(sK11(X0,X1,X1),X1)
| in(sK11(X0,X1,X1),X0)
| sP1(X0,X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_206])]) ).
fof(f3045,plain,
( ! [X0,X1] :
( in(sK11(X0,X1,X1),X1)
| sP1(X0,X1,X1)
| ~ empty(X0) )
| ~ spl15_17
| ~ spl15_206 ),
inference(resolution,[],[f3000,f275]) ).
fof(f3000,plain,
( ! [X0,X1] :
( in(sK11(X0,X1,X1),X1)
| in(sK11(X0,X1,X1),X0)
| sP1(X0,X1,X1) )
| ~ spl15_206 ),
inference(avatar_component_clause,[],[f2999]) ).
fof(f10271,plain,
( spl15_478
| ~ spl15_17
| ~ spl15_206 ),
inference(avatar_split_clause,[],[f3029,f2999,f274,f10269]) ).
fof(f10269,plain,
( spl15_478
<=> ! [X0,X1] :
( in(sK11(X0,X1,X1),X0)
| sP1(X0,X1,X1)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_478])]) ).
fof(f3029,plain,
( ! [X0,X1] :
( in(sK11(X0,X1,X1),X0)
| sP1(X0,X1,X1)
| ~ empty(X1) )
| ~ spl15_17
| ~ spl15_206 ),
inference(resolution,[],[f3000,f275]) ).
fof(f10267,plain,
( spl15_477
| ~ spl15_24
| ~ spl15_171 ),
inference(avatar_split_clause,[],[f2290,f2201,f314,f10265]) ).
fof(f10265,plain,
( spl15_477
<=> ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| ~ empty(X0)
| ~ in(X2,sK12(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_477])]) ).
fof(f314,plain,
( spl15_24
<=> ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_24])]) ).
fof(f2201,plain,
( spl15_171
<=> ! [X2,X0,X1] :
( in(sK12(X0,X1,X2),X2)
| sP2(X0,X1,X2)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_171])]) ).
fof(f2290,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| ~ empty(X0)
| ~ in(X2,sK12(X0,X1,X2)) )
| ~ spl15_24
| ~ spl15_171 ),
inference(resolution,[],[f2202,f315]) ).
fof(f315,plain,
( ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) )
| ~ spl15_24 ),
inference(avatar_component_clause,[],[f314]) ).
fof(f2202,plain,
( ! [X2,X0,X1] :
( in(sK12(X0,X1,X2),X2)
| sP2(X0,X1,X2)
| ~ empty(X0) )
| ~ spl15_171 ),
inference(avatar_component_clause,[],[f2201]) ).
fof(f10263,plain,
( spl15_476
| ~ spl15_24
| ~ spl15_170 ),
inference(avatar_split_clause,[],[f2276,f2197,f314,f10261]) ).
fof(f10261,plain,
( spl15_476
<=> ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| ~ empty(X2)
| ~ in(X0,sK12(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_476])]) ).
fof(f2197,plain,
( spl15_170
<=> ! [X2,X0,X1] :
( in(sK12(X0,X1,X2),X0)
| sP2(X0,X1,X2)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_170])]) ).
fof(f2276,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| ~ empty(X2)
| ~ in(X0,sK12(X0,X1,X2)) )
| ~ spl15_24
| ~ spl15_170 ),
inference(resolution,[],[f2198,f315]) ).
fof(f2198,plain,
( ! [X2,X0,X1] :
( in(sK12(X0,X1,X2),X0)
| sP2(X0,X1,X2)
| ~ empty(X2) )
| ~ spl15_170 ),
inference(avatar_component_clause,[],[f2197]) ).
fof(f10259,plain,
( spl15_475
| ~ spl15_24
| ~ spl15_169 ),
inference(avatar_split_clause,[],[f2251,f2193,f314,f10257]) ).
fof(f10257,plain,
( spl15_475
<=> ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| ~ empty(X1)
| ~ in(X2,sK12(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_475])]) ).
fof(f2193,plain,
( spl15_169
<=> ! [X2,X0,X1] :
( in(sK12(X0,X1,X2),X2)
| sP2(X0,X1,X2)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_169])]) ).
fof(f2251,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| ~ empty(X1)
| ~ in(X2,sK12(X0,X1,X2)) )
| ~ spl15_24
| ~ spl15_169 ),
inference(resolution,[],[f2194,f315]) ).
fof(f2194,plain,
( ! [X2,X0,X1] :
( in(sK12(X0,X1,X2),X2)
| sP2(X0,X1,X2)
| ~ empty(X1) )
| ~ spl15_169 ),
inference(avatar_component_clause,[],[f2193]) ).
fof(f10217,plain,
( spl15_474
| ~ spl15_24
| ~ spl15_168 ),
inference(avatar_split_clause,[],[f2237,f2189,f314,f10215]) ).
fof(f10215,plain,
( spl15_474
<=> ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| ~ empty(X2)
| ~ in(X1,sK12(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_474])]) ).
fof(f2189,plain,
( spl15_168
<=> ! [X2,X0,X1] :
( in(sK12(X0,X1,X2),X1)
| sP2(X0,X1,X2)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_168])]) ).
fof(f2237,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| ~ empty(X2)
| ~ in(X1,sK12(X0,X1,X2)) )
| ~ spl15_24
| ~ spl15_168 ),
inference(resolution,[],[f2190,f315]) ).
fof(f2190,plain,
( ! [X2,X0,X1] :
( in(sK12(X0,X1,X2),X1)
| sP2(X0,X1,X2)
| ~ empty(X2) )
| ~ spl15_168 ),
inference(avatar_component_clause,[],[f2189]) ).
fof(f10213,plain,
( spl15_473
| ~ spl15_24
| ~ spl15_167 ),
inference(avatar_split_clause,[],[f2222,f2185,f314,f10211]) ).
fof(f10211,plain,
( spl15_473
<=> ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ empty(X1)
| ~ in(X2,sK10(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_473])]) ).
fof(f2185,plain,
( spl15_167
<=> ! [X2,X0,X1] :
( in(sK10(X0,X1,X2),X2)
| sP0(X0,X1,X2)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_167])]) ).
fof(f2222,plain,
( ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ empty(X1)
| ~ in(X2,sK10(X0,X1,X2)) )
| ~ spl15_24
| ~ spl15_167 ),
inference(resolution,[],[f2186,f315]) ).
fof(f2186,plain,
( ! [X2,X0,X1] :
( in(sK10(X0,X1,X2),X2)
| sP0(X0,X1,X2)
| ~ empty(X1) )
| ~ spl15_167 ),
inference(avatar_component_clause,[],[f2185]) ).
fof(f10209,plain,
( spl15_472
| ~ spl15_24
| ~ spl15_166 ),
inference(avatar_split_clause,[],[f2206,f2181,f314,f10207]) ).
fof(f10207,plain,
( spl15_472
<=> ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ empty(X2)
| ~ in(X1,sK10(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_472])]) ).
fof(f2181,plain,
( spl15_166
<=> ! [X2,X0,X1] :
( in(sK10(X0,X1,X2),X1)
| sP0(X0,X1,X2)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_166])]) ).
fof(f2206,plain,
( ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ empty(X2)
| ~ in(X1,sK10(X0,X1,X2)) )
| ~ spl15_24
| ~ spl15_166 ),
inference(resolution,[],[f2182,f315]) ).
fof(f2182,plain,
( ! [X2,X0,X1] :
( in(sK10(X0,X1,X2),X1)
| sP0(X0,X1,X2)
| ~ empty(X2) )
| ~ spl15_166 ),
inference(avatar_component_clause,[],[f2181]) ).
fof(f10205,plain,
( spl15_471
| ~ spl15_130
| ~ spl15_135 ),
inference(avatar_split_clause,[],[f1563,f1448,f1428,f10203]) ).
fof(f10203,plain,
( spl15_471
<=> ! [X0,X1] :
( set_difference(X0,X1) = sK14
| in(sK8(sK14,set_difference(X0,X1)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_471])]) ).
fof(f1428,plain,
( spl15_130
<=> ! [X2,X0,X1] :
( ~ in(X0,set_difference(X1,X2))
| in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_130])]) ).
fof(f1448,plain,
( spl15_135
<=> ! [X0] :
( sK14 = X0
| in(sK8(sK14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_135])]) ).
fof(f1563,plain,
( ! [X0,X1] :
( set_difference(X0,X1) = sK14
| in(sK8(sK14,set_difference(X0,X1)),X0) )
| ~ spl15_130
| ~ spl15_135 ),
inference(resolution,[],[f1449,f1429]) ).
fof(f1429,plain,
( ! [X2,X0,X1] :
( ~ in(X0,set_difference(X1,X2))
| in(X0,X1) )
| ~ spl15_130 ),
inference(avatar_component_clause,[],[f1428]) ).
fof(f1449,plain,
( ! [X0] :
( in(sK8(sK14,X0),X0)
| sK14 = X0 )
| ~ spl15_135 ),
inference(avatar_component_clause,[],[f1448]) ).
fof(f10201,plain,
( spl15_470
| ~ spl15_131
| ~ spl15_135 ),
inference(avatar_split_clause,[],[f1562,f1448,f1432,f10199]) ).
fof(f10199,plain,
( spl15_470
<=> ! [X0,X1] :
( set_difference(X0,X1) = sK14
| ~ in(sK8(sK14,set_difference(X0,X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_470])]) ).
fof(f1432,plain,
( spl15_131
<=> ! [X2,X0,X1] :
( ~ in(X0,set_difference(X1,X2))
| ~ in(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_131])]) ).
fof(f1562,plain,
( ! [X0,X1] :
( set_difference(X0,X1) = sK14
| ~ in(sK8(sK14,set_difference(X0,X1)),X1) )
| ~ spl15_131
| ~ spl15_135 ),
inference(resolution,[],[f1449,f1433]) ).
fof(f1433,plain,
( ! [X2,X0,X1] :
( ~ in(X0,set_difference(X1,X2))
| ~ in(X0,X2) )
| ~ spl15_131 ),
inference(avatar_component_clause,[],[f1432]) ).
fof(f10197,plain,
( spl15_469
| ~ spl15_133
| ~ spl15_135 ),
inference(avatar_split_clause,[],[f1557,f1448,f1440,f10195]) ).
fof(f10195,plain,
( spl15_469
<=> ! [X0,X1] :
( set_intersection2(X0,X1) = sK14
| in(sK8(sK14,set_intersection2(X0,X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_469])]) ).
fof(f1440,plain,
( spl15_133
<=> ! [X2,X0,X1] :
( ~ in(X0,set_intersection2(X1,X2))
| in(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_133])]) ).
fof(f1557,plain,
( ! [X0,X1] :
( set_intersection2(X0,X1) = sK14
| in(sK8(sK14,set_intersection2(X0,X1)),X1) )
| ~ spl15_133
| ~ spl15_135 ),
inference(resolution,[],[f1449,f1441]) ).
fof(f1441,plain,
( ! [X2,X0,X1] :
( ~ in(X0,set_intersection2(X1,X2))
| in(X0,X2) )
| ~ spl15_133 ),
inference(avatar_component_clause,[],[f1440]) ).
fof(f10193,plain,
( spl15_468
| ~ spl15_130
| ~ spl15_134 ),
inference(avatar_split_clause,[],[f1551,f1444,f1428,f10191]) ).
fof(f10191,plain,
( spl15_468
<=> ! [X0,X1] :
( set_difference(X0,X1) = sK14
| in(sK8(set_difference(X0,X1),sK14),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_468])]) ).
fof(f1444,plain,
( spl15_134
<=> ! [X0] :
( sK14 = X0
| in(sK8(X0,sK14),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_134])]) ).
fof(f1551,plain,
( ! [X0,X1] :
( set_difference(X0,X1) = sK14
| in(sK8(set_difference(X0,X1),sK14),X0) )
| ~ spl15_130
| ~ spl15_134 ),
inference(resolution,[],[f1445,f1429]) ).
fof(f1445,plain,
( ! [X0] :
( in(sK8(X0,sK14),X0)
| sK14 = X0 )
| ~ spl15_134 ),
inference(avatar_component_clause,[],[f1444]) ).
fof(f10189,plain,
( spl15_467
| ~ spl15_131
| ~ spl15_134 ),
inference(avatar_split_clause,[],[f1550,f1444,f1432,f10187]) ).
fof(f10187,plain,
( spl15_467
<=> ! [X0,X1] :
( set_difference(X0,X1) = sK14
| ~ in(sK8(set_difference(X0,X1),sK14),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_467])]) ).
fof(f1550,plain,
( ! [X0,X1] :
( set_difference(X0,X1) = sK14
| ~ in(sK8(set_difference(X0,X1),sK14),X1) )
| ~ spl15_131
| ~ spl15_134 ),
inference(resolution,[],[f1445,f1433]) ).
fof(f10185,plain,
( spl15_466
| ~ spl15_133
| ~ spl15_134 ),
inference(avatar_split_clause,[],[f1545,f1444,f1440,f10183]) ).
fof(f10183,plain,
( spl15_466
<=> ! [X0,X1] :
( set_intersection2(X0,X1) = sK14
| in(sK8(set_intersection2(X0,X1),sK14),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_466])]) ).
fof(f1545,plain,
( ! [X0,X1] :
( set_intersection2(X0,X1) = sK14
| in(sK8(set_intersection2(X0,X1),sK14),X1) )
| ~ spl15_133
| ~ spl15_134 ),
inference(resolution,[],[f1445,f1441]) ).
fof(f10181,plain,
( spl15_465
| ~ spl15_46
| ~ spl15_133 ),
inference(avatar_split_clause,[],[f1524,f1440,f498,f10179]) ).
fof(f10179,plain,
( spl15_465
<=> ! [X2,X0,X1] :
( in(sK9(set_intersection2(X0,X1),X2),X1)
| subset(set_intersection2(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_465])]) ).
fof(f498,plain,
( spl15_46
<=> ! [X0,X1] :
( subset(X0,X1)
| in(sK9(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_46])]) ).
fof(f1524,plain,
( ! [X2,X0,X1] :
( in(sK9(set_intersection2(X0,X1),X2),X1)
| subset(set_intersection2(X0,X1),X2) )
| ~ spl15_46
| ~ spl15_133 ),
inference(resolution,[],[f1441,f499]) ).
fof(f499,plain,
( ! [X0,X1] :
( in(sK9(X0,X1),X0)
| subset(X0,X1) )
| ~ spl15_46 ),
inference(avatar_component_clause,[],[f498]) ).
fof(f10134,plain,
( spl15_464
| ~ spl15_47
| ~ spl15_132 ),
inference(avatar_split_clause,[],[f1508,f1436,f502,f10132]) ).
fof(f10132,plain,
( spl15_464
<=> ! [X2,X0,X1] :
( ~ in(sK9(X0,set_union2(X1,X2)),X2)
| subset(X0,set_union2(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_464])]) ).
fof(f1436,plain,
( spl15_132
<=> ! [X2,X0,X1] :
( ~ in(X0,X1)
| in(X0,set_union2(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_132])]) ).
fof(f1508,plain,
( ! [X2,X0,X1] :
( ~ in(sK9(X0,set_union2(X1,X2)),X2)
| subset(X0,set_union2(X1,X2)) )
| ~ spl15_47
| ~ spl15_132 ),
inference(resolution,[],[f1437,f503]) ).
fof(f1437,plain,
( ! [X2,X0,X1] :
( in(X0,set_union2(X2,X1))
| ~ in(X0,X1) )
| ~ spl15_132 ),
inference(avatar_component_clause,[],[f1436]) ).
fof(f10130,plain,
( spl15_463
| ~ spl15_46
| ~ spl15_131 ),
inference(avatar_split_clause,[],[f1488,f1432,f498,f10128]) ).
fof(f10128,plain,
( spl15_463
<=> ! [X2,X0,X1] :
( ~ in(sK9(set_difference(X0,X1),X2),X1)
| subset(set_difference(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_463])]) ).
fof(f1488,plain,
( ! [X2,X0,X1] :
( ~ in(sK9(set_difference(X0,X1),X2),X1)
| subset(set_difference(X0,X1),X2) )
| ~ spl15_46
| ~ spl15_131 ),
inference(resolution,[],[f1433,f499]) ).
fof(f10126,plain,
( spl15_462
| ~ spl15_46
| ~ spl15_130 ),
inference(avatar_split_clause,[],[f1468,f1428,f498,f10124]) ).
fof(f1468,plain,
( ! [X2,X0,X1] :
( in(sK9(set_difference(X0,X1),X2),X0)
| subset(set_difference(X0,X1),X2) )
| ~ spl15_46
| ~ spl15_130 ),
inference(resolution,[],[f1429,f499]) ).
fof(f9786,plain,
( spl15_461
| ~ spl15_35
| ~ spl15_433 ),
inference(avatar_split_clause,[],[f8902,f8511,f413,f9784]) ).
fof(f9784,plain,
( spl15_461
<=> ! [X0,X1] : disjoint(X0,set_difference(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_461])]) ).
fof(f413,plain,
( spl15_35
<=> ! [X0,X1] :
( in(sK6(X0,X1),X0)
| disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_35])]) ).
fof(f8511,plain,
( spl15_433
<=> ! [X2,X0,X1] :
( ~ in(sK6(X0,set_difference(X1,X2)),X2)
| disjoint(X0,set_difference(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_433])]) ).
fof(f8902,plain,
( ! [X0,X1] : disjoint(X0,set_difference(X1,X0))
| ~ spl15_35
| ~ spl15_433 ),
inference(duplicate_literal_removal,[],[f8872]) ).
fof(f8872,plain,
( ! [X0,X1] :
( disjoint(X0,set_difference(X1,X0))
| disjoint(X0,set_difference(X1,X0)) )
| ~ spl15_35
| ~ spl15_433 ),
inference(resolution,[],[f8512,f414]) ).
fof(f414,plain,
( ! [X0,X1] :
( in(sK6(X0,X1),X0)
| disjoint(X0,X1) )
| ~ spl15_35 ),
inference(avatar_component_clause,[],[f413]) ).
fof(f8512,plain,
( ! [X2,X0,X1] :
( ~ in(sK6(X0,set_difference(X1,X2)),X2)
| disjoint(X0,set_difference(X1,X2)) )
| ~ spl15_433 ),
inference(avatar_component_clause,[],[f8511]) ).
fof(f9121,plain,
( spl15_460
| ~ spl15_36
| ~ spl15_431 ),
inference(avatar_split_clause,[],[f8867,f8503,f417,f9119]) ).
fof(f9119,plain,
( spl15_460
<=> ! [X0,X1] : disjoint(set_difference(X0,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_460])]) ).
fof(f417,plain,
( spl15_36
<=> ! [X0,X1] :
( in(sK6(X0,X1),X1)
| disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_36])]) ).
fof(f8503,plain,
( spl15_431
<=> ! [X2,X0,X1] :
( ~ in(sK6(set_difference(X0,X1),X2),X1)
| disjoint(set_difference(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_431])]) ).
fof(f8867,plain,
( ! [X0,X1] : disjoint(set_difference(X0,X1),X1)
| ~ spl15_36
| ~ spl15_431 ),
inference(duplicate_literal_removal,[],[f8839]) ).
fof(f8839,plain,
( ! [X0,X1] :
( disjoint(set_difference(X0,X1),X1)
| disjoint(set_difference(X0,X1),X1) )
| ~ spl15_36
| ~ spl15_431 ),
inference(resolution,[],[f8504,f418]) ).
fof(f418,plain,
( ! [X0,X1] :
( in(sK6(X0,X1),X1)
| disjoint(X0,X1) )
| ~ spl15_36 ),
inference(avatar_component_clause,[],[f417]) ).
fof(f8504,plain,
( ! [X2,X0,X1] :
( ~ in(sK6(set_difference(X0,X1),X2),X1)
| disjoint(set_difference(X0,X1),X2) )
| ~ spl15_431 ),
inference(avatar_component_clause,[],[f8503]) ).
fof(f8769,plain,
( spl15_459
| ~ spl15_90
| ~ spl15_266 ),
inference(avatar_split_clause,[],[f4747,f4496,f922,f8767]) ).
fof(f8767,plain,
( spl15_459
<=> ! [X2,X0,X1] :
( subset(X0,X1)
| ~ empty(set_union2(X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_459])]) ).
fof(f922,plain,
( spl15_90
<=> ! [X0,X1] : subset(X0,set_union2(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_90])]) ).
fof(f4496,plain,
( spl15_266
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| subset(X1,X2)
| ~ subset(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_266])]) ).
fof(f4747,plain,
( ! [X2,X0,X1] :
( subset(X0,X1)
| ~ empty(set_union2(X2,X0)) )
| ~ spl15_90
| ~ spl15_266 ),
inference(resolution,[],[f4497,f923]) ).
fof(f923,plain,
( ! [X0,X1] : subset(X0,set_union2(X1,X0))
| ~ spl15_90 ),
inference(avatar_component_clause,[],[f922]) ).
fof(f4497,plain,
( ! [X2,X0,X1] :
( ~ subset(X1,X0)
| subset(X1,X2)
| ~ empty(X0) )
| ~ spl15_266 ),
inference(avatar_component_clause,[],[f4496]) ).
fof(f8613,plain,
( spl15_458
| ~ spl15_29
| ~ spl15_91
| ~ spl15_179 ),
inference(avatar_split_clause,[],[f2570,f2332,f926,f356,f8611]) ).
fof(f8611,plain,
( spl15_458
<=> ! [X2,X0,X1] :
( set_union2(X1,set_union2(set_intersection2(X2,X1),X0)) = X1
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_458])]) ).
fof(f356,plain,
( spl15_29
<=> ! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_29])]) ).
fof(f926,plain,
( spl15_91
<=> ! [X0,X1] : subset(set_intersection2(X1,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_91])]) ).
fof(f2332,plain,
( spl15_179
<=> ! [X2,X0,X1] :
( ~ subset(X0,X1)
| ~ subset(X2,X1)
| set_union2(set_union2(X2,X0),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_179])]) ).
fof(f2570,plain,
( ! [X2,X0,X1] :
( set_union2(X1,set_union2(set_intersection2(X2,X1),X0)) = X1
| ~ subset(X0,X1) )
| ~ spl15_29
| ~ spl15_91
| ~ spl15_179 ),
inference(forward_demodulation,[],[f2551,f357]) ).
fof(f357,plain,
( ! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0)
| ~ spl15_29 ),
inference(avatar_component_clause,[],[f356]) ).
fof(f2551,plain,
( ! [X2,X0,X1] :
( ~ subset(X0,X1)
| set_union2(set_union2(set_intersection2(X2,X1),X0),X1) = X1 )
| ~ spl15_91
| ~ spl15_179 ),
inference(resolution,[],[f2333,f927]) ).
fof(f927,plain,
( ! [X0,X1] : subset(set_intersection2(X1,X0),X0)
| ~ spl15_91 ),
inference(avatar_component_clause,[],[f926]) ).
fof(f2333,plain,
( ! [X2,X0,X1] :
( ~ subset(X2,X1)
| ~ subset(X0,X1)
| set_union2(set_union2(X2,X0),X1) = X1 )
| ~ spl15_179 ),
inference(avatar_component_clause,[],[f2332]) ).
fof(f8609,plain,
( spl15_457
| ~ spl15_9
| ~ spl15_29
| ~ spl15_179 ),
inference(avatar_split_clause,[],[f2566,f2332,f356,f242,f8607]) ).
fof(f8607,plain,
( spl15_457
<=> ! [X2,X0,X1] :
( set_union2(X1,set_union2(set_intersection2(X1,X2),X0)) = X1
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_457])]) ).
fof(f242,plain,
( spl15_9
<=> ! [X0,X1] : subset(set_intersection2(X0,X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_9])]) ).
fof(f2566,plain,
( ! [X2,X0,X1] :
( set_union2(X1,set_union2(set_intersection2(X1,X2),X0)) = X1
| ~ subset(X0,X1) )
| ~ spl15_9
| ~ spl15_29
| ~ spl15_179 ),
inference(forward_demodulation,[],[f2548,f357]) ).
fof(f2548,plain,
( ! [X2,X0,X1] :
( ~ subset(X0,X1)
| set_union2(set_union2(set_intersection2(X1,X2),X0),X1) = X1 )
| ~ spl15_9
| ~ spl15_179 ),
inference(resolution,[],[f2333,f243]) ).
fof(f243,plain,
( ! [X0,X1] : subset(set_intersection2(X0,X1),X0)
| ~ spl15_9 ),
inference(avatar_component_clause,[],[f242]) ).
fof(f8605,plain,
( spl15_456
| ~ spl15_98
| ~ spl15_179 ),
inference(avatar_split_clause,[],[f2552,f2332,f1004,f8603]) ).
fof(f8603,plain,
( spl15_456
<=> ! [X2,X0,X1] :
( ~ subset(X0,X1)
| set_union2(set_union2(X2,X0),X1) = X1
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_456])]) ).
fof(f1004,plain,
( spl15_98
<=> ! [X0,X1] :
( subset(X0,X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_98])]) ).
fof(f2552,plain,
( ! [X2,X0,X1] :
( ~ subset(X0,X1)
| set_union2(set_union2(X2,X0),X1) = X1
| ~ empty(X2) )
| ~ spl15_98
| ~ spl15_179 ),
inference(resolution,[],[f2333,f1005]) ).
fof(f1005,plain,
( ! [X0,X1] :
( subset(X0,X1)
| ~ empty(X0) )
| ~ spl15_98 ),
inference(avatar_component_clause,[],[f1004]) ).
fof(f8601,plain,
( spl15_455
| ~ spl15_98
| ~ spl15_178 ),
inference(avatar_split_clause,[],[f2532,f2328,f1004,f8599]) ).
fof(f8599,plain,
( spl15_455
<=> ! [X2,X0,X1] :
( ~ subset(X0,X1)
| sK14 = set_difference(set_union2(X2,X0),X1)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_455])]) ).
fof(f2328,plain,
( spl15_178
<=> ! [X2,X0,X1] :
( ~ subset(X0,X1)
| ~ subset(X2,X1)
| sK14 = set_difference(set_union2(X2,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_178])]) ).
fof(f2532,plain,
( ! [X2,X0,X1] :
( ~ subset(X0,X1)
| sK14 = set_difference(set_union2(X2,X0),X1)
| ~ empty(X2) )
| ~ spl15_98
| ~ spl15_178 ),
inference(resolution,[],[f2329,f1005]) ).
fof(f2329,plain,
( ! [X2,X0,X1] :
( ~ subset(X2,X1)
| ~ subset(X0,X1)
| sK14 = set_difference(set_union2(X2,X0),X1) )
| ~ spl15_178 ),
inference(avatar_component_clause,[],[f2328]) ).
fof(f8597,plain,
( spl15_454
| ~ spl15_8
| ~ spl15_266 ),
inference(avatar_split_clause,[],[f4746,f4496,f238,f8595]) ).
fof(f8595,plain,
( spl15_454
<=> ! [X2,X0,X1] :
( subset(X0,X1)
| ~ empty(set_union2(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_454])]) ).
fof(f238,plain,
( spl15_8
<=> ! [X0,X1] : subset(X0,set_union2(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_8])]) ).
fof(f4746,plain,
( ! [X2,X0,X1] :
( subset(X0,X1)
| ~ empty(set_union2(X0,X2)) )
| ~ spl15_8
| ~ spl15_266 ),
inference(resolution,[],[f4497,f239]) ).
fof(f239,plain,
( ! [X0,X1] : subset(X0,set_union2(X0,X1))
| ~ spl15_8 ),
inference(avatar_component_clause,[],[f238]) ).
fof(f8593,plain,
( spl15_453
| ~ spl15_91
| ~ spl15_178 ),
inference(avatar_split_clause,[],[f2531,f2328,f926,f8591]) ).
fof(f8591,plain,
( spl15_453
<=> ! [X2,X0,X1] :
( ~ subset(X0,X1)
| sK14 = set_difference(set_union2(set_intersection2(X2,X1),X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_453])]) ).
fof(f2531,plain,
( ! [X2,X0,X1] :
( ~ subset(X0,X1)
| sK14 = set_difference(set_union2(set_intersection2(X2,X1),X0),X1) )
| ~ spl15_91
| ~ spl15_178 ),
inference(resolution,[],[f2329,f927]) ).
fof(f8589,plain,
( spl15_452
| ~ spl15_9
| ~ spl15_178 ),
inference(avatar_split_clause,[],[f2528,f2328,f242,f8587]) ).
fof(f8587,plain,
( spl15_452
<=> ! [X2,X0,X1] :
( ~ subset(X0,X1)
| sK14 = set_difference(set_union2(set_intersection2(X1,X2),X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_452])]) ).
fof(f2528,plain,
( ! [X2,X0,X1] :
( ~ subset(X0,X1)
| sK14 = set_difference(set_union2(set_intersection2(X1,X2),X0),X1) )
| ~ spl15_9
| ~ spl15_178 ),
inference(resolution,[],[f2329,f243]) ).
fof(f8585,plain,
( spl15_451
| ~ spl15_90
| ~ spl15_177 ),
inference(avatar_split_clause,[],[f2516,f2324,f922,f8583]) ).
fof(f8583,plain,
( spl15_451
<=> ! [X2,X0,X1] :
( ~ subset(X0,X1)
| set_intersection2(X0,set_intersection2(set_union2(X2,X0),X1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_451])]) ).
fof(f2324,plain,
( spl15_177
<=> ! [X2,X0,X1] :
( ~ subset(X0,X1)
| ~ subset(X0,X2)
| set_intersection2(X0,set_intersection2(X2,X1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_177])]) ).
fof(f2516,plain,
( ! [X2,X0,X1] :
( ~ subset(X0,X1)
| set_intersection2(X0,set_intersection2(set_union2(X2,X0),X1)) = X0 )
| ~ spl15_90
| ~ spl15_177 ),
inference(resolution,[],[f2325,f923]) ).
fof(f2325,plain,
( ! [X2,X0,X1] :
( ~ subset(X0,X2)
| ~ subset(X0,X1)
| set_intersection2(X0,set_intersection2(X2,X1)) = X0 )
| ~ spl15_177 ),
inference(avatar_component_clause,[],[f2324]) ).
fof(f8581,plain,
( spl15_450
| ~ spl15_8
| ~ spl15_177 ),
inference(avatar_split_clause,[],[f2515,f2324,f238,f8579]) ).
fof(f8579,plain,
( spl15_450
<=> ! [X2,X0,X1] :
( ~ subset(X0,X1)
| set_intersection2(X0,set_intersection2(set_union2(X0,X2),X1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_450])]) ).
fof(f2515,plain,
( ! [X2,X0,X1] :
( ~ subset(X0,X1)
| set_intersection2(X0,set_intersection2(set_union2(X0,X2),X1)) = X0 )
| ~ spl15_8
| ~ spl15_177 ),
inference(resolution,[],[f2325,f239]) ).
fof(f8577,plain,
( spl15_449
| ~ spl15_90
| ~ spl15_176 ),
inference(avatar_split_clause,[],[f2497,f2320,f922,f8575]) ).
fof(f8575,plain,
( spl15_449
<=> ! [X2,X0,X1] :
( ~ subset(X0,X1)
| sK14 = set_difference(X0,set_intersection2(set_union2(X2,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_449])]) ).
fof(f2320,plain,
( spl15_176
<=> ! [X2,X0,X1] :
( ~ subset(X0,X1)
| ~ subset(X0,X2)
| sK14 = set_difference(X0,set_intersection2(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_176])]) ).
fof(f2497,plain,
( ! [X2,X0,X1] :
( ~ subset(X0,X1)
| sK14 = set_difference(X0,set_intersection2(set_union2(X2,X0),X1)) )
| ~ spl15_90
| ~ spl15_176 ),
inference(resolution,[],[f2321,f923]) ).
fof(f2321,plain,
( ! [X2,X0,X1] :
( ~ subset(X0,X2)
| ~ subset(X0,X1)
| sK14 = set_difference(X0,set_intersection2(X2,X1)) )
| ~ spl15_176 ),
inference(avatar_component_clause,[],[f2320]) ).
fof(f8573,plain,
( spl15_448
| ~ spl15_8
| ~ spl15_176 ),
inference(avatar_split_clause,[],[f2496,f2320,f238,f8571]) ).
fof(f8571,plain,
( spl15_448
<=> ! [X2,X0,X1] :
( ~ subset(X0,X1)
| sK14 = set_difference(X0,set_intersection2(set_union2(X0,X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_448])]) ).
fof(f2496,plain,
( ! [X2,X0,X1] :
( ~ subset(X0,X1)
| sK14 = set_difference(X0,set_intersection2(set_union2(X0,X2),X1)) )
| ~ spl15_8
| ~ spl15_176 ),
inference(resolution,[],[f2321,f239]) ).
fof(f8569,plain,
( spl15_447
| ~ spl15_91
| ~ spl15_175 ),
inference(avatar_split_clause,[],[f2475,f2316,f926,f8567]) ).
fof(f8567,plain,
( spl15_447
<=> ! [X0,X3,X2,X1] :
( subset(set_intersection2(X0,set_intersection2(X1,X2)),set_intersection2(X3,X2))
| ~ subset(X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_447])]) ).
fof(f2316,plain,
( spl15_175
<=> ! [X0,X3,X2,X1] :
( ~ subset(X0,X1)
| subset(X2,set_intersection2(X1,X3))
| ~ subset(X2,set_intersection2(X0,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_175])]) ).
fof(f2475,plain,
( ! [X2,X3,X0,X1] :
( subset(set_intersection2(X0,set_intersection2(X1,X2)),set_intersection2(X3,X2))
| ~ subset(X1,X3) )
| ~ spl15_91
| ~ spl15_175 ),
inference(resolution,[],[f2317,f927]) ).
fof(f2317,plain,
( ! [X2,X3,X0,X1] :
( ~ subset(X2,set_intersection2(X0,X3))
| subset(X2,set_intersection2(X1,X3))
| ~ subset(X0,X1) )
| ~ spl15_175 ),
inference(avatar_component_clause,[],[f2316]) ).
fof(f8565,plain,
( spl15_446
| ~ spl15_9
| ~ spl15_175 ),
inference(avatar_split_clause,[],[f2472,f2316,f242,f8563]) ).
fof(f8563,plain,
( spl15_446
<=> ! [X0,X3,X2,X1] :
( subset(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X3,X1))
| ~ subset(X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_446])]) ).
fof(f2472,plain,
( ! [X2,X3,X0,X1] :
( subset(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X3,X1))
| ~ subset(X0,X3) )
| ~ spl15_9
| ~ spl15_175 ),
inference(resolution,[],[f2317,f243]) ).
fof(f8561,plain,
( spl15_445
| ~ spl15_91
| ~ spl15_173 ),
inference(avatar_split_clause,[],[f2406,f2308,f926,f8559]) ).
fof(f8559,plain,
( spl15_445
<=> ! [X0,X3,X2,X1] :
( subset(set_intersection2(X0,set_difference(X1,X2)),set_difference(X3,X2))
| ~ subset(X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_445])]) ).
fof(f2308,plain,
( spl15_173
<=> ! [X0,X3,X2,X1] :
( ~ subset(X0,X1)
| subset(X2,set_difference(X1,X3))
| ~ subset(X2,set_difference(X0,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_173])]) ).
fof(f2406,plain,
( ! [X2,X3,X0,X1] :
( subset(set_intersection2(X0,set_difference(X1,X2)),set_difference(X3,X2))
| ~ subset(X1,X3) )
| ~ spl15_91
| ~ spl15_173 ),
inference(resolution,[],[f2309,f927]) ).
fof(f2309,plain,
( ! [X2,X3,X0,X1] :
( ~ subset(X2,set_difference(X0,X3))
| subset(X2,set_difference(X1,X3))
| ~ subset(X0,X1) )
| ~ spl15_173 ),
inference(avatar_component_clause,[],[f2308]) ).
fof(f8557,plain,
( spl15_444
| ~ spl15_9
| ~ spl15_173 ),
inference(avatar_split_clause,[],[f2403,f2308,f242,f8555]) ).
fof(f8555,plain,
( spl15_444
<=> ! [X0,X3,X2,X1] :
( subset(set_intersection2(set_difference(X0,X1),X2),set_difference(X3,X1))
| ~ subset(X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_444])]) ).
fof(f2403,plain,
( ! [X2,X3,X0,X1] :
( subset(set_intersection2(set_difference(X0,X1),X2),set_difference(X3,X1))
| ~ subset(X0,X3) )
| ~ spl15_9
| ~ spl15_173 ),
inference(resolution,[],[f2309,f243]) ).
fof(f8553,plain,
( spl15_443
| ~ spl15_91
| ~ spl15_266 ),
inference(avatar_split_clause,[],[f4741,f4496,f926,f8551]) ).
fof(f8551,plain,
( spl15_443
<=> ! [X2,X0,X1] :
( subset(set_intersection2(X0,X1),X2)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_443])]) ).
fof(f4741,plain,
( ! [X2,X0,X1] :
( subset(set_intersection2(X0,X1),X2)
| ~ empty(X1) )
| ~ spl15_91
| ~ spl15_266 ),
inference(resolution,[],[f4497,f927]) ).
fof(f8549,plain,
( spl15_442
| ~ spl15_137
| ~ spl15_144 ),
inference(avatar_split_clause,[],[f1751,f1658,f1571,f8547]) ).
fof(f8547,plain,
( spl15_442
<=> ! [X2,X0,X1] :
( subset(set_intersection2(X0,X1),set_intersection2(X0,X2))
| ~ subset(set_intersection2(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_442])]) ).
fof(f1571,plain,
( spl15_137
<=> ! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(set_intersection2(X0,X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_137])]) ).
fof(f1658,plain,
( spl15_144
<=> ! [X2,X0,X1] :
( subset(set_intersection2(X2,X1),set_intersection2(X1,X0))
| ~ subset(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_144])]) ).
fof(f1751,plain,
( ! [X2,X0,X1] :
( subset(set_intersection2(X0,X1),set_intersection2(X0,X2))
| ~ subset(set_intersection2(X0,X1),X2) )
| ~ spl15_137
| ~ spl15_144 ),
inference(superposition,[],[f1659,f1572]) ).
fof(f1572,plain,
( ! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(set_intersection2(X0,X1),X0)
| ~ spl15_137 ),
inference(avatar_component_clause,[],[f1571]) ).
fof(f1659,plain,
( ! [X2,X0,X1] :
( subset(set_intersection2(X2,X1),set_intersection2(X1,X0))
| ~ subset(X2,X0) )
| ~ spl15_144 ),
inference(avatar_component_clause,[],[f1658]) ).
fof(f8545,plain,
( spl15_441
| ~ spl15_42
| ~ spl15_144 ),
inference(avatar_split_clause,[],[f1742,f1658,f471,f8543]) ).
fof(f8543,plain,
( spl15_441
<=> ! [X2,X0,X1] :
( ~ subset(X0,X1)
| sK14 = set_difference(set_intersection2(X0,X2),set_intersection2(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_441])]) ).
fof(f471,plain,
( spl15_42
<=> ! [X0,X1] :
( set_difference(X0,X1) = sK14
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_42])]) ).
fof(f1742,plain,
( ! [X2,X0,X1] :
( ~ subset(X0,X1)
| sK14 = set_difference(set_intersection2(X0,X2),set_intersection2(X2,X1)) )
| ~ spl15_42
| ~ spl15_144 ),
inference(resolution,[],[f1659,f472]) ).
fof(f472,plain,
( ! [X0,X1] :
( ~ subset(X0,X1)
| set_difference(X0,X1) = sK14 )
| ~ spl15_42 ),
inference(avatar_component_clause,[],[f471]) ).
fof(f8541,plain,
( spl15_440
| ~ spl15_137
| ~ spl15_143 ),
inference(avatar_split_clause,[],[f1730,f1654,f1571,f8539]) ).
fof(f8539,plain,
( spl15_440
<=> ! [X2,X0,X1] :
( subset(set_intersection2(X0,X1),set_intersection2(X2,set_intersection2(X0,X1)))
| ~ subset(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_440])]) ).
fof(f1654,plain,
( spl15_143
<=> ! [X2,X0,X1] :
( subset(set_intersection2(X1,X0),set_intersection2(X2,X1))
| ~ subset(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_143])]) ).
fof(f1730,plain,
( ! [X2,X0,X1] :
( subset(set_intersection2(X0,X1),set_intersection2(X2,set_intersection2(X0,X1)))
| ~ subset(X0,X2) )
| ~ spl15_137
| ~ spl15_143 ),
inference(superposition,[],[f1655,f1572]) ).
fof(f1655,plain,
( ! [X2,X0,X1] :
( subset(set_intersection2(X1,X0),set_intersection2(X2,X1))
| ~ subset(X0,X2) )
| ~ spl15_143 ),
inference(avatar_component_clause,[],[f1654]) ).
fof(f8537,plain,
( spl15_439
| ~ spl15_42
| ~ spl15_143 ),
inference(avatar_split_clause,[],[f1721,f1654,f471,f8535]) ).
fof(f8535,plain,
( spl15_439
<=> ! [X2,X0,X1] :
( ~ subset(X0,X1)
| sK14 = set_difference(set_intersection2(X2,X0),set_intersection2(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_439])]) ).
fof(f1721,plain,
( ! [X2,X0,X1] :
( ~ subset(X0,X1)
| sK14 = set_difference(set_intersection2(X2,X0),set_intersection2(X1,X2)) )
| ~ spl15_42
| ~ spl15_143 ),
inference(resolution,[],[f1655,f472]) ).
fof(f8533,plain,
( spl15_438
| ~ spl15_59
| ~ spl15_137 ),
inference(avatar_split_clause,[],[f1615,f1571,f586,f8531]) ).
fof(f8531,plain,
( spl15_438
<=> ! [X2,X0,X1] :
( subset(set_intersection2(X0,X1),set_intersection2(X2,X0))
| ~ subset(set_intersection2(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_438])]) ).
fof(f586,plain,
( spl15_59
<=> ! [X2,X0,X1] :
( subset(set_intersection2(X0,X2),set_intersection2(X1,X2))
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_59])]) ).
fof(f1615,plain,
( ! [X2,X0,X1] :
( subset(set_intersection2(X0,X1),set_intersection2(X2,X0))
| ~ subset(set_intersection2(X0,X1),X2) )
| ~ spl15_59
| ~ spl15_137 ),
inference(superposition,[],[f587,f1572]) ).
fof(f587,plain,
( ! [X2,X0,X1] :
( subset(set_intersection2(X0,X2),set_intersection2(X1,X2))
| ~ subset(X0,X1) )
| ~ spl15_59 ),
inference(avatar_component_clause,[],[f586]) ).
fof(f8529,plain,
( spl15_437
| ~ spl15_122
| ~ spl15_135 ),
inference(avatar_split_clause,[],[f1558,f1448,f1235,f8527]) ).
fof(f8527,plain,
( spl15_437
<=> ! [X0,X1] :
( set_intersection2(X0,X1) = sK14
| in(sK8(sK14,set_intersection2(X0,X1)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_437])]) ).
fof(f1235,plain,
( spl15_122
<=> ! [X2,X0,X1] :
( ~ in(X0,set_intersection2(X1,X2))
| in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_122])]) ).
fof(f1558,plain,
( ! [X0,X1] :
( set_intersection2(X0,X1) = sK14
| in(sK8(sK14,set_intersection2(X0,X1)),X0) )
| ~ spl15_122
| ~ spl15_135 ),
inference(resolution,[],[f1449,f1236]) ).
