TSTP Solution File: SEU144+2 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU144+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% Computer : n025.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 : Sat Sep 2 00:06:47 EDT 2023
% Result : Theorem 0.16s 0.74s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 670
% Syntax : Number of formulae : 2210 ( 153 unt; 0 def)
% Number of atoms : 7091 ( 796 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 8791 (3910 ~;4041 |; 179 &)
% ( 629 <=>; 30 =>; 0 <=; 2 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 607 ( 605 usr; 597 prp; 0-3 aty)
% Number of functors : 20 ( 20 usr; 5 con; 0-3 aty)
% Number of variables : 3655 (;3609 !; 46 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f15752,plain,
$false,
inference(avatar_sat_refutation,[],[f285,f290,f295,f300,f304,f308,f312,f316,f320,f324,f328,f332,f336,f340,f344,f348,f352,f356,f360,f373,f377,f383,f387,f398,f406,f411,f415,f419,f423,f427,f431,f435,f439,f443,f456,f460,f465,f469,f473,f477,f481,f513,f517,f521,f525,f529,f533,f537,f541,f546,f551,f585,f589,f602,f607,f612,f616,f620,f636,f640,f644,f648,f652,f656,f660,f697,f707,f711,f715,f719,f723,f727,f731,f735,f739,f747,f751,f805,f809,f813,f862,f867,f871,f875,f879,f883,f887,f891,f895,f899,f903,f908,f915,f925,f957,f961,f965,f969,f973,f977,f985,f989,f993,f1009,f1013,f1021,f1025,f1029,f1033,f1037,f1041,f1085,f1089,f1093,f1097,f1105,f1141,f1145,f1149,f1153,f1157,f1161,f1165,f1169,f1173,f1177,f1290,f1294,f1298,f1333,f1337,f1342,f1346,f1371,f1375,f1379,f1383,f1387,f1431,f1435,f1439,f1443,f1447,f1451,f1455,f1459,f1463,f1652,f1656,f1660,f1664,f1668,f1672,f1676,f1680,f1684,f1688,f1692,f1700,f1734,f1738,f1742,f1746,f1750,f1754,f1758,f1762,f1766,f1770,f1774,f1778,f1782,f1786,f1790,f1794,f1798,f1802,f1806,f1810,f1936,f2042,f2046,f2062,f2066,f2070,f2074,f2078,f2082,f2270,f2274,f2278,f2282,f2314,f2318,f2322,f2326,f2330,f2334,f2338,f2342,f2346,f2350,f2354,f2358,f2362,f2366,f2370,f2374,f2378,f2544,f2674,f2678,f2682,f2686,f2695,f2699,f2767,f2772,f2820,f2824,f2828,f2832,f2836,f2840,f2961,f2969,f2973,f2977,f2981,f2985,f2993,f2997,f3300,f3308,f3312,f3316,f3320,f3324,f3396,f3401,f3472,f3477,f3536,f3541,f3637,f3641,f3645,f3649,f3653,f3657,f3661,f3665,f3669,f3964,f3968,f3972,f3976,f3980,f3984,f3988,f3992,f3996,f4000,f4004,f4231,f4235,f4239,f4243,f4247,f4251,f4362,f4366,f4371,f4375,f4379,f4482,f4486,f4490,f4494,f4498,f4502,f4506,f4510,f4514,f4518,f4522,f4613,f4617,f4621,f4625,f4629,f4633,f4637,f4641,f4645,f4649,f4653,f4788,f4940,f4944,f4948,f4952,f4956,f5053,f5057,f5061,f5065,f5069,f5073,f5077,f5081,f5085,f5403,f5407,f5411,f5459,f5468,f5472,f5476,f5480,f5484,f5488,f5492,f5496,f5500,f5507,f5511,f5515,f5519,f5618,f5708,f5712,f5716,f5746,f5750,f5754,f5758,f5762,f5766,f5770,f5774,f5778,f5782,f5786,f5859,f5876,f5880,f5884,f5888,f5892,f5896,f5900,f5908,f5912,f5916,f5920,f5924,f5928,f5932,f5936,f5940,f5944,f5952,f5956,f5960,f5964,f5968,f5972,f5976,f5980,f5984,f5988,f5992,f5996,f6423,f6637,f7232,f7236,f7241,f7245,f7249,f7253,f7257,f7261,f7265,f7269,f7273,f7277,f7281,f7285,f7289,f7293,f7297,f7301,f7305,f7309,f7313,f7317,f7321,f7325,f7329,f7333,f7337,f7341,f7345,f7349,f7353,f7357,f7361,f7365,f7369,f7373,f7377,f7381,f7385,f7389,f7393,f7397,f7401,f7405,f7409,f7413,f7417,f7421,f7425,f7429,f7433,f7437,f7441,f7445,f7997,f8205,f9065,f9069,f9073,f9077,f9081,f9085,f9089,f9093,f9097,f9275,f9279,f9283,f9287,f9291,f9295,f9299,f9303,f9307,f9311,f9315,f9334,f9339,f9343,f9347,f9351,f9355,f9359,f9363,f9367,f9371,f9395,f9399,f9403,f9407,f9411,f9415,f9419,f9423,f9427,f9431,f9455,f9459,f9463,f9467,f9471,f9475,f9479,f9483,f12030,f12112,f12116,f12129,f12133,f12155,f12159,f12163,f12167,f12171,f12175,f12179,f12183,f12187,f12191,f12195,f12199,f12203,f12207,f12211,f12215,f12219,f12224,f12228,f12232,f12237,f12312,f12317,f12321,f12325,f12329,f12333,f12337,f12341,f12345,f12378,f12382,f12386,f12390,f12394,f12398,f12402,f12406,f12410,f12414,f12426,f12430,f12434,f12438,f12442,f12446,f12450,f12454,f12458,f12462,f12503,f12507,f12511,f12515,f12519,f12523,f12528,f12532,f12536,f12540,f12544,f13080,f14099,f14560,f14759,f14763,f14767,f14771,f14775,f14779,f14783,f14787,f14791,f14795,f14799,f14803,f14807,f14811,f14815,f14819,f14838,f14842,f15006,f15086,f15093,f15097,f15101,f15105,f15109,f15113,f15117,f15121,f15125,f15129,f15130,f15162,f15167,f15173,f15178,f15421,f15426,f15430,f15434,f15679,f15685,f15714,f15721,f15724,f15734,f15739,f15744,f15749,f15751]) ).
fof(f15751,plain,
( spl18_2
| ~ spl18_211
| ~ spl18_587 ),
inference(avatar_split_clause,[],[f15601,f15432,f2542,f282]) ).
fof(f282,plain,
( spl18_2
<=> in(sK4,sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_2])]) ).
fof(f2542,plain,
( spl18_211
<=> ! [X0] : in(X0,singleton(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_211])]) ).
fof(f15432,plain,
( spl18_587
<=> ! [X1] :
( ~ in(X1,singleton(sK4))
| in(X1,sK5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_587])]) ).
fof(f15601,plain,
( in(sK4,sK5)
| ~ spl18_211
| ~ spl18_587 ),
inference(resolution,[],[f15433,f2543]) ).
fof(f2543,plain,
( ! [X0] : in(X0,singleton(X0))
| ~ spl18_211 ),
inference(avatar_component_clause,[],[f2542]) ).
fof(f15433,plain,
( ! [X1] :
( ~ in(X1,singleton(sK4))
| in(X1,sK5) )
| ~ spl18_587 ),
inference(avatar_component_clause,[],[f15432]) ).
fof(f15749,plain,
( spl18_596
| ~ spl18_157
| ~ spl18_589 ),
inference(avatar_split_clause,[],[f15698,f15676,f1682,f15747]) ).
fof(f15747,plain,
( spl18_596
<=> ! [X6] :
( ~ in(X6,sK5)
| sK4 = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_596])]) ).
fof(f1682,plain,
( spl18_157
<=> ! [X0,X1] :
( ~ in(X0,singleton(X1))
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_157])]) ).
fof(f15676,plain,
( spl18_589
<=> sK5 = singleton(sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_589])]) ).
fof(f15698,plain,
( ! [X6] :
( ~ in(X6,sK5)
| sK4 = X6 )
| ~ spl18_157
| ~ spl18_589 ),
inference(superposition,[],[f1683,f15678]) ).
fof(f15678,plain,
( sK5 = singleton(sK4)
| ~ spl18_589 ),
inference(avatar_component_clause,[],[f15676]) ).
fof(f1683,plain,
( ! [X0,X1] :
( ~ in(X0,singleton(X1))
| X0 = X1 )
| ~ spl18_157 ),
inference(avatar_component_clause,[],[f1682]) ).
fof(f15744,plain,
( spl18_595
| ~ spl18_123
| ~ spl18_586 ),
inference(avatar_split_clause,[],[f15591,f15428,f1159,f15742]) ).
fof(f15742,plain,
( spl18_595
<=> ! [X12] : subset(set_intersection2(X12,singleton(sK4)),sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_595])]) ).
fof(f1159,plain,
( spl18_123
<=> ! [X0,X1] : subset(set_intersection2(X1,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_123])]) ).
fof(f15428,plain,
( spl18_586
<=> ! [X0] :
( subset(X0,sK5)
| ~ subset(X0,singleton(sK4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_586])]) ).
fof(f15591,plain,
( ! [X12] : subset(set_intersection2(X12,singleton(sK4)),sK5)
| ~ spl18_123
| ~ spl18_586 ),
inference(resolution,[],[f15429,f1160]) ).
fof(f1160,plain,
( ! [X0,X1] : subset(set_intersection2(X1,X0),X0)
| ~ spl18_123 ),
inference(avatar_component_clause,[],[f1159]) ).
fof(f15429,plain,
( ! [X0] :
( ~ subset(X0,singleton(sK4))
| subset(X0,sK5) )
| ~ spl18_586 ),
inference(avatar_component_clause,[],[f15428]) ).
fof(f15739,plain,
( spl18_594
| ~ spl18_12
| ~ spl18_586 ),
inference(avatar_split_clause,[],[f15585,f15428,f326,f15737]) ).
fof(f15737,plain,
( spl18_594
<=> ! [X5] : subset(set_difference(singleton(sK4),X5),sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_594])]) ).
fof(f326,plain,
( spl18_12
<=> ! [X0,X1] : subset(set_difference(X0,X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_12])]) ).
fof(f15585,plain,
( ! [X5] : subset(set_difference(singleton(sK4),X5),sK5)
| ~ spl18_12
| ~ spl18_586 ),
inference(resolution,[],[f15429,f327]) ).
fof(f327,plain,
( ! [X0,X1] : subset(set_difference(X0,X1),X0)
| ~ spl18_12 ),
inference(avatar_component_clause,[],[f326]) ).
fof(f15734,plain,
( spl18_593
| ~ spl18_11
| ~ spl18_586 ),
inference(avatar_split_clause,[],[f15581,f15428,f322,f15732]) ).
fof(f15732,plain,
( spl18_593
<=> ! [X0] : subset(set_intersection2(singleton(sK4),X0),sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_593])]) ).
fof(f322,plain,
( spl18_11
<=> ! [X0,X1] : subset(set_intersection2(X0,X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_11])]) ).
fof(f15581,plain,
( ! [X0] : subset(set_intersection2(singleton(sK4),X0),sK5)
| ~ spl18_11
| ~ spl18_586 ),
inference(resolution,[],[f15429,f323]) ).
fof(f323,plain,
( ! [X0,X1] : subset(set_intersection2(X0,X1),X0)
| ~ spl18_11 ),
inference(avatar_component_clause,[],[f322]) ).
fof(f15724,plain,
( ~ spl18_8
| spl18_591 ),
inference(avatar_contradiction_clause,[],[f15722]) ).
fof(f15722,plain,
( $false
| ~ spl18_8
| spl18_591 ),
inference(resolution,[],[f15713,f311]) ).
fof(f311,plain,
( ! [X0] : subset(X0,X0)
| ~ spl18_8 ),
inference(avatar_component_clause,[],[f310]) ).
fof(f310,plain,
( spl18_8
<=> ! [X0] : subset(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_8])]) ).
fof(f15713,plain,
( ~ subset(sK5,sK5)
| spl18_591 ),
inference(avatar_component_clause,[],[f15711]) ).
fof(f15711,plain,
( spl18_591
<=> subset(sK5,sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_591])]) ).
fof(f15721,plain,
( ~ spl18_592
| ~ spl18_9
| ~ spl18_83
| ~ spl18_589 ),
inference(avatar_split_clause,[],[f15709,f15676,f864,f314,f15718]) ).
fof(f15718,plain,
( spl18_592
<=> sK5 = sK17 ),
introduced(avatar_definition,[new_symbols(naming,[spl18_592])]) ).
fof(f314,plain,
( spl18_9
<=> ! [X0] : singleton(X0) != empty_set ),
introduced(avatar_definition,[new_symbols(naming,[spl18_9])]) ).
fof(f864,plain,
( spl18_83
<=> empty_set = sK17 ),
introduced(avatar_definition,[new_symbols(naming,[spl18_83])]) ).
fof(f15709,plain,
( sK5 != sK17
| ~ spl18_9
| ~ spl18_83
| ~ spl18_589 ),
inference(forward_demodulation,[],[f15695,f866]) ).
fof(f866,plain,
( empty_set = sK17
| ~ spl18_83 ),
inference(avatar_component_clause,[],[f864]) ).
fof(f15695,plain,
( empty_set != sK5
| ~ spl18_9
| ~ spl18_589 ),
inference(superposition,[],[f315,f15678]) ).
fof(f315,plain,
( ! [X0] : singleton(X0) != empty_set
| ~ spl18_9 ),
inference(avatar_component_clause,[],[f314]) ).
fof(f15714,plain,
( ~ spl18_591
| spl18_588
| ~ spl18_589 ),
inference(avatar_split_clause,[],[f15694,f15676,f15672,f15711]) ).
fof(f15672,plain,
( spl18_588
<=> subset(sK5,singleton(sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_588])]) ).
fof(f15694,plain,
( ~ subset(sK5,sK5)
| spl18_588
| ~ spl18_589 ),
inference(superposition,[],[f15674,f15678]) ).
fof(f15674,plain,
( ~ subset(sK5,singleton(sK4))
| spl18_588 ),
inference(avatar_component_clause,[],[f15672]) ).
fof(f15685,plain,
( spl18_590
| spl18_589
| ~ spl18_1
| ~ spl18_69 ),
inference(avatar_split_clause,[],[f15137,f709,f278,f15676,f15682]) ).
fof(f15682,plain,
( spl18_590
<=> proper_subset(singleton(sK4),sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_590])]) ).
fof(f278,plain,
( spl18_1
<=> subset(singleton(sK4),sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_1])]) ).
fof(f709,plain,
( spl18_69
<=> ! [X0,X1] :
( proper_subset(X0,X1)
| X0 = X1
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_69])]) ).
fof(f15137,plain,
( sK5 = singleton(sK4)
| proper_subset(singleton(sK4),sK5)
| ~ spl18_1
| ~ spl18_69 ),
inference(resolution,[],[f280,f710]) ).
fof(f710,plain,
( ! [X0,X1] :
( ~ subset(X0,X1)
| X0 = X1
| proper_subset(X0,X1) )
| ~ spl18_69 ),
inference(avatar_component_clause,[],[f709]) ).
fof(f280,plain,
( subset(singleton(sK4),sK5)
| ~ spl18_1 ),
inference(avatar_component_clause,[],[f278]) ).
fof(f15679,plain,
( ~ spl18_588
| spl18_589
| ~ spl18_1
| ~ spl18_68 ),
inference(avatar_split_clause,[],[f15136,f705,f278,f15676,f15672]) ).
fof(f705,plain,
( spl18_68
<=> ! [X0,X1] :
( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_68])]) ).
fof(f15136,plain,
( sK5 = singleton(sK4)
| ~ subset(sK5,singleton(sK4))
| ~ spl18_1
| ~ spl18_68 ),
inference(resolution,[],[f280,f706]) ).
fof(f706,plain,
( ! [X0,X1] :
( ~ subset(X1,X0)
| X0 = X1
| ~ subset(X0,X1) )
| ~ spl18_68 ),
inference(avatar_component_clause,[],[f705]) ).
fof(f15434,plain,
( spl18_587
| ~ spl18_1
| ~ spl18_70 ),
inference(avatar_split_clause,[],[f15138,f713,f278,f15432]) ).
fof(f713,plain,
( spl18_70
<=> ! [X0,X1,X3] :
( in(X3,X1)
| ~ in(X3,X0)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_70])]) ).
fof(f15138,plain,
( ! [X1] :
( ~ in(X1,singleton(sK4))
| in(X1,sK5) )
| ~ spl18_1
| ~ spl18_70 ),
inference(resolution,[],[f280,f714]) ).
fof(f714,plain,
( ! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) )
| ~ spl18_70 ),
inference(avatar_component_clause,[],[f713]) ).
fof(f15430,plain,
( spl18_586
| ~ spl18_1
| ~ spl18_66 ),
inference(avatar_split_clause,[],[f15135,f658,f278,f15428]) ).
fof(f658,plain,
( spl18_66
<=> ! [X2,X0,X1] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_66])]) ).
fof(f15135,plain,
( ! [X0] :
( subset(X0,sK5)
| ~ subset(X0,singleton(sK4)) )
| ~ spl18_1
| ~ spl18_66 ),
inference(resolution,[],[f280,f659]) ).
fof(f659,plain,
( ! [X2,X0,X1] :
( ~ subset(X1,X2)
| subset(X0,X2)
| ~ subset(X0,X1) )
| ~ spl18_66 ),
inference(avatar_component_clause,[],[f658]) ).
fof(f15426,plain,
( spl18_585
| ~ spl18_138
| ~ spl18_582 ),
inference(avatar_split_clause,[],[f15191,f15170,f1381,f15423]) ).
fof(f15423,plain,
( spl18_585
<=> sP2(sK5,singleton(sK4),sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_585])]) ).
fof(f1381,plain,
( spl18_138
<=> ! [X0,X1] : sP2(X0,X1,set_union2(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_138])]) ).
fof(f15170,plain,
( spl18_582
<=> sK5 = set_union2(singleton(sK4),sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_582])]) ).
fof(f15191,plain,
( sP2(sK5,singleton(sK4),sK5)
| ~ spl18_138
| ~ spl18_582 ),
inference(superposition,[],[f1382,f15172]) ).
fof(f15172,plain,
( sK5 = set_union2(singleton(sK4),sK5)
| ~ spl18_582 ),
inference(avatar_component_clause,[],[f15170]) ).
fof(f1382,plain,
( ! [X0,X1] : sP2(X0,X1,set_union2(X1,X0))
| ~ spl18_138 ),
inference(avatar_component_clause,[],[f1381]) ).
fof(f15421,plain,
( spl18_584
| ~ spl18_1
| ~ spl18_47 ),
inference(avatar_split_clause,[],[f15133,f527,f278,f15418]) ).
fof(f15418,plain,
( spl18_584
<=> singleton(sK4) = set_intersection2(singleton(sK4),sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_584])]) ).
fof(f527,plain,
( spl18_47
<=> ! [X0,X1] :
( set_intersection2(X0,X1) = X0
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_47])]) ).
fof(f15133,plain,
( singleton(sK4) = set_intersection2(singleton(sK4),sK5)
| ~ spl18_1
| ~ spl18_47 ),
inference(resolution,[],[f280,f528]) ).
fof(f528,plain,
( ! [X0,X1] :
( ~ subset(X0,X1)
| set_intersection2(X0,X1) = X0 )
| ~ spl18_47 ),
inference(avatar_component_clause,[],[f527]) ).
fof(f15178,plain,
( spl18_583
| ~ spl18_1
| ~ spl18_54 ),
inference(avatar_split_clause,[],[f15134,f587,f278,f15175]) ).
fof(f15175,plain,
( spl18_583
<=> sK17 = set_difference(singleton(sK4),sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_583])]) ).
fof(f587,plain,
( spl18_54
<=> ! [X0,X1] :
( set_difference(X0,X1) = sK17
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_54])]) ).
fof(f15134,plain,
( sK17 = set_difference(singleton(sK4),sK5)
| ~ spl18_1
| ~ spl18_54 ),
inference(resolution,[],[f280,f588]) ).
fof(f588,plain,
( ! [X0,X1] :
( ~ subset(X0,X1)
| set_difference(X0,X1) = sK17 )
| ~ spl18_54 ),
inference(avatar_component_clause,[],[f587]) ).
fof(f15173,plain,
( spl18_582
| ~ spl18_1
| ~ spl18_46 ),
inference(avatar_split_clause,[],[f15132,f523,f278,f15170]) ).
fof(f523,plain,
( spl18_46
<=> ! [X0,X1] :
( set_union2(X0,X1) = X1
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_46])]) ).
fof(f15132,plain,
( sK5 = set_union2(singleton(sK4),sK5)
| ~ spl18_1
| ~ spl18_46 ),
inference(resolution,[],[f280,f524]) ).
fof(f524,plain,
( ! [X0,X1] :
( ~ subset(X0,X1)
| set_union2(X0,X1) = X1 )
| ~ spl18_46 ),
inference(avatar_component_clause,[],[f523]) ).
fof(f15167,plain,
( ~ spl18_581
| ~ spl18_1
| ~ spl18_23 ),
inference(avatar_split_clause,[],[f15131,f381,f278,f15164]) ).
fof(f15164,plain,
( spl18_581
<=> proper_subset(sK5,singleton(sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_581])]) ).
fof(f381,plain,
( spl18_23
<=> ! [X0,X1] :
( ~ proper_subset(X1,X0)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_23])]) ).
fof(f15131,plain,
( ~ proper_subset(sK5,singleton(sK4))
| ~ spl18_1
| ~ spl18_23 ),
inference(resolution,[],[f280,f382]) ).
fof(f382,plain,
( ! [X0,X1] :
( ~ subset(X0,X1)
| ~ proper_subset(X1,X0) )
| ~ spl18_23 ),
inference(avatar_component_clause,[],[f381]) ).
fof(f15162,plain,
( ~ spl18_1
| ~ spl18_2 ),
inference(avatar_split_clause,[],[f168,f282,f278]) ).
fof(f168,plain,
( ~ in(sK4,sK5)
| ~ subset(singleton(sK4),sK5) ),
inference(cnf_transformation,[],[f111]) ).
fof(f111,plain,
( ( ~ in(sK4,sK5)
| ~ subset(singleton(sK4),sK5) )
& ( in(sK4,sK5)
| subset(singleton(sK4),sK5) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f109,f110]) ).
fof(f110,plain,
( ? [X0,X1] :
( ( ~ in(X0,X1)
| ~ subset(singleton(X0),X1) )
& ( in(X0,X1)
| subset(singleton(X0),X1) ) )
=> ( ( ~ in(sK4,sK5)
| ~ subset(singleton(sK4),sK5) )
& ( in(sK4,sK5)
| subset(singleton(sK4),sK5) ) ) ),
introduced(choice_axiom,[]) ).
fof(f109,plain,
? [X0,X1] :
( ( ~ in(X0,X1)
| ~ subset(singleton(X0),X1) )
& ( in(X0,X1)
| subset(singleton(X0),X1) ) ),
inference(nnf_transformation,[],[f73]) ).
fof(f73,plain,
? [X0,X1] :
( subset(singleton(X0),X1)
<~> in(X0,X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f30,negated_conjecture,
~ ! [X0,X1] :
( subset(singleton(X0),X1)
<=> in(X0,X1) ),
inference(negated_conjecture,[],[f29]) ).
fof(f29,conjecture,
! [X0,X1] :
( subset(singleton(X0),X1)
<=> in(X0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.1596azFLbA/Vampire---4.8_25340',l2_zfmisc_1) ).
fof(f15130,plain,
( spl18_1
| ~ spl18_2
| ~ spl18_58
| ~ spl18_569 ),
inference(avatar_split_clause,[],[f15088,f15003,f614,f282,f278]) ).
fof(f614,plain,
( spl18_58
<=> ! [X0,X1] :
( subset(X0,X1)
| ~ in(sK10(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_58])]) ).
fof(f15003,plain,
( spl18_569
<=> sK4 = sK10(singleton(sK4),sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_569])]) ).
fof(f15088,plain,
( ~ in(sK4,sK5)
| subset(singleton(sK4),sK5)
| ~ spl18_58
| ~ spl18_569 ),
inference(superposition,[],[f615,f15005]) ).
fof(f15005,plain,
( sK4 = sK10(singleton(sK4),sK5)
| ~ spl18_569 ),
inference(avatar_component_clause,[],[f15003]) ).
fof(f615,plain,
( ! [X0,X1] :
( ~ in(sK10(X0,X1),X1)
| subset(X0,X1) )
| ~ spl18_58 ),
inference(avatar_component_clause,[],[f614]) ).
fof(f15129,plain,
( spl18_580
| ~ spl18_75
| ~ spl18_185 ),
inference(avatar_split_clause,[],[f2096,f2064,f733,f15127]) ).
fof(f15127,plain,
( spl18_580
<=> ! [X13,X12,X14] :
( set_union2(X12,X13) != X14
| sP2(set_union2(X12,X13),X12,X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_580])]) ).
fof(f733,plain,
( spl18_75
<=> ! [X2,X0,X1] :
( sP2(X1,X0,X2)
| set_union2(X0,X1) != X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_75])]) ).
fof(f2064,plain,
( spl18_185
<=> ! [X6,X7] : set_union2(X6,X7) = set_union2(X6,set_union2(X6,X7)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_185])]) ).
fof(f2096,plain,
( ! [X14,X12,X13] :
( set_union2(X12,X13) != X14
| sP2(set_union2(X12,X13),X12,X14) )
| ~ spl18_75
| ~ spl18_185 ),
inference(superposition,[],[f734,f2065]) ).
fof(f2065,plain,
( ! [X6,X7] : set_union2(X6,X7) = set_union2(X6,set_union2(X6,X7))
| ~ spl18_185 ),
inference(avatar_component_clause,[],[f2064]) ).
fof(f734,plain,
( ! [X2,X0,X1] :
( set_union2(X0,X1) != X2
| sP2(X1,X0,X2) )
| ~ spl18_75 ),
inference(avatar_component_clause,[],[f733]) ).
fof(f15125,plain,
( spl18_579
| ~ spl18_70
| ~ spl18_178 ),
inference(avatar_split_clause,[],[f2031,f1800,f713,f15123]) ).
fof(f15123,plain,
( spl18_579
<=> ! [X18,X17,X19] :
( ~ subset(X17,X18)
| ~ in(X19,X17)
| in(X19,set_intersection2(X18,X17)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_579])]) ).
fof(f1800,plain,
( spl18_178
<=> ! [X2,X3] :
( subset(X2,set_intersection2(X3,X2))
| ~ subset(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_178])]) ).
fof(f2031,plain,
( ! [X18,X19,X17] :
( ~ subset(X17,X18)
| ~ in(X19,X17)
| in(X19,set_intersection2(X18,X17)) )
| ~ spl18_70
| ~ spl18_178 ),
inference(resolution,[],[f1801,f714]) ).
fof(f1801,plain,
( ! [X2,X3] :
( subset(X2,set_intersection2(X3,X2))
| ~ subset(X2,X3) )
| ~ spl18_178 ),
inference(avatar_component_clause,[],[f1800]) ).
fof(f15121,plain,
( spl18_578
| ~ spl18_66
| ~ spl18_178 ),
inference(avatar_split_clause,[],[f2028,f1800,f658,f15119]) ).
fof(f15119,plain,
( spl18_578
<=> ! [X12,X11,X10] :
( ~ subset(X10,X11)
| subset(X12,set_intersection2(X11,X10))
| ~ subset(X12,X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_578])]) ).
fof(f2028,plain,
( ! [X10,X11,X12] :
( ~ subset(X10,X11)
| subset(X12,set_intersection2(X11,X10))
| ~ subset(X12,X10) )
| ~ spl18_66
| ~ spl18_178 ),
inference(resolution,[],[f1801,f659]) ).
fof(f15117,plain,
( spl18_577
| ~ spl18_42
| ~ spl18_174 ),
inference(avatar_split_clause,[],[f1981,f1784,f479,f15115]) ).
fof(f15115,plain,
( spl18_577
<=> ! [X6,X7] :
( in(sK8(set_difference(X6,X7)),X6)
| sK17 = set_difference(X6,X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_577])]) ).
fof(f479,plain,
( spl18_42
<=> ! [X0] :
( sK17 = X0
| in(sK8(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_42])]) ).
fof(f1784,plain,
( spl18_174
<=> ! [X9,X8,X7] :
( ~ in(X7,set_difference(X8,X9))
| in(X7,X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_174])]) ).
fof(f1981,plain,
( ! [X6,X7] :
( in(sK8(set_difference(X6,X7)),X6)
| sK17 = set_difference(X6,X7) )
| ~ spl18_42
| ~ spl18_174 ),
inference(resolution,[],[f1785,f480]) ).
fof(f480,plain,
( ! [X0] :
( in(sK8(X0),X0)
| sK17 = X0 )
| ~ spl18_42 ),
inference(avatar_component_clause,[],[f479]) ).
fof(f1785,plain,
( ! [X8,X9,X7] :
( ~ in(X7,set_difference(X8,X9))
| in(X7,X8) )
| ~ spl18_174 ),
inference(avatar_component_clause,[],[f1784]) ).
fof(f15113,plain,
( spl18_576
| ~ spl18_42
| ~ spl18_173 ),
inference(avatar_split_clause,[],[f1956,f1780,f479,f15111]) ).
fof(f15111,plain,
( spl18_576
<=> ! [X9,X8] :
( in(sK8(set_intersection2(X8,X9)),X8)
| sK17 = set_intersection2(X8,X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_576])]) ).
fof(f1780,plain,
( spl18_173
<=> ! [X4,X2,X3] :
( ~ in(X2,set_intersection2(X3,X4))
| in(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_173])]) ).
fof(f1956,plain,
( ! [X8,X9] :
( in(sK8(set_intersection2(X8,X9)),X8)
| sK17 = set_intersection2(X8,X9) )
| ~ spl18_42
| ~ spl18_173 ),
inference(resolution,[],[f1781,f480]) ).
fof(f1781,plain,
( ! [X2,X3,X4] :
( ~ in(X2,set_intersection2(X3,X4))
| in(X2,X3) )
| ~ spl18_173 ),
inference(avatar_component_clause,[],[f1780]) ).
fof(f15109,plain,
( spl18_575
| ~ spl18_70
| ~ spl18_172 ),
inference(avatar_split_clause,[],[f1944,f1776,f713,f15107]) ).
fof(f15107,plain,
( spl18_575
<=> ! [X24,X23,X25,X22] :
( ~ subset(X22,X23)
| ~ in(X24,X22)
| in(X24,set_union2(X23,X25)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_575])]) ).
fof(f1776,plain,
( spl18_172
<=> ! [X11,X12,X10] :
( subset(X10,set_union2(X11,X12))
| ~ subset(X10,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_172])]) ).
fof(f1944,plain,
( ! [X24,X22,X25,X23] :
( ~ subset(X22,X23)
| ~ in(X24,X22)
| in(X24,set_union2(X23,X25)) )
| ~ spl18_70
| ~ spl18_172 ),
inference(resolution,[],[f1777,f714]) ).
fof(f1777,plain,
( ! [X10,X11,X12] :
( subset(X10,set_union2(X11,X12))
| ~ subset(X10,X11) )
| ~ spl18_172 ),
inference(avatar_component_clause,[],[f1776]) ).
fof(f15105,plain,
( spl18_574
| ~ spl18_66
| ~ spl18_172 ),
inference(avatar_split_clause,[],[f1941,f1776,f658,f15103]) ).
fof(f15103,plain,
( spl18_574
<=> ! [X13,X14,X12,X15] :
( ~ subset(X12,X13)
| subset(X14,set_union2(X13,X15))
| ~ subset(X14,X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_574])]) ).
fof(f1941,plain,
( ! [X14,X15,X12,X13] :
( ~ subset(X12,X13)
| subset(X14,set_union2(X13,X15))
| ~ subset(X14,X12) )
| ~ spl18_66
| ~ spl18_172 ),
inference(resolution,[],[f1777,f659]) ).
fof(f15101,plain,
( spl18_573
| ~ spl18_66
| ~ spl18_167 ),
inference(avatar_split_clause,[],[f1873,f1756,f658,f15099]) ).
fof(f15099,plain,
( spl18_573
<=> ! [X13,X14,X12,X15] :
( ~ disjoint(X12,X13)
| subset(X14,X15)
| ~ subset(X14,set_intersection2(X12,X13)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_573])]) ).
fof(f1756,plain,
( spl18_167
<=> ! [X6,X4,X5] :
( subset(set_intersection2(X4,X5),X6)
| ~ disjoint(X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_167])]) ).
fof(f1873,plain,
( ! [X14,X15,X12,X13] :
( ~ disjoint(X12,X13)
| subset(X14,X15)
| ~ subset(X14,set_intersection2(X12,X13)) )
| ~ spl18_66
| ~ spl18_167 ),
inference(resolution,[],[f1757,f659]) ).
fof(f1757,plain,
( ! [X6,X4,X5] :
( subset(set_intersection2(X4,X5),X6)
| ~ disjoint(X4,X5) )
| ~ spl18_167 ),
inference(avatar_component_clause,[],[f1756]) ).
fof(f15097,plain,
( spl18_572
| ~ spl18_65
| ~ spl18_164 ),
inference(avatar_split_clause,[],[f1842,f1744,f654,f15095]) ).
fof(f15095,plain,
( spl18_572
<=> ! [X5,X4,X6,X3] :
( ~ disjoint(X3,X4)
| disjoint(X5,X6)
| ~ subset(X5,set_intersection2(X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_572])]) ).
fof(f654,plain,
( spl18_65
<=> ! [X2,X0,X1] :
( disjoint(X0,X2)
| ~ disjoint(X1,X2)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_65])]) ).
fof(f1744,plain,
( spl18_164
<=> ! [X6,X4,X5] :
( disjoint(set_intersection2(X4,X5),X6)
| ~ disjoint(X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_164])]) ).
fof(f1842,plain,
( ! [X3,X6,X4,X5] :
( ~ disjoint(X3,X4)
| disjoint(X5,X6)
| ~ subset(X5,set_intersection2(X3,X4)) )
| ~ spl18_65
| ~ spl18_164 ),
inference(resolution,[],[f1745,f655]) ).
fof(f655,plain,
( ! [X2,X0,X1] :
( ~ disjoint(X1,X2)
| disjoint(X0,X2)
| ~ subset(X0,X1) )
| ~ spl18_65 ),
inference(avatar_component_clause,[],[f654]) ).
fof(f1745,plain,
( ! [X6,X4,X5] :
( disjoint(set_intersection2(X4,X5),X6)
| ~ disjoint(X4,X5) )
| ~ spl18_164 ),
inference(avatar_component_clause,[],[f1744]) ).
fof(f15093,plain,
( spl18_571
| ~ spl18_63
| ~ spl18_141 ),
inference(avatar_split_clause,[],[f1492,f1433,f646,f15091]) ).
fof(f15091,plain,
( spl18_571
<=> ! [X4,X5] : set_union2(X4,X5) = set_union2(set_difference(X4,X5),set_union2(X4,X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_571])]) ).
fof(f646,plain,
( spl18_63
<=> ! [X0,X1] : set_difference(X0,X1) = set_difference(set_union2(X0,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_63])]) ).
fof(f1433,plain,
( spl18_141
<=> ! [X4,X5] : set_union2(set_difference(X4,X5),X4) = X4 ),
introduced(avatar_definition,[new_symbols(naming,[spl18_141])]) ).
fof(f1492,plain,
( ! [X4,X5] : set_union2(X4,X5) = set_union2(set_difference(X4,X5),set_union2(X4,X5))
| ~ spl18_63
| ~ spl18_141 ),
inference(superposition,[],[f1434,f647]) ).
fof(f647,plain,
( ! [X0,X1] : set_difference(X0,X1) = set_difference(set_union2(X0,X1),X1)
| ~ spl18_63 ),
inference(avatar_component_clause,[],[f646]) ).
fof(f1434,plain,
( ! [X4,X5] : set_union2(set_difference(X4,X5),X4) = X4
| ~ spl18_141 ),
inference(avatar_component_clause,[],[f1433]) ).
fof(f15086,plain,
( spl18_570
| ~ spl18_95
| ~ spl18_132 ),
inference(avatar_split_clause,[],[f1358,f1335,f923,f15084]) ).
fof(f15084,plain,
( spl18_570
<=> ! [X13,X12,X11] :
( subset(set_union2(X11,X12),X13)
| ~ subset(X12,sK17)
| ~ subset(X11,sK17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_570])]) ).
fof(f923,plain,
( spl18_95
<=> ! [X2,X0,X1] :
( subset(set_union2(X0,X2),X1)
| ~ subset(X2,X1)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_95])]) ).
fof(f1335,plain,
( spl18_132
<=> ! [X6,X5] :
( ~ subset(X5,sK17)
| subset(X5,X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_132])]) ).
fof(f1358,plain,
( ! [X11,X12,X13] :
( subset(set_union2(X11,X12),X13)
| ~ subset(X12,sK17)
| ~ subset(X11,sK17) )
| ~ spl18_95
| ~ spl18_132 ),
inference(resolution,[],[f1336,f924]) ).
fof(f924,plain,
( ! [X2,X0,X1] :
( subset(set_union2(X0,X2),X1)
| ~ subset(X2,X1)
| ~ subset(X0,X1) )
| ~ spl18_95 ),
inference(avatar_component_clause,[],[f923]) ).
fof(f1336,plain,
( ! [X6,X5] :
( ~ subset(X5,sK17)
| subset(X5,X6) )
| ~ spl18_132 ),
inference(avatar_component_clause,[],[f1335]) ).
fof(f15006,plain,
( spl18_569
| spl18_1
| ~ spl18_558 ),
inference(avatar_split_clause,[],[f14949,f14785,f278,f15003]) ).
fof(f14785,plain,
( spl18_558
<=> ! [X9,X10] :
( sK10(singleton(X9),X10) = X9
| subset(singleton(X9),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_558])]) ).
fof(f14949,plain,
( sK4 = sK10(singleton(sK4),sK5)
| spl18_1
| ~ spl18_558 ),
inference(resolution,[],[f14786,f279]) ).
fof(f279,plain,
( ~ subset(singleton(sK4),sK5)
| spl18_1 ),
inference(avatar_component_clause,[],[f278]) ).
fof(f14786,plain,
( ! [X10,X9] :
( subset(singleton(X9),X10)
| sK10(singleton(X9),X10) = X9 )
| ~ spl18_558 ),
inference(avatar_component_clause,[],[f14785]) ).
fof(f14842,plain,
( spl18_568
| ~ spl18_93
| ~ spl18_286 ),
inference(avatar_split_clause,[],[f4606,f4516,f906,f14840]) ).
fof(f14840,plain,
( spl18_568
<=> ! [X32] :
( in(sK14(sK17,sK17,X32),X32)
| sP2(sK17,sK17,X32) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_568])]) ).
fof(f906,plain,
( spl18_93
<=> ! [X0] : ~ in(X0,sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_93])]) ).
fof(f4516,plain,
( spl18_286
<=> ! [X4,X5] :
( in(sK14(X4,X4,X5),X5)
| in(sK14(X4,X4,X5),X4)
| sP2(X4,X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_286])]) ).
fof(f4606,plain,
( ! [X32] :
( in(sK14(sK17,sK17,X32),X32)
| sP2(sK17,sK17,X32) )
| ~ spl18_93
| ~ spl18_286 ),
inference(resolution,[],[f4517,f907]) ).
fof(f907,plain,
( ! [X0] : ~ in(X0,sK17)
| ~ spl18_93 ),
inference(avatar_component_clause,[],[f906]) ).
fof(f4517,plain,
( ! [X4,X5] :
( in(sK14(X4,X4,X5),X5)
| in(sK14(X4,X4,X5),X4)
| sP2(X4,X4,X5) )
| ~ spl18_286 ),
inference(avatar_component_clause,[],[f4516]) ).
fof(f14838,plain,
( spl18_567
| ~ spl18_93
| ~ spl18_286 ),
inference(avatar_split_clause,[],[f4593,f4516,f906,f14836]) ).
fof(f14836,plain,
( spl18_567
<=> ! [X34] :
( in(sK14(X34,X34,sK17),X34)
| sP2(X34,X34,sK17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_567])]) ).
fof(f4593,plain,
( ! [X34] :
( in(sK14(X34,X34,sK17),X34)
| sP2(X34,X34,sK17) )
| ~ spl18_93
| ~ spl18_286 ),
inference(resolution,[],[f4517,f907]) ).
fof(f14819,plain,
( spl18_566
| ~ spl18_93
| ~ spl18_285 ),
inference(avatar_split_clause,[],[f4577,f4512,f906,f14817]) ).
fof(f14817,plain,
( spl18_566
<=> ! [X34] :
( in(sK14(sK17,X34,sK17),X34)
| sP2(sK17,X34,sK17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_566])]) ).
fof(f4512,plain,
( spl18_285
<=> ! [X2,X3] :
( in(sK14(X2,X3,X2),X2)
| in(sK14(X2,X3,X2),X3)
| sP2(X2,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_285])]) ).
fof(f4577,plain,
( ! [X34] :
( in(sK14(sK17,X34,sK17),X34)
| sP2(sK17,X34,sK17) )
| ~ spl18_93
| ~ spl18_285 ),
inference(resolution,[],[f4513,f907]) ).
fof(f4513,plain,
( ! [X2,X3] :
( in(sK14(X2,X3,X2),X3)
| in(sK14(X2,X3,X2),X2)
| sP2(X2,X3,X2) )
| ~ spl18_285 ),
inference(avatar_component_clause,[],[f4512]) ).
fof(f14815,plain,
( spl18_565
| ~ spl18_93
| ~ spl18_284 ),
inference(avatar_split_clause,[],[f4535,f4508,f906,f14813]) ).
fof(f14813,plain,
( spl18_565
<=> ! [X34] :
( in(sK14(X34,sK17,sK17),X34)
| sP2(X34,sK17,sK17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_565])]) ).
fof(f4508,plain,
( spl18_284
<=> ! [X0,X1] :
( in(sK14(X0,X1,X1),X1)
| in(sK14(X0,X1,X1),X0)
| sP2(X0,X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_284])]) ).
fof(f4535,plain,
( ! [X34] :
( in(sK14(X34,sK17,sK17),X34)
| sP2(X34,sK17,sK17) )
| ~ spl18_93
| ~ spl18_284 ),
inference(resolution,[],[f4509,f907]) ).
fof(f4509,plain,
( ! [X0,X1] :
( in(sK14(X0,X1,X1),X1)
| in(sK14(X0,X1,X1),X0)
| sP2(X0,X1,X1) )
| ~ spl18_284 ),
inference(avatar_component_clause,[],[f4508]) ).
fof(f14811,plain,
( spl18_564
| ~ spl18_30
| ~ spl18_217 ),
inference(avatar_split_clause,[],[f2754,f2697,f421,f14809]) ).
fof(f14809,plain,
( spl18_564
<=> ! [X4,X3] :
( sP3(X3,X3,X4)
| ~ in(X4,sK15(X3,X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_564])]) ).
fof(f421,plain,
( spl18_30
<=> ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_30])]) ).
fof(f2697,plain,
( spl18_217
<=> ! [X2,X3] :
( sP3(X2,X2,X3)
| in(sK15(X2,X2,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_217])]) ).
fof(f2754,plain,
( ! [X3,X4] :
( sP3(X3,X3,X4)
| ~ in(X4,sK15(X3,X3,X4)) )
| ~ spl18_30
| ~ spl18_217 ),
inference(resolution,[],[f2698,f422]) ).
fof(f422,plain,
( ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) )
| ~ spl18_30 ),
inference(avatar_component_clause,[],[f421]) ).
fof(f2698,plain,
( ! [X2,X3] :
( in(sK15(X2,X2,X3),X3)
| sP3(X2,X2,X3) )
| ~ spl18_217 ),
inference(avatar_component_clause,[],[f2697]) ).
fof(f14807,plain,
( spl18_563
| ~ spl18_30
| ~ spl18_216 ),
inference(avatar_split_clause,[],[f2742,f2693,f421,f14805]) ).
fof(f14805,plain,
( spl18_563
<=> ! [X4,X3] :
( sP3(X3,X4,X4)
| ~ in(X4,sK15(X3,X4,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_563])]) ).
fof(f2693,plain,
( spl18_216
<=> ! [X0,X1] :
( in(sK15(X0,X1,X1),X1)
| sP3(X0,X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_216])]) ).
fof(f2742,plain,
( ! [X3,X4] :
( sP3(X3,X4,X4)
| ~ in(X4,sK15(X3,X4,X4)) )
| ~ spl18_30
| ~ spl18_216 ),
inference(resolution,[],[f2694,f422]) ).
fof(f2694,plain,
( ! [X0,X1] :
( in(sK15(X0,X1,X1),X1)
| sP3(X0,X1,X1) )
| ~ spl18_216 ),
inference(avatar_component_clause,[],[f2693]) ).
fof(f14803,plain,
( spl18_562
| ~ spl18_30
| ~ spl18_215 ),
inference(avatar_split_clause,[],[f2731,f2684,f421,f14801]) ).
fof(f14801,plain,
( spl18_562
<=> ! [X2,X3] :
( sP1(X2,X3,X2)
| ~ in(X2,sK13(X2,X3,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_562])]) ).
fof(f2684,plain,
( spl18_215
<=> ! [X0,X1] :
( in(sK13(X0,X1,X0),X0)
| sP1(X0,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_215])]) ).
fof(f2731,plain,
( ! [X2,X3] :
( sP1(X2,X3,X2)
| ~ in(X2,sK13(X2,X3,X2)) )
| ~ spl18_30
| ~ spl18_215 ),
inference(resolution,[],[f2685,f422]) ).
fof(f2685,plain,
( ! [X0,X1] :
( in(sK13(X0,X1,X0),X0)
| sP1(X0,X1,X0) )
| ~ spl18_215 ),
inference(avatar_component_clause,[],[f2684]) ).
fof(f14799,plain,
( spl18_561
| ~ spl18_30
| ~ spl18_214 ),
inference(avatar_split_clause,[],[f2721,f2680,f421,f14797]) ).
fof(f14797,plain,
( spl18_561
<=> ! [X2,X3] :
( sP1(X2,X3,X3)
| ~ in(X3,sK13(X2,X3,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_561])]) ).
fof(f2680,plain,
( spl18_214
<=> ! [X0,X1] :
( in(sK13(X0,X1,X1),X1)
| sP1(X0,X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_214])]) ).
fof(f2721,plain,
( ! [X2,X3] :
( sP1(X2,X3,X3)
| ~ in(X3,sK13(X2,X3,X3)) )
| ~ spl18_30
| ~ spl18_214 ),
inference(resolution,[],[f2681,f422]) ).
fof(f2681,plain,
( ! [X0,X1] :
( in(sK13(X0,X1,X1),X1)
| sP1(X0,X1,X1) )
| ~ spl18_214 ),
inference(avatar_component_clause,[],[f2680]) ).
fof(f14795,plain,
( spl18_560
| ~ spl18_30
| ~ spl18_213 ),
inference(avatar_split_clause,[],[f2711,f2676,f421,f14793]) ).
fof(f14793,plain,
( spl18_560
<=> ! [X2,X3] :
( X2 = X3
| ~ empty(X2)
| ~ in(X3,sK9(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_560])]) ).
fof(f2676,plain,
( spl18_213
<=> ! [X2,X3] :
( in(sK9(X2,X3),X3)
| X2 = X3
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_213])]) ).
fof(f2711,plain,
( ! [X2,X3] :
( X2 = X3
| ~ empty(X2)
| ~ in(X3,sK9(X2,X3)) )
| ~ spl18_30
| ~ spl18_213 ),
inference(resolution,[],[f2677,f422]) ).
fof(f2677,plain,
( ! [X2,X3] :
( in(sK9(X2,X3),X3)
| X2 = X3
| ~ empty(X2) )
| ~ spl18_213 ),
inference(avatar_component_clause,[],[f2676]) ).
fof(f14791,plain,
( spl18_559
| ~ spl18_30
| ~ spl18_212 ),
inference(avatar_split_clause,[],[f2701,f2672,f421,f14789]) ).
fof(f14789,plain,
( spl18_559
<=> ! [X2,X1] :
( X1 = X2
| ~ empty(X2)
| ~ in(X1,sK9(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_559])]) ).
fof(f2672,plain,
( spl18_212
<=> ! [X2,X3] :
( in(sK9(X2,X3),X2)
| X2 = X3
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_212])]) ).
fof(f2701,plain,
( ! [X2,X1] :
( X1 = X2
| ~ empty(X2)
| ~ in(X1,sK9(X1,X2)) )
| ~ spl18_30
| ~ spl18_212 ),
inference(resolution,[],[f2673,f422]) ).
fof(f2673,plain,
( ! [X2,X3] :
( in(sK9(X2,X3),X2)
| X2 = X3
| ~ empty(X3) )
| ~ spl18_212 ),
inference(avatar_component_clause,[],[f2672]) ).
fof(f14787,plain,
( spl18_558
| ~ spl18_57
| ~ spl18_157 ),
inference(avatar_split_clause,[],[f1712,f1682,f610,f14785]) ).
fof(f610,plain,
( spl18_57
<=> ! [X0,X1] :
( subset(X0,X1)
| in(sK10(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_57])]) ).
fof(f1712,plain,
( ! [X10,X9] :
( sK10(singleton(X9),X10) = X9
| subset(singleton(X9),X10) )
| ~ spl18_57
| ~ spl18_157 ),
inference(resolution,[],[f1683,f611]) ).
fof(f611,plain,
( ! [X0,X1] :
( in(sK10(X0,X1),X0)
| subset(X0,X1) )
| ~ spl18_57 ),
inference(avatar_component_clause,[],[f610]) ).
fof(f14783,plain,
( spl18_557
| ~ spl18_93
| ~ spl18_111 ),
inference(avatar_split_clause,[],[f1076,f1035,f906,f14781]) ).
fof(f14781,plain,
( spl18_557
<=> ! [X11,X10] :
( in(sK15(X10,sK17,X11),X11)
| sP3(X10,sK17,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_557])]) ).
fof(f1035,plain,
( spl18_111
<=> ! [X2,X0,X1] :
( sP3(X0,X1,X2)
| in(sK15(X0,X1,X2),X1)
| in(sK15(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_111])]) ).
fof(f1076,plain,
( ! [X10,X11] :
( in(sK15(X10,sK17,X11),X11)
| sP3(X10,sK17,X11) )
| ~ spl18_93
| ~ spl18_111 ),
inference(resolution,[],[f1036,f907]) ).
fof(f1036,plain,
( ! [X2,X0,X1] :
( in(sK15(X0,X1,X2),X2)
| in(sK15(X0,X1,X2),X1)
| sP3(X0,X1,X2) )
| ~ spl18_111 ),
inference(avatar_component_clause,[],[f1035]) ).
fof(f14779,plain,
( spl18_556
| ~ spl18_141
| ~ spl18_547 ),
inference(avatar_split_clause,[],[f13314,f12542,f1433,f14777]) ).
fof(f14777,plain,
( spl18_556
<=> ! [X29,X30] : ~ in(singleton(X29),set_difference(X29,X30)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_556])]) ).
fof(f12542,plain,
( spl18_547
<=> ! [X0,X1] : ~ in(singleton(set_union2(X0,X1)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_547])]) ).
fof(f13314,plain,
( ! [X29,X30] : ~ in(singleton(X29),set_difference(X29,X30))
| ~ spl18_141
| ~ spl18_547 ),
inference(superposition,[],[f12543,f1434]) ).
fof(f12543,plain,
( ! [X0,X1] : ~ in(singleton(set_union2(X0,X1)),X0)
| ~ spl18_547 ),
inference(avatar_component_clause,[],[f12542]) ).
fof(f14775,plain,
( spl18_555
| ~ spl18_93
| ~ spl18_111 ),
inference(avatar_split_clause,[],[f1072,f1035,f906,f14773]) ).
fof(f14773,plain,
( spl18_555
<=> ! [X11,X10] :
( in(sK15(X10,X11,sK17),X11)
| sP3(X10,X11,sK17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_555])]) ).
fof(f1072,plain,
( ! [X10,X11] :
( in(sK15(X10,X11,sK17),X11)
| sP3(X10,X11,sK17) )
| ~ spl18_93
| ~ spl18_111 ),
inference(resolution,[],[f1036,f907]) ).
fof(f14771,plain,
( spl18_554
| ~ spl18_93
| ~ spl18_108 ),
inference(avatar_split_clause,[],[f1067,f1023,f906,f14769]) ).
fof(f14769,plain,
( spl18_554
<=> ! [X11,X10] :
( in(sK13(sK17,X10,X11),X11)
| sP1(sK17,X10,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_554])]) ).
fof(f1023,plain,
( spl18_108
<=> ! [X2,X0,X1] :
( sP1(X0,X1,X2)
| in(sK13(X0,X1,X2),X0)
| in(sK13(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_108])]) ).
fof(f1067,plain,
( ! [X10,X11] :
( in(sK13(sK17,X10,X11),X11)
| sP1(sK17,X10,X11) )
| ~ spl18_93
| ~ spl18_108 ),
inference(resolution,[],[f1024,f907]) ).
fof(f1024,plain,
( ! [X2,X0,X1] :
( in(sK13(X0,X1,X2),X2)
| in(sK13(X0,X1,X2),X0)
| sP1(X0,X1,X2) )
| ~ spl18_108 ),
inference(avatar_component_clause,[],[f1023]) ).
fof(f14767,plain,
( spl18_553
| ~ spl18_93
| ~ spl18_108 ),
inference(avatar_split_clause,[],[f1063,f1023,f906,f14765]) ).
fof(f14765,plain,
( spl18_553
<=> ! [X11,X10] :
( in(sK13(X10,X11,sK17),X10)
| sP1(X10,X11,sK17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_553])]) ).
fof(f1063,plain,
( ! [X10,X11] :
( in(sK13(X10,X11,sK17),X10)
| sP1(X10,X11,sK17) )
| ~ spl18_93
| ~ spl18_108 ),
inference(resolution,[],[f1024,f907]) ).
fof(f14763,plain,
( spl18_552
| ~ spl18_93
| ~ spl18_107 ),
inference(avatar_split_clause,[],[f1049,f1019,f906,f14761]) ).
fof(f14761,plain,
( spl18_552
<=> ! [X11,X10] :
( in(sK13(X10,sK17,X11),X11)
| sP1(X10,sK17,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_552])]) ).
fof(f1019,plain,
( spl18_107
<=> ! [X2,X0,X1] :
( sP1(X0,X1,X2)
| in(sK13(X0,X1,X2),X1)
| in(sK13(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_107])]) ).
fof(f1049,plain,
( ! [X10,X11] :
( in(sK13(X10,sK17,X11),X11)
| sP1(X10,sK17,X11) )
| ~ spl18_93
| ~ spl18_107 ),
inference(resolution,[],[f1020,f907]) ).
fof(f1020,plain,
( ! [X2,X0,X1] :
( in(sK13(X0,X1,X2),X2)
| in(sK13(X0,X1,X2),X1)
| sP1(X0,X1,X2) )
| ~ spl18_107 ),
inference(avatar_component_clause,[],[f1019]) ).
