TSTP Solution File: SEU197+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU197+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n024.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 15:23:44 EDT 2024
% Result : Theorem 2.80s 0.69s
% Output : Refutation 2.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 569
% Syntax : Number of formulae : 2009 ( 63 unt; 0 def)
% Number of atoms : 9488 ( 542 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 13458 (5979 ~;6835 |; 74 &)
% ( 546 <=>; 23 =>; 0 <=; 1 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 541 ( 539 usr; 534 prp; 0-3 aty)
% Number of functors : 19 ( 19 usr; 8 con; 0-3 aty)
% Number of variables : 3946 (3903 !; 43 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f12730,plain,
$false,
inference(avatar_sat_refutation,[],[f154,f159,f164,f169,f174,f179,f184,f189,f194,f203,f208,f212,f216,f220,f224,f231,f235,f240,f244,f248,f261,f265,f269,f274,f282,f286,f290,f302,f306,f311,f316,f321,f326,f332,f337,f343,f349,f356,f362,f367,f373,f378,f384,f389,f403,f410,f421,f432,f438,f443,f451,f457,f462,f471,f476,f484,f492,f496,f509,f513,f534,f538,f542,f550,f554,f564,f575,f585,f599,f603,f608,f612,f617,f629,f633,f650,f654,f658,f694,f698,f703,f707,f712,f716,f722,f732,f736,f740,f744,f759,f778,f791,f795,f805,f809,f825,f834,f838,f842,f870,f874,f878,f901,f905,f909,f913,f917,f921,f955,f959,f963,f1003,f1007,f1027,f1031,f1035,f1045,f1065,f1069,f1073,f1077,f1081,f1124,f1128,f1156,f1174,f1186,f1190,f1194,f1199,f1212,f1216,f1220,f1224,f1242,f1246,f1269,f1296,f1300,f1304,f1308,f1344,f1348,f1352,f1356,f1413,f1417,f1421,f1425,f1429,f1445,f1487,f1491,f1495,f1499,f1503,f1507,f1594,f1598,f1630,f1634,f1652,f1656,f1660,f1669,f1707,f1711,f1715,f1719,f1763,f1767,f1771,f1775,f1779,f1839,f1862,f1866,f1870,f1874,f1878,f1972,f1976,f1980,f2013,f2046,f2050,f2054,f2058,f2062,f2066,f2070,f2074,f2135,f2150,f2154,f2158,f2162,f2166,f2170,f2174,f2178,f2182,f2186,f2190,f2202,f2206,f2216,f2226,f2230,f2234,f2403,f2488,f2492,f2496,f2516,f2531,f2535,f2539,f2543,f2547,f2551,f2617,f2627,f2631,f2635,f2639,f2643,f2647,f2651,f2665,f2792,f2801,f2805,f2809,f2813,f2817,f2821,f2825,f2829,f3006,f3010,f3060,f3061,f3065,f3069,f3073,f3077,f3081,f3229,f3233,f3237,f3357,f3361,f3365,f3370,f3444,f3448,f3452,f3456,f3460,f3461,f3465,f3645,f3649,f3653,f3745,f3749,f3753,f3757,f3761,f3792,f3841,f3845,f3849,f3853,f3971,f3975,f3979,f4100,f4104,f4112,f4120,f4124,f4128,f4132,f4136,f4140,f4144,f4148,f4357,f4379,f4383,f4387,f4439,f4443,f4447,f4451,f4455,f4613,f4617,f4621,f4625,f4652,f4673,f4677,f4725,f4729,f4733,f4806,f4810,f4814,f4818,f5020,f5024,f5040,f5044,f5048,f5052,f5056,f5060,f5064,f5188,f5238,f5254,f5258,f5274,f5332,f5336,f5340,f5344,f5495,f5511,f5527,f5531,f5559,f5563,f5579,f5595,f5611,f5615,f5619,f5623,f5685,f5698,f5756,f5760,f5765,f5769,f5831,f5835,f5839,f5843,f5847,f5969,f5973,f5977,f6009,f6031,f6071,f6075,f6128,f6132,f6136,f6140,f6161,f6165,f6170,f6174,f6178,f6210,f6214,f6218,f6222,f6226,f6230,f6234,f6238,f6242,f6246,f6641,f6762,f6766,f6770,f6774,f6778,f6782,f6786,f6790,f6794,f6817,f6821,f6825,f6829,f6863,f7059,f7063,f7067,f7099,f7103,f7107,f7111,f7115,f7119,f7123,f7127,f7131,f7141,f7707,f7771,f7775,f7779,f7797,f7801,f7805,f7810,f7849,f7853,f7886,f7917,f7921,f7922,f7927,f7932,f7934,f7935,f7940,f7944,f7948,f7952,f7956,f7960,f7964,f8510,f8514,f8518,f8522,f8526,f8530,f8534,f8538,f8542,f8546,f8550,f8567,f8571,f8575,f8579,f8583,f8587,f8591,f8595,f8599,f8603,f8607,f9138,f9142,f9146,f9150,f9154,f9158,f9162,f9166,f9170,f9174,f9178,f9273,f9277,f9281,f9285,f9529,f9972,f9976,f9991,f9995,f9999,f10003,f10007,f10011,f10015,f10019,f10023,f10027,f10031,f10035,f10039,f10043,f10047,f10508,f10512,f10516,f10520,f10524,f10528,f10532,f10536,f10540,f10544,f10548,f10562,f10566,f10570,f10574,f10578,f10582,f10586,f10590,f10594,f10598,f10599,f10603,f10607,f10611,f10615,f10619,f11706,f11711,f11715,f11719,f11723,f11727,f11731,f11735,f11739,f11743,f11776,f11806,f11836,f11840,f11844,f11848,f11852,f11856,f11860,f12708,f12712,f12716,f12720,f12724,f12728,f12729]) ).
fof(f12729,plain,
( ~ spl15_11
| ~ spl15_408
| ~ spl15_1
| ~ spl15_12
| spl15_10
| ~ spl15_443 ),
inference(avatar_split_clause,[],[f8696,f8581,f196,f205,f151,f7704,f200]) ).
fof(f200,plain,
( spl15_11
<=> in(sK2,sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_11])]) ).
fof(f7704,plain,
( spl15_408
<=> relation(relation_rng_restriction(sK3,sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_408])]) ).
fof(f151,plain,
( spl15_1
<=> relation(sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_1])]) ).
fof(f205,plain,
( spl15_12
<=> in(sK2,relation_rng(sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_12])]) ).
fof(f196,plain,
( spl15_10
<=> in(sK2,relation_rng(relation_rng_restriction(sK3,sK4))) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_10])]) ).
fof(f8581,plain,
( spl15_443
<=> ! [X2,X0,X1] :
( ~ in(X0,X1)
| ~ in(X0,relation_rng(X2))
| ~ relation(X2)
| ~ relation(relation_rng_restriction(X1,X2))
| in(X0,relation_rng(relation_rng_restriction(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_443])]) ).
fof(f8696,plain,
( ~ in(sK2,relation_rng(sK4))
| ~ relation(sK4)
| ~ relation(relation_rng_restriction(sK3,sK4))
| ~ in(sK2,sK3)
| spl15_10
| ~ spl15_443 ),
inference(resolution,[],[f8582,f197]) ).
fof(f197,plain,
( ~ in(sK2,relation_rng(relation_rng_restriction(sK3,sK4)))
| spl15_10 ),
inference(avatar_component_clause,[],[f196]) ).
fof(f8582,plain,
( ! [X2,X0,X1] :
( in(X0,relation_rng(relation_rng_restriction(X1,X2)))
| ~ in(X0,relation_rng(X2))
| ~ relation(X2)
| ~ relation(relation_rng_restriction(X1,X2))
| ~ in(X0,X1) )
| ~ spl15_443 ),
inference(avatar_component_clause,[],[f8581]) ).
fof(f12728,plain,
( spl15_533
| ~ spl15_24
| ~ spl15_258 ),
inference(avatar_split_clause,[],[f3489,f3446,f267,f12726]) ).
fof(f12726,plain,
( spl15_533
<=> ! [X2,X0,X1] :
( sP0(relation_rng_restriction(X0,X1),X2,relation_rng_restriction(X0,X1))
| ~ relation(relation_rng_restriction(X0,X1))
| ~ relation(X1)
| element(sK10(relation_rng_restriction(X0,X1),X2,relation_rng_restriction(X0,X1)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_533])]) ).
fof(f267,plain,
( spl15_24
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_24])]) ).
fof(f3446,plain,
( spl15_258
<=> ! [X2,X0,X1] :
( in(sK10(relation_rng_restriction(X0,X1),X2,relation_rng_restriction(X0,X1)),X0)
| sP0(relation_rng_restriction(X0,X1),X2,relation_rng_restriction(X0,X1))
| ~ relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_258])]) ).
fof(f3489,plain,
( ! [X2,X0,X1] :
( sP0(relation_rng_restriction(X0,X1),X2,relation_rng_restriction(X0,X1))
| ~ relation(relation_rng_restriction(X0,X1))
| ~ relation(X1)
| element(sK10(relation_rng_restriction(X0,X1),X2,relation_rng_restriction(X0,X1)),X0) )
| ~ spl15_24
| ~ spl15_258 ),
inference(resolution,[],[f3447,f268]) ).
fof(f268,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) )
| ~ spl15_24 ),
inference(avatar_component_clause,[],[f267]) ).
fof(f3447,plain,
( ! [X2,X0,X1] :
( in(sK10(relation_rng_restriction(X0,X1),X2,relation_rng_restriction(X0,X1)),X0)
| sP0(relation_rng_restriction(X0,X1),X2,relation_rng_restriction(X0,X1))
| ~ relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) )
| ~ spl15_258 ),
inference(avatar_component_clause,[],[f3446]) ).
fof(f12724,plain,
( spl15_532
| ~ spl15_23
| ~ spl15_257 ),
inference(avatar_split_clause,[],[f3469,f3442,f263,f12722]) ).
fof(f12722,plain,
( spl15_532
<=> ! [X0,X1] :
( ~ relation(X0)
| ~ relation(relation_rng(X0))
| relation_rng(relation_rng(relation_rng(X0))) = X1
| ~ empty(X0)
| ~ relation(relation_rng(relation_rng(X0)))
| ~ in(X1,sK5(relation_rng(relation_rng(X0)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_532])]) ).
fof(f263,plain,
( spl15_23
<=> ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_23])]) ).
fof(f3442,plain,
( spl15_257
<=> ! [X0,X1] :
( ~ empty(X0)
| ~ relation(X0)
| ~ relation(relation_rng(X0))
| relation_rng(relation_rng(relation_rng(X0))) = X1
| in(sK5(relation_rng(relation_rng(X0)),X1),X1)
| ~ relation(relation_rng(relation_rng(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_257])]) ).
fof(f3469,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ relation(relation_rng(X0))
| relation_rng(relation_rng(relation_rng(X0))) = X1
| ~ empty(X0)
| ~ relation(relation_rng(relation_rng(X0)))
| ~ in(X1,sK5(relation_rng(relation_rng(X0)),X1)) )
| ~ spl15_23
| ~ spl15_257 ),
inference(resolution,[],[f3443,f264]) ).
fof(f264,plain,
( ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) )
| ~ spl15_23 ),
inference(avatar_component_clause,[],[f263]) ).
fof(f3443,plain,
( ! [X0,X1] :
( in(sK5(relation_rng(relation_rng(X0)),X1),X1)
| ~ relation(X0)
| ~ relation(relation_rng(X0))
| relation_rng(relation_rng(relation_rng(X0))) = X1
| ~ empty(X0)
| ~ relation(relation_rng(relation_rng(X0))) )
| ~ spl15_257 ),
inference(avatar_component_clause,[],[f3442]) ).
fof(f12720,plain,
( spl15_531
| ~ spl15_101
| ~ spl15_232 ),
inference(avatar_split_clause,[],[f2844,f2790,f868,f12718]) ).
fof(f12718,plain,
( spl15_531
<=> ! [X2,X0,X1] :
( element(sK10(X0,relation_rng(relation_rng(X1)),X2),relation_rng(X2))
| ~ relation(X2)
| sP0(X0,relation_rng(relation_rng(X1)),X2)
| ~ empty(X1)
| ~ relation(X1)
| ~ relation(relation_rng(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_531])]) ).
fof(f868,plain,
( spl15_101
<=> ! [X0,X1] :
( ~ relation(X0)
| ~ empty(X0)
| ~ in(X1,relation_rng(relation_rng(X0)))
| ~ relation(relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_101])]) ).
fof(f2790,plain,
( spl15_232
<=> ! [X2,X0,X1] :
( in(sK10(X0,X1,X2),X1)
| sP0(X0,X1,X2)
| ~ relation(X2)
| element(sK10(X0,X1,X2),relation_rng(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_232])]) ).
fof(f2844,plain,
( ! [X2,X0,X1] :
( element(sK10(X0,relation_rng(relation_rng(X1)),X2),relation_rng(X2))
| ~ relation(X2)
| sP0(X0,relation_rng(relation_rng(X1)),X2)
| ~ empty(X1)
| ~ relation(X1)
| ~ relation(relation_rng(X1)) )
| ~ spl15_101
| ~ spl15_232 ),
inference(resolution,[],[f2791,f869]) ).
fof(f869,plain,
( ! [X0,X1] :
( ~ in(X1,relation_rng(relation_rng(X0)))
| ~ empty(X0)
| ~ relation(X0)
| ~ relation(relation_rng(X0)) )
| ~ spl15_101 ),
inference(avatar_component_clause,[],[f868]) ).
fof(f2791,plain,
( ! [X2,X0,X1] :
( element(sK10(X0,X1,X2),relation_rng(X2))
| in(sK10(X0,X1,X2),X1)
| ~ relation(X2)
| sP0(X0,X1,X2) )
| ~ spl15_232 ),
inference(avatar_component_clause,[],[f2790]) ).
fof(f12716,plain,
( spl15_530
| ~ spl15_65
| ~ spl15_224 ),
inference(avatar_split_clause,[],[f2666,f2625,f548,f12714]) ).
fof(f12714,plain,
( spl15_530
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| ~ relation(X0)
| ~ empty(X1)
| ~ relation(X1)
| ~ relation(relation_rng(X1))
| relation_rng(X0) = relation_rng_restriction(relation_rng(relation_rng(X1)),X2)
| ~ relation(relation_rng(X0))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_530])]) ).
fof(f548,plain,
( spl15_65
<=> ! [X2,X0,X1] :
( ~ sP0(X0,X1,X2)
| relation_rng_restriction(X1,X0) = X2
| ~ relation(X2)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_65])]) ).
fof(f2625,plain,
( spl15_224
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| sP0(X1,relation_rng(relation_rng(X2)),relation_rng(X0))
| ~ relation(X0)
| ~ empty(X2)
| ~ relation(X2)
| ~ relation(relation_rng(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_224])]) ).
fof(f2666,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| ~ relation(X0)
| ~ empty(X1)
| ~ relation(X1)
| ~ relation(relation_rng(X1))
| relation_rng(X0) = relation_rng_restriction(relation_rng(relation_rng(X1)),X2)
| ~ relation(relation_rng(X0))
| ~ relation(X2) )
| ~ spl15_65
| ~ spl15_224 ),
inference(resolution,[],[f2626,f549]) ).
fof(f549,plain,
( ! [X2,X0,X1] :
( ~ sP0(X0,X1,X2)
| relation_rng_restriction(X1,X0) = X2
| ~ relation(X2)
| ~ relation(X0) )
| ~ spl15_65 ),
inference(avatar_component_clause,[],[f548]) ).
fof(f2626,plain,
( ! [X2,X0,X1] :
( sP0(X1,relation_rng(relation_rng(X2)),relation_rng(X0))
| ~ empty(X0)
| ~ relation(X0)
| ~ empty(X2)
| ~ relation(X2)
| ~ relation(relation_rng(X2)) )
| ~ spl15_224 ),
inference(avatar_component_clause,[],[f2625]) ).
fof(f12712,plain,
( spl15_529
| ~ spl15_121
| ~ spl15_218 ),
inference(avatar_split_clause,[],[f2610,f2533,f1071,f12710]) ).
fof(f12710,plain,
( spl15_529
<=> ! [X0,X1] :
( ~ relation(X0)
| ~ relation(relation_rng(X0))
| ~ empty(X0)
| ~ relation(relation_rng(relation_rng(X0)))
| element(sK5(relation_rng(relation_rng(X0)),X1),X1)
| relation_rng(relation_rng(relation_rng(X0))) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_529])]) ).
fof(f1071,plain,
( spl15_121
<=> ! [X0,X1] :
( in(sK5(X0,X1),relation_rng(X0))
| ~ relation(X0)
| relation_rng(X0) = X1
| element(sK5(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_121])]) ).
fof(f2533,plain,
( spl15_218
<=> ! [X0,X1] :
( ~ empty(X0)
| ~ relation(X0)
| ~ relation(relation_rng(X0))
| ~ in(X1,relation_rng(relation_rng(relation_rng(X0))))
| ~ relation(relation_rng(relation_rng(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_218])]) ).
fof(f2610,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ relation(relation_rng(X0))
| ~ empty(X0)
| ~ relation(relation_rng(relation_rng(X0)))
| element(sK5(relation_rng(relation_rng(X0)),X1),X1)
| relation_rng(relation_rng(relation_rng(X0))) = X1 )
| ~ spl15_121
| ~ spl15_218 ),
inference(duplicate_literal_removal,[],[f2577]) ).
fof(f2577,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ relation(relation_rng(X0))
| ~ empty(X0)
| ~ relation(relation_rng(relation_rng(X0)))
| element(sK5(relation_rng(relation_rng(X0)),X1),X1)
| relation_rng(relation_rng(relation_rng(X0))) = X1
| ~ relation(relation_rng(relation_rng(X0))) )
| ~ spl15_121
| ~ spl15_218 ),
inference(resolution,[],[f2534,f1072]) ).
fof(f1072,plain,
( ! [X0,X1] :
( in(sK5(X0,X1),relation_rng(X0))
| element(sK5(X0,X1),X1)
| relation_rng(X0) = X1
| ~ relation(X0) )
| ~ spl15_121 ),
inference(avatar_component_clause,[],[f1071]) ).
fof(f2534,plain,
( ! [X0,X1] :
( ~ in(X1,relation_rng(relation_rng(relation_rng(X0))))
| ~ relation(X0)
| ~ relation(relation_rng(X0))
| ~ empty(X0)
| ~ relation(relation_rng(relation_rng(X0))) )
| ~ spl15_218 ),
inference(avatar_component_clause,[],[f2533]) ).
fof(f12708,plain,
( spl15_528
| ~ spl15_64
| ~ spl15_199 ),
inference(avatar_split_clause,[],[f2380,f2164,f540,f12706]) ).
fof(f12706,plain,
( spl15_528
<=> ! [X0,X3,X2,X1] :
( in(sK10(X0,relation_rng(relation_rng_restriction(X1,X2)),X3),X1)
| ~ relation(relation_rng_restriction(X1,X2))
| ~ relation(X2)
| sP0(X0,relation_rng(relation_rng_restriction(X1,X2)),X3)
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_528])]) ).
fof(f540,plain,
( spl15_64
<=> ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| in(sK10(X0,X1,X2),X1)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_64])]) ).
fof(f2164,plain,
( spl15_199
<=> ! [X2,X0,X1] :
( in(X0,X1)
| ~ in(X0,relation_rng(relation_rng_restriction(X1,X2)))
| ~ relation(relation_rng_restriction(X1,X2))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_199])]) ).
fof(f2380,plain,
( ! [X2,X3,X0,X1] :
( in(sK10(X0,relation_rng(relation_rng_restriction(X1,X2)),X3),X1)
| ~ relation(relation_rng_restriction(X1,X2))
| ~ relation(X2)
| sP0(X0,relation_rng(relation_rng_restriction(X1,X2)),X3)
| ~ empty(X3) )
| ~ spl15_64
| ~ spl15_199 ),
inference(resolution,[],[f2165,f541]) ).
fof(f541,plain,
( ! [X2,X0,X1] :
( in(sK10(X0,X1,X2),X1)
| sP0(X0,X1,X2)
| ~ empty(X2) )
| ~ spl15_64 ),
inference(avatar_component_clause,[],[f540]) ).
fof(f2165,plain,
( ! [X2,X0,X1] :
( ~ in(X0,relation_rng(relation_rng_restriction(X1,X2)))
| in(X0,X1)
| ~ relation(relation_rng_restriction(X1,X2))
| ~ relation(X2) )
| ~ spl15_199 ),
inference(avatar_component_clause,[],[f2164]) ).
fof(f11860,plain,
( spl15_527
| ~ spl15_18
| ~ spl15_478 ),
inference(avatar_split_clause,[],[f10142,f10029,f233,f11858]) ).
fof(f11858,plain,
( spl15_527
<=> ! [X0] :
( sK12 = relation_rng_restriction(relation_rng(relation_rng(relation_rng(X0))),relation_rng_restriction(sK3,sK4))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_527])]) ).
fof(f233,plain,
( spl15_18
<=> ! [X0] :
( empty(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_18])]) ).
fof(f10029,plain,
( spl15_478
<=> ! [X0] :
( sK12 = relation_rng_restriction(relation_rng(relation_rng(X0)),relation_rng_restriction(sK3,sK4))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_478])]) ).
fof(f10142,plain,
( ! [X0] :
( sK12 = relation_rng_restriction(relation_rng(relation_rng(relation_rng(X0))),relation_rng_restriction(sK3,sK4))
| ~ empty(X0) )
| ~ spl15_18
| ~ spl15_478 ),
inference(resolution,[],[f10030,f234]) ).
fof(f234,plain,
( ! [X0] :
( empty(relation_rng(X0))
| ~ empty(X0) )
| ~ spl15_18 ),
inference(avatar_component_clause,[],[f233]) ).
fof(f10030,plain,
( ! [X0] :
( ~ empty(X0)
| sK12 = relation_rng_restriction(relation_rng(relation_rng(X0)),relation_rng_restriction(sK3,sK4)) )
| ~ spl15_478 ),
inference(avatar_component_clause,[],[f10029]) ).
fof(f11856,plain,
( spl15_526
| ~ spl15_67
| ~ spl15_305 ),
inference(avatar_split_clause,[],[f4717,f4675,f562,f11854]) ).
fof(f11854,plain,
( spl15_526
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP0(X0,X1,relation_rng_restriction(X2,X3))
| ~ relation(relation_rng_restriction(X2,X3))
| ~ relation(X3)
| in(sK10(X0,X1,relation_rng_restriction(X2,X3)),relation_rng(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_526])]) ).
fof(f562,plain,
( spl15_67
<=> ! [X2,X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),X2)
| in(X1,relation_rng(X2))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_67])]) ).
fof(f4675,plain,
( spl15_305
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| in(unordered_pair(singleton(sK9(X0,X1,relation_rng_restriction(X2,X3))),unordered_pair(sK10(X0,X1,relation_rng_restriction(X2,X3)),sK9(X0,X1,relation_rng_restriction(X2,X3)))),X3)
| sP0(X0,X1,relation_rng_restriction(X2,X3))
| ~ relation(relation_rng_restriction(X2,X3))
| ~ relation(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_305])]) ).
fof(f4717,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP0(X0,X1,relation_rng_restriction(X2,X3))
| ~ relation(relation_rng_restriction(X2,X3))
| ~ relation(X3)
| in(sK10(X0,X1,relation_rng_restriction(X2,X3)),relation_rng(X3)) )
| ~ spl15_67
| ~ spl15_305 ),
inference(duplicate_literal_removal,[],[f4704]) ).
fof(f4704,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP0(X0,X1,relation_rng_restriction(X2,X3))
| ~ relation(relation_rng_restriction(X2,X3))
| ~ relation(X3)
| in(sK10(X0,X1,relation_rng_restriction(X2,X3)),relation_rng(X3))
| ~ relation(X3) )
| ~ spl15_67
| ~ spl15_305 ),
inference(resolution,[],[f4676,f563]) ).
fof(f563,plain,
( ! [X2,X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),X2)
| in(X1,relation_rng(X2))
| ~ relation(X2) )
| ~ spl15_67 ),
inference(avatar_component_clause,[],[f562]) ).
fof(f4676,plain,
( ! [X2,X3,X0,X1] :
( in(unordered_pair(singleton(sK9(X0,X1,relation_rng_restriction(X2,X3))),unordered_pair(sK10(X0,X1,relation_rng_restriction(X2,X3)),sK9(X0,X1,relation_rng_restriction(X2,X3)))),X3)
| ~ empty(X0)
| sP0(X0,X1,relation_rng_restriction(X2,X3))
| ~ relation(relation_rng_restriction(X2,X3))
| ~ relation(X3) )
| ~ spl15_305 ),
inference(avatar_component_clause,[],[f4675]) ).
fof(f11852,plain,
( spl15_525
| ~ spl15_67
| ~ spl15_304 ),
inference(avatar_split_clause,[],[f4695,f4671,f562,f11850]) ).
fof(f11850,plain,
( spl15_525
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP0(relation_rng_restriction(X1,X2),X3,X0)
| ~ relation(relation_rng_restriction(X1,X2))
| ~ relation(X2)
| in(sK10(relation_rng_restriction(X1,X2),X3,X0),relation_rng(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_525])]) ).
fof(f4671,plain,
( spl15_304
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| in(unordered_pair(singleton(sK9(relation_rng_restriction(X1,X2),X3,X0)),unordered_pair(sK10(relation_rng_restriction(X1,X2),X3,X0),sK9(relation_rng_restriction(X1,X2),X3,X0))),X2)
| sP0(relation_rng_restriction(X1,X2),X3,X0)
| ~ relation(relation_rng_restriction(X1,X2))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_304])]) ).
fof(f4695,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP0(relation_rng_restriction(X1,X2),X3,X0)
| ~ relation(relation_rng_restriction(X1,X2))
| ~ relation(X2)
| in(sK10(relation_rng_restriction(X1,X2),X3,X0),relation_rng(X2)) )
| ~ spl15_67
| ~ spl15_304 ),
inference(duplicate_literal_removal,[],[f4682]) ).
fof(f4682,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP0(relation_rng_restriction(X1,X2),X3,X0)
| ~ relation(relation_rng_restriction(X1,X2))
| ~ relation(X2)
| in(sK10(relation_rng_restriction(X1,X2),X3,X0),relation_rng(X2))
| ~ relation(X2) )
| ~ spl15_67
| ~ spl15_304 ),
inference(resolution,[],[f4672,f563]) ).
fof(f4672,plain,
( ! [X2,X3,X0,X1] :
( in(unordered_pair(singleton(sK9(relation_rng_restriction(X1,X2),X3,X0)),unordered_pair(sK10(relation_rng_restriction(X1,X2),X3,X0),sK9(relation_rng_restriction(X1,X2),X3,X0))),X2)
| ~ empty(X0)
| sP0(relation_rng_restriction(X1,X2),X3,X0)
| ~ relation(relation_rng_restriction(X1,X2))
| ~ relation(X2) )
| ~ spl15_304 ),
inference(avatar_component_clause,[],[f4671]) ).
fof(f11848,plain,
( spl15_524
| ~ spl15_68
| ~ spl15_288 ),
inference(avatar_split_clause,[],[f4283,f4142,f573,f11846]) ).
fof(f11846,plain,
( spl15_524
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ empty(X0)
| sP0(X0,X1,X2)
| ~ sP0(X2,relation_rng(X2),X3)
| ~ relation(X2)
| in(sK10(X0,X1,X2),X4)
| ~ sP0(X5,X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_524])]) ).
fof(f573,plain,
( spl15_68
<=> ! [X4,X0,X3,X2,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),X2)
| in(X1,X3)
| ~ sP0(X4,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_68])]) ).
fof(f4142,plain,
( spl15_288
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X3)
| sP0(X0,X1,X2)
| ~ sP0(X2,relation_rng(X2),X3)
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_288])]) ).
fof(f4283,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ empty(X0)
| sP0(X0,X1,X2)
| ~ sP0(X2,relation_rng(X2),X3)
| ~ relation(X2)
| in(sK10(X0,X1,X2),X4)
| ~ sP0(X5,X4,X3) )
| ~ spl15_68
| ~ spl15_288 ),
inference(resolution,[],[f4143,f574]) ).
fof(f574,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),X2)
| in(X1,X3)
| ~ sP0(X4,X3,X2) )
| ~ spl15_68 ),
inference(avatar_component_clause,[],[f573]) ).
fof(f4143,plain,
( ! [X2,X3,X0,X1] :
( in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X3)
| ~ empty(X0)
| sP0(X0,X1,X2)
| ~ sP0(X2,relation_rng(X2),X3)
| ~ relation(X2) )
| ~ spl15_288 ),
inference(avatar_component_clause,[],[f4142]) ).
fof(f11844,plain,
( spl15_523
| ~ spl15_68
| ~ spl15_287 ),
inference(avatar_split_clause,[],[f4243,f4138,f573,f11842]) ).
fof(f11842,plain,
( spl15_523
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ empty(X0)
| sP0(X1,X2,X0)
| ~ sP0(X1,relation_rng(X1),X3)
| ~ relation(X1)
| in(sK10(X1,X2,X0),X4)
| ~ sP0(X5,X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_523])]) ).
fof(f4138,plain,
( spl15_287
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| in(unordered_pair(singleton(sK9(X1,X2,X0)),unordered_pair(sK10(X1,X2,X0),sK9(X1,X2,X0))),X3)
| sP0(X1,X2,X0)
| ~ sP0(X1,relation_rng(X1),X3)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_287])]) ).
fof(f4243,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ empty(X0)
| sP0(X1,X2,X0)
| ~ sP0(X1,relation_rng(X1),X3)
| ~ relation(X1)
| in(sK10(X1,X2,X0),X4)
| ~ sP0(X5,X4,X3) )
| ~ spl15_68
| ~ spl15_287 ),
inference(resolution,[],[f4139,f574]) ).
fof(f4139,plain,
( ! [X2,X3,X0,X1] :
( in(unordered_pair(singleton(sK9(X1,X2,X0)),unordered_pair(sK10(X1,X2,X0),sK9(X1,X2,X0))),X3)
| ~ empty(X0)
| sP0(X1,X2,X0)
| ~ sP0(X1,relation_rng(X1),X3)
| ~ relation(X1) )
| ~ spl15_287 ),
inference(avatar_component_clause,[],[f4138]) ).
fof(f11840,plain,
( spl15_522
| ~ spl15_75
| ~ spl15_277 ),
inference(avatar_split_clause,[],[f4054,f3973,f627,f11838]) ).
fof(f11838,plain,
( spl15_522
<=> ! [X2,X0,X1] :
( ~ in(sK5(X0,X1),relation_rng(relation_rng_restriction(X2,X0)))
| ~ relation(relation_rng_restriction(X2,X0))
| ~ relation(X0)
| relation_rng(X0) = X1
| ~ in(sK5(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_522])]) ).
fof(f627,plain,
( spl15_75
<=> ! [X2,X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(sK5(X1,X2),X0)),X1)
| relation_rng(X1) = X2
| ~ in(sK5(X1,X2),X2)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_75])]) ).
fof(f3973,plain,
( spl15_277
<=> ! [X2,X0,X1] :
( in(unordered_pair(singleton(sK7(relation_rng_restriction(X0,X1),X2)),unordered_pair(X2,sK7(relation_rng_restriction(X0,X1),X2))),X1)
| ~ in(X2,relation_rng(relation_rng_restriction(X0,X1)))
| ~ relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_277])]) ).
fof(f4054,plain,
( ! [X2,X0,X1] :
( ~ in(sK5(X0,X1),relation_rng(relation_rng_restriction(X2,X0)))
| ~ relation(relation_rng_restriction(X2,X0))
| ~ relation(X0)
| relation_rng(X0) = X1
| ~ in(sK5(X0,X1),X1) )
| ~ spl15_75
| ~ spl15_277 ),
inference(duplicate_literal_removal,[],[f4042]) ).
fof(f4042,plain,
( ! [X2,X0,X1] :
( ~ in(sK5(X0,X1),relation_rng(relation_rng_restriction(X2,X0)))
| ~ relation(relation_rng_restriction(X2,X0))
| ~ relation(X0)
| relation_rng(X0) = X1
| ~ in(sK5(X0,X1),X1)
| ~ relation(X0) )
| ~ spl15_75
| ~ spl15_277 ),
inference(resolution,[],[f3974,f628]) ).
fof(f628,plain,
( ! [X2,X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(sK5(X1,X2),X0)),X1)
| relation_rng(X1) = X2
| ~ in(sK5(X1,X2),X2)
| ~ relation(X1) )
| ~ spl15_75 ),
inference(avatar_component_clause,[],[f627]) ).
fof(f3974,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(singleton(sK7(relation_rng_restriction(X0,X1),X2)),unordered_pair(X2,sK7(relation_rng_restriction(X0,X1),X2))),X1)
| ~ in(X2,relation_rng(relation_rng_restriction(X0,X1)))
| ~ relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) )
| ~ spl15_277 ),
inference(avatar_component_clause,[],[f3973]) ).
fof(f11836,plain,
( spl15_521
| ~ spl15_61
| ~ spl15_263 ),
inference(avatar_split_clause,[],[f3659,f3643,f511,f11834]) ).
fof(f11834,plain,
( spl15_521
<=> ! [X2,X0,X1] :
( ~ relation(relation_rng_restriction(relation_rng(X0),X1))
| relation_rng(X2) = relation_rng(relation_rng_restriction(relation_rng(X0),X1))
| ~ relation(X1)
| ~ relation(X2)
| ~ empty(X2)
| ~ relation(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_521])]) ).
fof(f511,plain,
( spl15_61
<=> ! [X0,X1] :
( ~ in(X0,relation_rng(X1))
| ~ relation(X1)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_61])]) ).
fof(f3643,plain,
( spl15_263
<=> ! [X2,X0,X1] :
( in(sK5(relation_rng_restriction(X0,X1),relation_rng(X2)),X0)
| ~ relation(relation_rng_restriction(X0,X1))
| relation_rng(X2) = relation_rng(relation_rng_restriction(X0,X1))
| ~ relation(X1)
| ~ relation(X2)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_263])]) ).
fof(f3659,plain,
( ! [X2,X0,X1] :
( ~ relation(relation_rng_restriction(relation_rng(X0),X1))
| relation_rng(X2) = relation_rng(relation_rng_restriction(relation_rng(X0),X1))
| ~ relation(X1)
| ~ relation(X2)
| ~ empty(X2)
| ~ relation(X0)
| ~ empty(X0) )
| ~ spl15_61
| ~ spl15_263 ),
inference(resolution,[],[f3644,f512]) ).
fof(f512,plain,
( ! [X0,X1] :
( ~ in(X0,relation_rng(X1))
| ~ relation(X1)
| ~ empty(X1) )
| ~ spl15_61 ),
inference(avatar_component_clause,[],[f511]) ).
fof(f3644,plain,
( ! [X2,X0,X1] :
( in(sK5(relation_rng_restriction(X0,X1),relation_rng(X2)),X0)
| ~ relation(relation_rng_restriction(X0,X1))
| relation_rng(X2) = relation_rng(relation_rng_restriction(X0,X1))
| ~ relation(X1)
| ~ relation(X2)
| ~ empty(X2) )
| ~ spl15_263 ),
inference(avatar_component_clause,[],[f3643]) ).
fof(f11806,plain,
( ~ spl15_19
| spl15_520
| ~ spl15_74
| ~ spl15_261 ),
inference(avatar_split_clause,[],[f3590,f3458,f614,f11804,f237]) ).
fof(f237,plain,
( spl15_19
<=> relation(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_19])]) ).
fof(f11804,plain,
( spl15_520
<=> ! [X0,X1] :
( in(sK10(relation_rng(relation_rng(X0)),X1,sK12),sK12)
| ~ relation(relation_rng(X0))
| ~ relation(X0)
| ~ empty(X0)
| sP0(relation_rng(relation_rng(X0)),X1,sK12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_520])]) ).
fof(f614,plain,
( spl15_74
<=> sK12 = relation_rng(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_74])]) ).
fof(f3458,plain,
( spl15_261
<=> ! [X2,X0,X1] :
( ~ relation(X0)
| in(sK10(relation_rng(relation_rng(X1)),X2,X0),relation_rng(X0))
| sP0(relation_rng(relation_rng(X1)),X2,X0)
| ~ empty(X1)
| ~ relation(X1)
| ~ relation(relation_rng(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_261])]) ).