fof(f1236,plain,
( ! [X2,X0,X1] :
( ~ in(X0,set_intersection2(X1,X2))
| in(X0,X1) )
| ~ spl15_122 ),
inference(avatar_component_clause,[],[f1235]) ).
fof(f8525,plain,
( spl15_436
| ~ spl15_122
| ~ spl15_134 ),
inference(avatar_split_clause,[],[f1546,f1444,f1235,f8523]) ).
fof(f8523,plain,
( spl15_436
<=> ! [X0,X1] :
( set_intersection2(X0,X1) = sK14
| in(sK8(set_intersection2(X0,X1),sK14),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_436])]) ).
fof(f1546,plain,
( ! [X0,X1] :
( set_intersection2(X0,X1) = sK14
| in(sK8(set_intersection2(X0,X1),sK14),X0) )
| ~ spl15_122
| ~ spl15_134 ),
inference(resolution,[],[f1445,f1236]) ).
fof(f8521,plain,
( spl15_435
| ~ spl15_36
| ~ spl15_133 ),
inference(avatar_split_clause,[],[f1527,f1440,f417,f8519]) ).
fof(f8519,plain,
( spl15_435
<=> ! [X2,X0,X1] :
( in(sK6(X0,set_intersection2(X1,X2)),X2)
| disjoint(X0,set_intersection2(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_435])]) ).
fof(f1527,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,set_intersection2(X1,X2)),X2)
| disjoint(X0,set_intersection2(X1,X2)) )
| ~ spl15_36
| ~ spl15_133 ),
inference(resolution,[],[f1441,f418]) ).
fof(f8517,plain,
( spl15_434
| ~ spl15_35
| ~ spl15_133 ),
inference(avatar_split_clause,[],[f1521,f1440,f413,f8515]) ).
fof(f8515,plain,
( spl15_434
<=> ! [X2,X0,X1] :
( in(sK6(set_intersection2(X0,X1),X2),X1)
| disjoint(set_intersection2(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_434])]) ).
fof(f1521,plain,
( ! [X2,X0,X1] :
( in(sK6(set_intersection2(X0,X1),X2),X1)
| disjoint(set_intersection2(X0,X1),X2) )
| ~ spl15_35
| ~ spl15_133 ),
inference(resolution,[],[f1441,f414]) ).
fof(f8513,plain,
( spl15_433
| ~ spl15_36
| ~ spl15_131 ),
inference(avatar_split_clause,[],[f1491,f1432,f417,f8511]) ).
fof(f1491,plain,
( ! [X2,X0,X1] :
( ~ in(sK6(X0,set_difference(X1,X2)),X2)
| disjoint(X0,set_difference(X1,X2)) )
| ~ spl15_36
| ~ spl15_131 ),
inference(resolution,[],[f1433,f418]) ).
fof(f8509,plain,
( spl15_432
| ~ spl15_9
| ~ spl15_266 ),
inference(avatar_split_clause,[],[f4737,f4496,f242,f8507]) ).
fof(f8507,plain,
( spl15_432
<=> ! [X2,X0,X1] :
( subset(set_intersection2(X0,X1),X2)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_432])]) ).
fof(f4737,plain,
( ! [X2,X0,X1] :
( subset(set_intersection2(X0,X1),X2)
| ~ empty(X0) )
| ~ spl15_9
| ~ spl15_266 ),
inference(resolution,[],[f4497,f243]) ).
fof(f8505,plain,
( spl15_431
| ~ spl15_35
| ~ spl15_131 ),
inference(avatar_split_clause,[],[f1485,f1432,f413,f8503]) ).
fof(f1485,plain,
( ! [X2,X0,X1] :
( ~ in(sK6(set_difference(X0,X1),X2),X1)
| disjoint(set_difference(X0,X1),X2) )
| ~ spl15_35
| ~ spl15_131 ),
inference(resolution,[],[f1433,f414]) ).
fof(f8501,plain,
( spl15_430
| ~ spl15_36
| ~ spl15_130 ),
inference(avatar_split_clause,[],[f1471,f1428,f417,f8499]) ).
fof(f8499,plain,
( spl15_430
<=> ! [X2,X0,X1] :
( in(sK6(X0,set_difference(X1,X2)),X1)
| disjoint(X0,set_difference(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_430])]) ).
fof(f1471,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,set_difference(X1,X2)),X1)
| disjoint(X0,set_difference(X1,X2)) )
| ~ spl15_36
| ~ spl15_130 ),
inference(resolution,[],[f1429,f418]) ).
fof(f8497,plain,
( spl15_429
| ~ spl15_35
| ~ spl15_130 ),
inference(avatar_split_clause,[],[f1465,f1428,f413,f8495]) ).
fof(f8495,plain,
( spl15_429
<=> ! [X2,X0,X1] :
( in(sK6(set_difference(X0,X1),X2),X0)
| disjoint(set_difference(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_429])]) ).
fof(f1465,plain,
( ! [X2,X0,X1] :
( in(sK6(set_difference(X0,X1),X2),X0)
| disjoint(set_difference(X0,X1),X2) )
| ~ spl15_35
| ~ spl15_130 ),
inference(resolution,[],[f1429,f414]) ).
fof(f8492,plain,
( spl15_428
| ~ spl15_37
| ~ spl15_126 ),
inference(avatar_split_clause,[],[f1412,f1251,f421,f8490]) ).
fof(f8490,plain,
( spl15_428
<=> ! [X0,X1] :
( ~ subset(X0,X1)
| set_intersection2(X1,X0) = set_union2(X0,set_intersection2(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_428])]) ).
fof(f421,plain,
( spl15_37
<=> ! [X0,X1] :
( set_union2(X0,X1) = X1
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_37])]) ).
fof(f1251,plain,
( spl15_126
<=> ! [X0,X1] :
( subset(X0,set_intersection2(X1,X0))
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_126])]) ).
fof(f1412,plain,
( ! [X0,X1] :
( ~ subset(X0,X1)
| set_intersection2(X1,X0) = set_union2(X0,set_intersection2(X1,X0)) )
| ~ spl15_37
| ~ spl15_126 ),
inference(resolution,[],[f1252,f422]) ).
fof(f422,plain,
( ! [X0,X1] :
( ~ subset(X0,X1)
| set_union2(X0,X1) = X1 )
| ~ spl15_37 ),
inference(avatar_component_clause,[],[f421]) ).
fof(f1252,plain,
( ! [X0,X1] :
( subset(X0,set_intersection2(X1,X0))
| ~ subset(X0,X1) )
| ~ spl15_126 ),
inference(avatar_component_clause,[],[f1251]) ).
fof(f8488,plain,
( spl15_427
| ~ spl15_47
| ~ spl15_123 ),
inference(avatar_split_clause,[],[f1374,f1239,f502,f8486]) ).
fof(f8486,plain,
( spl15_427
<=> ! [X2,X0,X1] :
( ~ in(sK9(X0,set_union2(X1,X2)),X1)
| subset(X0,set_union2(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_427])]) ).
fof(f1239,plain,
( spl15_123
<=> ! [X2,X0,X1] :
( ~ in(X0,X1)
| in(X0,set_union2(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_123])]) ).
fof(f1374,plain,
( ! [X2,X0,X1] :
( ~ in(sK9(X0,set_union2(X1,X2)),X1)
| subset(X0,set_union2(X1,X2)) )
| ~ spl15_47
| ~ spl15_123 ),
inference(resolution,[],[f1240,f503]) ).
fof(f1240,plain,
( ! [X2,X0,X1] :
( in(X0,set_union2(X1,X2))
| ~ in(X0,X1) )
| ~ spl15_123 ),
inference(avatar_component_clause,[],[f1239]) ).
fof(f8484,plain,
( spl15_426
| ~ spl15_36
| ~ spl15_122 ),
inference(avatar_split_clause,[],[f1356,f1235,f417,f8482]) ).
fof(f8482,plain,
( spl15_426
<=> ! [X2,X0,X1] :
( in(sK6(X0,set_intersection2(X1,X2)),X1)
| disjoint(X0,set_intersection2(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_426])]) ).
fof(f1356,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,set_intersection2(X1,X2)),X1)
| disjoint(X0,set_intersection2(X1,X2)) )
| ~ spl15_36
| ~ spl15_122 ),
inference(resolution,[],[f1236,f418]) ).
fof(f8480,plain,
( spl15_425
| ~ spl15_46
| ~ spl15_122 ),
inference(avatar_split_clause,[],[f1353,f1235,f498,f8478]) ).
fof(f8478,plain,
( spl15_425
<=> ! [X2,X0,X1] :
( in(sK9(set_intersection2(X0,X1),X2),X0)
| subset(set_intersection2(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_425])]) ).
fof(f1353,plain,
( ! [X2,X0,X1] :
( in(sK9(set_intersection2(X0,X1),X2),X0)
| subset(set_intersection2(X0,X1),X2) )
| ~ spl15_46
| ~ spl15_122 ),
inference(resolution,[],[f1236,f499]) ).
fof(f8476,plain,
( spl15_424
| ~ spl15_35
| ~ spl15_122 ),
inference(avatar_split_clause,[],[f1350,f1235,f413,f8474]) ).
fof(f8474,plain,
( spl15_424
<=> ! [X2,X0,X1] :
( in(sK6(set_intersection2(X0,X1),X2),X0)
| disjoint(set_intersection2(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_424])]) ).
fof(f1350,plain,
( ! [X2,X0,X1] :
( in(sK6(set_intersection2(X0,X1),X2),X0)
| disjoint(set_intersection2(X0,X1),X2) )
| ~ spl15_35
| ~ spl15_122 ),
inference(resolution,[],[f1236,f414]) ).
fof(f8472,plain,
( spl15_423
| ~ spl15_37
| ~ spl15_121 ),
inference(avatar_split_clause,[],[f1342,f1231,f421,f8470]) ).
fof(f8470,plain,
( spl15_423
<=> ! [X2,X0,X1] :
( ~ subset(X0,X1)
| set_union2(X1,X2) = set_union2(X0,set_union2(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_423])]) ).
fof(f1231,plain,
( spl15_121
<=> ! [X2,X0,X1] :
( subset(X0,set_union2(X1,X2))
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_121])]) ).
fof(f1342,plain,
( ! [X2,X0,X1] :
( ~ subset(X0,X1)
| set_union2(X1,X2) = set_union2(X0,set_union2(X1,X2)) )
| ~ spl15_37
| ~ spl15_121 ),
inference(resolution,[],[f1232,f422]) ).
fof(f1232,plain,
( ! [X2,X0,X1] :
( subset(X0,set_union2(X1,X2))
| ~ subset(X0,X1) )
| ~ spl15_121 ),
inference(avatar_component_clause,[],[f1231]) ).
fof(f8468,plain,
( spl15_422
| ~ spl15_38
| ~ spl15_119 ),
inference(avatar_split_clause,[],[f1312,f1223,f426,f8466]) ).
fof(f8466,plain,
( spl15_422
<=> ! [X2,X0,X1] :
( ~ disjoint(X0,X1)
| set_intersection2(X0,X1) = set_intersection2(set_intersection2(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_422])]) ).
fof(f426,plain,
( spl15_38
<=> ! [X0,X1] :
( set_intersection2(X0,X1) = X0
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_38])]) ).
fof(f1223,plain,
( spl15_119
<=> ! [X2,X0,X1] :
( subset(set_intersection2(X0,X1),X2)
| ~ disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_119])]) ).
fof(f1312,plain,
( ! [X2,X0,X1] :
( ~ disjoint(X0,X1)
| set_intersection2(X0,X1) = set_intersection2(set_intersection2(X0,X1),X2) )
| ~ spl15_38
| ~ spl15_119 ),
inference(resolution,[],[f1224,f427]) ).
fof(f427,plain,
( ! [X0,X1] :
( ~ subset(X0,X1)
| set_intersection2(X0,X1) = X0 )
| ~ spl15_38 ),
inference(avatar_component_clause,[],[f426]) ).
fof(f1224,plain,
( ! [X2,X0,X1] :
( subset(set_intersection2(X0,X1),X2)
| ~ disjoint(X0,X1) )
| ~ spl15_119 ),
inference(avatar_component_clause,[],[f1223]) ).
fof(f8464,plain,
( spl15_421
| ~ spl15_248
| ~ spl15_259 ),
inference(avatar_split_clause,[],[f4468,f4121,f4077,f8462]) ).
fof(f8462,plain,
( spl15_421
<=> ! [X2,X0,X1] :
( ~ empty(X1)
| ~ in(X2,set_intersection2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_421])]) ).
fof(f4077,plain,
( spl15_248
<=> ! [X0,X1] : set_union2(set_intersection2(X0,X1),X1) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl15_248])]) ).
fof(f4121,plain,
( spl15_259
<=> ! [X2,X0,X1] :
( ~ in(X0,X1)
| ~ empty(set_union2(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_259])]) ).
fof(f4468,plain,
( ! [X2,X0,X1] :
( ~ empty(X1)
| ~ in(X2,set_intersection2(X0,X1)) )
| ~ spl15_248
| ~ spl15_259 ),
inference(superposition,[],[f4122,f4078]) ).
fof(f4078,plain,
( ! [X0,X1] : set_union2(set_intersection2(X0,X1),X1) = X1
| ~ spl15_248 ),
inference(avatar_component_clause,[],[f4077]) ).
fof(f4122,plain,
( ! [X2,X0,X1] :
( ~ empty(set_union2(X1,X2))
| ~ in(X0,X1) )
| ~ spl15_259 ),
inference(avatar_component_clause,[],[f4121]) ).
fof(f8336,plain,
( spl15_420
| ~ spl15_24
| ~ spl15_163 ),
inference(avatar_split_clause,[],[f2076,f2013,f314,f8334]) ).
fof(f8334,plain,
( spl15_420
<=> ! [X2,X0,X1] :
( ~ in(X0,X1)
| ~ in(X0,X2)
| ~ in(set_intersection2(X1,X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_420])]) ).
fof(f2013,plain,
( spl15_163
<=> ! [X2,X0,X1] :
( ~ in(X0,X1)
| ~ in(X0,X2)
| in(X0,set_intersection2(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_163])]) ).
fof(f2076,plain,
( ! [X2,X0,X1] :
( ~ in(X0,X1)
| ~ in(X0,X2)
| ~ in(set_intersection2(X1,X2),X0) )
| ~ spl15_24
| ~ spl15_163 ),
inference(resolution,[],[f2014,f315]) ).
fof(f2014,plain,
( ! [X2,X0,X1] :
( in(X0,set_intersection2(X2,X1))
| ~ in(X0,X2)
| ~ in(X0,X1) )
| ~ spl15_163 ),
inference(avatar_component_clause,[],[f2013]) ).
fof(f8332,plain,
( spl15_419
| ~ spl15_24
| ~ spl15_161 ),
inference(avatar_split_clause,[],[f2018,f2005,f314,f8330]) ).
fof(f8330,plain,
( spl15_419
<=> ! [X2,X0,X1] :
( ~ in(X0,X1)
| in(X0,X2)
| ~ in(set_difference(X1,X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_419])]) ).
fof(f2005,plain,
( spl15_161
<=> ! [X2,X0,X1] :
( in(X0,X1)
| ~ in(X0,X2)
| in(X0,set_difference(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_161])]) ).
fof(f2018,plain,
( ! [X2,X0,X1] :
( ~ in(X0,X1)
| in(X0,X2)
| ~ in(set_difference(X1,X2),X0) )
| ~ spl15_24
| ~ spl15_161 ),
inference(resolution,[],[f2006,f315]) ).
fof(f2006,plain,
( ! [X2,X0,X1] :
( in(X0,set_difference(X2,X1))
| ~ in(X0,X2)
| in(X0,X1) )
| ~ spl15_161 ),
inference(avatar_component_clause,[],[f2005]) ).
fof(f8328,plain,
( spl15_418
| ~ spl15_33
| ~ spl15_133 ),
inference(avatar_split_clause,[],[f1522,f1440,f372,f8326]) ).
fof(f8326,plain,
( spl15_418
<=> ! [X0,X1] :
( in(sK7(set_intersection2(X0,X1)),X1)
| set_intersection2(X0,X1) = sK14 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_418])]) ).
fof(f372,plain,
( spl15_33
<=> ! [X0] :
( sK14 = X0
| in(sK7(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_33])]) ).
fof(f1522,plain,
( ! [X0,X1] :
( in(sK7(set_intersection2(X0,X1)),X1)
| set_intersection2(X0,X1) = sK14 )
| ~ spl15_33
| ~ spl15_133 ),
inference(resolution,[],[f1441,f373]) ).
fof(f373,plain,
( ! [X0] :
( in(sK7(X0),X0)
| sK14 = X0 )
| ~ spl15_33 ),
inference(avatar_component_clause,[],[f372]) ).
fof(f8324,plain,
( spl15_417
| ~ spl15_33
| ~ spl15_131 ),
inference(avatar_split_clause,[],[f1486,f1432,f372,f8322]) ).
fof(f8322,plain,
( spl15_417
<=> ! [X0,X1] :
( ~ in(sK7(set_difference(X0,X1)),X1)
| set_difference(X0,X1) = sK14 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_417])]) ).
fof(f1486,plain,
( ! [X0,X1] :
( ~ in(sK7(set_difference(X0,X1)),X1)
| set_difference(X0,X1) = sK14 )
| ~ spl15_33
| ~ spl15_131 ),
inference(resolution,[],[f1433,f373]) ).
fof(f8320,plain,
( spl15_416
| ~ spl15_33
| ~ spl15_130 ),
inference(avatar_split_clause,[],[f1466,f1428,f372,f8318]) ).
fof(f8318,plain,
( spl15_416
<=> ! [X0,X1] :
( in(sK7(set_difference(X0,X1)),X0)
| set_difference(X0,X1) = sK14 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_416])]) ).
fof(f1466,plain,
( ! [X0,X1] :
( in(sK7(set_difference(X0,X1)),X0)
| set_difference(X0,X1) = sK14 )
| ~ spl15_33
| ~ spl15_130 ),
inference(resolution,[],[f1429,f373]) ).
fof(f7211,plain,
( spl15_415
| ~ spl15_16
| ~ spl15_196 ),
inference(avatar_split_clause,[],[f2905,f2816,f270,f7209]) ).
fof(f7209,plain,
( spl15_415
<=> ! [X0,X1] :
( in(sK8(X0,X1),X1)
| X0 = X1
| ~ disjoint(X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_415])]) ).
fof(f270,plain,
( spl15_16
<=> ! [X0] : set_intersection2(X0,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl15_16])]) ).
fof(f2816,plain,
( spl15_196
<=> ! [X2,X0,X1] :
( in(sK8(set_intersection2(X0,X1),X2),X2)
| set_intersection2(X0,X1) = X2
| ~ disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_196])]) ).
fof(f2905,plain,
( ! [X0,X1] :
( in(sK8(X0,X1),X1)
| X0 = X1
| ~ disjoint(X0,X0) )
| ~ spl15_16
| ~ spl15_196 ),
inference(superposition,[],[f2817,f271]) ).
fof(f271,plain,
( ! [X0] : set_intersection2(X0,X0) = X0
| ~ spl15_16 ),
inference(avatar_component_clause,[],[f270]) ).
fof(f2817,plain,
( ! [X2,X0,X1] :
( in(sK8(set_intersection2(X0,X1),X2),X2)
| set_intersection2(X0,X1) = X2
| ~ disjoint(X0,X1) )
| ~ spl15_196 ),
inference(avatar_component_clause,[],[f2816]) ).
fof(f7207,plain,
( spl15_414
| ~ spl15_16
| ~ spl15_195 ),
inference(avatar_split_clause,[],[f2878,f2812,f270,f7205]) ).
fof(f7205,plain,
( spl15_414
<=> ! [X0,X1] :
( in(sK8(X1,X0),X1)
| X0 = X1
| ~ disjoint(X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_414])]) ).
fof(f2812,plain,
( spl15_195
<=> ! [X2,X0,X1] :
( in(sK8(X0,set_intersection2(X1,X2)),X0)
| set_intersection2(X1,X2) = X0
| ~ disjoint(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_195])]) ).
fof(f2878,plain,
( ! [X0,X1] :
( in(sK8(X1,X0),X1)
| X0 = X1
| ~ disjoint(X0,X0) )
| ~ spl15_16
| ~ spl15_195 ),
inference(superposition,[],[f2813,f271]) ).
fof(f2813,plain,
( ! [X2,X0,X1] :
( in(sK8(X0,set_intersection2(X1,X2)),X0)
| set_intersection2(X1,X2) = X0
| ~ disjoint(X1,X2) )
| ~ spl15_195 ),
inference(avatar_component_clause,[],[f2812]) ).
fof(f7203,plain,
( spl15_413
| ~ spl15_17
| ~ spl15_371 ),
inference(avatar_split_clause,[],[f7028,f6934,f274,f7201]) ).
fof(f7201,plain,
( spl15_413
<=> ! [X0] :
( sP1(sK14,sK14,X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_413])]) ).
fof(f6934,plain,
( spl15_371
<=> ! [X0] :
( sP1(sK14,sK14,X0)
| in(sK11(sK14,sK14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_371])]) ).
fof(f7028,plain,
( ! [X0] :
( sP1(sK14,sK14,X0)
| ~ empty(X0) )
| ~ spl15_17
| ~ spl15_371 ),
inference(resolution,[],[f6935,f275]) ).
fof(f6935,plain,
( ! [X0] :
( in(sK11(sK14,sK14,X0),X0)
| sP1(sK14,sK14,X0) )
| ~ spl15_371 ),
inference(avatar_component_clause,[],[f6934]) ).
fof(f7199,plain,
( spl15_412
| ~ spl15_6
| ~ spl15_187 ),
inference(avatar_split_clause,[],[f2699,f2600,f230,f7197]) ).
fof(f7197,plain,
( spl15_412
<=> ! [X2,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X2,X0)
| in(X2,set_intersection2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_412])]) ).
fof(f230,plain,
( spl15_6
<=> ! [X0] : subset(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_6])]) ).
fof(f2600,plain,
( spl15_187
<=> ! [X0,X3,X2,X1] :
( ~ subset(X0,X1)
| ~ subset(X0,X2)
| ~ in(X3,X0)
| in(X3,set_intersection2(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_187])]) ).
fof(f2699,plain,
( ! [X2,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X2,X0)
| in(X2,set_intersection2(X0,X1)) )
| ~ spl15_6
| ~ spl15_187 ),
inference(resolution,[],[f2601,f231]) ).
fof(f231,plain,
( ! [X0] : subset(X0,X0)
| ~ spl15_6 ),
inference(avatar_component_clause,[],[f230]) ).
fof(f2601,plain,
( ! [X2,X3,X0,X1] :
( ~ subset(X0,X2)
| ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,set_intersection2(X2,X1)) )
| ~ spl15_187 ),
inference(avatar_component_clause,[],[f2600]) ).
fof(f7195,plain,
( spl15_411
| ~ spl15_126
| ~ spl15_175 ),
inference(avatar_split_clause,[],[f2470,f2316,f1251,f7193]) ).
fof(f7193,plain,
( spl15_411
<=> ! [X2,X0,X1] :
( subset(X0,set_intersection2(X1,X0))
| ~ subset(X2,X1)
| ~ subset(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_411])]) ).
fof(f2470,plain,
( ! [X2,X0,X1] :
( subset(X0,set_intersection2(X1,X0))
| ~ subset(X2,X1)
| ~ subset(X0,X2) )
| ~ spl15_126
| ~ spl15_175 ),
inference(resolution,[],[f2317,f1252]) ).
fof(f7191,plain,
( spl15_410
| ~ spl15_34
| ~ spl15_171 ),
inference(avatar_split_clause,[],[f2296,f2201,f409,f7189]) ).
fof(f7189,plain,
( spl15_410
<=> ! [X0,X3,X2,X1] :
( sP2(X0,X1,set_intersection2(X2,X3))
| ~ empty(X0)
| ~ disjoint(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_410])]) ).
fof(f409,plain,
( spl15_34
<=> ! [X2,X0,X1] :
( ~ disjoint(X0,X1)
| ~ in(X2,set_intersection2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_34])]) ).
fof(f2296,plain,
( ! [X2,X3,X0,X1] :
( sP2(X0,X1,set_intersection2(X2,X3))
| ~ empty(X0)
| ~ disjoint(X2,X3) )
| ~ spl15_34
| ~ spl15_171 ),
inference(resolution,[],[f2202,f410]) ).
fof(f410,plain,
( ! [X2,X0,X1] :
( ~ in(X2,set_intersection2(X0,X1))
| ~ disjoint(X0,X1) )
| ~ spl15_34 ),
inference(avatar_component_clause,[],[f409]) ).
fof(f7187,plain,
( spl15_409
| ~ spl15_113
| ~ spl15_171 ),
inference(avatar_split_clause,[],[f2295,f2201,f1199,f7185]) ).
fof(f7185,plain,
( spl15_409
<=> ! [X0,X3,X2,X1] :
( sP2(X0,X1,set_intersection2(X2,X3))
| ~ empty(X0)
| ~ disjoint(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_409])]) ).
fof(f1199,plain,
( spl15_113
<=> ! [X2,X0,X1] :
( ~ in(X2,set_intersection2(X1,X0))
| ~ disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_113])]) ).
fof(f2295,plain,
( ! [X2,X3,X0,X1] :
( sP2(X0,X1,set_intersection2(X2,X3))
| ~ empty(X0)
| ~ disjoint(X3,X2) )
| ~ spl15_113
| ~ spl15_171 ),
inference(resolution,[],[f2202,f1200]) ).
fof(f1200,plain,
( ! [X2,X0,X1] :
( ~ in(X2,set_intersection2(X1,X0))
| ~ disjoint(X0,X1) )
| ~ spl15_113 ),
inference(avatar_component_clause,[],[f1199]) ).
fof(f7183,plain,
( spl15_408
| ~ spl15_34
| ~ spl15_170 ),
inference(avatar_split_clause,[],[f2282,f2197,f409,f7181]) ).
fof(f7181,plain,
( spl15_408
<=> ! [X0,X3,X2,X1] :
( sP2(set_intersection2(X0,X1),X2,X3)
| ~ empty(X3)
| ~ disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_408])]) ).
fof(f2282,plain,
( ! [X2,X3,X0,X1] :
( sP2(set_intersection2(X0,X1),X2,X3)
| ~ empty(X3)
| ~ disjoint(X0,X1) )
| ~ spl15_34
| ~ spl15_170 ),
inference(resolution,[],[f2198,f410]) ).
fof(f7179,plain,
( spl15_407
| ~ spl15_113
| ~ spl15_170 ),
inference(avatar_split_clause,[],[f2281,f2197,f1199,f7177]) ).
fof(f7177,plain,
( spl15_407
<=> ! [X0,X3,X2,X1] :
( sP2(set_intersection2(X0,X1),X2,X3)
| ~ empty(X3)
| ~ disjoint(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_407])]) ).
fof(f2281,plain,
( ! [X2,X3,X0,X1] :
( sP2(set_intersection2(X0,X1),X2,X3)
| ~ empty(X3)
| ~ disjoint(X1,X0) )
| ~ spl15_113
| ~ spl15_170 ),
inference(resolution,[],[f2198,f1200]) ).
fof(f7175,plain,
( spl15_406
| ~ spl15_34
| ~ spl15_169 ),
inference(avatar_split_clause,[],[f2257,f2193,f409,f7173]) ).
fof(f7173,plain,
( spl15_406
<=> ! [X0,X3,X2,X1] :
( sP2(X0,X1,set_intersection2(X2,X3))
| ~ empty(X1)
| ~ disjoint(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_406])]) ).
fof(f2257,plain,
( ! [X2,X3,X0,X1] :
( sP2(X0,X1,set_intersection2(X2,X3))
| ~ empty(X1)
| ~ disjoint(X2,X3) )
| ~ spl15_34
| ~ spl15_169 ),
inference(resolution,[],[f2194,f410]) ).
fof(f7171,plain,
( spl15_405
| ~ spl15_113
| ~ spl15_169 ),
inference(avatar_split_clause,[],[f2256,f2193,f1199,f7169]) ).
fof(f7169,plain,
( spl15_405
<=> ! [X0,X3,X2,X1] :
( sP2(X0,X1,set_intersection2(X2,X3))
| ~ empty(X1)
| ~ disjoint(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_405])]) ).
fof(f2256,plain,
( ! [X2,X3,X0,X1] :
( sP2(X0,X1,set_intersection2(X2,X3))
| ~ empty(X1)
| ~ disjoint(X3,X2) )
| ~ spl15_113
| ~ spl15_169 ),
inference(resolution,[],[f2194,f1200]) ).
fof(f7167,plain,
( spl15_404
| ~ spl15_34
| ~ spl15_168 ),
inference(avatar_split_clause,[],[f2243,f2189,f409,f7165]) ).
fof(f7165,plain,
( spl15_404
<=> ! [X0,X3,X2,X1] :
( sP2(X0,set_intersection2(X1,X2),X3)
| ~ empty(X3)
| ~ disjoint(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_404])]) ).
fof(f2243,plain,
( ! [X2,X3,X0,X1] :
( sP2(X0,set_intersection2(X1,X2),X3)
| ~ empty(X3)
| ~ disjoint(X1,X2) )
| ~ spl15_34
| ~ spl15_168 ),
inference(resolution,[],[f2190,f410]) ).
fof(f7163,plain,
( spl15_403
| ~ spl15_113
| ~ spl15_168 ),
inference(avatar_split_clause,[],[f2242,f2189,f1199,f7161]) ).
fof(f7161,plain,
( spl15_403
<=> ! [X0,X3,X2,X1] :
( sP2(X0,set_intersection2(X1,X2),X3)
| ~ empty(X3)
| ~ disjoint(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_403])]) ).
fof(f2242,plain,
( ! [X2,X3,X0,X1] :
( sP2(X0,set_intersection2(X1,X2),X3)
| ~ empty(X3)
| ~ disjoint(X2,X1) )
| ~ spl15_113
| ~ spl15_168 ),
inference(resolution,[],[f2190,f1200]) ).
fof(f7159,plain,
( spl15_402
| ~ spl15_17
| ~ spl15_370 ),
inference(avatar_split_clause,[],[f7009,f6930,f274,f7157]) ).
fof(f7157,plain,
( spl15_402
<=> ! [X0] :
( sP1(X0,X0,sK14)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_402])]) ).
fof(f6930,plain,
( spl15_370
<=> ! [X0] :
( sP1(X0,X0,sK14)
| in(sK11(X0,X0,sK14),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_370])]) ).
fof(f7009,plain,
( ! [X0] :
( sP1(X0,X0,sK14)
| ~ empty(X0) )
| ~ spl15_17
| ~ spl15_370 ),
inference(resolution,[],[f6931,f275]) ).
fof(f6931,plain,
( ! [X0] :
( in(sK11(X0,X0,sK14),X0)
| sP1(X0,X0,sK14) )
| ~ spl15_370 ),
inference(avatar_component_clause,[],[f6930]) ).
fof(f7155,plain,
( spl15_401
| ~ spl15_34
| ~ spl15_167 ),
inference(avatar_split_clause,[],[f2228,f2185,f409,f7153]) ).
fof(f7153,plain,
( spl15_401
<=> ! [X0,X3,X2,X1] :
( sP0(X0,X1,set_intersection2(X2,X3))
| ~ empty(X1)
| ~ disjoint(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_401])]) ).
fof(f2228,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,X1,set_intersection2(X2,X3))
| ~ empty(X1)
| ~ disjoint(X2,X3) )
| ~ spl15_34
| ~ spl15_167 ),
inference(resolution,[],[f2186,f410]) ).
fof(f7151,plain,
( spl15_400
| ~ spl15_113
| ~ spl15_167 ),
inference(avatar_split_clause,[],[f2227,f2185,f1199,f7149]) ).
fof(f7149,plain,
( spl15_400
<=> ! [X0,X3,X2,X1] :
( sP0(X0,X1,set_intersection2(X2,X3))
| ~ empty(X1)
| ~ disjoint(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_400])]) ).
fof(f2227,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,X1,set_intersection2(X2,X3))
| ~ empty(X1)
| ~ disjoint(X3,X2) )
| ~ spl15_113
| ~ spl15_167 ),
inference(resolution,[],[f2186,f1200]) ).
fof(f7147,plain,
( spl15_399
| ~ spl15_34
| ~ spl15_166 ),
inference(avatar_split_clause,[],[f2212,f2181,f409,f7145]) ).
fof(f7145,plain,
( spl15_399
<=> ! [X0,X3,X2,X1] :
( sP0(X0,set_intersection2(X1,X2),X3)
| ~ empty(X3)
| ~ disjoint(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_399])]) ).
fof(f2212,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,set_intersection2(X1,X2),X3)
| ~ empty(X3)
| ~ disjoint(X1,X2) )
| ~ spl15_34
| ~ spl15_166 ),
inference(resolution,[],[f2182,f410]) ).
fof(f7143,plain,
( spl15_398
| ~ spl15_113
| ~ spl15_166 ),
inference(avatar_split_clause,[],[f2211,f2181,f1199,f7141]) ).
fof(f7141,plain,
( spl15_398
<=> ! [X0,X3,X2,X1] :
( sP0(X0,set_intersection2(X1,X2),X3)
| ~ empty(X3)
| ~ disjoint(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_398])]) ).
fof(f2211,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,set_intersection2(X1,X2),X3)
| ~ empty(X3)
| ~ disjoint(X2,X1) )
| ~ spl15_113
| ~ spl15_166 ),
inference(resolution,[],[f2182,f1200]) ).
fof(f7139,plain,
( spl15_397
| ~ spl15_90
| ~ spl15_165 ),
inference(avatar_split_clause,[],[f2130,f2098,f922,f7137]) ).
fof(f7137,plain,
( spl15_397
<=> ! [X2,X0,X1] : sK14 = set_difference(set_intersection2(X0,X1),set_intersection2(set_union2(X2,X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_397])]) ).
fof(f2098,plain,
( spl15_165
<=> ! [X2,X0,X1] :
( ~ subset(X0,X1)
| sK14 = set_difference(set_intersection2(X0,X2),set_intersection2(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_165])]) ).
fof(f2130,plain,
( ! [X2,X0,X1] : sK14 = set_difference(set_intersection2(X0,X1),set_intersection2(set_union2(X2,X0),X1))
| ~ spl15_90
| ~ spl15_165 ),
inference(resolution,[],[f2099,f923]) ).
fof(f2099,plain,
( ! [X2,X0,X1] :
( ~ subset(X0,X1)
| sK14 = set_difference(set_intersection2(X0,X2),set_intersection2(X1,X2)) )
| ~ spl15_165 ),
inference(avatar_component_clause,[],[f2098]) ).
fof(f7135,plain,
( spl15_396
| ~ spl15_8
| ~ spl15_165 ),
inference(avatar_split_clause,[],[f2129,f2098,f238,f7133]) ).
fof(f7133,plain,
( spl15_396
<=> ! [X2,X0,X1] : sK14 = set_difference(set_intersection2(X0,X1),set_intersection2(set_union2(X0,X2),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_396])]) ).
fof(f2129,plain,
( ! [X2,X0,X1] : sK14 = set_difference(set_intersection2(X0,X1),set_intersection2(set_union2(X0,X2),X1))
| ~ spl15_8
| ~ spl15_165 ),
inference(resolution,[],[f2099,f239]) ).
fof(f7131,plain,
( spl15_395
| ~ spl15_91
| ~ spl15_165 ),
inference(avatar_split_clause,[],[f2125,f2098,f926,f7129]) ).
fof(f7129,plain,
( spl15_395
<=> ! [X2,X0,X1] : sK14 = set_difference(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_395])]) ).
fof(f2125,plain,
( ! [X2,X0,X1] : sK14 = set_difference(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X1,X2))
| ~ spl15_91
| ~ spl15_165 ),
inference(resolution,[],[f2099,f927]) ).
fof(f7127,plain,
( spl15_394
| ~ spl15_9
| ~ spl15_165 ),
inference(avatar_split_clause,[],[f2122,f2098,f242,f7125]) ).
fof(f7125,plain,
( spl15_394
<=> ! [X2,X0,X1] : sK14 = set_difference(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_394])]) ).
fof(f2122,plain,
( ! [X2,X0,X1] : sK14 = set_difference(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X2))
| ~ spl15_9
| ~ spl15_165 ),
inference(resolution,[],[f2099,f243]) ).
fof(f7123,plain,
( spl15_393
| ~ spl15_90
| ~ spl15_164 ),
inference(avatar_split_clause,[],[f2110,f2094,f922,f7121]) ).
fof(f7121,plain,
( spl15_393
<=> ! [X2,X0,X1] : sK14 = set_difference(set_difference(X0,X1),set_difference(set_union2(X2,X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_393])]) ).
fof(f2094,plain,
( spl15_164
<=> ! [X2,X0,X1] :
( ~ subset(X0,X1)
| sK14 = set_difference(set_difference(X0,X2),set_difference(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_164])]) ).
fof(f2110,plain,
( ! [X2,X0,X1] : sK14 = set_difference(set_difference(X0,X1),set_difference(set_union2(X2,X0),X1))
| ~ spl15_90
| ~ spl15_164 ),
inference(resolution,[],[f2095,f923]) ).
fof(f2095,plain,
( ! [X2,X0,X1] :
( ~ subset(X0,X1)
| sK14 = set_difference(set_difference(X0,X2),set_difference(X1,X2)) )
| ~ spl15_164 ),
inference(avatar_component_clause,[],[f2094]) ).
fof(f7119,plain,
( spl15_392
| ~ spl15_8
| ~ spl15_164 ),
inference(avatar_split_clause,[],[f2109,f2094,f238,f7117]) ).
fof(f7117,plain,
( spl15_392
<=> ! [X2,X0,X1] : sK14 = set_difference(set_difference(X0,X1),set_difference(set_union2(X0,X2),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_392])]) ).
fof(f2109,plain,
( ! [X2,X0,X1] : sK14 = set_difference(set_difference(X0,X1),set_difference(set_union2(X0,X2),X1))
| ~ spl15_8
| ~ spl15_164 ),
inference(resolution,[],[f2095,f239]) ).
fof(f7115,plain,
( spl15_391
| ~ spl15_17
| ~ spl15_369 ),
inference(avatar_split_clause,[],[f6990,f6926,f274,f7113]) ).
fof(f7113,plain,
( spl15_391
<=> ! [X0] :
( sP1(sK14,X0,sK14)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_391])]) ).
fof(f6926,plain,
( spl15_369
<=> ! [X0] :
( sP1(sK14,X0,sK14)
| in(sK11(sK14,X0,sK14),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_369])]) ).
fof(f6990,plain,
( ! [X0] :
( sP1(sK14,X0,sK14)
| ~ empty(X0) )
| ~ spl15_17
| ~ spl15_369 ),
inference(resolution,[],[f6927,f275]) ).
fof(f6927,plain,
( ! [X0] :
( in(sK11(sK14,X0,sK14),X0)
| sP1(sK14,X0,sK14) )
| ~ spl15_369 ),
inference(avatar_component_clause,[],[f6926]) ).
fof(f7111,plain,
( spl15_390
| ~ spl15_98
| ~ spl15_164 ),
inference(avatar_split_clause,[],[f2106,f2094,f1004,f7109]) ).
fof(f7109,plain,
( spl15_390
<=> ! [X2,X0,X1] :
( sK14 = set_difference(set_difference(X0,X1),set_difference(X2,X1))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_390])]) ).
fof(f2106,plain,
( ! [X2,X0,X1] :
( sK14 = set_difference(set_difference(X0,X1),set_difference(X2,X1))
| ~ empty(X0) )
| ~ spl15_98
| ~ spl15_164 ),
inference(resolution,[],[f2095,f1005]) ).
fof(f7107,plain,
( spl15_389
| ~ spl15_91
| ~ spl15_164 ),
inference(avatar_split_clause,[],[f2105,f2094,f926,f7105]) ).
fof(f7105,plain,
( spl15_389
<=> ! [X2,X0,X1] : sK14 = set_difference(set_difference(set_intersection2(X0,X1),X2),set_difference(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_389])]) ).
fof(f2105,plain,
( ! [X2,X0,X1] : sK14 = set_difference(set_difference(set_intersection2(X0,X1),X2),set_difference(X1,X2))
| ~ spl15_91
| ~ spl15_164 ),
inference(resolution,[],[f2095,f927]) ).
fof(f7103,plain,
( spl15_388
| ~ spl15_9
| ~ spl15_164 ),
inference(avatar_split_clause,[],[f2102,f2094,f242,f7101]) ).
fof(f7101,plain,
( spl15_388
<=> ! [X2,X0,X1] : sK14 = set_difference(set_difference(set_intersection2(X0,X1),X2),set_difference(X0,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_388])]) ).
fof(f2102,plain,
( ! [X2,X0,X1] : sK14 = set_difference(set_difference(set_intersection2(X0,X1),X2),set_difference(X0,X2))
| ~ spl15_9
| ~ spl15_164 ),
inference(resolution,[],[f2095,f243]) ).
fof(f7099,plain,
( spl15_387
| ~ spl15_34
| ~ spl15_156 ),
inference(avatar_split_clause,[],[f1944,f1800,f409,f7097]) ).
fof(f7097,plain,
( spl15_387
<=> ! [X2,X0,X1] :
( sP2(set_intersection2(X0,X1),X2,set_intersection2(X0,X1))
| ~ disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_387])]) ).
fof(f1800,plain,
( spl15_156
<=> ! [X0,X1] :
( in(sK12(X0,X1,X0),X0)
| sP2(X0,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_156])]) ).
fof(f1944,plain,
( ! [X2,X0,X1] :
( sP2(set_intersection2(X0,X1),X2,set_intersection2(X0,X1))
| ~ disjoint(X0,X1) )
| ~ spl15_34
| ~ spl15_156 ),
inference(resolution,[],[f1801,f410]) ).
fof(f1801,plain,
( ! [X0,X1] :
( in(sK12(X0,X1,X0),X0)
| sP2(X0,X1,X0) )
| ~ spl15_156 ),
inference(avatar_component_clause,[],[f1800]) ).
fof(f7095,plain,
( spl15_386
| ~ spl15_113
| ~ spl15_156 ),
inference(avatar_split_clause,[],[f1943,f1800,f1199,f7093]) ).
fof(f7093,plain,
( spl15_386
<=> ! [X2,X0,X1] :
( sP2(set_intersection2(X0,X1),X2,set_intersection2(X0,X1))
| ~ disjoint(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_386])]) ).
fof(f1943,plain,
( ! [X2,X0,X1] :
( sP2(set_intersection2(X0,X1),X2,set_intersection2(X0,X1))
| ~ disjoint(X1,X0) )
| ~ spl15_113
| ~ spl15_156 ),
inference(resolution,[],[f1801,f1200]) ).
fof(f7091,plain,
( spl15_385
| ~ spl15_34
| ~ spl15_153 ),
inference(avatar_split_clause,[],[f1905,f1788,f409,f7089]) ).
fof(f7089,plain,
( spl15_385
<=> ! [X2,X0,X1] :
( sP2(X0,set_intersection2(X1,X2),set_intersection2(X1,X2))
| ~ disjoint(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_385])]) ).
fof(f1788,plain,
( spl15_153
<=> ! [X0,X1] :
( in(sK12(X0,X1,X1),X1)
| sP2(X0,X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_153])]) ).