fof(f14759,plain,
( spl18_551
| ~ spl18_93
| ~ spl18_107 ),
inference(avatar_split_clause,[],[f1045,f1019,f906,f14757]) ).
fof(f14757,plain,
( spl18_551
<=> ! [X11,X10] :
( in(sK13(X10,X11,sK17),X11)
| sP1(X10,X11,sK17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_551])]) ).
fof(f1045,plain,
( ! [X10,X11] :
( in(sK13(X10,X11,sK17),X11)
| sP1(X10,X11,sK17) )
| ~ spl18_93
| ~ spl18_107 ),
inference(resolution,[],[f1020,f907]) ).
fof(f14560,plain,
( spl18_550
| ~ spl18_352
| ~ spl18_547 ),
inference(avatar_split_clause,[],[f13312,f12542,f5894,f14558]) ).
fof(f14558,plain,
( spl18_550
<=> ! [X25,X26] : ~ in(singleton(X26),set_intersection2(X25,X26)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_550])]) ).
fof(f5894,plain,
( spl18_352
<=> ! [X2,X3] : set_union2(set_intersection2(X2,X3),X3) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl18_352])]) ).
fof(f13312,plain,
( ! [X26,X25] : ~ in(singleton(X26),set_intersection2(X25,X26))
| ~ spl18_352
| ~ spl18_547 ),
inference(superposition,[],[f12543,f5895]) ).
fof(f5895,plain,
( ! [X2,X3] : set_union2(set_intersection2(X2,X3),X3) = X3
| ~ spl18_352 ),
inference(avatar_component_clause,[],[f5894]) ).
fof(f14099,plain,
( spl18_549
| ~ spl18_140
| ~ spl18_547 ),
inference(avatar_split_clause,[],[f13311,f12542,f1429,f14097]) ).
fof(f14097,plain,
( spl18_549
<=> ! [X24,X23] : ~ in(singleton(X23),set_intersection2(X23,X24)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_549])]) ).
fof(f1429,plain,
( spl18_140
<=> ! [X2,X1] : set_union2(set_intersection2(X1,X2),X1) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl18_140])]) ).
fof(f13311,plain,
( ! [X24,X23] : ~ in(singleton(X23),set_intersection2(X23,X24))
| ~ spl18_140
| ~ spl18_547 ),
inference(superposition,[],[f12543,f1430]) ).
fof(f1430,plain,
( ! [X2,X1] : set_union2(set_intersection2(X1,X2),X1) = X1
| ~ spl18_140 ),
inference(avatar_component_clause,[],[f1429]) ).
fof(f13080,plain,
( spl18_548
| ~ spl18_267
| ~ spl18_381 ),
inference(avatar_split_clause,[],[f7519,f7243,f4233,f13078]) ).
fof(f13078,plain,
( spl18_548
<=> ! [X16,X17] : ~ in(singleton(set_union2(X16,X17)),X17) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_548])]) ).
fof(f4233,plain,
( spl18_267
<=> ! [X1] : ~ in(singleton(X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_267])]) ).
fof(f7243,plain,
( spl18_381
<=> ! [X16,X17,X15] :
( ~ in(X15,X16)
| in(X15,set_union2(X17,X16)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_381])]) ).
fof(f7519,plain,
( ! [X16,X17] : ~ in(singleton(set_union2(X16,X17)),X17)
| ~ spl18_267
| ~ spl18_381 ),
inference(resolution,[],[f7244,f4234]) ).
fof(f4234,plain,
( ! [X1] : ~ in(singleton(X1),X1)
| ~ spl18_267 ),
inference(avatar_component_clause,[],[f4233]) ).
fof(f7244,plain,
( ! [X16,X17,X15] :
( in(X15,set_union2(X17,X16))
| ~ in(X15,X16) )
| ~ spl18_381 ),
inference(avatar_component_clause,[],[f7243]) ).
fof(f12544,plain,
( spl18_547
| ~ spl18_175
| ~ spl18_267 ),
inference(avatar_split_clause,[],[f4367,f4233,f1788,f12542]) ).
fof(f1788,plain,
( spl18_175
<=> ! [X12,X11,X10] :
( ~ in(X10,X11)
| in(X10,set_union2(X11,X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_175])]) ).
fof(f4367,plain,
( ! [X0,X1] : ~ in(singleton(set_union2(X0,X1)),X0)
| ~ spl18_175
| ~ spl18_267 ),
inference(resolution,[],[f4234,f1789]) ).
fof(f1789,plain,
( ! [X10,X11,X12] :
( in(X10,set_union2(X11,X12))
| ~ in(X10,X11) )
| ~ spl18_175 ),
inference(avatar_component_clause,[],[f1788]) ).
fof(f12540,plain,
( spl18_546
| ~ spl18_53
| ~ spl18_245 ),
inference(avatar_split_clause,[],[f3570,f3539,f583,f12538]) ).
fof(f12538,plain,
( spl18_546
<=> ! [X9,X8] :
( sK17 != X9
| subset(set_union2(X8,X9),set_difference(X8,X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_546])]) ).
fof(f583,plain,
( spl18_53
<=> ! [X0,X1] :
( set_difference(X0,X1) != sK17
| subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_53])]) ).
fof(f3539,plain,
( spl18_245
<=> ! [X0,X1] : set_difference(set_union2(X0,X1),set_difference(X0,X1)) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl18_245])]) ).
fof(f3570,plain,
( ! [X8,X9] :
( sK17 != X9
| subset(set_union2(X8,X9),set_difference(X8,X9)) )
| ~ spl18_53
| ~ spl18_245 ),
inference(superposition,[],[f584,f3540]) ).
fof(f3540,plain,
( ! [X0,X1] : set_difference(set_union2(X0,X1),set_difference(X0,X1)) = X1
| ~ spl18_245 ),
inference(avatar_component_clause,[],[f3539]) ).
fof(f584,plain,
( ! [X0,X1] :
( set_difference(X0,X1) != sK17
| subset(X0,X1) )
| ~ spl18_53 ),
inference(avatar_component_clause,[],[f583]) ).
fof(f12536,plain,
( spl18_545
| ~ spl18_60
| ~ spl18_196
| ~ spl18_243 ),
inference(avatar_split_clause,[],[f3525,f3475,f2320,f634,f12534]) ).
fof(f12534,plain,
( spl18_545
<=> ! [X43,X42] :
( subset(set_union2(X42,X43),set_difference(X43,X42))
| sK17 != X42 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_545])]) ).
fof(f634,plain,
( spl18_60
<=> ! [X0,X1] : set_union2(X0,X1) = set_union2(X0,set_difference(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_60])]) ).
fof(f2320,plain,
( spl18_196
<=> ! [X4,X5] :
( sK17 != set_difference(X4,X5)
| subset(set_union2(X4,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_196])]) ).
fof(f3475,plain,
( spl18_243
<=> ! [X6,X7] : set_difference(X6,set_difference(X7,X6)) = X6 ),
introduced(avatar_definition,[new_symbols(naming,[spl18_243])]) ).
fof(f3525,plain,
( ! [X42,X43] :
( subset(set_union2(X42,X43),set_difference(X43,X42))
| sK17 != X42 )
| ~ spl18_60
| ~ spl18_196
| ~ spl18_243 ),
inference(forward_demodulation,[],[f3509,f635]) ).
fof(f635,plain,
( ! [X0,X1] : set_union2(X0,X1) = set_union2(X0,set_difference(X1,X0))
| ~ spl18_60 ),
inference(avatar_component_clause,[],[f634]) ).
fof(f3509,plain,
( ! [X42,X43] :
( sK17 != X42
| subset(set_union2(X42,set_difference(X43,X42)),set_difference(X43,X42)) )
| ~ spl18_196
| ~ spl18_243 ),
inference(superposition,[],[f2321,f3476]) ).
fof(f3476,plain,
( ! [X6,X7] : set_difference(X6,set_difference(X7,X6)) = X6
| ~ spl18_243 ),
inference(avatar_component_clause,[],[f3475]) ).
fof(f2321,plain,
( ! [X4,X5] :
( sK17 != set_difference(X4,X5)
| subset(set_union2(X4,X5),X5) )
| ~ spl18_196 ),
inference(avatar_component_clause,[],[f2320]) ).
fof(f12532,plain,
( spl18_544
| ~ spl18_210
| ~ spl18_243 ),
inference(avatar_split_clause,[],[f3512,f3475,f2376,f12530]) ).
fof(f12530,plain,
( spl18_544
<=> ! [X50,X48,X49] :
( ~ proper_subset(set_difference(X50,set_difference(X49,X48)),X48)
| ~ subset(X48,X50) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_544])]) ).
fof(f2376,plain,
( spl18_210
<=> ! [X2,X0,X1] :
( ~ subset(X0,X1)
| ~ proper_subset(set_difference(X1,X2),set_difference(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_210])]) ).
fof(f3512,plain,
( ! [X50,X48,X49] :
( ~ proper_subset(set_difference(X50,set_difference(X49,X48)),X48)
| ~ subset(X48,X50) )
| ~ spl18_210
| ~ spl18_243 ),
inference(superposition,[],[f2377,f3476]) ).
fof(f2377,plain,
( ! [X2,X0,X1] :
( ~ proper_subset(set_difference(X1,X2),set_difference(X0,X2))
| ~ subset(X0,X1) )
| ~ spl18_210 ),
inference(avatar_component_clause,[],[f2376]) ).
fof(f12528,plain,
( spl18_543
| ~ spl18_81
| ~ spl18_243 ),
inference(avatar_split_clause,[],[f3499,f3475,f811,f12526]) ).
fof(f12526,plain,
( spl18_543
<=> ! [X20,X18,X19] :
( subset(X18,set_difference(X20,set_difference(X19,X18)))
| ~ subset(X18,X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_543])]) ).
fof(f811,plain,
( spl18_81
<=> ! [X2,X0,X1] :
( subset(set_difference(X0,X2),set_difference(X1,X2))
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_81])]) ).
fof(f3499,plain,
( ! [X18,X19,X20] :
( subset(X18,set_difference(X20,set_difference(X19,X18)))
| ~ subset(X18,X20) )
| ~ spl18_81
| ~ spl18_243 ),
inference(superposition,[],[f812,f3476]) ).
fof(f812,plain,
( ! [X2,X0,X1] :
( subset(set_difference(X0,X2),set_difference(X1,X2))
| ~ subset(X0,X1) )
| ~ spl18_81 ),
inference(avatar_component_clause,[],[f811]) ).
fof(f12523,plain,
( spl18_542
| ~ spl18_168
| ~ spl18_241 ),
inference(avatar_split_clause,[],[f3438,f3399,f1760,f12521]) ).
fof(f12521,plain,
( spl18_542
<=> ! [X30,X31] :
( ~ empty(X30)
| empty(set_difference(set_intersection2(X30,X31),set_difference(X30,X31))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_542])]) ).
fof(f1760,plain,
( spl18_168
<=> ! [X6,X7] :
( ~ empty(set_union2(X6,X7))
| empty(set_difference(X7,X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_168])]) ).
fof(f3399,plain,
( spl18_241
<=> ! [X0,X1] : set_union2(set_difference(X0,X1),set_intersection2(X0,X1)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl18_241])]) ).
fof(f3438,plain,
( ! [X31,X30] :
( ~ empty(X30)
| empty(set_difference(set_intersection2(X30,X31),set_difference(X30,X31))) )
| ~ spl18_168
| ~ spl18_241 ),
inference(superposition,[],[f1761,f3400]) ).
fof(f3400,plain,
( ! [X0,X1] : set_union2(set_difference(X0,X1),set_intersection2(X0,X1)) = X0
| ~ spl18_241 ),
inference(avatar_component_clause,[],[f3399]) ).
fof(f1761,plain,
( ! [X6,X7] :
( ~ empty(set_union2(X6,X7))
| empty(set_difference(X7,X6)) )
| ~ spl18_168 ),
inference(avatar_component_clause,[],[f1760]) ).
fof(f12519,plain,
( spl18_541
| ~ spl18_171
| ~ spl18_233 ),
inference(avatar_split_clause,[],[f3249,f2995,f1772,f12517]) ).
fof(f12517,plain,
( spl18_541
<=> ! [X2,X0,X1] :
( ~ subset(X0,set_union2(X1,X2))
| subset(set_difference(X0,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_541])]) ).
fof(f1772,plain,
( spl18_171
<=> ! [X9,X8,X7] :
( subset(X7,X8)
| ~ subset(X7,set_difference(X8,X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_171])]) ).
fof(f2995,plain,
( spl18_233
<=> ! [X9,X8,X7] :
( subset(set_difference(X9,X8),set_difference(X7,X8))
| ~ subset(X9,set_union2(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_233])]) ).
fof(f3249,plain,
( ! [X2,X0,X1] :
( ~ subset(X0,set_union2(X1,X2))
| subset(set_difference(X0,X2),X1) )
| ~ spl18_171
| ~ spl18_233 ),
inference(resolution,[],[f2996,f1773]) ).
fof(f1773,plain,
( ! [X8,X9,X7] :
( ~ subset(X7,set_difference(X8,X9))
| subset(X7,X8) )
| ~ spl18_171 ),
inference(avatar_component_clause,[],[f1772]) ).
fof(f2996,plain,
( ! [X8,X9,X7] :
( subset(set_difference(X9,X8),set_difference(X7,X8))
| ~ subset(X9,set_union2(X7,X8)) )
| ~ spl18_233 ),
inference(avatar_component_clause,[],[f2995]) ).
fof(f12515,plain,
( spl18_540
| ~ spl18_126
| ~ spl18_231 ),
inference(avatar_split_clause,[],[f3167,f2983,f1171,f12513]) ).
fof(f12513,plain,
( spl18_540
<=> ! [X0,X1] :
( subset(set_difference(X1,X0),sK17)
| ~ subset(set_union2(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_540])]) ).
fof(f1171,plain,
( spl18_126
<=> ! [X0] : sK17 = set_difference(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_126])]) ).
fof(f2983,plain,
( spl18_231
<=> ! [X9,X8,X7] :
( subset(set_difference(X7,X8),set_difference(X9,X8))
| ~ subset(set_union2(X7,X8),X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_231])]) ).
fof(f3167,plain,
( ! [X0,X1] :
( subset(set_difference(X1,X0),sK17)
| ~ subset(set_union2(X1,X0),X0) )
| ~ spl18_126
| ~ spl18_231 ),
inference(superposition,[],[f2984,f1172]) ).
fof(f1172,plain,
( ! [X0] : sK17 = set_difference(X0,X0)
| ~ spl18_126 ),
inference(avatar_component_clause,[],[f1171]) ).
fof(f2984,plain,
( ! [X8,X9,X7] :
( subset(set_difference(X7,X8),set_difference(X9,X8))
| ~ subset(set_union2(X7,X8),X9) )
| ~ spl18_231 ),
inference(avatar_component_clause,[],[f2983]) ).
fof(f12511,plain,
( spl18_539
| ~ spl18_171
| ~ spl18_231 ),
inference(avatar_split_clause,[],[f3144,f2983,f1772,f12509]) ).
fof(f12509,plain,
( spl18_539
<=> ! [X2,X0,X1] :
( ~ subset(set_union2(X0,X1),X2)
| subset(set_difference(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_539])]) ).
fof(f3144,plain,
( ! [X2,X0,X1] :
( ~ subset(set_union2(X0,X1),X2)
| subset(set_difference(X0,X1),X2) )
| ~ spl18_171
| ~ spl18_231 ),
inference(resolution,[],[f2984,f1773]) ).
fof(f12507,plain,
( spl18_538
| ~ spl18_130
| ~ spl18_225 ),
inference(avatar_split_clause,[],[f2945,f2838,f1296,f12505]) ).
fof(f12505,plain,
( spl18_538
<=> ! [X9,X10] :
( ~ subset(X9,sK17)
| sK17 = set_union2(X10,X9)
| ~ empty(X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_538])]) ).
fof(f1296,plain,
( spl18_130
<=> ! [X2,X3] :
( subset(X2,X3)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_130])]) ).
fof(f2838,plain,
( spl18_225
<=> ! [X27,X26] :
( ~ subset(X26,sK17)
| ~ subset(X27,sK17)
| sK17 = set_union2(X27,X26) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_225])]) ).
fof(f2945,plain,
( ! [X10,X9] :
( ~ subset(X9,sK17)
| sK17 = set_union2(X10,X9)
| ~ empty(X10) )
| ~ spl18_130
| ~ spl18_225 ),
inference(resolution,[],[f2839,f1297]) ).
fof(f1297,plain,
( ! [X2,X3] :
( subset(X2,X3)
| ~ empty(X2) )
| ~ spl18_130 ),
inference(avatar_component_clause,[],[f1296]) ).
fof(f2839,plain,
( ! [X26,X27] :
( ~ subset(X27,sK17)
| ~ subset(X26,sK17)
| sK17 = set_union2(X27,X26) )
| ~ spl18_225 ),
inference(avatar_component_clause,[],[f2838]) ).
fof(f12503,plain,
( spl18_537
| ~ spl18_53
| ~ spl18_219 ),
inference(avatar_split_clause,[],[f2787,f2770,f583,f12501]) ).
fof(f12501,plain,
( spl18_537
<=> ! [X4,X5] :
( sK17 != set_difference(X4,X5)
| subset(X4,set_intersection2(X4,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_537])]) ).
fof(f2770,plain,
( spl18_219
<=> ! [X2,X3] : set_difference(X2,X3) = set_difference(X2,set_intersection2(X2,X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_219])]) ).
fof(f2787,plain,
( ! [X4,X5] :
( sK17 != set_difference(X4,X5)
| subset(X4,set_intersection2(X4,X5)) )
| ~ spl18_53
| ~ spl18_219 ),
inference(superposition,[],[f584,f2771]) ).
fof(f2771,plain,
( ! [X2,X3] : set_difference(X2,X3) = set_difference(X2,set_intersection2(X2,X3))
| ~ spl18_219 ),
inference(avatar_component_clause,[],[f2770]) ).
fof(f12462,plain,
( spl18_536
| ~ spl18_49
| ~ spl18_219 ),
inference(avatar_split_clause,[],[f2786,f2770,f535,f12460]) ).
fof(f12460,plain,
( spl18_536
<=> ! [X2,X3] :
( set_difference(X2,X3) != X2
| disjoint(X2,set_intersection2(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_536])]) ).
fof(f535,plain,
( spl18_49
<=> ! [X0,X1] :
( disjoint(X0,X1)
| set_difference(X0,X1) != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_49])]) ).
fof(f2786,plain,
( ! [X2,X3] :
( set_difference(X2,X3) != X2
| disjoint(X2,set_intersection2(X2,X3)) )
| ~ spl18_49
| ~ spl18_219 ),
inference(superposition,[],[f536,f2771]) ).
fof(f536,plain,
( ! [X0,X1] :
( set_difference(X0,X1) != X0
| disjoint(X0,X1) )
| ~ spl18_49 ),
inference(avatar_component_clause,[],[f535]) ).
fof(f12458,plain,
( spl18_535
| ~ spl18_43
| ~ spl18_212 ),
inference(avatar_split_clause,[],[f2705,f2672,f511,f12456]) ).
fof(f12456,plain,
( spl18_535
<=> ! [X13,X12,X11] :
( set_intersection2(X11,X12) = X13
| ~ empty(X13)
| ~ disjoint(X11,X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_535])]) ).
fof(f511,plain,
( spl18_43
<=> ! [X2,X0,X1] :
( ~ disjoint(X0,X1)
| ~ in(X2,set_intersection2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_43])]) ).
fof(f2705,plain,
( ! [X11,X12,X13] :
( set_intersection2(X11,X12) = X13
| ~ empty(X13)
| ~ disjoint(X11,X12) )
| ~ spl18_43
| ~ spl18_212 ),
inference(resolution,[],[f2673,f512]) ).
fof(f512,plain,
( ! [X2,X0,X1] :
( ~ in(X2,set_intersection2(X0,X1))
| ~ disjoint(X0,X1) )
| ~ spl18_43 ),
inference(avatar_component_clause,[],[f511]) ).
fof(f12454,plain,
( spl18_534
| ~ spl18_162
| ~ spl18_212 ),
inference(avatar_split_clause,[],[f2704,f2672,f1736,f12452]) ).
fof(f12452,plain,
( spl18_534
<=> ! [X9,X8,X10] :
( set_intersection2(X8,X9) = X10
| ~ empty(X10)
| ~ disjoint(X9,X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_534])]) ).
fof(f1736,plain,
( spl18_162
<=> ! [X6,X4,X5] :
( ~ in(X6,set_intersection2(X5,X4))
| ~ disjoint(X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_162])]) ).
fof(f2704,plain,
( ! [X10,X8,X9] :
( set_intersection2(X8,X9) = X10
| ~ empty(X10)
| ~ disjoint(X9,X8) )
| ~ spl18_162
| ~ spl18_212 ),
inference(resolution,[],[f2673,f1737]) ).
fof(f1737,plain,
( ! [X6,X4,X5] :
( ~ in(X6,set_intersection2(X5,X4))
| ~ disjoint(X4,X5) )
| ~ spl18_162 ),
inference(avatar_component_clause,[],[f1736]) ).
fof(f12450,plain,
( spl18_533
| ~ spl18_144
| ~ spl18_210 ),
inference(avatar_split_clause,[],[f2654,f2376,f1445,f12448]) ).
fof(f12448,plain,
( spl18_533
<=> ! [X22,X21,X23] :
( ~ proper_subset(sK17,set_difference(X23,X21))
| ~ subset(X23,set_difference(X21,X22)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_533])]) ).
fof(f1445,plain,
( spl18_144
<=> ! [X4,X5] : sK17 = set_difference(set_difference(X4,X5),X4) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_144])]) ).
fof(f2654,plain,
( ! [X21,X22,X23] :
( ~ proper_subset(sK17,set_difference(X23,X21))
| ~ subset(X23,set_difference(X21,X22)) )
| ~ spl18_144
| ~ spl18_210 ),
inference(superposition,[],[f2377,f1446]) ).
fof(f1446,plain,
( ! [X4,X5] : sK17 = set_difference(set_difference(X4,X5),X4)
| ~ spl18_144 ),
inference(avatar_component_clause,[],[f1445]) ).
fof(f12446,plain,
( spl18_532
| ~ spl18_143
| ~ spl18_210 ),
inference(avatar_split_clause,[],[f2652,f2376,f1441,f12444]) ).
fof(f12444,plain,
( spl18_532
<=> ! [X18,X16,X17] :
( ~ proper_subset(sK17,set_difference(X18,X16))
| ~ subset(X18,set_intersection2(X16,X17)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_532])]) ).
fof(f1441,plain,
( spl18_143
<=> ! [X2,X1] : sK17 = set_difference(set_intersection2(X1,X2),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_143])]) ).
fof(f2652,plain,
( ! [X18,X16,X17] :
( ~ proper_subset(sK17,set_difference(X18,X16))
| ~ subset(X18,set_intersection2(X16,X17)) )
| ~ spl18_143
| ~ spl18_210 ),
inference(superposition,[],[f2377,f1442]) ).
fof(f1442,plain,
( ! [X2,X1] : sK17 = set_difference(set_intersection2(X1,X2),X1)
| ~ spl18_143 ),
inference(avatar_component_clause,[],[f1441]) ).
fof(f12442,plain,
( spl18_531
| ~ spl18_145
| ~ spl18_210 ),
inference(avatar_split_clause,[],[f2647,f2376,f1449,f12440]) ).
fof(f12440,plain,
( spl18_531
<=> ! [X2,X4,X3] :
( ~ proper_subset(sK17,set_difference(X4,set_union2(X2,X3)))
| ~ subset(X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_531])]) ).
fof(f1449,plain,
( spl18_145
<=> ! [X6,X7] : sK17 = set_difference(X6,set_union2(X6,X7)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_145])]) ).
fof(f2647,plain,
( ! [X2,X3,X4] :
( ~ proper_subset(sK17,set_difference(X4,set_union2(X2,X3)))
| ~ subset(X4,X2) )
| ~ spl18_145
| ~ spl18_210 ),
inference(superposition,[],[f2377,f1450]) ).
fof(f1450,plain,
( ! [X6,X7] : sK17 = set_difference(X6,set_union2(X6,X7))
| ~ spl18_145 ),
inference(avatar_component_clause,[],[f1449]) ).
fof(f12438,plain,
( spl18_530
| ~ spl18_142
| ~ spl18_208 ),
inference(avatar_split_clause,[],[f2630,f2368,f1437,f12436]) ).
fof(f12436,plain,
( spl18_530
<=> ! [X9,X8,X10] :
( subset(X8,set_intersection2(set_union2(X8,X9),X10))
| ~ subset(X8,X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_530])]) ).
fof(f1437,plain,
( spl18_142
<=> ! [X6,X7] : set_intersection2(X6,set_union2(X6,X7)) = X6 ),
introduced(avatar_definition,[new_symbols(naming,[spl18_142])]) ).
fof(f2368,plain,
( spl18_208
<=> ! [X6,X4,X5] :
( subset(set_intersection2(X6,X5),set_intersection2(X5,X4))
| ~ subset(X6,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_208])]) ).
fof(f2630,plain,
( ! [X10,X8,X9] :
( subset(X8,set_intersection2(set_union2(X8,X9),X10))
| ~ subset(X8,X10) )
| ~ spl18_142
| ~ spl18_208 ),
inference(superposition,[],[f2369,f1438]) ).
fof(f1438,plain,
( ! [X6,X7] : set_intersection2(X6,set_union2(X6,X7)) = X6
| ~ spl18_142 ),
inference(avatar_component_clause,[],[f1437]) ).
fof(f2369,plain,
( ! [X6,X4,X5] :
( subset(set_intersection2(X6,X5),set_intersection2(X5,X4))
| ~ subset(X6,X4) )
| ~ spl18_208 ),
inference(avatar_component_clause,[],[f2368]) ).
fof(f12434,plain,
( spl18_529
| ~ spl18_40
| ~ spl18_207 ),
inference(avatar_split_clause,[],[f2610,f2364,f471,f12432]) ).
fof(f12432,plain,
( spl18_529
<=> ! [X2,X4,X3] :
( subset(set_intersection2(X3,X4),set_intersection2(X3,X2))
| ~ subset(X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_529])]) ).
fof(f471,plain,
( spl18_40
<=> ! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_40])]) ).
fof(f2364,plain,
( spl18_207
<=> ! [X6,X4,X5] :
( subset(set_intersection2(X5,X4),set_intersection2(X6,X5))
| ~ subset(X4,X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_207])]) ).
fof(f2610,plain,
( ! [X2,X3,X4] :
( subset(set_intersection2(X3,X4),set_intersection2(X3,X2))
| ~ subset(X4,X2) )
| ~ spl18_40
| ~ spl18_207 ),
inference(superposition,[],[f2365,f472]) ).
fof(f472,plain,
( ! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0)
| ~ spl18_40 ),
inference(avatar_component_clause,[],[f471]) ).
fof(f2365,plain,
( ! [X6,X4,X5] :
( subset(set_intersection2(X5,X4),set_intersection2(X6,X5))
| ~ subset(X4,X6) )
| ~ spl18_207 ),
inference(avatar_component_clause,[],[f2364]) ).
fof(f12430,plain,
( spl18_528
| ~ spl18_142
| ~ spl18_207 ),
inference(avatar_split_clause,[],[f2603,f2364,f1437,f12428]) ).
fof(f12428,plain,
( spl18_528
<=> ! [X9,X8,X10] :
( subset(X8,set_intersection2(X10,X8))
| ~ subset(set_union2(X8,X9),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_528])]) ).
fof(f2603,plain,
( ! [X10,X8,X9] :
( subset(X8,set_intersection2(X10,X8))
| ~ subset(set_union2(X8,X9),X10) )
| ~ spl18_142
| ~ spl18_207 ),
inference(superposition,[],[f2365,f1438]) ).
fof(f12426,plain,
( spl18_527
| ~ spl18_142
| ~ spl18_206 ),
inference(avatar_split_clause,[],[f2583,f2360,f1437,f12424]) ).
fof(f12424,plain,
( spl18_527
<=> ! [X9,X8,X10] :
( ~ proper_subset(set_intersection2(X10,set_union2(X8,X9)),X8)
| ~ subset(X8,X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_527])]) ).
fof(f2360,plain,
( spl18_206
<=> ! [X2,X0,X1] :
( ~ subset(X0,X1)
| ~ proper_subset(set_intersection2(X1,X2),set_intersection2(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_206])]) ).
fof(f2583,plain,
( ! [X10,X8,X9] :
( ~ proper_subset(set_intersection2(X10,set_union2(X8,X9)),X8)
| ~ subset(X8,X10) )
| ~ spl18_142
| ~ spl18_206 ),
inference(superposition,[],[f2361,f1438]) ).
fof(f2361,plain,
( ! [X2,X0,X1] :
( ~ proper_subset(set_intersection2(X1,X2),set_intersection2(X0,X2))
| ~ subset(X0,X1) )
| ~ spl18_206 ),
inference(avatar_component_clause,[],[f2360]) ).
fof(f12414,plain,
( spl18_526
| ~ spl18_40
| ~ spl18_206 ),
inference(avatar_split_clause,[],[f2581,f2360,f471,f12412]) ).
fof(f12412,plain,
( spl18_526
<=> ! [X2,X4,X3] :
( ~ proper_subset(set_intersection2(X4,X3),set_intersection2(X3,X2))
| ~ subset(X2,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_526])]) ).
fof(f2581,plain,
( ! [X2,X3,X4] :
( ~ proper_subset(set_intersection2(X4,X3),set_intersection2(X3,X2))
| ~ subset(X2,X4) )
| ~ spl18_40
| ~ spl18_206 ),
inference(superposition,[],[f2361,f472]) ).
fof(f12410,plain,
( spl18_525
| ~ spl18_40
| ~ spl18_206 ),
inference(avatar_split_clause,[],[f2572,f2360,f471,f12408]) ).
fof(f12408,plain,
( spl18_525
<=> ! [X4,X2,X3] :
( ~ proper_subset(set_intersection2(X3,X2),set_intersection2(X4,X3))
| ~ subset(X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_525])]) ).
fof(f2572,plain,
( ! [X2,X3,X4] :
( ~ proper_subset(set_intersection2(X3,X2),set_intersection2(X4,X3))
| ~ subset(X4,X2) )
| ~ spl18_40
| ~ spl18_206 ),
inference(superposition,[],[f2361,f472]) ).
fof(f12406,plain,
( spl18_524
| ~ spl18_40
| ~ spl18_204 ),
inference(avatar_split_clause,[],[f2546,f2352,f471,f12404]) ).
fof(f12404,plain,
( spl18_524
<=> ! [X2,X1] :
( ~ in(set_intersection2(X2,X1),sK6(X1,X2))
| disjoint(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_524])]) ).
fof(f2352,plain,
( spl18_204
<=> ! [X2,X3] :
( disjoint(X2,X3)
| ~ in(set_intersection2(X2,X3),sK6(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_204])]) ).
fof(f2546,plain,
( ! [X2,X1] :
( ~ in(set_intersection2(X2,X1),sK6(X1,X2))
| disjoint(X1,X2) )
| ~ spl18_40
| ~ spl18_204 ),
inference(superposition,[],[f2353,f472]) ).
fof(f2353,plain,
( ! [X2,X3] :
( ~ in(set_intersection2(X2,X3),sK6(X2,X3))
| disjoint(X2,X3) )
| ~ spl18_204 ),
inference(avatar_component_clause,[],[f2352]) ).
fof(f12402,plain,
( spl18_523
| ~ spl18_40
| ~ spl18_195 ),
inference(avatar_split_clause,[],[f2399,f2316,f471,f12400]) ).
fof(f12400,plain,
( spl18_523
<=> ! [X2,X1] :
( set_intersection2(X2,X1) != X1
| disjoint(X1,set_difference(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_523])]) ).
fof(f2316,plain,
( spl18_195
<=> ! [X4,X5] :
( set_intersection2(X4,X5) != X4
| disjoint(X4,set_difference(X4,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_195])]) ).
fof(f2399,plain,
( ! [X2,X1] :
( set_intersection2(X2,X1) != X1
| disjoint(X1,set_difference(X1,X2)) )
| ~ spl18_40
| ~ spl18_195 ),
inference(superposition,[],[f2317,f472]) ).
fof(f2317,plain,
( ! [X4,X5] :
( set_intersection2(X4,X5) != X4
| disjoint(X4,set_difference(X4,X5)) )
| ~ spl18_195 ),
inference(avatar_component_clause,[],[f2316]) ).
fof(f12398,plain,
( spl18_522
| ~ spl18_40
| ~ spl18_194 ),
inference(avatar_split_clause,[],[f2380,f2312,f471,f12396]) ).
fof(f12396,plain,
( spl18_522
<=> ! [X2,X1] :
( sK17 != set_intersection2(X2,X1)
| subset(X1,set_difference(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_522])]) ).
fof(f2312,plain,
( spl18_194
<=> ! [X2,X3] :
( sK17 != set_intersection2(X2,X3)
| subset(X2,set_difference(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_194])]) ).
fof(f2380,plain,
( ! [X2,X1] :
( sK17 != set_intersection2(X2,X1)
| subset(X1,set_difference(X1,X2)) )
| ~ spl18_40
| ~ spl18_194 ),
inference(superposition,[],[f2313,f472]) ).
fof(f2313,plain,
( ! [X2,X3] :
( sK17 != set_intersection2(X2,X3)
| subset(X2,set_difference(X2,X3)) )
| ~ spl18_194 ),
inference(avatar_component_clause,[],[f2312]) ).
fof(f12394,plain,
( spl18_521
| ~ spl18_174
| ~ spl18_188 ),
inference(avatar_split_clause,[],[f2213,f2076,f1784,f12392]) ).
fof(f12392,plain,
( spl18_521
<=> ! [X34,X35,X33] :
( ~ in(X35,set_difference(X34,X33))
| in(X35,set_union2(X33,X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_521])]) ).
fof(f2076,plain,
( spl18_188
<=> ! [X2,X1] : set_difference(X1,X2) = set_difference(set_union2(X2,X1),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_188])]) ).
fof(f2213,plain,
( ! [X34,X35,X33] :
( ~ in(X35,set_difference(X34,X33))
| in(X35,set_union2(X33,X34)) )
| ~ spl18_174
| ~ spl18_188 ),
inference(superposition,[],[f1785,f2077]) ).
fof(f2077,plain,
( ! [X2,X1] : set_difference(X1,X2) = set_difference(set_union2(X2,X1),X2)
| ~ spl18_188 ),
inference(avatar_component_clause,[],[f2076]) ).
fof(f12390,plain,
( spl18_520
| ~ spl18_171
| ~ spl18_188 ),
inference(avatar_split_clause,[],[f2212,f2076,f1772,f12388]) ).
fof(f12388,plain,
( spl18_520
<=> ! [X32,X30,X31] :
( ~ subset(X32,set_difference(X31,X30))
| subset(X32,set_union2(X30,X31)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_520])]) ).
fof(f2212,plain,
( ! [X31,X32,X30] :
( ~ subset(X32,set_difference(X31,X30))
| subset(X32,set_union2(X30,X31)) )
| ~ spl18_171
| ~ spl18_188 ),
inference(superposition,[],[f1773,f2077]) ).
fof(f12386,plain,
( spl18_519
| ~ spl18_53
| ~ spl18_188 ),
inference(avatar_split_clause,[],[f2201,f2076,f583,f12384]) ).
fof(f12384,plain,
( spl18_519
<=> ! [X6,X5] :
( sK17 != set_difference(X6,X5)
| subset(set_union2(X5,X6),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_519])]) ).
fof(f2201,plain,
( ! [X6,X5] :
( sK17 != set_difference(X6,X5)
| subset(set_union2(X5,X6),X5) )
| ~ spl18_53
| ~ spl18_188 ),
inference(superposition,[],[f584,f2077]) ).
fof(f12382,plain,
( spl18_518
| ~ spl18_167
| ~ spl18_187 ),
inference(avatar_split_clause,[],[f2184,f2072,f1756,f12380]) ).
fof(f12380,plain,
( spl18_518
<=> ! [X48,X46,X47] :
( subset(set_difference(X46,X47),X48)
| ~ disjoint(set_difference(X46,X47),X46) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_518])]) ).
fof(f2072,plain,
( spl18_187
<=> ! [X4,X5] : set_difference(X4,X5) = set_intersection2(set_difference(X4,X5),X4) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_187])]) ).
fof(f2184,plain,
( ! [X48,X46,X47] :
( subset(set_difference(X46,X47),X48)
| ~ disjoint(set_difference(X46,X47),X46) )
| ~ spl18_167
| ~ spl18_187 ),
inference(superposition,[],[f1757,f2073]) ).
fof(f2073,plain,
( ! [X4,X5] : set_difference(X4,X5) = set_intersection2(set_difference(X4,X5),X4)
| ~ spl18_187 ),
inference(avatar_component_clause,[],[f2072]) ).
fof(f12378,plain,
( spl18_517
| ~ spl18_166
| ~ spl18_187 ),
inference(avatar_split_clause,[],[f2183,f2072,f1752,f12376]) ).
fof(f12376,plain,
( spl18_517
<=> ! [X45,X44,X43] :
( disjoint(X45,set_difference(X43,X44))
| ~ disjoint(set_difference(X43,X44),X43) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_517])]) ).
fof(f1752,plain,
( spl18_166
<=> ! [X6,X4,X5] :
( disjoint(X4,set_intersection2(X5,X6))
| ~ disjoint(X5,X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_166])]) ).
fof(f2183,plain,
( ! [X44,X45,X43] :
( disjoint(X45,set_difference(X43,X44))
| ~ disjoint(set_difference(X43,X44),X43) )
| ~ spl18_166
| ~ spl18_187 ),
inference(superposition,[],[f1753,f2073]) ).
fof(f1753,plain,
( ! [X6,X4,X5] :
( disjoint(X4,set_intersection2(X5,X6))
| ~ disjoint(X5,X6) )
| ~ spl18_166 ),
inference(avatar_component_clause,[],[f1752]) ).
fof(f12345,plain,
( spl18_516
| ~ spl18_164
| ~ spl18_187 ),
inference(avatar_split_clause,[],[f2182,f2072,f1744,f12343]) ).
fof(f12343,plain,
( spl18_516
<=> ! [X41,X40,X42] :
( disjoint(set_difference(X40,X41),X42)
| ~ disjoint(set_difference(X40,X41),X40) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_516])]) ).
fof(f2182,plain,
( ! [X40,X41,X42] :
( disjoint(set_difference(X40,X41),X42)
| ~ disjoint(set_difference(X40,X41),X40) )
| ~ spl18_164
| ~ spl18_187 ),
inference(superposition,[],[f1745,f2073]) ).
fof(f12341,plain,
( spl18_515
| ~ spl18_162
| ~ spl18_187 ),
inference(avatar_split_clause,[],[f2181,f2072,f1736,f12339]) ).
fof(f12339,plain,
( spl18_515
<=> ! [X38,X37,X39] :
( ~ in(X39,set_difference(X37,X38))
| ~ disjoint(X37,set_difference(X37,X38)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_515])]) ).
fof(f2181,plain,
( ! [X38,X39,X37] :
( ~ in(X39,set_difference(X37,X38))
| ~ disjoint(X37,set_difference(X37,X38)) )
| ~ spl18_162
| ~ spl18_187 ),
inference(superposition,[],[f1737,f2073]) ).
fof(f12337,plain,
( spl18_514
| ~ spl18_43
| ~ spl18_187 ),
inference(avatar_split_clause,[],[f2168,f2072,f511,f12335]) ).
fof(f12335,plain,
( spl18_514
<=> ! [X6,X7,X8] :
( ~ in(X8,set_difference(X6,X7))
| ~ disjoint(set_difference(X6,X7),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_514])]) ).
fof(f2168,plain,
( ! [X8,X6,X7] :
( ~ in(X8,set_difference(X6,X7))
| ~ disjoint(set_difference(X6,X7),X6) )
| ~ spl18_43
| ~ spl18_187 ),
inference(superposition,[],[f512,f2073]) ).
fof(f12333,plain,
( spl18_513
| ~ spl18_167
| ~ spl18_186 ),
inference(avatar_split_clause,[],[f2140,f2068,f1756,f12331]) ).
fof(f12331,plain,
( spl18_513
<=> ! [X48,X46,X47] :
( subset(set_intersection2(X46,X47),X48)
| ~ disjoint(set_intersection2(X46,X47),X46) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_513])]) ).
fof(f2068,plain,
( spl18_186
<=> ! [X2,X1] : set_intersection2(X1,X2) = set_intersection2(set_intersection2(X1,X2),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_186])]) ).
fof(f2140,plain,
( ! [X48,X46,X47] :
( subset(set_intersection2(X46,X47),X48)
| ~ disjoint(set_intersection2(X46,X47),X46) )
| ~ spl18_167
| ~ spl18_186 ),
inference(superposition,[],[f1757,f2069]) ).
fof(f2069,plain,
( ! [X2,X1] : set_intersection2(X1,X2) = set_intersection2(set_intersection2(X1,X2),X1)
| ~ spl18_186 ),
inference(avatar_component_clause,[],[f2068]) ).
fof(f12329,plain,
( spl18_512
| ~ spl18_166
| ~ spl18_186 ),
inference(avatar_split_clause,[],[f2139,f2068,f1752,f12327]) ).
fof(f12327,plain,
( spl18_512
<=> ! [X45,X44,X43] :
( disjoint(X45,set_intersection2(X43,X44))
| ~ disjoint(set_intersection2(X43,X44),X43) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_512])]) ).
fof(f2139,plain,
( ! [X44,X45,X43] :
( disjoint(X45,set_intersection2(X43,X44))
| ~ disjoint(set_intersection2(X43,X44),X43) )
| ~ spl18_166
| ~ spl18_186 ),
inference(superposition,[],[f1753,f2069]) ).
fof(f12325,plain,
( spl18_511
| ~ spl18_164
| ~ spl18_186 ),
inference(avatar_split_clause,[],[f2138,f2068,f1744,f12323]) ).
fof(f12323,plain,
( spl18_511
<=> ! [X41,X40,X42] :
( disjoint(set_intersection2(X40,X41),X42)
| ~ disjoint(set_intersection2(X40,X41),X40) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_511])]) ).
fof(f2138,plain,
( ! [X40,X41,X42] :
( disjoint(set_intersection2(X40,X41),X42)
| ~ disjoint(set_intersection2(X40,X41),X40) )
| ~ spl18_164
| ~ spl18_186 ),
inference(superposition,[],[f1745,f2069]) ).
fof(f12321,plain,
( spl18_510
| ~ spl18_162
| ~ spl18_186 ),
inference(avatar_split_clause,[],[f2137,f2068,f1736,f12319]) ).
fof(f12319,plain,
( spl18_510
<=> ! [X38,X37,X39] :
( ~ in(X39,set_intersection2(X37,X38))
| ~ disjoint(X37,set_intersection2(X37,X38)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_510])]) ).
fof(f2137,plain,
( ! [X38,X39,X37] :
( ~ in(X39,set_intersection2(X37,X38))
| ~ disjoint(X37,set_intersection2(X37,X38)) )
| ~ spl18_162
| ~ spl18_186 ),
inference(superposition,[],[f1737,f2069]) ).
fof(f12317,plain,
( spl18_509
| ~ spl18_43
| ~ spl18_186 ),
inference(avatar_split_clause,[],[f2124,f2068,f511,f12315]) ).
fof(f12315,plain,
( spl18_509
<=> ! [X6,X7,X8] :
( ~ in(X8,set_intersection2(X6,X7))
| ~ disjoint(set_intersection2(X6,X7),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_509])]) ).
fof(f2124,plain,
( ! [X8,X6,X7] :
( ~ in(X8,set_intersection2(X6,X7))
| ~ disjoint(set_intersection2(X6,X7),X6) )
| ~ spl18_43
| ~ spl18_186 ),
inference(superposition,[],[f512,f2069]) ).
fof(f12312,plain,
( spl18_508
| ~ spl18_54
| ~ spl18_178 ),
inference(avatar_split_clause,[],[f2027,f1800,f587,f12310]) ).
fof(f12310,plain,
( spl18_508
<=> ! [X9,X8] :
( ~ subset(X8,X9)
| sK17 = set_difference(X8,set_intersection2(X9,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_508])]) ).
fof(f2027,plain,
( ! [X8,X9] :
( ~ subset(X8,X9)
| sK17 = set_difference(X8,set_intersection2(X9,X8)) )
| ~ spl18_54
| ~ spl18_178 ),
inference(resolution,[],[f1801,f588]) ).
fof(f12237,plain,
( spl18_507
| ~ spl18_40
| ~ spl18_445
| ~ spl18_506 ),
inference(avatar_split_clause,[],[f12233,f12230,f9281,f471,f12235]) ).
fof(f12235,plain,
( spl18_507
<=> ! [X6,X7] :
( set_intersection2(X7,X6) = X6
| ~ subset(X6,X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_507])]) ).
fof(f9281,plain,
( spl18_445
<=> ! [X4,X5] : set_intersection2(X4,X5) = set_intersection2(set_intersection2(X4,X5),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_445])]) ).
fof(f12230,plain,
( spl18_506
<=> ! [X6,X7] :
( ~ subset(X6,X7)
| set_intersection2(X6,set_intersection2(X7,X6)) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_506])]) ).
fof(f12233,plain,
( ! [X6,X7] :
( set_intersection2(X7,X6) = X6
| ~ subset(X6,X7) )
| ~ spl18_40
| ~ spl18_445
| ~ spl18_506 ),
inference(forward_demodulation,[],[f12231,f9590]) ).
fof(f9590,plain,
( ! [X3,X4] : set_intersection2(X3,X4) = set_intersection2(X4,set_intersection2(X3,X4))
| ~ spl18_40
| ~ spl18_445 ),
inference(superposition,[],[f9282,f472]) ).
fof(f9282,plain,
( ! [X4,X5] : set_intersection2(X4,X5) = set_intersection2(set_intersection2(X4,X5),X5)
| ~ spl18_445 ),
inference(avatar_component_clause,[],[f9281]) ).
fof(f12231,plain,
( ! [X6,X7] :
( ~ subset(X6,X7)
| set_intersection2(X6,set_intersection2(X7,X6)) = X6 )
| ~ spl18_506 ),
inference(avatar_component_clause,[],[f12230]) ).
fof(f12232,plain,
( spl18_506
| ~ spl18_47
| ~ spl18_178 ),
inference(avatar_split_clause,[],[f2026,f1800,f527,f12230]) ).
fof(f2026,plain,
( ! [X6,X7] :
( ~ subset(X6,X7)
| set_intersection2(X6,set_intersection2(X7,X6)) = X6 )
| ~ spl18_47
| ~ spl18_178 ),
inference(resolution,[],[f1801,f528]) ).
fof(f12228,plain,
( spl18_505
| ~ spl18_54
| ~ spl18_172 ),
inference(avatar_split_clause,[],[f1940,f1776,f587,f12226]) ).
fof(f12226,plain,
( spl18_505
<=> ! [X9,X11,X10] :
( ~ subset(X9,X10)
| sK17 = set_difference(X9,set_union2(X10,X11)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_505])]) ).
fof(f1940,plain,
( ! [X10,X11,X9] :
( ~ subset(X9,X10)
| sK17 = set_difference(X9,set_union2(X10,X11)) )
| ~ spl18_54
| ~ spl18_172 ),
inference(resolution,[],[f1777,f588]) ).
fof(f12224,plain,
( spl18_504
| ~ spl18_47
| ~ spl18_172 ),
inference(avatar_split_clause,[],[f1939,f1776,f527,f12222]) ).
fof(f12222,plain,
( spl18_504
<=> ! [X6,X7,X8] :
( ~ subset(X6,X7)
| set_intersection2(X6,set_union2(X7,X8)) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_504])]) ).
fof(f1939,plain,
( ! [X8,X6,X7] :
( ~ subset(X6,X7)
| set_intersection2(X6,set_union2(X7,X8)) = X6 )
| ~ spl18_47
| ~ spl18_172 ),
inference(resolution,[],[f1777,f528]) ).
fof(f12219,plain,
( spl18_503
| ~ spl18_60
| ~ spl18_168 ),
inference(avatar_split_clause,[],[f1890,f1760,f634,f12217]) ).
fof(f12217,plain,
( spl18_503
<=> ! [X6,X7] :
( ~ empty(set_union2(X6,X7))
| empty(set_difference(set_difference(X7,X6),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_503])]) ).
fof(f1890,plain,
( ! [X6,X7] :
( ~ empty(set_union2(X6,X7))
| empty(set_difference(set_difference(X7,X6),X6)) )
| ~ spl18_60
| ~ spl18_168 ),
inference(superposition,[],[f1761,f635]) ).
fof(f12215,plain,
( spl18_502
| ~ spl18_54
| ~ spl18_167 ),
inference(avatar_split_clause,[],[f1872,f1756,f587,f12213]) ).
fof(f12213,plain,
( spl18_502
<=> ! [X9,X11,X10] :
( ~ disjoint(X9,X10)
| sK17 = set_difference(set_intersection2(X9,X10),X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_502])]) ).
fof(f1872,plain,
( ! [X10,X11,X9] :
( ~ disjoint(X9,X10)
| sK17 = set_difference(set_intersection2(X9,X10),X11) )
| ~ spl18_54
| ~ spl18_167 ),
inference(resolution,[],[f1757,f588]) ).
fof(f12211,plain,
( spl18_501
| ~ spl18_46
| ~ spl18_167 ),
inference(avatar_split_clause,[],[f1870,f1756,f523,f12209]) ).
fof(f12209,plain,
( spl18_501
<=> ! [X4,X5,X3] :
( ~ disjoint(X3,X4)
| set_union2(set_intersection2(X3,X4),X5) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_501])]) ).
fof(f1870,plain,
( ! [X3,X4,X5] :
( ~ disjoint(X3,X4)
| set_union2(set_intersection2(X3,X4),X5) = X5 )
| ~ spl18_46
| ~ spl18_167 ),
inference(resolution,[],[f1757,f524]) ).
fof(f12207,plain,
( spl18_500
| ~ spl18_48
| ~ spl18_166 ),
inference(avatar_split_clause,[],[f1858,f1752,f531,f12205]) ).
fof(f12205,plain,
( spl18_500
<=> ! [X11,X12,X13] :
( ~ disjoint(X11,X12)
| set_difference(X13,set_intersection2(X11,X12)) = X13 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_500])]) ).
fof(f531,plain,
( spl18_48
<=> ! [X0,X1] :
( set_difference(X0,X1) = X0
| ~ disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_48])]) ).
fof(f1858,plain,
( ! [X11,X12,X13] :
( ~ disjoint(X11,X12)
| set_difference(X13,set_intersection2(X11,X12)) = X13 )
| ~ spl18_48
| ~ spl18_166 ),
inference(resolution,[],[f1753,f532]) ).
fof(f532,plain,
( ! [X0,X1] :
( ~ disjoint(X0,X1)
| set_difference(X0,X1) = X0 )
| ~ spl18_48 ),
inference(avatar_component_clause,[],[f531]) ).
fof(f12203,plain,
( spl18_499
| ~ spl18_161
| ~ spl18_166 ),
inference(avatar_split_clause,[],[f1855,f1752,f1732,f12201]) ).
fof(f12201,plain,
( spl18_499
<=> ! [X2,X0,X1] :
( ~ disjoint(X0,X1)
| sK17 = set_intersection2(X2,set_intersection2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_499])]) ).
fof(f1732,plain,
( spl18_161
<=> ! [X0,X1] :
( ~ disjoint(X0,X1)
| set_intersection2(X0,X1) = sK17 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_161])]) ).
fof(f1855,plain,
( ! [X2,X0,X1] :
( ~ disjoint(X0,X1)
| sK17 = set_intersection2(X2,set_intersection2(X0,X1)) )
| ~ spl18_161
| ~ spl18_166 ),
inference(resolution,[],[f1753,f1733]) ).
fof(f1733,plain,
( ! [X0,X1] :
( ~ disjoint(X0,X1)
| set_intersection2(X0,X1) = sK17 )
| ~ spl18_161 ),
inference(avatar_component_clause,[],[f1732]) ).
fof(f12199,plain,
( spl18_498
| ~ spl18_161
| ~ spl18_164 ),
inference(avatar_split_clause,[],[f1841,f1744,f1732,f12197]) ).
fof(f12197,plain,
( spl18_498
<=> ! [X2,X0,X1] :
( ~ disjoint(X0,X1)
| sK17 = set_intersection2(set_intersection2(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_498])]) ).
fof(f1841,plain,
( ! [X2,X0,X1] :
( ~ disjoint(X0,X1)
| sK17 = set_intersection2(set_intersection2(X0,X1),X2) )
| ~ spl18_161
| ~ spl18_164 ),
inference(resolution,[],[f1745,f1733]) ).
fof(f12195,plain,
( spl18_497
| ~ spl18_128
| ~ spl18_406 ),
inference(avatar_split_clause,[],[f8351,f7343,f1288,f12193]) ).
fof(f12193,plain,
( spl18_497
<=> ! [X39,X40] :
( ~ proper_subset(X39,X40)
| ~ subset(X40,sK17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_497])]) ).
fof(f1288,plain,
( spl18_128
<=> ! [X0] : set_union2(sK17,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl18_128])]) ).
fof(f7343,plain,
( spl18_406
<=> ! [X2,X0,X1] :
( ~ subset(X0,X1)
| ~ proper_subset(set_union2(X1,X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_406])]) ).
fof(f8351,plain,
( ! [X40,X39] :
( ~ proper_subset(X39,X40)
| ~ subset(X40,sK17) )
| ~ spl18_128
| ~ spl18_406 ),
inference(superposition,[],[f7344,f1289]) ).
fof(f1289,plain,
( ! [X0] : set_union2(sK17,X0) = X0
| ~ spl18_128 ),
inference(avatar_component_clause,[],[f1288]) ).
fof(f7344,plain,
( ! [X2,X0,X1] :
( ~ proper_subset(set_union2(X1,X2),X0)
| ~ subset(X0,X1) )
| ~ spl18_406 ),
inference(avatar_component_clause,[],[f7343]) ).
fof(f12191,plain,
( spl18_496
| ~ spl18_45
| ~ spl18_157 ),
inference(avatar_split_clause,[],[f1708,f1682,f519,f12189]) ).
fof(f12189,plain,
( spl18_496
<=> ! [X2,X3] :
( sK7(X2,singleton(X3)) = X3
| disjoint(X2,singleton(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_496])]) ).
fof(f519,plain,
( spl18_45
<=> ! [X0,X1] :
( in(sK7(X0,X1),X1)
| disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_45])]) ).
fof(f1708,plain,
( ! [X2,X3] :
( sK7(X2,singleton(X3)) = X3
| disjoint(X2,singleton(X3)) )
| ~ spl18_45
| ~ spl18_157 ),
inference(resolution,[],[f1683,f520]) ).
fof(f520,plain,
( ! [X0,X1] :
( in(sK7(X0,X1),X1)
| disjoint(X0,X1) )
| ~ spl18_45 ),
inference(avatar_component_clause,[],[f519]) ).
