TSTP Solution File: SET801+4 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET801+4 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n012.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 : Tue Apr 30 15:13:14 EDT 2024
% Result : Theorem 9.17s 1.68s
% Output : Refutation 9.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 654
% Syntax : Number of formulae : 2206 ( 55 unt; 0 def)
% Number of atoms : 7970 ( 153 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 10096 (4332 ~;4887 |; 171 &)
% ( 665 <=>; 40 =>; 0 <=; 1 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 639 ( 637 usr; 630 prp; 0-4 aty)
% Number of functors : 19 ( 19 usr; 5 con; 0-4 aty)
% Number of variables : 4643 (4599 !; 44 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f20345,plain,
$false,
inference(avatar_sat_refutation,[],[f155,f160,f169,f174,f178,f182,f186,f190,f194,f198,f202,f206,f213,f217,f221,f225,f229,f233,f237,f241,f245,f261,f265,f269,f273,f277,f281,f285,f314,f318,f322,f326,f330,f334,f338,f368,f372,f376,f380,f384,f388,f392,f397,f424,f440,f446,f450,f466,f470,f474,f479,f483,f487,f491,f492,f498,f504,f521,f527,f531,f535,f550,f555,f559,f563,f567,f576,f580,f590,f594,f601,f605,f613,f617,f621,f625,f629,f633,f637,f641,f645,f671,f708,f712,f716,f720,f724,f728,f732,f736,f740,f744,f748,f752,f756,f760,f764,f768,f995,f1004,f1008,f1012,f1016,f1020,f1024,f1028,f1032,f1041,f1045,f1049,f1053,f1057,f1149,f1302,f1306,f1310,f1314,f1318,f1322,f1326,f1330,f1334,f1338,f1500,f1504,f1508,f1644,f1648,f1652,f1682,f1713,f1717,f1721,f1725,f1729,f1733,f1737,f1741,f1745,f1749,f1780,f1998,f2002,f2023,f2027,f2186,f2190,f2215,f2219,f2223,f2305,f2309,f2313,f2317,f2321,f2325,f2329,f2479,f2483,f2573,f2643,f2647,f2651,f2674,f2694,f2698,f2702,f2802,f2806,f2811,f2815,f2855,f2859,f2871,f2879,f2883,f2900,f2904,f2944,f2953,f2957,f2961,f2965,f2969,f2973,f2977,f2981,f2985,f2989,f2993,f2997,f3001,f3070,f3100,f3104,f3108,f3148,f3152,f3160,f3164,f3168,f3172,f3176,f3180,f3184,f3188,f3192,f3196,f3200,f3204,f3208,f3212,f3216,f3220,f3224,f3228,f3232,f3245,f3557,f3561,f3565,f3569,f3573,f3577,f3581,f3585,f3589,f3593,f3597,f3601,f3605,f3609,f3613,f3617,f3621,f3625,f3629,f3633,f3637,f3641,f3654,f3658,f3662,f3666,f3670,f3910,f4051,f4055,f4059,f4063,f4067,f4071,f4075,f4079,f4083,f4087,f4091,f4095,f4099,f4417,f4462,f4466,f4470,f4474,f4478,f4482,f4486,f4490,f4494,f4498,f4765,f4769,f4773,f4777,f4781,f4785,f4789,f4793,f4797,f4819,f5064,f5068,f5072,f5076,f5082,f5086,f5090,f5094,f5098,f5102,f5106,f5110,f5114,f5315,f5323,f5327,f5331,f5335,f5339,f5343,f5347,f5351,f5355,f5359,f5363,f5367,f5371,f5375,f5379,f5383,f5387,f6062,f6066,f6070,f6074,f6079,f6083,f6087,f6091,f6095,f6099,f6103,f6107,f6111,f6115,f6120,f6124,f6128,f6132,f6136,f6140,f6144,f6148,f6152,f6156,f6170,f6174,f6178,f6182,f6540,f6873,f7296,f7300,f7304,f7308,f7312,f7316,f7320,f7324,f7328,f7332,f7336,f7340,f7344,f7348,f7352,f7356,f7360,f7364,f7369,f7373,f7377,f7381,f7385,f7389,f7393,f7397,f7401,f7405,f7409,f7414,f7418,f7422,f7426,f7430,f7434,f7438,f7442,f7446,f7450,f7454,f7459,f7463,f7467,f7471,f7475,f7479,f7483,f7487,f7491,f7495,f7499,f7510,f9852,f9856,f9860,f9864,f9868,f9872,f9876,f9880,f9884,f9888,f9892,f9897,f9901,f9905,f9909,f9913,f9917,f9921,f9925,f9929,f9933,f9937,f9942,f9946,f9950,f9954,f9958,f9962,f9966,f9970,f9974,f9978,f9982,f9987,f9991,f9995,f9999,f10003,f10007,f10011,f10015,f10019,f10023,f10028,f10032,f10036,f10040,f10044,f10048,f10052,f10056,f10060,f10064,f10069,f10073,f10077,f10081,f10385,f11885,f12245,f12764,f13341,f13345,f13349,f13353,f13357,f13361,f13365,f13369,f13373,f13377,f13381,f13385,f13389,f13393,f13397,f13401,f13405,f13409,f13413,f13417,f13421,f13425,f13429,f13433,f13437,f13441,f13445,f13449,f13453,f13457,f13461,f13465,f13469,f13473,f13477,f13482,f13486,f13490,f13494,f13498,f13502,f13506,f13510,f13514,f13518,f13522,f13526,f13530,f13534,f13538,f13542,f13546,f13550,f13554,f13558,f13562,f13567,f13571,f13575,f13579,f13583,f13587,f13591,f13595,f13599,f13603,f13607,f13612,f13616,f13620,f13624,f13628,f13632,f13636,f13640,f13644,f13648,f13652,f13653,f13658,f13660,f13665,f13671,f13675,f13679,f13680,f13684,f13688,f13692,f13696,f13700,f13704,f13708,f13836,f14511,f19978,f19990,f19994,f19998,f20002,f20006,f20010,f20014,f20018,f20022,f20026,f20038,f20042,f20046,f20050,f20054,f20058,f20062,f20066,f20070,f20074,f20086,f20090,f20094,f20098,f20102,f20106,f20110,f20114,f20118,f20122,f20134,f20138,f20142,f20146,f20150,f20154,f20158,f20162,f20166,f20170,f20175,f20179,f20183,f20187,f20191,f20195,f20199,f20203,f20207,f20211,f20215,f20220,f20224,f20228,f20232,f20236,f20240,f20244,f20248,f20252,f20256,f20260,f20265,f20269,f20273,f20277,f20281,f20285,f20289,f20293,f20297,f20301,f20306,f20310,f20314,f20318,f20322,f20326,f20330,f20334,f20338,f20342,f20343,f20344]) ).
fof(f20344,plain,
( spl11_170
| ~ spl11_29
| ~ spl11_57 ),
inference(avatar_split_clause,[],[f13656,f501,f283,f2808]) ).
fof(f2808,plain,
( spl11_170
<=> upper_bound(sK4,sK1,sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_170])]) ).
fof(f283,plain,
( spl11_29
<=> ! [X0,X3,X2,X1] :
( upper_bound(X0,X1,X2)
| ~ sP0(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_29])]) ).
fof(f501,plain,
( spl11_57
<=> sP0(sK4,sK1,sK3,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_57])]) ).
fof(f13656,plain,
( upper_bound(sK4,sK1,sK3)
| ~ spl11_29
| ~ spl11_57 ),
inference(resolution,[],[f503,f284]) ).
fof(f284,plain,
( ! [X2,X3,X0,X1] :
( ~ sP0(X0,X1,X2,X3)
| upper_bound(X0,X1,X2) )
| ~ spl11_29 ),
inference(avatar_component_clause,[],[f283]) ).
fof(f503,plain,
( sP0(sK4,sK1,sK3,sK2)
| ~ spl11_57 ),
inference(avatar_component_clause,[],[f501]) ).
fof(f20343,plain,
( spl11_56
| ~ spl11_38
| ~ spl11_170 ),
inference(avatar_split_clause,[],[f2949,f2808,f370,f496]) ).
fof(f496,plain,
( spl11_56
<=> ! [X0] :
( ~ member(X0,sK3)
| apply(sK1,X0,sK4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_56])]) ).
fof(f370,plain,
( spl11_38
<=> ! [X4,X0,X2,X1] :
( apply(X0,X4,X2)
| ~ member(X4,X1)
| ~ upper_bound(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_38])]) ).
fof(f2949,plain,
( ! [X0] :
( ~ member(X0,sK3)
| apply(sK1,X0,sK4) )
| ~ spl11_38
| ~ spl11_170 ),
inference(resolution,[],[f2810,f371]) ).
fof(f371,plain,
( ! [X2,X0,X1,X4] :
( ~ upper_bound(X2,X0,X1)
| ~ member(X4,X1)
| apply(X0,X4,X2) )
| ~ spl11_38 ),
inference(avatar_component_clause,[],[f370]) ).
fof(f2810,plain,
( upper_bound(sK4,sK1,sK3)
| ~ spl11_170 ),
inference(avatar_component_clause,[],[f2808]) ).
fof(f20342,plain,
( spl11_629
| ~ spl11_11
| ~ spl11_127 ),
inference(avatar_split_clause,[],[f1660,f1642,f196,f20340]) ).
fof(f20340,plain,
( spl11_629
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,X1)
| greatest(X0,X2,X1)
| ~ subset(X1,power_set(X3))
| subset(sK8(X2,X1,X0),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_629])]) ).
fof(f196,plain,
( spl11_11
<=> ! [X0,X1] :
( subset(X0,X1)
| ~ member(X0,power_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_11])]) ).
fof(f1642,plain,
( spl11_127
<=> ! [X0,X3,X2,X1] :
( greatest(X0,X1,X2)
| ~ member(X0,X2)
| member(sK8(X1,X2,X0),X3)
| ~ subset(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_127])]) ).
fof(f1660,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,X1)
| greatest(X0,X2,X1)
| ~ subset(X1,power_set(X3))
| subset(sK8(X2,X1,X0),X3) )
| ~ spl11_11
| ~ spl11_127 ),
inference(resolution,[],[f1643,f197]) ).
fof(f197,plain,
( ! [X0,X1] :
( ~ member(X0,power_set(X1))
| subset(X0,X1) )
| ~ spl11_11 ),
inference(avatar_component_clause,[],[f196]) ).
fof(f1643,plain,
( ! [X2,X3,X0,X1] :
( member(sK8(X1,X2,X0),X3)
| ~ member(X0,X2)
| greatest(X0,X1,X2)
| ~ subset(X2,X3) )
| ~ spl11_127 ),
inference(avatar_component_clause,[],[f1642]) ).
fof(f20338,plain,
( spl11_628
| ~ spl11_14
| ~ spl11_126 ),
inference(avatar_split_clause,[],[f1615,f1506,f211,f20336]) ).
fof(f20336,plain,
( spl11_628
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,X1)
| ~ member(X0,X2)
| member(sK5(X0,X3),sum(intersection(X1,X2)))
| subset(X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_628])]) ).
fof(f211,plain,
( spl11_14
<=> ! [X0,X1] :
( subset(X0,X1)
| member(sK5(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_14])]) ).
fof(f1506,plain,
( spl11_126
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,X1)
| ~ member(X0,X2)
| ~ member(X3,X0)
| member(X3,sum(intersection(X2,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_126])]) ).
fof(f1615,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,X2)
| member(sK5(X0,X3),sum(intersection(X1,X2)))
| subset(X0,X3) )
| ~ spl11_14
| ~ spl11_126 ),
inference(resolution,[],[f1507,f212]) ).
fof(f212,plain,
( ! [X0,X1] :
( member(sK5(X0,X1),X0)
| subset(X0,X1) )
| ~ spl11_14 ),
inference(avatar_component_clause,[],[f211]) ).
fof(f1507,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X3,X0)
| ~ member(X0,X2)
| ~ member(X0,X1)
| member(X3,sum(intersection(X2,X1))) )
| ~ spl11_126 ),
inference(avatar_component_clause,[],[f1506]) ).
fof(f20334,plain,
( spl11_627
| ~ spl11_12
| ~ spl11_126 ),
inference(avatar_split_clause,[],[f1592,f1506,f200,f20332]) ).
fof(f20332,plain,
( spl11_627
<=> ! [X0,X3,X2,X1] :
( ~ member(power_set(X0),X1)
| ~ member(power_set(X0),X2)
| member(X3,sum(intersection(X1,X2)))
| ~ subset(X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_627])]) ).
fof(f200,plain,
( spl11_12
<=> ! [X0,X1] :
( member(X0,power_set(X1))
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_12])]) ).
fof(f1592,plain,
( ! [X2,X3,X0,X1] :
( ~ member(power_set(X0),X1)
| ~ member(power_set(X0),X2)
| member(X3,sum(intersection(X1,X2)))
| ~ subset(X3,X0) )
| ~ spl11_12
| ~ spl11_126 ),
inference(resolution,[],[f1507,f201]) ).
fof(f201,plain,
( ! [X0,X1] :
( member(X0,power_set(X1))
| ~ subset(X0,X1) )
| ~ spl11_12 ),
inference(avatar_component_clause,[],[f200]) ).
fof(f20330,plain,
( spl11_626
| ~ spl11_14
| ~ spl11_125 ),
inference(avatar_split_clause,[],[f1566,f1502,f211,f20328]) ).
fof(f20328,plain,
( spl11_626
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,X1)
| member(X0,X2)
| member(sK5(X0,X3),sum(difference(X1,X2)))
| subset(X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_626])]) ).
fof(f1502,plain,
( spl11_125
<=> ! [X0,X3,X2,X1] :
( member(X0,X1)
| ~ member(X0,X2)
| ~ member(X3,X0)
| member(X3,sum(difference(X2,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_125])]) ).
fof(f1566,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,X1)
| member(X0,X2)
| member(sK5(X0,X3),sum(difference(X1,X2)))
| subset(X0,X3) )
| ~ spl11_14
| ~ spl11_125 ),
inference(resolution,[],[f1503,f212]) ).
fof(f1503,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X3,X0)
| ~ member(X0,X2)
| member(X0,X1)
| member(X3,sum(difference(X2,X1))) )
| ~ spl11_125 ),
inference(avatar_component_clause,[],[f1502]) ).
fof(f20326,plain,
( spl11_625
| ~ spl11_12
| ~ spl11_125 ),
inference(avatar_split_clause,[],[f1543,f1502,f200,f20324]) ).
fof(f20324,plain,
( spl11_625
<=> ! [X0,X3,X2,X1] :
( ~ member(power_set(X0),X1)
| member(power_set(X0),X2)
| member(X3,sum(difference(X1,X2)))
| ~ subset(X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_625])]) ).
fof(f1543,plain,
( ! [X2,X3,X0,X1] :
( ~ member(power_set(X0),X1)
| member(power_set(X0),X2)
| member(X3,sum(difference(X1,X2)))
| ~ subset(X3,X0) )
| ~ spl11_12
| ~ spl11_125 ),
inference(resolution,[],[f1503,f201]) ).
fof(f20322,plain,
( spl11_624
| ~ spl11_16
| ~ spl11_124 ),
inference(avatar_split_clause,[],[f1520,f1498,f219,f20320]) ).
fof(f20320,plain,
( spl11_624
<=> ! [X4,X0,X3,X2,X1] :
( ~ member(difference(X0,X1),X2)
| upper_bound(X3,X4,product(X2))
| member(sK9(X4,product(X2),X3),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_624])]) ).
fof(f219,plain,
( spl11_16
<=> ! [X2,X0,X1] :
( member(X0,X2)
| ~ member(X0,difference(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_16])]) ).
fof(f1498,plain,
( spl11_124
<=> ! [X0,X3,X2,X1] :
( upper_bound(X0,X1,product(X2))
| ~ member(X3,X2)
| member(sK9(X1,product(X2),X0),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_124])]) ).
fof(f1520,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ member(difference(X0,X1),X2)
| upper_bound(X3,X4,product(X2))
| member(sK9(X4,product(X2),X3),X0) )
| ~ spl11_16
| ~ spl11_124 ),
inference(resolution,[],[f1499,f220]) ).
fof(f220,plain,
( ! [X2,X0,X1] :
( ~ member(X0,difference(X2,X1))
| member(X0,X2) )
| ~ spl11_16 ),
inference(avatar_component_clause,[],[f219]) ).
fof(f1499,plain,
( ! [X2,X3,X0,X1] :
( member(sK9(X1,product(X2),X0),X3)
| ~ member(X3,X2)
| upper_bound(X0,X1,product(X2)) )
| ~ spl11_124 ),
inference(avatar_component_clause,[],[f1498]) ).
fof(f20318,plain,
( spl11_623
| ~ spl11_17
| ~ spl11_124 ),
inference(avatar_split_clause,[],[f1519,f1498,f223,f20316]) ).
fof(f20316,plain,
( spl11_623
<=> ! [X4,X0,X3,X2,X1] :
( ~ member(difference(X0,X1),X2)
| upper_bound(X3,X4,product(X2))
| ~ member(sK9(X4,product(X2),X3),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_623])]) ).
fof(f223,plain,
( spl11_17
<=> ! [X2,X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,difference(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_17])]) ).
fof(f1519,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ member(difference(X0,X1),X2)
| upper_bound(X3,X4,product(X2))
| ~ member(sK9(X4,product(X2),X3),X1) )
| ~ spl11_17
| ~ spl11_124 ),
inference(resolution,[],[f1499,f224]) ).
fof(f224,plain,
( ! [X2,X0,X1] :
( ~ member(X0,difference(X2,X1))
| ~ member(X0,X1) )
| ~ spl11_17 ),
inference(avatar_component_clause,[],[f223]) ).
fof(f20314,plain,
( spl11_622
| ~ spl11_18
| ~ spl11_124 ),
inference(avatar_split_clause,[],[f1516,f1498,f227,f20312]) ).
fof(f20312,plain,
( spl11_622
<=> ! [X4,X0,X3,X2,X1] :
( ~ member(intersection(X0,X1),X2)
| upper_bound(X3,X4,product(X2))
| member(sK9(X4,product(X2),X3),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_622])]) ).
fof(f227,plain,
( spl11_18
<=> ! [X2,X0,X1] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_18])]) ).
fof(f1516,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ member(intersection(X0,X1),X2)
| upper_bound(X3,X4,product(X2))
| member(sK9(X4,product(X2),X3),X0) )
| ~ spl11_18
| ~ spl11_124 ),
inference(resolution,[],[f1499,f228]) ).
fof(f228,plain,
( ! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) )
| ~ spl11_18 ),
inference(avatar_component_clause,[],[f227]) ).
fof(f20310,plain,
( spl11_621
| ~ spl11_19
| ~ spl11_124 ),
inference(avatar_split_clause,[],[f1515,f1498,f231,f20308]) ).
fof(f20308,plain,
( spl11_621
<=> ! [X4,X0,X3,X2,X1] :
( ~ member(intersection(X0,X1),X2)
| upper_bound(X3,X4,product(X2))
| member(sK9(X4,product(X2),X3),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_621])]) ).
fof(f231,plain,
( spl11_19
<=> ! [X2,X0,X1] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_19])]) ).
fof(f1515,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ member(intersection(X0,X1),X2)
| upper_bound(X3,X4,product(X2))
| member(sK9(X4,product(X2),X3),X1) )
| ~ spl11_19
| ~ spl11_124 ),
inference(resolution,[],[f1499,f232]) ).
fof(f232,plain,
( ! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) )
| ~ spl11_19 ),
inference(avatar_component_clause,[],[f231]) ).
fof(f20306,plain,
( spl11_620
| ~ spl11_23
| ~ spl11_121 ),
inference(avatar_split_clause,[],[f1477,f1328,f259,f20304]) ).
fof(f20304,plain,
( spl11_620
<=> ! [X4,X0,X3,X2,X1] :
( upper_bound(X0,X1,difference(X2,X3))
| member(sK9(X1,difference(X2,X3),X0),X4)
| ~ subset(X2,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_620])]) ).
fof(f259,plain,
( spl11_23
<=> ! [X0,X1,X3] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_23])]) ).
fof(f1328,plain,
( spl11_121
<=> ! [X0,X3,X2,X1] :
( upper_bound(X0,X1,difference(X2,X3))
| member(sK9(X1,difference(X2,X3),X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_121])]) ).
fof(f1477,plain,
( ! [X2,X3,X0,X1,X4] :
( upper_bound(X0,X1,difference(X2,X3))
| member(sK9(X1,difference(X2,X3),X0),X4)
| ~ subset(X2,X4) )
| ~ spl11_23
| ~ spl11_121 ),
inference(resolution,[],[f1329,f260]) ).
fof(f260,plain,
( ! [X3,X0,X1] :
( ~ member(X3,X0)
| member(X3,X1)
| ~ subset(X0,X1) )
| ~ spl11_23 ),
inference(avatar_component_clause,[],[f259]) ).
fof(f1329,plain,
( ! [X2,X3,X0,X1] :
( member(sK9(X1,difference(X2,X3),X0),X2)
| upper_bound(X0,X1,difference(X2,X3)) )
| ~ spl11_121 ),
inference(avatar_component_clause,[],[f1328]) ).
fof(f20301,plain,
( spl11_619
| ~ spl11_23
| ~ spl11_119 ),
inference(avatar_split_clause,[],[f1439,f1320,f259,f20299]) ).
fof(f20299,plain,
( spl11_619
<=> ! [X4,X0,X3,X2,X1] :
( upper_bound(X0,X1,intersection(X2,X3))
| member(sK9(X1,intersection(X2,X3),X0),X4)
| ~ subset(X2,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_619])]) ).
fof(f1320,plain,
( spl11_119
<=> ! [X0,X3,X2,X1] :
( upper_bound(X0,X1,intersection(X2,X3))
| member(sK9(X1,intersection(X2,X3),X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_119])]) ).
fof(f1439,plain,
( ! [X2,X3,X0,X1,X4] :
( upper_bound(X0,X1,intersection(X2,X3))
| member(sK9(X1,intersection(X2,X3),X0),X4)
| ~ subset(X2,X4) )
| ~ spl11_23
| ~ spl11_119 ),
inference(resolution,[],[f1321,f260]) ).
fof(f1321,plain,
( ! [X2,X3,X0,X1] :
( member(sK9(X1,intersection(X2,X3),X0),X2)
| upper_bound(X0,X1,intersection(X2,X3)) )
| ~ spl11_119 ),
inference(avatar_component_clause,[],[f1320]) ).
fof(f20297,plain,
( spl11_618
| ~ spl11_23
| ~ spl11_118 ),
inference(avatar_split_clause,[],[f1418,f1316,f259,f20295]) ).
fof(f20295,plain,
( spl11_618
<=> ! [X4,X0,X3,X2,X1] :
( upper_bound(X0,X1,intersection(X2,X3))
| member(sK9(X1,intersection(X2,X3),X0),X4)
| ~ subset(X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_618])]) ).
fof(f1316,plain,
( spl11_118
<=> ! [X0,X3,X2,X1] :
( upper_bound(X0,X1,intersection(X2,X3))
| member(sK9(X1,intersection(X2,X3),X0),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_118])]) ).
fof(f1418,plain,
( ! [X2,X3,X0,X1,X4] :
( upper_bound(X0,X1,intersection(X2,X3))
| member(sK9(X1,intersection(X2,X3),X0),X4)
| ~ subset(X3,X4) )
| ~ spl11_23
| ~ spl11_118 ),
inference(resolution,[],[f1317,f260]) ).
fof(f1317,plain,
( ! [X2,X3,X0,X1] :
( member(sK9(X1,intersection(X2,X3),X0),X3)
| upper_bound(X0,X1,intersection(X2,X3)) )
| ~ spl11_118 ),
inference(avatar_component_clause,[],[f1316]) ).
fof(f20293,plain,
( spl11_617
| ~ spl11_23
| ~ spl11_115 ),
inference(avatar_split_clause,[],[f1364,f1304,f259,f20291]) ).
fof(f20291,plain,
( spl11_617
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,X1)
| ~ member(X2,sum(product(X1)))
| member(sK7(X2,product(X1)),X3)
| ~ subset(X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_617])]) ).
fof(f1304,plain,
( spl11_115
<=> ! [X2,X0,X1] :
( ~ member(X0,X1)
| member(sK7(X2,product(X1)),X0)
| ~ member(X2,sum(product(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_115])]) ).
fof(f1364,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,X1)
| ~ member(X2,sum(product(X1)))
| member(sK7(X2,product(X1)),X3)
| ~ subset(X0,X3) )
| ~ spl11_23
| ~ spl11_115 ),
inference(resolution,[],[f1305,f260]) ).
fof(f1305,plain,
( ! [X2,X0,X1] :
( member(sK7(X2,product(X1)),X0)
| ~ member(X0,X1)
| ~ member(X2,sum(product(X1))) )
| ~ spl11_115 ),
inference(avatar_component_clause,[],[f1304]) ).
fof(f20289,plain,
( spl11_616
| ~ spl11_23
| ~ spl11_114 ),
inference(avatar_split_clause,[],[f1343,f1300,f259,f20287]) ).
fof(f20287,plain,
( spl11_616
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,X1)
| member(X2,product(product(X1)))
| member(sK6(X2,product(X1)),X3)
| ~ subset(X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_616])]) ).
fof(f1300,plain,
( spl11_114
<=> ! [X2,X0,X1] :
( ~ member(X0,X1)
| member(sK6(X2,product(X1)),X0)
| member(X2,product(product(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_114])]) ).
fof(f1343,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,X1)
| member(X2,product(product(X1)))
| member(sK6(X2,product(X1)),X3)
| ~ subset(X0,X3) )
| ~ spl11_23
| ~ spl11_114 ),
inference(resolution,[],[f1301,f260]) ).
fof(f1301,plain,
( ! [X2,X0,X1] :
( member(sK6(X2,product(X1)),X0)
| ~ member(X0,X1)
| member(X2,product(product(X1))) )
| ~ spl11_114 ),
inference(avatar_component_clause,[],[f1300]) ).
fof(f20285,plain,
( spl11_615
| ~ spl11_32
| ~ spl11_112 ),
inference(avatar_split_clause,[],[f1294,f1055,f320,f20283]) ).
fof(f20283,plain,
( spl11_615
<=> ! [X4,X0,X3,X2,X1] :
( upper_bound(X0,X1,X2)
| ~ subset(X2,product(X3))
| ~ member(X4,X3)
| member(sK9(X1,X2,X0),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_615])]) ).
fof(f320,plain,
( spl11_32
<=> ! [X0,X1,X3] :
( member(X0,X3)
| ~ member(X3,X1)
| ~ member(X0,product(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_32])]) ).
fof(f1055,plain,
( spl11_112
<=> ! [X0,X3,X2,X1] :
( upper_bound(X0,X1,X2)
| member(sK9(X1,X2,X0),X3)
| ~ subset(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_112])]) ).
fof(f1294,plain,
( ! [X2,X3,X0,X1,X4] :
( upper_bound(X0,X1,X2)
| ~ subset(X2,product(X3))
| ~ member(X4,X3)
| member(sK9(X1,X2,X0),X4) )
| ~ spl11_32
| ~ spl11_112 ),
inference(resolution,[],[f1056,f321]) ).
fof(f321,plain,
( ! [X3,X0,X1] :
( ~ member(X0,product(X1))
| ~ member(X3,X1)
| member(X0,X3) )
| ~ spl11_32 ),
inference(avatar_component_clause,[],[f320]) ).
fof(f1056,plain,
( ! [X2,X3,X0,X1] :
( member(sK9(X1,X2,X0),X3)
| upper_bound(X0,X1,X2)
| ~ subset(X2,X3) )
| ~ spl11_112 ),
inference(avatar_component_clause,[],[f1055]) ).
fof(f20281,plain,
( spl11_614
| ~ spl11_33
| ~ spl11_112 ),
inference(avatar_split_clause,[],[f1281,f1055,f324,f20279]) ).
fof(f20279,plain,
( spl11_614
<=> ! [X4,X0,X3,X2,X1] :
( upper_bound(X0,X1,X2)
| ~ subset(X2,X3)
| ~ member(X4,sK9(X1,X2,X0))
| member(X4,sum(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_614])]) ).
fof(f324,plain,
( spl11_33
<=> ! [X2,X0,X1] :
( member(X0,sum(X1))
| ~ member(X0,X2)
| ~ member(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_33])]) ).
fof(f1281,plain,
( ! [X2,X3,X0,X1,X4] :
( upper_bound(X0,X1,X2)
| ~ subset(X2,X3)
| ~ member(X4,sK9(X1,X2,X0))
| member(X4,sum(X3)) )
| ~ spl11_33
| ~ spl11_112 ),
inference(resolution,[],[f1056,f325]) ).
fof(f325,plain,
( ! [X2,X0,X1] :
( ~ member(X2,X1)
| ~ member(X0,X2)
| member(X0,sum(X1)) )
| ~ spl11_33 ),
inference(avatar_component_clause,[],[f324]) ).
fof(f20277,plain,
( spl11_613
| ~ spl11_14
| ~ spl11_111 ),
inference(avatar_split_clause,[],[f1258,f1051,f211,f20275]) ).
fof(f20275,plain,
( spl11_613
<=> ! [X2,X0,X1] :
( member(sK5(sK7(X0,X1),X2),sum(X1))
| ~ member(X0,sum(X1))
| subset(sK7(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_613])]) ).
fof(f1051,plain,
( spl11_111
<=> ! [X2,X0,X1] :
( ~ member(X0,sK7(X1,X2))
| member(X0,sum(X2))
| ~ member(X1,sum(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_111])]) ).
fof(f1258,plain,
( ! [X2,X0,X1] :
( member(sK5(sK7(X0,X1),X2),sum(X1))
| ~ member(X0,sum(X1))
| subset(sK7(X0,X1),X2) )
| ~ spl11_14
| ~ spl11_111 ),
inference(resolution,[],[f1052,f212]) ).
fof(f1052,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sK7(X1,X2))
| member(X0,sum(X2))
| ~ member(X1,sum(X2)) )
| ~ spl11_111 ),
inference(avatar_component_clause,[],[f1051]) ).
fof(f20273,plain,
( spl11_612
| ~ spl11_14
| ~ spl11_110 ),
inference(avatar_split_clause,[],[f1238,f1047,f211,f20271]) ).
fof(f20271,plain,
( spl11_612
<=> ! [X2,X0,X1] :
( member(sK5(sK6(X0,X1),X2),sum(X1))
| member(X0,product(X1))
| subset(sK6(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_612])]) ).
fof(f1047,plain,
( spl11_110
<=> ! [X2,X0,X1] :
( ~ member(X0,sK6(X1,X2))
| member(X0,sum(X2))
| member(X1,product(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_110])]) ).
fof(f1238,plain,
( ! [X2,X0,X1] :
( member(sK5(sK6(X0,X1),X2),sum(X1))
| member(X0,product(X1))
| subset(sK6(X0,X1),X2) )
| ~ spl11_14
| ~ spl11_110 ),
inference(resolution,[],[f1048,f212]) ).
fof(f1048,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sK6(X1,X2))
| member(X0,sum(X2))
| member(X1,product(X2)) )
| ~ spl11_110 ),
inference(avatar_component_clause,[],[f1047]) ).
fof(f20269,plain,
( spl11_611
| ~ spl11_33
| ~ spl11_109 ),
inference(avatar_split_clause,[],[f1230,f1043,f324,f20267]) ).
fof(f20267,plain,
( spl11_611
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,X1)
| ~ member(X1,sum(X2))
| ~ member(X3,X0)
| member(X3,sum(sum(sK7(X1,X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_611])]) ).
fof(f1043,plain,
( spl11_109
<=> ! [X2,X0,X1] :
( ~ member(X0,X1)
| member(X0,sum(sK7(X1,X2)))
| ~ member(X1,sum(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_109])]) ).
fof(f1230,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,X1)
| ~ member(X1,sum(X2))
| ~ member(X3,X0)
| member(X3,sum(sum(sK7(X1,X2)))) )
| ~ spl11_33
| ~ spl11_109 ),
inference(resolution,[],[f1044,f325]) ).
fof(f1044,plain,
( ! [X2,X0,X1] :
( member(X0,sum(sK7(X1,X2)))
| ~ member(X0,X1)
| ~ member(X1,sum(X2)) )
| ~ spl11_109 ),
inference(avatar_component_clause,[],[f1043]) ).
fof(f20265,plain,
( spl11_610
| ~ spl11_32
| ~ spl11_108 ),
inference(avatar_split_clause,[],[f1221,f1039,f320,f20263]) ).
fof(f20263,plain,
( spl11_610
<=> ! [X0,X3,X2,X1] :
( ~ member(product(X0),X1)
| subset(product(X1),X2)
| ~ member(X3,X0)
| member(sK5(product(X1),X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_610])]) ).
fof(f1039,plain,
( spl11_108
<=> ! [X2,X0,X1] :
( ~ member(X0,X1)
| member(sK5(product(X1),X2),X0)
| subset(product(X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_108])]) ).
fof(f1221,plain,
( ! [X2,X3,X0,X1] :
( ~ member(product(X0),X1)
| subset(product(X1),X2)
| ~ member(X3,X0)
| member(sK5(product(X1),X2),X3) )
| ~ spl11_32
| ~ spl11_108 ),
inference(resolution,[],[f1040,f321]) ).
fof(f1040,plain,
( ! [X2,X0,X1] :
( member(sK5(product(X1),X2),X0)
| ~ member(X0,X1)
| subset(product(X1),X2) )
| ~ spl11_108 ),
inference(avatar_component_clause,[],[f1039]) ).
fof(f20260,plain,
( spl11_609
| ~ spl11_33
| ~ spl11_108 ),
inference(avatar_split_clause,[],[f1208,f1039,f324,f20258]) ).
fof(f20258,plain,
( spl11_609
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,X1)
| subset(product(X1),X2)
| ~ member(X3,sK5(product(X1),X2))
| member(X3,sum(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_609])]) ).
fof(f1208,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,X1)
| subset(product(X1),X2)
| ~ member(X3,sK5(product(X1),X2))
| member(X3,sum(X0)) )
| ~ spl11_33
| ~ spl11_108 ),
inference(resolution,[],[f1040,f325]) ).
fof(f20256,plain,
( spl11_608
| ~ spl11_16
| ~ spl11_107 ),
inference(avatar_split_clause,[],[f1194,f1030,f219,f20254]) ).
fof(f20254,plain,
( spl11_608
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,sum(difference(difference(X1,X2),X3)))
| member(sK7(X0,difference(difference(X1,X2),X3)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_608])]) ).
fof(f1030,plain,
( spl11_107
<=> ! [X2,X0,X1] :
( ~ member(X0,sum(difference(X1,X2)))
| member(sK7(X0,difference(X1,X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_107])]) ).
fof(f1194,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,sum(difference(difference(X1,X2),X3)))
| member(sK7(X0,difference(difference(X1,X2),X3)),X1) )
| ~ spl11_16
| ~ spl11_107 ),
inference(resolution,[],[f1031,f220]) ).
fof(f1031,plain,
( ! [X2,X0,X1] :
( member(sK7(X0,difference(X1,X2)),X1)
| ~ member(X0,sum(difference(X1,X2))) )
| ~ spl11_107 ),
inference(avatar_component_clause,[],[f1030]) ).
fof(f20252,plain,
( spl11_607
| ~ spl11_17
| ~ spl11_107 ),
inference(avatar_split_clause,[],[f1193,f1030,f223,f20250]) ).
fof(f20250,plain,
( spl11_607
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,sum(difference(difference(X1,X2),X3)))
| ~ member(sK7(X0,difference(difference(X1,X2),X3)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_607])]) ).
fof(f1193,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,sum(difference(difference(X1,X2),X3)))
| ~ member(sK7(X0,difference(difference(X1,X2),X3)),X2) )
| ~ spl11_17
| ~ spl11_107 ),
inference(resolution,[],[f1031,f224]) ).
fof(f20248,plain,
( spl11_606
| ~ spl11_18
| ~ spl11_107 ),
inference(avatar_split_clause,[],[f1190,f1030,f227,f20246]) ).
fof(f20246,plain,
( spl11_606
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,sum(difference(intersection(X1,X2),X3)))
| member(sK7(X0,difference(intersection(X1,X2),X3)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_606])]) ).
fof(f1190,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,sum(difference(intersection(X1,X2),X3)))
| member(sK7(X0,difference(intersection(X1,X2),X3)),X1) )
| ~ spl11_18
| ~ spl11_107 ),
inference(resolution,[],[f1031,f228]) ).
fof(f20244,plain,
( spl11_605
| ~ spl11_19
| ~ spl11_107 ),
inference(avatar_split_clause,[],[f1189,f1030,f231,f20242]) ).
fof(f20242,plain,
( spl11_605
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,sum(difference(intersection(X1,X2),X3)))
| member(sK7(X0,difference(intersection(X1,X2),X3)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_605])]) ).
fof(f1189,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,sum(difference(intersection(X1,X2),X3)))
| member(sK7(X0,difference(intersection(X1,X2),X3)),X2) )
| ~ spl11_19
| ~ spl11_107 ),
inference(resolution,[],[f1031,f232]) ).
fof(f20240,plain,
( spl11_604
| ~ spl11_33
| ~ spl11_107 ),
inference(avatar_split_clause,[],[f1186,f1030,f324,f20238]) ).
fof(f20238,plain,
( spl11_604
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,sum(difference(X1,X2)))
| ~ member(X3,sK7(X0,difference(X1,X2)))
| member(X3,sum(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_604])]) ).
fof(f1186,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,sum(difference(X1,X2)))
| ~ member(X3,sK7(X0,difference(X1,X2)))
| member(X3,sum(X1)) )
| ~ spl11_33
| ~ spl11_107 ),
inference(resolution,[],[f1031,f325]) ).
fof(f20236,plain,
( spl11_603
| ~ spl11_66
| ~ spl11_106 ),
inference(avatar_split_clause,[],[f1174,f1026,f565,f20234]) ).
fof(f20234,plain,
( spl11_603
<=> ! [X2,X0,X1] :
( ~ member(X0,sum(difference(X1,sum(singleton(X2)))))
| ~ member(sK7(X0,difference(X1,sum(singleton(X2)))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_603])]) ).
fof(f565,plain,
( spl11_66
<=> ! [X0,X1] :
( ~ member(X0,X1)
| member(X0,sum(singleton(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_66])]) ).
fof(f1026,plain,
( spl11_106
<=> ! [X2,X0,X1] :
( ~ member(X0,sum(difference(X1,X2)))
| ~ member(sK7(X0,difference(X1,X2)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_106])]) ).
fof(f1174,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sum(difference(X1,sum(singleton(X2)))))
| ~ member(sK7(X0,difference(X1,sum(singleton(X2)))),X2) )
| ~ spl11_66
| ~ spl11_106 ),
inference(resolution,[],[f1027,f566]) ).
fof(f566,plain,
( ! [X0,X1] :
( member(X0,sum(singleton(X1)))
| ~ member(X0,X1) )
| ~ spl11_66 ),
inference(avatar_component_clause,[],[f565]) ).
fof(f1027,plain,
( ! [X2,X0,X1] :
( ~ member(sK7(X0,difference(X1,X2)),X2)
| ~ member(X0,sum(difference(X1,X2))) )
| ~ spl11_106 ),
inference(avatar_component_clause,[],[f1026]) ).
fof(f20232,plain,
( spl11_602
| ~ spl11_20
| ~ spl11_106 ),
inference(avatar_split_clause,[],[f1172,f1026,f235,f20230]) ).
fof(f20230,plain,
( spl11_602
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,sum(difference(X1,union(X2,X3))))
| ~ member(sK7(X0,difference(X1,union(X2,X3))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_602])]) ).
fof(f235,plain,
( spl11_20
<=> ! [X2,X0,X1] :
( member(X0,union(X1,X2))
| ~ member(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_20])]) ).
fof(f1172,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,sum(difference(X1,union(X2,X3))))
| ~ member(sK7(X0,difference(X1,union(X2,X3))),X2) )
| ~ spl11_20
| ~ spl11_106 ),
inference(resolution,[],[f1027,f236]) ).
fof(f236,plain,
( ! [X2,X0,X1] :
( member(X0,union(X1,X2))
| ~ member(X0,X1) )
| ~ spl11_20 ),
inference(avatar_component_clause,[],[f235]) ).
fof(f20228,plain,
( spl11_601
| ~ spl11_21
| ~ spl11_106 ),
inference(avatar_split_clause,[],[f1171,f1026,f239,f20226]) ).
fof(f20226,plain,
( spl11_601
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,sum(difference(X1,union(X2,X3))))
| ~ member(sK7(X0,difference(X1,union(X2,X3))),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_601])]) ).
fof(f239,plain,
( spl11_21
<=> ! [X2,X0,X1] :
( member(X0,union(X1,X2))
| ~ member(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_21])]) ).
fof(f1171,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,sum(difference(X1,union(X2,X3))))
| ~ member(sK7(X0,difference(X1,union(X2,X3))),X3) )
| ~ spl11_21
| ~ spl11_106 ),
inference(resolution,[],[f1027,f240]) ).
fof(f240,plain,
( ! [X2,X0,X1] :
( member(X0,union(X1,X2))
| ~ member(X0,X2) )
| ~ spl11_21 ),
inference(avatar_component_clause,[],[f239]) ).
fof(f20224,plain,
( spl11_600
| ~ spl11_16
| ~ spl11_105 ),
inference(avatar_split_clause,[],[f1161,f1022,f219,f20222]) ).
fof(f20222,plain,
( spl11_600
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,sum(intersection(difference(X1,X2),X3)))
| member(sK7(X0,intersection(difference(X1,X2),X3)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_600])]) ).
fof(f1022,plain,
( spl11_105
<=> ! [X2,X0,X1] :
( ~ member(X0,sum(intersection(X1,X2)))
| member(sK7(X0,intersection(X1,X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_105])]) ).
fof(f1161,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,sum(intersection(difference(X1,X2),X3)))
| member(sK7(X0,intersection(difference(X1,X2),X3)),X1) )
| ~ spl11_16
| ~ spl11_105 ),
inference(resolution,[],[f1023,f220]) ).
fof(f1023,plain,
( ! [X2,X0,X1] :
( member(sK7(X0,intersection(X1,X2)),X1)
| ~ member(X0,sum(intersection(X1,X2))) )
| ~ spl11_105 ),
inference(avatar_component_clause,[],[f1022]) ).
fof(f20220,plain,
( spl11_599
| ~ spl11_155
| ~ spl11_544 ),
inference(avatar_split_clause,[],[f19973,f13706,f2319,f20217]) ).
fof(f20217,plain,
( spl11_599
<=> upper_bound(sK4,sK1,union(sum(empty_set),sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_599])]) ).
fof(f2319,plain,
( spl11_155
<=> ! [X0] :
( ~ member(sK9(sK1,X0,sK4),sK3)
| upper_bound(sK4,sK1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_155])]) ).
fof(f13706,plain,
( spl11_544
<=> ! [X2,X0,X1] :
( member(sK9(X0,union(sum(empty_set),X1),X2),X1)
| upper_bound(X2,X0,union(sum(empty_set),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_544])]) ).
fof(f19973,plain,
( upper_bound(sK4,sK1,union(sum(empty_set),sK3))
| ~ spl11_155
| ~ spl11_544 ),
inference(duplicate_literal_removal,[],[f19885]) ).
fof(f19885,plain,
( upper_bound(sK4,sK1,union(sum(empty_set),sK3))
| upper_bound(sK4,sK1,union(sum(empty_set),sK3))
| ~ spl11_155
| ~ spl11_544 ),
inference(resolution,[],[f13707,f2320]) ).
fof(f2320,plain,
( ! [X0] :
( ~ member(sK9(sK1,X0,sK4),sK3)
| upper_bound(sK4,sK1,X0) )
| ~ spl11_155 ),
inference(avatar_component_clause,[],[f2319]) ).
fof(f13707,plain,
( ! [X2,X0,X1] :
( member(sK9(X0,union(sum(empty_set),X1),X2),X1)
| upper_bound(X2,X0,union(sum(empty_set),X1)) )
| ~ spl11_544 ),
inference(avatar_component_clause,[],[f13706]) ).
fof(f20215,plain,
( spl11_598
| ~ spl11_17
| ~ spl11_105 ),
inference(avatar_split_clause,[],[f1160,f1022,f223,f20213]) ).
fof(f20213,plain,
( spl11_598
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,sum(intersection(difference(X1,X2),X3)))
| ~ member(sK7(X0,intersection(difference(X1,X2),X3)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_598])]) ).
fof(f1160,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,sum(intersection(difference(X1,X2),X3)))
| ~ member(sK7(X0,intersection(difference(X1,X2),X3)),X2) )
| ~ spl11_17
| ~ spl11_105 ),
inference(resolution,[],[f1023,f224]) ).
fof(f20211,plain,
( spl11_597
| ~ spl11_18
| ~ spl11_105 ),
inference(avatar_split_clause,[],[f1157,f1022,f227,f20209]) ).
fof(f20209,plain,
( spl11_597
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,sum(intersection(intersection(X1,X2),X3)))
| member(sK7(X0,intersection(intersection(X1,X2),X3)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_597])]) ).
fof(f1157,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,sum(intersection(intersection(X1,X2),X3)))
| member(sK7(X0,intersection(intersection(X1,X2),X3)),X1) )
| ~ spl11_18
| ~ spl11_105 ),
inference(resolution,[],[f1023,f228]) ).
fof(f20207,plain,
( spl11_596
| ~ spl11_19
| ~ spl11_105 ),
inference(avatar_split_clause,[],[f1156,f1022,f231,f20205]) ).
fof(f20205,plain,
( spl11_596
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,sum(intersection(intersection(X1,X2),X3)))
| member(sK7(X0,intersection(intersection(X1,X2),X3)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_596])]) ).
fof(f1156,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,sum(intersection(intersection(X1,X2),X3)))
| member(sK7(X0,intersection(intersection(X1,X2),X3)),X2) )
| ~ spl11_19
| ~ spl11_105 ),
inference(resolution,[],[f1023,f232]) ).
fof(f20203,plain,
( spl11_595
| ~ spl11_33
| ~ spl11_105 ),
inference(avatar_split_clause,[],[f1153,f1022,f324,f20201]) ).
fof(f20201,plain,
( spl11_595
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,sum(intersection(X1,X2)))
| ~ member(X3,sK7(X0,intersection(X1,X2)))
| member(X3,sum(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_595])]) ).
fof(f1153,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,sum(intersection(X1,X2)))
| ~ member(X3,sK7(X0,intersection(X1,X2)))
| member(X3,sum(X1)) )
| ~ spl11_33
| ~ spl11_105 ),
inference(resolution,[],[f1023,f325]) ).
fof(f20199,plain,
( spl11_594
| ~ spl11_16
| ~ spl11_104 ),
inference(avatar_split_clause,[],[f1139,f1018,f219,f20197]) ).
fof(f20197,plain,
( spl11_594
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,sum(intersection(X1,difference(X2,X3))))
| member(sK7(X0,intersection(X1,difference(X2,X3))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_594])]) ).
fof(f1018,plain,
( spl11_104
<=> ! [X2,X0,X1] :
( ~ member(X0,sum(intersection(X1,X2)))
| member(sK7(X0,intersection(X1,X2)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_104])]) ).
fof(f1139,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,sum(intersection(X1,difference(X2,X3))))
| member(sK7(X0,intersection(X1,difference(X2,X3))),X2) )
| ~ spl11_16
| ~ spl11_104 ),
inference(resolution,[],[f1019,f220]) ).
fof(f1019,plain,
( ! [X2,X0,X1] :
( member(sK7(X0,intersection(X1,X2)),X2)
| ~ member(X0,sum(intersection(X1,X2))) )
| ~ spl11_104 ),
inference(avatar_component_clause,[],[f1018]) ).
fof(f20195,plain,
( spl11_593
| ~ spl11_17
| ~ spl11_104 ),
inference(avatar_split_clause,[],[f1138,f1018,f223,f20193]) ).
fof(f20193,plain,
( spl11_593
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,sum(intersection(X1,difference(X2,X3))))
| ~ member(sK7(X0,intersection(X1,difference(X2,X3))),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_593])]) ).
fof(f1138,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,sum(intersection(X1,difference(X2,X3))))
| ~ member(sK7(X0,intersection(X1,difference(X2,X3))),X3) )
| ~ spl11_17
| ~ spl11_104 ),
inference(resolution,[],[f1019,f224]) ).
fof(f20191,plain,
( spl11_592
| ~ spl11_18
| ~ spl11_104 ),
inference(avatar_split_clause,[],[f1135,f1018,f227,f20189]) ).
fof(f20189,plain,
( spl11_592
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,sum(intersection(X1,intersection(X2,X3))))
| member(sK7(X0,intersection(X1,intersection(X2,X3))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_592])]) ).
fof(f1135,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,sum(intersection(X1,intersection(X2,X3))))
| member(sK7(X0,intersection(X1,intersection(X2,X3))),X2) )
| ~ spl11_18
| ~ spl11_104 ),
inference(resolution,[],[f1019,f228]) ).
fof(f20187,plain,
( spl11_591
| ~ spl11_19
| ~ spl11_104 ),
inference(avatar_split_clause,[],[f1134,f1018,f231,f20185]) ).
fof(f20185,plain,
( spl11_591
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,sum(intersection(X1,intersection(X2,X3))))
| member(sK7(X0,intersection(X1,intersection(X2,X3))),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_591])]) ).
fof(f1134,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,sum(intersection(X1,intersection(X2,X3))))
| member(sK7(X0,intersection(X1,intersection(X2,X3))),X3) )
| ~ spl11_19
| ~ spl11_104 ),
inference(resolution,[],[f1019,f232]) ).
fof(f20183,plain,
( spl11_590
| ~ spl11_33
| ~ spl11_104 ),
inference(avatar_split_clause,[],[f1131,f1018,f324,f20181]) ).
fof(f20181,plain,
( spl11_590
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,sum(intersection(X1,X2)))
| ~ member(X3,sK7(X0,intersection(X1,X2)))
| member(X3,sum(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_590])]) ).
fof(f1131,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,sum(intersection(X1,X2)))
| ~ member(X3,sK7(X0,intersection(X1,X2)))
| member(X3,sum(X2)) )
| ~ spl11_33
| ~ spl11_104 ),
inference(resolution,[],[f1019,f325]) ).
fof(f20179,plain,
( spl11_589
| ~ spl11_16
| ~ spl11_103 ),
inference(avatar_split_clause,[],[f1120,f1014,f219,f20177]) ).
fof(f20177,plain,
( spl11_589
<=> ! [X0,X3,X2,X1] :
( member(X0,product(difference(difference(X1,X2),X3)))
| member(sK6(X0,difference(difference(X1,X2),X3)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_589])]) ).
fof(f1014,plain,
( spl11_103
<=> ! [X2,X0,X1] :
( member(X0,product(difference(X1,X2)))
| member(sK6(X0,difference(X1,X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_103])]) ).
fof(f1120,plain,
( ! [X2,X3,X0,X1] :
( member(X0,product(difference(difference(X1,X2),X3)))
| member(sK6(X0,difference(difference(X1,X2),X3)),X1) )
| ~ spl11_16
| ~ spl11_103 ),
inference(resolution,[],[f1015,f220]) ).
fof(f1015,plain,
( ! [X2,X0,X1] :
( member(sK6(X0,difference(X1,X2)),X1)
| member(X0,product(difference(X1,X2))) )
| ~ spl11_103 ),
inference(avatar_component_clause,[],[f1014]) ).
fof(f20175,plain,
( spl11_588
| ~ spl11_155
| ~ spl11_543 ),
inference(avatar_split_clause,[],[f19882,f13702,f2319,f20172]) ).
fof(f20172,plain,
( spl11_588
<=> upper_bound(sK4,sK1,union(sK3,sum(empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_588])]) ).
fof(f13702,plain,
( spl11_543
<=> ! [X2,X0,X1] :
( member(sK9(X0,union(X1,sum(empty_set)),X2),X1)
| upper_bound(X2,X0,union(X1,sum(empty_set))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_543])]) ).
fof(f19882,plain,
( upper_bound(sK4,sK1,union(sK3,sum(empty_set)))
| ~ spl11_155
| ~ spl11_543 ),
inference(duplicate_literal_removal,[],[f19794]) ).
fof(f19794,plain,
( upper_bound(sK4,sK1,union(sK3,sum(empty_set)))
| upper_bound(sK4,sK1,union(sK3,sum(empty_set)))
| ~ spl11_155
| ~ spl11_543 ),
inference(resolution,[],[f13703,f2320]) ).
fof(f13703,plain,
( ! [X2,X0,X1] :
( member(sK9(X0,union(X1,sum(empty_set)),X2),X1)
| upper_bound(X2,X0,union(X1,sum(empty_set))) )
| ~ spl11_543 ),
inference(avatar_component_clause,[],[f13702]) ).
fof(f20170,plain,
( spl11_587
| ~ spl11_17
| ~ spl11_103 ),
inference(avatar_split_clause,[],[f1119,f1014,f223,f20168]) ).
fof(f20168,plain,
( spl11_587
<=> ! [X0,X3,X2,X1] :
( member(X0,product(difference(difference(X1,X2),X3)))
| ~ member(sK6(X0,difference(difference(X1,X2),X3)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_587])]) ).
fof(f1119,plain,
( ! [X2,X3,X0,X1] :
( member(X0,product(difference(difference(X1,X2),X3)))
| ~ member(sK6(X0,difference(difference(X1,X2),X3)),X2) )
| ~ spl11_17
| ~ spl11_103 ),
inference(resolution,[],[f1015,f224]) ).
fof(f20166,plain,
( spl11_586
| ~ spl11_18
| ~ spl11_103 ),
inference(avatar_split_clause,[],[f1116,f1014,f227,f20164]) ).
fof(f20164,plain,
( spl11_586
<=> ! [X0,X3,X2,X1] :
( member(X0,product(difference(intersection(X1,X2),X3)))
| member(sK6(X0,difference(intersection(X1,X2),X3)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_586])]) ).
fof(f1116,plain,
( ! [X2,X3,X0,X1] :
( member(X0,product(difference(intersection(X1,X2),X3)))
| member(sK6(X0,difference(intersection(X1,X2),X3)),X1) )
| ~ spl11_18
| ~ spl11_103 ),
inference(resolution,[],[f1015,f228]) ).
fof(f20162,plain,
( spl11_585
| ~ spl11_19
| ~ spl11_103 ),
inference(avatar_split_clause,[],[f1115,f1014,f231,f20160]) ).
fof(f20160,plain,
( spl11_585
<=> ! [X0,X3,X2,X1] :
( member(X0,product(difference(intersection(X1,X2),X3)))
| member(sK6(X0,difference(intersection(X1,X2),X3)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_585])]) ).
fof(f1115,plain,
( ! [X2,X3,X0,X1] :
( member(X0,product(difference(intersection(X1,X2),X3)))
| member(sK6(X0,difference(intersection(X1,X2),X3)),X2) )
| ~ spl11_19
| ~ spl11_103 ),
inference(resolution,[],[f1015,f232]) ).
fof(f20158,plain,
( spl11_584
| ~ spl11_33
| ~ spl11_103 ),
inference(avatar_split_clause,[],[f1112,f1014,f324,f20156]) ).
fof(f20156,plain,
( spl11_584
<=> ! [X0,X3,X2,X1] :
( member(X0,product(difference(X1,X2)))
| ~ member(X3,sK6(X0,difference(X1,X2)))
| member(X3,sum(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_584])]) ).
fof(f1112,plain,
( ! [X2,X3,X0,X1] :
( member(X0,product(difference(X1,X2)))
| ~ member(X3,sK6(X0,difference(X1,X2)))
| member(X3,sum(X1)) )
| ~ spl11_33
| ~ spl11_103 ),
inference(resolution,[],[f1015,f325]) ).
fof(f20154,plain,
( spl11_583
| ~ spl11_66
| ~ spl11_102 ),
inference(avatar_split_clause,[],[f1100,f1010,f565,f20152]) ).
fof(f20152,plain,
( spl11_583
<=> ! [X2,X0,X1] :
( member(X0,product(difference(X1,sum(singleton(X2)))))
| ~ member(sK6(X0,difference(X1,sum(singleton(X2)))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_583])]) ).
fof(f1010,plain,
( spl11_102
<=> ! [X2,X0,X1] :
( member(X0,product(difference(X1,X2)))
| ~ member(sK6(X0,difference(X1,X2)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_102])]) ).
fof(f1100,plain,
( ! [X2,X0,X1] :
( member(X0,product(difference(X1,sum(singleton(X2)))))
| ~ member(sK6(X0,difference(X1,sum(singleton(X2)))),X2) )
| ~ spl11_66
| ~ spl11_102 ),
inference(resolution,[],[f1011,f566]) ).
fof(f1011,plain,
( ! [X2,X0,X1] :
( ~ member(sK6(X0,difference(X1,X2)),X2)
| member(X0,product(difference(X1,X2))) )
| ~ spl11_102 ),
inference(avatar_component_clause,[],[f1010]) ).
fof(f20150,plain,
( spl11_582
| ~ spl11_20
| ~ spl11_102 ),
inference(avatar_split_clause,[],[f1098,f1010,f235,f20148]) ).
fof(f20148,plain,
( spl11_582
<=> ! [X0,X3,X2,X1] :
( member(X0,product(difference(X1,union(X2,X3))))
| ~ member(sK6(X0,difference(X1,union(X2,X3))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_582])]) ).
fof(f1098,plain,
( ! [X2,X3,X0,X1] :
( member(X0,product(difference(X1,union(X2,X3))))
| ~ member(sK6(X0,difference(X1,union(X2,X3))),X2) )
| ~ spl11_20
| ~ spl11_102 ),
inference(resolution,[],[f1011,f236]) ).
fof(f20146,plain,
( spl11_581
| ~ spl11_21
| ~ spl11_102 ),
inference(avatar_split_clause,[],[f1097,f1010,f239,f20144]) ).
fof(f20144,plain,
( spl11_581
<=> ! [X0,X3,X2,X1] :
( member(X0,product(difference(X1,union(X2,X3))))
| ~ member(sK6(X0,difference(X1,union(X2,X3))),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_581])]) ).
fof(f1097,plain,
( ! [X2,X3,X0,X1] :
( member(X0,product(difference(X1,union(X2,X3))))
| ~ member(sK6(X0,difference(X1,union(X2,X3))),X3) )
| ~ spl11_21
| ~ spl11_102 ),
inference(resolution,[],[f1011,f240]) ).
fof(f20142,plain,
( spl11_580
| ~ spl11_16
| ~ spl11_101 ),
inference(avatar_split_clause,[],[f1087,f1006,f219,f20140]) ).
fof(f20140,plain,
( spl11_580
<=> ! [X0,X3,X2,X1] :
( member(X0,product(intersection(difference(X1,X2),X3)))
| member(sK6(X0,intersection(difference(X1,X2),X3)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_580])]) ).
fof(f1006,plain,
( spl11_101
<=> ! [X2,X0,X1] :
( member(X0,product(intersection(X1,X2)))
| member(sK6(X0,intersection(X1,X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_101])]) ).
fof(f1087,plain,
( ! [X2,X3,X0,X1] :
( member(X0,product(intersection(difference(X1,X2),X3)))
| member(sK6(X0,intersection(difference(X1,X2),X3)),X1) )
| ~ spl11_16
| ~ spl11_101 ),
inference(resolution,[],[f1007,f220]) ).
fof(f1007,plain,
( ! [X2,X0,X1] :
( member(sK6(X0,intersection(X1,X2)),X1)
| member(X0,product(intersection(X1,X2))) )
| ~ spl11_101 ),
inference(avatar_component_clause,[],[f1006]) ).
fof(f20138,plain,
( spl11_579
| ~ spl11_17
| ~ spl11_101 ),
inference(avatar_split_clause,[],[f1086,f1006,f223,f20136]) ).
fof(f20136,plain,
( spl11_579
<=> ! [X0,X3,X2,X1] :
( member(X0,product(intersection(difference(X1,X2),X3)))
| ~ member(sK6(X0,intersection(difference(X1,X2),X3)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_579])]) ).
fof(f1086,plain,
( ! [X2,X3,X0,X1] :
( member(X0,product(intersection(difference(X1,X2),X3)))
| ~ member(sK6(X0,intersection(difference(X1,X2),X3)),X2) )
| ~ spl11_17
| ~ spl11_101 ),
inference(resolution,[],[f1007,f224]) ).
fof(f20134,plain,
( spl11_578
| ~ spl11_18
| ~ spl11_101 ),
inference(avatar_split_clause,[],[f1083,f1006,f227,f20132]) ).
fof(f20132,plain,
( spl11_578
<=> ! [X0,X3,X2,X1] :
( member(X0,product(intersection(intersection(X1,X2),X3)))
| member(sK6(X0,intersection(intersection(X1,X2),X3)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_578])]) ).
fof(f1083,plain,
( ! [X2,X3,X0,X1] :
( member(X0,product(intersection(intersection(X1,X2),X3)))
| member(sK6(X0,intersection(intersection(X1,X2),X3)),X1) )
| ~ spl11_18
| ~ spl11_101 ),
inference(resolution,[],[f1007,f228]) ).
fof(f20122,plain,
( spl11_577
| ~ spl11_19
| ~ spl11_101 ),
inference(avatar_split_clause,[],[f1082,f1006,f231,f20120]) ).
fof(f20120,plain,
( spl11_577
<=> ! [X0,X3,X2,X1] :
( member(X0,product(intersection(intersection(X1,X2),X3)))
| member(sK6(X0,intersection(intersection(X1,X2),X3)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_577])]) ).
fof(f1082,plain,
( ! [X2,X3,X0,X1] :
( member(X0,product(intersection(intersection(X1,X2),X3)))
| member(sK6(X0,intersection(intersection(X1,X2),X3)),X2) )
| ~ spl11_19
| ~ spl11_101 ),
inference(resolution,[],[f1007,f232]) ).
fof(f20118,plain,
( spl11_576
| ~ spl11_33
| ~ spl11_101 ),
inference(avatar_split_clause,[],[f1079,f1006,f324,f20116]) ).
fof(f20116,plain,
( spl11_576
<=> ! [X0,X3,X2,X1] :
( member(X0,product(intersection(X1,X2)))
| ~ member(X3,sK6(X0,intersection(X1,X2)))
| member(X3,sum(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_576])]) ).