fof(f1905,plain,
( ! [X2,X0,X1] :
( sP2(X0,set_intersection2(X1,X2),set_intersection2(X1,X2))
| ~ disjoint(X1,X2) )
| ~ spl15_34
| ~ spl15_153 ),
inference(resolution,[],[f1789,f410]) ).
fof(f1789,plain,
( ! [X0,X1] :
( in(sK12(X0,X1,X1),X1)
| sP2(X0,X1,X1) )
| ~ spl15_153 ),
inference(avatar_component_clause,[],[f1788]) ).
fof(f7087,plain,
( spl15_384
| ~ spl15_113
| ~ spl15_153 ),
inference(avatar_split_clause,[],[f1904,f1788,f1199,f7085]) ).
fof(f7085,plain,
( spl15_384
<=> ! [X2,X0,X1] :
( sP2(X0,set_intersection2(X1,X2),set_intersection2(X1,X2))
| ~ disjoint(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_384])]) ).
fof(f1904,plain,
( ! [X2,X0,X1] :
( sP2(X0,set_intersection2(X1,X2),set_intersection2(X1,X2))
| ~ disjoint(X2,X1) )
| ~ spl15_113
| ~ spl15_153 ),
inference(resolution,[],[f1789,f1200]) ).
fof(f7083,plain,
( spl15_383
| ~ spl15_34
| ~ spl15_148 ),
inference(avatar_split_clause,[],[f1842,f1768,f409,f7081]) ).
fof(f7081,plain,
( spl15_383
<=> ! [X2,X0,X1] :
( sP0(X0,set_intersection2(X1,X2),set_intersection2(X1,X2))
| ~ disjoint(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_383])]) ).
fof(f1768,plain,
( spl15_148
<=> ! [X0,X1] :
( in(sK10(X0,X1,X1),X1)
| sP0(X0,X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_148])]) ).
fof(f1842,plain,
( ! [X2,X0,X1] :
( sP0(X0,set_intersection2(X1,X2),set_intersection2(X1,X2))
| ~ disjoint(X1,X2) )
| ~ spl15_34
| ~ spl15_148 ),
inference(resolution,[],[f1769,f410]) ).
fof(f1769,plain,
( ! [X0,X1] :
( in(sK10(X0,X1,X1),X1)
| sP0(X0,X1,X1) )
| ~ spl15_148 ),
inference(avatar_component_clause,[],[f1768]) ).
fof(f7079,plain,
( spl15_382
| ~ spl15_113
| ~ spl15_148 ),
inference(avatar_split_clause,[],[f1841,f1768,f1199,f7077]) ).
fof(f7077,plain,
( spl15_382
<=> ! [X2,X0,X1] :
( sP0(X0,set_intersection2(X1,X2),set_intersection2(X1,X2))
| ~ disjoint(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_382])]) ).
fof(f1841,plain,
( ! [X2,X0,X1] :
( sP0(X0,set_intersection2(X1,X2),set_intersection2(X1,X2))
| ~ disjoint(X2,X1) )
| ~ spl15_113
| ~ spl15_148 ),
inference(resolution,[],[f1769,f1200]) ).
fof(f7075,plain,
( spl15_381
| ~ spl15_51
| ~ spl15_126 ),
inference(avatar_split_clause,[],[f1409,f1251,f531,f7073]) ).
fof(f7073,plain,
( spl15_381
<=> ! [X2,X0,X1] :
( ~ subset(X0,X1)
| subset(X2,set_intersection2(X1,X0))
| ~ subset(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_381])]) ).
fof(f531,plain,
( spl15_51
<=> ! [X2,X0,X1] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_51])]) ).
fof(f1409,plain,
( ! [X2,X0,X1] :
( ~ subset(X0,X1)
| subset(X2,set_intersection2(X1,X0))
| ~ subset(X2,X0) )
| ~ spl15_51
| ~ spl15_126 ),
inference(resolution,[],[f1252,f532]) ).
fof(f532,plain,
( ! [X2,X0,X1] :
( ~ subset(X1,X2)
| subset(X0,X2)
| ~ subset(X0,X1) )
| ~ spl15_51 ),
inference(avatar_component_clause,[],[f531]) ).
fof(f7071,plain,
( spl15_380
| ~ spl15_17
| ~ spl15_368 ),
inference(avatar_split_clause,[],[f6971,f6922,f274,f7069]) ).
fof(f7069,plain,
( spl15_380
<=> ! [X0] :
( sP1(X0,sK14,sK14)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_380])]) ).
fof(f6922,plain,
( spl15_368
<=> ! [X0] :
( sP1(X0,sK14,sK14)
| in(sK11(X0,sK14,sK14),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_368])]) ).
fof(f6971,plain,
( ! [X0] :
( sP1(X0,sK14,sK14)
| ~ empty(X0) )
| ~ spl15_17
| ~ spl15_368 ),
inference(resolution,[],[f6923,f275]) ).
fof(f6923,plain,
( ! [X0] :
( in(sK11(X0,sK14,sK14),X0)
| sP1(X0,sK14,sK14) )
| ~ spl15_368 ),
inference(avatar_component_clause,[],[f6922]) ).
fof(f7067,plain,
( spl15_379
| ~ spl15_53
| ~ spl15_126 ),
inference(avatar_split_clause,[],[f1407,f1251,f545,f7065]) ).
fof(f7065,plain,
( spl15_379
<=> ! [X2,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X2,X0)
| in(X2,set_intersection2(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_379])]) ).
fof(f545,plain,
( spl15_53
<=> ! [X0,X1,X3] :
( in(X3,X1)
| ~ in(X3,X0)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_53])]) ).
fof(f1407,plain,
( ! [X2,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X2,X0)
| in(X2,set_intersection2(X1,X0)) )
| ~ spl15_53
| ~ spl15_126 ),
inference(resolution,[],[f1252,f546]) ).
fof(f546,plain,
( ! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) )
| ~ spl15_53 ),
inference(avatar_component_clause,[],[f545]) ).
fof(f7063,plain,
( spl15_378
| ~ spl15_33
| ~ spl15_122 ),
inference(avatar_split_clause,[],[f1351,f1235,f372,f7061]) ).
fof(f7061,plain,
( spl15_378
<=> ! [X0,X1] :
( in(sK7(set_intersection2(X0,X1)),X0)
| set_intersection2(X0,X1) = sK14 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_378])]) ).
fof(f1351,plain,
( ! [X0,X1] :
( in(sK7(set_intersection2(X0,X1)),X0)
| set_intersection2(X0,X1) = sK14 )
| ~ spl15_33
| ~ spl15_122 ),
inference(resolution,[],[f1236,f373]) ).
fof(f7059,plain,
( spl15_377
| ~ spl15_51
| ~ spl15_121 ),
inference(avatar_split_clause,[],[f1339,f1231,f531,f7057]) ).
fof(f7057,plain,
( spl15_377
<=> ! [X0,X3,X2,X1] :
( ~ subset(X0,X1)
| subset(X2,set_union2(X1,X3))
| ~ subset(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_377])]) ).
fof(f1339,plain,
( ! [X2,X3,X0,X1] :
( ~ subset(X0,X1)
| subset(X2,set_union2(X1,X3))
| ~ subset(X2,X0) )
| ~ spl15_51
| ~ spl15_121 ),
inference(resolution,[],[f1232,f532]) ).
fof(f7055,plain,
( spl15_376
| ~ spl15_53
| ~ spl15_121 ),
inference(avatar_split_clause,[],[f1337,f1231,f545,f7053]) ).
fof(f7053,plain,
( spl15_376
<=> ! [X0,X3,X2,X1] :
( ~ subset(X0,X1)
| ~ in(X2,X0)
| in(X2,set_union2(X1,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_376])]) ).
fof(f1337,plain,
( ! [X2,X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X2,X0)
| in(X2,set_union2(X1,X3)) )
| ~ spl15_53
| ~ spl15_121 ),
inference(resolution,[],[f1232,f546]) ).
fof(f7051,plain,
( spl15_375
| ~ spl15_51
| ~ spl15_119 ),
inference(avatar_split_clause,[],[f1310,f1223,f531,f7049]) ).
fof(f7049,plain,
( spl15_375
<=> ! [X0,X3,X2,X1] :
( ~ disjoint(X0,X1)
| subset(X2,X3)
| ~ subset(X2,set_intersection2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_375])]) ).
fof(f1310,plain,
( ! [X2,X3,X0,X1] :
( ~ disjoint(X0,X1)
| subset(X2,X3)
| ~ subset(X2,set_intersection2(X0,X1)) )
| ~ spl15_51
| ~ spl15_119 ),
inference(resolution,[],[f1224,f532]) ).
fof(f7047,plain,
( spl15_374
| ~ spl15_68
| ~ spl15_101 ),
inference(avatar_split_clause,[],[f1056,f1042,f667,f7045]) ).
fof(f7045,plain,
( spl15_374
<=> ! [X2,X0,X1] :
( subset(set_union2(X0,X1),X2)
| ~ subset(X1,sK14)
| ~ subset(X0,sK14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_374])]) ).
fof(f667,plain,
( spl15_68
<=> ! [X2,X0,X1] :
( subset(set_union2(X0,X2),X1)
| ~ subset(X2,X1)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_68])]) ).
fof(f1042,plain,
( spl15_101
<=> ! [X0,X1] :
( ~ subset(X0,sK14)
| subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_101])]) ).
fof(f1056,plain,
( ! [X2,X0,X1] :
( subset(set_union2(X0,X1),X2)
| ~ subset(X1,sK14)
| ~ subset(X0,sK14) )
| ~ spl15_68
| ~ spl15_101 ),
inference(resolution,[],[f1043,f668]) ).
fof(f668,plain,
( ! [X2,X0,X1] :
( subset(set_union2(X0,X2),X1)
| ~ subset(X2,X1)
| ~ subset(X0,X1) )
| ~ spl15_68 ),
inference(avatar_component_clause,[],[f667]) ).
fof(f1043,plain,
( ! [X0,X1] :
( ~ subset(X0,sK14)
| subset(X0,X1) )
| ~ spl15_101 ),
inference(avatar_component_clause,[],[f1042]) ).
fof(f6967,plain,
( spl15_373
| ~ spl15_106
| ~ spl15_259 ),
inference(avatar_split_clause,[],[f4467,f4121,f1098,f6965]) ).
fof(f6965,plain,
( spl15_373
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| ~ in(X2,set_intersection2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_373])]) ).
fof(f1098,plain,
( spl15_106
<=> ! [X0,X1] : set_union2(set_intersection2(X0,X1),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl15_106])]) ).
fof(f4467,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| ~ in(X2,set_intersection2(X0,X1)) )
| ~ spl15_106
| ~ spl15_259 ),
inference(superposition,[],[f4122,f1099]) ).
fof(f1099,plain,
( ! [X0,X1] : set_union2(set_intersection2(X0,X1),X0) = X0
| ~ spl15_106 ),
inference(avatar_component_clause,[],[f1098]) ).
fof(f6940,plain,
( spl15_372
| ~ spl15_30
| ~ spl15_258 ),
inference(avatar_split_clause,[],[f4437,f4117,f360,f6938]) ).
fof(f6938,plain,
( spl15_372
<=> ! [X2,X0,X1] : subset(set_intersection2(X2,set_intersection2(X1,X0)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_372])]) ).
fof(f360,plain,
( spl15_30
<=> ! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_30])]) ).
fof(f4117,plain,
( spl15_258
<=> ! [X2,X0,X1] : subset(set_intersection2(X0,set_intersection2(X1,X2)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_258])]) ).
fof(f4437,plain,
( ! [X2,X0,X1] : subset(set_intersection2(X2,set_intersection2(X1,X0)),X0)
| ~ spl15_30
| ~ spl15_258 ),
inference(superposition,[],[f4118,f361]) ).
fof(f361,plain,
( ! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0)
| ~ spl15_30 ),
inference(avatar_component_clause,[],[f360]) ).
fof(f4118,plain,
( ! [X2,X0,X1] : subset(set_intersection2(X0,set_intersection2(X1,X2)),X1)
| ~ spl15_258 ),
inference(avatar_component_clause,[],[f4117]) ).
fof(f6936,plain,
( spl15_371
| ~ spl15_7
| ~ spl15_18
| ~ spl15_208 ),
inference(avatar_split_clause,[],[f3146,f3007,f284,f234,f6934]) ).
fof(f234,plain,
( spl15_7
<=> ! [X2] : ~ in(X2,empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_7])]) ).
fof(f284,plain,
( spl15_18
<=> empty_set = sK14 ),
introduced(avatar_definition,[new_symbols(naming,[spl15_18])]) ).
fof(f3146,plain,
( ! [X0] :
( sP1(sK14,sK14,X0)
| in(sK11(sK14,sK14,X0),X0) )
| ~ spl15_7
| ~ spl15_18
| ~ spl15_208 ),
inference(forward_demodulation,[],[f3145,f286]) ).
fof(f286,plain,
( empty_set = sK14
| ~ spl15_18 ),
inference(avatar_component_clause,[],[f284]) ).
fof(f3145,plain,
( ! [X0] :
( in(sK11(sK14,sK14,X0),X0)
| sP1(empty_set,empty_set,X0) )
| ~ spl15_7
| ~ spl15_18
| ~ spl15_208 ),
inference(forward_demodulation,[],[f3135,f286]) ).
fof(f3135,plain,
( ! [X0] :
( in(sK11(empty_set,empty_set,X0),X0)
| sP1(empty_set,empty_set,X0) )
| ~ spl15_7
| ~ spl15_208 ),
inference(resolution,[],[f3008,f235]) ).
fof(f235,plain,
( ! [X2] : ~ in(X2,empty_set)
| ~ spl15_7 ),
inference(avatar_component_clause,[],[f234]) ).
fof(f6932,plain,
( spl15_370
| ~ spl15_7
| ~ spl15_18
| ~ spl15_208 ),
inference(avatar_split_clause,[],[f3144,f3007,f284,f234,f6930]) ).
fof(f3144,plain,
( ! [X0] :
( sP1(X0,X0,sK14)
| in(sK11(X0,X0,sK14),X0) )
| ~ spl15_7
| ~ spl15_18
| ~ spl15_208 ),
inference(forward_demodulation,[],[f3143,f286]) ).
fof(f3143,plain,
( ! [X0] :
( in(sK11(X0,X0,sK14),X0)
| sP1(X0,X0,empty_set) )
| ~ spl15_7
| ~ spl15_18
| ~ spl15_208 ),
inference(forward_demodulation,[],[f3119,f286]) ).
fof(f3119,plain,
( ! [X0] :
( in(sK11(X0,X0,empty_set),X0)
| sP1(X0,X0,empty_set) )
| ~ spl15_7
| ~ spl15_208 ),
inference(resolution,[],[f3008,f235]) ).
fof(f6928,plain,
( spl15_369
| ~ spl15_7
| ~ spl15_18
| ~ spl15_207 ),
inference(avatar_split_clause,[],[f3103,f3003,f284,f234,f6926]) ).
fof(f3103,plain,
( ! [X0] :
( sP1(sK14,X0,sK14)
| in(sK11(sK14,X0,sK14),X0) )
| ~ spl15_7
| ~ spl15_18
| ~ spl15_207 ),
inference(forward_demodulation,[],[f3102,f286]) ).
fof(f3102,plain,
( ! [X0] :
( in(sK11(sK14,X0,sK14),X0)
| sP1(empty_set,X0,empty_set) )
| ~ spl15_7
| ~ spl15_18
| ~ spl15_207 ),
inference(forward_demodulation,[],[f3092,f286]) ).
fof(f3092,plain,
( ! [X0] :
( in(sK11(empty_set,X0,empty_set),X0)
| sP1(empty_set,X0,empty_set) )
| ~ spl15_7
| ~ spl15_207 ),
inference(resolution,[],[f3004,f235]) ).
fof(f6924,plain,
( spl15_368
| ~ spl15_7
| ~ spl15_18
| ~ spl15_206 ),
inference(avatar_split_clause,[],[f3062,f2999,f284,f234,f6922]) ).
fof(f3062,plain,
( ! [X0] :
( sP1(X0,sK14,sK14)
| in(sK11(X0,sK14,sK14),X0) )
| ~ spl15_7
| ~ spl15_18
| ~ spl15_206 ),
inference(forward_demodulation,[],[f3061,f286]) ).
fof(f3061,plain,
( ! [X0] :
( in(sK11(X0,sK14,sK14),X0)
| sP1(X0,empty_set,empty_set) )
| ~ spl15_7
| ~ spl15_18
| ~ spl15_206 ),
inference(forward_demodulation,[],[f3037,f286]) ).
fof(f3037,plain,
( ! [X0] :
( in(sK11(X0,empty_set,empty_set),X0)
| sP1(X0,empty_set,empty_set) )
| ~ spl15_7
| ~ spl15_206 ),
inference(resolution,[],[f3000,f235]) ).
fof(f6920,plain,
( spl15_367
| ~ spl15_17
| ~ spl15_163 ),
inference(avatar_split_clause,[],[f2077,f2013,f274,f6918]) ).
fof(f6918,plain,
( spl15_367
<=> ! [X2,X0,X1] :
( ~ in(X0,X1)
| ~ in(X0,X2)
| ~ empty(set_intersection2(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_367])]) ).
fof(f2077,plain,
( ! [X2,X0,X1] :
( ~ in(X0,X1)
| ~ in(X0,X2)
| ~ empty(set_intersection2(X1,X2)) )
| ~ spl15_17
| ~ spl15_163 ),
inference(resolution,[],[f2014,f275]) ).
fof(f6916,plain,
( spl15_366
| ~ spl15_17
| ~ spl15_161 ),
inference(avatar_split_clause,[],[f2019,f2005,f274,f6914]) ).
fof(f6914,plain,
( spl15_366
<=> ! [X2,X0,X1] :
( ~ in(X0,X1)
| in(X0,X2)
| ~ empty(set_difference(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_366])]) ).
fof(f2019,plain,
( ! [X2,X0,X1] :
( ~ in(X0,X1)
| in(X0,X2)
| ~ empty(set_difference(X1,X2)) )
| ~ spl15_17
| ~ spl15_161 ),
inference(resolution,[],[f2006,f275]) ).
fof(f6912,plain,
( spl15_365
| ~ spl15_30
| ~ spl15_257 ),
inference(avatar_split_clause,[],[f4380,f4113,f360,f6910]) ).
fof(f6910,plain,
( spl15_365
<=> ! [X2,X0,X1] : subset(set_intersection2(set_intersection2(X1,X0),X2),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_365])]) ).
fof(f4113,plain,
( spl15_257
<=> ! [X2,X0,X1] : subset(set_intersection2(set_intersection2(X0,X1),X2),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_257])]) ).
fof(f4380,plain,
( ! [X2,X0,X1] : subset(set_intersection2(set_intersection2(X1,X0),X2),X0)
| ~ spl15_30
| ~ spl15_257 ),
inference(superposition,[],[f4114,f361]) ).
fof(f4114,plain,
( ! [X2,X0,X1] : subset(set_intersection2(set_intersection2(X0,X1),X2),X0)
| ~ spl15_257 ),
inference(avatar_component_clause,[],[f4113]) ).
fof(f6908,plain,
( spl15_364
| ~ spl15_24
| ~ spl15_158 ),
inference(avatar_split_clause,[],[f1965,f1808,f314,f6906]) ).
fof(f6906,plain,
( spl15_364
<=> ! [X0,X1] :
( sP2(sK14,X0,X1)
| ~ in(X1,sK12(sK14,X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_364])]) ).
fof(f1808,plain,
( spl15_158
<=> ! [X0,X1] :
( sP2(sK14,X0,X1)
| in(sK12(sK14,X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_158])]) ).
fof(f1965,plain,
( ! [X0,X1] :
( sP2(sK14,X0,X1)
| ~ in(X1,sK12(sK14,X0,X1)) )
| ~ spl15_24
| ~ spl15_158 ),
inference(resolution,[],[f1809,f315]) ).
fof(f1809,plain,
( ! [X0,X1] :
( in(sK12(sK14,X0,X1),X1)
| sP2(sK14,X0,X1) )
| ~ spl15_158 ),
inference(avatar_component_clause,[],[f1808]) ).
fof(f6904,plain,
( spl15_363
| ~ spl15_24
| ~ spl15_157 ),
inference(avatar_split_clause,[],[f1952,f1804,f314,f6902]) ).
fof(f6902,plain,
( spl15_363
<=> ! [X0,X1] :
( sP2(X0,X1,sK14)
| ~ in(X0,sK12(X0,X1,sK14)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_363])]) ).
fof(f1804,plain,
( spl15_157
<=> ! [X0,X1] :
( sP2(X0,X1,sK14)
| in(sK12(X0,X1,sK14),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_157])]) ).
fof(f1952,plain,
( ! [X0,X1] :
( sP2(X0,X1,sK14)
| ~ in(X0,sK12(X0,X1,sK14)) )
| ~ spl15_24
| ~ spl15_157 ),
inference(resolution,[],[f1805,f315]) ).
fof(f1805,plain,
( ! [X0,X1] :
( in(sK12(X0,X1,sK14),X0)
| sP2(X0,X1,sK14) )
| ~ spl15_157 ),
inference(avatar_component_clause,[],[f1804]) ).
fof(f6900,plain,
( spl15_362
| ~ spl15_24
| ~ spl15_156 ),
inference(avatar_split_clause,[],[f1939,f1800,f314,f6898]) ).
fof(f6898,plain,
( spl15_362
<=> ! [X0,X1] :
( sP2(X0,X1,X0)
| ~ in(X0,sK12(X0,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_362])]) ).
fof(f1939,plain,
( ! [X0,X1] :
( sP2(X0,X1,X0)
| ~ in(X0,sK12(X0,X1,X0)) )
| ~ spl15_24
| ~ spl15_156 ),
inference(resolution,[],[f1801,f315]) ).
fof(f6896,plain,
( spl15_361
| ~ spl15_24
| ~ spl15_155 ),
inference(avatar_split_clause,[],[f1926,f1796,f314,f6894]) ).
fof(f6894,plain,
( spl15_361
<=> ! [X0,X1] :
( sP2(X0,sK14,X1)
| ~ in(X1,sK12(X0,sK14,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_361])]) ).
fof(f1796,plain,
( spl15_155
<=> ! [X0,X1] :
( sP2(X0,sK14,X1)
| in(sK12(X0,sK14,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_155])]) ).
fof(f1926,plain,
( ! [X0,X1] :
( sP2(X0,sK14,X1)
| ~ in(X1,sK12(X0,sK14,X1)) )
| ~ spl15_24
| ~ spl15_155 ),
inference(resolution,[],[f1797,f315]) ).
fof(f1797,plain,
( ! [X0,X1] :
( in(sK12(X0,sK14,X1),X1)
| sP2(X0,sK14,X1) )
| ~ spl15_155 ),
inference(avatar_component_clause,[],[f1796]) ).
fof(f6892,plain,
( spl15_360
| ~ spl15_24
| ~ spl15_154 ),
inference(avatar_split_clause,[],[f1913,f1792,f314,f6890]) ).
fof(f6890,plain,
( spl15_360
<=> ! [X0,X1] :
( sP2(X0,X1,sK14)
| ~ in(X1,sK12(X0,X1,sK14)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_360])]) ).
fof(f1792,plain,
( spl15_154
<=> ! [X0,X1] :
( sP2(X0,X1,sK14)
| in(sK12(X0,X1,sK14),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_154])]) ).
fof(f1913,plain,
( ! [X0,X1] :
( sP2(X0,X1,sK14)
| ~ in(X1,sK12(X0,X1,sK14)) )
| ~ spl15_24
| ~ spl15_154 ),
inference(resolution,[],[f1793,f315]) ).
fof(f1793,plain,
( ! [X0,X1] :
( in(sK12(X0,X1,sK14),X1)
| sP2(X0,X1,sK14) )
| ~ spl15_154 ),
inference(avatar_component_clause,[],[f1792]) ).
fof(f6888,plain,
( spl15_359
| ~ spl15_24
| ~ spl15_153 ),
inference(avatar_split_clause,[],[f1900,f1788,f314,f6886]) ).
fof(f6886,plain,
( spl15_359
<=> ! [X0,X1] :
( sP2(X0,X1,X1)
| ~ in(X1,sK12(X0,X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_359])]) ).
fof(f1900,plain,
( ! [X0,X1] :
( sP2(X0,X1,X1)
| ~ in(X1,sK12(X0,X1,X1)) )
| ~ spl15_24
| ~ spl15_153 ),
inference(resolution,[],[f1789,f315]) ).
fof(f6884,plain,
( spl15_358
| ~ spl15_24
| ~ spl15_151 ),
inference(avatar_split_clause,[],[f1886,f1780,f314,f6882]) ).
fof(f6882,plain,
( spl15_358
<=> ! [X0,X1] :
( sP0(X0,X0,X1)
| ~ in(X1,sK10(X0,X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_358])]) ).
fof(f1780,plain,
( spl15_151
<=> ! [X0,X1] :
( sP0(X0,X0,X1)
| in(sK10(X0,X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_151])]) ).
fof(f1886,plain,
( ! [X0,X1] :
( sP0(X0,X0,X1)
| ~ in(X1,sK10(X0,X0,X1)) )
| ~ spl15_24
| ~ spl15_151 ),
inference(resolution,[],[f1781,f315]) ).
fof(f1781,plain,
( ! [X0,X1] :
( in(sK10(X0,X0,X1),X1)
| sP0(X0,X0,X1) )
| ~ spl15_151 ),
inference(avatar_component_clause,[],[f1780]) ).
fof(f6880,plain,
( spl15_357
| ~ spl15_24
| ~ spl15_150 ),
inference(avatar_split_clause,[],[f1871,f1776,f314,f6878]) ).
fof(f6878,plain,
( spl15_357
<=> ! [X0,X1] :
( sP0(X0,sK14,X1)
| ~ in(X1,sK10(X0,sK14,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_357])]) ).
fof(f1776,plain,
( spl15_150
<=> ! [X0,X1] :
( sP0(X0,sK14,X1)
| in(sK10(X0,sK14,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_150])]) ).
fof(f1871,plain,
( ! [X0,X1] :
( sP0(X0,sK14,X1)
| ~ in(X1,sK10(X0,sK14,X1)) )
| ~ spl15_24
| ~ spl15_150 ),
inference(resolution,[],[f1777,f315]) ).
fof(f1777,plain,
( ! [X0,X1] :
( in(sK10(X0,sK14,X1),X1)
| sP0(X0,sK14,X1) )
| ~ spl15_150 ),
inference(avatar_component_clause,[],[f1776]) ).
fof(f6876,plain,
( spl15_356
| ~ spl15_24
| ~ spl15_149 ),
inference(avatar_split_clause,[],[f1852,f1772,f314,f6874]) ).
fof(f6874,plain,
( spl15_356
<=> ! [X0,X1] :
( sP0(X0,X1,sK14)
| ~ in(X1,sK10(X0,X1,sK14)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_356])]) ).
fof(f1772,plain,
( spl15_149
<=> ! [X0,X1] :
( sP0(X0,X1,sK14)
| in(sK10(X0,X1,sK14),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_149])]) ).
fof(f1852,plain,
( ! [X0,X1] :
( sP0(X0,X1,sK14)
| ~ in(X1,sK10(X0,X1,sK14)) )
| ~ spl15_24
| ~ spl15_149 ),
inference(resolution,[],[f1773,f315]) ).
fof(f1773,plain,
( ! [X0,X1] :
( in(sK10(X0,X1,sK14),X1)
| sP0(X0,X1,sK14) )
| ~ spl15_149 ),
inference(avatar_component_clause,[],[f1772]) ).
fof(f6872,plain,
( spl15_355
| ~ spl15_24
| ~ spl15_148 ),
inference(avatar_split_clause,[],[f1837,f1768,f314,f6870]) ).
fof(f6870,plain,
( spl15_355
<=> ! [X0,X1] :
( sP0(X0,X1,X1)
| ~ in(X1,sK10(X0,X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_355])]) ).
fof(f1837,plain,
( ! [X0,X1] :
( sP0(X0,X1,X1)
| ~ in(X1,sK10(X0,X1,X1)) )
| ~ spl15_24
| ~ spl15_148 ),
inference(resolution,[],[f1769,f315]) ).
fof(f6868,plain,
( spl15_354
| ~ spl15_29
| ~ spl15_248 ),
inference(avatar_split_clause,[],[f4250,f4077,f356,f6866]) ).
fof(f6866,plain,
( spl15_354
<=> ! [X0,X1] : set_union2(X1,set_intersection2(X0,X1)) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl15_354])]) ).
fof(f4250,plain,
( ! [X0,X1] : set_union2(X1,set_intersection2(X0,X1)) = X1
| ~ spl15_29
| ~ spl15_248 ),
inference(superposition,[],[f4078,f357]) ).
fof(f6864,plain,
( spl15_353
| ~ spl15_24
| ~ spl15_147 ),
inference(avatar_split_clause,[],[f1824,f1764,f314,f6862]) ).
fof(f6862,plain,
( spl15_353
<=> ! [X0,X1] :
( X0 = X1
| ~ empty(X0)
| ~ in(X1,sK8(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_353])]) ).
fof(f1764,plain,
( spl15_147
<=> ! [X0,X1] :
( in(sK8(X0,X1),X1)
| X0 = X1
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_147])]) ).
fof(f1824,plain,
( ! [X0,X1] :
( X0 = X1
| ~ empty(X0)
| ~ in(X1,sK8(X0,X1)) )
| ~ spl15_24
| ~ spl15_147 ),
inference(resolution,[],[f1765,f315]) ).
fof(f1765,plain,
( ! [X0,X1] :
( in(sK8(X0,X1),X1)
| X0 = X1
| ~ empty(X0) )
| ~ spl15_147 ),
inference(avatar_component_clause,[],[f1764]) ).
fof(f6860,plain,
( spl15_352
| ~ spl15_24
| ~ spl15_146 ),
inference(avatar_split_clause,[],[f1812,f1760,f314,f6858]) ).
fof(f6858,plain,
( spl15_352
<=> ! [X0,X1] :
( X0 = X1
| ~ empty(X1)
| ~ in(X0,sK8(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_352])]) ).
fof(f1760,plain,
( spl15_146
<=> ! [X0,X1] :
( in(sK8(X0,X1),X0)
| X0 = X1
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_146])]) ).
fof(f1812,plain,
( ! [X0,X1] :
( X0 = X1
| ~ empty(X1)
| ~ in(X0,sK8(X0,X1)) )
| ~ spl15_24
| ~ spl15_146 ),
inference(resolution,[],[f1761,f315]) ).
fof(f1761,plain,
( ! [X0,X1] :
( in(sK8(X0,X1),X0)
| X0 = X1
| ~ empty(X1) )
| ~ spl15_146 ),
inference(avatar_component_clause,[],[f1760]) ).
fof(f6581,plain,
( spl15_351
| ~ spl15_56
| ~ spl15_210 ),
inference(avatar_split_clause,[],[f3928,f3015,f557,f6579]) ).
fof(f6579,plain,
( spl15_351
<=> ! [X0,X1] : set_intersection2(set_union2(X0,X1),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl15_351])]) ).
fof(f557,plain,
( spl15_56
<=> ! [X2,X0,X1] :
( set_intersection2(X0,X1) = X2
| ~ sP2(X1,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_56])]) ).
fof(f3015,plain,
( spl15_210
<=> ! [X0,X1] : sP2(X0,set_union2(X0,X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_210])]) ).
fof(f3928,plain,
( ! [X0,X1] : set_intersection2(set_union2(X0,X1),X0) = X0
| ~ spl15_56
| ~ spl15_210 ),
inference(resolution,[],[f3016,f558]) ).
fof(f558,plain,
( ! [X2,X0,X1] :
( ~ sP2(X1,X0,X2)
| set_intersection2(X0,X1) = X2 )
| ~ spl15_56 ),
inference(avatar_component_clause,[],[f557]) ).
fof(f3016,plain,
( ! [X0,X1] : sP2(X0,set_union2(X0,X1),X0)
| ~ spl15_210 ),
inference(avatar_component_clause,[],[f3015]) ).
fof(f6104,plain,
( spl15_350
| ~ spl15_6
| ~ spl15_178 ),
inference(avatar_split_clause,[],[f2527,f2328,f230,f6102]) ).
fof(f6102,plain,
( spl15_350
<=> ! [X0,X1] :
( ~ subset(X0,X1)
| sK14 = set_difference(set_union2(X1,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_350])]) ).
fof(f2527,plain,
( ! [X0,X1] :
( ~ subset(X0,X1)
| sK14 = set_difference(set_union2(X1,X0),X1) )
| ~ spl15_6
| ~ spl15_178 ),
inference(resolution,[],[f2329,f231]) ).
fof(f6100,plain,
( spl15_349
| ~ spl15_6
| ~ spl15_176 ),
inference(avatar_split_clause,[],[f2488,f2320,f230,f6098]) ).
fof(f6098,plain,
( spl15_349
<=> ! [X0,X1] :
( ~ subset(X0,X1)
| sK14 = set_difference(X0,set_intersection2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_349])]) ).
fof(f2488,plain,
( ! [X0,X1] :
( ~ subset(X0,X1)
| sK14 = set_difference(X0,set_intersection2(X0,X1)) )
| ~ spl15_6
| ~ spl15_176 ),
inference(resolution,[],[f2321,f231]) ).
fof(f6081,plain,
( spl15_348
| ~ spl15_98
| ~ spl15_160 ),
inference(avatar_split_clause,[],[f1986,f1978,f1004,f6079]) ).
fof(f6079,plain,
( spl15_348
<=> ! [X0,X1] :
( ~ subset(X0,sK14)
| set_union2(X1,X0) = sK14
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_348])]) ).
fof(f1978,plain,
( spl15_160
<=> ! [X0,X1] :
( ~ subset(X0,sK14)
| ~ subset(X1,sK14)
| set_union2(X1,X0) = sK14 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_160])]) ).
fof(f1986,plain,
( ! [X0,X1] :
( ~ subset(X0,sK14)
| set_union2(X1,X0) = sK14
| ~ empty(X1) )
| ~ spl15_98
| ~ spl15_160 ),
inference(resolution,[],[f1979,f1005]) ).
fof(f1979,plain,
( ! [X0,X1] :
( ~ subset(X1,sK14)
| ~ subset(X0,sK14)
| set_union2(X1,X0) = sK14 )
| ~ spl15_160 ),
inference(avatar_component_clause,[],[f1978]) ).
fof(f6077,plain,
( spl15_347
| ~ spl15_34
| ~ spl15_146 ),
inference(avatar_split_clause,[],[f1817,f1760,f409,f6075]) ).
fof(f6075,plain,
( spl15_347
<=> ! [X2,X0,X1] :
( set_intersection2(X0,X1) = X2
| ~ empty(X2)
| ~ disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_347])]) ).
fof(f1817,plain,
( ! [X2,X0,X1] :
( set_intersection2(X0,X1) = X2
| ~ empty(X2)
| ~ disjoint(X0,X1) )
| ~ spl15_34
| ~ spl15_146 ),
inference(resolution,[],[f1761,f410]) ).
fof(f6073,plain,
( spl15_346
| ~ spl15_113
| ~ spl15_146 ),
inference(avatar_split_clause,[],[f1816,f1760,f1199,f6071]) ).
fof(f6071,plain,
( spl15_346
<=> ! [X2,X0,X1] :
( set_intersection2(X0,X1) = X2
| ~ empty(X2)
| ~ disjoint(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_346])]) ).
fof(f1816,plain,
( ! [X2,X0,X1] :
( set_intersection2(X0,X1) = X2
| ~ empty(X2)
| ~ disjoint(X1,X0) )
| ~ spl15_113
| ~ spl15_146 ),
inference(resolution,[],[f1761,f1200]) ).
fof(f6069,plain,
( spl15_345
| ~ spl15_107
| ~ spl15_144 ),
inference(avatar_split_clause,[],[f1748,f1658,f1102,f6067]) ).
fof(f6067,plain,
( spl15_345
<=> ! [X2,X0,X1] :
( subset(X0,set_intersection2(set_union2(X0,X1),X2))
| ~ subset(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_345])]) ).
fof(f1102,plain,
( spl15_107
<=> ! [X0,X1] : set_intersection2(X0,set_union2(X0,X1)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl15_107])]) ).
fof(f1748,plain,
( ! [X2,X0,X1] :
( subset(X0,set_intersection2(set_union2(X0,X1),X2))
| ~ subset(X0,X2) )
| ~ spl15_107
| ~ spl15_144 ),
inference(superposition,[],[f1659,f1103]) ).
fof(f1103,plain,
( ! [X0,X1] : set_intersection2(X0,set_union2(X0,X1)) = X0
| ~ spl15_107 ),
inference(avatar_component_clause,[],[f1102]) ).
fof(f6065,plain,
( spl15_344
| ~ spl15_30
| ~ spl15_143 ),
inference(avatar_split_clause,[],[f1732,f1654,f360,f6063]) ).
fof(f6063,plain,
( spl15_344
<=> ! [X2,X0,X1] :
( subset(set_intersection2(X1,X2),set_intersection2(X1,X0))
| ~ subset(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_344])]) ).
fof(f1732,plain,
( ! [X2,X0,X1] :
( subset(set_intersection2(X1,X2),set_intersection2(X1,X0))
| ~ subset(X2,X0) )
| ~ spl15_30
| ~ spl15_143 ),
inference(superposition,[],[f1655,f361]) ).
fof(f6061,plain,
( spl15_343
| ~ spl15_107
| ~ spl15_143 ),
inference(avatar_split_clause,[],[f1727,f1654,f1102,f6059]) ).
fof(f6059,plain,
( spl15_343
<=> ! [X2,X0,X1] :
( subset(X0,set_intersection2(X2,X0))
| ~ subset(set_union2(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_343])]) ).
fof(f1727,plain,
( ! [X2,X0,X1] :
( subset(X0,set_intersection2(X2,X0))
| ~ subset(set_union2(X0,X1),X2) )
| ~ spl15_107
| ~ spl15_143 ),
inference(superposition,[],[f1655,f1103]) ).
fof(f6057,plain,
( spl15_342
| ~ spl15_30
| ~ spl15_141 ),
inference(avatar_split_clause,[],[f1695,f1646,f360,f6055]) ).
fof(f6055,plain,
( spl15_342
<=> ! [X0,X1] :
( ~ in(set_intersection2(X1,X0),sK5(X0,X1))
| disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_342])]) ).
fof(f1646,plain,
( spl15_141
<=> ! [X0,X1] :
( disjoint(X0,X1)
| ~ in(set_intersection2(X0,X1),sK5(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_141])]) ).
fof(f1695,plain,
( ! [X0,X1] :
( ~ in(set_intersection2(X1,X0),sK5(X0,X1))
| disjoint(X0,X1) )
| ~ spl15_30
| ~ spl15_141 ),
inference(superposition,[],[f1647,f361]) ).
fof(f1647,plain,
( ! [X0,X1] :
( ~ in(set_intersection2(X0,X1),sK5(X0,X1))
| disjoint(X0,X1) )
| ~ spl15_141 ),
inference(avatar_component_clause,[],[f1646]) ).
fof(f6053,plain,
( spl15_341
| ~ spl15_119
| ~ spl15_137 ),
inference(avatar_split_clause,[],[f1625,f1571,f1223,f6051]) ).
fof(f6051,plain,
( spl15_341
<=> ! [X2,X0,X1] :
( subset(set_intersection2(X0,X1),X2)
| ~ disjoint(set_intersection2(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_341])]) ).
fof(f1625,plain,
( ! [X2,X0,X1] :
( subset(set_intersection2(X0,X1),X2)
| ~ disjoint(set_intersection2(X0,X1),X0) )
| ~ spl15_119
| ~ spl15_137 ),
inference(superposition,[],[f1224,f1572]) ).
fof(f6049,plain,
( spl15_340
| ~ spl15_118
| ~ spl15_137 ),
inference(avatar_split_clause,[],[f1624,f1571,f1219,f6047]) ).
fof(f6047,plain,
( spl15_340
<=> ! [X2,X0,X1] :
( disjoint(X2,set_intersection2(X0,X1))
| ~ disjoint(set_intersection2(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_340])]) ).
fof(f1219,plain,
( spl15_118
<=> ! [X2,X0,X1] :
( disjoint(X0,set_intersection2(X1,X2))
| ~ disjoint(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_118])]) ).
fof(f1624,plain,
( ! [X2,X0,X1] :
( disjoint(X2,set_intersection2(X0,X1))
| ~ disjoint(set_intersection2(X0,X1),X0) )
| ~ spl15_118
| ~ spl15_137 ),
inference(superposition,[],[f1220,f1572]) ).
fof(f1220,plain,
( ! [X2,X0,X1] :
( disjoint(X0,set_intersection2(X1,X2))
| ~ disjoint(X1,X2) )
| ~ spl15_118 ),
inference(avatar_component_clause,[],[f1219]) ).
fof(f6045,plain,
( spl15_339
| ~ spl15_115
| ~ spl15_137 ),
inference(avatar_split_clause,[],[f1623,f1571,f1207,f6043]) ).
fof(f6043,plain,
( spl15_339
<=> ! [X2,X0,X1] :
( disjoint(set_intersection2(X0,X1),X2)
| ~ disjoint(set_intersection2(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_339])]) ).
fof(f1207,plain,
( spl15_115
<=> ! [X2,X0,X1] :
( disjoint(set_intersection2(X0,X1),X2)
| ~ disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_115])]) ).
fof(f1623,plain,
( ! [X2,X0,X1] :
( disjoint(set_intersection2(X0,X1),X2)
| ~ disjoint(set_intersection2(X0,X1),X0) )
| ~ spl15_115
| ~ spl15_137 ),
inference(superposition,[],[f1208,f1572]) ).
fof(f1208,plain,
( ! [X2,X0,X1] :
( disjoint(set_intersection2(X0,X1),X2)
| ~ disjoint(X0,X1) )
| ~ spl15_115 ),
inference(avatar_component_clause,[],[f1207]) ).
fof(f6025,plain,
( spl15_338
| ~ spl15_113
| ~ spl15_137 ),
inference(avatar_split_clause,[],[f1622,f1571,f1199,f6023]) ).
fof(f6023,plain,
( spl15_338
<=> ! [X2,X0,X1] :
( ~ in(X2,set_intersection2(X0,X1))
| ~ disjoint(X0,set_intersection2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_338])]) ).
fof(f1622,plain,
( ! [X2,X0,X1] :
( ~ in(X2,set_intersection2(X0,X1))
| ~ disjoint(X0,set_intersection2(X0,X1)) )
| ~ spl15_113
| ~ spl15_137 ),
inference(superposition,[],[f1200,f1572]) ).
fof(f6021,plain,
( spl15_337
| ~ spl15_34
| ~ spl15_137 ),
inference(avatar_split_clause,[],[f1611,f1571,f409,f6019]) ).
fof(f6019,plain,
( spl15_337
<=> ! [X2,X0,X1] :
( ~ in(X2,set_intersection2(X0,X1))
| ~ disjoint(set_intersection2(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_337])]) ).
fof(f1611,plain,
( ! [X2,X0,X1] :
( ~ in(X2,set_intersection2(X0,X1))
| ~ disjoint(set_intersection2(X0,X1),X0) )
| ~ spl15_34
| ~ spl15_137 ),
inference(superposition,[],[f410,f1572]) ).
fof(f5988,plain,
( spl15_336
| ~ spl15_30
| ~ spl15_305
| ~ spl15_335 ),
inference(avatar_split_clause,[],[f5984,f5981,f5344,f360,f5986]) ).