fof(f3590,plain,
( ! [X0,X1] :
( in(sK10(relation_rng(relation_rng(X0)),X1,sK12),sK12)
| ~ relation(sK12)
| sP0(relation_rng(relation_rng(X0)),X1,sK12)
| ~ empty(X0)
| ~ relation(X0)
| ~ relation(relation_rng(X0)) )
| ~ spl15_74
| ~ spl15_261 ),
inference(superposition,[],[f3459,f616]) ).
fof(f616,plain,
( sK12 = relation_rng(sK12)
| ~ spl15_74 ),
inference(avatar_component_clause,[],[f614]) ).
fof(f3459,plain,
( ! [X2,X0,X1] :
( in(sK10(relation_rng(relation_rng(X1)),X2,X0),relation_rng(X0))
| ~ relation(X0)
| sP0(relation_rng(relation_rng(X1)),X2,X0)
| ~ empty(X1)
| ~ relation(X1)
| ~ relation(relation_rng(X1)) )
| ~ spl15_261 ),
inference(avatar_component_clause,[],[f3458]) ).
fof(f11776,plain,
( ~ spl15_19
| spl15_519
| ~ spl15_74
| ~ spl15_260 ),
inference(avatar_split_clause,[],[f3558,f3454,f614,f11774,f237]) ).
fof(f11774,plain,
( spl15_519
<=> ! [X0,X1] :
( in(sK10(sK12,X0,relation_rng(relation_rng(X1))),sK12)
| ~ relation(relation_rng(X1))
| ~ relation(X1)
| ~ empty(X1)
| sP0(sK12,X0,relation_rng(relation_rng(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_519])]) ).
fof(f3454,plain,
( spl15_260
<=> ! [X2,X0,X1] :
( ~ relation(X0)
| in(sK10(X0,X1,relation_rng(relation_rng(X2))),relation_rng(X0))
| sP0(X0,X1,relation_rng(relation_rng(X2)))
| ~ empty(X2)
| ~ relation(X2)
| ~ relation(relation_rng(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_260])]) ).
fof(f3558,plain,
( ! [X0,X1] :
( in(sK10(sK12,X0,relation_rng(relation_rng(X1))),sK12)
| ~ relation(sK12)
| sP0(sK12,X0,relation_rng(relation_rng(X1)))
| ~ empty(X1)
| ~ relation(X1)
| ~ relation(relation_rng(X1)) )
| ~ spl15_74
| ~ spl15_260 ),
inference(superposition,[],[f3455,f616]) ).
fof(f3455,plain,
( ! [X2,X0,X1] :
( in(sK10(X0,X1,relation_rng(relation_rng(X2))),relation_rng(X0))
| ~ relation(X0)
| sP0(X0,X1,relation_rng(relation_rng(X2)))
| ~ empty(X2)
| ~ relation(X2)
| ~ relation(relation_rng(X2)) )
| ~ spl15_260 ),
inference(avatar_component_clause,[],[f3454]) ).
fof(f11743,plain,
( ~ spl15_19
| spl15_518
| ~ spl15_74
| ~ spl15_259 ),
inference(avatar_split_clause,[],[f3526,f3450,f614,f11741,f237]) ).
fof(f11741,plain,
( spl15_518
<=> ! [X0,X1] :
( in(sK10(X0,relation_rng(relation_rng(X1)),sK12),sK12)
| ~ relation(relation_rng(X1))
| ~ relation(X1)
| ~ empty(X1)
| sP0(X0,relation_rng(relation_rng(X1)),sK12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_518])]) ).
fof(f3450,plain,
( spl15_259
<=> ! [X2,X0,X1] :
( in(sK10(X0,relation_rng(relation_rng(X1)),X2),relation_rng(X2))
| sP0(X0,relation_rng(relation_rng(X1)),X2)
| ~ relation(X2)
| ~ empty(X1)
| ~ relation(X1)
| ~ relation(relation_rng(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_259])]) ).
fof(f3526,plain,
( ! [X0,X1] :
( in(sK10(X0,relation_rng(relation_rng(X1)),sK12),sK12)
| sP0(X0,relation_rng(relation_rng(X1)),sK12)
| ~ relation(sK12)
| ~ empty(X1)
| ~ relation(X1)
| ~ relation(relation_rng(X1)) )
| ~ spl15_74
| ~ spl15_259 ),
inference(superposition,[],[f3451,f616]) ).
fof(f3451,plain,
( ! [X2,X0,X1] :
( in(sK10(X0,relation_rng(relation_rng(X1)),X2),relation_rng(X2))
| sP0(X0,relation_rng(relation_rng(X1)),X2)
| ~ relation(X2)
| ~ empty(X1)
| ~ relation(X1)
| ~ relation(relation_rng(X1)) )
| ~ spl15_259 ),
inference(avatar_component_clause,[],[f3450]) ).
fof(f11739,plain,
( spl15_517
| ~ spl15_23
| ~ spl15_253 ),
inference(avatar_split_clause,[],[f3378,f3355,f263,f11737]) ).
fof(f11737,plain,
( spl15_517
<=> ! [X0,X1] :
( ~ relation(X0)
| ~ relation(relation_rng(X0))
| ~ empty(X0)
| ~ relation(X1)
| relation_rng(X1) = relation_rng(relation_rng(X0))
| ~ in(relation_rng(X1),sK5(X1,relation_rng(relation_rng(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_517])]) ).
fof(f3355,plain,
( spl15_253
<=> ! [X0,X1] :
( ~ empty(X0)
| ~ relation(X0)
| ~ relation(relation_rng(X0))
| in(sK5(X1,relation_rng(relation_rng(X0))),relation_rng(X1))
| ~ relation(X1)
| relation_rng(X1) = relation_rng(relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_253])]) ).
fof(f3378,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ relation(relation_rng(X0))
| ~ empty(X0)
| ~ relation(X1)
| relation_rng(X1) = relation_rng(relation_rng(X0))
| ~ in(relation_rng(X1),sK5(X1,relation_rng(relation_rng(X0)))) )
| ~ spl15_23
| ~ spl15_253 ),
inference(resolution,[],[f3356,f264]) ).
fof(f3356,plain,
( ! [X0,X1] :
( in(sK5(X1,relation_rng(relation_rng(X0))),relation_rng(X1))
| ~ relation(X0)
| ~ relation(relation_rng(X0))
| ~ empty(X0)
| ~ relation(X1)
| relation_rng(X1) = relation_rng(relation_rng(X0)) )
| ~ spl15_253 ),
inference(avatar_component_clause,[],[f3355]) ).
fof(f11735,plain,
( spl15_516
| ~ spl15_101
| ~ spl15_249 ),
inference(avatar_split_clause,[],[f3217,f3079,f868,f11733]) ).
fof(f11733,plain,
( spl15_516
<=> ! [X2,X0,X1] :
( ~ relation(relation_rng_restriction(X0,X1))
| relation_rng(relation_rng_restriction(X0,X1)) = relation_rng(relation_rng(X2))
| ~ relation(X1)
| ~ empty(X1)
| ~ empty(X2)
| ~ relation(X2)
| ~ relation(relation_rng(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_516])]) ).
fof(f3079,plain,
( spl15_249
<=> ! [X2,X0,X1] :
( ~ relation(relation_rng_restriction(X0,X1))
| in(sK5(relation_rng_restriction(X0,X1),X2),X2)
| relation_rng(relation_rng_restriction(X0,X1)) = X2
| ~ relation(X1)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_249])]) ).
fof(f3217,plain,
( ! [X2,X0,X1] :
( ~ relation(relation_rng_restriction(X0,X1))
| relation_rng(relation_rng_restriction(X0,X1)) = relation_rng(relation_rng(X2))
| ~ relation(X1)
| ~ empty(X1)
| ~ empty(X2)
| ~ relation(X2)
| ~ relation(relation_rng(X2)) )
| ~ spl15_101
| ~ spl15_249 ),
inference(resolution,[],[f3080,f869]) ).
fof(f3080,plain,
( ! [X2,X0,X1] :
( in(sK5(relation_rng_restriction(X0,X1),X2),X2)
| ~ relation(relation_rng_restriction(X0,X1))
| relation_rng(relation_rng_restriction(X0,X1)) = X2
| ~ relation(X1)
| ~ empty(X1) )
| ~ spl15_249 ),
inference(avatar_component_clause,[],[f3079]) ).
fof(f11731,plain,
( spl15_515
| ~ spl15_101
| ~ spl15_247 ),
inference(avatar_split_clause,[],[f3135,f3071,f868,f11729]) ).
fof(f11729,plain,
( spl15_515
<=> ! [X2,X0,X1] :
( ~ relation(relation_rng_restriction(X0,X1))
| relation_rng(relation_rng_restriction(X0,X1)) = relation_rng(relation_rng(X2))
| ~ relation(X1)
| ~ empty(X0)
| ~ empty(X2)
| ~ relation(X2)
| ~ relation(relation_rng(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_515])]) ).
fof(f3071,plain,
( spl15_247
<=> ! [X2,X0,X1] :
( in(sK5(relation_rng_restriction(X0,X1),X2),X2)
| ~ relation(relation_rng_restriction(X0,X1))
| relation_rng(relation_rng_restriction(X0,X1)) = X2
| ~ relation(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_247])]) ).
fof(f3135,plain,
( ! [X2,X0,X1] :
( ~ relation(relation_rng_restriction(X0,X1))
| relation_rng(relation_rng_restriction(X0,X1)) = relation_rng(relation_rng(X2))
| ~ relation(X1)
| ~ empty(X0)
| ~ empty(X2)
| ~ relation(X2)
| ~ relation(relation_rng(X2)) )
| ~ spl15_101
| ~ spl15_247 ),
inference(resolution,[],[f3072,f869]) ).
fof(f3072,plain,
( ! [X2,X0,X1] :
( in(sK5(relation_rng_restriction(X0,X1),X2),X2)
| ~ relation(relation_rng_restriction(X0,X1))
| relation_rng(relation_rng_restriction(X0,X1)) = X2
| ~ relation(X1)
| ~ empty(X0) )
| ~ spl15_247 ),
inference(avatar_component_clause,[],[f3071]) ).
fof(f11727,plain,
( spl15_514
| ~ spl15_115
| ~ spl15_218 ),
inference(avatar_split_clause,[],[f2597,f2533,f1025,f11725]) ).
fof(f11725,plain,
( spl15_514
<=> ! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(relation_rng(X0))
| ~ empty(X0)
| ~ relation(relation_rng(relation_rng(X0)))
| ~ empty(X1)
| sP0(X2,relation_rng(relation_rng(relation_rng(X0))),relation_rng(X1))
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_514])]) ).
fof(f1025,plain,
( spl15_115
<=> ! [X2,X0,X1] :
( ~ relation(X0)
| ~ empty(X0)
| sP0(X1,X2,relation_rng(X0))
| in(sK10(X1,X2,relation_rng(X0)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_115])]) ).
fof(f2597,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(relation_rng(X0))
| ~ empty(X0)
| ~ relation(relation_rng(relation_rng(X0)))
| ~ empty(X1)
| sP0(X2,relation_rng(relation_rng(relation_rng(X0))),relation_rng(X1))
| ~ relation(X1) )
| ~ spl15_115
| ~ spl15_218 ),
inference(resolution,[],[f2534,f1026]) ).
fof(f1026,plain,
( ! [X2,X0,X1] :
( in(sK10(X1,X2,relation_rng(X0)),X2)
| ~ empty(X0)
| sP0(X1,X2,relation_rng(X0))
| ~ relation(X0) )
| ~ spl15_115 ),
inference(avatar_component_clause,[],[f1025]) ).
fof(f11723,plain,
( spl15_513
| ~ spl15_209
| ~ spl15_218 ),
inference(avatar_split_clause,[],[f2594,f2533,f2224,f11721]) ).
fof(f11721,plain,
( spl15_513
<=> ! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(relation_rng(X0))
| ~ empty(X0)
| ~ relation(relation_rng(relation_rng(X0)))
| sP0(X1,relation_rng(relation_rng(relation_rng(X0))),X2)
| ~ relation(X2)
| ~ empty(relation_rng(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_513])]) ).
fof(f2224,plain,
( spl15_209
<=> ! [X2,X0,X1] :
( in(sK10(X0,X1,X2),X1)
| sP0(X0,X1,X2)
| ~ relation(X2)
| ~ empty(relation_rng(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_209])]) ).
fof(f2594,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(relation_rng(X0))
| ~ empty(X0)
| ~ relation(relation_rng(relation_rng(X0)))
| sP0(X1,relation_rng(relation_rng(relation_rng(X0))),X2)
| ~ relation(X2)
| ~ empty(relation_rng(X2)) )
| ~ spl15_209
| ~ spl15_218 ),
inference(resolution,[],[f2534,f2225]) ).
fof(f2225,plain,
( ! [X2,X0,X1] :
( in(sK10(X0,X1,X2),X1)
| sP0(X0,X1,X2)
| ~ relation(X2)
| ~ empty(relation_rng(X2)) )
| ~ spl15_209 ),
inference(avatar_component_clause,[],[f2224]) ).
fof(f11719,plain,
( spl15_512
| ~ spl15_143
| ~ spl15_218 ),
inference(avatar_split_clause,[],[f2573,f2533,f1342,f11717]) ).
fof(f11717,plain,
( spl15_512
<=> ! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(relation_rng(X0))
| ~ empty(X0)
| ~ relation(relation_rng(relation_rng(X0)))
| ~ empty(X1)
| ~ relation(X1)
| sP0(relation_rng(X1),X2,relation_rng(relation_rng(relation_rng(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_512])]) ).
fof(f1342,plain,
( spl15_143
<=> ! [X2,X0,X1] :
( ~ relation(X0)
| ~ empty(X0)
| in(unordered_pair(singleton(sK9(relation_rng(X0),X1,X2)),unordered_pair(sK10(relation_rng(X0),X1,X2),sK9(relation_rng(X0),X1,X2))),X2)
| sP0(relation_rng(X0),X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_143])]) ).
fof(f2573,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(relation_rng(X0))
| ~ empty(X0)
| ~ relation(relation_rng(relation_rng(X0)))
| ~ empty(X1)
| ~ relation(X1)
| sP0(relation_rng(X1),X2,relation_rng(relation_rng(relation_rng(X0)))) )
| ~ spl15_143
| ~ spl15_218 ),
inference(resolution,[],[f2534,f1343]) ).
fof(f1343,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(singleton(sK9(relation_rng(X0),X1,X2)),unordered_pair(sK10(relation_rng(X0),X1,X2),sK9(relation_rng(X0),X1,X2))),X2)
| ~ empty(X0)
| ~ relation(X0)
| sP0(relation_rng(X0),X1,X2) )
| ~ spl15_143 ),
inference(avatar_component_clause,[],[f1342]) ).
fof(f11715,plain,
( spl15_511
| ~ spl15_144
| ~ spl15_218 ),
inference(avatar_split_clause,[],[f2567,f2533,f1346,f11713]) ).
fof(f11713,plain,
( spl15_511
<=> ! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(relation_rng(X0))
| ~ empty(X0)
| ~ relation(relation_rng(relation_rng(X0)))
| ~ empty(X1)
| ~ relation(X1)
| sP0(relation_rng(relation_rng(relation_rng(X0))),X2,relation_rng(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_511])]) ).
fof(f1346,plain,
( spl15_144
<=> ! [X2,X0,X1] :
( ~ relation(X0)
| ~ empty(X0)
| in(unordered_pair(singleton(sK9(X1,X2,relation_rng(X0))),unordered_pair(sK10(X1,X2,relation_rng(X0)),sK9(X1,X2,relation_rng(X0)))),X1)
| sP0(X1,X2,relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_144])]) ).
fof(f2567,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(relation_rng(X0))
| ~ empty(X0)
| ~ relation(relation_rng(relation_rng(X0)))
| ~ empty(X1)
| ~ relation(X1)
| sP0(relation_rng(relation_rng(relation_rng(X0))),X2,relation_rng(X1)) )
| ~ spl15_144
| ~ spl15_218 ),
inference(resolution,[],[f2534,f1347]) ).
fof(f1347,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(singleton(sK9(X1,X2,relation_rng(X0))),unordered_pair(sK10(X1,X2,relation_rng(X0)),sK9(X1,X2,relation_rng(X0)))),X1)
| ~ empty(X0)
| ~ relation(X0)
| sP0(X1,X2,relation_rng(X0)) )
| ~ spl15_144 ),
inference(avatar_component_clause,[],[f1346]) ).
fof(f11711,plain,
( spl15_510
| ~ spl15_38
| ~ spl15_218 ),
inference(avatar_split_clause,[],[f2560,f2533,f347,f11709]) ).
fof(f11709,plain,
( spl15_510
<=> ! [X0,X1] :
( ~ relation(X0)
| ~ relation(relation_rng(X0))
| ~ empty(X0)
| ~ relation(relation_rng(relation_rng(X0)))
| ~ in(X1,relation_rng(relation_rng(relation_rng(relation_rng(X0)))))
| ~ relation(relation_rng(relation_rng(relation_rng(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_510])]) ).
fof(f347,plain,
( spl15_38
<=> ! [X5,X0] :
( in(unordered_pair(singleton(sK7(X0,X5)),unordered_pair(X5,sK7(X0,X5))),X0)
| ~ in(X5,relation_rng(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_38])]) ).
fof(f2560,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ relation(relation_rng(X0))
| ~ empty(X0)
| ~ relation(relation_rng(relation_rng(X0)))
| ~ in(X1,relation_rng(relation_rng(relation_rng(relation_rng(X0)))))
| ~ relation(relation_rng(relation_rng(relation_rng(X0)))) )
| ~ spl15_38
| ~ spl15_218 ),
inference(resolution,[],[f2534,f348]) ).
fof(f348,plain,
( ! [X0,X5] :
( in(unordered_pair(singleton(sK7(X0,X5)),unordered_pair(X5,sK7(X0,X5))),X0)
| ~ in(X5,relation_rng(X0))
| ~ relation(X0) )
| ~ spl15_38 ),
inference(avatar_component_clause,[],[f347]) ).
fof(f11706,plain,
( ~ spl15_408
| ~ spl15_19
| ~ spl15_29
| spl15_484 ),
inference(avatar_split_clause,[],[f11031,f10505,f300,f237,f7704]) ).
fof(f300,plain,
( spl15_29
<=> ! [X2,X0,X1] :
( sP1(X2,X0,X1)
| ~ relation(X2)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_29])]) ).
fof(f10505,plain,
( spl15_484
<=> sP1(sK12,sK12,relation_rng_restriction(sK3,sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_484])]) ).
fof(f11031,plain,
( ~ relation(sK12)
| ~ relation(relation_rng_restriction(sK3,sK4))
| ~ spl15_29
| spl15_484 ),
inference(resolution,[],[f10507,f301]) ).
fof(f301,plain,
( ! [X2,X0,X1] :
( sP1(X2,X0,X1)
| ~ relation(X2)
| ~ relation(X1) )
| ~ spl15_29 ),
inference(avatar_component_clause,[],[f300]) ).
fof(f10507,plain,
( ~ sP1(sK12,sK12,relation_rng_restriction(sK3,sK4))
| spl15_484 ),
inference(avatar_component_clause,[],[f10505]) ).
fof(f10619,plain,
( spl15_509
| ~ spl15_21
| ~ spl15_318 ),
inference(avatar_split_clause,[],[f5130,f5050,f246,f10617]) ).
fof(f10617,plain,
( spl15_509
<=> ! [X0,X3,X2,X1] :
( sP0(X0,X1,relation_rng_restriction(X2,X3))
| in(sK10(X0,X1,relation_rng_restriction(X2,X3)),X1)
| ~ relation(relation_rng_restriction(X2,X3))
| ~ relation(X3)
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_509])]) ).
fof(f246,plain,
( spl15_21
<=> ! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_21])]) ).
fof(f5050,plain,
( spl15_318
<=> ! [X0,X3,X2,X1] :
( in(unordered_pair(singleton(sK9(X0,X1,relation_rng_restriction(X2,X3))),unordered_pair(sK10(X0,X1,relation_rng_restriction(X2,X3)),sK9(X0,X1,relation_rng_restriction(X2,X3)))),X3)
| sP0(X0,X1,relation_rng_restriction(X2,X3))
| in(sK10(X0,X1,relation_rng_restriction(X2,X3)),X1)
| ~ relation(relation_rng_restriction(X2,X3))
| ~ relation(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_318])]) ).
fof(f5130,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,X1,relation_rng_restriction(X2,X3))
| in(sK10(X0,X1,relation_rng_restriction(X2,X3)),X1)
| ~ relation(relation_rng_restriction(X2,X3))
| ~ relation(X3)
| ~ empty(X3) )
| ~ spl15_21
| ~ spl15_318 ),
inference(resolution,[],[f5051,f247]) ).
fof(f247,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) )
| ~ spl15_21 ),
inference(avatar_component_clause,[],[f246]) ).
fof(f5051,plain,
( ! [X2,X3,X0,X1] :
( in(unordered_pair(singleton(sK9(X0,X1,relation_rng_restriction(X2,X3))),unordered_pair(sK10(X0,X1,relation_rng_restriction(X2,X3)),sK9(X0,X1,relation_rng_restriction(X2,X3)))),X3)
| sP0(X0,X1,relation_rng_restriction(X2,X3))
| in(sK10(X0,X1,relation_rng_restriction(X2,X3)),X1)
| ~ relation(relation_rng_restriction(X2,X3))
| ~ relation(X3) )
| ~ spl15_318 ),
inference(avatar_component_clause,[],[f5050]) ).
fof(f10615,plain,
( spl15_508
| ~ spl15_61
| ~ spl15_315 ),
inference(avatar_split_clause,[],[f5073,f5038,f511,f10613]) ).
fof(f10613,plain,
( spl15_508
<=> ! [X2,X0,X1] :
( sP0(relation_rng_restriction(X0,relation_rng(X1)),X2,relation_rng_restriction(X0,relation_rng(X1)))
| ~ relation(relation_rng_restriction(X0,relation_rng(X1)))
| ~ relation(relation_rng(X1))
| ~ relation(X1)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_508])]) ).
fof(f5038,plain,
( spl15_315
<=> ! [X2,X0,X1] :
( in(unordered_pair(singleton(sK9(relation_rng_restriction(X0,X1),X2,relation_rng_restriction(X0,X1))),unordered_pair(sK10(relation_rng_restriction(X0,X1),X2,relation_rng_restriction(X0,X1)),sK9(relation_rng_restriction(X0,X1),X2,relation_rng_restriction(X0,X1)))),X1)
| sP0(relation_rng_restriction(X0,X1),X2,relation_rng_restriction(X0,X1))
| ~ relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_315])]) ).
fof(f5073,plain,
( ! [X2,X0,X1] :
( sP0(relation_rng_restriction(X0,relation_rng(X1)),X2,relation_rng_restriction(X0,relation_rng(X1)))
| ~ relation(relation_rng_restriction(X0,relation_rng(X1)))
| ~ relation(relation_rng(X1))
| ~ relation(X1)
| ~ empty(X1) )
| ~ spl15_61
| ~ spl15_315 ),
inference(resolution,[],[f5039,f512]) ).
fof(f5039,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(singleton(sK9(relation_rng_restriction(X0,X1),X2,relation_rng_restriction(X0,X1))),unordered_pair(sK10(relation_rng_restriction(X0,X1),X2,relation_rng_restriction(X0,X1)),sK9(relation_rng_restriction(X0,X1),X2,relation_rng_restriction(X0,X1)))),X1)
| sP0(relation_rng_restriction(X0,X1),X2,relation_rng_restriction(X0,X1))
| ~ relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) )
| ~ spl15_315 ),
inference(avatar_component_clause,[],[f5038]) ).
fof(f10611,plain,
( spl15_507
| ~ spl15_101
| ~ spl15_300 ),
inference(avatar_split_clause,[],[f4639,f4615,f868,f10609]) ).
fof(f10609,plain,
( spl15_507
<=> ! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(relation_rng(X0))
| ~ empty(X0)
| sP0(relation_rng(relation_rng(X0)),X1,relation_rng(relation_rng(X2)))
| ~ empty(X2)
| ~ relation(X2)
| ~ relation(relation_rng(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_507])]) ).
fof(f4615,plain,
( spl15_300
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| ~ relation(X0)
| ~ relation(relation_rng(X0))
| in(unordered_pair(singleton(sK9(relation_rng(relation_rng(X0)),X1,X2)),unordered_pair(sK10(relation_rng(relation_rng(X0)),X1,X2),sK9(relation_rng(relation_rng(X0)),X1,X2))),X2)
| sP0(relation_rng(relation_rng(X0)),X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_300])]) ).
fof(f4639,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(relation_rng(X0))
| ~ empty(X0)
| sP0(relation_rng(relation_rng(X0)),X1,relation_rng(relation_rng(X2)))
| ~ empty(X2)
| ~ relation(X2)
| ~ relation(relation_rng(X2)) )
| ~ spl15_101
| ~ spl15_300 ),
inference(resolution,[],[f4616,f869]) ).
fof(f4616,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(singleton(sK9(relation_rng(relation_rng(X0)),X1,X2)),unordered_pair(sK10(relation_rng(relation_rng(X0)),X1,X2),sK9(relation_rng(relation_rng(X0)),X1,X2))),X2)
| ~ relation(X0)
| ~ relation(relation_rng(X0))
| ~ empty(X0)
| sP0(relation_rng(relation_rng(X0)),X1,X2) )
| ~ spl15_300 ),
inference(avatar_component_clause,[],[f4615]) ).
fof(f10607,plain,
( spl15_506
| ~ spl15_61
| ~ spl15_297 ),
inference(avatar_split_clause,[],[f4578,f4449,f511,f10605]) ).
fof(f10605,plain,
( spl15_506
<=> ! [X0,X3,X2,X1] :
( ~ sP0(X0,relation_rng(X0),relation_rng(X1))
| sP0(X2,X3,X0)
| in(sK10(X2,X3,X0),X3)
| ~ relation(X0)
| ~ relation(X1)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_506])]) ).
fof(f4449,plain,
( spl15_297
<=> ! [X0,X3,X2,X1] :
( in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X3)
| ~ sP0(X2,relation_rng(X2),X3)
| sP0(X0,X1,X2)
| in(sK10(X0,X1,X2),X1)
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_297])]) ).
fof(f4578,plain,
( ! [X2,X3,X0,X1] :
( ~ sP0(X0,relation_rng(X0),relation_rng(X1))
| sP0(X2,X3,X0)
| in(sK10(X2,X3,X0),X3)
| ~ relation(X0)
| ~ relation(X1)
| ~ empty(X1) )
| ~ spl15_61
| ~ spl15_297 ),
inference(resolution,[],[f4450,f512]) ).
fof(f4450,plain,
( ! [X2,X3,X0,X1] :
( in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X3)
| ~ sP0(X2,relation_rng(X2),X3)
| sP0(X0,X1,X2)
| in(sK10(X0,X1,X2),X1)
| ~ relation(X2) )
| ~ spl15_297 ),
inference(avatar_component_clause,[],[f4449]) ).
fof(f10603,plain,
( spl15_505
| ~ spl15_101
| ~ spl15_288 ),
inference(avatar_split_clause,[],[f4304,f4142,f868,f10601]) ).
fof(f10601,plain,
( spl15_505
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP0(X0,X1,X2)
| ~ sP0(X2,relation_rng(X2),relation_rng(relation_rng(X3)))
| ~ relation(X2)
| ~ empty(X3)
| ~ relation(X3)
| ~ relation(relation_rng(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_505])]) ).
fof(f4304,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP0(X0,X1,X2)
| ~ sP0(X2,relation_rng(X2),relation_rng(relation_rng(X3)))
| ~ relation(X2)
| ~ empty(X3)
| ~ relation(X3)
| ~ relation(relation_rng(X3)) )
| ~ spl15_101
| ~ spl15_288 ),
inference(resolution,[],[f4143,f869]) ).
fof(f10599,plain,
( ~ spl15_5
| ~ spl15_93
| spl15_483 ),
inference(avatar_split_clause,[],[f10556,f10501,f789,f171]) ).
fof(f171,plain,
( spl15_5
<=> empty(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_5])]) ).
fof(f789,plain,
( spl15_93
<=> ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ empty(X2)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_93])]) ).
fof(f10501,plain,
( spl15_483
<=> sP0(relation_rng_restriction(sK3,sK4),sK12,sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_483])]) ).
fof(f10556,plain,
( ~ empty(sK12)
| ~ spl15_93
| spl15_483 ),
inference(duplicate_literal_removal,[],[f10553]) ).
fof(f10553,plain,
( ~ empty(sK12)
| ~ empty(sK12)
| ~ spl15_93
| spl15_483 ),
inference(resolution,[],[f10502,f790]) ).
fof(f790,plain,
( ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ empty(X2)
| ~ empty(X1) )
| ~ spl15_93 ),
inference(avatar_component_clause,[],[f789]) ).
fof(f10502,plain,
( ~ sP0(relation_rng_restriction(sK3,sK4),sK12,sK12)
| spl15_483 ),
inference(avatar_component_clause,[],[f10501]) ).
fof(f10598,plain,
( spl15_504
| ~ spl15_67
| ~ spl15_288 ),
inference(avatar_split_clause,[],[f4284,f4142,f562,f10596]) ).
fof(f10596,plain,
( spl15_504
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP0(X0,X1,X2)
| ~ sP0(X2,relation_rng(X2),X3)
| ~ relation(X2)
| in(sK10(X0,X1,X2),relation_rng(X3))
| ~ relation(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_504])]) ).
fof(f4284,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP0(X0,X1,X2)
| ~ sP0(X2,relation_rng(X2),X3)
| ~ relation(X2)
| in(sK10(X0,X1,X2),relation_rng(X3))
| ~ relation(X3) )
| ~ spl15_67
| ~ spl15_288 ),
inference(resolution,[],[f4143,f563]) ).
fof(f10594,plain,
( spl15_503
| ~ spl15_101
| ~ spl15_287 ),
inference(avatar_split_clause,[],[f4264,f4138,f868,f10592]) ).
fof(f10592,plain,
( spl15_503
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP0(X1,X2,X0)
| ~ sP0(X1,relation_rng(X1),relation_rng(relation_rng(X3)))
| ~ relation(X1)
| ~ empty(X3)
| ~ relation(X3)
| ~ relation(relation_rng(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_503])]) ).
fof(f4264,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP0(X1,X2,X0)
| ~ sP0(X1,relation_rng(X1),relation_rng(relation_rng(X3)))
| ~ relation(X1)
| ~ empty(X3)
| ~ relation(X3)
| ~ relation(relation_rng(X3)) )
| ~ spl15_101
| ~ spl15_287 ),
inference(resolution,[],[f4139,f869]) ).
fof(f10590,plain,
( spl15_502
| ~ spl15_67
| ~ spl15_287 ),
inference(avatar_split_clause,[],[f4244,f4138,f562,f10588]) ).
fof(f10588,plain,
( spl15_502
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP0(X1,X2,X0)
| ~ sP0(X1,relation_rng(X1),X3)
| ~ relation(X1)
| in(sK10(X1,X2,X0),relation_rng(X3))
| ~ relation(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_502])]) ).
fof(f4244,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP0(X1,X2,X0)
| ~ sP0(X1,relation_rng(X1),X3)
| ~ relation(X1)
| in(sK10(X1,X2,X0),relation_rng(X3))
| ~ relation(X3) )
| ~ spl15_67
| ~ spl15_287 ),
inference(resolution,[],[f4139,f563]) ).
fof(f10586,plain,
( spl15_501
| ~ spl15_21
| ~ spl15_276 ),
inference(avatar_split_clause,[],[f3991,f3969,f246,f10584]) ).
fof(f10584,plain,
( spl15_501
<=> ! [X0,X3,X2,X1] :
( in(sK10(X0,X1,relation_rng_restriction(X2,X3)),X1)
| sP0(X0,X1,relation_rng_restriction(X2,X3))
| ~ relation(relation_rng_restriction(X2,X3))
| ~ relation(X3)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_501])]) ).
fof(f3969,plain,
( spl15_276
<=> ! [X0,X3,X2,X1] :
( in(sK10(X0,X1,relation_rng_restriction(X2,X3)),X2)
| sP0(X0,X1,relation_rng_restriction(X2,X3))
| in(sK10(X0,X1,relation_rng_restriction(X2,X3)),X1)
| ~ relation(relation_rng_restriction(X2,X3))
| ~ relation(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_276])]) ).
fof(f3991,plain,
( ! [X2,X3,X0,X1] :
( in(sK10(X0,X1,relation_rng_restriction(X2,X3)),X1)
| sP0(X0,X1,relation_rng_restriction(X2,X3))
| ~ relation(relation_rng_restriction(X2,X3))
| ~ relation(X3)
| ~ empty(X2) )
| ~ spl15_21
| ~ spl15_276 ),
inference(resolution,[],[f3970,f247]) ).
fof(f3970,plain,
( ! [X2,X3,X0,X1] :
( in(sK10(X0,X1,relation_rng_restriction(X2,X3)),X2)
| in(sK10(X0,X1,relation_rng_restriction(X2,X3)),X1)
| sP0(X0,X1,relation_rng_restriction(X2,X3))
| ~ relation(relation_rng_restriction(X2,X3))
| ~ relation(X3) )
| ~ spl15_276 ),
inference(avatar_component_clause,[],[f3969]) ).
fof(f10582,plain,
( spl15_500
| ~ spl15_275 ),
inference(avatar_split_clause,[],[f3947,f3851,f10580]) ).
fof(f10580,plain,
( spl15_500
<=> ! [X0,X1] :
( in(sK5(relation_rng_restriction(X0,X1),relation_rng(X1)),relation_rng(X1))
| relation_rng(X1) = relation_rng(relation_rng_restriction(X0,X1))
| ~ relation(X1)
| ~ relation(relation_rng_restriction(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_500])]) ).
fof(f3851,plain,
( spl15_275
<=> ! [X2,X0,X1] :
( ~ relation(relation_rng_restriction(X0,X1))
| in(sK5(relation_rng_restriction(X0,X1),X2),X2)
| relation_rng(relation_rng_restriction(X0,X1)) = X2
| ~ relation(X1)
| in(sK5(relation_rng_restriction(X0,X1),X2),relation_rng(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_275])]) ).
fof(f3947,plain,
( ! [X0,X1] :
( in(sK5(relation_rng_restriction(X0,X1),relation_rng(X1)),relation_rng(X1))
| relation_rng(X1) = relation_rng(relation_rng_restriction(X0,X1))
| ~ relation(X1)
| ~ relation(relation_rng_restriction(X0,X1)) )
| ~ spl15_275 ),
inference(factoring,[],[f3852]) ).
fof(f3852,plain,
( ! [X2,X0,X1] :
( in(sK5(relation_rng_restriction(X0,X1),X2),relation_rng(X1))
| in(sK5(relation_rng_restriction(X0,X1),X2),X2)
| relation_rng(relation_rng_restriction(X0,X1)) = X2
| ~ relation(X1)
| ~ relation(relation_rng_restriction(X0,X1)) )
| ~ spl15_275 ),
inference(avatar_component_clause,[],[f3851]) ).
fof(f10578,plain,
( spl15_499
| ~ spl15_21
| ~ spl15_275 ),
inference(avatar_split_clause,[],[f3941,f3851,f246,f10576]) ).
fof(f10576,plain,
( spl15_499
<=> ! [X2,X0,X1] :
( in(sK5(relation_rng_restriction(X0,X1),X2),relation_rng(X1))
| relation_rng(relation_rng_restriction(X0,X1)) = X2
| ~ relation(X1)
| ~ relation(relation_rng_restriction(X0,X1))
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_499])]) ).
fof(f3941,plain,
( ! [X2,X0,X1] :
( in(sK5(relation_rng_restriction(X0,X1),X2),relation_rng(X1))
| relation_rng(relation_rng_restriction(X0,X1)) = X2
| ~ relation(X1)
| ~ relation(relation_rng_restriction(X0,X1))
| ~ empty(X2) )
| ~ spl15_21
| ~ spl15_275 ),
inference(resolution,[],[f3852,f247]) ).
fof(f10574,plain,
( spl15_498
| ~ spl15_21
| ~ spl15_275 ),
inference(avatar_split_clause,[],[f3936,f3851,f246,f10572]) ).