fof(f12187,plain,
( spl18_495
| ~ spl18_44
| ~ spl18_157 ),
inference(avatar_split_clause,[],[f1707,f1682,f515,f12185]) ).
fof(f12185,plain,
( spl18_495
<=> ! [X0,X1] :
( sK7(singleton(X0),X1) = X0
| disjoint(singleton(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_495])]) ).
fof(f515,plain,
( spl18_44
<=> ! [X0,X1] :
( in(sK7(X0,X1),X0)
| disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_44])]) ).
fof(f1707,plain,
( ! [X0,X1] :
( sK7(singleton(X0),X1) = X0
| disjoint(singleton(X0),X1) )
| ~ spl18_44
| ~ spl18_157 ),
inference(resolution,[],[f1683,f516]) ).
fof(f516,plain,
( ! [X0,X1] :
( in(sK7(X0,X1),X0)
| disjoint(X0,X1) )
| ~ spl18_44 ),
inference(avatar_component_clause,[],[f515]) ).
fof(f12183,plain,
( spl18_494
| ~ spl18_70
| ~ spl18_147 ),
inference(avatar_split_clause,[],[f1618,f1457,f713,f12181]) ).
fof(f12181,plain,
( spl18_494
<=> ! [X16,X17,X15] :
( ~ in(X15,set_difference(X16,X17))
| in(X15,set_union2(X16,X17)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_494])]) ).
fof(f1457,plain,
( spl18_147
<=> ! [X9,X8] : subset(set_difference(X8,X9),set_union2(X8,X9)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_147])]) ).
fof(f1618,plain,
( ! [X16,X17,X15] :
( ~ in(X15,set_difference(X16,X17))
| in(X15,set_union2(X16,X17)) )
| ~ spl18_70
| ~ spl18_147 ),
inference(resolution,[],[f1458,f714]) ).
fof(f1458,plain,
( ! [X8,X9] : subset(set_difference(X8,X9),set_union2(X8,X9))
| ~ spl18_147 ),
inference(avatar_component_clause,[],[f1457]) ).
fof(f12179,plain,
( spl18_493
| ~ spl18_66
| ~ spl18_147 ),
inference(avatar_split_clause,[],[f1615,f1457,f658,f12177]) ).
fof(f12177,plain,
( spl18_493
<=> ! [X9,X8,X10] :
( subset(X8,set_union2(X9,X10))
| ~ subset(X8,set_difference(X9,X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_493])]) ).
fof(f1615,plain,
( ! [X10,X8,X9] :
( subset(X8,set_union2(X9,X10))
| ~ subset(X8,set_difference(X9,X10)) )
| ~ spl18_66
| ~ spl18_147 ),
inference(resolution,[],[f1458,f659]) ).
fof(f12175,plain,
( spl18_492
| ~ spl18_81
| ~ spl18_145 ),
inference(avatar_split_clause,[],[f1601,f1449,f811,f12173]) ).
fof(f12173,plain,
( spl18_492
<=> ! [X18,X16,X17] :
( subset(set_difference(X18,set_union2(X16,X17)),sK17)
| ~ subset(X18,X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_492])]) ).
fof(f1601,plain,
( ! [X18,X16,X17] :
( subset(set_difference(X18,set_union2(X16,X17)),sK17)
| ~ subset(X18,X16) )
| ~ spl18_81
| ~ spl18_145 ),
inference(superposition,[],[f812,f1450]) ).
fof(f12171,plain,
( spl18_491
| ~ spl18_81
| ~ spl18_144 ),
inference(avatar_split_clause,[],[f1574,f1445,f811,f12169]) ).
fof(f12169,plain,
( spl18_491
<=> ! [X18,X16,X17] :
( subset(set_difference(X18,X16),sK17)
| ~ subset(X18,set_difference(X16,X17)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_491])]) ).
fof(f1574,plain,
( ! [X18,X16,X17] :
( subset(set_difference(X18,X16),sK17)
| ~ subset(X18,set_difference(X16,X17)) )
| ~ spl18_81
| ~ spl18_144 ),
inference(superposition,[],[f812,f1446]) ).
fof(f12167,plain,
( spl18_490
| ~ spl18_81
| ~ spl18_143 ),
inference(avatar_split_clause,[],[f1546,f1441,f811,f12165]) ).
fof(f12165,plain,
( spl18_490
<=> ! [X18,X16,X17] :
( subset(set_difference(X18,X16),sK17)
| ~ subset(X18,set_intersection2(X16,X17)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_490])]) ).
fof(f1546,plain,
( ! [X18,X16,X17] :
( subset(set_difference(X18,X16),sK17)
| ~ subset(X18,set_intersection2(X16,X17)) )
| ~ spl18_81
| ~ spl18_143 ),
inference(superposition,[],[f812,f1442]) ).
fof(f12163,plain,
( spl18_489
| ~ spl18_80
| ~ spl18_142 ),
inference(avatar_split_clause,[],[f1525,f1437,f807,f12161]) ).
fof(f12161,plain,
( spl18_489
<=> ! [X20,X21,X19] :
( subset(X19,set_intersection2(X21,set_union2(X19,X20)))
| ~ subset(X19,X21) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_489])]) ).
fof(f807,plain,
( spl18_80
<=> ! [X2,X0,X1] :
( subset(set_intersection2(X0,X2),set_intersection2(X1,X2))
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_80])]) ).
fof(f1525,plain,
( ! [X21,X19,X20] :
( subset(X19,set_intersection2(X21,set_union2(X19,X20)))
| ~ subset(X19,X21) )
| ~ spl18_80
| ~ spl18_142 ),
inference(superposition,[],[f808,f1438]) ).
fof(f808,plain,
( ! [X2,X0,X1] :
( subset(set_intersection2(X0,X2),set_intersection2(X1,X2))
| ~ subset(X0,X1) )
| ~ spl18_80 ),
inference(avatar_component_clause,[],[f807]) ).
fof(f12159,plain,
( spl18_488
| ~ spl18_69
| ~ spl18_123 ),
inference(avatar_split_clause,[],[f1240,f1159,f709,f12157]) ).
fof(f12157,plain,
( spl18_488
<=> ! [X13,X14] :
( set_intersection2(X13,X14) = X14
| proper_subset(set_intersection2(X13,X14),X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_488])]) ).
fof(f1240,plain,
( ! [X14,X13] :
( set_intersection2(X13,X14) = X14
| proper_subset(set_intersection2(X13,X14),X14) )
| ~ spl18_69
| ~ spl18_123 ),
inference(resolution,[],[f1160,f710]) ).
fof(f12155,plain,
( spl18_487
| ~ spl18_68
| ~ spl18_123 ),
inference(avatar_split_clause,[],[f1239,f1159,f705,f12153]) ).
fof(f12153,plain,
( spl18_487
<=> ! [X12,X11] :
( set_intersection2(X12,X11) = X11
| ~ subset(X11,set_intersection2(X12,X11)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_487])]) ).
fof(f1239,plain,
( ! [X11,X12] :
( set_intersection2(X12,X11) = X11
| ~ subset(X11,set_intersection2(X12,X11)) )
| ~ spl18_68
| ~ spl18_123 ),
inference(resolution,[],[f1160,f706]) ).
fof(f12133,plain,
( spl18_486
| ~ spl18_69
| ~ spl18_122 ),
inference(avatar_split_clause,[],[f1227,f1155,f709,f12131]) ).
fof(f12131,plain,
( spl18_486
<=> ! [X13,X14] :
( set_union2(X14,X13) = X13
| proper_subset(X13,set_union2(X14,X13)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_486])]) ).
fof(f1155,plain,
( spl18_122
<=> ! [X4,X5] : subset(X4,set_union2(X5,X4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_122])]) ).
fof(f1227,plain,
( ! [X14,X13] :
( set_union2(X14,X13) = X13
| proper_subset(X13,set_union2(X14,X13)) )
| ~ spl18_69
| ~ spl18_122 ),
inference(resolution,[],[f1156,f710]) ).
fof(f1156,plain,
( ! [X4,X5] : subset(X4,set_union2(X5,X4))
| ~ spl18_122 ),
inference(avatar_component_clause,[],[f1155]) ).
fof(f12129,plain,
( spl18_485
| ~ spl18_68
| ~ spl18_122 ),
inference(avatar_split_clause,[],[f1226,f1155,f705,f12127]) ).
fof(f12127,plain,
( spl18_485
<=> ! [X11,X12] :
( set_union2(X11,X12) = X12
| ~ subset(set_union2(X11,X12),X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_485])]) ).
fof(f1226,plain,
( ! [X11,X12] :
( set_union2(X11,X12) = X12
| ~ subset(set_union2(X11,X12),X12) )
| ~ spl18_68
| ~ spl18_122 ),
inference(resolution,[],[f1156,f706]) ).
fof(f12116,plain,
( spl18_484
| ~ spl18_42
| ~ spl18_157 ),
inference(avatar_split_clause,[],[f1709,f1682,f479,f12114]) ).
fof(f12114,plain,
( spl18_484
<=> ! [X4] :
( sK8(singleton(X4)) = X4
| sK17 = singleton(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_484])]) ).
fof(f1709,plain,
( ! [X4] :
( sK8(singleton(X4)) = X4
| sK17 = singleton(X4) )
| ~ spl18_42
| ~ spl18_157 ),
inference(resolution,[],[f1683,f480]) ).
fof(f12112,plain,
( spl18_483
| ~ spl18_93
| ~ spl18_106 ),
inference(avatar_split_clause,[],[f1017,f1011,f906,f12110]) ).
fof(f12110,plain,
( spl18_483
<=> ! [X7] :
( sK11(X7,sK17) = X7
| sK17 = singleton(X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_483])]) ).
fof(f1011,plain,
( spl18_106
<=> ! [X0,X1] :
( singleton(X0) = X1
| sK11(X0,X1) = X0
| in(sK11(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_106])]) ).
fof(f1017,plain,
( ! [X7] :
( sK11(X7,sK17) = X7
| sK17 = singleton(X7) )
| ~ spl18_93
| ~ spl18_106 ),
inference(resolution,[],[f1012,f907]) ).
fof(f1012,plain,
( ! [X0,X1] :
( in(sK11(X0,X1),X1)
| sK11(X0,X1) = X0
| singleton(X0) = X1 )
| ~ spl18_106 ),
inference(avatar_component_clause,[],[f1011]) ).
fof(f12030,plain,
( spl18_482
| ~ spl18_19
| ~ spl18_401 ),
inference(avatar_split_clause,[],[f8170,f7323,f354,f12028]) ).
fof(f12028,plain,
( spl18_482
<=> ! [X0,X1] :
( ~ proper_subset(X1,X0)
| ~ disjoint(X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_482])]) ).
fof(f354,plain,
( spl18_19
<=> ! [X0] : set_intersection2(X0,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl18_19])]) ).
fof(f7323,plain,
( spl18_401
<=> ! [X2,X0,X1] :
( ~ disjoint(X0,X1)
| ~ proper_subset(X2,set_intersection2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_401])]) ).
fof(f8170,plain,
( ! [X0,X1] :
( ~ proper_subset(X1,X0)
| ~ disjoint(X0,X0) )
| ~ spl18_19
| ~ spl18_401 ),
inference(superposition,[],[f7324,f355]) ).
fof(f355,plain,
( ! [X0] : set_intersection2(X0,X0) = X0
| ~ spl18_19 ),
inference(avatar_component_clause,[],[f354]) ).
fof(f7324,plain,
( ! [X2,X0,X1] :
( ~ proper_subset(X2,set_intersection2(X0,X1))
| ~ disjoint(X0,X1) )
| ~ spl18_401 ),
inference(avatar_component_clause,[],[f7323]) ).
fof(f9483,plain,
( spl18_481
| ~ spl18_93
| ~ spl18_298 ),
inference(avatar_split_clause,[],[f4923,f4651,f906,f9481]) ).
fof(f9481,plain,
( spl18_481
<=> ! [X57,X59,X58] :
( sP3(X57,set_intersection2(X58,X59),sK17)
| ~ disjoint(X58,X59) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_481])]) ).
fof(f4651,plain,
( spl18_298
<=> ! [X9,X7,X6,X8] :
( in(sK15(X6,set_intersection2(X7,X8),X9),X9)
| sP3(X6,set_intersection2(X7,X8),X9)
| ~ disjoint(X7,X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_298])]) ).
fof(f4923,plain,
( ! [X58,X59,X57] :
( sP3(X57,set_intersection2(X58,X59),sK17)
| ~ disjoint(X58,X59) )
| ~ spl18_93
| ~ spl18_298 ),
inference(resolution,[],[f4652,f907]) ).
fof(f4652,plain,
( ! [X8,X6,X9,X7] :
( in(sK15(X6,set_intersection2(X7,X8),X9),X9)
| sP3(X6,set_intersection2(X7,X8),X9)
| ~ disjoint(X7,X8) )
| ~ spl18_298 ),
inference(avatar_component_clause,[],[f4651]) ).
fof(f9479,plain,
( spl18_480
| ~ spl18_93
| ~ spl18_297 ),
inference(avatar_split_clause,[],[f4897,f4647,f906,f9477]) ).
fof(f9477,plain,
( spl18_480
<=> ! [X57,X56,X58] :
( sP3(X56,sK17,set_intersection2(X57,X58))
| ~ disjoint(X57,X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_480])]) ).
fof(f4647,plain,
( spl18_297
<=> ! [X9,X7,X6,X8] :
( in(sK15(X6,X7,set_intersection2(X8,X9)),X7)
| sP3(X6,X7,set_intersection2(X8,X9))
| ~ disjoint(X8,X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_297])]) ).
fof(f4897,plain,
( ! [X58,X56,X57] :
( sP3(X56,sK17,set_intersection2(X57,X58))
| ~ disjoint(X57,X58) )
| ~ spl18_93
| ~ spl18_297 ),
inference(resolution,[],[f4648,f907]) ).
fof(f4648,plain,
( ! [X8,X6,X9,X7] :
( in(sK15(X6,X7,set_intersection2(X8,X9)),X7)
| sP3(X6,X7,set_intersection2(X8,X9))
| ~ disjoint(X8,X9) )
| ~ spl18_297 ),
inference(avatar_component_clause,[],[f4647]) ).
fof(f9475,plain,
( spl18_479
| ~ spl18_93
| ~ spl18_296 ),
inference(avatar_split_clause,[],[f4872,f4643,f906,f9473]) ).
fof(f9473,plain,
( spl18_479
<=> ! [X54,X55,X56] :
( sP1(set_intersection2(X54,X55),X56,sK17)
| ~ disjoint(X54,X55) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_479])]) ).
fof(f4643,plain,
( spl18_296
<=> ! [X9,X7,X6,X8] :
( in(sK13(set_intersection2(X6,X7),X8,X9),X9)
| sP1(set_intersection2(X6,X7),X8,X9)
| ~ disjoint(X6,X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_296])]) ).
fof(f4872,plain,
( ! [X56,X54,X55] :
( sP1(set_intersection2(X54,X55),X56,sK17)
| ~ disjoint(X54,X55) )
| ~ spl18_93
| ~ spl18_296 ),
inference(resolution,[],[f4644,f907]) ).
fof(f4644,plain,
( ! [X8,X6,X9,X7] :
( in(sK13(set_intersection2(X6,X7),X8,X9),X9)
| sP1(set_intersection2(X6,X7),X8,X9)
| ~ disjoint(X6,X7) )
| ~ spl18_296 ),
inference(avatar_component_clause,[],[f4643]) ).
fof(f9471,plain,
( spl18_478
| ~ spl18_93
| ~ spl18_295 ),
inference(avatar_split_clause,[],[f4848,f4639,f906,f9469]) ).
fof(f9469,plain,
( spl18_478
<=> ! [X54,X53,X55] :
( sP1(sK17,X53,set_intersection2(X54,X55))
| ~ disjoint(X54,X55) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_478])]) ).
fof(f4639,plain,
( spl18_295
<=> ! [X9,X7,X6,X8] :
( in(sK13(X6,X7,set_intersection2(X8,X9)),X6)
| sP1(X6,X7,set_intersection2(X8,X9))
| ~ disjoint(X8,X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_295])]) ).
fof(f4848,plain,
( ! [X54,X55,X53] :
( sP1(sK17,X53,set_intersection2(X54,X55))
| ~ disjoint(X54,X55) )
| ~ spl18_93
| ~ spl18_295 ),
inference(resolution,[],[f4640,f907]) ).
fof(f4640,plain,
( ! [X8,X6,X9,X7] :
( in(sK13(X6,X7,set_intersection2(X8,X9)),X6)
| sP1(X6,X7,set_intersection2(X8,X9))
| ~ disjoint(X8,X9) )
| ~ spl18_295 ),
inference(avatar_component_clause,[],[f4639]) ).
fof(f9467,plain,
( spl18_477
| ~ spl18_93
| ~ spl18_294 ),
inference(avatar_split_clause,[],[f4824,f4635,f906,f9465]) ).
fof(f9465,plain,
( spl18_477
<=> ! [X54,X55,X56] :
( sP1(X54,set_intersection2(X55,X56),sK17)
| ~ disjoint(X55,X56) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_477])]) ).
fof(f4635,plain,
( spl18_294
<=> ! [X9,X7,X6,X8] :
( in(sK13(X6,set_intersection2(X7,X8),X9),X9)
| sP1(X6,set_intersection2(X7,X8),X9)
| ~ disjoint(X7,X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_294])]) ).
fof(f4824,plain,
( ! [X56,X54,X55] :
( sP1(X54,set_intersection2(X55,X56),sK17)
| ~ disjoint(X55,X56) )
| ~ spl18_93
| ~ spl18_294 ),
inference(resolution,[],[f4636,f907]) ).
fof(f4636,plain,
( ! [X8,X6,X9,X7] :
( in(sK13(X6,set_intersection2(X7,X8),X9),X9)
| sP1(X6,set_intersection2(X7,X8),X9)
| ~ disjoint(X7,X8) )
| ~ spl18_294 ),
inference(avatar_component_clause,[],[f4635]) ).
fof(f9463,plain,
( spl18_476
| ~ spl18_93
| ~ spl18_293 ),
inference(avatar_split_clause,[],[f4800,f4631,f906,f9461]) ).
fof(f9461,plain,
( spl18_476
<=> ! [X54,X53,X55] :
( sP1(X53,sK17,set_intersection2(X54,X55))
| ~ disjoint(X54,X55) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_476])]) ).
fof(f4631,plain,
( spl18_293
<=> ! [X9,X7,X6,X8] :
( in(sK13(X6,X7,set_intersection2(X8,X9)),X7)
| sP1(X6,X7,set_intersection2(X8,X9))
| ~ disjoint(X8,X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_293])]) ).
fof(f4800,plain,
( ! [X54,X55,X53] :
( sP1(X53,sK17,set_intersection2(X54,X55))
| ~ disjoint(X54,X55) )
| ~ spl18_93
| ~ spl18_293 ),
inference(resolution,[],[f4632,f907]) ).
fof(f4632,plain,
( ! [X8,X6,X9,X7] :
( in(sK13(X6,X7,set_intersection2(X8,X9)),X7)
| sP1(X6,X7,set_intersection2(X8,X9))
| ~ disjoint(X8,X9) )
| ~ spl18_293 ),
inference(avatar_component_clause,[],[f4631]) ).
fof(f9459,plain,
( spl18_475
| ~ spl18_62
| ~ spl18_63
| ~ spl18_241
| ~ spl18_245 ),
inference(avatar_split_clause,[],[f3629,f3539,f3399,f646,f642,f9457]) ).
fof(f9457,plain,
( spl18_475
<=> ! [X77,X76] : set_union2(X76,X77) = set_union2(X77,set_difference(X76,X77)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_475])]) ).
fof(f642,plain,
( spl18_62
<=> ! [X0,X1] : set_intersection2(X0,X1) = set_difference(X0,set_difference(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_62])]) ).
fof(f3629,plain,
( ! [X76,X77] : set_union2(X76,X77) = set_union2(X77,set_difference(X76,X77))
| ~ spl18_62
| ~ spl18_63
| ~ spl18_241
| ~ spl18_245 ),
inference(forward_demodulation,[],[f3597,f3625]) ).
fof(f3625,plain,
( ! [X12,X13] : set_difference(X12,X13) = set_intersection2(set_union2(X12,X13),set_difference(X12,X13))
| ~ spl18_62
| ~ spl18_63
| ~ spl18_245 ),
inference(forward_demodulation,[],[f3572,f647]) ).
fof(f3572,plain,
( ! [X12,X13] : set_intersection2(set_union2(X12,X13),set_difference(X12,X13)) = set_difference(set_union2(X12,X13),X13)
| ~ spl18_62
| ~ spl18_245 ),
inference(superposition,[],[f643,f3540]) ).
fof(f643,plain,
( ! [X0,X1] : set_intersection2(X0,X1) = set_difference(X0,set_difference(X0,X1))
| ~ spl18_62 ),
inference(avatar_component_clause,[],[f642]) ).
fof(f3597,plain,
( ! [X76,X77] : set_union2(X76,X77) = set_union2(X77,set_intersection2(set_union2(X76,X77),set_difference(X76,X77)))
| ~ spl18_241
| ~ spl18_245 ),
inference(superposition,[],[f3400,f3540]) ).
fof(f9455,plain,
( spl18_474
| ~ spl18_54
| ~ spl18_122
| ~ spl18_189
| ~ spl18_245 ),
inference(avatar_split_clause,[],[f3599,f3539,f2080,f1155,f587,f9453]) ).
fof(f9453,plain,
( spl18_474
<=> ! [X8,X7] : set_union2(X8,X7) = set_difference(set_union2(X7,X8),sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_474])]) ).
fof(f2080,plain,
( spl18_189
<=> ! [X2,X3] : set_union2(X3,X2) = set_union2(X3,set_union2(X2,X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_189])]) ).
fof(f3599,plain,
( ! [X8,X7] : set_union2(X8,X7) = set_difference(set_union2(X7,X8),sK17)
| ~ spl18_54
| ~ spl18_122
| ~ spl18_189
| ~ spl18_245 ),
inference(forward_demodulation,[],[f3546,f1224]) ).
fof(f1224,plain,
( ! [X6,X7] : sK17 = set_difference(X6,set_union2(X7,X6))
| ~ spl18_54
| ~ spl18_122 ),
inference(resolution,[],[f1156,f588]) ).
fof(f3546,plain,
( ! [X8,X7] : set_union2(X8,X7) = set_difference(set_union2(X7,X8),set_difference(X7,set_union2(X8,X7)))
| ~ spl18_189
| ~ spl18_245 ),
inference(superposition,[],[f3540,f2081]) ).
fof(f2081,plain,
( ! [X2,X3] : set_union2(X3,X2) = set_union2(X3,set_union2(X2,X3))
| ~ spl18_189 ),
inference(avatar_component_clause,[],[f2080]) ).
fof(f9431,plain,
( spl18_473
| ~ spl18_147
| ~ spl18_245 ),
inference(avatar_split_clause,[],[f3580,f3539,f1457,f9429]) ).
fof(f9429,plain,
( spl18_473
<=> ! [X32,X31] : subset(X32,set_union2(set_union2(X31,X32),set_difference(X31,X32))) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_473])]) ).
fof(f3580,plain,
( ! [X31,X32] : subset(X32,set_union2(set_union2(X31,X32),set_difference(X31,X32)))
| ~ spl18_147
| ~ spl18_245 ),
inference(superposition,[],[f1458,f3540]) ).
fof(f9427,plain,
( spl18_472
| ~ spl18_77
| ~ spl18_243 ),
inference(avatar_split_clause,[],[f3498,f3475,f745,f9425]) ).
fof(f9425,plain,
( spl18_472
<=> ! [X16,X17,X15] :
( X15 != X17
| sP3(set_difference(X16,X15),X15,X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_472])]) ).
fof(f745,plain,
( spl18_77
<=> ! [X2,X0,X1] :
( sP3(X1,X0,X2)
| set_difference(X0,X1) != X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_77])]) ).
fof(f3498,plain,
( ! [X16,X17,X15] :
( X15 != X17
| sP3(set_difference(X16,X15),X15,X17) )
| ~ spl18_77
| ~ spl18_243 ),
inference(superposition,[],[f746,f3476]) ).
fof(f746,plain,
( ! [X2,X0,X1] :
( set_difference(X0,X1) != X2
| sP3(X1,X0,X2) )
| ~ spl18_77 ),
inference(avatar_component_clause,[],[f745]) ).
fof(f9423,plain,
( spl18_471
| ~ spl18_40
| ~ spl18_47
| ~ spl18_63
| ~ spl18_122
| ~ spl18_241 ),
inference(avatar_split_clause,[],[f3454,f3399,f1155,f646,f527,f471,f9421]) ).
fof(f9421,plain,
( spl18_471
<=> ! [X9,X8] : set_union2(X8,X9) = set_union2(set_difference(X8,X9),X9) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_471])]) ).
fof(f3454,plain,
( ! [X8,X9] : set_union2(X8,X9) = set_union2(set_difference(X8,X9),X9)
| ~ spl18_40
| ~ spl18_47
| ~ spl18_63
| ~ spl18_122
| ~ spl18_241 ),
inference(forward_demodulation,[],[f3453,f1223]) ).
fof(f1223,plain,
( ! [X4,X5] : set_intersection2(X4,set_union2(X5,X4)) = X4
| ~ spl18_47
| ~ spl18_122 ),
inference(resolution,[],[f1156,f528]) ).
fof(f3453,plain,
( ! [X8,X9] : set_union2(X8,X9) = set_union2(set_difference(X8,X9),set_intersection2(X9,set_union2(X8,X9)))
| ~ spl18_40
| ~ spl18_63
| ~ spl18_241 ),
inference(forward_demodulation,[],[f3407,f472]) ).
fof(f3407,plain,
( ! [X8,X9] : set_union2(X8,X9) = set_union2(set_difference(X8,X9),set_intersection2(set_union2(X8,X9),X9))
| ~ spl18_63
| ~ spl18_241 ),
inference(superposition,[],[f3400,f647]) ).
fof(f9419,plain,
( spl18_470
| ~ spl18_40
| ~ spl18_241 ),
inference(avatar_split_clause,[],[f3414,f3399,f471,f9417]) ).
fof(f9417,plain,
( spl18_470
<=> ! [X2,X1] : set_union2(set_difference(X1,X2),set_intersection2(X2,X1)) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl18_470])]) ).
fof(f3414,plain,
( ! [X2,X1] : set_union2(set_difference(X1,X2),set_intersection2(X2,X1)) = X1
| ~ spl18_40
| ~ spl18_241 ),
inference(superposition,[],[f3400,f472]) ).
fof(f9415,plain,
( spl18_469
| ~ spl18_39
| ~ spl18_60
| ~ spl18_140
| ~ spl18_219 ),
inference(avatar_split_clause,[],[f2813,f2770,f1429,f634,f467,f9413]) ).
fof(f9413,plain,
( spl18_469
<=> ! [X6,X7] : set_union2(set_intersection2(X6,X7),set_difference(X6,X7)) = X6 ),
introduced(avatar_definition,[new_symbols(naming,[spl18_469])]) ).
fof(f467,plain,
( spl18_39
<=> ! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_39])]) ).
fof(f2813,plain,
( ! [X6,X7] : set_union2(set_intersection2(X6,X7),set_difference(X6,X7)) = X6
| ~ spl18_39
| ~ spl18_60
| ~ spl18_140
| ~ spl18_219 ),
inference(forward_demodulation,[],[f2812,f1470]) ).
fof(f1470,plain,
( ! [X2,X3] : set_union2(X2,set_intersection2(X2,X3)) = X2
| ~ spl18_39
| ~ spl18_140 ),
inference(superposition,[],[f1430,f468]) ).
fof(f468,plain,
( ! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0)
| ~ spl18_39 ),
inference(avatar_component_clause,[],[f467]) ).
fof(f2812,plain,
( ! [X6,X7] : set_union2(X6,set_intersection2(X6,X7)) = set_union2(set_intersection2(X6,X7),set_difference(X6,X7))
| ~ spl18_39
| ~ spl18_60
| ~ spl18_219 ),
inference(forward_demodulation,[],[f2788,f468]) ).
fof(f2788,plain,
( ! [X6,X7] : set_union2(set_intersection2(X6,X7),X6) = set_union2(set_intersection2(X6,X7),set_difference(X6,X7))
| ~ spl18_60
| ~ spl18_219 ),
inference(superposition,[],[f635,f2771]) ).
fof(f9411,plain,
( spl18_468
| ~ spl18_40
| ~ spl18_219 ),
inference(avatar_split_clause,[],[f2777,f2770,f471,f9409]) ).
fof(f9409,plain,
( spl18_468
<=> ! [X2,X1] : set_difference(X1,X2) = set_difference(X1,set_intersection2(X2,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_468])]) ).
fof(f2777,plain,
( ! [X2,X1] : set_difference(X1,X2) = set_difference(X1,set_intersection2(X2,X1))
| ~ spl18_40
| ~ spl18_219 ),
inference(superposition,[],[f2771,f472]) ).
fof(f9407,plain,
( spl18_467
| ~ spl18_43
| ~ spl18_217 ),
inference(avatar_split_clause,[],[f2758,f2697,f511,f9405]) ).
fof(f9405,plain,
( spl18_467
<=> ! [X13,X14,X15] :
( sP3(X13,X13,set_intersection2(X14,X15))
| ~ disjoint(X14,X15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_467])]) ).
fof(f2758,plain,
( ! [X14,X15,X13] :
( sP3(X13,X13,set_intersection2(X14,X15))
| ~ disjoint(X14,X15) )
| ~ spl18_43
| ~ spl18_217 ),
inference(resolution,[],[f2698,f512]) ).
fof(f9403,plain,
( spl18_466
| ~ spl18_162
| ~ spl18_217 ),
inference(avatar_split_clause,[],[f2757,f2697,f1736,f9401]) ).
fof(f9401,plain,
( spl18_466
<=> ! [X11,X12,X10] :
( sP3(X10,X10,set_intersection2(X11,X12))
| ~ disjoint(X12,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_466])]) ).
fof(f2757,plain,
( ! [X10,X11,X12] :
( sP3(X10,X10,set_intersection2(X11,X12))
| ~ disjoint(X12,X11) )
| ~ spl18_162
| ~ spl18_217 ),
inference(resolution,[],[f2698,f1737]) ).
fof(f9399,plain,
( spl18_465
| ~ spl18_130
| ~ spl18_200 ),
inference(avatar_split_clause,[],[f2488,f2336,f1296,f9397]) ).
fof(f9397,plain,
( spl18_465
<=> ! [X0,X1] :
( set_union2(X0,X1) = X0
| ~ empty(set_union2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_465])]) ).
fof(f2336,plain,
( spl18_200
<=> ! [X6,X7] :
( set_union2(X6,X7) = X6
| ~ subset(set_union2(X6,X7),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_200])]) ).
fof(f2488,plain,
( ! [X0,X1] :
( set_union2(X0,X1) = X0
| ~ empty(set_union2(X0,X1)) )
| ~ spl18_130
| ~ spl18_200 ),
inference(resolution,[],[f2337,f1297]) ).
fof(f2337,plain,
( ! [X6,X7] :
( ~ subset(set_union2(X6,X7),X6)
| set_union2(X6,X7) = X6 )
| ~ spl18_200 ),
inference(avatar_component_clause,[],[f2336]) ).
fof(f9395,plain,
( spl18_464
| ~ spl18_141
| ~ spl18_193 ),
inference(avatar_split_clause,[],[f2307,f2280,f1433,f9393]) ).
fof(f9393,plain,
( spl18_464
<=> ! [X22,X24,X23] :
( X22 != X24
| sP2(set_difference(X22,X23),X22,X24) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_464])]) ).
fof(f2280,plain,
( spl18_193
<=> ! [X4,X2,X3] :
( set_union2(X3,X2) != X4
| sP2(X3,X2,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_193])]) ).
fof(f2307,plain,
( ! [X24,X22,X23] :
( X22 != X24
| sP2(set_difference(X22,X23),X22,X24) )
| ~ spl18_141
| ~ spl18_193 ),
inference(superposition,[],[f2281,f1434]) ).
fof(f2281,plain,
( ! [X2,X3,X4] :
( set_union2(X3,X2) != X4
| sP2(X3,X2,X4) )
| ~ spl18_193 ),
inference(avatar_component_clause,[],[f2280]) ).
fof(f9371,plain,
( spl18_463
| ~ spl18_140
| ~ spl18_193 ),
inference(avatar_split_clause,[],[f2306,f2280,f1429,f9369]) ).
fof(f9369,plain,
( spl18_463
<=> ! [X20,X21,X19] :
( X19 != X21
| sP2(set_intersection2(X19,X20),X19,X21) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_463])]) ).
fof(f2306,plain,
( ! [X21,X19,X20] :
( X19 != X21
| sP2(set_intersection2(X19,X20),X19,X21) )
| ~ spl18_140
| ~ spl18_193 ),
inference(superposition,[],[f2281,f1430]) ).
fof(f9367,plain,
( spl18_462
| ~ spl18_142
| ~ spl18_192 ),
inference(avatar_split_clause,[],[f2290,f2276,f1437,f9365]) ).
fof(f9365,plain,
( spl18_462
<=> ! [X9,X8,X10] :
( X8 != X10
| sP1(X8,set_union2(X8,X9),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_462])]) ).
fof(f2276,plain,
( spl18_192
<=> ! [X6,X4,X5] :
( set_intersection2(X5,X4) != X6
| sP1(X5,X4,X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_192])]) ).
fof(f2290,plain,
( ! [X10,X8,X9] :
( X8 != X10
| sP1(X8,set_union2(X8,X9),X10) )
| ~ spl18_142
| ~ spl18_192 ),
inference(superposition,[],[f2277,f1438]) ).
fof(f2277,plain,
( ! [X6,X4,X5] :
( set_intersection2(X5,X4) != X6
| sP1(X5,X4,X6) )
| ~ spl18_192 ),
inference(avatar_component_clause,[],[f2276]) ).
fof(f9363,plain,
( spl18_461
| ~ spl18_54
| ~ spl18_63
| ~ spl18_122
| ~ spl18_189 ),
inference(avatar_split_clause,[],[f2263,f2080,f1155,f646,f587,f9361]) ).
fof(f9361,plain,
( spl18_461
<=> ! [X12,X11] : sK17 = set_difference(set_union2(X11,X12),set_union2(X12,X11)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_461])]) ).
fof(f2263,plain,
( ! [X11,X12] : sK17 = set_difference(set_union2(X11,X12),set_union2(X12,X11))
| ~ spl18_54
| ~ spl18_63
| ~ spl18_122
| ~ spl18_189 ),
inference(forward_demodulation,[],[f2241,f1224]) ).
fof(f2241,plain,
( ! [X11,X12] : set_difference(X11,set_union2(X12,X11)) = set_difference(set_union2(X11,X12),set_union2(X12,X11))
| ~ spl18_63
| ~ spl18_189 ),
inference(superposition,[],[f647,f2081]) ).
fof(f9359,plain,
( spl18_460
| ~ spl18_60
| ~ spl18_141
| ~ spl18_188
| ~ spl18_189 ),
inference(avatar_split_clause,[],[f2259,f2080,f2076,f1433,f634,f9357]) ).
fof(f9357,plain,
( spl18_460
<=> ! [X11,X10] : set_union2(X10,X11) = set_union2(set_difference(X11,X10),X10) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_460])]) ).
fof(f2259,plain,
( ! [X10,X11] : set_union2(X10,X11) = set_union2(set_difference(X11,X10),X10)
| ~ spl18_60
| ~ spl18_141
| ~ spl18_188
| ~ spl18_189 ),
inference(forward_demodulation,[],[f2233,f2209]) ).
fof(f2209,plain,
( ! [X24,X25] : set_union2(X24,X25) = set_union2(set_difference(X25,X24),set_union2(X24,X25))
| ~ spl18_141
| ~ spl18_188 ),
inference(superposition,[],[f1434,f2077]) ).
fof(f2233,plain,
( ! [X10,X11] : set_union2(set_difference(X11,X10),X10) = set_union2(set_difference(X11,X10),set_union2(X10,X11))
| ~ spl18_60
| ~ spl18_189 ),
inference(superposition,[],[f2081,f635]) ).
fof(f9355,plain,
( spl18_459
| ~ spl18_40
| ~ spl18_62
| ~ spl18_142
| ~ spl18_188 ),
inference(avatar_split_clause,[],[f2223,f2076,f1437,f642,f471,f9353]) ).
fof(f9353,plain,
( spl18_459
<=> ! [X9,X10] : set_difference(set_union2(X9,X10),set_difference(X10,X9)) = X9 ),
introduced(avatar_definition,[new_symbols(naming,[spl18_459])]) ).
fof(f2223,plain,
( ! [X10,X9] : set_difference(set_union2(X9,X10),set_difference(X10,X9)) = X9
| ~ spl18_40
| ~ spl18_62
| ~ spl18_142
| ~ spl18_188 ),
inference(forward_demodulation,[],[f2222,f1438]) ).
fof(f2222,plain,
( ! [X10,X9] : set_intersection2(X9,set_union2(X9,X10)) = set_difference(set_union2(X9,X10),set_difference(X10,X9))
| ~ spl18_40
| ~ spl18_62
| ~ spl18_188 ),
inference(forward_demodulation,[],[f2203,f472]) ).
fof(f2203,plain,
( ! [X10,X9] : set_intersection2(set_union2(X9,X10),X9) = set_difference(set_union2(X9,X10),set_difference(X10,X9))
| ~ spl18_62
| ~ spl18_188 ),
inference(superposition,[],[f643,f2077]) ).
fof(f9351,plain,
( spl18_458
| ~ spl18_60
| ~ spl18_188 ),
inference(avatar_split_clause,[],[f2218,f2076,f634,f9349]) ).
fof(f9349,plain,
( spl18_458
<=> ! [X9,X8] : set_difference(X9,X8) = set_difference(set_difference(X9,X8),X8) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_458])]) ).
fof(f2218,plain,
( ! [X8,X9] : set_difference(X9,X8) = set_difference(set_difference(X9,X8),X8)
| ~ spl18_60
| ~ spl18_188 ),
inference(forward_demodulation,[],[f2197,f2077]) ).
fof(f2197,plain,
( ! [X8,X9] : set_difference(set_difference(X9,X8),X8) = set_difference(set_union2(X8,X9),X8)
| ~ spl18_60
| ~ spl18_188 ),
inference(superposition,[],[f2077,f635]) ).
fof(f9347,plain,
( spl18_457
| ~ spl18_144
| ~ spl18_188 ),
inference(avatar_split_clause,[],[f2210,f2076,f1445,f9345]) ).
fof(f9345,plain,
( spl18_457
<=> ! [X27,X26] : sK17 = set_difference(set_difference(X27,X26),set_union2(X26,X27)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_457])]) ).
fof(f2210,plain,
( ! [X26,X27] : sK17 = set_difference(set_difference(X27,X26),set_union2(X26,X27))
| ~ spl18_144
| ~ spl18_188 ),
inference(superposition,[],[f1446,f2077]) ).
fof(f9343,plain,
( spl18_456
| ~ spl18_40
| ~ spl18_187 ),
inference(avatar_split_clause,[],[f2161,f2072,f471,f9341]) ).
fof(f9341,plain,
( spl18_456
<=> ! [X2,X3] : set_difference(X2,X3) = set_intersection2(X2,set_difference(X2,X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_456])]) ).
fof(f2161,plain,
( ! [X2,X3] : set_difference(X2,X3) = set_intersection2(X2,set_difference(X2,X3))
| ~ spl18_40
| ~ spl18_187 ),
inference(superposition,[],[f2073,f472]) ).
fof(f9339,plain,
( spl18_455
| ~ spl18_40
| ~ spl18_186 ),
inference(avatar_split_clause,[],[f2117,f2068,f471,f9337]) ).
fof(f9337,plain,
( spl18_455
<=> ! [X2,X3] : set_intersection2(X2,X3) = set_intersection2(X2,set_intersection2(X2,X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_455])]) ).
fof(f2117,plain,
( ! [X2,X3] : set_intersection2(X2,X3) = set_intersection2(X2,set_intersection2(X2,X3))
| ~ spl18_40
| ~ spl18_186 ),
inference(superposition,[],[f2069,f472]) ).
fof(f9334,plain,
( spl18_454
| ~ spl18_60
| ~ spl18_147 ),
inference(avatar_split_clause,[],[f1632,f1457,f634,f9332]) ).
fof(f9332,plain,
( spl18_454
<=> ! [X6,X7] : subset(set_difference(X6,set_difference(X7,X6)),set_union2(X6,X7)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_454])]) ).
fof(f1632,plain,
( ! [X6,X7] : subset(set_difference(X6,set_difference(X7,X6)),set_union2(X6,X7))
| ~ spl18_60
| ~ spl18_147 ),
inference(superposition,[],[f1458,f635]) ).
fof(f9315,plain,
( spl18_453
| ~ spl18_39
| ~ spl18_60
| ~ spl18_128
| ~ spl18_145 ),
inference(avatar_split_clause,[],[f1609,f1449,f1288,f634,f467,f9313]) ).
fof(f9313,plain,
( spl18_453
<=> ! [X6,X7] : set_union2(X6,X7) = set_union2(set_union2(X6,X7),X6) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_453])]) ).
fof(f1609,plain,
( ! [X6,X7] : set_union2(X6,X7) = set_union2(set_union2(X6,X7),X6)
| ~ spl18_39
| ~ spl18_60
| ~ spl18_128
| ~ spl18_145 ),
inference(forward_demodulation,[],[f1608,f1289]) ).
fof(f1608,plain,
( ! [X6,X7] : set_union2(set_union2(X6,X7),X6) = set_union2(sK17,set_union2(X6,X7))
| ~ spl18_39
| ~ spl18_60
| ~ spl18_145 ),
inference(forward_demodulation,[],[f1597,f468]) ).
fof(f1597,plain,
( ! [X6,X7] : set_union2(set_union2(X6,X7),X6) = set_union2(set_union2(X6,X7),sK17)
| ~ spl18_60
| ~ spl18_145 ),
inference(superposition,[],[f635,f1450]) ).
fof(f9311,plain,
( spl18_452
| ~ spl18_77
| ~ spl18_145 ),
inference(avatar_split_clause,[],[f1599,f1449,f745,f9309]) ).
fof(f9309,plain,
( spl18_452
<=> ! [X11,X12,X10] :
( sK17 != X12
| sP3(set_union2(X10,X11),X10,X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_452])]) ).
fof(f1599,plain,
( ! [X10,X11,X12] :
( sK17 != X12
| sP3(set_union2(X10,X11),X10,X12) )
| ~ spl18_77
| ~ spl18_145 ),
inference(superposition,[],[f746,f1450]) ).
fof(f9307,plain,
( spl18_451
| ~ spl18_77
| ~ spl18_144 ),
inference(avatar_split_clause,[],[f1572,f1445,f745,f9305]) ).
fof(f9305,plain,
( spl18_451
<=> ! [X11,X12,X10] :
( sK17 != X12
| sP3(X10,set_difference(X10,X11),X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_451])]) ).
fof(f1572,plain,
( ! [X10,X11,X12] :
( sK17 != X12
| sP3(X10,set_difference(X10,X11),X12) )
| ~ spl18_77
| ~ spl18_144 ),
inference(superposition,[],[f746,f1446]) ).
fof(f9303,plain,
( spl18_450
| ~ spl18_63
| ~ spl18_144 ),
inference(avatar_split_clause,[],[f1561,f1445,f646,f9301]) ).
fof(f9301,plain,
( spl18_450
<=> ! [X4,X5] : sK17 = set_difference(set_difference(X4,X5),set_union2(X4,X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_450])]) ).
fof(f1561,plain,
( ! [X4,X5] : sK17 = set_difference(set_difference(X4,X5),set_union2(X4,X5))
| ~ spl18_63
| ~ spl18_144 ),
inference(superposition,[],[f1446,f647]) ).
fof(f9299,plain,
( spl18_449
| ~ spl18_77
| ~ spl18_143 ),
inference(avatar_split_clause,[],[f1544,f1441,f745,f9297]) ).
fof(f9297,plain,
( spl18_449
<=> ! [X11,X12,X10] :
( sK17 != X12
| sP3(X10,set_intersection2(X10,X11),X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_449])]) ).
fof(f1544,plain,
( ! [X10,X11,X12] :
( sK17 != X12
| sP3(X10,set_intersection2(X10,X11),X12) )
| ~ spl18_77
| ~ spl18_143 ),
inference(superposition,[],[f746,f1442]) ).
fof(f9295,plain,
( spl18_448
| ~ spl18_73
| ~ spl18_142 ),
inference(avatar_split_clause,[],[f1522,f1437,f725,f9293]) ).
fof(f9293,plain,
( spl18_448
<=> ! [X13,X12,X11] :
( X11 != X13
| sP1(set_union2(X11,X12),X11,X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_448])]) ).
fof(f725,plain,
( spl18_73
<=> ! [X2,X0,X1] :
( sP1(X1,X0,X2)
| set_intersection2(X0,X1) != X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_73])]) ).
fof(f1522,plain,
( ! [X11,X12,X13] :
( X11 != X13
| sP1(set_union2(X11,X12),X11,X13) )
| ~ spl18_73
| ~ spl18_142 ),
inference(superposition,[],[f726,f1438]) ).
fof(f726,plain,
( ! [X2,X0,X1] :
( set_intersection2(X0,X1) != X2
| sP1(X1,X0,X2) )
| ~ spl18_73 ),
inference(avatar_component_clause,[],[f725]) ).
fof(f9291,plain,
( spl18_447
| ~ spl18_75
| ~ spl18_141 ),
inference(avatar_split_clause,[],[f1504,f1433,f733,f9289]) ).
fof(f9289,plain,
( spl18_447
<=> ! [X13,X12,X14] :
( X12 != X14
| sP2(X12,set_difference(X12,X13),X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_447])]) ).
fof(f1504,plain,
( ! [X14,X12,X13] :
( X12 != X14
| sP2(X12,set_difference(X12,X13),X14) )
| ~ spl18_75
| ~ spl18_141 ),
inference(superposition,[],[f734,f1434]) ).
fof(f9287,plain,
( spl18_446
| ~ spl18_75
| ~ spl18_140 ),
inference(avatar_split_clause,[],[f1479,f1429,f733,f9285]) ).
fof(f9285,plain,
( spl18_446
<=> ! [X13,X12,X14] :
( X12 != X14
| sP2(X12,set_intersection2(X12,X13),X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_446])]) ).
fof(f1479,plain,
( ! [X14,X12,X13] :
( X12 != X14
| sP2(X12,set_intersection2(X12,X13),X14) )
| ~ spl18_75
| ~ spl18_140 ),
inference(superposition,[],[f734,f1430]) ).
fof(f9283,plain,
( spl18_445
| ~ spl18_47
| ~ spl18_123 ),
inference(avatar_split_clause,[],[f1236,f1159,f527,f9281]) ).
fof(f1236,plain,
( ! [X4,X5] : set_intersection2(X4,X5) = set_intersection2(set_intersection2(X4,X5),X5)
| ~ spl18_47
| ~ spl18_123 ),
inference(resolution,[],[f1160,f528]) ).
fof(f9279,plain,
( spl18_444
| ~ spl18_46
| ~ spl18_122 ),
inference(avatar_split_clause,[],[f1222,f1155,f523,f9277]) ).
fof(f9277,plain,
( spl18_444
<=> ! [X2,X3] : set_union2(X3,X2) = set_union2(X2,set_union2(X3,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_444])]) ).
fof(f1222,plain,
( ! [X2,X3] : set_union2(X3,X2) = set_union2(X2,set_union2(X3,X2))
| ~ spl18_46
| ~ spl18_122 ),
inference(resolution,[],[f1156,f524]) ).
fof(f9275,plain,
( spl18_443
| ~ spl18_333
| ~ spl18_375 ),
inference(avatar_split_clause,[],[f7205,f5994,f5710,f9273]) ).
fof(f9273,plain,
( spl18_443
<=> ! [X205,X204] : sP1(X204,set_difference(X205,X204),sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_443])]) ).
fof(f5710,plain,
( spl18_333
<=> ! [X2,X1] : sP1(X2,X1,set_intersection2(X2,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_333])]) ).
fof(f5994,plain,
( spl18_375
<=> ! [X13,X14] : sK17 = set_intersection2(X13,set_difference(X14,X13)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_375])]) ).
fof(f7205,plain,
( ! [X205,X204] : sP1(X204,set_difference(X205,X204),sK17)
| ~ spl18_333
| ~ spl18_375 ),
inference(superposition,[],[f5711,f5995]) ).
fof(f5995,plain,
( ! [X14,X13] : sK17 = set_intersection2(X13,set_difference(X14,X13))
| ~ spl18_375 ),
inference(avatar_component_clause,[],[f5994]) ).
fof(f5711,plain,
( ! [X2,X1] : sP1(X2,X1,set_intersection2(X2,X1))
| ~ spl18_333 ),
inference(avatar_component_clause,[],[f5710]) ).
fof(f9097,plain,
( spl18_442
| ~ spl18_20
| ~ spl18_238 ),
inference(avatar_split_clause,[],[f3368,f3318,f358,f9095]) ).
fof(f9095,plain,
( spl18_442
<=> ! [X9,X8,X7] :
( sP3(X7,X8,X9)
| ~ empty(X9)
| ~ empty(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_442])]) ).
fof(f358,plain,
( spl18_20
<=> ! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_20])]) ).
fof(f3318,plain,
( spl18_238
<=> ! [X4,X5,X3] :
( in(sK15(X3,X4,X5),X4)
| sP3(X3,X4,X5)
| ~ empty(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_238])]) ).
fof(f3368,plain,
( ! [X8,X9,X7] :
( sP3(X7,X8,X9)
| ~ empty(X9)
| ~ empty(X8) )
| ~ spl18_20
| ~ spl18_238 ),
inference(resolution,[],[f3319,f359]) ).
fof(f359,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) )
| ~ spl18_20 ),
inference(avatar_component_clause,[],[f358]) ).
fof(f3319,plain,
( ! [X3,X4,X5] :
( in(sK15(X3,X4,X5),X4)
| sP3(X3,X4,X5)
| ~ empty(X5) )
| ~ spl18_238 ),
inference(avatar_component_clause,[],[f3318]) ).
fof(f9093,plain,
( spl18_441
| ~ spl18_20
| ~ spl18_236 ),
inference(avatar_split_clause,[],[f3347,f3310,f358,f9091]) ).
fof(f9091,plain,
( spl18_441
<=> ! [X6,X5,X7] :
( sP1(X5,X6,X7)
| ~ empty(X7)
| ~ empty(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_441])]) ).
fof(f3310,plain,
( spl18_236
<=> ! [X4,X5,X3] :
( in(sK13(X3,X4,X5),X3)
| sP1(X3,X4,X5)
| ~ empty(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_236])]) ).
fof(f3347,plain,
( ! [X6,X7,X5] :
( sP1(X5,X6,X7)
| ~ empty(X7)
| ~ empty(X5) )
| ~ spl18_20
| ~ spl18_236 ),
inference(resolution,[],[f3311,f359]) ).
fof(f3311,plain,
( ! [X3,X4,X5] :
( in(sK13(X3,X4,X5),X3)
| sP1(X3,X4,X5)
| ~ empty(X5) )
| ~ spl18_236 ),
inference(avatar_component_clause,[],[f3310]) ).
fof(f9089,plain,
( spl18_440
| ~ spl18_137
| ~ spl18_375 ),
inference(avatar_split_clause,[],[f7146,f5994,f1377,f9087]) ).
fof(f9087,plain,
( spl18_440
<=> ! [X32,X31] : sP1(set_difference(X32,X31),X31,sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_440])]) ).
fof(f1377,plain,
( spl18_137
<=> ! [X0,X1] : sP1(X0,X1,set_intersection2(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_137])]) ).
fof(f7146,plain,
( ! [X31,X32] : sP1(set_difference(X32,X31),X31,sK17)
| ~ spl18_137
| ~ spl18_375 ),
inference(superposition,[],[f1378,f5995]) ).
fof(f1378,plain,
( ! [X0,X1] : sP1(X0,X1,set_intersection2(X1,X0))
| ~ spl18_137 ),
inference(avatar_component_clause,[],[f1377]) ).
fof(f9085,plain,
( spl18_439
| ~ spl18_20
| ~ spl18_234 ),
inference(avatar_split_clause,[],[f3327,f3298,f358,f9083]) ).
fof(f9083,plain,
( spl18_439
<=> ! [X6,X5,X7] :
( sP1(X5,X6,X7)
| ~ empty(X7)
| ~ empty(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_439])]) ).
fof(f3298,plain,
( spl18_234
<=> ! [X4,X5,X3] :
( in(sK13(X3,X4,X5),X4)
| sP1(X3,X4,X5)
| ~ empty(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_234])]) ).
fof(f3327,plain,
( ! [X6,X7,X5] :
( sP1(X5,X6,X7)
| ~ empty(X7)
| ~ empty(X6) )
| ~ spl18_20
| ~ spl18_234 ),
inference(resolution,[],[f3299,f359]) ).
fof(f3299,plain,
( ! [X3,X4,X5] :
( in(sK13(X3,X4,X5),X4)
| sP1(X3,X4,X5)
| ~ empty(X5) )
| ~ spl18_234 ),
inference(avatar_component_clause,[],[f3298]) ).
fof(f9081,plain,
( spl18_438
| ~ spl18_92
| ~ spl18_139 ),
inference(avatar_split_clause,[],[f1417,f1385,f901,f9079]) ).
fof(f9079,plain,
( spl18_438
<=> ! [X4,X5,X3] :
( ~ in(X3,set_difference(X4,X5))
| ~ in(X3,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_438])]) ).
fof(f901,plain,
( spl18_92
<=> ! [X4,X0,X2,X1] :
( ~ in(X4,X0)
| ~ in(X4,X2)
| ~ sP3(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_92])]) ).
fof(f1385,plain,
( spl18_139
<=> ! [X0,X1] : sP3(X0,X1,set_difference(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_139])]) ).
fof(f1417,plain,
( ! [X3,X4,X5] :
( ~ in(X3,set_difference(X4,X5))
| ~ in(X3,X5) )
| ~ spl18_92
| ~ spl18_139 ),
inference(resolution,[],[f1386,f902]) ).
fof(f902,plain,
( ! [X2,X0,X1,X4] :
( ~ sP3(X0,X1,X2)
| ~ in(X4,X2)
| ~ in(X4,X0) )
| ~ spl18_92 ),
inference(avatar_component_clause,[],[f901]) ).
fof(f1386,plain,
( ! [X0,X1] : sP3(X0,X1,set_difference(X1,X0))
| ~ spl18_139 ),
inference(avatar_component_clause,[],[f1385]) ).
fof(f9077,plain,
( spl18_437
| ~ spl18_69
| ~ spl18_130 ),
inference(avatar_split_clause,[],[f1327,f1296,f709,f9075]) ).
fof(f9075,plain,
( spl18_437
<=> ! [X13,X14] :
( ~ empty(X13)
| X13 = X14
| proper_subset(X13,X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_437])]) ).