fof(f5986,plain,
( spl15_336
<=> ! [X0,X1] :
( set_intersection2(X1,X0) = X0
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_336])]) ).
fof(f5344,plain,
( spl15_305
<=> ! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(set_intersection2(X0,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_305])]) ).
fof(f5981,plain,
( spl15_335
<=> ! [X0,X1] :
( ~ subset(X0,X1)
| set_intersection2(X0,set_intersection2(X1,X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_335])]) ).
fof(f5984,plain,
( ! [X0,X1] :
( set_intersection2(X1,X0) = X0
| ~ subset(X0,X1) )
| ~ spl15_30
| ~ spl15_305
| ~ spl15_335 ),
inference(forward_demodulation,[],[f5982,f5473]) ).
fof(f5473,plain,
( ! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,set_intersection2(X0,X1))
| ~ spl15_30
| ~ spl15_305 ),
inference(superposition,[],[f5345,f361]) ).
fof(f5345,plain,
( ! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(set_intersection2(X0,X1),X1)
| ~ spl15_305 ),
inference(avatar_component_clause,[],[f5344]) ).
fof(f5982,plain,
( ! [X0,X1] :
( ~ subset(X0,X1)
| set_intersection2(X0,set_intersection2(X1,X0)) = X0 )
| ~ spl15_335 ),
inference(avatar_component_clause,[],[f5981]) ).
fof(f5983,plain,
( spl15_335
| ~ spl15_38
| ~ spl15_126 ),
inference(avatar_split_clause,[],[f1411,f1251,f426,f5981]) ).
fof(f1411,plain,
( ! [X0,X1] :
( ~ subset(X0,X1)
| set_intersection2(X0,set_intersection2(X1,X0)) = X0 )
| ~ spl15_38
| ~ spl15_126 ),
inference(resolution,[],[f1252,f427]) ).
fof(f5979,plain,
( spl15_334
| ~ spl15_42
| ~ spl15_126 ),
inference(avatar_split_clause,[],[f1410,f1251,f471,f5977]) ).
fof(f5977,plain,
( spl15_334
<=> ! [X0,X1] :
( ~ subset(X0,X1)
| sK14 = set_difference(X0,set_intersection2(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_334])]) ).
fof(f1410,plain,
( ! [X0,X1] :
( ~ subset(X0,X1)
| sK14 = set_difference(X0,set_intersection2(X1,X0)) )
| ~ spl15_42
| ~ spl15_126 ),
inference(resolution,[],[f1252,f472]) ).
fof(f5975,plain,
( spl15_333
| ~ spl15_38
| ~ spl15_121 ),
inference(avatar_split_clause,[],[f1341,f1231,f426,f5973]) ).
fof(f5973,plain,
( spl15_333
<=> ! [X2,X0,X1] :
( ~ subset(X0,X1)
| set_intersection2(X0,set_union2(X1,X2)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_333])]) ).
fof(f1341,plain,
( ! [X2,X0,X1] :
( ~ subset(X0,X1)
| set_intersection2(X0,set_union2(X1,X2)) = X0 )
| ~ spl15_38
| ~ spl15_121 ),
inference(resolution,[],[f1232,f427]) ).
fof(f5971,plain,
( spl15_332
| ~ spl15_42
| ~ spl15_121 ),
inference(avatar_split_clause,[],[f1340,f1231,f471,f5969]) ).
fof(f5969,plain,
( spl15_332
<=> ! [X2,X0,X1] :
( ~ subset(X0,X1)
| sK14 = set_difference(X0,set_union2(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_332])]) ).
fof(f1340,plain,
( ! [X2,X0,X1] :
( ~ subset(X0,X1)
| sK14 = set_difference(X0,set_union2(X1,X2)) )
| ~ spl15_42
| ~ spl15_121 ),
inference(resolution,[],[f1232,f472]) ).
fof(f5967,plain,
( spl15_331
| ~ spl15_37
| ~ spl15_119 ),
inference(avatar_split_clause,[],[f1313,f1223,f421,f5965]) ).
fof(f5965,plain,
( spl15_331
<=> ! [X2,X0,X1] :
( ~ disjoint(X0,X1)
| set_union2(set_intersection2(X0,X1),X2) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_331])]) ).
fof(f1313,plain,
( ! [X2,X0,X1] :
( ~ disjoint(X0,X1)
| set_union2(set_intersection2(X0,X1),X2) = X2 )
| ~ spl15_37
| ~ spl15_119 ),
inference(resolution,[],[f1224,f422]) ).
fof(f5963,plain,
( spl15_330
| ~ spl15_42
| ~ spl15_119 ),
inference(avatar_split_clause,[],[f1311,f1223,f471,f5961]) ).
fof(f5961,plain,
( spl15_330
<=> ! [X2,X0,X1] :
( ~ disjoint(X0,X1)
| sK14 = set_difference(set_intersection2(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_330])]) ).
fof(f1311,plain,
( ! [X2,X0,X1] :
( ~ disjoint(X0,X1)
| sK14 = set_difference(set_intersection2(X0,X1),X2) )
| ~ spl15_42
| ~ spl15_119 ),
inference(resolution,[],[f1224,f472]) ).
fof(f5943,plain,
( spl15_329
| ~ spl15_112
| ~ spl15_118 ),
inference(avatar_split_clause,[],[f1295,f1219,f1195,f5941]) ).
fof(f5941,plain,
( spl15_329
<=> ! [X2,X0,X1] :
( ~ disjoint(X0,X1)
| sK14 = set_intersection2(X2,set_intersection2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_329])]) ).
fof(f1195,plain,
( spl15_112
<=> ! [X0,X1] :
( ~ disjoint(X0,X1)
| set_intersection2(X0,X1) = sK14 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_112])]) ).
fof(f1295,plain,
( ! [X2,X0,X1] :
( ~ disjoint(X0,X1)
| sK14 = set_intersection2(X2,set_intersection2(X0,X1)) )
| ~ spl15_112
| ~ spl15_118 ),
inference(resolution,[],[f1220,f1196]) ).
fof(f1196,plain,
( ! [X0,X1] :
( ~ disjoint(X0,X1)
| set_intersection2(X0,X1) = sK14 )
| ~ spl15_112 ),
inference(avatar_component_clause,[],[f1195]) ).
fof(f5939,plain,
( spl15_328
| ~ spl15_112
| ~ spl15_115 ),
inference(avatar_split_clause,[],[f1284,f1207,f1195,f5937]) ).
fof(f5937,plain,
( spl15_328
<=> ! [X2,X0,X1] :
( ~ disjoint(X0,X1)
| sK14 = set_intersection2(set_intersection2(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_328])]) ).
fof(f1284,plain,
( ! [X2,X0,X1] :
( ~ disjoint(X0,X1)
| sK14 = set_intersection2(set_intersection2(X0,X1),X2) )
| ~ spl15_112
| ~ spl15_115 ),
inference(resolution,[],[f1208,f1196]) ).
fof(f5935,plain,
( spl15_327
| ~ spl15_58
| ~ spl15_109 ),
inference(avatar_split_clause,[],[f1178,f1110,f582,f5933]) ).
fof(f5933,plain,
( spl15_327
<=> ! [X2,X0,X1] :
( subset(set_difference(X2,set_union2(X0,X1)),sK14)
| ~ subset(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_327])]) ).
fof(f582,plain,
( spl15_58
<=> ! [X2,X0,X1] :
( subset(set_difference(X0,X2),set_difference(X1,X2))
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_58])]) ).
fof(f1110,plain,
( spl15_109
<=> ! [X0,X1] : sK14 = set_difference(X0,set_union2(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_109])]) ).
fof(f1178,plain,
( ! [X2,X0,X1] :
( subset(set_difference(X2,set_union2(X0,X1)),sK14)
| ~ subset(X2,X0) )
| ~ spl15_58
| ~ spl15_109 ),
inference(superposition,[],[f583,f1111]) ).
fof(f1111,plain,
( ! [X0,X1] : sK14 = set_difference(X0,set_union2(X0,X1))
| ~ spl15_109 ),
inference(avatar_component_clause,[],[f1110]) ).
fof(f583,plain,
( ! [X2,X0,X1] :
( subset(set_difference(X0,X2),set_difference(X1,X2))
| ~ subset(X0,X1) )
| ~ spl15_58 ),
inference(avatar_component_clause,[],[f582]) ).
fof(f5931,plain,
( spl15_326
| ~ spl15_58
| ~ spl15_108 ),
inference(avatar_split_clause,[],[f1163,f1106,f582,f5929]) ).
fof(f5929,plain,
( spl15_326
<=> ! [X2,X0,X1] :
( subset(set_difference(X2,X0),sK14)
| ~ subset(X2,set_intersection2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_326])]) ).
fof(f1106,plain,
( spl15_108
<=> ! [X0,X1] : sK14 = set_difference(set_intersection2(X0,X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_108])]) ).
fof(f1163,plain,
( ! [X2,X0,X1] :
( subset(set_difference(X2,X0),sK14)
| ~ subset(X2,set_intersection2(X0,X1)) )
| ~ spl15_58
| ~ spl15_108 ),
inference(superposition,[],[f583,f1107]) ).
fof(f1107,plain,
( ! [X0,X1] : sK14 = set_difference(set_intersection2(X0,X1),X0)
| ~ spl15_108 ),
inference(avatar_component_clause,[],[f1106]) ).
fof(f5927,plain,
( spl15_325
| ~ spl15_59
| ~ spl15_107 ),
inference(avatar_split_clause,[],[f1150,f1102,f586,f5925]) ).
fof(f5925,plain,
( spl15_325
<=> ! [X2,X0,X1] :
( subset(X0,set_intersection2(X2,set_union2(X0,X1)))
| ~ subset(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_325])]) ).
fof(f1150,plain,
( ! [X2,X0,X1] :
( subset(X0,set_intersection2(X2,set_union2(X0,X1)))
| ~ subset(X0,X2) )
| ~ spl15_59
| ~ spl15_107 ),
inference(superposition,[],[f587,f1103]) ).
fof(f5923,plain,
( spl15_324
| ~ spl15_52
| ~ spl15_91 ),
inference(avatar_split_clause,[],[f972,f926,f541,f5921]) ).
fof(f5921,plain,
( spl15_324
<=> ! [X0,X1] :
( set_intersection2(X1,X0) = X0
| ~ subset(X0,set_intersection2(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_324])]) ).
fof(f541,plain,
( spl15_52
<=> ! [X0,X1] :
( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_52])]) ).
fof(f972,plain,
( ! [X0,X1] :
( set_intersection2(X1,X0) = X0
| ~ subset(X0,set_intersection2(X1,X0)) )
| ~ spl15_52
| ~ spl15_91 ),
inference(resolution,[],[f927,f542]) ).
fof(f542,plain,
( ! [X0,X1] :
( ~ subset(X1,X0)
| X0 = X1
| ~ subset(X0,X1) )
| ~ spl15_52 ),
inference(avatar_component_clause,[],[f541]) ).
fof(f5919,plain,
( spl15_323
| ~ spl15_52
| ~ spl15_90 ),
inference(avatar_split_clause,[],[f961,f922,f541,f5917]) ).
fof(f5917,plain,
( spl15_323
<=> ! [X0,X1] :
( set_union2(X0,X1) = X1
| ~ subset(set_union2(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_323])]) ).
fof(f961,plain,
( ! [X0,X1] :
( set_union2(X0,X1) = X1
| ~ subset(set_union2(X0,X1),X1) )
| ~ spl15_52
| ~ spl15_90 ),
inference(resolution,[],[f923,f542]) ).
fof(f5415,plain,
( spl15_322
| ~ spl15_34
| ~ spl15_158 ),
inference(avatar_split_clause,[],[f1970,f1808,f409,f5413]) ).
fof(f5413,plain,
( spl15_322
<=> ! [X2,X0,X1] :
( sP2(sK14,X0,set_intersection2(X1,X2))
| ~ disjoint(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_322])]) ).
fof(f1970,plain,
( ! [X2,X0,X1] :
( sP2(sK14,X0,set_intersection2(X1,X2))
| ~ disjoint(X1,X2) )
| ~ spl15_34
| ~ spl15_158 ),
inference(resolution,[],[f1809,f410]) ).
fof(f5411,plain,
( spl15_321
| ~ spl15_113
| ~ spl15_158 ),
inference(avatar_split_clause,[],[f1969,f1808,f1199,f5409]) ).
fof(f5409,plain,
( spl15_321
<=> ! [X2,X0,X1] :
( sP2(sK14,X0,set_intersection2(X1,X2))
| ~ disjoint(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_321])]) ).
fof(f1969,plain,
( ! [X2,X0,X1] :
( sP2(sK14,X0,set_intersection2(X1,X2))
| ~ disjoint(X2,X1) )
| ~ spl15_113
| ~ spl15_158 ),
inference(resolution,[],[f1809,f1200]) ).
fof(f5407,plain,
( spl15_320
| ~ spl15_34
| ~ spl15_157 ),
inference(avatar_split_clause,[],[f1957,f1804,f409,f5405]) ).
fof(f5405,plain,
( spl15_320
<=> ! [X2,X0,X1] :
( sP2(set_intersection2(X0,X1),X2,sK14)
| ~ disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_320])]) ).
fof(f1957,plain,
( ! [X2,X0,X1] :
( sP2(set_intersection2(X0,X1),X2,sK14)
| ~ disjoint(X0,X1) )
| ~ spl15_34
| ~ spl15_157 ),
inference(resolution,[],[f1805,f410]) ).
fof(f5403,plain,
( spl15_319
| ~ spl15_113
| ~ spl15_157 ),
inference(avatar_split_clause,[],[f1956,f1804,f1199,f5401]) ).
fof(f5401,plain,
( spl15_319
<=> ! [X2,X0,X1] :
( sP2(set_intersection2(X0,X1),X2,sK14)
| ~ disjoint(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_319])]) ).
fof(f1956,plain,
( ! [X2,X0,X1] :
( sP2(set_intersection2(X0,X1),X2,sK14)
| ~ disjoint(X1,X0) )
| ~ spl15_113
| ~ spl15_157 ),
inference(resolution,[],[f1805,f1200]) ).
fof(f5399,plain,
( spl15_318
| ~ spl15_34
| ~ spl15_155 ),
inference(avatar_split_clause,[],[f1931,f1796,f409,f5397]) ).
fof(f5397,plain,
( spl15_318
<=> ! [X2,X0,X1] :
( sP2(X0,sK14,set_intersection2(X1,X2))
| ~ disjoint(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_318])]) ).
fof(f1931,plain,
( ! [X2,X0,X1] :
( sP2(X0,sK14,set_intersection2(X1,X2))
| ~ disjoint(X1,X2) )
| ~ spl15_34
| ~ spl15_155 ),
inference(resolution,[],[f1797,f410]) ).
fof(f5395,plain,
( spl15_317
| ~ spl15_113
| ~ spl15_155 ),
inference(avatar_split_clause,[],[f1930,f1796,f1199,f5393]) ).
fof(f5393,plain,
( spl15_317
<=> ! [X2,X0,X1] :
( sP2(X0,sK14,set_intersection2(X1,X2))
| ~ disjoint(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_317])]) ).
fof(f1930,plain,
( ! [X2,X0,X1] :
( sP2(X0,sK14,set_intersection2(X1,X2))
| ~ disjoint(X2,X1) )
| ~ spl15_113
| ~ spl15_155 ),
inference(resolution,[],[f1797,f1200]) ).
fof(f5391,plain,
( spl15_316
| ~ spl15_34
| ~ spl15_154 ),
inference(avatar_split_clause,[],[f1918,f1792,f409,f5389]) ).
fof(f5389,plain,
( spl15_316
<=> ! [X2,X0,X1] :
( sP2(X0,set_intersection2(X1,X2),sK14)
| ~ disjoint(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_316])]) ).
fof(f1918,plain,
( ! [X2,X0,X1] :
( sP2(X0,set_intersection2(X1,X2),sK14)
| ~ disjoint(X1,X2) )
| ~ spl15_34
| ~ spl15_154 ),
inference(resolution,[],[f1793,f410]) ).
fof(f5387,plain,
( spl15_315
| ~ spl15_113
| ~ spl15_154 ),
inference(avatar_split_clause,[],[f1917,f1792,f1199,f5385]) ).
fof(f5385,plain,
( spl15_315
<=> ! [X2,X0,X1] :
( sP2(X0,set_intersection2(X1,X2),sK14)
| ~ disjoint(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_315])]) ).
fof(f1917,plain,
( ! [X2,X0,X1] :
( sP2(X0,set_intersection2(X1,X2),sK14)
| ~ disjoint(X2,X1) )
| ~ spl15_113
| ~ spl15_154 ),
inference(resolution,[],[f1793,f1200]) ).
fof(f5383,plain,
( spl15_314
| ~ spl15_34
| ~ spl15_151 ),
inference(avatar_split_clause,[],[f1891,f1780,f409,f5381]) ).
fof(f5381,plain,
( spl15_314
<=> ! [X2,X0,X1] :
( sP0(X0,X0,set_intersection2(X1,X2))
| ~ disjoint(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_314])]) ).
fof(f1891,plain,
( ! [X2,X0,X1] :
( sP0(X0,X0,set_intersection2(X1,X2))
| ~ disjoint(X1,X2) )
| ~ spl15_34
| ~ spl15_151 ),
inference(resolution,[],[f1781,f410]) ).
fof(f5379,plain,
( spl15_313
| ~ spl15_113
| ~ spl15_151 ),
inference(avatar_split_clause,[],[f1890,f1780,f1199,f5377]) ).
fof(f5377,plain,
( spl15_313
<=> ! [X2,X0,X1] :
( sP0(X0,X0,set_intersection2(X1,X2))
| ~ disjoint(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_313])]) ).
fof(f1890,plain,
( ! [X2,X0,X1] :
( sP0(X0,X0,set_intersection2(X1,X2))
| ~ disjoint(X2,X1) )
| ~ spl15_113
| ~ spl15_151 ),
inference(resolution,[],[f1781,f1200]) ).
fof(f5375,plain,
( spl15_312
| ~ spl15_34
| ~ spl15_150 ),
inference(avatar_split_clause,[],[f1876,f1776,f409,f5373]) ).
fof(f5373,plain,
( spl15_312
<=> ! [X2,X0,X1] :
( sP0(X0,sK14,set_intersection2(X1,X2))
| ~ disjoint(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_312])]) ).
fof(f1876,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK14,set_intersection2(X1,X2))
| ~ disjoint(X1,X2) )
| ~ spl15_34
| ~ spl15_150 ),
inference(resolution,[],[f1777,f410]) ).
fof(f5371,plain,
( spl15_311
| ~ spl15_113
| ~ spl15_150 ),
inference(avatar_split_clause,[],[f1875,f1776,f1199,f5369]) ).
fof(f5369,plain,
( spl15_311
<=> ! [X2,X0,X1] :
( sP0(X0,sK14,set_intersection2(X1,X2))
| ~ disjoint(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_311])]) ).
fof(f1875,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK14,set_intersection2(X1,X2))
| ~ disjoint(X2,X1) )
| ~ spl15_113
| ~ spl15_150 ),
inference(resolution,[],[f1777,f1200]) ).
fof(f5367,plain,
( spl15_310
| ~ spl15_34
| ~ spl15_149 ),
inference(avatar_split_clause,[],[f1857,f1772,f409,f5365]) ).
fof(f5365,plain,
( spl15_310
<=> ! [X2,X0,X1] :
( sP0(X0,set_intersection2(X1,X2),sK14)
| ~ disjoint(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_310])]) ).
fof(f1857,plain,
( ! [X2,X0,X1] :
( sP0(X0,set_intersection2(X1,X2),sK14)
| ~ disjoint(X1,X2) )
| ~ spl15_34
| ~ spl15_149 ),
inference(resolution,[],[f1773,f410]) ).
fof(f5363,plain,
( spl15_309
| ~ spl15_113
| ~ spl15_149 ),
inference(avatar_split_clause,[],[f1856,f1772,f1199,f5361]) ).
fof(f5361,plain,
( spl15_309
<=> ! [X2,X0,X1] :
( sP0(X0,set_intersection2(X1,X2),sK14)
| ~ disjoint(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_309])]) ).
fof(f1856,plain,
( ! [X2,X0,X1] :
( sP0(X0,set_intersection2(X1,X2),sK14)
| ~ disjoint(X2,X1) )
| ~ spl15_113
| ~ spl15_149 ),
inference(resolution,[],[f1773,f1200]) ).
fof(f5359,plain,
( spl15_308
| ~ spl15_98
| ~ spl15_140 ),
inference(avatar_split_clause,[],[f1679,f1642,f1004,f5357]) ).
fof(f5357,plain,
( spl15_308
<=> ! [X0,X1] :
( set_union2(X0,X1) = X0
| ~ empty(set_union2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_308])]) ).
fof(f1642,plain,
( spl15_140
<=> ! [X0,X1] :
( set_union2(X0,X1) = X0
| ~ subset(set_union2(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_140])]) ).
fof(f1679,plain,
( ! [X0,X1] :
( set_union2(X0,X1) = X0
| ~ empty(set_union2(X0,X1)) )
| ~ spl15_98
| ~ spl15_140 ),
inference(resolution,[],[f1643,f1005]) ).
fof(f1643,plain,
( ! [X0,X1] :
( ~ subset(set_union2(X0,X1),X0)
| set_union2(X0,X1) = X0 )
| ~ spl15_140 ),
inference(avatar_component_clause,[],[f1642]) ).
fof(f5355,plain,
( ~ spl15_307
| ~ spl15_98
| spl15_296 ),
inference(avatar_split_clause,[],[f5287,f5170,f1004,f5352]) ).
fof(f5352,plain,
( spl15_307
<=> empty(sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_307])]) ).
fof(f5170,plain,
( spl15_296
<=> subset(sK3,sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_296])]) ).
fof(f5287,plain,
( ~ empty(sK3)
| ~ spl15_98
| spl15_296 ),
inference(resolution,[],[f5172,f1005]) ).
fof(f5172,plain,
( ~ subset(sK3,sK14)
| spl15_296 ),
inference(avatar_component_clause,[],[f5170]) ).
fof(f5350,plain,
( spl15_306
| ~ spl15_30
| ~ spl15_137 ),
inference(avatar_split_clause,[],[f1604,f1571,f360,f5348]) ).
fof(f5348,plain,
( spl15_306
<=> ! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X0,set_intersection2(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_306])]) ).
fof(f1604,plain,
( ! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X0,set_intersection2(X0,X1))
| ~ spl15_30
| ~ spl15_137 ),
inference(superposition,[],[f1572,f361]) ).
fof(f5346,plain,
( spl15_305
| ~ spl15_38
| ~ spl15_91 ),
inference(avatar_split_clause,[],[f975,f926,f426,f5344]) ).
fof(f975,plain,
( ! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(set_intersection2(X0,X1),X1)
| ~ spl15_38
| ~ spl15_91 ),
inference(resolution,[],[f927,f427]) ).
fof(f5342,plain,
( spl15_304
| ~ spl15_37
| ~ spl15_90 ),
inference(avatar_split_clause,[],[f965,f922,f421,f5340]) ).
fof(f5340,plain,
( spl15_304
<=> ! [X0,X1] : set_union2(X1,X0) = set_union2(X0,set_union2(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_304])]) ).
fof(f965,plain,
( ! [X0,X1] : set_union2(X1,X0) = set_union2(X0,set_union2(X1,X0))
| ~ spl15_37
| ~ spl15_90 ),
inference(resolution,[],[f923,f422]) ).
fof(f5286,plain,
( spl15_303
| ~ spl15_17
| ~ spl15_170 ),
inference(avatar_split_clause,[],[f2277,f2197,f274,f5284]) ).
fof(f5284,plain,
( spl15_303
<=> ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| ~ empty(X2)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_303])]) ).
fof(f2277,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| ~ empty(X2)
| ~ empty(X0) )
| ~ spl15_17
| ~ spl15_170 ),
inference(resolution,[],[f2198,f275]) ).
fof(f5282,plain,
( spl15_302
| ~ spl15_17
| ~ spl15_168 ),
inference(avatar_split_clause,[],[f2238,f2189,f274,f5280]) ).
fof(f5280,plain,
( spl15_302
<=> ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| ~ empty(X2)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_302])]) ).
fof(f2238,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| ~ empty(X2)
| ~ empty(X1) )
| ~ spl15_17
| ~ spl15_168 ),
inference(resolution,[],[f2190,f275]) ).
fof(f5278,plain,
( spl15_301
| ~ spl15_17
| ~ spl15_166 ),
inference(avatar_split_clause,[],[f2207,f2181,f274,f5276]) ).
fof(f5276,plain,
( spl15_301
<=> ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ empty(X2)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_301])]) ).
fof(f2207,plain,
( ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ empty(X2)
| ~ empty(X1) )
| ~ spl15_17
| ~ spl15_166 ),
inference(resolution,[],[f2182,f275]) ).
fof(f5274,plain,
( spl15_300
| ~ spl15_24
| ~ spl15_135 ),
inference(avatar_split_clause,[],[f1555,f1448,f314,f5272]) ).
fof(f5272,plain,
( spl15_300
<=> ! [X0] :
( sK14 = X0
| ~ in(X0,sK8(sK14,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_300])]) ).
fof(f1555,plain,
( ! [X0] :
( sK14 = X0
| ~ in(X0,sK8(sK14,X0)) )
| ~ spl15_24
| ~ spl15_135 ),
inference(resolution,[],[f1449,f315]) ).
fof(f5270,plain,
( spl15_299
| ~ spl15_24
| ~ spl15_134 ),
inference(avatar_split_clause,[],[f1543,f1444,f314,f5268]) ).
fof(f5268,plain,
( spl15_299
<=> ! [X0] :
( sK14 = X0
| ~ in(X0,sK8(X0,sK14)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_299])]) ).
fof(f1543,plain,
( ! [X0] :
( sK14 = X0
| ~ in(X0,sK8(X0,sK14)) )
| ~ spl15_24
| ~ spl15_134 ),
inference(resolution,[],[f1445,f315]) ).
fof(f5266,plain,
( spl15_298
| ~ spl15_24
| ~ spl15_132 ),
inference(avatar_split_clause,[],[f1505,f1436,f314,f5264]) ).
fof(f5264,plain,
( spl15_298
<=> ! [X2,X0,X1] :
( ~ in(X0,X1)
| ~ in(set_union2(X2,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_298])]) ).
fof(f1505,plain,
( ! [X2,X0,X1] :
( ~ in(X0,X1)
| ~ in(set_union2(X2,X1),X0) )
| ~ spl15_24
| ~ spl15_132 ),
inference(resolution,[],[f1437,f315]) ).
fof(f5262,plain,
( spl15_297
| ~ spl15_52
| ~ spl15_98 ),
inference(avatar_split_clause,[],[f1028,f1004,f541,f5260]) ).
fof(f5260,plain,
( spl15_297
<=> ! [X0,X1] :
( ~ empty(X0)
| X0 = X1
| ~ subset(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_297])]) ).
fof(f1028,plain,
( ! [X0,X1] :
( ~ empty(X0)
| X0 = X1
| ~ subset(X1,X0) )
| ~ spl15_52
| ~ spl15_98 ),
inference(resolution,[],[f1005,f542]) ).
fof(f5173,plain,
( ~ spl15_296
| spl15_1
| ~ spl15_282 ),
inference(avatar_split_clause,[],[f5011,f4560,f206,f5170]) ).
fof(f4560,plain,
( spl15_282
<=> ! [X2,X0,X1] :
( ~ subset(X0,sK14)
| subset(set_difference(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_282])]) ).
fof(f5011,plain,
( ~ subset(sK3,sK14)
| spl15_1
| ~ spl15_282 ),
inference(resolution,[],[f4561,f208]) ).
fof(f4561,plain,
( ! [X2,X0,X1] :
( subset(set_difference(X0,X1),X2)
| ~ subset(X0,sK14) )
| ~ spl15_282 ),
inference(avatar_component_clause,[],[f4560]) ).
fof(f4773,plain,
( spl15_295
| ~ spl15_29
| ~ spl15_220 ),
inference(avatar_split_clause,[],[f3955,f3291,f356,f4771]) ).
fof(f4771,plain,
( spl15_295
<=> ! [X0,X1] : sP0(set_union2(X1,X0),X0,sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_295])]) ).
fof(f3291,plain,
( spl15_220
<=> ! [X0,X1] : sP0(set_union2(X0,X1),X0,sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_220])]) ).
fof(f3955,plain,
( ! [X0,X1] : sP0(set_union2(X1,X0),X0,sK14)
| ~ spl15_29
| ~ spl15_220 ),
inference(superposition,[],[f3292,f357]) ).
fof(f3292,plain,
( ! [X0,X1] : sP0(set_union2(X0,X1),X0,sK14)
| ~ spl15_220 ),
inference(avatar_component_clause,[],[f3291]) ).
fof(f4610,plain,
( spl15_294
| ~ spl15_6
| ~ spl15_29
| ~ spl15_136
| ~ spl15_179 ),
inference(avatar_split_clause,[],[f2565,f2332,f1567,f356,f230,f4608]) ).
fof(f4608,plain,
( spl15_294
<=> ! [X0,X1] :
( set_union2(X1,X0) = X1
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_294])]) ).
fof(f1567,plain,
( spl15_136
<=> ! [X0,X1] : set_union2(X0,X1) = set_union2(X0,set_union2(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_136])]) ).
fof(f2565,plain,
( ! [X0,X1] :
( set_union2(X1,X0) = X1
| ~ subset(X0,X1) )
| ~ spl15_6
| ~ spl15_29
| ~ spl15_136
| ~ spl15_179 ),
inference(forward_demodulation,[],[f2564,f1568]) ).
fof(f1568,plain,
( ! [X0,X1] : set_union2(X0,X1) = set_union2(X0,set_union2(X0,X1))
| ~ spl15_136 ),
inference(avatar_component_clause,[],[f1567]) ).
fof(f2564,plain,
( ! [X0,X1] :
( set_union2(X1,set_union2(X1,X0)) = X1
| ~ subset(X0,X1) )
| ~ spl15_6
| ~ spl15_29
| ~ spl15_179 ),
inference(forward_demodulation,[],[f2547,f357]) ).
fof(f2547,plain,
( ! [X0,X1] :
( ~ subset(X0,X1)
| set_union2(set_union2(X1,X0),X1) = X1 )
| ~ spl15_6
| ~ spl15_179 ),
inference(resolution,[],[f2333,f231]) ).
fof(f4606,plain,
( spl15_293
| ~ spl15_120
| ~ spl15_143 ),
inference(avatar_split_clause,[],[f1716,f1654,f1227,f4604]) ).
fof(f4604,plain,
( spl15_293
<=> ! [X2,X0,X1] :
( ~ subset(X0,X1)
| subset(set_intersection2(X2,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_293])]) ).
fof(f1227,plain,
( spl15_120
<=> ! [X2,X0,X1] :
( subset(X0,X1)
| ~ subset(X0,set_intersection2(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_120])]) ).
fof(f1716,plain,
( ! [X2,X0,X1] :
( ~ subset(X0,X1)
| subset(set_intersection2(X2,X0),X1) )
| ~ spl15_120
| ~ spl15_143 ),
inference(resolution,[],[f1655,f1228]) ).
fof(f1228,plain,
( ! [X2,X0,X1] :
( ~ subset(X0,set_intersection2(X1,X2))
| subset(X0,X1) )
| ~ spl15_120 ),
inference(avatar_component_clause,[],[f1227]) ).
fof(f4602,plain,
( spl15_292
| ~ spl15_16
| ~ spl15_141 ),
inference(avatar_split_clause,[],[f1694,f1646,f270,f4600]) ).
fof(f4600,plain,
( spl15_292
<=> ! [X0] :
( ~ in(X0,sK5(X0,X0))
| disjoint(X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_292])]) ).
fof(f1694,plain,
( ! [X0] :
( ~ in(X0,sK5(X0,X0))
| disjoint(X0,X0) )
| ~ spl15_16
| ~ spl15_141 ),
inference(superposition,[],[f1647,f271]) ).
fof(f4598,plain,
( spl15_291
| ~ spl15_103
| ~ spl15_137 ),
inference(avatar_split_clause,[],[f1618,f1571,f1064,f4596]) ).
fof(f4596,plain,
( spl15_291
<=> ! [X0,X1] : sP2(set_intersection2(X0,X1),X0,set_intersection2(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_291])]) ).
fof(f1064,plain,
( spl15_103
<=> ! [X0,X1] : sP2(X1,X0,set_intersection2(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_103])]) ).
fof(f1618,plain,
( ! [X0,X1] : sP2(set_intersection2(X0,X1),X0,set_intersection2(X0,X1))
| ~ spl15_103
| ~ spl15_137 ),
inference(superposition,[],[f1065,f1572]) ).
fof(f1065,plain,
( ! [X0,X1] : sP2(X1,X0,set_intersection2(X1,X0))
| ~ spl15_103 ),
inference(avatar_component_clause,[],[f1064]) ).
fof(f4594,plain,
( spl15_290
| ~ spl15_27
| ~ spl15_137 ),
inference(avatar_split_clause,[],[f1608,f1571,f326,f4592]) ).
fof(f4592,plain,
( spl15_290
<=> ! [X0,X1] : sP2(X0,set_intersection2(X0,X1),set_intersection2(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_290])]) ).
fof(f326,plain,
( spl15_27
<=> ! [X0,X1] : sP2(X1,X0,set_intersection2(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_27])]) ).
fof(f1608,plain,
( ! [X0,X1] : sP2(X0,set_intersection2(X0,X1),set_intersection2(X0,X1))
| ~ spl15_27
| ~ spl15_137 ),
inference(superposition,[],[f327,f1572]) ).
fof(f327,plain,
( ! [X0,X1] : sP2(X1,X0,set_intersection2(X0,X1))
| ~ spl15_27 ),
inference(avatar_component_clause,[],[f326]) ).
fof(f4590,plain,
( spl15_289
| ~ spl15_30
| ~ spl15_213 ),
inference(avatar_split_clause,[],[f3942,f3105,f360,f4588]) ).
fof(f4588,plain,
( spl15_289
<=> ! [X0,X1] : sP0(X0,set_intersection2(X1,X0),sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_289])]) ).
fof(f3105,plain,
( spl15_213
<=> ! [X0,X1] : sP0(X0,set_intersection2(X0,X1),sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_213])]) ).
fof(f3942,plain,
( ! [X0,X1] : sP0(X0,set_intersection2(X1,X0),sK14)
| ~ spl15_30
| ~ spl15_213 ),
inference(superposition,[],[f3106,f361]) ).
fof(f3106,plain,
( ! [X0,X1] : sP0(X0,set_intersection2(X0,X1),sK14)
| ~ spl15_213 ),
inference(avatar_component_clause,[],[f3105]) ).
fof(f4586,plain,
( spl15_288
| ~ spl15_102
| ~ spl15_136 ),
inference(avatar_split_clause,[],[f1591,f1567,f1060,f4584]) ).
fof(f4584,plain,
( spl15_288
<=> ! [X0,X1] : sP1(X0,set_union2(X0,X1),set_union2(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_288])]) ).
fof(f1060,plain,
( spl15_102
<=> ! [X0,X1] : sP1(X1,X0,set_union2(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_102])]) ).
fof(f1591,plain,
( ! [X0,X1] : sP1(X0,set_union2(X0,X1),set_union2(X0,X1))
| ~ spl15_102
| ~ spl15_136 ),
inference(superposition,[],[f1061,f1568]) ).
fof(f1061,plain,
( ! [X0,X1] : sP1(X1,X0,set_union2(X1,X0))
| ~ spl15_102 ),
inference(avatar_component_clause,[],[f1060]) ).
fof(f4582,plain,
( spl15_287
| ~ spl15_26
| ~ spl15_136 ),
inference(avatar_split_clause,[],[f1588,f1567,f322,f4580]) ).
fof(f4580,plain,
( spl15_287
<=> ! [X0,X1] : sP1(set_union2(X0,X1),X0,set_union2(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_287])]) ).
fof(f322,plain,
( spl15_26
<=> ! [X0,X1] : sP1(X1,X0,set_union2(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_26])]) ).
fof(f1588,plain,
( ! [X0,X1] : sP1(set_union2(X0,X1),X0,set_union2(X0,X1))
| ~ spl15_26
| ~ spl15_136 ),
inference(superposition,[],[f323,f1568]) ).
fof(f323,plain,
( ! [X0,X1] : sP1(X1,X0,set_union2(X0,X1))
| ~ spl15_26 ),
inference(avatar_component_clause,[],[f322]) ).
fof(f4578,plain,
( spl15_286
| ~ spl15_57
| ~ spl15_133 ),
inference(avatar_split_clause,[],[f1520,f1440,f578,f4576]) ).
fof(f4576,plain,
( spl15_286
<=> ! [X0,X1] :
( in(sK5(X0,X1),X1)
| disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_286])]) ).
fof(f578,plain,
( spl15_57
<=> ! [X0,X1] :
( in(sK5(X0,X1),set_intersection2(X0,X1))
| disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_57])]) ).
fof(f1520,plain,
( ! [X0,X1] :
( in(sK5(X0,X1),X1)
| disjoint(X0,X1) )
| ~ spl15_57
| ~ spl15_133 ),
inference(resolution,[],[f1441,f579]) ).
fof(f579,plain,
( ! [X0,X1] :
( in(sK5(X0,X1),set_intersection2(X0,X1))
| disjoint(X0,X1) )
| ~ spl15_57 ),
inference(avatar_component_clause,[],[f578]) ).
fof(f4574,plain,
( spl15_285
| ~ spl15_107
| ~ spl15_129 ),
inference(avatar_split_clause,[],[f1458,f1424,f1102,f4572]) ).
fof(f4572,plain,
( spl15_285
<=> ! [X0,X1] :
( sK14 != X0
| disjoint(set_union2(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_285])]) ).
fof(f1424,plain,
( spl15_129
<=> ! [X0,X1] :
( set_intersection2(X1,X0) != sK14
| disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_129])]) ).
fof(f1458,plain,
( ! [X0,X1] :
( sK14 != X0
| disjoint(set_union2(X0,X1),X0) )
| ~ spl15_107
| ~ spl15_129 ),
inference(superposition,[],[f1425,f1103]) ).
fof(f1425,plain,
( ! [X0,X1] :
( set_intersection2(X1,X0) != sK14
| disjoint(X0,X1) )
| ~ spl15_129 ),
inference(avatar_component_clause,[],[f1424]) ).
fof(f4570,plain,
( spl15_284
| ~ spl15_30
| ~ spl15_126 ),
inference(avatar_split_clause,[],[f1414,f1251,f360,f4568]) ).
fof(f4568,plain,
( spl15_284
<=> ! [X0,X1] :
( subset(X1,set_intersection2(X1,X0))
| ~ subset(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_284])]) ).
fof(f1414,plain,
( ! [X0,X1] :
( subset(X1,set_intersection2(X1,X0))
| ~ subset(X1,X0) )
| ~ spl15_30
| ~ spl15_126 ),
inference(superposition,[],[f1252,f361]) ).
fof(f4566,plain,
( spl15_283
| ~ spl15_20
| ~ spl15_125 ),
inference(avatar_split_clause,[],[f1391,f1247,f295,f4564]) ).
fof(f4564,plain,
( spl15_283
<=> ! [X0,X1] :
( ~ subset(X0,sK14)
| set_difference(X0,X1) = sK14 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_283])]) ).
fof(f295,plain,
( spl15_20
<=> ! [X0] :
( ~ subset(X0,sK14)
| sK14 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_20])]) ).
fof(f1247,plain,
( spl15_125
<=> ! [X0,X1] :
( ~ subset(X1,sK14)
| subset(set_difference(X1,X0),sK14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_125])]) ).
fof(f1391,plain,
( ! [X0,X1] :
( ~ subset(X0,sK14)
| set_difference(X0,X1) = sK14 )
| ~ spl15_20
| ~ spl15_125 ),
inference(resolution,[],[f1248,f296]) ).
fof(f296,plain,
( ! [X0] :
( ~ subset(X0,sK14)
| sK14 = X0 )
| ~ spl15_20 ),
inference(avatar_component_clause,[],[f295]) ).
fof(f1248,plain,
( ! [X0,X1] :
( subset(set_difference(X1,X0),sK14)
| ~ subset(X1,sK14) )
| ~ spl15_125 ),
inference(avatar_component_clause,[],[f1247]) ).
fof(f4562,plain,
( spl15_282
| ~ spl15_101
| ~ spl15_125 ),
inference(avatar_split_clause,[],[f1390,f1247,f1042,f4560]) ).
fof(f1390,plain,
( ! [X2,X0,X1] :
( ~ subset(X0,sK14)
| subset(set_difference(X0,X1),X2) )
| ~ spl15_101
| ~ spl15_125 ),
inference(resolution,[],[f1248,f1043]) ).
fof(f4558,plain,
( spl15_281
| ~ spl15_24
| ~ spl15_123 ),
inference(avatar_split_clause,[],[f1371,f1239,f314,f4556]) ).
fof(f4556,plain,
( spl15_281
<=> ! [X2,X0,X1] :
( ~ in(X0,X1)
| ~ in(set_union2(X1,X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_281])]) ).
fof(f1371,plain,
( ! [X2,X0,X1] :
( ~ in(X0,X1)
| ~ in(set_union2(X1,X2),X0) )
| ~ spl15_24
| ~ spl15_123 ),
inference(resolution,[],[f1240,f315]) ).
fof(f4554,plain,
( spl15_280
| ~ spl15_57
| ~ spl15_122 ),
inference(avatar_split_clause,[],[f1349,f1235,f578,f4552]) ).
fof(f4552,plain,
( spl15_280
<=> ! [X0,X1] :
( in(sK5(X0,X1),X0)
| disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_280])]) ).
fof(f1349,plain,
( ! [X0,X1] :
( in(sK5(X0,X1),X0)
| disjoint(X0,X1) )
| ~ spl15_57
| ~ spl15_122 ),
inference(resolution,[],[f1236,f579]) ).
fof(f4550,plain,
( spl15_279
| ~ spl15_59
| ~ spl15_120 ),
inference(avatar_split_clause,[],[f1320,f1227,f586,f4548]) ).
fof(f4548,plain,
( spl15_279
<=> ! [X2,X0,X1] :
( subset(set_intersection2(X0,X1),X2)
| ~ subset(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_279])]) ).
fof(f1320,plain,
( ! [X2,X0,X1] :
( subset(set_intersection2(X0,X1),X2)
| ~ subset(X0,X2) )
| ~ spl15_59
| ~ spl15_120 ),
inference(resolution,[],[f1228,f587]) ).
fof(f4546,plain,
( spl15_278
| ~ spl15_29
| ~ spl15_210 ),
inference(avatar_split_clause,[],[f3930,f3015,f356,f4544]) ).
fof(f4544,plain,
( spl15_278
<=> ! [X0,X1] : sP2(X0,set_union2(X1,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_278])]) ).
fof(f3930,plain,
( ! [X0,X1] : sP2(X0,set_union2(X1,X0),X0)
| ~ spl15_29
| ~ spl15_210 ),
inference(superposition,[],[f3016,f357]) ).
fof(f4542,plain,
( spl15_277
| ~ spl15_107
| ~ spl15_119 ),
inference(avatar_split_clause,[],[f1317,f1223,f1102,f4540]) ).
fof(f4540,plain,
( spl15_277
<=> ! [X2,X0,X1] :
( subset(X0,X2)
| ~ disjoint(X0,set_union2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_277])]) ).