fof(f10572,plain,
( spl15_498
<=> ! [X2,X0,X1] :
( in(sK5(relation_rng_restriction(X0,X1),X2),X2)
| relation_rng(relation_rng_restriction(X0,X1)) = X2
| ~ relation(X1)
| ~ relation(relation_rng_restriction(X0,X1))
| ~ empty(relation_rng(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_498])]) ).
fof(f3936,plain,
( ! [X2,X0,X1] :
( in(sK5(relation_rng_restriction(X0,X1),X2),X2)
| relation_rng(relation_rng_restriction(X0,X1)) = X2
| ~ relation(X1)
| ~ relation(relation_rng_restriction(X0,X1))
| ~ empty(relation_rng(X1)) )
| ~ spl15_21
| ~ spl15_275 ),
inference(resolution,[],[f3852,f247]) ).
fof(f10570,plain,
( spl15_497
| ~ spl15_68
| ~ spl15_272 ),
inference(avatar_split_clause,[],[f3856,f3839,f573,f10568]) ).
fof(f10568,plain,
( spl15_497
<=> ! [X4,X0,X3,X2,X1] :
( ~ in(X0,X1)
| ~ in(X0,relation_rng(X2))
| ~ relation(X2)
| ~ relation(relation_rng_restriction(X1,X2))
| in(X0,X3)
| ~ sP0(X4,X3,relation_rng_restriction(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_497])]) ).
fof(f3839,plain,
( spl15_272
<=> ! [X2,X0,X1] :
( ~ in(X0,X1)
| in(unordered_pair(singleton(sK7(X2,X0)),unordered_pair(X0,sK7(X2,X0))),relation_rng_restriction(X1,X2))
| ~ in(X0,relation_rng(X2))
| ~ relation(X2)
| ~ relation(relation_rng_restriction(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_272])]) ).
fof(f3856,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ in(X0,X1)
| ~ in(X0,relation_rng(X2))
| ~ relation(X2)
| ~ relation(relation_rng_restriction(X1,X2))
| in(X0,X3)
| ~ sP0(X4,X3,relation_rng_restriction(X1,X2)) )
| ~ spl15_68
| ~ spl15_272 ),
inference(resolution,[],[f3840,f574]) ).
fof(f3840,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(singleton(sK7(X2,X0)),unordered_pair(X0,sK7(X2,X0))),relation_rng_restriction(X1,X2))
| ~ in(X0,X1)
| ~ in(X0,relation_rng(X2))
| ~ relation(X2)
| ~ relation(relation_rng_restriction(X1,X2)) )
| ~ spl15_272 ),
inference(avatar_component_clause,[],[f3839]) ).
fof(f10566,plain,
( spl15_496
| ~ spl15_23
| ~ spl15_252 ),
inference(avatar_split_clause,[],[f3326,f3235,f263,f10564]) ).
fof(f10564,plain,
( spl15_496
<=> ! [X2,X0,X1] :
( in(sK10(X0,X1,X2),relation_rng(X2))
| sP0(X0,X1,X2)
| ~ relation(X0)
| ~ relation(X2)
| ~ in(relation_rng(X0),sK10(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_496])]) ).
fof(f3235,plain,
( spl15_252
<=> ! [X2,X0,X1] :
( ~ relation(X0)
| in(sK10(X0,X1,X2),relation_rng(X0))
| sP0(X0,X1,X2)
| in(sK10(X0,X1,X2),relation_rng(X2))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_252])]) ).
fof(f3326,plain,
( ! [X2,X0,X1] :
( in(sK10(X0,X1,X2),relation_rng(X2))
| sP0(X0,X1,X2)
| ~ relation(X0)
| ~ relation(X2)
| ~ in(relation_rng(X0),sK10(X0,X1,X2)) )
| ~ spl15_23
| ~ spl15_252 ),
inference(resolution,[],[f3236,f264]) ).
fof(f3236,plain,
( ! [X2,X0,X1] :
( in(sK10(X0,X1,X2),relation_rng(X2))
| in(sK10(X0,X1,X2),relation_rng(X0))
| sP0(X0,X1,X2)
| ~ relation(X0)
| ~ relation(X2) )
| ~ spl15_252 ),
inference(avatar_component_clause,[],[f3235]) ).
fof(f10562,plain,
( spl15_495
| ~ spl15_24
| ~ spl15_252 ),
inference(avatar_split_clause,[],[f3325,f3235,f267,f10560]) ).
fof(f10560,plain,
( spl15_495
<=> ! [X2,X0,X1] :
( in(sK10(X0,X1,X2),relation_rng(X2))
| sP0(X0,X1,X2)
| ~ relation(X0)
| ~ relation(X2)
| element(sK10(X0,X1,X2),relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_495])]) ).
fof(f3325,plain,
( ! [X2,X0,X1] :
( in(sK10(X0,X1,X2),relation_rng(X2))
| sP0(X0,X1,X2)
| ~ relation(X0)
| ~ relation(X2)
| element(sK10(X0,X1,X2),relation_rng(X0)) )
| ~ spl15_24
| ~ spl15_252 ),
inference(resolution,[],[f3236,f268]) ).
fof(f10548,plain,
( spl15_494
| ~ spl15_23
| ~ spl15_252 ),
inference(avatar_split_clause,[],[f3310,f3235,f263,f10546]) ).
fof(f10546,plain,
( spl15_494
<=> ! [X2,X0,X1] :
( in(sK10(X0,X1,X2),relation_rng(X0))
| sP0(X0,X1,X2)
| ~ relation(X0)
| ~ relation(X2)
| ~ in(relation_rng(X2),sK10(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_494])]) ).
fof(f3310,plain,
( ! [X2,X0,X1] :
( in(sK10(X0,X1,X2),relation_rng(X0))
| sP0(X0,X1,X2)
| ~ relation(X0)
| ~ relation(X2)
| ~ in(relation_rng(X2),sK10(X0,X1,X2)) )
| ~ spl15_23
| ~ spl15_252 ),
inference(resolution,[],[f3236,f264]) ).
fof(f10544,plain,
( spl15_493
| ~ spl15_24
| ~ spl15_252 ),
inference(avatar_split_clause,[],[f3309,f3235,f267,f10542]) ).
fof(f10542,plain,
( spl15_493
<=> ! [X2,X0,X1] :
( in(sK10(X0,X1,X2),relation_rng(X0))
| sP0(X0,X1,X2)
| ~ relation(X0)
| ~ relation(X2)
| element(sK10(X0,X1,X2),relation_rng(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_493])]) ).
fof(f3309,plain,
( ! [X2,X0,X1] :
( in(sK10(X0,X1,X2),relation_rng(X0))
| sP0(X0,X1,X2)
| ~ relation(X0)
| ~ relation(X2)
| element(sK10(X0,X1,X2),relation_rng(X2)) )
| ~ spl15_24
| ~ spl15_252 ),
inference(resolution,[],[f3236,f268]) ).
fof(f10540,plain,
( spl15_492
| ~ spl15_23
| ~ spl15_251 ),
inference(avatar_split_clause,[],[f3277,f3231,f263,f10538]) ).
fof(f10538,plain,
( spl15_492
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP0(X0,X1,relation_rng_restriction(X2,X3))
| ~ relation(relation_rng_restriction(X2,X3))
| ~ relation(X3)
| ~ in(X2,sK10(X0,X1,relation_rng_restriction(X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_492])]) ).
fof(f3231,plain,
( spl15_251
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| in(sK10(X0,X1,relation_rng_restriction(X2,X3)),X2)
| sP0(X0,X1,relation_rng_restriction(X2,X3))
| ~ relation(relation_rng_restriction(X2,X3))
| ~ relation(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_251])]) ).
fof(f3277,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP0(X0,X1,relation_rng_restriction(X2,X3))
| ~ relation(relation_rng_restriction(X2,X3))
| ~ relation(X3)
| ~ in(X2,sK10(X0,X1,relation_rng_restriction(X2,X3))) )
| ~ spl15_23
| ~ spl15_251 ),
inference(resolution,[],[f3232,f264]) ).
fof(f3232,plain,
( ! [X2,X3,X0,X1] :
( in(sK10(X0,X1,relation_rng_restriction(X2,X3)),X2)
| ~ empty(X0)
| sP0(X0,X1,relation_rng_restriction(X2,X3))
| ~ relation(relation_rng_restriction(X2,X3))
| ~ relation(X3) )
| ~ spl15_251 ),
inference(avatar_component_clause,[],[f3231]) ).
fof(f10536,plain,
( spl15_491
| ~ spl15_24
| ~ spl15_251 ),
inference(avatar_split_clause,[],[f3276,f3231,f267,f10534]) ).
fof(f10534,plain,
( spl15_491
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP0(X0,X1,relation_rng_restriction(X2,X3))
| ~ relation(relation_rng_restriction(X2,X3))
| ~ relation(X3)
| element(sK10(X0,X1,relation_rng_restriction(X2,X3)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_491])]) ).
fof(f3276,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP0(X0,X1,relation_rng_restriction(X2,X3))
| ~ relation(relation_rng_restriction(X2,X3))
| ~ relation(X3)
| element(sK10(X0,X1,relation_rng_restriction(X2,X3)),X2) )
| ~ spl15_24
| ~ spl15_251 ),
inference(resolution,[],[f3232,f268]) ).
fof(f10532,plain,
( spl15_490
| ~ spl15_23
| ~ spl15_250 ),
inference(avatar_split_clause,[],[f3248,f3227,f263,f10530]) ).
fof(f10530,plain,
( spl15_490
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP0(relation_rng_restriction(X1,X2),X3,X0)
| ~ relation(relation_rng_restriction(X1,X2))
| ~ relation(X2)
| ~ in(X1,sK10(relation_rng_restriction(X1,X2),X3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_490])]) ).
fof(f3227,plain,
( spl15_250
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| in(sK10(relation_rng_restriction(X1,X2),X3,X0),X1)
| sP0(relation_rng_restriction(X1,X2),X3,X0)
| ~ relation(relation_rng_restriction(X1,X2))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_250])]) ).
fof(f3248,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP0(relation_rng_restriction(X1,X2),X3,X0)
| ~ relation(relation_rng_restriction(X1,X2))
| ~ relation(X2)
| ~ in(X1,sK10(relation_rng_restriction(X1,X2),X3,X0)) )
| ~ spl15_23
| ~ spl15_250 ),
inference(resolution,[],[f3228,f264]) ).
fof(f3228,plain,
( ! [X2,X3,X0,X1] :
( in(sK10(relation_rng_restriction(X1,X2),X3,X0),X1)
| ~ empty(X0)
| sP0(relation_rng_restriction(X1,X2),X3,X0)
| ~ relation(relation_rng_restriction(X1,X2))
| ~ relation(X2) )
| ~ spl15_250 ),
inference(avatar_component_clause,[],[f3227]) ).
fof(f10528,plain,
( spl15_489
| ~ spl15_24
| ~ spl15_250 ),
inference(avatar_split_clause,[],[f3247,f3227,f267,f10526]) ).
fof(f10526,plain,
( spl15_489
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP0(relation_rng_restriction(X1,X2),X3,X0)
| ~ relation(relation_rng_restriction(X1,X2))
| ~ relation(X2)
| element(sK10(relation_rng_restriction(X1,X2),X3,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_489])]) ).
fof(f3247,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP0(relation_rng_restriction(X1,X2),X3,X0)
| ~ relation(relation_rng_restriction(X1,X2))
| ~ relation(X2)
| element(sK10(relation_rng_restriction(X1,X2),X3,X0),X1) )
| ~ spl15_24
| ~ spl15_250 ),
inference(resolution,[],[f3228,f268]) ).
fof(f10524,plain,
( spl15_488
| ~ spl15_101
| ~ spl15_244 ),
inference(avatar_split_clause,[],[f3095,f3058,f868,f10522]) ).
fof(f10522,plain,
( spl15_488
<=> ! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(relation_rng(X0))
| sP0(X1,relation_rng(relation_rng(X2)),relation_rng(relation_rng(X0)))
| ~ empty(X0)
| ~ empty(X2)
| ~ relation(X2)
| ~ relation(relation_rng(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_488])]) ).
fof(f3058,plain,
( spl15_244
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| ~ relation(X0)
| ~ relation(relation_rng(X0))
| sP0(X1,X2,relation_rng(relation_rng(X0)))
| in(sK10(X1,X2,relation_rng(relation_rng(X0))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_244])]) ).
fof(f3095,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(relation_rng(X0))
| sP0(X1,relation_rng(relation_rng(X2)),relation_rng(relation_rng(X0)))
| ~ empty(X0)
| ~ empty(X2)
| ~ relation(X2)
| ~ relation(relation_rng(X2)) )
| ~ spl15_101
| ~ spl15_244 ),
inference(resolution,[],[f3059,f869]) ).
fof(f3059,plain,
( ! [X2,X0,X1] :
( in(sK10(X1,X2,relation_rng(relation_rng(X0))),X2)
| ~ relation(X0)
| ~ relation(relation_rng(X0))
| sP0(X1,X2,relation_rng(relation_rng(X0)))
| ~ empty(X0) )
| ~ spl15_244 ),
inference(avatar_component_clause,[],[f3058]) ).
fof(f10520,plain,
( spl15_487
| ~ spl15_199
| ~ spl15_210 ),
inference(avatar_split_clause,[],[f2445,f2228,f2164,f10518]) ).
fof(f10518,plain,
( spl15_487
<=> ! [X0,X3,X2,X1] :
( sP0(X0,X1,relation_rng_restriction(X2,X3))
| ~ relation(relation_rng_restriction(X2,X3))
| ~ empty(X1)
| in(sK10(X0,X1,relation_rng_restriction(X2,X3)),X2)
| ~ relation(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_487])]) ).
fof(f2228,plain,
( spl15_210
<=> ! [X2,X0,X1] :
( in(sK10(X0,X1,X2),relation_rng(X2))
| sP0(X0,X1,X2)
| ~ relation(X2)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_210])]) ).
fof(f2445,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,X1,relation_rng_restriction(X2,X3))
| ~ relation(relation_rng_restriction(X2,X3))
| ~ empty(X1)
| in(sK10(X0,X1,relation_rng_restriction(X2,X3)),X2)
| ~ relation(X3) )
| ~ spl15_199
| ~ spl15_210 ),
inference(duplicate_literal_removal,[],[f2440]) ).
fof(f2440,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,X1,relation_rng_restriction(X2,X3))
| ~ relation(relation_rng_restriction(X2,X3))
| ~ empty(X1)
| in(sK10(X0,X1,relation_rng_restriction(X2,X3)),X2)
| ~ relation(relation_rng_restriction(X2,X3))
| ~ relation(X3) )
| ~ spl15_199
| ~ spl15_210 ),
inference(resolution,[],[f2229,f2165]) ).
fof(f2229,plain,
( ! [X2,X0,X1] :
( in(sK10(X0,X1,X2),relation_rng(X2))
| sP0(X0,X1,X2)
| ~ relation(X2)
| ~ empty(X1) )
| ~ spl15_210 ),
inference(avatar_component_clause,[],[f2228]) ).
fof(f10516,plain,
( spl15_486
| ~ spl15_65
| ~ spl15_196 ),
inference(avatar_split_clause,[],[f2291,f2152,f548,f10514]) ).
fof(f10514,plain,
( spl15_486
<=> ! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(relation_rng(X0))
| ~ empty(X0)
| ~ empty(X1)
| relation_rng(relation_rng(X0)) = relation_rng_restriction(X2,X1)
| ~ relation(relation_rng(relation_rng(X0)))
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_486])]) ).
fof(f2152,plain,
( spl15_196
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| ~ relation(X0)
| ~ relation(relation_rng(X0))
| sP0(X1,X2,relation_rng(relation_rng(X0)))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_196])]) ).
fof(f2291,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(relation_rng(X0))
| ~ empty(X0)
| ~ empty(X1)
| relation_rng(relation_rng(X0)) = relation_rng_restriction(X2,X1)
| ~ relation(relation_rng(relation_rng(X0)))
| ~ relation(X1) )
| ~ spl15_65
| ~ spl15_196 ),
inference(resolution,[],[f2153,f549]) ).
fof(f2153,plain,
( ! [X2,X0,X1] :
( sP0(X1,X2,relation_rng(relation_rng(X0)))
| ~ relation(X0)
| ~ relation(relation_rng(X0))
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl15_196 ),
inference(avatar_component_clause,[],[f2152]) ).
fof(f10512,plain,
( spl15_485
| ~ spl15_65
| ~ spl15_194 ),
inference(avatar_split_clause,[],[f2242,f2133,f548,f10510]) ).
fof(f10510,plain,
( spl15_485
<=> ! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(relation_rng(X0))
| ~ empty(X0)
| ~ empty(X1)
| relation_rng_restriction(X2,relation_rng(relation_rng(X0))) = X1
| ~ relation(X1)
| ~ relation(relation_rng(relation_rng(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_485])]) ).
fof(f2133,plain,
( spl15_194
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| ~ relation(X0)
| ~ relation(relation_rng(X0))
| sP0(relation_rng(relation_rng(X0)),X1,X2)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_194])]) ).
fof(f2242,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(relation_rng(X0))
| ~ empty(X0)
| ~ empty(X1)
| relation_rng_restriction(X2,relation_rng(relation_rng(X0))) = X1
| ~ relation(X1)
| ~ relation(relation_rng(relation_rng(X0))) )
| ~ spl15_65
| ~ spl15_194 ),
inference(resolution,[],[f2134,f549]) ).
fof(f2134,plain,
( ! [X2,X0,X1] :
( sP0(relation_rng(relation_rng(X0)),X1,X2)
| ~ relation(X0)
| ~ relation(relation_rng(X0))
| ~ empty(X0)
| ~ empty(X2) )
| ~ spl15_194 ),
inference(avatar_component_clause,[],[f2133]) ).
fof(f10508,plain,
( spl15_483
| ~ spl15_484
| ~ spl15_31
| ~ spl15_450 ),
inference(avatar_split_clause,[],[f9180,f9135,f309,f10505,f10501]) ).
fof(f309,plain,
( spl15_31
<=> ! [X2,X1] :
( sP0(X2,X1,relation_rng_restriction(X1,X2))
| ~ sP1(relation_rng_restriction(X1,X2),X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_31])]) ).
fof(f9135,plain,
( spl15_450
<=> sK12 = relation_rng_restriction(sK12,relation_rng_restriction(sK3,sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_450])]) ).
fof(f9180,plain,
( ~ sP1(sK12,sK12,relation_rng_restriction(sK3,sK4))
| sP0(relation_rng_restriction(sK3,sK4),sK12,sK12)
| ~ spl15_31
| ~ spl15_450 ),
inference(superposition,[],[f310,f9137]) ).
fof(f9137,plain,
( sK12 = relation_rng_restriction(sK12,relation_rng_restriction(sK3,sK4))
| ~ spl15_450 ),
inference(avatar_component_clause,[],[f9135]) ).
fof(f310,plain,
( ! [X2,X1] :
( ~ sP1(relation_rng_restriction(X1,X2),X1,X2)
| sP0(X2,X1,relation_rng_restriction(X1,X2)) )
| ~ spl15_31 ),
inference(avatar_component_clause,[],[f309]) ).
fof(f10047,plain,
( spl15_482
| ~ spl15_61
| ~ spl15_305 ),
inference(avatar_split_clause,[],[f4709,f4675,f511,f10045]) ).
fof(f10045,plain,
( spl15_482
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP0(X0,X1,relation_rng_restriction(X2,relation_rng(X3)))
| ~ relation(relation_rng_restriction(X2,relation_rng(X3)))
| ~ relation(relation_rng(X3))
| ~ relation(X3)
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_482])]) ).
fof(f4709,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP0(X0,X1,relation_rng_restriction(X2,relation_rng(X3)))
| ~ relation(relation_rng_restriction(X2,relation_rng(X3)))
| ~ relation(relation_rng(X3))
| ~ relation(X3)
| ~ empty(X3) )
| ~ spl15_61
| ~ spl15_305 ),
inference(resolution,[],[f4676,f512]) ).
fof(f10043,plain,
( spl15_481
| ~ spl15_61
| ~ spl15_304 ),
inference(avatar_split_clause,[],[f4687,f4671,f511,f10041]) ).
fof(f10041,plain,
( spl15_481
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP0(relation_rng_restriction(X1,relation_rng(X2)),X3,X0)
| ~ relation(relation_rng_restriction(X1,relation_rng(X2)))
| ~ relation(relation_rng(X2))
| ~ relation(X2)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_481])]) ).
fof(f4687,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP0(relation_rng_restriction(X1,relation_rng(X2)),X3,X0)
| ~ relation(relation_rng_restriction(X1,relation_rng(X2)))
| ~ relation(relation_rng(X2))
| ~ relation(X2)
| ~ empty(X2) )
| ~ spl15_61
| ~ spl15_304 ),
inference(resolution,[],[f4672,f512]) ).
fof(f10039,plain,
( spl15_480
| ~ spl15_68
| ~ spl15_278 ),
inference(avatar_split_clause,[],[f4065,f3977,f573,f10037]) ).
fof(f10037,plain,
( spl15_480
<=> ! [X4,X0,X3,X2,X1] :
( ~ sP0(X0,relation_rng(X0),X1)
| sP0(X0,X2,X0)
| ~ relation(X0)
| in(sK10(X0,X2,X0),X3)
| ~ sP0(X4,X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_480])]) ).
fof(f3977,plain,
( spl15_278
<=> ! [X2,X0,X1] :
( in(unordered_pair(singleton(sK9(X0,X1,X0)),unordered_pair(sK10(X0,X1,X0),sK9(X0,X1,X0))),X2)
| ~ sP0(X0,relation_rng(X0),X2)
| sP0(X0,X1,X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_278])]) ).
fof(f4065,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ sP0(X0,relation_rng(X0),X1)
| sP0(X0,X2,X0)
| ~ relation(X0)
| in(sK10(X0,X2,X0),X3)
| ~ sP0(X4,X3,X1) )
| ~ spl15_68
| ~ spl15_278 ),
inference(resolution,[],[f3978,f574]) ).
fof(f3978,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(singleton(sK9(X0,X1,X0)),unordered_pair(sK10(X0,X1,X0),sK9(X0,X1,X0))),X2)
| ~ sP0(X0,relation_rng(X0),X2)
| sP0(X0,X1,X0)
| ~ relation(X0) )
| ~ spl15_278 ),
inference(avatar_component_clause,[],[f3977]) ).
fof(f10035,plain,
( spl15_479
| ~ spl15_21
| ~ spl15_274 ),
inference(avatar_split_clause,[],[f3906,f3847,f246,f10033]) ).
fof(f10033,plain,
( spl15_479
<=> ! [X2,X0,X1] :
( ~ relation(relation_rng_restriction(X0,relation_rng(X1)))
| relation_rng(relation_rng_restriction(X0,relation_rng(X1))) = X2
| ~ relation(relation_rng(X1))
| ~ relation(X1)
| ~ empty(X1)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_479])]) ).
fof(f3847,plain,
( spl15_274
<=> ! [X2,X0,X1] :
( ~ relation(relation_rng_restriction(X0,relation_rng(X1)))
| in(sK5(relation_rng_restriction(X0,relation_rng(X1)),X2),X2)
| relation_rng(relation_rng_restriction(X0,relation_rng(X1))) = X2
| ~ relation(relation_rng(X1))
| ~ relation(X1)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_274])]) ).
fof(f3906,plain,
( ! [X2,X0,X1] :
( ~ relation(relation_rng_restriction(X0,relation_rng(X1)))
| relation_rng(relation_rng_restriction(X0,relation_rng(X1))) = X2
| ~ relation(relation_rng(X1))
| ~ relation(X1)
| ~ empty(X1)
| ~ empty(X2) )
| ~ spl15_21
| ~ spl15_274 ),
inference(resolution,[],[f3848,f247]) ).
fof(f3848,plain,
( ! [X2,X0,X1] :
( in(sK5(relation_rng_restriction(X0,relation_rng(X1)),X2),X2)
| ~ relation(relation_rng_restriction(X0,relation_rng(X1)))
| relation_rng(relation_rng_restriction(X0,relation_rng(X1))) = X2
| ~ relation(relation_rng(X1))
| ~ relation(X1)
| ~ empty(X1) )
| ~ spl15_274 ),
inference(avatar_component_clause,[],[f3847]) ).
fof(f10031,plain,
( spl15_478
| ~ spl15_18
| ~ spl15_465 ),
inference(avatar_split_clause,[],[f9977,f9527,f233,f10029]) ).
fof(f9527,plain,
( spl15_465
<=> ! [X0] :
( sK12 = relation_rng_restriction(relation_rng(X0),relation_rng_restriction(sK3,sK4))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_465])]) ).
fof(f9977,plain,
( ! [X0] :
( sK12 = relation_rng_restriction(relation_rng(relation_rng(X0)),relation_rng_restriction(sK3,sK4))
| ~ empty(X0) )
| ~ spl15_18
| ~ spl15_465 ),
inference(resolution,[],[f9528,f234]) ).
fof(f9528,plain,
( ! [X0] :
( ~ empty(X0)
| sK12 = relation_rng_restriction(relation_rng(X0),relation_rng_restriction(sK3,sK4)) )
| ~ spl15_465 ),
inference(avatar_component_clause,[],[f9527]) ).
fof(f10027,plain,
( spl15_477
| ~ spl15_61
| ~ spl15_258 ),
inference(avatar_split_clause,[],[f3492,f3446,f511,f10025]) ).
fof(f10025,plain,
( spl15_477
<=> ! [X2,X0,X1] :
( sP0(relation_rng_restriction(relation_rng(X0),X1),X2,relation_rng_restriction(relation_rng(X0),X1))
| ~ relation(relation_rng_restriction(relation_rng(X0),X1))
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_477])]) ).
fof(f3492,plain,
( ! [X2,X0,X1] :
( sP0(relation_rng_restriction(relation_rng(X0),X1),X2,relation_rng_restriction(relation_rng(X0),X1))
| ~ relation(relation_rng_restriction(relation_rng(X0),X1))
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(X0) )
| ~ spl15_61
| ~ spl15_258 ),
inference(resolution,[],[f3447,f512]) ).
fof(f10023,plain,
( spl15_476
| ~ spl15_23
| ~ spl15_249 ),
inference(avatar_split_clause,[],[f3214,f3079,f263,f10021]) ).
fof(f10021,plain,
( spl15_476
<=> ! [X2,X0,X1] :
( ~ relation(relation_rng_restriction(X0,X1))
| relation_rng(relation_rng_restriction(X0,X1)) = X2
| ~ relation(X1)
| ~ empty(X1)
| ~ in(X2,sK5(relation_rng_restriction(X0,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_476])]) ).
fof(f3214,plain,
( ! [X2,X0,X1] :
( ~ relation(relation_rng_restriction(X0,X1))
| relation_rng(relation_rng_restriction(X0,X1)) = X2
| ~ relation(X1)
| ~ empty(X1)
| ~ in(X2,sK5(relation_rng_restriction(X0,X1),X2)) )
| ~ spl15_23
| ~ spl15_249 ),
inference(resolution,[],[f3080,f264]) ).
fof(f10019,plain,
( spl15_475
| ~ spl15_24
| ~ spl15_249 ),
inference(avatar_split_clause,[],[f3213,f3079,f267,f10017]) ).
fof(f10017,plain,
( spl15_475
<=> ! [X2,X0,X1] :
( ~ relation(relation_rng_restriction(X0,X1))
| relation_rng(relation_rng_restriction(X0,X1)) = X2
| ~ relation(X1)
| ~ empty(X1)
| element(sK5(relation_rng_restriction(X0,X1),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_475])]) ).
fof(f3213,plain,
( ! [X2,X0,X1] :
( ~ relation(relation_rng_restriction(X0,X1))
| relation_rng(relation_rng_restriction(X0,X1)) = X2
| ~ relation(X1)
| ~ empty(X1)
| element(sK5(relation_rng_restriction(X0,X1),X2),X2) )
| ~ spl15_24
| ~ spl15_249 ),
inference(resolution,[],[f3080,f268]) ).
fof(f10015,plain,
( spl15_474
| ~ spl15_23
| ~ spl15_247 ),
inference(avatar_split_clause,[],[f3132,f3071,f263,f10013]) ).
fof(f10013,plain,
( spl15_474
<=> ! [X2,X0,X1] :
( ~ relation(relation_rng_restriction(X0,X1))
| relation_rng(relation_rng_restriction(X0,X1)) = X2
| ~ relation(X1)
| ~ empty(X0)
| ~ in(X2,sK5(relation_rng_restriction(X0,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_474])]) ).
fof(f3132,plain,
( ! [X2,X0,X1] :
( ~ relation(relation_rng_restriction(X0,X1))
| relation_rng(relation_rng_restriction(X0,X1)) = X2
| ~ relation(X1)
| ~ empty(X0)
| ~ in(X2,sK5(relation_rng_restriction(X0,X1),X2)) )
| ~ spl15_23
| ~ spl15_247 ),
inference(resolution,[],[f3072,f264]) ).
fof(f10011,plain,
( spl15_473
| ~ spl15_24
| ~ spl15_247 ),
inference(avatar_split_clause,[],[f3131,f3071,f267,f10009]) ).
fof(f10009,plain,
( spl15_473
<=> ! [X2,X0,X1] :
( ~ relation(relation_rng_restriction(X0,X1))
| relation_rng(relation_rng_restriction(X0,X1)) = X2
| ~ relation(X1)
| ~ empty(X0)
| element(sK5(relation_rng_restriction(X0,X1),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_473])]) ).
fof(f3131,plain,
( ! [X2,X0,X1] :
( ~ relation(relation_rng_restriction(X0,X1))
| relation_rng(relation_rng_restriction(X0,X1)) = X2
| ~ relation(X1)
| ~ empty(X0)
| element(sK5(relation_rng_restriction(X0,X1),X2),X2) )
| ~ spl15_24
| ~ spl15_247 ),
inference(resolution,[],[f3072,f268]) ).
fof(f10007,plain,
( spl15_472
| ~ spl15_23
| ~ spl15_246 ),
inference(avatar_split_clause,[],[f3116,f3067,f263,f10005]) ).
fof(f10005,plain,
( spl15_472
<=> ! [X2,X0,X1] :
( ~ relation(relation_rng_restriction(X0,X1))
| relation_rng(relation_rng_restriction(X0,X1)) = X2
| ~ relation(X1)
| ~ empty(X2)
| ~ in(X0,sK5(relation_rng_restriction(X0,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_472])]) ).
fof(f3067,plain,
( spl15_246
<=> ! [X2,X0,X1] :
( in(sK5(relation_rng_restriction(X0,X1),X2),X0)
| ~ relation(relation_rng_restriction(X0,X1))
| relation_rng(relation_rng_restriction(X0,X1)) = X2
| ~ relation(X1)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_246])]) ).
fof(f3116,plain,
( ! [X2,X0,X1] :
( ~ relation(relation_rng_restriction(X0,X1))
| relation_rng(relation_rng_restriction(X0,X1)) = X2
| ~ relation(X1)
| ~ empty(X2)
| ~ in(X0,sK5(relation_rng_restriction(X0,X1),X2)) )
| ~ spl15_23
| ~ spl15_246 ),
inference(resolution,[],[f3068,f264]) ).
fof(f3068,plain,
( ! [X2,X0,X1] :
( in(sK5(relation_rng_restriction(X0,X1),X2),X0)
| ~ relation(relation_rng_restriction(X0,X1))
| relation_rng(relation_rng_restriction(X0,X1)) = X2
| ~ relation(X1)
| ~ empty(X2) )
| ~ spl15_246 ),
inference(avatar_component_clause,[],[f3067]) ).
fof(f10003,plain,
( spl15_471
| ~ spl15_24
| ~ spl15_246 ),
inference(avatar_split_clause,[],[f3115,f3067,f267,f10001]) ).
fof(f10001,plain,
( spl15_471
<=> ! [X2,X0,X1] :
( ~ relation(relation_rng_restriction(X0,X1))
| relation_rng(relation_rng_restriction(X0,X1)) = X2
| ~ relation(X1)
| ~ empty(X2)
| element(sK5(relation_rng_restriction(X0,X1),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_471])]) ).
fof(f3115,plain,
( ! [X2,X0,X1] :
( ~ relation(relation_rng_restriction(X0,X1))
| relation_rng(relation_rng_restriction(X0,X1)) = X2
| ~ relation(X1)
| ~ empty(X2)
| element(sK5(relation_rng_restriction(X0,X1),X2),X0) )
| ~ spl15_24
| ~ spl15_246 ),
inference(resolution,[],[f3068,f268]) ).
fof(f9999,plain,
( spl15_470
| ~ spl15_23
| ~ spl15_244 ),
inference(avatar_split_clause,[],[f3092,f3058,f263,f9997]) ).
fof(f9997,plain,
( spl15_470
<=> ! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(relation_rng(X0))
| sP0(X1,X2,relation_rng(relation_rng(X0)))
| ~ empty(X0)
| ~ in(X2,sK10(X1,X2,relation_rng(relation_rng(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_470])]) ).
fof(f3092,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(relation_rng(X0))
| sP0(X1,X2,relation_rng(relation_rng(X0)))
| ~ empty(X0)
| ~ in(X2,sK10(X1,X2,relation_rng(relation_rng(X0)))) )
| ~ spl15_23
| ~ spl15_244 ),
inference(resolution,[],[f3059,f264]) ).
fof(f9995,plain,
( spl15_469
| ~ spl15_24
| ~ spl15_244 ),
inference(avatar_split_clause,[],[f3091,f3058,f267,f9993]) ).
fof(f9993,plain,
( spl15_469
<=> ! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(relation_rng(X0))
| sP0(X1,X2,relation_rng(relation_rng(X0)))
| ~ empty(X0)
| element(sK10(X1,X2,relation_rng(relation_rng(X0))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_469])]) ).
fof(f3091,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(relation_rng(X0))
| sP0(X1,X2,relation_rng(relation_rng(X0)))
| ~ empty(X0)
| element(sK10(X1,X2,relation_rng(relation_rng(X0))),X2) )
| ~ spl15_24
| ~ spl15_244 ),
inference(resolution,[],[f3059,f268]) ).
fof(f9991,plain,
( spl15_468
| ~ spl15_63
| ~ spl15_231 ),
inference(avatar_split_clause,[],[f2778,f2663,f536,f9989]) ).
fof(f9989,plain,
( spl15_468
<=> ! [X0,X1] :
( in(sK5(X0,X1),X1)
| relation_rng(X0) = X1
| ~ relation(X0)
| ~ empty(relation_rng_restriction(relation_rng(X0),X0))
| ~ relation(relation_rng_restriction(relation_rng(X0),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_468])]) ).
fof(f536,plain,
( spl15_63
<=> ! [X0,X1] :
( sP0(X0,X1,relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_63])]) ).
fof(f2663,plain,
( spl15_231
<=> ! [X2,X0,X1] :
( ~ relation(X0)
| in(sK5(X0,X1),X1)
| relation_rng(X0) = X1
| ~ sP0(X0,relation_rng(X0),X2)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_231])]) ).
fof(f2778,plain,
( ! [X0,X1] :
( in(sK5(X0,X1),X1)
| relation_rng(X0) = X1
| ~ relation(X0)
| ~ empty(relation_rng_restriction(relation_rng(X0),X0))
| ~ relation(relation_rng_restriction(relation_rng(X0),X0)) )
| ~ spl15_63
| ~ spl15_231 ),
inference(duplicate_literal_removal,[],[f2763]) ).
fof(f2763,plain,
( ! [X0,X1] :
( in(sK5(X0,X1),X1)
| relation_rng(X0) = X1
| ~ relation(X0)
| ~ empty(relation_rng_restriction(relation_rng(X0),X0))
| ~ relation(relation_rng_restriction(relation_rng(X0),X0))
| ~ relation(X0) )
| ~ spl15_63
| ~ spl15_231 ),
inference(resolution,[],[f2664,f537]) ).
fof(f537,plain,
( ! [X0,X1] :
( sP0(X0,X1,relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ relation(X0) )
| ~ spl15_63 ),
inference(avatar_component_clause,[],[f536]) ).
fof(f2664,plain,
( ! [X2,X0,X1] :
( ~ sP0(X0,relation_rng(X0),X2)
| in(sK5(X0,X1),X1)
| relation_rng(X0) = X1
| ~ relation(X0)
| ~ empty(X2) )
| ~ spl15_231 ),
inference(avatar_component_clause,[],[f2663]) ).
fof(f9976,plain,
( spl15_467
| ~ spl15_76
| ~ spl15_218 ),
inference(avatar_split_clause,[],[f2566,f2533,f631,f9974]) ).