fof(f1079,plain,
( ! [X2,X3,X0,X1] :
( member(X0,product(intersection(X1,X2)))
| ~ member(X3,sK6(X0,intersection(X1,X2)))
| member(X3,sum(X1)) )
| ~ spl11_33
| ~ spl11_101 ),
inference(resolution,[],[f1007,f325]) ).
fof(f20114,plain,
( spl11_575
| ~ spl11_16
| ~ spl11_100 ),
inference(avatar_split_clause,[],[f1069,f1002,f219,f20112]) ).
fof(f20112,plain,
( spl11_575
<=> ! [X0,X3,X2,X1] :
( member(X0,product(intersection(X1,difference(X2,X3))))
| member(sK6(X0,intersection(X1,difference(X2,X3))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_575])]) ).
fof(f1002,plain,
( spl11_100
<=> ! [X2,X0,X1] :
( member(X0,product(intersection(X1,X2)))
| member(sK6(X0,intersection(X1,X2)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_100])]) ).
fof(f1069,plain,
( ! [X2,X3,X0,X1] :
( member(X0,product(intersection(X1,difference(X2,X3))))
| member(sK6(X0,intersection(X1,difference(X2,X3))),X2) )
| ~ spl11_16
| ~ spl11_100 ),
inference(resolution,[],[f1003,f220]) ).
fof(f1003,plain,
( ! [X2,X0,X1] :
( member(sK6(X0,intersection(X1,X2)),X2)
| member(X0,product(intersection(X1,X2))) )
| ~ spl11_100 ),
inference(avatar_component_clause,[],[f1002]) ).
fof(f20110,plain,
( spl11_574
| ~ spl11_17
| ~ spl11_100 ),
inference(avatar_split_clause,[],[f1068,f1002,f223,f20108]) ).
fof(f20108,plain,
( spl11_574
<=> ! [X0,X3,X2,X1] :
( member(X0,product(intersection(X1,difference(X2,X3))))
| ~ member(sK6(X0,intersection(X1,difference(X2,X3))),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_574])]) ).
fof(f1068,plain,
( ! [X2,X3,X0,X1] :
( member(X0,product(intersection(X1,difference(X2,X3))))
| ~ member(sK6(X0,intersection(X1,difference(X2,X3))),X3) )
| ~ spl11_17
| ~ spl11_100 ),
inference(resolution,[],[f1003,f224]) ).
fof(f20106,plain,
( spl11_573
| ~ spl11_18
| ~ spl11_100 ),
inference(avatar_split_clause,[],[f1065,f1002,f227,f20104]) ).
fof(f20104,plain,
( spl11_573
<=> ! [X0,X3,X2,X1] :
( member(X0,product(intersection(X1,intersection(X2,X3))))
| member(sK6(X0,intersection(X1,intersection(X2,X3))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_573])]) ).
fof(f1065,plain,
( ! [X2,X3,X0,X1] :
( member(X0,product(intersection(X1,intersection(X2,X3))))
| member(sK6(X0,intersection(X1,intersection(X2,X3))),X2) )
| ~ spl11_18
| ~ spl11_100 ),
inference(resolution,[],[f1003,f228]) ).
fof(f20102,plain,
( spl11_572
| ~ spl11_19
| ~ spl11_100 ),
inference(avatar_split_clause,[],[f1064,f1002,f231,f20100]) ).
fof(f20100,plain,
( spl11_572
<=> ! [X0,X3,X2,X1] :
( member(X0,product(intersection(X1,intersection(X2,X3))))
| member(sK6(X0,intersection(X1,intersection(X2,X3))),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_572])]) ).
fof(f1064,plain,
( ! [X2,X3,X0,X1] :
( member(X0,product(intersection(X1,intersection(X2,X3))))
| member(sK6(X0,intersection(X1,intersection(X2,X3))),X3) )
| ~ spl11_19
| ~ spl11_100 ),
inference(resolution,[],[f1003,f232]) ).
fof(f20098,plain,
( spl11_571
| ~ spl11_33
| ~ spl11_100 ),
inference(avatar_split_clause,[],[f1061,f1002,f324,f20096]) ).
fof(f20096,plain,
( spl11_571
<=> ! [X0,X3,X2,X1] :
( member(X0,product(intersection(X1,X2)))
| ~ member(X3,sK6(X0,intersection(X1,X2)))
| member(X3,sum(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_571])]) ).
fof(f1061,plain,
( ! [X2,X3,X0,X1] :
( member(X0,product(intersection(X1,X2)))
| ~ member(X3,sK6(X0,intersection(X1,X2)))
| member(X3,sum(X2)) )
| ~ spl11_33
| ~ spl11_100 ),
inference(resolution,[],[f1003,f325]) ).
fof(f20094,plain,
( spl11_570
| ~ spl11_27
| ~ spl11_95 ),
inference(avatar_split_clause,[],[f987,f754,f275,f20092]) ).
fof(f20092,plain,
( spl11_570
<=> ! [X2,X0,X1] :
( member(sK7(X0,sK5(X1,X2)),sum(X1))
| subset(X1,X2)
| ~ member(X0,sum(sK5(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_570])]) ).
fof(f275,plain,
( spl11_27
<=> ! [X0,X1] :
( member(sK7(X0,X1),X1)
| ~ member(X0,sum(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_27])]) ).
fof(f754,plain,
( spl11_95
<=> ! [X2,X0,X1] :
( ~ member(X0,sK5(X1,X2))
| member(X0,sum(X1))
| subset(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_95])]) ).
fof(f987,plain,
( ! [X2,X0,X1] :
( member(sK7(X0,sK5(X1,X2)),sum(X1))
| subset(X1,X2)
| ~ member(X0,sum(sK5(X1,X2))) )
| ~ spl11_27
| ~ spl11_95 ),
inference(resolution,[],[f755,f276]) ).
fof(f276,plain,
( ! [X0,X1] :
( member(sK7(X0,X1),X1)
| ~ member(X0,sum(X1)) )
| ~ spl11_27 ),
inference(avatar_component_clause,[],[f275]) ).
fof(f755,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sK5(X1,X2))
| member(X0,sum(X1))
| subset(X1,X2) )
| ~ spl11_95 ),
inference(avatar_component_clause,[],[f754]) ).
fof(f20090,plain,
( spl11_569
| ~ spl11_25
| ~ spl11_95 ),
inference(avatar_split_clause,[],[f985,f754,f267,f20088]) ).
fof(f20088,plain,
( spl11_569
<=> ! [X2,X0,X1] :
( member(sK6(X0,sK5(X1,X2)),sum(X1))
| subset(X1,X2)
| member(X0,product(sK5(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_569])]) ).
fof(f267,plain,
( spl11_25
<=> ! [X0,X1] :
( member(X0,product(X1))
| member(sK6(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_25])]) ).
fof(f985,plain,
( ! [X2,X0,X1] :
( member(sK6(X0,sK5(X1,X2)),sum(X1))
| subset(X1,X2)
| member(X0,product(sK5(X1,X2))) )
| ~ spl11_25
| ~ spl11_95 ),
inference(resolution,[],[f755,f268]) ).
fof(f268,plain,
( ! [X0,X1] :
( member(sK6(X0,X1),X1)
| member(X0,product(X1)) )
| ~ spl11_25 ),
inference(avatar_component_clause,[],[f267]) ).
fof(f20086,plain,
( spl11_568
| ~ spl11_75
| ~ spl11_95 ),
inference(avatar_split_clause,[],[f981,f754,f619,f20084]) ).
fof(f20084,plain,
( spl11_568
<=> ! [X0,X3,X2,X1] :
( member(sK5(X0,X1),sum(X2))
| subset(X2,X3)
| ~ subset(X0,sK5(X2,X3))
| subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_568])]) ).
fof(f619,plain,
( spl11_75
<=> ! [X2,X0,X1] :
( member(sK5(X0,X1),X2)
| ~ subset(X0,X2)
| subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_75])]) ).
fof(f981,plain,
( ! [X2,X3,X0,X1] :
( member(sK5(X0,X1),sum(X2))
| subset(X2,X3)
| ~ subset(X0,sK5(X2,X3))
| subset(X0,X1) )
| ~ spl11_75
| ~ spl11_95 ),
inference(resolution,[],[f755,f620]) ).
fof(f620,plain,
( ! [X2,X0,X1] :
( member(sK5(X0,X1),X2)
| ~ subset(X0,X2)
| subset(X0,X1) )
| ~ spl11_75 ),
inference(avatar_component_clause,[],[f619]) ).
fof(f20074,plain,
( spl11_567
| ~ spl11_75
| ~ spl11_94 ),
inference(avatar_split_clause,[],[f969,f750,f619,f20072]) ).
fof(f20072,plain,
( spl11_567
<=> ! [X4,X0,X3,X2,X1] :
( member(X0,sum(union(X1,X2)))
| ~ member(X0,sK5(X3,X4))
| ~ subset(X3,X1)
| subset(X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_567])]) ).
fof(f750,plain,
( spl11_94
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,X1)
| member(X0,sum(union(X2,X3)))
| ~ member(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_94])]) ).
fof(f969,plain,
( ! [X2,X3,X0,X1,X4] :
( member(X0,sum(union(X1,X2)))
| ~ member(X0,sK5(X3,X4))
| ~ subset(X3,X1)
| subset(X3,X4) )
| ~ spl11_75
| ~ spl11_94 ),
inference(resolution,[],[f751,f620]) ).
fof(f751,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X1,X2)
| member(X0,sum(union(X2,X3)))
| ~ member(X0,X1) )
| ~ spl11_94 ),
inference(avatar_component_clause,[],[f750]) ).
fof(f20070,plain,
( spl11_566
| ~ spl11_78
| ~ spl11_94 ),
inference(avatar_split_clause,[],[f963,f750,f631,f20068]) ).
fof(f20068,plain,
( spl11_566
<=> ! [X0,X3,X2,X1] :
( member(X0,sum(union(product(singleton(X1)),X2)))
| ~ member(X0,X3)
| sK6(X3,singleton(X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_566])]) ).
fof(f631,plain,
( spl11_78
<=> ! [X0,X1] :
( member(X0,product(singleton(X1)))
| sK6(X0,singleton(X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_78])]) ).
fof(f963,plain,
( ! [X2,X3,X0,X1] :
( member(X0,sum(union(product(singleton(X1)),X2)))
| ~ member(X0,X3)
| sK6(X3,singleton(X1)) = X1 )
| ~ spl11_78
| ~ spl11_94 ),
inference(resolution,[],[f751,f632]) ).
fof(f632,plain,
( ! [X0,X1] :
( member(X0,product(singleton(X1)))
| sK6(X0,singleton(X1)) = X1 )
| ~ spl11_78 ),
inference(avatar_component_clause,[],[f631]) ).
fof(f20066,plain,
( spl11_565
| ~ spl11_40
| ~ spl11_94 ),
inference(avatar_split_clause,[],[f953,f750,f378,f20064]) ).
fof(f20064,plain,
( spl11_565
<=> ! [X4,X0,X3,X2,X1] :
( member(X0,sum(union(difference(X1,X2),X3)))
| ~ member(X0,X4)
| member(X4,X2)
| ~ member(X4,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_565])]) ).
fof(f378,plain,
( spl11_40
<=> ! [X2,X0,X1] :
( member(X0,difference(X2,X1))
| member(X0,X1)
| ~ member(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_40])]) ).
fof(f953,plain,
( ! [X2,X3,X0,X1,X4] :
( member(X0,sum(union(difference(X1,X2),X3)))
| ~ member(X0,X4)
| member(X4,X2)
| ~ member(X4,X1) )
| ~ spl11_40
| ~ spl11_94 ),
inference(resolution,[],[f751,f379]) ).
fof(f379,plain,
( ! [X2,X0,X1] :
( member(X0,difference(X2,X1))
| member(X0,X1)
| ~ member(X0,X2) )
| ~ spl11_40 ),
inference(avatar_component_clause,[],[f378]) ).
fof(f20062,plain,
( spl11_564
| ~ spl11_41
| ~ spl11_94 ),
inference(avatar_split_clause,[],[f950,f750,f382,f20060]) ).
fof(f20060,plain,
( spl11_564
<=> ! [X4,X0,X3,X2,X1] :
( member(X0,sum(union(intersection(X1,X2),X3)))
| ~ member(X0,X4)
| ~ member(X4,X2)
| ~ member(X4,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_564])]) ).
fof(f382,plain,
( spl11_41
<=> ! [X2,X0,X1] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_41])]) ).
fof(f950,plain,
( ! [X2,X3,X0,X1,X4] :
( member(X0,sum(union(intersection(X1,X2),X3)))
| ~ member(X0,X4)
| ~ member(X4,X2)
| ~ member(X4,X1) )
| ~ spl11_41
| ~ spl11_94 ),
inference(resolution,[],[f751,f383]) ).
fof(f383,plain,
( ! [X2,X0,X1] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) )
| ~ spl11_41 ),
inference(avatar_component_clause,[],[f382]) ).
fof(f20058,plain,
( spl11_563
| ~ spl11_75
| ~ spl11_93 ),
inference(avatar_split_clause,[],[f938,f746,f619,f20056]) ).
fof(f20056,plain,
( spl11_563
<=> ! [X4,X0,X3,X2,X1] :
( member(X0,sum(union(X1,X2)))
| ~ member(X0,sK5(X3,X4))
| ~ subset(X3,X2)
| subset(X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_563])]) ).
fof(f746,plain,
( spl11_93
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,X1)
| member(X0,sum(union(X2,X3)))
| ~ member(X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_93])]) ).
fof(f938,plain,
( ! [X2,X3,X0,X1,X4] :
( member(X0,sum(union(X1,X2)))
| ~ member(X0,sK5(X3,X4))
| ~ subset(X3,X2)
| subset(X3,X4) )
| ~ spl11_75
| ~ spl11_93 ),
inference(resolution,[],[f747,f620]) ).
fof(f747,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X1,X3)
| member(X0,sum(union(X2,X3)))
| ~ member(X0,X1) )
| ~ spl11_93 ),
inference(avatar_component_clause,[],[f746]) ).
fof(f20054,plain,
( spl11_562
| ~ spl11_78
| ~ spl11_93 ),
inference(avatar_split_clause,[],[f932,f746,f631,f20052]) ).
fof(f20052,plain,
( spl11_562
<=> ! [X0,X3,X2,X1] :
( member(X0,sum(union(X1,product(singleton(X2)))))
| ~ member(X0,X3)
| sK6(X3,singleton(X2)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_562])]) ).
fof(f932,plain,
( ! [X2,X3,X0,X1] :
( member(X0,sum(union(X1,product(singleton(X2)))))
| ~ member(X0,X3)
| sK6(X3,singleton(X2)) = X2 )
| ~ spl11_78
| ~ spl11_93 ),
inference(resolution,[],[f747,f632]) ).
fof(f20050,plain,
( spl11_561
| ~ spl11_40
| ~ spl11_93 ),
inference(avatar_split_clause,[],[f922,f746,f378,f20048]) ).
fof(f20048,plain,
( spl11_561
<=> ! [X4,X0,X3,X2,X1] :
( member(X0,sum(union(X1,difference(X2,X3))))
| ~ member(X0,X4)
| member(X4,X3)
| ~ member(X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_561])]) ).
fof(f922,plain,
( ! [X2,X3,X0,X1,X4] :
( member(X0,sum(union(X1,difference(X2,X3))))
| ~ member(X0,X4)
| member(X4,X3)
| ~ member(X4,X2) )
| ~ spl11_40
| ~ spl11_93 ),
inference(resolution,[],[f747,f379]) ).
fof(f20046,plain,
( spl11_560
| ~ spl11_41
| ~ spl11_93 ),
inference(avatar_split_clause,[],[f919,f746,f382,f20044]) ).
fof(f20044,plain,
( spl11_560
<=> ! [X4,X0,X3,X2,X1] :
( member(X0,sum(union(X1,intersection(X2,X3))))
| ~ member(X0,X4)
| ~ member(X4,X3)
| ~ member(X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_560])]) ).
fof(f919,plain,
( ! [X2,X3,X0,X1,X4] :
( member(X0,sum(union(X1,intersection(X2,X3))))
| ~ member(X0,X4)
| ~ member(X4,X3)
| ~ member(X4,X2) )
| ~ spl11_41
| ~ spl11_93 ),
inference(resolution,[],[f747,f383]) ).
fof(f20042,plain,
( spl11_559
| ~ spl11_26
| ~ spl11_90 ),
inference(avatar_split_clause,[],[f914,f734,f271,f20040]) ).
fof(f20040,plain,
( spl11_559
<=> ! [X2,X0,X1] :
( ~ member(X0,sum(X1))
| ~ subset(X1,sK6(sK7(X0,X1),X2))
| member(sK7(X0,X1),product(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_559])]) ).
fof(f271,plain,
( spl11_26
<=> ! [X0,X1] :
( member(X0,product(X1))
| ~ member(X0,sK6(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_26])]) ).
fof(f734,plain,
( spl11_90
<=> ! [X2,X0,X1] :
( ~ member(X0,sum(X1))
| member(sK7(X0,X1),X2)
| ~ subset(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_90])]) ).
fof(f914,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sum(X1))
| ~ subset(X1,sK6(sK7(X0,X1),X2))
| member(sK7(X0,X1),product(X2)) )
| ~ spl11_26
| ~ spl11_90 ),
inference(resolution,[],[f735,f272]) ).
fof(f272,plain,
( ! [X0,X1] :
( ~ member(X0,sK6(X0,X1))
| member(X0,product(X1)) )
| ~ spl11_26 ),
inference(avatar_component_clause,[],[f271]) ).
fof(f735,plain,
( ! [X2,X0,X1] :
( member(sK7(X0,X1),X2)
| ~ member(X0,sum(X1))
| ~ subset(X1,X2) )
| ~ spl11_90 ),
inference(avatar_component_clause,[],[f734]) ).
fof(f20038,plain,
( spl11_558
| ~ spl11_80
| ~ spl11_90 ),
inference(avatar_split_clause,[],[f912,f734,f639,f20036]) ).
fof(f20036,plain,
( spl11_558
<=> ! [X2,X0,X1] :
( ~ member(X0,sum(X1))
| ~ subset(X1,sum(singleton(X2)))
| sK7(sK7(X0,X1),singleton(X2)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_558])]) ).
fof(f639,plain,
( spl11_80
<=> ! [X0,X1] :
( ~ member(X0,sum(singleton(X1)))
| sK7(X0,singleton(X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_80])]) ).
fof(f912,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sum(X1))
| ~ subset(X1,sum(singleton(X2)))
| sK7(sK7(X0,X1),singleton(X2)) = X2 )
| ~ spl11_80
| ~ spl11_90 ),
inference(resolution,[],[f735,f640]) ).
fof(f640,plain,
( ! [X0,X1] :
( ~ member(X0,sum(singleton(X1)))
| sK7(X0,singleton(X1)) = X1 )
| ~ spl11_80 ),
inference(avatar_component_clause,[],[f639]) ).
fof(f20026,plain,
( spl11_557
| ~ spl11_81
| ~ spl11_90 ),
inference(avatar_split_clause,[],[f899,f734,f643,f20024]) ).
fof(f20024,plain,
( spl11_557
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,sum(X1))
| ~ subset(X1,X2)
| member(sK7(X0,X1),sum(power_set(X3)))
| ~ subset(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_557])]) ).
fof(f643,plain,
( spl11_81
<=> ! [X2,X0,X1] :
( ~ member(X0,X1)
| member(X0,sum(power_set(X2)))
| ~ subset(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_81])]) ).
fof(f899,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,sum(X1))
| ~ subset(X1,X2)
| member(sK7(X0,X1),sum(power_set(X3)))
| ~ subset(X2,X3) )
| ~ spl11_81
| ~ spl11_90 ),
inference(resolution,[],[f735,f644]) ).
fof(f644,plain,
( ! [X2,X0,X1] :
( ~ member(X0,X1)
| member(X0,sum(power_set(X2)))
| ~ subset(X1,X2) )
| ~ spl11_81 ),
inference(avatar_component_clause,[],[f643]) ).
fof(f20022,plain,
( spl11_556
| ~ spl11_26
| ~ spl11_89 ),
inference(avatar_split_clause,[],[f898,f730,f271,f20020]) ).
fof(f20020,plain,
( spl11_556
<=> ! [X2,X0,X1] :
( member(X0,product(X1))
| ~ subset(X1,sK6(sK6(X0,X1),X2))
| member(sK6(X0,X1),product(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_556])]) ).
fof(f730,plain,
( spl11_89
<=> ! [X2,X0,X1] :
( member(X0,product(X1))
| member(sK6(X0,X1),X2)
| ~ subset(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_89])]) ).
fof(f898,plain,
( ! [X2,X0,X1] :
( member(X0,product(X1))
| ~ subset(X1,sK6(sK6(X0,X1),X2))
| member(sK6(X0,X1),product(X2)) )
| ~ spl11_26
| ~ spl11_89 ),
inference(resolution,[],[f731,f272]) ).
fof(f731,plain,
( ! [X2,X0,X1] :
( member(sK6(X0,X1),X2)
| member(X0,product(X1))
| ~ subset(X1,X2) )
| ~ spl11_89 ),
inference(avatar_component_clause,[],[f730]) ).
fof(f20018,plain,
( spl11_555
| ~ spl11_80
| ~ spl11_89 ),
inference(avatar_split_clause,[],[f896,f730,f639,f20016]) ).
fof(f20016,plain,
( spl11_555
<=> ! [X2,X0,X1] :
( member(X0,product(X1))
| ~ subset(X1,sum(singleton(X2)))
| sK7(sK6(X0,X1),singleton(X2)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_555])]) ).
fof(f896,plain,
( ! [X2,X0,X1] :
( member(X0,product(X1))
| ~ subset(X1,sum(singleton(X2)))
| sK7(sK6(X0,X1),singleton(X2)) = X2 )
| ~ spl11_80
| ~ spl11_89 ),
inference(resolution,[],[f731,f640]) ).
fof(f20014,plain,
( spl11_554
| ~ spl11_81
| ~ spl11_89 ),
inference(avatar_split_clause,[],[f883,f730,f643,f20012]) ).
fof(f20012,plain,
( spl11_554
<=> ! [X0,X3,X2,X1] :
( member(X0,product(X1))
| ~ subset(X1,X2)
| member(sK6(X0,X1),sum(power_set(X3)))
| ~ subset(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_554])]) ).
fof(f883,plain,
( ! [X2,X3,X0,X1] :
( member(X0,product(X1))
| ~ subset(X1,X2)
| member(sK6(X0,X1),sum(power_set(X3)))
| ~ subset(X2,X3) )
| ~ spl11_81
| ~ spl11_89 ),
inference(resolution,[],[f731,f644]) ).
fof(f20010,plain,
( spl11_553
| ~ spl11_32
| ~ spl11_86 ),
inference(avatar_split_clause,[],[f837,f718,f320,f20008]) ).
fof(f20008,plain,
( spl11_553
<=> ! [X0,X3,X2,X1] :
( subset(intersection(X0,product(X1)),X2)
| ~ member(X3,X1)
| member(sK5(intersection(X0,product(X1)),X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_553])]) ).
fof(f718,plain,
( spl11_86
<=> ! [X2,X0,X1] :
( member(sK5(intersection(X0,X1),X2),X1)
| subset(intersection(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_86])]) ).
fof(f837,plain,
( ! [X2,X3,X0,X1] :
( subset(intersection(X0,product(X1)),X2)
| ~ member(X3,X1)
| member(sK5(intersection(X0,product(X1)),X2),X3) )
| ~ spl11_32
| ~ spl11_86 ),
inference(resolution,[],[f719,f321]) ).
fof(f719,plain,
( ! [X2,X0,X1] :
( member(sK5(intersection(X0,X1),X2),X1)
| subset(intersection(X0,X1),X2) )
| ~ spl11_86 ),
inference(avatar_component_clause,[],[f718]) ).
fof(f20006,plain,
( spl11_552
| ~ spl11_81
| ~ spl11_86 ),
inference(avatar_split_clause,[],[f823,f718,f643,f20004]) ).
fof(f20004,plain,
( spl11_552
<=> ! [X0,X3,X2,X1] :
( subset(intersection(X0,X1),X2)
| member(sK5(intersection(X0,X1),X2),sum(power_set(X3)))
| ~ subset(X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_552])]) ).
fof(f823,plain,
( ! [X2,X3,X0,X1] :
( subset(intersection(X0,X1),X2)
| member(sK5(intersection(X0,X1),X2),sum(power_set(X3)))
| ~ subset(X1,X3) )
| ~ spl11_81
| ~ spl11_86 ),
inference(resolution,[],[f719,f644]) ).
fof(f20002,plain,
( spl11_551
| ~ spl11_32
| ~ spl11_85 ),
inference(avatar_split_clause,[],[f817,f714,f320,f20000]) ).
fof(f20000,plain,
( spl11_551
<=> ! [X0,X3,X2,X1] :
( subset(intersection(product(X0),X1),X2)
| ~ member(X3,X0)
| member(sK5(intersection(product(X0),X1),X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_551])]) ).
fof(f714,plain,
( spl11_85
<=> ! [X2,X0,X1] :
( member(sK5(intersection(X0,X1),X2),X0)
| subset(intersection(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_85])]) ).
fof(f817,plain,
( ! [X2,X3,X0,X1] :
( subset(intersection(product(X0),X1),X2)
| ~ member(X3,X0)
| member(sK5(intersection(product(X0),X1),X2),X3) )
| ~ spl11_32
| ~ spl11_85 ),
inference(resolution,[],[f715,f321]) ).
fof(f715,plain,
( ! [X2,X0,X1] :
( member(sK5(intersection(X0,X1),X2),X0)
| subset(intersection(X0,X1),X2) )
| ~ spl11_85 ),
inference(avatar_component_clause,[],[f714]) ).
fof(f19998,plain,
( spl11_550
| ~ spl11_81
| ~ spl11_85 ),
inference(avatar_split_clause,[],[f803,f714,f643,f19996]) ).
fof(f19996,plain,
( spl11_550
<=> ! [X0,X3,X2,X1] :
( subset(intersection(X0,X1),X2)
| member(sK5(intersection(X0,X1),X2),sum(power_set(X3)))
| ~ subset(X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_550])]) ).
fof(f803,plain,
( ! [X2,X3,X0,X1] :
( subset(intersection(X0,X1),X2)
| member(sK5(intersection(X0,X1),X2),sum(power_set(X3)))
| ~ subset(X0,X3) )
| ~ spl11_81
| ~ spl11_85 ),
inference(resolution,[],[f715,f644]) ).
fof(f19994,plain,
( spl11_549
| ~ spl11_32
| ~ spl11_83 ),
inference(avatar_split_clause,[],[f784,f706,f320,f19992]) ).
fof(f19992,plain,
( spl11_549
<=> ! [X0,X3,X2,X1] :
( subset(difference(product(X0),X1),X2)
| ~ member(X3,X0)
| member(sK5(difference(product(X0),X1),X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_549])]) ).
fof(f706,plain,
( spl11_83
<=> ! [X2,X0,X1] :
( member(sK5(difference(X0,X1),X2),X0)
| subset(difference(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_83])]) ).
fof(f784,plain,
( ! [X2,X3,X0,X1] :
( subset(difference(product(X0),X1),X2)
| ~ member(X3,X0)
| member(sK5(difference(product(X0),X1),X2),X3) )
| ~ spl11_32
| ~ spl11_83 ),
inference(resolution,[],[f707,f321]) ).
fof(f707,plain,
( ! [X2,X0,X1] :
( member(sK5(difference(X0,X1),X2),X0)
| subset(difference(X0,X1),X2) )
| ~ spl11_83 ),
inference(avatar_component_clause,[],[f706]) ).
fof(f19990,plain,
( spl11_548
| ~ spl11_81
| ~ spl11_83 ),
inference(avatar_split_clause,[],[f770,f706,f643,f19988]) ).
fof(f19988,plain,
( spl11_548
<=> ! [X0,X3,X2,X1] :
( subset(difference(X0,X1),X2)
| member(sK5(difference(X0,X1),X2),sum(power_set(X3)))
| ~ subset(X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_548])]) ).
fof(f770,plain,
( ! [X2,X3,X0,X1] :
( subset(difference(X0,X1),X2)
| member(sK5(difference(X0,X1),X2),sum(power_set(X3)))
| ~ subset(X0,X3) )
| ~ spl11_81
| ~ spl11_83 ),
inference(resolution,[],[f707,f644]) ).
fof(f19978,plain,
( spl11_547
| ~ spl11_34
| ~ spl11_80 ),
inference(avatar_split_clause,[],[f678,f639,f328,f19976]) ).
fof(f19976,plain,
( spl11_547
<=> ! [X2,X0,X1] :
( sK7(sK9(X0,sum(singleton(X1)),X2),singleton(X1)) = X1
| upper_bound(X2,X0,sum(singleton(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_547])]) ).
fof(f328,plain,
( spl11_34
<=> ! [X2,X0,X1] :
( upper_bound(X2,X0,X1)
| member(sK9(X0,X1,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_34])]) ).
fof(f678,plain,
( ! [X2,X0,X1] :
( sK7(sK9(X0,sum(singleton(X1)),X2),singleton(X1)) = X1
| upper_bound(X2,X0,sum(singleton(X1))) )
| ~ spl11_34
| ~ spl11_80 ),
inference(resolution,[],[f640,f329]) ).
fof(f329,plain,
( ! [X2,X0,X1] :
( member(sK9(X0,X1,X2),X1)
| upper_bound(X2,X0,X1) )
| ~ spl11_34 ),
inference(avatar_component_clause,[],[f328]) ).
fof(f14511,plain,
( spl11_546
| ~ spl11_82
| ~ spl11_391 ),
inference(avatar_split_clause,[],[f9649,f7489,f669,f14508]) ).
fof(f14508,plain,
( spl11_546
<=> subset(union(sum(empty_set),sK4),sum(sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_546])]) ).
fof(f669,plain,
( spl11_82
<=> ! [X0] :
( ~ member(sK5(X0,sum(sK3)),sK4)
| subset(X0,sum(sK3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_82])]) ).
fof(f7489,plain,
( spl11_391
<=> ! [X0,X1] :
( member(sK5(union(sum(empty_set),X0),X1),X0)
| subset(union(sum(empty_set),X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_391])]) ).
fof(f9649,plain,
( subset(union(sum(empty_set),sK4),sum(sK3))
| ~ spl11_82
| ~ spl11_391 ),
inference(duplicate_literal_removal,[],[f9589]) ).
fof(f9589,plain,
( subset(union(sum(empty_set),sK4),sum(sK3))
| subset(union(sum(empty_set),sK4),sum(sK3))
| ~ spl11_82
| ~ spl11_391 ),
inference(resolution,[],[f7490,f670]) ).
fof(f670,plain,
( ! [X0] :
( ~ member(sK5(X0,sum(sK3)),sK4)
| subset(X0,sum(sK3)) )
| ~ spl11_82 ),
inference(avatar_component_clause,[],[f669]) ).
fof(f7490,plain,
( ! [X0,X1] :
( member(sK5(union(sum(empty_set),X0),X1),X0)
| subset(union(sum(empty_set),X0),X1) )
| ~ spl11_391 ),
inference(avatar_component_clause,[],[f7489]) ).
fof(f13836,plain,
( spl11_545
| ~ spl11_82
| ~ spl11_390 ),
inference(avatar_split_clause,[],[f9558,f7485,f669,f13833]) ).
fof(f13833,plain,
( spl11_545
<=> subset(union(sK4,sum(empty_set)),sum(sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_545])]) ).
fof(f7485,plain,
( spl11_390
<=> ! [X0,X1] :
( member(sK5(union(X0,sum(empty_set)),X1),X0)
| subset(union(X0,sum(empty_set)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_390])]) ).
fof(f9558,plain,
( subset(union(sK4,sum(empty_set)),sum(sK3))
| ~ spl11_82
| ~ spl11_390 ),
inference(duplicate_literal_removal,[],[f9498]) ).
fof(f9498,plain,
( subset(union(sK4,sum(empty_set)),sum(sK3))
| subset(union(sK4,sum(empty_set)),sum(sK3))
| ~ spl11_82
| ~ spl11_390 ),
inference(resolution,[],[f7486,f670]) ).
fof(f7486,plain,
( ! [X0,X1] :
( member(sK5(union(X0,sum(empty_set)),X1),X0)
| subset(union(X0,sum(empty_set)),X1) )
| ~ spl11_390 ),
inference(avatar_component_clause,[],[f7485]) ).
fof(f13708,plain,
( spl11_544
| ~ spl11_60
| ~ spl11_149 ),
inference(avatar_split_clause,[],[f2266,f2217,f529,f13706]) ).
fof(f529,plain,
( spl11_60
<=> ! [X0] : ~ member(X0,sum(empty_set)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_60])]) ).
fof(f2217,plain,
( spl11_149
<=> ! [X0,X3,X2,X1] :
( member(sK9(X0,union(X1,X2),X3),X1)
| member(sK9(X0,union(X1,X2),X3),X2)
| upper_bound(X3,X0,union(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_149])]) ).
fof(f2266,plain,
( ! [X2,X0,X1] :
( member(sK9(X0,union(sum(empty_set),X1),X2),X1)
| upper_bound(X2,X0,union(sum(empty_set),X1)) )
| ~ spl11_60
| ~ spl11_149 ),
inference(resolution,[],[f2218,f530]) ).
fof(f530,plain,
( ! [X0] : ~ member(X0,sum(empty_set))
| ~ spl11_60 ),
inference(avatar_component_clause,[],[f529]) ).
fof(f2218,plain,
( ! [X2,X3,X0,X1] :
( member(sK9(X0,union(X1,X2),X3),X2)
| member(sK9(X0,union(X1,X2),X3),X1)
| upper_bound(X3,X0,union(X1,X2)) )
| ~ spl11_149 ),
inference(avatar_component_clause,[],[f2217]) ).
fof(f13704,plain,
( spl11_543
| ~ spl11_60
| ~ spl11_149 ),
inference(avatar_split_clause,[],[f2241,f2217,f529,f13702]) ).
fof(f2241,plain,
( ! [X2,X0,X1] :
( member(sK9(X0,union(X1,sum(empty_set)),X2),X1)
| upper_bound(X2,X0,union(X1,sum(empty_set))) )
| ~ spl11_60
| ~ spl11_149 ),
inference(resolution,[],[f2218,f530]) ).
fof(f13700,plain,
( spl11_542
| ~ spl11_127
| ~ spl11_138 ),
inference(avatar_split_clause,[],[f1943,f1739,f1642,f13698]) ).
fof(f13698,plain,
( spl11_542
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,difference(X1,X2))
| greatest(X0,X3,difference(X1,X2))
| ~ subset(difference(X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_542])]) ).
fof(f1739,plain,
( spl11_138
<=> ! [X0,X3,X2,X1] :
( greatest(X0,X1,difference(X2,X3))
| ~ member(X0,difference(X2,X3))
| ~ member(sK8(X1,difference(X2,X3),X0),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_138])]) ).
fof(f1943,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,difference(X1,X2))
| greatest(X0,X3,difference(X1,X2))
| ~ subset(difference(X1,X2),X2) )
| ~ spl11_127
| ~ spl11_138 ),
inference(duplicate_literal_removal,[],[f1927]) ).
fof(f1927,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,difference(X1,X2))
| greatest(X0,X3,difference(X1,X2))
| ~ member(X0,difference(X1,X2))
| greatest(X0,X3,difference(X1,X2))
| ~ subset(difference(X1,X2),X2) )
| ~ spl11_127
| ~ spl11_138 ),
inference(resolution,[],[f1740,f1643]) ).
fof(f1740,plain,
( ! [X2,X3,X0,X1] :
( ~ member(sK8(X1,difference(X2,X3),X0),X3)
| ~ member(X0,difference(X2,X3))
| greatest(X0,X1,difference(X2,X3)) )
| ~ spl11_138 ),
inference(avatar_component_clause,[],[f1739]) ).
fof(f13696,plain,
( spl11_541
| ~ spl11_87
| ~ spl11_135 ),
inference(avatar_split_clause,[],[f1877,f1727,f722,f13694]) ).
fof(f13694,plain,
( spl11_541
<=> ! [X2,X0,X1] :
( member(sK5(union(X0,X1),union(X1,X2)),X0)
| subset(union(X0,X1),union(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_541])]) ).
fof(f722,plain,
( spl11_87
<=> ! [X2,X0,X1] :
( ~ member(sK5(X0,union(X1,X2)),X1)
| subset(X0,union(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_87])]) ).
fof(f1727,plain,
( spl11_135
<=> ! [X2,X0,X1] :
( member(sK5(union(X0,X1),X2),X0)
| member(sK5(union(X0,X1),X2),X1)
| subset(union(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_135])]) ).
fof(f1877,plain,
( ! [X2,X0,X1] :
( member(sK5(union(X0,X1),union(X1,X2)),X0)
| subset(union(X0,X1),union(X1,X2)) )
| ~ spl11_87
| ~ spl11_135 ),
inference(duplicate_literal_removal,[],[f1811]) ).
fof(f1811,plain,
( ! [X2,X0,X1] :
( member(sK5(union(X0,X1),union(X1,X2)),X0)
| subset(union(X0,X1),union(X1,X2))
| subset(union(X0,X1),union(X1,X2)) )
| ~ spl11_87
| ~ spl11_135 ),
inference(resolution,[],[f1728,f723]) ).
fof(f723,plain,
( ! [X2,X0,X1] :
( ~ member(sK5(X0,union(X1,X2)),X1)
| subset(X0,union(X1,X2)) )
| ~ spl11_87 ),
inference(avatar_component_clause,[],[f722]) ).
fof(f1728,plain,
( ! [X2,X0,X1] :
( member(sK5(union(X0,X1),X2),X1)
| member(sK5(union(X0,X1),X2),X0)
| subset(union(X0,X1),X2) )
| ~ spl11_135 ),
inference(avatar_component_clause,[],[f1727]) ).
fof(f13692,plain,
( spl11_540
| ~ spl11_88
| ~ spl11_135 ),
inference(avatar_split_clause,[],[f1875,f1727,f726,f13690]) ).
fof(f13690,plain,
( spl11_540
<=> ! [X2,X0,X1] :
( member(sK5(union(X0,X1),union(X2,X1)),X0)
| subset(union(X0,X1),union(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_540])]) ).
fof(f726,plain,
( spl11_88
<=> ! [X2,X0,X1] :
( ~ member(sK5(X0,union(X1,X2)),X2)
| subset(X0,union(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_88])]) ).
fof(f1875,plain,
( ! [X2,X0,X1] :
( member(sK5(union(X0,X1),union(X2,X1)),X0)
| subset(union(X0,X1),union(X2,X1)) )
| ~ spl11_88
| ~ spl11_135 ),
inference(duplicate_literal_removal,[],[f1813]) ).
fof(f1813,plain,
( ! [X2,X0,X1] :
( member(sK5(union(X0,X1),union(X2,X1)),X0)
| subset(union(X0,X1),union(X2,X1))
| subset(union(X0,X1),union(X2,X1)) )
| ~ spl11_88
| ~ spl11_135 ),
inference(resolution,[],[f1728,f727]) ).
fof(f727,plain,
( ! [X2,X0,X1] :
( ~ member(sK5(X0,union(X1,X2)),X2)
| subset(X0,union(X1,X2)) )
| ~ spl11_88 ),
inference(avatar_component_clause,[],[f726]) ).
fof(f13688,plain,
( spl11_539
| ~ spl11_87
| ~ spl11_135 ),
inference(avatar_split_clause,[],[f1872,f1727,f722,f13686]) ).
fof(f13686,plain,
( spl11_539
<=> ! [X2,X0,X1] :
( member(sK5(union(X0,X1),union(X0,X2)),X1)
| subset(union(X0,X1),union(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_539])]) ).
fof(f1872,plain,
( ! [X2,X0,X1] :
( member(sK5(union(X0,X1),union(X0,X2)),X1)
| subset(union(X0,X1),union(X0,X2)) )
| ~ spl11_87
| ~ spl11_135 ),
inference(duplicate_literal_removal,[],[f1840]) ).
fof(f1840,plain,
( ! [X2,X0,X1] :
( member(sK5(union(X0,X1),union(X0,X2)),X1)
| subset(union(X0,X1),union(X0,X2))
| subset(union(X0,X1),union(X0,X2)) )
| ~ spl11_87
| ~ spl11_135 ),
inference(resolution,[],[f1728,f723]) ).
fof(f13684,plain,
( spl11_538
| ~ spl11_88
| ~ spl11_135 ),
inference(avatar_split_clause,[],[f1870,f1727,f726,f13682]) ).
fof(f13682,plain,
( spl11_538
<=> ! [X2,X0,X1] :
( member(sK5(union(X0,X1),union(X2,X0)),X1)
| subset(union(X0,X1),union(X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_538])]) ).
fof(f1870,plain,
( ! [X2,X0,X1] :
( member(sK5(union(X0,X1),union(X2,X0)),X1)
| subset(union(X0,X1),union(X2,X0)) )
| ~ spl11_88
| ~ spl11_135 ),
inference(duplicate_literal_removal,[],[f1842]) ).
fof(f1842,plain,
( ! [X2,X0,X1] :
( member(sK5(union(X0,X1),union(X2,X0)),X1)
| subset(union(X0,X1),union(X2,X0))
| subset(union(X0,X1),union(X2,X0)) )
| ~ spl11_88
| ~ spl11_135 ),
inference(resolution,[],[f1728,f727]) ).
fof(f13680,plain,
( ~ spl11_4
| spl11_3
| ~ spl11_45
| ~ spl11_165 ),
inference(avatar_split_clause,[],[f2718,f2692,f422,f162,f166]) ).
fof(f166,plain,
( spl11_4
<=> member(sK4,sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_4])]) ).
fof(f162,plain,
( spl11_3
<=> greatest(sK4,sK1,sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_3])]) ).
fof(f422,plain,
( spl11_45
<=> ! [X2,X0,X1] :
( greatest(X2,X0,X1)
| member(sK8(X0,X1,X2),X1)
| ~ member(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_45])]) ).
fof(f2692,plain,
( spl11_165
<=> ! [X0] :
( ~ member(sK8(sK1,X0,sK4),sK3)
| greatest(sK4,sK1,X0)
| ~ member(sK4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_165])]) ).
fof(f2718,plain,
( greatest(sK4,sK1,sK3)
| ~ member(sK4,sK3)
| ~ spl11_45
| ~ spl11_165 ),
inference(duplicate_literal_removal,[],[f2703]) ).
fof(f2703,plain,
( greatest(sK4,sK1,sK3)
| ~ member(sK4,sK3)
| greatest(sK4,sK1,sK3)
| ~ member(sK4,sK3)
| ~ spl11_45
| ~ spl11_165 ),
inference(resolution,[],[f2693,f423]) ).
fof(f423,plain,
( ! [X2,X0,X1] :
( member(sK8(X0,X1,X2),X1)
| greatest(X2,X0,X1)
| ~ member(X2,X1) )
| ~ spl11_45 ),
inference(avatar_component_clause,[],[f422]) ).
fof(f2693,plain,
( ! [X0] :
( ~ member(sK8(sK1,X0,sK4),sK3)
| greatest(sK4,sK1,X0)
| ~ member(sK4,X0) )
| ~ spl11_165 ),
inference(avatar_component_clause,[],[f2692]) ).
fof(f13679,plain,
( spl11_537
| ~ spl11_85
| ~ spl11_133 ),
inference(avatar_split_clause,[],[f1805,f1719,f714,f13677]) ).
fof(f13677,plain,
( spl11_537
<=> ! [X2,X0,X1] :
( ~ member(sK5(intersection(X0,X1),intersection(X2,X0)),X2)
| subset(intersection(X0,X1),intersection(X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_537])]) ).
fof(f1719,plain,
( spl11_133
<=> ! [X2,X0,X1] :
( ~ member(sK5(X0,intersection(X1,X2)),X2)
| ~ member(sK5(X0,intersection(X1,X2)),X1)
| subset(X0,intersection(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_133])]) ).
fof(f1805,plain,
( ! [X2,X0,X1] :
( ~ member(sK5(intersection(X0,X1),intersection(X2,X0)),X2)
| subset(intersection(X0,X1),intersection(X2,X0)) )
| ~ spl11_85
| ~ spl11_133 ),
inference(duplicate_literal_removal,[],[f1783]) ).
fof(f1783,plain,
( ! [X2,X0,X1] :
( ~ member(sK5(intersection(X0,X1),intersection(X2,X0)),X2)
| subset(intersection(X0,X1),intersection(X2,X0))
| subset(intersection(X0,X1),intersection(X2,X0)) )
| ~ spl11_85
| ~ spl11_133 ),
inference(resolution,[],[f1720,f715]) ).
fof(f1720,plain,
( ! [X2,X0,X1] :
( ~ member(sK5(X0,intersection(X1,X2)),X2)
| ~ member(sK5(X0,intersection(X1,X2)),X1)
| subset(X0,intersection(X1,X2)) )
| ~ spl11_133 ),
inference(avatar_component_clause,[],[f1719]) ).
fof(f13675,plain,
( spl11_536
| ~ spl11_86
| ~ spl11_133 ),
inference(avatar_split_clause,[],[f1804,f1719,f718,f13673]) ).
fof(f13673,plain,
( spl11_536
<=> ! [X2,X0,X1] :
( ~ member(sK5(intersection(X0,X1),intersection(X2,X1)),X2)
| subset(intersection(X0,X1),intersection(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_536])]) ).
fof(f1804,plain,
( ! [X2,X0,X1] :
( ~ member(sK5(intersection(X0,X1),intersection(X2,X1)),X2)
| subset(intersection(X0,X1),intersection(X2,X1)) )
| ~ spl11_86
| ~ spl11_133 ),
inference(duplicate_literal_removal,[],[f1784]) ).
fof(f1784,plain,
( ! [X2,X0,X1] :
( ~ member(sK5(intersection(X0,X1),intersection(X2,X1)),X2)
| subset(intersection(X0,X1),intersection(X2,X1))
| subset(intersection(X0,X1),intersection(X2,X1)) )
| ~ spl11_86
| ~ spl11_133 ),
inference(resolution,[],[f1720,f719]) ).
fof(f13671,plain,
( spl11_535
| ~ spl11_83
| ~ spl11_133 ),
inference(avatar_split_clause,[],[f1803,f1719,f706,f13669]) ).
fof(f13669,plain,
( spl11_535
<=> ! [X2,X0,X1] :
( ~ member(sK5(difference(X0,X1),intersection(X2,X0)),X2)
| subset(difference(X0,X1),intersection(X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_535])]) ).
fof(f1803,plain,
( ! [X2,X0,X1] :
( ~ member(sK5(difference(X0,X1),intersection(X2,X0)),X2)
| subset(difference(X0,X1),intersection(X2,X0)) )
| ~ spl11_83
| ~ spl11_133 ),
inference(duplicate_literal_removal,[],[f1785]) ).
fof(f1785,plain,
( ! [X2,X0,X1] :
( ~ member(sK5(difference(X0,X1),intersection(X2,X0)),X2)
| subset(difference(X0,X1),intersection(X2,X0))
| subset(difference(X0,X1),intersection(X2,X0)) )
| ~ spl11_83
| ~ spl11_133 ),
inference(resolution,[],[f1720,f707]) ).
fof(f13665,plain,
( spl11_534
| ~ spl11_47
| ~ spl11_57 ),
inference(avatar_split_clause,[],[f13654,f501,f444,f13663]) ).
fof(f13663,plain,
( spl11_534
<=> ! [X0] :
( ~ upper_bound(X0,sK1,sK3)
| ~ member(X0,sK2)
| apply(sK1,sK4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_534])]) ).
fof(f444,plain,
( spl11_47
<=> ! [X3,X0,X5,X2,X1] :
( apply(X1,X0,X5)
| ~ upper_bound(X5,X1,X2)
| ~ member(X5,X3)
| ~ sP0(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_47])]) ).
fof(f13654,plain,
( ! [X0] :
( ~ upper_bound(X0,sK1,sK3)
| ~ member(X0,sK2)
| apply(sK1,sK4,X0) )
| ~ spl11_47
| ~ spl11_57 ),
inference(resolution,[],[f503,f445]) ).
fof(f445,plain,
( ! [X2,X3,X0,X1,X5] :
( ~ sP0(X0,X1,X2,X3)
| ~ upper_bound(X5,X1,X2)
| ~ member(X5,X3)
| apply(X1,X0,X5) )
| ~ spl11_47 ),
inference(avatar_component_clause,[],[f444]) ).
fof(f13660,plain,
( ~ spl11_3
| ~ spl11_4
| ~ spl11_5 ),
inference(avatar_split_clause,[],[f103,f171,f166,f162]) ).
fof(f171,plain,
( spl11_5
<=> least_upper_bound(sK4,sK3,sK1,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_5])]) ).
fof(f103,plain,
( ~ least_upper_bound(sK4,sK3,sK1,sK2)
| ~ member(sK4,sK3)
| ~ greatest(sK4,sK1,sK3) ),
inference(cnf_transformation,[],[f61]) ).
fof(f61,plain,
( ( ~ least_upper_bound(sK4,sK3,sK1,sK2)
| ~ member(sK4,sK3)
| ~ greatest(sK4,sK1,sK3) )
& ( ( least_upper_bound(sK4,sK3,sK1,sK2)
& member(sK4,sK3) )
| greatest(sK4,sK1,sK3) )
& subset(sK3,sK2)
& order(sK1,sK2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4])],[f57,f60,f59,f58]) ).
fof(f58,plain,
( ? [X0,X1] :
( ? [X2] :
( ? [X3] :
( ( ~ least_upper_bound(X3,X2,X0,X1)
| ~ member(X3,X2)
| ~ greatest(X3,X0,X2) )
& ( ( least_upper_bound(X3,X2,X0,X1)
& member(X3,X2) )
| greatest(X3,X0,X2) ) )
& subset(X2,X1) )
& order(X0,X1) )
=> ( ? [X2] :
( ? [X3] :
( ( ~ least_upper_bound(X3,X2,sK1,sK2)
| ~ member(X3,X2)
| ~ greatest(X3,sK1,X2) )
& ( ( least_upper_bound(X3,X2,sK1,sK2)
& member(X3,X2) )
| greatest(X3,sK1,X2) ) )
& subset(X2,sK2) )
& order(sK1,sK2) ) ),
introduced(choice_axiom,[]) ).
fof(f59,plain,
( ? [X2] :
( ? [X3] :
( ( ~ least_upper_bound(X3,X2,sK1,sK2)
| ~ member(X3,X2)
| ~ greatest(X3,sK1,X2) )
& ( ( least_upper_bound(X3,X2,sK1,sK2)
& member(X3,X2) )
| greatest(X3,sK1,X2) ) )
& subset(X2,sK2) )
=> ( ? [X3] :
( ( ~ least_upper_bound(X3,sK3,sK1,sK2)
| ~ member(X3,sK3)
| ~ greatest(X3,sK1,sK3) )
& ( ( least_upper_bound(X3,sK3,sK1,sK2)
& member(X3,sK3) )
| greatest(X3,sK1,sK3) ) )
& subset(sK3,sK2) ) ),
introduced(choice_axiom,[]) ).
fof(f60,plain,
( ? [X3] :
( ( ~ least_upper_bound(X3,sK3,sK1,sK2)
| ~ member(X3,sK3)
| ~ greatest(X3,sK1,sK3) )
& ( ( least_upper_bound(X3,sK3,sK1,sK2)
& member(X3,sK3) )
| greatest(X3,sK1,sK3) ) )
=> ( ( ~ least_upper_bound(sK4,sK3,sK1,sK2)
| ~ member(sK4,sK3)
| ~ greatest(sK4,sK1,sK3) )
& ( ( least_upper_bound(sK4,sK3,sK1,sK2)
& member(sK4,sK3) )
| greatest(sK4,sK1,sK3) ) ) ),
introduced(choice_axiom,[]) ).
fof(f57,plain,
? [X0,X1] :
( ? [X2] :
( ? [X3] :
( ( ~ least_upper_bound(X3,X2,X0,X1)
| ~ member(X3,X2)
| ~ greatest(X3,X0,X2) )
& ( ( least_upper_bound(X3,X2,X0,X1)
& member(X3,X2) )
| greatest(X3,X0,X2) ) )
& subset(X2,X1) )
& order(X0,X1) ),
inference(flattening,[],[f56]) ).
fof(f56,plain,
? [X0,X1] :
( ? [X2] :
( ? [X3] :
( ( ~ least_upper_bound(X3,X2,X0,X1)
| ~ member(X3,X2)
| ~ greatest(X3,X0,X2) )
& ( ( least_upper_bound(X3,X2,X0,X1)
& member(X3,X2) )
| greatest(X3,X0,X2) ) )
& subset(X2,X1) )
& order(X0,X1) ),
inference(nnf_transformation,[],[f45]) ).
fof(f45,plain,
? [X0,X1] :
( ? [X2] :
( ? [X3] :
( greatest(X3,X0,X2)
<~> ( least_upper_bound(X3,X2,X0,X1)
& member(X3,X2) ) )
& subset(X2,X1) )
& order(X0,X1) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,plain,
~ ! [X0,X1] :
( order(X0,X1)
=> ! [X2] :
( subset(X2,X1)
=> ! [X3] :
( greatest(X3,X0,X2)
<=> ( least_upper_bound(X3,X2,X0,X1)
& member(X3,X2) ) ) ) ),
inference(rectify,[],[f23]) ).
fof(f23,negated_conjecture,
~ ! [X5,X3] :
( order(X5,X3)
=> ! [X2] :
( subset(X2,X3)
=> ! [X7] :
( greatest(X7,X5,X2)
<=> ( least_upper_bound(X7,X2,X5,X3)
& member(X7,X2) ) ) ) ),
inference(negated_conjecture,[],[f22]) ).
fof(f22,conjecture,
! [X5,X3] :
( order(X5,X3)
=> ! [X2] :
( subset(X2,X3)
=> ! [X7] :
( greatest(X7,X5,X2)
<=> ( least_upper_bound(X7,X2,X5,X3)
& member(X7,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIV13) ).
fof(f13658,plain,
( spl11_5
| ~ spl11_36
| ~ spl11_57 ),
inference(avatar_split_clause,[],[f13655,f501,f336,f171]) ).
fof(f336,plain,
( spl11_36
<=> ! [X0,X3,X2,X1] :
( least_upper_bound(X0,X1,X2,X3)
| ~ sP0(X0,X2,X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_36])]) ).
fof(f13655,plain,
( least_upper_bound(sK4,sK3,sK1,sK2)
| ~ spl11_36
| ~ spl11_57 ),
inference(resolution,[],[f503,f337]) ).
fof(f337,plain,
( ! [X2,X3,X0,X1] :
( ~ sP0(X0,X2,X1,X3)
| least_upper_bound(X0,X1,X2,X3) )
| ~ spl11_36 ),
inference(avatar_component_clause,[],[f336]) ).
fof(f13653,plain,
( ~ spl11_170
| ~ spl11_4
| spl11_57
| ~ spl11_312 ),
inference(avatar_split_clause,[],[f6058,f5385,f501,f166,f2808]) ).
fof(f5385,plain,
( spl11_312
<=> ! [X0,X3,X2,X1] :
( ~ upper_bound(X0,X1,X2)
| ~ member(X0,X2)
| sP0(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_312])]) ).
fof(f6058,plain,
( ~ member(sK4,sK3)
| ~ upper_bound(sK4,sK1,sK3)
| spl11_57
| ~ spl11_312 ),
inference(resolution,[],[f5386,f502]) ).
fof(f502,plain,
( ~ sP0(sK4,sK1,sK3,sK2)
| spl11_57 ),
inference(avatar_component_clause,[],[f501]) ).
fof(f5386,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,X1,X2,X3)
| ~ member(X0,X2)
| ~ upper_bound(X0,X1,X2) )
| ~ spl11_312 ),
inference(avatar_component_clause,[],[f5385]) ).
fof(f13652,plain,
( spl11_533
| ~ spl11_85
| ~ spl11_132 ),
inference(avatar_split_clause,[],[f1774,f1715,f714,f13650]) ).
fof(f13650,plain,
( spl11_533
<=> ! [X2,X0,X1] :
( member(sK5(intersection(X0,X1),difference(X0,X2)),X2)
| subset(intersection(X0,X1),difference(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_533])]) ).
fof(f1715,plain,
( spl11_132
<=> ! [X2,X0,X1] :
( member(sK5(X0,difference(X1,X2)),X2)
| ~ member(sK5(X0,difference(X1,X2)),X1)
| subset(X0,difference(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_132])]) ).
fof(f1774,plain,
( ! [X2,X0,X1] :
( member(sK5(intersection(X0,X1),difference(X0,X2)),X2)
| subset(intersection(X0,X1),difference(X0,X2)) )
| ~ spl11_85
| ~ spl11_132 ),
inference(duplicate_literal_removal,[],[f1752]) ).
fof(f1752,plain,
( ! [X2,X0,X1] :
( member(sK5(intersection(X0,X1),difference(X0,X2)),X2)
| subset(intersection(X0,X1),difference(X0,X2))
| subset(intersection(X0,X1),difference(X0,X2)) )
| ~ spl11_85
| ~ spl11_132 ),
inference(resolution,[],[f1716,f715]) ).
fof(f1716,plain,
( ! [X2,X0,X1] :
( ~ member(sK5(X0,difference(X1,X2)),X1)
| member(sK5(X0,difference(X1,X2)),X2)
| subset(X0,difference(X1,X2)) )
| ~ spl11_132 ),
inference(avatar_component_clause,[],[f1715]) ).
fof(f13648,plain,
( spl11_532
| ~ spl11_86
| ~ spl11_132 ),
inference(avatar_split_clause,[],[f1773,f1715,f718,f13646]) ).
fof(f13646,plain,
( spl11_532
<=> ! [X2,X0,X1] :
( member(sK5(intersection(X0,X1),difference(X1,X2)),X2)
| subset(intersection(X0,X1),difference(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_532])]) ).
fof(f1773,plain,
( ! [X2,X0,X1] :
( member(sK5(intersection(X0,X1),difference(X1,X2)),X2)
| subset(intersection(X0,X1),difference(X1,X2)) )
| ~ spl11_86
| ~ spl11_132 ),
inference(duplicate_literal_removal,[],[f1753]) ).
fof(f1753,plain,
( ! [X2,X0,X1] :
( member(sK5(intersection(X0,X1),difference(X1,X2)),X2)
| subset(intersection(X0,X1),difference(X1,X2))
| subset(intersection(X0,X1),difference(X1,X2)) )
| ~ spl11_86
| ~ spl11_132 ),
inference(resolution,[],[f1716,f719]) ).
fof(f13644,plain,
( spl11_531
| ~ spl11_83
| ~ spl11_132 ),
inference(avatar_split_clause,[],[f1772,f1715,f706,f13642]) ).
fof(f13642,plain,
( spl11_531
<=> ! [X2,X0,X1] :
( member(sK5(difference(X0,X1),difference(X0,X2)),X2)
| subset(difference(X0,X1),difference(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_531])]) ).
fof(f1772,plain,
( ! [X2,X0,X1] :
( member(sK5(difference(X0,X1),difference(X0,X2)),X2)
| subset(difference(X0,X1),difference(X0,X2)) )
| ~ spl11_83
| ~ spl11_132 ),
inference(duplicate_literal_removal,[],[f1754]) ).
fof(f1754,plain,
( ! [X2,X0,X1] :
( member(sK5(difference(X0,X1),difference(X0,X2)),X2)
| subset(difference(X0,X1),difference(X0,X2))
| subset(difference(X0,X1),difference(X0,X2)) )
| ~ spl11_83
| ~ spl11_132 ),
inference(resolution,[],[f1716,f707]) ).
fof(f13640,plain,
( spl11_530
| ~ spl11_9
| ~ spl11_126 ),
inference(avatar_split_clause,[],[f1599,f1506,f188,f13638]) ).
fof(f13638,plain,
( spl11_530
<=> ! [X0,X3,X2,X1] :
( ~ member(unordered_pair(X0,X1),X2)
| ~ member(unordered_pair(X0,X1),X3)
| member(X0,sum(intersection(X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_530])]) ).
fof(f188,plain,
( spl11_9
<=> ! [X2,X1] : member(X1,unordered_pair(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_9])]) ).
fof(f1599,plain,
( ! [X2,X3,X0,X1] :
( ~ member(unordered_pair(X0,X1),X2)
| ~ member(unordered_pair(X0,X1),X3)
| member(X0,sum(intersection(X2,X3))) )
| ~ spl11_9
| ~ spl11_126 ),
inference(resolution,[],[f1507,f189]) ).
fof(f189,plain,
( ! [X2,X1] : member(X1,unordered_pair(X1,X2))
| ~ spl11_9 ),
inference(avatar_component_clause,[],[f188]) ).
fof(f13636,plain,
( spl11_529
| ~ spl11_8
| ~ spl11_126 ),
inference(avatar_split_clause,[],[f1598,f1506,f184,f13634]) ).
fof(f13634,plain,
( spl11_529
<=> ! [X0,X3,X2,X1] :
( ~ member(unordered_pair(X0,X1),X2)
| ~ member(unordered_pair(X0,X1),X3)
| member(X1,sum(intersection(X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_529])]) ).
fof(f184,plain,
( spl11_8
<=> ! [X2,X1] : member(X2,unordered_pair(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_8])]) ).
fof(f1598,plain,
( ! [X2,X3,X0,X1] :
( ~ member(unordered_pair(X0,X1),X2)
| ~ member(unordered_pair(X0,X1),X3)
| member(X1,sum(intersection(X2,X3))) )
| ~ spl11_8
| ~ spl11_126 ),
inference(resolution,[],[f1507,f185]) ).
fof(f185,plain,
( ! [X2,X1] : member(X2,unordered_pair(X1,X2))
| ~ spl11_8 ),
inference(avatar_component_clause,[],[f184]) ).
fof(f13632,plain,
( spl11_528
| ~ spl11_9
| ~ spl11_125 ),
inference(avatar_split_clause,[],[f1550,f1502,f188,f13630]) ).
fof(f13630,plain,
( spl11_528
<=> ! [X0,X3,X2,X1] :
( ~ member(unordered_pair(X0,X1),X2)
| member(unordered_pair(X0,X1),X3)
| member(X0,sum(difference(X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_528])]) ).
fof(f1550,plain,
( ! [X2,X3,X0,X1] :
( ~ member(unordered_pair(X0,X1),X2)
| member(unordered_pair(X0,X1),X3)
| member(X0,sum(difference(X2,X3))) )
| ~ spl11_9
| ~ spl11_125 ),
inference(resolution,[],[f1503,f189]) ).