fof(f1317,plain,
( ! [X2,X0,X1] :
( subset(X0,X2)
| ~ disjoint(X0,set_union2(X0,X1)) )
| ~ spl15_107
| ~ spl15_119 ),
inference(superposition,[],[f1224,f1103]) ).
fof(f4538,plain,
( spl15_276
| ~ spl15_107
| ~ spl15_118 ),
inference(avatar_split_clause,[],[f1302,f1219,f1102,f4536]) ).
fof(f4536,plain,
( spl15_276
<=> ! [X2,X0,X1] :
( disjoint(X2,X0)
| ~ disjoint(X0,set_union2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_276])]) ).
fof(f1302,plain,
( ! [X2,X0,X1] :
( disjoint(X2,X0)
| ~ disjoint(X0,set_union2(X0,X1)) )
| ~ spl15_107
| ~ spl15_118 ),
inference(superposition,[],[f1220,f1103]) ).
fof(f4534,plain,
( spl15_275
| ~ spl15_107
| ~ spl15_115 ),
inference(avatar_split_clause,[],[f1291,f1207,f1102,f4532]) ).
fof(f1291,plain,
( ! [X2,X0,X1] :
( disjoint(X0,X2)
| ~ disjoint(X0,set_union2(X0,X1)) )
| ~ spl15_107
| ~ spl15_115 ),
inference(superposition,[],[f1208,f1103]) ).
fof(f4530,plain,
( spl15_274
| ~ spl15_107
| ~ spl15_113 ),
inference(avatar_split_clause,[],[f1281,f1199,f1102,f4528]) ).
fof(f4528,plain,
( spl15_274
<=> ! [X2,X0,X1] :
( ~ in(X2,X0)
| ~ disjoint(set_union2(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_274])]) ).
fof(f1281,plain,
( ! [X2,X0,X1] :
( ~ in(X2,X0)
| ~ disjoint(set_union2(X0,X1),X0) )
| ~ spl15_107
| ~ spl15_113 ),
inference(superposition,[],[f1200,f1103]) ).
fof(f4526,plain,
( spl15_273
| ~ spl15_36
| ~ spl15_113 ),
inference(avatar_split_clause,[],[f1269,f1199,f417,f4524]) ).
fof(f4524,plain,
( spl15_273
<=> ! [X2,X0,X1] :
( ~ disjoint(X0,X1)
| disjoint(X2,set_intersection2(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_273])]) ).
fof(f1269,plain,
( ! [X2,X0,X1] :
( ~ disjoint(X0,X1)
| disjoint(X2,set_intersection2(X1,X0)) )
| ~ spl15_36
| ~ spl15_113 ),
inference(resolution,[],[f1200,f418]) ).
fof(f4522,plain,
( spl15_272
| ~ spl15_46
| ~ spl15_113 ),
inference(avatar_split_clause,[],[f1266,f1199,f498,f4520]) ).
fof(f4520,plain,
( spl15_272
<=> ! [X2,X0,X1] :
( ~ disjoint(X0,X1)
| subset(set_intersection2(X1,X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_272])]) ).
fof(f1266,plain,
( ! [X2,X0,X1] :
( ~ disjoint(X0,X1)
| subset(set_intersection2(X1,X0),X2) )
| ~ spl15_46
| ~ spl15_113 ),
inference(resolution,[],[f1200,f499]) ).
fof(f4518,plain,
( spl15_271
| ~ spl15_33
| ~ spl15_113 ),
inference(avatar_split_clause,[],[f1264,f1199,f372,f4516]) ).
fof(f4516,plain,
( spl15_271
<=> ! [X0,X1] :
( ~ disjoint(X0,X1)
| set_intersection2(X1,X0) = sK14 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_271])]) ).
fof(f1264,plain,
( ! [X0,X1] :
( ~ disjoint(X0,X1)
| set_intersection2(X1,X0) = sK14 )
| ~ spl15_33
| ~ spl15_113 ),
inference(resolution,[],[f1200,f373]) ).
fof(f4514,plain,
( spl15_270
| ~ spl15_35
| ~ spl15_113 ),
inference(avatar_split_clause,[],[f1263,f1199,f413,f4512]) ).
fof(f4512,plain,
( spl15_270
<=> ! [X2,X0,X1] :
( ~ disjoint(X0,X1)
| disjoint(set_intersection2(X1,X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_270])]) ).
fof(f1263,plain,
( ! [X2,X0,X1] :
( ~ disjoint(X0,X1)
| disjoint(set_intersection2(X1,X0),X2) )
| ~ spl15_35
| ~ spl15_113 ),
inference(resolution,[],[f1200,f414]) ).
fof(f4510,plain,
( spl15_269
| ~ spl15_48
| ~ spl15_107 ),
inference(avatar_split_clause,[],[f1147,f1102,f506,f4508]) ).
fof(f4508,plain,
( spl15_269
<=> ! [X0,X1] :
( sK14 != X0
| disjoint(X0,set_union2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_269])]) ).
fof(f506,plain,
( spl15_48
<=> ! [X0,X1] :
( set_intersection2(X0,X1) != sK14
| disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_48])]) ).
fof(f1147,plain,
( ! [X0,X1] :
( sK14 != X0
| disjoint(X0,set_union2(X0,X1)) )
| ~ spl15_48
| ~ spl15_107 ),
inference(superposition,[],[f507,f1103]) ).
fof(f507,plain,
( ! [X0,X1] :
( set_intersection2(X0,X1) != sK14
| disjoint(X0,X1) )
| ~ spl15_48 ),
inference(avatar_component_clause,[],[f506]) ).
fof(f4506,plain,
( spl15_268
| ~ spl15_34
| ~ spl15_107 ),
inference(avatar_split_clause,[],[f1146,f1102,f409,f4504]) ).
fof(f4504,plain,
( spl15_268
<=> ! [X2,X0,X1] :
( ~ in(X2,X0)
| ~ disjoint(X0,set_union2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_268])]) ).
fof(f1146,plain,
( ! [X2,X0,X1] :
( ~ in(X2,X0)
| ~ disjoint(X0,set_union2(X0,X1)) )
| ~ spl15_34
| ~ spl15_107 ),
inference(superposition,[],[f410,f1103]) ).
fof(f4502,plain,
( spl15_267
| ~ spl15_29
| ~ spl15_199 ),
inference(avatar_split_clause,[],[f3918,f2971,f356,f4500]) ).
fof(f4500,plain,
( spl15_267
<=> ! [X0,X1] : sP2(set_union2(X1,X0),X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_267])]) ).
fof(f2971,plain,
( spl15_199
<=> ! [X0,X1] : sP2(set_union2(X0,X1),X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_199])]) ).
fof(f3918,plain,
( ! [X0,X1] : sP2(set_union2(X1,X0),X0,X0)
| ~ spl15_29
| ~ spl15_199 ),
inference(superposition,[],[f2972,f357]) ).
fof(f2972,plain,
( ! [X0,X1] : sP2(set_union2(X0,X1),X0,X0)
| ~ spl15_199 ),
inference(avatar_component_clause,[],[f2971]) ).
fof(f4498,plain,
( spl15_266
| ~ spl15_51
| ~ spl15_98 ),
inference(avatar_split_clause,[],[f1029,f1004,f531,f4496]) ).
fof(f1029,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| subset(X1,X2)
| ~ subset(X1,X0) )
| ~ spl15_51
| ~ spl15_98 ),
inference(resolution,[],[f1005,f532]) ).
fof(f4494,plain,
( spl15_265
| ~ spl15_58
| ~ spl15_94 ),
inference(avatar_split_clause,[],[f990,f938,f582,f4492]) ).
fof(f4492,plain,
( spl15_265
<=> ! [X0,X1] :
( subset(set_difference(X1,X0),sK14)
| ~ subset(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_265])]) ).
fof(f938,plain,
( spl15_94
<=> ! [X0] : sK14 = set_difference(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_94])]) ).
fof(f990,plain,
( ! [X0,X1] :
( subset(set_difference(X1,X0),sK14)
| ~ subset(X1,X0) )
| ~ spl15_58
| ~ spl15_94 ),
inference(superposition,[],[f583,f939]) ).
fof(f939,plain,
( ! [X0] : sK14 = set_difference(X0,X0)
| ~ spl15_94 ),
inference(avatar_component_clause,[],[f938]) ).
fof(f4490,plain,
( spl15_264
| ~ spl15_51
| ~ spl15_91 ),
inference(avatar_split_clause,[],[f973,f926,f531,f4488]) ).
fof(f4488,plain,
( spl15_264
<=> ! [X2,X0,X1] :
( subset(X0,X1)
| ~ subset(X0,set_intersection2(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_264])]) ).
fof(f973,plain,
( ! [X2,X0,X1] :
( subset(X0,X1)
| ~ subset(X0,set_intersection2(X2,X1)) )
| ~ spl15_51
| ~ spl15_91 ),
inference(resolution,[],[f927,f532]) ).
fof(f4486,plain,
( spl15_263
| ~ spl15_51
| ~ spl15_90 ),
inference(avatar_split_clause,[],[f962,f922,f531,f4484]) ).
fof(f4484,plain,
( spl15_263
<=> ! [X2,X0,X1] :
( subset(X0,set_union2(X1,X2))
| ~ subset(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_263])]) ).
fof(f962,plain,
( ! [X2,X0,X1] :
( subset(X0,set_union2(X1,X2))
| ~ subset(X0,X2) )
| ~ spl15_51
| ~ spl15_90 ),
inference(resolution,[],[f923,f532]) ).
fof(f4472,plain,
( spl15_262
| ~ spl15_17
| ~ spl15_132 ),
inference(avatar_split_clause,[],[f1506,f1436,f274,f4470]) ).
fof(f4470,plain,
( spl15_262
<=> ! [X2,X0,X1] :
( ~ in(X0,X1)
| ~ empty(set_union2(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_262])]) ).
fof(f1506,plain,
( ! [X2,X0,X1] :
( ~ in(X0,X1)
| ~ empty(set_union2(X2,X1)) )
| ~ spl15_17
| ~ spl15_132 ),
inference(resolution,[],[f1437,f275]) ).
fof(f4344,plain,
( spl15_261
| ~ spl15_30
| ~ spl15_194 ),
inference(avatar_split_clause,[],[f3905,f2808,f360,f4342]) ).
fof(f4342,plain,
( spl15_261
<=> ! [X0,X1] : sP1(set_intersection2(X1,X0),X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_261])]) ).
fof(f2808,plain,
( spl15_194
<=> ! [X0,X1] : sP1(set_intersection2(X0,X1),X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_194])]) ).
fof(f3905,plain,
( ! [X0,X1] : sP1(set_intersection2(X1,X0),X0,X0)
| ~ spl15_30
| ~ spl15_194 ),
inference(superposition,[],[f2809,f361]) ).
fof(f2809,plain,
( ! [X0,X1] : sP1(set_intersection2(X0,X1),X0,X0)
| ~ spl15_194 ),
inference(avatar_component_clause,[],[f2808]) ).
fof(f4127,plain,
( spl15_260
| ~ spl15_30
| ~ spl15_191 ),
inference(avatar_split_clause,[],[f3892,f2616,f360,f4125]) ).
fof(f4125,plain,
( spl15_260
<=> ! [X0,X1] : sP1(X0,set_intersection2(X1,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_260])]) ).
fof(f2616,plain,
( spl15_191
<=> ! [X0,X1] : sP1(X0,set_intersection2(X0,X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_191])]) ).
fof(f3892,plain,
( ! [X0,X1] : sP1(X0,set_intersection2(X1,X0),X0)
| ~ spl15_30
| ~ spl15_191 ),
inference(superposition,[],[f2617,f361]) ).
fof(f2617,plain,
( ! [X0,X1] : sP1(X0,set_intersection2(X0,X1),X0)
| ~ spl15_191 ),
inference(avatar_component_clause,[],[f2616]) ).
fof(f4123,plain,
( spl15_259
| ~ spl15_17
| ~ spl15_123 ),
inference(avatar_split_clause,[],[f1372,f1239,f274,f4121]) ).
fof(f1372,plain,
( ! [X2,X0,X1] :
( ~ in(X0,X1)
| ~ empty(set_union2(X1,X2)) )
| ~ spl15_17
| ~ spl15_123 ),
inference(resolution,[],[f1240,f275]) ).
fof(f4119,plain,
( spl15_258
| ~ spl15_91
| ~ spl15_120 ),
inference(avatar_split_clause,[],[f1326,f1227,f926,f4117]) ).
fof(f1326,plain,
( ! [X2,X0,X1] : subset(set_intersection2(X0,set_intersection2(X1,X2)),X1)
| ~ spl15_91
| ~ spl15_120 ),
inference(resolution,[],[f1228,f927]) ).
fof(f4115,plain,
( spl15_257
| ~ spl15_9
| ~ spl15_120 ),
inference(avatar_split_clause,[],[f1323,f1227,f242,f4113]) ).
fof(f1323,plain,
( ! [X2,X0,X1] : subset(set_intersection2(set_intersection2(X0,X1),X2),X0)
| ~ spl15_9
| ~ spl15_120 ),
inference(resolution,[],[f1228,f243]) ).
fof(f4111,plain,
( spl15_256
| ~ spl15_92
| ~ spl15_112 ),
inference(avatar_split_clause,[],[f1257,f1195,f930,f4109]) ).
fof(f4109,plain,
( spl15_256
<=> ! [X0,X1] :
( set_intersection2(X0,X1) = sK14
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_256])]) ).
fof(f930,plain,
( spl15_92
<=> ! [X0,X1] :
( disjoint(X0,X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_92])]) ).
fof(f1257,plain,
( ! [X0,X1] :
( set_intersection2(X0,X1) = sK14
| ~ empty(X0) )
| ~ spl15_92
| ~ spl15_112 ),
inference(resolution,[],[f1196,f931]) ).
fof(f931,plain,
( ! [X0,X1] :
( disjoint(X0,X1)
| ~ empty(X0) )
| ~ spl15_92 ),
inference(avatar_component_clause,[],[f930]) ).
fof(f4107,plain,
( spl15_255
| ~ spl15_93
| ~ spl15_112 ),
inference(avatar_split_clause,[],[f1256,f1195,f934,f4105]) ).
fof(f4105,plain,
( spl15_255
<=> ! [X0,X1] :
( set_intersection2(X0,X1) = sK14
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_255])]) ).
fof(f1256,plain,
( ! [X0,X1] :
( set_intersection2(X0,X1) = sK14
| ~ empty(X1) )
| ~ spl15_93
| ~ spl15_112 ),
inference(resolution,[],[f1196,f935]) ).
fof(f4103,plain,
( spl15_254
| ~ spl15_30
| ~ spl15_110 ),
inference(avatar_split_clause,[],[f1185,f1114,f360,f4101]) ).
fof(f4101,plain,
( spl15_254
<=> ! [X0,X1] :
( ~ empty(set_intersection2(X1,X0))
| disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_254])]) ).
fof(f1114,plain,
( spl15_110
<=> ! [X0,X1] :
( disjoint(X0,X1)
| ~ empty(set_intersection2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_110])]) ).
fof(f1185,plain,
( ! [X0,X1] :
( ~ empty(set_intersection2(X1,X0))
| disjoint(X0,X1) )
| ~ spl15_30
| ~ spl15_110 ),
inference(superposition,[],[f1115,f361]) ).
fof(f1115,plain,
( ! [X0,X1] :
( ~ empty(set_intersection2(X0,X1))
| disjoint(X0,X1) )
| ~ spl15_110 ),
inference(avatar_component_clause,[],[f1114]) ).
fof(f4099,plain,
( spl15_253
| ~ spl15_29
| ~ spl15_106 ),
inference(avatar_split_clause,[],[f1123,f1098,f356,f4097]) ).
fof(f4097,plain,
( spl15_253
<=> ! [X0,X1] : set_union2(X0,set_intersection2(X0,X1)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl15_253])]) ).
fof(f1123,plain,
( ! [X0,X1] : set_union2(X0,set_intersection2(X0,X1)) = X0
| ~ spl15_29
| ~ spl15_106 ),
inference(superposition,[],[f1099,f357]) ).
fof(f4095,plain,
( spl15_252
| ~ spl15_37
| ~ spl15_98 ),
inference(avatar_split_clause,[],[f1032,f1004,f421,f4093]) ).
fof(f4093,plain,
( spl15_252
<=> ! [X0,X1] :
( ~ empty(X0)
| set_union2(X0,X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_252])]) ).
fof(f1032,plain,
( ! [X0,X1] :
( ~ empty(X0)
| set_union2(X0,X1) = X1 )
| ~ spl15_37
| ~ spl15_98 ),
inference(resolution,[],[f1005,f422]) ).
fof(f4091,plain,
( spl15_251
| ~ spl15_38
| ~ spl15_98 ),
inference(avatar_split_clause,[],[f1031,f1004,f426,f4089]) ).
fof(f4089,plain,
( spl15_251
<=> ! [X0,X1] :
( ~ empty(X0)
| set_intersection2(X0,X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_251])]) ).
fof(f1031,plain,
( ! [X0,X1] :
( ~ empty(X0)
| set_intersection2(X0,X1) = X0 )
| ~ spl15_38
| ~ spl15_98 ),
inference(resolution,[],[f1005,f427]) ).
fof(f4087,plain,
( spl15_250
| ~ spl15_42
| ~ spl15_98 ),
inference(avatar_split_clause,[],[f1030,f1004,f471,f4085]) ).
fof(f4085,plain,
( spl15_250
<=> ! [X0,X1] :
( ~ empty(X0)
| set_difference(X0,X1) = sK14 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_250])]) ).
fof(f1030,plain,
( ! [X0,X1] :
( ~ empty(X0)
| set_difference(X0,X1) = sK14 )
| ~ spl15_42
| ~ spl15_98 ),
inference(resolution,[],[f1005,f472]) ).
fof(f4083,plain,
( spl15_249
| ~ spl15_30
| ~ spl15_182 ),
inference(avatar_split_clause,[],[f3879,f2580,f360,f4081]) ).
fof(f4081,plain,
( spl15_249
<=> ! [X0,X1] :
( empty(set_intersection2(X1,X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_249])]) ).
fof(f2580,plain,
( spl15_182
<=> ! [X0,X1] :
( ~ empty(X0)
| empty(set_intersection2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_182])]) ).
fof(f3879,plain,
( ! [X0,X1] :
( empty(set_intersection2(X1,X0))
| ~ empty(X0) )
| ~ spl15_30
| ~ spl15_182 ),
inference(superposition,[],[f2581,f361]) ).
fof(f2581,plain,
( ! [X0,X1] :
( empty(set_intersection2(X0,X1))
| ~ empty(X0) )
| ~ spl15_182 ),
inference(avatar_component_clause,[],[f2580]) ).
fof(f4079,plain,
( spl15_248
| ~ spl15_37
| ~ spl15_91 ),
inference(avatar_split_clause,[],[f976,f926,f421,f4077]) ).
fof(f976,plain,
( ! [X0,X1] : set_union2(set_intersection2(X0,X1),X1) = X1
| ~ spl15_37
| ~ spl15_91 ),
inference(resolution,[],[f927,f422]) ).
fof(f4075,plain,
( spl15_247
| ~ spl15_42
| ~ spl15_91 ),
inference(avatar_split_clause,[],[f974,f926,f471,f4073]) ).
fof(f4073,plain,
( spl15_247
<=> ! [X0,X1] : sK14 = set_difference(set_intersection2(X0,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_247])]) ).
fof(f974,plain,
( ! [X0,X1] : sK14 = set_difference(set_intersection2(X0,X1),X1)
| ~ spl15_42
| ~ spl15_91 ),
inference(resolution,[],[f927,f472]) ).
fof(f4071,plain,
( spl15_246
| ~ spl15_38
| ~ spl15_90 ),
inference(avatar_split_clause,[],[f964,f922,f426,f4069]) ).
fof(f4069,plain,
( spl15_246
<=> ! [X0,X1] : set_intersection2(X0,set_union2(X1,X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl15_246])]) ).
fof(f964,plain,
( ! [X0,X1] : set_intersection2(X0,set_union2(X1,X0)) = X0
| ~ spl15_38
| ~ spl15_90 ),
inference(resolution,[],[f923,f427]) ).
fof(f4067,plain,
( spl15_245
| ~ spl15_42
| ~ spl15_90 ),
inference(avatar_split_clause,[],[f963,f922,f471,f4065]) ).
fof(f4065,plain,
( spl15_245
<=> ! [X0,X1] : sK14 = set_difference(X0,set_union2(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_245])]) ).
fof(f963,plain,
( ! [X0,X1] : sK14 = set_difference(X0,set_union2(X1,X0))
| ~ spl15_42
| ~ spl15_90 ),
inference(resolution,[],[f923,f472]) ).
fof(f4019,plain,
( spl15_244
| ~ spl15_17
| ~ spl15_158 ),
inference(avatar_split_clause,[],[f1966,f1808,f274,f4017]) ).
fof(f4017,plain,
( spl15_244
<=> ! [X0,X1] :
( sP2(sK14,X0,X1)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_244])]) ).
fof(f1966,plain,
( ! [X0,X1] :
( sP2(sK14,X0,X1)
| ~ empty(X1) )
| ~ spl15_17
| ~ spl15_158 ),
inference(resolution,[],[f1809,f275]) ).
fof(f4015,plain,
( spl15_243
| ~ spl15_17
| ~ spl15_157 ),
inference(avatar_split_clause,[],[f1953,f1804,f274,f4013]) ).
fof(f4013,plain,
( spl15_243
<=> ! [X0,X1] :
( sP2(X0,X1,sK14)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_243])]) ).
fof(f1953,plain,
( ! [X0,X1] :
( sP2(X0,X1,sK14)
| ~ empty(X0) )
| ~ spl15_17
| ~ spl15_157 ),
inference(resolution,[],[f1805,f275]) ).
fof(f4011,plain,
( spl15_242
| ~ spl15_17
| ~ spl15_156 ),
inference(avatar_split_clause,[],[f1940,f1800,f274,f4009]) ).
fof(f4009,plain,
( spl15_242
<=> ! [X0,X1] :
( sP2(X0,X1,X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_242])]) ).
fof(f1940,plain,
( ! [X0,X1] :
( sP2(X0,X1,X0)
| ~ empty(X0) )
| ~ spl15_17
| ~ spl15_156 ),
inference(resolution,[],[f1801,f275]) ).
fof(f4007,plain,
( spl15_241
| ~ spl15_17
| ~ spl15_155 ),
inference(avatar_split_clause,[],[f1927,f1796,f274,f4005]) ).
fof(f4005,plain,
( spl15_241
<=> ! [X0,X1] :
( sP2(X0,sK14,X1)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_241])]) ).
fof(f1927,plain,
( ! [X0,X1] :
( sP2(X0,sK14,X1)
| ~ empty(X1) )
| ~ spl15_17
| ~ spl15_155 ),
inference(resolution,[],[f1797,f275]) ).
fof(f4003,plain,
( spl15_240
| ~ spl15_17
| ~ spl15_154 ),
inference(avatar_split_clause,[],[f1914,f1792,f274,f4001]) ).
fof(f4001,plain,
( spl15_240
<=> ! [X0,X1] :
( sP2(X0,X1,sK14)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_240])]) ).
fof(f1914,plain,
( ! [X0,X1] :
( sP2(X0,X1,sK14)
| ~ empty(X1) )
| ~ spl15_17
| ~ spl15_154 ),
inference(resolution,[],[f1793,f275]) ).
fof(f3999,plain,
( spl15_239
| ~ spl15_17
| ~ spl15_153 ),
inference(avatar_split_clause,[],[f1901,f1788,f274,f3997]) ).
fof(f3997,plain,
( spl15_239
<=> ! [X0,X1] :
( sP2(X0,X1,X1)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_239])]) ).
fof(f1901,plain,
( ! [X0,X1] :
( sP2(X0,X1,X1)
| ~ empty(X1) )
| ~ spl15_17
| ~ spl15_153 ),
inference(resolution,[],[f1789,f275]) ).
fof(f3995,plain,
( spl15_238
| ~ spl15_17
| ~ spl15_151 ),
inference(avatar_split_clause,[],[f1887,f1780,f274,f3993]) ).
fof(f3993,plain,
( spl15_238
<=> ! [X0,X1] :
( sP0(X0,X0,X1)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_238])]) ).
fof(f1887,plain,
( ! [X0,X1] :
( sP0(X0,X0,X1)
| ~ empty(X1) )
| ~ spl15_17
| ~ spl15_151 ),
inference(resolution,[],[f1781,f275]) ).
fof(f3991,plain,
( spl15_237
| ~ spl15_17
| ~ spl15_150 ),
inference(avatar_split_clause,[],[f1872,f1776,f274,f3989]) ).
fof(f3989,plain,
( spl15_237
<=> ! [X0,X1] :
( sP0(X0,sK14,X1)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_237])]) ).
fof(f1872,plain,
( ! [X0,X1] :
( sP0(X0,sK14,X1)
| ~ empty(X1) )
| ~ spl15_17
| ~ spl15_150 ),
inference(resolution,[],[f1777,f275]) ).
fof(f3987,plain,
( spl15_236
| ~ spl15_17
| ~ spl15_149 ),
inference(avatar_split_clause,[],[f1853,f1772,f274,f3985]) ).
fof(f3985,plain,
( spl15_236
<=> ! [X0,X1] :
( sP0(X0,X1,sK14)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_236])]) ).
fof(f1853,plain,
( ! [X0,X1] :
( sP0(X0,X1,sK14)
| ~ empty(X1) )
| ~ spl15_17
| ~ spl15_149 ),
inference(resolution,[],[f1773,f275]) ).
fof(f3983,plain,
( spl15_235
| ~ spl15_17
| ~ spl15_148 ),
inference(avatar_split_clause,[],[f1838,f1768,f274,f3981]) ).
fof(f3981,plain,
( spl15_235
<=> ! [X0,X1] :
( sP0(X0,X1,X1)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_235])]) ).
fof(f1838,plain,
( ! [X0,X1] :
( sP0(X0,X1,X1)
| ~ empty(X1) )
| ~ spl15_17
| ~ spl15_148 ),
inference(resolution,[],[f1769,f275]) ).
fof(f3873,plain,
( spl15_234
| ~ spl15_16
| ~ spl15_119 ),
inference(avatar_split_clause,[],[f1314,f1223,f270,f3871]) ).
fof(f3871,plain,
( spl15_234
<=> ! [X0,X1] :
( subset(X0,X1)
| ~ disjoint(X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_234])]) ).
fof(f1314,plain,
( ! [X0,X1] :
( subset(X0,X1)
| ~ disjoint(X0,X0) )
| ~ spl15_16
| ~ spl15_119 ),
inference(superposition,[],[f1224,f271]) ).
fof(f3684,plain,
( spl15_233
| ~ spl15_34
| ~ spl15_82 ),
inference(avatar_split_clause,[],[f852,f820,f409,f3682]) ).
fof(f3682,plain,
( spl15_233
<=> ! [X0,X3,X2,X1] :
( in(sK11(set_intersection2(X0,X1),X2,X3),X3)
| in(sK11(set_intersection2(X0,X1),X2,X3),X2)
| sP1(set_intersection2(X0,X1),X2,X3)
| ~ disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_233])]) ).
fof(f820,plain,
( spl15_82
<=> ! [X2,X0,X1] :
( sP1(X0,X1,X2)
| in(sK11(X0,X1,X2),X0)
| in(sK11(X0,X1,X2),X1)
| in(sK11(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_82])]) ).
fof(f852,plain,
( ! [X2,X3,X0,X1] :
( in(sK11(set_intersection2(X0,X1),X2,X3),X3)
| in(sK11(set_intersection2(X0,X1),X2,X3),X2)
| sP1(set_intersection2(X0,X1),X2,X3)
| ~ disjoint(X0,X1) )
| ~ spl15_34
| ~ spl15_82 ),
inference(resolution,[],[f821,f410]) ).
fof(f821,plain,
( ! [X2,X0,X1] :
( in(sK11(X0,X1,X2),X2)
| in(sK11(X0,X1,X2),X1)
| in(sK11(X0,X1,X2),X0)
| sP1(X0,X1,X2) )
| ~ spl15_82 ),
inference(avatar_component_clause,[],[f820]) ).
fof(f3680,plain,
( spl15_232
| ~ spl15_34
| ~ spl15_82 ),
inference(avatar_split_clause,[],[f845,f820,f409,f3678]) ).
fof(f3678,plain,
( spl15_232
<=> ! [X0,X3,X2,X1] :
( in(sK11(X0,set_intersection2(X1,X2),X3),X3)
| in(sK11(X0,set_intersection2(X1,X2),X3),X0)
| sP1(X0,set_intersection2(X1,X2),X3)
| ~ disjoint(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_232])]) ).
fof(f845,plain,
( ! [X2,X3,X0,X1] :
( in(sK11(X0,set_intersection2(X1,X2),X3),X3)
| in(sK11(X0,set_intersection2(X1,X2),X3),X0)
| sP1(X0,set_intersection2(X1,X2),X3)
| ~ disjoint(X1,X2) )
| ~ spl15_34
| ~ spl15_82 ),
inference(resolution,[],[f821,f410]) ).
fof(f3676,plain,
( spl15_231
| ~ spl15_34
| ~ spl15_82 ),
inference(avatar_split_clause,[],[f838,f820,f409,f3674]) ).
fof(f3674,plain,
( spl15_231
<=> ! [X0,X3,X2,X1] :
( in(sK11(X0,X1,set_intersection2(X2,X3)),X1)
| in(sK11(X0,X1,set_intersection2(X2,X3)),X0)
| sP1(X0,X1,set_intersection2(X2,X3))
| ~ disjoint(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_231])]) ).
fof(f838,plain,
( ! [X2,X3,X0,X1] :
( in(sK11(X0,X1,set_intersection2(X2,X3)),X1)
| in(sK11(X0,X1,set_intersection2(X2,X3)),X0)
| sP1(X0,X1,set_intersection2(X2,X3))
| ~ disjoint(X2,X3) )
| ~ spl15_34
| ~ spl15_82 ),
inference(resolution,[],[f821,f410]) ).
fof(f3672,plain,
( spl15_230
| ~ spl15_16
| ~ spl15_118 ),
inference(avatar_split_clause,[],[f1299,f1219,f270,f3670]) ).
fof(f3670,plain,
( spl15_230
<=> ! [X0,X1] :
( disjoint(X1,X0)
| ~ disjoint(X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_230])]) ).
fof(f1299,plain,
( ! [X0,X1] :
( disjoint(X1,X0)
| ~ disjoint(X0,X0) )
| ~ spl15_16
| ~ spl15_118 ),
inference(superposition,[],[f1220,f271]) ).
fof(f3668,plain,
( spl15_229
| ~ spl15_24
| ~ spl15_82 ),
inference(avatar_split_clause,[],[f850,f820,f314,f3666]) ).
fof(f3666,plain,
( spl15_229
<=> ! [X2,X0,X1] :
( in(sK11(X0,X1,X2),X2)
| in(sK11(X0,X1,X2),X1)
| sP1(X0,X1,X2)
| ~ in(X0,sK11(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_229])]) ).
fof(f850,plain,
( ! [X2,X0,X1] :
( in(sK11(X0,X1,X2),X2)
| in(sK11(X0,X1,X2),X1)
| sP1(X0,X1,X2)
| ~ in(X0,sK11(X0,X1,X2)) )
| ~ spl15_24
| ~ spl15_82 ),
inference(resolution,[],[f821,f315]) ).
fof(f3664,plain,
( spl15_228
| ~ spl15_24
| ~ spl15_82 ),
inference(avatar_split_clause,[],[f843,f820,f314,f3662]) ).
fof(f3662,plain,
( spl15_228
<=> ! [X2,X0,X1] :
( in(sK11(X0,X1,X2),X2)
| in(sK11(X0,X1,X2),X0)
| sP1(X0,X1,X2)
| ~ in(X1,sK11(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_228])]) ).
fof(f843,plain,
( ! [X2,X0,X1] :
( in(sK11(X0,X1,X2),X2)
| in(sK11(X0,X1,X2),X0)
| sP1(X0,X1,X2)
| ~ in(X1,sK11(X0,X1,X2)) )
| ~ spl15_24
| ~ spl15_82 ),
inference(resolution,[],[f821,f315]) ).
fof(f3660,plain,
( spl15_227
| ~ spl15_24
| ~ spl15_82 ),
inference(avatar_split_clause,[],[f836,f820,f314,f3658]) ).
fof(f3658,plain,
( spl15_227
<=> ! [X2,X0,X1] :
( in(sK11(X0,X1,X2),X1)
| in(sK11(X0,X1,X2),X0)
| sP1(X0,X1,X2)
| ~ in(X2,sK11(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_227])]) ).
fof(f836,plain,
( ! [X2,X0,X1] :
( in(sK11(X0,X1,X2),X1)
| in(sK11(X0,X1,X2),X0)
| sP1(X0,X1,X2)
| ~ in(X2,sK11(X0,X1,X2)) )
| ~ spl15_24
| ~ spl15_82 ),
inference(resolution,[],[f821,f315]) ).
fof(f3537,plain,
( spl15_226
| ~ spl15_17
| ~ spl15_82 ),
inference(avatar_split_clause,[],[f851,f820,f274,f3535]) ).
fof(f3535,plain,
( spl15_226
<=> ! [X2,X0,X1] :
( in(sK11(X0,X1,X2),X2)
| in(sK11(X0,X1,X2),X1)
| sP1(X0,X1,X2)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_226])]) ).
fof(f851,plain,
( ! [X2,X0,X1] :
( in(sK11(X0,X1,X2),X2)
| in(sK11(X0,X1,X2),X1)
| sP1(X0,X1,X2)
| ~ empty(X0) )
| ~ spl15_17
| ~ spl15_82 ),
inference(resolution,[],[f821,f275]) ).
fof(f3533,plain,
( spl15_225
| ~ spl15_17
| ~ spl15_82 ),
inference(avatar_split_clause,[],[f844,f820,f274,f3531]) ).
fof(f3531,plain,
( spl15_225
<=> ! [X2,X0,X1] :
( in(sK11(X0,X1,X2),X2)
| in(sK11(X0,X1,X2),X0)
| sP1(X0,X1,X2)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_225])]) ).
fof(f844,plain,
( ! [X2,X0,X1] :
( in(sK11(X0,X1,X2),X2)
| in(sK11(X0,X1,X2),X0)
| sP1(X0,X1,X2)
| ~ empty(X1) )
| ~ spl15_17
| ~ spl15_82 ),
inference(resolution,[],[f821,f275]) ).
fof(f3529,plain,
( spl15_224
| ~ spl15_17
| ~ spl15_82 ),
inference(avatar_split_clause,[],[f837,f820,f274,f3527]) ).
fof(f3527,plain,
( spl15_224
<=> ! [X2,X0,X1] :
( in(sK11(X0,X1,X2),X1)
| in(sK11(X0,X1,X2),X0)
| sP1(X0,X1,X2)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_224])]) ).
fof(f837,plain,
( ! [X2,X0,X1] :
( in(sK11(X0,X1,X2),X1)
| in(sK11(X0,X1,X2),X0)
| sP1(X0,X1,X2)
| ~ empty(X2) )
| ~ spl15_17
| ~ spl15_82 ),
inference(resolution,[],[f821,f275]) ).
fof(f3525,plain,
( spl15_223
| ~ spl15_16
| ~ spl15_115 ),
inference(avatar_split_clause,[],[f1288,f1207,f270,f3523]) ).
fof(f3523,plain,
( spl15_223
<=> ! [X0,X1] :
( disjoint(X0,X1)
| ~ disjoint(X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_223])]) ).
fof(f1288,plain,
( ! [X0,X1] :
( disjoint(X0,X1)
| ~ disjoint(X0,X0) )
| ~ spl15_16
| ~ spl15_115 ),
inference(superposition,[],[f1208,f271]) ).
fof(f3301,plain,
( spl15_222
| ~ spl15_34
| ~ spl15_80 ),
inference(avatar_split_clause,[],[f807,f763,f409,f3299]) ).
fof(f3299,plain,
( spl15_222
<=> ! [X0,X3,X2,X1] :
( in(sK12(set_intersection2(X0,X1),X2,X3),X3)
| sP2(set_intersection2(X0,X1),X2,X3)
| ~ disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_222])]) ).
fof(f763,plain,
( spl15_80
<=> ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| in(sK12(X0,X1,X2),X0)
| in(sK12(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_80])]) ).
fof(f807,plain,
( ! [X2,X3,X0,X1] :
( in(sK12(set_intersection2(X0,X1),X2,X3),X3)
| sP2(set_intersection2(X0,X1),X2,X3)
| ~ disjoint(X0,X1) )
| ~ spl15_34
| ~ spl15_80 ),
inference(resolution,[],[f764,f410]) ).
fof(f764,plain,
( ! [X2,X0,X1] :
( in(sK12(X0,X1,X2),X2)
| in(sK12(X0,X1,X2),X0)
| sP2(X0,X1,X2) )
| ~ spl15_80 ),
inference(avatar_component_clause,[],[f763]) ).
fof(f3297,plain,
( spl15_221
| ~ spl15_34
| ~ spl15_80 ),
inference(avatar_split_clause,[],[f802,f763,f409,f3295]) ).
fof(f3295,plain,
( spl15_221
<=> ! [X0,X3,X2,X1] :
( in(sK12(X0,X1,set_intersection2(X2,X3)),X0)
| sP2(X0,X1,set_intersection2(X2,X3))
| ~ disjoint(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_221])]) ).
fof(f802,plain,
( ! [X2,X3,X0,X1] :
( in(sK12(X0,X1,set_intersection2(X2,X3)),X0)
| sP2(X0,X1,set_intersection2(X2,X3))
| ~ disjoint(X2,X3) )
| ~ spl15_34
| ~ spl15_80 ),
inference(resolution,[],[f764,f410]) ).
fof(f3293,plain,
( spl15_220
| ~ spl15_25
| ~ spl15_109 ),
inference(avatar_split_clause,[],[f1181,f1110,f318,f3291]) ).
fof(f318,plain,
( spl15_25
<=> ! [X0,X1] : sP0(X1,X0,set_difference(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_25])]) ).
fof(f1181,plain,
( ! [X0,X1] : sP0(set_union2(X0,X1),X0,sK14)
| ~ spl15_25
| ~ spl15_109 ),
inference(superposition,[],[f319,f1111]) ).
fof(f319,plain,
( ! [X0,X1] : sP0(X1,X0,set_difference(X0,X1))
| ~ spl15_25 ),
inference(avatar_component_clause,[],[f318]) ).
fof(f3289,plain,
( spl15_219
| ~ spl15_34
| ~ spl15_79 ),
inference(avatar_split_clause,[],[f792,f759,f409,f3287]) ).
fof(f3287,plain,
( spl15_219
<=> ! [X0,X3,X2,X1] :
( in(sK12(X0,set_intersection2(X1,X2),X3),X3)
| sP2(X0,set_intersection2(X1,X2),X3)
| ~ disjoint(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_219])]) ).
fof(f759,plain,
( spl15_79
<=> ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| in(sK12(X0,X1,X2),X1)
| in(sK12(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_79])]) ).
fof(f792,plain,
( ! [X2,X3,X0,X1] :
( in(sK12(X0,set_intersection2(X1,X2),X3),X3)
| sP2(X0,set_intersection2(X1,X2),X3)
| ~ disjoint(X1,X2) )
| ~ spl15_34
| ~ spl15_79 ),
inference(resolution,[],[f760,f410]) ).
fof(f760,plain,
( ! [X2,X0,X1] :
( in(sK12(X0,X1,X2),X2)
| in(sK12(X0,X1,X2),X1)
| sP2(X0,X1,X2) )
| ~ spl15_79 ),
inference(avatar_component_clause,[],[f759]) ).
fof(f3285,plain,
( spl15_218
| ~ spl15_34
| ~ spl15_79 ),
inference(avatar_split_clause,[],[f787,f759,f409,f3283]) ).
fof(f3283,plain,
( spl15_218
<=> ! [X0,X3,X2,X1] :
( in(sK12(X0,X1,set_intersection2(X2,X3)),X1)
| sP2(X0,X1,set_intersection2(X2,X3))
| ~ disjoint(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_218])]) ).
fof(f787,plain,
( ! [X2,X3,X0,X1] :
( in(sK12(X0,X1,set_intersection2(X2,X3)),X1)
| sP2(X0,X1,set_intersection2(X2,X3))
| ~ disjoint(X2,X3) )
| ~ spl15_34
| ~ spl15_79 ),
inference(resolution,[],[f760,f410]) ).
fof(f3281,plain,
( spl15_217
| ~ spl15_34
| ~ spl15_74 ),
inference(avatar_split_clause,[],[f773,f739,f409,f3279]) ).
fof(f3279,plain,
( spl15_217
<=> ! [X0,X3,X2,X1] :
( in(sK10(X0,set_intersection2(X1,X2),X3),X3)
| sP0(X0,set_intersection2(X1,X2),X3)
| ~ disjoint(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_217])]) ).
fof(f739,plain,
( spl15_74
<=> ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| in(sK10(X0,X1,X2),X1)
| in(sK10(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_74])]) ).
fof(f773,plain,
( ! [X2,X3,X0,X1] :
( in(sK10(X0,set_intersection2(X1,X2),X3),X3)
| sP0(X0,set_intersection2(X1,X2),X3)
| ~ disjoint(X1,X2) )
| ~ spl15_34
| ~ spl15_74 ),
inference(resolution,[],[f740,f410]) ).
fof(f740,plain,
( ! [X2,X0,X1] :
( in(sK10(X0,X1,X2),X2)
| in(sK10(X0,X1,X2),X1)
| sP0(X0,X1,X2) )
| ~ spl15_74 ),
inference(avatar_component_clause,[],[f739]) ).
fof(f3277,plain,
( spl15_216
| ~ spl15_34
| ~ spl15_74 ),
inference(avatar_split_clause,[],[f768,f739,f409,f3275]) ).
fof(f3275,plain,
( spl15_216
<=> ! [X0,X3,X2,X1] :
( in(sK10(X0,X1,set_intersection2(X2,X3)),X1)
| sP0(X0,X1,set_intersection2(X2,X3))
| ~ disjoint(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_216])]) ).
fof(f768,plain,
( ! [X2,X3,X0,X1] :
( in(sK10(X0,X1,set_intersection2(X2,X3)),X1)
| sP0(X0,X1,set_intersection2(X2,X3))
| ~ disjoint(X2,X3) )
| ~ spl15_34
| ~ spl15_74 ),
inference(resolution,[],[f740,f410]) ).
fof(f3273,plain,
( spl15_215
| ~ spl15_52
| ~ spl15_59 ),
inference(avatar_split_clause,[],[f613,f586,f541,f3271]) ).
fof(f3271,plain,
( spl15_215
<=> ! [X2,X0,X1] :
( ~ subset(X0,X1)
| set_intersection2(X1,X2) = set_intersection2(X0,X2)
| ~ subset(set_intersection2(X1,X2),set_intersection2(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_215])]) ).
fof(f613,plain,
( ! [X2,X0,X1] :
( ~ subset(X0,X1)
| set_intersection2(X1,X2) = set_intersection2(X0,X2)
| ~ subset(set_intersection2(X1,X2),set_intersection2(X0,X2)) )
| ~ spl15_52
| ~ spl15_59 ),
inference(resolution,[],[f587,f542]) ).