fof(f9974,plain,
( spl15_467
<=> ! [X0,X1] :
( ~ relation(X0)
| ~ relation(relation_rng(X0))
| ~ empty(X0)
| ~ relation(relation_rng(relation_rng(X0)))
| sP0(relation_rng(relation_rng(relation_rng(X0))),X1,relation_rng(relation_rng(relation_rng(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_467])]) ).
fof(f631,plain,
( spl15_76
<=> ! [X0,X1] :
( in(unordered_pair(singleton(sK9(X0,X1,X0)),unordered_pair(sK10(X0,X1,X0),sK9(X0,X1,X0))),X0)
| sP0(X0,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_76])]) ).
fof(f2566,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ relation(relation_rng(X0))
| ~ empty(X0)
| ~ relation(relation_rng(relation_rng(X0)))
| sP0(relation_rng(relation_rng(relation_rng(X0))),X1,relation_rng(relation_rng(relation_rng(X0)))) )
| ~ spl15_76
| ~ spl15_218 ),
inference(resolution,[],[f2534,f632]) ).
fof(f632,plain,
( ! [X0,X1] :
( in(unordered_pair(singleton(sK9(X0,X1,X0)),unordered_pair(sK10(X0,X1,X0),sK9(X0,X1,X0))),X0)
| sP0(X0,X1,X0) )
| ~ spl15_76 ),
inference(avatar_component_clause,[],[f631]) ).
fof(f9972,plain,
( spl15_466
| ~ spl15_65
| ~ spl15_193 ),
inference(avatar_split_clause,[],[f2108,f2072,f548,f9970]) ).
fof(f9970,plain,
( spl15_466
<=> ! [X2,X0,X1] :
( ~ relation(X0)
| ~ empty(X0)
| ~ relation(X1)
| ~ empty(X1)
| relation_rng(X1) = relation_rng_restriction(X2,relation_rng(X0))
| ~ relation(relation_rng(X1))
| ~ relation(relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_466])]) ).
fof(f2072,plain,
( spl15_193
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| ~ relation(X0)
| sP0(relation_rng(X0),X1,relation_rng(X2))
| ~ relation(X2)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_193])]) ).
fof(f2108,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| ~ empty(X0)
| ~ relation(X1)
| ~ empty(X1)
| relation_rng(X1) = relation_rng_restriction(X2,relation_rng(X0))
| ~ relation(relation_rng(X1))
| ~ relation(relation_rng(X0)) )
| ~ spl15_65
| ~ spl15_193 ),
inference(resolution,[],[f2073,f549]) ).
fof(f2073,plain,
( ! [X2,X0,X1] :
( sP0(relation_rng(X0),X1,relation_rng(X2))
| ~ relation(X0)
| ~ empty(X0)
| ~ relation(X2)
| ~ empty(X2) )
| ~ spl15_193 ),
inference(avatar_component_clause,[],[f2072]) ).
fof(f9529,plain,
( spl15_465
| ~ spl15_18
| ~ spl15_449 ),
inference(avatar_split_clause,[],[f8652,f8605,f233,f9527]) ).
fof(f8605,plain,
( spl15_449
<=> ! [X0] :
( sK12 = relation_rng_restriction(X0,relation_rng_restriction(sK3,sK4))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_449])]) ).
fof(f8652,plain,
( ! [X0] :
( sK12 = relation_rng_restriction(relation_rng(X0),relation_rng_restriction(sK3,sK4))
| ~ empty(X0) )
| ~ spl15_18
| ~ spl15_449 ),
inference(resolution,[],[f8606,f234]) ).
fof(f8606,plain,
( ! [X0] :
( ~ empty(X0)
| sK12 = relation_rng_restriction(X0,relation_rng_restriction(sK3,sK4)) )
| ~ spl15_449 ),
inference(avatar_component_clause,[],[f8605]) ).
fof(f9285,plain,
( spl15_464
| ~ spl15_101
| ~ spl15_278 ),
inference(avatar_split_clause,[],[f4081,f3977,f868,f9283]) ).
fof(f9283,plain,
( spl15_464
<=> ! [X2,X0,X1] :
( ~ sP0(X0,relation_rng(X0),relation_rng(relation_rng(X1)))
| sP0(X0,X2,X0)
| ~ relation(X0)
| ~ empty(X1)
| ~ relation(X1)
| ~ relation(relation_rng(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_464])]) ).
fof(f4081,plain,
( ! [X2,X0,X1] :
( ~ sP0(X0,relation_rng(X0),relation_rng(relation_rng(X1)))
| sP0(X0,X2,X0)
| ~ relation(X0)
| ~ empty(X1)
| ~ relation(X1)
| ~ relation(relation_rng(X1)) )
| ~ spl15_101
| ~ spl15_278 ),
inference(resolution,[],[f3978,f869]) ).
fof(f9281,plain,
( spl15_463
| ~ spl15_67
| ~ spl15_278 ),
inference(avatar_split_clause,[],[f4066,f3977,f562,f9279]) ).
fof(f9279,plain,
( spl15_463
<=> ! [X2,X0,X1] :
( ~ sP0(X0,relation_rng(X0),X1)
| sP0(X0,X2,X0)
| ~ relation(X0)
| in(sK10(X0,X2,X0),relation_rng(X1))
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_463])]) ).
fof(f4066,plain,
( ! [X2,X0,X1] :
( ~ sP0(X0,relation_rng(X0),X1)
| sP0(X0,X2,X0)
| ~ relation(X0)
| in(sK10(X0,X2,X0),relation_rng(X1))
| ~ relation(X1) )
| ~ spl15_67
| ~ spl15_278 ),
inference(resolution,[],[f3978,f563]) ).
fof(f9277,plain,
( spl15_462
| ~ spl15_276 ),
inference(avatar_split_clause,[],[f4014,f3969,f9275]) ).
fof(f9275,plain,
( spl15_462
<=> ! [X2,X0,X1] :
( in(sK10(X0,X1,relation_rng_restriction(X1,X2)),X1)
| sP0(X0,X1,relation_rng_restriction(X1,X2))
| ~ relation(relation_rng_restriction(X1,X2))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_462])]) ).
fof(f4014,plain,
( ! [X2,X0,X1] :
( in(sK10(X0,X1,relation_rng_restriction(X1,X2)),X1)
| sP0(X0,X1,relation_rng_restriction(X1,X2))
| ~ relation(relation_rng_restriction(X1,X2))
| ~ relation(X2) )
| ~ spl15_276 ),
inference(factoring,[],[f3970]) ).
fof(f9273,plain,
( spl15_461
| ~ spl15_68
| ~ spl15_273 ),
inference(avatar_split_clause,[],[f3870,f3843,f573,f9271]) ).
fof(f9271,plain,
( spl15_461
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ empty(X0)
| sP0(X1,X2,X0)
| ~ sP0(X1,X2,X3)
| in(sK10(X1,X2,X0),X4)
| ~ sP0(X5,X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_461])]) ).
fof(f3843,plain,
( spl15_273
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| in(unordered_pair(singleton(sK9(X1,X2,X0)),unordered_pair(sK10(X1,X2,X0),sK9(X1,X2,X0))),X3)
| sP0(X1,X2,X0)
| ~ sP0(X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_273])]) ).
fof(f3870,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ empty(X0)
| sP0(X1,X2,X0)
| ~ sP0(X1,X2,X3)
| in(sK10(X1,X2,X0),X4)
| ~ sP0(X5,X4,X3) )
| ~ spl15_68
| ~ spl15_273 ),
inference(resolution,[],[f3844,f574]) ).
fof(f3844,plain,
( ! [X2,X3,X0,X1] :
( in(unordered_pair(singleton(sK9(X1,X2,X0)),unordered_pair(sK10(X1,X2,X0),sK9(X1,X2,X0))),X3)
| ~ empty(X0)
| sP0(X1,X2,X0)
| ~ sP0(X1,X2,X3) )
| ~ spl15_273 ),
inference(avatar_component_clause,[],[f3843]) ).
fof(f9178,plain,
( spl15_460
| ~ spl15_61
| ~ spl15_251 ),
inference(avatar_split_clause,[],[f3279,f3231,f511,f9176]) ).
fof(f9176,plain,
( spl15_460
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP0(X0,X1,relation_rng_restriction(relation_rng(X2),X3))
| ~ relation(relation_rng_restriction(relation_rng(X2),X3))
| ~ relation(X3)
| ~ relation(X2)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_460])]) ).
fof(f3279,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP0(X0,X1,relation_rng_restriction(relation_rng(X2),X3))
| ~ relation(relation_rng_restriction(relation_rng(X2),X3))
| ~ relation(X3)
| ~ relation(X2)
| ~ empty(X2) )
| ~ spl15_61
| ~ spl15_251 ),
inference(resolution,[],[f3232,f512]) ).
fof(f9174,plain,
( spl15_459
| ~ spl15_61
| ~ spl15_250 ),
inference(avatar_split_clause,[],[f3250,f3227,f511,f9172]) ).
fof(f9172,plain,
( spl15_459
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP0(relation_rng_restriction(relation_rng(X1),X2),X3,X0)
| ~ relation(relation_rng_restriction(relation_rng(X1),X2))
| ~ relation(X2)
| ~ relation(X1)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_459])]) ).
fof(f3250,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP0(relation_rng_restriction(relation_rng(X1),X2),X3,X0)
| ~ relation(relation_rng_restriction(relation_rng(X1),X2))
| ~ relation(X2)
| ~ relation(X1)
| ~ empty(X1) )
| ~ spl15_61
| ~ spl15_250 ),
inference(resolution,[],[f3228,f512]) ).
fof(f9170,plain,
( spl15_458
| ~ spl15_61
| ~ spl15_246 ),
inference(avatar_split_clause,[],[f3118,f3067,f511,f9168]) ).
fof(f9168,plain,
( spl15_458
<=> ! [X2,X0,X1] :
( ~ relation(relation_rng_restriction(relation_rng(X0),X1))
| relation_rng(relation_rng_restriction(relation_rng(X0),X1)) = X2
| ~ relation(X1)
| ~ empty(X2)
| ~ relation(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_458])]) ).
fof(f3118,plain,
( ! [X2,X0,X1] :
( ~ relation(relation_rng_restriction(relation_rng(X0),X1))
| relation_rng(relation_rng_restriction(relation_rng(X0),X1)) = X2
| ~ relation(X1)
| ~ empty(X2)
| ~ relation(X0)
| ~ empty(X0) )
| ~ spl15_61
| ~ spl15_246 ),
inference(resolution,[],[f3068,f512]) ).
fof(f9166,plain,
( spl15_457
| ~ spl15_211
| ~ spl15_218 ),
inference(avatar_split_clause,[],[f2601,f2533,f2232,f9164]) ).
fof(f9164,plain,
( spl15_457
<=> ! [X0,X1] :
( ~ relation(X0)
| ~ relation(relation_rng(X0))
| ~ empty(X0)
| ~ relation(relation_rng(relation_rng(X0)))
| sP0(X1,relation_rng(relation_rng(relation_rng(X0))),relation_rng(relation_rng(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_457])]) ).
fof(f2232,plain,
( spl15_211
<=> ! [X0,X1] :
( in(sK10(X0,relation_rng(X1),X1),relation_rng(X1))
| sP0(X0,relation_rng(X1),X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_211])]) ).
fof(f2601,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ relation(relation_rng(X0))
| ~ empty(X0)
| ~ relation(relation_rng(relation_rng(X0)))
| sP0(X1,relation_rng(relation_rng(relation_rng(X0))),relation_rng(relation_rng(X0))) )
| ~ spl15_211
| ~ spl15_218 ),
inference(duplicate_literal_removal,[],[f2598]) ).
fof(f2598,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ relation(relation_rng(X0))
| ~ empty(X0)
| ~ relation(relation_rng(relation_rng(X0)))
| sP0(X1,relation_rng(relation_rng(relation_rng(X0))),relation_rng(relation_rng(X0)))
| ~ relation(relation_rng(relation_rng(X0))) )
| ~ spl15_211
| ~ spl15_218 ),
inference(resolution,[],[f2534,f2233]) ).
fof(f2233,plain,
( ! [X0,X1] :
( in(sK10(X0,relation_rng(X1),X1),relation_rng(X1))
| sP0(X0,relation_rng(X1),X1)
| ~ relation(X1) )
| ~ spl15_211 ),
inference(avatar_component_clause,[],[f2232]) ).
fof(f9162,plain,
( spl15_456
| ~ spl15_64
| ~ spl15_218 ),
inference(avatar_split_clause,[],[f2596,f2533,f540,f9160]) ).
fof(f9160,plain,
( spl15_456
<=> ! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(relation_rng(X0))
| ~ empty(X0)
| ~ relation(relation_rng(relation_rng(X0)))
| sP0(X1,relation_rng(relation_rng(relation_rng(X0))),X2)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_456])]) ).
fof(f2596,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(relation_rng(X0))
| ~ empty(X0)
| ~ relation(relation_rng(relation_rng(X0)))
| sP0(X1,relation_rng(relation_rng(relation_rng(X0))),X2)
| ~ empty(X2) )
| ~ spl15_64
| ~ spl15_218 ),
inference(resolution,[],[f2534,f541]) ).
fof(f9158,plain,
( spl15_455
| ~ spl15_79
| ~ spl15_218 ),
inference(avatar_split_clause,[],[f2570,f2533,f656,f9156]) ).
fof(f9156,plain,
( spl15_455
<=> ! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(relation_rng(X0))
| ~ empty(X0)
| ~ relation(relation_rng(relation_rng(X0)))
| sP0(X1,X2,relation_rng(relation_rng(relation_rng(X0))))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_455])]) ).
fof(f656,plain,
( spl15_79
<=> ! [X2,X0,X1] :
( in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X2)
| sP0(X0,X1,X2)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_79])]) ).
fof(f2570,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(relation_rng(X0))
| ~ empty(X0)
| ~ relation(relation_rng(relation_rng(X0)))
| sP0(X1,X2,relation_rng(relation_rng(relation_rng(X0))))
| ~ empty(X1) )
| ~ spl15_79
| ~ spl15_218 ),
inference(resolution,[],[f2534,f657]) ).
fof(f657,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X2)
| sP0(X0,X1,X2)
| ~ empty(X0) )
| ~ spl15_79 ),
inference(avatar_component_clause,[],[f656]) ).
fof(f9154,plain,
( spl15_454
| ~ spl15_78
| ~ spl15_218 ),
inference(avatar_split_clause,[],[f2564,f2533,f652,f9152]) ).
fof(f9152,plain,
( spl15_454
<=> ! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(relation_rng(X0))
| ~ empty(X0)
| ~ relation(relation_rng(relation_rng(X0)))
| sP0(relation_rng(relation_rng(relation_rng(X0))),X1,X2)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_454])]) ).
fof(f652,plain,
( spl15_78
<=> ! [X2,X0,X1] :
( in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X0)
| sP0(X0,X1,X2)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_78])]) ).
fof(f2564,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(relation_rng(X0))
| ~ empty(X0)
| ~ relation(relation_rng(relation_rng(X0)))
| sP0(relation_rng(relation_rng(relation_rng(X0))),X1,X2)
| ~ empty(X2) )
| ~ spl15_78
| ~ spl15_218 ),
inference(resolution,[],[f2534,f653]) ).
fof(f653,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X0)
| sP0(X0,X1,X2)
| ~ empty(X2) )
| ~ spl15_78 ),
inference(avatar_component_clause,[],[f652]) ).
fof(f9150,plain,
( spl15_453
| ~ spl15_65
| ~ spl15_197 ),
inference(avatar_split_clause,[],[f2315,f2156,f548,f9148]) ).
fof(f9148,plain,
( spl15_453
<=> ! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(relation_rng(X0))
| ~ empty(X0)
| ~ empty(X1)
| relation_rng_restriction(relation_rng(relation_rng(X0)),X2) = X1
| ~ relation(X1)
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_453])]) ).
fof(f2156,plain,
( spl15_197
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| ~ relation(X0)
| ~ relation(relation_rng(X0))
| sP0(X1,relation_rng(relation_rng(X0)),X2)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_197])]) ).
fof(f2315,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(relation_rng(X0))
| ~ empty(X0)
| ~ empty(X1)
| relation_rng_restriction(relation_rng(relation_rng(X0)),X2) = X1
| ~ relation(X1)
| ~ relation(X2) )
| ~ spl15_65
| ~ spl15_197 ),
inference(resolution,[],[f2157,f549]) ).
fof(f2157,plain,
( ! [X2,X0,X1] :
( sP0(X1,relation_rng(relation_rng(X0)),X2)
| ~ relation(X0)
| ~ relation(relation_rng(X0))
| ~ empty(X0)
| ~ empty(X2) )
| ~ spl15_197 ),
inference(avatar_component_clause,[],[f2156]) ).
fof(f9146,plain,
( spl15_452
| ~ spl15_65
| ~ spl15_195 ),
inference(avatar_split_clause,[],[f2290,f2148,f548,f9144]) ).
fof(f9144,plain,
( spl15_452
<=> ! [X0,X1] :
( ~ relation(X0)
| ~ relation(relation_rng(X0))
| ~ empty(X0)
| relation_rng(relation_rng(X0)) = relation_rng_restriction(X1,relation_rng(relation_rng(X0)))
| ~ relation(relation_rng(relation_rng(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_452])]) ).
fof(f2148,plain,
( spl15_195
<=> ! [X0,X1] :
( ~ empty(X0)
| ~ relation(X0)
| ~ relation(relation_rng(X0))
| sP0(relation_rng(relation_rng(X0)),X1,relation_rng(relation_rng(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_195])]) ).
fof(f2290,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ relation(relation_rng(X0))
| ~ empty(X0)
| relation_rng(relation_rng(X0)) = relation_rng_restriction(X1,relation_rng(relation_rng(X0)))
| ~ relation(relation_rng(relation_rng(X0))) )
| ~ spl15_65
| ~ spl15_195 ),
inference(duplicate_literal_removal,[],[f2266]) ).
fof(f2266,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ relation(relation_rng(X0))
| ~ empty(X0)
| relation_rng(relation_rng(X0)) = relation_rng_restriction(X1,relation_rng(relation_rng(X0)))
| ~ relation(relation_rng(relation_rng(X0)))
| ~ relation(relation_rng(relation_rng(X0))) )
| ~ spl15_65
| ~ spl15_195 ),
inference(resolution,[],[f2149,f549]) ).
fof(f2149,plain,
( ! [X0,X1] :
( sP0(relation_rng(relation_rng(X0)),X1,relation_rng(relation_rng(X0)))
| ~ relation(X0)
| ~ relation(relation_rng(X0))
| ~ empty(X0) )
| ~ spl15_195 ),
inference(avatar_component_clause,[],[f2148]) ).
fof(f9142,plain,
( spl15_451
| ~ spl15_65
| ~ spl15_192 ),
inference(avatar_split_clause,[],[f2084,f2068,f548,f9140]) ).
fof(f9140,plain,
( spl15_451
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| ~ relation(X0)
| ~ relation(X1)
| ~ empty(X1)
| relation_rng(X0) = relation_rng_restriction(relation_rng(X1),X2)
| ~ relation(relation_rng(X0))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_451])]) ).
fof(f2068,plain,
( spl15_192
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| sP0(X1,relation_rng(X2),relation_rng(X0))
| ~ relation(X0)
| ~ relation(X2)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_192])]) ).
fof(f2084,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| ~ relation(X0)
| ~ relation(X1)
| ~ empty(X1)
| relation_rng(X0) = relation_rng_restriction(relation_rng(X1),X2)
| ~ relation(relation_rng(X0))
| ~ relation(X2) )
| ~ spl15_65
| ~ spl15_192 ),
inference(resolution,[],[f2069,f549]) ).
fof(f2069,plain,
( ! [X2,X0,X1] :
( sP0(X1,relation_rng(X2),relation_rng(X0))
| ~ empty(X0)
| ~ relation(X0)
| ~ relation(X2)
| ~ empty(X2) )
| ~ spl15_192 ),
inference(avatar_component_clause,[],[f2068]) ).
fof(f9138,plain,
( spl15_450
| ~ spl15_2
| ~ spl15_55
| ~ spl15_449 ),
inference(avatar_split_clause,[],[f8658,f8605,f468,f156,f9135]) ).
fof(f156,plain,
( spl15_2
<=> empty(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_2])]) ).
fof(f468,plain,
( spl15_55
<=> empty_set = sK12 ),
introduced(avatar_definition,[new_symbols(naming,[spl15_55])]) ).
fof(f8658,plain,
( sK12 = relation_rng_restriction(sK12,relation_rng_restriction(sK3,sK4))
| ~ spl15_2
| ~ spl15_55
| ~ spl15_449 ),
inference(forward_demodulation,[],[f8655,f470]) ).
fof(f470,plain,
( empty_set = sK12
| ~ spl15_55 ),
inference(avatar_component_clause,[],[f468]) ).
fof(f8655,plain,
( sK12 = relation_rng_restriction(empty_set,relation_rng_restriction(sK3,sK4))
| ~ spl15_2
| ~ spl15_449 ),
inference(resolution,[],[f8606,f158]) ).
fof(f158,plain,
( empty(empty_set)
| ~ spl15_2 ),
inference(avatar_component_clause,[],[f156]) ).
fof(f8607,plain,
( spl15_449
| ~ spl15_5
| ~ spl15_3
| ~ spl15_55
| ~ spl15_428 ),
inference(avatar_split_clause,[],[f8561,f8508,f468,f161,f171,f8605]) ).
fof(f161,plain,
( spl15_3
<=> relation(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_3])]) ).
fof(f8508,plain,
( spl15_428
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_rng_restriction(X0,relation_rng_restriction(sK3,sK4)) = X1
| ~ relation(X1)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_428])]) ).
fof(f8561,plain,
( ! [X0] :
( ~ empty(sK12)
| sK12 = relation_rng_restriction(X0,relation_rng_restriction(sK3,sK4))
| ~ empty(X0) )
| ~ spl15_3
| ~ spl15_55
| ~ spl15_428 ),
inference(forward_demodulation,[],[f8560,f470]) ).
fof(f8560,plain,
( ! [X0] :
( sK12 = relation_rng_restriction(X0,relation_rng_restriction(sK3,sK4))
| ~ empty(X0)
| ~ empty(empty_set) )
| ~ spl15_3
| ~ spl15_55
| ~ spl15_428 ),
inference(forward_demodulation,[],[f8555,f470]) ).
fof(f8555,plain,
( ! [X0] :
( empty_set = relation_rng_restriction(X0,relation_rng_restriction(sK3,sK4))
| ~ empty(X0)
| ~ empty(empty_set) )
| ~ spl15_3
| ~ spl15_428 ),
inference(resolution,[],[f8509,f163]) ).
fof(f163,plain,
( relation(empty_set)
| ~ spl15_3 ),
inference(avatar_component_clause,[],[f161]) ).
fof(f8509,plain,
( ! [X0,X1] :
( ~ relation(X1)
| relation_rng_restriction(X0,relation_rng_restriction(sK3,sK4)) = X1
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl15_428 ),
inference(avatar_component_clause,[],[f8508]) ).
fof(f8603,plain,
( spl15_448
| ~ spl15_21
| ~ spl15_297 ),
inference(avatar_split_clause,[],[f4562,f4449,f246,f8601]) ).
fof(f8601,plain,
( spl15_448
<=> ! [X0,X3,X2,X1] :
( ~ sP0(X0,relation_rng(X0),X1)
| sP0(X2,X3,X0)
| in(sK10(X2,X3,X0),X3)
| ~ relation(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_448])]) ).
fof(f4562,plain,
( ! [X2,X3,X0,X1] :
( ~ sP0(X0,relation_rng(X0),X1)
| sP0(X2,X3,X0)
| in(sK10(X2,X3,X0),X3)
| ~ relation(X0)
| ~ empty(X1) )
| ~ spl15_21
| ~ spl15_297 ),
inference(resolution,[],[f4450,f247]) ).
fof(f8599,plain,
( spl15_447
| ~ spl15_61
| ~ spl15_277 ),
inference(avatar_split_clause,[],[f4046,f3973,f511,f8597]) ).
fof(f8597,plain,
( spl15_447
<=> ! [X2,X0,X1] :
( ~ in(X0,relation_rng(relation_rng_restriction(X1,relation_rng(X2))))
| ~ relation(relation_rng_restriction(X1,relation_rng(X2)))
| ~ relation(relation_rng(X2))
| ~ relation(X2)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_447])]) ).
fof(f4046,plain,
( ! [X2,X0,X1] :
( ~ in(X0,relation_rng(relation_rng_restriction(X1,relation_rng(X2))))
| ~ relation(relation_rng_restriction(X1,relation_rng(X2)))
| ~ relation(relation_rng(X2))
| ~ relation(X2)
| ~ empty(X2) )
| ~ spl15_61
| ~ spl15_277 ),
inference(resolution,[],[f3974,f512]) ).
fof(f8595,plain,
( spl15_446
| ~ spl15_68
| ~ spl15_277 ),
inference(avatar_split_clause,[],[f4040,f3973,f573,f8593]) ).
fof(f8593,plain,
( spl15_446
<=> ! [X4,X0,X3,X2,X1] :
( ~ in(X0,relation_rng(relation_rng_restriction(X1,X2)))
| ~ relation(relation_rng_restriction(X1,X2))
| ~ relation(X2)
| in(X0,X3)
| ~ sP0(X4,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_446])]) ).
fof(f4040,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ in(X0,relation_rng(relation_rng_restriction(X1,X2)))
| ~ relation(relation_rng_restriction(X1,X2))
| ~ relation(X2)
| in(X0,X3)
| ~ sP0(X4,X3,X2) )
| ~ spl15_68
| ~ spl15_277 ),
inference(resolution,[],[f3974,f574]) ).
fof(f8591,plain,
( spl15_445
| ~ spl15_101
| ~ spl15_273 ),
inference(avatar_split_clause,[],[f3886,f3843,f868,f8589]) ).
fof(f8589,plain,
( spl15_445
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP0(X1,X2,X0)
| ~ sP0(X1,X2,relation_rng(relation_rng(X3)))
| ~ empty(X3)
| ~ relation(X3)
| ~ relation(relation_rng(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_445])]) ).
fof(f3886,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP0(X1,X2,X0)
| ~ sP0(X1,X2,relation_rng(relation_rng(X3)))
| ~ empty(X3)
| ~ relation(X3)
| ~ relation(relation_rng(X3)) )
| ~ spl15_101
| ~ spl15_273 ),
inference(resolution,[],[f3844,f869]) ).
fof(f8587,plain,
( spl15_444
| ~ spl15_67
| ~ spl15_273 ),
inference(avatar_split_clause,[],[f3871,f3843,f562,f8585]) ).
fof(f8585,plain,
( spl15_444
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP0(X1,X2,X0)
| ~ sP0(X1,X2,X3)
| in(sK10(X1,X2,X0),relation_rng(X3))
| ~ relation(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_444])]) ).
fof(f3871,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP0(X1,X2,X0)
| ~ sP0(X1,X2,X3)
| in(sK10(X1,X2,X0),relation_rng(X3))
| ~ relation(X3) )
| ~ spl15_67
| ~ spl15_273 ),
inference(resolution,[],[f3844,f563]) ).
fof(f8583,plain,
( spl15_443
| ~ spl15_67
| ~ spl15_272 ),
inference(avatar_split_clause,[],[f3866,f3839,f562,f8581]) ).
fof(f3866,plain,
( ! [X2,X0,X1] :
( ~ in(X0,X1)
| ~ in(X0,relation_rng(X2))
| ~ relation(X2)
| ~ relation(relation_rng_restriction(X1,X2))
| in(X0,relation_rng(relation_rng_restriction(X1,X2))) )
| ~ spl15_67
| ~ spl15_272 ),
inference(duplicate_literal_removal,[],[f3857]) ).
fof(f3857,plain,
( ! [X2,X0,X1] :
( ~ in(X0,X1)
| ~ in(X0,relation_rng(X2))
| ~ relation(X2)
| ~ relation(relation_rng_restriction(X1,X2))
| in(X0,relation_rng(relation_rng_restriction(X1,X2)))
| ~ relation(relation_rng_restriction(X1,X2)) )
| ~ spl15_67
| ~ spl15_272 ),
inference(resolution,[],[f3840,f563]) ).
fof(f8579,plain,
( spl15_442
| ~ spl15_61
| ~ spl15_249 ),
inference(avatar_split_clause,[],[f3216,f3079,f511,f8577]) ).
fof(f8577,plain,
( spl15_442
<=> ! [X2,X0,X1] :
( ~ relation(relation_rng_restriction(X0,X1))
| relation_rng(X2) = relation_rng(relation_rng_restriction(X0,X1))
| ~ relation(X1)
| ~ empty(X1)
| ~ relation(X2)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_442])]) ).
fof(f3216,plain,
( ! [X2,X0,X1] :
( ~ relation(relation_rng_restriction(X0,X1))
| relation_rng(X2) = relation_rng(relation_rng_restriction(X0,X1))
| ~ relation(X1)
| ~ empty(X1)
| ~ relation(X2)
| ~ empty(X2) )
| ~ spl15_61
| ~ spl15_249 ),
inference(resolution,[],[f3080,f512]) ).
fof(f8575,plain,
( spl15_441
| ~ spl15_61
| ~ spl15_247 ),
inference(avatar_split_clause,[],[f3134,f3071,f511,f8573]) ).
fof(f8573,plain,
( spl15_441
<=> ! [X2,X0,X1] :
( ~ relation(relation_rng_restriction(X0,X1))
| relation_rng(X2) = relation_rng(relation_rng_restriction(X0,X1))
| ~ relation(X1)
| ~ empty(X0)
| ~ relation(X2)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_441])]) ).
fof(f3134,plain,
( ! [X2,X0,X1] :
( ~ relation(relation_rng_restriction(X0,X1))
| relation_rng(X2) = relation_rng(relation_rng_restriction(X0,X1))
| ~ relation(X1)
| ~ empty(X0)
| ~ relation(X2)
| ~ empty(X2) )
| ~ spl15_61
| ~ spl15_247 ),
inference(resolution,[],[f3072,f512]) ).
fof(f8571,plain,
( spl15_440
| ~ spl15_23
| ~ spl15_241 ),
inference(avatar_split_clause,[],[f2986,f2827,f263,f8569]) ).
fof(f8569,plain,
( spl15_440
<=> ! [X2,X0,X1] :
( ~ relation(X0)
| sP0(X1,X2,relation_rng(X0))
| ~ empty(X0)
| ~ relation(X1)
| ~ in(relation_rng(X1),sK10(X1,X2,relation_rng(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_440])]) ).
fof(f2827,plain,
( spl15_241
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| ~ relation(X0)
| sP0(X1,X2,relation_rng(X0))
| in(sK10(X1,X2,relation_rng(X0)),relation_rng(X1))
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_241])]) ).
fof(f2986,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| sP0(X1,X2,relation_rng(X0))
| ~ empty(X0)
| ~ relation(X1)
| ~ in(relation_rng(X1),sK10(X1,X2,relation_rng(X0))) )
| ~ spl15_23
| ~ spl15_241 ),
inference(resolution,[],[f2828,f264]) ).
fof(f2828,plain,
( ! [X2,X0,X1] :
( in(sK10(X1,X2,relation_rng(X0)),relation_rng(X1))
| ~ relation(X0)
| sP0(X1,X2,relation_rng(X0))
| ~ empty(X0)
| ~ relation(X1) )
| ~ spl15_241 ),
inference(avatar_component_clause,[],[f2827]) ).
fof(f8567,plain,
( spl15_439
| ~ spl15_24
| ~ spl15_241 ),
inference(avatar_split_clause,[],[f2985,f2827,f267,f8565]) ).
fof(f8565,plain,
( spl15_439
<=> ! [X2,X0,X1] :
( ~ relation(X0)
| sP0(X1,X2,relation_rng(X0))
| ~ empty(X0)
| ~ relation(X1)
| element(sK10(X1,X2,relation_rng(X0)),relation_rng(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_439])]) ).
fof(f2985,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| sP0(X1,X2,relation_rng(X0))
| ~ empty(X0)
| ~ relation(X1)
| element(sK10(X1,X2,relation_rng(X0)),relation_rng(X1)) )
| ~ spl15_24
| ~ spl15_241 ),
inference(resolution,[],[f2828,f268]) ).
fof(f8550,plain,
( spl15_438
| ~ spl15_23
| ~ spl15_240 ),
inference(avatar_split_clause,[],[f2955,f2823,f263,f8548]) ).
fof(f8548,plain,
( spl15_438
<=> ! [X2,X0,X1] :
( ~ relation(X0)
| sP0(relation_rng(X0),X1,X2)
| ~ empty(X0)
| ~ relation(X2)
| ~ in(relation_rng(X2),sK10(relation_rng(X0),X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_438])]) ).
fof(f2823,plain,
( spl15_240
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| ~ relation(X0)
| sP0(relation_rng(X0),X1,X2)
| in(sK10(relation_rng(X0),X1,X2),relation_rng(X2))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_240])]) ).
fof(f2955,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| sP0(relation_rng(X0),X1,X2)
| ~ empty(X0)
| ~ relation(X2)
| ~ in(relation_rng(X2),sK10(relation_rng(X0),X1,X2)) )
| ~ spl15_23
| ~ spl15_240 ),
inference(resolution,[],[f2824,f264]) ).
fof(f2824,plain,
( ! [X2,X0,X1] :
( in(sK10(relation_rng(X0),X1,X2),relation_rng(X2))
| ~ relation(X0)
| sP0(relation_rng(X0),X1,X2)
| ~ empty(X0)
| ~ relation(X2) )
| ~ spl15_240 ),
inference(avatar_component_clause,[],[f2823]) ).
fof(f8546,plain,
( spl15_437
| ~ spl15_24
| ~ spl15_240 ),
inference(avatar_split_clause,[],[f2954,f2823,f267,f8544]) ).
fof(f8544,plain,
( spl15_437
<=> ! [X2,X0,X1] :
( ~ relation(X0)
| sP0(relation_rng(X0),X1,X2)
| ~ empty(X0)
| ~ relation(X2)
| element(sK10(relation_rng(X0),X1,X2),relation_rng(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_437])]) ).
fof(f2954,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| sP0(relation_rng(X0),X1,X2)
| ~ empty(X0)
| ~ relation(X2)
| element(sK10(relation_rng(X0),X1,X2),relation_rng(X2)) )
| ~ spl15_24
| ~ spl15_240 ),
inference(resolution,[],[f2824,f268]) ).
fof(f8542,plain,
( spl15_436
| ~ spl15_61
| ~ spl15_239 ),
inference(avatar_split_clause,[],[f2931,f2819,f511,f8540]) ).
fof(f8540,plain,
( spl15_436
<=> ! [X0,X1] :
( ~ relation(relation_rng_restriction(relation_rng(X0),X1))
| relation_rng(X0) = relation_rng(relation_rng_restriction(relation_rng(X0),X1))
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_436])]) ).
fof(f2819,plain,
( spl15_239
<=> ! [X0,X1] :
( in(sK5(relation_rng_restriction(X0,X1),X0),X0)
| ~ relation(relation_rng_restriction(X0,X1))
| relation_rng(relation_rng_restriction(X0,X1)) = X0
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_239])]) ).
fof(f2931,plain,
( ! [X0,X1] :
( ~ relation(relation_rng_restriction(relation_rng(X0),X1))
| relation_rng(X0) = relation_rng(relation_rng_restriction(relation_rng(X0),X1))
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(X0) )
| ~ spl15_61
| ~ spl15_239 ),
inference(resolution,[],[f2820,f512]) ).
fof(f2820,plain,
( ! [X0,X1] :
( in(sK5(relation_rng_restriction(X0,X1),X0),X0)
| ~ relation(relation_rng_restriction(X0,X1))
| relation_rng(relation_rng_restriction(X0,X1)) = X0
| ~ relation(X1) )
| ~ spl15_239 ),
inference(avatar_component_clause,[],[f2819]) ).
fof(f8538,plain,
( spl15_435
| ~ spl15_23
| ~ spl15_239 ),
inference(avatar_split_clause,[],[f2929,f2819,f263,f8536]) ).
fof(f8536,plain,
( spl15_435
<=> ! [X0,X1] :
( ~ relation(relation_rng_restriction(X0,X1))
| relation_rng(relation_rng_restriction(X0,X1)) = X0
| ~ relation(X1)
| ~ in(X0,sK5(relation_rng_restriction(X0,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_435])]) ).