fof(f13628,plain,
( spl11_527
| ~ spl11_8
| ~ spl11_125 ),
inference(avatar_split_clause,[],[f1549,f1502,f184,f13626]) ).
fof(f13626,plain,
( spl11_527
<=> ! [X0,X3,X2,X1] :
( ~ member(unordered_pair(X0,X1),X2)
| member(unordered_pair(X0,X1),X3)
| member(X1,sum(difference(X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_527])]) ).
fof(f1549,plain,
( ! [X2,X3,X0,X1] :
( ~ member(unordered_pair(X0,X1),X2)
| member(unordered_pair(X0,X1),X3)
| member(X1,sum(difference(X2,X3))) )
| ~ spl11_8
| ~ spl11_125 ),
inference(resolution,[],[f1503,f185]) ).
fof(f13624,plain,
( spl11_526
| ~ spl11_10
| ~ spl11_124 ),
inference(avatar_split_clause,[],[f1521,f1498,f192,f13622]) ).
fof(f13622,plain,
( spl11_526
<=> ! [X0,X3,X2,X1] :
( ~ member(singleton(X0),X1)
| upper_bound(X2,X3,product(X1))
| sK9(X3,product(X1),X2) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_526])]) ).
fof(f192,plain,
( spl11_10
<=> ! [X0,X1] :
( X0 = X1
| ~ member(X0,singleton(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_10])]) ).
fof(f1521,plain,
( ! [X2,X3,X0,X1] :
( ~ member(singleton(X0),X1)
| upper_bound(X2,X3,product(X1))
| sK9(X3,product(X1),X2) = X0 )
| ~ spl11_10
| ~ spl11_124 ),
inference(resolution,[],[f1499,f193]) ).
fof(f193,plain,
( ! [X0,X1] :
( ~ member(X0,singleton(X1))
| X0 = X1 )
| ~ spl11_10 ),
inference(avatar_component_clause,[],[f192]) ).
fof(f13620,plain,
( spl11_525
| ~ spl11_11
| ~ spl11_124 ),
inference(avatar_split_clause,[],[f1514,f1498,f196,f13618]) ).
fof(f13618,plain,
( spl11_525
<=> ! [X0,X3,X2,X1] :
( ~ member(power_set(X0),X1)
| upper_bound(X2,X3,product(X1))
| subset(sK9(X3,product(X1),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_525])]) ).
fof(f1514,plain,
( ! [X2,X3,X0,X1] :
( ~ member(power_set(X0),X1)
| upper_bound(X2,X3,product(X1))
| subset(sK9(X3,product(X1),X2),X0) )
| ~ spl11_11
| ~ spl11_124 ),
inference(resolution,[],[f1499,f197]) ).
fof(f13616,plain,
( spl11_524
| ~ spl11_10
| ~ spl11_121 ),
inference(avatar_split_clause,[],[f1485,f1328,f192,f13614]) ).
fof(f13614,plain,
( spl11_524
<=> ! [X0,X3,X2,X1] :
( upper_bound(X0,X1,difference(singleton(X2),X3))
| sK9(X1,difference(singleton(X2),X3),X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_524])]) ).
fof(f1485,plain,
( ! [X2,X3,X0,X1] :
( upper_bound(X0,X1,difference(singleton(X2),X3))
| sK9(X1,difference(singleton(X2),X3),X0) = X2 )
| ~ spl11_10
| ~ spl11_121 ),
inference(resolution,[],[f1329,f193]) ).
fof(f13612,plain,
( spl11_523
| ~ spl11_82
| ~ spl11_310 ),
inference(avatar_split_clause,[],[f6041,f5377,f669,f13609]) ).
fof(f13609,plain,
( spl11_523
<=> subset(union(sK4,sum(sK3)),sum(sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_523])]) ).
fof(f5377,plain,
( spl11_310
<=> ! [X0,X1] :
( member(sK5(union(X0,X1),X1),X0)
| subset(union(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_310])]) ).
fof(f6041,plain,
( subset(union(sK4,sum(sK3)),sum(sK3))
| ~ spl11_82
| ~ spl11_310 ),
inference(duplicate_literal_removal,[],[f5995]) ).
fof(f5995,plain,
( subset(union(sK4,sum(sK3)),sum(sK3))
| subset(union(sK4,sum(sK3)),sum(sK3))
| ~ spl11_82
| ~ spl11_310 ),
inference(resolution,[],[f5378,f670]) ).
fof(f5378,plain,
( ! [X0,X1] :
( member(sK5(union(X0,X1),X1),X0)
| subset(union(X0,X1),X1) )
| ~ spl11_310 ),
inference(avatar_component_clause,[],[f5377]) ).
fof(f13607,plain,
( spl11_522
| ~ spl11_11
| ~ spl11_121 ),
inference(avatar_split_clause,[],[f1478,f1328,f196,f13605]) ).
fof(f13605,plain,
( spl11_522
<=> ! [X0,X3,X2,X1] :
( upper_bound(X0,X1,difference(power_set(X2),X3))
| subset(sK9(X1,difference(power_set(X2),X3),X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_522])]) ).
fof(f1478,plain,
( ! [X2,X3,X0,X1] :
( upper_bound(X0,X1,difference(power_set(X2),X3))
| subset(sK9(X1,difference(power_set(X2),X3),X0),X2) )
| ~ spl11_11
| ~ spl11_121 ),
inference(resolution,[],[f1329,f197]) ).
fof(f13603,plain,
( spl11_521
| ~ spl11_12
| ~ spl11_120 ),
inference(avatar_split_clause,[],[f1457,f1324,f200,f13601]) ).
fof(f13601,plain,
( spl11_521
<=> ! [X0,X3,X2,X1] :
( upper_bound(X0,X1,difference(X2,power_set(X3)))
| ~ subset(sK9(X1,difference(X2,power_set(X3)),X0),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_521])]) ).
fof(f1324,plain,
( spl11_120
<=> ! [X0,X3,X2,X1] :
( upper_bound(X0,X1,difference(X2,X3))
| ~ member(sK9(X1,difference(X2,X3),X0),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_120])]) ).
fof(f1457,plain,
( ! [X2,X3,X0,X1] :
( upper_bound(X0,X1,difference(X2,power_set(X3)))
| ~ subset(sK9(X1,difference(X2,power_set(X3)),X0),X3) )
| ~ spl11_12
| ~ spl11_120 ),
inference(resolution,[],[f1325,f201]) ).
fof(f1325,plain,
( ! [X2,X3,X0,X1] :
( ~ member(sK9(X1,difference(X2,X3),X0),X3)
| upper_bound(X0,X1,difference(X2,X3)) )
| ~ spl11_120 ),
inference(avatar_component_clause,[],[f1324]) ).
fof(f13599,plain,
( spl11_520
| ~ spl11_10
| ~ spl11_119 ),
inference(avatar_split_clause,[],[f1447,f1320,f192,f13597]) ).
fof(f13597,plain,
( spl11_520
<=> ! [X0,X3,X2,X1] :
( upper_bound(X0,X1,intersection(singleton(X2),X3))
| sK9(X1,intersection(singleton(X2),X3),X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_520])]) ).
fof(f1447,plain,
( ! [X2,X3,X0,X1] :
( upper_bound(X0,X1,intersection(singleton(X2),X3))
| sK9(X1,intersection(singleton(X2),X3),X0) = X2 )
| ~ spl11_10
| ~ spl11_119 ),
inference(resolution,[],[f1321,f193]) ).
fof(f13595,plain,
( spl11_519
| ~ spl11_11
| ~ spl11_119 ),
inference(avatar_split_clause,[],[f1440,f1320,f196,f13593]) ).
fof(f13593,plain,
( spl11_519
<=> ! [X0,X3,X2,X1] :
( upper_bound(X0,X1,intersection(power_set(X2),X3))
| subset(sK9(X1,intersection(power_set(X2),X3),X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_519])]) ).
fof(f1440,plain,
( ! [X2,X3,X0,X1] :
( upper_bound(X0,X1,intersection(power_set(X2),X3))
| subset(sK9(X1,intersection(power_set(X2),X3),X0),X2) )
| ~ spl11_11
| ~ spl11_119 ),
inference(resolution,[],[f1321,f197]) ).
fof(f13591,plain,
( spl11_518
| ~ spl11_10
| ~ spl11_118 ),
inference(avatar_split_clause,[],[f1426,f1316,f192,f13589]) ).
fof(f13589,plain,
( spl11_518
<=> ! [X0,X3,X2,X1] :
( upper_bound(X0,X1,intersection(X2,singleton(X3)))
| sK9(X1,intersection(X2,singleton(X3)),X0) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_518])]) ).
fof(f1426,plain,
( ! [X2,X3,X0,X1] :
( upper_bound(X0,X1,intersection(X2,singleton(X3)))
| sK9(X1,intersection(X2,singleton(X3)),X0) = X3 )
| ~ spl11_10
| ~ spl11_118 ),
inference(resolution,[],[f1317,f193]) ).
fof(f13587,plain,
( spl11_517
| ~ spl11_11
| ~ spl11_118 ),
inference(avatar_split_clause,[],[f1419,f1316,f196,f13585]) ).
fof(f13585,plain,
( spl11_517
<=> ! [X0,X3,X2,X1] :
( upper_bound(X0,X1,intersection(X2,power_set(X3)))
| subset(sK9(X1,intersection(X2,power_set(X3)),X0),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_517])]) ).
fof(f1419,plain,
( ! [X2,X3,X0,X1] :
( upper_bound(X0,X1,intersection(X2,power_set(X3)))
| subset(sK9(X1,intersection(X2,power_set(X3)),X0),X3) )
| ~ spl11_11
| ~ spl11_118 ),
inference(resolution,[],[f1317,f197]) ).
fof(f13583,plain,
( spl11_516
| ~ spl11_16
| ~ spl11_115 ),
inference(avatar_split_clause,[],[f1371,f1304,f219,f13581]) ).
fof(f13581,plain,
( spl11_516
<=> ! [X0,X3,X2,X1] :
( ~ member(difference(X0,X1),X2)
| ~ member(X3,sum(product(X2)))
| member(sK7(X3,product(X2)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_516])]) ).
fof(f1371,plain,
( ! [X2,X3,X0,X1] :
( ~ member(difference(X0,X1),X2)
| ~ member(X3,sum(product(X2)))
| member(sK7(X3,product(X2)),X0) )
| ~ spl11_16
| ~ spl11_115 ),
inference(resolution,[],[f1305,f220]) ).
fof(f13579,plain,
( spl11_515
| ~ spl11_17
| ~ spl11_115 ),
inference(avatar_split_clause,[],[f1370,f1304,f223,f13577]) ).
fof(f13577,plain,
( spl11_515
<=> ! [X0,X3,X2,X1] :
( ~ member(difference(X0,X1),X2)
| ~ member(X3,sum(product(X2)))
| ~ member(sK7(X3,product(X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_515])]) ).
fof(f1370,plain,
( ! [X2,X3,X0,X1] :
( ~ member(difference(X0,X1),X2)
| ~ member(X3,sum(product(X2)))
| ~ member(sK7(X3,product(X2)),X1) )
| ~ spl11_17
| ~ spl11_115 ),
inference(resolution,[],[f1305,f224]) ).
fof(f13575,plain,
( spl11_514
| ~ spl11_18
| ~ spl11_115 ),
inference(avatar_split_clause,[],[f1367,f1304,f227,f13573]) ).
fof(f13573,plain,
( spl11_514
<=> ! [X0,X3,X2,X1] :
( ~ member(intersection(X0,X1),X2)
| ~ member(X3,sum(product(X2)))
| member(sK7(X3,product(X2)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_514])]) ).
fof(f1367,plain,
( ! [X2,X3,X0,X1] :
( ~ member(intersection(X0,X1),X2)
| ~ member(X3,sum(product(X2)))
| member(sK7(X3,product(X2)),X0) )
| ~ spl11_18
| ~ spl11_115 ),
inference(resolution,[],[f1305,f228]) ).
fof(f13571,plain,
( spl11_513
| ~ spl11_19
| ~ spl11_115 ),
inference(avatar_split_clause,[],[f1366,f1304,f231,f13569]) ).
fof(f13569,plain,
( spl11_513
<=> ! [X0,X3,X2,X1] :
( ~ member(intersection(X0,X1),X2)
| ~ member(X3,sum(product(X2)))
| member(sK7(X3,product(X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_513])]) ).
fof(f1366,plain,
( ! [X2,X3,X0,X1] :
( ~ member(intersection(X0,X1),X2)
| ~ member(X3,sum(product(X2)))
| member(sK7(X3,product(X2)),X1) )
| ~ spl11_19
| ~ spl11_115 ),
inference(resolution,[],[f1305,f232]) ).
fof(f13567,plain,
( spl11_512
| ~ spl11_82
| ~ spl11_309 ),
inference(avatar_split_clause,[],[f5974,f5373,f669,f13564]) ).
fof(f13564,plain,
( spl11_512
<=> subset(union(sum(sK3),sK4),sum(sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_512])]) ).
fof(f5373,plain,
( spl11_309
<=> ! [X0,X1] :
( member(sK5(union(X0,X1),X0),X1)
| subset(union(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_309])]) ).
fof(f5974,plain,
( subset(union(sum(sK3),sK4),sum(sK3))
| ~ spl11_82
| ~ spl11_309 ),
inference(duplicate_literal_removal,[],[f5928]) ).
fof(f5928,plain,
( subset(union(sum(sK3),sK4),sum(sK3))
| subset(union(sum(sK3),sK4),sum(sK3))
| ~ spl11_82
| ~ spl11_309 ),
inference(resolution,[],[f5374,f670]) ).
fof(f5374,plain,
( ! [X0,X1] :
( member(sK5(union(X0,X1),X0),X1)
| subset(union(X0,X1),X0) )
| ~ spl11_309 ),
inference(avatar_component_clause,[],[f5373]) ).
fof(f13562,plain,
( spl11_511
| ~ spl11_16
| ~ spl11_114 ),
inference(avatar_split_clause,[],[f1350,f1300,f219,f13560]) ).
fof(f13560,plain,
( spl11_511
<=> ! [X0,X3,X2,X1] :
( ~ member(difference(X0,X1),X2)
| member(X3,product(product(X2)))
| member(sK6(X3,product(X2)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_511])]) ).
fof(f1350,plain,
( ! [X2,X3,X0,X1] :
( ~ member(difference(X0,X1),X2)
| member(X3,product(product(X2)))
| member(sK6(X3,product(X2)),X0) )
| ~ spl11_16
| ~ spl11_114 ),
inference(resolution,[],[f1301,f220]) ).
fof(f13558,plain,
( spl11_510
| ~ spl11_17
| ~ spl11_114 ),
inference(avatar_split_clause,[],[f1349,f1300,f223,f13556]) ).
fof(f13556,plain,
( spl11_510
<=> ! [X0,X3,X2,X1] :
( ~ member(difference(X0,X1),X2)
| member(X3,product(product(X2)))
| ~ member(sK6(X3,product(X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_510])]) ).
fof(f1349,plain,
( ! [X2,X3,X0,X1] :
( ~ member(difference(X0,X1),X2)
| member(X3,product(product(X2)))
| ~ member(sK6(X3,product(X2)),X1) )
| ~ spl11_17
| ~ spl11_114 ),
inference(resolution,[],[f1301,f224]) ).
fof(f13554,plain,
( spl11_509
| ~ spl11_18
| ~ spl11_114 ),
inference(avatar_split_clause,[],[f1346,f1300,f227,f13552]) ).
fof(f13552,plain,
( spl11_509
<=> ! [X0,X3,X2,X1] :
( ~ member(intersection(X0,X1),X2)
| member(X3,product(product(X2)))
| member(sK6(X3,product(X2)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_509])]) ).
fof(f1346,plain,
( ! [X2,X3,X0,X1] :
( ~ member(intersection(X0,X1),X2)
| member(X3,product(product(X2)))
| member(sK6(X3,product(X2)),X0) )
| ~ spl11_18
| ~ spl11_114 ),
inference(resolution,[],[f1301,f228]) ).
fof(f13550,plain,
( spl11_508
| ~ spl11_19
| ~ spl11_114 ),
inference(avatar_split_clause,[],[f1345,f1300,f231,f13548]) ).
fof(f13548,plain,
( spl11_508
<=> ! [X0,X3,X2,X1] :
( ~ member(intersection(X0,X1),X2)
| member(X3,product(product(X2)))
| member(sK6(X3,product(X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_508])]) ).
fof(f1345,plain,
( ! [X2,X3,X0,X1] :
( ~ member(intersection(X0,X1),X2)
| member(X3,product(product(X2)))
| member(sK6(X3,product(X2)),X1) )
| ~ spl11_19
| ~ spl11_114 ),
inference(resolution,[],[f1301,f232]) ).
fof(f13546,plain,
( spl11_507
| ~ spl11_23
| ~ spl11_112 ),
inference(avatar_split_clause,[],[f1282,f1055,f259,f13544]) ).
fof(f13544,plain,
( spl11_507
<=> ! [X4,X0,X3,X2,X1] :
( upper_bound(X0,X1,X2)
| ~ subset(X2,X3)
| member(sK9(X1,X2,X0),X4)
| ~ subset(X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_507])]) ).
fof(f1282,plain,
( ! [X2,X3,X0,X1,X4] :
( upper_bound(X0,X1,X2)
| ~ subset(X2,X3)
| member(sK9(X1,X2,X0),X4)
| ~ subset(X3,X4) )
| ~ spl11_23
| ~ spl11_112 ),
inference(resolution,[],[f1056,f260]) ).
fof(f13542,plain,
( spl11_506
| ~ spl11_23
| ~ spl11_109 ),
inference(avatar_split_clause,[],[f1231,f1043,f259,f13540]) ).
fof(f13540,plain,
( spl11_506
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,X1)
| ~ member(X1,sum(X2))
| member(X0,X3)
| ~ subset(sum(sK7(X1,X2)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_506])]) ).
fof(f1231,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,X1)
| ~ member(X1,sum(X2))
| member(X0,X3)
| ~ subset(sum(sK7(X1,X2)),X3) )
| ~ spl11_23
| ~ spl11_109 ),
inference(resolution,[],[f1044,f260]) ).
fof(f13538,plain,
( spl11_505
| ~ spl11_23
| ~ spl11_108 ),
inference(avatar_split_clause,[],[f1209,f1039,f259,f13536]) ).
fof(f13536,plain,
( spl11_505
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,X1)
| subset(product(X1),X2)
| member(sK5(product(X1),X2),X3)
| ~ subset(X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_505])]) ).
fof(f1209,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,X1)
| subset(product(X1),X2)
| member(sK5(product(X1),X2),X3)
| ~ subset(X0,X3) )
| ~ spl11_23
| ~ spl11_108 ),
inference(resolution,[],[f1040,f260]) ).
fof(f13534,plain,
( spl11_504
| ~ spl11_23
| ~ spl11_107 ),
inference(avatar_split_clause,[],[f1187,f1030,f259,f13532]) ).
fof(f13532,plain,
( spl11_504
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,sum(difference(X1,X2)))
| member(sK7(X0,difference(X1,X2)),X3)
| ~ subset(X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_504])]) ).
fof(f1187,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,sum(difference(X1,X2)))
| member(sK7(X0,difference(X1,X2)),X3)
| ~ subset(X1,X3) )
| ~ spl11_23
| ~ spl11_107 ),
inference(resolution,[],[f1031,f260]) ).
fof(f13530,plain,
( spl11_503
| ~ spl11_23
| ~ spl11_105 ),
inference(avatar_split_clause,[],[f1154,f1022,f259,f13528]) ).
fof(f13528,plain,
( spl11_503
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,sum(intersection(X1,X2)))
| member(sK7(X0,intersection(X1,X2)),X3)
| ~ subset(X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_503])]) ).
fof(f1154,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,sum(intersection(X1,X2)))
| member(sK7(X0,intersection(X1,X2)),X3)
| ~ subset(X1,X3) )
| ~ spl11_23
| ~ spl11_105 ),
inference(resolution,[],[f1023,f260]) ).
fof(f13526,plain,
( spl11_502
| ~ spl11_23
| ~ spl11_104 ),
inference(avatar_split_clause,[],[f1132,f1018,f259,f13524]) ).
fof(f13524,plain,
( spl11_502
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,sum(intersection(X1,X2)))
| member(sK7(X0,intersection(X1,X2)),X3)
| ~ subset(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_502])]) ).
fof(f1132,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,sum(intersection(X1,X2)))
| member(sK7(X0,intersection(X1,X2)),X3)
| ~ subset(X2,X3) )
| ~ spl11_23
| ~ spl11_104 ),
inference(resolution,[],[f1019,f260]) ).
fof(f13522,plain,
( spl11_501
| ~ spl11_23
| ~ spl11_103 ),
inference(avatar_split_clause,[],[f1113,f1014,f259,f13520]) ).
fof(f13520,plain,
( spl11_501
<=> ! [X0,X3,X2,X1] :
( member(X0,product(difference(X1,X2)))
| member(sK6(X0,difference(X1,X2)),X3)
| ~ subset(X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_501])]) ).
fof(f1113,plain,
( ! [X2,X3,X0,X1] :
( member(X0,product(difference(X1,X2)))
| member(sK6(X0,difference(X1,X2)),X3)
| ~ subset(X1,X3) )
| ~ spl11_23
| ~ spl11_103 ),
inference(resolution,[],[f1015,f260]) ).
fof(f13518,plain,
( spl11_500
| ~ spl11_23
| ~ spl11_101 ),
inference(avatar_split_clause,[],[f1080,f1006,f259,f13516]) ).
fof(f13516,plain,
( spl11_500
<=> ! [X0,X3,X2,X1] :
( member(X0,product(intersection(X1,X2)))
| member(sK6(X0,intersection(X1,X2)),X3)
| ~ subset(X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_500])]) ).
fof(f1080,plain,
( ! [X2,X3,X0,X1] :
( member(X0,product(intersection(X1,X2)))
| member(sK6(X0,intersection(X1,X2)),X3)
| ~ subset(X1,X3) )
| ~ spl11_23
| ~ spl11_101 ),
inference(resolution,[],[f1007,f260]) ).
fof(f13514,plain,
( spl11_499
| ~ spl11_23
| ~ spl11_100 ),
inference(avatar_split_clause,[],[f1062,f1002,f259,f13512]) ).
fof(f13512,plain,
( spl11_499
<=> ! [X0,X3,X2,X1] :
( member(X0,product(intersection(X1,X2)))
| member(sK6(X0,intersection(X1,X2)),X3)
| ~ subset(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_499])]) ).
fof(f1062,plain,
( ! [X2,X3,X0,X1] :
( member(X0,product(intersection(X1,X2)))
| member(sK6(X0,intersection(X1,X2)),X3)
| ~ subset(X2,X3) )
| ~ spl11_23
| ~ spl11_100 ),
inference(resolution,[],[f1003,f260]) ).
fof(f13510,plain,
( spl11_498
| ~ spl11_14
| ~ spl11_95 ),
inference(avatar_split_clause,[],[f980,f754,f211,f13508]) ).
fof(f13508,plain,
( spl11_498
<=> ! [X2,X0,X1] :
( member(sK5(sK5(X0,X1),X2),sum(X0))
| subset(X0,X1)
| subset(sK5(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_498])]) ).
fof(f980,plain,
( ! [X2,X0,X1] :
( member(sK5(sK5(X0,X1),X2),sum(X0))
| subset(X0,X1)
| subset(sK5(X0,X1),X2) )
| ~ spl11_14
| ~ spl11_95 ),
inference(resolution,[],[f755,f212]) ).
fof(f13506,plain,
( spl11_497
| ~ spl11_34
| ~ spl11_94 ),
inference(avatar_split_clause,[],[f978,f750,f328,f13504]) ).
fof(f13504,plain,
( spl11_497
<=> ! [X4,X0,X3,X2,X1] :
( member(X0,sum(union(X1,X2)))
| ~ member(X0,sK9(X3,X1,X4))
| upper_bound(X4,X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_497])]) ).
fof(f978,plain,
( ! [X2,X3,X0,X1,X4] :
( member(X0,sum(union(X1,X2)))
| ~ member(X0,sK9(X3,X1,X4))
| upper_bound(X4,X3,X1) )
| ~ spl11_34
| ~ spl11_94 ),
inference(resolution,[],[f751,f329]) ).
fof(f13502,plain,
( spl11_496
| ~ spl11_34
| ~ spl11_93 ),
inference(avatar_split_clause,[],[f947,f746,f328,f13500]) ).
fof(f13500,plain,
( spl11_496
<=> ! [X4,X0,X3,X2,X1] :
( member(X0,sum(union(X1,X2)))
| ~ member(X0,sK9(X3,X2,X4))
| upper_bound(X4,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_496])]) ).
fof(f947,plain,
( ! [X2,X3,X0,X1,X4] :
( member(X0,sum(union(X1,X2)))
| ~ member(X0,sK9(X3,X2,X4))
| upper_bound(X4,X3,X2) )
| ~ spl11_34
| ~ spl11_93 ),
inference(resolution,[],[f747,f329]) ).
fof(f13498,plain,
( spl11_495
| ~ spl11_32
| ~ spl11_90 ),
inference(avatar_split_clause,[],[f913,f734,f320,f13496]) ).
fof(f13496,plain,
( spl11_495
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,sum(X1))
| ~ subset(X1,product(X2))
| ~ member(X3,X2)
| member(sK7(X0,X1),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_495])]) ).
fof(f913,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,sum(X1))
| ~ subset(X1,product(X2))
| ~ member(X3,X2)
| member(sK7(X0,X1),X3) )
| ~ spl11_32
| ~ spl11_90 ),
inference(resolution,[],[f735,f321]) ).
fof(f13494,plain,
( spl11_494
| ~ spl11_33
| ~ spl11_90 ),
inference(avatar_split_clause,[],[f900,f734,f324,f13492]) ).
fof(f13492,plain,
( spl11_494
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,sum(X1))
| ~ subset(X1,X2)
| ~ member(X3,sK7(X0,X1))
| member(X3,sum(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_494])]) ).
fof(f900,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,sum(X1))
| ~ subset(X1,X2)
| ~ member(X3,sK7(X0,X1))
| member(X3,sum(X2)) )
| ~ spl11_33
| ~ spl11_90 ),
inference(resolution,[],[f735,f325]) ).
fof(f13490,plain,
( spl11_493
| ~ spl11_32
| ~ spl11_89 ),
inference(avatar_split_clause,[],[f897,f730,f320,f13488]) ).
fof(f13488,plain,
( spl11_493
<=> ! [X0,X3,X2,X1] :
( member(X0,product(X1))
| ~ subset(X1,product(X2))
| ~ member(X3,X2)
| member(sK6(X0,X1),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_493])]) ).
fof(f897,plain,
( ! [X2,X3,X0,X1] :
( member(X0,product(X1))
| ~ subset(X1,product(X2))
| ~ member(X3,X2)
| member(sK6(X0,X1),X3) )
| ~ spl11_32
| ~ spl11_89 ),
inference(resolution,[],[f731,f321]) ).
fof(f13486,plain,
( spl11_492
| ~ spl11_33
| ~ spl11_89 ),
inference(avatar_split_clause,[],[f884,f730,f324,f13484]) ).
fof(f13484,plain,
( spl11_492
<=> ! [X0,X3,X2,X1] :
( member(X0,product(X1))
| ~ subset(X1,X2)
| ~ member(X3,sK6(X0,X1))
| member(X3,sum(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_492])]) ).
fof(f884,plain,
( ! [X2,X3,X0,X1] :
( member(X0,product(X1))
| ~ subset(X1,X2)
| ~ member(X3,sK6(X0,X1))
| member(X3,sum(X2)) )
| ~ spl11_33
| ~ spl11_89 ),
inference(resolution,[],[f731,f325]) ).
fof(f13482,plain,
( spl11_294
| ~ spl11_491
| ~ spl11_55
| ~ spl11_252 ),
inference(avatar_split_clause,[],[f4247,f4069,f489,f13479,f5309]) ).
fof(f5309,plain,
( spl11_294
<=> ! [X0] : ~ member(X0,sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_294])]) ).
fof(f13479,plain,
( spl11_491
<=> subset(sK3,sum(empty_set)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_491])]) ).
fof(f489,plain,
( spl11_55
<=> ! [X0] :
( ~ member(X0,sK4)
| member(X0,sum(sK3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_55])]) ).
fof(f4069,plain,
( spl11_252
<=> ! [X0,X1] :
( ~ member(X0,sum(X1))
| ~ subset(X1,sum(empty_set)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_252])]) ).
fof(f4247,plain,
( ! [X0] :
( ~ subset(sK3,sum(empty_set))
| ~ member(X0,sK4) )
| ~ spl11_55
| ~ spl11_252 ),
inference(resolution,[],[f4070,f490]) ).
fof(f490,plain,
( ! [X0] :
( member(X0,sum(sK3))
| ~ member(X0,sK4) )
| ~ spl11_55 ),
inference(avatar_component_clause,[],[f489]) ).
fof(f4070,plain,
( ! [X0,X1] :
( ~ member(X0,sum(X1))
| ~ subset(X1,sum(empty_set)) )
| ~ spl11_252 ),
inference(avatar_component_clause,[],[f4069]) ).
fof(f13477,plain,
( spl11_490
| ~ spl11_66
| ~ spl11_88 ),
inference(avatar_split_clause,[],[f871,f726,f565,f13475]) ).
fof(f13475,plain,
( spl11_490
<=> ! [X2,X0,X1] :
( subset(X0,union(X1,sum(singleton(X2))))
| ~ member(sK5(X0,union(X1,sum(singleton(X2)))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_490])]) ).
fof(f871,plain,
( ! [X2,X0,X1] :
( subset(X0,union(X1,sum(singleton(X2))))
| ~ member(sK5(X0,union(X1,sum(singleton(X2)))),X2) )
| ~ spl11_66
| ~ spl11_88 ),
inference(resolution,[],[f727,f566]) ).
fof(f13473,plain,
( spl11_489
| ~ spl11_20
| ~ spl11_88 ),
inference(avatar_split_clause,[],[f869,f726,f235,f13471]) ).
fof(f13471,plain,
( spl11_489
<=> ! [X0,X3,X2,X1] :
( subset(X0,union(X1,union(X2,X3)))
| ~ member(sK5(X0,union(X1,union(X2,X3))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_489])]) ).
fof(f869,plain,
( ! [X2,X3,X0,X1] :
( subset(X0,union(X1,union(X2,X3)))
| ~ member(sK5(X0,union(X1,union(X2,X3))),X2) )
| ~ spl11_20
| ~ spl11_88 ),
inference(resolution,[],[f727,f236]) ).
fof(f13469,plain,
( spl11_488
| ~ spl11_21
| ~ spl11_88 ),
inference(avatar_split_clause,[],[f868,f726,f239,f13467]) ).
fof(f13467,plain,
( spl11_488
<=> ! [X0,X3,X2,X1] :
( subset(X0,union(X1,union(X2,X3)))
| ~ member(sK5(X0,union(X1,union(X2,X3))),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_488])]) ).
fof(f868,plain,
( ! [X2,X3,X0,X1] :
( subset(X0,union(X1,union(X2,X3)))
| ~ member(sK5(X0,union(X1,union(X2,X3))),X3) )
| ~ spl11_21
| ~ spl11_88 ),
inference(resolution,[],[f727,f240]) ).
fof(f13465,plain,
( spl11_487
| ~ spl11_66
| ~ spl11_87 ),
inference(avatar_split_clause,[],[f849,f722,f565,f13463]) ).
fof(f13463,plain,
( spl11_487
<=> ! [X2,X0,X1] :
( subset(X0,union(sum(singleton(X1)),X2))
| ~ member(sK5(X0,union(sum(singleton(X1)),X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_487])]) ).
fof(f849,plain,
( ! [X2,X0,X1] :
( subset(X0,union(sum(singleton(X1)),X2))
| ~ member(sK5(X0,union(sum(singleton(X1)),X2)),X1) )
| ~ spl11_66
| ~ spl11_87 ),
inference(resolution,[],[f723,f566]) ).
fof(f13461,plain,
( spl11_486
| ~ spl11_20
| ~ spl11_87 ),
inference(avatar_split_clause,[],[f847,f722,f235,f13459]) ).
fof(f13459,plain,
( spl11_486
<=> ! [X0,X3,X2,X1] :
( subset(X0,union(union(X1,X2),X3))
| ~ member(sK5(X0,union(union(X1,X2),X3)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_486])]) ).
fof(f847,plain,
( ! [X2,X3,X0,X1] :
( subset(X0,union(union(X1,X2),X3))
| ~ member(sK5(X0,union(union(X1,X2),X3)),X1) )
| ~ spl11_20
| ~ spl11_87 ),
inference(resolution,[],[f723,f236]) ).
fof(f13457,plain,
( spl11_485
| ~ spl11_21
| ~ spl11_87 ),
inference(avatar_split_clause,[],[f846,f722,f239,f13455]) ).
fof(f13455,plain,
( spl11_485
<=> ! [X0,X3,X2,X1] :
( subset(X0,union(union(X1,X2),X3))
| ~ member(sK5(X0,union(union(X1,X2),X3)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_485])]) ).
fof(f846,plain,
( ! [X2,X3,X0,X1] :
( subset(X0,union(union(X1,X2),X3))
| ~ member(sK5(X0,union(union(X1,X2),X3)),X2) )
| ~ spl11_21
| ~ spl11_87 ),
inference(resolution,[],[f723,f240]) ).
fof(f13453,plain,
( spl11_484
| ~ spl11_16
| ~ spl11_86 ),
inference(avatar_split_clause,[],[f832,f718,f219,f13451]) ).
fof(f13451,plain,
( spl11_484
<=> ! [X0,X3,X2,X1] :
( subset(intersection(X0,difference(X1,X2)),X3)
| member(sK5(intersection(X0,difference(X1,X2)),X3),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_484])]) ).
fof(f832,plain,
( ! [X2,X3,X0,X1] :
( subset(intersection(X0,difference(X1,X2)),X3)
| member(sK5(intersection(X0,difference(X1,X2)),X3),X1) )
| ~ spl11_16
| ~ spl11_86 ),
inference(resolution,[],[f719,f220]) ).
fof(f13449,plain,
( spl11_483
| ~ spl11_17
| ~ spl11_86 ),
inference(avatar_split_clause,[],[f831,f718,f223,f13447]) ).
fof(f13447,plain,
( spl11_483
<=> ! [X0,X3,X2,X1] :
( subset(intersection(X0,difference(X1,X2)),X3)
| ~ member(sK5(intersection(X0,difference(X1,X2)),X3),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_483])]) ).
fof(f831,plain,
( ! [X2,X3,X0,X1] :
( subset(intersection(X0,difference(X1,X2)),X3)
| ~ member(sK5(intersection(X0,difference(X1,X2)),X3),X2) )
| ~ spl11_17
| ~ spl11_86 ),
inference(resolution,[],[f719,f224]) ).
fof(f13445,plain,
( spl11_482
| ~ spl11_18
| ~ spl11_86 ),
inference(avatar_split_clause,[],[f828,f718,f227,f13443]) ).
fof(f13443,plain,
( spl11_482
<=> ! [X0,X3,X2,X1] :
( subset(intersection(X0,intersection(X1,X2)),X3)
| member(sK5(intersection(X0,intersection(X1,X2)),X3),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_482])]) ).
fof(f828,plain,
( ! [X2,X3,X0,X1] :
( subset(intersection(X0,intersection(X1,X2)),X3)
| member(sK5(intersection(X0,intersection(X1,X2)),X3),X1) )
| ~ spl11_18
| ~ spl11_86 ),
inference(resolution,[],[f719,f228]) ).
fof(f13441,plain,
( spl11_481
| ~ spl11_19
| ~ spl11_86 ),
inference(avatar_split_clause,[],[f827,f718,f231,f13439]) ).
fof(f13439,plain,
( spl11_481
<=> ! [X0,X3,X2,X1] :
( subset(intersection(X0,intersection(X1,X2)),X3)
| member(sK5(intersection(X0,intersection(X1,X2)),X3),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_481])]) ).
fof(f827,plain,
( ! [X2,X3,X0,X1] :
( subset(intersection(X0,intersection(X1,X2)),X3)
| member(sK5(intersection(X0,intersection(X1,X2)),X3),X2) )
| ~ spl11_19
| ~ spl11_86 ),
inference(resolution,[],[f719,f232]) ).
fof(f13437,plain,
( spl11_480
| ~ spl11_91
| ~ spl11_229 ),
inference(avatar_split_clause,[],[f3746,f3595,f738,f13435]) ).
fof(f13435,plain,
( spl11_480
<=> ! [X0] :
( ~ subset(power_set(X0),empty_set)
| ~ subset(sK3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_480])]) ).
fof(f738,plain,
( spl11_91
<=> ! [X0] :
( member(sK4,sum(power_set(X0)))
| ~ subset(sK3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_91])]) ).
fof(f3595,plain,
( spl11_229
<=> ! [X0,X1] :
( ~ member(X0,sum(X1))
| ~ subset(X1,empty_set) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_229])]) ).
fof(f3746,plain,
( ! [X0] :
( ~ subset(power_set(X0),empty_set)
| ~ subset(sK3,X0) )
| ~ spl11_91
| ~ spl11_229 ),
inference(resolution,[],[f3596,f739]) ).
fof(f739,plain,
( ! [X0] :
( member(sK4,sum(power_set(X0)))
| ~ subset(sK3,X0) )
| ~ spl11_91 ),
inference(avatar_component_clause,[],[f738]) ).
fof(f3596,plain,
( ! [X0,X1] :
( ~ member(X0,sum(X1))
| ~ subset(X1,empty_set) )
| ~ spl11_229 ),
inference(avatar_component_clause,[],[f3595]) ).
fof(f13433,plain,
( spl11_479
| ~ spl11_33
| ~ spl11_86 ),
inference(avatar_split_clause,[],[f824,f718,f324,f13431]) ).
fof(f13431,plain,
( spl11_479
<=> ! [X0,X3,X2,X1] :
( subset(intersection(X0,X1),X2)
| ~ member(X3,sK5(intersection(X0,X1),X2))
| member(X3,sum(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_479])]) ).
fof(f824,plain,
( ! [X2,X3,X0,X1] :
( subset(intersection(X0,X1),X2)
| ~ member(X3,sK5(intersection(X0,X1),X2))
| member(X3,sum(X1)) )
| ~ spl11_33
| ~ spl11_86 ),
inference(resolution,[],[f719,f325]) ).
fof(f13429,plain,
( spl11_478
| ~ spl11_16
| ~ spl11_85 ),
inference(avatar_split_clause,[],[f812,f714,f219,f13427]) ).
fof(f13427,plain,
( spl11_478
<=> ! [X0,X3,X2,X1] :
( subset(intersection(difference(X0,X1),X2),X3)
| member(sK5(intersection(difference(X0,X1),X2),X3),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_478])]) ).
fof(f812,plain,
( ! [X2,X3,X0,X1] :
( subset(intersection(difference(X0,X1),X2),X3)
| member(sK5(intersection(difference(X0,X1),X2),X3),X0) )
| ~ spl11_16
| ~ spl11_85 ),
inference(resolution,[],[f715,f220]) ).
fof(f13425,plain,
( spl11_477
| ~ spl11_17
| ~ spl11_85 ),
inference(avatar_split_clause,[],[f811,f714,f223,f13423]) ).
fof(f13423,plain,
( spl11_477
<=> ! [X0,X3,X2,X1] :
( subset(intersection(difference(X0,X1),X2),X3)
| ~ member(sK5(intersection(difference(X0,X1),X2),X3),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_477])]) ).
fof(f811,plain,
( ! [X2,X3,X0,X1] :
( subset(intersection(difference(X0,X1),X2),X3)
| ~ member(sK5(intersection(difference(X0,X1),X2),X3),X1) )
| ~ spl11_17
| ~ spl11_85 ),
inference(resolution,[],[f715,f224]) ).
fof(f13421,plain,
( spl11_476
| ~ spl11_18
| ~ spl11_85 ),
inference(avatar_split_clause,[],[f808,f714,f227,f13419]) ).
fof(f13419,plain,
( spl11_476
<=> ! [X0,X3,X2,X1] :
( subset(intersection(intersection(X0,X1),X2),X3)
| member(sK5(intersection(intersection(X0,X1),X2),X3),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_476])]) ).
fof(f808,plain,
( ! [X2,X3,X0,X1] :
( subset(intersection(intersection(X0,X1),X2),X3)
| member(sK5(intersection(intersection(X0,X1),X2),X3),X0) )
| ~ spl11_18
| ~ spl11_85 ),
inference(resolution,[],[f715,f228]) ).
fof(f13417,plain,
( spl11_475
| ~ spl11_19
| ~ spl11_85 ),
inference(avatar_split_clause,[],[f807,f714,f231,f13415]) ).
fof(f13415,plain,
( spl11_475
<=> ! [X0,X3,X2,X1] :
( subset(intersection(intersection(X0,X1),X2),X3)
| member(sK5(intersection(intersection(X0,X1),X2),X3),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_475])]) ).
fof(f807,plain,
( ! [X2,X3,X0,X1] :
( subset(intersection(intersection(X0,X1),X2),X3)
| member(sK5(intersection(intersection(X0,X1),X2),X3),X1) )
| ~ spl11_19
| ~ spl11_85 ),
inference(resolution,[],[f715,f232]) ).
fof(f13413,plain,
( spl11_474
| ~ spl11_33
| ~ spl11_85 ),
inference(avatar_split_clause,[],[f804,f714,f324,f13411]) ).
fof(f13411,plain,
( spl11_474
<=> ! [X0,X3,X2,X1] :
( subset(intersection(X0,X1),X2)
| ~ member(X3,sK5(intersection(X0,X1),X2))
| member(X3,sum(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_474])]) ).
fof(f804,plain,
( ! [X2,X3,X0,X1] :
( subset(intersection(X0,X1),X2)
| ~ member(X3,sK5(intersection(X0,X1),X2))
| member(X3,sum(X0)) )
| ~ spl11_33
| ~ spl11_85 ),
inference(resolution,[],[f715,f325]) ).
fof(f13409,plain,
( spl11_473
| ~ spl11_66
| ~ spl11_84 ),
inference(avatar_split_clause,[],[f793,f710,f565,f13407]) ).
fof(f13407,plain,
( spl11_473
<=> ! [X2,X0,X1] :
( subset(difference(X0,sum(singleton(X1))),X2)
| ~ member(sK5(difference(X0,sum(singleton(X1))),X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_473])]) ).
fof(f710,plain,
( spl11_84
<=> ! [X2,X0,X1] :
( ~ member(sK5(difference(X0,X1),X2),X1)
| subset(difference(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_84])]) ).
fof(f793,plain,
( ! [X2,X0,X1] :
( subset(difference(X0,sum(singleton(X1))),X2)
| ~ member(sK5(difference(X0,sum(singleton(X1))),X2),X1) )
| ~ spl11_66
| ~ spl11_84 ),
inference(resolution,[],[f711,f566]) ).
fof(f711,plain,
( ! [X2,X0,X1] :
( ~ member(sK5(difference(X0,X1),X2),X1)
| subset(difference(X0,X1),X2) )
| ~ spl11_84 ),
inference(avatar_component_clause,[],[f710]) ).
fof(f13405,plain,
( spl11_472
| ~ spl11_20
| ~ spl11_84 ),
inference(avatar_split_clause,[],[f791,f710,f235,f13403]) ).
fof(f13403,plain,
( spl11_472
<=> ! [X0,X3,X2,X1] :
( subset(difference(X0,union(X1,X2)),X3)
| ~ member(sK5(difference(X0,union(X1,X2)),X3),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_472])]) ).
fof(f791,plain,
( ! [X2,X3,X0,X1] :
( subset(difference(X0,union(X1,X2)),X3)
| ~ member(sK5(difference(X0,union(X1,X2)),X3),X1) )
| ~ spl11_20
| ~ spl11_84 ),
inference(resolution,[],[f711,f236]) ).
fof(f13401,plain,
( spl11_471
| ~ spl11_21
| ~ spl11_84 ),
inference(avatar_split_clause,[],[f790,f710,f239,f13399]) ).
fof(f13399,plain,
( spl11_471
<=> ! [X0,X3,X2,X1] :
( subset(difference(X0,union(X1,X2)),X3)
| ~ member(sK5(difference(X0,union(X1,X2)),X3),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_471])]) ).
fof(f790,plain,
( ! [X2,X3,X0,X1] :
( subset(difference(X0,union(X1,X2)),X3)
| ~ member(sK5(difference(X0,union(X1,X2)),X3),X2) )
| ~ spl11_21
| ~ spl11_84 ),
inference(resolution,[],[f711,f240]) ).
fof(f13397,plain,
( spl11_470
| ~ spl11_16
| ~ spl11_83 ),
inference(avatar_split_clause,[],[f779,f706,f219,f13395]) ).
fof(f13395,plain,
( spl11_470
<=> ! [X0,X3,X2,X1] :
( subset(difference(difference(X0,X1),X2),X3)
| member(sK5(difference(difference(X0,X1),X2),X3),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_470])]) ).
fof(f779,plain,
( ! [X2,X3,X0,X1] :
( subset(difference(difference(X0,X1),X2),X3)
| member(sK5(difference(difference(X0,X1),X2),X3),X0) )
| ~ spl11_16
| ~ spl11_83 ),
inference(resolution,[],[f707,f220]) ).
fof(f13393,plain,
( spl11_469
| ~ spl11_121
| ~ spl11_174 ),
inference(avatar_split_clause,[],[f2875,f2869,f1328,f13391]) ).
fof(f13391,plain,
( spl11_469
<=> ! [X0,X1] : upper_bound(X0,X1,difference(sK4,sum(sK3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_469])]) ).
fof(f2869,plain,
( spl11_174
<=> ! [X2,X0,X1] :
( upper_bound(X0,X1,difference(X2,sum(sK3)))
| ~ member(sK9(X1,difference(X2,sum(sK3)),X0),sK4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_174])]) ).
fof(f2875,plain,
( ! [X0,X1] : upper_bound(X0,X1,difference(sK4,sum(sK3)))
| ~ spl11_121
| ~ spl11_174 ),
inference(duplicate_literal_removal,[],[f2872]) ).
fof(f2872,plain,
( ! [X0,X1] :
( upper_bound(X0,X1,difference(sK4,sum(sK3)))
| upper_bound(X0,X1,difference(sK4,sum(sK3))) )
| ~ spl11_121
| ~ spl11_174 ),
inference(resolution,[],[f2870,f1329]) ).
fof(f2870,plain,
( ! [X2,X0,X1] :
( ~ member(sK9(X1,difference(X2,sum(sK3)),X0),sK4)
| upper_bound(X0,X1,difference(X2,sum(sK3))) )
| ~ spl11_174 ),
inference(avatar_component_clause,[],[f2869]) ).
fof(f13389,plain,
( spl11_468
| ~ spl11_17
| ~ spl11_83 ),
inference(avatar_split_clause,[],[f778,f706,f223,f13387]) ).
fof(f13387,plain,
( spl11_468
<=> ! [X0,X3,X2,X1] :
( subset(difference(difference(X0,X1),X2),X3)
| ~ member(sK5(difference(difference(X0,X1),X2),X3),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_468])]) ).
fof(f778,plain,
( ! [X2,X3,X0,X1] :
( subset(difference(difference(X0,X1),X2),X3)
| ~ member(sK5(difference(difference(X0,X1),X2),X3),X1) )
| ~ spl11_17
| ~ spl11_83 ),
inference(resolution,[],[f707,f224]) ).
fof(f13385,plain,
( spl11_467
| ~ spl11_18
| ~ spl11_83 ),
inference(avatar_split_clause,[],[f775,f706,f227,f13383]) ).
fof(f13383,plain,
( spl11_467
<=> ! [X0,X3,X2,X1] :
( subset(difference(intersection(X0,X1),X2),X3)
| member(sK5(difference(intersection(X0,X1),X2),X3),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_467])]) ).
fof(f775,plain,
( ! [X2,X3,X0,X1] :
( subset(difference(intersection(X0,X1),X2),X3)
| member(sK5(difference(intersection(X0,X1),X2),X3),X0) )
| ~ spl11_18
| ~ spl11_83 ),
inference(resolution,[],[f707,f228]) ).
fof(f13381,plain,
( spl11_466
| ~ spl11_19
| ~ spl11_83 ),
inference(avatar_split_clause,[],[f774,f706,f231,f13379]) ).
fof(f13379,plain,
( spl11_466
<=> ! [X0,X3,X2,X1] :
( subset(difference(intersection(X0,X1),X2),X3)
| member(sK5(difference(intersection(X0,X1),X2),X3),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_466])]) ).
fof(f774,plain,
( ! [X2,X3,X0,X1] :
( subset(difference(intersection(X0,X1),X2),X3)
| member(sK5(difference(intersection(X0,X1),X2),X3),X1) )
| ~ spl11_19
| ~ spl11_83 ),
inference(resolution,[],[f707,f232]) ).
fof(f13377,plain,
( spl11_465
| ~ spl11_33
| ~ spl11_83 ),
inference(avatar_split_clause,[],[f771,f706,f324,f13375]) ).
fof(f13375,plain,
( spl11_465
<=> ! [X0,X3,X2,X1] :
( subset(difference(X0,X1),X2)
| ~ member(X3,sK5(difference(X0,X1),X2))
| member(X3,sum(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_465])]) ).
fof(f771,plain,
( ! [X2,X3,X0,X1] :
( subset(difference(X0,X1),X2)
| ~ member(X3,sK5(difference(X0,X1),X2))
| member(X3,sum(X0)) )
| ~ spl11_33
| ~ spl11_83 ),
inference(resolution,[],[f707,f325]) ).
fof(f13373,plain,
( spl11_464
| ~ spl11_75
| ~ spl11_81 ),
inference(avatar_split_clause,[],[f699,f643,f619,f13371]) ).
fof(f13371,plain,
( spl11_464
<=> ! [X0,X3,X2,X1] :
( member(sK5(X0,X1),sum(power_set(X2)))
| ~ subset(X3,X2)
| ~ subset(X0,X3)
| subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_464])]) ).
fof(f699,plain,
( ! [X2,X3,X0,X1] :
( member(sK5(X0,X1),sum(power_set(X2)))
| ~ subset(X3,X2)
| ~ subset(X0,X3)
| subset(X0,X1) )
| ~ spl11_75
| ~ spl11_81 ),
inference(resolution,[],[f644,f620]) ).
fof(f13369,plain,
( spl11_463
| ~ spl11_78
| ~ spl11_81 ),
inference(avatar_split_clause,[],[f694,f643,f631,f13367]) ).
fof(f13367,plain,
( spl11_463
<=> ! [X2,X0,X1] :
( member(X0,sum(power_set(X1)))
| ~ subset(product(singleton(X2)),X1)
| sK6(X0,singleton(X2)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_463])]) ).
fof(f694,plain,
( ! [X2,X0,X1] :
( member(X0,sum(power_set(X1)))
| ~ subset(product(singleton(X2)),X1)
| sK6(X0,singleton(X2)) = X2 )
| ~ spl11_78
| ~ spl11_81 ),
inference(resolution,[],[f644,f632]) ).
fof(f13365,plain,
( spl11_462
| ~ spl11_40
| ~ spl11_81 ),
inference(avatar_split_clause,[],[f684,f643,f378,f13363]) ).
fof(f13363,plain,
( spl11_462
<=> ! [X0,X3,X2,X1] :
( member(X0,sum(power_set(X1)))
| ~ subset(difference(X2,X3),X1)
| member(X0,X3)
| ~ member(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_462])]) ).
fof(f684,plain,
( ! [X2,X3,X0,X1] :
( member(X0,sum(power_set(X1)))
| ~ subset(difference(X2,X3),X1)
| member(X0,X3)
| ~ member(X0,X2) )
| ~ spl11_40
| ~ spl11_81 ),
inference(resolution,[],[f644,f379]) ).
fof(f13361,plain,
( spl11_461
| ~ spl11_41
| ~ spl11_81 ),
inference(avatar_split_clause,[],[f681,f643,f382,f13359]) ).
fof(f13359,plain,
( spl11_461
<=> ! [X0,X3,X2,X1] :
( member(X0,sum(power_set(X1)))
| ~ subset(intersection(X2,X3),X1)
| ~ member(X0,X3)
| ~ member(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_461])]) ).
fof(f681,plain,
( ! [X2,X3,X0,X1] :
( member(X0,sum(power_set(X1)))
| ~ subset(intersection(X2,X3),X1)
| ~ member(X0,X3)
| ~ member(X0,X2) )
| ~ spl11_41
| ~ spl11_81 ),
inference(resolution,[],[f644,f383]) ).
fof(f13357,plain,
( spl11_460
| ~ spl11_27
| ~ spl11_80 ),
inference(avatar_split_clause,[],[f676,f639,f275,f13355]) ).
fof(f13355,plain,
( spl11_460
<=> ! [X0,X1] :
( sK7(sK7(X0,sum(singleton(X1))),singleton(X1)) = X1
| ~ member(X0,sum(sum(singleton(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_460])]) ).
fof(f676,plain,
( ! [X0,X1] :
( sK7(sK7(X0,sum(singleton(X1))),singleton(X1)) = X1
| ~ member(X0,sum(sum(singleton(X1)))) )
| ~ spl11_27
| ~ spl11_80 ),
inference(resolution,[],[f640,f276]) ).
fof(f13353,plain,
( spl11_459
| ~ spl11_25
| ~ spl11_80 ),
inference(avatar_split_clause,[],[f675,f639,f267,f13351]) ).
fof(f13351,plain,
( spl11_459
<=> ! [X0,X1] :
( sK7(sK6(X0,sum(singleton(X1))),singleton(X1)) = X1
| member(X0,product(sum(singleton(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_459])]) ).
fof(f675,plain,
( ! [X0,X1] :
( sK7(sK6(X0,sum(singleton(X1))),singleton(X1)) = X1
| member(X0,product(sum(singleton(X1)))) )
| ~ spl11_25
| ~ spl11_80 ),
inference(resolution,[],[f640,f268]) ).
fof(f13349,plain,
( spl11_458
| ~ spl11_107
| ~ spl11_173 ),
inference(avatar_split_clause,[],[f2867,f2857,f1030,f13347]) ).
fof(f13347,plain,
( spl11_458
<=> ! [X0] : ~ member(X0,sum(difference(sK4,sum(sK3)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_458])]) ).
fof(f2857,plain,
( spl11_173
<=> ! [X0,X1] :
( ~ member(X0,sum(difference(X1,sum(sK3))))
| ~ member(sK7(X0,difference(X1,sum(sK3))),sK4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_173])]) ).
fof(f2867,plain,
( ! [X0] : ~ member(X0,sum(difference(sK4,sum(sK3))))
| ~ spl11_107
| ~ spl11_173 ),
inference(duplicate_literal_removal,[],[f2864]) ).
fof(f2864,plain,
( ! [X0] :
( ~ member(X0,sum(difference(sK4,sum(sK3))))
| ~ member(X0,sum(difference(sK4,sum(sK3)))) )
| ~ spl11_107
| ~ spl11_173 ),
inference(resolution,[],[f2858,f1031]) ).
fof(f2858,plain,
( ! [X0,X1] :
( ~ member(sK7(X0,difference(X1,sum(sK3))),sK4)
| ~ member(X0,sum(difference(X1,sum(sK3)))) )
| ~ spl11_173 ),
inference(avatar_component_clause,[],[f2857]) ).
fof(f13345,plain,
( spl11_457
| ~ spl11_75
| ~ spl11_80 ),
inference(avatar_split_clause,[],[f674,f639,f619,f13343]) ).
fof(f13343,plain,
( spl11_457
<=> ! [X2,X0,X1] :
( sK7(sK5(X0,X1),singleton(X2)) = X2
| ~ subset(X0,sum(singleton(X2)))
| subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_457])]) ).
fof(f674,plain,
( ! [X2,X0,X1] :
( sK7(sK5(X0,X1),singleton(X2)) = X2
| ~ subset(X0,sum(singleton(X2)))
| subset(X0,X1) )
| ~ spl11_75
| ~ spl11_80 ),
inference(resolution,[],[f640,f620]) ).
fof(f13341,plain,
( spl11_456
| ~ spl11_26
| ~ spl11_75 ),
inference(avatar_split_clause,[],[f662,f619,f271,f13339]) ).
fof(f13339,plain,
( spl11_456
<=> ! [X2,X0,X1] :
( ~ subset(X0,sK6(sK5(X0,X1),X2))
| subset(X0,X1)
| member(sK5(X0,X1),product(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_456])]) ).
fof(f662,plain,
( ! [X2,X0,X1] :
( ~ subset(X0,sK6(sK5(X0,X1),X2))
| subset(X0,X1)
| member(sK5(X0,X1),product(X2)) )
| ~ spl11_26
| ~ spl11_75 ),
inference(resolution,[],[f620,f272]) ).
fof(f12764,plain,
( spl11_455
| ~ spl11_103
| ~ spl11_172 ),
inference(avatar_split_clause,[],[f2863,f2853,f1014,f12762]) ).
fof(f12762,plain,
( spl11_455
<=> ! [X0] : member(X0,product(difference(sK4,sum(sK3)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_455])]) ).
fof(f2853,plain,
( spl11_172
<=> ! [X0,X1] :
( member(X0,product(difference(X1,sum(sK3))))
| ~ member(sK6(X0,difference(X1,sum(sK3))),sK4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_172])]) ).
fof(f2863,plain,
( ! [X0] : member(X0,product(difference(sK4,sum(sK3))))
| ~ spl11_103
| ~ spl11_172 ),
inference(duplicate_literal_removal,[],[f2860]) ).
fof(f2860,plain,
( ! [X0] :
( member(X0,product(difference(sK4,sum(sK3))))
| member(X0,product(difference(sK4,sum(sK3)))) )
| ~ spl11_103
| ~ spl11_172 ),
inference(resolution,[],[f2854,f1015]) ).
fof(f2854,plain,
( ! [X0,X1] :
( ~ member(sK6(X0,difference(X1,sum(sK3))),sK4)
| member(X0,product(difference(X1,sum(sK3)))) )
| ~ spl11_172 ),
inference(avatar_component_clause,[],[f2853]) ).
fof(f12245,plain,
( spl11_454
| ~ spl11_112
| ~ spl11_155 ),
inference(avatar_split_clause,[],[f2568,f2319,f1055,f12243]) ).
fof(f12243,plain,
( spl11_454
<=> ! [X0] :
( upper_bound(sK4,sK1,X0)
| ~ subset(X0,sK3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_454])]) ).
fof(f2568,plain,
( ! [X0] :
( upper_bound(sK4,sK1,X0)
| ~ subset(X0,sK3) )
| ~ spl11_112
| ~ spl11_155 ),
inference(duplicate_literal_removal,[],[f2555]) ).
fof(f2555,plain,
( ! [X0] :
( upper_bound(sK4,sK1,X0)
| upper_bound(sK4,sK1,X0)
| ~ subset(X0,sK3) )
| ~ spl11_112
| ~ spl11_155 ),
inference(resolution,[],[f2320,f1056]) ).
fof(f11885,plain,
( spl11_453
| ~ spl11_75
| ~ spl11_82 ),
inference(avatar_split_clause,[],[f2552,f669,f619,f11883]) ).
fof(f11883,plain,
( spl11_453
<=> ! [X0] :
( subset(X0,sum(sK3))
| ~ subset(X0,sK4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_453])]) ).
fof(f2552,plain,
( ! [X0] :
( subset(X0,sum(sK3))
| ~ subset(X0,sK4) )
| ~ spl11_75
| ~ spl11_82 ),
inference(duplicate_literal_removal,[],[f2539]) ).
fof(f2539,plain,
( ! [X0] :
( subset(X0,sum(sK3))
| ~ subset(X0,sK4)
| subset(X0,sum(sK3)) )
| ~ spl11_75
| ~ spl11_82 ),
inference(resolution,[],[f670,f620]) ).
fof(f10385,plain,
( spl11_294
| ~ spl11_452
| ~ spl11_65
| ~ spl11_229 ),
inference(avatar_split_clause,[],[f3742,f3595,f561,f10382,f5309]) ).
fof(f10382,plain,
( spl11_452
<=> subset(sK2,empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_452])]) ).
fof(f561,plain,
( spl11_65
<=> ! [X0] :
( ~ member(X0,sK4)
| member(X0,sum(sK2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_65])]) ).
fof(f3742,plain,
( ! [X0] :
( ~ subset(sK2,empty_set)
| ~ member(X0,sK4) )
| ~ spl11_65
| ~ spl11_229 ),
inference(resolution,[],[f3596,f562]) ).
fof(f562,plain,
( ! [X0] :
( member(X0,sum(sK2))
| ~ member(X0,sK4) )
| ~ spl11_65 ),
inference(avatar_component_clause,[],[f561]) ).
fof(f10081,plain,
( spl11_451
| ~ spl11_60
| ~ spl11_145 ),
inference(avatar_split_clause,[],[f2173,f2025,f529,f10079]) ).
fof(f10079,plain,
( spl11_451
<=> ! [X0,X1] :
( member(sK7(X0,union(sum(empty_set),X1)),X1)
| ~ member(X0,sum(union(sum(empty_set),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_451])]) ).
fof(f2025,plain,
( spl11_145
<=> ! [X2,X0,X1] :
( member(sK7(X0,union(X1,X2)),X1)
| member(sK7(X0,union(X1,X2)),X2)
| ~ member(X0,sum(union(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_145])]) ).
fof(f2173,plain,
( ! [X0,X1] :
( member(sK7(X0,union(sum(empty_set),X1)),X1)
| ~ member(X0,sum(union(sum(empty_set),X1))) )
| ~ spl11_60
| ~ spl11_145 ),
inference(resolution,[],[f2026,f530]) ).
fof(f2026,plain,
( ! [X2,X0,X1] :
( member(sK7(X0,union(X1,X2)),X2)
| member(sK7(X0,union(X1,X2)),X1)
| ~ member(X0,sum(union(X1,X2))) )
| ~ spl11_145 ),
inference(avatar_component_clause,[],[f2025]) ).
fof(f10077,plain,
( spl11_450
| ~ spl11_60
| ~ spl11_145 ),
inference(avatar_split_clause,[],[f2148,f2025,f529,f10075]) ).