fof(f3269,plain,
( spl15_214
| ~ spl15_52
| ~ spl15_58 ),
inference(avatar_split_clause,[],[f599,f582,f541,f3267]) ).
fof(f3267,plain,
( spl15_214
<=> ! [X2,X0,X1] :
( ~ subset(X0,X1)
| set_difference(X0,X2) = set_difference(X1,X2)
| ~ subset(set_difference(X1,X2),set_difference(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_214])]) ).
fof(f599,plain,
( ! [X2,X0,X1] :
( ~ subset(X0,X1)
| set_difference(X0,X2) = set_difference(X1,X2)
| ~ subset(set_difference(X1,X2),set_difference(X0,X2)) )
| ~ spl15_52
| ~ spl15_58 ),
inference(resolution,[],[f583,f542]) ).
fof(f3107,plain,
( spl15_213
| ~ spl15_25
| ~ spl15_108 ),
inference(avatar_split_clause,[],[f1166,f1106,f318,f3105]) ).
fof(f1166,plain,
( ! [X0,X1] : sP0(X0,set_intersection2(X0,X1),sK14)
| ~ spl15_25
| ~ spl15_108 ),
inference(superposition,[],[f319,f1107]) ).
fof(f3025,plain,
( spl15_212
| ~ spl15_7
| ~ spl15_18
| ~ spl15_82 ),
inference(avatar_split_clause,[],[f868,f820,f284,f234,f3023]) ).
fof(f868,plain,
( ! [X0,X1] :
( sP1(sK14,X0,X1)
| in(sK11(sK14,X0,X1),X0)
| in(sK11(sK14,X0,X1),X1) )
| ~ spl15_7
| ~ spl15_18
| ~ spl15_82 ),
inference(forward_demodulation,[],[f867,f286]) ).
fof(f867,plain,
( ! [X0,X1] :
( in(sK11(sK14,X0,X1),X0)
| in(sK11(sK14,X0,X1),X1)
| sP1(empty_set,X0,X1) )
| ~ spl15_7
| ~ spl15_18
| ~ spl15_82 ),
inference(forward_demodulation,[],[f866,f286]) ).
fof(f866,plain,
( ! [X0,X1] :
( in(sK11(sK14,X0,X1),X1)
| in(sK11(empty_set,X0,X1),X0)
| sP1(empty_set,X0,X1) )
| ~ spl15_7
| ~ spl15_18
| ~ spl15_82 ),
inference(forward_demodulation,[],[f853,f286]) ).
fof(f853,plain,
( ! [X0,X1] :
( in(sK11(empty_set,X0,X1),X1)
| in(sK11(empty_set,X0,X1),X0)
| sP1(empty_set,X0,X1) )
| ~ spl15_7
| ~ spl15_82 ),
inference(resolution,[],[f821,f235]) ).
fof(f3021,plain,
( spl15_211
| ~ spl15_7
| ~ spl15_18
| ~ spl15_82 ),
inference(avatar_split_clause,[],[f865,f820,f284,f234,f3019]) ).
fof(f865,plain,
( ! [X0,X1] :
( sP1(X0,sK14,X1)
| in(sK11(X0,sK14,X1),X0)
| in(sK11(X0,sK14,X1),X1) )
| ~ spl15_7
| ~ spl15_18
| ~ spl15_82 ),
inference(forward_demodulation,[],[f864,f286]) ).
fof(f864,plain,
( ! [X0,X1] :
( in(sK11(X0,sK14,X1),X0)
| in(sK11(X0,sK14,X1),X1)
| sP1(X0,empty_set,X1) )
| ~ spl15_7
| ~ spl15_18
| ~ spl15_82 ),
inference(forward_demodulation,[],[f863,f286]) ).
fof(f863,plain,
( ! [X0,X1] :
( in(sK11(X0,sK14,X1),X1)
| in(sK11(X0,empty_set,X1),X0)
| sP1(X0,empty_set,X1) )
| ~ spl15_7
| ~ spl15_18
| ~ spl15_82 ),
inference(forward_demodulation,[],[f846,f286]) ).
fof(f846,plain,
( ! [X0,X1] :
( in(sK11(X0,empty_set,X1),X1)
| in(sK11(X0,empty_set,X1),X0)
| sP1(X0,empty_set,X1) )
| ~ spl15_7
| ~ spl15_82 ),
inference(resolution,[],[f821,f235]) ).
fof(f3017,plain,
( spl15_210
| ~ spl15_103
| ~ spl15_107 ),
inference(avatar_split_clause,[],[f1153,f1102,f1064,f3015]) ).
fof(f1153,plain,
( ! [X0,X1] : sP2(X0,set_union2(X0,X1),X0)
| ~ spl15_103
| ~ spl15_107 ),
inference(superposition,[],[f1065,f1103]) ).
fof(f3013,plain,
( spl15_209
| ~ spl15_7
| ~ spl15_18
| ~ spl15_82 ),
inference(avatar_split_clause,[],[f862,f820,f284,f234,f3011]) ).
fof(f862,plain,
( ! [X0,X1] :
( sP1(X0,X1,sK14)
| in(sK11(X0,X1,sK14),X0)
| in(sK11(X0,X1,sK14),X1) )
| ~ spl15_7
| ~ spl15_18
| ~ spl15_82 ),
inference(forward_demodulation,[],[f861,f286]) ).
fof(f861,plain,
( ! [X0,X1] :
( in(sK11(X0,X1,sK14),X0)
| in(sK11(X0,X1,sK14),X1)
| sP1(X0,X1,empty_set) )
| ~ spl15_7
| ~ spl15_18
| ~ spl15_82 ),
inference(forward_demodulation,[],[f860,f286]) ).
fof(f860,plain,
( ! [X0,X1] :
( in(sK11(X0,X1,sK14),X1)
| in(sK11(X0,X1,empty_set),X0)
| sP1(X0,X1,empty_set) )
| ~ spl15_7
| ~ spl15_18
| ~ spl15_82 ),
inference(forward_demodulation,[],[f839,f286]) ).
fof(f839,plain,
( ! [X0,X1] :
( in(sK11(X0,X1,empty_set),X1)
| in(sK11(X0,X1,empty_set),X0)
| sP1(X0,X1,empty_set) )
| ~ spl15_7
| ~ spl15_82 ),
inference(resolution,[],[f821,f235]) ).
fof(f3009,plain,
( spl15_208
| ~ spl15_82 ),
inference(avatar_split_clause,[],[f857,f820,f3007]) ).
fof(f857,plain,
( ! [X4,X5] :
( in(sK11(X4,X4,X5),X5)
| in(sK11(X4,X4,X5),X4)
| sP1(X4,X4,X5) )
| ~ spl15_82 ),
inference(factoring,[],[f821]) ).
fof(f3005,plain,
( spl15_207
| ~ spl15_82 ),
inference(avatar_split_clause,[],[f856,f820,f3003]) ).
fof(f856,plain,
( ! [X2,X3] :
( in(sK11(X2,X3,X2),X2)
| in(sK11(X2,X3,X2),X3)
| sP1(X2,X3,X2) )
| ~ spl15_82 ),
inference(factoring,[],[f821]) ).
fof(f3001,plain,
( spl15_206
| ~ spl15_82 ),
inference(avatar_split_clause,[],[f855,f820,f2999]) ).
fof(f855,plain,
( ! [X0,X1] :
( in(sK11(X0,X1,X1),X1)
| in(sK11(X0,X1,X1),X0)
| sP1(X0,X1,X1) )
| ~ spl15_82 ),
inference(factoring,[],[f821]) ).
fof(f2997,plain,
( spl15_205
| ~ spl15_24
| ~ spl15_80 ),
inference(avatar_split_clause,[],[f805,f763,f314,f2995]) ).
fof(f2995,plain,
( spl15_205
<=> ! [X2,X0,X1] :
( in(sK12(X0,X1,X2),X2)
| sP2(X0,X1,X2)
| ~ in(X0,sK12(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_205])]) ).
fof(f805,plain,
( ! [X2,X0,X1] :
( in(sK12(X0,X1,X2),X2)
| sP2(X0,X1,X2)
| ~ in(X0,sK12(X0,X1,X2)) )
| ~ spl15_24
| ~ spl15_80 ),
inference(resolution,[],[f764,f315]) ).
fof(f2993,plain,
( spl15_204
| ~ spl15_24
| ~ spl15_80 ),
inference(avatar_split_clause,[],[f800,f763,f314,f2991]) ).
fof(f2991,plain,
( spl15_204
<=> ! [X2,X0,X1] :
( in(sK12(X0,X1,X2),X0)
| sP2(X0,X1,X2)
| ~ in(X2,sK12(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_204])]) ).
fof(f800,plain,
( ! [X2,X0,X1] :
( in(sK12(X0,X1,X2),X0)
| sP2(X0,X1,X2)
| ~ in(X2,sK12(X0,X1,X2)) )
| ~ spl15_24
| ~ spl15_80 ),
inference(resolution,[],[f764,f315]) ).
fof(f2989,plain,
( spl15_203
| ~ spl15_24
| ~ spl15_79 ),
inference(avatar_split_clause,[],[f790,f759,f314,f2987]) ).
fof(f2987,plain,
( spl15_203
<=> ! [X2,X0,X1] :
( in(sK12(X0,X1,X2),X2)
| sP2(X0,X1,X2)
| ~ in(X1,sK12(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_203])]) ).
fof(f790,plain,
( ! [X2,X0,X1] :
( in(sK12(X0,X1,X2),X2)
| sP2(X0,X1,X2)
| ~ in(X1,sK12(X0,X1,X2)) )
| ~ spl15_24
| ~ spl15_79 ),
inference(resolution,[],[f760,f315]) ).
fof(f2985,plain,
( spl15_202
| ~ spl15_24
| ~ spl15_79 ),
inference(avatar_split_clause,[],[f785,f759,f314,f2983]) ).
fof(f2983,plain,
( spl15_202
<=> ! [X2,X0,X1] :
( in(sK12(X0,X1,X2),X1)
| sP2(X0,X1,X2)
| ~ in(X2,sK12(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_202])]) ).
fof(f785,plain,
( ! [X2,X0,X1] :
( in(sK12(X0,X1,X2),X1)
| sP2(X0,X1,X2)
| ~ in(X2,sK12(X0,X1,X2)) )
| ~ spl15_24
| ~ spl15_79 ),
inference(resolution,[],[f760,f315]) ).
fof(f2981,plain,
( spl15_201
| ~ spl15_24
| ~ spl15_74 ),
inference(avatar_split_clause,[],[f771,f739,f314,f2979]) ).
fof(f2979,plain,
( spl15_201
<=> ! [X2,X0,X1] :
( in(sK10(X0,X1,X2),X2)
| sP0(X0,X1,X2)
| ~ in(X1,sK10(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_201])]) ).
fof(f771,plain,
( ! [X2,X0,X1] :
( in(sK10(X0,X1,X2),X2)
| sP0(X0,X1,X2)
| ~ in(X1,sK10(X0,X1,X2)) )
| ~ spl15_24
| ~ spl15_74 ),
inference(resolution,[],[f740,f315]) ).
fof(f2977,plain,
( spl15_200
| ~ spl15_24
| ~ spl15_74 ),
inference(avatar_split_clause,[],[f766,f739,f314,f2975]) ).
fof(f2975,plain,
( spl15_200
<=> ! [X2,X0,X1] :
( in(sK10(X0,X1,X2),X1)
| sP0(X0,X1,X2)
| ~ in(X2,sK10(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_200])]) ).
fof(f766,plain,
( ! [X2,X0,X1] :
( in(sK10(X0,X1,X2),X1)
| sP0(X0,X1,X2)
| ~ in(X2,sK10(X0,X1,X2)) )
| ~ spl15_24
| ~ spl15_74 ),
inference(resolution,[],[f740,f315]) ).
fof(f2973,plain,
( spl15_199
| ~ spl15_27
| ~ spl15_107 ),
inference(avatar_split_clause,[],[f1145,f1102,f326,f2971]) ).
fof(f1145,plain,
( ! [X0,X1] : sP2(set_union2(X0,X1),X0,X0)
| ~ spl15_27
| ~ spl15_107 ),
inference(superposition,[],[f327,f1103]) ).
fof(f2924,plain,
( spl15_198
| ~ spl15_52
| ~ spl15_68 ),
inference(avatar_split_clause,[],[f683,f667,f541,f2922]) ).
fof(f2922,plain,
( spl15_198
<=> ! [X2,X0,X1] :
( ~ subset(X0,X1)
| ~ subset(X2,X1)
| set_union2(X2,X0) = X1
| ~ subset(X1,set_union2(X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_198])]) ).
fof(f683,plain,
( ! [X2,X0,X1] :
( ~ subset(X0,X1)
| ~ subset(X2,X1)
| set_union2(X2,X0) = X1
| ~ subset(X1,set_union2(X2,X0)) )
| ~ spl15_52
| ~ spl15_68 ),
inference(resolution,[],[f668,f542]) ).
fof(f2920,plain,
( spl15_197
| ~ spl15_52
| ~ spl15_67 ),
inference(avatar_split_clause,[],[f671,f663,f541,f2918]) ).
fof(f2918,plain,
( spl15_197
<=> ! [X2,X0,X1] :
( ~ subset(X0,X1)
| ~ subset(X0,X2)
| set_intersection2(X2,X1) = X0
| ~ subset(set_intersection2(X2,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_197])]) ).
fof(f663,plain,
( spl15_67
<=> ! [X2,X0,X1] :
( subset(X0,set_intersection2(X1,X2))
| ~ subset(X0,X2)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_67])]) ).
fof(f671,plain,
( ! [X2,X0,X1] :
( ~ subset(X0,X1)
| ~ subset(X0,X2)
| set_intersection2(X2,X1) = X0
| ~ subset(set_intersection2(X2,X1),X0) )
| ~ spl15_52
| ~ spl15_67 ),
inference(resolution,[],[f664,f542]) ).
fof(f664,plain,
( ! [X2,X0,X1] :
( subset(X0,set_intersection2(X1,X2))
| ~ subset(X0,X2)
| ~ subset(X0,X1) )
| ~ spl15_67 ),
inference(avatar_component_clause,[],[f663]) ).
fof(f2818,plain,
( spl15_196
| ~ spl15_34
| ~ spl15_69 ),
inference(avatar_split_clause,[],[f724,f694,f409,f2816]) ).
fof(f694,plain,
( spl15_69
<=> ! [X0,X1] :
( X0 = X1
| in(sK8(X0,X1),X1)
| in(sK8(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_69])]) ).
fof(f724,plain,
( ! [X2,X0,X1] :
( in(sK8(set_intersection2(X0,X1),X2),X2)
| set_intersection2(X0,X1) = X2
| ~ disjoint(X0,X1) )
| ~ spl15_34
| ~ spl15_69 ),
inference(resolution,[],[f695,f410]) ).
fof(f695,plain,
( ! [X0,X1] :
( in(sK8(X0,X1),X1)
| in(sK8(X0,X1),X0)
| X0 = X1 )
| ~ spl15_69 ),
inference(avatar_component_clause,[],[f694]) ).
fof(f2814,plain,
( spl15_195
| ~ spl15_34
| ~ spl15_69 ),
inference(avatar_split_clause,[],[f719,f694,f409,f2812]) ).
fof(f719,plain,
( ! [X2,X0,X1] :
( in(sK8(X0,set_intersection2(X1,X2)),X0)
| set_intersection2(X1,X2) = X0
| ~ disjoint(X1,X2) )
| ~ spl15_34
| ~ spl15_69 ),
inference(resolution,[],[f695,f410]) ).
fof(f2810,plain,
( spl15_194
| ~ spl15_102
| ~ spl15_106 ),
inference(avatar_split_clause,[],[f1133,f1098,f1060,f2808]) ).
fof(f1133,plain,
( ! [X0,X1] : sP1(set_intersection2(X0,X1),X0,X0)
| ~ spl15_102
| ~ spl15_106 ),
inference(superposition,[],[f1061,f1099]) ).
fof(f2806,plain,
( spl15_193
| ~ spl15_38
| ~ spl15_68 ),
inference(avatar_split_clause,[],[f686,f667,f426,f2804]) ).
fof(f2804,plain,
( spl15_193
<=> ! [X2,X0,X1] :
( ~ subset(X0,X1)
| ~ subset(X2,X1)
| set_union2(X2,X0) = set_intersection2(set_union2(X2,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_193])]) ).
fof(f686,plain,
( ! [X2,X0,X1] :
( ~ subset(X0,X1)
| ~ subset(X2,X1)
| set_union2(X2,X0) = set_intersection2(set_union2(X2,X0),X1) )
| ~ spl15_38
| ~ spl15_68 ),
inference(resolution,[],[f668,f427]) ).
fof(f2802,plain,
( spl15_192
| ~ spl15_37
| ~ spl15_67 ),
inference(avatar_split_clause,[],[f675,f663,f421,f2800]) ).
fof(f2800,plain,
( spl15_192
<=> ! [X2,X0,X1] :
( ~ subset(X0,X1)
| ~ subset(X0,X2)
| set_intersection2(X2,X1) = set_union2(X0,set_intersection2(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_192])]) ).
fof(f675,plain,
( ! [X2,X0,X1] :
( ~ subset(X0,X1)
| ~ subset(X0,X2)
| set_intersection2(X2,X1) = set_union2(X0,set_intersection2(X2,X1)) )
| ~ spl15_37
| ~ spl15_67 ),
inference(resolution,[],[f664,f422]) ).
fof(f2618,plain,
( spl15_191
| ~ spl15_26
| ~ spl15_106 ),
inference(avatar_split_clause,[],[f1128,f1098,f322,f2616]) ).
fof(f1128,plain,
( ! [X0,X1] : sP1(X0,set_intersection2(X0,X1),X0)
| ~ spl15_26
| ~ spl15_106 ),
inference(superposition,[],[f323,f1099]) ).
fof(f2614,plain,
( spl15_190
| ~ spl15_51
| ~ spl15_68 ),
inference(avatar_split_clause,[],[f684,f667,f531,f2612]) ).
fof(f2612,plain,
( spl15_190
<=> ! [X0,X3,X2,X1] :
( ~ subset(X0,X1)
| ~ subset(X2,X1)
| subset(X3,X1)
| ~ subset(X3,set_union2(X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_190])]) ).
fof(f684,plain,
( ! [X2,X3,X0,X1] :
( ~ subset(X0,X1)
| ~ subset(X2,X1)
| subset(X3,X1)
| ~ subset(X3,set_union2(X2,X0)) )
| ~ spl15_51
| ~ spl15_68 ),
inference(resolution,[],[f668,f532]) ).
fof(f2610,plain,
( spl15_189
| ~ spl15_53
| ~ spl15_68 ),
inference(avatar_split_clause,[],[f682,f667,f545,f2608]) ).
fof(f2608,plain,
( spl15_189
<=> ! [X0,X3,X2,X1] :
( ~ subset(X0,X1)
| ~ subset(X2,X1)
| ~ in(X3,set_union2(X2,X0))
| in(X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_189])]) ).
fof(f682,plain,
( ! [X2,X3,X0,X1] :
( ~ subset(X0,X1)
| ~ subset(X2,X1)
| ~ in(X3,set_union2(X2,X0))
| in(X3,X1) )
| ~ spl15_53
| ~ spl15_68 ),
inference(resolution,[],[f668,f546]) ).
fof(f2606,plain,
( spl15_188
| ~ spl15_51
| ~ spl15_67 ),
inference(avatar_split_clause,[],[f672,f663,f531,f2604]) ).
fof(f2604,plain,
( spl15_188
<=> ! [X0,X3,X2,X1] :
( ~ subset(X0,X1)
| ~ subset(X0,X2)
| subset(X3,set_intersection2(X2,X1))
| ~ subset(X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_188])]) ).
fof(f672,plain,
( ! [X2,X3,X0,X1] :
( ~ subset(X0,X1)
| ~ subset(X0,X2)
| subset(X3,set_intersection2(X2,X1))
| ~ subset(X3,X0) )
| ~ spl15_51
| ~ spl15_67 ),
inference(resolution,[],[f664,f532]) ).
fof(f2602,plain,
( spl15_187
| ~ spl15_53
| ~ spl15_67 ),
inference(avatar_split_clause,[],[f670,f663,f545,f2600]) ).
fof(f670,plain,
( ! [X2,X3,X0,X1] :
( ~ subset(X0,X1)
| ~ subset(X0,X2)
| ~ in(X3,X0)
| in(X3,set_intersection2(X2,X1)) )
| ~ spl15_53
| ~ spl15_67 ),
inference(resolution,[],[f664,f546]) ).
fof(f2598,plain,
( spl15_186
| ~ spl15_37
| ~ spl15_59 ),
inference(avatar_split_clause,[],[f617,f586,f421,f2596]) ).
fof(f2596,plain,
( spl15_186
<=> ! [X2,X0,X1] :
( ~ subset(X0,X1)
| set_intersection2(X1,X2) = set_union2(set_intersection2(X0,X2),set_intersection2(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_186])]) ).
fof(f617,plain,
( ! [X2,X0,X1] :
( ~ subset(X0,X1)
| set_intersection2(X1,X2) = set_union2(set_intersection2(X0,X2),set_intersection2(X1,X2)) )
| ~ spl15_37
| ~ spl15_59 ),
inference(resolution,[],[f587,f422]) ).
fof(f2594,plain,
( spl15_185
| ~ spl15_38
| ~ spl15_59 ),
inference(avatar_split_clause,[],[f616,f586,f426,f2592]) ).
fof(f2592,plain,
( spl15_185
<=> ! [X2,X0,X1] :
( ~ subset(X0,X1)
| set_intersection2(X0,X2) = set_intersection2(set_intersection2(X0,X2),set_intersection2(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_185])]) ).
fof(f616,plain,
( ! [X2,X0,X1] :
( ~ subset(X0,X1)
| set_intersection2(X0,X2) = set_intersection2(set_intersection2(X0,X2),set_intersection2(X1,X2)) )
| ~ spl15_38
| ~ spl15_59 ),
inference(resolution,[],[f587,f427]) ).
fof(f2590,plain,
( spl15_184
| ~ spl15_37
| ~ spl15_58 ),
inference(avatar_split_clause,[],[f603,f582,f421,f2588]) ).
fof(f2588,plain,
( spl15_184
<=> ! [X2,X0,X1] :
( ~ subset(X0,X1)
| set_difference(X1,X2) = set_union2(set_difference(X0,X2),set_difference(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_184])]) ).
fof(f603,plain,
( ! [X2,X0,X1] :
( ~ subset(X0,X1)
| set_difference(X1,X2) = set_union2(set_difference(X0,X2),set_difference(X1,X2)) )
| ~ spl15_37
| ~ spl15_58 ),
inference(resolution,[],[f583,f422]) ).
fof(f2586,plain,
( spl15_183
| ~ spl15_38
| ~ spl15_58 ),
inference(avatar_split_clause,[],[f602,f582,f426,f2584]) ).
fof(f2584,plain,
( spl15_183
<=> ! [X2,X0,X1] :
( ~ subset(X0,X1)
| set_difference(X0,X2) = set_intersection2(set_difference(X0,X2),set_difference(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_183])]) ).
fof(f602,plain,
( ! [X2,X0,X1] :
( ~ subset(X0,X1)
| set_difference(X0,X2) = set_intersection2(set_difference(X0,X2),set_difference(X1,X2)) )
| ~ spl15_38
| ~ spl15_58 ),
inference(resolution,[],[f583,f427]) ).
fof(f2582,plain,
( spl15_182
| ~ spl15_22
| ~ spl15_106 ),
inference(avatar_split_clause,[],[f1127,f1098,f306,f2580]) ).
fof(f306,plain,
( spl15_22
<=> ! [X0,X1] :
( ~ empty(set_union2(X0,X1))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_22])]) ).
fof(f1127,plain,
( ! [X0,X1] :
( ~ empty(X0)
| empty(set_intersection2(X0,X1)) )
| ~ spl15_22
| ~ spl15_106 ),
inference(superposition,[],[f307,f1099]) ).
fof(f307,plain,
( ! [X0,X1] :
( ~ empty(set_union2(X0,X1))
| empty(X0) )
| ~ spl15_22 ),
inference(avatar_component_clause,[],[f306]) ).
fof(f2578,plain,
( spl15_181
| ~ spl15_24
| ~ spl15_69 ),
inference(avatar_split_clause,[],[f722,f694,f314,f2576]) ).
fof(f2576,plain,
( spl15_181
<=> ! [X0,X1] :
( in(sK8(X0,X1),X1)
| X0 = X1
| ~ in(X0,sK8(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_181])]) ).
fof(f722,plain,
( ! [X0,X1] :
( in(sK8(X0,X1),X1)
| X0 = X1
| ~ in(X0,sK8(X0,X1)) )
| ~ spl15_24
| ~ spl15_69 ),
inference(resolution,[],[f695,f315]) ).
fof(f2574,plain,
( spl15_180
| ~ spl15_24
| ~ spl15_69 ),
inference(avatar_split_clause,[],[f717,f694,f314,f2572]) ).
fof(f2572,plain,
( spl15_180
<=> ! [X0,X1] :
( in(sK8(X0,X1),X0)
| X0 = X1
| ~ in(X1,sK8(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_180])]) ).
fof(f717,plain,
( ! [X0,X1] :
( in(sK8(X0,X1),X0)
| X0 = X1
| ~ in(X1,sK8(X0,X1)) )
| ~ spl15_24
| ~ spl15_69 ),
inference(resolution,[],[f695,f315]) ).
fof(f2334,plain,
( spl15_179
| ~ spl15_37
| ~ spl15_68 ),
inference(avatar_split_clause,[],[f687,f667,f421,f2332]) ).
fof(f687,plain,
( ! [X2,X0,X1] :
( ~ subset(X0,X1)
| ~ subset(X2,X1)
| set_union2(set_union2(X2,X0),X1) = X1 )
| ~ spl15_37
| ~ spl15_68 ),
inference(resolution,[],[f668,f422]) ).
fof(f2330,plain,
( spl15_178
| ~ spl15_42
| ~ spl15_68 ),
inference(avatar_split_clause,[],[f685,f667,f471,f2328]) ).
fof(f685,plain,
( ! [X2,X0,X1] :
( ~ subset(X0,X1)
| ~ subset(X2,X1)
| sK14 = set_difference(set_union2(X2,X0),X1) )
| ~ spl15_42
| ~ spl15_68 ),
inference(resolution,[],[f668,f472]) ).
fof(f2326,plain,
( spl15_177
| ~ spl15_38
| ~ spl15_67 ),
inference(avatar_split_clause,[],[f674,f663,f426,f2324]) ).
fof(f674,plain,
( ! [X2,X0,X1] :
( ~ subset(X0,X1)
| ~ subset(X0,X2)
| set_intersection2(X0,set_intersection2(X2,X1)) = X0 )
| ~ spl15_38
| ~ spl15_67 ),
inference(resolution,[],[f664,f427]) ).
fof(f2322,plain,
( spl15_176
| ~ spl15_42
| ~ spl15_67 ),
inference(avatar_split_clause,[],[f673,f663,f471,f2320]) ).
fof(f673,plain,
( ! [X2,X0,X1] :
( ~ subset(X0,X1)
| ~ subset(X0,X2)
| sK14 = set_difference(X0,set_intersection2(X2,X1)) )
| ~ spl15_42
| ~ spl15_67 ),
inference(resolution,[],[f664,f472]) ).
fof(f2318,plain,
( spl15_175
| ~ spl15_51
| ~ spl15_59 ),
inference(avatar_split_clause,[],[f614,f586,f531,f2316]) ).
fof(f614,plain,
( ! [X2,X3,X0,X1] :
( ~ subset(X0,X1)
| subset(X2,set_intersection2(X1,X3))
| ~ subset(X2,set_intersection2(X0,X3)) )
| ~ spl15_51
| ~ spl15_59 ),
inference(resolution,[],[f587,f532]) ).
fof(f2314,plain,
( spl15_174
| ~ spl15_53
| ~ spl15_59 ),
inference(avatar_split_clause,[],[f612,f586,f545,f2312]) ).
fof(f2312,plain,
( spl15_174
<=> ! [X0,X3,X2,X1] :
( ~ subset(X0,X1)
| ~ in(X2,set_intersection2(X0,X3))
| in(X2,set_intersection2(X1,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_174])]) ).
fof(f612,plain,
( ! [X2,X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X2,set_intersection2(X0,X3))
| in(X2,set_intersection2(X1,X3)) )
| ~ spl15_53
| ~ spl15_59 ),
inference(resolution,[],[f587,f546]) ).
fof(f2310,plain,
( spl15_173
| ~ spl15_51
| ~ spl15_58 ),
inference(avatar_split_clause,[],[f600,f582,f531,f2308]) ).
fof(f600,plain,
( ! [X2,X3,X0,X1] :
( ~ subset(X0,X1)
| subset(X2,set_difference(X1,X3))
| ~ subset(X2,set_difference(X0,X3)) )
| ~ spl15_51
| ~ spl15_58 ),
inference(resolution,[],[f583,f532]) ).
fof(f2306,plain,
( spl15_172
| ~ spl15_53
| ~ spl15_58 ),
inference(avatar_split_clause,[],[f598,f582,f545,f2304]) ).
fof(f2304,plain,
( spl15_172
<=> ! [X0,X3,X2,X1] :
( ~ subset(X0,X1)
| ~ in(X2,set_difference(X0,X3))
| in(X2,set_difference(X1,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_172])]) ).
fof(f598,plain,
( ! [X2,X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X2,set_difference(X0,X3))
| in(X2,set_difference(X1,X3)) )
| ~ spl15_53
| ~ spl15_58 ),
inference(resolution,[],[f583,f546]) ).
fof(f2203,plain,
( spl15_171
| ~ spl15_17
| ~ spl15_80 ),
inference(avatar_split_clause,[],[f806,f763,f274,f2201]) ).
fof(f806,plain,
( ! [X2,X0,X1] :
( in(sK12(X0,X1,X2),X2)
| sP2(X0,X1,X2)
| ~ empty(X0) )
| ~ spl15_17
| ~ spl15_80 ),
inference(resolution,[],[f764,f275]) ).
fof(f2199,plain,
( spl15_170
| ~ spl15_17
| ~ spl15_80 ),
inference(avatar_split_clause,[],[f801,f763,f274,f2197]) ).
fof(f801,plain,
( ! [X2,X0,X1] :
( in(sK12(X0,X1,X2),X0)
| sP2(X0,X1,X2)
| ~ empty(X2) )
| ~ spl15_17
| ~ spl15_80 ),
inference(resolution,[],[f764,f275]) ).
fof(f2195,plain,
( spl15_169
| ~ spl15_17
| ~ spl15_79 ),
inference(avatar_split_clause,[],[f791,f759,f274,f2193]) ).
fof(f791,plain,
( ! [X2,X0,X1] :
( in(sK12(X0,X1,X2),X2)
| sP2(X0,X1,X2)
| ~ empty(X1) )
| ~ spl15_17
| ~ spl15_79 ),
inference(resolution,[],[f760,f275]) ).
fof(f2191,plain,
( spl15_168
| ~ spl15_17
| ~ spl15_79 ),
inference(avatar_split_clause,[],[f786,f759,f274,f2189]) ).
fof(f786,plain,
( ! [X2,X0,X1] :
( in(sK12(X0,X1,X2),X1)
| sP2(X0,X1,X2)
| ~ empty(X2) )
| ~ spl15_17
| ~ spl15_79 ),
inference(resolution,[],[f760,f275]) ).
fof(f2187,plain,
( spl15_167
| ~ spl15_17
| ~ spl15_74 ),
inference(avatar_split_clause,[],[f772,f739,f274,f2185]) ).
fof(f772,plain,
( ! [X2,X0,X1] :
( in(sK10(X0,X1,X2),X2)
| sP0(X0,X1,X2)
| ~ empty(X1) )
| ~ spl15_17
| ~ spl15_74 ),
inference(resolution,[],[f740,f275]) ).
fof(f2183,plain,
( spl15_166
| ~ spl15_17
| ~ spl15_74 ),
inference(avatar_split_clause,[],[f767,f739,f274,f2181]) ).
fof(f767,plain,
( ! [X2,X0,X1] :
( in(sK10(X0,X1,X2),X1)
| sP0(X0,X1,X2)
| ~ empty(X2) )
| ~ spl15_17
| ~ spl15_74 ),
inference(resolution,[],[f740,f275]) ).
fof(f2100,plain,
( spl15_165
| ~ spl15_42
| ~ spl15_59 ),
inference(avatar_split_clause,[],[f615,f586,f471,f2098]) ).
fof(f615,plain,
( ! [X2,X0,X1] :
( ~ subset(X0,X1)
| sK14 = set_difference(set_intersection2(X0,X2),set_intersection2(X1,X2)) )
| ~ spl15_42
| ~ spl15_59 ),
inference(resolution,[],[f587,f472]) ).
fof(f2096,plain,
( spl15_164
| ~ spl15_42
| ~ spl15_58 ),
inference(avatar_split_clause,[],[f601,f582,f471,f2094]) ).
fof(f601,plain,
( ! [X2,X0,X1] :
( ~ subset(X0,X1)
| sK14 = set_difference(set_difference(X0,X2),set_difference(X1,X2)) )
| ~ spl15_42
| ~ spl15_58 ),
inference(resolution,[],[f583,f472]) ).
fof(f2015,plain,
( spl15_163
| ~ spl15_27
| ~ spl15_73 ),
inference(avatar_split_clause,[],[f737,f714,f326,f2013]) ).
fof(f714,plain,
( spl15_73
<=> ! [X4,X0,X2,X1] :
( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1)
| ~ sP2(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_73])]) ).
fof(f737,plain,
( ! [X2,X0,X1] :
( ~ in(X0,X1)
| ~ in(X0,X2)
| in(X0,set_intersection2(X2,X1)) )
| ~ spl15_27
| ~ spl15_73 ),
inference(resolution,[],[f715,f327]) ).
fof(f715,plain,
( ! [X2,X0,X1,X4] :
( ~ sP2(X0,X1,X2)
| ~ in(X4,X0)
| ~ in(X4,X1)
| in(X4,X2) )
| ~ spl15_73 ),
inference(avatar_component_clause,[],[f714]) ).
fof(f2011,plain,
( spl15_162
| ~ spl15_26
| ~ spl15_72 ),
inference(avatar_split_clause,[],[f736,f706,f322,f2009]) ).
fof(f2009,plain,
( spl15_162
<=> ! [X2,X0,X1] :
( in(X0,X1)
| ~ in(X0,set_union2(X1,X2))
| in(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_162])]) ).
fof(f706,plain,
( spl15_72
<=> ! [X2,X4,X0,X1] :
( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2)
| ~ sP1(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_72])]) ).
fof(f736,plain,
( ! [X2,X0,X1] :
( in(X0,X1)
| ~ in(X0,set_union2(X1,X2))
| in(X0,X2) )
| ~ spl15_26
| ~ spl15_72 ),
inference(resolution,[],[f707,f323]) ).
fof(f707,plain,
( ! [X2,X0,X1,X4] :
( ~ sP1(X0,X1,X2)
| in(X4,X1)
| ~ in(X4,X2)
| in(X4,X0) )
| ~ spl15_72 ),
inference(avatar_component_clause,[],[f706]) ).
fof(f2007,plain,
( spl15_161
| ~ spl15_25
| ~ spl15_71 ),
inference(avatar_split_clause,[],[f735,f702,f318,f2005]) ).
fof(f702,plain,
( spl15_71
<=> ! [X4,X0,X2,X1] :
( in(X4,X2)
| in(X4,X0)
| ~ in(X4,X1)
| ~ sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_71])]) ).
fof(f735,plain,
( ! [X2,X0,X1] :
( in(X0,X1)
| ~ in(X0,X2)
| in(X0,set_difference(X2,X1)) )
| ~ spl15_25
| ~ spl15_71 ),
inference(resolution,[],[f703,f319]) ).
fof(f703,plain,
( ! [X2,X0,X1,X4] :
( ~ sP0(X0,X1,X2)
| in(X4,X0)
| ~ in(X4,X1)
| in(X4,X2) )
| ~ spl15_71 ),
inference(avatar_component_clause,[],[f702]) ).
fof(f1980,plain,
( spl15_160
| ~ spl15_20
| ~ spl15_68 ),
inference(avatar_split_clause,[],[f681,f667,f295,f1978]) ).
fof(f681,plain,
( ! [X0,X1] :
( ~ subset(X0,sK14)
| ~ subset(X1,sK14)
| set_union2(X1,X0) = sK14 )
| ~ spl15_20
| ~ spl15_68 ),
inference(resolution,[],[f668,f296]) ).
fof(f1868,plain,
( spl15_159
| ~ spl15_13
| ~ spl15_18 ),
inference(avatar_split_clause,[],[f335,f284,f258,f1866]) ).
fof(f1866,plain,
( spl15_159
<=> ! [X0] : set_union2(X0,sK14) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl15_159])]) ).
fof(f258,plain,
( spl15_13
<=> ! [X0] : set_union2(X0,empty_set) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl15_13])]) ).
fof(f335,plain,
( ! [X0] : set_union2(X0,sK14) = X0
| ~ spl15_13
| ~ spl15_18 ),
inference(superposition,[],[f259,f286]) ).
fof(f259,plain,
( ! [X0] : set_union2(X0,empty_set) = X0
| ~ spl15_13 ),
inference(avatar_component_clause,[],[f258]) ).
fof(f1810,plain,
( spl15_158
| ~ spl15_7
| ~ spl15_18
| ~ spl15_80 ),
inference(avatar_split_clause,[],[f814,f763,f284,f234,f1808]) ).
fof(f814,plain,
( ! [X0,X1] :
( sP2(sK14,X0,X1)
| in(sK12(sK14,X0,X1),X1) )
| ~ spl15_7
| ~ spl15_18
| ~ spl15_80 ),
inference(forward_demodulation,[],[f813,f286]) ).
fof(f813,plain,
( ! [X0,X1] :
( in(sK12(sK14,X0,X1),X1)
| sP2(empty_set,X0,X1) )
| ~ spl15_7
| ~ spl15_18
| ~ spl15_80 ),
inference(forward_demodulation,[],[f808,f286]) ).
fof(f808,plain,
( ! [X0,X1] :
( in(sK12(empty_set,X0,X1),X1)
| sP2(empty_set,X0,X1) )
| ~ spl15_7
| ~ spl15_80 ),
inference(resolution,[],[f764,f235]) ).
fof(f1806,plain,
( spl15_157
| ~ spl15_7
| ~ spl15_18
| ~ spl15_80 ),
inference(avatar_split_clause,[],[f812,f763,f284,f234,f1804]) ).
fof(f812,plain,
( ! [X0,X1] :
( sP2(X0,X1,sK14)
| in(sK12(X0,X1,sK14),X0) )
| ~ spl15_7
| ~ spl15_18
| ~ spl15_80 ),
inference(forward_demodulation,[],[f811,f286]) ).
fof(f811,plain,
( ! [X0,X1] :
( in(sK12(X0,X1,sK14),X0)
| sP2(X0,X1,empty_set) )
| ~ spl15_7
| ~ spl15_18
| ~ spl15_80 ),
inference(forward_demodulation,[],[f803,f286]) ).
fof(f803,plain,
( ! [X0,X1] :
( in(sK12(X0,X1,empty_set),X0)
| sP2(X0,X1,empty_set) )
| ~ spl15_7
| ~ spl15_80 ),
inference(resolution,[],[f764,f235]) ).
fof(f1802,plain,
( spl15_156
| ~ spl15_80 ),
inference(avatar_split_clause,[],[f810,f763,f1800]) ).
fof(f810,plain,
( ! [X0,X1] :
( in(sK12(X0,X1,X0),X0)
| sP2(X0,X1,X0) )
| ~ spl15_80 ),
inference(factoring,[],[f764]) ).
fof(f1798,plain,
( spl15_155
| ~ spl15_7
| ~ spl15_18
| ~ spl15_79 ),
inference(avatar_split_clause,[],[f799,f759,f284,f234,f1796]) ).
fof(f799,plain,
( ! [X0,X1] :
( sP2(X0,sK14,X1)
| in(sK12(X0,sK14,X1),X1) )
| ~ spl15_7
| ~ spl15_18
| ~ spl15_79 ),
inference(forward_demodulation,[],[f798,f286]) ).
fof(f798,plain,
( ! [X0,X1] :
( in(sK12(X0,sK14,X1),X1)
| sP2(X0,empty_set,X1) )
| ~ spl15_7
| ~ spl15_18
| ~ spl15_79 ),
inference(forward_demodulation,[],[f793,f286]) ).
fof(f793,plain,
( ! [X0,X1] :
( in(sK12(X0,empty_set,X1),X1)
| sP2(X0,empty_set,X1) )
| ~ spl15_7
| ~ spl15_79 ),
inference(resolution,[],[f760,f235]) ).
fof(f1794,plain,
( spl15_154
| ~ spl15_7
| ~ spl15_18
| ~ spl15_79 ),
inference(avatar_split_clause,[],[f797,f759,f284,f234,f1792]) ).
fof(f797,plain,
( ! [X0,X1] :
( sP2(X0,X1,sK14)
| in(sK12(X0,X1,sK14),X1) )
| ~ spl15_7
| ~ spl15_18
| ~ spl15_79 ),
inference(forward_demodulation,[],[f796,f286]) ).
fof(f796,plain,
( ! [X0,X1] :
( in(sK12(X0,X1,sK14),X1)
| sP2(X0,X1,empty_set) )
| ~ spl15_7
| ~ spl15_18
| ~ spl15_79 ),
inference(forward_demodulation,[],[f788,f286]) ).
fof(f788,plain,
( ! [X0,X1] :
( in(sK12(X0,X1,empty_set),X1)
| sP2(X0,X1,empty_set) )
| ~ spl15_7
| ~ spl15_79 ),
inference(resolution,[],[f760,f235]) ).
fof(f1790,plain,
( spl15_153
| ~ spl15_79 ),
inference(avatar_split_clause,[],[f795,f759,f1788]) ).
fof(f795,plain,
( ! [X0,X1] :
( in(sK12(X0,X1,X1),X1)
| sP2(X0,X1,X1) )
| ~ spl15_79 ),
inference(factoring,[],[f760]) ).
fof(f1786,plain,
( spl15_152
| ~ spl15_12
| ~ spl15_18 ),
inference(avatar_split_clause,[],[f334,f284,f254,f1784]) ).
fof(f1784,plain,
( spl15_152
<=> ! [X0] : set_difference(X0,sK14) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl15_152])]) ).
fof(f254,plain,
( spl15_12
<=> ! [X0] : set_difference(X0,empty_set) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl15_12])]) ).
fof(f334,plain,
( ! [X0] : set_difference(X0,sK14) = X0
| ~ spl15_12
| ~ spl15_18 ),
inference(superposition,[],[f255,f286]) ).
fof(f255,plain,
( ! [X0] : set_difference(X0,empty_set) = X0
| ~ spl15_12 ),
inference(avatar_component_clause,[],[f254]) ).
fof(f1782,plain,
( spl15_151
| ~ spl15_74
| ~ spl15_75 ),
inference(avatar_split_clause,[],[f784,f743,f739,f1780]) ).
fof(f743,plain,
( spl15_75
<=> ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ in(sK10(X0,X1,X2),X0)
| in(sK10(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_75])]) ).