fof(f2929,plain,
( ! [X0,X1] :
( ~ relation(relation_rng_restriction(X0,X1))
| relation_rng(relation_rng_restriction(X0,X1)) = X0
| ~ relation(X1)
| ~ in(X0,sK5(relation_rng_restriction(X0,X1),X0)) )
| ~ spl15_23
| ~ spl15_239 ),
inference(resolution,[],[f2820,f264]) ).
fof(f8534,plain,
( spl15_434
| ~ spl15_24
| ~ spl15_239 ),
inference(avatar_split_clause,[],[f2928,f2819,f267,f8532]) ).
fof(f8532,plain,
( spl15_434
<=> ! [X0,X1] :
( ~ relation(relation_rng_restriction(X0,X1))
| relation_rng(relation_rng_restriction(X0,X1)) = X0
| ~ relation(X1)
| element(sK5(relation_rng_restriction(X0,X1),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_434])]) ).
fof(f2928,plain,
( ! [X0,X1] :
( ~ relation(relation_rng_restriction(X0,X1))
| relation_rng(relation_rng_restriction(X0,X1)) = X0
| ~ relation(X1)
| element(sK5(relation_rng_restriction(X0,X1),X0),X0) )
| ~ spl15_24
| ~ spl15_239 ),
inference(resolution,[],[f2820,f268]) ).
fof(f8530,plain,
( spl15_433
| ~ spl15_23
| ~ spl15_238 ),
inference(avatar_split_clause,[],[f2910,f2815,f263,f8528]) ).
fof(f8528,plain,
( spl15_433
<=> ! [X2,X0,X1] :
( sP0(X0,relation_rng(X1),X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ empty(X1)
| ~ in(relation_rng(X2),sK10(X0,relation_rng(X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_433])]) ).
fof(f2815,plain,
( spl15_238
<=> ! [X2,X0,X1] :
( in(sK10(X0,relation_rng(X1),X2),relation_rng(X2))
| sP0(X0,relation_rng(X1),X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_238])]) ).
fof(f2910,plain,
( ! [X2,X0,X1] :
( sP0(X0,relation_rng(X1),X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ empty(X1)
| ~ in(relation_rng(X2),sK10(X0,relation_rng(X1),X2)) )
| ~ spl15_23
| ~ spl15_238 ),
inference(resolution,[],[f2816,f264]) ).
fof(f2816,plain,
( ! [X2,X0,X1] :
( in(sK10(X0,relation_rng(X1),X2),relation_rng(X2))
| sP0(X0,relation_rng(X1),X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ empty(X1) )
| ~ spl15_238 ),
inference(avatar_component_clause,[],[f2815]) ).
fof(f8526,plain,
( spl15_432
| ~ spl15_23
| ~ spl15_236 ),
inference(avatar_split_clause,[],[f2873,f2807,f263,f8524]) ).
fof(f8524,plain,
( spl15_432
<=> ! [X2,X0,X1] :
( element(sK10(X0,X1,X2),X1)
| ~ relation(X2)
| sP0(X0,X1,X2)
| ~ in(relation_rng(X2),sK10(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_432])]) ).
fof(f2807,plain,
( spl15_236
<=> ! [X2,X0,X1] :
( in(sK10(X0,X1,X2),relation_rng(X2))
| sP0(X0,X1,X2)
| ~ relation(X2)
| element(sK10(X0,X1,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_236])]) ).
fof(f2873,plain,
( ! [X2,X0,X1] :
( element(sK10(X0,X1,X2),X1)
| ~ relation(X2)
| sP0(X0,X1,X2)
| ~ in(relation_rng(X2),sK10(X0,X1,X2)) )
| ~ spl15_23
| ~ spl15_236 ),
inference(resolution,[],[f2808,f264]) ).
fof(f2808,plain,
( ! [X2,X0,X1] :
( in(sK10(X0,X1,X2),relation_rng(X2))
| element(sK10(X0,X1,X2),X1)
| ~ relation(X2)
| sP0(X0,X1,X2) )
| ~ spl15_236 ),
inference(avatar_component_clause,[],[f2807]) ).
fof(f8522,plain,
( spl15_431
| ~ spl15_61
| ~ spl15_232 ),
inference(avatar_split_clause,[],[f2843,f2790,f511,f8520]) ).
fof(f8520,plain,
( spl15_431
<=> ! [X2,X0,X1] :
( element(sK10(X0,relation_rng(X1),X2),relation_rng(X2))
| ~ relation(X2)
| sP0(X0,relation_rng(X1),X2)
| ~ relation(X1)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_431])]) ).
fof(f2843,plain,
( ! [X2,X0,X1] :
( element(sK10(X0,relation_rng(X1),X2),relation_rng(X2))
| ~ relation(X2)
| sP0(X0,relation_rng(X1),X2)
| ~ relation(X1)
| ~ empty(X1) )
| ~ spl15_61
| ~ spl15_232 ),
inference(resolution,[],[f2791,f512]) ).
fof(f8518,plain,
( spl15_430
| ~ spl15_23
| ~ spl15_232 ),
inference(avatar_split_clause,[],[f2841,f2790,f263,f8516]) ).
fof(f8516,plain,
( spl15_430
<=> ! [X2,X0,X1] :
( element(sK10(X0,X1,X2),relation_rng(X2))
| ~ relation(X2)
| sP0(X0,X1,X2)
| ~ in(X1,sK10(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_430])]) ).
fof(f2841,plain,
( ! [X2,X0,X1] :
( element(sK10(X0,X1,X2),relation_rng(X2))
| ~ relation(X2)
| sP0(X0,X1,X2)
| ~ in(X1,sK10(X0,X1,X2)) )
| ~ spl15_23
| ~ spl15_232 ),
inference(resolution,[],[f2791,f264]) ).
fof(f8514,plain,
( spl15_429
| ~ spl15_24
| ~ spl15_232 ),
inference(avatar_split_clause,[],[f2840,f2790,f267,f8512]) ).
fof(f8512,plain,
( spl15_429
<=> ! [X2,X0,X1] :
( element(sK10(X0,X1,X2),relation_rng(X2))
| ~ relation(X2)
| sP0(X0,X1,X2)
| element(sK10(X0,X1,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_429])]) ).
fof(f2840,plain,
( ! [X2,X0,X1] :
( element(sK10(X0,X1,X2),relation_rng(X2))
| ~ relation(X2)
| sP0(X0,X1,X2)
| element(sK10(X0,X1,X2),X1) )
| ~ spl15_24
| ~ spl15_232 ),
inference(resolution,[],[f2791,f268]) ).
fof(f8510,plain,
( spl15_428
| ~ spl15_182
| ~ spl15_408 ),
inference(avatar_split_clause,[],[f7985,f7704,f1970,f8508]) ).
fof(f1970,plain,
( spl15_182
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| ~ empty(X1)
| relation_rng_restriction(X1,X2) = X0
| ~ relation(X0)
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_182])]) ).
fof(f7985,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_rng_restriction(X0,relation_rng_restriction(sK3,sK4)) = X1
| ~ relation(X1)
| ~ empty(X1) )
| ~ spl15_182
| ~ spl15_408 ),
inference(resolution,[],[f7705,f1971]) ).
fof(f1971,plain,
( ! [X2,X0,X1] :
( ~ relation(X2)
| ~ empty(X1)
| relation_rng_restriction(X1,X2) = X0
| ~ relation(X0)
| ~ empty(X0) )
| ~ spl15_182 ),
inference(avatar_component_clause,[],[f1970]) ).
fof(f7705,plain,
( relation(relation_rng_restriction(sK3,sK4))
| ~ spl15_408 ),
inference(avatar_component_clause,[],[f7704]) ).
fof(f7964,plain,
( spl15_427
| ~ spl15_61
| ~ spl15_288 ),
inference(avatar_split_clause,[],[f4303,f4142,f511,f7962]) ).
fof(f7962,plain,
( spl15_427
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP0(X0,X1,X2)
| ~ sP0(X2,relation_rng(X2),relation_rng(X3))
| ~ relation(X2)
| ~ relation(X3)
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_427])]) ).
fof(f4303,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP0(X0,X1,X2)
| ~ sP0(X2,relation_rng(X2),relation_rng(X3))
| ~ relation(X2)
| ~ relation(X3)
| ~ empty(X3) )
| ~ spl15_61
| ~ spl15_288 ),
inference(resolution,[],[f4143,f512]) ).
fof(f7960,plain,
( spl15_426
| ~ spl15_61
| ~ spl15_287 ),
inference(avatar_split_clause,[],[f4263,f4138,f511,f7958]) ).
fof(f7958,plain,
( spl15_426
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP0(X1,X2,X0)
| ~ sP0(X1,relation_rng(X1),relation_rng(X3))
| ~ relation(X1)
| ~ relation(X3)
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_426])]) ).
fof(f4263,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP0(X1,X2,X0)
| ~ sP0(X1,relation_rng(X1),relation_rng(X3))
| ~ relation(X1)
| ~ relation(X3)
| ~ empty(X3) )
| ~ spl15_61
| ~ spl15_287 ),
inference(resolution,[],[f4139,f512]) ).
fof(f7956,plain,
( spl15_425
| ~ spl15_21
| ~ spl15_261 ),
inference(avatar_split_clause,[],[f3588,f3458,f246,f7954]) ).
fof(f7954,plain,
( spl15_425
<=> ! [X2,X0,X1] :
( ~ relation(X0)
| sP0(relation_rng(relation_rng(X1)),X2,X0)
| ~ empty(X1)
| ~ relation(X1)
| ~ relation(relation_rng(X1))
| ~ empty(relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_425])]) ).
fof(f3588,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| sP0(relation_rng(relation_rng(X1)),X2,X0)
| ~ empty(X1)
| ~ relation(X1)
| ~ relation(relation_rng(X1))
| ~ empty(relation_rng(X0)) )
| ~ spl15_21
| ~ spl15_261 ),
inference(resolution,[],[f3459,f247]) ).
fof(f7952,plain,
( spl15_424
| ~ spl15_21
| ~ spl15_260 ),
inference(avatar_split_clause,[],[f3556,f3454,f246,f7950]) ).
fof(f7950,plain,
( spl15_424
<=> ! [X2,X0,X1] :
( ~ relation(X0)
| sP0(X0,X1,relation_rng(relation_rng(X2)))
| ~ empty(X2)
| ~ relation(X2)
| ~ relation(relation_rng(X2))
| ~ empty(relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_424])]) ).
fof(f3556,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| sP0(X0,X1,relation_rng(relation_rng(X2)))
| ~ empty(X2)
| ~ relation(X2)
| ~ relation(relation_rng(X2))
| ~ empty(relation_rng(X0)) )
| ~ spl15_21
| ~ spl15_260 ),
inference(resolution,[],[f3455,f247]) ).
fof(f7948,plain,
( spl15_423
| ~ spl15_21
| ~ spl15_252 ),
inference(avatar_split_clause,[],[f3327,f3235,f246,f7946]) ).
fof(f7946,plain,
( spl15_423
<=> ! [X2,X0,X1] :
( in(sK10(X0,X1,X2),relation_rng(X2))
| sP0(X0,X1,X2)
| ~ relation(X0)
| ~ relation(X2)
| ~ empty(relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_423])]) ).
fof(f3327,plain,
( ! [X2,X0,X1] :
( in(sK10(X0,X1,X2),relation_rng(X2))
| sP0(X0,X1,X2)
| ~ relation(X0)
| ~ relation(X2)
| ~ empty(relation_rng(X0)) )
| ~ spl15_21
| ~ spl15_252 ),
inference(resolution,[],[f3236,f247]) ).
fof(f7944,plain,
( spl15_422
| ~ spl15_21
| ~ spl15_252 ),
inference(avatar_split_clause,[],[f3311,f3235,f246,f7942]) ).
fof(f7942,plain,
( spl15_422
<=> ! [X2,X0,X1] :
( in(sK10(X0,X1,X2),relation_rng(X0))
| sP0(X0,X1,X2)
| ~ relation(X0)
| ~ relation(X2)
| ~ empty(relation_rng(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_422])]) ).
fof(f3311,plain,
( ! [X2,X0,X1] :
( in(sK10(X0,X1,X2),relation_rng(X0))
| sP0(X0,X1,X2)
| ~ relation(X0)
| ~ relation(X2)
| ~ empty(relation_rng(X2)) )
| ~ spl15_21
| ~ spl15_252 ),
inference(resolution,[],[f3236,f247]) ).
fof(f7940,plain,
( spl15_10
| spl15_49
| ~ spl15_30
| ~ spl15_51 ),
inference(avatar_split_clause,[],[f466,f440,f304,f429,f196]) ).
fof(f429,plain,
( spl15_49
<=> empty(relation_rng(relation_rng_restriction(sK3,sK4))) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_49])]) ).
fof(f304,plain,
( spl15_30
<=> ! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_30])]) ).
fof(f440,plain,
( spl15_51
<=> element(sK2,relation_rng(relation_rng_restriction(sK3,sK4))) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_51])]) ).
fof(f466,plain,
( empty(relation_rng(relation_rng_restriction(sK3,sK4)))
| in(sK2,relation_rng(relation_rng_restriction(sK3,sK4)))
| ~ spl15_30
| ~ spl15_51 ),
inference(resolution,[],[f442,f305]) ).
fof(f305,plain,
( ! [X0,X1] :
( ~ element(X0,X1)
| empty(X1)
| in(X0,X1) )
| ~ spl15_30 ),
inference(avatar_component_clause,[],[f304]) ).
fof(f442,plain,
( element(sK2,relation_rng(relation_rng_restriction(sK3,sK4)))
| ~ spl15_51 ),
inference(avatar_component_clause,[],[f440]) ).
fof(f7935,plain,
( ~ spl15_1
| ~ spl15_408
| spl15_11
| ~ spl15_10
| ~ spl15_199 ),
inference(avatar_split_clause,[],[f2361,f2164,f196,f200,f7704,f151]) ).
fof(f2361,plain,
( in(sK2,sK3)
| ~ relation(relation_rng_restriction(sK3,sK4))
| ~ relation(sK4)
| ~ spl15_10
| ~ spl15_199 ),
inference(resolution,[],[f2165,f198]) ).
fof(f198,plain,
( in(sK2,relation_rng(relation_rng_restriction(sK3,sK4)))
| ~ spl15_10 ),
inference(avatar_component_clause,[],[f196]) ).
fof(f7934,plain,
( spl15_11
| spl15_25
| ~ spl15_30
| ~ spl15_43 ),
inference(avatar_split_clause,[],[f427,f375,f304,f271,f200]) ).
fof(f271,plain,
( spl15_25
<=> empty(sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_25])]) ).
fof(f375,plain,
( spl15_43
<=> element(sK2,sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_43])]) ).
fof(f427,plain,
( empty(sK3)
| in(sK2,sK3)
| ~ spl15_30
| ~ spl15_43 ),
inference(resolution,[],[f377,f305]) ).
fof(f377,plain,
( element(sK2,sK3)
| ~ spl15_43 ),
inference(avatar_component_clause,[],[f375]) ).
fof(f7932,plain,
( ~ spl15_421
| ~ spl15_12
| ~ spl15_23 ),
inference(avatar_split_clause,[],[f445,f263,f205,f7929]) ).
fof(f7929,plain,
( spl15_421
<=> in(relation_rng(sK4),sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_421])]) ).
fof(f445,plain,
( ~ in(relation_rng(sK4),sK2)
| ~ spl15_12
| ~ spl15_23 ),
inference(resolution,[],[f207,f264]) ).
fof(f207,plain,
( in(sK2,relation_rng(sK4))
| ~ spl15_12 ),
inference(avatar_component_clause,[],[f205]) ).
fof(f7927,plain,
( ~ spl15_10
| ~ spl15_11
| ~ spl15_12 ),
inference(avatar_split_clause,[],[f81,f205,f200,f196]) ).
fof(f81,plain,
( ~ in(sK2,relation_rng(sK4))
| ~ in(sK2,sK3)
| ~ in(sK2,relation_rng(relation_rng_restriction(sK3,sK4))) ),
inference(cnf_transformation,[],[f54]) ).
fof(f54,plain,
( ( ~ in(sK2,relation_rng(sK4))
| ~ in(sK2,sK3)
| ~ in(sK2,relation_rng(relation_rng_restriction(sK3,sK4))) )
& ( ( in(sK2,relation_rng(sK4))
& in(sK2,sK3) )
| in(sK2,relation_rng(relation_rng_restriction(sK3,sK4))) )
& relation(sK4) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f52,f53]) ).
fof(f53,plain,
( ? [X0,X1,X2] :
( ( ~ in(X0,relation_rng(X2))
| ~ in(X0,X1)
| ~ in(X0,relation_rng(relation_rng_restriction(X1,X2))) )
& ( ( in(X0,relation_rng(X2))
& in(X0,X1) )
| in(X0,relation_rng(relation_rng_restriction(X1,X2))) )
& relation(X2) )
=> ( ( ~ in(sK2,relation_rng(sK4))
| ~ in(sK2,sK3)
| ~ in(sK2,relation_rng(relation_rng_restriction(sK3,sK4))) )
& ( ( in(sK2,relation_rng(sK4))
& in(sK2,sK3) )
| in(sK2,relation_rng(relation_rng_restriction(sK3,sK4))) )
& relation(sK4) ) ),
introduced(choice_axiom,[]) ).
fof(f52,plain,
? [X0,X1,X2] :
( ( ~ in(X0,relation_rng(X2))
| ~ in(X0,X1)
| ~ in(X0,relation_rng(relation_rng_restriction(X1,X2))) )
& ( ( in(X0,relation_rng(X2))
& in(X0,X1) )
| in(X0,relation_rng(relation_rng_restriction(X1,X2))) )
& relation(X2) ),
inference(flattening,[],[f51]) ).
fof(f51,plain,
? [X0,X1,X2] :
( ( ~ in(X0,relation_rng(X2))
| ~ in(X0,X1)
| ~ in(X0,relation_rng(relation_rng_restriction(X1,X2))) )
& ( ( in(X0,relation_rng(X2))
& in(X0,X1) )
| in(X0,relation_rng(relation_rng_restriction(X1,X2))) )
& relation(X2) ),
inference(nnf_transformation,[],[f33]) ).
fof(f33,plain,
? [X0,X1,X2] :
( ( in(X0,relation_rng(relation_rng_restriction(X1,X2)))
<~> ( in(X0,relation_rng(X2))
& in(X0,X1) ) )
& relation(X2) ),
inference(ennf_transformation,[],[f27]) ).
fof(f27,negated_conjecture,
~ ! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_rng(relation_rng_restriction(X1,X2)))
<=> ( in(X0,relation_rng(X2))
& in(X0,X1) ) ) ),
inference(negated_conjecture,[],[f26]) ).
fof(f26,conjecture,
! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_rng(relation_rng_restriction(X1,X2)))
<=> ( in(X0,relation_rng(X2))
& in(X0,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t115_relat_1) ).
fof(f7922,plain,
( ~ spl15_1
| ~ spl15_22
| spl15_408 ),
inference(avatar_split_clause,[],[f7806,f7704,f259,f151]) ).
fof(f259,plain,
( spl15_22
<=> ! [X0,X1] :
( relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_22])]) ).
fof(f7806,plain,
( ~ relation(sK4)
| ~ spl15_22
| spl15_408 ),
inference(resolution,[],[f7706,f260]) ).
fof(f260,plain,
( ! [X0,X1] :
( relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) )
| ~ spl15_22 ),
inference(avatar_component_clause,[],[f259]) ).
fof(f7706,plain,
( ~ relation(relation_rng_restriction(sK3,sK4))
| spl15_408 ),
inference(avatar_component_clause,[],[f7704]) ).
fof(f7921,plain,
( spl15_420
| ~ spl15_20
| ~ spl15_245 ),
inference(avatar_split_clause,[],[f3113,f3063,f242,f7919]) ).
fof(f7919,plain,
( spl15_420
<=> ! [X0,X1] :
( relation_rng(relation_rng(X0)) = relation_rng(relation_rng(X1))
| ~ relation(X0)
| ~ relation(relation_rng(X0))
| ~ empty(X1)
| ~ relation(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_420])]) ).
fof(f242,plain,
( spl15_20
<=> ! [X0] :
( relation(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_20])]) ).
fof(f3063,plain,
( spl15_245
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_rng(relation_rng(X0)) = relation_rng(relation_rng(X1))
| ~ relation(X0)
| ~ relation(relation_rng(X0))
| ~ empty(X1)
| ~ relation(X1)
| ~ relation(relation_rng(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_245])]) ).
fof(f3113,plain,
( ! [X0,X1] :
( relation_rng(relation_rng(X0)) = relation_rng(relation_rng(X1))
| ~ relation(X0)
| ~ relation(relation_rng(X0))
| ~ empty(X1)
| ~ relation(X1)
| ~ empty(X0) )
| ~ spl15_20
| ~ spl15_245 ),
inference(duplicate_literal_removal,[],[f3110]) ).
fof(f3110,plain,
( ! [X0,X1] :
( relation_rng(relation_rng(X0)) = relation_rng(relation_rng(X1))
| ~ relation(X0)
| ~ relation(relation_rng(X0))
| ~ empty(X1)
| ~ relation(X1)
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl15_20
| ~ spl15_245 ),
inference(resolution,[],[f3064,f243]) ).
fof(f243,plain,
( ! [X0] :
( relation(relation_rng(X0))
| ~ empty(X0) )
| ~ spl15_20 ),
inference(avatar_component_clause,[],[f242]) ).
fof(f3064,plain,
( ! [X0,X1] :
( ~ relation(relation_rng(X1))
| relation_rng(relation_rng(X0)) = relation_rng(relation_rng(X1))
| ~ relation(X0)
| ~ relation(relation_rng(X0))
| ~ empty(X1)
| ~ relation(X1)
| ~ empty(X0) )
| ~ spl15_245 ),
inference(avatar_component_clause,[],[f3063]) ).
fof(f7917,plain,
( spl15_419
| ~ spl15_61
| ~ spl15_244 ),
inference(avatar_split_clause,[],[f3094,f3058,f511,f7915]) ).
fof(f7915,plain,
( spl15_419
<=> ! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(relation_rng(X0))
| sP0(X1,relation_rng(X2),relation_rng(relation_rng(X0)))
| ~ empty(X0)
| ~ relation(X2)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_419])]) ).
fof(f3094,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(relation_rng(X0))
| sP0(X1,relation_rng(X2),relation_rng(relation_rng(X0)))
| ~ empty(X0)
| ~ relation(X2)
| ~ empty(X2) )
| ~ spl15_61
| ~ spl15_244 ),
inference(resolution,[],[f3059,f512]) ).
fof(f7886,plain,
( ~ spl15_19
| spl15_418
| ~ spl15_74
| ~ spl15_238 ),
inference(avatar_split_clause,[],[f2913,f2815,f614,f7884,f237]) ).
fof(f7884,plain,
( spl15_418
<=> ! [X0,X1] :
( in(sK10(X0,relation_rng(X1),sK12),sK12)
| ~ empty(X1)
| ~ relation(X1)
| sP0(X0,relation_rng(X1),sK12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_418])]) ).
fof(f2913,plain,
( ! [X0,X1] :
( in(sK10(X0,relation_rng(X1),sK12),sK12)
| sP0(X0,relation_rng(X1),sK12)
| ~ relation(sK12)
| ~ relation(X1)
| ~ empty(X1) )
| ~ spl15_74
| ~ spl15_238 ),
inference(superposition,[],[f2816,f616]) ).
fof(f7853,plain,
( ~ spl15_19
| spl15_417
| ~ spl15_74
| ~ spl15_236 ),
inference(avatar_split_clause,[],[f2876,f2807,f614,f7851,f237]) ).
fof(f7851,plain,
( spl15_417
<=> ! [X0,X1] :
( in(sK10(X0,X1,sK12),sK12)
| sP0(X0,X1,sK12)
| element(sK10(X0,X1,sK12),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_417])]) ).
fof(f2876,plain,
( ! [X0,X1] :
( in(sK10(X0,X1,sK12),sK12)
| element(sK10(X0,X1,sK12),X1)
| ~ relation(sK12)
| sP0(X0,X1,sK12) )
| ~ spl15_74
| ~ spl15_236 ),
inference(superposition,[],[f2808,f616]) ).
fof(f7849,plain,
( ~ spl15_19
| spl15_416
| ~ spl15_74
| ~ spl15_235 ),
inference(avatar_split_clause,[],[f2858,f2803,f614,f7847,f237]) ).
fof(f7847,plain,
( spl15_416
<=> ! [X0,X1] :
( ~ in(sK12,sK10(X0,X1,sK12))
| in(sK10(X0,X1,sK12),X1)
| sP0(X0,X1,sK12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_416])]) ).
fof(f2803,plain,
( spl15_235
<=> ! [X2,X0,X1] :
( in(sK10(X0,X1,X2),X1)
| sP0(X0,X1,X2)
| ~ relation(X2)
| ~ in(relation_rng(X2),sK10(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_235])]) ).
fof(f2858,plain,
( ! [X0,X1] :
( ~ in(sK12,sK10(X0,X1,sK12))
| sP0(X0,X1,sK12)
| ~ relation(sK12)
| in(sK10(X0,X1,sK12),X1) )
| ~ spl15_74
| ~ spl15_235 ),
inference(superposition,[],[f2804,f616]) ).
fof(f2804,plain,
( ! [X2,X0,X1] :
( ~ in(relation_rng(X2),sK10(X0,X1,X2))
| sP0(X0,X1,X2)
| ~ relation(X2)
| in(sK10(X0,X1,X2),X1) )
| ~ spl15_235 ),
inference(avatar_component_clause,[],[f2803]) ).
fof(f7810,plain,
( ~ spl15_19
| spl15_415
| ~ spl15_74
| ~ spl15_232 ),
inference(avatar_split_clause,[],[f2848,f2790,f614,f7808,f237]) ).
fof(f7808,plain,
( spl15_415
<=> ! [X0,X1] :
( element(sK10(X0,X1,sK12),sK12)
| sP0(X0,X1,sK12)
| in(sK10(X0,X1,sK12),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_415])]) ).
fof(f2848,plain,
( ! [X0,X1] :
( element(sK10(X0,X1,sK12),sK12)
| in(sK10(X0,X1,sK12),X1)
| ~ relation(sK12)
| sP0(X0,X1,sK12) )
| ~ spl15_74
| ~ spl15_232 ),
inference(superposition,[],[f2791,f616]) ).
fof(f7805,plain,
( spl15_414
| ~ spl15_22
| ~ spl15_213 ),
inference(avatar_split_clause,[],[f2497,f2486,f259,f7803]) ).
fof(f7803,plain,
( spl15_414
<=> ! [X0,X3,X2,X1] :
( ~ relation(X0)
| ~ empty(X0)
| relation_rng_restriction(relation_rng(X0),relation_rng_restriction(X1,X2)) = X3
| ~ relation(X3)
| ~ empty(X3)
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_414])]) ).
fof(f2486,plain,
( spl15_213
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| ~ relation(X1)
| ~ empty(X1)
| relation_rng_restriction(relation_rng(X1),X2) = X0
| ~ relation(X0)
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_213])]) ).
fof(f2497,plain,
( ! [X2,X3,X0,X1] :
( ~ relation(X0)
| ~ empty(X0)
| relation_rng_restriction(relation_rng(X0),relation_rng_restriction(X1,X2)) = X3
| ~ relation(X3)
| ~ empty(X3)
| ~ relation(X2) )
| ~ spl15_22
| ~ spl15_213 ),
inference(resolution,[],[f2487,f260]) ).
fof(f2487,plain,
( ! [X2,X0,X1] :
( ~ relation(X2)
| ~ relation(X1)
| ~ empty(X1)
| relation_rng_restriction(relation_rng(X1),X2) = X0
| ~ relation(X0)
| ~ empty(X0) )
| ~ spl15_213 ),
inference(avatar_component_clause,[],[f2486]) ).
fof(f7801,plain,
( spl15_413
| ~ spl15_101
| ~ spl15_209 ),
inference(avatar_split_clause,[],[f2417,f2224,f868,f7799]) ).
fof(f7799,plain,
( spl15_413
<=> ! [X2,X0,X1] :
( sP0(X0,relation_rng(relation_rng(X1)),X2)
| ~ relation(X2)
| ~ empty(relation_rng(X2))
| ~ empty(X1)
| ~ relation(X1)
| ~ relation(relation_rng(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_413])]) ).
fof(f2417,plain,
( ! [X2,X0,X1] :
( sP0(X0,relation_rng(relation_rng(X1)),X2)
| ~ relation(X2)
| ~ empty(relation_rng(X2))
| ~ empty(X1)
| ~ relation(X1)
| ~ relation(relation_rng(X1)) )
| ~ spl15_101
| ~ spl15_209 ),
inference(resolution,[],[f2225,f869]) ).
fof(f7797,plain,
( spl15_412
| ~ spl15_59
| ~ spl15_199 ),
inference(avatar_split_clause,[],[f2374,f2164,f494,f7795]) ).
fof(f7795,plain,
( spl15_412
<=> ! [X0,X1] :
( in(sK8(relation_rng(relation_rng_restriction(X0,X1))),X0)
| ~ relation(relation_rng_restriction(X0,X1))
| ~ relation(X1)
| empty(relation_rng(relation_rng_restriction(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_412])]) ).
fof(f494,plain,
( spl15_59
<=> ! [X0] :
( empty(X0)
| in(sK8(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_59])]) ).
fof(f2374,plain,
( ! [X0,X1] :
( in(sK8(relation_rng(relation_rng_restriction(X0,X1))),X0)
| ~ relation(relation_rng_restriction(X0,X1))
| ~ relation(X1)
| empty(relation_rng(relation_rng_restriction(X0,X1))) )
| ~ spl15_59
| ~ spl15_199 ),
inference(resolution,[],[f2165,f495]) ).
fof(f495,plain,
( ! [X0] :
( in(sK8(X0),X0)
| empty(X0) )
| ~ spl15_59 ),
inference(avatar_component_clause,[],[f494]) ).
fof(f7779,plain,
( spl15_411
| ~ spl15_21
| ~ spl15_272 ),
inference(avatar_split_clause,[],[f3861,f3839,f246,f7777]) ).
fof(f7777,plain,
( spl15_411
<=> ! [X2,X0,X1] :
( ~ in(X0,X1)
| ~ in(X0,relation_rng(X2))
| ~ relation(X2)
| ~ relation(relation_rng_restriction(X1,X2))
| ~ empty(relation_rng_restriction(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_411])]) ).
fof(f3861,plain,
( ! [X2,X0,X1] :
( ~ in(X0,X1)
| ~ in(X0,relation_rng(X2))
| ~ relation(X2)
| ~ relation(relation_rng_restriction(X1,X2))
| ~ empty(relation_rng_restriction(X1,X2)) )
| ~ spl15_21
| ~ spl15_272 ),
inference(resolution,[],[f3840,f247]) ).
fof(f7775,plain,
( spl15_410
| ~ spl15_22
| ~ spl15_183 ),
inference(avatar_split_clause,[],[f2026,f1974,f259,f7773]) ).
fof(f7773,plain,
( spl15_410
<=> ! [X0,X3,X2,X1] :
( ~ empty(relation_rng_restriction(X0,X1))
| relation_rng_restriction(X2,relation_rng_restriction(X0,X1)) = X3
| ~ relation(X3)
| ~ empty(X3)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_410])]) ).
fof(f1974,plain,
( spl15_183
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| ~ empty(X1)
| relation_rng_restriction(X2,X1) = X0
| ~ relation(X0)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_183])]) ).
fof(f2026,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(relation_rng_restriction(X0,X1))
| relation_rng_restriction(X2,relation_rng_restriction(X0,X1)) = X3
| ~ relation(X3)
| ~ empty(X3)
| ~ relation(X1) )
| ~ spl15_22
| ~ spl15_183 ),
inference(resolution,[],[f1975,f260]) ).
fof(f1975,plain,
( ! [X2,X0,X1] :
( ~ relation(X1)
| ~ empty(X1)
| relation_rng_restriction(X2,X1) = X0
| ~ relation(X0)
| ~ empty(X0) )
| ~ spl15_183 ),
inference(avatar_component_clause,[],[f1974]) ).
fof(f7771,plain,
( spl15_409
| ~ spl15_65
| ~ spl15_181 ),
inference(avatar_split_clause,[],[f1946,f1876,f548,f7769]) ).
fof(f7769,plain,
( spl15_409
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| ~ relation(X0)
| ~ empty(X1)
| relation_rng(X0) = relation_rng_restriction(X1,X2)
| ~ relation(relation_rng(X0))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_409])]) ).
fof(f1876,plain,
( spl15_181
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| sP0(X1,X2,relation_rng(X0))
| ~ relation(X0)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_181])]) ).
fof(f1946,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| ~ relation(X0)
| ~ empty(X1)
| relation_rng(X0) = relation_rng_restriction(X1,X2)
| ~ relation(relation_rng(X0))
| ~ relation(X2) )
| ~ spl15_65
| ~ spl15_181 ),
inference(resolution,[],[f1877,f549]) ).
fof(f1877,plain,
( ! [X2,X0,X1] :
( sP0(X1,X2,relation_rng(X0))
| ~ empty(X0)
| ~ relation(X0)
| ~ empty(X2) )
| ~ spl15_181 ),
inference(avatar_component_clause,[],[f1876]) ).
fof(f7707,plain,
( spl15_12
| ~ spl15_1
| ~ spl15_408
| ~ spl15_10
| ~ spl15_402 ),
inference(avatar_split_clause,[],[f7426,f7113,f196,f7704,f151,f205]) ).
fof(f7113,plain,
( spl15_402
<=> ! [X2,X0,X1] :
( ~ in(X0,relation_rng(relation_rng_restriction(X1,X2)))
| ~ relation(relation_rng_restriction(X1,X2))
| ~ relation(X2)
| in(X0,relation_rng(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_402])]) ).
fof(f7426,plain,
( ~ relation(relation_rng_restriction(sK3,sK4))
| ~ relation(sK4)
| in(sK2,relation_rng(sK4))
| ~ spl15_10
| ~ spl15_402 ),
inference(resolution,[],[f7114,f198]) ).
fof(f7114,plain,
( ! [X2,X0,X1] :
( ~ in(X0,relation_rng(relation_rng_restriction(X1,X2)))
| ~ relation(relation_rng_restriction(X1,X2))
| ~ relation(X2)
| in(X0,relation_rng(X2)) )
| ~ spl15_402 ),
inference(avatar_component_clause,[],[f7113]) ).
fof(f7141,plain,
( spl15_407
| ~ spl15_22
| ~ spl15_191 ),
inference(avatar_split_clause,[],[f2136,f2064,f259,f7139]) ).
fof(f7139,plain,
( spl15_407
<=> ! [X2,X0,X1] :
( relation_rng_restriction(X1,X2) = relation_rng_restriction(X0,sK4)
| ~ empty(X0)
| ~ empty(relation_rng_restriction(X1,X2))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_407])]) ).
fof(f2064,plain,
( spl15_191
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_rng_restriction(X0,sK4) = X1
| ~ relation(X1)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_191])]) ).
fof(f2136,plain,
( ! [X2,X0,X1] :
( relation_rng_restriction(X1,X2) = relation_rng_restriction(X0,sK4)
| ~ empty(X0)
| ~ empty(relation_rng_restriction(X1,X2))
| ~ relation(X2) )
| ~ spl15_22
| ~ spl15_191 ),
inference(resolution,[],[f2065,f260]) ).
fof(f2065,plain,
( ! [X0,X1] :
( ~ relation(X1)
| relation_rng_restriction(X0,sK4) = X1
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl15_191 ),
inference(avatar_component_clause,[],[f2064]) ).
fof(f7131,plain,
( spl15_406
| ~ spl15_21
| ~ spl15_315 ),
inference(avatar_split_clause,[],[f5071,f5038,f246,f7129]) ).
fof(f7129,plain,
( spl15_406
<=> ! [X2,X0,X1] :
( sP0(relation_rng_restriction(X0,X1),X2,relation_rng_restriction(X0,X1))
| ~ relation(relation_rng_restriction(X0,X1))
| ~ relation(X1)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_406])]) ).