fof(f1327,plain,
( ! [X14,X13] :
( ~ empty(X13)
| X13 = X14
| proper_subset(X13,X14) )
| ~ spl18_69
| ~ spl18_130 ),
inference(resolution,[],[f1297,f710]) ).
fof(f9073,plain,
( spl18_436
| ~ spl18_68
| ~ spl18_130 ),
inference(avatar_split_clause,[],[f1326,f1296,f705,f9071]) ).
fof(f9071,plain,
( spl18_436
<=> ! [X12,X11] :
( ~ empty(X11)
| X11 = X12
| ~ subset(X12,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_436])]) ).
fof(f1326,plain,
( ! [X11,X12] :
( ~ empty(X11)
| X11 = X12
| ~ subset(X12,X11) )
| ~ spl18_68
| ~ spl18_130 ),
inference(resolution,[],[f1297,f706]) ).
fof(f9069,plain,
( spl18_435
| ~ spl18_93
| ~ spl18_97 ),
inference(avatar_split_clause,[],[f1001,f959,f906,f9067]) ).
fof(f9067,plain,
( spl18_435
<=> ! [X7] :
( in(sK9(sK17,X7),X7)
| sK17 = X7 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_435])]) ).
fof(f959,plain,
( spl18_97
<=> ! [X0,X1] :
( X0 = X1
| in(sK9(X0,X1),X1)
| in(sK9(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_97])]) ).
fof(f1001,plain,
( ! [X7] :
( in(sK9(sK17,X7),X7)
| sK17 = X7 )
| ~ spl18_93
| ~ spl18_97 ),
inference(resolution,[],[f960,f907]) ).
fof(f960,plain,
( ! [X0,X1] :
( in(sK9(X0,X1),X1)
| in(sK9(X0,X1),X0)
| X0 = X1 )
| ~ spl18_97 ),
inference(avatar_component_clause,[],[f959]) ).
fof(f9065,plain,
( spl18_434
| ~ spl18_93
| ~ spl18_97 ),
inference(avatar_split_clause,[],[f997,f959,f906,f9063]) ).
fof(f9063,plain,
( spl18_434
<=> ! [X7] :
( in(sK9(X7,sK17),X7)
| sK17 = X7 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_434])]) ).
fof(f997,plain,
( ! [X7] :
( in(sK9(X7,sK17),X7)
| sK17 = X7 )
| ~ spl18_93
| ~ spl18_97 ),
inference(resolution,[],[f960,f907]) ).
fof(f8205,plain,
( spl18_433
| ~ spl18_334
| ~ spl18_352 ),
inference(avatar_split_clause,[],[f6315,f5894,f5714,f8203]) ).
fof(f8203,plain,
( spl18_433
<=> ! [X80,X81] : sP2(set_intersection2(X80,X81),X81,X81) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_433])]) ).
fof(f5714,plain,
( spl18_334
<=> ! [X2,X1] : sP2(X2,X1,set_union2(X2,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_334])]) ).
fof(f6315,plain,
( ! [X80,X81] : sP2(set_intersection2(X80,X81),X81,X81)
| ~ spl18_334
| ~ spl18_352 ),
inference(superposition,[],[f5715,f5895]) ).
fof(f5715,plain,
( ! [X2,X1] : sP2(X2,X1,set_union2(X2,X1))
| ~ spl18_334 ),
inference(avatar_component_clause,[],[f5714]) ).
fof(f7997,plain,
( spl18_432
| ~ spl18_333
| ~ spl18_349 ),
inference(avatar_split_clause,[],[f6119,f5882,f5710,f7995]) ).
fof(f7995,plain,
( spl18_432
<=> ! [X203,X204] : sP1(X203,set_union2(X204,X203),X203) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_432])]) ).
fof(f5882,plain,
( spl18_349
<=> ! [X4,X5] : set_intersection2(X4,set_union2(X5,X4)) = X4 ),
introduced(avatar_definition,[new_symbols(naming,[spl18_349])]) ).
fof(f6119,plain,
( ! [X203,X204] : sP1(X203,set_union2(X204,X203),X203)
| ~ spl18_333
| ~ spl18_349 ),
inference(superposition,[],[f5711,f5883]) ).
fof(f5883,plain,
( ! [X4,X5] : set_intersection2(X4,set_union2(X5,X4)) = X4
| ~ spl18_349 ),
inference(avatar_component_clause,[],[f5882]) ).
fof(f7445,plain,
( spl18_431
| ~ spl18_12
| ~ spl18_254 ),
inference(avatar_split_clause,[],[f3923,f3667,f326,f7443]) ).
fof(f7443,plain,
( spl18_431
<=> ! [X0,X1] :
( subset(set_union2(X0,X1),X1)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_431])]) ).
fof(f3667,plain,
( spl18_254
<=> ! [X11,X12,X10] :
( subset(set_union2(X10,X11),X12)
| ~ subset(set_difference(X11,X10),X12)
| ~ subset(X10,X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_254])]) ).
fof(f3923,plain,
( ! [X0,X1] :
( subset(set_union2(X0,X1),X1)
| ~ subset(X0,X1) )
| ~ spl18_12
| ~ spl18_254 ),
inference(resolution,[],[f3668,f327]) ).
fof(f3668,plain,
( ! [X10,X11,X12] :
( ~ subset(set_difference(X11,X10),X12)
| subset(set_union2(X10,X11),X12)
| ~ subset(X10,X12) )
| ~ spl18_254 ),
inference(avatar_component_clause,[],[f3667]) ).
fof(f7441,plain,
( spl18_430
| ~ spl18_8
| ~ spl18_39
| ~ spl18_185
| ~ spl18_252 ),
inference(avatar_split_clause,[],[f3887,f3659,f2064,f467,f310,f7439]) ).
fof(f7439,plain,
( spl18_430
<=> ! [X0,X1] :
( set_union2(X1,X0) = X1
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_430])]) ).
fof(f3659,plain,
( spl18_252
<=> ! [X4,X5,X3] :
( ~ subset(X3,X4)
| ~ subset(X5,X4)
| set_union2(set_union2(X5,X3),X4) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_252])]) ).
fof(f3887,plain,
( ! [X0,X1] :
( set_union2(X1,X0) = X1
| ~ subset(X0,X1) )
| ~ spl18_8
| ~ spl18_39
| ~ spl18_185
| ~ spl18_252 ),
inference(forward_demodulation,[],[f3886,f2065]) ).
fof(f3886,plain,
( ! [X0,X1] :
( set_union2(X1,set_union2(X1,X0)) = X1
| ~ subset(X0,X1) )
| ~ spl18_8
| ~ spl18_39
| ~ spl18_252 ),
inference(forward_demodulation,[],[f3863,f468]) ).
fof(f3863,plain,
( ! [X0,X1] :
( ~ subset(X0,X1)
| set_union2(set_union2(X1,X0),X1) = X1 )
| ~ spl18_8
| ~ spl18_252 ),
inference(resolution,[],[f3660,f311]) ).
fof(f3660,plain,
( ! [X3,X4,X5] :
( ~ subset(X5,X4)
| ~ subset(X3,X4)
| set_union2(set_union2(X5,X3),X4) = X4 )
| ~ spl18_252 ),
inference(avatar_component_clause,[],[f3659]) ).
fof(f7437,plain,
( spl18_429
| ~ spl18_139
| ~ spl18_245 ),
inference(avatar_split_clause,[],[f3577,f3539,f1385,f7435]) ).
fof(f7435,plain,
( spl18_429
<=> ! [X25,X26] : sP3(set_difference(X25,X26),set_union2(X25,X26),X26) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_429])]) ).
fof(f3577,plain,
( ! [X26,X25] : sP3(set_difference(X25,X26),set_union2(X25,X26),X26)
| ~ spl18_139
| ~ spl18_245 ),
inference(superposition,[],[f1386,f3540]) ).
fof(f7433,plain,
( spl18_428
| ~ spl18_53
| ~ spl18_243 ),
inference(avatar_split_clause,[],[f3496,f3475,f583,f7431]) ).
fof(f7431,plain,
( spl18_428
<=> ! [X9,X10] :
( sK17 != X9
| subset(X9,set_difference(X10,X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_428])]) ).
fof(f3496,plain,
( ! [X10,X9] :
( sK17 != X9
| subset(X9,set_difference(X10,X9)) )
| ~ spl18_53
| ~ spl18_243 ),
inference(superposition,[],[f584,f3476]) ).
fof(f7429,plain,
( spl18_427
| ~ spl18_138
| ~ spl18_241 ),
inference(avatar_split_clause,[],[f3434,f3399,f1381,f7427]) ).
fof(f7427,plain,
( spl18_427
<=> ! [X22,X23] : sP2(set_intersection2(X22,X23),set_difference(X22,X23),X22) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_427])]) ).
fof(f3434,plain,
( ! [X22,X23] : sP2(set_intersection2(X22,X23),set_difference(X22,X23),X22)
| ~ spl18_138
| ~ spl18_241 ),
inference(superposition,[],[f1382,f3400]) ).
fof(f7425,plain,
( spl18_426
| ~ spl18_139
| ~ spl18_219 ),
inference(avatar_split_clause,[],[f2794,f2770,f1385,f7423]) ).
fof(f7423,plain,
( spl18_426
<=> ! [X22,X21] : sP3(set_intersection2(X21,X22),X21,set_difference(X21,X22)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_426])]) ).
fof(f2794,plain,
( ! [X21,X22] : sP3(set_intersection2(X21,X22),X21,set_difference(X21,X22))
| ~ spl18_139
| ~ spl18_219 ),
inference(superposition,[],[f1386,f2771]) ).
fof(f7421,plain,
( spl18_425
| ~ spl18_14
| ~ spl18_83
| ~ spl18_210 ),
inference(avatar_split_clause,[],[f2668,f2376,f864,f334,f7419]) ).
fof(f7419,plain,
( spl18_425
<=> ! [X20,X19] :
( ~ subset(X20,sK17)
| ~ proper_subset(sK17,set_difference(X20,X19)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_425])]) ).
fof(f334,plain,
( spl18_14
<=> ! [X0] : empty_set = set_difference(empty_set,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_14])]) ).
fof(f2668,plain,
( ! [X19,X20] :
( ~ subset(X20,sK17)
| ~ proper_subset(sK17,set_difference(X20,X19)) )
| ~ spl18_14
| ~ spl18_83
| ~ spl18_210 ),
inference(forward_demodulation,[],[f2667,f866]) ).
fof(f2667,plain,
( ! [X19,X20] :
( ~ proper_subset(sK17,set_difference(X20,X19))
| ~ subset(X20,empty_set) )
| ~ spl18_14
| ~ spl18_83
| ~ spl18_210 ),
inference(forward_demodulation,[],[f2653,f866]) ).
fof(f2653,plain,
( ! [X19,X20] :
( ~ proper_subset(empty_set,set_difference(X20,X19))
| ~ subset(X20,empty_set) )
| ~ spl18_14
| ~ spl18_210 ),
inference(superposition,[],[f2377,f335]) ).
fof(f335,plain,
( ! [X0] : empty_set = set_difference(empty_set,X0)
| ~ spl18_14 ),
inference(avatar_component_clause,[],[f334]) ).
fof(f7417,plain,
( spl18_424
| ~ spl18_126
| ~ spl18_210 ),
inference(avatar_split_clause,[],[f2646,f2376,f1171,f7415]) ).
fof(f7415,plain,
( spl18_424
<=> ! [X0,X1] :
( ~ proper_subset(sK17,set_difference(X1,X0))
| ~ subset(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_424])]) ).
fof(f2646,plain,
( ! [X0,X1] :
( ~ proper_subset(sK17,set_difference(X1,X0))
| ~ subset(X1,X0) )
| ~ spl18_126
| ~ spl18_210 ),
inference(superposition,[],[f2377,f1172]) ).
fof(f7413,plain,
( spl18_423
| ~ spl18_170
| ~ spl18_207 ),
inference(avatar_split_clause,[],[f2590,f2364,f1768,f7411]) ).
fof(f7411,plain,
( spl18_423
<=> ! [X2,X0,X1] :
( ~ subset(X0,X1)
| subset(set_intersection2(X2,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_423])]) ).
fof(f1768,plain,
( spl18_170
<=> ! [X2,X4,X3] :
( subset(X2,X3)
| ~ subset(X2,set_intersection2(X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_170])]) ).
fof(f2590,plain,
( ! [X2,X0,X1] :
( ~ subset(X0,X1)
| subset(set_intersection2(X2,X0),X1) )
| ~ spl18_170
| ~ spl18_207 ),
inference(resolution,[],[f2365,f1769]) ).
fof(f1769,plain,
( ! [X2,X3,X4] :
( ~ subset(X2,set_intersection2(X3,X4))
| subset(X2,X3) )
| ~ spl18_170 ),
inference(avatar_component_clause,[],[f1768]) ).
fof(f7409,plain,
( spl18_422
| ~ spl18_141
| ~ spl18_334 ),
inference(avatar_split_clause,[],[f5821,f5714,f1433,f7407]) ).
fof(f7407,plain,
( spl18_422
<=> ! [X16,X15] : sP2(set_difference(X15,X16),X15,X15) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_422])]) ).
fof(f5821,plain,
( ! [X16,X15] : sP2(set_difference(X15,X16),X15,X15)
| ~ spl18_141
| ~ spl18_334 ),
inference(superposition,[],[f5715,f1434]) ).
fof(f7405,plain,
( spl18_421
| ~ spl18_120
| ~ spl18_206 ),
inference(avatar_split_clause,[],[f2579,f2360,f1147,f7403]) ).
fof(f7403,plain,
( spl18_421
<=> ! [X22,X21] :
( ~ proper_subset(sK17,set_intersection2(X22,X21))
| ~ subset(X22,sK17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_421])]) ).
fof(f1147,plain,
( spl18_120
<=> ! [X0] : sK17 = set_intersection2(sK17,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_120])]) ).
fof(f2579,plain,
( ! [X21,X22] :
( ~ proper_subset(sK17,set_intersection2(X22,X21))
| ~ subset(X22,sK17) )
| ~ spl18_120
| ~ spl18_206 ),
inference(superposition,[],[f2361,f1148]) ).
fof(f1148,plain,
( ! [X0] : sK17 = set_intersection2(sK17,X0)
| ~ spl18_120 ),
inference(avatar_component_clause,[],[f1147]) ).
fof(f7401,plain,
( spl18_420
| ~ spl18_173
| ~ spl18_205 ),
inference(avatar_split_clause,[],[f2556,f2356,f1780,f7399]) ).
fof(f7399,plain,
( spl18_420
<=> ! [X0,X1] :
( disjoint(X0,X1)
| in(sK6(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_420])]) ).
fof(f2356,plain,
( spl18_205
<=> ! [X2,X3] :
( in(sK6(X2,X3),set_intersection2(X3,X2))
| disjoint(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_205])]) ).
fof(f2556,plain,
( ! [X0,X1] :
( disjoint(X0,X1)
| in(sK6(X0,X1),X1) )
| ~ spl18_173
| ~ spl18_205 ),
inference(resolution,[],[f2357,f1781]) ).
fof(f2357,plain,
( ! [X2,X3] :
( in(sK6(X2,X3),set_intersection2(X3,X2))
| disjoint(X2,X3) )
| ~ spl18_205 ),
inference(avatar_component_clause,[],[f2356]) ).
fof(f7397,plain,
( spl18_419
| ~ spl18_19
| ~ spl18_204 ),
inference(avatar_split_clause,[],[f2545,f2352,f354,f7395]) ).
fof(f7395,plain,
( spl18_419
<=> ! [X0] :
( ~ in(X0,sK6(X0,X0))
| disjoint(X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_419])]) ).
fof(f2545,plain,
( ! [X0] :
( ~ in(X0,sK6(X0,X0))
| disjoint(X0,X0) )
| ~ spl18_19
| ~ spl18_204 ),
inference(superposition,[],[f2353,f355]) ).
fof(f7393,plain,
( spl18_418
| ~ spl18_138
| ~ spl18_189 ),
inference(avatar_split_clause,[],[f2246,f2080,f1381,f7391]) ).
fof(f7391,plain,
( spl18_418
<=> ! [X24,X23] : sP2(set_union2(X24,X23),X23,set_union2(X23,X24)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_418])]) ).
fof(f2246,plain,
( ! [X24,X23] : sP2(set_union2(X24,X23),X23,set_union2(X23,X24))
| ~ spl18_138
| ~ spl18_189 ),
inference(superposition,[],[f1382,f2081]) ).
fof(f7389,plain,
( spl18_417
| ~ spl18_27
| ~ spl18_189 ),
inference(avatar_split_clause,[],[f2239,f2080,f409,f7387]) ).
fof(f7387,plain,
( spl18_417
<=> ! [X4,X3] :
( ~ empty(set_union2(X3,X4))
| empty(set_union2(X4,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_417])]) ).
fof(f409,plain,
( spl18_27
<=> ! [X0,X1] :
( ~ empty(set_union2(X1,X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_27])]) ).
fof(f2239,plain,
( ! [X3,X4] :
( ~ empty(set_union2(X3,X4))
| empty(set_union2(X4,X3)) )
| ~ spl18_27
| ~ spl18_189 ),
inference(superposition,[],[f410,f2081]) ).
fof(f410,plain,
( ! [X0,X1] :
( ~ empty(set_union2(X1,X0))
| empty(X0) )
| ~ spl18_27 ),
inference(avatar_component_clause,[],[f409]) ).
fof(f7385,plain,
( spl18_416
| ~ spl18_139
| ~ spl18_188 ),
inference(avatar_split_clause,[],[f2208,f2076,f1385,f7383]) ).
fof(f7383,plain,
( spl18_416
<=> ! [X22,X23] : sP3(X22,set_union2(X22,X23),set_difference(X23,X22)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_416])]) ).
fof(f2208,plain,
( ! [X22,X23] : sP3(X22,set_union2(X22,X23),set_difference(X23,X22))
| ~ spl18_139
| ~ spl18_188 ),
inference(superposition,[],[f1386,f2077]) ).
fof(f7381,plain,
( spl18_415
| ~ spl18_137
| ~ spl18_187 ),
inference(avatar_split_clause,[],[f2177,f2072,f1377,f7379]) ).
fof(f7379,plain,
( spl18_415
<=> ! [X29,X30] : sP1(X29,set_difference(X29,X30),set_difference(X29,X30)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_415])]) ).
fof(f2177,plain,
( ! [X29,X30] : sP1(X29,set_difference(X29,X30),set_difference(X29,X30))
| ~ spl18_137
| ~ spl18_187 ),
inference(superposition,[],[f1378,f2073]) ).
fof(f7377,plain,
( spl18_414
| ~ spl18_137
| ~ spl18_186 ),
inference(avatar_split_clause,[],[f2133,f2068,f1377,f7375]) ).
fof(f7375,plain,
( spl18_414
<=> ! [X29,X30] : sP1(X29,set_intersection2(X29,X30),set_intersection2(X29,X30)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_414])]) ).
fof(f2133,plain,
( ! [X29,X30] : sP1(X29,set_intersection2(X29,X30),set_intersection2(X29,X30))
| ~ spl18_137
| ~ spl18_186 ),
inference(superposition,[],[f1378,f2069]) ).
fof(f7373,plain,
( spl18_413
| ~ spl18_138
| ~ spl18_185 ),
inference(avatar_split_clause,[],[f2100,f2064,f1381,f7371]) ).
fof(f7371,plain,
( spl18_413
<=> ! [X22,X23] : sP2(set_union2(X22,X23),X22,set_union2(X22,X23)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_413])]) ).
fof(f2100,plain,
( ! [X22,X23] : sP2(set_union2(X22,X23),X22,set_union2(X22,X23))
| ~ spl18_138
| ~ spl18_185 ),
inference(superposition,[],[f1382,f2065]) ).
fof(f7369,plain,
( spl18_412
| ~ spl18_142
| ~ spl18_183 ),
inference(avatar_split_clause,[],[f2050,f2044,f1437,f7367]) ).
fof(f7367,plain,
( spl18_412
<=> ! [X6,X5] :
( sK17 != X5
| disjoint(set_union2(X5,X6),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_412])]) ).
fof(f2044,plain,
( spl18_183
<=> ! [X2,X3] :
( sK17 != set_intersection2(X3,X2)
| disjoint(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_183])]) ).
fof(f2050,plain,
( ! [X6,X5] :
( sK17 != X5
| disjoint(set_union2(X5,X6),X5) )
| ~ spl18_142
| ~ spl18_183 ),
inference(superposition,[],[f2045,f1438]) ).
fof(f2045,plain,
( ! [X2,X3] :
( sK17 != set_intersection2(X3,X2)
| disjoint(X2,X3) )
| ~ spl18_183 ),
inference(avatar_component_clause,[],[f2044]) ).
fof(f7365,plain,
( spl18_411
| ~ spl18_140
| ~ spl18_334 ),
inference(avatar_split_clause,[],[f5820,f5714,f1429,f7363]) ).
fof(f7363,plain,
( spl18_411
<=> ! [X13,X14] : sP2(set_intersection2(X13,X14),X13,X13) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_411])]) ).
fof(f5820,plain,
( ! [X14,X13] : sP2(set_intersection2(X13,X14),X13,X13)
| ~ spl18_140
| ~ spl18_334 ),
inference(superposition,[],[f5715,f1430]) ).
fof(f7361,plain,
( spl18_410
| ~ spl18_40
| ~ spl18_178 ),
inference(avatar_split_clause,[],[f2033,f1800,f471,f7359]) ).
fof(f7359,plain,
( spl18_410
<=> ! [X2,X1] :
( subset(X2,set_intersection2(X2,X1))
| ~ subset(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_410])]) ).
fof(f2033,plain,
( ! [X2,X1] :
( subset(X2,set_intersection2(X2,X1))
| ~ subset(X2,X1) )
| ~ spl18_40
| ~ spl18_178 ),
inference(superposition,[],[f1801,f472]) ).
fof(f7357,plain,
( spl18_409
| ~ spl18_23
| ~ spl18_178 ),
inference(avatar_split_clause,[],[f2024,f1800,f381,f7355]) ).
fof(f7355,plain,
( spl18_409
<=> ! [X2,X3] :
( ~ subset(X2,X3)
| ~ proper_subset(set_intersection2(X3,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_409])]) ).
fof(f2024,plain,
( ! [X2,X3] :
( ~ subset(X2,X3)
| ~ proper_subset(set_intersection2(X3,X2),X2) )
| ~ spl18_23
| ~ spl18_178 ),
inference(resolution,[],[f1801,f382]) ).
fof(f7353,plain,
( spl18_408
| ~ spl18_30
| ~ spl18_175 ),
inference(avatar_split_clause,[],[f2005,f1788,f421,f7351]) ).
fof(f7351,plain,
( spl18_408
<=> ! [X2,X0,X1] :
( ~ in(X0,X1)
| ~ in(set_union2(X1,X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_408])]) ).
fof(f2005,plain,
( ! [X2,X0,X1] :
( ~ in(X0,X1)
| ~ in(set_union2(X1,X2),X0) )
| ~ spl18_30
| ~ spl18_175 ),
inference(resolution,[],[f1789,f422]) ).
fof(f7349,plain,
( spl18_407
| ~ spl18_79
| ~ spl18_173 ),
inference(avatar_split_clause,[],[f1953,f1780,f803,f7347]) ).
fof(f7347,plain,
( spl18_407
<=> ! [X0,X1] :
( in(sK6(X0,X1),X0)
| disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_407])]) ).
fof(f803,plain,
( spl18_79
<=> ! [X0,X1] :
( in(sK6(X0,X1),set_intersection2(X0,X1))
| disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_79])]) ).
fof(f1953,plain,
( ! [X0,X1] :
( in(sK6(X0,X1),X0)
| disjoint(X0,X1) )
| ~ spl18_79
| ~ spl18_173 ),
inference(resolution,[],[f1781,f804]) ).
fof(f804,plain,
( ! [X0,X1] :
( in(sK6(X0,X1),set_intersection2(X0,X1))
| disjoint(X0,X1) )
| ~ spl18_79 ),
inference(avatar_component_clause,[],[f803]) ).
fof(f7345,plain,
( spl18_406
| ~ spl18_23
| ~ spl18_172 ),
inference(avatar_split_clause,[],[f1937,f1776,f381,f7343]) ).
fof(f1937,plain,
( ! [X2,X0,X1] :
( ~ subset(X0,X1)
| ~ proper_subset(set_union2(X1,X2),X0) )
| ~ spl18_23
| ~ spl18_172 ),
inference(resolution,[],[f1777,f382]) ).
fof(f7341,plain,
( spl18_405
| ~ spl18_81
| ~ spl18_171 ),
inference(avatar_split_clause,[],[f1914,f1772,f811,f7339]) ).
fof(f7339,plain,
( spl18_405
<=> ! [X2,X0,X1] :
( subset(set_difference(X0,X1),X2)
| ~ subset(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_405])]) ).
fof(f1914,plain,
( ! [X2,X0,X1] :
( subset(set_difference(X0,X1),X2)
| ~ subset(X0,X2) )
| ~ spl18_81
| ~ spl18_171 ),
inference(resolution,[],[f1773,f812]) ).
fof(f7337,plain,
( spl18_404
| ~ spl18_80
| ~ spl18_170 ),
inference(avatar_split_clause,[],[f1895,f1768,f807,f7335]) ).
fof(f7335,plain,
( spl18_404
<=> ! [X2,X0,X1] :
( subset(set_intersection2(X0,X1),X2)
| ~ subset(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_404])]) ).
fof(f1895,plain,
( ! [X2,X0,X1] :
( subset(set_intersection2(X0,X1),X2)
| ~ subset(X0,X2) )
| ~ spl18_80
| ~ spl18_170 ),
inference(resolution,[],[f1769,f808]) ).
fof(f7333,plain,
( spl18_403
| ~ spl18_39
| ~ spl18_168 ),
inference(avatar_split_clause,[],[f1887,f1760,f467,f7331]) ).
fof(f7331,plain,
( spl18_403
<=> ! [X2,X1] :
( ~ empty(set_union2(X2,X1))
| empty(set_difference(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_403])]) ).
fof(f1887,plain,
( ! [X2,X1] :
( ~ empty(set_union2(X2,X1))
| empty(set_difference(X2,X1)) )
| ~ spl18_39
| ~ spl18_168 ),
inference(superposition,[],[f1761,f468]) ).
fof(f7329,plain,
( spl18_402
| ~ spl18_142
| ~ spl18_167 ),
inference(avatar_split_clause,[],[f1882,f1756,f1437,f7327]) ).
fof(f7327,plain,
( spl18_402
<=> ! [X9,X8,X10] :
( subset(X8,X10)
| ~ disjoint(X8,set_union2(X8,X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_402])]) ).
fof(f1882,plain,
( ! [X10,X8,X9] :
( subset(X8,X10)
| ~ disjoint(X8,set_union2(X8,X9)) )
| ~ spl18_142
| ~ spl18_167 ),
inference(superposition,[],[f1757,f1438]) ).
fof(f7325,plain,
( spl18_401
| ~ spl18_23
| ~ spl18_167 ),
inference(avatar_split_clause,[],[f1869,f1756,f381,f7323]) ).
fof(f1869,plain,
( ! [X2,X0,X1] :
( ~ disjoint(X0,X1)
| ~ proper_subset(X2,set_intersection2(X0,X1)) )
| ~ spl18_23
| ~ spl18_167 ),
inference(resolution,[],[f1757,f382]) ).
fof(f7321,plain,
( spl18_400
| ~ spl18_142
| ~ spl18_333 ),
inference(avatar_split_clause,[],[f5801,f5710,f1437,f7319]) ).
fof(f7319,plain,
( spl18_400
<=> ! [X6,X5] : sP1(X5,set_union2(X5,X6),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_400])]) ).
fof(f5801,plain,
( ! [X6,X5] : sP1(X5,set_union2(X5,X6),X5)
| ~ spl18_142
| ~ spl18_333 ),
inference(superposition,[],[f5711,f1438]) ).
fof(f7317,plain,
( spl18_399
| ~ spl18_142
| ~ spl18_166 ),
inference(avatar_split_clause,[],[f1864,f1752,f1437,f7315]) ).
fof(f7315,plain,
( spl18_399
<=> ! [X9,X8,X10] :
( disjoint(X10,X8)
| ~ disjoint(X8,set_union2(X8,X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_399])]) ).
fof(f1864,plain,
( ! [X10,X8,X9] :
( disjoint(X10,X8)
| ~ disjoint(X8,set_union2(X8,X9)) )
| ~ spl18_142
| ~ spl18_166 ),
inference(superposition,[],[f1753,f1438]) ).
fof(f7313,plain,
( spl18_398
| ~ spl18_142
| ~ spl18_164 ),
inference(avatar_split_clause,[],[f1850,f1744,f1437,f7311]) ).
fof(f7311,plain,
( spl18_398
<=> ! [X9,X8,X10] :
( disjoint(X8,X10)
| ~ disjoint(X8,set_union2(X8,X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_398])]) ).
fof(f1850,plain,
( ! [X10,X8,X9] :
( disjoint(X8,X10)
| ~ disjoint(X8,set_union2(X8,X9)) )
| ~ spl18_142
| ~ spl18_164 ),
inference(superposition,[],[f1745,f1438]) ).
fof(f7309,plain,
( spl18_397
| ~ spl18_142
| ~ spl18_162 ),
inference(avatar_split_clause,[],[f1836,f1736,f1437,f7307]) ).
fof(f7307,plain,
( spl18_397
<=> ! [X9,X8,X10] :
( ~ in(X10,X8)
| ~ disjoint(set_union2(X8,X9),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_397])]) ).
fof(f1836,plain,
( ! [X10,X8,X9] :
( ~ in(X10,X8)
| ~ disjoint(set_union2(X8,X9),X8) )
| ~ spl18_142
| ~ spl18_162 ),
inference(superposition,[],[f1737,f1438]) ).
fof(f7305,plain,
( spl18_396
| ~ spl18_57
| ~ spl18_162 ),
inference(avatar_split_clause,[],[f1821,f1736,f610,f7303]) ).
fof(f7303,plain,
( spl18_396
<=> ! [X18,X16,X17] :
( ~ disjoint(X16,X17)
| subset(set_intersection2(X17,X16),X18) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_396])]) ).
fof(f1821,plain,
( ! [X18,X16,X17] :
( ~ disjoint(X16,X17)
| subset(set_intersection2(X17,X16),X18) )
| ~ spl18_57
| ~ spl18_162 ),
inference(resolution,[],[f1737,f611]) ).
fof(f7301,plain,
( spl18_395
| ~ spl18_42
| ~ spl18_162 ),
inference(avatar_split_clause,[],[f1818,f1736,f479,f7299]) ).
fof(f7299,plain,
( spl18_395
<=> ! [X9,X8] :
( ~ disjoint(X8,X9)
| sK17 = set_intersection2(X9,X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_395])]) ).
fof(f1818,plain,
( ! [X8,X9] :
( ~ disjoint(X8,X9)
| sK17 = set_intersection2(X9,X8) )
| ~ spl18_42
| ~ spl18_162 ),
inference(resolution,[],[f1737,f480]) ).
fof(f7297,plain,
( spl18_394
| ~ spl18_45
| ~ spl18_162 ),
inference(avatar_split_clause,[],[f1817,f1736,f519,f7295]) ).
fof(f7295,plain,
( spl18_394
<=> ! [X6,X5,X7] :
( ~ disjoint(X5,X6)
| disjoint(X7,set_intersection2(X6,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_394])]) ).
fof(f1817,plain,
( ! [X6,X7,X5] :
( ~ disjoint(X5,X6)
| disjoint(X7,set_intersection2(X6,X5)) )
| ~ spl18_45
| ~ spl18_162 ),
inference(resolution,[],[f1737,f520]) ).
fof(f7293,plain,
( spl18_393
| ~ spl18_44
| ~ spl18_162 ),
inference(avatar_split_clause,[],[f1816,f1736,f515,f7291]) ).
fof(f7291,plain,
( spl18_393
<=> ! [X2,X4,X3] :
( ~ disjoint(X2,X3)
| disjoint(set_intersection2(X3,X2),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_393])]) ).
fof(f1816,plain,
( ! [X2,X3,X4] :
( ~ disjoint(X2,X3)
| disjoint(set_intersection2(X3,X2),X4) )
| ~ spl18_44
| ~ spl18_162 ),
inference(resolution,[],[f1737,f516]) ).
fof(f7289,plain,
( spl18_392
| ~ spl18_59
| ~ spl18_142 ),
inference(avatar_split_clause,[],[f1521,f1437,f618,f7287]) ).
fof(f7287,plain,
( spl18_392
<=> ! [X9,X10] :
( sK17 != X9
| disjoint(X9,set_union2(X9,X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_392])]) ).
fof(f618,plain,
( spl18_59
<=> ! [X0,X1] :
( set_intersection2(X0,X1) != sK17
| disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_59])]) ).
fof(f1521,plain,
( ! [X10,X9] :
( sK17 != X9
| disjoint(X9,set_union2(X9,X10)) )
| ~ spl18_59
| ~ spl18_142 ),
inference(superposition,[],[f619,f1438]) ).
fof(f619,plain,
( ! [X0,X1] :
( set_intersection2(X0,X1) != sK17
| disjoint(X0,X1) )
| ~ spl18_59 ),
inference(avatar_component_clause,[],[f618]) ).
fof(f7285,plain,
( spl18_391
| ~ spl18_43
| ~ spl18_142 ),
inference(avatar_split_clause,[],[f1520,f1437,f511,f7283]) ).
fof(f7283,plain,
( spl18_391
<=> ! [X6,X8,X7] :
( ~ in(X8,X6)
| ~ disjoint(X6,set_union2(X6,X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_391])]) ).
fof(f1520,plain,
( ! [X8,X6,X7] :
( ~ in(X8,X6)
| ~ disjoint(X6,set_union2(X6,X7)) )
| ~ spl18_43
| ~ spl18_142 ),
inference(superposition,[],[f512,f1438]) ).
fof(f7281,plain,
( spl18_390
| ~ spl18_63
| ~ spl18_139 ),
inference(avatar_split_clause,[],[f1423,f1385,f646,f7279]) ).
fof(f7279,plain,
( spl18_390
<=> ! [X4,X5] : sP3(X5,set_union2(X4,X5),set_difference(X4,X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_390])]) ).
fof(f1423,plain,
( ! [X4,X5] : sP3(X5,set_union2(X4,X5),set_difference(X4,X5))
| ~ spl18_63
| ~ spl18_139 ),
inference(superposition,[],[f1386,f647]) ).
fof(f7277,plain,
( spl18_389
| ~ spl18_245
| ~ spl18_325 ),
inference(avatar_split_clause,[],[f5646,f5494,f3539,f7275]) ).
fof(f7275,plain,
( spl18_389
<=> ! [X16,X15] : sP3(set_union2(X15,X16),X16,sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_389])]) ).
fof(f5494,plain,
( spl18_325
<=> ! [X22,X21] : sP3(X21,set_difference(X21,X22),sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_325])]) ).
fof(f5646,plain,
( ! [X16,X15] : sP3(set_union2(X15,X16),X16,sK17)
| ~ spl18_245
| ~ spl18_325 ),
inference(superposition,[],[f5495,f3540]) ).
fof(f5495,plain,
( ! [X21,X22] : sP3(X21,set_difference(X21,X22),sK17)
| ~ spl18_325 ),
inference(avatar_component_clause,[],[f5494]) ).
fof(f7273,plain,
( spl18_388
| ~ spl18_62
| ~ spl18_139 ),
inference(avatar_split_clause,[],[f1421,f1385,f642,f7271]) ).
fof(f7271,plain,
( spl18_388
<=> ! [X2,X1] : sP3(set_difference(X1,X2),X1,set_intersection2(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_388])]) ).
fof(f1421,plain,
( ! [X2,X1] : sP3(set_difference(X1,X2),X1,set_intersection2(X1,X2))
| ~ spl18_62
| ~ spl18_139 ),
inference(superposition,[],[f1386,f643]) ).
fof(f7269,plain,
( spl18_387
| ~ spl18_60
| ~ spl18_138 ),
inference(avatar_split_clause,[],[f1413,f1381,f634,f7267]) ).
fof(f7267,plain,
( spl18_387
<=> ! [X6,X7] : sP2(set_difference(X7,X6),X6,set_union2(X6,X7)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_387])]) ).
fof(f1413,plain,
( ! [X6,X7] : sP2(set_difference(X7,X6),X6,set_union2(X6,X7))
| ~ spl18_60
| ~ spl18_138 ),
inference(superposition,[],[f1382,f635]) ).
fof(f7265,plain,
( spl18_386
| ~ spl18_66
| ~ spl18_130 ),
inference(avatar_split_clause,[],[f1325,f1296,f658,f7263]) ).
fof(f7263,plain,
( spl18_386
<=> ! [X9,X8,X10] :
( ~ empty(X8)
| subset(X9,X10)
| ~ subset(X9,X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_386])]) ).
fof(f1325,plain,
( ! [X10,X8,X9] :
( ~ empty(X8)
| subset(X9,X10)
| ~ subset(X9,X8) )
| ~ spl18_66
| ~ spl18_130 ),
inference(resolution,[],[f1297,f659]) ).
fof(f7261,plain,
( spl18_385
| ~ spl18_81
| ~ spl18_126 ),
inference(avatar_split_clause,[],[f1265,f1171,f811,f7259]) ).
fof(f7259,plain,
( spl18_385
<=> ! [X9,X10] :
( subset(set_difference(X10,X9),sK17)
| ~ subset(X10,X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_385])]) ).
fof(f1265,plain,
( ! [X10,X9] :
( subset(set_difference(X10,X9),sK17)
| ~ subset(X10,X9) )
| ~ spl18_81
| ~ spl18_126 ),
inference(superposition,[],[f812,f1172]) ).
fof(f7257,plain,
( spl18_384
| ~ spl18_65
| ~ spl18_124 ),
inference(avatar_split_clause,[],[f1248,f1163,f654,f7255]) ).
fof(f7255,plain,
( spl18_384
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| disjoint(X1,X2)
| ~ subset(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_384])]) ).
fof(f1163,plain,
( spl18_124
<=> ! [X2,X3] :
( disjoint(X2,X3)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_124])]) ).
fof(f1248,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| disjoint(X1,X2)
| ~ subset(X1,X0) )
| ~ spl18_65
| ~ spl18_124 ),
inference(resolution,[],[f1164,f655]) ).
fof(f1164,plain,
( ! [X2,X3] :
( disjoint(X2,X3)
| ~ empty(X2) )
| ~ spl18_124 ),
inference(avatar_component_clause,[],[f1163]) ).
fof(f7253,plain,
( spl18_383
| ~ spl18_70
| ~ spl18_123 ),
inference(avatar_split_clause,[],[f1241,f1159,f713,f7251]) ).
fof(f7251,plain,
( spl18_383
<=> ! [X16,X17,X15] :
( ~ in(X15,set_intersection2(X16,X17))
| in(X15,X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_383])]) ).
fof(f1241,plain,
( ! [X16,X17,X15] :
( ~ in(X15,set_intersection2(X16,X17))
| in(X15,X17) )
| ~ spl18_70
| ~ spl18_123 ),
inference(resolution,[],[f1160,f714]) ).
fof(f7249,plain,
( spl18_382
| ~ spl18_66
| ~ spl18_123 ),
inference(avatar_split_clause,[],[f1238,f1159,f658,f7247]) ).
fof(f7247,plain,
( spl18_382
<=> ! [X9,X8,X10] :
( subset(X8,X9)
| ~ subset(X8,set_intersection2(X10,X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_382])]) ).
fof(f1238,plain,
( ! [X10,X8,X9] :
( subset(X8,X9)
| ~ subset(X8,set_intersection2(X10,X9)) )
| ~ spl18_66
| ~ spl18_123 ),
inference(resolution,[],[f1160,f659]) ).
fof(f7245,plain,
( spl18_381
| ~ spl18_70
| ~ spl18_122 ),
inference(avatar_split_clause,[],[f1228,f1155,f713,f7243]) ).
fof(f1228,plain,
( ! [X16,X17,X15] :
( ~ in(X15,X16)
| in(X15,set_union2(X17,X16)) )
| ~ spl18_70
| ~ spl18_122 ),
inference(resolution,[],[f1156,f714]) ).
fof(f7241,plain,
( spl18_380
| ~ spl18_66
| ~ spl18_122 ),
inference(avatar_split_clause,[],[f1225,f1155,f658,f7239]) ).
fof(f7239,plain,
( spl18_380
<=> ! [X9,X8,X10] :
( subset(X8,set_union2(X9,X10))
| ~ subset(X8,X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_380])]) ).
fof(f1225,plain,
( ! [X10,X8,X9] :
( subset(X8,set_union2(X9,X10))
| ~ subset(X8,X10) )
| ~ spl18_66
| ~ spl18_122 ),
inference(resolution,[],[f1156,f659]) ).
fof(f7236,plain,
( spl18_379
| ~ spl18_40
| ~ spl18_324 ),
inference(avatar_split_clause,[],[f5624,f5490,f471,f7234]) ).
fof(f7234,plain,
( spl18_379
<=> ! [X2,X1] : sP3(X1,set_intersection2(X2,X1),sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_379])]) ).
fof(f5490,plain,
( spl18_324
<=> ! [X22,X21] : sP3(X21,set_intersection2(X21,X22),sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_324])]) ).
fof(f5624,plain,
( ! [X2,X1] : sP3(X1,set_intersection2(X2,X1),sK17)
| ~ spl18_40
| ~ spl18_324 ),
inference(superposition,[],[f5491,f472]) ).
fof(f5491,plain,
( ! [X21,X22] : sP3(X21,set_intersection2(X21,X22),sK17)
| ~ spl18_324 ),
inference(avatar_component_clause,[],[f5490]) ).
fof(f7232,plain,
( spl18_378
| ~ spl18_75
| ~ spl18_128 ),
inference(avatar_split_clause,[],[f1309,f1288,f733,f7230]) ).
fof(f7230,plain,
( spl18_378
<=> ! [X6,X7] :
( X6 != X7
| sP2(X6,sK17,X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_378])]) ).
fof(f1309,plain,
( ! [X6,X7] :
( X6 != X7
| sP2(X6,sK17,X7) )
| ~ spl18_75
| ~ spl18_128 ),
inference(superposition,[],[f734,f1289]) ).
fof(f6637,plain,
( spl18_377
| ~ spl18_39
| ~ spl18_323 ),
inference(avatar_split_clause,[],[f5604,f5486,f467,f6635]) ).
fof(f6635,plain,
( spl18_377
<=> ! [X2,X1] : sP1(set_union2(X2,X1),X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_377])]) ).
fof(f5486,plain,
( spl18_323
<=> ! [X29,X30] : sP1(set_union2(X29,X30),X29,X29) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_323])]) ).
fof(f5604,plain,
( ! [X2,X1] : sP1(set_union2(X2,X1),X1,X1)
| ~ spl18_39
| ~ spl18_323 ),
inference(superposition,[],[f5487,f468]) ).
fof(f5487,plain,
( ! [X29,X30] : sP1(set_union2(X29,X30),X29,X29)
| ~ spl18_323 ),
inference(avatar_component_clause,[],[f5486]) ).
fof(f6423,plain,
( spl18_376
| ~ spl18_40
| ~ spl18_320 ),
inference(avatar_split_clause,[],[f5553,f5474,f471,f6421]) ).
fof(f6421,plain,
( spl18_376
<=> ! [X2,X1] : sP2(X1,set_intersection2(X2,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_376])]) ).
fof(f5474,plain,
( spl18_320
<=> ! [X22,X23] : sP2(X22,set_intersection2(X22,X23),X22) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_320])]) ).
fof(f5553,plain,
( ! [X2,X1] : sP2(X1,set_intersection2(X2,X1),X1)
| ~ spl18_40
| ~ spl18_320 ),
inference(superposition,[],[f5475,f472]) ).
fof(f5475,plain,
( ! [X22,X23] : sP2(X22,set_intersection2(X22,X23),X22)
| ~ spl18_320 ),
inference(avatar_component_clause,[],[f5474]) ).
fof(f5996,plain,
( spl18_375
| ~ spl18_62
| ~ spl18_126
| ~ spl18_243 ),
inference(avatar_split_clause,[],[f3524,f3475,f1171,f642,f5994]) ).
fof(f3524,plain,
( ! [X14,X13] : sK17 = set_intersection2(X13,set_difference(X14,X13))
| ~ spl18_62
| ~ spl18_126
| ~ spl18_243 ),
inference(forward_demodulation,[],[f3497,f1172]) ).
fof(f3497,plain,
( ! [X14,X13] : set_intersection2(X13,set_difference(X14,X13)) = set_difference(X13,X13)
| ~ spl18_62
| ~ spl18_243 ),
inference(superposition,[],[f643,f3476]) ).
fof(f5992,plain,
( spl18_374
| ~ spl18_40
| ~ spl18_319 ),
inference(avatar_split_clause,[],[f5539,f5470,f471,f5990]) ).
fof(f5990,plain,
( spl18_374
<=> ! [X2,X1] :
( empty(set_intersection2(X2,X1))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_374])]) ).
fof(f5470,plain,
( spl18_319
<=> ! [X4,X5] :
( ~ empty(X4)
| empty(set_intersection2(X4,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_319])]) ).
fof(f5539,plain,
( ! [X2,X1] :
( empty(set_intersection2(X2,X1))
| ~ empty(X1) )
| ~ spl18_40
| ~ spl18_319 ),
inference(superposition,[],[f5471,f472]) ).
fof(f5471,plain,
( ! [X4,X5] :
( empty(set_intersection2(X4,X5))
| ~ empty(X4) )
| ~ spl18_319 ),
inference(avatar_component_clause,[],[f5470]) ).
fof(f5988,plain,
( spl18_373
| ~ spl18_122
| ~ spl18_189 ),
inference(avatar_split_clause,[],[f2245,f2080,f1155,f5986]) ).
fof(f5986,plain,
( spl18_373
<=> ! [X22,X21] : subset(set_union2(X22,X21),set_union2(X21,X22)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_373])]) ).
fof(f2245,plain,
( ! [X21,X22] : subset(set_union2(X22,X21),set_union2(X21,X22))
| ~ spl18_122
| ~ spl18_189 ),
inference(superposition,[],[f1156,f2081]) ).
fof(f5984,plain,
( spl18_372
| ~ spl18_118
| ~ spl18_188 ),
inference(avatar_split_clause,[],[f2207,f2076,f1139,f5982]) ).
fof(f5982,plain,
( spl18_372
<=> ! [X20,X21] : ~ proper_subset(set_union2(X20,X21),set_difference(X21,X20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_372])]) ).
fof(f1139,plain,
( spl18_118
<=> ! [X4,X5] : ~ proper_subset(X4,set_difference(X4,X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_118])]) ).
fof(f2207,plain,
( ! [X21,X20] : ~ proper_subset(set_union2(X20,X21),set_difference(X21,X20))
| ~ spl18_118
| ~ spl18_188 ),
inference(superposition,[],[f1140,f2077]) ).
fof(f1140,plain,
( ! [X4,X5] : ~ proper_subset(X4,set_difference(X4,X5))
| ~ spl18_118 ),
inference(avatar_component_clause,[],[f1139]) ).
fof(f5980,plain,
( spl18_371
| ~ spl18_20
| ~ spl18_175 ),
inference(avatar_split_clause,[],[f2006,f1788,f358,f5978]) ).
fof(f5978,plain,
( spl18_371
<=> ! [X4,X5,X3] :
( ~ in(X3,X4)
| ~ empty(set_union2(X4,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_371])]) ).
fof(f2006,plain,
( ! [X3,X4,X5] :
( ~ in(X3,X4)
| ~ empty(set_union2(X4,X5)) )
| ~ spl18_20
| ~ spl18_175 ),
inference(resolution,[],[f1789,f359]) ).
fof(f5976,plain,
( spl18_370
| ~ spl18_123
| ~ spl18_171 ),
inference(avatar_split_clause,[],[f1920,f1772,f1159,f5974]) ).
fof(f5974,plain,
( spl18_370
<=> ! [X13,X14,X15] : subset(set_intersection2(X13,set_difference(X14,X15)),X14) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_370])]) ).
fof(f1920,plain,
( ! [X14,X15,X13] : subset(set_intersection2(X13,set_difference(X14,X15)),X14)
| ~ spl18_123
| ~ spl18_171 ),
inference(resolution,[],[f1773,f1160]) ).
fof(f5972,plain,
( spl18_369
| ~ spl18_12
| ~ spl18_171 ),
inference(avatar_split_clause,[],[f1918,f1772,f326,f5970]) ).
fof(f5970,plain,
( spl18_369
<=> ! [X9,X11,X10] : subset(set_difference(set_difference(X9,X10),X11),X9) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_369])]) ).
fof(f1918,plain,
( ! [X10,X11,X9] : subset(set_difference(set_difference(X9,X10),X11),X9)
| ~ spl18_12
| ~ spl18_171 ),
inference(resolution,[],[f1773,f327]) ).
fof(f5968,plain,
( spl18_368
| ~ spl18_11
| ~ spl18_171 ),
inference(avatar_split_clause,[],[f1916,f1772,f322,f5966]) ).
fof(f5966,plain,
( spl18_368
<=> ! [X6,X5,X7] : subset(set_intersection2(set_difference(X5,X6),X7),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_368])]) ).
fof(f1916,plain,
( ! [X6,X7,X5] : subset(set_intersection2(set_difference(X5,X6),X7),X5)
| ~ spl18_11
| ~ spl18_171 ),
inference(resolution,[],[f1773,f323]) ).
fof(f5964,plain,
( spl18_367
| ~ spl18_123
| ~ spl18_170 ),
inference(avatar_split_clause,[],[f1902,f1768,f1159,f5962]) ).
fof(f5962,plain,
( spl18_367
<=> ! [X18,X16,X17] : subset(set_intersection2(X16,set_intersection2(X17,X18)),X17) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_367])]) ).
fof(f1902,plain,
( ! [X18,X16,X17] : subset(set_intersection2(X16,set_intersection2(X17,X18)),X17)
| ~ spl18_123
| ~ spl18_170 ),
inference(resolution,[],[f1769,f1160]) ).
fof(f5960,plain,
( spl18_366
| ~ spl18_12
| ~ spl18_170 ),
inference(avatar_split_clause,[],[f1900,f1768,f326,f5958]) ).
fof(f5958,plain,
( spl18_366
<=> ! [X13,X12,X14] : subset(set_difference(set_intersection2(X12,X13),X14),X12) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_366])]) ).
fof(f1900,plain,
( ! [X14,X12,X13] : subset(set_difference(set_intersection2(X12,X13),X14),X12)
| ~ spl18_12
| ~ spl18_170 ),
inference(resolution,[],[f1769,f327]) ).
fof(f5956,plain,
( spl18_365
| ~ spl18_11
| ~ spl18_170 ),
inference(avatar_split_clause,[],[f1898,f1768,f322,f5954]) ).
fof(f5954,plain,
( spl18_365
<=> ! [X9,X8,X10] : subset(set_intersection2(set_intersection2(X8,X9),X10),X8) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_365])]) ).
fof(f1898,plain,
( ! [X10,X8,X9] : subset(set_intersection2(set_intersection2(X8,X9),X10),X8)
| ~ spl18_11
| ~ spl18_170 ),
inference(resolution,[],[f1769,f323]) ).
fof(f5952,plain,
( spl18_364
| ~ spl18_124
| ~ spl18_161 ),
inference(avatar_split_clause,[],[f1814,f1732,f1163,f5950]) ).
fof(f5950,plain,
( spl18_364
<=> ! [X4,X5] :
( sK17 = set_intersection2(X4,X5)
| ~ empty(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_364])]) ).
fof(f1814,plain,
( ! [X4,X5] :
( sK17 = set_intersection2(X4,X5)
| ~ empty(X4) )
| ~ spl18_124
| ~ spl18_161 ),
inference(resolution,[],[f1733,f1164]) ).
fof(f5944,plain,
( spl18_363
| ~ spl18_125
| ~ spl18_161 ),
inference(avatar_split_clause,[],[f1813,f1732,f1167,f5942]) ).
fof(f5942,plain,
( spl18_363
<=> ! [X2,X3] :
( sK17 = set_intersection2(X2,X3)
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_363])]) ).
fof(f1167,plain,
( spl18_125
<=> ! [X2,X3] :
( disjoint(X2,X3)
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_125])]) ).
fof(f1813,plain,
( ! [X2,X3] :
( sK17 = set_intersection2(X2,X3)
| ~ empty(X3) )
| ~ spl18_125
| ~ spl18_161 ),
inference(resolution,[],[f1733,f1168]) ).
fof(f1168,plain,
( ! [X2,X3] :
( disjoint(X2,X3)
| ~ empty(X3) )
| ~ spl18_125 ),
inference(avatar_component_clause,[],[f1167]) ).
fof(f5940,plain,
( spl18_362
| ~ spl18_40
| ~ spl18_148 ),
inference(avatar_split_clause,[],[f1643,f1461,f471,f5938]) ).
fof(f5938,plain,
( spl18_362
<=> ! [X2,X1] :
( ~ empty(set_intersection2(X2,X1))
| disjoint(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_362])]) ).
fof(f1461,plain,
( spl18_148
<=> ! [X4,X5] :
( disjoint(X4,X5)
| ~ empty(set_intersection2(X4,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_148])]) ).
fof(f1643,plain,
( ! [X2,X1] :
( ~ empty(set_intersection2(X2,X1))
| disjoint(X1,X2) )
| ~ spl18_40
| ~ spl18_148 ),
inference(superposition,[],[f1462,f472]) ).
fof(f1462,plain,
( ! [X4,X5] :
( ~ empty(set_intersection2(X4,X5))
| disjoint(X4,X5) )
| ~ spl18_148 ),
inference(avatar_component_clause,[],[f1461]) ).
fof(f5936,plain,
( spl18_361
| ~ spl18_39
| ~ spl18_141 ),
inference(avatar_split_clause,[],[f1495,f1433,f467,f5934]) ).
fof(f5934,plain,
( spl18_361
<=> ! [X2,X3] : set_union2(X2,set_difference(X2,X3)) = X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl18_361])]) ).
fof(f1495,plain,
( ! [X2,X3] : set_union2(X2,set_difference(X2,X3)) = X2
| ~ spl18_39
| ~ spl18_141 ),
inference(superposition,[],[f1434,f468]) ).
fof(f5932,plain,
( spl18_360
| ~ spl18_39
| ~ spl18_140 ),
inference(avatar_split_clause,[],[f1470,f1429,f467,f5930]) ).
fof(f5930,plain,
( spl18_360
<=> ! [X2,X3] : set_union2(X2,set_intersection2(X2,X3)) = X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl18_360])]) ).
fof(f5928,plain,
( spl18_359
| ~ spl18_54
| ~ spl18_130 ),
inference(avatar_split_clause,[],[f1324,f1296,f587,f5926]) ).
fof(f5926,plain,
( spl18_359
<=> ! [X6,X7] :
( ~ empty(X6)
| sK17 = set_difference(X6,X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_359])]) ).
fof(f1324,plain,
( ! [X6,X7] :
( ~ empty(X6)
| sK17 = set_difference(X6,X7) )
| ~ spl18_54
| ~ spl18_130 ),
inference(resolution,[],[f1297,f588]) ).