fof(f10075,plain,
( spl11_450
<=> ! [X0,X1] :
( member(sK7(X0,union(X1,sum(empty_set))),X1)
| ~ member(X0,sum(union(X1,sum(empty_set)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_450])]) ).
fof(f2148,plain,
( ! [X0,X1] :
( member(sK7(X0,union(X1,sum(empty_set))),X1)
| ~ member(X0,sum(union(X1,sum(empty_set)))) )
| ~ spl11_60
| ~ spl11_145 ),
inference(resolution,[],[f2026,f530]) ).
fof(f10073,plain,
( spl11_449
| ~ spl11_60
| ~ spl11_144 ),
inference(avatar_split_clause,[],[f2122,f2021,f529,f10071]) ).
fof(f10071,plain,
( spl11_449
<=> ! [X0,X1] :
( member(sK6(X0,union(sum(empty_set),X1)),X1)
| member(X0,product(union(sum(empty_set),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_449])]) ).
fof(f2021,plain,
( spl11_144
<=> ! [X2,X0,X1] :
( member(sK6(X0,union(X1,X2)),X1)
| member(sK6(X0,union(X1,X2)),X2)
| member(X0,product(union(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_144])]) ).
fof(f2122,plain,
( ! [X0,X1] :
( member(sK6(X0,union(sum(empty_set),X1)),X1)
| member(X0,product(union(sum(empty_set),X1))) )
| ~ spl11_60
| ~ spl11_144 ),
inference(resolution,[],[f2022,f530]) ).
fof(f2022,plain,
( ! [X2,X0,X1] :
( member(sK6(X0,union(X1,X2)),X2)
| member(sK6(X0,union(X1,X2)),X1)
| member(X0,product(union(X1,X2))) )
| ~ spl11_144 ),
inference(avatar_component_clause,[],[f2021]) ).
fof(f10069,plain,
( spl11_448
| ~ spl11_60
| ~ spl11_144 ),
inference(avatar_split_clause,[],[f2097,f2021,f529,f10067]) ).
fof(f10067,plain,
( spl11_448
<=> ! [X0,X1] :
( member(sK6(X0,union(X1,sum(empty_set))),X1)
| member(X0,product(union(X1,sum(empty_set)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_448])]) ).
fof(f2097,plain,
( ! [X0,X1] :
( member(sK6(X0,union(X1,sum(empty_set))),X1)
| member(X0,product(union(X1,sum(empty_set)))) )
| ~ spl11_60
| ~ spl11_144 ),
inference(resolution,[],[f2022,f530]) ).
fof(f10064,plain,
( spl11_447
| ~ spl11_75
| ~ spl11_133 ),
inference(avatar_split_clause,[],[f1806,f1719,f619,f10062]) ).
fof(f10062,plain,
( spl11_447
<=> ! [X2,X0,X1] :
( ~ member(sK5(X0,intersection(X1,X2)),X1)
| subset(X0,intersection(X1,X2))
| ~ subset(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_447])]) ).
fof(f1806,plain,
( ! [X2,X0,X1] :
( ~ member(sK5(X0,intersection(X1,X2)),X1)
| subset(X0,intersection(X1,X2))
| ~ subset(X0,X2) )
| ~ spl11_75
| ~ spl11_133 ),
inference(duplicate_literal_removal,[],[f1782]) ).
fof(f1782,plain,
( ! [X2,X0,X1] :
( ~ member(sK5(X0,intersection(X1,X2)),X1)
| subset(X0,intersection(X1,X2))
| ~ subset(X0,X2)
| subset(X0,intersection(X1,X2)) )
| ~ spl11_75
| ~ spl11_133 ),
inference(resolution,[],[f1720,f620]) ).
fof(f10060,plain,
( spl11_446
| ~ spl11_75
| ~ spl11_132 ),
inference(avatar_split_clause,[],[f1775,f1715,f619,f10058]) ).
fof(f10058,plain,
( spl11_446
<=> ! [X2,X0,X1] :
( member(sK5(X0,difference(X1,X2)),X2)
| subset(X0,difference(X1,X2))
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_446])]) ).
fof(f1775,plain,
( ! [X2,X0,X1] :
( member(sK5(X0,difference(X1,X2)),X2)
| subset(X0,difference(X1,X2))
| ~ subset(X0,X1) )
| ~ spl11_75
| ~ spl11_132 ),
inference(duplicate_literal_removal,[],[f1751]) ).
fof(f1751,plain,
( ! [X2,X0,X1] :
( member(sK5(X0,difference(X1,X2)),X2)
| subset(X0,difference(X1,X2))
| ~ subset(X0,X1)
| subset(X0,difference(X1,X2)) )
| ~ spl11_75
| ~ spl11_132 ),
inference(resolution,[],[f1716,f620]) ).
fof(f10056,plain,
( spl11_445
| ~ spl11_10
| ~ spl11_115 ),
inference(avatar_split_clause,[],[f1372,f1304,f192,f10054]) ).
fof(f10054,plain,
( spl11_445
<=> ! [X2,X0,X1] :
( ~ member(singleton(X0),X1)
| ~ member(X2,sum(product(X1)))
| sK7(X2,product(X1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_445])]) ).
fof(f1372,plain,
( ! [X2,X0,X1] :
( ~ member(singleton(X0),X1)
| ~ member(X2,sum(product(X1)))
| sK7(X2,product(X1)) = X0 )
| ~ spl11_10
| ~ spl11_115 ),
inference(resolution,[],[f1305,f193]) ).
fof(f10052,plain,
( spl11_444
| ~ spl11_11
| ~ spl11_115 ),
inference(avatar_split_clause,[],[f1365,f1304,f196,f10050]) ).
fof(f10050,plain,
( spl11_444
<=> ! [X2,X0,X1] :
( ~ member(power_set(X0),X1)
| ~ member(X2,sum(product(X1)))
| subset(sK7(X2,product(X1)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_444])]) ).
fof(f1365,plain,
( ! [X2,X0,X1] :
( ~ member(power_set(X0),X1)
| ~ member(X2,sum(product(X1)))
| subset(sK7(X2,product(X1)),X0) )
| ~ spl11_11
| ~ spl11_115 ),
inference(resolution,[],[f1305,f197]) ).
fof(f10048,plain,
( spl11_443
| ~ spl11_10
| ~ spl11_114 ),
inference(avatar_split_clause,[],[f1351,f1300,f192,f10046]) ).
fof(f10046,plain,
( spl11_443
<=> ! [X2,X0,X1] :
( ~ member(singleton(X0),X1)
| member(X2,product(product(X1)))
| sK6(X2,product(X1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_443])]) ).
fof(f1351,plain,
( ! [X2,X0,X1] :
( ~ member(singleton(X0),X1)
| member(X2,product(product(X1)))
| sK6(X2,product(X1)) = X0 )
| ~ spl11_10
| ~ spl11_114 ),
inference(resolution,[],[f1301,f193]) ).
fof(f10044,plain,
( spl11_442
| ~ spl11_11
| ~ spl11_114 ),
inference(avatar_split_clause,[],[f1344,f1300,f196,f10042]) ).
fof(f10042,plain,
( spl11_442
<=> ! [X2,X0,X1] :
( ~ member(power_set(X0),X1)
| member(X2,product(product(X1)))
| subset(sK6(X2,product(X1)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_442])]) ).
fof(f1344,plain,
( ! [X2,X0,X1] :
( ~ member(power_set(X0),X1)
| member(X2,product(product(X1)))
| subset(sK6(X2,product(X1)),X0) )
| ~ spl11_11
| ~ spl11_114 ),
inference(resolution,[],[f1301,f197]) ).
fof(f10040,plain,
( spl11_441
| ~ spl11_16
| ~ spl11_112 ),
inference(avatar_split_clause,[],[f1289,f1055,f219,f10038]) ).
fof(f10038,plain,
( spl11_441
<=> ! [X4,X0,X3,X2,X1] :
( upper_bound(X0,X1,X2)
| ~ subset(X2,difference(X3,X4))
| member(sK9(X1,X2,X0),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_441])]) ).
fof(f1289,plain,
( ! [X2,X3,X0,X1,X4] :
( upper_bound(X0,X1,X2)
| ~ subset(X2,difference(X3,X4))
| member(sK9(X1,X2,X0),X3) )
| ~ spl11_16
| ~ spl11_112 ),
inference(resolution,[],[f1056,f220]) ).
fof(f10036,plain,
( spl11_440
| ~ spl11_17
| ~ spl11_112 ),
inference(avatar_split_clause,[],[f1288,f1055,f223,f10034]) ).
fof(f10034,plain,
( spl11_440
<=> ! [X4,X0,X3,X2,X1] :
( upper_bound(X0,X1,X2)
| ~ subset(X2,difference(X3,X4))
| ~ member(sK9(X1,X2,X0),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_440])]) ).
fof(f1288,plain,
( ! [X2,X3,X0,X1,X4] :
( upper_bound(X0,X1,X2)
| ~ subset(X2,difference(X3,X4))
| ~ member(sK9(X1,X2,X0),X4) )
| ~ spl11_17
| ~ spl11_112 ),
inference(resolution,[],[f1056,f224]) ).
fof(f10032,plain,
( spl11_439
| ~ spl11_18
| ~ spl11_112 ),
inference(avatar_split_clause,[],[f1285,f1055,f227,f10030]) ).
fof(f10030,plain,
( spl11_439
<=> ! [X4,X0,X3,X2,X1] :
( upper_bound(X0,X1,X2)
| ~ subset(X2,intersection(X3,X4))
| member(sK9(X1,X2,X0),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_439])]) ).
fof(f1285,plain,
( ! [X2,X3,X0,X1,X4] :
( upper_bound(X0,X1,X2)
| ~ subset(X2,intersection(X3,X4))
| member(sK9(X1,X2,X0),X3) )
| ~ spl11_18
| ~ spl11_112 ),
inference(resolution,[],[f1056,f228]) ).
fof(f10028,plain,
( spl11_438
| ~ spl11_19
| ~ spl11_112 ),
inference(avatar_split_clause,[],[f1284,f1055,f231,f10026]) ).
fof(f10026,plain,
( spl11_438
<=> ! [X4,X0,X3,X2,X1] :
( upper_bound(X0,X1,X2)
| ~ subset(X2,intersection(X3,X4))
| member(sK9(X1,X2,X0),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_438])]) ).
fof(f1284,plain,
( ! [X2,X3,X0,X1,X4] :
( upper_bound(X0,X1,X2)
| ~ subset(X2,intersection(X3,X4))
| member(sK9(X1,X2,X0),X4) )
| ~ spl11_19
| ~ spl11_112 ),
inference(resolution,[],[f1056,f232]) ).
fof(f10023,plain,
( spl11_437
| ~ spl11_16
| ~ spl11_108 ),
inference(avatar_split_clause,[],[f1216,f1039,f219,f10021]) ).
fof(f10021,plain,
( spl11_437
<=> ! [X0,X3,X2,X1] :
( ~ member(difference(X0,X1),X2)
| subset(product(X2),X3)
| member(sK5(product(X2),X3),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_437])]) ).
fof(f1216,plain,
( ! [X2,X3,X0,X1] :
( ~ member(difference(X0,X1),X2)
| subset(product(X2),X3)
| member(sK5(product(X2),X3),X0) )
| ~ spl11_16
| ~ spl11_108 ),
inference(resolution,[],[f1040,f220]) ).
fof(f10019,plain,
( spl11_436
| ~ spl11_17
| ~ spl11_108 ),
inference(avatar_split_clause,[],[f1215,f1039,f223,f10017]) ).
fof(f10017,plain,
( spl11_436
<=> ! [X0,X3,X2,X1] :
( ~ member(difference(X0,X1),X2)
| subset(product(X2),X3)
| ~ member(sK5(product(X2),X3),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_436])]) ).
fof(f1215,plain,
( ! [X2,X3,X0,X1] :
( ~ member(difference(X0,X1),X2)
| subset(product(X2),X3)
| ~ member(sK5(product(X2),X3),X1) )
| ~ spl11_17
| ~ spl11_108 ),
inference(resolution,[],[f1040,f224]) ).
fof(f10015,plain,
( spl11_435
| ~ spl11_18
| ~ spl11_108 ),
inference(avatar_split_clause,[],[f1212,f1039,f227,f10013]) ).
fof(f10013,plain,
( spl11_435
<=> ! [X0,X3,X2,X1] :
( ~ member(intersection(X0,X1),X2)
| subset(product(X2),X3)
| member(sK5(product(X2),X3),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_435])]) ).
fof(f1212,plain,
( ! [X2,X3,X0,X1] :
( ~ member(intersection(X0,X1),X2)
| subset(product(X2),X3)
| member(sK5(product(X2),X3),X0) )
| ~ spl11_18
| ~ spl11_108 ),
inference(resolution,[],[f1040,f228]) ).
fof(f10011,plain,
( spl11_434
| ~ spl11_19
| ~ spl11_108 ),
inference(avatar_split_clause,[],[f1211,f1039,f231,f10009]) ).
fof(f10009,plain,
( spl11_434
<=> ! [X0,X3,X2,X1] :
( ~ member(intersection(X0,X1),X2)
| subset(product(X2),X3)
| member(sK5(product(X2),X3),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_434])]) ).
fof(f1211,plain,
( ! [X2,X3,X0,X1] :
( ~ member(intersection(X0,X1),X2)
| subset(product(X2),X3)
| member(sK5(product(X2),X3),X1) )
| ~ spl11_19
| ~ spl11_108 ),
inference(resolution,[],[f1040,f232]) ).
fof(f10007,plain,
( spl11_433
| ~ spl11_10
| ~ spl11_107 ),
inference(avatar_split_clause,[],[f1195,f1030,f192,f10005]) ).
fof(f10005,plain,
( spl11_433
<=> ! [X2,X0,X1] :
( ~ member(X0,sum(difference(singleton(X1),X2)))
| sK7(X0,difference(singleton(X1),X2)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_433])]) ).
fof(f1195,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sum(difference(singleton(X1),X2)))
| sK7(X0,difference(singleton(X1),X2)) = X1 )
| ~ spl11_10
| ~ spl11_107 ),
inference(resolution,[],[f1031,f193]) ).
fof(f10003,plain,
( spl11_432
| ~ spl11_11
| ~ spl11_107 ),
inference(avatar_split_clause,[],[f1188,f1030,f196,f10001]) ).
fof(f10001,plain,
( spl11_432
<=> ! [X2,X0,X1] :
( ~ member(X0,sum(difference(power_set(X1),X2)))
| subset(sK7(X0,difference(power_set(X1),X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_432])]) ).
fof(f1188,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sum(difference(power_set(X1),X2)))
| subset(sK7(X0,difference(power_set(X1),X2)),X1) )
| ~ spl11_11
| ~ spl11_107 ),
inference(resolution,[],[f1031,f197]) ).
fof(f9999,plain,
( spl11_431
| ~ spl11_12
| ~ spl11_106 ),
inference(avatar_split_clause,[],[f1169,f1026,f200,f9997]) ).
fof(f9997,plain,
( spl11_431
<=> ! [X2,X0,X1] :
( ~ member(X0,sum(difference(X1,power_set(X2))))
| ~ subset(sK7(X0,difference(X1,power_set(X2))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_431])]) ).
fof(f1169,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sum(difference(X1,power_set(X2))))
| ~ subset(sK7(X0,difference(X1,power_set(X2))),X2) )
| ~ spl11_12
| ~ spl11_106 ),
inference(resolution,[],[f1027,f201]) ).
fof(f9995,plain,
( spl11_430
| ~ spl11_10
| ~ spl11_105 ),
inference(avatar_split_clause,[],[f1162,f1022,f192,f9993]) ).
fof(f9993,plain,
( spl11_430
<=> ! [X2,X0,X1] :
( ~ member(X0,sum(intersection(singleton(X1),X2)))
| sK7(X0,intersection(singleton(X1),X2)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_430])]) ).
fof(f1162,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sum(intersection(singleton(X1),X2)))
| sK7(X0,intersection(singleton(X1),X2)) = X1 )
| ~ spl11_10
| ~ spl11_105 ),
inference(resolution,[],[f1023,f193]) ).
fof(f9991,plain,
( spl11_429
| ~ spl11_11
| ~ spl11_105 ),
inference(avatar_split_clause,[],[f1155,f1022,f196,f9989]) ).
fof(f9989,plain,
( spl11_429
<=> ! [X2,X0,X1] :
( ~ member(X0,sum(intersection(power_set(X1),X2)))
| subset(sK7(X0,intersection(power_set(X1),X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_429])]) ).
fof(f1155,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sum(intersection(power_set(X1),X2)))
| subset(sK7(X0,intersection(power_set(X1),X2)),X1) )
| ~ spl11_11
| ~ spl11_105 ),
inference(resolution,[],[f1023,f197]) ).
fof(f9987,plain,
( spl11_428
| ~ spl11_10
| ~ spl11_104 ),
inference(avatar_split_clause,[],[f1140,f1018,f192,f9985]) ).
fof(f9985,plain,
( spl11_428
<=> ! [X2,X0,X1] :
( ~ member(X0,sum(intersection(X1,singleton(X2))))
| sK7(X0,intersection(X1,singleton(X2))) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_428])]) ).
fof(f1140,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sum(intersection(X1,singleton(X2))))
| sK7(X0,intersection(X1,singleton(X2))) = X2 )
| ~ spl11_10
| ~ spl11_104 ),
inference(resolution,[],[f1019,f193]) ).
fof(f9982,plain,
( spl11_427
| ~ spl11_11
| ~ spl11_104 ),
inference(avatar_split_clause,[],[f1133,f1018,f196,f9980]) ).
fof(f9980,plain,
( spl11_427
<=> ! [X2,X0,X1] :
( ~ member(X0,sum(intersection(X1,power_set(X2))))
| subset(sK7(X0,intersection(X1,power_set(X2))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_427])]) ).
fof(f1133,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sum(intersection(X1,power_set(X2))))
| subset(sK7(X0,intersection(X1,power_set(X2))),X2) )
| ~ spl11_11
| ~ spl11_104 ),
inference(resolution,[],[f1019,f197]) ).
fof(f9978,plain,
( spl11_426
| ~ spl11_10
| ~ spl11_103 ),
inference(avatar_split_clause,[],[f1121,f1014,f192,f9976]) ).
fof(f9976,plain,
( spl11_426
<=> ! [X2,X0,X1] :
( member(X0,product(difference(singleton(X1),X2)))
| sK6(X0,difference(singleton(X1),X2)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_426])]) ).
fof(f1121,plain,
( ! [X2,X0,X1] :
( member(X0,product(difference(singleton(X1),X2)))
| sK6(X0,difference(singleton(X1),X2)) = X1 )
| ~ spl11_10
| ~ spl11_103 ),
inference(resolution,[],[f1015,f193]) ).
fof(f9974,plain,
( spl11_425
| ~ spl11_11
| ~ spl11_103 ),
inference(avatar_split_clause,[],[f1114,f1014,f196,f9972]) ).
fof(f9972,plain,
( spl11_425
<=> ! [X2,X0,X1] :
( member(X0,product(difference(power_set(X1),X2)))
| subset(sK6(X0,difference(power_set(X1),X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_425])]) ).
fof(f1114,plain,
( ! [X2,X0,X1] :
( member(X0,product(difference(power_set(X1),X2)))
| subset(sK6(X0,difference(power_set(X1),X2)),X1) )
| ~ spl11_11
| ~ spl11_103 ),
inference(resolution,[],[f1015,f197]) ).
fof(f9970,plain,
( spl11_424
| ~ spl11_12
| ~ spl11_102 ),
inference(avatar_split_clause,[],[f1095,f1010,f200,f9968]) ).
fof(f9968,plain,
( spl11_424
<=> ! [X2,X0,X1] :
( member(X0,product(difference(X1,power_set(X2))))
| ~ subset(sK6(X0,difference(X1,power_set(X2))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_424])]) ).
fof(f1095,plain,
( ! [X2,X0,X1] :
( member(X0,product(difference(X1,power_set(X2))))
| ~ subset(sK6(X0,difference(X1,power_set(X2))),X2) )
| ~ spl11_12
| ~ spl11_102 ),
inference(resolution,[],[f1011,f201]) ).
fof(f9966,plain,
( spl11_423
| ~ spl11_10
| ~ spl11_101 ),
inference(avatar_split_clause,[],[f1088,f1006,f192,f9964]) ).
fof(f9964,plain,
( spl11_423
<=> ! [X2,X0,X1] :
( member(X0,product(intersection(singleton(X1),X2)))
| sK6(X0,intersection(singleton(X1),X2)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_423])]) ).
fof(f1088,plain,
( ! [X2,X0,X1] :
( member(X0,product(intersection(singleton(X1),X2)))
| sK6(X0,intersection(singleton(X1),X2)) = X1 )
| ~ spl11_10
| ~ spl11_101 ),
inference(resolution,[],[f1007,f193]) ).
fof(f9962,plain,
( spl11_422
| ~ spl11_11
| ~ spl11_101 ),
inference(avatar_split_clause,[],[f1081,f1006,f196,f9960]) ).
fof(f9960,plain,
( spl11_422
<=> ! [X2,X0,X1] :
( member(X0,product(intersection(power_set(X1),X2)))
| subset(sK6(X0,intersection(power_set(X1),X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_422])]) ).
fof(f1081,plain,
( ! [X2,X0,X1] :
( member(X0,product(intersection(power_set(X1),X2)))
| subset(sK6(X0,intersection(power_set(X1),X2)),X1) )
| ~ spl11_11
| ~ spl11_101 ),
inference(resolution,[],[f1007,f197]) ).
fof(f9958,plain,
( spl11_421
| ~ spl11_10
| ~ spl11_100 ),
inference(avatar_split_clause,[],[f1070,f1002,f192,f9956]) ).
fof(f9956,plain,
( spl11_421
<=> ! [X2,X0,X1] :
( member(X0,product(intersection(X1,singleton(X2))))
| sK6(X0,intersection(X1,singleton(X2))) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_421])]) ).
fof(f1070,plain,
( ! [X2,X0,X1] :
( member(X0,product(intersection(X1,singleton(X2))))
| sK6(X0,intersection(X1,singleton(X2))) = X2 )
| ~ spl11_10
| ~ spl11_100 ),
inference(resolution,[],[f1003,f193]) ).
fof(f9954,plain,
( spl11_420
| ~ spl11_11
| ~ spl11_100 ),
inference(avatar_split_clause,[],[f1063,f1002,f196,f9952]) ).
fof(f9952,plain,
( spl11_420
<=> ! [X2,X0,X1] :
( member(X0,product(intersection(X1,power_set(X2))))
| subset(sK6(X0,intersection(X1,power_set(X2))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_420])]) ).
fof(f1063,plain,
( ! [X2,X0,X1] :
( member(X0,product(intersection(X1,power_set(X2))))
| subset(sK6(X0,intersection(X1,power_set(X2))),X2) )
| ~ spl11_11
| ~ spl11_100 ),
inference(resolution,[],[f1003,f197]) ).
fof(f9950,plain,
( spl11_419
| ~ spl11_38
| ~ spl11_97 ),
inference(avatar_split_clause,[],[f996,f762,f370,f9948]) ).
fof(f9948,plain,
( spl11_419
<=> ! [X0,X3,X2,X1] :
( sK9(X0,singleton(X1),X2) = X1
| ~ member(X3,singleton(X1))
| apply(X0,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_419])]) ).
fof(f762,plain,
( spl11_97
<=> ! [X2,X0,X1] :
( upper_bound(X0,X1,singleton(X2))
| sK9(X1,singleton(X2),X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_97])]) ).
fof(f996,plain,
( ! [X2,X3,X0,X1] :
( sK9(X0,singleton(X1),X2) = X1
| ~ member(X3,singleton(X1))
| apply(X0,X3,X2) )
| ~ spl11_38
| ~ spl11_97 ),
inference(resolution,[],[f763,f371]) ).
fof(f763,plain,
( ! [X2,X0,X1] :
( upper_bound(X0,X1,singleton(X2))
| sK9(X1,singleton(X2),X0) = X2 )
| ~ spl11_97 ),
inference(avatar_component_clause,[],[f762]) ).
fof(f9946,plain,
( spl11_418
| ~ spl11_27
| ~ spl11_94 ),
inference(avatar_split_clause,[],[f975,f750,f275,f9944]) ).
fof(f9944,plain,
( spl11_418
<=> ! [X0,X3,X2,X1] :
( member(X0,sum(union(X1,X2)))
| ~ member(X0,sK7(X3,X1))
| ~ member(X3,sum(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_418])]) ).
fof(f975,plain,
( ! [X2,X3,X0,X1] :
( member(X0,sum(union(X1,X2)))
| ~ member(X0,sK7(X3,X1))
| ~ member(X3,sum(X1)) )
| ~ spl11_27
| ~ spl11_94 ),
inference(resolution,[],[f751,f276]) ).
fof(f9942,plain,
( spl11_417
| ~ spl11_155
| ~ spl11_394 ),
inference(avatar_split_clause,[],[f9847,f7508,f2319,f9939]) ).
fof(f9939,plain,
( spl11_417
<=> upper_bound(sK4,sK1,union(sK3,sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_417])]) ).
fof(f7508,plain,
( spl11_394
<=> ! [X2,X0,X1] :
( member(sK9(X0,union(X1,X1),X2),X1)
| upper_bound(X2,X0,union(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_394])]) ).
fof(f9847,plain,
( upper_bound(sK4,sK1,union(sK3,sK3))
| ~ spl11_155
| ~ spl11_394 ),
inference(duplicate_literal_removal,[],[f9787]) ).
fof(f9787,plain,
( upper_bound(sK4,sK1,union(sK3,sK3))
| upper_bound(sK4,sK1,union(sK3,sK3))
| ~ spl11_155
| ~ spl11_394 ),
inference(resolution,[],[f7509,f2320]) ).
fof(f7509,plain,
( ! [X2,X0,X1] :
( member(sK9(X0,union(X1,X1),X2),X1)
| upper_bound(X2,X0,union(X1,X1)) )
| ~ spl11_394 ),
inference(avatar_component_clause,[],[f7508]) ).
fof(f9937,plain,
( spl11_416
| ~ spl11_25
| ~ spl11_94 ),
inference(avatar_split_clause,[],[f973,f750,f267,f9935]) ).
fof(f9935,plain,
( spl11_416
<=> ! [X0,X3,X2,X1] :
( member(X0,sum(union(X1,X2)))
| ~ member(X0,sK6(X3,X1))
| member(X3,product(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_416])]) ).
fof(f973,plain,
( ! [X2,X3,X0,X1] :
( member(X0,sum(union(X1,X2)))
| ~ member(X0,sK6(X3,X1))
| member(X3,product(X1)) )
| ~ spl11_25
| ~ spl11_94 ),
inference(resolution,[],[f751,f268]) ).
fof(f9933,plain,
( spl11_415
| ~ spl11_28
| ~ spl11_94 ),
inference(avatar_split_clause,[],[f964,f750,f279,f9931]) ).
fof(f9931,plain,
( spl11_415
<=> ! [X0,X3,X2,X1] :
( member(X0,sum(union(sK7(X1,X2),X3)))
| ~ member(X0,X1)
| ~ member(X1,sum(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_415])]) ).
fof(f279,plain,
( spl11_28
<=> ! [X0,X1] :
( member(X0,sK7(X0,X1))
| ~ member(X0,sum(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_28])]) ).
fof(f964,plain,
( ! [X2,X3,X0,X1] :
( member(X0,sum(union(sK7(X1,X2),X3)))
| ~ member(X0,X1)
| ~ member(X1,sum(X2)) )
| ~ spl11_28
| ~ spl11_94 ),
inference(resolution,[],[f751,f280]) ).
fof(f280,plain,
( ! [X0,X1] :
( member(X0,sK7(X0,X1))
| ~ member(X0,sum(X1)) )
| ~ spl11_28 ),
inference(avatar_component_clause,[],[f279]) ).
fof(f9929,plain,
( spl11_414
| ~ spl11_67
| ~ spl11_94 ),
inference(avatar_split_clause,[],[f959,f750,f574,f9927]) ).
fof(f9927,plain,
( spl11_414
<=> ! [X4,X0,X3,X2,X1] :
( member(X0,sum(union(sum(unordered_pair(X1,X2)),X3)))
| ~ member(X0,X4)
| ~ member(X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_414])]) ).
fof(f574,plain,
( spl11_67
<=> ! [X2,X0,X1] :
( ~ member(X0,X1)
| member(X0,sum(unordered_pair(X2,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_67])]) ).
fof(f959,plain,
( ! [X2,X3,X0,X1,X4] :
( member(X0,sum(union(sum(unordered_pair(X1,X2)),X3)))
| ~ member(X0,X4)
| ~ member(X4,X2) )
| ~ spl11_67
| ~ spl11_94 ),
inference(resolution,[],[f751,f575]) ).
fof(f575,plain,
( ! [X2,X0,X1] :
( member(X0,sum(unordered_pair(X2,X1)))
| ~ member(X0,X1) )
| ~ spl11_67 ),
inference(avatar_component_clause,[],[f574]) ).
fof(f9925,plain,
( spl11_413
| ~ spl11_68
| ~ spl11_94 ),
inference(avatar_split_clause,[],[f958,f750,f578,f9923]) ).
fof(f9923,plain,
( spl11_413
<=> ! [X4,X0,X3,X2,X1] :
( member(X0,sum(union(sum(unordered_pair(X1,X2)),X3)))
| ~ member(X0,X4)
| ~ member(X4,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_413])]) ).
fof(f578,plain,
( spl11_68
<=> ! [X2,X0,X1] :
( ~ member(X0,X1)
| member(X0,sum(unordered_pair(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_68])]) ).
fof(f958,plain,
( ! [X2,X3,X0,X1,X4] :
( member(X0,sum(union(sum(unordered_pair(X1,X2)),X3)))
| ~ member(X0,X4)
| ~ member(X4,X1) )
| ~ spl11_68
| ~ spl11_94 ),
inference(resolution,[],[f751,f579]) ).
fof(f579,plain,
( ! [X2,X0,X1] :
( member(X0,sum(unordered_pair(X1,X2)))
| ~ member(X0,X1) )
| ~ spl11_68 ),
inference(avatar_component_clause,[],[f578]) ).
fof(f9921,plain,
( spl11_412
| ~ spl11_27
| ~ spl11_93 ),
inference(avatar_split_clause,[],[f944,f746,f275,f9919]) ).
fof(f9919,plain,
( spl11_412
<=> ! [X0,X3,X2,X1] :
( member(X0,sum(union(X1,X2)))
| ~ member(X0,sK7(X3,X2))
| ~ member(X3,sum(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_412])]) ).
fof(f944,plain,
( ! [X2,X3,X0,X1] :
( member(X0,sum(union(X1,X2)))
| ~ member(X0,sK7(X3,X2))
| ~ member(X3,sum(X2)) )
| ~ spl11_27
| ~ spl11_93 ),
inference(resolution,[],[f747,f276]) ).
fof(f9917,plain,
( spl11_411
| ~ spl11_25
| ~ spl11_93 ),
inference(avatar_split_clause,[],[f942,f746,f267,f9915]) ).
fof(f9915,plain,
( spl11_411
<=> ! [X0,X3,X2,X1] :
( member(X0,sum(union(X1,X2)))
| ~ member(X0,sK6(X3,X2))
| member(X3,product(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_411])]) ).
fof(f942,plain,
( ! [X2,X3,X0,X1] :
( member(X0,sum(union(X1,X2)))
| ~ member(X0,sK6(X3,X2))
| member(X3,product(X2)) )
| ~ spl11_25
| ~ spl11_93 ),
inference(resolution,[],[f747,f268]) ).
fof(f9913,plain,
( spl11_410
| ~ spl11_28
| ~ spl11_93 ),
inference(avatar_split_clause,[],[f933,f746,f279,f9911]) ).
fof(f9911,plain,
( spl11_410
<=> ! [X0,X3,X2,X1] :
( member(X0,sum(union(X1,sK7(X2,X3))))
| ~ member(X0,X2)
| ~ member(X2,sum(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_410])]) ).
fof(f933,plain,
( ! [X2,X3,X0,X1] :
( member(X0,sum(union(X1,sK7(X2,X3))))
| ~ member(X0,X2)
| ~ member(X2,sum(X3)) )
| ~ spl11_28
| ~ spl11_93 ),
inference(resolution,[],[f747,f280]) ).
fof(f9909,plain,
( spl11_409
| ~ spl11_67
| ~ spl11_93 ),
inference(avatar_split_clause,[],[f928,f746,f574,f9907]) ).
fof(f9907,plain,
( spl11_409
<=> ! [X4,X0,X3,X2,X1] :
( member(X0,sum(union(X1,sum(unordered_pair(X2,X3)))))
| ~ member(X0,X4)
| ~ member(X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_409])]) ).
fof(f928,plain,
( ! [X2,X3,X0,X1,X4] :
( member(X0,sum(union(X1,sum(unordered_pair(X2,X3)))))
| ~ member(X0,X4)
| ~ member(X4,X3) )
| ~ spl11_67
| ~ spl11_93 ),
inference(resolution,[],[f747,f575]) ).
fof(f9905,plain,
( spl11_408
| ~ spl11_68
| ~ spl11_93 ),
inference(avatar_split_clause,[],[f927,f746,f578,f9903]) ).
fof(f9903,plain,
( spl11_408
<=> ! [X4,X0,X3,X2,X1] :
( member(X0,sum(union(X1,sum(unordered_pair(X2,X3)))))
| ~ member(X0,X4)
| ~ member(X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_408])]) ).
fof(f927,plain,
( ! [X2,X3,X0,X1,X4] :
( member(X0,sum(union(X1,sum(unordered_pair(X2,X3)))))
| ~ member(X0,X4)
| ~ member(X4,X2) )
| ~ spl11_68
| ~ spl11_93 ),
inference(resolution,[],[f747,f579]) ).
fof(f9901,plain,
( spl11_407
| ~ spl11_23
| ~ spl11_90 ),
inference(avatar_split_clause,[],[f901,f734,f259,f9899]) ).
fof(f9899,plain,
( spl11_407
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,sum(X1))
| ~ subset(X1,X2)
| member(sK7(X0,X1),X3)
| ~ subset(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_407])]) ).
fof(f901,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,sum(X1))
| ~ subset(X1,X2)
| member(sK7(X0,X1),X3)
| ~ subset(X2,X3) )
| ~ spl11_23
| ~ spl11_90 ),
inference(resolution,[],[f735,f260]) ).
fof(f9897,plain,
( spl11_406
| ~ spl11_155
| ~ spl11_393 ),
inference(avatar_split_clause,[],[f9786,f7497,f2319,f9894]) ).
fof(f9894,plain,
( spl11_406
<=> upper_bound(sK4,sK1,union(empty_set,sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_406])]) ).
fof(f7497,plain,
( spl11_393
<=> ! [X2,X0,X1] :
( member(sK9(X0,union(empty_set,X1),X2),X1)
| upper_bound(X2,X0,union(empty_set,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_393])]) ).
fof(f9786,plain,
( upper_bound(sK4,sK1,union(empty_set,sK3))
| ~ spl11_155
| ~ spl11_393 ),
inference(duplicate_literal_removal,[],[f9726]) ).
fof(f9726,plain,
( upper_bound(sK4,sK1,union(empty_set,sK3))
| upper_bound(sK4,sK1,union(empty_set,sK3))
| ~ spl11_155
| ~ spl11_393 ),
inference(resolution,[],[f7498,f2320]) ).
fof(f7498,plain,
( ! [X2,X0,X1] :
( member(sK9(X0,union(empty_set,X1),X2),X1)
| upper_bound(X2,X0,union(empty_set,X1)) )
| ~ spl11_393 ),
inference(avatar_component_clause,[],[f7497]) ).
fof(f9892,plain,
( spl11_405
| ~ spl11_23
| ~ spl11_89 ),
inference(avatar_split_clause,[],[f885,f730,f259,f9890]) ).
fof(f9890,plain,
( spl11_405
<=> ! [X0,X3,X2,X1] :
( member(X0,product(X1))
| ~ subset(X1,X2)
| member(sK6(X0,X1),X3)
| ~ subset(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_405])]) ).
fof(f885,plain,
( ! [X2,X3,X0,X1] :
( member(X0,product(X1))
| ~ subset(X1,X2)
| member(sK6(X0,X1),X3)
| ~ subset(X2,X3) )
| ~ spl11_23
| ~ spl11_89 ),
inference(resolution,[],[f731,f260]) ).
fof(f9888,plain,
( spl11_404
| ~ spl11_23
| ~ spl11_86 ),
inference(avatar_split_clause,[],[f825,f718,f259,f9886]) ).
fof(f9886,plain,
( spl11_404
<=> ! [X0,X3,X2,X1] :
( subset(intersection(X0,X1),X2)
| member(sK5(intersection(X0,X1),X2),X3)
| ~ subset(X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_404])]) ).
fof(f825,plain,
( ! [X2,X3,X0,X1] :
( subset(intersection(X0,X1),X2)
| member(sK5(intersection(X0,X1),X2),X3)
| ~ subset(X1,X3) )
| ~ spl11_23
| ~ spl11_86 ),
inference(resolution,[],[f719,f260]) ).
fof(f9884,plain,
( spl11_403
| ~ spl11_23
| ~ spl11_85 ),
inference(avatar_split_clause,[],[f805,f714,f259,f9882]) ).
fof(f9882,plain,
( spl11_403
<=> ! [X0,X3,X2,X1] :
( subset(intersection(X0,X1),X2)
| member(sK5(intersection(X0,X1),X2),X3)
| ~ subset(X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_403])]) ).
fof(f805,plain,
( ! [X2,X3,X0,X1] :
( subset(intersection(X0,X1),X2)
| member(sK5(intersection(X0,X1),X2),X3)
| ~ subset(X0,X3) )
| ~ spl11_23
| ~ spl11_85 ),
inference(resolution,[],[f715,f260]) ).
fof(f9880,plain,
( spl11_402
| ~ spl11_23
| ~ spl11_83 ),
inference(avatar_split_clause,[],[f772,f706,f259,f9878]) ).
fof(f9878,plain,
( spl11_402
<=> ! [X0,X3,X2,X1] :
( subset(difference(X0,X1),X2)
| member(sK5(difference(X0,X1),X2),X3)
| ~ subset(X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_402])]) ).
fof(f772,plain,
( ! [X2,X3,X0,X1] :
( subset(difference(X0,X1),X2)
| member(sK5(difference(X0,X1),X2),X3)
| ~ subset(X0,X3) )
| ~ spl11_23
| ~ spl11_83 ),
inference(resolution,[],[f707,f260]) ).
fof(f9876,plain,
( spl11_401
| ~ spl11_34
| ~ spl11_81 ),
inference(avatar_split_clause,[],[f703,f643,f328,f9874]) ).
fof(f9874,plain,
( spl11_401
<=> ! [X0,X3,X2,X1] :
( member(sK9(X0,X1,X2),sum(power_set(X3)))
| ~ subset(X1,X3)
| upper_bound(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_401])]) ).
fof(f703,plain,
( ! [X2,X3,X0,X1] :
( member(sK9(X0,X1,X2),sum(power_set(X3)))
| ~ subset(X1,X3)
| upper_bound(X2,X0,X1) )
| ~ spl11_34
| ~ spl11_81 ),
inference(resolution,[],[f644,f329]) ).
fof(f9872,plain,
( spl11_400
| ~ spl11_14
| ~ spl11_80 ),
inference(avatar_split_clause,[],[f673,f639,f211,f9870]) ).
fof(f9870,plain,
( spl11_400
<=> ! [X0,X1] :
( sK7(sK5(sum(singleton(X0)),X1),singleton(X0)) = X0
| subset(sum(singleton(X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_400])]) ).
fof(f673,plain,
( ! [X0,X1] :
( sK7(sK5(sum(singleton(X0)),X1),singleton(X0)) = X0
| subset(sum(singleton(X0)),X1) )
| ~ spl11_14
| ~ spl11_80 ),
inference(resolution,[],[f640,f212]) ).
fof(f9868,plain,
( spl11_399
| ~ spl11_15
| ~ spl11_78 ),
inference(avatar_split_clause,[],[f667,f631,f215,f9866]) ).
fof(f9866,plain,
( spl11_399
<=> ! [X0,X1] :
( sK6(sK5(X0,product(singleton(X1))),singleton(X1)) = X1
| subset(X0,product(singleton(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_399])]) ).
fof(f215,plain,
( spl11_15
<=> ! [X0,X1] :
( subset(X0,X1)
| ~ member(sK5(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_15])]) ).
fof(f667,plain,
( ! [X0,X1] :
( sK6(sK5(X0,product(singleton(X1))),singleton(X1)) = X1
| subset(X0,product(singleton(X1))) )
| ~ spl11_15
| ~ spl11_78 ),
inference(resolution,[],[f632,f216]) ).
fof(f216,plain,
( ! [X0,X1] :
( ~ member(sK5(X0,X1),X1)
| subset(X0,X1) )
| ~ spl11_15 ),
inference(avatar_component_clause,[],[f215]) ).
fof(f9864,plain,
( spl11_398
| ~ spl11_33
| ~ spl11_78 ),
inference(avatar_split_clause,[],[f665,f631,f324,f9862]) ).
fof(f9862,plain,
( spl11_398
<=> ! [X2,X0,X1] :
( sK6(X0,singleton(X1)) = X1
| ~ member(X2,X0)
| member(X2,sum(product(singleton(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_398])]) ).
fof(f665,plain,
( ! [X2,X0,X1] :
( sK6(X0,singleton(X1)) = X1
| ~ member(X2,X0)
| member(X2,sum(product(singleton(X1)))) )
| ~ spl11_33
| ~ spl11_78 ),
inference(resolution,[],[f632,f325]) ).
fof(f9860,plain,
( spl11_397
| ~ spl11_32
| ~ spl11_75 ),
inference(avatar_split_clause,[],[f661,f619,f320,f9858]) ).
fof(f9858,plain,
( spl11_397
<=> ! [X0,X3,X2,X1] :
( ~ subset(X0,product(X1))
| subset(X0,X2)
| ~ member(X3,X1)
| member(sK5(X0,X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_397])]) ).
fof(f661,plain,
( ! [X2,X3,X0,X1] :
( ~ subset(X0,product(X1))
| subset(X0,X2)
| ~ member(X3,X1)
| member(sK5(X0,X2),X3) )
| ~ spl11_32
| ~ spl11_75 ),
inference(resolution,[],[f620,f321]) ).
fof(f9856,plain,
( spl11_396
| ~ spl11_33
| ~ spl11_75 ),
inference(avatar_split_clause,[],[f649,f619,f324,f9854]) ).
fof(f9854,plain,
( spl11_396
<=> ! [X0,X3,X2,X1] :
( ~ subset(X0,X1)
| subset(X0,X2)
| ~ member(X3,sK5(X0,X2))
| member(X3,sum(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_396])]) ).
fof(f649,plain,
( ! [X2,X3,X0,X1] :
( ~ subset(X0,X1)
| subset(X0,X2)
| ~ member(X3,sK5(X0,X2))
| member(X3,sum(X1)) )
| ~ spl11_33
| ~ spl11_75 ),
inference(resolution,[],[f620,f325]) ).
fof(f9852,plain,
( spl11_395
| ~ spl11_155
| ~ spl11_392 ),
inference(avatar_split_clause,[],[f9725,f7493,f2319,f9849]) ).
fof(f9849,plain,
( spl11_395
<=> upper_bound(sK4,sK1,union(sK3,empty_set)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_395])]) ).
fof(f7493,plain,
( spl11_392
<=> ! [X2,X0,X1] :
( member(sK9(X0,union(X1,empty_set),X2),X1)
| upper_bound(X2,X0,union(X1,empty_set)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_392])]) ).
fof(f9725,plain,
( upper_bound(sK4,sK1,union(sK3,empty_set))
| ~ spl11_155
| ~ spl11_392 ),
inference(duplicate_literal_removal,[],[f9665]) ).
fof(f9665,plain,
( upper_bound(sK4,sK1,union(sK3,empty_set))
| upper_bound(sK4,sK1,union(sK3,empty_set))
| ~ spl11_155
| ~ spl11_392 ),
inference(resolution,[],[f7494,f2320]) ).
fof(f7494,plain,
( ! [X2,X0,X1] :
( member(sK9(X0,union(X1,empty_set),X2),X1)
| upper_bound(X2,X0,union(X1,empty_set)) )
| ~ spl11_392 ),
inference(avatar_component_clause,[],[f7493]) ).
fof(f7510,plain,
( spl11_394
| ~ spl11_149 ),
inference(avatar_split_clause,[],[f2275,f2217,f7508]) ).
fof(f2275,plain,
( ! [X2,X0,X1] :
( member(sK9(X0,union(X1,X1),X2),X1)
| upper_bound(X2,X0,union(X1,X1)) )
| ~ spl11_149 ),
inference(factoring,[],[f2218]) ).
fof(f7499,plain,
( spl11_393
| ~ spl11_6
| ~ spl11_149 ),
inference(avatar_split_clause,[],[f2261,f2217,f176,f7497]) ).
fof(f176,plain,
( spl11_6
<=> ! [X0] : ~ member(X0,empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_6])]) ).
fof(f2261,plain,
( ! [X2,X0,X1] :
( member(sK9(X0,union(empty_set,X1),X2),X1)
| upper_bound(X2,X0,union(empty_set,X1)) )
| ~ spl11_6
| ~ spl11_149 ),
inference(resolution,[],[f2218,f177]) ).
fof(f177,plain,
( ! [X0] : ~ member(X0,empty_set)
| ~ spl11_6 ),
inference(avatar_component_clause,[],[f176]) ).
fof(f7495,plain,
( spl11_392
| ~ spl11_6
| ~ spl11_149 ),
inference(avatar_split_clause,[],[f2236,f2217,f176,f7493]) ).
fof(f2236,plain,
( ! [X2,X0,X1] :
( member(sK9(X0,union(X1,empty_set),X2),X1)
| upper_bound(X2,X0,union(X1,empty_set)) )
| ~ spl11_6
| ~ spl11_149 ),
inference(resolution,[],[f2218,f177]) ).
fof(f7491,plain,
( spl11_391
| ~ spl11_60
| ~ spl11_135 ),
inference(avatar_split_clause,[],[f1860,f1727,f529,f7489]) ).
fof(f1860,plain,
( ! [X0,X1] :
( member(sK5(union(sum(empty_set),X0),X1),X0)
| subset(union(sum(empty_set),X0),X1) )
| ~ spl11_60
| ~ spl11_135 ),
inference(resolution,[],[f1728,f530]) ).
fof(f7487,plain,
( spl11_390
| ~ spl11_60
| ~ spl11_135 ),
inference(avatar_split_clause,[],[f1831,f1727,f529,f7485]) ).
fof(f1831,plain,
( ! [X0,X1] :
( member(sK5(union(X0,sum(empty_set)),X1),X0)
| subset(union(X0,sum(empty_set)),X1) )
| ~ spl11_60
| ~ spl11_135 ),
inference(resolution,[],[f1728,f530]) ).
fof(f7483,plain,
( spl11_389
| ~ spl11_59
| ~ spl11_133 ),
inference(avatar_split_clause,[],[f1800,f1719,f525,f7481]) ).
fof(f7481,plain,
( spl11_389
<=> ! [X0,X1] :
( ~ member(sK5(X0,intersection(X1,product(empty_set))),X1)
| subset(X0,intersection(X1,product(empty_set))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_389])]) ).
fof(f525,plain,
( spl11_59
<=> ! [X0] : member(X0,product(empty_set)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_59])]) ).
fof(f1800,plain,
( ! [X0,X1] :
( ~ member(sK5(X0,intersection(X1,product(empty_set))),X1)
| subset(X0,intersection(X1,product(empty_set))) )
| ~ spl11_59
| ~ spl11_133 ),
inference(resolution,[],[f1720,f526]) ).
fof(f526,plain,
( ! [X0] : member(X0,product(empty_set))
| ~ spl11_59 ),
inference(avatar_component_clause,[],[f525]) ).
fof(f7479,plain,
( spl11_388
| ~ spl11_59
| ~ spl11_132 ),
inference(avatar_split_clause,[],[f1769,f1715,f525,f7477]) ).
fof(f7477,plain,
( spl11_388
<=> ! [X0,X1] :
( member(sK5(X0,difference(product(empty_set),X1)),X1)
| subset(X0,difference(product(empty_set),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_388])]) ).
fof(f1769,plain,
( ! [X0,X1] :
( member(sK5(X0,difference(product(empty_set),X1)),X1)
| subset(X0,difference(product(empty_set),X1)) )
| ~ spl11_59
| ~ spl11_132 ),
inference(resolution,[],[f1716,f526]) ).
fof(f7475,plain,
( spl11_387
| ~ spl11_59
| ~ spl11_126 ),
inference(avatar_split_clause,[],[f1608,f1506,f525,f7473]) ).
fof(f7473,plain,
( spl11_387
<=> ! [X2,X0,X1] :
( ~ member(product(empty_set),X0)
| ~ member(product(empty_set),X1)
| member(X2,sum(intersection(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_387])]) ).
fof(f1608,plain,
( ! [X2,X0,X1] :
( ~ member(product(empty_set),X0)
| ~ member(product(empty_set),X1)
| member(X2,sum(intersection(X0,X1))) )
| ~ spl11_59
| ~ spl11_126 ),
inference(resolution,[],[f1507,f526]) ).
fof(f7471,plain,
( spl11_386
| ~ spl11_7
| ~ spl11_126 ),
inference(avatar_split_clause,[],[f1597,f1506,f180,f7469]) ).
fof(f7469,plain,
( spl11_386
<=> ! [X2,X0,X1] :
( ~ member(singleton(X0),X1)
| ~ member(singleton(X0),X2)
| member(X0,sum(intersection(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_386])]) ).
fof(f180,plain,
( spl11_7
<=> ! [X1] : member(X1,singleton(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_7])]) ).
fof(f1597,plain,
( ! [X2,X0,X1] :
( ~ member(singleton(X0),X1)
| ~ member(singleton(X0),X2)
| member(X0,sum(intersection(X1,X2))) )
| ~ spl11_7
| ~ spl11_126 ),
inference(resolution,[],[f1507,f181]) ).
fof(f181,plain,
( ! [X1] : member(X1,singleton(X1))
| ~ spl11_7 ),
inference(avatar_component_clause,[],[f180]) ).
fof(f7467,plain,
( spl11_385
| ~ spl11_59
| ~ spl11_125 ),
inference(avatar_split_clause,[],[f1559,f1502,f525,f7465]) ).
fof(f7465,plain,
( spl11_385
<=> ! [X2,X0,X1] :
( ~ member(product(empty_set),X0)
| member(product(empty_set),X1)
| member(X2,sum(difference(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_385])]) ).
fof(f1559,plain,
( ! [X2,X0,X1] :
( ~ member(product(empty_set),X0)
| member(product(empty_set),X1)
| member(X2,sum(difference(X0,X1))) )
| ~ spl11_59
| ~ spl11_125 ),
inference(resolution,[],[f1503,f526]) ).
fof(f7463,plain,
( spl11_384
| ~ spl11_7
| ~ spl11_125 ),
inference(avatar_split_clause,[],[f1548,f1502,f180,f7461]) ).
fof(f7461,plain,
( spl11_384
<=> ! [X2,X0,X1] :
( ~ member(singleton(X0),X1)
| member(singleton(X0),X2)
| member(X0,sum(difference(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_384])]) ).
fof(f1548,plain,
( ! [X2,X0,X1] :
( ~ member(singleton(X0),X1)
| member(singleton(X0),X2)
| member(X0,sum(difference(X1,X2))) )
| ~ spl11_7
| ~ spl11_125 ),
inference(resolution,[],[f1503,f181]) ).
fof(f7459,plain,
( spl11_383
| ~ spl11_82
| ~ spl11_308 ),
inference(avatar_split_clause,[],[f5906,f5369,f669,f7456]) ).
fof(f7456,plain,
( spl11_383
<=> subset(union(sK4,sK4),sum(sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_383])]) ).
fof(f5369,plain,
( spl11_308
<=> ! [X0,X1] :
( member(sK5(union(X0,X0),X1),X0)
| subset(union(X0,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_308])]) ).
fof(f5906,plain,
( subset(union(sK4,sK4),sum(sK3))
| ~ spl11_82
| ~ spl11_308 ),
inference(duplicate_literal_removal,[],[f5860]) ).
fof(f5860,plain,
( subset(union(sK4,sK4),sum(sK3))
| subset(union(sK4,sK4),sum(sK3))
| ~ spl11_82
| ~ spl11_308 ),
inference(resolution,[],[f5370,f670]) ).
fof(f5370,plain,
( ! [X0,X1] :
( member(sK5(union(X0,X0),X1),X0)
| subset(union(X0,X0),X1) )
| ~ spl11_308 ),
inference(avatar_component_clause,[],[f5369]) ).
fof(f7454,plain,
( spl11_382
| ~ spl11_10
| ~ spl11_112 ),
inference(avatar_split_clause,[],[f1290,f1055,f192,f7452]) ).
fof(f7452,plain,
( spl11_382
<=> ! [X0,X3,X2,X1] :
( upper_bound(X0,X1,X2)
| ~ subset(X2,singleton(X3))
| sK9(X1,X2,X0) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_382])]) ).
fof(f1290,plain,
( ! [X2,X3,X0,X1] :
( upper_bound(X0,X1,X2)
| ~ subset(X2,singleton(X3))
| sK9(X1,X2,X0) = X3 )
| ~ spl11_10
| ~ spl11_112 ),
inference(resolution,[],[f1056,f193]) ).
fof(f7450,plain,
( spl11_381
| ~ spl11_11
| ~ spl11_112 ),
inference(avatar_split_clause,[],[f1283,f1055,f196,f7448]) ).
fof(f7448,plain,
( spl11_381
<=> ! [X0,X3,X2,X1] :
( upper_bound(X0,X1,X2)
| ~ subset(X2,power_set(X3))
| subset(sK9(X1,X2,X0),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_381])]) ).
fof(f1283,plain,
( ! [X2,X3,X0,X1] :
( upper_bound(X0,X1,X2)
| ~ subset(X2,power_set(X3))
| subset(sK9(X1,X2,X0),X3) )
| ~ spl11_11
| ~ spl11_112 ),
inference(resolution,[],[f1056,f197]) ).
fof(f7446,plain,
( spl11_380
| ~ spl11_10
| ~ spl11_108 ),
inference(avatar_split_clause,[],[f1217,f1039,f192,f7444]) ).
fof(f7444,plain,
( spl11_380
<=> ! [X2,X0,X1] :
( ~ member(singleton(X0),X1)
| subset(product(X1),X2)
| sK5(product(X1),X2) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_380])]) ).
fof(f1217,plain,
( ! [X2,X0,X1] :
( ~ member(singleton(X0),X1)
| subset(product(X1),X2)
| sK5(product(X1),X2) = X0 )
| ~ spl11_10
| ~ spl11_108 ),
inference(resolution,[],[f1040,f193]) ).
fof(f7442,plain,
( spl11_379
| ~ spl11_11
| ~ spl11_108 ),
inference(avatar_split_clause,[],[f1210,f1039,f196,f7440]) ).
fof(f7440,plain,
( spl11_379
<=> ! [X2,X0,X1] :
( ~ member(power_set(X0),X1)
| subset(product(X1),X2)
| subset(sK5(product(X1),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_379])]) ).
fof(f1210,plain,
( ! [X2,X0,X1] :
( ~ member(power_set(X0),X1)
| subset(product(X1),X2)
| subset(sK5(product(X1),X2),X0) )
| ~ spl11_11
| ~ spl11_108 ),
inference(resolution,[],[f1040,f197]) ).
fof(f7438,plain,
( spl11_378
| ~ spl11_14
| ~ spl11_94 ),
inference(avatar_split_clause,[],[f968,f750,f211,f7436]) ).
fof(f7436,plain,
( spl11_378
<=> ! [X0,X3,X2,X1] :
( member(X0,sum(union(X1,X2)))
| ~ member(X0,sK5(X1,X3))
| subset(X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_378])]) ).
fof(f968,plain,
( ! [X2,X3,X0,X1] :
( member(X0,sum(union(X1,X2)))
| ~ member(X0,sK5(X1,X3))
| subset(X1,X3) )
| ~ spl11_14
| ~ spl11_94 ),
inference(resolution,[],[f751,f212]) ).
fof(f7434,plain,
( spl11_377
| ~ spl11_66
| ~ spl11_94 ),
inference(avatar_split_clause,[],[f957,f750,f565,f7432]) ).
fof(f7432,plain,
( spl11_377
<=> ! [X0,X3,X2,X1] :
( member(X0,sum(union(sum(singleton(X1)),X2)))
| ~ member(X0,X3)
| ~ member(X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_377])]) ).
fof(f957,plain,
( ! [X2,X3,X0,X1] :
( member(X0,sum(union(sum(singleton(X1)),X2)))
| ~ member(X0,X3)
| ~ member(X3,X1) )
| ~ spl11_66
| ~ spl11_94 ),
inference(resolution,[],[f751,f566]) ).
fof(f7430,plain,
( spl11_376
| ~ spl11_20
| ~ spl11_94 ),
inference(avatar_split_clause,[],[f952,f750,f235,f7428]) ).
fof(f7428,plain,
( spl11_376
<=> ! [X4,X0,X3,X2,X1] :
( member(X0,sum(union(union(X1,X2),X3)))
| ~ member(X0,X4)
| ~ member(X4,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_376])]) ).
fof(f952,plain,
( ! [X2,X3,X0,X1,X4] :
( member(X0,sum(union(union(X1,X2),X3)))
| ~ member(X0,X4)
| ~ member(X4,X1) )
| ~ spl11_20
| ~ spl11_94 ),
inference(resolution,[],[f751,f236]) ).
fof(f7426,plain,
( spl11_375
| ~ spl11_21
| ~ spl11_94 ),
inference(avatar_split_clause,[],[f951,f750,f239,f7424]) ).
fof(f7424,plain,
( spl11_375
<=> ! [X4,X0,X3,X2,X1] :
( member(X0,sum(union(union(X1,X2),X3)))
| ~ member(X0,X4)
| ~ member(X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_375])]) ).
fof(f951,plain,
( ! [X2,X3,X0,X1,X4] :
( member(X0,sum(union(union(X1,X2),X3)))
| ~ member(X0,X4)
| ~ member(X4,X2) )
| ~ spl11_21
| ~ spl11_94 ),
inference(resolution,[],[f751,f240]) ).
fof(f7422,plain,
( spl11_374
| ~ spl11_14
| ~ spl11_93 ),
inference(avatar_split_clause,[],[f937,f746,f211,f7420]) ).
fof(f7420,plain,
( spl11_374
<=> ! [X0,X3,X2,X1] :
( member(X0,sum(union(X1,X2)))
| ~ member(X0,sK5(X2,X3))
| subset(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_374])]) ).
fof(f937,plain,
( ! [X2,X3,X0,X1] :
( member(X0,sum(union(X1,X2)))
| ~ member(X0,sK5(X2,X3))
| subset(X2,X3) )
| ~ spl11_14
| ~ spl11_93 ),
inference(resolution,[],[f747,f212]) ).
fof(f7418,plain,
( spl11_373
| ~ spl11_66
| ~ spl11_93 ),
inference(avatar_split_clause,[],[f926,f746,f565,f7416]) ).
fof(f7416,plain,
( spl11_373
<=> ! [X0,X3,X2,X1] :
( member(X0,sum(union(X1,sum(singleton(X2)))))
| ~ member(X0,X3)
| ~ member(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_373])]) ).
fof(f926,plain,
( ! [X2,X3,X0,X1] :
( member(X0,sum(union(X1,sum(singleton(X2)))))
| ~ member(X0,X3)
| ~ member(X3,X2) )
| ~ spl11_66
| ~ spl11_93 ),
inference(resolution,[],[f747,f566]) ).
fof(f7414,plain,
( spl11_372
| ~ spl11_82
| ~ spl11_307 ),
inference(avatar_split_clause,[],[f5837,f5365,f669,f7411]) ).
fof(f7411,plain,
( spl11_372
<=> subset(union(empty_set,sK4),sum(sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_372])]) ).
fof(f5365,plain,
( spl11_307
<=> ! [X0,X1] :
( member(sK5(union(empty_set,X0),X1),X0)
| subset(union(empty_set,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_307])]) ).
fof(f5837,plain,
( subset(union(empty_set,sK4),sum(sK3))
| ~ spl11_82
| ~ spl11_307 ),
inference(duplicate_literal_removal,[],[f5791]) ).
fof(f5791,plain,
( subset(union(empty_set,sK4),sum(sK3))
| subset(union(empty_set,sK4),sum(sK3))
| ~ spl11_82
| ~ spl11_307 ),
inference(resolution,[],[f5366,f670]) ).
fof(f5366,plain,
( ! [X0,X1] :
( member(sK5(union(empty_set,X0),X1),X0)
| subset(union(empty_set,X0),X1) )
| ~ spl11_307 ),
inference(avatar_component_clause,[],[f5365]) ).
fof(f7409,plain,
( spl11_371
| ~ spl11_20
| ~ spl11_93 ),
inference(avatar_split_clause,[],[f921,f746,f235,f7407]) ).
fof(f7407,plain,
( spl11_371
<=> ! [X4,X0,X3,X2,X1] :
( member(X0,sum(union(X1,union(X2,X3))))
| ~ member(X0,X4)
| ~ member(X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_371])]) ).
fof(f921,plain,
( ! [X2,X3,X0,X1,X4] :
( member(X0,sum(union(X1,union(X2,X3))))
| ~ member(X0,X4)
| ~ member(X4,X2) )
| ~ spl11_20
| ~ spl11_93 ),
inference(resolution,[],[f747,f236]) ).
fof(f7405,plain,
( spl11_370
| ~ spl11_21
| ~ spl11_93 ),
inference(avatar_split_clause,[],[f920,f746,f239,f7403]) ).
fof(f7403,plain,
( spl11_370
<=> ! [X4,X0,X3,X2,X1] :
( member(X0,sum(union(X1,union(X2,X3))))
| ~ member(X0,X4)
| ~ member(X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_370])]) ).
fof(f920,plain,
( ! [X2,X3,X0,X1,X4] :
( member(X0,sum(union(X1,union(X2,X3))))
| ~ member(X0,X4)
| ~ member(X4,X3) )
| ~ spl11_21
| ~ spl11_93 ),
inference(resolution,[],[f747,f240]) ).