fof(f5071,plain,
( ! [X2,X0,X1] :
( sP0(relation_rng_restriction(X0,X1),X2,relation_rng_restriction(X0,X1))
| ~ relation(relation_rng_restriction(X0,X1))
| ~ relation(X1)
| ~ empty(X1) )
| ~ spl15_21
| ~ spl15_315 ),
inference(resolution,[],[f5039,f247]) ).
fof(f7127,plain,
( spl15_405
| ~ spl15_21
| ~ spl15_305 ),
inference(avatar_split_clause,[],[f4707,f4675,f246,f7125]) ).
fof(f7125,plain,
( spl15_405
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP0(X0,X1,relation_rng_restriction(X2,X3))
| ~ relation(relation_rng_restriction(X2,X3))
| ~ relation(X3)
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_405])]) ).
fof(f4707,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP0(X0,X1,relation_rng_restriction(X2,X3))
| ~ relation(relation_rng_restriction(X2,X3))
| ~ relation(X3)
| ~ empty(X3) )
| ~ spl15_21
| ~ spl15_305 ),
inference(resolution,[],[f4676,f247]) ).
fof(f7123,plain,
( spl15_404
| ~ spl15_21
| ~ spl15_304 ),
inference(avatar_split_clause,[],[f4685,f4671,f246,f7121]) ).
fof(f7121,plain,
( spl15_404
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP0(relation_rng_restriction(X1,X2),X3,X0)
| ~ relation(relation_rng_restriction(X1,X2))
| ~ relation(X2)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_404])]) ).
fof(f4685,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP0(relation_rng_restriction(X1,X2),X3,X0)
| ~ relation(relation_rng_restriction(X1,X2))
| ~ relation(X2)
| ~ empty(X2) )
| ~ spl15_21
| ~ spl15_304 ),
inference(resolution,[],[f4672,f247]) ).
fof(f7119,plain,
( spl15_403
| ~ spl15_61
| ~ spl15_278 ),
inference(avatar_split_clause,[],[f4080,f3977,f511,f7117]) ).
fof(f7117,plain,
( spl15_403
<=> ! [X2,X0,X1] :
( ~ sP0(X0,relation_rng(X0),relation_rng(X1))
| sP0(X0,X2,X0)
| ~ relation(X0)
| ~ relation(X1)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_403])]) ).
fof(f4080,plain,
( ! [X2,X0,X1] :
( ~ sP0(X0,relation_rng(X0),relation_rng(X1))
| sP0(X0,X2,X0)
| ~ relation(X0)
| ~ relation(X1)
| ~ empty(X1) )
| ~ spl15_61
| ~ spl15_278 ),
inference(resolution,[],[f3978,f512]) ).
fof(f7115,plain,
( spl15_402
| ~ spl15_67
| ~ spl15_277 ),
inference(avatar_split_clause,[],[f4055,f3973,f562,f7113]) ).
fof(f4055,plain,
( ! [X2,X0,X1] :
( ~ in(X0,relation_rng(relation_rng_restriction(X1,X2)))
| ~ relation(relation_rng_restriction(X1,X2))
| ~ relation(X2)
| in(X0,relation_rng(X2)) )
| ~ spl15_67
| ~ spl15_277 ),
inference(duplicate_literal_removal,[],[f4041]) ).
fof(f4041,plain,
( ! [X2,X0,X1] :
( ~ in(X0,relation_rng(relation_rng_restriction(X1,X2)))
| ~ relation(relation_rng_restriction(X1,X2))
| ~ relation(X2)
| in(X0,relation_rng(X2))
| ~ relation(X2) )
| ~ spl15_67
| ~ spl15_277 ),
inference(resolution,[],[f3974,f563]) ).
fof(f7111,plain,
( spl15_401
| ~ spl15_21
| ~ spl15_258 ),
inference(avatar_split_clause,[],[f3491,f3446,f246,f7109]) ).
fof(f7109,plain,
( spl15_401
<=> ! [X2,X0,X1] :
( sP0(relation_rng_restriction(X0,X1),X2,relation_rng_restriction(X0,X1))
| ~ relation(relation_rng_restriction(X0,X1))
| ~ relation(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_401])]) ).
fof(f3491,plain,
( ! [X2,X0,X1] :
( sP0(relation_rng_restriction(X0,X1),X2,relation_rng_restriction(X0,X1))
| ~ relation(relation_rng_restriction(X0,X1))
| ~ relation(X1)
| ~ empty(X0) )
| ~ spl15_21
| ~ spl15_258 ),
inference(resolution,[],[f3447,f247]) ).
fof(f7107,plain,
( spl15_400
| ~ spl15_21
| ~ spl15_251 ),
inference(avatar_split_clause,[],[f3278,f3231,f246,f7105]) ).
fof(f7105,plain,
( spl15_400
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP0(X0,X1,relation_rng_restriction(X2,X3))
| ~ relation(relation_rng_restriction(X2,X3))
| ~ relation(X3)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_400])]) ).
fof(f3278,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP0(X0,X1,relation_rng_restriction(X2,X3))
| ~ relation(relation_rng_restriction(X2,X3))
| ~ relation(X3)
| ~ empty(X2) )
| ~ spl15_21
| ~ spl15_251 ),
inference(resolution,[],[f3232,f247]) ).
fof(f7103,plain,
( spl15_399
| ~ spl15_21
| ~ spl15_250 ),
inference(avatar_split_clause,[],[f3249,f3227,f246,f7101]) ).
fof(f7101,plain,
( spl15_399
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP0(relation_rng_restriction(X1,X2),X3,X0)
| ~ relation(relation_rng_restriction(X1,X2))
| ~ relation(X2)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_399])]) ).
fof(f3249,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP0(relation_rng_restriction(X1,X2),X3,X0)
| ~ relation(relation_rng_restriction(X1,X2))
| ~ relation(X2)
| ~ empty(X1) )
| ~ spl15_21
| ~ spl15_250 ),
inference(resolution,[],[f3228,f247]) ).
fof(f7099,plain,
( spl15_398
| ~ spl15_21
| ~ spl15_249 ),
inference(avatar_split_clause,[],[f3215,f3079,f246,f7097]) ).
fof(f7097,plain,
( spl15_398
<=> ! [X2,X0,X1] :
( ~ relation(relation_rng_restriction(X0,X1))
| relation_rng(relation_rng_restriction(X0,X1)) = X2
| ~ relation(X1)
| ~ empty(X1)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_398])]) ).
fof(f3215,plain,
( ! [X2,X0,X1] :
( ~ relation(relation_rng_restriction(X0,X1))
| relation_rng(relation_rng_restriction(X0,X1)) = X2
| ~ relation(X1)
| ~ empty(X1)
| ~ empty(X2) )
| ~ spl15_21
| ~ spl15_249 ),
inference(resolution,[],[f3080,f247]) ).
fof(f7067,plain,
( spl15_397
| ~ spl15_21
| ~ spl15_246 ),
inference(avatar_split_clause,[],[f3117,f3067,f246,f7065]) ).
fof(f7065,plain,
( spl15_397
<=> ! [X2,X0,X1] :
( ~ relation(relation_rng_restriction(X0,X1))
| relation_rng(relation_rng_restriction(X0,X1)) = X2
| ~ relation(X1)
| ~ empty(X2)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_397])]) ).
fof(f3117,plain,
( ! [X2,X0,X1] :
( ~ relation(relation_rng_restriction(X0,X1))
| relation_rng(relation_rng_restriction(X0,X1)) = X2
| ~ relation(X1)
| ~ empty(X2)
| ~ empty(X0) )
| ~ spl15_21
| ~ spl15_246 ),
inference(resolution,[],[f3068,f247]) ).
fof(f7063,plain,
( spl15_396
| ~ spl15_59
| ~ spl15_218 ),
inference(avatar_split_clause,[],[f2588,f2533,f494,f7061]) ).
fof(f7061,plain,
( spl15_396
<=> ! [X0] :
( ~ relation(X0)
| ~ relation(relation_rng(X0))
| ~ empty(X0)
| ~ relation(relation_rng(relation_rng(X0)))
| empty(relation_rng(relation_rng(relation_rng(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_396])]) ).
fof(f2588,plain,
( ! [X0] :
( ~ relation(X0)
| ~ relation(relation_rng(X0))
| ~ empty(X0)
| ~ relation(relation_rng(relation_rng(X0)))
| empty(relation_rng(relation_rng(relation_rng(X0)))) )
| ~ spl15_59
| ~ spl15_218 ),
inference(resolution,[],[f2534,f495]) ).
fof(f7059,plain,
( spl15_395
| ~ spl15_96
| ~ spl15_177 ),
inference(avatar_split_clause,[],[f1888,f1860,f807,f7057]) ).
fof(f7057,plain,
( spl15_395
<=> ! [X0,X1] :
( ~ relation(X0)
| ~ relation(relation_rng(X0))
| ~ empty(X0)
| relation_rng(relation_rng(relation_rng(relation_rng(X0)))) = X1
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_395])]) ).
fof(f807,plain,
( spl15_96
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_rng(relation_rng(X1)) = X0
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_96])]) ).
fof(f1860,plain,
( spl15_177
<=> ! [X0] :
( ~ empty(X0)
| ~ relation(X0)
| ~ relation(relation_rng(X0))
| empty(relation_rng(relation_rng(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_177])]) ).
fof(f1888,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ relation(relation_rng(X0))
| ~ empty(X0)
| relation_rng(relation_rng(relation_rng(relation_rng(X0)))) = X1
| ~ empty(X1) )
| ~ spl15_96
| ~ spl15_177 ),
inference(resolution,[],[f1861,f808]) ).
fof(f808,plain,
( ! [X0,X1] :
( ~ empty(X1)
| relation_rng(relation_rng(X1)) = X0
| ~ empty(X0) )
| ~ spl15_96 ),
inference(avatar_component_clause,[],[f807]) ).
fof(f1861,plain,
( ! [X0] :
( empty(relation_rng(relation_rng(X0)))
| ~ relation(X0)
| ~ relation(relation_rng(X0))
| ~ empty(X0) )
| ~ spl15_177 ),
inference(avatar_component_clause,[],[f1860]) ).
fof(f6863,plain,
( spl15_394
| ~ spl15_18
| ~ spl15_371 ),
inference(avatar_split_clause,[],[f6255,f6212,f233,f6861]) ).
fof(f6861,plain,
( spl15_394
<=> ! [X0] :
( sK12 = relation_rng_restriction(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(X0))))))),sK4)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_394])]) ).
fof(f6212,plain,
( spl15_371
<=> ! [X0] :
( sK12 = relation_rng_restriction(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(X0)))))),sK4)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_371])]) ).
fof(f6255,plain,
( ! [X0] :
( sK12 = relation_rng_restriction(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(X0))))))),sK4)
| ~ empty(X0) )
| ~ spl15_18
| ~ spl15_371 ),
inference(resolution,[],[f6213,f234]) ).
fof(f6213,plain,
( ! [X0] :
( ~ empty(X0)
| sK12 = relation_rng_restriction(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(X0)))))),sK4) )
| ~ spl15_371 ),
inference(avatar_component_clause,[],[f6212]) ).
fof(f6829,plain,
( spl15_393
| ~ spl15_21
| ~ spl15_288 ),
inference(avatar_split_clause,[],[f4287,f4142,f246,f6827]) ).
fof(f6827,plain,
( spl15_393
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP0(X0,X1,X2)
| ~ sP0(X2,relation_rng(X2),X3)
| ~ relation(X2)
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_393])]) ).
fof(f4287,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP0(X0,X1,X2)
| ~ sP0(X2,relation_rng(X2),X3)
| ~ relation(X2)
| ~ empty(X3) )
| ~ spl15_21
| ~ spl15_288 ),
inference(resolution,[],[f4143,f247]) ).
fof(f6825,plain,
( spl15_392
| ~ spl15_21
| ~ spl15_287 ),
inference(avatar_split_clause,[],[f4247,f4138,f246,f6823]) ).
fof(f6823,plain,
( spl15_392
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP0(X1,X2,X0)
| ~ sP0(X1,relation_rng(X1),X3)
| ~ relation(X1)
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_392])]) ).
fof(f4247,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP0(X1,X2,X0)
| ~ sP0(X1,relation_rng(X1),X3)
| ~ relation(X1)
| ~ empty(X3) )
| ~ spl15_21
| ~ spl15_287 ),
inference(resolution,[],[f4139,f247]) ).
fof(f6821,plain,
( spl15_391
| ~ spl15_61
| ~ spl15_273 ),
inference(avatar_split_clause,[],[f3885,f3843,f511,f6819]) ).
fof(f6819,plain,
( spl15_391
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP0(X1,X2,X0)
| ~ sP0(X1,X2,relation_rng(X3))
| ~ relation(X3)
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_391])]) ).
fof(f3885,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP0(X1,X2,X0)
| ~ sP0(X1,X2,relation_rng(X3))
| ~ relation(X3)
| ~ empty(X3) )
| ~ spl15_61
| ~ spl15_273 ),
inference(resolution,[],[f3844,f512]) ).
fof(f6817,plain,
( spl15_390
| ~ spl15_21
| ~ spl15_244 ),
inference(avatar_split_clause,[],[f3093,f3058,f246,f6815]) ).
fof(f6815,plain,
( spl15_390
<=> ! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(relation_rng(X0))
| sP0(X1,X2,relation_rng(relation_rng(X0)))
| ~ empty(X0)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_390])]) ).
fof(f3093,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(relation_rng(X0))
| sP0(X1,X2,relation_rng(relation_rng(X0)))
| ~ empty(X0)
| ~ empty(X2) )
| ~ spl15_21
| ~ spl15_244 ),
inference(resolution,[],[f3059,f247]) ).
fof(f6794,plain,
( spl15_389
| ~ spl15_23
| ~ spl15_211 ),
inference(avatar_split_clause,[],[f2470,f2232,f263,f6792]) ).
fof(f6792,plain,
( spl15_389
<=> ! [X0,X1] :
( sP0(X0,relation_rng(X1),X1)
| ~ relation(X1)
| ~ in(relation_rng(X1),sK10(X0,relation_rng(X1),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_389])]) ).
fof(f2470,plain,
( ! [X0,X1] :
( sP0(X0,relation_rng(X1),X1)
| ~ relation(X1)
| ~ in(relation_rng(X1),sK10(X0,relation_rng(X1),X1)) )
| ~ spl15_23
| ~ spl15_211 ),
inference(resolution,[],[f2233,f264]) ).
fof(f6790,plain,
( spl15_388
| ~ spl15_24
| ~ spl15_211 ),
inference(avatar_split_clause,[],[f2469,f2232,f267,f6788]) ).
fof(f6788,plain,
( spl15_388
<=> ! [X0,X1] :
( sP0(X0,relation_rng(X1),X1)
| ~ relation(X1)
| element(sK10(X0,relation_rng(X1),X1),relation_rng(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_388])]) ).
fof(f2469,plain,
( ! [X0,X1] :
( sP0(X0,relation_rng(X1),X1)
| ~ relation(X1)
| element(sK10(X0,relation_rng(X1),X1),relation_rng(X1)) )
| ~ spl15_24
| ~ spl15_211 ),
inference(resolution,[],[f2233,f268]) ).
fof(f6786,plain,
( spl15_387
| ~ spl15_23
| ~ spl15_210 ),
inference(avatar_split_clause,[],[f2442,f2228,f263,f6784]) ).
fof(f6784,plain,
( spl15_387
<=> ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ relation(X2)
| ~ empty(X1)
| ~ in(relation_rng(X2),sK10(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_387])]) ).
fof(f2442,plain,
( ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ relation(X2)
| ~ empty(X1)
| ~ in(relation_rng(X2),sK10(X0,X1,X2)) )
| ~ spl15_23
| ~ spl15_210 ),
inference(resolution,[],[f2229,f264]) ).
fof(f6782,plain,
( spl15_386
| ~ spl15_24
| ~ spl15_210 ),
inference(avatar_split_clause,[],[f2441,f2228,f267,f6780]) ).
fof(f6780,plain,
( spl15_386
<=> ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ relation(X2)
| ~ empty(X1)
| element(sK10(X0,X1,X2),relation_rng(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_386])]) ).
fof(f2441,plain,
( ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ relation(X2)
| ~ empty(X1)
| element(sK10(X0,X1,X2),relation_rng(X2)) )
| ~ spl15_24
| ~ spl15_210 ),
inference(resolution,[],[f2229,f268]) ).
fof(f6778,plain,
( spl15_385
| ~ spl15_23
| ~ spl15_209 ),
inference(avatar_split_clause,[],[f2414,f2224,f263,f6776]) ).
fof(f6776,plain,
( spl15_385
<=> ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ relation(X2)
| ~ empty(relation_rng(X2))
| ~ in(X1,sK10(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_385])]) ).
fof(f2414,plain,
( ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ relation(X2)
| ~ empty(relation_rng(X2))
| ~ in(X1,sK10(X0,X1,X2)) )
| ~ spl15_23
| ~ spl15_209 ),
inference(resolution,[],[f2225,f264]) ).
fof(f6774,plain,
( spl15_384
| ~ spl15_24
| ~ spl15_209 ),
inference(avatar_split_clause,[],[f2413,f2224,f267,f6772]) ).
fof(f6772,plain,
( spl15_384
<=> ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ relation(X2)
| ~ empty(relation_rng(X2))
| element(sK10(X0,X1,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_384])]) ).
fof(f2413,plain,
( ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ relation(X2)
| ~ empty(relation_rng(X2))
| element(sK10(X0,X1,X2),X1) )
| ~ spl15_24
| ~ spl15_209 ),
inference(resolution,[],[f2225,f268]) ).
fof(f6770,plain,
( spl15_383
| ~ spl15_20
| ~ spl15_183 ),
inference(avatar_split_clause,[],[f2027,f1974,f242,f6768]) ).
fof(f6768,plain,
( spl15_383
<=> ! [X2,X0,X1] :
( ~ empty(relation_rng(X0))
| relation_rng_restriction(X1,relation_rng(X0)) = X2
| ~ relation(X2)
| ~ empty(X2)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_383])]) ).
fof(f2027,plain,
( ! [X2,X0,X1] :
( ~ empty(relation_rng(X0))
| relation_rng_restriction(X1,relation_rng(X0)) = X2
| ~ relation(X2)
| ~ empty(X2)
| ~ empty(X0) )
| ~ spl15_20
| ~ spl15_183 ),
inference(resolution,[],[f1975,f243]) ).
fof(f6766,plain,
( spl15_382
| ~ spl15_22
| ~ spl15_182 ),
inference(avatar_split_clause,[],[f2014,f1970,f259,f6764]) ).
fof(f6764,plain,
( spl15_382
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| relation_rng_restriction(X0,relation_rng_restriction(X1,X2)) = X3
| ~ relation(X3)
| ~ empty(X3)
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_382])]) ).
fof(f2014,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| relation_rng_restriction(X0,relation_rng_restriction(X1,X2)) = X3
| ~ relation(X3)
| ~ empty(X3)
| ~ relation(X2) )
| ~ spl15_22
| ~ spl15_182 ),
inference(resolution,[],[f1971,f260]) ).
fof(f6762,plain,
( spl15_381
| ~ spl15_22
| ~ spl15_108 ),
inference(avatar_split_clause,[],[f971,f915,f259,f6760]) ).
fof(f6760,plain,
( spl15_381
<=> ! [X2,X0,X1] :
( relation_rng_restriction(X1,X2) = relation_rng_restriction(X0,relation_rng_restriction(X1,X2))
| ~ empty(relation_rng_restriction(X1,X2))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_381])]) ).
fof(f915,plain,
( spl15_108
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_rng_restriction(X1,X0) = X0
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_108])]) ).
fof(f971,plain,
( ! [X2,X0,X1] :
( relation_rng_restriction(X1,X2) = relation_rng_restriction(X0,relation_rng_restriction(X1,X2))
| ~ empty(relation_rng_restriction(X1,X2))
| ~ relation(X2) )
| ~ spl15_22
| ~ spl15_108 ),
inference(resolution,[],[f916,f260]) ).
fof(f916,plain,
( ! [X0,X1] :
( ~ relation(X0)
| relation_rng_restriction(X1,X0) = X0
| ~ empty(X0) )
| ~ spl15_108 ),
inference(avatar_component_clause,[],[f915]) ).
fof(f6641,plain,
( spl15_380
| ~ spl15_18
| ~ spl15_358 ),
inference(avatar_split_clause,[],[f6142,f6029,f233,f6639]) ).
fof(f6639,plain,
( spl15_380
<=> ! [X0,X1] :
( relation_rng(relation_rng(X0)) = relation_rng_restriction(relation_rng(relation_rng(relation_rng(X1))),sK4)
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_380])]) ).
fof(f6029,plain,
( spl15_358
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_rng(relation_rng(X0)) = relation_rng_restriction(relation_rng(relation_rng(X1)),sK4)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_358])]) ).
fof(f6142,plain,
( ! [X0,X1] :
( relation_rng(relation_rng(X0)) = relation_rng_restriction(relation_rng(relation_rng(relation_rng(X1))),sK4)
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl15_18
| ~ spl15_358 ),
inference(resolution,[],[f6030,f234]) ).
fof(f6030,plain,
( ! [X0,X1] :
( ~ empty(X1)
| relation_rng(relation_rng(X0)) = relation_rng_restriction(relation_rng(relation_rng(X1)),sK4)
| ~ empty(X0) )
| ~ spl15_358 ),
inference(avatar_component_clause,[],[f6029]) ).
fof(f6246,plain,
( spl15_379
| ~ spl15_21
| ~ spl15_277 ),
inference(avatar_split_clause,[],[f4045,f3973,f246,f6244]) ).
fof(f6244,plain,
( spl15_379
<=> ! [X2,X0,X1] :
( ~ in(X0,relation_rng(relation_rng_restriction(X1,X2)))
| ~ relation(relation_rng_restriction(X1,X2))
| ~ relation(X2)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_379])]) ).
fof(f4045,plain,
( ! [X2,X0,X1] :
( ~ in(X0,relation_rng(relation_rng_restriction(X1,X2)))
| ~ relation(relation_rng_restriction(X1,X2))
| ~ relation(X2)
| ~ empty(X2) )
| ~ spl15_21
| ~ spl15_277 ),
inference(resolution,[],[f3974,f247]) ).
fof(f6242,plain,
( spl15_378
| ~ spl15_176
| ~ spl15_258 ),
inference(avatar_split_clause,[],[f3500,f3446,f1837,f6240]) ).
fof(f6240,plain,
( spl15_378
<=> ! [X0,X1] :
( sP0(relation_rng_restriction(X0,X1),X0,relation_rng_restriction(X0,X1))
| ~ relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_378])]) ).
fof(f1837,plain,
( spl15_176
<=> ! [X0,X1] :
( sP0(X0,X1,X0)
| ~ in(sK10(X0,X1,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_176])]) ).
fof(f3500,plain,
( ! [X0,X1] :
( sP0(relation_rng_restriction(X0,X1),X0,relation_rng_restriction(X0,X1))
| ~ relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) )
| ~ spl15_176
| ~ spl15_258 ),
inference(duplicate_literal_removal,[],[f3488]) ).
fof(f3488,plain,
( ! [X0,X1] :
( sP0(relation_rng_restriction(X0,X1),X0,relation_rng_restriction(X0,X1))
| ~ relation(relation_rng_restriction(X0,X1))
| ~ relation(X1)
| sP0(relation_rng_restriction(X0,X1),X0,relation_rng_restriction(X0,X1)) )
| ~ spl15_176
| ~ spl15_258 ),
inference(resolution,[],[f3447,f1838]) ).
fof(f1838,plain,
( ! [X0,X1] :
( ~ in(sK10(X0,X1,X0),X1)
| sP0(X0,X1,X0) )
| ~ spl15_176 ),
inference(avatar_component_clause,[],[f1837]) ).
fof(f6238,plain,
( spl15_377
| ~ spl15_21
| ~ spl15_241 ),
inference(avatar_split_clause,[],[f2987,f2827,f246,f6236]) ).
fof(f6236,plain,
( spl15_377
<=> ! [X2,X0,X1] :
( ~ relation(X0)
| sP0(X1,X2,relation_rng(X0))
| ~ empty(X0)
| ~ relation(X1)
| ~ empty(relation_rng(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_377])]) ).
fof(f2987,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| sP0(X1,X2,relation_rng(X0))
| ~ empty(X0)
| ~ relation(X1)
| ~ empty(relation_rng(X1)) )
| ~ spl15_21
| ~ spl15_241 ),
inference(resolution,[],[f2828,f247]) ).
fof(f6234,plain,
( spl15_376
| ~ spl15_21
| ~ spl15_240 ),
inference(avatar_split_clause,[],[f2956,f2823,f246,f6232]) ).
fof(f6232,plain,
( spl15_376
<=> ! [X2,X0,X1] :
( ~ relation(X0)
| sP0(relation_rng(X0),X1,X2)
| ~ empty(X0)
| ~ relation(X2)
| ~ empty(relation_rng(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_376])]) ).
fof(f2956,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| sP0(relation_rng(X0),X1,X2)
| ~ empty(X0)
| ~ relation(X2)
| ~ empty(relation_rng(X2)) )
| ~ spl15_21
| ~ spl15_240 ),
inference(resolution,[],[f2824,f247]) ).
fof(f6230,plain,
( spl15_375
| ~ spl15_21
| ~ spl15_239 ),
inference(avatar_split_clause,[],[f2930,f2819,f246,f6228]) ).
fof(f6228,plain,
( spl15_375
<=> ! [X0,X1] :
( ~ relation(relation_rng_restriction(X0,X1))
| relation_rng(relation_rng_restriction(X0,X1)) = X0
| ~ relation(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_375])]) ).
fof(f2930,plain,
( ! [X0,X1] :
( ~ relation(relation_rng_restriction(X0,X1))
| relation_rng(relation_rng_restriction(X0,X1)) = X0
| ~ relation(X1)
| ~ empty(X0) )
| ~ spl15_21
| ~ spl15_239 ),
inference(resolution,[],[f2820,f247]) ).
fof(f6226,plain,
( spl15_374
| ~ spl15_20
| ~ spl15_217 ),
inference(avatar_split_clause,[],[f2559,f2529,f242,f6224]) ).
fof(f6224,plain,
( spl15_374
<=> ! [X2,X0,X1] :
( ~ relation(X0)
| ~ empty(X0)
| relation_rng(X0) = relation_rng_restriction(X1,X2)
| ~ empty(X2)
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_374])]) ).
fof(f2529,plain,
( spl15_217
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| ~ relation(X1)
| ~ empty(X1)
| relation_rng(X1) = relation_rng_restriction(X2,X0)
| ~ relation(relation_rng(X1))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_217])]) ).
fof(f2559,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| ~ empty(X0)
| relation_rng(X0) = relation_rng_restriction(X1,X2)
| ~ empty(X2)
| ~ relation(X2) )
| ~ spl15_20
| ~ spl15_217 ),
inference(duplicate_literal_removal,[],[f2556]) ).
fof(f2556,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| ~ empty(X0)
| relation_rng(X0) = relation_rng_restriction(X1,X2)
| ~ empty(X2)
| ~ relation(X2)
| ~ empty(X0) )
| ~ spl15_20
| ~ spl15_217 ),
inference(resolution,[],[f2530,f243]) ).
fof(f2530,plain,
( ! [X2,X0,X1] :
( ~ relation(relation_rng(X1))
| ~ relation(X1)
| ~ empty(X1)
| relation_rng(X1) = relation_rng_restriction(X2,X0)
| ~ empty(X0)
| ~ relation(X0) )
| ~ spl15_217 ),
inference(avatar_component_clause,[],[f2529]) ).
fof(f6222,plain,
( spl15_373
| ~ spl15_20
| ~ spl15_216 ),
inference(avatar_split_clause,[],[f2555,f2514,f242,f6220]) ).
fof(f6220,plain,
( spl15_373
<=> ! [X2,X0,X1] :
( ~ relation(X0)
| ~ empty(X0)
| relation_rng_restriction(X1,relation_rng(X0)) = X2
| ~ relation(X2)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_373])]) ).
fof(f2514,plain,
( spl15_216
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| ~ relation(X1)
| ~ empty(X1)
| relation_rng_restriction(X2,relation_rng(X1)) = X0
| ~ relation(X0)
| ~ relation(relation_rng(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_216])]) ).
fof(f2555,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| ~ empty(X0)
| relation_rng_restriction(X1,relation_rng(X0)) = X2
| ~ relation(X2)
| ~ empty(X2) )
| ~ spl15_20
| ~ spl15_216 ),
inference(duplicate_literal_removal,[],[f2552]) ).
fof(f2552,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| ~ empty(X0)
| relation_rng_restriction(X1,relation_rng(X0)) = X2
| ~ relation(X2)
| ~ empty(X2)
| ~ empty(X0) )
| ~ spl15_20
| ~ spl15_216 ),
inference(resolution,[],[f2515,f243]) ).
fof(f2515,plain,
( ! [X2,X0,X1] :
( ~ relation(relation_rng(X1))
| ~ relation(X1)
| ~ empty(X1)
| relation_rng_restriction(X2,relation_rng(X1)) = X0
| ~ relation(X0)
| ~ empty(X0) )
| ~ spl15_216 ),
inference(avatar_component_clause,[],[f2514]) ).
fof(f6218,plain,
( spl15_372
| ~ spl15_7
| ~ spl15_213 ),
inference(avatar_split_clause,[],[f2502,f2486,f181,f6216]) ).
fof(f6216,plain,
( spl15_372
<=> ! [X0,X1] :
( ~ relation(X0)
| ~ empty(X0)
| relation_rng_restriction(relation_rng(X0),sK13) = X1
| ~ relation(X1)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_372])]) ).
fof(f181,plain,
( spl15_7
<=> relation(sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_7])]) ).
fof(f2502,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ empty(X0)
| relation_rng_restriction(relation_rng(X0),sK13) = X1
| ~ relation(X1)
| ~ empty(X1) )
| ~ spl15_7
| ~ spl15_213 ),
inference(resolution,[],[f2487,f183]) ).
fof(f183,plain,
( relation(sK13)
| ~ spl15_7 ),
inference(avatar_component_clause,[],[f181]) ).
fof(f6214,plain,
( spl15_371
| ~ spl15_18
| ~ spl15_303 ),
inference(avatar_split_clause,[],[f4771,f4650,f233,f6212]) ).
fof(f4650,plain,
( spl15_303
<=> ! [X0] :
( sK12 = relation_rng_restriction(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(X0))))),sK4)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_303])]) ).
fof(f4771,plain,
( ! [X0] :
( sK12 = relation_rng_restriction(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(X0)))))),sK4)
| ~ empty(X0) )
| ~ spl15_18
| ~ spl15_303 ),
inference(resolution,[],[f4651,f234]) ).
fof(f4651,plain,
( ! [X0] :
( ~ empty(X0)
| sK12 = relation_rng_restriction(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(X0))))),sK4) )
| ~ spl15_303 ),
inference(avatar_component_clause,[],[f4650]) ).
fof(f6210,plain,
( spl15_370
| ~ spl15_101
| ~ spl15_211 ),
inference(avatar_split_clause,[],[f2474,f2232,f868,f6208]) ).
fof(f6208,plain,
( spl15_370
<=> ! [X0,X1] :
( sP0(X0,relation_rng(relation_rng(X1)),relation_rng(X1))
| ~ relation(relation_rng(X1))
| ~ empty(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_370])]) ).
fof(f2474,plain,
( ! [X0,X1] :
( sP0(X0,relation_rng(relation_rng(X1)),relation_rng(X1))
| ~ relation(relation_rng(X1))
| ~ empty(X1)
| ~ relation(X1) )
| ~ spl15_101
| ~ spl15_211 ),
inference(duplicate_literal_removal,[],[f2467]) ).
fof(f2467,plain,
( ! [X0,X1] :
( sP0(X0,relation_rng(relation_rng(X1)),relation_rng(X1))
| ~ relation(relation_rng(X1))
| ~ empty(X1)
| ~ relation(X1)
| ~ relation(relation_rng(X1)) )
| ~ spl15_101
| ~ spl15_211 ),
inference(resolution,[],[f2233,f869]) ).
fof(f6178,plain,
( ~ spl15_19
| spl15_369
| ~ spl15_74
| ~ spl15_210 ),
inference(avatar_split_clause,[],[f2444,f2228,f614,f6176,f237]) ).
fof(f6176,plain,
( spl15_369
<=> ! [X0,X1] :
( in(sK10(X0,X1,sK12),sK12)
| ~ empty(X1)
| sP0(X0,X1,sK12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_369])]) ).
fof(f2444,plain,
( ! [X0,X1] :
( in(sK10(X0,X1,sK12),sK12)
| sP0(X0,X1,sK12)
| ~ relation(sK12)
| ~ empty(X1) )
| ~ spl15_74
| ~ spl15_210 ),
inference(superposition,[],[f2229,f616]) ).
fof(f6174,plain,
( spl15_368
| ~ spl15_61
| ~ spl15_209 ),
inference(avatar_split_clause,[],[f2416,f2224,f511,f6172]) ).
fof(f6172,plain,
( spl15_368
<=> ! [X2,X0,X1] :
( sP0(X0,relation_rng(X1),X2)
| ~ relation(X2)
| ~ empty(relation_rng(X2))
| ~ relation(X1)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_368])]) ).
fof(f2416,plain,
( ! [X2,X0,X1] :
( sP0(X0,relation_rng(X1),X2)
| ~ relation(X2)
| ~ empty(relation_rng(X2))
| ~ relation(X1)
| ~ empty(X1) )
| ~ spl15_61
| ~ spl15_209 ),
inference(resolution,[],[f2225,f512]) ).
fof(f6170,plain,
( ~ spl15_19
| spl15_367
| ~ spl15_74
| ~ spl15_203 ),
inference(avatar_split_clause,[],[f2398,f2180,f614,f6168,f237]) ).
fof(f6168,plain,
( spl15_367
<=> ! [X0,X1] :
( ~ in(sK12,sK10(X0,X1,sK12))
| ~ empty(X0)
| sP0(X0,X1,sK12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_367])]) ).
fof(f2180,plain,
( spl15_203
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| sP0(X0,X1,X2)
| ~ relation(X2)
| ~ in(relation_rng(X2),sK10(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_203])]) ).
fof(f2398,plain,
( ! [X0,X1] :
( ~ in(sK12,sK10(X0,X1,sK12))
| sP0(X0,X1,sK12)
| ~ relation(sK12)
| ~ empty(X0) )
| ~ spl15_74
| ~ spl15_203 ),
inference(superposition,[],[f2181,f616]) ).
fof(f2181,plain,
( ! [X2,X0,X1] :
( ~ in(relation_rng(X2),sK10(X0,X1,X2))
| sP0(X0,X1,X2)
| ~ relation(X2)
| ~ empty(X0) )
| ~ spl15_203 ),
inference(avatar_component_clause,[],[f2180]) ).
fof(f6165,plain,
( ~ spl15_19
| spl15_366
| ~ spl15_74
| ~ spl15_202 ),
inference(avatar_split_clause,[],[f2397,f2176,f614,f6163,f237]) ).
fof(f6163,plain,
( spl15_366
<=> ! [X0,X1] :
( element(sK10(X0,X1,sK12),sK12)
| ~ empty(X0)
| sP0(X0,X1,sK12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_366])]) ).
fof(f2176,plain,
( spl15_202
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| sP0(X0,X1,X2)
| ~ relation(X2)
| element(sK10(X0,X1,X2),relation_rng(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_202])]) ).
fof(f2397,plain,
( ! [X0,X1] :
( element(sK10(X0,X1,sK12),sK12)
| sP0(X0,X1,sK12)
| ~ relation(sK12)
| ~ empty(X0) )
| ~ spl15_74
| ~ spl15_202 ),
inference(superposition,[],[f2177,f616]) ).
fof(f2177,plain,
( ! [X2,X0,X1] :
( element(sK10(X0,X1,X2),relation_rng(X2))
| sP0(X0,X1,X2)
| ~ relation(X2)
| ~ empty(X0) )
| ~ spl15_202 ),
inference(avatar_component_clause,[],[f2176]) ).
fof(f6161,plain,
( ~ spl15_19
| spl15_365
| ~ spl15_74
| ~ spl15_201 ),
inference(avatar_split_clause,[],[f2395,f2172,f614,f6159,f237]) ).
fof(f6159,plain,
( spl15_365
<=> ! [X0,X1] :
( ~ in(sK12,sK10(sK12,X0,X1))
| ~ empty(X1)
| sP0(sK12,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_365])]) ).