fof(f784,plain,
( ! [X0,X1] :
( sP0(X0,X0,X1)
| in(sK10(X0,X0,X1),X1) )
| ~ spl15_74
| ~ spl15_75 ),
inference(duplicate_literal_removal,[],[f781]) ).
fof(f781,plain,
( ! [X0,X1] :
( sP0(X0,X0,X1)
| in(sK10(X0,X0,X1),X1)
| in(sK10(X0,X0,X1),X1)
| sP0(X0,X0,X1) )
| ~ spl15_74
| ~ spl15_75 ),
inference(resolution,[],[f744,f740]) ).
fof(f744,plain,
( ! [X2,X0,X1] :
( ~ in(sK10(X0,X1,X2),X0)
| sP0(X0,X1,X2)
| in(sK10(X0,X1,X2),X2) )
| ~ spl15_75 ),
inference(avatar_component_clause,[],[f743]) ).
fof(f1778,plain,
( spl15_150
| ~ spl15_7
| ~ spl15_18
| ~ spl15_74 ),
inference(avatar_split_clause,[],[f780,f739,f284,f234,f1776]) ).
fof(f780,plain,
( ! [X0,X1] :
( sP0(X0,sK14,X1)
| in(sK10(X0,sK14,X1),X1) )
| ~ spl15_7
| ~ spl15_18
| ~ spl15_74 ),
inference(forward_demodulation,[],[f779,f286]) ).
fof(f779,plain,
( ! [X0,X1] :
( in(sK10(X0,sK14,X1),X1)
| sP0(X0,empty_set,X1) )
| ~ spl15_7
| ~ spl15_18
| ~ spl15_74 ),
inference(forward_demodulation,[],[f774,f286]) ).
fof(f774,plain,
( ! [X0,X1] :
( in(sK10(X0,empty_set,X1),X1)
| sP0(X0,empty_set,X1) )
| ~ spl15_7
| ~ spl15_74 ),
inference(resolution,[],[f740,f235]) ).
fof(f1774,plain,
( spl15_149
| ~ spl15_7
| ~ spl15_18
| ~ spl15_74 ),
inference(avatar_split_clause,[],[f778,f739,f284,f234,f1772]) ).
fof(f778,plain,
( ! [X0,X1] :
( sP0(X0,X1,sK14)
| in(sK10(X0,X1,sK14),X1) )
| ~ spl15_7
| ~ spl15_18
| ~ spl15_74 ),
inference(forward_demodulation,[],[f777,f286]) ).
fof(f777,plain,
( ! [X0,X1] :
( in(sK10(X0,X1,sK14),X1)
| sP0(X0,X1,empty_set) )
| ~ spl15_7
| ~ spl15_18
| ~ spl15_74 ),
inference(forward_demodulation,[],[f769,f286]) ).
fof(f769,plain,
( ! [X0,X1] :
( in(sK10(X0,X1,empty_set),X1)
| sP0(X0,X1,empty_set) )
| ~ spl15_7
| ~ spl15_74 ),
inference(resolution,[],[f740,f235]) ).
fof(f1770,plain,
( spl15_148
| ~ spl15_74 ),
inference(avatar_split_clause,[],[f776,f739,f1768]) ).
fof(f776,plain,
( ! [X0,X1] :
( in(sK10(X0,X1,X1),X1)
| sP0(X0,X1,X1) )
| ~ spl15_74 ),
inference(factoring,[],[f740]) ).
fof(f1766,plain,
( spl15_147
| ~ spl15_17
| ~ spl15_69 ),
inference(avatar_split_clause,[],[f723,f694,f274,f1764]) ).
fof(f723,plain,
( ! [X0,X1] :
( in(sK8(X0,X1),X1)
| X0 = X1
| ~ empty(X0) )
| ~ spl15_17
| ~ spl15_69 ),
inference(resolution,[],[f695,f275]) ).
fof(f1762,plain,
( spl15_146
| ~ spl15_17
| ~ spl15_69 ),
inference(avatar_split_clause,[],[f718,f694,f274,f1760]) ).
fof(f718,plain,
( ! [X0,X1] :
( in(sK8(X0,X1),X0)
| X0 = X1
| ~ empty(X1) )
| ~ spl15_17
| ~ spl15_69 ),
inference(resolution,[],[f695,f275]) ).
fof(f1693,plain,
( spl15_145
| ~ spl15_11
| ~ spl15_18 ),
inference(avatar_split_clause,[],[f333,f284,f250,f1691]) ).
fof(f1691,plain,
( spl15_145
<=> ! [X0] : sK14 = set_intersection2(X0,sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_145])]) ).
fof(f250,plain,
( spl15_11
<=> ! [X0] : empty_set = set_intersection2(X0,empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_11])]) ).
fof(f333,plain,
( ! [X0] : sK14 = set_intersection2(X0,sK14)
| ~ spl15_11
| ~ spl15_18 ),
inference(superposition,[],[f251,f286]) ).
fof(f251,plain,
( ! [X0] : empty_set = set_intersection2(X0,empty_set)
| ~ spl15_11 ),
inference(avatar_component_clause,[],[f250]) ).
fof(f1660,plain,
( spl15_144
| ~ spl15_30
| ~ spl15_59 ),
inference(avatar_split_clause,[],[f624,f586,f360,f1658]) ).
fof(f624,plain,
( ! [X2,X0,X1] :
( subset(set_intersection2(X2,X1),set_intersection2(X1,X0))
| ~ subset(X2,X0) )
| ~ spl15_30
| ~ spl15_59 ),
inference(superposition,[],[f587,f361]) ).
fof(f1656,plain,
( spl15_143
| ~ spl15_30
| ~ spl15_59 ),
inference(avatar_split_clause,[],[f620,f586,f360,f1654]) ).
fof(f620,plain,
( ! [X2,X0,X1] :
( subset(set_intersection2(X1,X0),set_intersection2(X2,X1))
| ~ subset(X0,X2) )
| ~ spl15_30
| ~ spl15_59 ),
inference(superposition,[],[f587,f361]) ).
fof(f1652,plain,
( spl15_142
| ~ spl15_30
| ~ spl15_57 ),
inference(avatar_split_clause,[],[f594,f578,f360,f1650]) ).
fof(f1650,plain,
( spl15_142
<=> ! [X0,X1] :
( in(sK5(X0,X1),set_intersection2(X1,X0))
| disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_142])]) ).
fof(f594,plain,
( ! [X0,X1] :
( in(sK5(X0,X1),set_intersection2(X1,X0))
| disjoint(X0,X1) )
| ~ spl15_30
| ~ spl15_57 ),
inference(superposition,[],[f579,f361]) ).
fof(f1648,plain,
( spl15_141
| ~ spl15_24
| ~ spl15_57 ),
inference(avatar_split_clause,[],[f590,f578,f314,f1646]) ).
fof(f590,plain,
( ! [X0,X1] :
( disjoint(X0,X1)
| ~ in(set_intersection2(X0,X1),sK5(X0,X1)) )
| ~ spl15_24
| ~ spl15_57 ),
inference(resolution,[],[f579,f315]) ).
fof(f1644,plain,
( spl15_140
| ~ spl15_8
| ~ spl15_52 ),
inference(avatar_split_clause,[],[f564,f541,f238,f1642]) ).
fof(f564,plain,
( ! [X0,X1] :
( set_union2(X0,X1) = X0
| ~ subset(set_union2(X0,X1),X0) )
| ~ spl15_8
| ~ spl15_52 ),
inference(resolution,[],[f542,f239]) ).
fof(f1640,plain,
( spl15_139
| ~ spl15_9
| ~ spl15_52 ),
inference(avatar_split_clause,[],[f561,f541,f242,f1638]) ).
fof(f1638,plain,
( spl15_139
<=> ! [X0,X1] :
( set_intersection2(X0,X1) = X0
| ~ subset(X0,set_intersection2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_139])]) ).
fof(f561,plain,
( ! [X0,X1] :
( set_intersection2(X0,X1) = X0
| ~ subset(X0,set_intersection2(X0,X1)) )
| ~ spl15_9
| ~ spl15_52 ),
inference(resolution,[],[f542,f243]) ).
fof(f1577,plain,
( spl15_138
| ~ spl15_10
| ~ spl15_18 ),
inference(avatar_split_clause,[],[f332,f284,f246,f1575]) ).
fof(f1575,plain,
( spl15_138
<=> ! [X0] : sK14 = set_difference(sK14,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_138])]) ).
fof(f246,plain,
( spl15_10
<=> ! [X0] : empty_set = set_difference(empty_set,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_10])]) ).
fof(f332,plain,
( ! [X0] : sK14 = set_difference(sK14,X0)
| ~ spl15_10
| ~ spl15_18 ),
inference(superposition,[],[f247,f286]) ).
fof(f247,plain,
( ! [X0] : empty_set = set_difference(empty_set,X0)
| ~ spl15_10 ),
inference(avatar_component_clause,[],[f246]) ).
fof(f1573,plain,
( spl15_137
| ~ spl15_9
| ~ spl15_38 ),
inference(avatar_split_clause,[],[f461,f426,f242,f1571]) ).
fof(f461,plain,
( ! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(set_intersection2(X0,X1),X0)
| ~ spl15_9
| ~ spl15_38 ),
inference(resolution,[],[f427,f243]) ).
fof(f1569,plain,
( spl15_136
| ~ spl15_8
| ~ spl15_37 ),
inference(avatar_split_clause,[],[f458,f421,f238,f1567]) ).
fof(f458,plain,
( ! [X0,X1] : set_union2(X0,X1) = set_union2(X0,set_union2(X0,X1))
| ~ spl15_8
| ~ spl15_37 ),
inference(resolution,[],[f422,f239]) ).
fof(f1450,plain,
( spl15_135
| ~ spl15_7
| ~ spl15_18
| ~ spl15_69 ),
inference(avatar_split_clause,[],[f731,f694,f284,f234,f1448]) ).
fof(f731,plain,
( ! [X0] :
( sK14 = X0
| in(sK8(sK14,X0),X0) )
| ~ spl15_7
| ~ spl15_18
| ~ spl15_69 ),
inference(forward_demodulation,[],[f730,f286]) ).
fof(f730,plain,
( ! [X0] :
( in(sK8(sK14,X0),X0)
| empty_set = X0 )
| ~ spl15_7
| ~ spl15_18
| ~ spl15_69 ),
inference(forward_demodulation,[],[f725,f286]) ).
fof(f725,plain,
( ! [X0] :
( in(sK8(empty_set,X0),X0)
| empty_set = X0 )
| ~ spl15_7
| ~ spl15_69 ),
inference(resolution,[],[f695,f235]) ).
fof(f1446,plain,
( spl15_134
| ~ spl15_7
| ~ spl15_18
| ~ spl15_69 ),
inference(avatar_split_clause,[],[f729,f694,f284,f234,f1444]) ).
fof(f729,plain,
( ! [X0] :
( sK14 = X0
| in(sK8(X0,sK14),X0) )
| ~ spl15_7
| ~ spl15_18
| ~ spl15_69 ),
inference(forward_demodulation,[],[f728,f286]) ).
fof(f728,plain,
( ! [X0] :
( in(sK8(X0,sK14),X0)
| empty_set = X0 )
| ~ spl15_7
| ~ spl15_18
| ~ spl15_69 ),
inference(forward_demodulation,[],[f720,f286]) ).
fof(f720,plain,
( ! [X0] :
( in(sK8(X0,empty_set),X0)
| empty_set = X0 )
| ~ spl15_7
| ~ spl15_69 ),
inference(resolution,[],[f695,f235]) ).
fof(f1442,plain,
( spl15_133
| ~ spl15_27
| ~ spl15_65 ),
inference(avatar_split_clause,[],[f661,f649,f326,f1440]) ).
fof(f649,plain,
( spl15_65
<=> ! [X4,X0,X2,X1] :
( in(X4,X0)
| ~ in(X4,X2)
| ~ sP2(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_65])]) ).
fof(f661,plain,
( ! [X2,X0,X1] :
( ~ in(X0,set_intersection2(X1,X2))
| in(X0,X2) )
| ~ spl15_27
| ~ spl15_65 ),
inference(resolution,[],[f650,f327]) ).
fof(f650,plain,
( ! [X2,X0,X1,X4] :
( ~ sP2(X0,X1,X2)
| ~ in(X4,X2)
| in(X4,X0) )
| ~ spl15_65 ),
inference(avatar_component_clause,[],[f649]) ).
fof(f1438,plain,
( spl15_132
| ~ spl15_26
| ~ spl15_63 ),
inference(avatar_split_clause,[],[f655,f641,f322,f1436]) ).
fof(f641,plain,
( spl15_63
<=> ! [X4,X0,X2,X1] :
( in(X4,X2)
| ~ in(X4,X0)
| ~ sP1(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_63])]) ).
fof(f655,plain,
( ! [X2,X0,X1] :
( ~ in(X0,X1)
| in(X0,set_union2(X2,X1)) )
| ~ spl15_26
| ~ spl15_63 ),
inference(resolution,[],[f642,f323]) ).
fof(f642,plain,
( ! [X2,X0,X1,X4] :
( ~ sP1(X0,X1,X2)
| ~ in(X4,X0)
| in(X4,X2) )
| ~ spl15_63 ),
inference(avatar_component_clause,[],[f641]) ).
fof(f1434,plain,
( spl15_131
| ~ spl15_25
| ~ spl15_61 ),
inference(avatar_split_clause,[],[f653,f633,f318,f1432]) ).
fof(f633,plain,
( spl15_61
<=> ! [X4,X0,X2,X1] :
( ~ in(X4,X0)
| ~ in(X4,X2)
| ~ sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_61])]) ).
fof(f653,plain,
( ! [X2,X0,X1] :
( ~ in(X0,set_difference(X1,X2))
| ~ in(X0,X2) )
| ~ spl15_25
| ~ spl15_61 ),
inference(resolution,[],[f634,f319]) ).
fof(f634,plain,
( ! [X2,X0,X1,X4] :
( ~ sP0(X0,X1,X2)
| ~ in(X4,X2)
| ~ in(X4,X0) )
| ~ spl15_61 ),
inference(avatar_component_clause,[],[f633]) ).
fof(f1430,plain,
( spl15_130
| ~ spl15_25
| ~ spl15_60 ),
inference(avatar_split_clause,[],[f652,f629,f318,f1428]) ).
fof(f629,plain,
( spl15_60
<=> ! [X4,X0,X1,X2] :
( in(X4,X1)
| ~ in(X4,X2)
| ~ sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_60])]) ).
fof(f652,plain,
( ! [X2,X0,X1] :
( ~ in(X0,set_difference(X1,X2))
| in(X0,X1) )
| ~ spl15_25
| ~ spl15_60 ),
inference(resolution,[],[f630,f319]) ).
fof(f630,plain,
( ! [X2,X0,X1,X4] :
( ~ sP0(X0,X1,X2)
| ~ in(X4,X2)
| in(X4,X1) )
| ~ spl15_60 ),
inference(avatar_component_clause,[],[f629]) ).
fof(f1426,plain,
( spl15_129
| ~ spl15_30
| ~ spl15_48 ),
inference(avatar_split_clause,[],[f517,f506,f360,f1424]) ).
fof(f517,plain,
( ! [X0,X1] :
( set_intersection2(X1,X0) != sK14
| disjoint(X0,X1) )
| ~ spl15_30
| ~ spl15_48 ),
inference(superposition,[],[f507,f361]) ).
fof(f1422,plain,
( spl15_128
| ~ spl15_24
| ~ spl15_46 ),
inference(avatar_split_clause,[],[f510,f498,f314,f1420]) ).
fof(f1420,plain,
( spl15_128
<=> ! [X0,X1] :
( subset(X0,X1)
| ~ in(X0,sK9(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_128])]) ).
fof(f510,plain,
( ! [X0,X1] :
( subset(X0,X1)
| ~ in(X0,sK9(X0,X1)) )
| ~ spl15_24
| ~ spl15_46 ),
inference(resolution,[],[f499,f315]) ).
fof(f1389,plain,
( spl15_127
| ~ spl15_26
| ~ spl15_96 ),
inference(avatar_split_clause,[],[f1013,f996,f322,f1387]) ).
fof(f1387,plain,
( spl15_127
<=> ! [X0] : sP1(X0,sK14,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_127])]) ).
fof(f996,plain,
( spl15_96
<=> ! [X0] : set_union2(sK14,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl15_96])]) ).
fof(f1013,plain,
( ! [X0] : sP1(X0,sK14,X0)
| ~ spl15_26
| ~ spl15_96 ),
inference(superposition,[],[f323,f997]) ).
fof(f997,plain,
( ! [X0] : set_union2(sK14,X0) = X0
| ~ spl15_96 ),
inference(avatar_component_clause,[],[f996]) ).
fof(f1253,plain,
( spl15_126
| ~ spl15_16
| ~ spl15_59 ),
inference(avatar_split_clause,[],[f619,f586,f270,f1251]) ).
fof(f619,plain,
( ! [X0,X1] :
( subset(X0,set_intersection2(X1,X0))
| ~ subset(X0,X1) )
| ~ spl15_16
| ~ spl15_59 ),
inference(superposition,[],[f587,f271]) ).
fof(f1249,plain,
( spl15_125
| ~ spl15_10
| ~ spl15_18
| ~ spl15_58 ),
inference(avatar_split_clause,[],[f610,f582,f284,f246,f1247]) ).
fof(f610,plain,
( ! [X0,X1] :
( ~ subset(X1,sK14)
| subset(set_difference(X1,X0),sK14) )
| ~ spl15_10
| ~ spl15_18
| ~ spl15_58 ),
inference(forward_demodulation,[],[f609,f286]) ).
fof(f609,plain,
( ! [X0,X1] :
( subset(set_difference(X1,X0),sK14)
| ~ subset(X1,empty_set) )
| ~ spl15_10
| ~ spl15_18
| ~ spl15_58 ),
inference(forward_demodulation,[],[f606,f286]) ).
fof(f606,plain,
( ! [X0,X1] :
( subset(set_difference(X1,X0),empty_set)
| ~ subset(X1,empty_set) )
| ~ spl15_10
| ~ spl15_58 ),
inference(superposition,[],[f583,f247]) ).
fof(f1245,plain,
( spl15_124
| ~ spl15_16
| ~ spl15_57 ),
inference(avatar_split_clause,[],[f593,f578,f270,f1243]) ).
fof(f1243,plain,
( spl15_124
<=> ! [X0] :
( in(sK5(X0,X0),X0)
| disjoint(X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_124])]) ).
fof(f593,plain,
( ! [X0] :
( in(sK5(X0,X0),X0)
| disjoint(X0,X0) )
| ~ spl15_16
| ~ spl15_57 ),
inference(superposition,[],[f579,f271]) ).
fof(f1241,plain,
( spl15_123
| ~ spl15_8
| ~ spl15_53 ),
inference(avatar_split_clause,[],[f573,f545,f238,f1239]) ).
fof(f573,plain,
( ! [X2,X0,X1] :
( ~ in(X0,X1)
| in(X0,set_union2(X1,X2)) )
| ~ spl15_8
| ~ spl15_53 ),
inference(resolution,[],[f546,f239]) ).
fof(f1237,plain,
( spl15_122
| ~ spl15_9
| ~ spl15_53 ),
inference(avatar_split_clause,[],[f570,f545,f242,f1235]) ).
fof(f570,plain,
( ! [X2,X0,X1] :
( ~ in(X0,set_intersection2(X1,X2))
| in(X0,X1) )
| ~ spl15_9
| ~ spl15_53 ),
inference(resolution,[],[f546,f243]) ).
fof(f1233,plain,
( spl15_121
| ~ spl15_8
| ~ spl15_51 ),
inference(avatar_split_clause,[],[f538,f531,f238,f1231]) ).
fof(f538,plain,
( ! [X2,X0,X1] :
( subset(X0,set_union2(X1,X2))
| ~ subset(X0,X1) )
| ~ spl15_8
| ~ spl15_51 ),
inference(resolution,[],[f532,f239]) ).
fof(f1229,plain,
( spl15_120
| ~ spl15_9
| ~ spl15_51 ),
inference(avatar_split_clause,[],[f535,f531,f242,f1227]) ).
fof(f535,plain,
( ! [X2,X0,X1] :
( subset(X0,X1)
| ~ subset(X0,set_intersection2(X1,X2)) )
| ~ spl15_9
| ~ spl15_51 ),
inference(resolution,[],[f532,f243]) ).
fof(f1225,plain,
( spl15_119
| ~ spl15_34
| ~ spl15_46 ),
inference(avatar_split_clause,[],[f512,f498,f409,f1223]) ).
fof(f512,plain,
( ! [X2,X0,X1] :
( subset(set_intersection2(X0,X1),X2)
| ~ disjoint(X0,X1) )
| ~ spl15_34
| ~ spl15_46 ),
inference(resolution,[],[f499,f410]) ).
fof(f1221,plain,
( spl15_118
| ~ spl15_34
| ~ spl15_36 ),
inference(avatar_split_clause,[],[f452,f417,f409,f1219]) ).
fof(f452,plain,
( ! [X2,X0,X1] :
( disjoint(X0,set_intersection2(X1,X2))
| ~ disjoint(X1,X2) )
| ~ spl15_34
| ~ spl15_36 ),
inference(resolution,[],[f418,f410]) ).
fof(f1217,plain,
( spl15_117
| ~ spl15_25
| ~ spl15_94 ),
inference(avatar_split_clause,[],[f993,f938,f318,f1215]) ).
fof(f1215,plain,
( spl15_117
<=> ! [X0] : sP0(X0,X0,sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_117])]) ).
fof(f993,plain,
( ! [X0] : sP0(X0,X0,sK14)
| ~ spl15_25
| ~ spl15_94 ),
inference(superposition,[],[f319,f939]) ).
fof(f1213,plain,
( spl15_116
| ~ spl15_24
| ~ spl15_36 ),
inference(avatar_split_clause,[],[f450,f417,f314,f1211]) ).
fof(f1211,plain,
( spl15_116
<=> ! [X0,X1] :
( disjoint(X0,X1)
| ~ in(X1,sK6(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_116])]) ).
fof(f450,plain,
( ! [X0,X1] :
( disjoint(X0,X1)
| ~ in(X1,sK6(X0,X1)) )
| ~ spl15_24
| ~ spl15_36 ),
inference(resolution,[],[f418,f315]) ).
fof(f1209,plain,
( spl15_115
| ~ spl15_34
| ~ spl15_35 ),
inference(avatar_split_clause,[],[f447,f413,f409,f1207]) ).
fof(f447,plain,
( ! [X2,X0,X1] :
( disjoint(set_intersection2(X0,X1),X2)
| ~ disjoint(X0,X1) )
| ~ spl15_34
| ~ spl15_35 ),
inference(resolution,[],[f414,f410]) ).
fof(f1205,plain,
( spl15_114
| ~ spl15_24
| ~ spl15_35 ),
inference(avatar_split_clause,[],[f445,f413,f314,f1203]) ).
fof(f1203,plain,
( spl15_114
<=> ! [X0,X1] :
( disjoint(X0,X1)
| ~ in(X0,sK6(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_114])]) ).
fof(f445,plain,
( ! [X0,X1] :
( disjoint(X0,X1)
| ~ in(X0,sK6(X0,X1)) )
| ~ spl15_24
| ~ spl15_35 ),
inference(resolution,[],[f414,f315]) ).
fof(f1201,plain,
( spl15_113
| ~ spl15_30
| ~ spl15_34 ),
inference(avatar_split_clause,[],[f442,f409,f360,f1199]) ).
fof(f442,plain,
( ! [X2,X0,X1] :
( ~ in(X2,set_intersection2(X1,X0))
| ~ disjoint(X0,X1) )
| ~ spl15_30
| ~ spl15_34 ),
inference(superposition,[],[f410,f361]) ).
fof(f1197,plain,
( spl15_112
| ~ spl15_33
| ~ spl15_34 ),
inference(avatar_split_clause,[],[f439,f409,f372,f1195]) ).
fof(f439,plain,
( ! [X0,X1] :
( ~ disjoint(X0,X1)
| set_intersection2(X0,X1) = sK14 )
| ~ spl15_33
| ~ spl15_34 ),
inference(resolution,[],[f410,f373]) ).
fof(f1193,plain,
( spl15_111
| ~ spl15_24
| ~ spl15_33 ),
inference(avatar_split_clause,[],[f406,f372,f314,f1191]) ).
fof(f1191,plain,
( spl15_111
<=> ! [X0] :
( sK14 = X0
| ~ in(X0,sK7(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_111])]) ).
fof(f406,plain,
( ! [X0] :
( sK14 = X0
| ~ in(X0,sK7(X0)) )
| ~ spl15_24
| ~ spl15_33 ),
inference(resolution,[],[f373,f315]) ).
fof(f1116,plain,
( spl15_110
| ~ spl15_17
| ~ spl15_57 ),
inference(avatar_split_clause,[],[f591,f578,f274,f1114]) ).
fof(f591,plain,
( ! [X0,X1] :
( disjoint(X0,X1)
| ~ empty(set_intersection2(X0,X1)) )
| ~ spl15_17
| ~ spl15_57 ),
inference(resolution,[],[f579,f275]) ).
fof(f1112,plain,
( spl15_109
| ~ spl15_8
| ~ spl15_42 ),
inference(avatar_split_clause,[],[f485,f471,f238,f1110]) ).
fof(f485,plain,
( ! [X0,X1] : sK14 = set_difference(X0,set_union2(X0,X1))
| ~ spl15_8
| ~ spl15_42 ),
inference(resolution,[],[f472,f239]) ).
fof(f1108,plain,
( spl15_108
| ~ spl15_9
| ~ spl15_42 ),
inference(avatar_split_clause,[],[f482,f471,f242,f1106]) ).
fof(f482,plain,
( ! [X0,X1] : sK14 = set_difference(set_intersection2(X0,X1),X0)
| ~ spl15_9
| ~ spl15_42 ),
inference(resolution,[],[f472,f243]) ).
fof(f1104,plain,
( spl15_107
| ~ spl15_8
| ~ spl15_38 ),
inference(avatar_split_clause,[],[f464,f426,f238,f1102]) ).
fof(f464,plain,
( ! [X0,X1] : set_intersection2(X0,set_union2(X0,X1)) = X0
| ~ spl15_8
| ~ spl15_38 ),
inference(resolution,[],[f427,f239]) ).
fof(f1100,plain,
( spl15_106
| ~ spl15_9
| ~ spl15_37 ),
inference(avatar_split_clause,[],[f455,f421,f242,f1098]) ).
fof(f455,plain,
( ! [X0,X1] : set_union2(set_intersection2(X0,X1),X0) = X0
| ~ spl15_9
| ~ spl15_37 ),
inference(resolution,[],[f422,f243]) ).
fof(f1075,plain,
( ~ spl15_105
| spl15_1
| ~ spl15_98 ),
inference(avatar_split_clause,[],[f1025,f1004,f206,f1072]) ).
fof(f1072,plain,
( spl15_105
<=> empty(set_difference(sK3,sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_105])]) ).
fof(f1025,plain,
( ~ empty(set_difference(sK3,sK4))
| spl15_1
| ~ spl15_98 ),
inference(resolution,[],[f1005,f208]) ).
fof(f1070,plain,
( spl15_104
| ~ spl15_16
| ~ spl15_48 ),
inference(avatar_split_clause,[],[f516,f506,f270,f1068]) ).
fof(f1068,plain,
( spl15_104
<=> ! [X0] :
( sK14 != X0
| disjoint(X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_104])]) ).
fof(f516,plain,
( ! [X0] :
( sK14 != X0
| disjoint(X0,X0) )
| ~ spl15_16
| ~ spl15_48 ),
inference(superposition,[],[f507,f271]) ).
fof(f1066,plain,
( spl15_103
| ~ spl15_27
| ~ spl15_30 ),
inference(avatar_split_clause,[],[f393,f360,f326,f1064]) ).
fof(f393,plain,
( ! [X0,X1] : sP2(X1,X0,set_intersection2(X1,X0))
| ~ spl15_27
| ~ spl15_30 ),
inference(superposition,[],[f327,f361]) ).
fof(f1062,plain,
( spl15_102
| ~ spl15_26
| ~ spl15_29 ),
inference(avatar_split_clause,[],[f377,f356,f322,f1060]) ).
fof(f377,plain,
( ! [X0,X1] : sP1(X1,X0,set_union2(X1,X0))
| ~ spl15_26
| ~ spl15_29 ),
inference(superposition,[],[f323,f357]) ).
fof(f1044,plain,
( spl15_101
| ~ spl15_5
| ~ spl15_18
| ~ spl15_51 ),
inference(avatar_split_clause,[],[f539,f531,f284,f226,f1042]) ).
fof(f226,plain,
( spl15_5
<=> ! [X0] : subset(empty_set,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_5])]) ).
fof(f539,plain,
( ! [X0,X1] :
( ~ subset(X0,sK14)
| subset(X0,X1) )
| ~ spl15_5
| ~ spl15_18
| ~ spl15_51 ),
inference(forward_demodulation,[],[f536,f286]) ).
fof(f536,plain,
( ! [X0,X1] :
( subset(X0,X1)
| ~ subset(X0,empty_set) )
| ~ spl15_5
| ~ spl15_51 ),
inference(resolution,[],[f532,f227]) ).
fof(f227,plain,
( ! [X0] : subset(empty_set,X0)
| ~ spl15_5 ),
inference(avatar_component_clause,[],[f226]) ).
fof(f1040,plain,
( spl15_100
| ~ spl15_12
| ~ spl15_18
| ~ spl15_41 ),
inference(avatar_split_clause,[],[f480,f467,f284,f254,f1038]) ).
fof(f1038,plain,
( spl15_100
<=> ! [X0] :
( subset(X0,sK14)
| sK14 != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_100])]) ).
fof(f467,plain,
( spl15_41
<=> ! [X0,X1] :
( set_difference(X0,X1) != sK14
| subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_41])]) ).
fof(f480,plain,
( ! [X0] :
( subset(X0,sK14)
| sK14 != X0 )
| ~ spl15_12
| ~ spl15_18
| ~ spl15_41 ),
inference(forward_demodulation,[],[f479,f286]) ).
fof(f479,plain,
( ! [X0] :
( sK14 != X0
| subset(X0,empty_set) )
| ~ spl15_12
| ~ spl15_41 ),
inference(superposition,[],[f468,f255]) ).
fof(f468,plain,
( ! [X0,X1] :
( set_difference(X0,X1) != sK14
| subset(X0,X1) )
| ~ spl15_41 ),
inference(avatar_component_clause,[],[f467]) ).
fof(f1036,plain,
( spl15_99
| ~ spl15_16
| ~ spl15_34 ),
inference(avatar_split_clause,[],[f441,f409,f270,f1034]) ).
fof(f1034,plain,
( spl15_99
<=> ! [X0,X1] :
( ~ in(X1,X0)
| ~ disjoint(X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_99])]) ).
fof(f441,plain,
( ! [X0,X1] :
( ~ in(X1,X0)
| ~ disjoint(X0,X0) )
| ~ spl15_16
| ~ spl15_34 ),
inference(superposition,[],[f410,f271]) ).
fof(f1006,plain,
( spl15_98
| ~ spl15_17
| ~ spl15_46 ),
inference(avatar_split_clause,[],[f511,f498,f274,f1004]) ).
fof(f511,plain,
( ! [X0,X1] :
( subset(X0,X1)
| ~ empty(X0) )
| ~ spl15_17
| ~ spl15_46 ),
inference(resolution,[],[f499,f275]) ).
fof(f1002,plain,
( spl15_97
| ~ spl15_4
| ~ spl15_32 ),
inference(avatar_split_clause,[],[f404,f368,f221,f1000]) ).
fof(f1000,plain,
( spl15_97
<=> ! [X0] :
( sK14 = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_97])]) ).
fof(f221,plain,
( spl15_4
<=> empty(sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_4])]) ).
fof(f368,plain,
( spl15_32
<=> ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_32])]) ).
fof(f404,plain,
( ! [X0] :
( sK14 = X0
| ~ empty(X0) )
| ~ spl15_4
| ~ spl15_32 ),
inference(resolution,[],[f369,f223]) ).
fof(f223,plain,
( empty(sK14)
| ~ spl15_4 ),
inference(avatar_component_clause,[],[f221]) ).
fof(f369,plain,
( ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) )
| ~ spl15_32 ),
inference(avatar_component_clause,[],[f368]) ).
fof(f998,plain,
( spl15_96
| ~ spl15_13
| ~ spl15_18
| ~ spl15_29 ),
inference(avatar_split_clause,[],[f387,f356,f284,f258,f996]) ).
fof(f387,plain,
( ! [X0] : set_union2(sK14,X0) = X0
| ~ spl15_13
| ~ spl15_18
| ~ spl15_29 ),
inference(forward_demodulation,[],[f375,f286]) ).
fof(f375,plain,
( ! [X0] : set_union2(empty_set,X0) = X0
| ~ spl15_13
| ~ spl15_29 ),
inference(superposition,[],[f357,f259]) ).
fof(f959,plain,
( spl15_95
| ~ spl15_27
| ~ spl15_89 ),
inference(avatar_split_clause,[],[f945,f918,f326,f957]) ).
fof(f957,plain,
( spl15_95
<=> ! [X0] : sP2(X0,sK14,sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_95])]) ).
fof(f918,plain,
( spl15_89
<=> ! [X0] : sK14 = set_intersection2(sK14,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_89])]) ).
fof(f945,plain,
( ! [X0] : sP2(X0,sK14,sK14)
| ~ spl15_27
| ~ spl15_89 ),
inference(superposition,[],[f327,f919]) ).
fof(f919,plain,
( ! [X0] : sK14 = set_intersection2(sK14,X0)
| ~ spl15_89 ),
inference(avatar_component_clause,[],[f918]) ).
fof(f940,plain,
( spl15_94
| ~ spl15_6
| ~ spl15_42 ),
inference(avatar_split_clause,[],[f481,f471,f230,f938]) ).
fof(f481,plain,
( ! [X0] : sK14 = set_difference(X0,X0)
| ~ spl15_6
| ~ spl15_42 ),
inference(resolution,[],[f472,f231]) ).
fof(f936,plain,
( spl15_93
| ~ spl15_17
| ~ spl15_36 ),
inference(avatar_split_clause,[],[f451,f417,f274,f934]) ).
fof(f451,plain,
( ! [X0,X1] :
( disjoint(X0,X1)
| ~ empty(X1) )
| ~ spl15_17
| ~ spl15_36 ),
inference(resolution,[],[f418,f275]) ).
fof(f932,plain,
( spl15_92
| ~ spl15_17
| ~ spl15_35 ),
inference(avatar_split_clause,[],[f446,f413,f274,f930]) ).
fof(f446,plain,
( ! [X0,X1] :
( disjoint(X0,X1)
| ~ empty(X0) )
| ~ spl15_17
| ~ spl15_35 ),
inference(resolution,[],[f414,f275]) ).
fof(f928,plain,
( spl15_91
| ~ spl15_9
| ~ spl15_30 ),
inference(avatar_split_clause,[],[f394,f360,f242,f926]) ).
fof(f394,plain,
( ! [X0,X1] : subset(set_intersection2(X1,X0),X0)
| ~ spl15_9
| ~ spl15_30 ),
inference(superposition,[],[f243,f361]) ).
fof(f924,plain,
( spl15_90
| ~ spl15_8
| ~ spl15_29 ),
inference(avatar_split_clause,[],[f380,f356,f238,f922]) ).
fof(f380,plain,
( ! [X0,X1] : subset(X0,set_union2(X1,X0))
| ~ spl15_8
| ~ spl15_29 ),
inference(superposition,[],[f239,f357]) ).
fof(f920,plain,
( spl15_89
| ~ spl15_9
| ~ spl15_20 ),
inference(avatar_split_clause,[],[f300,f295,f242,f918]) ).
fof(f300,plain,
( ! [X0] : sK14 = set_intersection2(sK14,X0)
| ~ spl15_9
| ~ spl15_20 ),
inference(resolution,[],[f296,f243]) ).
fof(f890,plain,
( spl15_88
| ~ spl15_11
| ~ spl15_18
| ~ spl15_27 ),
inference(avatar_split_clause,[],[f349,f326,f284,f250,f888]) ).
fof(f888,plain,
( spl15_88
<=> ! [X0] : sP2(sK14,X0,sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_88])]) ).
fof(f349,plain,
( ! [X0] : sP2(sK14,X0,sK14)
| ~ spl15_11
| ~ spl15_18
| ~ spl15_27 ),
inference(forward_demodulation,[],[f347,f286]) ).
fof(f347,plain,
( ! [X0] : sP2(empty_set,X0,empty_set)
| ~ spl15_11
| ~ spl15_27 ),
inference(superposition,[],[f327,f251]) ).
fof(f886,plain,
( spl15_87
| ~ spl15_16
| ~ spl15_27 ),
inference(avatar_split_clause,[],[f348,f326,f270,f884]) ).
fof(f884,plain,
( spl15_87
<=> ! [X0] : sP2(X0,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_87])]) ).
fof(f348,plain,
( ! [X0] : sP2(X0,X0,X0)
| ~ spl15_16
| ~ spl15_27 ),
inference(superposition,[],[f327,f271]) ).
fof(f882,plain,
( spl15_86
| ~ spl15_13
| ~ spl15_18
| ~ spl15_26 ),
inference(avatar_split_clause,[],[f346,f322,f284,f258,f880]) ).
fof(f880,plain,
( spl15_86
<=> ! [X0] : sP1(sK14,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_86])]) ).
fof(f346,plain,
( ! [X0] : sP1(sK14,X0,X0)
| ~ spl15_13
| ~ spl15_18
| ~ spl15_26 ),
inference(forward_demodulation,[],[f344,f286]) ).
fof(f344,plain,
( ! [X0] : sP1(empty_set,X0,X0)
| ~ spl15_13
| ~ spl15_26 ),
inference(superposition,[],[f323,f259]) ).
fof(f878,plain,
( spl15_85
| ~ spl15_15
| ~ spl15_26 ),
inference(avatar_split_clause,[],[f345,f322,f266,f876]) ).
fof(f876,plain,
( spl15_85
<=> ! [X0] : sP1(X0,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_85])]) ).
fof(f266,plain,
( spl15_15
<=> ! [X0] : set_union2(X0,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl15_15])]) ).
fof(f345,plain,
( ! [X0] : sP1(X0,X0,X0)
| ~ spl15_15
| ~ spl15_26 ),
inference(superposition,[],[f323,f267]) ).
fof(f267,plain,
( ! [X0] : set_union2(X0,X0) = X0
| ~ spl15_15 ),
inference(avatar_component_clause,[],[f266]) ).
fof(f830,plain,
spl15_84,
inference(avatar_split_clause,[],[f194,f828]) ).
fof(f828,plain,
( spl15_84
<=> ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| ~ in(sK12(X0,X1,X2),X0)
| ~ in(sK12(X0,X1,X2),X1)
| ~ in(sK12(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_84])]) ).
fof(f194,plain,
! [X2,X0,X1] :
( sP2(X0,X1,X2)
| ~ in(sK12(X0,X1,X2),X0)
| ~ in(sK12(X0,X1,X2),X1)
| ~ in(sK12(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f119]) ).
fof(f119,plain,
! [X0,X1,X2] :
( ( sP2(X0,X1,X2)
| ( ( ~ in(sK12(X0,X1,X2),X0)
| ~ in(sK12(X0,X1,X2),X1)
| ~ in(sK12(X0,X1,X2),X2) )
& ( ( in(sK12(X0,X1,X2),X0)
& in(sK12(X0,X1,X2),X1) )
| in(sK12(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1) )
& ( ( in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| ~ sP2(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f117,f118]) ).
fof(f118,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) )
=> ( ( ~ in(sK12(X0,X1,X2),X0)
| ~ in(sK12(X0,X1,X2),X1)
| ~ in(sK12(X0,X1,X2),X2) )
& ( ( in(sK12(X0,X1,X2),X0)
& in(sK12(X0,X1,X2),X1) )
| in(sK12(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f117,plain,
! [X0,X1,X2] :
( ( sP2(X0,X1,X2)
| ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1) )
& ( ( in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| ~ sP2(X0,X1,X2) ) ),
inference(rectify,[],[f116]) ).
fof(f116,plain,
! [X1,X0,X2] :
( ( sP2(X1,X0,X2)
| ? [X3] :
( ( ~ in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) )
& ( ( in(X3,X1)
& in(X3,X0) )
| ~ in(X3,X2) ) )
| ~ sP2(X1,X0,X2) ) ),
inference(flattening,[],[f115]) ).
fof(f115,plain,
! [X1,X0,X2] :
( ( sP2(X1,X0,X2)
| ? [X3] :
( ( ~ in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) )
& ( ( in(X3,X1)
& in(X3,X0) )
| ~ in(X3,X2) ) )
| ~ sP2(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f80]) ).
fof(f80,plain,
! [X1,X0,X2] :
( sP2(X1,X0,X2)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
& in(X3,X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f826,plain,
( spl15_83
| ~ spl15_12
| ~ spl15_18
| ~ spl15_25 ),
inference(avatar_split_clause,[],[f343,f318,f284,f254,f824]) ).
fof(f824,plain,
( spl15_83
<=> ! [X0] : sP0(sK14,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_83])]) ).
fof(f343,plain,
( ! [X0] : sP0(sK14,X0,X0)
| ~ spl15_12
| ~ spl15_18
| ~ spl15_25 ),
inference(forward_demodulation,[],[f341,f286]) ).
fof(f341,plain,
( ! [X0] : sP0(empty_set,X0,X0)
| ~ spl15_12
| ~ spl15_25 ),
inference(superposition,[],[f319,f255]) ).
fof(f822,plain,
spl15_82,
inference(avatar_split_clause,[],[f184,f820]) ).
fof(f184,plain,
! [X2,X0,X1] :
( sP1(X0,X1,X2)
| in(sK11(X0,X1,X2),X0)
| in(sK11(X0,X1,X2),X1)
| in(sK11(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f113]) ).
fof(f113,plain,
! [X0,X1,X2] :
( ( sP1(X0,X1,X2)
| ( ( ( ~ in(sK11(X0,X1,X2),X0)
& ~ in(sK11(X0,X1,X2),X1) )
| ~ in(sK11(X0,X1,X2),X2) )
& ( in(sK11(X0,X1,X2),X0)
| in(sK11(X0,X1,X2),X1)
| in(sK11(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( ~ in(X4,X0)
& ~ in(X4,X1) ) )
& ( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2) ) )
| ~ sP1(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f111,f112]) ).
fof(f112,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ( ~ in(X3,X0)
& ~ in(X3,X1) )
| ~ in(X3,X2) )
& ( in(X3,X0)
| in(X3,X1)
| in(X3,X2) ) )
=> ( ( ( ~ in(sK11(X0,X1,X2),X0)
& ~ in(sK11(X0,X1,X2),X1) )
| ~ in(sK11(X0,X1,X2),X2) )
& ( in(sK11(X0,X1,X2),X0)
| in(sK11(X0,X1,X2),X1)
| in(sK11(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f111,plain,
! [X0,X1,X2] :
( ( sP1(X0,X1,X2)
| ? [X3] :
( ( ( ~ in(X3,X0)
& ~ in(X3,X1) )
| ~ in(X3,X2) )
& ( in(X3,X0)
| in(X3,X1)
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( ~ in(X4,X0)
& ~ in(X4,X1) ) )
& ( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2) ) )
| ~ sP1(X0,X1,X2) ) ),
inference(rectify,[],[f110]) ).