fof(f7401,plain,
( spl11_369
| ~ spl11_16
| ~ spl11_90 ),
inference(avatar_split_clause,[],[f908,f734,f219,f7399]) ).
fof(f7399,plain,
( spl11_369
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,sum(X1))
| ~ subset(X1,difference(X2,X3))
| member(sK7(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_369])]) ).
fof(f908,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,sum(X1))
| ~ subset(X1,difference(X2,X3))
| member(sK7(X0,X1),X2) )
| ~ spl11_16
| ~ spl11_90 ),
inference(resolution,[],[f735,f220]) ).
fof(f7397,plain,
( spl11_368
| ~ spl11_17
| ~ spl11_90 ),
inference(avatar_split_clause,[],[f907,f734,f223,f7395]) ).
fof(f7395,plain,
( spl11_368
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,sum(X1))
| ~ subset(X1,difference(X2,X3))
| ~ member(sK7(X0,X1),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_368])]) ).
fof(f907,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,sum(X1))
| ~ subset(X1,difference(X2,X3))
| ~ member(sK7(X0,X1),X3) )
| ~ spl11_17
| ~ spl11_90 ),
inference(resolution,[],[f735,f224]) ).
fof(f7393,plain,
( spl11_367
| ~ spl11_18
| ~ spl11_90 ),
inference(avatar_split_clause,[],[f904,f734,f227,f7391]) ).
fof(f7391,plain,
( spl11_367
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,sum(X1))
| ~ subset(X1,intersection(X2,X3))
| member(sK7(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_367])]) ).
fof(f904,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,sum(X1))
| ~ subset(X1,intersection(X2,X3))
| member(sK7(X0,X1),X2) )
| ~ spl11_18
| ~ spl11_90 ),
inference(resolution,[],[f735,f228]) ).
fof(f7389,plain,
( spl11_366
| ~ spl11_19
| ~ spl11_90 ),
inference(avatar_split_clause,[],[f903,f734,f231,f7387]) ).
fof(f7387,plain,
( spl11_366
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,sum(X1))
| ~ subset(X1,intersection(X2,X3))
| member(sK7(X0,X1),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_366])]) ).
fof(f903,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,sum(X1))
| ~ subset(X1,intersection(X2,X3))
| member(sK7(X0,X1),X3) )
| ~ spl11_19
| ~ spl11_90 ),
inference(resolution,[],[f735,f232]) ).
fof(f7385,plain,
( spl11_365
| ~ spl11_16
| ~ spl11_89 ),
inference(avatar_split_clause,[],[f892,f730,f219,f7383]) ).
fof(f7383,plain,
( spl11_365
<=> ! [X0,X3,X2,X1] :
( member(X0,product(X1))
| ~ subset(X1,difference(X2,X3))
| member(sK6(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_365])]) ).
fof(f892,plain,
( ! [X2,X3,X0,X1] :
( member(X0,product(X1))
| ~ subset(X1,difference(X2,X3))
| member(sK6(X0,X1),X2) )
| ~ spl11_16
| ~ spl11_89 ),
inference(resolution,[],[f731,f220]) ).
fof(f7381,plain,
( spl11_364
| ~ spl11_17
| ~ spl11_89 ),
inference(avatar_split_clause,[],[f891,f730,f223,f7379]) ).
fof(f7379,plain,
( spl11_364
<=> ! [X0,X3,X2,X1] :
( member(X0,product(X1))
| ~ subset(X1,difference(X2,X3))
| ~ member(sK6(X0,X1),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_364])]) ).
fof(f891,plain,
( ! [X2,X3,X0,X1] :
( member(X0,product(X1))
| ~ subset(X1,difference(X2,X3))
| ~ member(sK6(X0,X1),X3) )
| ~ spl11_17
| ~ spl11_89 ),
inference(resolution,[],[f731,f224]) ).
fof(f7377,plain,
( spl11_363
| ~ spl11_18
| ~ spl11_89 ),
inference(avatar_split_clause,[],[f888,f730,f227,f7375]) ).
fof(f7375,plain,
( spl11_363
<=> ! [X0,X3,X2,X1] :
( member(X0,product(X1))
| ~ subset(X1,intersection(X2,X3))
| member(sK6(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_363])]) ).
fof(f888,plain,
( ! [X2,X3,X0,X1] :
( member(X0,product(X1))
| ~ subset(X1,intersection(X2,X3))
| member(sK6(X0,X1),X2) )
| ~ spl11_18
| ~ spl11_89 ),
inference(resolution,[],[f731,f228]) ).
fof(f7373,plain,
( spl11_362
| ~ spl11_19
| ~ spl11_89 ),
inference(avatar_split_clause,[],[f887,f730,f231,f7371]) ).
fof(f7371,plain,
( spl11_362
<=> ! [X0,X3,X2,X1] :
( member(X0,product(X1))
| ~ subset(X1,intersection(X2,X3))
| member(sK6(X0,X1),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_362])]) ).
fof(f887,plain,
( ! [X2,X3,X0,X1] :
( member(X0,product(X1))
| ~ subset(X1,intersection(X2,X3))
| member(sK6(X0,X1),X3) )
| ~ spl11_19
| ~ spl11_89 ),
inference(resolution,[],[f731,f232]) ).
fof(f7369,plain,
( spl11_361
| ~ spl11_82
| ~ spl11_306 ),
inference(avatar_split_clause,[],[f5767,f5361,f669,f7366]) ).
fof(f7366,plain,
( spl11_361
<=> subset(union(sK4,empty_set),sum(sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_361])]) ).
fof(f5361,plain,
( spl11_306
<=> ! [X0,X1] :
( member(sK5(union(X0,empty_set),X1),X0)
| subset(union(X0,empty_set),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_306])]) ).
fof(f5767,plain,
( subset(union(sK4,empty_set),sum(sK3))
| ~ spl11_82
| ~ spl11_306 ),
inference(duplicate_literal_removal,[],[f5721]) ).
fof(f5721,plain,
( subset(union(sK4,empty_set),sum(sK3))
| subset(union(sK4,empty_set),sum(sK3))
| ~ spl11_82
| ~ spl11_306 ),
inference(resolution,[],[f5362,f670]) ).
fof(f5362,plain,
( ! [X0,X1] :
( member(sK5(union(X0,empty_set),X1),X0)
| subset(union(X0,empty_set),X1) )
| ~ spl11_306 ),
inference(avatar_component_clause,[],[f5361]) ).
fof(f7364,plain,
( spl11_360
| ~ spl11_12
| ~ spl11_88 ),
inference(avatar_split_clause,[],[f866,f726,f200,f7362]) ).
fof(f7362,plain,
( spl11_360
<=> ! [X2,X0,X1] :
( subset(X0,union(X1,power_set(X2)))
| ~ subset(sK5(X0,union(X1,power_set(X2))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_360])]) ).
fof(f866,plain,
( ! [X2,X0,X1] :
( subset(X0,union(X1,power_set(X2)))
| ~ subset(sK5(X0,union(X1,power_set(X2))),X2) )
| ~ spl11_12
| ~ spl11_88 ),
inference(resolution,[],[f727,f201]) ).
fof(f7360,plain,
( spl11_359
| ~ spl11_12
| ~ spl11_87 ),
inference(avatar_split_clause,[],[f844,f722,f200,f7358]) ).
fof(f7358,plain,
( spl11_359
<=> ! [X2,X0,X1] :
( subset(X0,union(power_set(X1),X2))
| ~ subset(sK5(X0,union(power_set(X1),X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_359])]) ).
fof(f844,plain,
( ! [X2,X0,X1] :
( subset(X0,union(power_set(X1),X2))
| ~ subset(sK5(X0,union(power_set(X1),X2)),X1) )
| ~ spl11_12
| ~ spl11_87 ),
inference(resolution,[],[f723,f201]) ).
fof(f7356,plain,
( spl11_358
| ~ spl11_10
| ~ spl11_86 ),
inference(avatar_split_clause,[],[f833,f718,f192,f7354]) ).
fof(f7354,plain,
( spl11_358
<=> ! [X2,X0,X1] :
( subset(intersection(X0,singleton(X1)),X2)
| sK5(intersection(X0,singleton(X1)),X2) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_358])]) ).
fof(f833,plain,
( ! [X2,X0,X1] :
( subset(intersection(X0,singleton(X1)),X2)
| sK5(intersection(X0,singleton(X1)),X2) = X1 )
| ~ spl11_10
| ~ spl11_86 ),
inference(resolution,[],[f719,f193]) ).
fof(f7352,plain,
( spl11_357
| ~ spl11_11
| ~ spl11_86 ),
inference(avatar_split_clause,[],[f826,f718,f196,f7350]) ).
fof(f7350,plain,
( spl11_357
<=> ! [X2,X0,X1] :
( subset(intersection(X0,power_set(X1)),X2)
| subset(sK5(intersection(X0,power_set(X1)),X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_357])]) ).
fof(f826,plain,
( ! [X2,X0,X1] :
( subset(intersection(X0,power_set(X1)),X2)
| subset(sK5(intersection(X0,power_set(X1)),X2),X1) )
| ~ spl11_11
| ~ spl11_86 ),
inference(resolution,[],[f719,f197]) ).
fof(f7348,plain,
( spl11_356
| ~ spl11_10
| ~ spl11_85 ),
inference(avatar_split_clause,[],[f813,f714,f192,f7346]) ).
fof(f7346,plain,
( spl11_356
<=> ! [X2,X0,X1] :
( subset(intersection(singleton(X0),X1),X2)
| sK5(intersection(singleton(X0),X1),X2) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_356])]) ).
fof(f813,plain,
( ! [X2,X0,X1] :
( subset(intersection(singleton(X0),X1),X2)
| sK5(intersection(singleton(X0),X1),X2) = X0 )
| ~ spl11_10
| ~ spl11_85 ),
inference(resolution,[],[f715,f193]) ).
fof(f7344,plain,
( spl11_355
| ~ spl11_11
| ~ spl11_85 ),
inference(avatar_split_clause,[],[f806,f714,f196,f7342]) ).
fof(f7342,plain,
( spl11_355
<=> ! [X2,X0,X1] :
( subset(intersection(power_set(X0),X1),X2)
| subset(sK5(intersection(power_set(X0),X1),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_355])]) ).
fof(f806,plain,
( ! [X2,X0,X1] :
( subset(intersection(power_set(X0),X1),X2)
| subset(sK5(intersection(power_set(X0),X1),X2),X0) )
| ~ spl11_11
| ~ spl11_85 ),
inference(resolution,[],[f715,f197]) ).
fof(f7340,plain,
( spl11_354
| ~ spl11_12
| ~ spl11_84 ),
inference(avatar_split_clause,[],[f788,f710,f200,f7338]) ).
fof(f7338,plain,
( spl11_354
<=> ! [X2,X0,X1] :
( subset(difference(X0,power_set(X1)),X2)
| ~ subset(sK5(difference(X0,power_set(X1)),X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_354])]) ).
fof(f788,plain,
( ! [X2,X0,X1] :
( subset(difference(X0,power_set(X1)),X2)
| ~ subset(sK5(difference(X0,power_set(X1)),X2),X1) )
| ~ spl11_12
| ~ spl11_84 ),
inference(resolution,[],[f711,f201]) ).
fof(f7336,plain,
( spl11_353
| ~ spl11_10
| ~ spl11_83 ),
inference(avatar_split_clause,[],[f780,f706,f192,f7334]) ).
fof(f7334,plain,
( spl11_353
<=> ! [X2,X0,X1] :
( subset(difference(singleton(X0),X1),X2)
| sK5(difference(singleton(X0),X1),X2) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_353])]) ).
fof(f780,plain,
( ! [X2,X0,X1] :
( subset(difference(singleton(X0),X1),X2)
| sK5(difference(singleton(X0),X1),X2) = X0 )
| ~ spl11_10
| ~ spl11_83 ),
inference(resolution,[],[f707,f193]) ).
fof(f7332,plain,
( spl11_352
| ~ spl11_11
| ~ spl11_83 ),
inference(avatar_split_clause,[],[f773,f706,f196,f7330]) ).
fof(f7330,plain,
( spl11_352
<=> ! [X2,X0,X1] :
( subset(difference(power_set(X0),X1),X2)
| subset(sK5(difference(power_set(X0),X1),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_352])]) ).
fof(f773,plain,
( ! [X2,X0,X1] :
( subset(difference(power_set(X0),X1),X2)
| subset(sK5(difference(power_set(X0),X1),X2),X0) )
| ~ spl11_11
| ~ spl11_83 ),
inference(resolution,[],[f707,f197]) ).
fof(f7328,plain,
( spl11_351
| ~ spl11_27
| ~ spl11_81 ),
inference(avatar_split_clause,[],[f701,f643,f275,f7326]) ).
fof(f7326,plain,
( spl11_351
<=> ! [X2,X0,X1] :
( member(sK7(X0,X1),sum(power_set(X2)))
| ~ subset(X1,X2)
| ~ member(X0,sum(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_351])]) ).
fof(f701,plain,
( ! [X2,X0,X1] :
( member(sK7(X0,X1),sum(power_set(X2)))
| ~ subset(X1,X2)
| ~ member(X0,sum(X1)) )
| ~ spl11_27
| ~ spl11_81 ),
inference(resolution,[],[f644,f276]) ).
fof(f7324,plain,
( spl11_350
| ~ spl11_25
| ~ spl11_81 ),
inference(avatar_split_clause,[],[f700,f643,f267,f7322]) ).
fof(f7322,plain,
( spl11_350
<=> ! [X2,X0,X1] :
( member(sK6(X0,X1),sum(power_set(X2)))
| ~ subset(X1,X2)
| member(X0,product(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_350])]) ).
fof(f700,plain,
( ! [X2,X0,X1] :
( member(sK6(X0,X1),sum(power_set(X2)))
| ~ subset(X1,X2)
| member(X0,product(X1)) )
| ~ spl11_25
| ~ spl11_81 ),
inference(resolution,[],[f644,f268]) ).
fof(f7320,plain,
( spl11_349
| ~ spl11_28
| ~ spl11_81 ),
inference(avatar_split_clause,[],[f695,f643,f279,f7318]) ).
fof(f7318,plain,
( spl11_349
<=> ! [X2,X0,X1] :
( member(X0,sum(power_set(X1)))
| ~ subset(sK7(X0,X2),X1)
| ~ member(X0,sum(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_349])]) ).
fof(f695,plain,
( ! [X2,X0,X1] :
( member(X0,sum(power_set(X1)))
| ~ subset(sK7(X0,X2),X1)
| ~ member(X0,sum(X2)) )
| ~ spl11_28
| ~ spl11_81 ),
inference(resolution,[],[f644,f280]) ).
fof(f7316,plain,
( spl11_348
| ~ spl11_67
| ~ spl11_81 ),
inference(avatar_split_clause,[],[f690,f643,f574,f7314]) ).
fof(f7314,plain,
( spl11_348
<=> ! [X0,X3,X2,X1] :
( member(X0,sum(power_set(X1)))
| ~ subset(sum(unordered_pair(X2,X3)),X1)
| ~ member(X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_348])]) ).
fof(f690,plain,
( ! [X2,X3,X0,X1] :
( member(X0,sum(power_set(X1)))
| ~ subset(sum(unordered_pair(X2,X3)),X1)
| ~ member(X0,X3) )
| ~ spl11_67
| ~ spl11_81 ),
inference(resolution,[],[f644,f575]) ).
fof(f7312,plain,
( spl11_347
| ~ spl11_68
| ~ spl11_81 ),
inference(avatar_split_clause,[],[f689,f643,f578,f7310]) ).
fof(f7310,plain,
( spl11_347
<=> ! [X0,X3,X2,X1] :
( member(X0,sum(power_set(X1)))
| ~ subset(sum(unordered_pair(X2,X3)),X1)
| ~ member(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_347])]) ).
fof(f689,plain,
( ! [X2,X3,X0,X1] :
( member(X0,sum(power_set(X1)))
| ~ subset(sum(unordered_pair(X2,X3)),X1)
| ~ member(X0,X2) )
| ~ spl11_68
| ~ spl11_81 ),
inference(resolution,[],[f644,f579]) ).
fof(f7308,plain,
( spl11_346
| ~ spl11_23
| ~ spl11_78 ),
inference(avatar_split_clause,[],[f666,f631,f259,f7306]) ).
fof(f7306,plain,
( spl11_346
<=> ! [X2,X0,X1] :
( sK6(X0,singleton(X1)) = X1
| member(X0,X2)
| ~ subset(product(singleton(X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_346])]) ).
fof(f666,plain,
( ! [X2,X0,X1] :
( sK6(X0,singleton(X1)) = X1
| member(X0,X2)
| ~ subset(product(singleton(X1)),X2) )
| ~ spl11_23
| ~ spl11_78 ),
inference(resolution,[],[f632,f260]) ).
fof(f7304,plain,
( spl11_345
| ~ spl11_23
| ~ spl11_75 ),
inference(avatar_split_clause,[],[f650,f619,f259,f7302]) ).
fof(f7302,plain,
( spl11_345
<=> ! [X0,X3,X2,X1] :
( ~ subset(X0,X1)
| subset(X0,X2)
| member(sK5(X0,X2),X3)
| ~ subset(X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_345])]) ).
fof(f650,plain,
( ! [X2,X3,X0,X1] :
( ~ subset(X0,X1)
| subset(X0,X2)
| member(sK5(X0,X2),X3)
| ~ subset(X1,X3) )
| ~ spl11_23
| ~ spl11_75 ),
inference(resolution,[],[f620,f260]) ).
fof(f7300,plain,
( spl11_344
| ~ spl11_15
| ~ spl11_68 ),
inference(avatar_split_clause,[],[f586,f578,f215,f7298]) ).
fof(f7298,plain,
( spl11_344
<=> ! [X2,X0,X1] :
( ~ member(sK5(X0,sum(unordered_pair(X1,X2))),X1)
| subset(X0,sum(unordered_pair(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_344])]) ).
fof(f586,plain,
( ! [X2,X0,X1] :
( ~ member(sK5(X0,sum(unordered_pair(X1,X2))),X1)
| subset(X0,sum(unordered_pair(X1,X2))) )
| ~ spl11_15
| ~ spl11_68 ),
inference(resolution,[],[f579,f216]) ).
fof(f7296,plain,
( spl11_343
| ~ spl11_15
| ~ spl11_67 ),
inference(avatar_split_clause,[],[f583,f574,f215,f7294]) ).
fof(f7294,plain,
( spl11_343
<=> ! [X2,X0,X1] :
( ~ member(sK5(X0,sum(unordered_pair(X1,X2))),X2)
| subset(X0,sum(unordered_pair(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_343])]) ).
fof(f583,plain,
( ! [X2,X0,X1] :
( ~ member(sK5(X0,sum(unordered_pair(X1,X2))),X2)
| subset(X0,sum(unordered_pair(X1,X2))) )
| ~ spl11_15
| ~ spl11_67 ),
inference(resolution,[],[f575,f216]) ).
fof(f6873,plain,
( spl11_342
| ~ spl11_4
| ~ spl11_262 ),
inference(avatar_split_clause,[],[f4610,f4464,f166,f6870]) ).
fof(f6870,plain,
( spl11_342
<=> sK3 = sK7(sK4,singleton(sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_342])]) ).
fof(f4464,plain,
( spl11_262
<=> ! [X0,X1] :
( sK7(X0,singleton(X1)) = X1
| ~ member(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_262])]) ).
fof(f4610,plain,
( sK3 = sK7(sK4,singleton(sK3))
| ~ spl11_4
| ~ spl11_262 ),
inference(resolution,[],[f4465,f168]) ).
fof(f168,plain,
( member(sK4,sK3)
| ~ spl11_4 ),
inference(avatar_component_clause,[],[f166]) ).
fof(f4465,plain,
( ! [X0,X1] :
( ~ member(X0,X1)
| sK7(X0,singleton(X1)) = X1 )
| ~ spl11_262 ),
inference(avatar_component_clause,[],[f4464]) ).
fof(f6540,plain,
( spl11_341
| ~ spl11_44
| ~ spl11_262 ),
inference(avatar_split_clause,[],[f4609,f4464,f394,f6537]) ).
fof(f6537,plain,
( spl11_341
<=> sK2 = sK7(sK4,singleton(sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_341])]) ).
fof(f394,plain,
( spl11_44
<=> member(sK4,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_44])]) ).
fof(f4609,plain,
( sK2 = sK7(sK4,singleton(sK2))
| ~ spl11_44
| ~ spl11_262 ),
inference(resolution,[],[f4465,f396]) ).
fof(f396,plain,
( member(sK4,sK2)
| ~ spl11_44 ),
inference(avatar_component_clause,[],[f394]) ).
fof(f6182,plain,
( spl11_340
| ~ spl11_145 ),
inference(avatar_split_clause,[],[f2182,f2025,f6180]) ).
fof(f6180,plain,
( spl11_340
<=> ! [X0,X1] :
( member(sK7(X0,union(X1,X1)),X1)
| ~ member(X0,sum(union(X1,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_340])]) ).
fof(f2182,plain,
( ! [X0,X1] :
( member(sK7(X0,union(X1,X1)),X1)
| ~ member(X0,sum(union(X1,X1))) )
| ~ spl11_145 ),
inference(factoring,[],[f2026]) ).
fof(f6178,plain,
( spl11_339
| ~ spl11_6
| ~ spl11_145 ),
inference(avatar_split_clause,[],[f2168,f2025,f176,f6176]) ).
fof(f6176,plain,
( spl11_339
<=> ! [X0,X1] :
( member(sK7(X0,union(empty_set,X1)),X1)
| ~ member(X0,sum(union(empty_set,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_339])]) ).
fof(f2168,plain,
( ! [X0,X1] :
( member(sK7(X0,union(empty_set,X1)),X1)
| ~ member(X0,sum(union(empty_set,X1))) )
| ~ spl11_6
| ~ spl11_145 ),
inference(resolution,[],[f2026,f177]) ).
fof(f6174,plain,
( spl11_338
| ~ spl11_6
| ~ spl11_145 ),
inference(avatar_split_clause,[],[f2143,f2025,f176,f6172]) ).
fof(f6172,plain,
( spl11_338
<=> ! [X0,X1] :
( member(sK7(X0,union(X1,empty_set)),X1)
| ~ member(X0,sum(union(X1,empty_set))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_338])]) ).
fof(f2143,plain,
( ! [X0,X1] :
( member(sK7(X0,union(X1,empty_set)),X1)
| ~ member(X0,sum(union(X1,empty_set))) )
| ~ spl11_6
| ~ spl11_145 ),
inference(resolution,[],[f2026,f177]) ).
fof(f6170,plain,
( spl11_337
| ~ spl11_144 ),
inference(avatar_split_clause,[],[f2131,f2021,f6168]) ).
fof(f6168,plain,
( spl11_337
<=> ! [X0,X1] :
( member(sK6(X0,union(X1,X1)),X1)
| member(X0,product(union(X1,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_337])]) ).
fof(f2131,plain,
( ! [X0,X1] :
( member(sK6(X0,union(X1,X1)),X1)
| member(X0,product(union(X1,X1))) )
| ~ spl11_144 ),
inference(factoring,[],[f2022]) ).
fof(f6156,plain,
( spl11_336
| ~ spl11_6
| ~ spl11_144 ),
inference(avatar_split_clause,[],[f2117,f2021,f176,f6154]) ).
fof(f6154,plain,
( spl11_336
<=> ! [X0,X1] :
( member(sK6(X0,union(empty_set,X1)),X1)
| member(X0,product(union(empty_set,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_336])]) ).
fof(f2117,plain,
( ! [X0,X1] :
( member(sK6(X0,union(empty_set,X1)),X1)
| member(X0,product(union(empty_set,X1))) )
| ~ spl11_6
| ~ spl11_144 ),
inference(resolution,[],[f2022,f177]) ).
fof(f6152,plain,
( spl11_335
| ~ spl11_6
| ~ spl11_144 ),
inference(avatar_split_clause,[],[f2092,f2021,f176,f6150]) ).
fof(f6150,plain,
( spl11_335
<=> ! [X0,X1] :
( member(sK6(X0,union(X1,empty_set)),X1)
| member(X0,product(union(X1,empty_set))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_335])]) ).
fof(f2092,plain,
( ! [X0,X1] :
( member(sK6(X0,union(X1,empty_set)),X1)
| member(X0,product(union(X1,empty_set))) )
| ~ spl11_6
| ~ spl11_144 ),
inference(resolution,[],[f2022,f177]) ).
fof(f6148,plain,
( spl11_334
| ~ spl11_60
| ~ spl11_140 ),
inference(avatar_split_clause,[],[f1986,f1747,f529,f6146]) ).
fof(f6146,plain,
( spl11_334
<=> ! [X2,X0,X1] :
( ~ member(X0,product(X1))
| ~ member(sum(empty_set),X1)
| greatest(X0,X2,product(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_334])]) ).
fof(f1747,plain,
( spl11_140
<=> ! [X0,X3,X2,X1] :
( greatest(X0,X1,product(X2))
| ~ member(X0,product(X2))
| ~ member(X3,X2)
| member(sK8(X1,product(X2),X0),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_140])]) ).
fof(f1986,plain,
( ! [X2,X0,X1] :
( ~ member(X0,product(X1))
| ~ member(sum(empty_set),X1)
| greatest(X0,X2,product(X1)) )
| ~ spl11_60
| ~ spl11_140 ),
inference(resolution,[],[f1748,f530]) ).
fof(f1748,plain,
( ! [X2,X3,X0,X1] :
( member(sK8(X1,product(X2),X0),X3)
| ~ member(X0,product(X2))
| ~ member(X3,X2)
| greatest(X0,X1,product(X2)) )
| ~ spl11_140 ),
inference(avatar_component_clause,[],[f1747]) ).
fof(f6144,plain,
( spl11_333
| ~ spl11_60
| ~ spl11_139 ),
inference(avatar_split_clause,[],[f1961,f1743,f529,f6142]) ).
fof(f6142,plain,
( spl11_333
<=> ! [X2,X0,X1] :
( ~ member(X0,difference(sum(empty_set),X1))
| greatest(X0,X2,difference(sum(empty_set),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_333])]) ).
fof(f1743,plain,
( spl11_139
<=> ! [X0,X3,X2,X1] :
( greatest(X0,X1,difference(X2,X3))
| ~ member(X0,difference(X2,X3))
| member(sK8(X1,difference(X2,X3),X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_139])]) ).
fof(f1961,plain,
( ! [X2,X0,X1] :
( ~ member(X0,difference(sum(empty_set),X1))
| greatest(X0,X2,difference(sum(empty_set),X1)) )
| ~ spl11_60
| ~ spl11_139 ),
inference(resolution,[],[f1744,f530]) ).
fof(f1744,plain,
( ! [X2,X3,X0,X1] :
( member(sK8(X1,difference(X2,X3),X0),X2)
| ~ member(X0,difference(X2,X3))
| greatest(X0,X1,difference(X2,X3)) )
| ~ spl11_139 ),
inference(avatar_component_clause,[],[f1743]) ).
fof(f6140,plain,
( spl11_332
| ~ spl11_59
| ~ spl11_138 ),
inference(avatar_split_clause,[],[f1941,f1739,f525,f6138]) ).
fof(f6138,plain,
( spl11_332
<=> ! [X2,X0,X1] :
( ~ member(X0,difference(X1,product(empty_set)))
| greatest(X0,X2,difference(X1,product(empty_set))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_332])]) ).
fof(f1941,plain,
( ! [X2,X0,X1] :
( ~ member(X0,difference(X1,product(empty_set)))
| greatest(X0,X2,difference(X1,product(empty_set))) )
| ~ spl11_59
| ~ spl11_138 ),
inference(resolution,[],[f1740,f526]) ).
fof(f6136,plain,
( spl11_331
| ~ spl11_60
| ~ spl11_137 ),
inference(avatar_split_clause,[],[f1919,f1735,f529,f6134]) ).
fof(f6134,plain,
( spl11_331
<=> ! [X2,X0,X1] :
( ~ member(X0,intersection(sum(empty_set),X1))
| greatest(X0,X2,intersection(sum(empty_set),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_331])]) ).
fof(f1735,plain,
( spl11_137
<=> ! [X0,X3,X2,X1] :
( greatest(X0,X1,intersection(X2,X3))
| ~ member(X0,intersection(X2,X3))
| member(sK8(X1,intersection(X2,X3),X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_137])]) ).
fof(f1919,plain,
( ! [X2,X0,X1] :
( ~ member(X0,intersection(sum(empty_set),X1))
| greatest(X0,X2,intersection(sum(empty_set),X1)) )
| ~ spl11_60
| ~ spl11_137 ),
inference(resolution,[],[f1736,f530]) ).
fof(f1736,plain,
( ! [X2,X3,X0,X1] :
( member(sK8(X1,intersection(X2,X3),X0),X2)
| ~ member(X0,intersection(X2,X3))
| greatest(X0,X1,intersection(X2,X3)) )
| ~ spl11_137 ),
inference(avatar_component_clause,[],[f1735]) ).
fof(f6132,plain,
( spl11_330
| ~ spl11_60
| ~ spl11_136 ),
inference(avatar_split_clause,[],[f1895,f1731,f529,f6130]) ).
fof(f6130,plain,
( spl11_330
<=> ! [X2,X0,X1] :
( ~ member(X0,intersection(X1,sum(empty_set)))
| greatest(X0,X2,intersection(X1,sum(empty_set))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_330])]) ).
fof(f1731,plain,
( spl11_136
<=> ! [X0,X3,X2,X1] :
( greatest(X0,X1,intersection(X2,X3))
| ~ member(X0,intersection(X2,X3))
| member(sK8(X1,intersection(X2,X3),X0),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_136])]) ).
fof(f1895,plain,
( ! [X2,X0,X1] :
( ~ member(X0,intersection(X1,sum(empty_set)))
| greatest(X0,X2,intersection(X1,sum(empty_set))) )
| ~ spl11_60
| ~ spl11_136 ),
inference(resolution,[],[f1732,f530]) ).
fof(f1732,plain,
( ! [X2,X3,X0,X1] :
( member(sK8(X1,intersection(X2,X3),X0),X3)
| ~ member(X0,intersection(X2,X3))
| greatest(X0,X1,intersection(X2,X3)) )
| ~ spl11_136 ),
inference(avatar_component_clause,[],[f1731]) ).
fof(f6128,plain,
( spl11_329
| ~ spl11_12
| ~ spl11_94 ),
inference(avatar_split_clause,[],[f949,f750,f200,f6126]) ).
fof(f6126,plain,
( spl11_329
<=> ! [X0,X3,X2,X1] :
( member(X0,sum(union(power_set(X1),X2)))
| ~ member(X0,X3)
| ~ subset(X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_329])]) ).
fof(f949,plain,
( ! [X2,X3,X0,X1] :
( member(X0,sum(union(power_set(X1),X2)))
| ~ member(X0,X3)
| ~ subset(X3,X1) )
| ~ spl11_12
| ~ spl11_94 ),
inference(resolution,[],[f751,f201]) ).
fof(f6124,plain,
( spl11_328
| ~ spl11_12
| ~ spl11_93 ),
inference(avatar_split_clause,[],[f918,f746,f200,f6122]) ).
fof(f6122,plain,
( spl11_328
<=> ! [X0,X3,X2,X1] :
( member(X0,sum(union(X1,power_set(X2))))
| ~ member(X0,X3)
| ~ subset(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_328])]) ).
fof(f918,plain,
( ! [X2,X3,X0,X1] :
( member(X0,sum(union(X1,power_set(X2))))
| ~ member(X0,X3)
| ~ subset(X3,X2) )
| ~ spl11_12
| ~ spl11_93 ),
inference(resolution,[],[f747,f201]) ).
fof(f6120,plain,
( spl11_327
| ~ spl11_10
| ~ spl11_90 ),
inference(avatar_split_clause,[],[f909,f734,f192,f6118]) ).
fof(f6118,plain,
( spl11_327
<=> ! [X2,X0,X1] :
( ~ member(X0,sum(X1))
| ~ subset(X1,singleton(X2))
| sK7(X0,X1) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_327])]) ).
fof(f909,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sum(X1))
| ~ subset(X1,singleton(X2))
| sK7(X0,X1) = X2 )
| ~ spl11_10
| ~ spl11_90 ),
inference(resolution,[],[f735,f193]) ).
fof(f6115,plain,
( spl11_326
| ~ spl11_11
| ~ spl11_90 ),
inference(avatar_split_clause,[],[f902,f734,f196,f6113]) ).
fof(f6113,plain,
( spl11_326
<=> ! [X2,X0,X1] :
( ~ member(X0,sum(X1))
| ~ subset(X1,power_set(X2))
| subset(sK7(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_326])]) ).
fof(f902,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sum(X1))
| ~ subset(X1,power_set(X2))
| subset(sK7(X0,X1),X2) )
| ~ spl11_11
| ~ spl11_90 ),
inference(resolution,[],[f735,f197]) ).
fof(f6111,plain,
( spl11_325
| ~ spl11_10
| ~ spl11_89 ),
inference(avatar_split_clause,[],[f893,f730,f192,f6109]) ).
fof(f6109,plain,
( spl11_325
<=> ! [X2,X0,X1] :
( member(X0,product(X1))
| ~ subset(X1,singleton(X2))
| sK6(X0,X1) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_325])]) ).
fof(f893,plain,
( ! [X2,X0,X1] :
( member(X0,product(X1))
| ~ subset(X1,singleton(X2))
| sK6(X0,X1) = X2 )
| ~ spl11_10
| ~ spl11_89 ),
inference(resolution,[],[f731,f193]) ).
fof(f6107,plain,
( spl11_324
| ~ spl11_11
| ~ spl11_89 ),
inference(avatar_split_clause,[],[f886,f730,f196,f6105]) ).
fof(f6105,plain,
( spl11_324
<=> ! [X2,X0,X1] :
( member(X0,product(X1))
| ~ subset(X1,power_set(X2))
| subset(sK6(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_324])]) ).
fof(f886,plain,
( ! [X2,X0,X1] :
( member(X0,product(X1))
| ~ subset(X1,power_set(X2))
| subset(sK6(X0,X1),X2) )
| ~ spl11_11
| ~ spl11_89 ),
inference(resolution,[],[f731,f197]) ).
fof(f6103,plain,
( spl11_323
| ~ spl11_14
| ~ spl11_81 ),
inference(avatar_split_clause,[],[f698,f643,f211,f6101]) ).
fof(f6101,plain,
( spl11_323
<=> ! [X2,X0,X1] :
( member(sK5(X0,X1),sum(power_set(X2)))
| ~ subset(X0,X2)
| subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_323])]) ).
fof(f698,plain,
( ! [X2,X0,X1] :
( member(sK5(X0,X1),sum(power_set(X2)))
| ~ subset(X0,X2)
| subset(X0,X1) )
| ~ spl11_14
| ~ spl11_81 ),
inference(resolution,[],[f644,f212]) ).
fof(f6099,plain,
( spl11_322
| ~ spl11_66
| ~ spl11_81 ),
inference(avatar_split_clause,[],[f688,f643,f565,f6097]) ).
fof(f6097,plain,
( spl11_322
<=> ! [X2,X0,X1] :
( member(X0,sum(power_set(X1)))
| ~ subset(sum(singleton(X2)),X1)
| ~ member(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_322])]) ).
fof(f688,plain,
( ! [X2,X0,X1] :
( member(X0,sum(power_set(X1)))
| ~ subset(sum(singleton(X2)),X1)
| ~ member(X0,X2) )
| ~ spl11_66
| ~ spl11_81 ),
inference(resolution,[],[f644,f566]) ).
fof(f6095,plain,
( spl11_321
| ~ spl11_20
| ~ spl11_81 ),
inference(avatar_split_clause,[],[f683,f643,f235,f6093]) ).
fof(f6093,plain,
( spl11_321
<=> ! [X0,X3,X2,X1] :
( member(X0,sum(power_set(X1)))
| ~ subset(union(X2,X3),X1)
| ~ member(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_321])]) ).
fof(f683,plain,
( ! [X2,X3,X0,X1] :
( member(X0,sum(power_set(X1)))
| ~ subset(union(X2,X3),X1)
| ~ member(X0,X2) )
| ~ spl11_20
| ~ spl11_81 ),
inference(resolution,[],[f644,f236]) ).
fof(f6091,plain,
( spl11_320
| ~ spl11_21
| ~ spl11_81 ),
inference(avatar_split_clause,[],[f682,f643,f239,f6089]) ).
fof(f6089,plain,
( spl11_320
<=> ! [X0,X3,X2,X1] :
( member(X0,sum(power_set(X1)))
| ~ subset(union(X2,X3),X1)
| ~ member(X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_320])]) ).
fof(f682,plain,
( ! [X2,X3,X0,X1] :
( member(X0,sum(power_set(X1)))
| ~ subset(union(X2,X3),X1)
| ~ member(X0,X3) )
| ~ spl11_21
| ~ spl11_81 ),
inference(resolution,[],[f644,f240]) ).
fof(f6087,plain,
( spl11_319
| ~ spl11_32
| ~ spl11_78 ),
inference(avatar_split_clause,[],[f664,f631,f320,f6085]) ).
fof(f6085,plain,
( spl11_319
<=> ! [X2,X0,X1] :
( sK6(X0,singleton(X1)) = X1
| ~ member(X2,singleton(X1))
| member(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_319])]) ).
fof(f664,plain,
( ! [X2,X0,X1] :
( sK6(X0,singleton(X1)) = X1
| ~ member(X2,singleton(X1))
| member(X0,X2) )
| ~ spl11_32
| ~ spl11_78 ),
inference(resolution,[],[f632,f321]) ).
fof(f6083,plain,
( spl11_318
| ~ spl11_16
| ~ spl11_75 ),
inference(avatar_split_clause,[],[f657,f619,f219,f6081]) ).
fof(f6081,plain,
( spl11_318
<=> ! [X0,X3,X2,X1] :
( ~ subset(X0,difference(X1,X2))
| subset(X0,X3)
| member(sK5(X0,X3),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_318])]) ).
fof(f657,plain,
( ! [X2,X3,X0,X1] :
( ~ subset(X0,difference(X1,X2))
| subset(X0,X3)
| member(sK5(X0,X3),X1) )
| ~ spl11_16
| ~ spl11_75 ),
inference(resolution,[],[f620,f220]) ).
fof(f6079,plain,
( spl11_317
| ~ spl11_17
| ~ spl11_75 ),
inference(avatar_split_clause,[],[f656,f619,f223,f6077]) ).
fof(f6077,plain,
( spl11_317
<=> ! [X0,X3,X2,X1] :
( ~ subset(X0,difference(X1,X2))
| subset(X0,X3)
| ~ member(sK5(X0,X3),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_317])]) ).
fof(f656,plain,
( ! [X2,X3,X0,X1] :
( ~ subset(X0,difference(X1,X2))
| subset(X0,X3)
| ~ member(sK5(X0,X3),X2) )
| ~ spl11_17
| ~ spl11_75 ),
inference(resolution,[],[f620,f224]) ).
fof(f6074,plain,
( spl11_316
| ~ spl11_18
| ~ spl11_75 ),
inference(avatar_split_clause,[],[f653,f619,f227,f6072]) ).
fof(f6072,plain,
( spl11_316
<=> ! [X0,X3,X2,X1] :
( ~ subset(X0,intersection(X1,X2))
| subset(X0,X3)
| member(sK5(X0,X3),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_316])]) ).
fof(f653,plain,
( ! [X2,X3,X0,X1] :
( ~ subset(X0,intersection(X1,X2))
| subset(X0,X3)
| member(sK5(X0,X3),X1) )
| ~ spl11_18
| ~ spl11_75 ),
inference(resolution,[],[f620,f228]) ).
fof(f6070,plain,
( spl11_315
| ~ spl11_19
| ~ spl11_75 ),
inference(avatar_split_clause,[],[f652,f619,f231,f6068]) ).
fof(f6068,plain,
( spl11_315
<=> ! [X0,X3,X2,X1] :
( ~ subset(X0,intersection(X1,X2))
| subset(X0,X3)
| member(sK5(X0,X3),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_315])]) ).
fof(f652,plain,
( ! [X2,X3,X0,X1] :
( ~ subset(X0,intersection(X1,X2))
| subset(X0,X3)
| member(sK5(X0,X3),X2) )
| ~ spl11_19
| ~ spl11_75 ),
inference(resolution,[],[f620,f232]) ).
fof(f6066,plain,
( spl11_314
| ~ spl11_33
| ~ spl11_68 ),
inference(avatar_split_clause,[],[f584,f578,f324,f6064]) ).
fof(f6064,plain,
( spl11_314
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,X1)
| ~ member(X2,X0)
| member(X2,sum(sum(unordered_pair(X1,X3)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_314])]) ).
fof(f584,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,X1)
| ~ member(X2,X0)
| member(X2,sum(sum(unordered_pair(X1,X3)))) )
| ~ spl11_33
| ~ spl11_68 ),
inference(resolution,[],[f579,f325]) ).
fof(f6062,plain,
( spl11_313
| ~ spl11_33
| ~ spl11_67 ),
inference(avatar_split_clause,[],[f581,f574,f324,f6060]) ).
fof(f6060,plain,
( spl11_313
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,X1)
| ~ member(X2,X0)
| member(X2,sum(sum(unordered_pair(X3,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_313])]) ).
fof(f581,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,X1)
| ~ member(X2,X0)
| member(X2,sum(sum(unordered_pair(X3,X1)))) )
| ~ spl11_33
| ~ spl11_67 ),
inference(resolution,[],[f575,f325]) ).
fof(f5387,plain,
( spl11_312
| ~ spl11_51
| ~ spl11_157 ),
inference(avatar_split_clause,[],[f2475,f2327,f472,f5385]) ).
fof(f472,plain,
( spl11_51
<=> ! [X0,X3,X2,X1] :
( sP0(X0,X1,X2,X3)
| ~ apply(X1,X0,sK10(X0,X1,X2,X3))
| ~ upper_bound(X0,X1,X2)
| ~ member(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_51])]) ).
fof(f2327,plain,
( spl11_157
<=> ! [X4,X0,X3,X2,X1] :
( sP0(X0,X1,X2,X3)
| ~ upper_bound(X0,X1,X2)
| ~ member(X0,X2)
| ~ member(X4,X2)
| apply(X1,X4,sK10(X0,X1,X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_157])]) ).
fof(f2475,plain,
( ! [X2,X3,X0,X1] :
( ~ upper_bound(X0,X1,X2)
| ~ member(X0,X2)
| sP0(X0,X1,X2,X3) )
| ~ spl11_51
| ~ spl11_157 ),
inference(duplicate_literal_removal,[],[f2470]) ).
fof(f2470,plain,
( ! [X2,X3,X0,X1] :
( ~ upper_bound(X0,X1,X2)
| ~ member(X0,X2)
| ~ member(X0,X2)
| sP0(X0,X1,X2,X3)
| sP0(X0,X1,X2,X3)
| ~ upper_bound(X0,X1,X2)
| ~ member(X0,X2) )
| ~ spl11_51
| ~ spl11_157 ),
inference(resolution,[],[f2328,f473]) ).
fof(f473,plain,
( ! [X2,X3,X0,X1] :
( ~ apply(X1,X0,sK10(X0,X1,X2,X3))
| sP0(X0,X1,X2,X3)
| ~ upper_bound(X0,X1,X2)
| ~ member(X0,X2) )
| ~ spl11_51 ),
inference(avatar_component_clause,[],[f472]) ).
fof(f2328,plain,
( ! [X2,X3,X0,X1,X4] :
( apply(X1,X4,sK10(X0,X1,X2,X3))
| ~ upper_bound(X0,X1,X2)
| ~ member(X0,X2)
| ~ member(X4,X2)
| sP0(X0,X1,X2,X3) )
| ~ spl11_157 ),
inference(avatar_component_clause,[],[f2327]) ).
fof(f5383,plain,
( spl11_311
| ~ spl11_6
| ~ spl11_140 ),
inference(avatar_split_clause,[],[f1981,f1747,f176,f5381]) ).
fof(f5381,plain,
( spl11_311
<=> ! [X2,X0,X1] :
( ~ member(X0,product(X1))
| ~ member(empty_set,X1)
| greatest(X0,X2,product(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_311])]) ).
fof(f1981,plain,
( ! [X2,X0,X1] :
( ~ member(X0,product(X1))
| ~ member(empty_set,X1)
| greatest(X0,X2,product(X1)) )
| ~ spl11_6
| ~ spl11_140 ),
inference(resolution,[],[f1748,f177]) ).
fof(f5379,plain,
( spl11_310
| ~ spl11_15
| ~ spl11_135 ),
inference(avatar_split_clause,[],[f1878,f1727,f215,f5377]) ).
fof(f1878,plain,
( ! [X0,X1] :
( member(sK5(union(X0,X1),X1),X0)
| subset(union(X0,X1),X1) )
| ~ spl11_15
| ~ spl11_135 ),
inference(duplicate_literal_removal,[],[f1810]) ).
fof(f1810,plain,
( ! [X0,X1] :
( member(sK5(union(X0,X1),X1),X0)
| subset(union(X0,X1),X1)
| subset(union(X0,X1),X1) )
| ~ spl11_15
| ~ spl11_135 ),
inference(resolution,[],[f1728,f216]) ).
fof(f5375,plain,
( spl11_309
| ~ spl11_15
| ~ spl11_135 ),
inference(avatar_split_clause,[],[f1873,f1727,f215,f5373]) ).
fof(f1873,plain,
( ! [X0,X1] :
( member(sK5(union(X0,X1),X0),X1)
| subset(union(X0,X1),X0) )
| ~ spl11_15
| ~ spl11_135 ),
inference(duplicate_literal_removal,[],[f1839]) ).
fof(f1839,plain,
( ! [X0,X1] :
( member(sK5(union(X0,X1),X0),X1)
| subset(union(X0,X1),X0)
| subset(union(X0,X1),X0) )
| ~ spl11_15
| ~ spl11_135 ),
inference(resolution,[],[f1728,f216]) ).
fof(f5371,plain,
( spl11_308
| ~ spl11_135 ),
inference(avatar_split_clause,[],[f1868,f1727,f5369]) ).
fof(f1868,plain,
( ! [X0,X1] :
( member(sK5(union(X0,X0),X1),X0)
| subset(union(X0,X0),X1) )
| ~ spl11_135 ),
inference(factoring,[],[f1728]) ).
fof(f5367,plain,
( spl11_307
| ~ spl11_6
| ~ spl11_135 ),
inference(avatar_split_clause,[],[f1855,f1727,f176,f5365]) ).
fof(f1855,plain,
( ! [X0,X1] :
( member(sK5(union(empty_set,X0),X1),X0)
| subset(union(empty_set,X0),X1) )
| ~ spl11_6
| ~ spl11_135 ),
inference(resolution,[],[f1728,f177]) ).
fof(f5363,plain,
( spl11_306
| ~ spl11_6
| ~ spl11_135 ),
inference(avatar_split_clause,[],[f1826,f1727,f176,f5361]) ).
fof(f1826,plain,
( ! [X0,X1] :
( member(sK5(union(X0,empty_set),X1),X0)
| subset(union(X0,empty_set),X1) )
| ~ spl11_6
| ~ spl11_135 ),
inference(resolution,[],[f1728,f177]) ).
fof(f5359,plain,
( spl11_305
| ~ spl11_14
| ~ spl11_133 ),
inference(avatar_split_clause,[],[f1807,f1719,f211,f5357]) ).
fof(f5357,plain,
( spl11_305
<=> ! [X0,X1] :
( ~ member(sK5(X0,intersection(X1,X0)),X1)
| subset(X0,intersection(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_305])]) ).
fof(f1807,plain,
( ! [X0,X1] :
( ~ member(sK5(X0,intersection(X1,X0)),X1)
| subset(X0,intersection(X1,X0)) )
| ~ spl11_14
| ~ spl11_133 ),
inference(duplicate_literal_removal,[],[f1781]) ).
fof(f1781,plain,
( ! [X0,X1] :
( ~ member(sK5(X0,intersection(X1,X0)),X1)
| subset(X0,intersection(X1,X0))
| subset(X0,intersection(X1,X0)) )
| ~ spl11_14
| ~ spl11_133 ),
inference(resolution,[],[f1720,f212]) ).
fof(f5355,plain,
( spl11_304
| ~ spl11_14
| ~ spl11_132 ),
inference(avatar_split_clause,[],[f1776,f1715,f211,f5353]) ).
fof(f5353,plain,
( spl11_304
<=> ! [X0,X1] :
( member(sK5(X0,difference(X0,X1)),X1)
| subset(X0,difference(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_304])]) ).
fof(f1776,plain,
( ! [X0,X1] :
( member(sK5(X0,difference(X0,X1)),X1)
| subset(X0,difference(X0,X1)) )
| ~ spl11_14
| ~ spl11_132 ),
inference(duplicate_literal_removal,[],[f1750]) ).
fof(f1750,plain,
( ! [X0,X1] :
( member(sK5(X0,difference(X0,X1)),X1)
| subset(X0,difference(X0,X1))
| subset(X0,difference(X0,X1)) )
| ~ spl11_14
| ~ spl11_132 ),
inference(resolution,[],[f1716,f212]) ).
fof(f5351,plain,
( spl11_303
| ~ spl11_36
| ~ spl11_98 ),
inference(avatar_split_clause,[],[f998,f766,f336,f5349]) ).
fof(f5349,plain,
( spl11_303
<=> ! [X2,X0,X1] :
( ~ upper_bound(X0,X1,X2)
| ~ member(X0,X2)
| least_upper_bound(X0,X2,X1,empty_set) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_303])]) ).
fof(f766,plain,
( spl11_98
<=> ! [X2,X0,X1] :
( sP0(X0,X1,X2,empty_set)
| ~ upper_bound(X0,X1,X2)
| ~ member(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_98])]) ).
fof(f998,plain,
( ! [X2,X0,X1] :
( ~ upper_bound(X0,X1,X2)
| ~ member(X0,X2)
| least_upper_bound(X0,X2,X1,empty_set) )
| ~ spl11_36
| ~ spl11_98 ),
inference(resolution,[],[f767,f337]) ).
fof(f767,plain,
( ! [X2,X0,X1] :
( sP0(X0,X1,X2,empty_set)
| ~ upper_bound(X0,X1,X2)
| ~ member(X0,X2) )
| ~ spl11_98 ),
inference(avatar_component_clause,[],[f766]) ).
fof(f5347,plain,
( spl11_302
| ~ spl11_12
| ~ spl11_81 ),
inference(avatar_split_clause,[],[f680,f643,f200,f5345]) ).
fof(f5345,plain,
( spl11_302
<=> ! [X2,X0,X1] :
( member(X0,sum(power_set(X1)))
| ~ subset(power_set(X2),X1)
| ~ subset(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_302])]) ).
fof(f680,plain,
( ! [X2,X0,X1] :
( member(X0,sum(power_set(X1)))
| ~ subset(power_set(X2),X1)
| ~ subset(X0,X2) )
| ~ spl11_12
| ~ spl11_81 ),
inference(resolution,[],[f644,f201]) ).
fof(f5343,plain,
( spl11_301
| ~ spl11_10
| ~ spl11_75 ),
inference(avatar_split_clause,[],[f658,f619,f192,f5341]) ).
fof(f5341,plain,
( spl11_301
<=> ! [X2,X0,X1] :
( ~ subset(X0,singleton(X1))
| subset(X0,X2)
| sK5(X0,X2) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_301])]) ).
fof(f658,plain,
( ! [X2,X0,X1] :
( ~ subset(X0,singleton(X1))
| subset(X0,X2)
| sK5(X0,X2) = X1 )
| ~ spl11_10
| ~ spl11_75 ),
inference(resolution,[],[f620,f193]) ).
fof(f5339,plain,
( spl11_300
| ~ spl11_11
| ~ spl11_75 ),
inference(avatar_split_clause,[],[f651,f619,f196,f5337]) ).
fof(f5337,plain,
( spl11_300
<=> ! [X2,X0,X1] :
( ~ subset(X0,power_set(X1))
| subset(X0,X2)
| subset(sK5(X0,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_300])]) ).
fof(f651,plain,
( ! [X2,X0,X1] :
( ~ subset(X0,power_set(X1))
| subset(X0,X2)
| subset(sK5(X0,X2),X1) )
| ~ spl11_11
| ~ spl11_75 ),
inference(resolution,[],[f620,f197]) ).
fof(f5335,plain,
( spl11_299
| ~ spl11_23
| ~ spl11_68 ),
inference(avatar_split_clause,[],[f585,f578,f259,f5333]) ).
fof(f5333,plain,
( spl11_299
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,X1)
| member(X0,X2)
| ~ subset(sum(unordered_pair(X1,X3)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_299])]) ).
fof(f585,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,X1)
| member(X0,X2)
| ~ subset(sum(unordered_pair(X1,X3)),X2) )
| ~ spl11_23
| ~ spl11_68 ),
inference(resolution,[],[f579,f260]) ).
fof(f5331,plain,
( spl11_298
| ~ spl11_23
| ~ spl11_67 ),
inference(avatar_split_clause,[],[f582,f574,f259,f5329]) ).
fof(f5329,plain,
( spl11_298
<=> ! [X2,X0,X1,X3] :
( ~ member(X0,X1)
| member(X0,X2)
| ~ subset(sum(unordered_pair(X3,X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_298])]) ).
fof(f582,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,X1)
| member(X0,X2)
| ~ subset(sum(unordered_pair(X3,X1)),X2) )
| ~ spl11_23
| ~ spl11_67 ),
inference(resolution,[],[f575,f260]) ).
fof(f5327,plain,
( spl11_297
| ~ spl11_15
| ~ spl11_66 ),
inference(avatar_split_clause,[],[f572,f565,f215,f5325]) ).
fof(f5325,plain,
( spl11_297
<=> ! [X0,X1] :
( ~ member(sK5(X0,sum(singleton(X1))),X1)
| subset(X0,sum(singleton(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_297])]) ).
fof(f572,plain,
( ! [X0,X1] :
( ~ member(sK5(X0,sum(singleton(X1))),X1)
| subset(X0,sum(singleton(X1))) )
| ~ spl11_15
| ~ spl11_66 ),
inference(resolution,[],[f566,f216]) ).
fof(f5323,plain,
( spl11_296
| ~ spl11_33
| ~ spl11_66 ),
inference(avatar_split_clause,[],[f570,f565,f324,f5321]) ).
fof(f5321,plain,
( spl11_296
<=> ! [X2,X0,X1] :
( ~ member(X0,X1)
| ~ member(X2,X0)
| member(X2,sum(sum(singleton(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_296])]) ).
fof(f570,plain,
( ! [X2,X0,X1] :
( ~ member(X0,X1)
| ~ member(X2,X0)
| member(X2,sum(sum(singleton(X1)))) )
| ~ spl11_33
| ~ spl11_66 ),
inference(resolution,[],[f566,f325]) ).
fof(f5315,plain,
( spl11_294
| ~ spl11_295
| ~ spl11_55
| ~ spl11_229 ),
inference(avatar_split_clause,[],[f3743,f3595,f489,f5312,f5309]) ).
fof(f5312,plain,
( spl11_295
<=> subset(sK3,empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_295])]) ).
fof(f3743,plain,
( ! [X0] :
( ~ subset(sK3,empty_set)
| ~ member(X0,sK4) )
| ~ spl11_55
| ~ spl11_229 ),
inference(resolution,[],[f3596,f490]) ).
fof(f5114,plain,
( spl11_293
| ~ spl11_138
| ~ spl11_139 ),
inference(avatar_split_clause,[],[f1969,f1743,f1739,f5112]) ).
fof(f5112,plain,
( spl11_293
<=> ! [X2,X0,X1] :
( ~ member(X0,difference(X1,X1))
| greatest(X0,X2,difference(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_293])]) ).
fof(f1969,plain,
( ! [X2,X0,X1] :
( ~ member(X0,difference(X1,X1))
| greatest(X0,X2,difference(X1,X1)) )
| ~ spl11_138
| ~ spl11_139 ),
inference(duplicate_literal_removal,[],[f1944]) ).
fof(f1944,plain,
( ! [X2,X0,X1] :
( ~ member(X0,difference(X1,X1))
| greatest(X0,X2,difference(X1,X1))
| ~ member(X0,difference(X1,X1))
| greatest(X0,X2,difference(X1,X1)) )
| ~ spl11_138
| ~ spl11_139 ),
inference(resolution,[],[f1744,f1740]) ).
fof(f5110,plain,
( spl11_292
| ~ spl11_6
| ~ spl11_139 ),
inference(avatar_split_clause,[],[f1956,f1743,f176,f5108]) ).
fof(f5108,plain,
( spl11_292
<=> ! [X2,X0,X1] :
( ~ member(X0,difference(empty_set,X1))
| greatest(X0,X2,difference(empty_set,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_292])]) ).
fof(f1956,plain,
( ! [X2,X0,X1] :
( ~ member(X0,difference(empty_set,X1))
| greatest(X0,X2,difference(empty_set,X1)) )
| ~ spl11_6
| ~ spl11_139 ),
inference(resolution,[],[f1744,f177]) ).
fof(f5106,plain,
( spl11_291
| ~ spl11_6
| ~ spl11_137 ),
inference(avatar_split_clause,[],[f1914,f1735,f176,f5104]) ).
fof(f5104,plain,
( spl11_291
<=> ! [X2,X0,X1] :
( ~ member(X0,intersection(empty_set,X1))
| greatest(X0,X2,intersection(empty_set,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_291])]) ).
fof(f1914,plain,
( ! [X2,X0,X1] :
( ~ member(X0,intersection(empty_set,X1))
| greatest(X0,X2,intersection(empty_set,X1)) )
| ~ spl11_6
| ~ spl11_137 ),
inference(resolution,[],[f1736,f177]) ).
fof(f5102,plain,
( spl11_290
| ~ spl11_6
| ~ spl11_136 ),
inference(avatar_split_clause,[],[f1890,f1731,f176,f5100]) ).
fof(f5100,plain,
( spl11_290
<=> ! [X2,X0,X1] :
( ~ member(X0,intersection(X1,empty_set))
| greatest(X0,X2,intersection(X1,empty_set)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_290])]) ).
fof(f1890,plain,
( ! [X2,X0,X1] :
( ~ member(X0,intersection(X1,empty_set))
| greatest(X0,X2,intersection(X1,empty_set)) )
| ~ spl11_6
| ~ spl11_136 ),
inference(resolution,[],[f1732,f177]) ).
fof(f5098,plain,
( spl11_289
| ~ spl11_60
| ~ spl11_127 ),
inference(avatar_split_clause,[],[f1669,f1642,f529,f5096]) ).
fof(f5096,plain,
( spl11_289
<=> ! [X2,X0,X1] :
( ~ member(X0,X1)
| greatest(X0,X2,X1)
| ~ subset(X1,sum(empty_set)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_289])]) ).
fof(f1669,plain,
( ! [X2,X0,X1] :
( ~ member(X0,X1)
| greatest(X0,X2,X1)
| ~ subset(X1,sum(empty_set)) )
| ~ spl11_60
| ~ spl11_127 ),
inference(resolution,[],[f1643,f530]) ).
fof(f5094,plain,
( spl11_288
| ~ spl11_112
| ~ spl11_120 ),
inference(avatar_split_clause,[],[f1471,f1324,f1055,f5092]) ).
fof(f5092,plain,
( spl11_288
<=> ! [X0,X3,X2,X1] :
( upper_bound(X0,X1,difference(X2,X3))
| ~ subset(difference(X2,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_288])]) ).
fof(f1471,plain,
( ! [X2,X3,X0,X1] :
( upper_bound(X0,X1,difference(X2,X3))
| ~ subset(difference(X2,X3),X3) )
| ~ spl11_112
| ~ spl11_120 ),
inference(duplicate_literal_removal,[],[f1456]) ).
fof(f1456,plain,
( ! [X2,X3,X0,X1] :
( upper_bound(X0,X1,difference(X2,X3))
| upper_bound(X0,X1,difference(X2,X3))
| ~ subset(difference(X2,X3),X3) )
| ~ spl11_112
| ~ spl11_120 ),
inference(resolution,[],[f1325,f1056]) ).
fof(f5090,plain,
( spl11_287
| ~ spl11_90
| ~ spl11_106 ),
inference(avatar_split_clause,[],[f1181,f1026,f734,f5088]) ).
fof(f5088,plain,
( spl11_287
<=> ! [X2,X0,X1] :
( ~ member(X0,sum(difference(X1,X2)))
| ~ subset(difference(X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_287])]) ).
fof(f1181,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sum(difference(X1,X2)))
| ~ subset(difference(X1,X2),X2) )
| ~ spl11_90
| ~ spl11_106 ),
inference(duplicate_literal_removal,[],[f1168]) ).
fof(f1168,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sum(difference(X1,X2)))
| ~ member(X0,sum(difference(X1,X2)))
| ~ subset(difference(X1,X2),X2) )
| ~ spl11_90
| ~ spl11_106 ),
inference(resolution,[],[f1027,f735]) ).
fof(f5086,plain,
( spl11_286
| ~ spl11_89
| ~ spl11_102 ),
inference(avatar_split_clause,[],[f1107,f1010,f730,f5084]) ).
fof(f5084,plain,
( spl11_286
<=> ! [X2,X0,X1] :
( member(X0,product(difference(X1,X2)))
| ~ subset(difference(X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_286])]) ).
fof(f1107,plain,
( ! [X2,X0,X1] :
( member(X0,product(difference(X1,X2)))
| ~ subset(difference(X1,X2),X2) )
| ~ spl11_89
| ~ spl11_102 ),
inference(duplicate_literal_removal,[],[f1094]) ).
fof(f1094,plain,
( ! [X2,X0,X1] :
( member(X0,product(difference(X1,X2)))
| member(X0,product(difference(X1,X2)))
| ~ subset(difference(X1,X2),X2) )
| ~ spl11_89
| ~ spl11_102 ),
inference(resolution,[],[f1011,f731]) ).
fof(f5082,plain,
( spl11_285
| ~ spl11_9
| ~ spl11_94 ),
inference(avatar_split_clause,[],[f956,f750,f188,f5080]) ).
fof(f5080,plain,
( spl11_285
<=> ! [X0,X3,X2,X1] :
( member(X0,sum(union(unordered_pair(X1,X2),X3)))
| ~ member(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_285])]) ).