fof(f2172,plain,
( spl15_201
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| sP0(X1,X2,X0)
| ~ relation(X1)
| ~ in(relation_rng(X1),sK10(X1,X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_201])]) ).
fof(f2395,plain,
( ! [X0,X1] :
( ~ in(sK12,sK10(sK12,X0,X1))
| sP0(sK12,X0,X1)
| ~ relation(sK12)
| ~ empty(X1) )
| ~ spl15_74
| ~ spl15_201 ),
inference(superposition,[],[f2173,f616]) ).
fof(f2173,plain,
( ! [X2,X0,X1] :
( ~ in(relation_rng(X1),sK10(X1,X2,X0))
| sP0(X1,X2,X0)
| ~ relation(X1)
| ~ empty(X0) )
| ~ spl15_201 ),
inference(avatar_component_clause,[],[f2172]) ).
fof(f6140,plain,
( ~ spl15_19
| spl15_364
| ~ spl15_74
| ~ spl15_200 ),
inference(avatar_split_clause,[],[f2394,f2168,f614,f6138,f237]) ).
fof(f6138,plain,
( spl15_364
<=> ! [X0,X1] :
( element(sK10(sK12,X0,X1),sK12)
| ~ empty(X1)
| sP0(sK12,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_364])]) ).
fof(f2168,plain,
( spl15_200
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| sP0(X1,X2,X0)
| ~ relation(X1)
| element(sK10(X1,X2,X0),relation_rng(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_200])]) ).
fof(f2394,plain,
( ! [X0,X1] :
( element(sK10(sK12,X0,X1),sK12)
| sP0(sK12,X0,X1)
| ~ relation(sK12)
| ~ empty(X1) )
| ~ spl15_74
| ~ spl15_200 ),
inference(superposition,[],[f2169,f616]) ).
fof(f2169,plain,
( ! [X2,X0,X1] :
( element(sK10(X1,X2,X0),relation_rng(X1))
| sP0(X1,X2,X0)
| ~ relation(X1)
| ~ empty(X0) )
| ~ spl15_200 ),
inference(avatar_component_clause,[],[f2168]) ).
fof(f6136,plain,
( spl15_363
| ~ spl15_20
| ~ spl15_182 ),
inference(avatar_split_clause,[],[f2015,f1970,f242,f6134]) ).
fof(f6134,plain,
( spl15_363
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| relation_rng_restriction(X0,relation_rng(X1)) = X2
| ~ relation(X2)
| ~ empty(X2)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_363])]) ).
fof(f2015,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| relation_rng_restriction(X0,relation_rng(X1)) = X2
| ~ relation(X2)
| ~ empty(X2)
| ~ empty(X1) )
| ~ spl15_20
| ~ spl15_182 ),
inference(resolution,[],[f1971,f243]) ).
fof(f6132,plain,
( spl15_362
| ~ spl15_65
| ~ spl15_180 ),
inference(avatar_split_clause,[],[f1945,f1872,f548,f6130]) ).
fof(f6130,plain,
( spl15_362
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| ~ relation(X1)
| ~ empty(relation_rng(X1))
| relation_rng_restriction(X2,X0) = X1
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_362])]) ).
fof(f1872,plain,
( spl15_180
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| sP0(X0,X1,X2)
| ~ relation(X2)
| ~ empty(relation_rng(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_180])]) ).
fof(f1945,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| ~ relation(X1)
| ~ empty(relation_rng(X1))
| relation_rng_restriction(X2,X0) = X1
| ~ relation(X0) )
| ~ spl15_65
| ~ spl15_180 ),
inference(duplicate_literal_removal,[],[f1919]) ).
fof(f1919,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| ~ relation(X1)
| ~ empty(relation_rng(X1))
| relation_rng_restriction(X2,X0) = X1
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl15_65
| ~ spl15_180 ),
inference(resolution,[],[f1873,f549]) ).
fof(f1873,plain,
( ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ empty(X0)
| ~ relation(X2)
| ~ empty(relation_rng(X2)) )
| ~ spl15_180 ),
inference(avatar_component_clause,[],[f1872]) ).
fof(f6128,plain,
( spl15_361
| ~ spl15_65
| ~ spl15_179 ),
inference(avatar_split_clause,[],[f1918,f1868,f548,f6126]) ).
fof(f6126,plain,
( spl15_361
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| ~ relation(X1)
| ~ empty(relation_rng(X1))
| relation_rng_restriction(X2,X1) = X0
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_361])]) ).
fof(f1868,plain,
( spl15_179
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| sP0(X1,X2,X0)
| ~ relation(X1)
| ~ empty(relation_rng(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_179])]) ).
fof(f1918,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| ~ relation(X1)
| ~ empty(relation_rng(X1))
| relation_rng_restriction(X2,X1) = X0
| ~ relation(X0) )
| ~ spl15_65
| ~ spl15_179 ),
inference(duplicate_literal_removal,[],[f1895]) ).
fof(f1895,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| ~ relation(X1)
| ~ empty(relation_rng(X1))
| relation_rng_restriction(X2,X1) = X0
| ~ relation(X0)
| ~ relation(X1) )
| ~ spl15_65
| ~ spl15_179 ),
inference(resolution,[],[f1869,f549]) ).
fof(f1869,plain,
( ! [X2,X0,X1] :
( sP0(X1,X2,X0)
| ~ empty(X0)
| ~ relation(X1)
| ~ empty(relation_rng(X1)) )
| ~ spl15_179 ),
inference(avatar_component_clause,[],[f1868]) ).
fof(f6075,plain,
( spl15_360
| ~ spl15_21
| ~ spl15_278 ),
inference(avatar_split_clause,[],[f4069,f3977,f246,f6073]) ).
fof(f6073,plain,
( spl15_360
<=> ! [X2,X0,X1] :
( ~ sP0(X0,relation_rng(X0),X1)
| sP0(X0,X2,X0)
| ~ relation(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_360])]) ).
fof(f4069,plain,
( ! [X2,X0,X1] :
( ~ sP0(X0,relation_rng(X0),X1)
| sP0(X0,X2,X0)
| ~ relation(X0)
| ~ empty(X1) )
| ~ spl15_21
| ~ spl15_278 ),
inference(resolution,[],[f3978,f247]) ).
fof(f6071,plain,
( spl15_359
| ~ spl15_23
| ~ spl15_204 ),
inference(avatar_split_clause,[],[f2194,f2184,f263,f6069]) ).
fof(f6069,plain,
( spl15_359
<=> ! [X0] :
( sK12 = X0
| element(sK5(sK12,X0),sK12)
| ~ in(X0,sK5(sK12,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_359])]) ).
fof(f2184,plain,
( spl15_204
<=> ! [X0] :
( element(sK5(sK12,X0),sK12)
| sK12 = X0
| in(sK5(sK12,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_204])]) ).
fof(f2194,plain,
( ! [X0] :
( sK12 = X0
| element(sK5(sK12,X0),sK12)
| ~ in(X0,sK5(sK12,X0)) )
| ~ spl15_23
| ~ spl15_204 ),
inference(resolution,[],[f2185,f264]) ).
fof(f2185,plain,
( ! [X0] :
( in(sK5(sK12,X0),X0)
| sK12 = X0
| element(sK5(sK12,X0),sK12) )
| ~ spl15_204 ),
inference(avatar_component_clause,[],[f2184]) ).
fof(f6031,plain,
( spl15_358
| ~ spl15_18
| ~ spl15_347 ),
inference(avatar_split_clause,[],[f5867,f5763,f233,f6029]) ).
fof(f5763,plain,
( spl15_347
<=> ! [X0,X1] :
( relation_rng(relation_rng(X0)) = relation_rng_restriction(relation_rng(X1),sK4)
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_347])]) ).
fof(f5867,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_rng(relation_rng(X0)) = relation_rng_restriction(relation_rng(relation_rng(X1)),sK4)
| ~ empty(X1) )
| ~ spl15_18
| ~ spl15_347 ),
inference(resolution,[],[f5764,f234]) ).
fof(f5764,plain,
( ! [X0,X1] :
( ~ empty(X1)
| ~ empty(X0)
| relation_rng(relation_rng(X0)) = relation_rng_restriction(relation_rng(X1),sK4) )
| ~ spl15_347 ),
inference(avatar_component_clause,[],[f5763]) ).
fof(f6009,plain,
( spl15_357
| ~ spl15_21
| ~ spl15_273 ),
inference(avatar_split_clause,[],[f3874,f3843,f246,f6007]) ).
fof(f6007,plain,
( spl15_357
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP0(X1,X2,X0)
| ~ sP0(X1,X2,X3)
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_357])]) ).
fof(f3874,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP0(X1,X2,X0)
| ~ sP0(X1,X2,X3)
| ~ empty(X3) )
| ~ spl15_21
| ~ spl15_273 ),
inference(resolution,[],[f3844,f247]) ).
fof(f5977,plain,
( ~ spl15_19
| spl15_356
| ~ spl15_74
| ~ spl15_211 ),
inference(avatar_split_clause,[],[f2472,f2232,f614,f5975,f237]) ).
fof(f5975,plain,
( spl15_356
<=> ! [X0] :
( in(sK10(X0,sK12,sK12),sK12)
| sP0(X0,sK12,sK12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_356])]) ).
fof(f2472,plain,
( ! [X0] :
( in(sK10(X0,sK12,sK12),sK12)
| sP0(X0,sK12,sK12)
| ~ relation(sK12) )
| ~ spl15_74
| ~ spl15_211 ),
inference(superposition,[],[f2233,f616]) ).
fof(f5973,plain,
( spl15_355
| ~ spl15_18
| ~ spl15_198 ),
inference(avatar_split_clause,[],[f2343,f2160,f233,f5971]) ).
fof(f5971,plain,
( spl15_355
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_rng(X0) = relation_rng(relation_rng(X1))
| ~ relation(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_355])]) ).
fof(f2160,plain,
( spl15_198
<=> ! [X0,X1] :
( ~ relation(X0)
| ~ empty(X0)
| relation_rng(X0) = relation_rng(relation_rng(X1))
| ~ empty(relation_rng(X1))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_198])]) ).
fof(f2343,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_rng(X0) = relation_rng(relation_rng(X1))
| ~ relation(X0)
| ~ empty(X1) )
| ~ spl15_18
| ~ spl15_198 ),
inference(duplicate_literal_removal,[],[f2339]) ).
fof(f2339,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_rng(X0) = relation_rng(relation_rng(X1))
| ~ relation(X0)
| ~ empty(X1)
| ~ empty(X1) )
| ~ spl15_18
| ~ spl15_198 ),
inference(resolution,[],[f2161,f234]) ).
fof(f2161,plain,
( ! [X0,X1] :
( ~ empty(relation_rng(X1))
| ~ empty(X0)
| relation_rng(X0) = relation_rng(relation_rng(X1))
| ~ relation(X0)
| ~ empty(X1) )
| ~ spl15_198 ),
inference(avatar_component_clause,[],[f2160]) ).
fof(f5969,plain,
( spl15_354
| ~ spl15_20
| ~ spl15_108 ),
inference(avatar_split_clause,[],[f972,f915,f242,f5967]) ).
fof(f5967,plain,
( spl15_354
<=> ! [X0,X1] :
( relation_rng(X1) = relation_rng_restriction(X0,relation_rng(X1))
| ~ empty(relation_rng(X1))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_354])]) ).
fof(f972,plain,
( ! [X0,X1] :
( relation_rng(X1) = relation_rng_restriction(X0,relation_rng(X1))
| ~ empty(relation_rng(X1))
| ~ empty(X1) )
| ~ spl15_20
| ~ spl15_108 ),
inference(resolution,[],[f916,f243]) ).
fof(f5847,plain,
( spl15_353
| ~ spl15_21
| ~ spl15_209 ),
inference(avatar_split_clause,[],[f2415,f2224,f246,f5845]) ).
fof(f5845,plain,
( spl15_353
<=> ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ relation(X2)
| ~ empty(relation_rng(X2))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_353])]) ).
fof(f2415,plain,
( ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ relation(X2)
| ~ empty(relation_rng(X2))
| ~ empty(X1) )
| ~ spl15_21
| ~ spl15_209 ),
inference(resolution,[],[f2225,f247]) ).
fof(f5843,plain,
( spl15_352
| ~ spl15_20
| ~ spl15_186 ),
inference(avatar_split_clause,[],[f2078,f2044,f242,f5841]) ).
fof(f5841,plain,
( spl15_352
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_rng(X0) = relation_rng_restriction(X1,relation_rng(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_352])]) ).
fof(f2044,plain,
( spl15_186
<=> ! [X0,X1] :
( ~ relation(X0)
| ~ empty(X0)
| relation_rng(X0) = relation_rng_restriction(X1,relation_rng(X0))
| ~ relation(relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_186])]) ).
fof(f2078,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_rng(X0) = relation_rng_restriction(X1,relation_rng(X0))
| ~ relation(X0) )
| ~ spl15_20
| ~ spl15_186 ),
inference(duplicate_literal_removal,[],[f2075]) ).
fof(f2075,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_rng(X0) = relation_rng_restriction(X1,relation_rng(X0))
| ~ relation(X0)
| ~ empty(X0) )
| ~ spl15_20
| ~ spl15_186 ),
inference(resolution,[],[f2045,f243]) ).
fof(f2045,plain,
( ! [X0,X1] :
( ~ relation(relation_rng(X0))
| ~ empty(X0)
| relation_rng(X0) = relation_rng_restriction(X1,relation_rng(X0))
| ~ relation(X0) )
| ~ spl15_186 ),
inference(avatar_component_clause,[],[f2044]) ).
fof(f5839,plain,
( spl15_351
| ~ spl15_7
| ~ spl15_182 ),
inference(avatar_split_clause,[],[f2019,f1970,f181,f5837]) ).
fof(f5837,plain,
( spl15_351
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_rng_restriction(X0,sK13) = X1
| ~ relation(X1)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_351])]) ).
fof(f2019,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_rng_restriction(X0,sK13) = X1
| ~ relation(X1)
| ~ empty(X1) )
| ~ spl15_7
| ~ spl15_182 ),
inference(resolution,[],[f1971,f183]) ).
fof(f5835,plain,
( spl15_350
| ~ spl15_14
| ~ spl15_177 ),
inference(avatar_split_clause,[],[f1880,f1860,f214,f5833]) ).
fof(f5833,plain,
( spl15_350
<=> ! [X0] :
( ~ relation(X0)
| ~ relation(relation_rng(X0))
| ~ empty(X0)
| relation(relation_rng(relation_rng(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_350])]) ).
fof(f214,plain,
( spl15_14
<=> ! [X0] :
( relation(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_14])]) ).
fof(f1880,plain,
( ! [X0] :
( ~ relation(X0)
| ~ relation(relation_rng(X0))
| ~ empty(X0)
| relation(relation_rng(relation_rng(X0))) )
| ~ spl15_14
| ~ spl15_177 ),
inference(resolution,[],[f1861,f215]) ).
fof(f215,plain,
( ! [X0] :
( ~ empty(X0)
| relation(X0) )
| ~ spl15_14 ),
inference(avatar_component_clause,[],[f214]) ).
fof(f5831,plain,
( spl15_349
| ~ spl15_18
| ~ spl15_173 ),
inference(avatar_split_clause,[],[f1840,f1769,f233,f5829]) ).
fof(f5829,plain,
( spl15_349
<=> ! [X0,X1] :
( relation_rng(X1) = relation_rng(relation_rng(relation_rng(X0)))
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_349])]) ).
fof(f1769,plain,
( spl15_173
<=> ! [X0,X1] :
( relation_rng(relation_rng(relation_rng(X0))) = X1
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_173])]) ).
fof(f1840,plain,
( ! [X0,X1] :
( relation_rng(X1) = relation_rng(relation_rng(relation_rng(X0)))
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl15_18
| ~ spl15_173 ),
inference(resolution,[],[f1770,f234]) ).
fof(f1770,plain,
( ! [X0,X1] :
( ~ empty(X1)
| relation_rng(relation_rng(relation_rng(X0))) = X1
| ~ empty(X0) )
| ~ spl15_173 ),
inference(avatar_component_clause,[],[f1769]) ).
fof(f5769,plain,
( spl15_348
| ~ spl15_21
| ~ spl15_211 ),
inference(avatar_split_clause,[],[f2471,f2232,f246,f5767]) ).
fof(f5767,plain,
( spl15_348
<=> ! [X0,X1] :
( sP0(X0,relation_rng(X1),X1)
| ~ relation(X1)
| ~ empty(relation_rng(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_348])]) ).
fof(f2471,plain,
( ! [X0,X1] :
( sP0(X0,relation_rng(X1),X1)
| ~ relation(X1)
| ~ empty(relation_rng(X1)) )
| ~ spl15_21
| ~ spl15_211 ),
inference(resolution,[],[f2233,f247]) ).
fof(f5765,plain,
( spl15_347
| ~ spl15_18
| ~ spl15_336 ),
inference(avatar_split_clause,[],[f5636,f5561,f233,f5763]) ).
fof(f5561,plain,
( spl15_336
<=> ! [X0,X1] :
( relation_rng(relation_rng(X0)) = relation_rng_restriction(X1,sK4)
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_336])]) ).
fof(f5636,plain,
( ! [X0,X1] :
( relation_rng(relation_rng(X0)) = relation_rng_restriction(relation_rng(X1),sK4)
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl15_18
| ~ spl15_336 ),
inference(resolution,[],[f5562,f234]) ).
fof(f5562,plain,
( ! [X0,X1] :
( ~ empty(X1)
| relation_rng(relation_rng(X0)) = relation_rng_restriction(X1,sK4)
| ~ empty(X0) )
| ~ spl15_336 ),
inference(avatar_component_clause,[],[f5561]) ).
fof(f5760,plain,
( ~ spl15_5
| spl15_346
| ~ spl15_21
| ~ spl15_207 ),
inference(avatar_split_clause,[],[f2212,f2204,f246,f5758,f171]) ).
fof(f5758,plain,
( spl15_346
<=> ! [X0] :
( element(sK5(sK12,X0),X0)
| sK12 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_346])]) ).
fof(f2204,plain,
( spl15_207
<=> ! [X0] :
( in(sK5(sK12,X0),sK12)
| sK12 = X0
| element(sK5(sK12,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_207])]) ).
fof(f2212,plain,
( ! [X0] :
( element(sK5(sK12,X0),X0)
| sK12 = X0
| ~ empty(sK12) )
| ~ spl15_21
| ~ spl15_207 ),
inference(resolution,[],[f2205,f247]) ).
fof(f2205,plain,
( ! [X0] :
( element(sK5(sK12,X0),X0)
| in(sK5(sK12,X0),sK12)
| sK12 = X0 )
| ~ spl15_207 ),
inference(avatar_component_clause,[],[f2204]) ).
fof(f5756,plain,
( spl15_345
| ~ spl15_65
| ~ spl15_152 ),
inference(avatar_split_clause,[],[f1526,f1443,f548,f5754]) ).
fof(f5754,plain,
( spl15_345
<=> ! [X0,X1] :
( ~ relation(X0)
| ~ empty(relation_rng(X0))
| relation_rng_restriction(X1,X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_345])]) ).
fof(f1443,plain,
( spl15_152
<=> ! [X0,X1] :
( sP0(X0,X1,X0)
| ~ relation(X0)
| ~ empty(relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_152])]) ).
fof(f1526,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ empty(relation_rng(X0))
| relation_rng_restriction(X1,X0) = X0 )
| ~ spl15_65
| ~ spl15_152 ),
inference(duplicate_literal_removal,[],[f1508]) ).
fof(f1508,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ empty(relation_rng(X0))
| relation_rng_restriction(X1,X0) = X0
| ~ relation(X0)
| ~ relation(X0) )
| ~ spl15_65
| ~ spl15_152 ),
inference(resolution,[],[f1444,f549]) ).
fof(f1444,plain,
( ! [X0,X1] :
( sP0(X0,X1,X0)
| ~ relation(X0)
| ~ empty(relation_rng(X0)) )
| ~ spl15_152 ),
inference(avatar_component_clause,[],[f1443]) ).
fof(f5698,plain,
( spl15_344
| ~ spl15_61
| ~ spl15_211 ),
inference(avatar_split_clause,[],[f2475,f2232,f511,f5696]) ).
fof(f5696,plain,
( spl15_344
<=> ! [X0,X1] :
( sP0(X0,relation_rng(X1),X1)
| ~ relation(X1)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_344])]) ).
fof(f2475,plain,
( ! [X0,X1] :
( sP0(X0,relation_rng(X1),X1)
| ~ relation(X1)
| ~ empty(X1) )
| ~ spl15_61
| ~ spl15_211 ),
inference(duplicate_literal_removal,[],[f2466]) ).
fof(f2466,plain,
( ! [X0,X1] :
( sP0(X0,relation_rng(X1),X1)
| ~ relation(X1)
| ~ relation(X1)
| ~ empty(X1) )
| ~ spl15_61
| ~ spl15_211 ),
inference(resolution,[],[f2233,f512]) ).
fof(f5685,plain,
( spl15_343
| ~ spl15_1
| ~ spl15_213 ),
inference(avatar_split_clause,[],[f2500,f2486,f151,f5683]) ).
fof(f5683,plain,
( spl15_343
<=> ! [X0,X1] :
( ~ relation(X0)
| ~ empty(X0)
| relation_rng_restriction(relation_rng(X0),sK4) = X1
| ~ relation(X1)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_343])]) ).
fof(f2500,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ empty(X0)
| relation_rng_restriction(relation_rng(X0),sK4) = X1
| ~ relation(X1)
| ~ empty(X1) )
| ~ spl15_1
| ~ spl15_213 ),
inference(resolution,[],[f2487,f153]) ).
fof(f153,plain,
( relation(sK4)
| ~ spl15_1 ),
inference(avatar_component_clause,[],[f151]) ).
fof(f5623,plain,
( spl15_342
| ~ spl15_149
| ~ spl15_165 ),
inference(avatar_split_clause,[],[f1665,f1658,f1419,f5621]) ).
fof(f5621,plain,
( spl15_342
<=> ! [X0,X3,X2,X1] :
( sP0(X0,X1,unordered_pair(singleton(sK6(X2,X3)),unordered_pair(sK6(X2,X3),sK5(X2,X3))))
| element(unordered_pair(singleton(sK9(X0,X1,unordered_pair(singleton(sK6(X2,X3)),unordered_pair(sK6(X2,X3),sK5(X2,X3))))),unordered_pair(sK10(X0,X1,unordered_pair(singleton(sK6(X2,X3)),unordered_pair(sK6(X2,X3),sK5(X2,X3)))),sK9(X0,X1,unordered_pair(singleton(sK6(X2,X3)),unordered_pair(sK6(X2,X3),sK5(X2,X3)))))),X0)
| ~ relation(X2)
| in(sK5(X2,X3),X3)
| relation_rng(X2) = X3
| ~ sP0(X2,relation_rng(X2),unordered_pair(singleton(sK9(X0,X1,unordered_pair(singleton(sK6(X2,X3)),unordered_pair(sK6(X2,X3),sK5(X2,X3))))),unordered_pair(sK10(X0,X1,unordered_pair(singleton(sK6(X2,X3)),unordered_pair(sK6(X2,X3),sK5(X2,X3)))),sK9(X0,X1,unordered_pair(singleton(sK6(X2,X3)),unordered_pair(sK6(X2,X3),sK5(X2,X3))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_342])]) ).
fof(f1419,plain,
( spl15_149
<=> ! [X2,X0,X1] :
( in(sK5(X0,X1),X1)
| ~ relation(X0)
| in(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X2)
| relation_rng(X0) = X1
| ~ sP0(X0,relation_rng(X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_149])]) ).
fof(f1658,plain,
( spl15_165
<=> ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X0)
| sP0(X0,X1,X2)
| ~ in(X2,unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_165])]) ).
fof(f1665,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,X1,unordered_pair(singleton(sK6(X2,X3)),unordered_pair(sK6(X2,X3),sK5(X2,X3))))
| element(unordered_pair(singleton(sK9(X0,X1,unordered_pair(singleton(sK6(X2,X3)),unordered_pair(sK6(X2,X3),sK5(X2,X3))))),unordered_pair(sK10(X0,X1,unordered_pair(singleton(sK6(X2,X3)),unordered_pair(sK6(X2,X3),sK5(X2,X3)))),sK9(X0,X1,unordered_pair(singleton(sK6(X2,X3)),unordered_pair(sK6(X2,X3),sK5(X2,X3)))))),X0)
| ~ relation(X2)
| in(sK5(X2,X3),X3)
| relation_rng(X2) = X3
| ~ sP0(X2,relation_rng(X2),unordered_pair(singleton(sK9(X0,X1,unordered_pair(singleton(sK6(X2,X3)),unordered_pair(sK6(X2,X3),sK5(X2,X3))))),unordered_pair(sK10(X0,X1,unordered_pair(singleton(sK6(X2,X3)),unordered_pair(sK6(X2,X3),sK5(X2,X3)))),sK9(X0,X1,unordered_pair(singleton(sK6(X2,X3)),unordered_pair(sK6(X2,X3),sK5(X2,X3))))))) )
| ~ spl15_149
| ~ spl15_165 ),
inference(resolution,[],[f1659,f1420]) ).
fof(f1420,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X2)
| ~ relation(X0)
| in(sK5(X0,X1),X1)
| relation_rng(X0) = X1
| ~ sP0(X0,relation_rng(X0),X2) )
| ~ spl15_149 ),
inference(avatar_component_clause,[],[f1419]) ).
fof(f1659,plain,
( ! [X2,X0,X1] :
( ~ in(X2,unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))))
| sP0(X0,X1,X2)
| element(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X0) )
| ~ spl15_165 ),
inference(avatar_component_clause,[],[f1658]) ).
fof(f5619,plain,
( spl15_341
| ~ spl15_149
| ~ spl15_164 ),
inference(avatar_split_clause,[],[f1664,f1654,f1419,f5617]) ).
fof(f5617,plain,
( spl15_341
<=> ! [X0,X3,X2,X1] :
( sP0(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X2,X3)
| element(unordered_pair(singleton(sK9(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X2,X3)),unordered_pair(sK10(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X2,X3),sK9(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X2,X3))),X3)
| ~ relation(X0)
| in(sK5(X0,X1),X1)
| relation_rng(X0) = X1
| ~ sP0(X0,relation_rng(X0),unordered_pair(singleton(sK9(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X2,X3)),unordered_pair(sK10(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X2,X3),sK9(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X2,X3)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_341])]) ).
fof(f1654,plain,
( spl15_164
<=> ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X2)
| sP0(X0,X1,X2)
| ~ in(X0,unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_164])]) ).
fof(f1664,plain,
( ! [X2,X3,X0,X1] :
( sP0(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X2,X3)
| element(unordered_pair(singleton(sK9(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X2,X3)),unordered_pair(sK10(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X2,X3),sK9(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X2,X3))),X3)
| ~ relation(X0)
| in(sK5(X0,X1),X1)
| relation_rng(X0) = X1
| ~ sP0(X0,relation_rng(X0),unordered_pair(singleton(sK9(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X2,X3)),unordered_pair(sK10(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X2,X3),sK9(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X2,X3)))) )
| ~ spl15_149
| ~ spl15_164 ),
inference(resolution,[],[f1655,f1420]) ).
fof(f1655,plain,
( ! [X2,X0,X1] :
( ~ in(X0,unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))))
| sP0(X0,X1,X2)
| element(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X2) )
| ~ spl15_164 ),
inference(avatar_component_clause,[],[f1654]) ).
fof(f5615,plain,
( spl15_340
| ~ spl15_90
| ~ spl15_149 ),
inference(avatar_split_clause,[],[f1472,f1419,f742,f5613]) ).
fof(f5613,plain,
( spl15_340
<=> ! [X0,X3,X2,X1] :
( ~ relation(X0)
| in(sK5(X0,X1),X1)
| relation_rng(X0) = X1
| ~ sP0(X0,relation_rng(X0),unordered_pair(singleton(sK9(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X2,X3)),unordered_pair(sK10(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X2,X3),sK9(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X2,X3))))
| sP0(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X2,X3)
| in(unordered_pair(singleton(sK9(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X2,X3)),unordered_pair(sK10(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X2,X3),sK9(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X2,X3))),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_340])]) ).
fof(f742,plain,
( spl15_90
<=> ! [X2,X0,X1] :
( in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X2)
| sP0(X0,X1,X2)
| ~ in(X0,unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_90])]) ).
fof(f1472,plain,
( ! [X2,X3,X0,X1] :
( ~ relation(X0)
| in(sK5(X0,X1),X1)
| relation_rng(X0) = X1
| ~ sP0(X0,relation_rng(X0),unordered_pair(singleton(sK9(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X2,X3)),unordered_pair(sK10(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X2,X3),sK9(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X2,X3))))
| sP0(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X2,X3)
| in(unordered_pair(singleton(sK9(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X2,X3)),unordered_pair(sK10(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X2,X3),sK9(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X2,X3))),X3) )
| ~ spl15_90
| ~ spl15_149 ),
inference(resolution,[],[f1420,f743]) ).
fof(f743,plain,
( ! [X2,X0,X1] :
( ~ in(X0,unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))))
| sP0(X0,X1,X2)
| in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X2) )
| ~ spl15_90 ),
inference(avatar_component_clause,[],[f742]) ).
fof(f5611,plain,
( spl15_339
| ~ spl15_88
| ~ spl15_149 ),
inference(avatar_split_clause,[],[f1469,f1419,f734,f5609]) ).
fof(f5609,plain,
( spl15_339
<=> ! [X0,X3,X2,X1] :
( ~ relation(X0)
| in(sK5(X0,X1),X1)
| relation_rng(X0) = X1
| ~ sP0(X0,relation_rng(X0),unordered_pair(singleton(sK9(X2,X3,unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))))),unordered_pair(sK10(X2,X3,unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1)))),sK9(X2,X3,unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1)))))))
| sP0(X2,X3,unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))))
| in(unordered_pair(singleton(sK9(X2,X3,unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))))),unordered_pair(sK10(X2,X3,unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1)))),sK9(X2,X3,unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1)))))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_339])]) ).
fof(f734,plain,
( spl15_88
<=> ! [X2,X0,X1] :
( in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X0)
| sP0(X0,X1,X2)
| ~ in(X2,unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_88])]) ).
fof(f1469,plain,
( ! [X2,X3,X0,X1] :
( ~ relation(X0)
| in(sK5(X0,X1),X1)
| relation_rng(X0) = X1
| ~ sP0(X0,relation_rng(X0),unordered_pair(singleton(sK9(X2,X3,unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))))),unordered_pair(sK10(X2,X3,unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1)))),sK9(X2,X3,unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1)))))))
| sP0(X2,X3,unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))))
| in(unordered_pair(singleton(sK9(X2,X3,unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))))),unordered_pair(sK10(X2,X3,unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1)))),sK9(X2,X3,unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1)))))),X2) )
| ~ spl15_88
| ~ spl15_149 ),
inference(resolution,[],[f1420,f735]) ).
fof(f735,plain,
( ! [X2,X0,X1] :
( ~ in(X2,unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))))
| sP0(X0,X1,X2)
| in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X0) )
| ~ spl15_88 ),
inference(avatar_component_clause,[],[f734]) ).
fof(f5595,plain,
( spl15_338
| ~ spl15_130
| ~ spl15_149 ),
inference(avatar_split_clause,[],[f1473,f1419,f1192,f5593]) ).
fof(f5593,plain,
( spl15_338
<=> ! [X2,X0,X1] :
( ~ relation(X0)
| in(sK5(X0,X1),X1)
| relation_rng(X0) = X1
| ~ sP0(X0,relation_rng(X0),unordered_pair(singleton(sK9(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X2,unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))))),unordered_pair(sK10(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X2,unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1)))),sK9(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X2,unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1)))))))
| sP0(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X2,unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_338])]) ).
fof(f1192,plain,
( spl15_130
<=> ! [X0,X1] :
( sP0(X0,X1,X0)
| ~ in(X0,unordered_pair(singleton(sK9(X0,X1,X0)),unordered_pair(sK10(X0,X1,X0),sK9(X0,X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_130])]) ).
fof(f1473,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| in(sK5(X0,X1),X1)
| relation_rng(X0) = X1
| ~ sP0(X0,relation_rng(X0),unordered_pair(singleton(sK9(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X2,unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))))),unordered_pair(sK10(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X2,unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1)))),sK9(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X2,unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1)))))))
| sP0(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X2,unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1)))) )
| ~ spl15_130
| ~ spl15_149 ),
inference(resolution,[],[f1420,f1193]) ).
fof(f1193,plain,
( ! [X0,X1] :
( ~ in(X0,unordered_pair(singleton(sK9(X0,X1,X0)),unordered_pair(sK10(X0,X1,X0),sK9(X0,X1,X0))))
| sP0(X0,X1,X0) )
| ~ spl15_130 ),
inference(avatar_component_clause,[],[f1192]) ).
fof(f5579,plain,
( spl15_337
| ~ spl15_81
| ~ spl15_149 ),
inference(avatar_split_clause,[],[f1467,f1419,f696,f5577]) ).
fof(f5577,plain,
( spl15_337
<=> ! [X2,X0,X1] :
( ~ relation(X0)
| in(sK5(X0,X1),X1)
| relation_rng(X0) = X1
| ~ sP0(X0,relation_rng(X0),unordered_pair(singleton(sK6(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X2)),unordered_pair(sK6(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X2),sK5(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X2))))
| in(sK5(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X2),X2)
| ~ relation(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))))
| relation_rng(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1)))) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_337])]) ).
fof(f696,plain,
( spl15_81
<=> ! [X0,X1] :
( relation_rng(X0) = X1
| in(sK5(X0,X1),X1)
| ~ relation(X0)
| ~ in(X0,unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_81])]) ).
fof(f1467,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| in(sK5(X0,X1),X1)
| relation_rng(X0) = X1
| ~ sP0(X0,relation_rng(X0),unordered_pair(singleton(sK6(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X2)),unordered_pair(sK6(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X2),sK5(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X2))))
| in(sK5(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X2),X2)
| ~ relation(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))))
| relation_rng(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1)))) = X2 )
| ~ spl15_81
| ~ spl15_149 ),
inference(resolution,[],[f1420,f697]) ).
fof(f697,plain,
( ! [X0,X1] :
( ~ in(X0,unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))))
| in(sK5(X0,X1),X1)
| ~ relation(X0)
| relation_rng(X0) = X1 )
| ~ spl15_81 ),
inference(avatar_component_clause,[],[f696]) ).
fof(f5563,plain,
( spl15_336
| ~ spl15_18
| ~ spl15_325 ),
inference(avatar_split_clause,[],[f5456,f5256,f233,f5561]) ).
fof(f5256,plain,
( spl15_325
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_rng(X1) = relation_rng_restriction(X0,sK4)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_325])]) ).
fof(f5456,plain,
( ! [X0,X1] :
( relation_rng(relation_rng(X0)) = relation_rng_restriction(X1,sK4)
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl15_18
| ~ spl15_325 ),
inference(resolution,[],[f5257,f234]) ).
fof(f5257,plain,
( ! [X0,X1] :
( ~ empty(X1)
| relation_rng(X1) = relation_rng_restriction(X0,sK4)
| ~ empty(X0) )
| ~ spl15_325 ),
inference(avatar_component_clause,[],[f5256]) ).
fof(f5559,plain,
( spl15_335
| ~ spl15_83
| ~ spl15_149 ),
inference(avatar_split_clause,[],[f1470,f1419,f705,f5557]) ).
fof(f5557,plain,
( spl15_335
<=> ! [X0,X3,X2,X1] :
( ~ relation(X0)
| in(sK5(X0,X1),X1)
| relation_rng(X0) = X1
| ~ sP0(X0,relation_rng(X0),unordered_pair(singleton(sK9(X2,X3,unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))))),unordered_pair(sK10(X2,X3,unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1)))),sK9(X2,X3,unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1)))))))
| in(sK10(X2,X3,unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1)))),X3)
| sP0(X2,X3,unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_335])]) ).
fof(f705,plain,
( spl15_83
<=> ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| in(sK10(X0,X1,X2),X1)
| ~ in(X2,unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_83])]) ).
fof(f1470,plain,
( ! [X2,X3,X0,X1] :
( ~ relation(X0)
| in(sK5(X0,X1),X1)
| relation_rng(X0) = X1
| ~ sP0(X0,relation_rng(X0),unordered_pair(singleton(sK9(X2,X3,unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))))),unordered_pair(sK10(X2,X3,unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1)))),sK9(X2,X3,unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1)))))))
| in(sK10(X2,X3,unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1)))),X3)
| sP0(X2,X3,unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1)))) )
| ~ spl15_83
| ~ spl15_149 ),
inference(resolution,[],[f1420,f706]) ).