fof(f5924,plain,
( spl18_358
| ~ spl18_47
| ~ spl18_130 ),
inference(avatar_split_clause,[],[f1323,f1296,f527,f5922]) ).
fof(f5922,plain,
( spl18_358
<=> ! [X4,X5] :
( ~ empty(X4)
| set_intersection2(X4,X5) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_358])]) ).
fof(f1323,plain,
( ! [X4,X5] :
( ~ empty(X4)
| set_intersection2(X4,X5) = X4 )
| ~ spl18_47
| ~ spl18_130 ),
inference(resolution,[],[f1297,f528]) ).
fof(f5920,plain,
( spl18_357
| ~ spl18_46
| ~ spl18_130 ),
inference(avatar_split_clause,[],[f1322,f1296,f523,f5918]) ).
fof(f5918,plain,
( spl18_357
<=> ! [X2,X3] :
( ~ empty(X2)
| set_union2(X2,X3) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_357])]) ).
fof(f1322,plain,
( ! [X2,X3] :
( ~ empty(X2)
| set_union2(X2,X3) = X3 )
| ~ spl18_46
| ~ spl18_130 ),
inference(resolution,[],[f1297,f524]) ).
fof(f5916,plain,
( spl18_356
| ~ spl18_77
| ~ spl18_126 ),
inference(avatar_split_clause,[],[f1263,f1171,f745,f5914]) ).
fof(f5914,plain,
( spl18_356
<=> ! [X6,X5] :
( sK17 != X6
| sP3(X5,X5,X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_356])]) ).
fof(f1263,plain,
( ! [X6,X5] :
( sK17 != X6
| sP3(X5,X5,X6) )
| ~ spl18_77
| ~ spl18_126 ),
inference(superposition,[],[f746,f1172]) ).
fof(f5912,plain,
( spl18_355
| ~ spl18_48
| ~ spl18_125 ),
inference(avatar_split_clause,[],[f1254,f1167,f531,f5910]) ).
fof(f5910,plain,
( spl18_355
<=> ! [X6,X7] :
( ~ empty(X6)
| set_difference(X7,X6) = X7 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_355])]) ).
fof(f1254,plain,
( ! [X6,X7] :
( ~ empty(X6)
| set_difference(X7,X6) = X7 )
| ~ spl18_48
| ~ spl18_125 ),
inference(resolution,[],[f1168,f532]) ).
fof(f5908,plain,
( spl18_354
| ~ spl18_48
| ~ spl18_124 ),
inference(avatar_split_clause,[],[f1250,f1163,f531,f5906]) ).
fof(f5906,plain,
( spl18_354
<=> ! [X6,X7] :
( ~ empty(X6)
| set_difference(X6,X7) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_354])]) ).
fof(f1250,plain,
( ! [X6,X7] :
( ~ empty(X6)
| set_difference(X6,X7) = X6 )
| ~ spl18_48
| ~ spl18_124 ),
inference(resolution,[],[f1164,f532]) ).
fof(f5900,plain,
( spl18_353
| ~ spl18_54
| ~ spl18_123 ),
inference(avatar_split_clause,[],[f1237,f1159,f587,f5898]) ).
fof(f5898,plain,
( spl18_353
<=> ! [X6,X7] : sK17 = set_difference(set_intersection2(X6,X7),X7) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_353])]) ).
fof(f1237,plain,
( ! [X6,X7] : sK17 = set_difference(set_intersection2(X6,X7),X7)
| ~ spl18_54
| ~ spl18_123 ),
inference(resolution,[],[f1160,f588]) ).
fof(f5896,plain,
( spl18_352
| ~ spl18_46
| ~ spl18_123 ),
inference(avatar_split_clause,[],[f1235,f1159,f523,f5894]) ).
fof(f1235,plain,
( ! [X2,X3] : set_union2(set_intersection2(X2,X3),X3) = X3
| ~ spl18_46
| ~ spl18_123 ),
inference(resolution,[],[f1160,f524]) ).
fof(f5892,plain,
( spl18_351
| ~ spl18_60
| ~ spl18_122 ),
inference(avatar_split_clause,[],[f1233,f1155,f634,f5890]) ).
fof(f5890,plain,
( spl18_351
<=> ! [X6,X7] : subset(set_difference(X7,X6),set_union2(X6,X7)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_351])]) ).
fof(f1233,plain,
( ! [X6,X7] : subset(set_difference(X7,X6),set_union2(X6,X7))
| ~ spl18_60
| ~ spl18_122 ),
inference(superposition,[],[f1156,f635]) ).
fof(f5888,plain,
( spl18_350
| ~ spl18_54
| ~ spl18_122 ),
inference(avatar_split_clause,[],[f1224,f1155,f587,f5886]) ).
fof(f5886,plain,
( spl18_350
<=> ! [X6,X7] : sK17 = set_difference(X6,set_union2(X7,X6)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_350])]) ).
fof(f5884,plain,
( spl18_349
| ~ spl18_47
| ~ spl18_122 ),
inference(avatar_split_clause,[],[f1223,f1155,f527,f5882]) ).
fof(f5880,plain,
( spl18_348
| ~ spl18_73
| ~ spl18_120 ),
inference(avatar_split_clause,[],[f1200,f1147,f725,f5878]) ).
fof(f5878,plain,
( spl18_348
<=> ! [X6,X7] :
( sK17 != X7
| sP1(X6,sK17,X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_348])]) ).
fof(f1200,plain,
( ! [X6,X7] :
( sK17 != X7
| sP1(X6,sK17,X7) )
| ~ spl18_73
| ~ spl18_120 ),
inference(superposition,[],[f726,f1148]) ).
fof(f5876,plain,
( spl18_347
| ~ spl18_63
| ~ spl18_118 ),
inference(avatar_split_clause,[],[f1186,f1139,f646,f5874]) ).
fof(f5874,plain,
( spl18_347
<=> ! [X4,X5] : ~ proper_subset(set_union2(X4,X5),set_difference(X4,X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_347])]) ).
fof(f1186,plain,
( ! [X4,X5] : ~ proper_subset(set_union2(X4,X5),set_difference(X4,X5))
| ~ spl18_63
| ~ spl18_118 ),
inference(superposition,[],[f1140,f647]) ).
fof(f5859,plain,
( spl18_346
| ~ spl18_30
| ~ spl18_316 ),
inference(avatar_split_clause,[],[f5460,f5409,f421,f5857]) ).
fof(f5857,plain,
( spl18_346
<=> ! [X0,X1] : ~ in(unordered_pair(X0,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_346])]) ).
fof(f5409,plain,
( spl18_316
<=> ! [X0,X1] : in(X0,unordered_pair(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_316])]) ).
fof(f5460,plain,
( ! [X0,X1] : ~ in(unordered_pair(X0,X1),X1)
| ~ spl18_30
| ~ spl18_316 ),
inference(resolution,[],[f5410,f422]) ).
fof(f5410,plain,
( ! [X0,X1] : in(X0,unordered_pair(X1,X0))
| ~ spl18_316 ),
inference(avatar_component_clause,[],[f5409]) ).
fof(f5786,plain,
( spl18_345
| ~ spl18_30
| ~ spl18_315 ),
inference(avatar_split_clause,[],[f5451,f5405,f421,f5784]) ).
fof(f5784,plain,
( spl18_345
<=> ! [X0,X1] : ~ in(unordered_pair(X0,X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_345])]) ).
fof(f5405,plain,
( spl18_315
<=> ! [X0,X1] : in(X0,unordered_pair(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_315])]) ).
fof(f5451,plain,
( ! [X0,X1] : ~ in(unordered_pair(X0,X1),X0)
| ~ spl18_30
| ~ spl18_315 ),
inference(resolution,[],[f5406,f422]) ).
fof(f5406,plain,
( ! [X0,X1] : in(X0,unordered_pair(X0,X1))
| ~ spl18_315 ),
inference(avatar_component_clause,[],[f5405]) ).
fof(f5782,plain,
( spl18_344
| ~ spl18_93
| ~ spl18_239 ),
inference(avatar_split_clause,[],[f3390,f3322,f906,f5780]) ).
fof(f5780,plain,
( spl18_344
<=> ! [X30,X31] :
( sP3(X30,X31,sK17)
| ~ empty(X31) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_344])]) ).
fof(f3322,plain,
( spl18_239
<=> ! [X4,X5,X3] :
( in(sK15(X3,X4,X5),X5)
| sP3(X3,X4,X5)
| ~ empty(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_239])]) ).
fof(f3390,plain,
( ! [X31,X30] :
( sP3(X30,X31,sK17)
| ~ empty(X31) )
| ~ spl18_93
| ~ spl18_239 ),
inference(resolution,[],[f3323,f907]) ).
fof(f3323,plain,
( ! [X3,X4,X5] :
( in(sK15(X3,X4,X5),X5)
| sP3(X3,X4,X5)
| ~ empty(X4) )
| ~ spl18_239 ),
inference(avatar_component_clause,[],[f3322]) ).
fof(f5778,plain,
( spl18_343
| ~ spl18_93
| ~ spl18_238 ),
inference(avatar_split_clause,[],[f3374,f3318,f906,f5776]) ).
fof(f5776,plain,
( spl18_343
<=> ! [X29,X30] :
( sP3(X29,sK17,X30)
| ~ empty(X30) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_343])]) ).
fof(f3374,plain,
( ! [X29,X30] :
( sP3(X29,sK17,X30)
| ~ empty(X30) )
| ~ spl18_93
| ~ spl18_238 ),
inference(resolution,[],[f3319,f907]) ).
fof(f5774,plain,
( spl18_342
| ~ spl18_93
| ~ spl18_237 ),
inference(avatar_split_clause,[],[f3363,f3314,f906,f5772]) ).
fof(f5772,plain,
( spl18_342
<=> ! [X29,X28] :
( sP1(X28,X29,sK17)
| ~ empty(X28) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_342])]) ).
fof(f3314,plain,
( spl18_237
<=> ! [X4,X5,X3] :
( in(sK13(X3,X4,X5),X5)
| sP1(X3,X4,X5)
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_237])]) ).
fof(f3363,plain,
( ! [X28,X29] :
( sP1(X28,X29,sK17)
| ~ empty(X28) )
| ~ spl18_93
| ~ spl18_237 ),
inference(resolution,[],[f3315,f907]) ).
fof(f3315,plain,
( ! [X3,X4,X5] :
( in(sK13(X3,X4,X5),X5)
| sP1(X3,X4,X5)
| ~ empty(X3) )
| ~ spl18_237 ),
inference(avatar_component_clause,[],[f3314]) ).
fof(f5770,plain,
( spl18_341
| ~ spl18_93
| ~ spl18_236 ),
inference(avatar_split_clause,[],[f3353,f3310,f906,f5768]) ).
fof(f5768,plain,
( spl18_341
<=> ! [X27,X28] :
( sP1(sK17,X27,X28)
| ~ empty(X28) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_341])]) ).
fof(f3353,plain,
( ! [X28,X27] :
( sP1(sK17,X27,X28)
| ~ empty(X28) )
| ~ spl18_93
| ~ spl18_236 ),
inference(resolution,[],[f3311,f907]) ).
fof(f5766,plain,
( spl18_340
| ~ spl18_93
| ~ spl18_235 ),
inference(avatar_split_clause,[],[f3343,f3306,f906,f5764]) ).
fof(f5764,plain,
( spl18_340
<=> ! [X29,X28] :
( sP1(X28,X29,sK17)
| ~ empty(X29) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_340])]) ).
fof(f3306,plain,
( spl18_235
<=> ! [X4,X5,X3] :
( in(sK13(X3,X4,X5),X5)
| sP1(X3,X4,X5)
| ~ empty(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_235])]) ).
fof(f3343,plain,
( ! [X28,X29] :
( sP1(X28,X29,sK17)
| ~ empty(X29) )
| ~ spl18_93
| ~ spl18_235 ),
inference(resolution,[],[f3307,f907]) ).
fof(f3307,plain,
( ! [X3,X4,X5] :
( in(sK13(X3,X4,X5),X5)
| sP1(X3,X4,X5)
| ~ empty(X4) )
| ~ spl18_235 ),
inference(avatar_component_clause,[],[f3306]) ).
fof(f5762,plain,
( spl18_339
| ~ spl18_93
| ~ spl18_234 ),
inference(avatar_split_clause,[],[f3333,f3298,f906,f5760]) ).
fof(f5760,plain,
( spl18_339
<=> ! [X27,X28] :
( sP1(X27,sK17,X28)
| ~ empty(X28) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_339])]) ).
fof(f3333,plain,
( ! [X28,X27] :
( sP1(X27,sK17,X28)
| ~ empty(X28) )
| ~ spl18_93
| ~ spl18_234 ),
inference(resolution,[],[f3299,f907]) ).
fof(f5758,plain,
( spl18_338
| ~ spl18_20
| ~ spl18_217 ),
inference(avatar_split_clause,[],[f2755,f2697,f358,f5756]) ).
fof(f5756,plain,
( spl18_338
<=> ! [X6,X5] :
( sP3(X5,X5,X6)
| ~ empty(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_338])]) ).
fof(f2755,plain,
( ! [X6,X5] :
( sP3(X5,X5,X6)
| ~ empty(X6) )
| ~ spl18_20
| ~ spl18_217 ),
inference(resolution,[],[f2698,f359]) ).
fof(f5754,plain,
( spl18_337
| ~ spl18_20
| ~ spl18_216 ),
inference(avatar_split_clause,[],[f2743,f2693,f358,f5752]) ).
fof(f5752,plain,
( spl18_337
<=> ! [X6,X5] :
( sP3(X5,X6,X6)
| ~ empty(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_337])]) ).
fof(f2743,plain,
( ! [X6,X5] :
( sP3(X5,X6,X6)
| ~ empty(X6) )
| ~ spl18_20
| ~ spl18_216 ),
inference(resolution,[],[f2694,f359]) ).
fof(f5750,plain,
( spl18_336
| ~ spl18_20
| ~ spl18_215 ),
inference(avatar_split_clause,[],[f2732,f2684,f358,f5748]) ).
fof(f5748,plain,
( spl18_336
<=> ! [X4,X5] :
( sP1(X4,X5,X4)
| ~ empty(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_336])]) ).
fof(f2732,plain,
( ! [X4,X5] :
( sP1(X4,X5,X4)
| ~ empty(X4) )
| ~ spl18_20
| ~ spl18_215 ),
inference(resolution,[],[f2685,f359]) ).
fof(f5746,plain,
( spl18_335
| ~ spl18_20
| ~ spl18_214 ),
inference(avatar_split_clause,[],[f2722,f2680,f358,f5744]) ).
fof(f5744,plain,
( spl18_335
<=> ! [X4,X5] :
( sP1(X4,X5,X5)
| ~ empty(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_335])]) ).
fof(f2722,plain,
( ! [X4,X5] :
( sP1(X4,X5,X5)
| ~ empty(X5) )
| ~ spl18_20
| ~ spl18_214 ),
inference(resolution,[],[f2681,f359]) ).
fof(f5716,plain,
( spl18_334
| ~ spl18_39
| ~ spl18_138 ),
inference(avatar_split_clause,[],[f1410,f1381,f467,f5714]) ).
fof(f1410,plain,
( ! [X2,X1] : sP2(X2,X1,set_union2(X2,X1))
| ~ spl18_39
| ~ spl18_138 ),
inference(superposition,[],[f1382,f468]) ).
fof(f5712,plain,
( spl18_333
| ~ spl18_40
| ~ spl18_137 ),
inference(avatar_split_clause,[],[f1399,f1377,f471,f5710]) ).
fof(f1399,plain,
( ! [X2,X1] : sP1(X2,X1,set_intersection2(X2,X1))
| ~ spl18_40
| ~ spl18_137 ),
inference(superposition,[],[f1378,f472]) ).
fof(f5708,plain,
( spl18_332
| ~ spl18_38
| ~ spl18_136 ),
inference(avatar_split_clause,[],[f1392,f1373,f463,f5706]) ).
fof(f5706,plain,
( spl18_332
<=> ! [X2,X1] : sP0(X2,X1,unordered_pair(X2,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_332])]) ).
fof(f463,plain,
( spl18_38
<=> ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_38])]) ).
fof(f1373,plain,
( spl18_136
<=> ! [X0,X1] : sP0(X0,X1,unordered_pair(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_136])]) ).
fof(f1392,plain,
( ! [X2,X1] : sP0(X2,X1,unordered_pair(X2,X1))
| ~ spl18_38
| ~ spl18_136 ),
inference(superposition,[],[f1374,f464]) ).
fof(f464,plain,
( ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0)
| ~ spl18_38 ),
inference(avatar_component_clause,[],[f463]) ).
fof(f1374,plain,
( ! [X0,X1] : sP0(X0,X1,unordered_pair(X1,X0))
| ~ spl18_136 ),
inference(avatar_component_clause,[],[f1373]) ).
fof(f5618,plain,
( spl18_331
| ~ spl18_31
| ~ spl18_309 ),
inference(avatar_split_clause,[],[f5381,f5067,f425,f5616]) ).
fof(f5616,plain,
( spl18_331
<=> ! [X13,X14] : disjoint(set_difference(X13,X14),X14) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_331])]) ).
fof(f425,plain,
( spl18_31
<=> ! [X0,X1] :
( disjoint(X1,X0)
| ~ disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_31])]) ).
fof(f5067,plain,
( spl18_309
<=> ! [X7,X8] : disjoint(X7,set_difference(X8,X7)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_309])]) ).
fof(f5381,plain,
( ! [X14,X13] : disjoint(set_difference(X13,X14),X14)
| ~ spl18_31
| ~ spl18_309 ),
inference(resolution,[],[f5068,f426]) ).
fof(f426,plain,
( ! [X0,X1] :
( ~ disjoint(X0,X1)
| disjoint(X1,X0) )
| ~ spl18_31 ),
inference(avatar_component_clause,[],[f425]) ).
fof(f5068,plain,
( ! [X8,X7] : disjoint(X7,set_difference(X8,X7))
| ~ spl18_309 ),
inference(avatar_component_clause,[],[f5067]) ).
fof(f5519,plain,
( spl18_330
| ~ spl18_139
| ~ spl18_243 ),
inference(avatar_split_clause,[],[f3502,f3475,f1385,f5517]) ).
fof(f5517,plain,
( spl18_330
<=> ! [X27,X26] : sP3(set_difference(X27,X26),X26,X26) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_330])]) ).
fof(f3502,plain,
( ! [X26,X27] : sP3(set_difference(X27,X26),X26,X26)
| ~ spl18_139
| ~ spl18_243 ),
inference(superposition,[],[f1386,f3476]) ).
fof(f5515,plain,
( spl18_329
| ~ spl18_19
| ~ spl18_167 ),
inference(avatar_split_clause,[],[f1879,f1756,f354,f5513]) ).
fof(f5513,plain,
( spl18_329
<=> ! [X0,X1] :
( subset(X0,X1)
| ~ disjoint(X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_329])]) ).
fof(f1879,plain,
( ! [X0,X1] :
( subset(X0,X1)
| ~ disjoint(X0,X0) )
| ~ spl18_19
| ~ spl18_167 ),
inference(superposition,[],[f1757,f355]) ).
fof(f5511,plain,
( spl18_328
| ~ spl18_19
| ~ spl18_166 ),
inference(avatar_split_clause,[],[f1861,f1752,f354,f5509]) ).
fof(f5509,plain,
( spl18_328
<=> ! [X0,X1] :
( disjoint(X1,X0)
| ~ disjoint(X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_328])]) ).
fof(f1861,plain,
( ! [X0,X1] :
( disjoint(X1,X0)
| ~ disjoint(X0,X0) )
| ~ spl18_19
| ~ spl18_166 ),
inference(superposition,[],[f1753,f355]) ).
fof(f5507,plain,
( spl18_327
| ~ spl18_19
| ~ spl18_164 ),
inference(avatar_split_clause,[],[f1847,f1744,f354,f5505]) ).
fof(f5505,plain,
( spl18_327
<=> ! [X0,X1] :
( disjoint(X0,X1)
| ~ disjoint(X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_327])]) ).
fof(f1847,plain,
( ! [X0,X1] :
( disjoint(X0,X1)
| ~ disjoint(X0,X0) )
| ~ spl18_19
| ~ spl18_164 ),
inference(superposition,[],[f1745,f355]) ).
fof(f5500,plain,
( spl18_326
| ~ spl18_139
| ~ spl18_145 ),
inference(avatar_split_clause,[],[f1603,f1449,f1385,f5498]) ).
fof(f5498,plain,
( spl18_326
<=> ! [X22,X21] : sP3(set_union2(X21,X22),X21,sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_326])]) ).
fof(f1603,plain,
( ! [X21,X22] : sP3(set_union2(X21,X22),X21,sK17)
| ~ spl18_139
| ~ spl18_145 ),
inference(superposition,[],[f1386,f1450]) ).
fof(f5496,plain,
( spl18_325
| ~ spl18_139
| ~ spl18_144 ),
inference(avatar_split_clause,[],[f1576,f1445,f1385,f5494]) ).
fof(f1576,plain,
( ! [X21,X22] : sP3(X21,set_difference(X21,X22),sK17)
| ~ spl18_139
| ~ spl18_144 ),
inference(superposition,[],[f1386,f1446]) ).
fof(f5492,plain,
( spl18_324
| ~ spl18_139
| ~ spl18_143 ),
inference(avatar_split_clause,[],[f1548,f1441,f1385,f5490]) ).
fof(f1548,plain,
( ! [X21,X22] : sP3(X21,set_intersection2(X21,X22),sK17)
| ~ spl18_139
| ~ spl18_143 ),
inference(superposition,[],[f1386,f1442]) ).
fof(f5488,plain,
( spl18_323
| ~ spl18_137
| ~ spl18_142 ),
inference(avatar_split_clause,[],[f1529,f1437,f1377,f5486]) ).
fof(f1529,plain,
( ! [X29,X30] : sP1(set_union2(X29,X30),X29,X29)
| ~ spl18_137
| ~ spl18_142 ),
inference(superposition,[],[f1378,f1438]) ).
fof(f5484,plain,
( spl18_322
| ~ spl18_138
| ~ spl18_141 ),
inference(avatar_split_clause,[],[f1508,f1433,f1381,f5482]) ).
fof(f5482,plain,
( spl18_322
<=> ! [X22,X23] : sP2(X22,set_difference(X22,X23),X22) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_322])]) ).
fof(f1508,plain,
( ! [X22,X23] : sP2(X22,set_difference(X22,X23),X22)
| ~ spl18_138
| ~ spl18_141 ),
inference(superposition,[],[f1382,f1434]) ).
fof(f5480,plain,
( spl18_321
| ~ spl18_28
| ~ spl18_141 ),
inference(avatar_split_clause,[],[f1500,f1433,f413,f5478]) ).
fof(f5478,plain,
( spl18_321
<=> ! [X4,X5] :
( ~ empty(X4)
| empty(set_difference(X4,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_321])]) ).
fof(f413,plain,
( spl18_28
<=> ! [X0,X1] :
( ~ empty(set_union2(X0,X1))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_28])]) ).
fof(f1500,plain,
( ! [X4,X5] :
( ~ empty(X4)
| empty(set_difference(X4,X5)) )
| ~ spl18_28
| ~ spl18_141 ),
inference(superposition,[],[f414,f1434]) ).
fof(f414,plain,
( ! [X0,X1] :
( ~ empty(set_union2(X0,X1))
| empty(X0) )
| ~ spl18_28 ),
inference(avatar_component_clause,[],[f413]) ).
fof(f5476,plain,
( spl18_320
| ~ spl18_138
| ~ spl18_140 ),
inference(avatar_split_clause,[],[f1483,f1429,f1381,f5474]) ).
fof(f1483,plain,
( ! [X22,X23] : sP2(X22,set_intersection2(X22,X23),X22)
| ~ spl18_138
| ~ spl18_140 ),
inference(superposition,[],[f1382,f1430]) ).
fof(f5472,plain,
( spl18_319
| ~ spl18_28
| ~ spl18_140 ),
inference(avatar_split_clause,[],[f1475,f1429,f413,f5470]) ).
fof(f1475,plain,
( ! [X4,X5] :
( ~ empty(X4)
| empty(set_intersection2(X4,X5)) )
| ~ spl18_28
| ~ spl18_140 ),
inference(superposition,[],[f414,f1430]) ).
fof(f5468,plain,
( spl18_318
| ~ spl18_61
| ~ spl18_65 ),
inference(avatar_split_clause,[],[f740,f654,f638,f5466]) ).
fof(f5466,plain,
( spl18_318
<=> ! [X0,X1] :
( disjoint(X0,X1)
| ~ subset(X0,sK17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_318])]) ).
fof(f638,plain,
( spl18_61
<=> ! [X0] : disjoint(sK17,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_61])]) ).
fof(f740,plain,
( ! [X0,X1] :
( disjoint(X0,X1)
| ~ subset(X0,sK17) )
| ~ spl18_61
| ~ spl18_65 ),
inference(resolution,[],[f639,f655]) ).
fof(f639,plain,
( ! [X0] : disjoint(sK17,X0)
| ~ spl18_61 ),
inference(avatar_component_clause,[],[f638]) ).
fof(f5459,plain,
( spl18_317
| ~ spl18_20
| ~ spl18_315 ),
inference(avatar_split_clause,[],[f5452,f5405,f358,f5457]) ).
fof(f5457,plain,
( spl18_317
<=> ! [X2,X3] : ~ empty(unordered_pair(X2,X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_317])]) ).
fof(f5452,plain,
( ! [X2,X3] : ~ empty(unordered_pair(X2,X3))
| ~ spl18_20
| ~ spl18_315 ),
inference(resolution,[],[f5406,f359]) ).
fof(f5411,plain,
( spl18_316
| ~ spl18_136
| ~ spl18_160 ),
inference(avatar_split_clause,[],[f1730,f1698,f1373,f5409]) ).
fof(f1698,plain,
( spl18_160
<=> ! [X2,X0,X1] :
( in(X0,X1)
| ~ sP0(X0,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_160])]) ).
fof(f1730,plain,
( ! [X0,X1] : in(X0,unordered_pair(X1,X0))
| ~ spl18_136
| ~ spl18_160 ),
inference(resolution,[],[f1699,f1374]) ).
fof(f1699,plain,
( ! [X2,X0,X1] :
( ~ sP0(X0,X2,X1)
| in(X0,X1) )
| ~ spl18_160 ),
inference(avatar_component_clause,[],[f1698]) ).
fof(f5407,plain,
( spl18_315
| ~ spl18_136
| ~ spl18_159 ),
inference(avatar_split_clause,[],[f1729,f1690,f1373,f5405]) ).
fof(f1690,plain,
( spl18_159
<=> ! [X2,X0,X1] :
( in(X0,X1)
| ~ sP0(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_159])]) ).
fof(f1729,plain,
( ! [X0,X1] : in(X0,unordered_pair(X0,X1))
| ~ spl18_136
| ~ spl18_159 ),
inference(resolution,[],[f1691,f1374]) ).
fof(f1691,plain,
( ! [X2,X0,X1] :
( ~ sP0(X2,X0,X1)
| in(X0,X1) )
| ~ spl18_159 ),
inference(avatar_component_clause,[],[f1690]) ).
fof(f5403,plain,
( spl18_314
| ~ spl18_15
| ~ spl18_83 ),
inference(avatar_split_clause,[],[f920,f864,f338,f5401]) ).
fof(f5401,plain,
( spl18_314
<=> ! [X3] : set_union2(X3,sK17) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl18_314])]) ).
fof(f338,plain,
( spl18_15
<=> ! [X0] : set_union2(X0,empty_set) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl18_15])]) ).
fof(f920,plain,
( ! [X3] : set_union2(X3,sK17) = X3
| ~ spl18_15
| ~ spl18_83 ),
inference(superposition,[],[f339,f866]) ).
fof(f339,plain,
( ! [X0] : set_union2(X0,empty_set) = X0
| ~ spl18_15 ),
inference(avatar_component_clause,[],[f338]) ).
fof(f5085,plain,
( spl18_313
| ~ spl18_43
| ~ spl18_115 ),
inference(avatar_split_clause,[],[f1128,f1091,f511,f5083]) ).
fof(f5083,plain,
( spl18_313
<=> ! [X10,X11,X13,X12] :
( in(sK14(set_intersection2(X10,X11),X12,X13),X13)
| in(sK14(set_intersection2(X10,X11),X12,X13),X12)
| sP2(set_intersection2(X10,X11),X12,X13)
| ~ disjoint(X10,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_313])]) ).
fof(f1091,plain,
( spl18_115
<=> ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| in(sK14(X0,X1,X2),X0)
| in(sK14(X0,X1,X2),X1)
| in(sK14(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_115])]) ).
fof(f1128,plain,
( ! [X10,X11,X12,X13] :
( in(sK14(set_intersection2(X10,X11),X12,X13),X13)
| in(sK14(set_intersection2(X10,X11),X12,X13),X12)
| sP2(set_intersection2(X10,X11),X12,X13)
| ~ disjoint(X10,X11) )
| ~ spl18_43
| ~ spl18_115 ),
inference(resolution,[],[f1092,f512]) ).
fof(f1092,plain,
( ! [X2,X0,X1] :
( in(sK14(X0,X1,X2),X2)
| in(sK14(X0,X1,X2),X1)
| in(sK14(X0,X1,X2),X0)
| sP2(X0,X1,X2) )
| ~ spl18_115 ),
inference(avatar_component_clause,[],[f1091]) ).
fof(f5081,plain,
( spl18_312
| ~ spl18_43
| ~ spl18_115 ),
inference(avatar_split_clause,[],[f1122,f1091,f511,f5079]) ).
fof(f5079,plain,
( spl18_312
<=> ! [X10,X11,X13,X12] :
( in(sK14(X10,set_intersection2(X11,X12),X13),X13)
| in(sK14(X10,set_intersection2(X11,X12),X13),X10)
| sP2(X10,set_intersection2(X11,X12),X13)
| ~ disjoint(X11,X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_312])]) ).
fof(f1122,plain,
( ! [X10,X11,X12,X13] :
( in(sK14(X10,set_intersection2(X11,X12),X13),X13)
| in(sK14(X10,set_intersection2(X11,X12),X13),X10)
| sP2(X10,set_intersection2(X11,X12),X13)
| ~ disjoint(X11,X12) )
| ~ spl18_43
| ~ spl18_115 ),
inference(resolution,[],[f1092,f512]) ).
fof(f5077,plain,
( spl18_311
| ~ spl18_43
| ~ spl18_115 ),
inference(avatar_split_clause,[],[f1116,f1091,f511,f5075]) ).
fof(f5075,plain,
( spl18_311
<=> ! [X13,X14,X12,X15] :
( in(sK14(X12,X13,set_intersection2(X14,X15)),X13)
| in(sK14(X12,X13,set_intersection2(X14,X15)),X12)
| sP2(X12,X13,set_intersection2(X14,X15))
| ~ disjoint(X14,X15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_311])]) ).
fof(f1116,plain,
( ! [X14,X15,X12,X13] :
( in(sK14(X12,X13,set_intersection2(X14,X15)),X13)
| in(sK14(X12,X13,set_intersection2(X14,X15)),X12)
| sP2(X12,X13,set_intersection2(X14,X15))
| ~ disjoint(X14,X15) )
| ~ spl18_43
| ~ spl18_115 ),
inference(resolution,[],[f1092,f512]) ).
fof(f5073,plain,
( spl18_310
| ~ spl18_43
| ~ spl18_113 ),
inference(avatar_split_clause,[],[f1100,f1083,f511,f5071]) ).
fof(f5071,plain,
( spl18_310
<=> ! [X9,X7,X6,X8] :
( sK12(X6,X7,set_intersection2(X8,X9)) = X6
| sK12(X6,X7,set_intersection2(X8,X9)) = X7
| sP0(X6,X7,set_intersection2(X8,X9))
| ~ disjoint(X8,X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_310])]) ).
fof(f1083,plain,
( spl18_113
<=> ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| sK12(X0,X1,X2) = X0
| sK12(X0,X1,X2) = X1
| in(sK12(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_113])]) ).
fof(f1100,plain,
( ! [X8,X6,X9,X7] :
( sK12(X6,X7,set_intersection2(X8,X9)) = X6
| sK12(X6,X7,set_intersection2(X8,X9)) = X7
| sP0(X6,X7,set_intersection2(X8,X9))
| ~ disjoint(X8,X9) )
| ~ spl18_43
| ~ spl18_113 ),
inference(resolution,[],[f1084,f512]) ).
fof(f1084,plain,
( ! [X2,X0,X1] :
( in(sK12(X0,X1,X2),X2)
| sK12(X0,X1,X2) = X0
| sK12(X0,X1,X2) = X1
| sP0(X0,X1,X2) )
| ~ spl18_113 ),
inference(avatar_component_clause,[],[f1083]) ).
fof(f5069,plain,
( spl18_309
| ~ spl18_49
| ~ spl18_243 ),
inference(avatar_split_clause,[],[f3523,f3475,f535,f5067]) ).
fof(f3523,plain,
( ! [X8,X7] : disjoint(X7,set_difference(X8,X7))
| ~ spl18_49
| ~ spl18_243 ),
inference(trivial_inequality_removal,[],[f3495]) ).
fof(f3495,plain,
( ! [X8,X7] :
( X7 != X7
| disjoint(X7,set_difference(X8,X7)) )
| ~ spl18_49
| ~ spl18_243 ),
inference(superposition,[],[f536,f3476]) ).
fof(f5065,plain,
( spl18_308
| ~ spl18_30
| ~ spl18_115 ),
inference(avatar_split_clause,[],[f1126,f1091,f421,f5063]) ).
fof(f5063,plain,
( spl18_308
<=> ! [X6,X4,X5] :
( in(sK14(X4,X5,X6),X6)
| in(sK14(X4,X5,X6),X5)
| sP2(X4,X5,X6)
| ~ in(X4,sK14(X4,X5,X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_308])]) ).
fof(f1126,plain,
( ! [X6,X4,X5] :
( in(sK14(X4,X5,X6),X6)
| in(sK14(X4,X5,X6),X5)
| sP2(X4,X5,X6)
| ~ in(X4,sK14(X4,X5,X6)) )
| ~ spl18_30
| ~ spl18_115 ),
inference(resolution,[],[f1092,f422]) ).
fof(f5061,plain,
( spl18_307
| ~ spl18_30
| ~ spl18_115 ),
inference(avatar_split_clause,[],[f1120,f1091,f421,f5059]) ).
fof(f5059,plain,
( spl18_307
<=> ! [X6,X4,X5] :
( in(sK14(X4,X5,X6),X6)
| in(sK14(X4,X5,X6),X4)
| sP2(X4,X5,X6)
| ~ in(X5,sK14(X4,X5,X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_307])]) ).
fof(f1120,plain,
( ! [X6,X4,X5] :
( in(sK14(X4,X5,X6),X6)
| in(sK14(X4,X5,X6),X4)
| sP2(X4,X5,X6)
| ~ in(X5,sK14(X4,X5,X6)) )
| ~ spl18_30
| ~ spl18_115 ),
inference(resolution,[],[f1092,f422]) ).
fof(f5057,plain,
( spl18_306
| ~ spl18_30
| ~ spl18_115 ),
inference(avatar_split_clause,[],[f1114,f1091,f421,f5055]) ).
fof(f5055,plain,
( spl18_306
<=> ! [X6,X7,X8] :
( in(sK14(X6,X7,X8),X7)
| in(sK14(X6,X7,X8),X6)
| sP2(X6,X7,X8)
| ~ in(X8,sK14(X6,X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_306])]) ).
fof(f1114,plain,
( ! [X8,X6,X7] :
( in(sK14(X6,X7,X8),X7)
| in(sK14(X6,X7,X8),X6)
| sP2(X6,X7,X8)
| ~ in(X8,sK14(X6,X7,X8)) )
| ~ spl18_30
| ~ spl18_115 ),
inference(resolution,[],[f1092,f422]) ).
fof(f5053,plain,
( spl18_305
| ~ spl18_30
| ~ spl18_113 ),
inference(avatar_split_clause,[],[f1098,f1083,f421,f5051]) ).
fof(f5051,plain,
( spl18_305
<=> ! [X2,X0,X1] :
( sK12(X0,X1,X2) = X0
| sK12(X0,X1,X2) = X1
| sP0(X0,X1,X2)
| ~ in(X2,sK12(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_305])]) ).
fof(f1098,plain,
( ! [X2,X0,X1] :
( sK12(X0,X1,X2) = X0
| sK12(X0,X1,X2) = X1
| sP0(X0,X1,X2)
| ~ in(X2,sK12(X0,X1,X2)) )
| ~ spl18_30
| ~ spl18_113 ),
inference(resolution,[],[f1084,f422]) ).
fof(f4956,plain,
( spl18_304
| ~ spl18_21
| ~ spl18_136 ),
inference(avatar_split_clause,[],[f1391,f1373,f371,f4954]) ).
fof(f4954,plain,
( spl18_304
<=> ! [X0] : sP0(X0,X0,singleton(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_304])]) ).
fof(f371,plain,
( spl18_21
<=> ! [X0] : singleton(X0) = unordered_pair(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_21])]) ).
fof(f1391,plain,
( ! [X0] : sP0(X0,X0,singleton(X0))
| ~ spl18_21
| ~ spl18_136 ),
inference(superposition,[],[f1374,f372]) ).
fof(f372,plain,
( ! [X0] : singleton(X0) = unordered_pair(X0,X0)
| ~ spl18_21 ),
inference(avatar_component_clause,[],[f371]) ).
fof(f4952,plain,
( spl18_303
| ~ spl18_20
| ~ spl18_115 ),
inference(avatar_split_clause,[],[f1127,f1091,f358,f4950]) ).
fof(f4950,plain,
( spl18_303
<=> ! [X9,X8,X7] :
( in(sK14(X7,X8,X9),X9)
| in(sK14(X7,X8,X9),X8)
| sP2(X7,X8,X9)
| ~ empty(X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_303])]) ).
fof(f1127,plain,
( ! [X8,X9,X7] :
( in(sK14(X7,X8,X9),X9)
| in(sK14(X7,X8,X9),X8)
| sP2(X7,X8,X9)
| ~ empty(X7) )
| ~ spl18_20
| ~ spl18_115 ),
inference(resolution,[],[f1092,f359]) ).
fof(f4948,plain,
( spl18_302
| ~ spl18_20
| ~ spl18_115 ),
inference(avatar_split_clause,[],[f1121,f1091,f358,f4946]) ).
fof(f4946,plain,
( spl18_302
<=> ! [X9,X8,X7] :
( in(sK14(X7,X8,X9),X9)
| in(sK14(X7,X8,X9),X7)
| sP2(X7,X8,X9)
| ~ empty(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_302])]) ).
fof(f1121,plain,
( ! [X8,X9,X7] :
( in(sK14(X7,X8,X9),X9)
| in(sK14(X7,X8,X9),X7)
| sP2(X7,X8,X9)
| ~ empty(X8) )
| ~ spl18_20
| ~ spl18_115 ),
inference(resolution,[],[f1092,f359]) ).
fof(f4944,plain,
( spl18_301
| ~ spl18_20
| ~ spl18_115 ),
inference(avatar_split_clause,[],[f1115,f1091,f358,f4942]) ).
fof(f4942,plain,
( spl18_301
<=> ! [X9,X11,X10] :
( in(sK14(X9,X10,X11),X10)
| in(sK14(X9,X10,X11),X9)
| sP2(X9,X10,X11)
| ~ empty(X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_301])]) ).
fof(f1115,plain,
( ! [X10,X11,X9] :
( in(sK14(X9,X10,X11),X10)
| in(sK14(X9,X10,X11),X9)
| sP2(X9,X10,X11)
| ~ empty(X11) )
| ~ spl18_20
| ~ spl18_115 ),
inference(resolution,[],[f1092,f359]) ).
fof(f4940,plain,
( spl18_300
| ~ spl18_20
| ~ spl18_113 ),
inference(avatar_split_clause,[],[f1099,f1083,f358,f4938]) ).
fof(f4938,plain,
( spl18_300
<=> ! [X4,X5,X3] :
( sK12(X3,X4,X5) = X3
| sK12(X3,X4,X5) = X4
| sP0(X3,X4,X5)
| ~ empty(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_300])]) ).
fof(f1099,plain,
( ! [X3,X4,X5] :
( sK12(X3,X4,X5) = X3
| sK12(X3,X4,X5) = X4
| sP0(X3,X4,X5)
| ~ empty(X5) )
| ~ spl18_20
| ~ spl18_113 ),
inference(resolution,[],[f1084,f359]) ).
fof(f4788,plain,
( spl18_299
| ~ spl18_23
| ~ spl18_130 ),
inference(avatar_split_clause,[],[f1321,f1296,f381,f4786]) ).
fof(f4786,plain,
( spl18_299
<=> ! [X0,X1] :
( ~ empty(X0)
| ~ proper_subset(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_299])]) ).
fof(f1321,plain,
( ! [X0,X1] :
( ~ empty(X0)
| ~ proper_subset(X1,X0) )
| ~ spl18_23
| ~ spl18_130 ),
inference(resolution,[],[f1297,f382]) ).
fof(f4653,plain,
( spl18_298
| ~ spl18_43
| ~ spl18_111 ),
inference(avatar_split_clause,[],[f1075,f1035,f511,f4651]) ).
fof(f1075,plain,
( ! [X8,X6,X9,X7] :
( in(sK15(X6,set_intersection2(X7,X8),X9),X9)
| sP3(X6,set_intersection2(X7,X8),X9)
| ~ disjoint(X7,X8) )
| ~ spl18_43
| ~ spl18_111 ),
inference(resolution,[],[f1036,f512]) ).
fof(f4649,plain,
( spl18_297
| ~ spl18_43
| ~ spl18_111 ),
inference(avatar_split_clause,[],[f1071,f1035,f511,f4647]) ).
fof(f1071,plain,
( ! [X8,X6,X9,X7] :
( in(sK15(X6,X7,set_intersection2(X8,X9)),X7)
| sP3(X6,X7,set_intersection2(X8,X9))
| ~ disjoint(X8,X9) )
| ~ spl18_43
| ~ spl18_111 ),
inference(resolution,[],[f1036,f512]) ).
fof(f4645,plain,
( spl18_296
| ~ spl18_43
| ~ spl18_108 ),
inference(avatar_split_clause,[],[f1066,f1023,f511,f4643]) ).
fof(f1066,plain,
( ! [X8,X6,X9,X7] :
( in(sK13(set_intersection2(X6,X7),X8,X9),X9)
| sP1(set_intersection2(X6,X7),X8,X9)
| ~ disjoint(X6,X7) )
| ~ spl18_43
| ~ spl18_108 ),
inference(resolution,[],[f1024,f512]) ).
fof(f4641,plain,
( spl18_295
| ~ spl18_43
| ~ spl18_108 ),
inference(avatar_split_clause,[],[f1062,f1023,f511,f4639]) ).
fof(f1062,plain,
( ! [X8,X6,X9,X7] :
( in(sK13(X6,X7,set_intersection2(X8,X9)),X6)
| sP1(X6,X7,set_intersection2(X8,X9))
| ~ disjoint(X8,X9) )
| ~ spl18_43
| ~ spl18_108 ),
inference(resolution,[],[f1024,f512]) ).
fof(f4637,plain,
( spl18_294
| ~ spl18_43
| ~ spl18_107 ),
inference(avatar_split_clause,[],[f1048,f1019,f511,f4635]) ).
fof(f1048,plain,
( ! [X8,X6,X9,X7] :
( in(sK13(X6,set_intersection2(X7,X8),X9),X9)
| sP1(X6,set_intersection2(X7,X8),X9)
| ~ disjoint(X7,X8) )
| ~ spl18_43
| ~ spl18_107 ),
inference(resolution,[],[f1020,f512]) ).
fof(f4633,plain,
( spl18_293
| ~ spl18_43
| ~ spl18_107 ),
inference(avatar_split_clause,[],[f1044,f1019,f511,f4631]) ).
fof(f1044,plain,
( ! [X8,X6,X9,X7] :
( in(sK13(X6,X7,set_intersection2(X8,X9)),X7)
| sP1(X6,X7,set_intersection2(X8,X9))
| ~ disjoint(X8,X9) )
| ~ spl18_43
| ~ spl18_107 ),
inference(resolution,[],[f1020,f512]) ).
fof(f4629,plain,
( spl18_292
| ~ spl18_39
| ~ spl18_119 ),
inference(avatar_split_clause,[],[f1188,f1143,f467,f4627]) ).
fof(f4627,plain,
( spl18_292
<=> ! [X2,X1] : ~ proper_subset(set_union2(X2,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_292])]) ).
fof(f1143,plain,
( spl18_119
<=> ! [X6,X7] : ~ proper_subset(set_union2(X6,X7),X6) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_119])]) ).
fof(f1188,plain,
( ! [X2,X1] : ~ proper_subset(set_union2(X2,X1),X1)
| ~ spl18_39
| ~ spl18_119 ),
inference(superposition,[],[f1144,f468]) ).
fof(f1144,plain,
( ! [X6,X7] : ~ proper_subset(set_union2(X6,X7),X6)
| ~ spl18_119 ),
inference(avatar_component_clause,[],[f1143]) ).
fof(f4625,plain,
( spl18_291
| ~ spl18_69
| ~ spl18_81 ),
inference(avatar_split_clause,[],[f845,f811,f709,f4623]) ).
fof(f4623,plain,
( spl18_291
<=> ! [X20,X21,X19] :
( ~ subset(X19,X20)
| set_difference(X19,X21) = set_difference(X20,X21)
| proper_subset(set_difference(X19,X21),set_difference(X20,X21)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_291])]) ).
fof(f845,plain,
( ! [X21,X19,X20] :
( ~ subset(X19,X20)
| set_difference(X19,X21) = set_difference(X20,X21)
| proper_subset(set_difference(X19,X21),set_difference(X20,X21)) )
| ~ spl18_69
| ~ spl18_81 ),
inference(resolution,[],[f812,f710]) ).
fof(f4621,plain,
( spl18_290
| ~ spl18_68
| ~ spl18_81 ),
inference(avatar_split_clause,[],[f844,f811,f705,f4619]) ).
fof(f4619,plain,
( spl18_290
<=> ! [X18,X16,X17] :
( ~ subset(X16,X17)
| set_difference(X17,X18) = set_difference(X16,X18)
| ~ subset(set_difference(X17,X18),set_difference(X16,X18)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_290])]) ).
fof(f844,plain,
( ! [X18,X16,X17] :
( ~ subset(X16,X17)
| set_difference(X17,X18) = set_difference(X16,X18)
| ~ subset(set_difference(X17,X18),set_difference(X16,X18)) )
| ~ spl18_68
| ~ spl18_81 ),
inference(resolution,[],[f812,f706]) ).
fof(f4617,plain,
( spl18_289
| ~ spl18_69
| ~ spl18_80 ),
inference(avatar_split_clause,[],[f829,f807,f709,f4615]) ).
fof(f4615,plain,
( spl18_289
<=> ! [X20,X21,X19] :
( ~ subset(X19,X20)
| set_intersection2(X19,X21) = set_intersection2(X20,X21)
| proper_subset(set_intersection2(X19,X21),set_intersection2(X20,X21)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_289])]) ).
fof(f829,plain,
( ! [X21,X19,X20] :
( ~ subset(X19,X20)
| set_intersection2(X19,X21) = set_intersection2(X20,X21)
| proper_subset(set_intersection2(X19,X21),set_intersection2(X20,X21)) )
| ~ spl18_69
| ~ spl18_80 ),
inference(resolution,[],[f808,f710]) ).
fof(f4613,plain,
( spl18_288
| ~ spl18_68
| ~ spl18_80 ),
inference(avatar_split_clause,[],[f828,f807,f705,f4611]) ).
fof(f4611,plain,
( spl18_288
<=> ! [X18,X16,X17] :
( ~ subset(X16,X17)
| set_intersection2(X17,X18) = set_intersection2(X16,X18)
| ~ subset(set_intersection2(X17,X18),set_intersection2(X16,X18)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_288])]) ).
fof(f828,plain,
( ! [X18,X16,X17] :
( ~ subset(X16,X17)
| set_intersection2(X17,X18) = set_intersection2(X16,X18)
| ~ subset(set_intersection2(X17,X18),set_intersection2(X16,X18)) )
| ~ spl18_68
| ~ spl18_80 ),
inference(resolution,[],[f808,f706]) ).
fof(f4522,plain,
( spl18_287
| ~ spl18_40
| ~ spl18_117 ),
inference(avatar_split_clause,[],[f1180,f1103,f471,f4520]) ).
fof(f4520,plain,
( spl18_287
<=> ! [X2,X3] : ~ proper_subset(X2,set_intersection2(X3,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_287])]) ).
fof(f1103,plain,
( spl18_117
<=> ! [X2,X1] : ~ proper_subset(X1,set_intersection2(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_117])]) ).
fof(f1180,plain,
( ! [X2,X3] : ~ proper_subset(X2,set_intersection2(X3,X2))
| ~ spl18_40
| ~ spl18_117 ),
inference(superposition,[],[f1104,f472]) ).
fof(f1104,plain,
( ! [X2,X1] : ~ proper_subset(X1,set_intersection2(X1,X2))
| ~ spl18_117 ),
inference(avatar_component_clause,[],[f1103]) ).
fof(f4518,plain,
( spl18_286
| ~ spl18_115 ),
inference(avatar_split_clause,[],[f1132,f1091,f4516]) ).
fof(f1132,plain,
( ! [X4,X5] :
( in(sK14(X4,X4,X5),X5)
| in(sK14(X4,X4,X5),X4)
| sP2(X4,X4,X5) )
| ~ spl18_115 ),
inference(factoring,[],[f1092]) ).
fof(f4514,plain,
( spl18_285
| ~ spl18_115 ),
inference(avatar_split_clause,[],[f1131,f1091,f4512]) ).
fof(f1131,plain,
( ! [X2,X3] :
( in(sK14(X2,X3,X2),X2)
| in(sK14(X2,X3,X2),X3)
| sP2(X2,X3,X2) )
| ~ spl18_115 ),
inference(factoring,[],[f1092]) ).
fof(f4510,plain,
( spl18_284
| ~ spl18_115 ),
inference(avatar_split_clause,[],[f1130,f1091,f4508]) ).
fof(f1130,plain,
( ! [X0,X1] :
( in(sK14(X0,X1,X1),X1)
| in(sK14(X0,X1,X1),X0)
| sP2(X0,X1,X1) )
| ~ spl18_115 ),
inference(factoring,[],[f1092]) ).
fof(f4506,plain,
( spl18_283
| ~ spl18_30
| ~ spl18_111 ),
inference(avatar_split_clause,[],[f1073,f1035,f421,f4504]) ).
fof(f4504,plain,
( spl18_283
<=> ! [X2,X0,X1] :
( in(sK15(X0,X1,X2),X2)
| sP3(X0,X1,X2)
| ~ in(X1,sK15(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_283])]) ).
fof(f1073,plain,
( ! [X2,X0,X1] :
( in(sK15(X0,X1,X2),X2)
| sP3(X0,X1,X2)
| ~ in(X1,sK15(X0,X1,X2)) )
| ~ spl18_30
| ~ spl18_111 ),
inference(resolution,[],[f1036,f422]) ).
fof(f4502,plain,
( spl18_282
| ~ spl18_30
| ~ spl18_111 ),
inference(avatar_split_clause,[],[f1069,f1035,f421,f4500]) ).
fof(f4500,plain,
( spl18_282
<=> ! [X2,X0,X1] :
( in(sK15(X0,X1,X2),X1)
| sP3(X0,X1,X2)
| ~ in(X2,sK15(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_282])]) ).
fof(f1069,plain,
( ! [X2,X0,X1] :
( in(sK15(X0,X1,X2),X1)
| sP3(X0,X1,X2)
| ~ in(X2,sK15(X0,X1,X2)) )
| ~ spl18_30
| ~ spl18_111 ),
inference(resolution,[],[f1036,f422]) ).
fof(f4498,plain,
( spl18_281
| ~ spl18_30
| ~ spl18_108 ),
inference(avatar_split_clause,[],[f1064,f1023,f421,f4496]) ).
fof(f4496,plain,
( spl18_281
<=> ! [X2,X0,X1] :
( in(sK13(X0,X1,X2),X2)
| sP1(X0,X1,X2)
| ~ in(X0,sK13(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_281])]) ).
fof(f1064,plain,
( ! [X2,X0,X1] :
( in(sK13(X0,X1,X2),X2)
| sP1(X0,X1,X2)
| ~ in(X0,sK13(X0,X1,X2)) )
| ~ spl18_30
| ~ spl18_108 ),
inference(resolution,[],[f1024,f422]) ).
fof(f4494,plain,
( spl18_280
| ~ spl18_30
| ~ spl18_108 ),
inference(avatar_split_clause,[],[f1060,f1023,f421,f4492]) ).
fof(f4492,plain,
( spl18_280
<=> ! [X2,X0,X1] :
( in(sK13(X0,X1,X2),X0)
| sP1(X0,X1,X2)
| ~ in(X2,sK13(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_280])]) ).
fof(f1060,plain,
( ! [X2,X0,X1] :
( in(sK13(X0,X1,X2),X0)
| sP1(X0,X1,X2)
| ~ in(X2,sK13(X0,X1,X2)) )
| ~ spl18_30
| ~ spl18_108 ),
inference(resolution,[],[f1024,f422]) ).
fof(f4490,plain,
( spl18_279
| ~ spl18_48
| ~ spl18_67 ),
inference(avatar_split_clause,[],[f792,f695,f531,f4488]) ).
fof(f4488,plain,
( spl18_279
<=> ! [X4] : set_difference(X4,sK17) = X4 ),
introduced(avatar_definition,[new_symbols(naming,[spl18_279])]) ).
fof(f695,plain,
( spl18_67
<=> ! [X1] : disjoint(X1,sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_67])]) ).
fof(f792,plain,
( ! [X4] : set_difference(X4,sK17) = X4
| ~ spl18_48
| ~ spl18_67 ),
inference(resolution,[],[f696,f532]) ).
fof(f696,plain,
( ! [X1] : disjoint(X1,sK17)
| ~ spl18_67 ),
inference(avatar_component_clause,[],[f695]) ).
fof(f4486,plain,
( spl18_278
| ~ spl18_30
| ~ spl18_107 ),
inference(avatar_split_clause,[],[f1046,f1019,f421,f4484]) ).
fof(f4484,plain,
( spl18_278
<=> ! [X2,X0,X1] :
( in(sK13(X0,X1,X2),X2)
| sP1(X0,X1,X2)
| ~ in(X1,sK13(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_278])]) ).
fof(f1046,plain,
( ! [X2,X0,X1] :
( in(sK13(X0,X1,X2),X2)
| sP1(X0,X1,X2)
| ~ in(X1,sK13(X0,X1,X2)) )
| ~ spl18_30
| ~ spl18_107 ),
inference(resolution,[],[f1020,f422]) ).
fof(f4482,plain,
( spl18_277
| ~ spl18_30
| ~ spl18_107 ),
inference(avatar_split_clause,[],[f1042,f1019,f421,f4480]) ).