fof(f956,plain,
( ! [X2,X3,X0,X1] :
( member(X0,sum(union(unordered_pair(X1,X2),X3)))
| ~ member(X0,X1) )
| ~ spl11_9
| ~ spl11_94 ),
inference(resolution,[],[f751,f189]) ).
fof(f5076,plain,
( spl11_284
| ~ spl11_8
| ~ spl11_94 ),
inference(avatar_split_clause,[],[f955,f750,f184,f5074]) ).
fof(f5074,plain,
( spl11_284
<=> ! [X0,X3,X2,X1] :
( member(X0,sum(union(unordered_pair(X1,X2),X3)))
| ~ member(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_284])]) ).
fof(f955,plain,
( ! [X2,X3,X0,X1] :
( member(X0,sum(union(unordered_pair(X1,X2),X3)))
| ~ member(X0,X2) )
| ~ spl11_8
| ~ spl11_94 ),
inference(resolution,[],[f751,f185]) ).
fof(f5072,plain,
( spl11_283
| ~ spl11_9
| ~ spl11_93 ),
inference(avatar_split_clause,[],[f925,f746,f188,f5070]) ).
fof(f5070,plain,
( spl11_283
<=> ! [X0,X3,X2,X1] :
( member(X0,sum(union(X1,unordered_pair(X2,X3))))
| ~ member(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_283])]) ).
fof(f925,plain,
( ! [X2,X3,X0,X1] :
( member(X0,sum(union(X1,unordered_pair(X2,X3))))
| ~ member(X0,X2) )
| ~ spl11_9
| ~ spl11_93 ),
inference(resolution,[],[f747,f189]) ).
fof(f5068,plain,
( spl11_282
| ~ spl11_8
| ~ spl11_93 ),
inference(avatar_split_clause,[],[f924,f746,f184,f5066]) ).
fof(f5066,plain,
( spl11_282
<=> ! [X0,X3,X2,X1] :
( member(X0,sum(union(X1,unordered_pair(X2,X3))))
| ~ member(X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_282])]) ).
fof(f924,plain,
( ! [X2,X3,X0,X1] :
( member(X0,sum(union(X1,unordered_pair(X2,X3))))
| ~ member(X0,X3) )
| ~ spl11_8
| ~ spl11_93 ),
inference(resolution,[],[f747,f185]) ).
fof(f5064,plain,
( spl11_281
| ~ spl11_23
| ~ spl11_66 ),
inference(avatar_split_clause,[],[f571,f565,f259,f5062]) ).
fof(f5062,plain,
( spl11_281
<=> ! [X2,X0,X1] :
( ~ member(X0,X1)
| member(X0,X2)
| ~ subset(sum(singleton(X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_281])]) ).
fof(f571,plain,
( ! [X2,X0,X1] :
( ~ member(X0,X1)
| member(X0,X2)
| ~ subset(sum(singleton(X1)),X2) )
| ~ spl11_23
| ~ spl11_66 ),
inference(resolution,[],[f566,f260]) ).
fof(f4819,plain,
( spl11_280
| ~ spl11_14
| ~ spl11_171 ),
inference(avatar_split_clause,[],[f2851,f2813,f211,f4817]) ).
fof(f4817,plain,
( spl11_280
<=> ! [X0] : subset(sK4,union(X0,sum(sK3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_280])]) ).
fof(f2813,plain,
( spl11_171
<=> ! [X0,X1] :
( subset(X0,union(X1,sum(sK3)))
| ~ member(sK5(X0,union(X1,sum(sK3))),sK4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_171])]) ).
fof(f2851,plain,
( ! [X0] : subset(sK4,union(X0,sum(sK3)))
| ~ spl11_14
| ~ spl11_171 ),
inference(duplicate_literal_removal,[],[f2836]) ).
fof(f2836,plain,
( ! [X0] :
( subset(sK4,union(X0,sum(sK3)))
| subset(sK4,union(X0,sum(sK3))) )
| ~ spl11_14
| ~ spl11_171 ),
inference(resolution,[],[f2814,f212]) ).
fof(f2814,plain,
( ! [X0,X1] :
( ~ member(sK5(X0,union(X1,sum(sK3))),sK4)
| subset(X0,union(X1,sum(sK3))) )
| ~ spl11_171 ),
inference(avatar_component_clause,[],[f2813]) ).
fof(f4797,plain,
( spl11_279
| ~ spl11_6
| ~ spl11_127 ),
inference(avatar_split_clause,[],[f1664,f1642,f176,f4795]) ).
fof(f4795,plain,
( spl11_279
<=> ! [X2,X0,X1] :
( ~ member(X0,X1)
| greatest(X0,X2,X1)
| ~ subset(X1,empty_set) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_279])]) ).
fof(f1664,plain,
( ! [X2,X0,X1] :
( ~ member(X0,X1)
| greatest(X0,X2,X1)
| ~ subset(X1,empty_set) )
| ~ spl11_6
| ~ spl11_127 ),
inference(resolution,[],[f1643,f177]) ).
fof(f4793,plain,
( spl11_278
| ~ spl11_59
| ~ spl11_94 ),
inference(avatar_split_clause,[],[f962,f750,f525,f4791]) ).
fof(f4791,plain,
( spl11_278
<=> ! [X2,X0,X1] :
( member(X0,sum(union(product(empty_set),X1)))
| ~ member(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_278])]) ).
fof(f962,plain,
( ! [X2,X0,X1] :
( member(X0,sum(union(product(empty_set),X1)))
| ~ member(X0,X2) )
| ~ spl11_59
| ~ spl11_94 ),
inference(resolution,[],[f751,f526]) ).
fof(f4789,plain,
( spl11_277
| ~ spl11_7
| ~ spl11_94 ),
inference(avatar_split_clause,[],[f954,f750,f180,f4787]) ).
fof(f4787,plain,
( spl11_277
<=> ! [X2,X0,X1] :
( member(X0,sum(union(singleton(X1),X2)))
| ~ member(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_277])]) ).
fof(f954,plain,
( ! [X2,X0,X1] :
( member(X0,sum(union(singleton(X1),X2)))
| ~ member(X0,X1) )
| ~ spl11_7
| ~ spl11_94 ),
inference(resolution,[],[f751,f181]) ).
fof(f4785,plain,
( spl11_276
| ~ spl11_59
| ~ spl11_93 ),
inference(avatar_split_clause,[],[f931,f746,f525,f4783]) ).
fof(f4783,plain,
( spl11_276
<=> ! [X2,X0,X1] :
( member(X0,sum(union(X1,product(empty_set))))
| ~ member(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_276])]) ).
fof(f931,plain,
( ! [X2,X0,X1] :
( member(X0,sum(union(X1,product(empty_set))))
| ~ member(X0,X2) )
| ~ spl11_59
| ~ spl11_93 ),
inference(resolution,[],[f747,f526]) ).
fof(f4781,plain,
( spl11_275
| ~ spl11_7
| ~ spl11_93 ),
inference(avatar_split_clause,[],[f923,f746,f180,f4779]) ).
fof(f4779,plain,
( spl11_275
<=> ! [X2,X0,X1] :
( member(X0,sum(union(X1,singleton(X2))))
| ~ member(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_275])]) ).
fof(f923,plain,
( ! [X2,X0,X1] :
( member(X0,sum(union(X1,singleton(X2))))
| ~ member(X0,X2) )
| ~ spl11_7
| ~ spl11_93 ),
inference(resolution,[],[f747,f181]) ).
fof(f4777,plain,
( spl11_274
| ~ spl11_75
| ~ spl11_84 ),
inference(avatar_split_clause,[],[f800,f710,f619,f4775]) ).
fof(f4775,plain,
( spl11_274
<=> ! [X2,X0,X1] :
( subset(difference(X0,X1),X2)
| ~ subset(difference(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_274])]) ).
fof(f800,plain,
( ! [X2,X0,X1] :
( subset(difference(X0,X1),X2)
| ~ subset(difference(X0,X1),X1) )
| ~ spl11_75
| ~ spl11_84 ),
inference(duplicate_literal_removal,[],[f787]) ).
fof(f787,plain,
( ! [X2,X0,X1] :
( subset(difference(X0,X1),X2)
| ~ subset(difference(X0,X1),X1)
| subset(difference(X0,X1),X2) )
| ~ spl11_75
| ~ spl11_84 ),
inference(resolution,[],[f711,f620]) ).
fof(f4773,plain,
( spl11_273
| ~ spl11_9
| ~ spl11_81 ),
inference(avatar_split_clause,[],[f687,f643,f188,f4771]) ).
fof(f4771,plain,
( spl11_273
<=> ! [X2,X0,X1] :
( member(X0,sum(power_set(X1)))
| ~ subset(unordered_pair(X0,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_273])]) ).
fof(f687,plain,
( ! [X2,X0,X1] :
( member(X0,sum(power_set(X1)))
| ~ subset(unordered_pair(X0,X2),X1) )
| ~ spl11_9
| ~ spl11_81 ),
inference(resolution,[],[f644,f189]) ).
fof(f4769,plain,
( spl11_272
| ~ spl11_8
| ~ spl11_81 ),
inference(avatar_split_clause,[],[f686,f643,f184,f4767]) ).
fof(f4767,plain,
( spl11_272
<=> ! [X2,X0,X1] :
( member(X0,sum(power_set(X1)))
| ~ subset(unordered_pair(X2,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_272])]) ).
fof(f686,plain,
( ! [X2,X0,X1] :
( member(X0,sum(power_set(X1)))
| ~ subset(unordered_pair(X2,X0),X1) )
| ~ spl11_8
| ~ spl11_81 ),
inference(resolution,[],[f644,f185]) ).
fof(f4765,plain,
( spl11_271
| ~ spl11_14
| ~ spl11_169 ),
inference(avatar_split_clause,[],[f2835,f2804,f211,f4763]) ).
fof(f4763,plain,
( spl11_271
<=> ! [X0] : subset(sK4,union(sum(sK3),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_271])]) ).
fof(f2804,plain,
( spl11_169
<=> ! [X0,X1] :
( subset(X0,union(sum(sK3),X1))
| ~ member(sK5(X0,union(sum(sK3),X1)),sK4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_169])]) ).
fof(f2835,plain,
( ! [X0] : subset(sK4,union(sum(sK3),X0))
| ~ spl11_14
| ~ spl11_169 ),
inference(duplicate_literal_removal,[],[f2820]) ).
fof(f2820,plain,
( ! [X0] :
( subset(sK4,union(sum(sK3),X0))
| subset(sK4,union(sum(sK3),X0)) )
| ~ spl11_14
| ~ spl11_169 ),
inference(resolution,[],[f2805,f212]) ).
fof(f2805,plain,
( ! [X0,X1] :
( ~ member(sK5(X0,union(sum(sK3),X1)),sK4)
| subset(X0,union(sum(sK3),X1)) )
| ~ spl11_169 ),
inference(avatar_component_clause,[],[f2804]) ).
fof(f4498,plain,
( spl11_270
| ~ spl11_60
| ~ spl11_124 ),
inference(avatar_split_clause,[],[f1523,f1498,f529,f4496]) ).
fof(f4496,plain,
( spl11_270
<=> ! [X2,X0,X1] :
( ~ member(sum(empty_set),X0)
| upper_bound(X1,X2,product(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_270])]) ).
fof(f1523,plain,
( ! [X2,X0,X1] :
( ~ member(sum(empty_set),X0)
| upper_bound(X1,X2,product(X0)) )
| ~ spl11_60
| ~ spl11_124 ),
inference(resolution,[],[f1499,f530]) ).
fof(f4494,plain,
( spl11_269
| ~ spl11_83
| ~ spl11_168 ),
inference(avatar_split_clause,[],[f2819,f2800,f706,f4492]) ).
fof(f4492,plain,
( spl11_269
<=> ! [X0] : subset(difference(sK4,sum(sK3)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_269])]) ).
fof(f2800,plain,
( spl11_168
<=> ! [X0,X1] :
( subset(difference(X0,sum(sK3)),X1)
| ~ member(sK5(difference(X0,sum(sK3)),X1),sK4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_168])]) ).
fof(f2819,plain,
( ! [X0] : subset(difference(sK4,sum(sK3)),X0)
| ~ spl11_83
| ~ spl11_168 ),
inference(duplicate_literal_removal,[],[f2816]) ).
fof(f2816,plain,
( ! [X0] :
( subset(difference(sK4,sum(sK3)),X0)
| subset(difference(sK4,sum(sK3)),X0) )
| ~ spl11_83
| ~ spl11_168 ),
inference(resolution,[],[f2801,f707]) ).
fof(f2801,plain,
( ! [X0,X1] :
( ~ member(sK5(difference(X0,sum(sK3)),X1),sK4)
| subset(difference(X0,sum(sK3)),X1) )
| ~ spl11_168 ),
inference(avatar_component_clause,[],[f2800]) ).
fof(f4490,plain,
( spl11_268
| ~ spl11_60
| ~ spl11_115 ),
inference(avatar_split_clause,[],[f1374,f1304,f529,f4488]) ).
fof(f4488,plain,
( spl11_268
<=> ! [X0,X1] :
( ~ member(sum(empty_set),X0)
| ~ member(X1,sum(product(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_268])]) ).
fof(f1374,plain,
( ! [X0,X1] :
( ~ member(sum(empty_set),X0)
| ~ member(X1,sum(product(X0))) )
| ~ spl11_60
| ~ spl11_115 ),
inference(resolution,[],[f1305,f530]) ).
fof(f4486,plain,
( spl11_267
| ~ spl11_60
| ~ spl11_114 ),
inference(avatar_split_clause,[],[f1353,f1300,f529,f4484]) ).
fof(f4484,plain,
( spl11_267
<=> ! [X0,X1] :
( ~ member(sum(empty_set),X0)
| member(X1,product(product(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_267])]) ).
fof(f1353,plain,
( ! [X0,X1] :
( ~ member(sum(empty_set),X0)
| member(X1,product(product(X0))) )
| ~ spl11_60
| ~ spl11_114 ),
inference(resolution,[],[f1301,f530]) ).
fof(f4482,plain,
( spl11_266
| ~ spl11_87
| ~ spl11_108 ),
inference(avatar_split_clause,[],[f1225,f1039,f722,f4480]) ).
fof(f4480,plain,
( spl11_266
<=> ! [X2,X0,X1] :
( ~ member(X0,X1)
| subset(product(X1),union(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_266])]) ).
fof(f1225,plain,
( ! [X2,X0,X1] :
( ~ member(X0,X1)
| subset(product(X1),union(X0,X2)) )
| ~ spl11_87
| ~ spl11_108 ),
inference(duplicate_literal_removal,[],[f1203]) ).
fof(f1203,plain,
( ! [X2,X0,X1] :
( ~ member(X0,X1)
| subset(product(X1),union(X0,X2))
| subset(product(X1),union(X0,X2)) )
| ~ spl11_87
| ~ spl11_108 ),
inference(resolution,[],[f1040,f723]) ).
fof(f4478,plain,
( spl11_265
| ~ spl11_88
| ~ spl11_108 ),
inference(avatar_split_clause,[],[f1224,f1039,f726,f4476]) ).
fof(f4476,plain,
( spl11_265
<=> ! [X2,X0,X1] :
( ~ member(X0,X1)
| subset(product(X1),union(X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_265])]) ).
fof(f1224,plain,
( ! [X2,X0,X1] :
( ~ member(X0,X1)
| subset(product(X1),union(X2,X0)) )
| ~ spl11_88
| ~ spl11_108 ),
inference(duplicate_literal_removal,[],[f1204]) ).
fof(f1204,plain,
( ! [X2,X0,X1] :
( ~ member(X0,X1)
| subset(product(X1),union(X2,X0))
| subset(product(X1),union(X2,X0)) )
| ~ spl11_88
| ~ spl11_108 ),
inference(resolution,[],[f1040,f727]) ).
fof(f4474,plain,
( spl11_264
| ~ spl11_59
| ~ spl11_81 ),
inference(avatar_split_clause,[],[f693,f643,f525,f4472]) ).
fof(f4472,plain,
( spl11_264
<=> ! [X0,X1] :
( member(X0,sum(power_set(X1)))
| ~ subset(product(empty_set),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_264])]) ).
fof(f693,plain,
( ! [X0,X1] :
( member(X0,sum(power_set(X1)))
| ~ subset(product(empty_set),X1) )
| ~ spl11_59
| ~ spl11_81 ),
inference(resolution,[],[f644,f526]) ).
fof(f4470,plain,
( spl11_263
| ~ spl11_7
| ~ spl11_81 ),
inference(avatar_split_clause,[],[f685,f643,f180,f4468]) ).
fof(f4468,plain,
( spl11_263
<=> ! [X0,X1] :
( member(X0,sum(power_set(X1)))
| ~ subset(singleton(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_263])]) ).
fof(f685,plain,
( ! [X0,X1] :
( member(X0,sum(power_set(X1)))
| ~ subset(singleton(X0),X1) )
| ~ spl11_7
| ~ spl11_81 ),
inference(resolution,[],[f644,f181]) ).
fof(f4466,plain,
( spl11_262
| ~ spl11_66
| ~ spl11_80 ),
inference(avatar_split_clause,[],[f672,f639,f565,f4464]) ).
fof(f672,plain,
( ! [X0,X1] :
( sK7(X0,singleton(X1)) = X1
| ~ member(X0,X1) )
| ~ spl11_66
| ~ spl11_80 ),
inference(resolution,[],[f640,f566]) ).
fof(f4462,plain,
( spl11_261
| ~ spl11_62
| ~ spl11_69 ),
inference(avatar_split_clause,[],[f606,f588,f548,f4460]) ).
fof(f4460,plain,
( spl11_261
<=> ! [X0,X1] :
( sK5(singleton(X0),X1) = X0
| member(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_261])]) ).
fof(f548,plain,
( spl11_62
<=> ! [X0,X1] :
( member(X0,X1)
| ~ subset(singleton(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_62])]) ).
fof(f588,plain,
( spl11_69
<=> ! [X0,X1] :
( subset(singleton(X0),X1)
| sK5(singleton(X0),X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_69])]) ).
fof(f606,plain,
( ! [X0,X1] :
( sK5(singleton(X0),X1) = X0
| member(X0,X1) )
| ~ spl11_62
| ~ spl11_69 ),
inference(resolution,[],[f589,f549]) ).
fof(f549,plain,
( ! [X0,X1] :
( ~ subset(singleton(X0),X1)
| member(X0,X1) )
| ~ spl11_62 ),
inference(avatar_component_clause,[],[f548]) ).
fof(f589,plain,
( ! [X0,X1] :
( subset(singleton(X0),X1)
| sK5(singleton(X0),X1) = X0 )
| ~ spl11_69 ),
inference(avatar_component_clause,[],[f588]) ).
fof(f4417,plain,
( spl11_260
| ~ spl11_118
| ~ spl11_155 ),
inference(avatar_split_clause,[],[f2567,f2319,f1316,f4415]) ).
fof(f4415,plain,
( spl11_260
<=> ! [X0] : upper_bound(sK4,sK1,intersection(X0,sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_260])]) ).
fof(f2567,plain,
( ! [X0] : upper_bound(sK4,sK1,intersection(X0,sK3))
| ~ spl11_118
| ~ spl11_155 ),
inference(duplicate_literal_removal,[],[f2556]) ).
fof(f2556,plain,
( ! [X0] :
( upper_bound(sK4,sK1,intersection(X0,sK3))
| upper_bound(sK4,sK1,intersection(X0,sK3)) )
| ~ spl11_118
| ~ spl11_155 ),
inference(resolution,[],[f2320,f1317]) ).
fof(f4099,plain,
( spl11_259
| ~ spl11_6
| ~ spl11_124 ),
inference(avatar_split_clause,[],[f1518,f1498,f176,f4097]) ).
fof(f4097,plain,
( spl11_259
<=> ! [X2,X0,X1] :
( ~ member(empty_set,X0)
| upper_bound(X1,X2,product(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_259])]) ).
fof(f1518,plain,
( ! [X2,X0,X1] :
( ~ member(empty_set,X0)
| upper_bound(X1,X2,product(X0)) )
| ~ spl11_6
| ~ spl11_124 ),
inference(resolution,[],[f1499,f177]) ).
fof(f4095,plain,
( spl11_258
| ~ spl11_119
| ~ spl11_155 ),
inference(avatar_split_clause,[],[f2566,f2319,f1320,f4093]) ).
fof(f4093,plain,
( spl11_258
<=> ! [X0] : upper_bound(sK4,sK1,intersection(sK3,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_258])]) ).
fof(f2566,plain,
( ! [X0] : upper_bound(sK4,sK1,intersection(sK3,X0))
| ~ spl11_119
| ~ spl11_155 ),
inference(duplicate_literal_removal,[],[f2557]) ).
fof(f2557,plain,
( ! [X0] :
( upper_bound(sK4,sK1,intersection(sK3,X0))
| upper_bound(sK4,sK1,intersection(sK3,X0)) )
| ~ spl11_119
| ~ spl11_155 ),
inference(resolution,[],[f2320,f1321]) ).
fof(f4091,plain,
( spl11_257
| ~ spl11_6
| ~ spl11_115 ),
inference(avatar_split_clause,[],[f1369,f1304,f176,f4089]) ).
fof(f4089,plain,
( spl11_257
<=> ! [X0,X1] :
( ~ member(empty_set,X0)
| ~ member(X1,sum(product(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_257])]) ).
fof(f1369,plain,
( ! [X0,X1] :
( ~ member(empty_set,X0)
| ~ member(X1,sum(product(X0))) )
| ~ spl11_6
| ~ spl11_115 ),
inference(resolution,[],[f1305,f177]) ).
fof(f4087,plain,
( spl11_256
| ~ spl11_6
| ~ spl11_114 ),
inference(avatar_split_clause,[],[f1348,f1300,f176,f4085]) ).
fof(f4085,plain,
( spl11_256
<=> ! [X0,X1] :
( ~ member(empty_set,X0)
| member(X1,product(product(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_256])]) ).
fof(f1348,plain,
( ! [X0,X1] :
( ~ member(empty_set,X0)
| member(X1,product(product(X0))) )
| ~ spl11_6
| ~ spl11_114 ),
inference(resolution,[],[f1301,f177]) ).
fof(f4083,plain,
( spl11_255
| ~ spl11_60
| ~ spl11_112 ),
inference(avatar_split_clause,[],[f1292,f1055,f529,f4081]) ).
fof(f4081,plain,
( spl11_255
<=> ! [X2,X0,X1] :
( upper_bound(X0,X1,X2)
| ~ subset(X2,sum(empty_set)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_255])]) ).
fof(f1292,plain,
( ! [X2,X0,X1] :
( upper_bound(X0,X1,X2)
| ~ subset(X2,sum(empty_set)) )
| ~ spl11_60
| ~ spl11_112 ),
inference(resolution,[],[f1056,f530]) ).
fof(f4079,plain,
( spl11_254
| ~ spl11_60
| ~ spl11_108 ),
inference(avatar_split_clause,[],[f1219,f1039,f529,f4077]) ).
fof(f4077,plain,
( spl11_254
<=> ! [X0,X1] :
( ~ member(sum(empty_set),X0)
| subset(product(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_254])]) ).
fof(f1219,plain,
( ! [X0,X1] :
( ~ member(sum(empty_set),X0)
| subset(product(X0),X1) )
| ~ spl11_60
| ~ spl11_108 ),
inference(resolution,[],[f1040,f530]) ).
fof(f4075,plain,
( spl11_253
| ~ spl11_79
| ~ spl11_92 ),
inference(avatar_split_clause,[],[f917,f742,f635,f4073]) ).
fof(f4073,plain,
( spl11_253
<=> ! [X0,X1] :
( member(X0,X1)
| ~ member(X0,sum(power_set(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_253])]) ).
fof(f635,plain,
( spl11_79
<=> ! [X0,X1] :
( ~ member(X0,sum(power_set(X1)))
| subset(sK7(X0,power_set(X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_79])]) ).
fof(f742,plain,
( spl11_92
<=> ! [X2,X0,X1] :
( ~ member(X0,sum(X1))
| member(X0,X2)
| ~ subset(sK7(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_92])]) ).
fof(f917,plain,
( ! [X0,X1] :
( member(X0,X1)
| ~ member(X0,sum(power_set(X1))) )
| ~ spl11_79
| ~ spl11_92 ),
inference(duplicate_literal_removal,[],[f915]) ).
fof(f915,plain,
( ! [X0,X1] :
( member(X0,X1)
| ~ member(X0,sum(power_set(X1)))
| ~ member(X0,sum(power_set(X1))) )
| ~ spl11_79
| ~ spl11_92 ),
inference(resolution,[],[f743,f636]) ).
fof(f636,plain,
( ! [X0,X1] :
( subset(sK7(X0,power_set(X1)),X1)
| ~ member(X0,sum(power_set(X1))) )
| ~ spl11_79 ),
inference(avatar_component_clause,[],[f635]) ).
fof(f743,plain,
( ! [X2,X0,X1] :
( ~ subset(sK7(X0,X1),X2)
| member(X0,X2)
| ~ member(X0,sum(X1)) )
| ~ spl11_92 ),
inference(avatar_component_clause,[],[f742]) ).
fof(f4071,plain,
( spl11_252
| ~ spl11_60
| ~ spl11_90 ),
inference(avatar_split_clause,[],[f911,f734,f529,f4069]) ).
fof(f911,plain,
( ! [X0,X1] :
( ~ member(X0,sum(X1))
| ~ subset(X1,sum(empty_set)) )
| ~ spl11_60
| ~ spl11_90 ),
inference(resolution,[],[f735,f530]) ).
fof(f4067,plain,
( spl11_251
| ~ spl11_60
| ~ spl11_89 ),
inference(avatar_split_clause,[],[f895,f730,f529,f4065]) ).
fof(f4065,plain,
( spl11_251
<=> ! [X0,X1] :
( member(X0,product(X1))
| ~ subset(X1,sum(empty_set)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_251])]) ).
fof(f895,plain,
( ! [X0,X1] :
( member(X0,product(X1))
| ~ subset(X1,sum(empty_set)) )
| ~ spl11_60
| ~ spl11_89 ),
inference(resolution,[],[f731,f530]) ).
fof(f4063,plain,
( spl11_250
| ~ spl11_75
| ~ spl11_88 ),
inference(avatar_split_clause,[],[f881,f726,f619,f4061]) ).
fof(f4061,plain,
( spl11_250
<=> ! [X2,X0,X1] :
( subset(X0,union(X1,X2))
| ~ subset(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_250])]) ).
fof(f881,plain,
( ! [X2,X0,X1] :
( subset(X0,union(X1,X2))
| ~ subset(X0,X2) )
| ~ spl11_75
| ~ spl11_88 ),
inference(duplicate_literal_removal,[],[f862]) ).
fof(f862,plain,
( ! [X2,X0,X1] :
( subset(X0,union(X1,X2))
| ~ subset(X0,X2)
| subset(X0,union(X1,X2)) )
| ~ spl11_75
| ~ spl11_88 ),
inference(resolution,[],[f727,f620]) ).
fof(f4059,plain,
( spl11_249
| ~ spl11_75
| ~ spl11_87 ),
inference(avatar_split_clause,[],[f859,f722,f619,f4057]) ).
fof(f4057,plain,
( spl11_249
<=> ! [X2,X0,X1] :
( subset(X0,union(X1,X2))
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_249])]) ).
fof(f859,plain,
( ! [X2,X0,X1] :
( subset(X0,union(X1,X2))
| ~ subset(X0,X1) )
| ~ spl11_75
| ~ spl11_87 ),
inference(duplicate_literal_removal,[],[f840]) ).
fof(f840,plain,
( ! [X2,X0,X1] :
( subset(X0,union(X1,X2))
| ~ subset(X0,X1)
| subset(X0,union(X1,X2)) )
| ~ spl11_75
| ~ spl11_87 ),
inference(resolution,[],[f723,f620]) ).
fof(f4055,plain,
( spl11_248
| ~ spl11_33
| ~ spl11_59 ),
inference(avatar_split_clause,[],[f537,f525,f324,f4053]) ).
fof(f4053,plain,
( spl11_248
<=> ! [X0,X1] :
( ~ member(X0,X1)
| member(X0,sum(product(empty_set))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_248])]) ).
fof(f537,plain,
( ! [X0,X1] :
( ~ member(X0,X1)
| member(X0,sum(product(empty_set))) )
| ~ spl11_33
| ~ spl11_59 ),
inference(resolution,[],[f526,f325]) ).
fof(f4051,plain,
( spl11_247
| ~ spl11_121
| ~ spl11_155 ),
inference(avatar_split_clause,[],[f2563,f2319,f1328,f4049]) ).
fof(f4049,plain,
( spl11_247
<=> ! [X0] : upper_bound(sK4,sK1,difference(sK3,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_247])]) ).
fof(f2563,plain,
( ! [X0] : upper_bound(sK4,sK1,difference(sK3,X0))
| ~ spl11_121
| ~ spl11_155 ),
inference(duplicate_literal_removal,[],[f2560]) ).
fof(f2560,plain,
( ! [X0] :
( upper_bound(sK4,sK1,difference(sK3,X0))
| upper_bound(sK4,sK1,difference(sK3,X0)) )
| ~ spl11_121
| ~ spl11_155 ),
inference(resolution,[],[f2320,f1329]) ).
fof(f3910,plain,
( spl11_246
| ~ spl11_82
| ~ spl11_85 ),
inference(avatar_split_clause,[],[f2551,f714,f669,f3908]) ).
fof(f3908,plain,
( spl11_246
<=> ! [X0] : subset(intersection(sK4,X0),sum(sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_246])]) ).
fof(f2551,plain,
( ! [X0] : subset(intersection(sK4,X0),sum(sK3))
| ~ spl11_82
| ~ spl11_85 ),
inference(duplicate_literal_removal,[],[f2540]) ).
fof(f2540,plain,
( ! [X0] :
( subset(intersection(sK4,X0),sum(sK3))
| subset(intersection(sK4,X0),sum(sK3)) )
| ~ spl11_82
| ~ spl11_85 ),
inference(resolution,[],[f670,f715]) ).
fof(f3670,plain,
( spl11_245
| ~ spl11_60
| ~ spl11_121 ),
inference(avatar_split_clause,[],[f1487,f1328,f529,f3668]) ).
fof(f3668,plain,
( spl11_245
<=> ! [X2,X0,X1] : upper_bound(X0,X1,difference(sum(empty_set),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_245])]) ).
fof(f1487,plain,
( ! [X2,X0,X1] : upper_bound(X0,X1,difference(sum(empty_set),X2))
| ~ spl11_60
| ~ spl11_121 ),
inference(resolution,[],[f1329,f530]) ).
fof(f3666,plain,
( spl11_244
| ~ spl11_59
| ~ spl11_120 ),
inference(avatar_split_clause,[],[f1469,f1324,f525,f3664]) ).
fof(f3664,plain,
( spl11_244
<=> ! [X2,X0,X1] : upper_bound(X0,X1,difference(X2,product(empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_244])]) ).
fof(f1469,plain,
( ! [X2,X0,X1] : upper_bound(X0,X1,difference(X2,product(empty_set)))
| ~ spl11_59
| ~ spl11_120 ),
inference(resolution,[],[f1325,f526]) ).
fof(f3662,plain,
( spl11_243
| ~ spl11_60
| ~ spl11_119 ),
inference(avatar_split_clause,[],[f1449,f1320,f529,f3660]) ).
fof(f3660,plain,
( spl11_243
<=> ! [X2,X0,X1] : upper_bound(X0,X1,intersection(sum(empty_set),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_243])]) ).
fof(f1449,plain,
( ! [X2,X0,X1] : upper_bound(X0,X1,intersection(sum(empty_set),X2))
| ~ spl11_60
| ~ spl11_119 ),
inference(resolution,[],[f1321,f530]) ).
fof(f3658,plain,
( spl11_242
| ~ spl11_60
| ~ spl11_118 ),
inference(avatar_split_clause,[],[f1428,f1316,f529,f3656]) ).
fof(f3656,plain,
( spl11_242
<=> ! [X2,X0,X1] : upper_bound(X0,X1,intersection(X2,sum(empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_242])]) ).
fof(f1428,plain,
( ! [X2,X0,X1] : upper_bound(X0,X1,intersection(X2,sum(empty_set)))
| ~ spl11_60
| ~ spl11_118 ),
inference(resolution,[],[f1317,f530]) ).
fof(f3654,plain,
( spl11_241
| ~ spl11_6
| ~ spl11_112 ),
inference(avatar_split_clause,[],[f1287,f1055,f176,f3652]) ).
fof(f3652,plain,
( spl11_241
<=> ! [X2,X0,X1] :
( upper_bound(X0,X1,X2)
| ~ subset(X2,empty_set) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_241])]) ).
fof(f1287,plain,
( ! [X2,X0,X1] :
( upper_bound(X0,X1,X2)
| ~ subset(X2,empty_set) )
| ~ spl11_6
| ~ spl11_112 ),
inference(resolution,[],[f1056,f177]) ).
fof(f3641,plain,
( spl11_240
| ~ spl11_15
| ~ spl11_108 ),
inference(avatar_split_clause,[],[f1226,f1039,f215,f3639]) ).
fof(f3639,plain,
( spl11_240
<=> ! [X0,X1] :
( ~ member(X0,X1)
| subset(product(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_240])]) ).
fof(f1226,plain,
( ! [X0,X1] :
( ~ member(X0,X1)
| subset(product(X1),X0) )
| ~ spl11_15
| ~ spl11_108 ),
inference(duplicate_literal_removal,[],[f1202]) ).
fof(f1202,plain,
( ! [X0,X1] :
( ~ member(X0,X1)
| subset(product(X1),X0)
| subset(product(X1),X0) )
| ~ spl11_15
| ~ spl11_108 ),
inference(resolution,[],[f1040,f216]) ).
fof(f3637,plain,
( spl11_239
| ~ spl11_6
| ~ spl11_108 ),
inference(avatar_split_clause,[],[f1214,f1039,f176,f3635]) ).
fof(f3635,plain,
( spl11_239
<=> ! [X0,X1] :
( ~ member(empty_set,X0)
| subset(product(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_239])]) ).
fof(f1214,plain,
( ! [X0,X1] :
( ~ member(empty_set,X0)
| subset(product(X0),X1) )
| ~ spl11_6
| ~ spl11_108 ),
inference(resolution,[],[f1040,f177]) ).
fof(f3633,plain,
( spl11_238
| ~ spl11_60
| ~ spl11_107 ),
inference(avatar_split_clause,[],[f1197,f1030,f529,f3631]) ).
fof(f3631,plain,
( spl11_238
<=> ! [X0,X1] : ~ member(X0,sum(difference(sum(empty_set),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_238])]) ).
fof(f1197,plain,
( ! [X0,X1] : ~ member(X0,sum(difference(sum(empty_set),X1)))
| ~ spl11_60
| ~ spl11_107 ),
inference(resolution,[],[f1031,f530]) ).
fof(f3629,plain,
( spl11_237
| ~ spl11_59
| ~ spl11_106 ),
inference(avatar_split_clause,[],[f1179,f1026,f525,f3627]) ).
fof(f3627,plain,
( spl11_237
<=> ! [X0,X1] : ~ member(X0,sum(difference(X1,product(empty_set)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_237])]) ).
fof(f1179,plain,
( ! [X0,X1] : ~ member(X0,sum(difference(X1,product(empty_set))))
| ~ spl11_59
| ~ spl11_106 ),
inference(resolution,[],[f1027,f526]) ).
fof(f3625,plain,
( spl11_236
| ~ spl11_60
| ~ spl11_105 ),
inference(avatar_split_clause,[],[f1164,f1022,f529,f3623]) ).
fof(f3623,plain,
( spl11_236
<=> ! [X0,X1] : ~ member(X0,sum(intersection(sum(empty_set),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_236])]) ).
fof(f1164,plain,
( ! [X0,X1] : ~ member(X0,sum(intersection(sum(empty_set),X1)))
| ~ spl11_60
| ~ spl11_105 ),
inference(resolution,[],[f1023,f530]) ).
fof(f3621,plain,
( spl11_235
| ~ spl11_60
| ~ spl11_104 ),
inference(avatar_split_clause,[],[f1142,f1018,f529,f3619]) ).
fof(f3619,plain,
( spl11_235
<=> ! [X0,X1] : ~ member(X0,sum(intersection(X1,sum(empty_set)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_235])]) ).
fof(f1142,plain,
( ! [X0,X1] : ~ member(X0,sum(intersection(X1,sum(empty_set))))
| ~ spl11_60
| ~ spl11_104 ),
inference(resolution,[],[f1019,f530]) ).
fof(f3617,plain,
( spl11_234
| ~ spl11_60
| ~ spl11_103 ),
inference(avatar_split_clause,[],[f1123,f1014,f529,f3615]) ).
fof(f3615,plain,
( spl11_234
<=> ! [X0,X1] : member(X0,product(difference(sum(empty_set),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_234])]) ).
fof(f1123,plain,
( ! [X0,X1] : member(X0,product(difference(sum(empty_set),X1)))
| ~ spl11_60
| ~ spl11_103 ),
inference(resolution,[],[f1015,f530]) ).
fof(f3613,plain,
( spl11_233
| ~ spl11_59
| ~ spl11_102 ),
inference(avatar_split_clause,[],[f1105,f1010,f525,f3611]) ).
fof(f3611,plain,
( spl11_233
<=> ! [X0,X1] : member(X0,product(difference(X1,product(empty_set)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_233])]) ).
fof(f1105,plain,
( ! [X0,X1] : member(X0,product(difference(X1,product(empty_set))))
| ~ spl11_59
| ~ spl11_102 ),
inference(resolution,[],[f1011,f526]) ).
fof(f3609,plain,
( spl11_232
| ~ spl11_60
| ~ spl11_101 ),
inference(avatar_split_clause,[],[f1090,f1006,f529,f3607]) ).
fof(f3607,plain,
( spl11_232
<=> ! [X0,X1] : member(X0,product(intersection(sum(empty_set),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_232])]) ).
fof(f1090,plain,
( ! [X0,X1] : member(X0,product(intersection(sum(empty_set),X1)))
| ~ spl11_60
| ~ spl11_101 ),
inference(resolution,[],[f1007,f530]) ).
fof(f3605,plain,
( spl11_231
| ~ spl11_60
| ~ spl11_100 ),
inference(avatar_split_clause,[],[f1072,f1002,f529,f3603]) ).
fof(f3603,plain,
( spl11_231
<=> ! [X0,X1] : member(X0,product(intersection(X1,sum(empty_set)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_231])]) ).
fof(f1072,plain,
( ! [X0,X1] : member(X0,product(intersection(X1,sum(empty_set))))
| ~ spl11_60
| ~ spl11_100 ),
inference(resolution,[],[f1003,f530]) ).
fof(f3601,plain,
( spl11_230
| ~ spl11_52
| ~ spl11_192 ),
inference(avatar_split_clause,[],[f3086,f2999,f477,f3599]) ).
fof(f3599,plain,
( spl11_230
<=> ! [X0] : member(sK4,union(X0,sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_230])]) ).
fof(f477,plain,
( spl11_52
<=> ! [X0] :
( member(sK4,X0)
| ~ subset(sK2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_52])]) ).
fof(f2999,plain,
( spl11_192
<=> ! [X0,X1] : subset(X0,union(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_192])]) ).
fof(f3086,plain,
( ! [X0] : member(sK4,union(X0,sK2))
| ~ spl11_52
| ~ spl11_192 ),
inference(resolution,[],[f3000,f478]) ).
fof(f478,plain,
( ! [X0] :
( ~ subset(sK2,X0)
| member(sK4,X0) )
| ~ spl11_52 ),
inference(avatar_component_clause,[],[f477]) ).
fof(f3000,plain,
( ! [X0,X1] : subset(X0,union(X1,X0))
| ~ spl11_192 ),
inference(avatar_component_clause,[],[f2999]) ).
fof(f3597,plain,
( spl11_229
| ~ spl11_6
| ~ spl11_90 ),
inference(avatar_split_clause,[],[f906,f734,f176,f3595]) ).
fof(f906,plain,
( ! [X0,X1] :
( ~ member(X0,sum(X1))
| ~ subset(X1,empty_set) )
| ~ spl11_6
| ~ spl11_90 ),
inference(resolution,[],[f735,f177]) ).
fof(f3593,plain,
( spl11_228
| ~ spl11_6
| ~ spl11_89 ),
inference(avatar_split_clause,[],[f890,f730,f176,f3591]) ).
fof(f3591,plain,
( spl11_228
<=> ! [X0,X1] :
( member(X0,product(X1))
| ~ subset(X1,empty_set) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_228])]) ).
fof(f890,plain,
( ! [X0,X1] :
( member(X0,product(X1))
| ~ subset(X1,empty_set) )
| ~ spl11_6
| ~ spl11_89 ),
inference(resolution,[],[f731,f177]) ).
fof(f3589,plain,
( spl11_227
| ~ spl11_83
| ~ spl11_88 ),
inference(avatar_split_clause,[],[f880,f726,f706,f3587]) ).
fof(f3587,plain,
( spl11_227
<=> ! [X2,X0,X1] : subset(difference(X0,X1),union(X2,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_227])]) ).
fof(f880,plain,
( ! [X2,X0,X1] : subset(difference(X0,X1),union(X2,X0))
| ~ spl11_83
| ~ spl11_88 ),
inference(duplicate_literal_removal,[],[f863]) ).
fof(f863,plain,
( ! [X2,X0,X1] :
( subset(difference(X0,X1),union(X2,X0))
| subset(difference(X0,X1),union(X2,X0)) )
| ~ spl11_83
| ~ spl11_88 ),
inference(resolution,[],[f727,f707]) ).
fof(f3585,plain,
( spl11_226
| ~ spl11_85
| ~ spl11_88 ),
inference(avatar_split_clause,[],[f879,f726,f714,f3583]) ).
fof(f3583,plain,
( spl11_226
<=> ! [X2,X0,X1] : subset(intersection(X0,X1),union(X2,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_226])]) ).
fof(f879,plain,
( ! [X2,X0,X1] : subset(intersection(X0,X1),union(X2,X0))
| ~ spl11_85
| ~ spl11_88 ),
inference(duplicate_literal_removal,[],[f864]) ).
fof(f864,plain,
( ! [X2,X0,X1] :
( subset(intersection(X0,X1),union(X2,X0))
| subset(intersection(X0,X1),union(X2,X0)) )
| ~ spl11_85
| ~ spl11_88 ),
inference(resolution,[],[f727,f715]) ).
fof(f3581,plain,
( spl11_225
| ~ spl11_86
| ~ spl11_88 ),
inference(avatar_split_clause,[],[f878,f726,f718,f3579]) ).
fof(f3579,plain,
( spl11_225
<=> ! [X2,X0,X1] : subset(intersection(X0,X1),union(X2,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_225])]) ).
fof(f878,plain,
( ! [X2,X0,X1] : subset(intersection(X0,X1),union(X2,X1))
| ~ spl11_86
| ~ spl11_88 ),
inference(duplicate_literal_removal,[],[f865]) ).
fof(f865,plain,
( ! [X2,X0,X1] :
( subset(intersection(X0,X1),union(X2,X1))
| subset(intersection(X0,X1),union(X2,X1)) )
| ~ spl11_86
| ~ spl11_88 ),
inference(resolution,[],[f727,f719]) ).
fof(f3577,plain,
( spl11_224
| ~ spl11_83
| ~ spl11_87 ),
inference(avatar_split_clause,[],[f858,f722,f706,f3575]) ).
fof(f3575,plain,
( spl11_224
<=> ! [X2,X0,X1] : subset(difference(X0,X1),union(X0,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_224])]) ).
fof(f858,plain,
( ! [X2,X0,X1] : subset(difference(X0,X1),union(X0,X2))
| ~ spl11_83
| ~ spl11_87 ),
inference(duplicate_literal_removal,[],[f841]) ).
fof(f841,plain,
( ! [X2,X0,X1] :
( subset(difference(X0,X1),union(X0,X2))
| subset(difference(X0,X1),union(X0,X2)) )
| ~ spl11_83
| ~ spl11_87 ),
inference(resolution,[],[f723,f707]) ).
fof(f3573,plain,
( spl11_223
| ~ spl11_85
| ~ spl11_87 ),
inference(avatar_split_clause,[],[f857,f722,f714,f3571]) ).
fof(f3571,plain,
( spl11_223
<=> ! [X2,X0,X1] : subset(intersection(X0,X1),union(X0,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_223])]) ).
fof(f857,plain,
( ! [X2,X0,X1] : subset(intersection(X0,X1),union(X0,X2))
| ~ spl11_85
| ~ spl11_87 ),
inference(duplicate_literal_removal,[],[f842]) ).
fof(f842,plain,
( ! [X2,X0,X1] :
( subset(intersection(X0,X1),union(X0,X2))
| subset(intersection(X0,X1),union(X0,X2)) )
| ~ spl11_85
| ~ spl11_87 ),
inference(resolution,[],[f723,f715]) ).
fof(f3569,plain,
( spl11_222
| ~ spl11_86
| ~ spl11_87 ),
inference(avatar_split_clause,[],[f856,f722,f718,f3567]) ).
fof(f3567,plain,
( spl11_222
<=> ! [X2,X0,X1] : subset(intersection(X0,X1),union(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_222])]) ).
fof(f856,plain,
( ! [X2,X0,X1] : subset(intersection(X0,X1),union(X1,X2))
| ~ spl11_86
| ~ spl11_87 ),
inference(duplicate_literal_removal,[],[f843]) ).
fof(f843,plain,
( ! [X2,X0,X1] :
( subset(intersection(X0,X1),union(X1,X2))
| subset(intersection(X0,X1),union(X1,X2)) )
| ~ spl11_86
| ~ spl11_87 ),
inference(resolution,[],[f723,f719]) ).
fof(f3565,plain,
( spl11_221
| ~ spl11_60
| ~ spl11_75 ),
inference(avatar_split_clause,[],[f660,f619,f529,f3563]) ).
fof(f3563,plain,
( spl11_221
<=> ! [X0,X1] :
( ~ subset(X0,sum(empty_set))
| subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_221])]) ).
fof(f660,plain,
( ! [X0,X1] :
( ~ subset(X0,sum(empty_set))
| subset(X0,X1) )
| ~ spl11_60
| ~ spl11_75 ),
inference(resolution,[],[f620,f530]) ).
fof(f3561,plain,
( spl11_220
| ~ spl11_23
| ~ spl11_59 ),
inference(avatar_split_clause,[],[f538,f525,f259,f3559]) ).
fof(f3559,plain,
( spl11_220
<=> ! [X0,X1] :
( member(X0,X1)
| ~ subset(product(empty_set),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_220])]) ).
fof(f538,plain,
( ! [X0,X1] :
( member(X0,X1)
| ~ subset(product(empty_set),X1) )
| ~ spl11_23
| ~ spl11_59 ),
inference(resolution,[],[f526,f260]) ).
fof(f3557,plain,
( spl11_219
| ~ spl11_52
| ~ spl11_191 ),
inference(avatar_split_clause,[],[f3074,f2995,f477,f3555]) ).
fof(f3555,plain,
( spl11_219
<=> ! [X0] : member(sK4,union(sK2,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_219])]) ).
fof(f2995,plain,
( spl11_191
<=> ! [X0,X1] : subset(X0,union(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_191])]) ).
fof(f3074,plain,
( ! [X0] : member(sK4,union(sK2,X0))
| ~ spl11_52
| ~ spl11_191 ),
inference(resolution,[],[f2996,f478]) ).
fof(f2996,plain,
( ! [X0,X1] : subset(X0,union(X0,X1))
| ~ spl11_191 ),
inference(avatar_component_clause,[],[f2995]) ).
fof(f3245,plain,
( spl11_218
| ~ spl11_120
| ~ spl11_121 ),
inference(avatar_split_clause,[],[f1494,f1328,f1324,f3243]) ).
fof(f3243,plain,
( spl11_218
<=> ! [X2,X0,X1] : upper_bound(X0,X1,difference(X2,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_218])]) ).
fof(f1494,plain,
( ! [X2,X0,X1] : upper_bound(X0,X1,difference(X2,X2))
| ~ spl11_120
| ~ spl11_121 ),
inference(duplicate_literal_removal,[],[f1472]) ).
fof(f1472,plain,
( ! [X2,X0,X1] :
( upper_bound(X0,X1,difference(X2,X2))
| upper_bound(X0,X1,difference(X2,X2)) )
| ~ spl11_120
| ~ spl11_121 ),
inference(resolution,[],[f1329,f1325]) ).
fof(f3232,plain,
( spl11_217
| ~ spl11_6
| ~ spl11_121 ),
inference(avatar_split_clause,[],[f1482,f1328,f176,f3230]) ).
fof(f3230,plain,
( spl11_217
<=> ! [X2,X0,X1] : upper_bound(X0,X1,difference(empty_set,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_217])]) ).
fof(f1482,plain,
( ! [X2,X0,X1] : upper_bound(X0,X1,difference(empty_set,X2))
| ~ spl11_6
| ~ spl11_121 ),
inference(resolution,[],[f1329,f177]) ).
fof(f3228,plain,
( spl11_216
| ~ spl11_6
| ~ spl11_119 ),
inference(avatar_split_clause,[],[f1444,f1320,f176,f3226]) ).
fof(f3226,plain,
( spl11_216
<=> ! [X2,X0,X1] : upper_bound(X0,X1,intersection(empty_set,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_216])]) ).
fof(f1444,plain,
( ! [X2,X0,X1] : upper_bound(X0,X1,intersection(empty_set,X2))
| ~ spl11_6
| ~ spl11_119 ),
inference(resolution,[],[f1321,f177]) ).
fof(f3224,plain,
( spl11_215
| ~ spl11_6
| ~ spl11_118 ),
inference(avatar_split_clause,[],[f1423,f1316,f176,f3222]) ).
fof(f3222,plain,
( spl11_215
<=> ! [X2,X0,X1] : upper_bound(X0,X1,intersection(X2,empty_set)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_215])]) ).
fof(f1423,plain,
( ! [X2,X0,X1] : upper_bound(X0,X1,intersection(X2,empty_set))
| ~ spl11_6
| ~ spl11_118 ),
inference(resolution,[],[f1317,f177]) ).
fof(f3220,plain,
( spl11_214
| ~ spl11_106
| ~ spl11_107 ),
inference(avatar_split_clause,[],[f1201,f1030,f1026,f3218]) ).
fof(f3218,plain,
( spl11_214
<=> ! [X0,X1] : ~ member(X0,sum(difference(X1,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_214])]) ).
fof(f1201,plain,
( ! [X0,X1] : ~ member(X0,sum(difference(X1,X1)))
| ~ spl11_106
| ~ spl11_107 ),
inference(duplicate_literal_removal,[],[f1182]) ).
fof(f1182,plain,
( ! [X0,X1] :
( ~ member(X0,sum(difference(X1,X1)))
| ~ member(X0,sum(difference(X1,X1))) )
| ~ spl11_106
| ~ spl11_107 ),
inference(resolution,[],[f1031,f1027]) ).
fof(f3216,plain,
( spl11_213
| ~ spl11_6
| ~ spl11_107 ),
inference(avatar_split_clause,[],[f1192,f1030,f176,f3214]) ).
fof(f3214,plain,
( spl11_213
<=> ! [X0,X1] : ~ member(X0,sum(difference(empty_set,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_213])]) ).
fof(f1192,plain,
( ! [X0,X1] : ~ member(X0,sum(difference(empty_set,X1)))
| ~ spl11_6
| ~ spl11_107 ),
inference(resolution,[],[f1031,f177]) ).
fof(f3212,plain,
( spl11_212
| ~ spl11_6
| ~ spl11_105 ),
inference(avatar_split_clause,[],[f1159,f1022,f176,f3210]) ).
fof(f3210,plain,
( spl11_212
<=> ! [X0,X1] : ~ member(X0,sum(intersection(empty_set,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_212])]) ).
fof(f1159,plain,
( ! [X0,X1] : ~ member(X0,sum(intersection(empty_set,X1)))
| ~ spl11_6
| ~ spl11_105 ),
inference(resolution,[],[f1023,f177]) ).
fof(f3208,plain,
( spl11_211
| ~ spl11_6
| ~ spl11_104 ),
inference(avatar_split_clause,[],[f1137,f1018,f176,f3206]) ).
fof(f3206,plain,
( spl11_211
<=> ! [X0,X1] : ~ member(X0,sum(intersection(X1,empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_211])]) ).
fof(f1137,plain,
( ! [X0,X1] : ~ member(X0,sum(intersection(X1,empty_set)))
| ~ spl11_6
| ~ spl11_104 ),
inference(resolution,[],[f1019,f177]) ).
fof(f3204,plain,
( spl11_210
| ~ spl11_102
| ~ spl11_103 ),
inference(avatar_split_clause,[],[f1127,f1014,f1010,f3202]) ).
fof(f3202,plain,
( spl11_210
<=> ! [X0,X1] : member(X0,product(difference(X1,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_210])]) ).
fof(f1127,plain,
( ! [X0,X1] : member(X0,product(difference(X1,X1)))
| ~ spl11_102
| ~ spl11_103 ),
inference(duplicate_literal_removal,[],[f1108]) ).
fof(f1108,plain,
( ! [X0,X1] :
( member(X0,product(difference(X1,X1)))
| member(X0,product(difference(X1,X1))) )
| ~ spl11_102
| ~ spl11_103 ),
inference(resolution,[],[f1015,f1011]) ).
fof(f3200,plain,
( spl11_209
| ~ spl11_6
| ~ spl11_103 ),
inference(avatar_split_clause,[],[f1118,f1014,f176,f3198]) ).
fof(f3198,plain,
( spl11_209
<=> ! [X0,X1] : member(X0,product(difference(empty_set,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_209])]) ).
fof(f1118,plain,
( ! [X0,X1] : member(X0,product(difference(empty_set,X1)))
| ~ spl11_6
| ~ spl11_103 ),
inference(resolution,[],[f1015,f177]) ).
fof(f3196,plain,
( spl11_208
| ~ spl11_6
| ~ spl11_101 ),
inference(avatar_split_clause,[],[f1085,f1006,f176,f3194]) ).
fof(f3194,plain,
( spl11_208
<=> ! [X0,X1] : member(X0,product(intersection(empty_set,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_208])]) ).
fof(f1085,plain,
( ! [X0,X1] : member(X0,product(intersection(empty_set,X1)))
| ~ spl11_6
| ~ spl11_101 ),
inference(resolution,[],[f1007,f177]) ).
fof(f3192,plain,
( spl11_207
| ~ spl11_30
| ~ spl11_192 ),
inference(avatar_split_clause,[],[f3085,f2999,f312,f3190]) ).
fof(f3190,plain,
( spl11_207
<=> ! [X0] : member(sK4,union(X0,sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_207])]) ).
fof(f312,plain,
( spl11_30
<=> ! [X0] :
( member(sK4,X0)
| ~ subset(sK3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_30])]) ).
fof(f3085,plain,
( ! [X0] : member(sK4,union(X0,sK3))
| ~ spl11_30
| ~ spl11_192 ),
inference(resolution,[],[f3000,f313]) ).
fof(f313,plain,
( ! [X0] :
( ~ subset(sK3,X0)
| member(sK4,X0) )
| ~ spl11_30 ),
inference(avatar_component_clause,[],[f312]) ).
fof(f3188,plain,
( spl11_206
| ~ spl11_6
| ~ spl11_100 ),
inference(avatar_split_clause,[],[f1067,f1002,f176,f3186]) ).
fof(f3186,plain,
( spl11_206
<=> ! [X0,X1] : member(X0,product(intersection(X1,empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_206])]) ).
fof(f1067,plain,
( ! [X0,X1] : member(X0,product(intersection(X1,empty_set)))
| ~ spl11_6
| ~ spl11_100 ),
inference(resolution,[],[f1003,f177]) ).
fof(f3184,plain,
( spl11_205
| ~ spl11_59
| ~ spl11_88 ),
inference(avatar_split_clause,[],[f876,f726,f525,f3182]) ).
fof(f3182,plain,
( spl11_205
<=> ! [X0,X1] : subset(X0,union(X1,product(empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_205])]) ).
fof(f876,plain,
( ! [X0,X1] : subset(X0,union(X1,product(empty_set)))
| ~ spl11_59
| ~ spl11_88 ),
inference(resolution,[],[f727,f526]) ).
fof(f3180,plain,
( spl11_204
| ~ spl11_59
| ~ spl11_87 ),
inference(avatar_split_clause,[],[f854,f722,f525,f3178]) ).
fof(f3178,plain,
( spl11_204
<=> ! [X0,X1] : subset(X0,union(product(empty_set),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_204])]) ).
fof(f854,plain,
( ! [X0,X1] : subset(X0,union(product(empty_set),X1))
| ~ spl11_59
| ~ spl11_87 ),
inference(resolution,[],[f723,f526]) ).
fof(f3176,plain,
( spl11_203
| ~ spl11_60
| ~ spl11_86 ),
inference(avatar_split_clause,[],[f835,f718,f529,f3174]) ).
fof(f3174,plain,
( spl11_203
<=> ! [X0,X1] : subset(intersection(X0,sum(empty_set)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_203])]) ).
fof(f835,plain,
( ! [X0,X1] : subset(intersection(X0,sum(empty_set)),X1)
| ~ spl11_60
| ~ spl11_86 ),
inference(resolution,[],[f719,f530]) ).
fof(f3172,plain,
( spl11_202
| ~ spl11_60
| ~ spl11_85 ),
inference(avatar_split_clause,[],[f815,f714,f529,f3170]) ).
fof(f3170,plain,
( spl11_202
<=> ! [X0,X1] : subset(intersection(sum(empty_set),X0),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_202])]) ).
fof(f815,plain,
( ! [X0,X1] : subset(intersection(sum(empty_set),X0),X1)
| ~ spl11_60
| ~ spl11_85 ),
inference(resolution,[],[f715,f530]) ).
fof(f3168,plain,
( spl11_201
| ~ spl11_59
| ~ spl11_84 ),
inference(avatar_split_clause,[],[f798,f710,f525,f3166]) ).
fof(f3166,plain,
( spl11_201
<=> ! [X0,X1] : subset(difference(X0,product(empty_set)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_201])]) ).
fof(f798,plain,
( ! [X0,X1] : subset(difference(X0,product(empty_set)),X1)
| ~ spl11_59
| ~ spl11_84 ),
inference(resolution,[],[f711,f526]) ).
fof(f3164,plain,
( spl11_200
| ~ spl11_60
| ~ spl11_83 ),
inference(avatar_split_clause,[],[f782,f706,f529,f3162]) ).
fof(f3162,plain,
( spl11_200
<=> ! [X0,X1] : subset(difference(sum(empty_set),X0),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_200])]) ).
fof(f782,plain,
( ! [X0,X1] : subset(difference(sum(empty_set),X0),X1)
| ~ spl11_60
| ~ spl11_83 ),
inference(resolution,[],[f707,f530]) ).
fof(f3160,plain,
( spl11_199
| ~ spl11_6
| ~ spl11_75 ),
inference(avatar_split_clause,[],[f655,f619,f176,f3158]) ).
fof(f3158,plain,
( spl11_199
<=> ! [X0,X1] :
( ~ subset(X0,empty_set)
| subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_199])]) ).
fof(f655,plain,
( ! [X0,X1] :
( ~ subset(X0,empty_set)
| subset(X0,X1) )
| ~ spl11_6
| ~ spl11_75 ),
inference(resolution,[],[f620,f177]) ).
fof(f3152,plain,
( spl11_198
| ~ spl11_53
| ~ spl11_56 ),
inference(avatar_split_clause,[],[f516,f496,f481,f3150]) ).
fof(f3150,plain,
( spl11_198
<=> ! [X2,X0,X1] :
( ~ member(X0,sK3)
| apply(sK1,X1,sK4)
| ~ apply(sK1,X1,X0)
| ~ member(sK4,X2)
| ~ member(X0,X2)
| ~ member(X1,X2)
| ~ order(sK1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_198])]) ).
fof(f481,plain,
( spl11_53
<=> ! [X4,X0,X3,X2,X1] :
( apply(X0,X2,X4)
| ~ apply(X0,X3,X4)
| ~ apply(X0,X2,X3)
| ~ member(X4,X1)
| ~ member(X3,X1)
| ~ member(X2,X1)
| ~ order(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_53])]) ).
fof(f516,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sK3)
| apply(sK1,X1,sK4)
| ~ apply(sK1,X1,X0)
| ~ member(sK4,X2)
| ~ member(X0,X2)
| ~ member(X1,X2)
| ~ order(sK1,X2) )
| ~ spl11_53
| ~ spl11_56 ),
inference(resolution,[],[f497,f482]) ).
fof(f482,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ apply(X0,X3,X4)
| apply(X0,X2,X4)
| ~ apply(X0,X2,X3)
| ~ member(X4,X1)
| ~ member(X3,X1)
| ~ member(X2,X1)
| ~ order(X0,X1) )
| ~ spl11_53 ),
inference(avatar_component_clause,[],[f481]) ).
fof(f497,plain,
( ! [X0] :
( apply(sK1,X0,sK4)
| ~ member(X0,sK3) )
| ~ spl11_56 ),
inference(avatar_component_clause,[],[f496]) ).
fof(f3148,plain,
( spl11_197
| ~ spl11_30
| ~ spl11_191 ),
inference(avatar_split_clause,[],[f3073,f2995,f312,f3146]) ).
fof(f3146,plain,
( spl11_197
<=> ! [X0] : member(sK4,union(sK3,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_197])]) ).
fof(f3073,plain,
( ! [X0] : member(sK4,union(sK3,X0))
| ~ spl11_30
| ~ spl11_191 ),
inference(resolution,[],[f2996,f313]) ).
fof(f3108,plain,
( spl11_196
| ~ spl11_55
| ~ spl11_138 ),
inference(avatar_split_clause,[],[f1939,f1739,f489,f3106]) ).
fof(f3106,plain,
( spl11_196
<=> ! [X2,X0,X1] :
( ~ member(X0,difference(X1,sum(sK3)))
| greatest(X0,X2,difference(X1,sum(sK3)))
| ~ member(sK8(X2,difference(X1,sum(sK3)),X0),sK4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_196])]) ).
fof(f1939,plain,
( ! [X2,X0,X1] :
( ~ member(X0,difference(X1,sum(sK3)))
| greatest(X0,X2,difference(X1,sum(sK3)))
| ~ member(sK8(X2,difference(X1,sum(sK3)),X0),sK4) )
| ~ spl11_55
| ~ spl11_138 ),
inference(resolution,[],[f1740,f490]) ).