fof(f110,plain,
! [X1,X0,X2] :
( ( sP1(X1,X0,X2)
| ? [X3] :
( ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| ~ in(X3,X2) )
& ( in(X3,X1)
| in(X3,X0)
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) )
& ( in(X3,X1)
| in(X3,X0)
| ~ in(X3,X2) ) )
| ~ sP1(X1,X0,X2) ) ),
inference(flattening,[],[f109]) ).
fof(f109,plain,
! [X1,X0,X2] :
( ( sP1(X1,X0,X2)
| ? [X3] :
( ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| ~ in(X3,X2) )
& ( in(X3,X1)
| in(X3,X0)
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) )
& ( in(X3,X1)
| in(X3,X0)
| ~ in(X3,X2) ) )
| ~ sP1(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f78]) ).
fof(f78,plain,
! [X1,X0,X2] :
( sP1(X1,X0,X2)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
| in(X3,X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f818,plain,
spl15_81,
inference(avatar_split_clause,[],[f178,f816]) ).
fof(f816,plain,
( spl15_81
<=> ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| in(sK10(X0,X1,X2),X0)
| ~ in(sK10(X0,X1,X2),X1)
| ~ in(sK10(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_81])]) ).
fof(f178,plain,
! [X2,X0,X1] :
( sP0(X0,X1,X2)
| in(sK10(X0,X1,X2),X0)
| ~ in(sK10(X0,X1,X2),X1)
| ~ in(sK10(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f107]) ).
fof(f107,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ( ( in(sK10(X0,X1,X2),X0)
| ~ in(sK10(X0,X1,X2),X1)
| ~ in(sK10(X0,X1,X2),X2) )
& ( ( ~ in(sK10(X0,X1,X2),X0)
& in(sK10(X0,X1,X2),X1) )
| in(sK10(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| in(X4,X0)
| ~ in(X4,X1) )
& ( ( ~ in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f105,f106]) ).
fof(f106,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( ~ in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) )
=> ( ( in(sK10(X0,X1,X2),X0)
| ~ in(sK10(X0,X1,X2),X1)
| ~ in(sK10(X0,X1,X2),X2) )
& ( ( ~ in(sK10(X0,X1,X2),X0)
& in(sK10(X0,X1,X2),X1) )
| in(sK10(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f105,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ? [X3] :
( ( in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( ~ in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| in(X4,X0)
| ~ in(X4,X1) )
& ( ( ~ in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(rectify,[],[f104]) ).
fof(f104,plain,
! [X1,X0,X2] :
( ( sP0(X1,X0,X2)
| ? [X3] :
( ( in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| in(X3,X1)
| ~ in(X3,X0) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| ~ in(X3,X2) ) )
| ~ sP0(X1,X0,X2) ) ),
inference(flattening,[],[f103]) ).
fof(f103,plain,
! [X1,X0,X2] :
( ( sP0(X1,X0,X2)
| ? [X3] :
( ( in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| in(X3,X1)
| ~ in(X3,X0) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| ~ in(X3,X2) ) )
| ~ sP0(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f76]) ).
fof(f76,plain,
! [X1,X0,X2] :
( sP0(X1,X0,X2)
<=> ! [X3] :
( in(X3,X2)
<=> ( ~ in(X3,X1)
& in(X3,X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f765,plain,
spl15_80,
inference(avatar_split_clause,[],[f193,f763]) ).
fof(f193,plain,
! [X2,X0,X1] :
( sP2(X0,X1,X2)
| in(sK12(X0,X1,X2),X0)
| in(sK12(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f119]) ).
fof(f761,plain,
spl15_79,
inference(avatar_split_clause,[],[f192,f759]) ).
fof(f192,plain,
! [X2,X0,X1] :
( sP2(X0,X1,X2)
| in(sK12(X0,X1,X2),X1)
| in(sK12(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f119]) ).
fof(f757,plain,
( spl15_78
| ~ spl15_10
| ~ spl15_18
| ~ spl15_25 ),
inference(avatar_split_clause,[],[f342,f318,f284,f246,f755]) ).
fof(f755,plain,
( spl15_78
<=> ! [X0] : sP0(X0,sK14,sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_78])]) ).
fof(f342,plain,
( ! [X0] : sP0(X0,sK14,sK14)
| ~ spl15_10
| ~ spl15_18
| ~ spl15_25 ),
inference(forward_demodulation,[],[f340,f286]) ).
fof(f340,plain,
( ! [X0] : sP0(X0,empty_set,empty_set)
| ~ spl15_10
| ~ spl15_25 ),
inference(superposition,[],[f319,f247]) ).
fof(f753,plain,
spl15_77,
inference(avatar_split_clause,[],[f186,f751]) ).
fof(f751,plain,
( spl15_77
<=> ! [X2,X0,X1] :
( sP1(X0,X1,X2)
| ~ in(sK11(X0,X1,X2),X0)
| ~ in(sK11(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_77])]) ).
fof(f186,plain,
! [X2,X0,X1] :
( sP1(X0,X1,X2)
| ~ in(sK11(X0,X1,X2),X0)
| ~ in(sK11(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f113]) ).
fof(f749,plain,
spl15_76,
inference(avatar_split_clause,[],[f185,f747]) ).
fof(f747,plain,
( spl15_76
<=> ! [X2,X0,X1] :
( sP1(X0,X1,X2)
| ~ in(sK11(X0,X1,X2),X1)
| ~ in(sK11(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_76])]) ).
fof(f185,plain,
! [X2,X0,X1] :
( sP1(X0,X1,X2)
| ~ in(sK11(X0,X1,X2),X1)
| ~ in(sK11(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f113]) ).
fof(f745,plain,
spl15_75,
inference(avatar_split_clause,[],[f177,f743]) ).
fof(f177,plain,
! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ in(sK10(X0,X1,X2),X0)
| in(sK10(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f107]) ).
fof(f741,plain,
spl15_74,
inference(avatar_split_clause,[],[f176,f739]) ).
fof(f176,plain,
! [X2,X0,X1] :
( sP0(X0,X1,X2)
| in(sK10(X0,X1,X2),X1)
| in(sK10(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f107]) ).
fof(f716,plain,
spl15_73,
inference(avatar_split_clause,[],[f191,f714]) ).
fof(f191,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1)
| ~ sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f119]) ).
fof(f708,plain,
spl15_72,
inference(avatar_split_clause,[],[f181,f706]) ).
fof(f181,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2)
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f113]) ).
fof(f704,plain,
spl15_71,
inference(avatar_split_clause,[],[f175,f702]) ).
fof(f175,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| in(X4,X0)
| ~ in(X4,X1)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f107]) ).
fof(f700,plain,
spl15_70,
inference(avatar_split_clause,[],[f162,f698]) ).
fof(f698,plain,
( spl15_70
<=> ! [X0,X1] :
( X0 = X1
| ~ in(sK8(X0,X1),X1)
| ~ in(sK8(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_70])]) ).
fof(f162,plain,
! [X0,X1] :
( X0 = X1
| ~ in(sK8(X0,X1),X1)
| ~ in(sK8(X0,X1),X0) ),
inference(cnf_transformation,[],[f95]) ).
fof(f95,plain,
! [X0,X1] :
( X0 = X1
| ( ( ~ in(sK8(X0,X1),X1)
| ~ in(sK8(X0,X1),X0) )
& ( in(sK8(X0,X1),X1)
| in(sK8(X0,X1),X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f93,f94]) ).
fof(f94,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ in(X2,X1)
| ~ in(X2,X0) )
& ( in(X2,X1)
| in(X2,X0) ) )
=> ( ( ~ in(sK8(X0,X1),X1)
| ~ in(sK8(X0,X1),X0) )
& ( in(sK8(X0,X1),X1)
| in(sK8(X0,X1),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f93,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( ( ~ in(X2,X1)
| ~ in(X2,X0) )
& ( in(X2,X1)
| in(X2,X0) ) ) ),
inference(nnf_transformation,[],[f72]) ).
fof(f72,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( in(X2,X0)
<~> in(X2,X1) ) ),
inference(ennf_transformation,[],[f33]) ).
fof(f33,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
<=> in(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
fof(f696,plain,
spl15_69,
inference(avatar_split_clause,[],[f161,f694]) ).
fof(f161,plain,
! [X0,X1] :
( X0 = X1
| in(sK8(X0,X1),X1)
| in(sK8(X0,X1),X0) ),
inference(cnf_transformation,[],[f95]) ).
fof(f669,plain,
spl15_68,
inference(avatar_split_clause,[],[f143,f667]) ).
fof(f143,plain,
! [X2,X0,X1] :
( subset(set_union2(X0,X2),X1)
| ~ subset(X2,X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f66]) ).
fof(f66,plain,
! [X0,X1,X2] :
( subset(set_union2(X0,X2),X1)
| ~ subset(X2,X1)
| ~ subset(X0,X1) ),
inference(flattening,[],[f65]) ).
fof(f65,plain,
! [X0,X1,X2] :
( subset(set_union2(X0,X2),X1)
| ~ subset(X2,X1)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f47]) ).
fof(f47,axiom,
! [X0,X1,X2] :
( ( subset(X2,X1)
& subset(X0,X1) )
=> subset(set_union2(X0,X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_xboole_1) ).
fof(f665,plain,
spl15_67,
inference(avatar_split_clause,[],[f142,f663]) ).
fof(f142,plain,
! [X2,X0,X1] :
( subset(X0,set_intersection2(X1,X2))
| ~ subset(X0,X2)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f64]) ).
fof(f64,plain,
! [X0,X1,X2] :
( subset(X0,set_intersection2(X1,X2))
| ~ subset(X0,X2)
| ~ subset(X0,X1) ),
inference(flattening,[],[f63]) ).
fof(f63,plain,
! [X0,X1,X2] :
( subset(X0,set_intersection2(X1,X2))
| ~ subset(X0,X2)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f27]) ).
fof(f27,axiom,
! [X0,X1,X2] :
( ( subset(X0,X2)
& subset(X0,X1) )
=> subset(X0,set_intersection2(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_xboole_1) ).
fof(f659,plain,
( spl15_66
| ~ spl15_7
| ~ spl15_18 ),
inference(avatar_split_clause,[],[f331,f284,f234,f657]) ).
fof(f657,plain,
( spl15_66
<=> ! [X0] : ~ in(X0,sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_66])]) ).
fof(f331,plain,
( ! [X0] : ~ in(X0,sK14)
| ~ spl15_7
| ~ spl15_18 ),
inference(superposition,[],[f235,f286]) ).
fof(f651,plain,
spl15_65,
inference(avatar_split_clause,[],[f190,f649]) ).
fof(f190,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| ~ in(X4,X2)
| ~ sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f119]) ).
fof(f647,plain,
spl15_64,
inference(avatar_split_clause,[],[f189,f645]) ).
fof(f645,plain,
( spl15_64
<=> ! [X4,X0,X1,X2] :
( in(X4,X1)
| ~ in(X4,X2)
| ~ sP2(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_64])]) ).
fof(f189,plain,
! [X2,X0,X1,X4] :
( in(X4,X1)
| ~ in(X4,X2)
| ~ sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f119]) ).
fof(f643,plain,
spl15_63,
inference(avatar_split_clause,[],[f183,f641]) ).
fof(f183,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f113]) ).
fof(f639,plain,
spl15_62,
inference(avatar_split_clause,[],[f182,f637]) ).
fof(f637,plain,
( spl15_62
<=> ! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X1)
| ~ sP1(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_62])]) ).
fof(f182,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X1)
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f113]) ).
fof(f635,plain,
spl15_61,
inference(avatar_split_clause,[],[f174,f633]) ).
fof(f174,plain,
! [X2,X0,X1,X4] :
( ~ in(X4,X0)
| ~ in(X4,X2)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f107]) ).
fof(f631,plain,
spl15_60,
inference(avatar_split_clause,[],[f173,f629]) ).
fof(f173,plain,
! [X2,X0,X1,X4] :
( in(X4,X1)
| ~ in(X4,X2)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f107]) ).
fof(f588,plain,
spl15_59,
inference(avatar_split_clause,[],[f140,f586]) ).
fof(f140,plain,
! [X2,X0,X1] :
( subset(set_intersection2(X0,X2),set_intersection2(X1,X2))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f60]) ).
fof(f60,plain,
! [X0,X1,X2] :
( subset(set_intersection2(X0,X2),set_intersection2(X1,X2))
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f30,axiom,
! [X0,X1,X2] :
( subset(X0,X1)
=> subset(set_intersection2(X0,X2),set_intersection2(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_xboole_1) ).
fof(f584,plain,
spl15_58,
inference(avatar_split_clause,[],[f139,f582]) ).
fof(f139,plain,
! [X2,X0,X1] :
( subset(set_difference(X0,X2),set_difference(X1,X2))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f59]) ).
fof(f59,plain,
! [X0,X1,X2] :
( subset(set_difference(X0,X2),set_difference(X1,X2))
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f35]) ).
fof(f35,axiom,
! [X0,X1,X2] :
( subset(X0,X1)
=> subset(set_difference(X0,X2),set_difference(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_xboole_1) ).
fof(f580,plain,
spl15_57,
inference(avatar_split_clause,[],[f130,f578]) ).
fof(f130,plain,
! [X0,X1] :
( in(sK5(X0,X1),set_intersection2(X0,X1))
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f85]) ).
fof(f85,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| ! [X2] : ~ in(X2,set_intersection2(X0,X1)) )
& ( in(sK5(X0,X1),set_intersection2(X0,X1))
| disjoint(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f55,f84]) ).
fof(f84,plain,
! [X0,X1] :
( ? [X3] : in(X3,set_intersection2(X0,X1))
=> in(sK5(X0,X1),set_intersection2(X0,X1)) ),
introduced(choice_axiom,[]) ).
fof(f55,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| ! [X2] : ~ in(X2,set_intersection2(X0,X1)) )
& ( ? [X3] : in(X3,set_intersection2(X0,X1))
| disjoint(X0,X1) ) ),
inference(ennf_transformation,[],[f48]) ).
fof(f48,plain,
! [X0,X1] :
( ~ ( disjoint(X0,X1)
& ? [X2] : in(X2,set_intersection2(X0,X1)) )
& ~ ( ! [X3] : ~ in(X3,set_intersection2(X0,X1))
& ~ disjoint(X0,X1) ) ),
inference(rectify,[],[f42]) ).
fof(f42,axiom,
! [X0,X1] :
( ~ ( disjoint(X0,X1)
& ? [X2] : in(X2,set_intersection2(X0,X1)) )
& ~ ( ! [X2] : ~ in(X2,set_intersection2(X0,X1))
& ~ disjoint(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_xboole_0) ).
fof(f559,plain,
spl15_56,
inference(avatar_split_clause,[],[f196,f557]) ).
fof(f196,plain,
! [X2,X0,X1] :
( set_intersection2(X0,X1) = X2
| ~ sP2(X1,X0,X2) ),
inference(cnf_transformation,[],[f120]) ).
fof(f120,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) = X2
| ~ sP2(X1,X0,X2) )
& ( sP2(X1,X0,X2)
| set_intersection2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f81]) ).
fof(f81,plain,
! [X0,X1,X2] :
( set_intersection2(X0,X1) = X2
<=> sP2(X1,X0,X2) ),
inference(definition_folding,[],[f8,f80]) ).
fof(f8,axiom,
! [X0,X1,X2] :
( set_intersection2(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f555,plain,
spl15_55,
inference(avatar_split_clause,[],[f188,f553]) ).
fof(f553,plain,
( spl15_55
<=> ! [X2,X0,X1] :
( set_union2(X0,X1) = X2
| ~ sP1(X1,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_55])]) ).
fof(f188,plain,
! [X2,X0,X1] :
( set_union2(X0,X1) = X2
| ~ sP1(X1,X0,X2) ),
inference(cnf_transformation,[],[f114]) ).
fof(f114,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) = X2
| ~ sP1(X1,X0,X2) )
& ( sP1(X1,X0,X2)
| set_union2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f79]) ).
fof(f79,plain,
! [X0,X1,X2] :
( set_union2(X0,X1) = X2
<=> sP1(X1,X0,X2) ),
inference(definition_folding,[],[f6,f78]) ).
fof(f6,axiom,
! [X0,X1,X2] :
( set_union2(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
| in(X3,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f551,plain,
spl15_54,
inference(avatar_split_clause,[],[f180,f549]) ).
fof(f549,plain,
( spl15_54
<=> ! [X2,X0,X1] :
( set_difference(X0,X1) = X2
| ~ sP0(X1,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_54])]) ).
fof(f180,plain,
! [X2,X0,X1] :
( set_difference(X0,X1) = X2
| ~ sP0(X1,X0,X2) ),
inference(cnf_transformation,[],[f108]) ).
fof(f108,plain,
! [X0,X1,X2] :
( ( set_difference(X0,X1) = X2
| ~ sP0(X1,X0,X2) )
& ( sP0(X1,X0,X2)
| set_difference(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f77]) ).
fof(f77,plain,
! [X0,X1,X2] :
( set_difference(X0,X1) = X2
<=> sP0(X1,X0,X2) ),
inference(definition_folding,[],[f9,f76]) ).
fof(f9,axiom,
! [X0,X1,X2] :
( set_difference(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( ~ in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(f547,plain,
spl15_53,
inference(avatar_split_clause,[],[f168,f545]) ).
fof(f168,plain,
! [X3,X0,X1] :
( in(X3,X1)
| ~ in(X3,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f102]) ).
fof(f102,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK9(X0,X1),X1)
& in(sK9(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f100,f101]) ).
fof(f101,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) )
=> ( ~ in(sK9(X0,X1),X1)
& in(sK9(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f100,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f99]) ).
fof(f99,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f73]) ).
fof(f73,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f543,plain,
spl15_52,
inference(avatar_split_clause,[],[f165,f541]) ).
fof(f165,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f97]) ).
fof(f97,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 ) ),
inference(flattening,[],[f96]) ).
fof(f96,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(f533,plain,
spl15_51,
inference(avatar_split_clause,[],[f141,f531]) ).
fof(f141,plain,
! [X2,X0,X1] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f62]) ).
fof(f62,plain,
! [X0,X1,X2] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(flattening,[],[f61]) ).
fof(f61,plain,
! [X0,X1,X2] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f29]) ).
fof(f29,axiom,
! [X0,X1,X2] :
( ( subset(X1,X2)
& subset(X0,X1) )
=> subset(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_xboole_1) ).
fof(f529,plain,
spl15_50,
inference(avatar_split_clause,[],[f134,f527]) ).
fof(f527,plain,
( spl15_50
<=> ! [X2,X0,X1] :
( ~ disjoint(X0,X1)
| ~ in(X2,X1)
| ~ in(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_50])]) ).
fof(f134,plain,
! [X2,X0,X1] :
( ~ disjoint(X0,X1)
| ~ in(X2,X1)
| ~ in(X2,X0) ),
inference(cnf_transformation,[],[f87]) ).
fof(f87,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| ! [X2] :
( ~ in(X2,X1)
| ~ in(X2,X0) ) )
& ( ( in(sK6(X0,X1),X1)
& in(sK6(X0,X1),X0) )
| disjoint(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f56,f86]) ).
fof(f86,plain,
! [X0,X1] :
( ? [X3] :
( in(X3,X1)
& in(X3,X0) )
=> ( in(sK6(X0,X1),X1)
& in(sK6(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f56,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| ! [X2] :
( ~ in(X2,X1)
| ~ in(X2,X0) ) )
& ( ? [X3] :
( in(X3,X1)
& in(X3,X0) )
| disjoint(X0,X1) ) ),
inference(ennf_transformation,[],[f49]) ).
fof(f49,plain,
! [X0,X1] :
( ~ ( disjoint(X0,X1)
& ? [X2] :
( in(X2,X1)
& in(X2,X0) ) )
& ~ ( ! [X3] :
~ ( in(X3,X1)
& in(X3,X0) )
& ~ disjoint(X0,X1) ) ),
inference(rectify,[],[f39]) ).
fof(f39,axiom,
! [X0,X1] :
( ~ ( disjoint(X0,X1)
& ? [X2] :
( in(X2,X1)
& in(X2,X0) ) )
& ~ ( ! [X2] :
~ ( in(X2,X1)
& in(X2,X0) )
& ~ disjoint(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_0) ).
fof(f525,plain,
( spl15_49
| ~ spl15_7
| ~ spl15_18
| ~ spl15_36 ),
inference(avatar_split_clause,[],[f453,f417,f284,f234,f523]) ).
fof(f523,plain,
( spl15_49
<=> ! [X0] : disjoint(X0,sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_49])]) ).
fof(f453,plain,
( ! [X0] : disjoint(X0,sK14)
| ~ spl15_7
| ~ spl15_18
| ~ spl15_36 ),
inference(forward_demodulation,[],[f449,f286]) ).
fof(f449,plain,
( ! [X0] : disjoint(X0,empty_set)
| ~ spl15_7
| ~ spl15_36 ),
inference(resolution,[],[f418,f235]) ).
fof(f508,plain,
( spl15_48
| ~ spl15_18
| ~ spl15_45 ),
inference(avatar_split_clause,[],[f496,f493,f284,f506]) ).
fof(f493,plain,
( spl15_45
<=> ! [X0,X1] :
( disjoint(X0,X1)
| set_intersection2(X0,X1) != empty_set ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_45])]) ).
fof(f496,plain,
( ! [X0,X1] :
( set_intersection2(X0,X1) != sK14
| disjoint(X0,X1) )
| ~ spl15_18
| ~ spl15_45 ),
inference(forward_demodulation,[],[f494,f286]) ).
fof(f494,plain,
( ! [X0,X1] :
( disjoint(X0,X1)
| set_intersection2(X0,X1) != empty_set )
| ~ spl15_45 ),
inference(avatar_component_clause,[],[f493]) ).
fof(f504,plain,
spl15_47,
inference(avatar_split_clause,[],[f170,f502]) ).
fof(f170,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sK9(X0,X1),X1) ),
inference(cnf_transformation,[],[f102]) ).
fof(f500,plain,
spl15_46,
inference(avatar_split_clause,[],[f169,f498]) ).
fof(f169,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sK9(X0,X1),X0) ),
inference(cnf_transformation,[],[f102]) ).
fof(f495,plain,
spl15_45,
inference(avatar_split_clause,[],[f167,f493]) ).
fof(f167,plain,
! [X0,X1] :
( disjoint(X0,X1)
| set_intersection2(X0,X1) != empty_set ),
inference(cnf_transformation,[],[f98]) ).
fof(f98,plain,
! [X0,X1] :
( ( disjoint(X0,X1)
| set_intersection2(X0,X1) != empty_set )
& ( set_intersection2(X0,X1) = empty_set
| ~ disjoint(X0,X1) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> set_intersection2(X0,X1) = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_xboole_0) ).
fof(f490,plain,
spl15_44,
inference(avatar_split_clause,[],[f166,f488]) ).
fof(f488,plain,
( spl15_44
<=> ! [X0,X1] :
( set_intersection2(X0,X1) = empty_set
| ~ disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_44])]) ).
fof(f166,plain,
! [X0,X1] :
( set_intersection2(X0,X1) = empty_set
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f98]) ).
fof(f477,plain,
( spl15_43
| ~ spl15_7
| ~ spl15_18
| ~ spl15_35 ),
inference(avatar_split_clause,[],[f448,f413,f284,f234,f475]) ).
fof(f475,plain,
( spl15_43
<=> ! [X0] : disjoint(sK14,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_43])]) ).
fof(f448,plain,
( ! [X0] : disjoint(sK14,X0)
| ~ spl15_7
| ~ spl15_18
| ~ spl15_35 ),
inference(forward_demodulation,[],[f444,f286]) ).
fof(f444,plain,
( ! [X0] : disjoint(empty_set,X0)
| ~ spl15_7
| ~ spl15_35 ),
inference(resolution,[],[f414,f235]) ).
fof(f473,plain,
( spl15_42
| ~ spl15_18
| ~ spl15_40 ),
inference(avatar_split_clause,[],[f438,f435,f284,f471]) ).
fof(f435,plain,
( spl15_40
<=> ! [X0,X1] :
( empty_set = set_difference(X0,X1)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_40])]) ).
fof(f438,plain,
( ! [X0,X1] :
( set_difference(X0,X1) = sK14
| ~ subset(X0,X1) )
| ~ spl15_18
| ~ spl15_40 ),
inference(forward_demodulation,[],[f436,f286]) ).
fof(f436,plain,
( ! [X0,X1] :
( empty_set = set_difference(X0,X1)
| ~ subset(X0,X1) )
| ~ spl15_40 ),
inference(avatar_component_clause,[],[f435]) ).
fof(f469,plain,
( spl15_41
| ~ spl15_18
| ~ spl15_39 ),
inference(avatar_split_clause,[],[f433,f430,f284,f467]) ).
fof(f430,plain,
( spl15_39
<=> ! [X0,X1] :
( subset(X0,X1)
| empty_set != set_difference(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_39])]) ).
fof(f433,plain,
( ! [X0,X1] :
( set_difference(X0,X1) != sK14
| subset(X0,X1) )
| ~ spl15_18
| ~ spl15_39 ),
inference(forward_demodulation,[],[f431,f286]) ).
fof(f431,plain,
( ! [X0,X1] :
( subset(X0,X1)
| empty_set != set_difference(X0,X1) )
| ~ spl15_39 ),
inference(avatar_component_clause,[],[f430]) ).
fof(f437,plain,
spl15_40,
inference(avatar_split_clause,[],[f138,f435]) ).
fof(f138,plain,
! [X0,X1] :
( empty_set = set_difference(X0,X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f88]) ).
fof(f88,plain,
! [X0,X1] :
( ( empty_set = set_difference(X0,X1)
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| empty_set != set_difference(X0,X1) ) ),
inference(nnf_transformation,[],[f20]) ).
fof(f20,axiom,
! [X0,X1] :
( empty_set = set_difference(X0,X1)
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l32_xboole_1) ).
fof(f432,plain,
spl15_39,
inference(avatar_split_clause,[],[f137,f430]) ).
fof(f137,plain,
! [X0,X1] :
( subset(X0,X1)
| empty_set != set_difference(X0,X1) ),
inference(cnf_transformation,[],[f88]) ).
fof(f428,plain,
spl15_38,
inference(avatar_split_clause,[],[f136,f426]) ).
fof(f136,plain,
! [X0,X1] :
( set_intersection2(X0,X1) = X0
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f58]) ).
fof(f58,plain,
! [X0,X1] :
( set_intersection2(X0,X1) = X0
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,axiom,
! [X0,X1] :
( subset(X0,X1)
=> set_intersection2(X0,X1) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_xboole_1) ).
fof(f423,plain,
spl15_37,
inference(avatar_split_clause,[],[f135,f421]) ).
fof(f135,plain,
! [X0,X1] :
( set_union2(X0,X1) = X1
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f57]) ).
fof(f57,plain,
! [X0,X1] :
( set_union2(X0,X1) = X1
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f25]) ).
fof(f25,axiom,
! [X0,X1] :
( subset(X0,X1)
=> set_union2(X0,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_xboole_1) ).
fof(f419,plain,
spl15_36,
inference(avatar_split_clause,[],[f133,f417]) ).
fof(f133,plain,
! [X0,X1] :
( in(sK6(X0,X1),X1)
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f87]) ).
fof(f415,plain,
spl15_35,
inference(avatar_split_clause,[],[f132,f413]) ).
fof(f132,plain,
! [X0,X1] :
( in(sK6(X0,X1),X0)
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f87]) ).
fof(f411,plain,
spl15_34,
inference(avatar_split_clause,[],[f131,f409]) ).
fof(f131,plain,
! [X2,X0,X1] :
( ~ disjoint(X0,X1)
| ~ in(X2,set_intersection2(X0,X1)) ),
inference(cnf_transformation,[],[f85]) ).
fof(f374,plain,
( spl15_33
| ~ spl15_18
| ~ spl15_28 ),
inference(avatar_split_clause,[],[f354,f351,f284,f372]) ).
fof(f351,plain,
( spl15_28
<=> ! [X0] :
( empty_set = X0
| in(sK7(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_28])]) ).
fof(f354,plain,
( ! [X0] :
( sK14 = X0
| in(sK7(X0),X0) )
| ~ spl15_18
| ~ spl15_28 ),
inference(forward_demodulation,[],[f352,f286]) ).
fof(f352,plain,
( ! [X0] :
( empty_set = X0
| in(sK7(X0),X0) )
| ~ spl15_28 ),
inference(avatar_component_clause,[],[f351]) ).
fof(f370,plain,
spl15_32,
inference(avatar_split_clause,[],[f171,f368]) ).
fof(f171,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f74]) ).
fof(f74,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(ennf_transformation,[],[f46]) ).
fof(f46,axiom,
! [X0,X1] :
~ ( empty(X1)
& X0 != X1
& empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
fof(f366,plain,
( spl15_31
| ~ spl15_5
| ~ spl15_18 ),
inference(avatar_split_clause,[],[f330,f284,f226,f364]) ).
fof(f364,plain,
( spl15_31
<=> ! [X0] : subset(sK14,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_31])]) ).
fof(f330,plain,
( ! [X0] : subset(sK14,X0)
| ~ spl15_5
| ~ spl15_18 ),
inference(superposition,[],[f227,f286]) ).
fof(f362,plain,
spl15_30,
inference(avatar_split_clause,[],[f156,f360]) ).
fof(f156,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f358,plain,
spl15_29,
inference(avatar_split_clause,[],[f155,f356]) ).
fof(f155,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f353,plain,
spl15_28,
inference(avatar_split_clause,[],[f151,f351]) ).
fof(f151,plain,
! [X0] :
( empty_set = X0
| in(sK7(X0),X0) ),
inference(cnf_transformation,[],[f92]) ).
fof(f92,plain,
! [X0] :
( ( empty_set = X0
| in(sK7(X0),X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f90,f91]) ).
fof(f91,plain,
! [X0] :
( ? [X1] : in(X1,X0)
=> in(sK7(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f90,plain,
! [X0] :
( ( empty_set = X0
| ? [X1] : in(X1,X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(rectify,[],[f89]) ).
fof(f89,plain,
! [X0] :
( ( empty_set = X0
| ? [X1] : in(X1,X0) )
& ( ! [X1] : ~ in(X1,X0)
| empty_set != X0 ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0] :
( empty_set = X0
<=> ! [X1] : ~ in(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f328,plain,
spl15_27,
inference(avatar_split_clause,[],[f204,f326]) ).
fof(f204,plain,
! [X0,X1] : sP2(X1,X0,set_intersection2(X0,X1)),
inference(equality_resolution,[],[f195]) ).
fof(f195,plain,
! [X2,X0,X1] :
( sP2(X1,X0,X2)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f120]) ).
fof(f324,plain,
spl15_26,
inference(avatar_split_clause,[],[f203,f322]) ).
fof(f203,plain,
! [X0,X1] : sP1(X1,X0,set_union2(X0,X1)),
inference(equality_resolution,[],[f187]) ).
fof(f187,plain,
! [X2,X0,X1] :
( sP1(X1,X0,X2)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f114]) ).
fof(f320,plain,
spl15_25,
inference(avatar_split_clause,[],[f202,f318]) ).
fof(f202,plain,
! [X0,X1] : sP0(X1,X0,set_difference(X0,X1)),
inference(equality_resolution,[],[f179]) ).
fof(f179,plain,
! [X2,X0,X1] :
( sP0(X1,X0,X2)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f108]) ).
fof(f316,plain,
spl15_24,
inference(avatar_split_clause,[],[f160,f314]) ).
fof(f160,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f71]) ).
fof(f71,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f312,plain,
spl15_23,
inference(avatar_split_clause,[],[f159,f310]) ).
fof(f310,plain,
( spl15_23
<=> ! [X0,X1] :
( disjoint(X1,X0)
| ~ disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_23])]) ).
fof(f159,plain,
! [X0,X1] :
( disjoint(X1,X0)
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f70]) ).
fof(f70,plain,
! [X0,X1] :
( disjoint(X1,X0)
| ~ disjoint(X0,X1) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,axiom,
! [X0,X1] :
( disjoint(X0,X1)
=> disjoint(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
fof(f308,plain,
spl15_22,
inference(avatar_split_clause,[],[f158,f306]) ).
fof(f158,plain,
! [X0,X1] :
( ~ empty(set_union2(X0,X1))
| empty(X0) ),
inference(cnf_transformation,[],[f69]) ).
fof(f69,plain,
! [X0,X1] :
( ~ empty(set_union2(X0,X1))
| empty(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0,X1] :
( ~ empty(X0)
=> ~ empty(set_union2(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_xboole_0) ).
fof(f304,plain,
spl15_21,
inference(avatar_split_clause,[],[f157,f302]) ).
fof(f302,plain,
( spl15_21
<=> ! [X0,X1] :
( ~ empty(set_union2(X1,X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_21])]) ).
fof(f157,plain,
! [X0,X1] :
( ~ empty(set_union2(X1,X0))
| empty(X0) ),
inference(cnf_transformation,[],[f68]) ).
fof(f68,plain,
! [X0,X1] :
( ~ empty(set_union2(X1,X0))
| empty(X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f17,axiom,
! [X0,X1] :
( ~ empty(X0)
=> ~ empty(set_union2(X1,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_xboole_0) ).
fof(f297,plain,
( spl15_20
| ~ spl15_18
| ~ spl15_19 ),
inference(avatar_split_clause,[],[f293,f289,f284,f295]) ).
fof(f289,plain,
( spl15_19
<=> ! [X0] :
( empty_set = X0
| ~ subset(X0,empty_set) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_19])]) ).
fof(f293,plain,
( ! [X0] :
( ~ subset(X0,sK14)
| sK14 = X0 )
| ~ spl15_18
| ~ spl15_19 ),
inference(forward_demodulation,[],[f292,f286]) ).
fof(f292,plain,
( ! [X0] :
( sK14 = X0
| ~ subset(X0,empty_set) )
| ~ spl15_18
| ~ spl15_19 ),
inference(forward_demodulation,[],[f290,f286]) ).
fof(f290,plain,
( ! [X0] :
( empty_set = X0
| ~ subset(X0,empty_set) )
| ~ spl15_19 ),
inference(avatar_component_clause,[],[f289]) ).
fof(f291,plain,
spl15_19,
inference(avatar_split_clause,[],[f127,f289]) ).
fof(f127,plain,
! [X0] :
( empty_set = X0
| ~ subset(X0,empty_set) ),
inference(cnf_transformation,[],[f54]) ).
fof(f54,plain,
! [X0] :
( empty_set = X0
| ~ subset(X0,empty_set) ),
inference(ennf_transformation,[],[f40]) ).
fof(f40,axiom,
! [X0] :
( subset(X0,empty_set)
=> empty_set = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_1) ).
fof(f287,plain,
( spl15_18
| ~ spl15_4
| ~ spl15_14 ),
inference(avatar_split_clause,[],[f280,f262,f221,f284]) ).
fof(f262,plain,
( spl15_14
<=> ! [X0] :
( empty_set = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_14])]) ).
fof(f280,plain,
( empty_set = sK14
| ~ spl15_4
| ~ spl15_14 ),
inference(resolution,[],[f263,f223]) ).
fof(f263,plain,
( ! [X0] :
( ~ empty(X0)
| empty_set = X0 )
| ~ spl15_14 ),
inference(avatar_component_clause,[],[f262]) ).
fof(f276,plain,
spl15_17,
inference(avatar_split_clause,[],[f172,f274]) ).
fof(f172,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f75]) ).
fof(f75,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f44]) ).
fof(f44,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f272,plain,
spl15_16,
inference(avatar_split_clause,[],[f154,f270]) ).
fof(f154,plain,
! [X0] : set_intersection2(X0,X0) = X0,
inference(cnf_transformation,[],[f52]) ).
fof(f52,plain,
! [X0] : set_intersection2(X0,X0) = X0,
inference(rectify,[],[f19]) ).
fof(f19,axiom,
! [X0,X1] : set_intersection2(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
fof(f268,plain,
spl15_15,
inference(avatar_split_clause,[],[f153,f266]) ).
fof(f153,plain,
! [X0] : set_union2(X0,X0) = X0,
inference(cnf_transformation,[],[f51]) ).
fof(f51,plain,
! [X0] : set_union2(X0,X0) = X0,
inference(rectify,[],[f18]) ).
fof(f18,axiom,
! [X0,X1] : set_union2(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
fof(f264,plain,
spl15_14,
inference(avatar_split_clause,[],[f149,f262]) ).
fof(f149,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f67,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(ennf_transformation,[],[f43]) ).
fof(f43,axiom,
! [X0] :
( empty(X0)
=> empty_set = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(f260,plain,
spl15_13,
inference(avatar_split_clause,[],[f148,f258]) ).
fof(f148,plain,
! [X0] : set_union2(X0,empty_set) = X0,
inference(cnf_transformation,[],[f28]) ).
fof(f28,axiom,
! [X0] : set_union2(X0,empty_set) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_boole) ).
fof(f256,plain,
spl15_12,
inference(avatar_split_clause,[],[f147,f254]) ).
fof(f147,plain,
! [X0] : set_difference(X0,empty_set) = X0,
inference(cnf_transformation,[],[f38]) ).
fof(f38,axiom,
! [X0] : set_difference(X0,empty_set) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_boole) ).
fof(f252,plain,
spl15_11,
inference(avatar_split_clause,[],[f146,f250]) ).
fof(f146,plain,
! [X0] : empty_set = set_intersection2(X0,empty_set),
inference(cnf_transformation,[],[f32]) ).
fof(f32,axiom,
! [X0] : empty_set = set_intersection2(X0,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_boole) ).
fof(f248,plain,
spl15_10,
inference(avatar_split_clause,[],[f145,f246]) ).
fof(f145,plain,
! [X0] : empty_set = set_difference(empty_set,X0),
inference(cnf_transformation,[],[f41]) ).
fof(f41,axiom,
! [X0] : empty_set = set_difference(empty_set,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_boole) ).
fof(f244,plain,
spl15_9,
inference(avatar_split_clause,[],[f129,f242]) ).
fof(f129,plain,
! [X0,X1] : subset(set_intersection2(X0,X1),X0),
inference(cnf_transformation,[],[f26]) ).
fof(f26,axiom,
! [X0,X1] : subset(set_intersection2(X0,X1),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_xboole_1) ).
fof(f240,plain,
spl15_8,
inference(avatar_split_clause,[],[f128,f238]) ).
fof(f128,plain,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
inference(cnf_transformation,[],[f45]) ).
fof(f45,axiom,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_xboole_1) ).
fof(f236,plain,
spl15_7,
inference(avatar_split_clause,[],[f199,f234]) ).
fof(f199,plain,
! [X2] : ~ in(X2,empty_set),
inference(equality_resolution,[],[f150]) ).
fof(f150,plain,
! [X2,X0] :
( ~ in(X2,X0)
| empty_set != X0 ),
inference(cnf_transformation,[],[f92]) ).
fof(f232,plain,
spl15_6,
inference(avatar_split_clause,[],[f152,f230]) ).
fof(f152,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f50]) ).
fof(f50,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f23]) ).
fof(f23,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f228,plain,
spl15_5,
inference(avatar_split_clause,[],[f126,f226]) ).
fof(f126,plain,
! [X0] : subset(empty_set,X0),
inference(cnf_transformation,[],[f34]) ).
fof(f34,axiom,
! [X0] : subset(empty_set,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_xboole_1) ).
fof(f224,plain,
spl15_4,
inference(avatar_split_clause,[],[f198,f221]) ).
fof(f198,plain,
empty(sK14),
inference(cnf_transformation,[],[f124]) ).
fof(f124,plain,
empty(sK14),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f21,f123]) ).
fof(f123,plain,
( ? [X0] : empty(X0)
=> empty(sK14) ),
introduced(choice_axiom,[]) ).
fof(f21,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f219,plain,
~ spl15_3,
inference(avatar_split_clause,[],[f197,f216]) ).
fof(f216,plain,
( spl15_3
<=> empty(sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_3])]) ).
fof(f197,plain,
~ empty(sK13),
inference(cnf_transformation,[],[f122]) ).
fof(f122,plain,
~ empty(sK13),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f22,f121]) ).
fof(f121,plain,
( ? [X0] : ~ empty(X0)
=> ~ empty(sK13) ),
introduced(choice_axiom,[]) ).
fof(f22,axiom,
? [X0] : ~ empty(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f214,plain,
spl15_2,
inference(avatar_split_clause,[],[f144,f211]) ).
fof(f211,plain,
( spl15_2
<=> empty(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_2])]) ).
fof(f144,plain,
empty(empty_set),
inference(cnf_transformation,[],[f15]) ).
fof(f15,axiom,
empty(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f209,plain,
~ spl15_1,
inference(avatar_split_clause,[],[f125,f206]) ).
fof(f125,plain,
~ subset(set_difference(sK3,sK4),sK3),
inference(cnf_transformation,[],[f83]) ).
fof(f83,plain,
~ subset(set_difference(sK3,sK4),sK3),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f53,f82]) ).
fof(f82,plain,
( ? [X0,X1] : ~ subset(set_difference(X0,X1),X0)
=> ~ subset(set_difference(sK3,sK4),sK3) ),
introduced(choice_axiom,[]) ).
fof(f53,plain,
? [X0,X1] : ~ subset(set_difference(X0,X1),X0),
inference(ennf_transformation,[],[f37]) ).
fof(f37,negated_conjecture,
~ ! [X0,X1] : subset(set_difference(X0,X1),X0),
inference(negated_conjecture,[],[f36]) ).
fof(f36,conjecture,
! [X0,X1] : subset(set_difference(X0,X1),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_xboole_1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU133+2 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n011.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri May 3 11:33:49 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.36 % (31891)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37 % (31894)WARNING: value z3 for option sas not known
% 0.14/0.37 % (31894)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.38 % (31892)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.38 % (31893)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.38 % (31895)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38 % (31896)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.14/0.38 % (31897)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.14/0.38 % (31898)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.14/0.38 TRYING [1]
% 0.14/0.38 TRYING [2]
% 0.14/0.38 TRYING [3]
% 0.20/0.39 TRYING [4]
% 0.20/0.39 TRYING [1]
% 0.20/0.40 TRYING [2]
% 0.20/0.43 TRYING [5]
% 0.20/0.43 TRYING [3]
% 0.20/0.46 TRYING [1]
% 0.20/0.46 TRYING [2]
% 0.20/0.46 TRYING [3]
% 0.20/0.47 TRYING [4]
% 0.20/0.49 TRYING [6]
% 0.20/0.50 TRYING [5]
% 1.33/0.54 TRYING [4]
% 1.33/0.56 TRYING [6]
% 1.33/0.60 TRYING [7]
% 2.02/0.66 % (31896)First to succeed.
% 2.02/0.67 % (31896)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-31891"
% 2.02/0.67 % (31896)Refutation found. Thanks to Tanya!
% 2.02/0.67 % SZS status Theorem for theBenchmark
% 2.02/0.67 % SZS output start Proof for theBenchmark
% See solution above
% 2.02/0.68 % (31896)------------------------------
% 2.02/0.68 % (31896)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 2.02/0.68 % (31896)Termination reason: Refutation
% 2.02/0.68
% 2.02/0.68 % (31896)Memory used [KB]: 5652
% 2.02/0.68 % (31896)Time elapsed: 0.295 s
% 2.02/0.68 % (31896)Instructions burned: 721 (million)
% 2.02/0.68 % (31891)Success in time 0.297 s
%------------------------------------------------------------------------------