fof(f4480,plain,
( spl18_277
<=> ! [X2,X0,X1] :
( in(sK13(X0,X1,X2),X1)
| sP1(X0,X1,X2)
| ~ in(X2,sK13(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_277])]) ).
fof(f1042,plain,
( ! [X2,X0,X1] :
( in(sK13(X0,X1,X2),X1)
| sP1(X0,X1,X2)
| ~ in(X2,sK13(X0,X1,X2)) )
| ~ spl18_30
| ~ spl18_107 ),
inference(resolution,[],[f1020,f422]) ).
fof(f4379,plain,
( spl18_276
| ~ spl18_43
| ~ spl18_106 ),
inference(avatar_split_clause,[],[f1016,f1011,f511,f4377]) ).
fof(f4377,plain,
( spl18_276
<=> ! [X6,X4,X5] :
( sK11(X4,set_intersection2(X5,X6)) = X4
| set_intersection2(X5,X6) = singleton(X4)
| ~ disjoint(X5,X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_276])]) ).
fof(f1016,plain,
( ! [X6,X4,X5] :
( sK11(X4,set_intersection2(X5,X6)) = X4
| set_intersection2(X5,X6) = singleton(X4)
| ~ disjoint(X5,X6) )
| ~ spl18_43
| ~ spl18_106 ),
inference(resolution,[],[f1012,f512]) ).
fof(f4375,plain,
( spl18_275
| ~ spl18_69
| ~ spl18_95 ),
inference(avatar_split_clause,[],[f945,f923,f709,f4373]) ).
fof(f4373,plain,
( spl18_275
<=> ! [X20,X21,X19] :
( ~ subset(X19,X20)
| ~ subset(X21,X20)
| set_union2(X21,X19) = X20
| proper_subset(set_union2(X21,X19),X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_275])]) ).
fof(f945,plain,
( ! [X21,X19,X20] :
( ~ subset(X19,X20)
| ~ subset(X21,X20)
| set_union2(X21,X19) = X20
| proper_subset(set_union2(X21,X19),X20) )
| ~ spl18_69
| ~ spl18_95 ),
inference(resolution,[],[f924,f710]) ).
fof(f4371,plain,
( spl18_274
| ~ spl18_68
| ~ spl18_95 ),
inference(avatar_split_clause,[],[f944,f923,f705,f4369]) ).
fof(f4369,plain,
( spl18_274
<=> ! [X18,X16,X17] :
( ~ subset(X16,X17)
| ~ subset(X18,X17)
| set_union2(X18,X16) = X17
| ~ subset(X17,set_union2(X18,X16)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_274])]) ).
fof(f944,plain,
( ! [X18,X16,X17] :
( ~ subset(X16,X17)
| ~ subset(X18,X17)
| set_union2(X18,X16) = X17
| ~ subset(X17,set_union2(X18,X16)) )
| ~ spl18_68
| ~ spl18_95 ),
inference(resolution,[],[f924,f706]) ).
fof(f4366,plain,
( spl18_273
| ~ spl18_69
| ~ spl18_94 ),
inference(avatar_split_clause,[],[f932,f913,f709,f4364]) ).
fof(f4364,plain,
( spl18_273
<=> ! [X20,X21,X19] :
( ~ subset(X19,X20)
| ~ subset(X19,X21)
| set_intersection2(X21,X20) = X19
| proper_subset(X19,set_intersection2(X21,X20)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_273])]) ).
fof(f913,plain,
( spl18_94
<=> ! [X2,X0,X1] :
( subset(X0,set_intersection2(X1,X2))
| ~ subset(X0,X2)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_94])]) ).
fof(f932,plain,
( ! [X21,X19,X20] :
( ~ subset(X19,X20)
| ~ subset(X19,X21)
| set_intersection2(X21,X20) = X19
| proper_subset(X19,set_intersection2(X21,X20)) )
| ~ spl18_69
| ~ spl18_94 ),
inference(resolution,[],[f914,f710]) ).
fof(f914,plain,
( ! [X2,X0,X1] :
( subset(X0,set_intersection2(X1,X2))
| ~ subset(X0,X2)
| ~ subset(X0,X1) )
| ~ spl18_94 ),
inference(avatar_component_clause,[],[f913]) ).
fof(f4362,plain,
( spl18_272
| ~ spl18_68
| ~ spl18_94 ),
inference(avatar_split_clause,[],[f931,f913,f705,f4360]) ).
fof(f4360,plain,
( spl18_272
<=> ! [X18,X16,X17] :
( ~ subset(X16,X17)
| ~ subset(X16,X18)
| set_intersection2(X18,X17) = X16
| ~ subset(set_intersection2(X18,X17),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_272])]) ).
fof(f931,plain,
( ! [X18,X16,X17] :
( ~ subset(X16,X17)
| ~ subset(X16,X18)
| set_intersection2(X18,X17) = X16
| ~ subset(set_intersection2(X18,X17),X16) )
| ~ spl18_68
| ~ spl18_94 ),
inference(resolution,[],[f914,f706]) ).
fof(f4251,plain,
( spl18_271
| ~ spl18_43
| ~ spl18_97 ),
inference(avatar_split_clause,[],[f1000,f959,f511,f4249]) ).
fof(f4249,plain,
( spl18_271
<=> ! [X6,X4,X5] :
( in(sK9(set_intersection2(X4,X5),X6),X6)
| set_intersection2(X4,X5) = X6
| ~ disjoint(X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_271])]) ).
fof(f1000,plain,
( ! [X6,X4,X5] :
( in(sK9(set_intersection2(X4,X5),X6),X6)
| set_intersection2(X4,X5) = X6
| ~ disjoint(X4,X5) )
| ~ spl18_43
| ~ spl18_97 ),
inference(resolution,[],[f960,f512]) ).
fof(f4247,plain,
( spl18_270
| ~ spl18_43
| ~ spl18_97 ),
inference(avatar_split_clause,[],[f996,f959,f511,f4245]) ).
fof(f4245,plain,
( spl18_270
<=> ! [X6,X4,X5] :
( in(sK9(X4,set_intersection2(X5,X6)),X4)
| set_intersection2(X5,X6) = X4
| ~ disjoint(X5,X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_270])]) ).
fof(f996,plain,
( ! [X6,X4,X5] :
( in(sK9(X4,set_intersection2(X5,X6)),X4)
| set_intersection2(X5,X6) = X4
| ~ disjoint(X5,X6) )
| ~ spl18_43
| ~ spl18_97 ),
inference(resolution,[],[f960,f512]) ).
fof(f4243,plain,
( spl18_269
| ~ spl18_47
| ~ spl18_95 ),
inference(avatar_split_clause,[],[f941,f923,f527,f4241]) ).
fof(f4241,plain,
( spl18_269
<=> ! [X6,X7,X8] :
( ~ subset(X6,X7)
| ~ subset(X8,X7)
| set_union2(X8,X6) = set_intersection2(set_union2(X8,X6),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_269])]) ).
fof(f941,plain,
( ! [X8,X6,X7] :
( ~ subset(X6,X7)
| ~ subset(X8,X7)
| set_union2(X8,X6) = set_intersection2(set_union2(X8,X6),X7) )
| ~ spl18_47
| ~ spl18_95 ),
inference(resolution,[],[f924,f528]) ).
fof(f4239,plain,
( spl18_268
| ~ spl18_46
| ~ spl18_94 ),
inference(avatar_split_clause,[],[f927,f913,f523,f4237]) ).
fof(f4237,plain,
( spl18_268
<=> ! [X4,X5,X3] :
( ~ subset(X3,X4)
| ~ subset(X3,X5)
| set_intersection2(X5,X4) = set_union2(X3,set_intersection2(X5,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_268])]) ).
fof(f927,plain,
( ! [X3,X4,X5] :
( ~ subset(X3,X4)
| ~ subset(X3,X5)
| set_intersection2(X5,X4) = set_union2(X3,set_intersection2(X5,X4)) )
| ~ spl18_46
| ~ spl18_94 ),
inference(resolution,[],[f914,f524]) ).
fof(f4235,plain,
( spl18_267
| ~ spl18_30
| ~ spl18_211 ),
inference(avatar_split_clause,[],[f3696,f2542,f421,f4233]) ).
fof(f3696,plain,
( ! [X1] : ~ in(singleton(X1),X1)
| ~ spl18_30
| ~ spl18_211 ),
inference(resolution,[],[f2543,f422]) ).
fof(f4231,plain,
( spl18_266
| ~ spl18_30
| ~ spl18_106 ),
inference(avatar_split_clause,[],[f1014,f1011,f421,f4229]) ).
fof(f4229,plain,
( spl18_266
<=> ! [X0,X1] :
( sK11(X0,X1) = X0
| singleton(X0) = X1
| ~ in(X1,sK11(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_266])]) ).
fof(f1014,plain,
( ! [X0,X1] :
( sK11(X0,X1) = X0
| singleton(X0) = X1
| ~ in(X1,sK11(X0,X1)) )
| ~ spl18_30
| ~ spl18_106 ),
inference(resolution,[],[f1012,f422]) ).
fof(f4004,plain,
( spl18_265
| ~ spl18_70
| ~ spl18_95 ),
inference(avatar_split_clause,[],[f946,f923,f713,f4002]) ).
fof(f4002,plain,
( spl18_265
<=> ! [X24,X23,X25,X22] :
( ~ subset(X22,X23)
| ~ subset(X24,X23)
| ~ in(X25,set_union2(X24,X22))
| in(X25,X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_265])]) ).
fof(f946,plain,
( ! [X24,X22,X25,X23] :
( ~ subset(X22,X23)
| ~ subset(X24,X23)
| ~ in(X25,set_union2(X24,X22))
| in(X25,X23) )
| ~ spl18_70
| ~ spl18_95 ),
inference(resolution,[],[f924,f714]) ).
fof(f4000,plain,
( spl18_264
| ~ spl18_66
| ~ spl18_95 ),
inference(avatar_split_clause,[],[f943,f923,f658,f3998]) ).
fof(f3998,plain,
( spl18_264
<=> ! [X13,X14,X12,X15] :
( ~ subset(X12,X13)
| ~ subset(X14,X13)
| subset(X15,X13)
| ~ subset(X15,set_union2(X14,X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_264])]) ).
fof(f943,plain,
( ! [X14,X15,X12,X13] :
( ~ subset(X12,X13)
| ~ subset(X14,X13)
| subset(X15,X13)
| ~ subset(X15,set_union2(X14,X12)) )
| ~ spl18_66
| ~ spl18_95 ),
inference(resolution,[],[f924,f659]) ).
fof(f3996,plain,
( spl18_263
| ~ spl18_70
| ~ spl18_94 ),
inference(avatar_split_clause,[],[f933,f913,f713,f3994]) ).
fof(f3994,plain,
( spl18_263
<=> ! [X24,X23,X25,X22] :
( ~ subset(X22,X23)
| ~ subset(X22,X24)
| ~ in(X25,X22)
| in(X25,set_intersection2(X24,X23)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_263])]) ).
fof(f933,plain,
( ! [X24,X22,X25,X23] :
( ~ subset(X22,X23)
| ~ subset(X22,X24)
| ~ in(X25,X22)
| in(X25,set_intersection2(X24,X23)) )
| ~ spl18_70
| ~ spl18_94 ),
inference(resolution,[],[f914,f714]) ).
fof(f3992,plain,
( spl18_262
| ~ spl18_66
| ~ spl18_94 ),
inference(avatar_split_clause,[],[f930,f913,f658,f3990]) ).
fof(f3990,plain,
( spl18_262
<=> ! [X13,X14,X12,X15] :
( ~ subset(X12,X13)
| ~ subset(X12,X14)
| subset(X15,set_intersection2(X14,X13))
| ~ subset(X15,X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_262])]) ).
fof(f930,plain,
( ! [X14,X15,X12,X13] :
( ~ subset(X12,X13)
| ~ subset(X12,X14)
| subset(X15,set_intersection2(X14,X13))
| ~ subset(X15,X12) )
| ~ spl18_66
| ~ spl18_94 ),
inference(resolution,[],[f914,f659]) ).
fof(f3988,plain,
( spl18_261
| ~ spl18_47
| ~ spl18_81 ),
inference(avatar_split_clause,[],[f841,f811,f527,f3986]) ).
fof(f3986,plain,
( spl18_261
<=> ! [X6,X7,X8] :
( ~ subset(X6,X7)
| set_difference(X6,X8) = set_intersection2(set_difference(X6,X8),set_difference(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_261])]) ).
fof(f841,plain,
( ! [X8,X6,X7] :
( ~ subset(X6,X7)
| set_difference(X6,X8) = set_intersection2(set_difference(X6,X8),set_difference(X7,X8)) )
| ~ spl18_47
| ~ spl18_81 ),
inference(resolution,[],[f812,f528]) ).
fof(f3984,plain,
( spl18_260
| ~ spl18_46
| ~ spl18_81 ),
inference(avatar_split_clause,[],[f840,f811,f523,f3982]) ).
fof(f3982,plain,
( spl18_260
<=> ! [X4,X5,X3] :
( ~ subset(X3,X4)
| set_difference(X4,X5) = set_union2(set_difference(X3,X5),set_difference(X4,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_260])]) ).
fof(f840,plain,
( ! [X3,X4,X5] :
( ~ subset(X3,X4)
| set_difference(X4,X5) = set_union2(set_difference(X3,X5),set_difference(X4,X5)) )
| ~ spl18_46
| ~ spl18_81 ),
inference(resolution,[],[f812,f524]) ).
fof(f3980,plain,
( spl18_259
| ~ spl18_47
| ~ spl18_80 ),
inference(avatar_split_clause,[],[f825,f807,f527,f3978]) ).
fof(f3978,plain,
( spl18_259
<=> ! [X6,X7,X8] :
( ~ subset(X6,X7)
| set_intersection2(X6,X8) = set_intersection2(set_intersection2(X6,X8),set_intersection2(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_259])]) ).
fof(f825,plain,
( ! [X8,X6,X7] :
( ~ subset(X6,X7)
| set_intersection2(X6,X8) = set_intersection2(set_intersection2(X6,X8),set_intersection2(X7,X8)) )
| ~ spl18_47
| ~ spl18_80 ),
inference(resolution,[],[f808,f528]) ).
fof(f3976,plain,
( spl18_258
| ~ spl18_46
| ~ spl18_80 ),
inference(avatar_split_clause,[],[f824,f807,f523,f3974]) ).
fof(f3974,plain,
( spl18_258
<=> ! [X4,X5,X3] :
( ~ subset(X3,X4)
| set_intersection2(X4,X5) = set_union2(set_intersection2(X3,X5),set_intersection2(X4,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_258])]) ).
fof(f824,plain,
( ! [X3,X4,X5] :
( ~ subset(X3,X4)
| set_intersection2(X4,X5) = set_union2(set_intersection2(X3,X5),set_intersection2(X4,X5)) )
| ~ spl18_46
| ~ spl18_80 ),
inference(resolution,[],[f808,f524]) ).
fof(f3972,plain,
( spl18_257
| ~ spl18_20
| ~ spl18_211 ),
inference(avatar_split_clause,[],[f3697,f2542,f358,f3970]) ).
fof(f3970,plain,
( spl18_257
<=> ! [X2] : ~ empty(singleton(X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_257])]) ).
fof(f3697,plain,
( ! [X2] : ~ empty(singleton(X2))
| ~ spl18_20
| ~ spl18_211 ),
inference(resolution,[],[f2543,f359]) ).
fof(f3968,plain,
( spl18_256
| ~ spl18_30
| ~ spl18_97 ),
inference(avatar_split_clause,[],[f998,f959,f421,f3966]) ).
fof(f3966,plain,
( spl18_256
<=> ! [X0,X1] :
( in(sK9(X0,X1),X1)
| X0 = X1
| ~ in(X0,sK9(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_256])]) ).
fof(f998,plain,
( ! [X0,X1] :
( in(sK9(X0,X1),X1)
| X0 = X1
| ~ in(X0,sK9(X0,X1)) )
| ~ spl18_30
| ~ spl18_97 ),
inference(resolution,[],[f960,f422]) ).
fof(f3964,plain,
( spl18_255
| ~ spl18_30
| ~ spl18_97 ),
inference(avatar_split_clause,[],[f994,f959,f421,f3962]) ).
fof(f3962,plain,
( spl18_255
<=> ! [X0,X1] :
( in(sK9(X0,X1),X0)
| X0 = X1
| ~ in(X1,sK9(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_255])]) ).
fof(f994,plain,
( ! [X0,X1] :
( in(sK9(X0,X1),X0)
| X0 = X1
| ~ in(X1,sK9(X0,X1)) )
| ~ spl18_30
| ~ spl18_97 ),
inference(resolution,[],[f960,f422]) ).
fof(f3669,plain,
( spl18_254
| ~ spl18_60
| ~ spl18_95 ),
inference(avatar_split_clause,[],[f952,f923,f634,f3667]) ).
fof(f952,plain,
( ! [X10,X11,X12] :
( subset(set_union2(X10,X11),X12)
| ~ subset(set_difference(X11,X10),X12)
| ~ subset(X10,X12) )
| ~ spl18_60
| ~ spl18_95 ),
inference(superposition,[],[f924,f635]) ).
fof(f3665,plain,
( spl18_253
| ~ spl18_54
| ~ spl18_95 ),
inference(avatar_split_clause,[],[f942,f923,f587,f3663]) ).
fof(f3663,plain,
( spl18_253
<=> ! [X9,X11,X10] :
( ~ subset(X9,X10)
| ~ subset(X11,X10)
| sK17 = set_difference(set_union2(X11,X9),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_253])]) ).
fof(f942,plain,
( ! [X10,X11,X9] :
( ~ subset(X9,X10)
| ~ subset(X11,X10)
| sK17 = set_difference(set_union2(X11,X9),X10) )
| ~ spl18_54
| ~ spl18_95 ),
inference(resolution,[],[f924,f588]) ).
fof(f3661,plain,
( spl18_252
| ~ spl18_46
| ~ spl18_95 ),
inference(avatar_split_clause,[],[f940,f923,f523,f3659]) ).
fof(f940,plain,
( ! [X3,X4,X5] :
( ~ subset(X3,X4)
| ~ subset(X5,X4)
| set_union2(set_union2(X5,X3),X4) = X4 )
| ~ spl18_46
| ~ spl18_95 ),
inference(resolution,[],[f924,f524]) ).
fof(f3657,plain,
( spl18_251
| ~ spl18_54
| ~ spl18_94 ),
inference(avatar_split_clause,[],[f929,f913,f587,f3655]) ).
fof(f3655,plain,
( spl18_251
<=> ! [X9,X11,X10] :
( ~ subset(X9,X10)
| ~ subset(X9,X11)
| sK17 = set_difference(X9,set_intersection2(X11,X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_251])]) ).
fof(f929,plain,
( ! [X10,X11,X9] :
( ~ subset(X9,X10)
| ~ subset(X9,X11)
| sK17 = set_difference(X9,set_intersection2(X11,X10)) )
| ~ spl18_54
| ~ spl18_94 ),
inference(resolution,[],[f914,f588]) ).
fof(f3653,plain,
( spl18_250
| ~ spl18_47
| ~ spl18_94 ),
inference(avatar_split_clause,[],[f928,f913,f527,f3651]) ).
fof(f3651,plain,
( spl18_250
<=> ! [X6,X7,X8] :
( ~ subset(X6,X7)
| ~ subset(X6,X8)
| set_intersection2(X6,set_intersection2(X8,X7)) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_250])]) ).
fof(f928,plain,
( ! [X8,X6,X7] :
( ~ subset(X6,X7)
| ~ subset(X6,X8)
| set_intersection2(X6,set_intersection2(X8,X7)) = X6 )
| ~ spl18_47
| ~ spl18_94 ),
inference(resolution,[],[f914,f528]) ).
fof(f3649,plain,
( spl18_249
| ~ spl18_70
| ~ spl18_81 ),
inference(avatar_split_clause,[],[f846,f811,f713,f3647]) ).
fof(f3647,plain,
( spl18_249
<=> ! [X24,X23,X25,X22] :
( ~ subset(X22,X23)
| ~ in(X24,set_difference(X22,X25))
| in(X24,set_difference(X23,X25)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_249])]) ).
fof(f846,plain,
( ! [X24,X22,X25,X23] :
( ~ subset(X22,X23)
| ~ in(X24,set_difference(X22,X25))
| in(X24,set_difference(X23,X25)) )
| ~ spl18_70
| ~ spl18_81 ),
inference(resolution,[],[f812,f714]) ).
fof(f3645,plain,
( spl18_248
| ~ spl18_66
| ~ spl18_81 ),
inference(avatar_split_clause,[],[f843,f811,f658,f3643]) ).
fof(f3643,plain,
( spl18_248
<=> ! [X13,X14,X12,X15] :
( ~ subset(X12,X13)
| subset(X14,set_difference(X13,X15))
| ~ subset(X14,set_difference(X12,X15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_248])]) ).
fof(f843,plain,
( ! [X14,X15,X12,X13] :
( ~ subset(X12,X13)
| subset(X14,set_difference(X13,X15))
| ~ subset(X14,set_difference(X12,X15)) )
| ~ spl18_66
| ~ spl18_81 ),
inference(resolution,[],[f812,f659]) ).
fof(f3641,plain,
( spl18_247
| ~ spl18_70
| ~ spl18_80 ),
inference(avatar_split_clause,[],[f830,f807,f713,f3639]) ).
fof(f3639,plain,
( spl18_247
<=> ! [X24,X23,X25,X22] :
( ~ subset(X22,X23)
| ~ in(X24,set_intersection2(X22,X25))
| in(X24,set_intersection2(X23,X25)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_247])]) ).
fof(f830,plain,
( ! [X24,X22,X25,X23] :
( ~ subset(X22,X23)
| ~ in(X24,set_intersection2(X22,X25))
| in(X24,set_intersection2(X23,X25)) )
| ~ spl18_70
| ~ spl18_80 ),
inference(resolution,[],[f808,f714]) ).
fof(f3637,plain,
( spl18_246
| ~ spl18_66
| ~ spl18_80 ),
inference(avatar_split_clause,[],[f827,f807,f658,f3635]) ).
fof(f3635,plain,
( spl18_246
<=> ! [X13,X14,X12,X15] :
( ~ subset(X12,X13)
| subset(X14,set_intersection2(X13,X15))
| ~ subset(X14,set_intersection2(X12,X15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_246])]) ).
fof(f827,plain,
( ! [X14,X15,X12,X13] :
( ~ subset(X12,X13)
| subset(X14,set_intersection2(X13,X15))
| ~ subset(X14,set_intersection2(X12,X15)) )
| ~ spl18_66
| ~ spl18_80 ),
inference(resolution,[],[f808,f659]) ).
fof(f3541,plain,
( spl18_245
| ~ spl18_47
| ~ spl18_122
| ~ spl18_244 ),
inference(avatar_split_clause,[],[f3537,f3534,f1155,f527,f3539]) ).
fof(f3534,plain,
( spl18_244
<=> ! [X0,X1] : set_difference(set_union2(X0,X1),set_difference(X0,X1)) = set_intersection2(X1,set_union2(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_244])]) ).
fof(f3537,plain,
( ! [X0,X1] : set_difference(set_union2(X0,X1),set_difference(X0,X1)) = X1
| ~ spl18_47
| ~ spl18_122
| ~ spl18_244 ),
inference(forward_demodulation,[],[f3535,f1223]) ).
fof(f3535,plain,
( ! [X0,X1] : set_difference(set_union2(X0,X1),set_difference(X0,X1)) = set_intersection2(X1,set_union2(X0,X1))
| ~ spl18_244 ),
inference(avatar_component_clause,[],[f3534]) ).
fof(f3536,plain,
( spl18_244
| ~ spl18_40
| ~ spl18_62
| ~ spl18_63 ),
inference(avatar_split_clause,[],[f691,f646,f642,f471,f3534]) ).
fof(f691,plain,
( ! [X0,X1] : set_difference(set_union2(X0,X1),set_difference(X0,X1)) = set_intersection2(X1,set_union2(X0,X1))
| ~ spl18_40
| ~ spl18_62
| ~ spl18_63 ),
inference(forward_demodulation,[],[f684,f472]) ).
fof(f684,plain,
( ! [X0,X1] : set_intersection2(set_union2(X0,X1),X1) = set_difference(set_union2(X0,X1),set_difference(X0,X1))
| ~ spl18_62
| ~ spl18_63 ),
inference(superposition,[],[f643,f647]) ).
fof(f3477,plain,
( spl18_243
| ~ spl18_40
| ~ spl18_62
| ~ spl18_142
| ~ spl18_188
| ~ spl18_242 ),
inference(avatar_split_clause,[],[f3473,f3470,f2076,f1437,f642,f471,f3475]) ).
fof(f3470,plain,
( spl18_242
<=> ! [X6,X7] : set_difference(X6,set_difference(X7,X6)) = set_difference(set_union2(X6,X7),set_difference(X7,X6)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_242])]) ).
fof(f3473,plain,
( ! [X6,X7] : set_difference(X6,set_difference(X7,X6)) = X6
| ~ spl18_40
| ~ spl18_62
| ~ spl18_142
| ~ spl18_188
| ~ spl18_242 ),
inference(forward_demodulation,[],[f3471,f2223]) ).
fof(f3471,plain,
( ! [X6,X7] : set_difference(X6,set_difference(X7,X6)) = set_difference(set_union2(X6,X7),set_difference(X7,X6))
| ~ spl18_242 ),
inference(avatar_component_clause,[],[f3470]) ).
fof(f3472,plain,
( spl18_242
| ~ spl18_60
| ~ spl18_63 ),
inference(avatar_split_clause,[],[f682,f646,f634,f3470]) ).
fof(f682,plain,
( ! [X6,X7] : set_difference(X6,set_difference(X7,X6)) = set_difference(set_union2(X6,X7),set_difference(X7,X6))
| ~ spl18_60
| ~ spl18_63 ),
inference(superposition,[],[f647,f635]) ).
fof(f3401,plain,
( spl18_241
| ~ spl18_39
| ~ spl18_141
| ~ spl18_240 ),
inference(avatar_split_clause,[],[f3397,f3394,f1433,f467,f3399]) ).
fof(f3394,plain,
( spl18_240
<=> ! [X0,X1] : set_union2(set_difference(X0,X1),set_intersection2(X0,X1)) = set_union2(X0,set_difference(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_240])]) ).
fof(f3397,plain,
( ! [X0,X1] : set_union2(set_difference(X0,X1),set_intersection2(X0,X1)) = X0
| ~ spl18_39
| ~ spl18_141
| ~ spl18_240 ),
inference(forward_demodulation,[],[f3395,f1495]) ).
fof(f3395,plain,
( ! [X0,X1] : set_union2(set_difference(X0,X1),set_intersection2(X0,X1)) = set_union2(X0,set_difference(X0,X1))
| ~ spl18_240 ),
inference(avatar_component_clause,[],[f3394]) ).
fof(f3396,plain,
( spl18_240
| ~ spl18_39
| ~ spl18_60
| ~ spl18_62 ),
inference(avatar_split_clause,[],[f678,f642,f634,f467,f3394]) ).
fof(f678,plain,
( ! [X0,X1] : set_union2(set_difference(X0,X1),set_intersection2(X0,X1)) = set_union2(X0,set_difference(X0,X1))
| ~ spl18_39
| ~ spl18_60
| ~ spl18_62 ),
inference(forward_demodulation,[],[f668,f468]) ).
fof(f668,plain,
( ! [X0,X1] : set_union2(set_difference(X0,X1),X0) = set_union2(set_difference(X0,X1),set_intersection2(X0,X1))
| ~ spl18_60
| ~ spl18_62 ),
inference(superposition,[],[f635,f643]) ).
fof(f3324,plain,
( spl18_239
| ~ spl18_20
| ~ spl18_111 ),
inference(avatar_split_clause,[],[f1074,f1035,f358,f3322]) ).
fof(f1074,plain,
( ! [X3,X4,X5] :
( in(sK15(X3,X4,X5),X5)
| sP3(X3,X4,X5)
| ~ empty(X4) )
| ~ spl18_20
| ~ spl18_111 ),
inference(resolution,[],[f1036,f359]) ).
fof(f3320,plain,
( spl18_238
| ~ spl18_20
| ~ spl18_111 ),
inference(avatar_split_clause,[],[f1070,f1035,f358,f3318]) ).
fof(f1070,plain,
( ! [X3,X4,X5] :
( in(sK15(X3,X4,X5),X4)
| sP3(X3,X4,X5)
| ~ empty(X5) )
| ~ spl18_20
| ~ spl18_111 ),
inference(resolution,[],[f1036,f359]) ).
fof(f3316,plain,
( spl18_237
| ~ spl18_20
| ~ spl18_108 ),
inference(avatar_split_clause,[],[f1065,f1023,f358,f3314]) ).
fof(f1065,plain,
( ! [X3,X4,X5] :
( in(sK13(X3,X4,X5),X5)
| sP1(X3,X4,X5)
| ~ empty(X3) )
| ~ spl18_20
| ~ spl18_108 ),
inference(resolution,[],[f1024,f359]) ).
fof(f3312,plain,
( spl18_236
| ~ spl18_20
| ~ spl18_108 ),
inference(avatar_split_clause,[],[f1061,f1023,f358,f3310]) ).
fof(f1061,plain,
( ! [X3,X4,X5] :
( in(sK13(X3,X4,X5),X3)
| sP1(X3,X4,X5)
| ~ empty(X5) )
| ~ spl18_20
| ~ spl18_108 ),
inference(resolution,[],[f1024,f359]) ).
fof(f3308,plain,
( spl18_235
| ~ spl18_20
| ~ spl18_107 ),
inference(avatar_split_clause,[],[f1047,f1019,f358,f3306]) ).
fof(f1047,plain,
( ! [X3,X4,X5] :
( in(sK13(X3,X4,X5),X5)
| sP1(X3,X4,X5)
| ~ empty(X4) )
| ~ spl18_20
| ~ spl18_107 ),
inference(resolution,[],[f1020,f359]) ).
fof(f3300,plain,
( spl18_234
| ~ spl18_20
| ~ spl18_107 ),
inference(avatar_split_clause,[],[f1043,f1019,f358,f3298]) ).
fof(f1043,plain,
( ! [X3,X4,X5] :
( in(sK13(X3,X4,X5),X4)
| sP1(X3,X4,X5)
| ~ empty(X5) )
| ~ spl18_20
| ~ spl18_107 ),
inference(resolution,[],[f1020,f359]) ).
fof(f2997,plain,
( spl18_233
| ~ spl18_63
| ~ spl18_81 ),
inference(avatar_split_clause,[],[f854,f811,f646,f2995]) ).
fof(f854,plain,
( ! [X8,X9,X7] :
( subset(set_difference(X9,X8),set_difference(X7,X8))
| ~ subset(X9,set_union2(X7,X8)) )
| ~ spl18_63
| ~ spl18_81 ),
inference(superposition,[],[f812,f647]) ).
fof(f2993,plain,
( spl18_232
| ~ spl18_62
| ~ spl18_81 ),
inference(avatar_split_clause,[],[f853,f811,f642,f2991]) ).
fof(f2991,plain,
( spl18_232
<=> ! [X6,X4,X5] :
( subset(set_difference(X6,set_difference(X4,X5)),set_intersection2(X4,X5))
| ~ subset(X6,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_232])]) ).
fof(f853,plain,
( ! [X6,X4,X5] :
( subset(set_difference(X6,set_difference(X4,X5)),set_intersection2(X4,X5))
| ~ subset(X6,X4) )
| ~ spl18_62
| ~ spl18_81 ),
inference(superposition,[],[f812,f643]) ).
fof(f2985,plain,
( spl18_231
| ~ spl18_63
| ~ spl18_81 ),
inference(avatar_split_clause,[],[f850,f811,f646,f2983]) ).
fof(f850,plain,
( ! [X8,X9,X7] :
( subset(set_difference(X7,X8),set_difference(X9,X8))
| ~ subset(set_union2(X7,X8),X9) )
| ~ spl18_63
| ~ spl18_81 ),
inference(superposition,[],[f812,f647]) ).
fof(f2981,plain,
( spl18_230
| ~ spl18_62
| ~ spl18_81 ),
inference(avatar_split_clause,[],[f849,f811,f642,f2979]) ).
fof(f2979,plain,
( spl18_230
<=> ! [X6,X4,X5] :
( subset(set_intersection2(X4,X5),set_difference(X6,set_difference(X4,X5)))
| ~ subset(X4,X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_230])]) ).
fof(f849,plain,
( ! [X6,X4,X5] :
( subset(set_intersection2(X4,X5),set_difference(X6,set_difference(X4,X5)))
| ~ subset(X4,X6) )
| ~ spl18_62
| ~ spl18_81 ),
inference(superposition,[],[f812,f643]) ).
fof(f2977,plain,
( spl18_229
| ~ spl18_54
| ~ spl18_81 ),
inference(avatar_split_clause,[],[f842,f811,f587,f2975]) ).
fof(f2975,plain,
( spl18_229
<=> ! [X9,X11,X10] :
( ~ subset(X9,X10)
| sK17 = set_difference(set_difference(X9,X11),set_difference(X10,X11)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_229])]) ).
fof(f842,plain,
( ! [X10,X11,X9] :
( ~ subset(X9,X10)
| sK17 = set_difference(set_difference(X9,X11),set_difference(X10,X11)) )
| ~ spl18_54
| ~ spl18_81 ),
inference(resolution,[],[f812,f588]) ).
fof(f2973,plain,
( spl18_228
| ~ spl18_54
| ~ spl18_80 ),
inference(avatar_split_clause,[],[f826,f807,f587,f2971]) ).
fof(f2971,plain,
( spl18_228
<=> ! [X9,X11,X10] :
( ~ subset(X9,X10)
| sK17 = set_difference(set_intersection2(X9,X11),set_intersection2(X10,X11)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_228])]) ).
fof(f826,plain,
( ! [X10,X11,X9] :
( ~ subset(X9,X10)
| sK17 = set_difference(set_intersection2(X9,X11),set_intersection2(X10,X11)) )
| ~ spl18_54
| ~ spl18_80 ),
inference(resolution,[],[f808,f588]) ).
fof(f2969,plain,
( spl18_227
| ~ spl18_49
| ~ spl18_63 ),
inference(avatar_split_clause,[],[f687,f646,f535,f2967]) ).
fof(f2967,plain,
( spl18_227
<=> ! [X6,X7] :
( set_union2(X6,X7) != set_difference(X6,X7)
| disjoint(set_union2(X6,X7),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_227])]) ).
fof(f687,plain,
( ! [X6,X7] :
( set_union2(X6,X7) != set_difference(X6,X7)
| disjoint(set_union2(X6,X7),X7) )
| ~ spl18_49
| ~ spl18_63 ),
inference(superposition,[],[f536,f647]) ).
fof(f2961,plain,
( spl18_226
| ~ spl18_20
| ~ spl18_106 ),
inference(avatar_split_clause,[],[f1015,f1011,f358,f2959]) ).
fof(f2959,plain,
( spl18_226
<=> ! [X2,X3] :
( sK11(X2,X3) = X2
| singleton(X2) = X3
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_226])]) ).
fof(f1015,plain,
( ! [X2,X3] :
( sK11(X2,X3) = X2
| singleton(X2) = X3
| ~ empty(X3) )
| ~ spl18_20
| ~ spl18_106 ),
inference(resolution,[],[f1012,f359]) ).
fof(f2840,plain,
( spl18_225
| ~ spl18_24
| ~ spl18_95 ),
inference(avatar_split_clause,[],[f947,f923,f385,f2838]) ).
fof(f385,plain,
( spl18_24
<=> ! [X0] :
( ~ subset(X0,sK17)
| sK17 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_24])]) ).
fof(f947,plain,
( ! [X26,X27] :
( ~ subset(X26,sK17)
| ~ subset(X27,sK17)
| sK17 = set_union2(X27,X26) )
| ~ spl18_24
| ~ spl18_95 ),
inference(resolution,[],[f924,f386]) ).
fof(f386,plain,
( ! [X0] :
( ~ subset(X0,sK17)
| sK17 = X0 )
| ~ spl18_24 ),
inference(avatar_component_clause,[],[f385]) ).
fof(f2836,plain,
( spl18_224
| ~ spl18_23
| ~ spl18_95 ),
inference(avatar_split_clause,[],[f939,f923,f381,f2834]) ).
fof(f2834,plain,
( spl18_224
<=> ! [X2,X0,X1] :
( ~ subset(X0,X1)
| ~ subset(X2,X1)
| ~ proper_subset(X1,set_union2(X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_224])]) ).
fof(f939,plain,
( ! [X2,X0,X1] :
( ~ subset(X0,X1)
| ~ subset(X2,X1)
| ~ proper_subset(X1,set_union2(X2,X0)) )
| ~ spl18_23
| ~ spl18_95 ),
inference(resolution,[],[f924,f382]) ).
fof(f2832,plain,
( spl18_223
| ~ spl18_23
| ~ spl18_94 ),
inference(avatar_split_clause,[],[f926,f913,f381,f2830]) ).
fof(f2830,plain,
( spl18_223
<=> ! [X2,X0,X1] :
( ~ subset(X0,X1)
| ~ subset(X0,X2)
| ~ proper_subset(set_intersection2(X2,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_223])]) ).
fof(f926,plain,
( ! [X2,X0,X1] :
( ~ subset(X0,X1)
| ~ subset(X0,X2)
| ~ proper_subset(set_intersection2(X2,X1),X0) )
| ~ spl18_23
| ~ spl18_94 ),
inference(resolution,[],[f914,f382]) ).
fof(f2828,plain,
( spl18_222
| ~ spl18_63
| ~ spl18_77 ),
inference(avatar_split_clause,[],[f797,f745,f646,f2826]) ).
fof(f2826,plain,
( spl18_222
<=> ! [X9,X8,X7] :
( set_difference(X7,X8) != X9
| sP3(X8,set_union2(X7,X8),X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_222])]) ).
fof(f797,plain,
( ! [X8,X9,X7] :
( set_difference(X7,X8) != X9
| sP3(X8,set_union2(X7,X8),X9) )
| ~ spl18_63
| ~ spl18_77 ),
inference(superposition,[],[f746,f647]) ).
fof(f2824,plain,
( spl18_221
| ~ spl18_62
| ~ spl18_77 ),
inference(avatar_split_clause,[],[f796,f745,f642,f2822]) ).
fof(f2822,plain,
( spl18_221
<=> ! [X6,X4,X5] :
( set_intersection2(X4,X5) != X6
| sP3(set_difference(X4,X5),X4,X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_221])]) ).
fof(f796,plain,
( ! [X6,X4,X5] :
( set_intersection2(X4,X5) != X6
| sP3(set_difference(X4,X5),X4,X6) )
| ~ spl18_62
| ~ spl18_77 ),
inference(superposition,[],[f746,f643]) ).
fof(f2820,plain,
( spl18_220
| ~ spl18_60
| ~ spl18_75 ),
inference(avatar_split_clause,[],[f787,f733,f634,f2818]) ).
fof(f2818,plain,
( spl18_220
<=> ! [X11,X12,X10] :
( set_union2(X10,X11) != X12
| sP2(set_difference(X11,X10),X10,X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_220])]) ).
fof(f787,plain,
( ! [X10,X11,X12] :
( set_union2(X10,X11) != X12
| sP2(set_difference(X11,X10),X10,X12) )
| ~ spl18_60
| ~ spl18_75 ),
inference(superposition,[],[f734,f635]) ).
fof(f2772,plain,
( spl18_219
| ~ spl18_40
| ~ spl18_187
| ~ spl18_218 ),
inference(avatar_split_clause,[],[f2768,f2765,f2072,f471,f2770]) ).
fof(f2765,plain,
( spl18_218
<=> ! [X2,X3] : set_intersection2(X2,set_difference(X2,X3)) = set_difference(X2,set_intersection2(X2,X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_218])]) ).
fof(f2768,plain,
( ! [X2,X3] : set_difference(X2,X3) = set_difference(X2,set_intersection2(X2,X3))
| ~ spl18_40
| ~ spl18_187
| ~ spl18_218 ),
inference(forward_demodulation,[],[f2766,f2161]) ).
fof(f2766,plain,
( ! [X2,X3] : set_intersection2(X2,set_difference(X2,X3)) = set_difference(X2,set_intersection2(X2,X3))
| ~ spl18_218 ),
inference(avatar_component_clause,[],[f2765]) ).
fof(f2767,plain,
( spl18_218
| ~ spl18_62 ),
inference(avatar_split_clause,[],[f666,f642,f2765]) ).
fof(f666,plain,
( ! [X2,X3] : set_intersection2(X2,set_difference(X2,X3)) = set_difference(X2,set_intersection2(X2,X3))
| ~ spl18_62 ),
inference(superposition,[],[f643,f643]) ).
fof(f2699,plain,
( spl18_217
| ~ spl18_111
| ~ spl18_112 ),
inference(avatar_split_clause,[],[f1080,f1039,f1035,f2697]) ).
fof(f1039,plain,
( spl18_112
<=> ! [X2,X0,X1] :
( sP3(X0,X1,X2)
| ~ in(sK15(X0,X1,X2),X0)
| in(sK15(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_112])]) ).
fof(f1080,plain,
( ! [X2,X3] :
( sP3(X2,X2,X3)
| in(sK15(X2,X2,X3),X3) )
| ~ spl18_111
| ~ spl18_112 ),
inference(duplicate_literal_removal,[],[f1079]) ).
fof(f1079,plain,
( ! [X2,X3] :
( sP3(X2,X2,X3)
| in(sK15(X2,X2,X3),X3)
| in(sK15(X2,X2,X3),X3)
| sP3(X2,X2,X3) )
| ~ spl18_111
| ~ spl18_112 ),
inference(resolution,[],[f1040,f1036]) ).
fof(f1040,plain,
( ! [X2,X0,X1] :
( ~ in(sK15(X0,X1,X2),X0)
| sP3(X0,X1,X2)
| in(sK15(X0,X1,X2),X2) )
| ~ spl18_112 ),
inference(avatar_component_clause,[],[f1039]) ).
fof(f2695,plain,
( spl18_216
| ~ spl18_111 ),
inference(avatar_split_clause,[],[f1077,f1035,f2693]) ).
fof(f1077,plain,
( ! [X0,X1] :
( in(sK15(X0,X1,X1),X1)
| sP3(X0,X1,X1) )
| ~ spl18_111 ),
inference(factoring,[],[f1036]) ).
fof(f2686,plain,
( spl18_215
| ~ spl18_108 ),
inference(avatar_split_clause,[],[f1068,f1023,f2684]) ).
fof(f1068,plain,
( ! [X0,X1] :
( in(sK13(X0,X1,X0),X0)
| sP1(X0,X1,X0) )
| ~ spl18_108 ),
inference(factoring,[],[f1024]) ).
fof(f2682,plain,
( spl18_214
| ~ spl18_107 ),
inference(avatar_split_clause,[],[f1050,f1019,f2680]) ).
fof(f1050,plain,
( ! [X0,X1] :
( in(sK13(X0,X1,X1),X1)
| sP1(X0,X1,X1) )
| ~ spl18_107 ),
inference(factoring,[],[f1020]) ).
fof(f2678,plain,
( spl18_213
| ~ spl18_20
| ~ spl18_97 ),
inference(avatar_split_clause,[],[f999,f959,f358,f2676]) ).
fof(f999,plain,
( ! [X2,X3] :
( in(sK9(X2,X3),X3)
| X2 = X3
| ~ empty(X2) )
| ~ spl18_20
| ~ spl18_97 ),
inference(resolution,[],[f960,f359]) ).
fof(f2674,plain,
( spl18_212
| ~ spl18_20
| ~ spl18_97 ),
inference(avatar_split_clause,[],[f995,f959,f358,f2672]) ).
fof(f995,plain,
( ! [X2,X3] :
( in(sK9(X2,X3),X2)
| X2 = X3
| ~ empty(X3) )
| ~ spl18_20
| ~ spl18_97 ),
inference(resolution,[],[f960,f359]) ).
fof(f2544,plain,
( spl18_211
| ~ spl18_158 ),
inference(avatar_split_clause,[],[f1724,f1686,f2542]) ).
fof(f1686,plain,
( spl18_158
<=> ! [X0,X1] :
( X0 != X1
| in(X1,singleton(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_158])]) ).
fof(f1724,plain,
( ! [X0] : in(X0,singleton(X0))
| ~ spl18_158 ),
inference(equality_resolution,[],[f1687]) ).
fof(f1687,plain,
( ! [X0,X1] :
( X0 != X1
| in(X1,singleton(X0)) )
| ~ spl18_158 ),
inference(avatar_component_clause,[],[f1686]) ).
fof(f2378,plain,
( spl18_210
| ~ spl18_23
| ~ spl18_81 ),
inference(avatar_split_clause,[],[f839,f811,f381,f2376]) ).
fof(f839,plain,
( ! [X2,X0,X1] :
( ~ subset(X0,X1)
| ~ proper_subset(set_difference(X1,X2),set_difference(X0,X2)) )
| ~ spl18_23
| ~ spl18_81 ),
inference(resolution,[],[f812,f382]) ).
fof(f2374,plain,
( spl18_209
| ~ spl18_14
| ~ spl18_83
| ~ spl18_139 ),
inference(avatar_split_clause,[],[f1427,f1385,f864,f334,f2372]) ).
fof(f2372,plain,
( spl18_209
<=> ! [X6] : sP3(X6,sK17,sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_209])]) ).
fof(f1427,plain,
( ! [X6] : sP3(X6,sK17,sK17)
| ~ spl18_14
| ~ spl18_83
| ~ spl18_139 ),
inference(forward_demodulation,[],[f1424,f866]) ).
fof(f1424,plain,
( ! [X6] : sP3(X6,empty_set,empty_set)
| ~ spl18_14
| ~ spl18_139 ),
inference(superposition,[],[f1386,f335]) ).
fof(f2370,plain,
( spl18_208
| ~ spl18_40
| ~ spl18_80 ),
inference(avatar_split_clause,[],[f837,f807,f471,f2368]) ).
fof(f837,plain,
( ! [X6,X4,X5] :
( subset(set_intersection2(X6,X5),set_intersection2(X5,X4))
| ~ subset(X6,X4) )
| ~ spl18_40
| ~ spl18_80 ),
inference(superposition,[],[f808,f472]) ).
fof(f2366,plain,
( spl18_207
| ~ spl18_40
| ~ spl18_80 ),
inference(avatar_split_clause,[],[f833,f807,f471,f2364]) ).
fof(f833,plain,
( ! [X6,X4,X5] :
( subset(set_intersection2(X5,X4),set_intersection2(X6,X5))
| ~ subset(X4,X6) )
| ~ spl18_40
| ~ spl18_80 ),
inference(superposition,[],[f808,f472]) ).
fof(f2362,plain,
( spl18_206
| ~ spl18_23
| ~ spl18_80 ),
inference(avatar_split_clause,[],[f823,f807,f381,f2360]) ).
fof(f823,plain,
( ! [X2,X0,X1] :
( ~ subset(X0,X1)
| ~ proper_subset(set_intersection2(X1,X2),set_intersection2(X0,X2)) )
| ~ spl18_23
| ~ spl18_80 ),
inference(resolution,[],[f808,f382]) ).
fof(f2358,plain,
( spl18_205
| ~ spl18_40
| ~ spl18_79 ),
inference(avatar_split_clause,[],[f819,f803,f471,f2356]) ).
fof(f819,plain,
( ! [X2,X3] :
( in(sK6(X2,X3),set_intersection2(X3,X2))
| disjoint(X2,X3) )
| ~ spl18_40
| ~ spl18_79 ),
inference(superposition,[],[f804,f472]) ).
fof(f2354,plain,
( spl18_204
| ~ spl18_30
| ~ spl18_79 ),
inference(avatar_split_clause,[],[f815,f803,f421,f2352]) ).
fof(f815,plain,
( ! [X2,X3] :
( disjoint(X2,X3)
| ~ in(set_intersection2(X2,X3),sK6(X2,X3)) )
| ~ spl18_30
| ~ spl18_79 ),
inference(resolution,[],[f804,f422]) ).
fof(f2350,plain,
( spl18_203
| ~ spl18_10
| ~ spl18_69 ),
inference(avatar_split_clause,[],[f763,f709,f318,f2348]) ).
fof(f2348,plain,
( spl18_203
<=> ! [X6,X7] :
( set_union2(X6,X7) = X6
| proper_subset(X6,set_union2(X6,X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_203])]) ).
fof(f318,plain,
( spl18_10
<=> ! [X0,X1] : subset(X0,set_union2(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_10])]) ).
fof(f763,plain,
( ! [X6,X7] :
( set_union2(X6,X7) = X6
| proper_subset(X6,set_union2(X6,X7)) )
| ~ spl18_10
| ~ spl18_69 ),
inference(resolution,[],[f710,f319]) ).
fof(f319,plain,
( ! [X0,X1] : subset(X0,set_union2(X0,X1))
| ~ spl18_10 ),
inference(avatar_component_clause,[],[f318]) ).
fof(f2346,plain,
( spl18_202
| ~ spl18_12
| ~ spl18_69 ),
inference(avatar_split_clause,[],[f762,f709,f326,f2344]) ).
fof(f2344,plain,
( spl18_202
<=> ! [X4,X5] :
( set_difference(X4,X5) = X4
| proper_subset(set_difference(X4,X5),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_202])]) ).
fof(f762,plain,
( ! [X4,X5] :
( set_difference(X4,X5) = X4
| proper_subset(set_difference(X4,X5),X4) )
| ~ spl18_12
| ~ spl18_69 ),
inference(resolution,[],[f710,f327]) ).
fof(f2342,plain,
( spl18_201
| ~ spl18_11
| ~ spl18_69 ),
inference(avatar_split_clause,[],[f760,f709,f322,f2340]) ).
fof(f2340,plain,
( spl18_201
<=> ! [X2,X1] :
( set_intersection2(X1,X2) = X1
| proper_subset(set_intersection2(X1,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_201])]) ).
fof(f760,plain,
( ! [X2,X1] :
( set_intersection2(X1,X2) = X1
| proper_subset(set_intersection2(X1,X2),X1) )
| ~ spl18_11
| ~ spl18_69 ),
inference(resolution,[],[f710,f323]) ).
fof(f2338,plain,
( spl18_200
| ~ spl18_10
| ~ spl18_68 ),
inference(avatar_split_clause,[],[f756,f705,f318,f2336]) ).
fof(f756,plain,
( ! [X6,X7] :
( set_union2(X6,X7) = X6
| ~ subset(set_union2(X6,X7),X6) )
| ~ spl18_10
| ~ spl18_68 ),
inference(resolution,[],[f706,f319]) ).
fof(f2334,plain,
( spl18_199
| ~ spl18_12
| ~ spl18_68 ),
inference(avatar_split_clause,[],[f755,f705,f326,f2332]) ).
fof(f2332,plain,
( spl18_199
<=> ! [X4,X5] :
( set_difference(X4,X5) = X4
| ~ subset(X4,set_difference(X4,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_199])]) ).
fof(f755,plain,
( ! [X4,X5] :
( set_difference(X4,X5) = X4
| ~ subset(X4,set_difference(X4,X5)) )
| ~ spl18_12
| ~ spl18_68 ),
inference(resolution,[],[f706,f327]) ).
fof(f2330,plain,
( spl18_198
| ~ spl18_16
| ~ spl18_83
| ~ spl18_139 ),
inference(avatar_split_clause,[],[f1426,f1385,f864,f342,f2328]) ).
fof(f2328,plain,
( spl18_198
<=> ! [X0] : sP3(sK17,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_198])]) ).
fof(f342,plain,
( spl18_16
<=> ! [X0] : set_difference(X0,empty_set) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl18_16])]) ).
fof(f1426,plain,
( ! [X0] : sP3(sK17,X0,X0)
| ~ spl18_16
| ~ spl18_83
| ~ spl18_139 ),
inference(forward_demodulation,[],[f1420,f866]) ).
fof(f1420,plain,
( ! [X0] : sP3(empty_set,X0,X0)
| ~ spl18_16
| ~ spl18_139 ),
inference(superposition,[],[f1386,f343]) ).
fof(f343,plain,
( ! [X0] : set_difference(X0,empty_set) = X0
| ~ spl18_16 ),
inference(avatar_component_clause,[],[f342]) ).
fof(f2326,plain,
( spl18_197
| ~ spl18_11
| ~ spl18_68 ),
inference(avatar_split_clause,[],[f753,f705,f322,f2324]) ).
fof(f2324,plain,
( spl18_197
<=> ! [X2,X1] :
( set_intersection2(X1,X2) = X1
| ~ subset(X1,set_intersection2(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_197])]) ).
fof(f753,plain,
( ! [X2,X1] :
( set_intersection2(X1,X2) = X1
| ~ subset(X1,set_intersection2(X1,X2)) )
| ~ spl18_11
| ~ spl18_68 ),
inference(resolution,[],[f706,f323]) ).
fof(f2322,plain,
( spl18_196
| ~ spl18_53
| ~ spl18_63 ),
inference(avatar_split_clause,[],[f686,f646,f583,f2320]) ).
fof(f686,plain,
( ! [X4,X5] :
( sK17 != set_difference(X4,X5)
| subset(set_union2(X4,X5),X5) )
| ~ spl18_53
| ~ spl18_63 ),
inference(superposition,[],[f584,f647]) ).
fof(f2318,plain,
( spl18_195
| ~ spl18_49
| ~ spl18_62 ),
inference(avatar_split_clause,[],[f670,f642,f535,f2316]) ).
fof(f670,plain,
( ! [X4,X5] :
( set_intersection2(X4,X5) != X4
| disjoint(X4,set_difference(X4,X5)) )
| ~ spl18_49
| ~ spl18_62 ),
inference(superposition,[],[f536,f643]) ).
fof(f2314,plain,
( spl18_194
| ~ spl18_53
| ~ spl18_62 ),
inference(avatar_split_clause,[],[f669,f642,f583,f2312]) ).
fof(f669,plain,
( ! [X2,X3] :
( sK17 != set_intersection2(X2,X3)
| subset(X2,set_difference(X2,X3)) )
| ~ spl18_53
| ~ spl18_62 ),
inference(superposition,[],[f584,f643]) ).
fof(f2282,plain,
( spl18_193
| ~ spl18_39
| ~ spl18_75 ),
inference(avatar_split_clause,[],[f784,f733,f467,f2280]) ).
fof(f784,plain,
( ! [X2,X3,X4] :
( set_union2(X3,X2) != X4
| sP2(X3,X2,X4) )
| ~ spl18_39
| ~ spl18_75 ),
inference(superposition,[],[f734,f468]) ).
fof(f2278,plain,
( spl18_192
| ~ spl18_40
| ~ spl18_73 ),
inference(avatar_split_clause,[],[f778,f725,f471,f2276]) ).
fof(f778,plain,
( ! [X6,X4,X5] :
( set_intersection2(X5,X4) != X6
| sP1(X5,X4,X6) )
| ~ spl18_40
| ~ spl18_73 ),
inference(superposition,[],[f726,f472]) ).
fof(f2274,plain,
( spl18_191
| ~ spl18_38
| ~ spl18_71 ),
inference(avatar_split_clause,[],[f773,f717,f463,f2272]) ).