fof(f3104,plain,
( spl11_195
| ~ spl11_55
| ~ spl11_133 ),
inference(avatar_split_clause,[],[f1798,f1719,f489,f3102]) ).
fof(f3102,plain,
( spl11_195
<=> ! [X0,X1] :
( ~ member(sK5(X0,intersection(X1,sum(sK3))),X1)
| subset(X0,intersection(X1,sum(sK3)))
| ~ member(sK5(X0,intersection(X1,sum(sK3))),sK4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_195])]) ).
fof(f1798,plain,
( ! [X0,X1] :
( ~ member(sK5(X0,intersection(X1,sum(sK3))),X1)
| subset(X0,intersection(X1,sum(sK3)))
| ~ member(sK5(X0,intersection(X1,sum(sK3))),sK4) )
| ~ spl11_55
| ~ spl11_133 ),
inference(resolution,[],[f1720,f490]) ).
fof(f3100,plain,
( spl11_194
| ~ spl11_55
| ~ spl11_132 ),
inference(avatar_split_clause,[],[f1767,f1715,f489,f3098]) ).
fof(f3098,plain,
( spl11_194
<=> ! [X0,X1] :
( member(sK5(X0,difference(sum(sK3),X1)),X1)
| subset(X0,difference(sum(sK3),X1))
| ~ member(sK5(X0,difference(sum(sK3),X1)),sK4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_194])]) ).
fof(f1767,plain,
( ! [X0,X1] :
( member(sK5(X0,difference(sum(sK3),X1)),X1)
| subset(X0,difference(sum(sK3),X1))
| ~ member(sK5(X0,difference(sum(sK3),X1)),sK4) )
| ~ spl11_55
| ~ spl11_132 ),
inference(resolution,[],[f1716,f490]) ).
fof(f3070,plain,
( spl11_193
| ~ spl11_82
| ~ spl11_86 ),
inference(avatar_split_clause,[],[f2550,f718,f669,f3068]) ).
fof(f3068,plain,
( spl11_193
<=> ! [X0] : subset(intersection(X0,sK4),sum(sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_193])]) ).
fof(f2550,plain,
( ! [X0] : subset(intersection(X0,sK4),sum(sK3))
| ~ spl11_82
| ~ spl11_86 ),
inference(duplicate_literal_removal,[],[f2541]) ).
fof(f2541,plain,
( ! [X0] :
( subset(intersection(X0,sK4),sum(sK3))
| subset(intersection(X0,sK4),sum(sK3)) )
| ~ spl11_82
| ~ spl11_86 ),
inference(resolution,[],[f670,f719]) ).
fof(f3001,plain,
( spl11_192
| ~ spl11_14
| ~ spl11_88 ),
inference(avatar_split_clause,[],[f882,f726,f211,f2999]) ).
fof(f882,plain,
( ! [X0,X1] : subset(X0,union(X1,X0))
| ~ spl11_14
| ~ spl11_88 ),
inference(duplicate_literal_removal,[],[f861]) ).
fof(f861,plain,
( ! [X0,X1] :
( subset(X0,union(X1,X0))
| subset(X0,union(X1,X0)) )
| ~ spl11_14
| ~ spl11_88 ),
inference(resolution,[],[f727,f212]) ).
fof(f2997,plain,
( spl11_191
| ~ spl11_14
| ~ spl11_87 ),
inference(avatar_split_clause,[],[f860,f722,f211,f2995]) ).
fof(f860,plain,
( ! [X0,X1] : subset(X0,union(X0,X1))
| ~ spl11_14
| ~ spl11_87 ),
inference(duplicate_literal_removal,[],[f839]) ).
fof(f839,plain,
( ! [X0,X1] :
( subset(X0,union(X0,X1))
| subset(X0,union(X0,X1)) )
| ~ spl11_14
| ~ spl11_87 ),
inference(resolution,[],[f723,f212]) ).
fof(f2993,plain,
( spl11_190
| ~ spl11_82
| ~ spl11_83 ),
inference(avatar_split_clause,[],[f2547,f706,f669,f2991]) ).
fof(f2991,plain,
( spl11_190
<=> ! [X0] : subset(difference(sK4,X0),sum(sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_190])]) ).
fof(f2547,plain,
( ! [X0] : subset(difference(sK4,X0),sum(sK3))
| ~ spl11_82
| ~ spl11_83 ),
inference(duplicate_literal_removal,[],[f2544]) ).
fof(f2544,plain,
( ! [X0] :
( subset(difference(sK4,X0),sum(sK3))
| subset(difference(sK4,X0),sum(sK3)) )
| ~ spl11_82
| ~ spl11_83 ),
inference(resolution,[],[f670,f707]) ).
fof(f2989,plain,
( spl11_189
| ~ spl11_15
| ~ spl11_86 ),
inference(avatar_split_clause,[],[f838,f718,f215,f2987]) ).
fof(f2987,plain,
( spl11_189
<=> ! [X0,X1] : subset(intersection(X0,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_189])]) ).
fof(f838,plain,
( ! [X0,X1] : subset(intersection(X0,X1),X1)
| ~ spl11_15
| ~ spl11_86 ),
inference(duplicate_literal_removal,[],[f822]) ).
fof(f822,plain,
( ! [X0,X1] :
( subset(intersection(X0,X1),X1)
| subset(intersection(X0,X1),X1) )
| ~ spl11_15
| ~ spl11_86 ),
inference(resolution,[],[f719,f216]) ).
fof(f2985,plain,
( spl11_188
| ~ spl11_6
| ~ spl11_86 ),
inference(avatar_split_clause,[],[f830,f718,f176,f2983]) ).
fof(f2983,plain,
( spl11_188
<=> ! [X0,X1] : subset(intersection(X0,empty_set),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_188])]) ).
fof(f830,plain,
( ! [X0,X1] : subset(intersection(X0,empty_set),X1)
| ~ spl11_6
| ~ spl11_86 ),
inference(resolution,[],[f719,f177]) ).
fof(f2981,plain,
( spl11_187
| ~ spl11_15
| ~ spl11_85 ),
inference(avatar_split_clause,[],[f818,f714,f215,f2979]) ).
fof(f2979,plain,
( spl11_187
<=> ! [X0,X1] : subset(intersection(X0,X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_187])]) ).
fof(f818,plain,
( ! [X0,X1] : subset(intersection(X0,X1),X0)
| ~ spl11_15
| ~ spl11_85 ),
inference(duplicate_literal_removal,[],[f802]) ).
fof(f802,plain,
( ! [X0,X1] :
( subset(intersection(X0,X1),X0)
| subset(intersection(X0,X1),X0) )
| ~ spl11_15
| ~ spl11_85 ),
inference(resolution,[],[f715,f216]) ).
fof(f2977,plain,
( spl11_186
| ~ spl11_6
| ~ spl11_85 ),
inference(avatar_split_clause,[],[f810,f714,f176,f2975]) ).
fof(f2975,plain,
( spl11_186
<=> ! [X0,X1] : subset(intersection(empty_set,X0),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_186])]) ).
fof(f810,plain,
( ! [X0,X1] : subset(intersection(empty_set,X0),X1)
| ~ spl11_6
| ~ spl11_85 ),
inference(resolution,[],[f715,f177]) ).
fof(f2973,plain,
( spl11_185
| ~ spl11_83
| ~ spl11_84 ),
inference(avatar_split_clause,[],[f801,f710,f706,f2971]) ).
fof(f2971,plain,
( spl11_185
<=> ! [X0,X1] : subset(difference(X0,X0),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_185])]) ).
fof(f801,plain,
( ! [X0,X1] : subset(difference(X0,X0),X1)
| ~ spl11_83
| ~ spl11_84 ),
inference(duplicate_literal_removal,[],[f786]) ).
fof(f786,plain,
( ! [X0,X1] :
( subset(difference(X0,X0),X1)
| subset(difference(X0,X0),X1) )
| ~ spl11_83
| ~ spl11_84 ),
inference(resolution,[],[f711,f707]) ).
fof(f2969,plain,
( spl11_184
| ~ spl11_15
| ~ spl11_83 ),
inference(avatar_split_clause,[],[f785,f706,f215,f2967]) ).
fof(f2967,plain,
( spl11_184
<=> ! [X0,X1] : subset(difference(X0,X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_184])]) ).
fof(f785,plain,
( ! [X0,X1] : subset(difference(X0,X1),X0)
| ~ spl11_15
| ~ spl11_83 ),
inference(duplicate_literal_removal,[],[f769]) ).
fof(f769,plain,
( ! [X0,X1] :
( subset(difference(X0,X1),X0)
| subset(difference(X0,X1),X0) )
| ~ spl11_15
| ~ spl11_83 ),
inference(resolution,[],[f707,f216]) ).
fof(f2965,plain,
( spl11_183
| ~ spl11_6
| ~ spl11_83 ),
inference(avatar_split_clause,[],[f777,f706,f176,f2963]) ).
fof(f2963,plain,
( spl11_183
<=> ! [X0,X1] : subset(difference(empty_set,X0),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_183])]) ).
fof(f777,plain,
( ! [X0,X1] : subset(difference(empty_set,X0),X1)
| ~ spl11_6
| ~ spl11_83 ),
inference(resolution,[],[f707,f177]) ).
fof(f2961,plain,
( spl11_182
| ~ spl11_34
| ~ spl11_60 ),
inference(avatar_split_clause,[],[f544,f529,f328,f2959]) ).
fof(f2959,plain,
( spl11_182
<=> ! [X0,X1] : upper_bound(X0,X1,sum(empty_set)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_182])]) ).
fof(f544,plain,
( ! [X0,X1] : upper_bound(X0,X1,sum(empty_set))
| ~ spl11_34
| ~ spl11_60 ),
inference(resolution,[],[f530,f329]) ).
fof(f2957,plain,
( spl11_181
| ~ spl11_27
| ~ spl11_60 ),
inference(avatar_split_clause,[],[f542,f529,f275,f2955]) ).
fof(f2955,plain,
( spl11_181
<=> ! [X0] : ~ member(X0,sum(sum(empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_181])]) ).
fof(f542,plain,
( ! [X0] : ~ member(X0,sum(sum(empty_set)))
| ~ spl11_27
| ~ spl11_60 ),
inference(resolution,[],[f530,f276]) ).
fof(f2953,plain,
( spl11_180
| ~ spl11_25
| ~ spl11_60 ),
inference(avatar_split_clause,[],[f541,f529,f267,f2951]) ).
fof(f2951,plain,
( spl11_180
<=> ! [X0] : member(X0,product(sum(empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_180])]) ).
fof(f541,plain,
( ! [X0] : member(X0,product(sum(empty_set)))
| ~ spl11_25
| ~ spl11_60 ),
inference(resolution,[],[f530,f268]) ).
fof(f2944,plain,
( spl11_179
| ~ spl11_49
| ~ spl11_56 ),
inference(avatar_split_clause,[],[f517,f496,f464,f2942]) ).
fof(f2942,plain,
( spl11_179
<=> ! [X0,X1] :
( ~ member(X0,sK3)
| sK4 = X0
| ~ apply(sK1,sK4,X0)
| ~ member(X0,X1)
| ~ member(sK4,X1)
| ~ order(sK1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_179])]) ).
fof(f464,plain,
( spl11_49
<=> ! [X5,X0,X6,X1] :
( X5 = X6
| ~ apply(X0,X6,X5)
| ~ apply(X0,X5,X6)
| ~ member(X6,X1)
| ~ member(X5,X1)
| ~ order(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_49])]) ).
fof(f517,plain,
( ! [X0,X1] :
( ~ member(X0,sK3)
| sK4 = X0
| ~ apply(sK1,sK4,X0)
| ~ member(X0,X1)
| ~ member(sK4,X1)
| ~ order(sK1,X1) )
| ~ spl11_49
| ~ spl11_56 ),
inference(resolution,[],[f497,f465]) ).
fof(f465,plain,
( ! [X0,X1,X6,X5] :
( ~ apply(X0,X6,X5)
| X5 = X6
| ~ apply(X0,X5,X6)
| ~ member(X6,X1)
| ~ member(X5,X1)
| ~ order(X0,X1) )
| ~ spl11_49 ),
inference(avatar_component_clause,[],[f464]) ).
fof(f2904,plain,
( spl11_178
| ~ spl11_55
| ~ spl11_126 ),
inference(avatar_split_clause,[],[f1606,f1506,f489,f2902]) ).
fof(f2902,plain,
( spl11_178
<=> ! [X2,X0,X1] :
( ~ member(sum(sK3),X0)
| ~ member(sum(sK3),X1)
| member(X2,sum(intersection(X0,X1)))
| ~ member(X2,sK4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_178])]) ).
fof(f1606,plain,
( ! [X2,X0,X1] :
( ~ member(sum(sK3),X0)
| ~ member(sum(sK3),X1)
| member(X2,sum(intersection(X0,X1)))
| ~ member(X2,sK4) )
| ~ spl11_55
| ~ spl11_126 ),
inference(resolution,[],[f1507,f490]) ).
fof(f2900,plain,
( spl11_177
| ~ spl11_55
| ~ spl11_125 ),
inference(avatar_split_clause,[],[f1557,f1502,f489,f2898]) ).
fof(f2898,plain,
( spl11_177
<=> ! [X2,X0,X1] :
( ~ member(sum(sK3),X0)
| member(sum(sK3),X1)
| member(X2,sum(difference(X0,X1)))
| ~ member(X2,sK4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_177])]) ).
fof(f1557,plain,
( ! [X2,X0,X1] :
( ~ member(sum(sK3),X0)
| member(sum(sK3),X1)
| member(X2,sum(difference(X0,X1)))
| ~ member(X2,sK4) )
| ~ spl11_55
| ~ spl11_125 ),
inference(resolution,[],[f1503,f490]) ).
fof(f2883,plain,
( spl11_176
| ~ spl11_14
| ~ spl11_60 ),
inference(avatar_split_clause,[],[f540,f529,f211,f2881]) ).
fof(f2881,plain,
( spl11_176
<=> ! [X0] : subset(sum(empty_set),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_176])]) ).
fof(f540,plain,
( ! [X0] : subset(sum(empty_set),X0)
| ~ spl11_14
| ~ spl11_60 ),
inference(resolution,[],[f530,f212]) ).
fof(f2879,plain,
( spl11_175
| ~ spl11_15
| ~ spl11_59 ),
inference(avatar_split_clause,[],[f539,f525,f215,f2877]) ).
fof(f2877,plain,
( spl11_175
<=> ! [X0] : subset(X0,product(empty_set)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_175])]) ).
fof(f539,plain,
( ! [X0] : subset(X0,product(empty_set))
| ~ spl11_15
| ~ spl11_59 ),
inference(resolution,[],[f526,f216]) ).
fof(f2871,plain,
( spl11_174
| ~ spl11_55
| ~ spl11_120 ),
inference(avatar_split_clause,[],[f1467,f1324,f489,f2869]) ).
fof(f1467,plain,
( ! [X2,X0,X1] :
( upper_bound(X0,X1,difference(X2,sum(sK3)))
| ~ member(sK9(X1,difference(X2,sum(sK3)),X0),sK4) )
| ~ spl11_55
| ~ spl11_120 ),
inference(resolution,[],[f1325,f490]) ).
fof(f2859,plain,
( spl11_173
| ~ spl11_55
| ~ spl11_106 ),
inference(avatar_split_clause,[],[f1178,f1026,f489,f2857]) ).
fof(f1178,plain,
( ! [X0,X1] :
( ~ member(X0,sum(difference(X1,sum(sK3))))
| ~ member(sK7(X0,difference(X1,sum(sK3))),sK4) )
| ~ spl11_55
| ~ spl11_106 ),
inference(resolution,[],[f1027,f490]) ).
fof(f2855,plain,
( spl11_172
| ~ spl11_55
| ~ spl11_102 ),
inference(avatar_split_clause,[],[f1104,f1010,f489,f2853]) ).
fof(f1104,plain,
( ! [X0,X1] :
( member(X0,product(difference(X1,sum(sK3))))
| ~ member(sK6(X0,difference(X1,sum(sK3))),sK4) )
| ~ spl11_55
| ~ spl11_102 ),
inference(resolution,[],[f1011,f490]) ).
fof(f2815,plain,
( spl11_171
| ~ spl11_55
| ~ spl11_88 ),
inference(avatar_split_clause,[],[f875,f726,f489,f2813]) ).
fof(f875,plain,
( ! [X0,X1] :
( subset(X0,union(X1,sum(sK3)))
| ~ member(sK5(X0,union(X1,sum(sK3))),sK4) )
| ~ spl11_55
| ~ spl11_88 ),
inference(resolution,[],[f727,f490]) ).
fof(f2811,plain,
( spl11_170
| ~ spl11_34
| ~ spl11_155 ),
inference(avatar_split_clause,[],[f2569,f2319,f328,f2808]) ).
fof(f2569,plain,
( upper_bound(sK4,sK1,sK3)
| ~ spl11_34
| ~ spl11_155 ),
inference(duplicate_literal_removal,[],[f2554]) ).
fof(f2554,plain,
( upper_bound(sK4,sK1,sK3)
| upper_bound(sK4,sK1,sK3)
| ~ spl11_34
| ~ spl11_155 ),
inference(resolution,[],[f2320,f329]) ).
fof(f2806,plain,
( spl11_169
| ~ spl11_55
| ~ spl11_87 ),
inference(avatar_split_clause,[],[f853,f722,f489,f2804]) ).
fof(f853,plain,
( ! [X0,X1] :
( subset(X0,union(sum(sK3),X1))
| ~ member(sK5(X0,union(sum(sK3),X1)),sK4) )
| ~ spl11_55
| ~ spl11_87 ),
inference(resolution,[],[f723,f490]) ).
fof(f2802,plain,
( spl11_168
| ~ spl11_55
| ~ spl11_84 ),
inference(avatar_split_clause,[],[f797,f710,f489,f2800]) ).
fof(f797,plain,
( ! [X0,X1] :
( subset(difference(X0,sum(sK3)),X1)
| ~ member(sK5(difference(X0,sum(sK3)),X1),sK4) )
| ~ spl11_55
| ~ spl11_84 ),
inference(resolution,[],[f711,f490]) ).
fof(f2702,plain,
( spl11_167
| ~ spl11_55
| ~ spl11_94 ),
inference(avatar_split_clause,[],[f961,f750,f489,f2700]) ).
fof(f2700,plain,
( spl11_167
<=> ! [X2,X0,X1] :
( member(X0,sum(union(sum(sK3),X1)))
| ~ member(X0,X2)
| ~ member(X2,sK4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_167])]) ).
fof(f961,plain,
( ! [X2,X0,X1] :
( member(X0,sum(union(sum(sK3),X1)))
| ~ member(X0,X2)
| ~ member(X2,sK4) )
| ~ spl11_55
| ~ spl11_94 ),
inference(resolution,[],[f751,f490]) ).
fof(f2698,plain,
( spl11_166
| ~ spl11_55
| ~ spl11_93 ),
inference(avatar_split_clause,[],[f930,f746,f489,f2696]) ).
fof(f2696,plain,
( spl11_166
<=> ! [X2,X0,X1] :
( member(X0,sum(union(X1,sum(sK3))))
| ~ member(X0,X2)
| ~ member(X2,sK4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_166])]) ).
fof(f930,plain,
( ! [X2,X0,X1] :
( member(X0,sum(union(X1,sum(sK3))))
| ~ member(X0,X2)
| ~ member(X2,sK4) )
| ~ spl11_55
| ~ spl11_93 ),
inference(resolution,[],[f747,f490]) ).
fof(f2694,plain,
( spl11_165
| ~ spl11_46
| ~ spl11_56 ),
inference(avatar_split_clause,[],[f515,f496,f438,f2692]) ).
fof(f438,plain,
( spl11_46
<=> ! [X2,X0,X1] :
( greatest(X2,X0,X1)
| ~ apply(X0,sK8(X0,X1,X2),X2)
| ~ member(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_46])]) ).
fof(f515,plain,
( ! [X0] :
( ~ member(sK8(sK1,X0,sK4),sK3)
| greatest(sK4,sK1,X0)
| ~ member(sK4,X0) )
| ~ spl11_46
| ~ spl11_56 ),
inference(resolution,[],[f497,f439]) ).
fof(f439,plain,
( ! [X2,X0,X1] :
( ~ apply(X0,sK8(X0,X1,X2),X2)
| greatest(X2,X0,X1)
| ~ member(X2,X1) )
| ~ spl11_46 ),
inference(avatar_component_clause,[],[f438]) ).
fof(f2674,plain,
( spl11_164
| ~ spl11_14
| ~ spl11_82 ),
inference(avatar_split_clause,[],[f2553,f669,f211,f2671]) ).
fof(f2671,plain,
( spl11_164
<=> subset(sK4,sum(sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_164])]) ).
fof(f2553,plain,
( subset(sK4,sum(sK3))
| ~ spl11_14
| ~ spl11_82 ),
inference(duplicate_literal_removal,[],[f2538]) ).
fof(f2538,plain,
( subset(sK4,sum(sK3))
| subset(sK4,sum(sK3))
| ~ spl11_14
| ~ spl11_82 ),
inference(resolution,[],[f670,f212]) ).
fof(f2651,plain,
( spl11_163
| ~ spl11_4
| ~ spl11_126 ),
inference(avatar_split_clause,[],[f1612,f1506,f166,f2649]) ).
fof(f2649,plain,
( spl11_163
<=> ! [X0,X1] :
( ~ member(sK3,X0)
| ~ member(sK3,X1)
| member(sK4,sum(intersection(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_163])]) ).
fof(f1612,plain,
( ! [X0,X1] :
( ~ member(sK3,X0)
| ~ member(sK3,X1)
| member(sK4,sum(intersection(X0,X1))) )
| ~ spl11_4
| ~ spl11_126 ),
inference(resolution,[],[f1507,f168]) ).
fof(f2647,plain,
( spl11_162
| ~ spl11_4
| ~ spl11_125 ),
inference(avatar_split_clause,[],[f1563,f1502,f166,f2645]) ).
fof(f2645,plain,
( spl11_162
<=> ! [X0,X1] :
( ~ member(sK3,X0)
| member(sK3,X1)
| member(sK4,sum(difference(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_162])]) ).
fof(f1563,plain,
( ! [X0,X1] :
( ~ member(sK3,X0)
| member(sK3,X1)
| member(sK4,sum(difference(X0,X1))) )
| ~ spl11_4
| ~ spl11_125 ),
inference(resolution,[],[f1503,f168]) ).
fof(f2643,plain,
( spl11_161
| ~ spl11_55
| ~ spl11_81 ),
inference(avatar_split_clause,[],[f692,f643,f489,f2641]) ).
fof(f2641,plain,
( spl11_161
<=> ! [X0,X1] :
( member(X0,sum(power_set(X1)))
| ~ subset(sum(sK3),X1)
| ~ member(X0,sK4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_161])]) ).
fof(f692,plain,
( ! [X0,X1] :
( member(X0,sum(power_set(X1)))
| ~ subset(sum(sK3),X1)
| ~ member(X0,sK4) )
| ~ spl11_55
| ~ spl11_81 ),
inference(resolution,[],[f644,f490]) ).
fof(f2573,plain,
( spl11_160
| ~ spl11_33
| ~ spl11_55 ),
inference(avatar_split_clause,[],[f511,f489,f324,f2571]) ).
fof(f2571,plain,
( spl11_160
<=> ! [X0,X1] :
( ~ member(X0,sK4)
| ~ member(X1,X0)
| member(X1,sum(sum(sK3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_160])]) ).
fof(f511,plain,
( ! [X0,X1] :
( ~ member(X0,sK4)
| ~ member(X1,X0)
| member(X1,sum(sum(sK3))) )
| ~ spl11_33
| ~ spl11_55 ),
inference(resolution,[],[f490,f325]) ).
fof(f2483,plain,
( spl11_159
| ~ spl11_42
| ~ spl11_45 ),
inference(avatar_split_clause,[],[f435,f422,f386,f2481]) ).
fof(f2481,plain,
( spl11_159
<=> ! [X0,X3,X2,X1] :
( greatest(X0,X1,unordered_pair(X2,X3))
| ~ member(X0,unordered_pair(X2,X3))
| sK8(X1,unordered_pair(X2,X3),X0) = X2
| sK8(X1,unordered_pair(X2,X3),X0) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_159])]) ).
fof(f386,plain,
( spl11_42
<=> ! [X2,X0,X1] :
( X0 = X2
| X0 = X1
| ~ member(X0,unordered_pair(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_42])]) ).
fof(f435,plain,
( ! [X2,X3,X0,X1] :
( greatest(X0,X1,unordered_pair(X2,X3))
| ~ member(X0,unordered_pair(X2,X3))
| sK8(X1,unordered_pair(X2,X3),X0) = X2
| sK8(X1,unordered_pair(X2,X3),X0) = X3 )
| ~ spl11_42
| ~ spl11_45 ),
inference(resolution,[],[f423,f387]) ).
fof(f387,plain,
( ! [X2,X0,X1] :
( ~ member(X0,unordered_pair(X1,X2))
| X0 = X1
| X0 = X2 )
| ~ spl11_42 ),
inference(avatar_component_clause,[],[f386]) ).
fof(f2479,plain,
( spl11_158
| ~ spl11_43
| ~ spl11_45 ),
inference(avatar_split_clause,[],[f430,f422,f390,f2477]) ).
fof(f2477,plain,
( spl11_158
<=> ! [X0,X3,X2,X1] :
( greatest(X0,X1,union(X2,X3))
| ~ member(X0,union(X2,X3))
| member(sK8(X1,union(X2,X3),X0),X2)
| member(sK8(X1,union(X2,X3),X0),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_158])]) ).
fof(f390,plain,
( spl11_43
<=> ! [X2,X0,X1] :
( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_43])]) ).
fof(f430,plain,
( ! [X2,X3,X0,X1] :
( greatest(X0,X1,union(X2,X3))
| ~ member(X0,union(X2,X3))
| member(sK8(X1,union(X2,X3),X0),X2)
| member(sK8(X1,union(X2,X3),X0),X3) )
| ~ spl11_43
| ~ spl11_45 ),
inference(resolution,[],[f423,f391]) ).
fof(f391,plain,
( ! [X2,X0,X1] :
( ~ member(X0,union(X1,X2))
| member(X0,X1)
| member(X0,X2) )
| ~ spl11_43 ),
inference(avatar_component_clause,[],[f390]) ).
fof(f2329,plain,
( spl11_157
| ~ spl11_38
| ~ spl11_50 ),
inference(avatar_split_clause,[],[f475,f468,f370,f2327]) ).
fof(f468,plain,
( spl11_50
<=> ! [X0,X3,X2,X1] :
( sP0(X0,X1,X2,X3)
| upper_bound(sK10(X0,X1,X2,X3),X1,X2)
| ~ upper_bound(X0,X1,X2)
| ~ member(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_50])]) ).
fof(f475,plain,
( ! [X2,X3,X0,X1,X4] :
( sP0(X0,X1,X2,X3)
| ~ upper_bound(X0,X1,X2)
| ~ member(X0,X2)
| ~ member(X4,X2)
| apply(X1,X4,sK10(X0,X1,X2,X3)) )
| ~ spl11_38
| ~ spl11_50 ),
inference(resolution,[],[f469,f371]) ).
fof(f469,plain,
( ! [X2,X3,X0,X1] :
( upper_bound(sK10(X0,X1,X2,X3),X1,X2)
| sP0(X0,X1,X2,X3)
| ~ upper_bound(X0,X1,X2)
| ~ member(X0,X2) )
| ~ spl11_50 ),
inference(avatar_component_clause,[],[f468]) ).
fof(f2325,plain,
( spl11_156
| ~ spl11_16
| ~ spl11_48 ),
inference(avatar_split_clause,[],[f459,f448,f219,f2323]) ).
fof(f2323,plain,
( spl11_156
<=> ! [X4,X0,X3,X2,X1] :
( sP0(X0,X1,X2,difference(X3,X4))
| ~ upper_bound(X0,X1,X2)
| ~ member(X0,X2)
| member(sK10(X0,X1,X2,difference(X3,X4)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_156])]) ).
fof(f448,plain,
( spl11_48
<=> ! [X0,X3,X2,X1] :
( sP0(X0,X1,X2,X3)
| member(sK10(X0,X1,X2,X3),X3)
| ~ upper_bound(X0,X1,X2)
| ~ member(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_48])]) ).
fof(f459,plain,
( ! [X2,X3,X0,X1,X4] :
( sP0(X0,X1,X2,difference(X3,X4))
| ~ upper_bound(X0,X1,X2)
| ~ member(X0,X2)
| member(sK10(X0,X1,X2,difference(X3,X4)),X3) )
| ~ spl11_16
| ~ spl11_48 ),
inference(resolution,[],[f449,f220]) ).
fof(f449,plain,
( ! [X2,X3,X0,X1] :
( member(sK10(X0,X1,X2,X3),X3)
| sP0(X0,X1,X2,X3)
| ~ upper_bound(X0,X1,X2)
| ~ member(X0,X2) )
| ~ spl11_48 ),
inference(avatar_component_clause,[],[f448]) ).
fof(f2321,plain,
( spl11_155
| ~ spl11_39
| ~ spl11_56 ),
inference(avatar_split_clause,[],[f514,f496,f374,f2319]) ).
fof(f374,plain,
( spl11_39
<=> ! [X2,X0,X1] :
( upper_bound(X2,X0,X1)
| ~ apply(X0,sK9(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_39])]) ).
fof(f514,plain,
( ! [X0] :
( ~ member(sK9(sK1,X0,sK4),sK3)
| upper_bound(sK4,sK1,X0) )
| ~ spl11_39
| ~ spl11_56 ),
inference(resolution,[],[f497,f375]) ).
fof(f375,plain,
( ! [X2,X0,X1] :
( ~ apply(X0,sK9(X0,X1,X2),X2)
| upper_bound(X2,X0,X1) )
| ~ spl11_39 ),
inference(avatar_component_clause,[],[f374]) ).
fof(f2317,plain,
( spl11_154
| ~ spl11_17
| ~ spl11_48 ),
inference(avatar_split_clause,[],[f458,f448,f223,f2315]) ).
fof(f2315,plain,
( spl11_154
<=> ! [X4,X0,X3,X2,X1] :
( sP0(X0,X1,X2,difference(X3,X4))
| ~ upper_bound(X0,X1,X2)
| ~ member(X0,X2)
| ~ member(sK10(X0,X1,X2,difference(X3,X4)),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_154])]) ).
fof(f458,plain,
( ! [X2,X3,X0,X1,X4] :
( sP0(X0,X1,X2,difference(X3,X4))
| ~ upper_bound(X0,X1,X2)
| ~ member(X0,X2)
| ~ member(sK10(X0,X1,X2,difference(X3,X4)),X4) )
| ~ spl11_17
| ~ spl11_48 ),
inference(resolution,[],[f449,f224]) ).
fof(f2313,plain,
( spl11_153
| ~ spl11_18
| ~ spl11_48 ),
inference(avatar_split_clause,[],[f455,f448,f227,f2311]) ).
fof(f2311,plain,
( spl11_153
<=> ! [X4,X0,X3,X2,X1] :
( sP0(X0,X1,X2,intersection(X3,X4))
| ~ upper_bound(X0,X1,X2)
| ~ member(X0,X2)
| member(sK10(X0,X1,X2,intersection(X3,X4)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_153])]) ).
fof(f455,plain,
( ! [X2,X3,X0,X1,X4] :
( sP0(X0,X1,X2,intersection(X3,X4))
| ~ upper_bound(X0,X1,X2)
| ~ member(X0,X2)
| member(sK10(X0,X1,X2,intersection(X3,X4)),X3) )
| ~ spl11_18
| ~ spl11_48 ),
inference(resolution,[],[f449,f228]) ).
fof(f2309,plain,
( spl11_152
| ~ spl11_19
| ~ spl11_48 ),
inference(avatar_split_clause,[],[f454,f448,f231,f2307]) ).
fof(f2307,plain,
( spl11_152
<=> ! [X4,X0,X3,X2,X1] :
( sP0(X0,X1,X2,intersection(X3,X4))
| ~ upper_bound(X0,X1,X2)
| ~ member(X0,X2)
| member(sK10(X0,X1,X2,intersection(X3,X4)),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_152])]) ).
fof(f454,plain,
( ! [X2,X3,X0,X1,X4] :
( sP0(X0,X1,X2,intersection(X3,X4))
| ~ upper_bound(X0,X1,X2)
| ~ member(X0,X2)
| member(sK10(X0,X1,X2,intersection(X3,X4)),X4) )
| ~ spl11_19
| ~ spl11_48 ),
inference(resolution,[],[f449,f232]) ).
fof(f2305,plain,
( spl11_151
| ~ spl11_33
| ~ spl11_48 ),
inference(avatar_split_clause,[],[f451,f448,f324,f2303]) ).
fof(f2303,plain,
( spl11_151
<=> ! [X4,X0,X3,X2,X1] :
( sP0(X0,X1,X2,X3)
| ~ upper_bound(X0,X1,X2)
| ~ member(X0,X2)
| ~ member(X4,sK10(X0,X1,X2,X3))
| member(X4,sum(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_151])]) ).
fof(f451,plain,
( ! [X2,X3,X0,X1,X4] :
( sP0(X0,X1,X2,X3)
| ~ upper_bound(X0,X1,X2)
| ~ member(X0,X2)
| ~ member(X4,sK10(X0,X1,X2,X3))
| member(X4,sum(X3)) )
| ~ spl11_33
| ~ spl11_48 ),
inference(resolution,[],[f449,f325]) ).
fof(f2223,plain,
( spl11_150
| ~ spl11_23
| ~ spl11_48 ),
inference(avatar_split_clause,[],[f452,f448,f259,f2221]) ).
fof(f2221,plain,
( spl11_150
<=> ! [X4,X0,X3,X2,X1] :
( sP0(X0,X1,X2,X3)
| ~ upper_bound(X0,X1,X2)
| ~ member(X0,X2)
| member(sK10(X0,X1,X2,X3),X4)
| ~ subset(X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_150])]) ).
fof(f452,plain,
( ! [X2,X3,X0,X1,X4] :
( sP0(X0,X1,X2,X3)
| ~ upper_bound(X0,X1,X2)
| ~ member(X0,X2)
| member(sK10(X0,X1,X2,X3),X4)
| ~ subset(X3,X4) )
| ~ spl11_23
| ~ spl11_48 ),
inference(resolution,[],[f449,f260]) ).
fof(f2219,plain,
( spl11_149
| ~ spl11_34
| ~ spl11_43 ),
inference(avatar_split_clause,[],[f420,f390,f328,f2217]) ).
fof(f420,plain,
( ! [X2,X3,X0,X1] :
( member(sK9(X0,union(X1,X2),X3),X1)
| member(sK9(X0,union(X1,X2),X3),X2)
| upper_bound(X3,X0,union(X1,X2)) )
| ~ spl11_34
| ~ spl11_43 ),
inference(resolution,[],[f391,f329]) ).
fof(f2215,plain,
( spl11_148
| ~ spl11_34
| ~ spl11_42 ),
inference(avatar_split_clause,[],[f414,f386,f328,f2213]) ).
fof(f2213,plain,
( spl11_148
<=> ! [X0,X3,X2,X1] :
( sK9(X0,unordered_pair(X1,X2),X3) = X1
| sK9(X0,unordered_pair(X1,X2),X3) = X2
| upper_bound(X3,X0,unordered_pair(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_148])]) ).
fof(f414,plain,
( ! [X2,X3,X0,X1] :
( sK9(X0,unordered_pair(X1,X2),X3) = X1
| sK9(X0,unordered_pair(X1,X2),X3) = X2
| upper_bound(X3,X0,unordered_pair(X1,X2)) )
| ~ spl11_34
| ~ spl11_42 ),
inference(resolution,[],[f387,f329]) ).
fof(f2190,plain,
( spl11_147
| ~ spl11_10
| ~ spl11_48 ),
inference(avatar_split_clause,[],[f460,f448,f192,f2188]) ).
fof(f2188,plain,
( spl11_147
<=> ! [X0,X3,X2,X1] :
( sP0(X0,X1,X2,singleton(X3))
| ~ upper_bound(X0,X1,X2)
| ~ member(X0,X2)
| sK10(X0,X1,X2,singleton(X3)) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_147])]) ).
fof(f460,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,X1,X2,singleton(X3))
| ~ upper_bound(X0,X1,X2)
| ~ member(X0,X2)
| sK10(X0,X1,X2,singleton(X3)) = X3 )
| ~ spl11_10
| ~ spl11_48 ),
inference(resolution,[],[f449,f193]) ).
fof(f2186,plain,
( spl11_146
| ~ spl11_11
| ~ spl11_48 ),
inference(avatar_split_clause,[],[f453,f448,f196,f2184]) ).
fof(f2184,plain,
( spl11_146
<=> ! [X0,X3,X2,X1] :
( sP0(X0,X1,X2,power_set(X3))
| ~ upper_bound(X0,X1,X2)
| ~ member(X0,X2)
| subset(sK10(X0,X1,X2,power_set(X3)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_146])]) ).
fof(f453,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,X1,X2,power_set(X3))
| ~ upper_bound(X0,X1,X2)
| ~ member(X0,X2)
| subset(sK10(X0,X1,X2,power_set(X3)),X3) )
| ~ spl11_11
| ~ spl11_48 ),
inference(resolution,[],[f449,f197]) ).
fof(f2027,plain,
( spl11_145
| ~ spl11_27
| ~ spl11_43 ),
inference(avatar_split_clause,[],[f419,f390,f275,f2025]) ).
fof(f419,plain,
( ! [X2,X0,X1] :
( member(sK7(X0,union(X1,X2)),X1)
| member(sK7(X0,union(X1,X2)),X2)
| ~ member(X0,sum(union(X1,X2))) )
| ~ spl11_27
| ~ spl11_43 ),
inference(resolution,[],[f391,f276]) ).
fof(f2023,plain,
( spl11_144
| ~ spl11_25
| ~ spl11_43 ),
inference(avatar_split_clause,[],[f418,f390,f267,f2021]) ).
fof(f418,plain,
( ! [X2,X0,X1] :
( member(sK6(X0,union(X1,X2)),X1)
| member(sK6(X0,union(X1,X2)),X2)
| member(X0,product(union(X1,X2))) )
| ~ spl11_25
| ~ spl11_43 ),
inference(resolution,[],[f391,f268]) ).
fof(f2002,plain,
( spl11_143
| ~ spl11_27
| ~ spl11_42 ),
inference(avatar_split_clause,[],[f413,f386,f275,f2000]) ).
fof(f2000,plain,
( spl11_143
<=> ! [X2,X0,X1] :
( sK7(X0,unordered_pair(X1,X2)) = X1
| sK7(X0,unordered_pair(X1,X2)) = X2
| ~ member(X0,sum(unordered_pair(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_143])]) ).
fof(f413,plain,
( ! [X2,X0,X1] :
( sK7(X0,unordered_pair(X1,X2)) = X1
| sK7(X0,unordered_pair(X1,X2)) = X2
| ~ member(X0,sum(unordered_pair(X1,X2))) )
| ~ spl11_27
| ~ spl11_42 ),
inference(resolution,[],[f387,f276]) ).
fof(f1998,plain,
( spl11_142
| ~ spl11_25
| ~ spl11_42 ),
inference(avatar_split_clause,[],[f412,f386,f267,f1996]) ).
fof(f1996,plain,
( spl11_142
<=> ! [X2,X0,X1] :
( sK6(X0,unordered_pair(X1,X2)) = X1
| sK6(X0,unordered_pair(X1,X2)) = X2
| member(X0,product(unordered_pair(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_142])]) ).
fof(f412,plain,
( ! [X2,X0,X1] :
( sK6(X0,unordered_pair(X1,X2)) = X1
| sK6(X0,unordered_pair(X1,X2)) = X2
| member(X0,product(unordered_pair(X1,X2))) )
| ~ spl11_25
| ~ spl11_42 ),
inference(resolution,[],[f387,f268]) ).
fof(f1780,plain,
( spl11_141
| ~ spl11_44
| ~ spl11_94 ),
inference(avatar_split_clause,[],[f965,f750,f394,f1778]) ).
fof(f1778,plain,
( spl11_141
<=> ! [X0,X1] :
( member(X0,sum(union(sK2,X1)))
| ~ member(X0,sK4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_141])]) ).
fof(f965,plain,
( ! [X0,X1] :
( member(X0,sum(union(sK2,X1)))
| ~ member(X0,sK4) )
| ~ spl11_44
| ~ spl11_94 ),
inference(resolution,[],[f751,f396]) ).
fof(f1749,plain,
( spl11_140
| ~ spl11_32
| ~ spl11_45 ),
inference(avatar_split_clause,[],[f436,f422,f320,f1747]) ).
fof(f436,plain,
( ! [X2,X3,X0,X1] :
( greatest(X0,X1,product(X2))
| ~ member(X0,product(X2))
| ~ member(X3,X2)
| member(sK8(X1,product(X2),X0),X3) )
| ~ spl11_32
| ~ spl11_45 ),
inference(resolution,[],[f423,f321]) ).
fof(f1745,plain,
( spl11_139
| ~ spl11_16
| ~ spl11_45 ),
inference(avatar_split_clause,[],[f433,f422,f219,f1743]) ).
fof(f433,plain,
( ! [X2,X3,X0,X1] :
( greatest(X0,X1,difference(X2,X3))
| ~ member(X0,difference(X2,X3))
| member(sK8(X1,difference(X2,X3),X0),X2) )
| ~ spl11_16
| ~ spl11_45 ),
inference(resolution,[],[f423,f220]) ).
fof(f1741,plain,
( spl11_138
| ~ spl11_17
| ~ spl11_45 ),
inference(avatar_split_clause,[],[f432,f422,f223,f1739]) ).
fof(f432,plain,
( ! [X2,X3,X0,X1] :
( greatest(X0,X1,difference(X2,X3))
| ~ member(X0,difference(X2,X3))
| ~ member(sK8(X1,difference(X2,X3),X0),X3) )
| ~ spl11_17
| ~ spl11_45 ),
inference(resolution,[],[f423,f224]) ).
fof(f1737,plain,
( spl11_137
| ~ spl11_18
| ~ spl11_45 ),
inference(avatar_split_clause,[],[f429,f422,f227,f1735]) ).
fof(f429,plain,
( ! [X2,X3,X0,X1] :
( greatest(X0,X1,intersection(X2,X3))
| ~ member(X0,intersection(X2,X3))
| member(sK8(X1,intersection(X2,X3),X0),X2) )
| ~ spl11_18
| ~ spl11_45 ),
inference(resolution,[],[f423,f228]) ).
fof(f1733,plain,
( spl11_136
| ~ spl11_19
| ~ spl11_45 ),
inference(avatar_split_clause,[],[f428,f422,f231,f1731]) ).
fof(f428,plain,
( ! [X2,X3,X0,X1] :
( greatest(X0,X1,intersection(X2,X3))
| ~ member(X0,intersection(X2,X3))
| member(sK8(X1,intersection(X2,X3),X0),X3) )
| ~ spl11_19
| ~ spl11_45 ),
inference(resolution,[],[f423,f232]) ).
fof(f1729,plain,
( spl11_135
| ~ spl11_14
| ~ spl11_43 ),
inference(avatar_split_clause,[],[f417,f390,f211,f1727]) ).
fof(f417,plain,
( ! [X2,X0,X1] :
( member(sK5(union(X0,X1),X2),X0)
| member(sK5(union(X0,X1),X2),X1)
| subset(union(X0,X1),X2) )
| ~ spl11_14
| ~ spl11_43 ),
inference(resolution,[],[f391,f212]) ).
fof(f1725,plain,
( spl11_134
| ~ spl11_14
| ~ spl11_42 ),
inference(avatar_split_clause,[],[f411,f386,f211,f1723]) ).
fof(f1723,plain,
( spl11_134
<=> ! [X2,X0,X1] :
( sK5(unordered_pair(X0,X1),X2) = X0
| sK5(unordered_pair(X0,X1),X2) = X1
| subset(unordered_pair(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_134])]) ).
fof(f411,plain,
( ! [X2,X0,X1] :
( sK5(unordered_pair(X0,X1),X2) = X0
| sK5(unordered_pair(X0,X1),X2) = X1
| subset(unordered_pair(X0,X1),X2) )
| ~ spl11_14
| ~ spl11_42 ),
inference(resolution,[],[f387,f212]) ).
fof(f1721,plain,
( spl11_133
| ~ spl11_15
| ~ spl11_41 ),
inference(avatar_split_clause,[],[f408,f382,f215,f1719]) ).
fof(f408,plain,
( ! [X2,X0,X1] :
( ~ member(sK5(X0,intersection(X1,X2)),X2)
| ~ member(sK5(X0,intersection(X1,X2)),X1)
| subset(X0,intersection(X1,X2)) )
| ~ spl11_15
| ~ spl11_41 ),
inference(resolution,[],[f383,f216]) ).
fof(f1717,plain,
( spl11_132
| ~ spl11_15
| ~ spl11_40 ),
inference(avatar_split_clause,[],[f403,f378,f215,f1715]) ).
fof(f403,plain,
( ! [X2,X0,X1] :
( member(sK5(X0,difference(X1,X2)),X2)
| ~ member(sK5(X0,difference(X1,X2)),X1)
| subset(X0,difference(X1,X2)) )
| ~ spl11_15
| ~ spl11_40 ),
inference(resolution,[],[f379,f216]) ).
fof(f1713,plain,
( spl11_131
| ~ spl11_44
| ~ spl11_93 ),
inference(avatar_split_clause,[],[f934,f746,f394,f1711]) ).
fof(f1711,plain,
( spl11_131
<=> ! [X0,X1] :
( member(X0,sum(union(X1,sK2)))
| ~ member(X0,sK4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_131])]) ).
fof(f934,plain,
( ! [X0,X1] :
( member(X0,sum(union(X1,sK2)))
| ~ member(X0,sK4) )
| ~ spl11_44
| ~ spl11_93 ),
inference(resolution,[],[f747,f396]) ).
fof(f1682,plain,
( spl11_130
| ~ spl11_33
| ~ spl11_45 ),
inference(avatar_split_clause,[],[f425,f422,f324,f1680]) ).
fof(f1680,plain,
( spl11_130
<=> ! [X0,X3,X2,X1] :
( greatest(X0,X1,X2)
| ~ member(X0,X2)
| ~ member(X3,sK8(X1,X2,X0))
| member(X3,sum(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_130])]) ).
fof(f425,plain,
( ! [X2,X3,X0,X1] :
( greatest(X0,X1,X2)
| ~ member(X0,X2)
| ~ member(X3,sK8(X1,X2,X0))
| member(X3,sum(X2)) )
| ~ spl11_33
| ~ spl11_45 ),
inference(resolution,[],[f423,f325]) ).
fof(f1652,plain,
( spl11_129
| ~ spl11_10
| ~ spl11_45 ),
inference(avatar_split_clause,[],[f434,f422,f192,f1650]) ).
fof(f1650,plain,
( spl11_129
<=> ! [X2,X0,X1] :
( greatest(X0,X1,singleton(X2))
| ~ member(X0,singleton(X2))
| sK8(X1,singleton(X2),X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_129])]) ).
fof(f434,plain,
( ! [X2,X0,X1] :
( greatest(X0,X1,singleton(X2))
| ~ member(X0,singleton(X2))
| sK8(X1,singleton(X2),X0) = X2 )
| ~ spl11_10
| ~ spl11_45 ),
inference(resolution,[],[f423,f193]) ).
fof(f1648,plain,
( spl11_128
| ~ spl11_11
| ~ spl11_45 ),
inference(avatar_split_clause,[],[f427,f422,f196,f1646]) ).
fof(f1646,plain,
( spl11_128
<=> ! [X2,X0,X1] :
( greatest(X0,X1,power_set(X2))
| ~ member(X0,power_set(X2))
| subset(sK8(X1,power_set(X2),X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_128])]) ).
fof(f427,plain,
( ! [X2,X0,X1] :
( greatest(X0,X1,power_set(X2))
| ~ member(X0,power_set(X2))
| subset(sK8(X1,power_set(X2),X0),X2) )
| ~ spl11_11
| ~ spl11_45 ),
inference(resolution,[],[f423,f197]) ).
fof(f1644,plain,
( spl11_127
| ~ spl11_23
| ~ spl11_45 ),
inference(avatar_split_clause,[],[f426,f422,f259,f1642]) ).
fof(f426,plain,
( ! [X2,X3,X0,X1] :
( greatest(X0,X1,X2)
| ~ member(X0,X2)
| member(sK8(X1,X2,X0),X3)
| ~ subset(X2,X3) )
| ~ spl11_23
| ~ spl11_45 ),
inference(resolution,[],[f423,f260]) ).
fof(f1508,plain,
( spl11_126
| ~ spl11_33
| ~ spl11_41 ),
inference(avatar_split_clause,[],[f406,f382,f324,f1506]) ).
fof(f406,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,X2)
| ~ member(X3,X0)
| member(X3,sum(intersection(X2,X1))) )
| ~ spl11_33
| ~ spl11_41 ),
inference(resolution,[],[f383,f325]) ).
fof(f1504,plain,
( spl11_125
| ~ spl11_33
| ~ spl11_40 ),
inference(avatar_split_clause,[],[f401,f378,f324,f1502]) ).
fof(f401,plain,
( ! [X2,X3,X0,X1] :
( member(X0,X1)
| ~ member(X0,X2)
| ~ member(X3,X0)
| member(X3,sum(difference(X2,X1))) )
| ~ spl11_33
| ~ spl11_40 ),
inference(resolution,[],[f379,f325]) ).
fof(f1500,plain,
( spl11_124
| ~ spl11_32
| ~ spl11_34 ),
inference(avatar_split_clause,[],[f364,f328,f320,f1498]) ).
fof(f364,plain,
( ! [X2,X3,X0,X1] :
( upper_bound(X0,X1,product(X2))
| ~ member(X3,X2)
| member(sK9(X1,product(X2),X0),X3) )
| ~ spl11_32
| ~ spl11_34 ),
inference(resolution,[],[f329,f321]) ).
fof(f1338,plain,
( spl11_123
| ~ spl11_23
| ~ spl11_41 ),
inference(avatar_split_clause,[],[f407,f382,f259,f1336]) ).
fof(f1336,plain,
( spl11_123
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,X1)
| ~ member(X0,X2)
| member(X0,X3)
| ~ subset(intersection(X2,X1),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_123])]) ).
fof(f407,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,X2)
| member(X0,X3)
| ~ subset(intersection(X2,X1),X3) )
| ~ spl11_23
| ~ spl11_41 ),
inference(resolution,[],[f383,f260]) ).
fof(f1334,plain,
( spl11_122
| ~ spl11_23
| ~ spl11_40 ),
inference(avatar_split_clause,[],[f402,f378,f259,f1332]) ).
fof(f1332,plain,
( spl11_122
<=> ! [X0,X3,X2,X1] :
( member(X0,X1)
| ~ member(X0,X2)
| member(X0,X3)
| ~ subset(difference(X2,X1),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_122])]) ).
fof(f402,plain,
( ! [X2,X3,X0,X1] :
( member(X0,X1)
| ~ member(X0,X2)
| member(X0,X3)
| ~ subset(difference(X2,X1),X3) )
| ~ spl11_23
| ~ spl11_40 ),
inference(resolution,[],[f379,f260]) ).
fof(f1330,plain,
( spl11_121
| ~ spl11_16
| ~ spl11_34 ),
inference(avatar_split_clause,[],[f362,f328,f219,f1328]) ).
fof(f362,plain,
( ! [X2,X3,X0,X1] :
( upper_bound(X0,X1,difference(X2,X3))
| member(sK9(X1,difference(X2,X3),X0),X2) )
| ~ spl11_16
| ~ spl11_34 ),
inference(resolution,[],[f329,f220]) ).
fof(f1326,plain,
( spl11_120
| ~ spl11_17
| ~ spl11_34 ),
inference(avatar_split_clause,[],[f361,f328,f223,f1324]) ).
fof(f361,plain,
( ! [X2,X3,X0,X1] :
( upper_bound(X0,X1,difference(X2,X3))
| ~ member(sK9(X1,difference(X2,X3),X0),X3) )
| ~ spl11_17
| ~ spl11_34 ),
inference(resolution,[],[f329,f224]) ).
fof(f1322,plain,
( spl11_119
| ~ spl11_18
| ~ spl11_34 ),
inference(avatar_split_clause,[],[f359,f328,f227,f1320]) ).
fof(f359,plain,
( ! [X2,X3,X0,X1] :
( upper_bound(X0,X1,intersection(X2,X3))
| member(sK9(X1,intersection(X2,X3),X0),X2) )
| ~ spl11_18
| ~ spl11_34 ),
inference(resolution,[],[f329,f228]) ).
fof(f1318,plain,
( spl11_118
| ~ spl11_19
| ~ spl11_34 ),
inference(avatar_split_clause,[],[f358,f328,f231,f1316]) ).
fof(f358,plain,
( ! [X2,X3,X0,X1] :
( upper_bound(X0,X1,intersection(X2,X3))
| member(sK9(X1,intersection(X2,X3),X0),X3) )
| ~ spl11_19
| ~ spl11_34 ),
inference(resolution,[],[f329,f232]) ).
fof(f1314,plain,
( spl11_117
| ~ spl11_33
| ~ spl11_34 ),
inference(avatar_split_clause,[],[f355,f328,f324,f1312]) ).
fof(f1312,plain,
( spl11_117
<=> ! [X0,X3,X2,X1] :
( upper_bound(X0,X1,X2)
| ~ member(X3,sK9(X1,X2,X0))
| member(X3,sum(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_117])]) ).
fof(f355,plain,
( ! [X2,X3,X0,X1] :
( upper_bound(X0,X1,X2)
| ~ member(X3,sK9(X1,X2,X0))
| member(X3,sum(X2)) )
| ~ spl11_33
| ~ spl11_34 ),
inference(resolution,[],[f329,f325]) ).
fof(f1310,plain,
( spl11_116
| ~ spl11_4
| ~ spl11_94 ),
inference(avatar_split_clause,[],[f966,f750,f166,f1308]) ).
fof(f1308,plain,
( spl11_116
<=> ! [X0,X1] :
( member(X0,sum(union(sK3,X1)))
| ~ member(X0,sK4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_116])]) ).
fof(f966,plain,
( ! [X0,X1] :
( member(X0,sum(union(sK3,X1)))
| ~ member(X0,sK4) )
| ~ spl11_4
| ~ spl11_94 ),
inference(resolution,[],[f751,f168]) ).
fof(f1306,plain,
( spl11_115
| ~ spl11_27
| ~ spl11_32 ),
inference(avatar_split_clause,[],[f342,f320,f275,f1304]) ).
fof(f342,plain,
( ! [X2,X0,X1] :
( ~ member(X0,X1)
| member(sK7(X2,product(X1)),X0)
| ~ member(X2,sum(product(X1))) )
| ~ spl11_27
| ~ spl11_32 ),
inference(resolution,[],[f321,f276]) ).
fof(f1302,plain,
( spl11_114
| ~ spl11_25
| ~ spl11_32 ),
inference(avatar_split_clause,[],[f341,f320,f267,f1300]) ).
fof(f341,plain,
( ! [X2,X0,X1] :
( ~ member(X0,X1)
| member(sK6(X2,product(X1)),X0)
| member(X2,product(product(X1))) )
| ~ spl11_25
| ~ spl11_32 ),
inference(resolution,[],[f321,f268]) ).
fof(f1149,plain,
( spl11_113
| ~ spl11_4
| ~ spl11_93 ),
inference(avatar_split_clause,[],[f935,f746,f166,f1147]) ).
fof(f1147,plain,
( spl11_113
<=> ! [X0,X1] :
( member(X0,sum(union(X1,sK3)))
| ~ member(X0,sK4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_113])]) ).
fof(f935,plain,
( ! [X0,X1] :
( member(X0,sum(union(X1,sK3)))
| ~ member(X0,sK4) )
| ~ spl11_4
| ~ spl11_93 ),
inference(resolution,[],[f747,f168]) ).
fof(f1057,plain,
( spl11_112
| ~ spl11_23
| ~ spl11_34 ),
inference(avatar_split_clause,[],[f356,f328,f259,f1055]) ).
fof(f356,plain,
( ! [X2,X3,X0,X1] :
( upper_bound(X0,X1,X2)
| member(sK9(X1,X2,X0),X3)
| ~ subset(X2,X3) )
| ~ spl11_23
| ~ spl11_34 ),
inference(resolution,[],[f329,f260]) ).
fof(f1053,plain,
( spl11_111
| ~ spl11_27
| ~ spl11_33 ),
inference(avatar_split_clause,[],[f353,f324,f275,f1051]) ).
fof(f353,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sK7(X1,X2))
| member(X0,sum(X2))
| ~ member(X1,sum(X2)) )
| ~ spl11_27
| ~ spl11_33 ),
inference(resolution,[],[f325,f276]) ).
fof(f1049,plain,
( spl11_110
| ~ spl11_25
| ~ spl11_33 ),
inference(avatar_split_clause,[],[f352,f324,f267,f1047]) ).
fof(f352,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sK6(X1,X2))
| member(X0,sum(X2))
| member(X1,product(X2)) )
| ~ spl11_25
| ~ spl11_33 ),
inference(resolution,[],[f325,f268]) ).
fof(f1045,plain,
( spl11_109
| ~ spl11_28
| ~ spl11_33 ),
inference(avatar_split_clause,[],[f349,f324,f279,f1043]) ).
fof(f349,plain,
( ! [X2,X0,X1] :
( ~ member(X0,X1)
| member(X0,sum(sK7(X1,X2)))
| ~ member(X1,sum(X2)) )
| ~ spl11_28
| ~ spl11_33 ),
inference(resolution,[],[f325,f280]) ).
fof(f1041,plain,
( spl11_108
| ~ spl11_14
| ~ spl11_32 ),
inference(avatar_split_clause,[],[f340,f320,f211,f1039]) ).
fof(f340,plain,
( ! [X2,X0,X1] :
( ~ member(X0,X1)
| member(sK5(product(X1),X2),X0)
| subset(product(X1),X2) )
| ~ spl11_14
| ~ spl11_32 ),
inference(resolution,[],[f321,f212]) ).
fof(f1032,plain,
( spl11_107
| ~ spl11_16
| ~ spl11_27 ),
inference(avatar_split_clause,[],[f308,f275,f219,f1030]) ).
fof(f308,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sum(difference(X1,X2)))
| member(sK7(X0,difference(X1,X2)),X1) )
| ~ spl11_16
| ~ spl11_27 ),
inference(resolution,[],[f276,f220]) ).
fof(f1028,plain,
( spl11_106
| ~ spl11_17
| ~ spl11_27 ),
inference(avatar_split_clause,[],[f307,f275,f223,f1026]) ).
fof(f307,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sum(difference(X1,X2)))
| ~ member(sK7(X0,difference(X1,X2)),X2) )
| ~ spl11_17
| ~ spl11_27 ),
inference(resolution,[],[f276,f224]) ).
fof(f1024,plain,
( spl11_105
| ~ spl11_18
| ~ spl11_27 ),
inference(avatar_split_clause,[],[f305,f275,f227,f1022]) ).
fof(f305,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sum(intersection(X1,X2)))
| member(sK7(X0,intersection(X1,X2)),X1) )
| ~ spl11_18
| ~ spl11_27 ),
inference(resolution,[],[f276,f228]) ).
fof(f1020,plain,
( spl11_104
| ~ spl11_19
| ~ spl11_27 ),
inference(avatar_split_clause,[],[f304,f275,f231,f1018]) ).
fof(f304,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sum(intersection(X1,X2)))
| member(sK7(X0,intersection(X1,X2)),X2) )
| ~ spl11_19
| ~ spl11_27 ),
inference(resolution,[],[f276,f232]) ).
fof(f1016,plain,
( spl11_103
| ~ spl11_16
| ~ spl11_25 ),
inference(avatar_split_clause,[],[f300,f267,f219,f1014]) ).
fof(f300,plain,
( ! [X2,X0,X1] :
( member(X0,product(difference(X1,X2)))
| member(sK6(X0,difference(X1,X2)),X1) )
| ~ spl11_16
| ~ spl11_25 ),
inference(resolution,[],[f268,f220]) ).
fof(f1012,plain,
( spl11_102
| ~ spl11_17
| ~ spl11_25 ),
inference(avatar_split_clause,[],[f299,f267,f223,f1010]) ).
fof(f299,plain,
( ! [X2,X0,X1] :
( member(X0,product(difference(X1,X2)))
| ~ member(sK6(X0,difference(X1,X2)),X2) )
| ~ spl11_17
| ~ spl11_25 ),
inference(resolution,[],[f268,f224]) ).
fof(f1008,plain,
( spl11_101
| ~ spl11_18
| ~ spl11_25 ),
inference(avatar_split_clause,[],[f297,f267,f227,f1006]) ).
fof(f297,plain,
( ! [X2,X0,X1] :
( member(X0,product(intersection(X1,X2)))
| member(sK6(X0,intersection(X1,X2)),X1) )
| ~ spl11_18
| ~ spl11_25 ),
inference(resolution,[],[f268,f228]) ).
fof(f1004,plain,
( spl11_100
| ~ spl11_19
| ~ spl11_25 ),
inference(avatar_split_clause,[],[f296,f267,f231,f1002]) ).
fof(f296,plain,
( ! [X2,X0,X1] :
( member(X0,product(intersection(X1,X2)))
| member(sK6(X0,intersection(X1,X2)),X2) )
| ~ spl11_19
| ~ spl11_25 ),
inference(resolution,[],[f268,f232]) ).
fof(f995,plain,
( spl11_99
| ~ spl11_44
| ~ spl11_81 ),
inference(avatar_split_clause,[],[f696,f643,f394,f993]) ).
fof(f993,plain,
( spl11_99
<=> ! [X0] :
( member(sK4,sum(power_set(X0)))
| ~ subset(sK2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_99])]) ).
fof(f696,plain,
( ! [X0] :
( member(sK4,sum(power_set(X0)))
| ~ subset(sK2,X0) )
| ~ spl11_44
| ~ spl11_81 ),
inference(resolution,[],[f644,f396]) ).
fof(f768,plain,
( spl11_98
| ~ spl11_6
| ~ spl11_48 ),
inference(avatar_split_clause,[],[f457,f448,f176,f766]) ).