fof(f2272,plain,
( spl18_191
<=> ! [X4,X2,X3] :
( unordered_pair(X3,X2) != X4
| sP0(X3,X2,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_191])]) ).
fof(f717,plain,
( spl18_71
<=> ! [X2,X0,X1] :
( sP0(X1,X0,X2)
| unordered_pair(X0,X1) != X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_71])]) ).
fof(f773,plain,
( ! [X2,X3,X4] :
( unordered_pair(X3,X2) != X4
| sP0(X3,X2,X4) )
| ~ spl18_38
| ~ spl18_71 ),
inference(superposition,[],[f718,f464]) ).
fof(f718,plain,
( ! [X2,X0,X1] :
( unordered_pair(X0,X1) != X2
| sP0(X1,X0,X2) )
| ~ spl18_71 ),
inference(avatar_component_clause,[],[f717]) ).
fof(f2270,plain,
( spl18_190
| ~ spl18_15
| ~ spl18_83
| ~ spl18_138 ),
inference(avatar_split_clause,[],[f1415,f1381,f864,f338,f2268]) ).
fof(f2268,plain,
( spl18_190
<=> ! [X5] : sP2(sK17,X5,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_190])]) ).
fof(f1415,plain,
( ! [X5] : sP2(sK17,X5,X5)
| ~ spl18_15
| ~ spl18_83
| ~ spl18_138 ),
inference(forward_demodulation,[],[f1412,f866]) ).
fof(f1412,plain,
( ! [X5] : sP2(empty_set,X5,X5)
| ~ spl18_15
| ~ spl18_138 ),
inference(superposition,[],[f1382,f339]) ).
fof(f2082,plain,
( spl18_189
| ~ spl18_60
| ~ spl18_63 ),
inference(avatar_split_clause,[],[f692,f646,f634,f2080]) ).
fof(f692,plain,
( ! [X2,X3] : set_union2(X3,X2) = set_union2(X3,set_union2(X2,X3))
| ~ spl18_60
| ~ spl18_63 ),
inference(forward_demodulation,[],[f685,f635]) ).
fof(f685,plain,
( ! [X2,X3] : set_union2(X3,set_union2(X2,X3)) = set_union2(X3,set_difference(X2,X3))
| ~ spl18_60
| ~ spl18_63 ),
inference(superposition,[],[f635,f647]) ).
fof(f2078,plain,
( spl18_188
| ~ spl18_39
| ~ spl18_63 ),
inference(avatar_split_clause,[],[f680,f646,f467,f2076]) ).
fof(f680,plain,
( ! [X2,X1] : set_difference(X1,X2) = set_difference(set_union2(X2,X1),X2)
| ~ spl18_39
| ~ spl18_63 ),
inference(superposition,[],[f647,f468]) ).
fof(f2074,plain,
( spl18_187
| ~ spl18_12
| ~ spl18_47 ),
inference(avatar_split_clause,[],[f573,f527,f326,f2072]) ).
fof(f573,plain,
( ! [X4,X5] : set_difference(X4,X5) = set_intersection2(set_difference(X4,X5),X4)
| ~ spl18_12
| ~ spl18_47 ),
inference(resolution,[],[f528,f327]) ).
fof(f2070,plain,
( spl18_186
| ~ spl18_11
| ~ spl18_47 ),
inference(avatar_split_clause,[],[f571,f527,f322,f2068]) ).
fof(f571,plain,
( ! [X2,X1] : set_intersection2(X1,X2) = set_intersection2(set_intersection2(X1,X2),X1)
| ~ spl18_11
| ~ spl18_47 ),
inference(resolution,[],[f528,f323]) ).
fof(f2066,plain,
( spl18_185
| ~ spl18_10
| ~ spl18_46 ),
inference(avatar_split_clause,[],[f568,f523,f318,f2064]) ).
fof(f568,plain,
( ! [X6,X7] : set_union2(X6,X7) = set_union2(X6,set_union2(X6,X7))
| ~ spl18_10
| ~ spl18_46 ),
inference(resolution,[],[f524,f319]) ).
fof(f2062,plain,
( spl18_184
| ~ spl18_128
| ~ spl18_138 ),
inference(avatar_split_clause,[],[f1414,f1381,f1288,f2060]) ).
fof(f2060,plain,
( spl18_184
<=> ! [X8] : sP2(X8,sK17,X8) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_184])]) ).
fof(f1414,plain,
( ! [X8] : sP2(X8,sK17,X8)
| ~ spl18_128
| ~ spl18_138 ),
inference(superposition,[],[f1382,f1289]) ).
fof(f2046,plain,
( spl18_183
| ~ spl18_40
| ~ spl18_59 ),
inference(avatar_split_clause,[],[f628,f618,f471,f2044]) ).
fof(f628,plain,
( ! [X2,X3] :
( sK17 != set_intersection2(X3,X2)
| disjoint(X2,X3) )
| ~ spl18_40
| ~ spl18_59 ),
inference(superposition,[],[f619,f472]) ).
fof(f2042,plain,
( spl18_182
| ~ spl18_30
| ~ spl18_57 ),
inference(avatar_split_clause,[],[f621,f610,f421,f2040]) ).
fof(f2040,plain,
( spl18_182
<=> ! [X0,X1] :
( subset(X0,X1)
| ~ in(X0,sK10(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_182])]) ).
fof(f621,plain,
( ! [X0,X1] :
( subset(X0,X1)
| ~ in(X0,sK10(X0,X1)) )
| ~ spl18_30
| ~ spl18_57 ),
inference(resolution,[],[f611,f422]) ).
fof(f1936,plain,
( spl18_181
| ~ spl18_18
| ~ spl18_138 ),
inference(avatar_split_clause,[],[f1409,f1381,f350,f1934]) ).
fof(f1934,plain,
( spl18_181
<=> ! [X0] : sP2(X0,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_181])]) ).
fof(f350,plain,
( spl18_18
<=> ! [X0] : set_union2(X0,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl18_18])]) ).
fof(f1409,plain,
( ! [X0] : sP2(X0,X0,X0)
| ~ spl18_18
| ~ spl18_138 ),
inference(superposition,[],[f1382,f351]) ).
fof(f351,plain,
( ! [X0] : set_union2(X0,X0) = X0
| ~ spl18_18 ),
inference(avatar_component_clause,[],[f350]) ).
fof(f1810,plain,
( spl18_180
| ~ spl18_13
| ~ spl18_83
| ~ spl18_137 ),
inference(avatar_split_clause,[],[f1404,f1377,f864,f330,f1808]) ).
fof(f1808,plain,
( spl18_180
<=> ! [X5] : sP1(sK17,X5,sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_180])]) ).
fof(f330,plain,
( spl18_13
<=> ! [X0] : empty_set = set_intersection2(X0,empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_13])]) ).
fof(f1404,plain,
( ! [X5] : sP1(sK17,X5,sK17)
| ~ spl18_13
| ~ spl18_83
| ~ spl18_137 ),
inference(forward_demodulation,[],[f1401,f866]) ).
fof(f1401,plain,
( ! [X5] : sP1(empty_set,X5,empty_set)
| ~ spl18_13
| ~ spl18_137 ),
inference(superposition,[],[f1378,f331]) ).
fof(f331,plain,
( ! [X0] : empty_set = set_intersection2(X0,empty_set)
| ~ spl18_13 ),
inference(avatar_component_clause,[],[f330]) ).
fof(f1806,plain,
( spl18_179
| ~ spl18_5
| ~ spl18_14
| ~ spl18_17
| ~ spl18_81 ),
inference(avatar_split_clause,[],[f857,f811,f346,f334,f297,f1804]) ).
fof(f1804,plain,
( spl18_179
<=> ! [X0,X1] :
( ~ subset(X1,sK17)
| subset(set_difference(X1,X0),sK17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_179])]) ).
fof(f297,plain,
( spl18_5
<=> empty(sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_5])]) ).
fof(f346,plain,
( spl18_17
<=> ! [X0] :
( empty_set = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_17])]) ).
fof(f857,plain,
( ! [X0,X1] :
( ~ subset(X1,sK17)
| subset(set_difference(X1,X0),sK17) )
| ~ spl18_5
| ~ spl18_14
| ~ spl18_17
| ~ spl18_81 ),
inference(forward_demodulation,[],[f856,f366]) ).
fof(f366,plain,
( empty_set = sK17
| ~ spl18_5
| ~ spl18_17 ),
inference(resolution,[],[f347,f299]) ).
fof(f299,plain,
( empty(sK17)
| ~ spl18_5 ),
inference(avatar_component_clause,[],[f297]) ).
fof(f347,plain,
( ! [X0] :
( ~ empty(X0)
| empty_set = X0 )
| ~ spl18_17 ),
inference(avatar_component_clause,[],[f346]) ).
fof(f856,plain,
( ! [X0,X1] :
( subset(set_difference(X1,X0),sK17)
| ~ subset(X1,empty_set) )
| ~ spl18_5
| ~ spl18_14
| ~ spl18_17
| ~ spl18_81 ),
inference(forward_demodulation,[],[f851,f366]) ).
fof(f851,plain,
( ! [X0,X1] :
( subset(set_difference(X1,X0),empty_set)
| ~ subset(X1,empty_set) )
| ~ spl18_14
| ~ spl18_81 ),
inference(superposition,[],[f812,f335]) ).
fof(f1802,plain,
( spl18_178
| ~ spl18_19
| ~ spl18_80 ),
inference(avatar_split_clause,[],[f832,f807,f354,f1800]) ).
fof(f832,plain,
( ! [X2,X3] :
( subset(X2,set_intersection2(X3,X2))
| ~ subset(X2,X3) )
| ~ spl18_19
| ~ spl18_80 ),
inference(superposition,[],[f808,f355]) ).
fof(f1798,plain,
( spl18_177
| ~ spl18_19
| ~ spl18_79 ),
inference(avatar_split_clause,[],[f818,f803,f354,f1796]) ).
fof(f1796,plain,
( spl18_177
<=> ! [X1] :
( in(sK6(X1,X1),X1)
| disjoint(X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_177])]) ).
fof(f818,plain,
( ! [X1] :
( in(sK6(X1,X1),X1)
| disjoint(X1,X1) )
| ~ spl18_19
| ~ spl18_79 ),
inference(superposition,[],[f804,f355]) ).
fof(f1794,plain,
( spl18_176
| ~ spl18_21
| ~ spl18_71 ),
inference(avatar_split_clause,[],[f772,f717,f371,f1792]) ).
fof(f1792,plain,
( spl18_176
<=> ! [X0,X1] :
( singleton(X0) != X1
| sP0(X0,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_176])]) ).
fof(f772,plain,
( ! [X0,X1] :
( singleton(X0) != X1
| sP0(X0,X0,X1) )
| ~ spl18_21
| ~ spl18_71 ),
inference(superposition,[],[f718,f372]) ).
fof(f1790,plain,
( spl18_175
| ~ spl18_10
| ~ spl18_70 ),
inference(avatar_split_clause,[],[f770,f713,f318,f1788]) ).
fof(f770,plain,
( ! [X10,X11,X12] :
( ~ in(X10,X11)
| in(X10,set_union2(X11,X12)) )
| ~ spl18_10
| ~ spl18_70 ),
inference(resolution,[],[f714,f319]) ).
fof(f1786,plain,
( spl18_174
| ~ spl18_12
| ~ spl18_70 ),
inference(avatar_split_clause,[],[f769,f713,f326,f1784]) ).
fof(f769,plain,
( ! [X8,X9,X7] :
( ~ in(X7,set_difference(X8,X9))
| in(X7,X8) )
| ~ spl18_12
| ~ spl18_70 ),
inference(resolution,[],[f714,f327]) ).
fof(f1782,plain,
( spl18_173
| ~ spl18_11
| ~ spl18_70 ),
inference(avatar_split_clause,[],[f767,f713,f322,f1780]) ).
fof(f767,plain,
( ! [X2,X3,X4] :
( ~ in(X2,set_intersection2(X3,X4))
| in(X2,X3) )
| ~ spl18_11
| ~ spl18_70 ),
inference(resolution,[],[f714,f323]) ).
fof(f1778,plain,
( spl18_172
| ~ spl18_10
| ~ spl18_66 ),
inference(avatar_split_clause,[],[f702,f658,f318,f1776]) ).
fof(f702,plain,
( ! [X10,X11,X12] :
( subset(X10,set_union2(X11,X12))
| ~ subset(X10,X11) )
| ~ spl18_10
| ~ spl18_66 ),
inference(resolution,[],[f659,f319]) ).
fof(f1774,plain,
( spl18_171
| ~ spl18_12
| ~ spl18_66 ),
inference(avatar_split_clause,[],[f701,f658,f326,f1772]) ).
fof(f701,plain,
( ! [X8,X9,X7] :
( subset(X7,X8)
| ~ subset(X7,set_difference(X8,X9)) )
| ~ spl18_12
| ~ spl18_66 ),
inference(resolution,[],[f659,f327]) ).
fof(f1770,plain,
( spl18_170
| ~ spl18_11
| ~ spl18_66 ),
inference(avatar_split_clause,[],[f699,f658,f322,f1768]) ).
fof(f699,plain,
( ! [X2,X3,X4] :
( subset(X2,X3)
| ~ subset(X2,set_intersection2(X3,X4)) )
| ~ spl18_11
| ~ spl18_66 ),
inference(resolution,[],[f659,f323]) ).
fof(f1766,plain,
( spl18_169
| ~ spl18_19
| ~ spl18_137 ),
inference(avatar_split_clause,[],[f1398,f1377,f354,f1764]) ).
fof(f1764,plain,
( spl18_169
<=> ! [X0] : sP1(X0,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_169])]) ).
fof(f1398,plain,
( ! [X0] : sP1(X0,X0,X0)
| ~ spl18_19
| ~ spl18_137 ),
inference(superposition,[],[f1378,f355]) ).
fof(f1762,plain,
( spl18_168
| ~ spl18_27
| ~ spl18_60 ),
inference(avatar_split_clause,[],[f662,f634,f409,f1760]) ).
fof(f662,plain,
( ! [X6,X7] :
( ~ empty(set_union2(X6,X7))
| empty(set_difference(X7,X6)) )
| ~ spl18_27
| ~ spl18_60 ),
inference(superposition,[],[f410,f635]) ).
fof(f1758,plain,
( spl18_167
| ~ spl18_43
| ~ spl18_57 ),
inference(avatar_split_clause,[],[f623,f610,f511,f1756]) ).
fof(f623,plain,
( ! [X6,X4,X5] :
( subset(set_intersection2(X4,X5),X6)
| ~ disjoint(X4,X5) )
| ~ spl18_43
| ~ spl18_57 ),
inference(resolution,[],[f611,f512]) ).
fof(f1754,plain,
( spl18_166
| ~ spl18_43
| ~ spl18_45 ),
inference(avatar_split_clause,[],[f563,f519,f511,f1752]) ).
fof(f563,plain,
( ! [X6,X4,X5] :
( disjoint(X4,set_intersection2(X5,X6))
| ~ disjoint(X5,X6) )
| ~ spl18_43
| ~ spl18_45 ),
inference(resolution,[],[f520,f512]) ).
fof(f1750,plain,
( spl18_165
| ~ spl18_30
| ~ spl18_45 ),
inference(avatar_split_clause,[],[f561,f519,f421,f1748]) ).
fof(f1748,plain,
( spl18_165
<=> ! [X0,X1] :
( disjoint(X0,X1)
| ~ in(X1,sK7(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_165])]) ).
fof(f561,plain,
( ! [X0,X1] :
( disjoint(X0,X1)
| ~ in(X1,sK7(X0,X1)) )
| ~ spl18_30
| ~ spl18_45 ),
inference(resolution,[],[f520,f422]) ).
fof(f1746,plain,
( spl18_164
| ~ spl18_43
| ~ spl18_44 ),
inference(avatar_split_clause,[],[f560,f515,f511,f1744]) ).
fof(f560,plain,
( ! [X6,X4,X5] :
( disjoint(set_intersection2(X4,X5),X6)
| ~ disjoint(X4,X5) )
| ~ spl18_43
| ~ spl18_44 ),
inference(resolution,[],[f516,f512]) ).
fof(f1742,plain,
( spl18_163
| ~ spl18_30
| ~ spl18_44 ),
inference(avatar_split_clause,[],[f558,f515,f421,f1740]) ).
fof(f1740,plain,
( spl18_163
<=> ! [X0,X1] :
( disjoint(X0,X1)
| ~ in(X0,sK7(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_163])]) ).
fof(f558,plain,
( ! [X0,X1] :
( disjoint(X0,X1)
| ~ in(X0,sK7(X0,X1)) )
| ~ spl18_30
| ~ spl18_44 ),
inference(resolution,[],[f516,f422]) ).
fof(f1738,plain,
( spl18_162
| ~ spl18_40
| ~ spl18_43 ),
inference(avatar_split_clause,[],[f555,f511,f471,f1736]) ).
fof(f555,plain,
( ! [X6,X4,X5] :
( ~ in(X6,set_intersection2(X5,X4))
| ~ disjoint(X4,X5) )
| ~ spl18_40
| ~ spl18_43 ),
inference(superposition,[],[f512,f472]) ).
fof(f1734,plain,
( spl18_161
| ~ spl18_42
| ~ spl18_43 ),
inference(avatar_split_clause,[],[f552,f511,f479,f1732]) ).
fof(f552,plain,
( ! [X0,X1] :
( ~ disjoint(X0,X1)
| set_intersection2(X0,X1) = sK17 )
| ~ spl18_42
| ~ spl18_43 ),
inference(resolution,[],[f512,f480]) ).
fof(f1700,plain,
( spl18_160
| ~ spl18_86 ),
inference(avatar_split_clause,[],[f911,f877,f1698]) ).
fof(f877,plain,
( spl18_86
<=> ! [X4,X0,X2,X1] :
( in(X4,X2)
| X0 != X4
| ~ sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_86])]) ).
fof(f911,plain,
( ! [X2,X0,X1] :
( in(X0,X1)
| ~ sP0(X0,X2,X1) )
| ~ spl18_86 ),
inference(equality_resolution,[],[f878]) ).
fof(f878,plain,
( ! [X2,X0,X1,X4] :
( X0 != X4
| in(X4,X2)
| ~ sP0(X0,X1,X2) )
| ~ spl18_86 ),
inference(avatar_component_clause,[],[f877]) ).
fof(f1692,plain,
( spl18_159
| ~ spl18_85 ),
inference(avatar_split_clause,[],[f910,f873,f1690]) ).
fof(f873,plain,
( spl18_85
<=> ! [X2,X0,X1,X4] :
( in(X4,X2)
| X1 != X4
| ~ sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_85])]) ).
fof(f910,plain,
( ! [X2,X0,X1] :
( in(X0,X1)
| ~ sP0(X2,X0,X1) )
| ~ spl18_85 ),
inference(equality_resolution,[],[f874]) ).
fof(f874,plain,
( ! [X2,X0,X1,X4] :
( X1 != X4
| in(X4,X2)
| ~ sP0(X0,X1,X2) )
| ~ spl18_85 ),
inference(avatar_component_clause,[],[f873]) ).
fof(f1688,plain,
( spl18_158
| ~ spl18_84 ),
inference(avatar_split_clause,[],[f909,f869,f1686]) ).
fof(f869,plain,
( spl18_84
<=> ! [X0,X1,X3] :
( in(X3,X1)
| X0 != X3
| singleton(X0) != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_84])]) ).
fof(f909,plain,
( ! [X0,X1] :
( X0 != X1
| in(X1,singleton(X0)) )
| ~ spl18_84 ),
inference(equality_resolution,[],[f870]) ).
fof(f870,plain,
( ! [X3,X0,X1] :
( singleton(X0) != X1
| X0 != X3
| in(X3,X1) )
| ~ spl18_84 ),
inference(avatar_component_clause,[],[f869]) ).
fof(f1684,plain,
( spl18_157
| ~ spl18_82 ),
inference(avatar_split_clause,[],[f904,f860,f1682]) ).
fof(f860,plain,
( spl18_82
<=> ! [X0,X1,X3] :
( X0 = X3
| ~ in(X3,X1)
| singleton(X0) != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_82])]) ).
fof(f904,plain,
( ! [X0,X1] :
( ~ in(X0,singleton(X1))
| X0 = X1 )
| ~ spl18_82 ),
inference(equality_resolution,[],[f861]) ).
fof(f861,plain,
( ! [X3,X0,X1] :
( singleton(X0) != X1
| ~ in(X3,X1)
| X0 = X3 )
| ~ spl18_82 ),
inference(avatar_component_clause,[],[f860]) ).
fof(f1680,plain,
( spl18_156
| ~ spl18_5
| ~ spl18_16
| ~ spl18_17
| ~ spl18_77 ),
inference(avatar_split_clause,[],[f801,f745,f346,f342,f297,f1678]) ).
fof(f1678,plain,
( spl18_156
<=> ! [X2,X3] :
( sP3(sK17,X2,X3)
| X2 != X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_156])]) ).
fof(f801,plain,
( ! [X2,X3] :
( sP3(sK17,X2,X3)
| X2 != X3 )
| ~ spl18_5
| ~ spl18_16
| ~ spl18_17
| ~ spl18_77 ),
inference(forward_demodulation,[],[f795,f366]) ).
fof(f795,plain,
( ! [X2,X3] :
( X2 != X3
| sP3(empty_set,X2,X3) )
| ~ spl18_16
| ~ spl18_77 ),
inference(superposition,[],[f746,f343]) ).
fof(f1676,plain,
( spl18_155
| ~ spl18_5
| ~ spl18_14
| ~ spl18_17
| ~ spl18_77 ),
inference(avatar_split_clause,[],[f800,f745,f346,f334,f297,f1674]) ).
fof(f1674,plain,
( spl18_155
<=> ! [X0,X1] :
( sP3(X0,sK17,X1)
| sK17 != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_155])]) ).
fof(f800,plain,
( ! [X0,X1] :
( sP3(X0,sK17,X1)
| sK17 != X1 )
| ~ spl18_5
| ~ spl18_14
| ~ spl18_17
| ~ spl18_77 ),
inference(forward_demodulation,[],[f799,f366]) ).
fof(f799,plain,
( ! [X0,X1] :
( sK17 != X1
| sP3(X0,empty_set,X1) )
| ~ spl18_5
| ~ spl18_14
| ~ spl18_17
| ~ spl18_77 ),
inference(forward_demodulation,[],[f794,f366]) ).
fof(f794,plain,
( ! [X0,X1] :
( empty_set != X1
| sP3(X0,empty_set,X1) )
| ~ spl18_14
| ~ spl18_77 ),
inference(superposition,[],[f746,f335]) ).
fof(f1672,plain,
( spl18_154
| ~ spl18_5
| ~ spl18_15
| ~ spl18_17
| ~ spl18_75 ),
inference(avatar_split_clause,[],[f789,f733,f346,f338,f297,f1670]) ).
fof(f1670,plain,
( spl18_154
<=> ! [X9,X8] :
( sP2(sK17,X8,X9)
| X8 != X9 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_154])]) ).
fof(f789,plain,
( ! [X8,X9] :
( sP2(sK17,X8,X9)
| X8 != X9 )
| ~ spl18_5
| ~ spl18_15
| ~ spl18_17
| ~ spl18_75 ),
inference(forward_demodulation,[],[f786,f366]) ).
fof(f786,plain,
( ! [X8,X9] :
( X8 != X9
| sP2(empty_set,X8,X9) )
| ~ spl18_15
| ~ spl18_75 ),
inference(superposition,[],[f734,f339]) ).
fof(f1668,plain,
( spl18_153
| ~ spl18_18
| ~ spl18_75 ),
inference(avatar_split_clause,[],[f783,f733,f350,f1666]) ).
fof(f1666,plain,
( spl18_153
<=> ! [X0,X1] :
( X0 != X1
| sP2(X0,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_153])]) ).
fof(f783,plain,
( ! [X0,X1] :
( X0 != X1
| sP2(X0,X0,X1) )
| ~ spl18_18
| ~ spl18_75 ),
inference(superposition,[],[f734,f351]) ).
fof(f1664,plain,
( spl18_152
| ~ spl18_5
| ~ spl18_13
| ~ spl18_17
| ~ spl18_73 ),
inference(avatar_split_clause,[],[f782,f725,f346,f330,f297,f1662]) ).
fof(f1662,plain,
( spl18_152
<=> ! [X0,X1] :
( sP1(sK17,X0,X1)
| sK17 != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_152])]) ).
fof(f782,plain,
( ! [X0,X1] :
( sP1(sK17,X0,X1)
| sK17 != X1 )
| ~ spl18_5
| ~ spl18_13
| ~ spl18_17
| ~ spl18_73 ),
inference(forward_demodulation,[],[f781,f366]) ).
fof(f781,plain,
( ! [X0,X1] :
( sK17 != X1
| sP1(empty_set,X0,X1) )
| ~ spl18_5
| ~ spl18_13
| ~ spl18_17
| ~ spl18_73 ),
inference(forward_demodulation,[],[f776,f366]) ).
fof(f776,plain,
( ! [X0,X1] :
( empty_set != X1
| sP1(empty_set,X0,X1) )
| ~ spl18_13
| ~ spl18_73 ),
inference(superposition,[],[f726,f331]) ).
fof(f1660,plain,
( spl18_151
| ~ spl18_19
| ~ spl18_73 ),
inference(avatar_split_clause,[],[f777,f725,f354,f1658]) ).
fof(f1658,plain,
( spl18_151
<=> ! [X2,X3] :
( X2 != X3
| sP1(X2,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_151])]) ).
fof(f777,plain,
( ! [X2,X3] :
( X2 != X3
| sP1(X2,X2,X3) )
| ~ spl18_19
| ~ spl18_73 ),
inference(superposition,[],[f726,f355]) ).
fof(f1656,plain,
( spl18_150
| ~ spl18_30
| ~ spl18_42 ),
inference(avatar_split_clause,[],[f508,f479,f421,f1654]) ).
fof(f1654,plain,
( spl18_150
<=> ! [X0] :
( sK17 = X0
| ~ in(X0,sK8(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_150])]) ).
fof(f508,plain,
( ! [X0] :
( sK17 = X0
| ~ in(X0,sK8(X0)) )
| ~ spl18_30
| ~ spl18_42 ),
inference(resolution,[],[f480,f422]) ).
fof(f1652,plain,
( spl18_149
| ~ spl18_126
| ~ spl18_139 ),
inference(avatar_split_clause,[],[f1422,f1385,f1171,f1650]) ).
fof(f1650,plain,
( spl18_149
<=> ! [X3] : sP3(X3,X3,sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_149])]) ).
fof(f1422,plain,
( ! [X3] : sP3(X3,X3,sK17)
| ~ spl18_126
| ~ spl18_139 ),
inference(superposition,[],[f1386,f1172]) ).
fof(f1463,plain,
( spl18_148
| ~ spl18_20
| ~ spl18_79 ),
inference(avatar_split_clause,[],[f816,f803,f358,f1461]) ).
fof(f816,plain,
( ! [X4,X5] :
( disjoint(X4,X5)
| ~ empty(set_intersection2(X4,X5)) )
| ~ spl18_20
| ~ spl18_79 ),
inference(resolution,[],[f804,f359]) ).
fof(f1459,plain,
( spl18_147
| ~ spl18_12
| ~ spl18_63 ),
inference(avatar_split_clause,[],[f688,f646,f326,f1457]) ).
fof(f688,plain,
( ! [X8,X9] : subset(set_difference(X8,X9),set_union2(X8,X9))
| ~ spl18_12
| ~ spl18_63 ),
inference(superposition,[],[f327,f647]) ).
fof(f1455,plain,
( spl18_146
| ~ spl18_120
| ~ spl18_137 ),
inference(avatar_split_clause,[],[f1403,f1377,f1147,f1453]) ).
fof(f1453,plain,
( spl18_146
<=> ! [X7] : sP1(X7,sK17,sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_146])]) ).
fof(f1403,plain,
( ! [X7] : sP1(X7,sK17,sK17)
| ~ spl18_120
| ~ spl18_137 ),
inference(superposition,[],[f1378,f1148]) ).
fof(f1451,plain,
( spl18_145
| ~ spl18_10
| ~ spl18_54 ),
inference(avatar_split_clause,[],[f597,f587,f318,f1449]) ).
fof(f597,plain,
( ! [X6,X7] : sK17 = set_difference(X6,set_union2(X6,X7))
| ~ spl18_10
| ~ spl18_54 ),
inference(resolution,[],[f588,f319]) ).
fof(f1447,plain,
( spl18_144
| ~ spl18_12
| ~ spl18_54 ),
inference(avatar_split_clause,[],[f596,f587,f326,f1445]) ).
fof(f596,plain,
( ! [X4,X5] : sK17 = set_difference(set_difference(X4,X5),X4)
| ~ spl18_12
| ~ spl18_54 ),
inference(resolution,[],[f588,f327]) ).
fof(f1443,plain,
( spl18_143
| ~ spl18_11
| ~ spl18_54 ),
inference(avatar_split_clause,[],[f594,f587,f322,f1441]) ).
fof(f594,plain,
( ! [X2,X1] : sK17 = set_difference(set_intersection2(X1,X2),X1)
| ~ spl18_11
| ~ spl18_54 ),
inference(resolution,[],[f588,f323]) ).
fof(f1439,plain,
( spl18_142
| ~ spl18_10
| ~ spl18_47 ),
inference(avatar_split_clause,[],[f574,f527,f318,f1437]) ).
fof(f574,plain,
( ! [X6,X7] : set_intersection2(X6,set_union2(X6,X7)) = X6
| ~ spl18_10
| ~ spl18_47 ),
inference(resolution,[],[f528,f319]) ).
fof(f1435,plain,
( spl18_141
| ~ spl18_12
| ~ spl18_46 ),
inference(avatar_split_clause,[],[f567,f523,f326,f1433]) ).
fof(f567,plain,
( ! [X4,X5] : set_union2(set_difference(X4,X5),X4) = X4
| ~ spl18_12
| ~ spl18_46 ),
inference(resolution,[],[f524,f327]) ).
fof(f1431,plain,
( spl18_140
| ~ spl18_11
| ~ spl18_46 ),
inference(avatar_split_clause,[],[f565,f523,f322,f1429]) ).
fof(f565,plain,
( ! [X2,X1] : set_union2(set_intersection2(X1,X2),X1) = X1
| ~ spl18_11
| ~ spl18_46 ),
inference(resolution,[],[f524,f323]) ).
fof(f1387,plain,
( spl18_139
| ~ spl18_77 ),
inference(avatar_split_clause,[],[f798,f745,f1385]) ).
fof(f798,plain,
( ! [X0,X1] : sP3(X0,X1,set_difference(X1,X0))
| ~ spl18_77 ),
inference(equality_resolution,[],[f746]) ).
fof(f1383,plain,
( spl18_138
| ~ spl18_75 ),
inference(avatar_split_clause,[],[f788,f733,f1381]) ).
fof(f788,plain,
( ! [X0,X1] : sP2(X0,X1,set_union2(X1,X0))
| ~ spl18_75 ),
inference(equality_resolution,[],[f734]) ).
fof(f1379,plain,
( spl18_137
| ~ spl18_73 ),
inference(avatar_split_clause,[],[f780,f725,f1377]) ).
fof(f780,plain,
( ! [X0,X1] : sP1(X0,X1,set_intersection2(X1,X0))
| ~ spl18_73 ),
inference(equality_resolution,[],[f726]) ).
fof(f1375,plain,
( spl18_136
| ~ spl18_71 ),
inference(avatar_split_clause,[],[f775,f717,f1373]) ).
fof(f775,plain,
( ! [X0,X1] : sP0(X0,X1,unordered_pair(X1,X0))
| ~ spl18_71 ),
inference(equality_resolution,[],[f718]) ).
fof(f1371,plain,
( spl18_135
| ~ spl18_19
| ~ spl18_59 ),
inference(avatar_split_clause,[],[f627,f618,f354,f1369]) ).
fof(f1369,plain,
( spl18_135
<=> ! [X1] :
( sK17 != X1
| disjoint(X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_135])]) ).
fof(f627,plain,
( ! [X1] :
( sK17 != X1
| disjoint(X1,X1) )
| ~ spl18_19
| ~ spl18_59 ),
inference(superposition,[],[f619,f355]) ).
fof(f1346,plain,
( spl18_134
| ~ spl18_5
| ~ spl18_6
| ~ spl18_17
| ~ spl18_69 ),
inference(avatar_split_clause,[],[f765,f709,f346,f302,f297,f1344]) ).
fof(f1344,plain,
( spl18_134
<=> ! [X3] :
( proper_subset(sK17,X3)
| sK17 = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_134])]) ).
fof(f302,plain,
( spl18_6
<=> ! [X0] : subset(empty_set,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_6])]) ).
fof(f765,plain,
( ! [X3] :
( proper_subset(sK17,X3)
| sK17 = X3 )
| ~ spl18_5
| ~ spl18_6
| ~ spl18_17
| ~ spl18_69 ),
inference(forward_demodulation,[],[f764,f366]) ).
fof(f764,plain,
( ! [X3] :
( sK17 = X3
| proper_subset(empty_set,X3) )
| ~ spl18_5
| ~ spl18_6
| ~ spl18_17
| ~ spl18_69 ),
inference(forward_demodulation,[],[f761,f366]) ).
fof(f761,plain,
( ! [X3] :
( empty_set = X3
| proper_subset(empty_set,X3) )
| ~ spl18_6
| ~ spl18_69 ),
inference(resolution,[],[f710,f303]) ).
fof(f303,plain,
( ! [X0] : subset(empty_set,X0)
| ~ spl18_6 ),
inference(avatar_component_clause,[],[f302]) ).
fof(f1342,plain,
( ~ spl18_133
| spl18_1
| ~ spl18_130 ),
inference(avatar_split_clause,[],[f1320,f1296,f278,f1339]) ).
fof(f1339,plain,
( spl18_133
<=> empty(singleton(sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_133])]) ).
fof(f1320,plain,
( ~ empty(singleton(sK4))
| spl18_1
| ~ spl18_130 ),
inference(resolution,[],[f1297,f279]) ).
fof(f1337,plain,
( spl18_132
| ~ spl18_5
| ~ spl18_6
| ~ spl18_17
| ~ spl18_66 ),
inference(avatar_split_clause,[],[f703,f658,f346,f302,f297,f1335]) ).
fof(f703,plain,
( ! [X6,X5] :
( ~ subset(X5,sK17)
| subset(X5,X6) )
| ~ spl18_5
| ~ spl18_6
| ~ spl18_17
| ~ spl18_66 ),
inference(forward_demodulation,[],[f700,f366]) ).
fof(f700,plain,
( ! [X6,X5] :
( subset(X5,X6)
| ~ subset(X5,empty_set) )
| ~ spl18_6
| ~ spl18_66 ),
inference(resolution,[],[f659,f303]) ).
fof(f1333,plain,
( spl18_131
| ~ spl18_19
| ~ spl18_43 ),
inference(avatar_split_clause,[],[f554,f511,f354,f1331]) ).
fof(f1331,plain,
( spl18_131
<=> ! [X2,X3] :
( ~ in(X3,X2)
| ~ disjoint(X2,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_131])]) ).
fof(f554,plain,
( ! [X2,X3] :
( ~ in(X3,X2)
| ~ disjoint(X2,X2) )
| ~ spl18_19
| ~ spl18_43 ),
inference(superposition,[],[f512,f355]) ).
fof(f1298,plain,
( spl18_130
| ~ spl18_20
| ~ spl18_57 ),
inference(avatar_split_clause,[],[f622,f610,f358,f1296]) ).
fof(f622,plain,
( ! [X2,X3] :
( subset(X2,X3)
| ~ empty(X2) )
| ~ spl18_20
| ~ spl18_57 ),
inference(resolution,[],[f611,f359]) ).
fof(f1294,plain,
( spl18_129
| ~ spl18_5
| ~ spl18_41 ),
inference(avatar_split_clause,[],[f507,f475,f297,f1292]) ).
fof(f1292,plain,
( spl18_129
<=> ! [X1] :
( sK17 = X1
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_129])]) ).
fof(f475,plain,
( spl18_41
<=> ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_41])]) ).
fof(f507,plain,
( ! [X1] :
( sK17 = X1
| ~ empty(X1) )
| ~ spl18_5
| ~ spl18_41 ),
inference(resolution,[],[f476,f299]) ).
fof(f476,plain,
( ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) )
| ~ spl18_41 ),
inference(avatar_component_clause,[],[f475]) ).
fof(f1290,plain,
( spl18_128
| ~ spl18_5
| ~ spl18_15
| ~ spl18_17
| ~ spl18_39 ),
inference(avatar_split_clause,[],[f492,f467,f346,f338,f297,f1288]) ).
fof(f492,plain,
( ! [X0] : set_union2(sK17,X0) = X0
| ~ spl18_5
| ~ spl18_15
| ~ spl18_17
| ~ spl18_39 ),
inference(forward_demodulation,[],[f482,f366]) ).
fof(f482,plain,
( ! [X0] : set_union2(empty_set,X0) = X0
| ~ spl18_15
| ~ spl18_39 ),
inference(superposition,[],[f468,f339]) ).
fof(f1177,plain,
( spl18_127
| ~ spl18_5
| ~ spl18_8
| ~ spl18_16
| ~ spl18_17
| ~ spl18_54
| ~ spl18_62 ),
inference(avatar_split_clause,[],[f676,f642,f587,f346,f342,f310,f297,f1175]) ).
fof(f1175,plain,
( spl18_127
<=> ! [X1] : sK17 = set_intersection2(X1,sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_127])]) ).
fof(f676,plain,
( ! [X1] : sK17 = set_intersection2(X1,sK17)
| ~ spl18_5
| ~ spl18_8
| ~ spl18_16
| ~ spl18_17
| ~ spl18_54
| ~ spl18_62 ),
inference(forward_demodulation,[],[f675,f366]) ).
fof(f675,plain,
( ! [X1] : sK17 = set_intersection2(X1,empty_set)
| ~ spl18_8
| ~ spl18_16
| ~ spl18_54
| ~ spl18_62 ),
inference(forward_demodulation,[],[f665,f593]) ).
fof(f593,plain,
( ! [X0] : sK17 = set_difference(X0,X0)
| ~ spl18_8
| ~ spl18_54 ),
inference(resolution,[],[f588,f311]) ).
fof(f665,plain,
( ! [X1] : set_intersection2(X1,empty_set) = set_difference(X1,X1)
| ~ spl18_16
| ~ spl18_62 ),
inference(superposition,[],[f643,f343]) ).
fof(f1173,plain,
( spl18_126
| ~ spl18_8
| ~ spl18_54 ),
inference(avatar_split_clause,[],[f593,f587,f310,f1171]) ).
fof(f1169,plain,
( spl18_125
| ~ spl18_20
| ~ spl18_45 ),
inference(avatar_split_clause,[],[f562,f519,f358,f1167]) ).
fof(f562,plain,
( ! [X2,X3] :
( disjoint(X2,X3)
| ~ empty(X3) )
| ~ spl18_20
| ~ spl18_45 ),
inference(resolution,[],[f520,f359]) ).
fof(f1165,plain,
( spl18_124
| ~ spl18_20
| ~ spl18_44 ),
inference(avatar_split_clause,[],[f559,f515,f358,f1163]) ).
fof(f559,plain,
( ! [X2,X3] :
( disjoint(X2,X3)
| ~ empty(X2) )
| ~ spl18_20
| ~ spl18_44 ),
inference(resolution,[],[f516,f359]) ).
fof(f1161,plain,
( spl18_123
| ~ spl18_11
| ~ spl18_40 ),
inference(avatar_split_clause,[],[f498,f471,f322,f1159]) ).
fof(f498,plain,
( ! [X0,X1] : subset(set_intersection2(X1,X0),X0)
| ~ spl18_11
| ~ spl18_40 ),
inference(superposition,[],[f323,f472]) ).
fof(f1157,plain,
( spl18_122
| ~ spl18_10
| ~ spl18_39 ),
inference(avatar_split_clause,[],[f486,f467,f318,f1155]) ).
fof(f486,plain,
( ! [X4,X5] : subset(X4,set_union2(X5,X4))
| ~ spl18_10
| ~ spl18_39 ),
inference(superposition,[],[f319,f468]) ).
fof(f1153,plain,
( spl18_121
| ~ spl18_12
| ~ spl18_24 ),
inference(avatar_split_clause,[],[f402,f385,f326,f1151]) ).
fof(f1151,plain,
( spl18_121
<=> ! [X1] : sK17 = set_difference(sK17,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_121])]) ).
fof(f402,plain,
( ! [X1] : sK17 = set_difference(sK17,X1)
| ~ spl18_12
| ~ spl18_24 ),
inference(resolution,[],[f386,f327]) ).
fof(f1149,plain,
( spl18_120
| ~ spl18_11
| ~ spl18_24 ),
inference(avatar_split_clause,[],[f400,f385,f322,f1147]) ).
fof(f400,plain,
( ! [X0] : sK17 = set_intersection2(sK17,X0)
| ~ spl18_11
| ~ spl18_24 ),
inference(resolution,[],[f386,f323]) ).
fof(f1145,plain,
( spl18_119
| ~ spl18_10
| ~ spl18_23 ),
inference(avatar_split_clause,[],[f392,f381,f318,f1143]) ).
fof(f392,plain,
( ! [X6,X7] : ~ proper_subset(set_union2(X6,X7),X6)
| ~ spl18_10
| ~ spl18_23 ),
inference(resolution,[],[f382,f319]) ).
fof(f1141,plain,
( spl18_118
| ~ spl18_12
| ~ spl18_23 ),
inference(avatar_split_clause,[],[f391,f381,f326,f1139]) ).
fof(f391,plain,
( ! [X4,X5] : ~ proper_subset(X4,set_difference(X4,X5))
| ~ spl18_12
| ~ spl18_23 ),
inference(resolution,[],[f382,f327]) ).
fof(f1105,plain,
( spl18_117
| ~ spl18_11
| ~ spl18_23 ),
inference(avatar_split_clause,[],[f389,f381,f322,f1103]) ).
fof(f389,plain,
( ! [X2,X1] : ~ proper_subset(X1,set_intersection2(X1,X2))
| ~ spl18_11
| ~ spl18_23 ),
inference(resolution,[],[f382,f323]) ).
fof(f1097,plain,
spl18_116,
inference(avatar_split_clause,[],[f268,f1095]) ).
fof(f1095,plain,
( spl18_116
<=> ! [X2,X0,X1] :
( sP3(X0,X1,X2)
| in(sK15(X0,X1,X2),X0)
| ~ in(sK15(X0,X1,X2),X1)
| ~ in(sK15(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_116])]) ).
fof(f268,plain,
! [X2,X0,X1] :
( sP3(X0,X1,X2)
| in(sK15(X0,X1,X2),X0)
| ~ in(sK15(X0,X1,X2),X1)
| ~ in(sK15(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f161]) ).
fof(f161,plain,
! [X0,X1,X2] :
( ( sP3(X0,X1,X2)
| ( ( in(sK15(X0,X1,X2),X0)
| ~ in(sK15(X0,X1,X2),X1)
| ~ in(sK15(X0,X1,X2),X2) )
& ( ( ~ in(sK15(X0,X1,X2),X0)
& in(sK15(X0,X1,X2),X1) )
| in(sK15(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| in(X4,X0)
| ~ in(X4,X1) )
& ( ( ~ in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| ~ sP3(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15])],[f159,f160]) ).
fof(f160,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( ~ in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) )
=> ( ( in(sK15(X0,X1,X2),X0)
| ~ in(sK15(X0,X1,X2),X1)
| ~ in(sK15(X0,X1,X2),X2) )
& ( ( ~ in(sK15(X0,X1,X2),X0)
& in(sK15(X0,X1,X2),X1) )
| in(sK15(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f159,plain,
! [X0,X1,X2] :
( ( sP3(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) ) )
| ~ sP3(X0,X1,X2) ) ),
inference(rectify,[],[f158]) ).
fof(f158,plain,
! [X1,X0,X2] :
( ( sP3(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) ) )
| ~ sP3(X1,X0,X2) ) ),
inference(flattening,[],[f157]) ).
fof(f157,plain,
! [X1,X0,X2] :
( ( sP3(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) ) )
| ~ sP3(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f107]) ).
fof(f107,plain,
! [X1,X0,X2] :
( sP3(X1,X0,X2)
<=> ! [X3] :
( in(X3,X2)
<=> ( ~ in(X3,X1)
& in(X3,X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f1093,plain,
spl18_115,
inference(avatar_split_clause,[],[f258,f1091]) ).
fof(f258,plain,
! [X2,X0,X1] :
( sP2(X0,X1,X2)
| in(sK14(X0,X1,X2),X0)
| in(sK14(X0,X1,X2),X1)
| in(sK14(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f155]) ).
fof(f155,plain,
! [X0,X1,X2] :
( ( sP2(X0,X1,X2)
| ( ( ( ~ in(sK14(X0,X1,X2),X0)
& ~ in(sK14(X0,X1,X2),X1) )
| ~ in(sK14(X0,X1,X2),X2) )
& ( in(sK14(X0,X1,X2),X0)
| in(sK14(X0,X1,X2),X1)
| in(sK14(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,[sK14])],[f153,f154]) ).
fof(f154,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ( ~ in(X3,X0)
& ~ in(X3,X1) )
| ~ in(X3,X2) )
& ( in(X3,X0)
| in(X3,X1)
| in(X3,X2) ) )
=> ( ( ( ~ in(sK14(X0,X1,X2),X0)
& ~ in(sK14(X0,X1,X2),X1) )
| ~ in(sK14(X0,X1,X2),X2) )
& ( in(sK14(X0,X1,X2),X0)
| in(sK14(X0,X1,X2),X1)
| in(sK14(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f153,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,[],[f152]) ).
fof(f152,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,[],[f151]) ).
fof(f151,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,[],[f105]) ).
fof(f105,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(f1089,plain,
spl18_114,
inference(avatar_split_clause,[],[f252,f1087]) ).
fof(f1087,plain,
( spl18_114
<=> ! [X2,X0,X1] :
( sP1(X0,X1,X2)
| ~ in(sK13(X0,X1,X2),X0)
| ~ in(sK13(X0,X1,X2),X1)
| ~ in(sK13(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_114])]) ).
fof(f252,plain,
! [X2,X0,X1] :
( sP1(X0,X1,X2)
| ~ in(sK13(X0,X1,X2),X0)
| ~ in(sK13(X0,X1,X2),X1)
| ~ in(sK13(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f149]) ).
fof(f149,plain,
! [X0,X1,X2] :
( ( sP1(X0,X1,X2)
| ( ( ~ in(sK13(X0,X1,X2),X0)
| ~ in(sK13(X0,X1,X2),X1)
| ~ in(sK13(X0,X1,X2),X2) )
& ( ( in(sK13(X0,X1,X2),X0)
& in(sK13(X0,X1,X2),X1) )
| in(sK13(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,[sK13])],[f147,f148]) ).
fof(f148,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) )
=> ( ( ~ in(sK13(X0,X1,X2),X0)
| ~ in(sK13(X0,X1,X2),X1)
| ~ in(sK13(X0,X1,X2),X2) )
& ( ( in(sK13(X0,X1,X2),X0)
& in(sK13(X0,X1,X2),X1) )
| in(sK13(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f147,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,[],[f146]) ).
fof(f146,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,[],[f145]) ).
fof(f145,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,[],[f103]) ).
fof(f103,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(f1085,plain,
spl18_113,
inference(avatar_split_clause,[],[f242,f1083]) ).
fof(f242,plain,
! [X2,X0,X1] :
( sP0(X0,X1,X2)
| sK12(X0,X1,X2) = X0
| sK12(X0,X1,X2) = X1
| in(sK12(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f143]) ).
fof(f143,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ( ( ( sK12(X0,X1,X2) != X0
& sK12(X0,X1,X2) != X1 )
| ~ in(sK12(X0,X1,X2),X2) )
& ( sK12(X0,X1,X2) = X0
| sK12(X0,X1,X2) = X1
| in(sK12(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( X0 != X4
& X1 != X4 ) )
& ( X0 = X4
| X1 = X4
| ~ in(X4,X2) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f141,f142]) ).
fof(f142,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ( X0 != X3
& X1 != X3 )
| ~ in(X3,X2) )
& ( X0 = X3
| X1 = X3
| in(X3,X2) ) )
=> ( ( ( sK12(X0,X1,X2) != X0
& sK12(X0,X1,X2) != X1 )
| ~ in(sK12(X0,X1,X2),X2) )
& ( sK12(X0,X1,X2) = X0
| sK12(X0,X1,X2) = X1
| in(sK12(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f141,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ? [X3] :
( ( ( X0 != X3
& X1 != X3 )
| ~ in(X3,X2) )
& ( X0 = X3
| X1 = X3
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( X0 != X4
& X1 != X4 ) )
& ( X0 = X4
| X1 = X4
| ~ in(X4,X2) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(rectify,[],[f140]) ).
fof(f140,plain,
! [X1,X0,X2] :
( ( sP0(X1,X0,X2)
| ? [X3] :
( ( ( X1 != X3
& X0 != X3 )
| ~ in(X3,X2) )
& ( X1 = X3
| X0 = X3
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( X1 != X3
& X0 != X3 ) )
& ( X1 = X3
| X0 = X3
| ~ in(X3,X2) ) )
| ~ sP0(X1,X0,X2) ) ),
inference(flattening,[],[f139]) ).
fof(f139,plain,
! [X1,X0,X2] :
( ( sP0(X1,X0,X2)
| ? [X3] :
( ( ( X1 != X3
& X0 != X3 )
| ~ in(X3,X2) )
& ( X1 = X3
| X0 = X3
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( X1 != X3
& X0 != X3 ) )
& ( X1 = X3
| X0 = X3
| ~ in(X3,X2) ) )
| ~ sP0(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f101]) ).
fof(f101,plain,
! [X1,X0,X2] :
( sP0(X1,X0,X2)
<=> ! [X3] :
( in(X3,X2)
<=> ( X1 = X3
| X0 = X3 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f1041,plain,
spl18_112,
inference(avatar_split_clause,[],[f267,f1039]) ).
fof(f267,plain,
! [X2,X0,X1] :
( sP3(X0,X1,X2)
| ~ in(sK15(X0,X1,X2),X0)
| in(sK15(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f161]) ).
fof(f1037,plain,
spl18_111,
inference(avatar_split_clause,[],[f266,f1035]) ).
fof(f266,plain,
! [X2,X0,X1] :
( sP3(X0,X1,X2)
| in(sK15(X0,X1,X2),X1)
| in(sK15(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f161]) ).
fof(f1033,plain,
spl18_110,
inference(avatar_split_clause,[],[f260,f1031]) ).
fof(f1031,plain,
( spl18_110
<=> ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| ~ in(sK14(X0,X1,X2),X0)
| ~ in(sK14(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_110])]) ).
fof(f260,plain,
! [X2,X0,X1] :
( sP2(X0,X1,X2)
| ~ in(sK14(X0,X1,X2),X0)
| ~ in(sK14(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f155]) ).
fof(f1029,plain,
spl18_109,
inference(avatar_split_clause,[],[f259,f1027]) ).
fof(f1027,plain,
( spl18_109
<=> ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| ~ in(sK14(X0,X1,X2),X1)
| ~ in(sK14(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_109])]) ).
fof(f259,plain,
! [X2,X0,X1] :
( sP2(X0,X1,X2)
| ~ in(sK14(X0,X1,X2),X1)
| ~ in(sK14(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f155]) ).
fof(f1025,plain,
spl18_108,
inference(avatar_split_clause,[],[f251,f1023]) ).
fof(f251,plain,
! [X2,X0,X1] :
( sP1(X0,X1,X2)
| in(sK13(X0,X1,X2),X0)
| in(sK13(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f149]) ).
fof(f1021,plain,
spl18_107,
inference(avatar_split_clause,[],[f250,f1019]) ).
fof(f250,plain,
! [X2,X0,X1] :
( sP1(X0,X1,X2)
| in(sK13(X0,X1,X2),X1)
| in(sK13(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f149]) ).
fof(f1013,plain,
spl18_106,
inference(avatar_split_clause,[],[f235,f1011]) ).
fof(f235,plain,
! [X0,X1] :
( singleton(X0) = X1
| sK11(X0,X1) = X0
| in(sK11(X0,X1),X1) ),
inference(cnf_transformation,[],[f138]) ).
fof(f138,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ( ( sK11(X0,X1) != X0
| ~ in(sK11(X0,X1),X1) )
& ( sK11(X0,X1) = X0
| in(sK11(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f136,f137]) ).
fof(f137,plain,
! [X0,X1] :
( ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) )
=> ( ( sK11(X0,X1) != X0
| ~ in(sK11(X0,X1),X1) )
& ( sK11(X0,X1) = X0
| in(sK11(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f136,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(rectify,[],[f135]) ).
fof(f135,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| X0 != X2 )
& ( X0 = X2
| ~ in(X2,X1) ) )
| singleton(X0) != X1 ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0,X1] :
( singleton(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> X0 = X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.1596azFLbA/Vampire---4.8_25340',d1_tarski) ).
fof(f1009,plain,
( spl18_105
| ~ spl18_6
| ~ spl18_83 ),
inference(avatar_split_clause,[],[f917,f864,f302,f1007]) ).
fof(f1007,plain,
( spl18_105
<=> ! [X0] : subset(sK17,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_105])]) ).
fof(f917,plain,
( ! [X0] : subset(sK17,X0)
| ~ spl18_6
| ~ spl18_83 ),
inference(superposition,[],[f303,f866]) ).
fof(f993,plain,
spl18_104,
inference(avatar_split_clause,[],[f276,f991]) ).
fof(f991,plain,
( spl18_104
<=> ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| sK12(X0,X1,X2) != X1
| ~ in(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_104])]) ).
fof(f276,plain,
! [X2,X0,X1] :
( sP0(X0,X1,X2)
| sK12(X0,X1,X2) != X1
| ~ in(X1,X2) ),
inference(inner_rewriting,[],[f243]) ).
fof(f243,plain,
! [X2,X0,X1] :
( sP0(X0,X1,X2)
| sK12(X0,X1,X2) != X1
| ~ in(sK12(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f143]) ).
fof(f989,plain,
spl18_103,
inference(avatar_split_clause,[],[f275,f987]) ).
fof(f987,plain,
( spl18_103
<=> ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| sK12(X0,X1,X2) != X0
| ~ in(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_103])]) ).
fof(f275,plain,
! [X2,X0,X1] :
( sP0(X0,X1,X2)
| sK12(X0,X1,X2) != X0
| ~ in(X0,X2) ),
inference(inner_rewriting,[],[f244]) ).
fof(f244,plain,
! [X2,X0,X1] :
( sP0(X0,X1,X2)
| sK12(X0,X1,X2) != X0
| ~ in(sK12(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f143]) ).
fof(f985,plain,
spl18_102,
inference(avatar_split_clause,[],[f265,f983]) ).
fof(f983,plain,
( spl18_102
<=> ! [X4,X0,X2,X1] :
( in(X4,X2)
| in(X4,X0)
| ~ in(X4,X1)
| ~ sP3(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_102])]) ).
fof(f265,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| in(X4,X0)
| ~ in(X4,X1)
| ~ sP3(X0,X1,X2) ),
inference(cnf_transformation,[],[f161]) ).
fof(f977,plain,
spl18_101,
inference(avatar_split_clause,[],[f255,f975]) ).
fof(f975,plain,
( spl18_101
<=> ! [X2,X4,X0,X1] :
( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2)
| ~ sP2(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_101])]) ).
fof(f255,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2)
| ~ sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f155]) ).
fof(f973,plain,
spl18_100,
inference(avatar_split_clause,[],[f249,f971]) ).
fof(f971,plain,
( spl18_100
<=> ! [X4,X0,X2,X1] :
( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1)
| ~ sP1(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_100])]) ).
fof(f249,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1)
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f149]) ).
fof(f969,plain,
spl18_99,
inference(avatar_split_clause,[],[f239,f967]) ).
fof(f967,plain,
( spl18_99
<=> ! [X2,X4,X0,X1] :
( X0 = X4
| X1 = X4
| ~ in(X4,X2)
| ~ sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_99])]) ).
fof(f239,plain,
! [X2,X0,X1,X4] :
( X0 = X4
| X1 = X4
| ~ in(X4,X2)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f143]) ).
fof(f965,plain,
spl18_98,
inference(avatar_split_clause,[],[f221,f963]) ).
fof(f963,plain,
( spl18_98
<=> ! [X0,X1] :
( X0 = X1
| ~ in(sK9(X0,X1),X1)
| ~ in(sK9(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_98])]) ).
fof(f221,plain,
! [X0,X1] :
( X0 = X1
| ~ in(sK9(X0,X1),X1)
| ~ in(sK9(X0,X1),X0) ),
inference(cnf_transformation,[],[f125]) ).
fof(f125,plain,
! [X0,X1] :
( X0 = X1
| ( ( ~ in(sK9(X0,X1),X1)
| ~ in(sK9(X0,X1),X0) )
& ( in(sK9(X0,X1),X1)
| in(sK9(X0,X1),X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f123,f124]) ).
fof(f124,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ in(X2,X1)
| ~ in(X2,X0) )
& ( in(X2,X1)
| in(X2,X0) ) )
=> ( ( ~ in(sK9(X0,X1),X1)
| ~ in(sK9(X0,X1),X0) )
& ( in(sK9(X0,X1),X1)
| in(sK9(X0,X1),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f123,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( ( ~ in(X2,X1)
| ~ in(X2,X0) )
& ( in(X2,X1)
| in(X2,X0) ) ) ),
inference(nnf_transformation,[],[f97]) ).
fof(f97,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( in(X2,X0)
<~> in(X2,X1) ) ),
inference(ennf_transformation,[],[f44]) ).
fof(f44,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
<=> in(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox/tmp/tmp.1596azFLbA/Vampire---4.8_25340',t2_tarski) ).
fof(f961,plain,
spl18_97,
inference(avatar_split_clause,[],[f220,f959]) ).
fof(f220,plain,
! [X0,X1] :
( X0 = X1
| in(sK9(X0,X1),X1)
| in(sK9(X0,X1),X0) ),
inference(cnf_transformation,[],[f125]) ).
fof(f957,plain,
spl18_96,
inference(avatar_split_clause,[],[f274,f955]) ).
fof(f955,plain,
( spl18_96
<=> ! [X0,X1] :
( singleton(X0) = X1
| sK11(X0,X1) != X0
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_96])]) ).
fof(f274,plain,
! [X0,X1] :
( singleton(X0) = X1
| sK11(X0,X1) != X0
| ~ in(X0,X1) ),
inference(inner_rewriting,[],[f236]) ).
fof(f236,plain,
! [X0,X1] :
( singleton(X0) = X1
| sK11(X0,X1) != X0
| ~ in(sK11(X0,X1),X1) ),
inference(cnf_transformation,[],[f138]) ).
fof(f925,plain,
spl18_95,
inference(avatar_split_clause,[],[f199,f923]) ).
fof(f199,plain,
! [X2,X0,X1] :
( subset(set_union2(X0,X2),X1)
| ~ subset(X2,X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f90]) ).
fof(f90,plain,
! [X0,X1,X2] :
( subset(set_union2(X0,X2),X1)
| ~ subset(X2,X1)
| ~ subset(X0,X1) ),
inference(flattening,[],[f89]) ).
fof(f89,plain,
! [X0,X1,X2] :
( subset(set_union2(X0,X2),X1)
| ~ subset(X2,X1)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f66]) ).
fof(f66,axiom,
! [X0,X1,X2] :
( ( subset(X2,X1)
& subset(X0,X1) )
=> subset(set_union2(X0,X2),X1) ),
file('/export/starexec/sandbox/tmp/tmp.1596azFLbA/Vampire---4.8_25340',t8_xboole_1) ).
fof(f915,plain,
spl18_94,
inference(avatar_split_clause,[],[f198,f913]) ).
fof(f198,plain,
! [X2,X0,X1] :
( subset(X0,set_intersection2(X1,X2))
| ~ subset(X0,X2)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f88]) ).
fof(f88,plain,
! [X0,X1,X2] :
( subset(X0,set_intersection2(X1,X2))
| ~ subset(X0,X2)
| ~ subset(X0,X1) ),
inference(flattening,[],[f87]) ).
fof(f87,plain,
! [X0,X1,X2] :
( subset(X0,set_intersection2(X1,X2))
| ~ subset(X0,X2)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f38]) ).
fof(f38,axiom,
! [X0,X1,X2] :
( ( subset(X0,X2)
& subset(X0,X1) )
=> subset(X0,set_intersection2(X1,X2)) ),
file('/export/starexec/sandbox/tmp/tmp.1596azFLbA/Vampire---4.8_25340',t19_xboole_1) ).
fof(f908,plain,
( spl18_93
| ~ spl18_35 ),
inference(avatar_split_clause,[],[f451,f441,f906]) ).
fof(f441,plain,
( spl18_35
<=> ! [X2,X0] :
( sK17 != X0
| ~ in(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_35])]) ).
fof(f451,plain,
( ! [X0] : ~ in(X0,sK17)
| ~ spl18_35 ),
inference(equality_resolution,[],[f442]) ).
fof(f442,plain,
( ! [X2,X0] :
( sK17 != X0
| ~ in(X2,X0) )
| ~ spl18_35 ),
inference(avatar_component_clause,[],[f441]) ).
fof(f903,plain,
spl18_92,
inference(avatar_split_clause,[],[f264,f901]) ).
fof(f264,plain,
! [X2,X0,X1,X4] :
( ~ in(X4,X0)
| ~ in(X4,X2)
| ~ sP3(X0,X1,X2) ),
inference(cnf_transformation,[],[f161]) ).
fof(f899,plain,
spl18_91,
inference(avatar_split_clause,[],[f263,f897]) ).
fof(f897,plain,
( spl18_91
<=> ! [X4,X0,X1,X2] :
( in(X4,X1)
| ~ in(X4,X2)
| ~ sP3(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_91])]) ).
fof(f263,plain,
! [X2,X0,X1,X4] :
( in(X4,X1)
| ~ in(X4,X2)
| ~ sP3(X0,X1,X2) ),
inference(cnf_transformation,[],[f161]) ).
fof(f895,plain,
spl18_90,
inference(avatar_split_clause,[],[f257,f893]) ).
fof(f893,plain,
( spl18_90
<=> ! [X4,X0,X2,X1] :
( in(X4,X2)
| ~ in(X4,X0)
| ~ sP2(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_90])]) ).
fof(f257,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| ~ sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f155]) ).
fof(f891,plain,
spl18_89,
inference(avatar_split_clause,[],[f256,f889]) ).
fof(f889,plain,
( spl18_89
<=> ! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X1)
| ~ sP2(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_89])]) ).
fof(f256,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X1)
| ~ sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f155]) ).
fof(f887,plain,
spl18_88,
inference(avatar_split_clause,[],[f248,f885]) ).
fof(f885,plain,
( spl18_88
<=> ! [X4,X0,X2,X1] :
( in(X4,X0)
| ~ in(X4,X2)
| ~ sP1(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_88])]) ).
fof(f248,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| ~ in(X4,X2)
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f149]) ).
fof(f883,plain,
spl18_87,
inference(avatar_split_clause,[],[f247,f881]) ).
fof(f881,plain,
( spl18_87
<=> ! [X4,X0,X1,X2] :
( in(X4,X1)
| ~ in(X4,X2)
| ~ sP1(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_87])]) ).
fof(f247,plain,
! [X2,X0,X1,X4] :
( in(X4,X1)
| ~ in(X4,X2)
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f149]) ).
fof(f879,plain,
spl18_86,
inference(avatar_split_clause,[],[f241,f877]) ).
fof(f241,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| X0 != X4
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f143]) ).
fof(f875,plain,
spl18_85,
inference(avatar_split_clause,[],[f240,f873]) ).
fof(f240,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| X1 != X4
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f143]) ).
fof(f871,plain,
spl18_84,
inference(avatar_split_clause,[],[f234,f869]) ).
fof(f234,plain,
! [X3,X0,X1] :
( in(X3,X1)
| X0 != X3
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f138]) ).
fof(f867,plain,
( spl18_83
| ~ spl18_5
| ~ spl18_17 ),
inference(avatar_split_clause,[],[f366,f346,f297,f864]) ).
fof(f862,plain,
spl18_82,
inference(avatar_split_clause,[],[f233,f860]) ).
fof(f233,plain,
! [X3,X0,X1] :
( X0 = X3
| ~ in(X3,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f138]) ).
fof(f813,plain,
spl18_81,
inference(avatar_split_clause,[],[f195,f811]) ).
fof(f195,plain,
! [X2,X0,X1] :
( subset(set_difference(X0,X2),set_difference(X1,X2))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f82]) ).
fof(f82,plain,
! [X0,X1,X2] :
( subset(set_difference(X0,X2),set_difference(X1,X2))
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f46]) ).
fof(f46,axiom,
! [X0,X1,X2] :
( subset(X0,X1)
=> subset(set_difference(X0,X2),set_difference(X1,X2)) ),
file('/export/starexec/sandbox/tmp/tmp.1596azFLbA/Vampire---4.8_25340',t33_xboole_1) ).
fof(f809,plain,
spl18_80,
inference(avatar_split_clause,[],[f194,f807]) ).
fof(f194,plain,
! [X2,X0,X1] :
( subset(set_intersection2(X0,X2),set_intersection2(X1,X2))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f81]) ).
fof(f81,plain,
! [X0,X1,X2] :
( subset(set_intersection2(X0,X2),set_intersection2(X1,X2))
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f41]) ).
fof(f41,axiom,
! [X0,X1,X2] :
( subset(X0,X1)
=> subset(set_intersection2(X0,X2),set_intersection2(X1,X2)) ),
file('/export/starexec/sandbox/tmp/tmp.1596azFLbA/Vampire---4.8_25340',t26_xboole_1) ).
fof(f805,plain,
spl18_79,
inference(avatar_split_clause,[],[f179,f803]) ).
fof(f179,plain,
! [X0,X1] :
( in(sK6(X0,X1),set_intersection2(X0,X1))
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f113]) ).
fof(f113,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| ! [X2] : ~ in(X2,set_intersection2(X0,X1)) )
& ( in(sK6(X0,X1),set_intersection2(X0,X1))
| disjoint(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f75,f112]) ).
fof(f112,plain,
! [X0,X1] :
( ? [X3] : in(X3,set_intersection2(X0,X1))
=> in(sK6(X0,X1),set_intersection2(X0,X1)) ),
introduced(choice_axiom,[]) ).
fof(f75,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,[],[f67]) ).
fof(f67,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,[],[f57]) ).
fof(f57,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/tmp/tmp.1596azFLbA/Vampire---4.8_25340',t4_xboole_0) ).
fof(f751,plain,
spl18_78,
inference(avatar_split_clause,[],[f270,f749]) ).
fof(f749,plain,
( spl18_78
<=> ! [X2,X0,X1] :
( set_difference(X0,X1) = X2
| ~ sP3(X1,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_78])]) ).
fof(f270,plain,
! [X2,X0,X1] :
( set_difference(X0,X1) = X2
| ~ sP3(X1,X0,X2) ),
inference(cnf_transformation,[],[f162]) ).
fof(f162,plain,
! [X0,X1,X2] :
( ( set_difference(X0,X1) = X2
| ~ sP3(X1,X0,X2) )
& ( sP3(X1,X0,X2)
| set_difference(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f108]) ).
fof(f108,plain,
! [X0,X1,X2] :
( set_difference(X0,X1) = X2
<=> sP3(X1,X0,X2) ),
inference(definition_folding,[],[f13,f107]) ).
fof(f13,axiom,
! [X0,X1,X2] :
( set_difference(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( ~ in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.1596azFLbA/Vampire---4.8_25340',d4_xboole_0) ).
fof(f747,plain,
spl18_77,
inference(avatar_split_clause,[],[f269,f745]) ).
fof(f269,plain,
! [X2,X0,X1] :
( sP3(X1,X0,X2)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f162]) ).
fof(f739,plain,
spl18_76,
inference(avatar_split_clause,[],[f262,f737]) ).
fof(f737,plain,
( spl18_76
<=> ! [X2,X0,X1] :
( set_union2(X0,X1) = X2
| ~ sP2(X1,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_76])]) ).
fof(f262,plain,
! [X2,X0,X1] :
( set_union2(X0,X1) = X2
| ~ sP2(X1,X0,X2) ),
inference(cnf_transformation,[],[f156]) ).
fof(f156,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) = X2
| ~ sP2(X1,X0,X2) )
& ( sP2(X1,X0,X2)
| set_union2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f106]) ).
fof(f106,plain,
! [X0,X1,X2] :
( set_union2(X0,X1) = X2
<=> sP2(X1,X0,X2) ),
inference(definition_folding,[],[f10,f105]) ).
fof(f10,axiom,
! [X0,X1,X2] :
( set_union2(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
| in(X3,X0) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.1596azFLbA/Vampire---4.8_25340',d2_xboole_0) ).
fof(f735,plain,
spl18_75,
inference(avatar_split_clause,[],[f261,f733]) ).
fof(f261,plain,
! [X2,X0,X1] :
( sP2(X1,X0,X2)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f156]) ).
fof(f731,plain,
spl18_74,
inference(avatar_split_clause,[],[f254,f729]) ).
fof(f729,plain,
( spl18_74
<=> ! [X2,X0,X1] :
( set_intersection2(X0,X1) = X2
| ~ sP1(X1,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_74])]) ).
fof(f254,plain,
! [X2,X0,X1] :
( set_intersection2(X0,X1) = X2
| ~ sP1(X1,X0,X2) ),
inference(cnf_transformation,[],[f150]) ).
fof(f150,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) = X2
| ~ sP1(X1,X0,X2) )
& ( sP1(X1,X0,X2)
| set_intersection2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f104]) ).
fof(f104,plain,
! [X0,X1,X2] :
( set_intersection2(X0,X1) = X2
<=> sP1(X1,X0,X2) ),
inference(definition_folding,[],[f12,f103]) ).
fof(f12,axiom,
! [X0,X1,X2] :
( set_intersection2(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.1596azFLbA/Vampire---4.8_25340',d3_xboole_0) ).
fof(f727,plain,
spl18_73,
inference(avatar_split_clause,[],[f253,f725]) ).
fof(f253,plain,
! [X2,X0,X1] :
( sP1(X1,X0,X2)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f150]) ).
fof(f723,plain,
spl18_72,
inference(avatar_split_clause,[],[f246,f721]) ).
fof(f721,plain,
( spl18_72
<=> ! [X2,X0,X1] :
( unordered_pair(X0,X1) = X2
| ~ sP0(X1,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_72])]) ).
fof(f246,plain,
! [X2,X0,X1] :
( unordered_pair(X0,X1) = X2
| ~ sP0(X1,X0,X2) ),
inference(cnf_transformation,[],[f144]) ).
fof(f144,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) = X2
| ~ sP0(X1,X0,X2) )
& ( sP0(X1,X0,X2)
| unordered_pair(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f102]) ).
fof(f102,plain,
! [X0,X1,X2] :
( unordered_pair(X0,X1) = X2
<=> sP0(X1,X0,X2) ),
inference(definition_folding,[],[f9,f101]) ).
fof(f9,axiom,
! [X0,X1,X2] :
( unordered_pair(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( X1 = X3
| X0 = X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.1596azFLbA/Vampire---4.8_25340',d2_tarski) ).
fof(f719,plain,
spl18_71,
inference(avatar_split_clause,[],[f245,f717]) ).
fof(f245,plain,
! [X2,X0,X1] :
( sP0(X1,X0,X2)
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f144]) ).
fof(f715,plain,
spl18_70,
inference(avatar_split_clause,[],[f230,f713]) ).
fof(f230,plain,
! [X3,X0,X1] :
( in(X3,X1)
| ~ in(X3,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f134]) ).
fof(f134,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK10(X0,X1),X1)
& in(sK10(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f132,f133]) ).
fof(f133,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) )
=> ( ~ in(sK10(X0,X1),X1)
& in(sK10(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f132,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,[],[f131]) ).
fof(f131,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,[],[f98]) ).
fof(f98,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/tmp/tmp.1596azFLbA/Vampire---4.8_25340',d3_tarski) ).
fof(f711,plain,
spl18_69,
inference(avatar_split_clause,[],[f227,f709]) ).
fof(f227,plain,
! [X0,X1] :
( proper_subset(X0,X1)
| X0 = X1
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f129]) ).
fof(f129,plain,
! [X0,X1] :
( ( proper_subset(X0,X1)
| X0 = X1
| ~ subset(X0,X1) )
& ( ( X0 != X1
& subset(X0,X1) )
| ~ proper_subset(X0,X1) ) ),
inference(flattening,[],[f128]) ).
fof(f128,plain,
! [X0,X1] :
( ( proper_subset(X0,X1)
| X0 = X1
| ~ subset(X0,X1) )
& ( ( X0 != X1
& subset(X0,X1) )
| ~ proper_subset(X0,X1) ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0,X1] :
( proper_subset(X0,X1)
<=> ( X0 != X1
& subset(X0,X1) ) ),
file('/export/starexec/sandbox/tmp/tmp.1596azFLbA/Vampire---4.8_25340',d8_xboole_0) ).
fof(f707,plain,
spl18_68,
inference(avatar_split_clause,[],[f224,f705]) ).
fof(f224,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f127]) ).
fof(f127,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 ) ),
inference(flattening,[],[f126]) ).
fof(f126,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox/tmp/tmp.1596azFLbA/Vampire---4.8_25340',d10_xboole_0) ).
fof(f697,plain,
( spl18_67
| ~ spl18_5
| ~ spl18_16
| ~ spl18_17
| ~ spl18_49 ),
inference(avatar_split_clause,[],[f581,f535,f346,f342,f297,f695]) ).
fof(f581,plain,
( ! [X1] : disjoint(X1,sK17)
| ~ spl18_5
| ~ spl18_16
| ~ spl18_17
| ~ spl18_49 ),
inference(forward_demodulation,[],[f578,f366]) ).
fof(f578,plain,
( ! [X1] : disjoint(X1,empty_set)
| ~ spl18_16
| ~ spl18_49 ),
inference(trivial_inequality_removal,[],[f577]) ).
fof(f577,plain,
( ! [X1] :
( X1 != X1
| disjoint(X1,empty_set) )
| ~ spl18_16
| ~ spl18_49 ),
inference(superposition,[],[f536,f343]) ).
fof(f660,plain,
spl18_66,
inference(avatar_split_clause,[],[f197,f658]) ).
fof(f197,plain,
! [X2,X0,X1] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f86]) ).
fof(f86,plain,
! [X0,X1,X2] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(flattening,[],[f85]) ).
fof(f85,plain,
! [X0,X1,X2] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f40]) ).
fof(f40,axiom,
! [X0,X1,X2] :
( ( subset(X1,X2)
& subset(X0,X1) )
=> subset(X0,X2) ),
file('/export/starexec/sandbox/tmp/tmp.1596azFLbA/Vampire---4.8_25340',t1_xboole_1) ).
fof(f656,plain,
spl18_65,
inference(avatar_split_clause,[],[f196,f654]) ).
fof(f196,plain,
! [X2,X0,X1] :
( disjoint(X0,X2)
| ~ disjoint(X1,X2)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f84]) ).
fof(f84,plain,
! [X0,X1,X2] :
( disjoint(X0,X2)
| ~ disjoint(X1,X2)
| ~ subset(X0,X1) ),
inference(flattening,[],[f83]) ).
fof(f83,plain,
! [X0,X1,X2] :
( disjoint(X0,X2)
| ~ disjoint(X1,X2)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f59]) ).
fof(f59,axiom,
! [X0,X1,X2] :
( ( disjoint(X1,X2)
& subset(X0,X1) )
=> disjoint(X0,X2) ),
file('/export/starexec/sandbox/tmp/tmp.1596azFLbA/Vampire---4.8_25340',t63_xboole_1) ).
fof(f652,plain,
spl18_64,
inference(avatar_split_clause,[],[f183,f650]) ).
fof(f650,plain,
( spl18_64
<=> ! [X2,X0,X1] :
( ~ disjoint(X0,X1)
| ~ in(X2,X1)
| ~ in(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_64])]) ).
fof(f183,plain,
! [X2,X0,X1] :
( ~ disjoint(X0,X1)
| ~ in(X2,X1)
| ~ in(X2,X0) ),
inference(cnf_transformation,[],[f115]) ).
fof(f115,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| ! [X2] :
( ~ in(X2,X1)
| ~ in(X2,X0) ) )
& ( ( in(sK7(X0,X1),X1)
& in(sK7(X0,X1),X0) )
| disjoint(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f76,f114]) ).
fof(f114,plain,
! [X0,X1] :
( ? [X3] :
( in(X3,X1)
& in(X3,X0) )
=> ( in(sK7(X0,X1),X1)
& in(sK7(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f76,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,[],[f68]) ).
fof(f68,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,[],[f51]) ).
fof(f51,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/tmp/tmp.1596azFLbA/Vampire---4.8_25340',t3_xboole_0) ).
fof(f648,plain,
spl18_63,
inference(avatar_split_clause,[],[f178,f646]) ).
fof(f178,plain,
! [X0,X1] : set_difference(X0,X1) = set_difference(set_union2(X0,X1),X1),
inference(cnf_transformation,[],[f53]) ).
fof(f53,axiom,
! [X0,X1] : set_difference(X0,X1) = set_difference(set_union2(X0,X1),X1),
file('/export/starexec/sandbox/tmp/tmp.1596azFLbA/Vampire---4.8_25340',t40_xboole_1) ).
fof(f644,plain,
spl18_62,
inference(avatar_split_clause,[],[f177,f642]) ).
fof(f177,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_difference(X0,set_difference(X0,X1)),
inference(cnf_transformation,[],[f55]) ).
fof(f55,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_difference(X0,set_difference(X0,X1)),
file('/export/starexec/sandbox/tmp/tmp.1596azFLbA/Vampire---4.8_25340',t48_xboole_1) ).
fof(f640,plain,
( spl18_61
| ~ spl18_5
| ~ spl18_14
| ~ spl18_17
| ~ spl18_49 ),
inference(avatar_split_clause,[],[f580,f535,f346,f334,f297,f638]) ).
fof(f580,plain,
( ! [X0] : disjoint(sK17,X0)
| ~ spl18_5
| ~ spl18_14
| ~ spl18_17
| ~ spl18_49 ),
inference(forward_demodulation,[],[f579,f366]) ).
fof(f579,plain,
( ! [X0] : disjoint(empty_set,X0)
| ~ spl18_14
| ~ spl18_49 ),
inference(trivial_inequality_removal,[],[f576]) ).
fof(f576,plain,
( ! [X0] :
( empty_set != empty_set
| disjoint(empty_set,X0) )
| ~ spl18_14
| ~ spl18_49 ),
inference(superposition,[],[f536,f335]) ).
fof(f636,plain,
spl18_60,
inference(avatar_split_clause,[],[f176,f634]) ).
fof(f176,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X0,set_difference(X1,X0)),
inference(cnf_transformation,[],[f49]) ).
fof(f49,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X0,set_difference(X1,X0)),
file('/export/starexec/sandbox/tmp/tmp.1596azFLbA/Vampire---4.8_25340',t39_xboole_1) ).
fof(f620,plain,
( spl18_59
| ~ spl18_5
| ~ spl18_17
| ~ spl18_56 ),
inference(avatar_split_clause,[],[f608,f605,f346,f297,f618]) ).
fof(f605,plain,
( spl18_56
<=> ! [X0,X1] :
( disjoint(X0,X1)
| set_intersection2(X0,X1) != empty_set ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_56])]) ).
fof(f608,plain,
( ! [X0,X1] :
( set_intersection2(X0,X1) != sK17
| disjoint(X0,X1) )
| ~ spl18_5
| ~ spl18_17
| ~ spl18_56 ),
inference(forward_demodulation,[],[f606,f366]) ).
fof(f606,plain,
( ! [X0,X1] :
( disjoint(X0,X1)
| set_intersection2(X0,X1) != empty_set )
| ~ spl18_56 ),
inference(avatar_component_clause,[],[f605]) ).
fof(f616,plain,
spl18_58,
inference(avatar_split_clause,[],[f232,f614]) ).
fof(f232,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sK10(X0,X1),X1) ),
inference(cnf_transformation,[],[f134]) ).
fof(f612,plain,
spl18_57,
inference(avatar_split_clause,[],[f231,f610]) ).
fof(f231,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sK10(X0,X1),X0) ),
inference(cnf_transformation,[],[f134]) ).
fof(f607,plain,
spl18_56,
inference(avatar_split_clause,[],[f229,f605]) ).
fof(f229,plain,
! [X0,X1] :
( disjoint(X0,X1)
| set_intersection2(X0,X1) != empty_set ),
inference(cnf_transformation,[],[f130]) ).
fof(f130,plain,
! [X0,X1] :
( ( disjoint(X0,X1)
| set_intersection2(X0,X1) != empty_set )
& ( set_intersection2(X0,X1) = empty_set
| ~ disjoint(X0,X1) ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> set_intersection2(X0,X1) = empty_set ),
file('/export/starexec/sandbox/tmp/tmp.1596azFLbA/Vampire---4.8_25340',d7_xboole_0) ).
fof(f602,plain,
spl18_55,
inference(avatar_split_clause,[],[f228,f600]) ).
fof(f600,plain,
( spl18_55
<=> ! [X0,X1] :
( set_intersection2(X0,X1) = empty_set
| ~ disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_55])]) ).
fof(f228,plain,
! [X0,X1] :
( set_intersection2(X0,X1) = empty_set
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f130]) ).
fof(f589,plain,
( spl18_54
| ~ spl18_5
| ~ spl18_17
| ~ spl18_51 ),
inference(avatar_split_clause,[],[f547,f544,f346,f297,f587]) ).
fof(f544,plain,
( spl18_51
<=> ! [X0,X1] :
( empty_set = set_difference(X0,X1)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_51])]) ).
fof(f547,plain,
( ! [X0,X1] :
( set_difference(X0,X1) = sK17
| ~ subset(X0,X1) )
| ~ spl18_5
| ~ spl18_17
| ~ spl18_51 ),
inference(forward_demodulation,[],[f545,f366]) ).
fof(f545,plain,
( ! [X0,X1] :
( empty_set = set_difference(X0,X1)
| ~ subset(X0,X1) )
| ~ spl18_51 ),
inference(avatar_component_clause,[],[f544]) ).
fof(f585,plain,
( spl18_53
| ~ spl18_5
| ~ spl18_17
| ~ spl18_50 ),
inference(avatar_split_clause,[],[f542,f539,f346,f297,f583]) ).
fof(f539,plain,
( spl18_50
<=> ! [X0,X1] :
( subset(X0,X1)
| empty_set != set_difference(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_50])]) ).
fof(f542,plain,
( ! [X0,X1] :
( set_difference(X0,X1) != sK17
| subset(X0,X1) )
| ~ spl18_5
| ~ spl18_17
| ~ spl18_50 ),
inference(forward_demodulation,[],[f540,f366]) ).
fof(f540,plain,
( ! [X0,X1] :
( subset(X0,X1)
| empty_set != set_difference(X0,X1) )
| ~ spl18_50 ),
inference(avatar_component_clause,[],[f539]) ).
fof(f551,plain,
( spl18_52
| ~ spl18_5
| ~ spl18_6
| ~ spl18_17
| ~ spl18_23 ),
inference(avatar_split_clause,[],[f393,f381,f346,f302,f297,f549]) ).
fof(f549,plain,
( spl18_52
<=> ! [X3] : ~ proper_subset(X3,sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_52])]) ).
fof(f393,plain,
( ! [X3] : ~ proper_subset(X3,sK17)
| ~ spl18_5
| ~ spl18_6
| ~ spl18_17
| ~ spl18_23 ),
inference(forward_demodulation,[],[f390,f366]) ).
fof(f390,plain,
( ! [X3] : ~ proper_subset(X3,empty_set)
| ~ spl18_6
| ~ spl18_23 ),
inference(resolution,[],[f382,f303]) ).
fof(f546,plain,
spl18_51,
inference(avatar_split_clause,[],[f190,f544]) ).
fof(f190,plain,
! [X0,X1] :
( empty_set = set_difference(X0,X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f117]) ).
fof(f117,plain,
! [X0,X1] :
( ( empty_set = set_difference(X0,X1)
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| empty_set != set_difference(X0,X1) ) ),
inference(nnf_transformation,[],[f31]) ).
fof(f31,axiom,
! [X0,X1] :
( empty_set = set_difference(X0,X1)
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.1596azFLbA/Vampire---4.8_25340',l32_xboole_1) ).
fof(f541,plain,
spl18_50,
inference(avatar_split_clause,[],[f189,f539]) ).
fof(f189,plain,
! [X0,X1] :
( subset(X0,X1)
| empty_set != set_difference(X0,X1) ),
inference(cnf_transformation,[],[f117]) ).
fof(f537,plain,
spl18_49,
inference(avatar_split_clause,[],[f188,f535]) ).
fof(f188,plain,
! [X0,X1] :
( disjoint(X0,X1)
| set_difference(X0,X1) != X0 ),
inference(cnf_transformation,[],[f116]) ).
fof(f116,plain,
! [X0,X1] :
( ( disjoint(X0,X1)
| set_difference(X0,X1) != X0 )
& ( set_difference(X0,X1) = X0
| ~ disjoint(X0,X1) ) ),
inference(nnf_transformation,[],[f64]) ).
fof(f64,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> set_difference(X0,X1) = X0 ),
file('/export/starexec/sandbox/tmp/tmp.1596azFLbA/Vampire---4.8_25340',t83_xboole_1) ).
fof(f533,plain,
spl18_48,
inference(avatar_split_clause,[],[f187,f531]) ).
fof(f187,plain,
! [X0,X1] :
( set_difference(X0,X1) = X0
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f116]) ).
fof(f529,plain,
spl18_47,
inference(avatar_split_clause,[],[f185,f527]) ).
fof(f185,plain,
! [X0,X1] :
( set_intersection2(X0,X1) = X0
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f78]) ).
fof(f78,plain,
! [X0,X1] :
( set_intersection2(X0,X1) = X0
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f42]) ).
fof(f42,axiom,
! [X0,X1] :
( subset(X0,X1)
=> set_intersection2(X0,X1) = X0 ),
file('/export/starexec/sandbox/tmp/tmp.1596azFLbA/Vampire---4.8_25340',t28_xboole_1) ).
fof(f525,plain,
spl18_46,
inference(avatar_split_clause,[],[f184,f523]) ).
fof(f184,plain,
! [X0,X1] :
( set_union2(X0,X1) = X1
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f77]) ).
fof(f77,plain,
! [X0,X1] :
( set_union2(X0,X1) = X1
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f36]) ).
fof(f36,axiom,
! [X0,X1] :
( subset(X0,X1)
=> set_union2(X0,X1) = X1 ),
file('/export/starexec/sandbox/tmp/tmp.1596azFLbA/Vampire---4.8_25340',t12_xboole_1) ).
fof(f521,plain,
spl18_45,
inference(avatar_split_clause,[],[f182,f519]) ).
fof(f182,plain,
! [X0,X1] :
( in(sK7(X0,X1),X1)
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f115]) ).
fof(f517,plain,
spl18_44,
inference(avatar_split_clause,[],[f181,f515]) ).
fof(f181,plain,
! [X0,X1] :
( in(sK7(X0,X1),X0)
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f115]) ).
fof(f513,plain,
spl18_43,
inference(avatar_split_clause,[],[f180,f511]) ).
fof(f180,plain,
! [X2,X0,X1] :
( ~ disjoint(X0,X1)
| ~ in(X2,set_intersection2(X0,X1)) ),
inference(cnf_transformation,[],[f113]) ).
fof(f481,plain,
( spl18_42
| ~ spl18_5
| ~ spl18_17
| ~ spl18_37 ),
inference(avatar_split_clause,[],[f461,f458,f346,f297,f479]) ).
fof(f458,plain,
( spl18_37
<=> ! [X0] :
( empty_set = X0
| in(sK8(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_37])]) ).
fof(f461,plain,
( ! [X0] :
( sK17 = X0
| in(sK8(X0),X0) )
| ~ spl18_5
| ~ spl18_17
| ~ spl18_37 ),
inference(forward_demodulation,[],[f459,f366]) ).
fof(f459,plain,
( ! [X0] :
( empty_set = X0
| in(sK8(X0),X0) )
| ~ spl18_37 ),
inference(avatar_component_clause,[],[f458]) ).
fof(f477,plain,
spl18_41,
inference(avatar_split_clause,[],[f237,f475]) ).
fof(f237,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f99]) ).
fof(f99,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(ennf_transformation,[],[f65]) ).
fof(f65,axiom,
! [X0,X1] :
~ ( empty(X1)
& X0 != X1
& empty(X0) ),
file('/export/starexec/sandbox/tmp/tmp.1596azFLbA/Vampire---4.8_25340',t8_boole) ).
fof(f473,plain,
spl18_40,
inference(avatar_split_clause,[],[f214,f471]) ).
fof(f214,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox/tmp/tmp.1596azFLbA/Vampire---4.8_25340',commutativity_k3_xboole_0) ).
fof(f469,plain,
spl18_39,
inference(avatar_split_clause,[],[f213,f467]) ).
fof(f213,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox/tmp/tmp.1596azFLbA/Vampire---4.8_25340',commutativity_k2_xboole_0) ).
fof(f465,plain,
spl18_38,
inference(avatar_split_clause,[],[f212,f463]) ).
fof(f212,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/tmp/tmp.1596azFLbA/Vampire---4.8_25340',commutativity_k2_tarski) ).
fof(f460,plain,
spl18_37,
inference(avatar_split_clause,[],[f207,f458]) ).
fof(f207,plain,
! [X0] :
( empty_set = X0
| in(sK8(X0),X0) ),
inference(cnf_transformation,[],[f122]) ).
fof(f122,plain,
! [X0] :
( ( empty_set = X0
| in(sK8(X0),X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f120,f121]) ).
fof(f121,plain,
! [X0] :
( ? [X1] : in(X1,X0)
=> in(sK8(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f120,plain,
! [X0] :
( ( empty_set = X0
| ? [X1] : in(X1,X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(rectify,[],[f119]) ).
fof(f119,plain,
! [X0] :
( ( empty_set = X0
| ? [X1] : in(X1,X0) )
& ( ! [X1] : ~ in(X1,X0)
| empty_set != X0 ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0] :
( empty_set = X0
<=> ! [X1] : ~ in(X1,X0) ),
file('/export/starexec/sandbox/tmp/tmp.1596azFLbA/Vampire---4.8_25340',d1_xboole_0) ).
fof(f456,plain,
( ~ spl18_36
| ~ spl18_2
| ~ spl18_30 ),
inference(avatar_split_clause,[],[f448,f421,f282,f453]) ).
fof(f453,plain,
( spl18_36
<=> in(sK5,sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_36])]) ).
fof(f448,plain,
( ~ in(sK5,sK4)
| ~ spl18_2
| ~ spl18_30 ),
inference(resolution,[],[f422,f284]) ).
fof(f284,plain,
( in(sK4,sK5)
| ~ spl18_2 ),
inference(avatar_component_clause,[],[f282]) ).
fof(f443,plain,
( spl18_35
| ~ spl18_5
| ~ spl18_17
| ~ spl18_26 ),
inference(avatar_split_clause,[],[f407,f404,f346,f297,f441]) ).
fof(f404,plain,
( spl18_26
<=> ! [X2,X0] :
( ~ in(X2,X0)
| empty_set != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_26])]) ).
fof(f407,plain,
( ! [X2,X0] :
( sK17 != X0
| ~ in(X2,X0) )
| ~ spl18_5
| ~ spl18_17
| ~ spl18_26 ),
inference(forward_demodulation,[],[f405,f366]) ).
fof(f405,plain,
( ! [X2,X0] :
( ~ in(X2,X0)
| empty_set != X0 )
| ~ spl18_26 ),
inference(avatar_component_clause,[],[f404]) ).
fof(f439,plain,
spl18_34,
inference(avatar_split_clause,[],[f226,f437]) ).
fof(f437,plain,
( spl18_34
<=> ! [X0,X1] :
( X0 != X1
| ~ proper_subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_34])]) ).
fof(f226,plain,
! [X0,X1] :
( X0 != X1
| ~ proper_subset(X0,X1) ),
inference(cnf_transformation,[],[f129]) ).
fof(f435,plain,
spl18_33,
inference(avatar_split_clause,[],[f225,f433]) ).
fof(f433,plain,
( spl18_33
<=> ! [X0,X1] :
( subset(X0,X1)
| ~ proper_subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_33])]) ).
fof(f225,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ proper_subset(X0,X1) ),
inference(cnf_transformation,[],[f129]) ).
fof(f431,plain,
spl18_32,
inference(avatar_split_clause,[],[f223,f429]) ).
fof(f429,plain,
( spl18_32
<=> ! [X0,X1] :
( subset(X1,X0)
| X0 != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_32])]) ).
fof(f223,plain,
! [X0,X1] :
( subset(X1,X0)
| X0 != X1 ),
inference(cnf_transformation,[],[f127]) ).
fof(f427,plain,
spl18_31,
inference(avatar_split_clause,[],[f219,f425]) ).
fof(f219,plain,
! [X0,X1] :
( disjoint(X1,X0)
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f96]) ).
fof(f96,plain,
! [X0,X1] :
( disjoint(X1,X0)
| ~ disjoint(X0,X1) ),
inference(ennf_transformation,[],[f35]) ).
fof(f35,axiom,
! [X0,X1] :
( disjoint(X0,X1)
=> disjoint(X1,X0) ),
file('/export/starexec/sandbox/tmp/tmp.1596azFLbA/Vampire---4.8_25340',symmetry_r1_xboole_0) ).
fof(f423,plain,
spl18_30,
inference(avatar_split_clause,[],[f218,f421]) ).
fof(f218,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f95]) ).
fof(f95,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/tmp/tmp.1596azFLbA/Vampire---4.8_25340',antisymmetry_r2_hidden) ).
fof(f419,plain,
spl18_29,
inference(avatar_split_clause,[],[f217,f417]) ).
fof(f417,plain,
( spl18_29
<=> ! [X0,X1] :
( ~ proper_subset(X1,X0)
| ~ proper_subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_29])]) ).
fof(f217,plain,
! [X0,X1] :
( ~ proper_subset(X1,X0)
| ~ proper_subset(X0,X1) ),
inference(cnf_transformation,[],[f94]) ).
fof(f94,plain,
! [X0,X1] :
( ~ proper_subset(X1,X0)
| ~ proper_subset(X0,X1) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0,X1] :
( proper_subset(X0,X1)
=> ~ proper_subset(X1,X0) ),
file('/export/starexec/sandbox/tmp/tmp.1596azFLbA/Vampire---4.8_25340',antisymmetry_r2_xboole_0) ).
fof(f415,plain,
spl18_28,
inference(avatar_split_clause,[],[f216,f413]) ).
fof(f216,plain,
! [X0,X1] :
( ~ empty(set_union2(X0,X1))
| empty(X0) ),
inference(cnf_transformation,[],[f93]) ).
fof(f93,plain,
! [X0,X1] :
( ~ empty(set_union2(X0,X1))
| empty(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f23,axiom,
! [X0,X1] :
( ~ empty(X0)
=> ~ empty(set_union2(X0,X1)) ),
file('/export/starexec/sandbox/tmp/tmp.1596azFLbA/Vampire---4.8_25340',fc2_xboole_0) ).
fof(f411,plain,
spl18_27,
inference(avatar_split_clause,[],[f215,f409]) ).
fof(f215,plain,
! [X0,X1] :
( ~ empty(set_union2(X1,X0))
| empty(X0) ),
inference(cnf_transformation,[],[f92]) ).
fof(f92,plain,
! [X0,X1] :
( ~ empty(set_union2(X1,X0))
| empty(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,axiom,
! [X0,X1] :
( ~ empty(X0)
=> ~ empty(set_union2(X1,X0)) ),
file('/export/starexec/sandbox/tmp/tmp.1596azFLbA/Vampire---4.8_25340',fc3_xboole_0) ).
fof(f406,plain,
spl18_26,
inference(avatar_split_clause,[],[f206,f404]) ).
fof(f206,plain,
! [X2,X0] :
( ~ in(X2,X0)
| empty_set != X0 ),
inference(cnf_transformation,[],[f122]) ).
fof(f398,plain,
( ~ spl18_25
| ~ spl18_2
| ~ spl18_20 ),
inference(avatar_split_clause,[],[f369,f358,f282,f395]) ).
fof(f395,plain,
( spl18_25
<=> empty(sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_25])]) ).
fof(f369,plain,
( ~ empty(sK5)
| ~ spl18_2
| ~ spl18_20 ),
inference(resolution,[],[f359,f284]) ).
fof(f387,plain,
( spl18_24
| ~ spl18_5
| ~ spl18_17
| ~ spl18_22 ),
inference(avatar_split_clause,[],[f379,f375,f346,f297,f385]) ).
fof(f375,plain,
( spl18_22
<=> ! [X0] :
( empty_set = X0
| ~ subset(X0,empty_set) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_22])]) ).
fof(f379,plain,
( ! [X0] :
( ~ subset(X0,sK17)
| sK17 = X0 )
| ~ spl18_5
| ~ spl18_17
| ~ spl18_22 ),
inference(forward_demodulation,[],[f378,f366]) ).
fof(f378,plain,
( ! [X0] :
( sK17 = X0
| ~ subset(X0,empty_set) )
| ~ spl18_5
| ~ spl18_17
| ~ spl18_22 ),
inference(forward_demodulation,[],[f376,f366]) ).
fof(f376,plain,
( ! [X0] :
( empty_set = X0
| ~ subset(X0,empty_set) )
| ~ spl18_22 ),
inference(avatar_component_clause,[],[f375]) ).
fof(f383,plain,
spl18_23,
inference(avatar_split_clause,[],[f193,f381]) ).
fof(f193,plain,
! [X0,X1] :
( ~ proper_subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f80]) ).
fof(f80,plain,
! [X0,X1] :
( ~ proper_subset(X1,X0)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f58]) ).
fof(f58,axiom,
! [X0,X1] :
~ ( proper_subset(X1,X0)
& subset(X0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.1596azFLbA/Vampire---4.8_25340',t60_xboole_1) ).
fof(f377,plain,
spl18_22,
inference(avatar_split_clause,[],[f172,f375]) ).
fof(f172,plain,
! [X0] :
( empty_set = X0
| ~ subset(X0,empty_set) ),
inference(cnf_transformation,[],[f74]) ).
fof(f74,plain,
! [X0] :
( empty_set = X0
| ~ subset(X0,empty_set) ),
inference(ennf_transformation,[],[f52]) ).
fof(f52,axiom,
! [X0] :
( subset(X0,empty_set)
=> empty_set = X0 ),
file('/export/starexec/sandbox/tmp/tmp.1596azFLbA/Vampire---4.8_25340',t3_xboole_1) ).
fof(f373,plain,
spl18_21,
inference(avatar_split_clause,[],[f171,f371]) ).
fof(f171,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f60]) ).
fof(f60,axiom,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
file('/export/starexec/sandbox/tmp/tmp.1596azFLbA/Vampire---4.8_25340',t69_enumset1) ).
fof(f360,plain,
spl18_20,
inference(avatar_split_clause,[],[f238,f358]) ).
fof(f238,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f100]) ).
fof(f100,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f62]) ).
fof(f62,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.1596azFLbA/Vampire---4.8_25340',t7_boole) ).
fof(f356,plain,
spl18_19,
inference(avatar_split_clause,[],[f211,f354]) ).
fof(f211,plain,
! [X0] : set_intersection2(X0,X0) = X0,
inference(cnf_transformation,[],[f72]) ).
fof(f72,plain,
! [X0] : set_intersection2(X0,X0) = X0,
inference(rectify,[],[f26]) ).
fof(f26,axiom,
! [X0,X1] : set_intersection2(X0,X0) = X0,
file('/export/starexec/sandbox/tmp/tmp.1596azFLbA/Vampire---4.8_25340',idempotence_k3_xboole_0) ).
fof(f352,plain,
spl18_18,
inference(avatar_split_clause,[],[f210,f350]) ).
fof(f210,plain,
! [X0] : set_union2(X0,X0) = X0,
inference(cnf_transformation,[],[f71]) ).
fof(f71,plain,
! [X0] : set_union2(X0,X0) = X0,
inference(rectify,[],[f25]) ).
fof(f25,axiom,
! [X0,X1] : set_union2(X0,X0) = X0,
file('/export/starexec/sandbox/tmp/tmp.1596azFLbA/Vampire---4.8_25340',idempotence_k2_xboole_0) ).
fof(f348,plain,
spl18_17,
inference(avatar_split_clause,[],[f205,f346]) ).
fof(f205,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(cnf_transformation,[],[f91]) ).
fof(f91,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(ennf_transformation,[],[f61]) ).
fof(f61,axiom,
! [X0] :
( empty(X0)
=> empty_set = X0 ),
file('/export/starexec/sandbox/tmp/tmp.1596azFLbA/Vampire---4.8_25340',t6_boole) ).
fof(f344,plain,
spl18_16,
inference(avatar_split_clause,[],[f204,f342]) ).
fof(f204,plain,
! [X0] : set_difference(X0,empty_set) = X0,
inference(cnf_transformation,[],[f50]) ).
fof(f50,axiom,
! [X0] : set_difference(X0,empty_set) = X0,
file('/export/starexec/sandbox/tmp/tmp.1596azFLbA/Vampire---4.8_25340',t3_boole) ).
fof(f340,plain,
spl18_15,
inference(avatar_split_clause,[],[f203,f338]) ).
fof(f203,plain,
! [X0] : set_union2(X0,empty_set) = X0,
inference(cnf_transformation,[],[f39]) ).
fof(f39,axiom,
! [X0] : set_union2(X0,empty_set) = X0,
file('/export/starexec/sandbox/tmp/tmp.1596azFLbA/Vampire---4.8_25340',t1_boole) ).
fof(f336,plain,
spl18_14,
inference(avatar_split_clause,[],[f202,f334]) ).
fof(f202,plain,
! [X0] : empty_set = set_difference(empty_set,X0),
inference(cnf_transformation,[],[f56]) ).
fof(f56,axiom,
! [X0] : empty_set = set_difference(empty_set,X0),
file('/export/starexec/sandbox/tmp/tmp.1596azFLbA/Vampire---4.8_25340',t4_boole) ).
fof(f332,plain,
spl18_13,
inference(avatar_split_clause,[],[f201,f330]) ).
fof(f201,plain,
! [X0] : empty_set = set_intersection2(X0,empty_set),
inference(cnf_transformation,[],[f43]) ).
fof(f43,axiom,
! [X0] : empty_set = set_intersection2(X0,empty_set),
file('/export/starexec/sandbox/tmp/tmp.1596azFLbA/Vampire---4.8_25340',t2_boole) ).
fof(f328,plain,
spl18_12,
inference(avatar_split_clause,[],[f175,f326]) ).
fof(f175,plain,
! [X0,X1] : subset(set_difference(X0,X1),X0),
inference(cnf_transformation,[],[f47]) ).
fof(f47,axiom,
! [X0,X1] : subset(set_difference(X0,X1),X0),
file('/export/starexec/sandbox/tmp/tmp.1596azFLbA/Vampire---4.8_25340',t36_xboole_1) ).
fof(f324,plain,
spl18_11,
inference(avatar_split_clause,[],[f174,f322]) ).
fof(f174,plain,
! [X0,X1] : subset(set_intersection2(X0,X1),X0),
inference(cnf_transformation,[],[f37]) ).
fof(f37,axiom,
! [X0,X1] : subset(set_intersection2(X0,X1),X0),
file('/export/starexec/sandbox/tmp/tmp.1596azFLbA/Vampire---4.8_25340',t17_xboole_1) ).
fof(f320,plain,
spl18_10,
inference(avatar_split_clause,[],[f173,f318]) ).
fof(f173,plain,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
inference(cnf_transformation,[],[f63]) ).
fof(f63,axiom,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
file('/export/starexec/sandbox/tmp/tmp.1596azFLbA/Vampire---4.8_25340',t7_xboole_1) ).
fof(f316,plain,
spl18_9,
inference(avatar_split_clause,[],[f170,f314]) ).
fof(f170,plain,
! [X0] : singleton(X0) != empty_set,
inference(cnf_transformation,[],[f28]) ).
fof(f28,axiom,
! [X0] : singleton(X0) != empty_set,
file('/export/starexec/sandbox/tmp/tmp.1596azFLbA/Vampire---4.8_25340',l1_zfmisc_1) ).
fof(f312,plain,
spl18_8,
inference(avatar_split_clause,[],[f209,f310]) ).
fof(f209,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f70]) ).
fof(f70,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f34]) ).
fof(f34,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox/tmp/tmp.1596azFLbA/Vampire---4.8_25340',reflexivity_r1_tarski) ).
fof(f308,plain,
spl18_7,
inference(avatar_split_clause,[],[f208,f306]) ).
fof(f306,plain,
( spl18_7
<=> ! [X0] : ~ proper_subset(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_7])]) ).
fof(f208,plain,
! [X0] : ~ proper_subset(X0,X0),
inference(cnf_transformation,[],[f69]) ).
fof(f69,plain,
! [X0] : ~ proper_subset(X0,X0),
inference(rectify,[],[f27]) ).
fof(f27,axiom,
! [X0,X1] : ~ proper_subset(X0,X0),
file('/export/starexec/sandbox/tmp/tmp.1596azFLbA/Vampire---4.8_25340',irreflexivity_r2_xboole_0) ).
fof(f304,plain,
spl18_6,
inference(avatar_split_clause,[],[f169,f302]) ).
fof(f169,plain,
! [X0] : subset(empty_set,X0),
inference(cnf_transformation,[],[f45]) ).
fof(f45,axiom,
! [X0] : subset(empty_set,X0),
file('/export/starexec/sandbox/tmp/tmp.1596azFLbA/Vampire---4.8_25340',t2_xboole_1) ).
fof(f300,plain,
spl18_5,
inference(avatar_split_clause,[],[f272,f297]) ).
fof(f272,plain,
empty(sK17),
inference(cnf_transformation,[],[f166]) ).
fof(f166,plain,
empty(sK17),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17])],[f32,f165]) ).
fof(f165,plain,
( ? [X0] : empty(X0)
=> empty(sK17) ),
introduced(choice_axiom,[]) ).
fof(f32,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox/tmp/tmp.1596azFLbA/Vampire---4.8_25340',rc1_xboole_0) ).
fof(f295,plain,
~ spl18_4,
inference(avatar_split_clause,[],[f271,f292]) ).
fof(f292,plain,
( spl18_4
<=> empty(sK16) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_4])]) ).
fof(f271,plain,
~ empty(sK16),
inference(cnf_transformation,[],[f164]) ).
fof(f164,plain,
~ empty(sK16),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f33,f163]) ).
fof(f163,plain,
( ? [X0] : ~ empty(X0)
=> ~ empty(sK16) ),
introduced(choice_axiom,[]) ).
fof(f33,axiom,
? [X0] : ~ empty(X0),
file('/export/starexec/sandbox/tmp/tmp.1596azFLbA/Vampire---4.8_25340',rc2_xboole_0) ).
fof(f290,plain,
spl18_3,
inference(avatar_split_clause,[],[f200,f287]) ).
fof(f287,plain,
( spl18_3
<=> empty(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_3])]) ).
fof(f200,plain,
empty(empty_set),
inference(cnf_transformation,[],[f22]) ).
fof(f22,axiom,
empty(empty_set),
file('/export/starexec/sandbox/tmp/tmp.1596azFLbA/Vampire---4.8_25340',fc1_xboole_0) ).
fof(f285,plain,
( spl18_1
| spl18_2 ),
inference(avatar_split_clause,[],[f167,f282,f278]) ).
fof(f167,plain,
( in(sK4,sK5)
| subset(singleton(sK4),sK5) ),
inference(cnf_transformation,[],[f111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU144+2 : TPTP v8.1.2. Released v3.3.0.
% 0.10/0.12 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.11/0.32 % Computer : n025.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Wed Aug 30 14:16:26 EDT 2023
% 0.11/0.32 % CPUTime :
% 0.16/0.36 % (26648)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.36 % (26857)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on Vampire---4 for (846ds/0Mi)
% 0.16/0.36 % (26861)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on Vampire---4 for (531ds/0Mi)
% 0.16/0.36 % (26860)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on Vampire---4 for (533ds/0Mi)
% 0.16/0.36 % (26863)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on Vampire---4 for (522ds/0Mi)
% 0.16/0.36 % (26859)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on Vampire---4 for (569ds/0Mi)
% 0.16/0.36 % (26864)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on Vampire---4 for (497ds/0Mi)
% 0.16/0.36 % (26858)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on Vampire---4 for (793ds/0Mi)
% 0.16/0.36 TRYING [1]
% 0.16/0.36 TRYING [2]
% 0.16/0.37 TRYING [3]
% 0.16/0.38 TRYING [4]
% 0.16/0.38 TRYING [1]
% 0.16/0.38 TRYING [2]
% 0.16/0.41 TRYING [5]
% 0.16/0.42 TRYING [3]
% 0.16/0.47 TRYING [6]
% 0.16/0.54 TRYING [4]
% 0.16/0.68 TRYING [7]
% 0.16/0.72 % (26861)First to succeed.
% 0.16/0.74 % (26861)Refutation found. Thanks to Tanya!
% 0.16/0.74 % SZS status Theorem for Vampire---4
% 0.16/0.74 % SZS output start Proof for Vampire---4
% See solution above
% 0.16/0.76 % (26861)------------------------------
% 0.16/0.76 % (26861)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.16/0.76 % (26861)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.16/0.76 % (26861)Termination reason: Refutation
% 0.16/0.76
% 0.16/0.76 % (26861)Memory used [KB]: 15479
% 0.16/0.76 % (26861)Time elapsed: 0.384 s
% 0.16/0.76 % (26861)------------------------------
% 0.16/0.76 % (26861)------------------------------
% 0.16/0.76 % (26648)Success in time 0.431 s
% 0.16/0.76 % Vampire---4.8 exiting
%------------------------------------------------------------------------------