fof(f457,plain,
( ! [X2,X0,X1] :
( sP0(X0,X1,X2,empty_set)
| ~ upper_bound(X0,X1,X2)
| ~ member(X0,X2) )
| ~ spl11_6
| ~ spl11_48 ),
inference(resolution,[],[f449,f177]) ).
fof(f764,plain,
( spl11_97
| ~ spl11_10
| ~ spl11_34 ),
inference(avatar_split_clause,[],[f363,f328,f192,f762]) ).
fof(f363,plain,
( ! [X2,X0,X1] :
( upper_bound(X0,X1,singleton(X2))
| sK9(X1,singleton(X2),X0) = X2 )
| ~ spl11_10
| ~ spl11_34 ),
inference(resolution,[],[f329,f193]) ).
fof(f760,plain,
( spl11_96
| ~ spl11_11
| ~ spl11_34 ),
inference(avatar_split_clause,[],[f357,f328,f196,f758]) ).
fof(f758,plain,
( spl11_96
<=> ! [X2,X0,X1] :
( upper_bound(X0,X1,power_set(X2))
| subset(sK9(X1,power_set(X2),X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_96])]) ).
fof(f357,plain,
( ! [X2,X0,X1] :
( upper_bound(X0,X1,power_set(X2))
| subset(sK9(X1,power_set(X2),X0),X2) )
| ~ spl11_11
| ~ spl11_34 ),
inference(resolution,[],[f329,f197]) ).
fof(f756,plain,
( spl11_95
| ~ spl11_14
| ~ spl11_33 ),
inference(avatar_split_clause,[],[f351,f324,f211,f754]) ).
fof(f351,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sK5(X1,X2))
| member(X0,sum(X1))
| subset(X1,X2) )
| ~ spl11_14
| ~ spl11_33 ),
inference(resolution,[],[f325,f212]) ).
fof(f752,plain,
( spl11_94
| ~ spl11_20
| ~ spl11_33 ),
inference(avatar_split_clause,[],[f345,f324,f235,f750]) ).
fof(f345,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,X1)
| member(X0,sum(union(X2,X3)))
| ~ member(X1,X2) )
| ~ spl11_20
| ~ spl11_33 ),
inference(resolution,[],[f325,f236]) ).
fof(f748,plain,
( spl11_93
| ~ spl11_21
| ~ spl11_33 ),
inference(avatar_split_clause,[],[f344,f324,f239,f746]) ).
fof(f344,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,X1)
| member(X0,sum(union(X2,X3)))
| ~ member(X1,X3) )
| ~ spl11_21
| ~ spl11_33 ),
inference(resolution,[],[f325,f240]) ).
fof(f744,plain,
( spl11_92
| ~ spl11_23
| ~ spl11_28 ),
inference(avatar_split_clause,[],[f310,f279,f259,f742]) ).
fof(f310,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sum(X1))
| member(X0,X2)
| ~ subset(sK7(X0,X1),X2) )
| ~ spl11_23
| ~ spl11_28 ),
inference(resolution,[],[f280,f260]) ).
fof(f740,plain,
( spl11_91
| ~ spl11_4
| ~ spl11_81 ),
inference(avatar_split_clause,[],[f697,f643,f166,f738]) ).
fof(f697,plain,
( ! [X0] :
( member(sK4,sum(power_set(X0)))
| ~ subset(sK3,X0) )
| ~ spl11_4
| ~ spl11_81 ),
inference(resolution,[],[f644,f168]) ).
fof(f736,plain,
( spl11_90
| ~ spl11_23
| ~ spl11_27 ),
inference(avatar_split_clause,[],[f302,f275,f259,f734]) ).
fof(f302,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sum(X1))
| member(sK7(X0,X1),X2)
| ~ subset(X1,X2) )
| ~ spl11_23
| ~ spl11_27 ),
inference(resolution,[],[f276,f260]) ).
fof(f732,plain,
( spl11_89
| ~ spl11_23
| ~ spl11_25 ),
inference(avatar_split_clause,[],[f294,f267,f259,f730]) ).
fof(f294,plain,
( ! [X2,X0,X1] :
( member(X0,product(X1))
| member(sK6(X0,X1),X2)
| ~ subset(X1,X2) )
| ~ spl11_23
| ~ spl11_25 ),
inference(resolution,[],[f268,f260]) ).
fof(f728,plain,
( spl11_88
| ~ spl11_15
| ~ spl11_21 ),
inference(avatar_split_clause,[],[f257,f239,f215,f726]) ).
fof(f257,plain,
( ! [X2,X0,X1] :
( ~ member(sK5(X0,union(X1,X2)),X2)
| subset(X0,union(X1,X2)) )
| ~ spl11_15
| ~ spl11_21 ),
inference(resolution,[],[f240,f216]) ).
fof(f724,plain,
( spl11_87
| ~ spl11_15
| ~ spl11_20 ),
inference(avatar_split_clause,[],[f256,f235,f215,f722]) ).
fof(f256,plain,
( ! [X2,X0,X1] :
( ~ member(sK5(X0,union(X1,X2)),X1)
| subset(X0,union(X1,X2)) )
| ~ spl11_15
| ~ spl11_20 ),
inference(resolution,[],[f236,f216]) ).
fof(f720,plain,
( spl11_86
| ~ spl11_14
| ~ spl11_19 ),
inference(avatar_split_clause,[],[f255,f231,f211,f718]) ).
fof(f255,plain,
( ! [X2,X0,X1] :
( member(sK5(intersection(X0,X1),X2),X1)
| subset(intersection(X0,X1),X2) )
| ~ spl11_14
| ~ spl11_19 ),
inference(resolution,[],[f232,f212]) ).
fof(f716,plain,
( spl11_85
| ~ spl11_14
| ~ spl11_18 ),
inference(avatar_split_clause,[],[f254,f227,f211,f714]) ).
fof(f254,plain,
( ! [X2,X0,X1] :
( member(sK5(intersection(X0,X1),X2),X0)
| subset(intersection(X0,X1),X2) )
| ~ spl11_14
| ~ spl11_18 ),
inference(resolution,[],[f228,f212]) ).
fof(f712,plain,
( spl11_84
| ~ spl11_14
| ~ spl11_17 ),
inference(avatar_split_clause,[],[f253,f223,f211,f710]) ).
fof(f253,plain,
( ! [X2,X0,X1] :
( ~ member(sK5(difference(X0,X1),X2),X1)
| subset(difference(X0,X1),X2) )
| ~ spl11_14
| ~ spl11_17 ),
inference(resolution,[],[f224,f212]) ).
fof(f708,plain,
( spl11_83
| ~ spl11_14
| ~ spl11_16 ),
inference(avatar_split_clause,[],[f252,f219,f211,f706]) ).
fof(f252,plain,
( ! [X2,X0,X1] :
( member(sK5(difference(X0,X1),X2),X0)
| subset(difference(X0,X1),X2) )
| ~ spl11_14
| ~ spl11_16 ),
inference(resolution,[],[f220,f212]) ).
fof(f671,plain,
( spl11_82
| ~ spl11_15
| ~ spl11_55 ),
inference(avatar_split_clause,[],[f513,f489,f215,f669]) ).
fof(f513,plain,
( ! [X0] :
( ~ member(sK5(X0,sum(sK3)),sK4)
| subset(X0,sum(sK3)) )
| ~ spl11_15
| ~ spl11_55 ),
inference(resolution,[],[f490,f216]) ).
fof(f645,plain,
( spl11_81
| ~ spl11_12
| ~ spl11_33 ),
inference(avatar_split_clause,[],[f343,f324,f200,f643]) ).
fof(f343,plain,
( ! [X2,X0,X1] :
( ~ member(X0,X1)
| member(X0,sum(power_set(X2)))
| ~ subset(X1,X2) )
| ~ spl11_12
| ~ spl11_33 ),
inference(resolution,[],[f325,f201]) ).
fof(f641,plain,
( spl11_80
| ~ spl11_10
| ~ spl11_27 ),
inference(avatar_split_clause,[],[f309,f275,f192,f639]) ).
fof(f309,plain,
( ! [X0,X1] :
( ~ member(X0,sum(singleton(X1)))
| sK7(X0,singleton(X1)) = X1 )
| ~ spl11_10
| ~ spl11_27 ),
inference(resolution,[],[f276,f193]) ).
fof(f637,plain,
( spl11_79
| ~ spl11_11
| ~ spl11_27 ),
inference(avatar_split_clause,[],[f303,f275,f196,f635]) ).
fof(f303,plain,
( ! [X0,X1] :
( ~ member(X0,sum(power_set(X1)))
| subset(sK7(X0,power_set(X1)),X1) )
| ~ spl11_11
| ~ spl11_27 ),
inference(resolution,[],[f276,f197]) ).
fof(f633,plain,
( spl11_78
| ~ spl11_10
| ~ spl11_25 ),
inference(avatar_split_clause,[],[f301,f267,f192,f631]) ).
fof(f301,plain,
( ! [X0,X1] :
( member(X0,product(singleton(X1)))
| sK6(X0,singleton(X1)) = X1 )
| ~ spl11_10
| ~ spl11_25 ),
inference(resolution,[],[f268,f193]) ).
fof(f629,plain,
( spl11_77
| ~ spl11_23
| ~ spl11_55 ),
inference(avatar_split_clause,[],[f512,f489,f259,f627]) ).
fof(f627,plain,
( spl11_77
<=> ! [X0,X1] :
( ~ member(X0,sK4)
| member(X0,X1)
| ~ subset(sum(sK3),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_77])]) ).
fof(f512,plain,
( ! [X0,X1] :
( ~ member(X0,sK4)
| member(X0,X1)
| ~ subset(sum(sK3),X1) )
| ~ spl11_23
| ~ spl11_55 ),
inference(resolution,[],[f490,f260]) ).
fof(f625,plain,
( spl11_76
| ~ spl11_11
| ~ spl11_25 ),
inference(avatar_split_clause,[],[f295,f267,f196,f623]) ).
fof(f623,plain,
( spl11_76
<=> ! [X0,X1] :
( member(X0,product(power_set(X1)))
| subset(sK6(X0,power_set(X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_76])]) ).
fof(f295,plain,
( ! [X0,X1] :
( member(X0,product(power_set(X1)))
| subset(sK6(X0,power_set(X1)),X1) )
| ~ spl11_11
| ~ spl11_25 ),
inference(resolution,[],[f268,f197]) ).
fof(f621,plain,
( spl11_75
| ~ spl11_14
| ~ spl11_23 ),
inference(avatar_split_clause,[],[f293,f259,f211,f619]) ).
fof(f293,plain,
( ! [X2,X0,X1] :
( member(sK5(X0,X1),X2)
| ~ subset(X0,X2)
| subset(X0,X1) )
| ~ spl11_14
| ~ spl11_23 ),
inference(resolution,[],[f260,f212]) ).
fof(f617,plain,
( spl11_74
| ~ spl11_20
| ~ spl11_23 ),
inference(avatar_split_clause,[],[f289,f259,f235,f615]) ).
fof(f615,plain,
( spl11_74
<=> ! [X0,X3,X2,X1] :
( member(X0,X1)
| ~ subset(union(X2,X3),X1)
| ~ member(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_74])]) ).
fof(f289,plain,
( ! [X2,X3,X0,X1] :
( member(X0,X1)
| ~ subset(union(X2,X3),X1)
| ~ member(X0,X2) )
| ~ spl11_20
| ~ spl11_23 ),
inference(resolution,[],[f260,f236]) ).
fof(f613,plain,
( spl11_73
| ~ spl11_21
| ~ spl11_23 ),
inference(avatar_split_clause,[],[f288,f259,f239,f611]) ).
fof(f611,plain,
( spl11_73
<=> ! [X0,X3,X2,X1] :
( member(X0,X1)
| ~ subset(union(X2,X3),X1)
| ~ member(X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_73])]) ).
fof(f288,plain,
( ! [X2,X3,X0,X1] :
( member(X0,X1)
| ~ subset(union(X2,X3),X1)
| ~ member(X0,X3) )
| ~ spl11_21
| ~ spl11_23 ),
inference(resolution,[],[f260,f240]) ).
fof(f605,plain,
( spl11_72
| ~ spl11_12
| ~ spl11_23 ),
inference(avatar_split_clause,[],[f287,f259,f200,f603]) ).
fof(f603,plain,
( spl11_72
<=> ! [X2,X0,X1] :
( member(X0,X1)
| ~ subset(power_set(X2),X1)
| ~ subset(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_72])]) ).
fof(f287,plain,
( ! [X2,X0,X1] :
( member(X0,X1)
| ~ subset(power_set(X2),X1)
| ~ subset(X0,X2) )
| ~ spl11_12
| ~ spl11_23 ),
inference(resolution,[],[f260,f201]) ).
fof(f601,plain,
( spl11_71
| ~ spl11_12
| ~ spl11_15 ),
inference(avatar_split_clause,[],[f250,f215,f200,f599]) ).
fof(f599,plain,
( spl11_71
<=> ! [X0,X1] :
( subset(X0,power_set(X1))
| ~ subset(sK5(X0,power_set(X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_71])]) ).
fof(f250,plain,
( ! [X0,X1] :
( subset(X0,power_set(X1))
| ~ subset(sK5(X0,power_set(X1)),X1) )
| ~ spl11_12
| ~ spl11_15 ),
inference(resolution,[],[f216,f201]) ).
fof(f594,plain,
( spl11_70
| ~ spl11_11
| ~ spl11_14 ),
inference(avatar_split_clause,[],[f248,f211,f196,f592]) ).
fof(f592,plain,
( spl11_70
<=> ! [X0,X1] :
( subset(power_set(X0),X1)
| subset(sK5(power_set(X0),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_70])]) ).
fof(f248,plain,
( ! [X0,X1] :
( subset(power_set(X0),X1)
| subset(sK5(power_set(X0),X1),X0) )
| ~ spl11_11
| ~ spl11_14 ),
inference(resolution,[],[f212,f197]) ).
fof(f590,plain,
( spl11_69
| ~ spl11_10
| ~ spl11_14 ),
inference(avatar_split_clause,[],[f247,f211,f192,f588]) ).
fof(f247,plain,
( ! [X0,X1] :
( subset(singleton(X0),X1)
| sK5(singleton(X0),X1) = X0 )
| ~ spl11_10
| ~ spl11_14 ),
inference(resolution,[],[f212,f193]) ).
fof(f580,plain,
( spl11_68
| ~ spl11_9
| ~ spl11_33 ),
inference(avatar_split_clause,[],[f348,f324,f188,f578]) ).
fof(f348,plain,
( ! [X2,X0,X1] :
( ~ member(X0,X1)
| member(X0,sum(unordered_pair(X1,X2))) )
| ~ spl11_9
| ~ spl11_33 ),
inference(resolution,[],[f325,f189]) ).
fof(f576,plain,
( spl11_67
| ~ spl11_8
| ~ spl11_33 ),
inference(avatar_split_clause,[],[f347,f324,f184,f574]) ).
fof(f347,plain,
( ! [X2,X0,X1] :
( ~ member(X0,X1)
| member(X0,sum(unordered_pair(X2,X1))) )
| ~ spl11_8
| ~ spl11_33 ),
inference(resolution,[],[f325,f185]) ).
fof(f567,plain,
( spl11_66
| ~ spl11_7
| ~ spl11_33 ),
inference(avatar_split_clause,[],[f346,f324,f180,f565]) ).
fof(f346,plain,
( ! [X0,X1] :
( ~ member(X0,X1)
| member(X0,sum(singleton(X1))) )
| ~ spl11_7
| ~ spl11_33 ),
inference(resolution,[],[f325,f181]) ).
fof(f563,plain,
( spl11_65
| ~ spl11_33
| ~ spl11_44 ),
inference(avatar_split_clause,[],[f441,f394,f324,f561]) ).
fof(f441,plain,
( ! [X0] :
( ~ member(X0,sK4)
| member(X0,sum(sK2)) )
| ~ spl11_33
| ~ spl11_44 ),
inference(resolution,[],[f396,f325]) ).
fof(f559,plain,
( spl11_64
| ~ spl11_9
| ~ spl11_23 ),
inference(avatar_split_clause,[],[f292,f259,f188,f557]) ).
fof(f557,plain,
( spl11_64
<=> ! [X2,X0,X1] :
( member(X0,X1)
| ~ subset(unordered_pair(X0,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_64])]) ).
fof(f292,plain,
( ! [X2,X0,X1] :
( member(X0,X1)
| ~ subset(unordered_pair(X0,X2),X1) )
| ~ spl11_9
| ~ spl11_23 ),
inference(resolution,[],[f260,f189]) ).
fof(f555,plain,
( spl11_63
| ~ spl11_8
| ~ spl11_23 ),
inference(avatar_split_clause,[],[f291,f259,f184,f553]) ).
fof(f553,plain,
( spl11_63
<=> ! [X2,X0,X1] :
( member(X0,X1)
| ~ subset(unordered_pair(X2,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_63])]) ).
fof(f291,plain,
( ! [X2,X0,X1] :
( member(X0,X1)
| ~ subset(unordered_pair(X2,X0),X1) )
| ~ spl11_8
| ~ spl11_23 ),
inference(resolution,[],[f260,f185]) ).
fof(f550,plain,
( spl11_62
| ~ spl11_7
| ~ spl11_23 ),
inference(avatar_split_clause,[],[f290,f259,f180,f548]) ).
fof(f290,plain,
( ! [X0,X1] :
( member(X0,X1)
| ~ subset(singleton(X0),X1) )
| ~ spl11_7
| ~ spl11_23 ),
inference(resolution,[],[f260,f181]) ).
fof(f535,plain,
( spl11_61
| ~ spl11_6
| ~ spl11_34 ),
inference(avatar_split_clause,[],[f360,f328,f176,f533]) ).
fof(f533,plain,
( spl11_61
<=> ! [X0,X1] : upper_bound(X0,X1,empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_61])]) ).
fof(f360,plain,
( ! [X0,X1] : upper_bound(X0,X1,empty_set)
| ~ spl11_6
| ~ spl11_34 ),
inference(resolution,[],[f329,f177]) ).
fof(f531,plain,
( spl11_60
| ~ spl11_6
| ~ spl11_27 ),
inference(avatar_split_clause,[],[f306,f275,f176,f529]) ).
fof(f306,plain,
( ! [X0] : ~ member(X0,sum(empty_set))
| ~ spl11_6
| ~ spl11_27 ),
inference(resolution,[],[f276,f177]) ).
fof(f527,plain,
( spl11_59
| ~ spl11_6
| ~ spl11_25 ),
inference(avatar_split_clause,[],[f298,f267,f176,f525]) ).
fof(f298,plain,
( ! [X0] : member(X0,product(empty_set))
| ~ spl11_6
| ~ spl11_25 ),
inference(resolution,[],[f268,f177]) ).
fof(f521,plain,
( spl11_58
| ~ spl11_14
| ~ spl11_15 ),
inference(avatar_split_clause,[],[f251,f215,f211,f519]) ).
fof(f519,plain,
( spl11_58
<=> ! [X0] : subset(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_58])]) ).
fof(f251,plain,
( ! [X0] : subset(X0,X0)
| ~ spl11_14
| ~ spl11_15 ),
inference(duplicate_literal_removal,[],[f249]) ).
fof(f249,plain,
( ! [X0] :
( subset(X0,X0)
| subset(X0,X0) )
| ~ spl11_14
| ~ spl11_15 ),
inference(resolution,[],[f216,f212]) ).
fof(f504,plain,
( spl11_57
| ~ spl11_5
| ~ spl11_35 ),
inference(avatar_split_clause,[],[f499,f332,f171,f501]) ).
fof(f332,plain,
( spl11_35
<=> ! [X0,X3,X2,X1] :
( sP0(X0,X2,X1,X3)
| ~ least_upper_bound(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_35])]) ).
fof(f499,plain,
( sP0(sK4,sK1,sK3,sK2)
| ~ spl11_5
| ~ spl11_35 ),
inference(resolution,[],[f173,f333]) ).
fof(f333,plain,
( ! [X2,X3,X0,X1] :
( ~ least_upper_bound(X0,X1,X2,X3)
| sP0(X0,X2,X1,X3) )
| ~ spl11_35 ),
inference(avatar_component_clause,[],[f332]) ).
fof(f173,plain,
( least_upper_bound(sK4,sK3,sK1,sK2)
| ~ spl11_5 ),
inference(avatar_component_clause,[],[f171]) ).
fof(f498,plain,
( spl11_56
| ~ spl11_3
| ~ spl11_37 ),
inference(avatar_split_clause,[],[f398,f366,f162,f496]) ).
fof(f366,plain,
( spl11_37
<=> ! [X4,X0,X2,X1] :
( apply(X0,X4,X2)
| ~ member(X4,X1)
| ~ greatest(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_37])]) ).
fof(f398,plain,
( ! [X0] :
( ~ member(X0,sK3)
| apply(sK1,X0,sK4) )
| ~ spl11_3
| ~ spl11_37 ),
inference(resolution,[],[f367,f164]) ).
fof(f164,plain,
( greatest(sK4,sK1,sK3)
| ~ spl11_3 ),
inference(avatar_component_clause,[],[f162]) ).
fof(f367,plain,
( ! [X2,X0,X1,X4] :
( ~ greatest(X2,X0,X1)
| ~ member(X4,X1)
| apply(X0,X4,X2) )
| ~ spl11_37 ),
inference(avatar_component_clause,[],[f366]) ).
fof(f492,plain,
( spl11_4
| ~ spl11_3
| ~ spl11_13 ),
inference(avatar_split_clause,[],[f209,f204,f162,f166]) ).
fof(f204,plain,
( spl11_13
<=> ! [X2,X0,X1] :
( member(X2,X1)
| ~ greatest(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_13])]) ).
fof(f209,plain,
( member(sK4,sK3)
| ~ spl11_3
| ~ spl11_13 ),
inference(resolution,[],[f205,f164]) ).
fof(f205,plain,
( ! [X2,X0,X1] :
( ~ greatest(X2,X0,X1)
| member(X2,X1) )
| ~ spl11_13 ),
inference(avatar_component_clause,[],[f204]) ).
fof(f491,plain,
( spl11_55
| ~ spl11_4
| ~ spl11_33 ),
inference(avatar_split_clause,[],[f350,f324,f166,f489]) ).
fof(f350,plain,
( ! [X0] :
( ~ member(X0,sK4)
| member(X0,sum(sK3)) )
| ~ spl11_4
| ~ spl11_33 ),
inference(resolution,[],[f325,f168]) ).
fof(f487,plain,
( spl11_54
| ~ spl11_1
| ~ spl11_31 ),
inference(avatar_split_clause,[],[f339,f316,f152,f485]) ).
fof(f485,plain,
( spl11_54
<=> ! [X0] :
( ~ member(X0,sK2)
| apply(sK1,X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_54])]) ).
fof(f152,plain,
( spl11_1
<=> order(sK1,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_1])]) ).
fof(f316,plain,
( spl11_31
<=> ! [X0,X1,X7] :
( apply(X0,X7,X7)
| ~ member(X7,X1)
| ~ order(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_31])]) ).
fof(f339,plain,
( ! [X0] :
( ~ member(X0,sK2)
| apply(sK1,X0,X0) )
| ~ spl11_1
| ~ spl11_31 ),
inference(resolution,[],[f317,f154]) ).
fof(f154,plain,
( order(sK1,sK2)
| ~ spl11_1 ),
inference(avatar_component_clause,[],[f152]) ).
fof(f317,plain,
( ! [X0,X1,X7] :
( ~ order(X0,X1)
| ~ member(X7,X1)
| apply(X0,X7,X7) )
| ~ spl11_31 ),
inference(avatar_component_clause,[],[f316]) ).
fof(f483,plain,
spl11_53,
inference(avatar_split_clause,[],[f107,f481]) ).
fof(f107,plain,
! [X2,X3,X0,X1,X4] :
( apply(X0,X2,X4)
| ~ apply(X0,X3,X4)
| ~ apply(X0,X2,X3)
| ~ member(X4,X1)
| ~ member(X3,X1)
| ~ member(X2,X1)
| ~ order(X0,X1) ),
inference(cnf_transformation,[],[f47]) ).
fof(f47,plain,
! [X0,X1] :
( ( ! [X2,X3,X4] :
( apply(X0,X2,X4)
| ~ apply(X0,X3,X4)
| ~ apply(X0,X2,X3)
| ~ member(X4,X1)
| ~ member(X3,X1)
| ~ member(X2,X1) )
& ! [X5,X6] :
( X5 = X6
| ~ apply(X0,X6,X5)
| ~ apply(X0,X5,X6)
| ~ member(X6,X1)
| ~ member(X5,X1) )
& ! [X7] :
( apply(X0,X7,X7)
| ~ member(X7,X1) ) )
| ~ order(X0,X1) ),
inference(flattening,[],[f46]) ).
fof(f46,plain,
! [X0,X1] :
( ( ! [X2,X3,X4] :
( apply(X0,X2,X4)
| ~ apply(X0,X3,X4)
| ~ apply(X0,X2,X3)
| ~ member(X4,X1)
| ~ member(X3,X1)
| ~ member(X2,X1) )
& ! [X5,X6] :
( X5 = X6
| ~ apply(X0,X6,X5)
| ~ apply(X0,X5,X6)
| ~ member(X6,X1)
| ~ member(X5,X1) )
& ! [X7] :
( apply(X0,X7,X7)
| ~ member(X7,X1) ) )
| ~ order(X0,X1) ),
inference(ennf_transformation,[],[f44]) ).
fof(f44,plain,
! [X0,X1] :
( order(X0,X1)
=> ( ! [X2,X3,X4] :
( ( member(X4,X1)
& member(X3,X1)
& member(X2,X1) )
=> ( ( apply(X0,X3,X4)
& apply(X0,X2,X3) )
=> apply(X0,X2,X4) ) )
& ! [X5,X6] :
( ( member(X6,X1)
& member(X5,X1) )
=> ( ( apply(X0,X6,X5)
& apply(X0,X5,X6) )
=> X5 = X6 ) )
& ! [X7] :
( member(X7,X1)
=> apply(X0,X7,X7) ) ) ),
inference(unused_predicate_definition_removal,[],[f27]) ).
fof(f27,plain,
! [X0,X1] :
( order(X0,X1)
<=> ( ! [X2,X3,X4] :
( ( member(X4,X1)
& member(X3,X1)
& member(X2,X1) )
=> ( ( apply(X0,X3,X4)
& apply(X0,X2,X3) )
=> apply(X0,X2,X4) ) )
& ! [X5,X6] :
( ( member(X6,X1)
& member(X5,X1) )
=> ( ( apply(X0,X6,X5)
& apply(X0,X5,X6) )
=> X5 = X6 ) )
& ! [X7] :
( member(X7,X1)
=> apply(X0,X7,X7) ) ) ),
inference(rectify,[],[f12]) ).
fof(f12,axiom,
! [X5,X3] :
( order(X5,X3)
<=> ( ! [X2,X4,X6] :
( ( member(X6,X3)
& member(X4,X3)
& member(X2,X3) )
=> ( ( apply(X5,X4,X6)
& apply(X5,X2,X4) )
=> apply(X5,X2,X6) ) )
& ! [X2,X4] :
( ( member(X4,X3)
& member(X2,X3) )
=> ( ( apply(X5,X4,X2)
& apply(X5,X2,X4) )
=> X2 = X4 ) )
& ! [X2] :
( member(X2,X3)
=> apply(X5,X2,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',order) ).
fof(f479,plain,
( spl11_52
| ~ spl11_23
| ~ spl11_44 ),
inference(avatar_split_clause,[],[f442,f394,f259,f477]) ).
fof(f442,plain,
( ! [X0] :
( member(sK4,X0)
| ~ subset(sK2,X0) )
| ~ spl11_23
| ~ spl11_44 ),
inference(resolution,[],[f396,f260]) ).
fof(f474,plain,
spl11_51,
inference(avatar_split_clause,[],[f145,f472]) ).
fof(f145,plain,
! [X2,X3,X0,X1] :
( sP0(X0,X1,X2,X3)
| ~ apply(X1,X0,sK10(X0,X1,X2,X3))
| ~ upper_bound(X0,X1,X2)
| ~ member(X0,X2) ),
inference(cnf_transformation,[],[f97]) ).
fof(f97,plain,
! [X0,X1,X2,X3] :
( ( sP0(X0,X1,X2,X3)
| ( ~ apply(X1,X0,sK10(X0,X1,X2,X3))
& upper_bound(sK10(X0,X1,X2,X3),X1,X2)
& member(sK10(X0,X1,X2,X3),X3) )
| ~ upper_bound(X0,X1,X2)
| ~ member(X0,X2) )
& ( ( ! [X5] :
( apply(X1,X0,X5)
| ~ upper_bound(X5,X1,X2)
| ~ member(X5,X3) )
& upper_bound(X0,X1,X2)
& member(X0,X2) )
| ~ sP0(X0,X1,X2,X3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f95,f96]) ).
fof(f96,plain,
! [X0,X1,X2,X3] :
( ? [X4] :
( ~ apply(X1,X0,X4)
& upper_bound(X4,X1,X2)
& member(X4,X3) )
=> ( ~ apply(X1,X0,sK10(X0,X1,X2,X3))
& upper_bound(sK10(X0,X1,X2,X3),X1,X2)
& member(sK10(X0,X1,X2,X3),X3) ) ),
introduced(choice_axiom,[]) ).
fof(f95,plain,
! [X0,X1,X2,X3] :
( ( sP0(X0,X1,X2,X3)
| ? [X4] :
( ~ apply(X1,X0,X4)
& upper_bound(X4,X1,X2)
& member(X4,X3) )
| ~ upper_bound(X0,X1,X2)
| ~ member(X0,X2) )
& ( ( ! [X5] :
( apply(X1,X0,X5)
| ~ upper_bound(X5,X1,X2)
| ~ member(X5,X3) )
& upper_bound(X0,X1,X2)
& member(X0,X2) )
| ~ sP0(X0,X1,X2,X3) ) ),
inference(rectify,[],[f94]) ).
fof(f94,plain,
! [X0,X2,X1,X3] :
( ( sP0(X0,X2,X1,X3)
| ? [X4] :
( ~ apply(X2,X0,X4)
& upper_bound(X4,X2,X1)
& member(X4,X3) )
| ~ upper_bound(X0,X2,X1)
| ~ member(X0,X1) )
& ( ( ! [X4] :
( apply(X2,X0,X4)
| ~ upper_bound(X4,X2,X1)
| ~ member(X4,X3) )
& upper_bound(X0,X2,X1)
& member(X0,X1) )
| ~ sP0(X0,X2,X1,X3) ) ),
inference(flattening,[],[f93]) ).
fof(f93,plain,
! [X0,X2,X1,X3] :
( ( sP0(X0,X2,X1,X3)
| ? [X4] :
( ~ apply(X2,X0,X4)
& upper_bound(X4,X2,X1)
& member(X4,X3) )
| ~ upper_bound(X0,X2,X1)
| ~ member(X0,X1) )
& ( ( ! [X4] :
( apply(X2,X0,X4)
| ~ upper_bound(X4,X2,X1)
| ~ member(X4,X3) )
& upper_bound(X0,X2,X1)
& member(X0,X1) )
| ~ sP0(X0,X2,X1,X3) ) ),
inference(nnf_transformation,[],[f54]) ).
fof(f54,plain,
! [X0,X2,X1,X3] :
( sP0(X0,X2,X1,X3)
<=> ( ! [X4] :
( apply(X2,X0,X4)
| ~ upper_bound(X4,X2,X1)
| ~ member(X4,X3) )
& upper_bound(X0,X2,X1)
& member(X0,X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f470,plain,
spl11_50,
inference(avatar_split_clause,[],[f144,f468]) ).
fof(f144,plain,
! [X2,X3,X0,X1] :
( sP0(X0,X1,X2,X3)
| upper_bound(sK10(X0,X1,X2,X3),X1,X2)
| ~ upper_bound(X0,X1,X2)
| ~ member(X0,X2) ),
inference(cnf_transformation,[],[f97]) ).
fof(f466,plain,
spl11_49,
inference(avatar_split_clause,[],[f106,f464]) ).
fof(f106,plain,
! [X0,X1,X6,X5] :
( X5 = X6
| ~ apply(X0,X6,X5)
| ~ apply(X0,X5,X6)
| ~ member(X6,X1)
| ~ member(X5,X1)
| ~ order(X0,X1) ),
inference(cnf_transformation,[],[f47]) ).
fof(f450,plain,
spl11_48,
inference(avatar_split_clause,[],[f143,f448]) ).
fof(f143,plain,
! [X2,X3,X0,X1] :
( sP0(X0,X1,X2,X3)
| member(sK10(X0,X1,X2,X3),X3)
| ~ upper_bound(X0,X1,X2)
| ~ member(X0,X2) ),
inference(cnf_transformation,[],[f97]) ).
fof(f446,plain,
spl11_47,
inference(avatar_split_clause,[],[f142,f444]) ).
fof(f142,plain,
! [X2,X3,X0,X1,X5] :
( apply(X1,X0,X5)
| ~ upper_bound(X5,X1,X2)
| ~ member(X5,X3)
| ~ sP0(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f97]) ).
fof(f440,plain,
spl11_46,
inference(avatar_split_clause,[],[f124,f438]) ).
fof(f124,plain,
! [X2,X0,X1] :
( greatest(X2,X0,X1)
| ~ apply(X0,sK8(X0,X1,X2),X2)
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f80]) ).
fof(f80,plain,
! [X0,X1,X2] :
( ( greatest(X2,X0,X1)
| ( ~ apply(X0,sK8(X0,X1,X2),X2)
& member(sK8(X0,X1,X2),X1) )
| ~ member(X2,X1) )
& ( ( ! [X4] :
( apply(X0,X4,X2)
| ~ member(X4,X1) )
& member(X2,X1) )
| ~ greatest(X2,X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f78,f79]) ).
fof(f79,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ apply(X0,X3,X2)
& member(X3,X1) )
=> ( ~ apply(X0,sK8(X0,X1,X2),X2)
& member(sK8(X0,X1,X2),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f78,plain,
! [X0,X1,X2] :
( ( greatest(X2,X0,X1)
| ? [X3] :
( ~ apply(X0,X3,X2)
& member(X3,X1) )
| ~ member(X2,X1) )
& ( ( ! [X4] :
( apply(X0,X4,X2)
| ~ member(X4,X1) )
& member(X2,X1) )
| ~ greatest(X2,X0,X1) ) ),
inference(rectify,[],[f77]) ).
fof(f77,plain,
! [X0,X1,X2] :
( ( greatest(X2,X0,X1)
| ? [X3] :
( ~ apply(X0,X3,X2)
& member(X3,X1) )
| ~ member(X2,X1) )
& ( ( ! [X3] :
( apply(X0,X3,X2)
| ~ member(X3,X1) )
& member(X2,X1) )
| ~ greatest(X2,X0,X1) ) ),
inference(flattening,[],[f76]) ).
fof(f76,plain,
! [X0,X1,X2] :
( ( greatest(X2,X0,X1)
| ? [X3] :
( ~ apply(X0,X3,X2)
& member(X3,X1) )
| ~ member(X2,X1) )
& ( ( ! [X3] :
( apply(X0,X3,X2)
| ~ member(X3,X1) )
& member(X2,X1) )
| ~ greatest(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f50]) ).
fof(f50,plain,
! [X0,X1,X2] :
( greatest(X2,X0,X1)
<=> ( ! [X3] :
( apply(X0,X3,X2)
| ~ member(X3,X1) )
& member(X2,X1) ) ),
inference(ennf_transformation,[],[f35]) ).
fof(f35,plain,
! [X0,X1,X2] :
( greatest(X2,X0,X1)
<=> ( ! [X3] :
( member(X3,X1)
=> apply(X0,X3,X2) )
& member(X2,X1) ) ),
inference(rectify,[],[f16]) ).
fof(f16,axiom,
! [X5,X3,X7] :
( greatest(X7,X5,X3)
<=> ( ! [X2] :
( member(X2,X3)
=> apply(X5,X2,X7) )
& member(X7,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',greatest) ).
fof(f424,plain,
spl11_45,
inference(avatar_split_clause,[],[f123,f422]) ).
fof(f123,plain,
! [X2,X0,X1] :
( greatest(X2,X0,X1)
| member(sK8(X0,X1,X2),X1)
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f80]) ).
fof(f397,plain,
( spl11_44
| ~ spl11_2
| ~ spl11_30 ),
inference(avatar_split_clause,[],[f354,f312,f157,f394]) ).
fof(f157,plain,
( spl11_2
<=> subset(sK3,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_2])]) ).
fof(f354,plain,
( member(sK4,sK2)
| ~ spl11_2
| ~ spl11_30 ),
inference(resolution,[],[f313,f159]) ).
fof(f159,plain,
( subset(sK3,sK2)
| ~ spl11_2 ),
inference(avatar_component_clause,[],[f157]) ).
fof(f392,plain,
spl11_43,
inference(avatar_split_clause,[],[f137,f390]) ).
fof(f137,plain,
! [X2,X0,X1] :
( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ),
inference(cnf_transformation,[],[f92]) ).
fof(f92,plain,
! [X0,X1,X2] :
( ( member(X0,union(X1,X2))
| ( ~ member(X0,X2)
& ~ member(X0,X1) ) )
& ( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ) ),
inference(flattening,[],[f91]) ).
fof(f91,plain,
! [X0,X1,X2] :
( ( member(X0,union(X1,X2))
| ( ~ member(X0,X2)
& ~ member(X0,X1) ) )
& ( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ) ),
inference(nnf_transformation,[],[f41]) ).
fof(f41,plain,
! [X0,X1,X2] :
( member(X0,union(X1,X2))
<=> ( member(X0,X2)
| member(X0,X1) ) ),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X2,X0,X1] :
( member(X2,union(X0,X1))
<=> ( member(X2,X1)
| member(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union) ).
fof(f388,plain,
spl11_42,
inference(avatar_split_clause,[],[f134,f386]) ).
fof(f134,plain,
! [X2,X0,X1] :
( X0 = X2
| X0 = X1
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f90]) ).
fof(f90,plain,
! [X0,X1,X2] :
( ( member(X0,unordered_pair(X1,X2))
| ( X0 != X2
& X0 != X1 ) )
& ( X0 = X2
| X0 = X1
| ~ member(X0,unordered_pair(X1,X2)) ) ),
inference(flattening,[],[f89]) ).
fof(f89,plain,
! [X0,X1,X2] :
( ( member(X0,unordered_pair(X1,X2))
| ( X0 != X2
& X0 != X1 ) )
& ( X0 = X2
| X0 = X1
| ~ member(X0,unordered_pair(X1,X2)) ) ),
inference(nnf_transformation,[],[f40]) ).
fof(f40,plain,
! [X0,X1,X2] :
( member(X0,unordered_pair(X1,X2))
<=> ( X0 = X2
| X0 = X1 ) ),
inference(rectify,[],[f9]) ).
fof(f9,axiom,
! [X2,X0,X1] :
( member(X2,unordered_pair(X0,X1))
<=> ( X1 = X2
| X0 = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair) ).
fof(f384,plain,
spl11_41,
inference(avatar_split_clause,[],[f133,f382]) ).
fof(f133,plain,
! [X2,X0,X1] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f88]) ).
fof(f88,plain,
! [X0,X1,X2] :
( ( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) )
& ( ( member(X0,X2)
& member(X0,X1) )
| ~ member(X0,intersection(X1,X2)) ) ),
inference(flattening,[],[f87]) ).
fof(f87,plain,
! [X0,X1,X2] :
( ( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) )
& ( ( member(X0,X2)
& member(X0,X1) )
| ~ member(X0,intersection(X1,X2)) ) ),
inference(nnf_transformation,[],[f39]) ).
fof(f39,plain,
! [X0,X1,X2] :
( member(X0,intersection(X1,X2))
<=> ( member(X0,X2)
& member(X0,X1) ) ),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
! [X2,X0,X1] :
( member(X2,intersection(X0,X1))
<=> ( member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection) ).
fof(f380,plain,
spl11_40,
inference(avatar_split_clause,[],[f130,f378]) ).
fof(f130,plain,
! [X2,X0,X1] :
( member(X0,difference(X2,X1))
| member(X0,X1)
| ~ member(X0,X2) ),
inference(cnf_transformation,[],[f86]) ).
fof(f86,plain,
! [X0,X1,X2] :
( ( member(X0,difference(X2,X1))
| member(X0,X1)
| ~ member(X0,X2) )
& ( ( ~ member(X0,X1)
& member(X0,X2) )
| ~ member(X0,difference(X2,X1)) ) ),
inference(flattening,[],[f85]) ).
fof(f85,plain,
! [X0,X1,X2] :
( ( member(X0,difference(X2,X1))
| member(X0,X1)
| ~ member(X0,X2) )
& ( ( ~ member(X0,X1)
& member(X0,X2) )
| ~ member(X0,difference(X2,X1)) ) ),
inference(nnf_transformation,[],[f38]) ).
fof(f38,plain,
! [X0,X1,X2] :
( member(X0,difference(X2,X1))
<=> ( ~ member(X0,X1)
& member(X0,X2) ) ),
inference(rectify,[],[f7]) ).
fof(f7,axiom,
! [X1,X0,X3] :
( member(X1,difference(X3,X0))
<=> ( ~ member(X1,X0)
& member(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference) ).
fof(f376,plain,
spl11_39,
inference(avatar_split_clause,[],[f127,f374]) ).
fof(f127,plain,
! [X2,X0,X1] :
( upper_bound(X2,X0,X1)
| ~ apply(X0,sK9(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f84]) ).
fof(f84,plain,
! [X0,X1,X2] :
( ( upper_bound(X2,X0,X1)
| ( ~ apply(X0,sK9(X0,X1,X2),X2)
& member(sK9(X0,X1,X2),X1) ) )
& ( ! [X4] :
( apply(X0,X4,X2)
| ~ member(X4,X1) )
| ~ upper_bound(X2,X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f82,f83]) ).
fof(f83,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ apply(X0,X3,X2)
& member(X3,X1) )
=> ( ~ apply(X0,sK9(X0,X1,X2),X2)
& member(sK9(X0,X1,X2),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f82,plain,
! [X0,X1,X2] :
( ( upper_bound(X2,X0,X1)
| ? [X3] :
( ~ apply(X0,X3,X2)
& member(X3,X1) ) )
& ( ! [X4] :
( apply(X0,X4,X2)
| ~ member(X4,X1) )
| ~ upper_bound(X2,X0,X1) ) ),
inference(rectify,[],[f81]) ).
fof(f81,plain,
! [X0,X1,X2] :
( ( upper_bound(X2,X0,X1)
| ? [X3] :
( ~ apply(X0,X3,X2)
& member(X3,X1) ) )
& ( ! [X3] :
( apply(X0,X3,X2)
| ~ member(X3,X1) )
| ~ upper_bound(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f51]) ).
fof(f51,plain,
! [X0,X1,X2] :
( upper_bound(X2,X0,X1)
<=> ! [X3] :
( apply(X0,X3,X2)
| ~ member(X3,X1) ) ),
inference(ennf_transformation,[],[f36]) ).
fof(f36,plain,
! [X0,X1,X2] :
( upper_bound(X2,X0,X1)
<=> ! [X3] :
( member(X3,X1)
=> apply(X0,X3,X2) ) ),
inference(rectify,[],[f14]) ).
fof(f14,axiom,
! [X5,X3,X7] :
( upper_bound(X7,X5,X3)
<=> ! [X2] :
( member(X2,X3)
=> apply(X5,X2,X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upper_bound) ).
fof(f372,plain,
spl11_38,
inference(avatar_split_clause,[],[f125,f370]) ).
fof(f125,plain,
! [X2,X0,X1,X4] :
( apply(X0,X4,X2)
| ~ member(X4,X1)
| ~ upper_bound(X2,X0,X1) ),
inference(cnf_transformation,[],[f84]) ).
fof(f368,plain,
spl11_37,
inference(avatar_split_clause,[],[f122,f366]) ).
fof(f122,plain,
! [X2,X0,X1,X4] :
( apply(X0,X4,X2)
| ~ member(X4,X1)
| ~ greatest(X2,X0,X1) ),
inference(cnf_transformation,[],[f80]) ).
fof(f338,plain,
spl11_36,
inference(avatar_split_clause,[],[f147,f336]) ).
fof(f147,plain,
! [X2,X3,X0,X1] :
( least_upper_bound(X0,X1,X2,X3)
| ~ sP0(X0,X2,X1,X3) ),
inference(cnf_transformation,[],[f98]) ).
fof(f98,plain,
! [X0,X1,X2,X3] :
( ( least_upper_bound(X0,X1,X2,X3)
| ~ sP0(X0,X2,X1,X3) )
& ( sP0(X0,X2,X1,X3)
| ~ least_upper_bound(X0,X1,X2,X3) ) ),
inference(nnf_transformation,[],[f55]) ).
fof(f55,plain,
! [X0,X1,X2,X3] :
( least_upper_bound(X0,X1,X2,X3)
<=> sP0(X0,X2,X1,X3) ),
inference(definition_folding,[],[f53,f54]) ).
fof(f53,plain,
! [X0,X1,X2,X3] :
( least_upper_bound(X0,X1,X2,X3)
<=> ( ! [X4] :
( apply(X2,X0,X4)
| ~ upper_bound(X4,X2,X1)
| ~ member(X4,X3) )
& upper_bound(X0,X2,X1)
& member(X0,X1) ) ),
inference(flattening,[],[f52]) ).
fof(f52,plain,
! [X0,X1,X2,X3] :
( least_upper_bound(X0,X1,X2,X3)
<=> ( ! [X4] :
( apply(X2,X0,X4)
| ~ upper_bound(X4,X2,X1)
| ~ member(X4,X3) )
& upper_bound(X0,X2,X1)
& member(X0,X1) ) ),
inference(ennf_transformation,[],[f43]) ).
fof(f43,plain,
! [X0,X1,X2,X3] :
( least_upper_bound(X0,X1,X2,X3)
<=> ( ! [X4] :
( ( upper_bound(X4,X2,X1)
& member(X4,X3) )
=> apply(X2,X0,X4) )
& upper_bound(X0,X2,X1)
& member(X0,X1) ) ),
inference(rectify,[],[f20]) ).
fof(f20,axiom,
! [X0,X2,X5,X3] :
( least_upper_bound(X0,X2,X5,X3)
<=> ( ! [X7] :
( ( upper_bound(X7,X5,X2)
& member(X7,X3) )
=> apply(X5,X0,X7) )
& upper_bound(X0,X5,X2)
& member(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',least_upper_bound) ).
fof(f334,plain,
spl11_35,
inference(avatar_split_clause,[],[f146,f332]) ).
fof(f146,plain,
! [X2,X3,X0,X1] :
( sP0(X0,X2,X1,X3)
| ~ least_upper_bound(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f98]) ).
fof(f330,plain,
spl11_34,
inference(avatar_split_clause,[],[f126,f328]) ).
fof(f126,plain,
! [X2,X0,X1] :
( upper_bound(X2,X0,X1)
| member(sK9(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f84]) ).
fof(f326,plain,
spl11_33,
inference(avatar_split_clause,[],[f120,f324]) ).
fof(f120,plain,
! [X2,X0,X1] :
( member(X0,sum(X1))
| ~ member(X0,X2)
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f75]) ).
fof(f75,plain,
! [X0,X1] :
( ( member(X0,sum(X1))
| ! [X2] :
( ~ member(X0,X2)
| ~ member(X2,X1) ) )
& ( ( member(X0,sK7(X0,X1))
& member(sK7(X0,X1),X1) )
| ~ member(X0,sum(X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f73,f74]) ).
fof(f74,plain,
! [X0,X1] :
( ? [X3] :
( member(X0,X3)
& member(X3,X1) )
=> ( member(X0,sK7(X0,X1))
& member(sK7(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f73,plain,
! [X0,X1] :
( ( member(X0,sum(X1))
| ! [X2] :
( ~ member(X0,X2)
| ~ member(X2,X1) ) )
& ( ? [X3] :
( member(X0,X3)
& member(X3,X1) )
| ~ member(X0,sum(X1)) ) ),
inference(rectify,[],[f72]) ).
fof(f72,plain,
! [X0,X1] :
( ( member(X0,sum(X1))
| ! [X2] :
( ~ member(X0,X2)
| ~ member(X2,X1) ) )
& ( ? [X2] :
( member(X0,X2)
& member(X2,X1) )
| ~ member(X0,sum(X1)) ) ),
inference(nnf_transformation,[],[f31]) ).
fof(f31,plain,
! [X0,X1] :
( member(X0,sum(X1))
<=> ? [X2] :
( member(X0,X2)
& member(X2,X1) ) ),
inference(rectify,[],[f10]) ).
fof(f10,axiom,
! [X2,X0] :
( member(X2,sum(X0))
<=> ? [X4] :
( member(X2,X4)
& member(X4,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum) ).
fof(f322,plain,
spl11_32,
inference(avatar_split_clause,[],[f115,f320]) ).
fof(f115,plain,
! [X3,X0,X1] :
( member(X0,X3)
| ~ member(X3,X1)
| ~ member(X0,product(X1)) ),
inference(cnf_transformation,[],[f71]) ).
fof(f71,plain,
! [X0,X1] :
( ( member(X0,product(X1))
| ( ~ member(X0,sK6(X0,X1))
& member(sK6(X0,X1),X1) ) )
& ( ! [X3] :
( member(X0,X3)
| ~ member(X3,X1) )
| ~ member(X0,product(X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f69,f70]) ).
fof(f70,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X0,X2)
& member(X2,X1) )
=> ( ~ member(X0,sK6(X0,X1))
& member(sK6(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f69,plain,
! [X0,X1] :
( ( member(X0,product(X1))
| ? [X2] :
( ~ member(X0,X2)
& member(X2,X1) ) )
& ( ! [X3] :
( member(X0,X3)
| ~ member(X3,X1) )
| ~ member(X0,product(X1)) ) ),
inference(rectify,[],[f68]) ).
fof(f68,plain,
! [X0,X1] :
( ( member(X0,product(X1))
| ? [X2] :
( ~ member(X0,X2)
& member(X2,X1) ) )
& ( ! [X2] :
( member(X0,X2)
| ~ member(X2,X1) )
| ~ member(X0,product(X1)) ) ),
inference(nnf_transformation,[],[f49]) ).
fof(f49,plain,
! [X0,X1] :
( member(X0,product(X1))
<=> ! [X2] :
( member(X0,X2)
| ~ member(X2,X1) ) ),
inference(ennf_transformation,[],[f30]) ).
fof(f30,plain,
! [X0,X1] :
( member(X0,product(X1))
<=> ! [X2] :
( member(X2,X1)
=> member(X0,X2) ) ),
inference(rectify,[],[f11]) ).
fof(f11,axiom,
! [X2,X0] :
( member(X2,product(X0))
<=> ! [X4] :
( member(X4,X0)
=> member(X2,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product) ).
fof(f318,plain,
spl11_31,
inference(avatar_split_clause,[],[f105,f316]) ).
fof(f105,plain,
! [X0,X1,X7] :
( apply(X0,X7,X7)
| ~ member(X7,X1)
| ~ order(X0,X1) ),
inference(cnf_transformation,[],[f47]) ).
fof(f314,plain,
( spl11_30
| ~ spl11_4
| ~ spl11_23 ),
inference(avatar_split_clause,[],[f286,f259,f166,f312]) ).
fof(f286,plain,
( ! [X0] :
( member(sK4,X0)
| ~ subset(sK3,X0) )
| ~ spl11_4
| ~ spl11_23 ),
inference(resolution,[],[f260,f168]) ).
fof(f285,plain,
spl11_29,
inference(avatar_split_clause,[],[f141,f283]) ).
fof(f141,plain,
! [X2,X3,X0,X1] :
( upper_bound(X0,X1,X2)
| ~ sP0(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f97]) ).
fof(f281,plain,
spl11_28,
inference(avatar_split_clause,[],[f119,f279]) ).
fof(f119,plain,
! [X0,X1] :
( member(X0,sK7(X0,X1))
| ~ member(X0,sum(X1)) ),
inference(cnf_transformation,[],[f75]) ).
fof(f277,plain,
spl11_27,
inference(avatar_split_clause,[],[f118,f275]) ).
fof(f118,plain,
! [X0,X1] :
( member(sK7(X0,X1),X1)
| ~ member(X0,sum(X1)) ),
inference(cnf_transformation,[],[f75]) ).
fof(f273,plain,
spl11_26,
inference(avatar_split_clause,[],[f117,f271]) ).
fof(f117,plain,
! [X0,X1] :
( member(X0,product(X1))
| ~ member(X0,sK6(X0,X1)) ),
inference(cnf_transformation,[],[f71]) ).
fof(f269,plain,
spl11_25,
inference(avatar_split_clause,[],[f116,f267]) ).
fof(f116,plain,
! [X0,X1] :
( member(X0,product(X1))
| member(sK6(X0,X1),X1) ),
inference(cnf_transformation,[],[f71]) ).
fof(f265,plain,
( spl11_24
| ~ spl11_6
| ~ spl11_14 ),
inference(avatar_split_clause,[],[f246,f211,f176,f263]) ).
fof(f263,plain,
( spl11_24
<=> ! [X0] : subset(empty_set,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_24])]) ).
fof(f246,plain,
( ! [X0] : subset(empty_set,X0)
| ~ spl11_6
| ~ spl11_14 ),
inference(resolution,[],[f212,f177]) ).
fof(f261,plain,
spl11_23,
inference(avatar_split_clause,[],[f108,f259]) ).
fof(f108,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f65]) ).
fof(f65,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK5(X0,X1),X1)
& member(sK5(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f63,f64]) ).
fof(f64,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) )
=> ( ~ member(sK5(X0,X1),X1)
& member(sK5(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f63,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f62]) ).
fof(f62,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f48]) ).
fof(f48,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset) ).
fof(f245,plain,
spl11_22,
inference(avatar_split_clause,[],[f140,f243]) ).
fof(f243,plain,
( spl11_22
<=> ! [X0,X3,X2,X1] :
( member(X0,X2)
| ~ sP0(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_22])]) ).
fof(f140,plain,
! [X2,X3,X0,X1] :
( member(X0,X2)
| ~ sP0(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f97]) ).
fof(f241,plain,
spl11_21,
inference(avatar_split_clause,[],[f139,f239]) ).
fof(f139,plain,
! [X2,X0,X1] :
( member(X0,union(X1,X2))
| ~ member(X0,X2) ),
inference(cnf_transformation,[],[f92]) ).
fof(f237,plain,
spl11_20,
inference(avatar_split_clause,[],[f138,f235]) ).
fof(f138,plain,
! [X2,X0,X1] :
( member(X0,union(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f92]) ).
fof(f233,plain,
spl11_19,
inference(avatar_split_clause,[],[f132,f231]) ).
fof(f132,plain,
! [X2,X0,X1] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f88]) ).
fof(f229,plain,
spl11_18,
inference(avatar_split_clause,[],[f131,f227]) ).
fof(f131,plain,
! [X2,X0,X1] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f88]) ).
fof(f225,plain,
spl11_17,
inference(avatar_split_clause,[],[f129,f223]) ).
fof(f129,plain,
! [X2,X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,difference(X2,X1)) ),
inference(cnf_transformation,[],[f86]) ).
fof(f221,plain,
spl11_16,
inference(avatar_split_clause,[],[f128,f219]) ).
fof(f128,plain,
! [X2,X0,X1] :
( member(X0,X2)
| ~ member(X0,difference(X2,X1)) ),
inference(cnf_transformation,[],[f86]) ).
fof(f217,plain,
spl11_15,
inference(avatar_split_clause,[],[f110,f215]) ).
fof(f110,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK5(X0,X1),X1) ),
inference(cnf_transformation,[],[f65]) ).
fof(f213,plain,
spl11_14,
inference(avatar_split_clause,[],[f109,f211]) ).
fof(f109,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK5(X0,X1),X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f206,plain,
spl11_13,
inference(avatar_split_clause,[],[f121,f204]) ).
fof(f121,plain,
! [X2,X0,X1] :
( member(X2,X1)
| ~ greatest(X2,X0,X1) ),
inference(cnf_transformation,[],[f80]) ).
fof(f202,plain,
spl11_12,
inference(avatar_split_clause,[],[f114,f200]) ).
fof(f114,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f67]) ).
fof(f67,plain,
! [X0,X1] :
( ( member(X0,power_set(X1))
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ member(X0,power_set(X1)) ) ),
inference(nnf_transformation,[],[f29]) ).
fof(f29,plain,
! [X0,X1] :
( member(X0,power_set(X1))
<=> subset(X0,X1) ),
inference(rectify,[],[f3]) ).
fof(f3,axiom,
! [X2,X0] :
( member(X2,power_set(X0))
<=> subset(X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',power_set) ).
fof(f198,plain,
spl11_11,
inference(avatar_split_clause,[],[f113,f196]) ).
fof(f113,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(X0,power_set(X1)) ),
inference(cnf_transformation,[],[f67]) ).
fof(f194,plain,
spl11_10,
inference(avatar_split_clause,[],[f111,f192]) ).
fof(f111,plain,
! [X0,X1] :
( X0 = X1
| ~ member(X0,singleton(X1)) ),
inference(cnf_transformation,[],[f66]) ).
fof(f66,plain,
! [X0,X1] :
( ( member(X0,singleton(X1))
| X0 != X1 )
& ( X0 = X1
| ~ member(X0,singleton(X1)) ) ),
inference(nnf_transformation,[],[f28]) ).
fof(f28,plain,
! [X0,X1] :
( member(X0,singleton(X1))
<=> X0 = X1 ),
inference(rectify,[],[f8]) ).
fof(f8,axiom,
! [X2,X0] :
( member(X2,singleton(X0))
<=> X0 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton) ).
fof(f190,plain,
spl11_9,
inference(avatar_split_clause,[],[f150,f188]) ).
fof(f150,plain,
! [X2,X1] : member(X1,unordered_pair(X1,X2)),
inference(equality_resolution,[],[f135]) ).
fof(f135,plain,
! [X2,X0,X1] :
( member(X0,unordered_pair(X1,X2))
| X0 != X1 ),
inference(cnf_transformation,[],[f90]) ).
fof(f186,plain,
spl11_8,
inference(avatar_split_clause,[],[f149,f184]) ).
fof(f149,plain,
! [X2,X1] : member(X2,unordered_pair(X1,X2)),
inference(equality_resolution,[],[f136]) ).
fof(f136,plain,
! [X2,X0,X1] :
( member(X0,unordered_pair(X1,X2))
| X0 != X2 ),
inference(cnf_transformation,[],[f90]) ).
fof(f182,plain,
spl11_7,
inference(avatar_split_clause,[],[f148,f180]) ).
fof(f148,plain,
! [X1] : member(X1,singleton(X1)),
inference(equality_resolution,[],[f112]) ).
fof(f112,plain,
! [X0,X1] :
( member(X0,singleton(X1))
| X0 != X1 ),
inference(cnf_transformation,[],[f66]) ).
fof(f178,plain,
spl11_6,
inference(avatar_split_clause,[],[f104,f176]) ).
fof(f104,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f25]) ).
fof(f25,plain,
! [X0] : ~ member(X0,empty_set),
inference(rectify,[],[f6]) ).
fof(f6,axiom,
! [X2] : ~ member(X2,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set) ).
fof(f174,plain,
( spl11_3
| spl11_5 ),
inference(avatar_split_clause,[],[f102,f171,f162]) ).
fof(f102,plain,
( least_upper_bound(sK4,sK3,sK1,sK2)
| greatest(sK4,sK1,sK3) ),
inference(cnf_transformation,[],[f61]) ).
fof(f169,plain,
( spl11_3
| spl11_4 ),
inference(avatar_split_clause,[],[f101,f166,f162]) ).
fof(f101,plain,
( member(sK4,sK3)
| greatest(sK4,sK1,sK3) ),
inference(cnf_transformation,[],[f61]) ).
fof(f160,plain,
spl11_2,
inference(avatar_split_clause,[],[f100,f157]) ).
fof(f100,plain,
subset(sK3,sK2),
inference(cnf_transformation,[],[f61]) ).
fof(f155,plain,
spl11_1,
inference(avatar_split_clause,[],[f99,f152]) ).
fof(f99,plain,
order(sK1,sK2),
inference(cnf_transformation,[],[f61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET801+4 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35 % Computer : n012.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Tue Apr 30 01:33:57 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (12756)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38 % (12759)WARNING: value z3 for option sas not known
% 0.15/0.38 % (12760)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.38 % (12757)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38 % (12758)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.38 % (12759)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.15/0.38 % (12761)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.15/0.38 % (12762)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.15/0.38 % (12763)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.22/0.38 TRYING [1]
% 0.22/0.38 TRYING [2]
% 0.22/0.38 TRYING [3]
% 0.22/0.39 TRYING [1]
% 0.22/0.39 TRYING [4]
% 0.22/0.39 TRYING [2]
% 0.22/0.41 TRYING [5]
% 0.22/0.42 TRYING [3]
% 0.22/0.45 TRYING [6]
% 0.22/0.50 TRYING [4]
% 0.22/0.52 TRYING [7]
% 1.97/0.63 TRYING [8]
% 2.38/0.68 TRYING [5]
% 3.50/0.87 TRYING [9]
% 6.18/1.24 TRYING [6]
% 6.50/1.30 TRYING [10]
% 7.76/1.48 TRYING [1]
% 7.76/1.48 TRYING [2]
% 7.76/1.48 TRYING [3]
% 7.76/1.48 TRYING [4]
% 7.76/1.50 TRYING [5]
% 8.29/1.54 TRYING [6]
% 8.62/1.61 TRYING [7]
% 9.17/1.65 % (12761)First to succeed.
% 9.17/1.68 % (12761)Refutation found. Thanks to Tanya!
% 9.17/1.68 % SZS status Theorem for theBenchmark
% 9.17/1.68 % SZS output start Proof for theBenchmark
% See solution above
% 9.36/1.69 % (12761)------------------------------
% 9.36/1.69 % (12761)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 9.36/1.69 % (12761)Termination reason: Refutation
% 9.36/1.69
% 9.36/1.69 % (12761)Memory used [KB]: 15236
% 9.36/1.69 % (12761)Time elapsed: 1.298 s
% 9.36/1.69 % (12761)Instructions burned: 3873 (million)
% 9.36/1.69 % (12761)------------------------------
% 9.36/1.69 % (12761)------------------------------
% 9.36/1.69 % (12756)Success in time 1.3 s
%------------------------------------------------------------------------------