fof(f706,plain,
( ! [X2,X0,X1] :
( ~ in(X2,unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))))
| in(sK10(X0,X1,X2),X1)
| sP0(X0,X1,X2) )
| ~ spl15_83 ),
inference(avatar_component_clause,[],[f705]) ).
fof(f5531,plain,
( spl15_334
| ~ spl15_133
| ~ spl15_149 ),
inference(avatar_split_clause,[],[f1471,f1419,f1214,f5529]) ).
fof(f5529,plain,
( spl15_334
<=> ! [X0,X3,X2,X1] :
( ~ relation(X0)
| in(sK5(X0,X1),X1)
| relation_rng(X0) = X1
| ~ sP0(X0,relation_rng(X0),unordered_pair(singleton(sK9(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X2,X3)),unordered_pair(sK10(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X2,X3),sK9(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X2,X3))))
| ~ empty(X3)
| sP0(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_334])]) ).
fof(f1214,plain,
( spl15_133
<=> ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ empty(X2)
| ~ in(X0,unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_133])]) ).
fof(f1471,plain,
( ! [X2,X3,X0,X1] :
( ~ relation(X0)
| in(sK5(X0,X1),X1)
| relation_rng(X0) = X1
| ~ sP0(X0,relation_rng(X0),unordered_pair(singleton(sK9(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X2,X3)),unordered_pair(sK10(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X2,X3),sK9(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X2,X3))))
| ~ empty(X3)
| sP0(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X2,X3) )
| ~ spl15_133
| ~ spl15_149 ),
inference(resolution,[],[f1420,f1215]) ).
fof(f1215,plain,
( ! [X2,X0,X1] :
( ~ in(X0,unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))))
| ~ empty(X2)
| sP0(X0,X1,X2) )
| ~ spl15_133 ),
inference(avatar_component_clause,[],[f1214]) ).
fof(f5527,plain,
( spl15_333
| ~ spl15_135
| ~ spl15_149 ),
inference(avatar_split_clause,[],[f1468,f1419,f1222,f5525]) ).
fof(f5525,plain,
( spl15_333
<=> ! [X0,X3,X2,X1] :
( ~ relation(X0)
| in(sK5(X0,X1),X1)
| relation_rng(X0) = X1
| ~ sP0(X0,relation_rng(X0),unordered_pair(singleton(sK9(X2,X3,unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))))),unordered_pair(sK10(X2,X3,unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1)))),sK9(X2,X3,unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1)))))))
| ~ empty(X2)
| sP0(X2,X3,unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_333])]) ).
fof(f1222,plain,
( spl15_135
<=> ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ empty(X0)
| ~ in(X2,unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_135])]) ).
fof(f1468,plain,
( ! [X2,X3,X0,X1] :
( ~ relation(X0)
| in(sK5(X0,X1),X1)
| relation_rng(X0) = X1
| ~ sP0(X0,relation_rng(X0),unordered_pair(singleton(sK9(X2,X3,unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))))),unordered_pair(sK10(X2,X3,unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1)))),sK9(X2,X3,unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1)))))))
| ~ empty(X2)
| sP0(X2,X3,unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1)))) )
| ~ spl15_135
| ~ spl15_149 ),
inference(resolution,[],[f1420,f1223]) ).
fof(f1223,plain,
( ! [X2,X0,X1] :
( ~ in(X2,unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))))
| ~ empty(X0)
| sP0(X0,X1,X2) )
| ~ spl15_135 ),
inference(avatar_component_clause,[],[f1222]) ).
fof(f5511,plain,
( spl15_332
| ~ spl15_71
| ~ spl15_149 ),
inference(avatar_split_clause,[],[f1466,f1419,f601,f5509]) ).
fof(f5509,plain,
( spl15_332
<=> ! [X2,X0,X1] :
( ~ relation(X0)
| in(sK5(X0,X1),X1)
| relation_rng(X0) = X1
| ~ sP0(X0,relation_rng(X0),unordered_pair(singleton(sK7(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X2)),unordered_pair(X2,sK7(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X2))))
| ~ relation(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))))
| ~ in(X2,relation_rng(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_332])]) ).
fof(f601,plain,
( spl15_71
<=> ! [X0,X1] :
( ~ in(X0,relation_rng(X1))
| ~ relation(X1)
| ~ in(X1,unordered_pair(singleton(sK7(X1,X0)),unordered_pair(X0,sK7(X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_71])]) ).
fof(f1466,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| in(sK5(X0,X1),X1)
| relation_rng(X0) = X1
| ~ sP0(X0,relation_rng(X0),unordered_pair(singleton(sK7(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X2)),unordered_pair(X2,sK7(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X2))))
| ~ relation(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))))
| ~ in(X2,relation_rng(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))))) )
| ~ spl15_71
| ~ spl15_149 ),
inference(resolution,[],[f1420,f602]) ).
fof(f602,plain,
( ! [X0,X1] :
( ~ in(X1,unordered_pair(singleton(sK7(X1,X0)),unordered_pair(X0,sK7(X1,X0))))
| ~ relation(X1)
| ~ in(X0,relation_rng(X1)) )
| ~ spl15_71 ),
inference(avatar_component_clause,[],[f601]) ).
fof(f5495,plain,
( spl15_331
| ~ spl15_122
| ~ spl15_149 ),
inference(avatar_split_clause,[],[f1476,f1419,f1075,f5493]) ).
fof(f5493,plain,
( spl15_331
<=> ! [X2,X0,X1] :
( ~ relation(X0)
| in(sK5(X0,X1),X1)
| relation_rng(X0) = X1
| ~ sP0(X0,relation_rng(X0),sK5(X2,unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1)))))
| ~ relation(X2)
| relation_rng(X2) = unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1)))
| in(sK5(X2,unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1)))),relation_rng(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_331])]) ).
fof(f1075,plain,
( spl15_122
<=> ! [X0,X1] :
( in(sK5(X0,X1),relation_rng(X0))
| ~ relation(X0)
| relation_rng(X0) = X1
| ~ in(X1,sK5(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_122])]) ).
fof(f1476,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| in(sK5(X0,X1),X1)
| relation_rng(X0) = X1
| ~ sP0(X0,relation_rng(X0),sK5(X2,unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1)))))
| ~ relation(X2)
| relation_rng(X2) = unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1)))
| in(sK5(X2,unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1)))),relation_rng(X2)) )
| ~ spl15_122
| ~ spl15_149 ),
inference(resolution,[],[f1420,f1076]) ).
fof(f1076,plain,
( ! [X0,X1] :
( ~ in(X1,sK5(X0,X1))
| ~ relation(X0)
| relation_rng(X0) = X1
| in(sK5(X0,X1),relation_rng(X0)) )
| ~ spl15_122 ),
inference(avatar_component_clause,[],[f1075]) ).
fof(f5344,plain,
( spl15_330
| ~ spl15_63
| ~ spl15_170 ),
inference(avatar_split_clause,[],[f1754,f1717,f536,f5342]) ).
fof(f5342,plain,
( spl15_330
<=> ! [X0,X3,X2,X1] :
( sP0(X0,X1,relation_rng_restriction(X2,X3))
| in(unordered_pair(singleton(sK9(X0,X1,relation_rng_restriction(X2,X3))),unordered_pair(sK10(X0,X1,relation_rng_restriction(X2,X3)),sK9(X0,X1,relation_rng_restriction(X2,X3)))),X3)
| element(unordered_pair(singleton(sK9(X0,X1,relation_rng_restriction(X2,X3))),unordered_pair(sK10(X0,X1,relation_rng_restriction(X2,X3)),sK9(X0,X1,relation_rng_restriction(X2,X3)))),X0)
| ~ relation(relation_rng_restriction(X2,X3))
| ~ relation(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_330])]) ).
fof(f1717,plain,
( spl15_170
<=> ! [X4,X0,X3,X2,X1] :
( element(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X0)
| sP0(X0,X1,X2)
| in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X3)
| ~ sP0(X3,X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_170])]) ).
fof(f1754,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,X1,relation_rng_restriction(X2,X3))
| in(unordered_pair(singleton(sK9(X0,X1,relation_rng_restriction(X2,X3))),unordered_pair(sK10(X0,X1,relation_rng_restriction(X2,X3)),sK9(X0,X1,relation_rng_restriction(X2,X3)))),X3)
| element(unordered_pair(singleton(sK9(X0,X1,relation_rng_restriction(X2,X3))),unordered_pair(sK10(X0,X1,relation_rng_restriction(X2,X3)),sK9(X0,X1,relation_rng_restriction(X2,X3)))),X0)
| ~ relation(relation_rng_restriction(X2,X3))
| ~ relation(X3) )
| ~ spl15_63
| ~ spl15_170 ),
inference(resolution,[],[f1718,f537]) ).
fof(f1718,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ sP0(X3,X4,X2)
| sP0(X0,X1,X2)
| in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X3)
| element(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X0) )
| ~ spl15_170 ),
inference(avatar_component_clause,[],[f1717]) ).
fof(f5340,plain,
( spl15_329
| ~ spl15_63
| ~ spl15_169 ),
inference(avatar_split_clause,[],[f1744,f1713,f536,f5338]) ).
fof(f5338,plain,
( spl15_329
<=> ! [X0,X3,X2,X1] :
( sP0(relation_rng_restriction(X0,X1),X2,X3)
| in(unordered_pair(singleton(sK9(relation_rng_restriction(X0,X1),X2,X3)),unordered_pair(sK10(relation_rng_restriction(X0,X1),X2,X3),sK9(relation_rng_restriction(X0,X1),X2,X3))),X1)
| element(unordered_pair(singleton(sK9(relation_rng_restriction(X0,X1),X2,X3)),unordered_pair(sK10(relation_rng_restriction(X0,X1),X2,X3),sK9(relation_rng_restriction(X0,X1),X2,X3))),X3)
| ~ relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_329])]) ).
fof(f1713,plain,
( spl15_169
<=> ! [X4,X0,X3,X2,X1] :
( element(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X2)
| sP0(X0,X1,X2)
| in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X3)
| ~ sP0(X3,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_169])]) ).
fof(f1744,plain,
( ! [X2,X3,X0,X1] :
( sP0(relation_rng_restriction(X0,X1),X2,X3)
| in(unordered_pair(singleton(sK9(relation_rng_restriction(X0,X1),X2,X3)),unordered_pair(sK10(relation_rng_restriction(X0,X1),X2,X3),sK9(relation_rng_restriction(X0,X1),X2,X3))),X1)
| element(unordered_pair(singleton(sK9(relation_rng_restriction(X0,X1),X2,X3)),unordered_pair(sK10(relation_rng_restriction(X0,X1),X2,X3),sK9(relation_rng_restriction(X0,X1),X2,X3))),X3)
| ~ relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) )
| ~ spl15_63
| ~ spl15_169 ),
inference(resolution,[],[f1714,f537]) ).
fof(f1714,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ sP0(X3,X4,X0)
| sP0(X0,X1,X2)
| in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X3)
| element(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X2) )
| ~ spl15_169 ),
inference(avatar_component_clause,[],[f1713]) ).
fof(f5336,plain,
( spl15_328
| ~ spl15_63
| ~ spl15_168 ),
inference(avatar_split_clause,[],[f1734,f1709,f536,f5334]) ).
fof(f5334,plain,
( spl15_328
<=> ! [X0,X3,X2,X1] :
( in(unordered_pair(singleton(sK9(X0,X1,relation_rng_restriction(X2,X3))),unordered_pair(sK10(X0,X1,relation_rng_restriction(X2,X3)),sK9(X0,X1,relation_rng_restriction(X2,X3)))),X3)
| in(unordered_pair(singleton(sK9(X0,X1,relation_rng_restriction(X2,X3))),unordered_pair(sK10(X0,X1,relation_rng_restriction(X2,X3)),sK9(X0,X1,relation_rng_restriction(X2,X3)))),X0)
| sP0(X0,X1,relation_rng_restriction(X2,X3))
| ~ relation(relation_rng_restriction(X2,X3))
| ~ relation(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_328])]) ).
fof(f1709,plain,
( spl15_168
<=> ! [X4,X0,X3,X2,X1] :
( in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X3)
| ~ sP0(X3,X4,X2)
| in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X0)
| sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_168])]) ).
fof(f1734,plain,
( ! [X2,X3,X0,X1] :
( in(unordered_pair(singleton(sK9(X0,X1,relation_rng_restriction(X2,X3))),unordered_pair(sK10(X0,X1,relation_rng_restriction(X2,X3)),sK9(X0,X1,relation_rng_restriction(X2,X3)))),X3)
| in(unordered_pair(singleton(sK9(X0,X1,relation_rng_restriction(X2,X3))),unordered_pair(sK10(X0,X1,relation_rng_restriction(X2,X3)),sK9(X0,X1,relation_rng_restriction(X2,X3)))),X0)
| sP0(X0,X1,relation_rng_restriction(X2,X3))
| ~ relation(relation_rng_restriction(X2,X3))
| ~ relation(X3) )
| ~ spl15_63
| ~ spl15_168 ),
inference(resolution,[],[f1710,f537]) ).
fof(f1710,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ sP0(X3,X4,X2)
| in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X3)
| in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X0)
| sP0(X0,X1,X2) )
| ~ spl15_168 ),
inference(avatar_component_clause,[],[f1709]) ).
fof(f5332,plain,
( spl15_327
| ~ spl15_63
| ~ spl15_167 ),
inference(avatar_split_clause,[],[f1724,f1705,f536,f5330]) ).
fof(f5330,plain,
( spl15_327
<=> ! [X0,X3,X2,X1] :
( in(unordered_pair(singleton(sK9(relation_rng_restriction(X0,X1),X2,X3)),unordered_pair(sK10(relation_rng_restriction(X0,X1),X2,X3),sK9(relation_rng_restriction(X0,X1),X2,X3))),X1)
| in(unordered_pair(singleton(sK9(relation_rng_restriction(X0,X1),X2,X3)),unordered_pair(sK10(relation_rng_restriction(X0,X1),X2,X3),sK9(relation_rng_restriction(X0,X1),X2,X3))),X3)
| sP0(relation_rng_restriction(X0,X1),X2,X3)
| ~ relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_327])]) ).
fof(f1705,plain,
( spl15_167
<=> ! [X4,X0,X3,X2,X1] :
( in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X3)
| ~ sP0(X3,X4,X0)
| in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X2)
| sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_167])]) ).
fof(f1724,plain,
( ! [X2,X3,X0,X1] :
( in(unordered_pair(singleton(sK9(relation_rng_restriction(X0,X1),X2,X3)),unordered_pair(sK10(relation_rng_restriction(X0,X1),X2,X3),sK9(relation_rng_restriction(X0,X1),X2,X3))),X1)
| in(unordered_pair(singleton(sK9(relation_rng_restriction(X0,X1),X2,X3)),unordered_pair(sK10(relation_rng_restriction(X0,X1),X2,X3),sK9(relation_rng_restriction(X0,X1),X2,X3))),X3)
| sP0(relation_rng_restriction(X0,X1),X2,X3)
| ~ relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) )
| ~ spl15_63
| ~ spl15_167 ),
inference(resolution,[],[f1706,f537]) ).
fof(f1706,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ sP0(X3,X4,X0)
| in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X3)
| in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X2)
| sP0(X0,X1,X2) )
| ~ spl15_167 ),
inference(avatar_component_clause,[],[f1705]) ).
fof(f5274,plain,
( spl15_326
| ~ spl15_42
| ~ spl15_166 ),
inference(avatar_split_clause,[],[f1670,f1667,f371,f5272]) ).
fof(f5272,plain,
( spl15_326
<=> ! [X4,X0,X3,X2,X1] :
( ~ relation(relation_rng_restriction(X0,X1))
| in(sK5(relation_rng_restriction(X0,X1),X2),X2)
| relation_rng(relation_rng_restriction(X0,X1)) = X2
| ~ relation(X1)
| in(unordered_pair(singleton(sK6(relation_rng_restriction(X0,X1),X2)),unordered_pair(sK6(relation_rng_restriction(X0,X1),X2),sK5(relation_rng_restriction(X0,X1),X2))),X3)
| ~ in(sK5(relation_rng_restriction(X0,X1),X2),X4)
| ~ sP0(X1,X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_326])]) ).
fof(f371,plain,
( spl15_42
<=> ! [X5,X0,X6,X2,X1] :
( ~ in(unordered_pair(singleton(X5),unordered_pair(X5,X6)),X0)
| in(unordered_pair(singleton(X5),unordered_pair(X5,X6)),X2)
| ~ in(X6,X1)
| ~ sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_42])]) ).
fof(f1667,plain,
( spl15_166
<=> ! [X2,X0,X1] :
( in(sK5(relation_rng_restriction(X0,X1),X2),X2)
| ~ relation(relation_rng_restriction(X0,X1))
| in(unordered_pair(singleton(sK6(relation_rng_restriction(X0,X1),X2)),unordered_pair(sK6(relation_rng_restriction(X0,X1),X2),sK5(relation_rng_restriction(X0,X1),X2))),X1)
| relation_rng(relation_rng_restriction(X0,X1)) = X2
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_166])]) ).
fof(f1670,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ relation(relation_rng_restriction(X0,X1))
| in(sK5(relation_rng_restriction(X0,X1),X2),X2)
| relation_rng(relation_rng_restriction(X0,X1)) = X2
| ~ relation(X1)
| in(unordered_pair(singleton(sK6(relation_rng_restriction(X0,X1),X2)),unordered_pair(sK6(relation_rng_restriction(X0,X1),X2),sK5(relation_rng_restriction(X0,X1),X2))),X3)
| ~ in(sK5(relation_rng_restriction(X0,X1),X2),X4)
| ~ sP0(X1,X4,X3) )
| ~ spl15_42
| ~ spl15_166 ),
inference(resolution,[],[f1668,f372]) ).
fof(f372,plain,
( ! [X2,X0,X1,X6,X5] :
( ~ in(unordered_pair(singleton(X5),unordered_pair(X5,X6)),X0)
| in(unordered_pair(singleton(X5),unordered_pair(X5,X6)),X2)
| ~ in(X6,X1)
| ~ sP0(X0,X1,X2) )
| ~ spl15_42 ),
inference(avatar_component_clause,[],[f371]) ).
fof(f1668,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(singleton(sK6(relation_rng_restriction(X0,X1),X2)),unordered_pair(sK6(relation_rng_restriction(X0,X1),X2),sK5(relation_rng_restriction(X0,X1),X2))),X1)
| ~ relation(relation_rng_restriction(X0,X1))
| in(sK5(relation_rng_restriction(X0,X1),X2),X2)
| relation_rng(relation_rng_restriction(X0,X1)) = X2
| ~ relation(X1) )
| ~ spl15_166 ),
inference(avatar_component_clause,[],[f1667]) ).
fof(f5258,plain,
( spl15_325
| ~ spl15_18
| ~ spl15_314 ),
inference(avatar_split_clause,[],[f5105,f5022,f233,f5256]) ).
fof(f5022,plain,
( spl15_314
<=> ! [X0,X1] :
( relation_rng(X1) = relation_rng_restriction(X0,sK4)
| ~ empty(X0)
| ~ empty(relation_rng(X1))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_314])]) ).
fof(f5105,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_rng(X1) = relation_rng_restriction(X0,sK4)
| ~ empty(X1) )
| ~ spl15_18
| ~ spl15_314 ),
inference(duplicate_literal_removal,[],[f5101]) ).
fof(f5101,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_rng(X1) = relation_rng_restriction(X0,sK4)
| ~ empty(X1)
| ~ empty(X1) )
| ~ spl15_18
| ~ spl15_314 ),
inference(resolution,[],[f5023,f234]) ).
fof(f5023,plain,
( ! [X0,X1] :
( ~ empty(relation_rng(X1))
| ~ empty(X0)
| relation_rng(X1) = relation_rng_restriction(X0,sK4)
| ~ empty(X1) )
| ~ spl15_314 ),
inference(avatar_component_clause,[],[f5022]) ).
fof(f5254,plain,
( spl15_324
| ~ spl15_105
| ~ spl15_149 ),
inference(avatar_split_clause,[],[f1477,f1419,f903,f5252]) ).
fof(f5252,plain,
( spl15_324
<=> ! [X2,X0,X1] :
( ~ relation(X0)
| in(sK5(X0,X1),X1)
| relation_rng(X0) = X1
| ~ sP0(X0,relation_rng(X0),sK5(X2,unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1)))))
| ~ relation(X2)
| ~ empty(X2)
| relation_rng(X2) = unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_324])]) ).
fof(f903,plain,
( spl15_105
<=> ! [X0,X1] :
( relation_rng(X0) = X1
| ~ relation(X0)
| ~ empty(X0)
| ~ in(X1,sK5(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_105])]) ).
fof(f1477,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| in(sK5(X0,X1),X1)
| relation_rng(X0) = X1
| ~ sP0(X0,relation_rng(X0),sK5(X2,unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1)))))
| ~ relation(X2)
| ~ empty(X2)
| relation_rng(X2) = unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))) )
| ~ spl15_105
| ~ spl15_149 ),
inference(resolution,[],[f1420,f904]) ).
fof(f904,plain,
( ! [X0,X1] :
( ~ in(X1,sK5(X0,X1))
| ~ relation(X0)
| ~ empty(X0)
| relation_rng(X0) = X1 )
| ~ spl15_105 ),
inference(avatar_component_clause,[],[f903]) ).
fof(f5238,plain,
( spl15_323
| ~ spl15_103
| ~ spl15_149 ),
inference(avatar_split_clause,[],[f1479,f1419,f876,f5236]) ).
fof(f5236,plain,
( spl15_323
<=> ! [X0,X3,X2,X1] :
( ~ relation(X0)
| in(sK5(X0,X1),X1)
| relation_rng(X0) = X1
| ~ sP0(X0,relation_rng(X0),sK10(X2,unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X3))
| ~ empty(X3)
| sP0(X2,unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_323])]) ).
fof(f876,plain,
( spl15_103
<=> ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ empty(X2)
| ~ in(X1,sK10(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_103])]) ).
fof(f1479,plain,
( ! [X2,X3,X0,X1] :
( ~ relation(X0)
| in(sK5(X0,X1),X1)
| relation_rng(X0) = X1
| ~ sP0(X0,relation_rng(X0),sK10(X2,unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X3))
| ~ empty(X3)
| sP0(X2,unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X3) )
| ~ spl15_103
| ~ spl15_149 ),
inference(resolution,[],[f1420,f877]) ).
fof(f877,plain,
( ! [X2,X0,X1] :
( ~ in(X1,sK10(X0,X1,X2))
| ~ empty(X2)
| sP0(X0,X1,X2) )
| ~ spl15_103 ),
inference(avatar_component_clause,[],[f876]) ).
fof(f5188,plain,
( spl15_322
| ~ spl15_86
| ~ spl15_138 ),
inference(avatar_split_clause,[],[f1288,f1267,f720,f5186]) ).
fof(f5186,plain,
( spl15_322
<=> ! [X0,X3,X2,X1] :
( in(sK5(relation_rng_restriction(X0,X1),X2),X2)
| ~ relation(relation_rng_restriction(X0,X1))
| relation_rng(relation_rng_restriction(X0,X1)) = X2
| ~ relation(X1)
| in(unordered_pair(singleton(sK6(relation_rng_restriction(X0,X1),X2)),unordered_pair(sK6(relation_rng_restriction(X0,X1),X2),sK5(relation_rng_restriction(X0,X1),X2))),X3)
| ~ sP0(relation_rng_restriction(X0,X1),X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_322])]) ).
fof(f720,plain,
( spl15_86
<=> ! [X0,X3,X2,X1] :
( relation_rng(X0) = X1
| in(sK5(X0,X1),X1)
| ~ relation(X0)
| in(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X2)
| ~ in(sK5(X0,X1),X3)
| ~ sP0(X0,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_86])]) ).
fof(f1267,plain,
( spl15_138
<=> ! [X2,X0,X1] :
( in(sK5(relation_rng_restriction(X0,X1),X2),X2)
| ~ relation(relation_rng_restriction(X0,X1))
| in(sK5(relation_rng_restriction(X0,X1),X2),X0)
| relation_rng(relation_rng_restriction(X0,X1)) = X2
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_138])]) ).
fof(f1288,plain,
( ! [X2,X3,X0,X1] :
( in(sK5(relation_rng_restriction(X0,X1),X2),X2)
| ~ relation(relation_rng_restriction(X0,X1))
| relation_rng(relation_rng_restriction(X0,X1)) = X2
| ~ relation(X1)
| in(unordered_pair(singleton(sK6(relation_rng_restriction(X0,X1),X2)),unordered_pair(sK6(relation_rng_restriction(X0,X1),X2),sK5(relation_rng_restriction(X0,X1),X2))),X3)
| ~ sP0(relation_rng_restriction(X0,X1),X0,X3) )
| ~ spl15_86
| ~ spl15_138 ),
inference(duplicate_literal_removal,[],[f1277]) ).
fof(f1277,plain,
( ! [X2,X3,X0,X1] :
( in(sK5(relation_rng_restriction(X0,X1),X2),X2)
| ~ relation(relation_rng_restriction(X0,X1))
| relation_rng(relation_rng_restriction(X0,X1)) = X2
| ~ relation(X1)
| in(sK5(relation_rng_restriction(X0,X1),X2),X2)
| ~ relation(relation_rng_restriction(X0,X1))
| in(unordered_pair(singleton(sK6(relation_rng_restriction(X0,X1),X2)),unordered_pair(sK6(relation_rng_restriction(X0,X1),X2),sK5(relation_rng_restriction(X0,X1),X2))),X3)
| relation_rng(relation_rng_restriction(X0,X1)) = X2
| ~ sP0(relation_rng_restriction(X0,X1),X0,X3) )
| ~ spl15_86
| ~ spl15_138 ),
inference(resolution,[],[f1268,f721]) ).
fof(f721,plain,
( ! [X2,X3,X0,X1] :
( ~ in(sK5(X0,X1),X3)
| in(sK5(X0,X1),X1)
| ~ relation(X0)
| in(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X2)
| relation_rng(X0) = X1
| ~ sP0(X0,X3,X2) )
| ~ spl15_86 ),
inference(avatar_component_clause,[],[f720]) ).
fof(f1268,plain,
( ! [X2,X0,X1] :
( in(sK5(relation_rng_restriction(X0,X1),X2),X2)
| in(sK5(relation_rng_restriction(X0,X1),X2),X0)
| ~ relation(relation_rng_restriction(X0,X1))
| relation_rng(relation_rng_restriction(X0,X1)) = X2
| ~ relation(X1) )
| ~ spl15_138 ),
inference(avatar_component_clause,[],[f1267]) ).
fof(f5064,plain,
( spl15_321
| ~ spl15_39
| ~ spl15_166 ),
inference(avatar_split_clause,[],[f1671,f1667,f354,f5062]) ).
fof(f5062,plain,
( spl15_321
<=> ! [X4,X0,X3,X2,X1] :
( ~ relation(relation_rng_restriction(X0,X1))
| in(sK5(relation_rng_restriction(X0,X1),X2),X2)
| relation_rng(relation_rng_restriction(X0,X1)) = X2
| ~ relation(X1)
| in(unordered_pair(singleton(sK6(relation_rng_restriction(X0,X1),X2)),unordered_pair(sK6(relation_rng_restriction(X0,X1),X2),sK5(relation_rng_restriction(X0,X1),X2))),X3)
| ~ sP0(X3,X4,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_321])]) ).
fof(f354,plain,
( spl15_39
<=> ! [X5,X0,X6,X2,X1] :
( ~ in(unordered_pair(singleton(X5),unordered_pair(X5,X6)),X2)
| in(unordered_pair(singleton(X5),unordered_pair(X5,X6)),X0)
| ~ sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_39])]) ).
fof(f1671,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ relation(relation_rng_restriction(X0,X1))
| in(sK5(relation_rng_restriction(X0,X1),X2),X2)
| relation_rng(relation_rng_restriction(X0,X1)) = X2
| ~ relation(X1)
| in(unordered_pair(singleton(sK6(relation_rng_restriction(X0,X1),X2)),unordered_pair(sK6(relation_rng_restriction(X0,X1),X2),sK5(relation_rng_restriction(X0,X1),X2))),X3)
| ~ sP0(X3,X4,X1) )
| ~ spl15_39
| ~ spl15_166 ),
inference(resolution,[],[f1668,f355]) ).
fof(f355,plain,
( ! [X2,X0,X1,X6,X5] :
( ~ in(unordered_pair(singleton(X5),unordered_pair(X5,X6)),X2)
| in(unordered_pair(singleton(X5),unordered_pair(X5,X6)),X0)
| ~ sP0(X0,X1,X2) )
| ~ spl15_39 ),
inference(avatar_component_clause,[],[f354]) ).
fof(f5060,plain,
( spl15_320
| ~ spl15_63
| ~ spl15_158 ),
inference(avatar_split_clause,[],[f1585,f1505,f536,f5058]) ).
fof(f5058,plain,
( spl15_320
<=> ! [X0,X3,X2,X1] :
( sP0(X0,X1,relation_rng_restriction(X2,X3))
| in(sK10(X0,X1,relation_rng_restriction(X2,X3)),X2)
| element(unordered_pair(singleton(sK9(X0,X1,relation_rng_restriction(X2,X3))),unordered_pair(sK10(X0,X1,relation_rng_restriction(X2,X3)),sK9(X0,X1,relation_rng_restriction(X2,X3)))),X0)
| ~ relation(relation_rng_restriction(X2,X3))
| ~ relation(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_320])]) ).
fof(f1505,plain,
( spl15_158
<=> ! [X4,X0,X3,X2,X1] :
( element(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X0)
| sP0(X0,X1,X2)
| in(sK10(X0,X1,X2),X3)
| ~ sP0(X4,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_158])]) ).
fof(f1585,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,X1,relation_rng_restriction(X2,X3))
| in(sK10(X0,X1,relation_rng_restriction(X2,X3)),X2)
| element(unordered_pair(singleton(sK9(X0,X1,relation_rng_restriction(X2,X3))),unordered_pair(sK10(X0,X1,relation_rng_restriction(X2,X3)),sK9(X0,X1,relation_rng_restriction(X2,X3)))),X0)
| ~ relation(relation_rng_restriction(X2,X3))
| ~ relation(X3) )
| ~ spl15_63
| ~ spl15_158 ),
inference(resolution,[],[f1506,f537]) ).
fof(f1506,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ sP0(X4,X3,X2)
| sP0(X0,X1,X2)
| in(sK10(X0,X1,X2),X3)
| element(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X0) )
| ~ spl15_158 ),
inference(avatar_component_clause,[],[f1505]) ).
fof(f5056,plain,
( spl15_319
| ~ spl15_63
| ~ spl15_157 ),
inference(avatar_split_clause,[],[f1575,f1501,f536,f5054]) ).
fof(f5054,plain,
( spl15_319
<=> ! [X0,X3,X2,X1] :
( sP0(relation_rng_restriction(X0,X1),X2,X3)
| in(sK10(relation_rng_restriction(X0,X1),X2,X3),X0)
| element(unordered_pair(singleton(sK9(relation_rng_restriction(X0,X1),X2,X3)),unordered_pair(sK10(relation_rng_restriction(X0,X1),X2,X3),sK9(relation_rng_restriction(X0,X1),X2,X3))),X3)
| ~ relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_319])]) ).
fof(f1501,plain,
( spl15_157
<=> ! [X4,X0,X3,X2,X1] :
( element(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X2)
| sP0(X0,X1,X2)
| in(sK10(X0,X1,X2),X3)
| ~ sP0(X4,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_157])]) ).
fof(f1575,plain,
( ! [X2,X3,X0,X1] :
( sP0(relation_rng_restriction(X0,X1),X2,X3)
| in(sK10(relation_rng_restriction(X0,X1),X2,X3),X0)
| element(unordered_pair(singleton(sK9(relation_rng_restriction(X0,X1),X2,X3)),unordered_pair(sK10(relation_rng_restriction(X0,X1),X2,X3),sK9(relation_rng_restriction(X0,X1),X2,X3))),X3)
| ~ relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) )
| ~ spl15_63
| ~ spl15_157 ),
inference(resolution,[],[f1502,f537]) ).
fof(f1502,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ sP0(X4,X3,X0)
| sP0(X0,X1,X2)
| in(sK10(X0,X1,X2),X3)
| element(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X2) )
| ~ spl15_157 ),
inference(avatar_component_clause,[],[f1501]) ).
fof(f5052,plain,
( spl15_318
| ~ spl15_63
| ~ spl15_155 ),
inference(avatar_split_clause,[],[f1551,f1493,f536,f5050]) ).
fof(f1493,plain,
( spl15_155
<=> ! [X4,X0,X3,X2,X1] :
( in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X3)
| ~ sP0(X3,X4,X2)
| sP0(X0,X1,X2)
| in(sK10(X0,X1,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_155])]) ).
fof(f1551,plain,
( ! [X2,X3,X0,X1] :
( in(unordered_pair(singleton(sK9(X0,X1,relation_rng_restriction(X2,X3))),unordered_pair(sK10(X0,X1,relation_rng_restriction(X2,X3)),sK9(X0,X1,relation_rng_restriction(X2,X3)))),X3)
| sP0(X0,X1,relation_rng_restriction(X2,X3))
| in(sK10(X0,X1,relation_rng_restriction(X2,X3)),X1)
| ~ relation(relation_rng_restriction(X2,X3))
| ~ relation(X3) )
| ~ spl15_63
| ~ spl15_155 ),
inference(resolution,[],[f1494,f537]) ).
fof(f1494,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ sP0(X3,X4,X2)
| in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X3)
| sP0(X0,X1,X2)
| in(sK10(X0,X1,X2),X1) )
| ~ spl15_155 ),
inference(avatar_component_clause,[],[f1493]) ).
fof(f5048,plain,
( spl15_317
| ~ spl15_63
| ~ spl15_154 ),
inference(avatar_split_clause,[],[f1541,f1489,f536,f5046]) ).
fof(f5046,plain,
( spl15_317
<=> ! [X0,X3,X2,X1] :
( in(sK10(X0,X1,relation_rng_restriction(X2,X3)),X2)
| in(unordered_pair(singleton(sK9(X0,X1,relation_rng_restriction(X2,X3))),unordered_pair(sK10(X0,X1,relation_rng_restriction(X2,X3)),sK9(X0,X1,relation_rng_restriction(X2,X3)))),X0)
| sP0(X0,X1,relation_rng_restriction(X2,X3))
| ~ relation(relation_rng_restriction(X2,X3))
| ~ relation(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_317])]) ).
fof(f1489,plain,
( spl15_154
<=> ! [X4,X0,X3,X2,X1] :
( in(sK10(X0,X1,X2),X3)
| ~ sP0(X4,X3,X2)
| in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X0)
| sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_154])]) ).
fof(f1541,plain,
( ! [X2,X3,X0,X1] :
( in(sK10(X0,X1,relation_rng_restriction(X2,X3)),X2)
| in(unordered_pair(singleton(sK9(X0,X1,relation_rng_restriction(X2,X3))),unordered_pair(sK10(X0,X1,relation_rng_restriction(X2,X3)),sK9(X0,X1,relation_rng_restriction(X2,X3)))),X0)
| sP0(X0,X1,relation_rng_restriction(X2,X3))
| ~ relation(relation_rng_restriction(X2,X3))
| ~ relation(X3) )
| ~ spl15_63
| ~ spl15_154 ),
inference(resolution,[],[f1490,f537]) ).
fof(f1490,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ sP0(X4,X3,X2)
| in(sK10(X0,X1,X2),X3)
| in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X0)
| sP0(X0,X1,X2) )
| ~ spl15_154 ),
inference(avatar_component_clause,[],[f1489]) ).
fof(f5044,plain,
( spl15_316
| ~ spl15_63
| ~ spl15_153 ),
inference(avatar_split_clause,[],[f1531,f1485,f536,f5042]) ).
fof(f5042,plain,
( spl15_316
<=> ! [X0,X3,X2,X1] :
( in(sK10(relation_rng_restriction(X0,X1),X2,X3),X0)
| in(unordered_pair(singleton(sK9(relation_rng_restriction(X0,X1),X2,X3)),unordered_pair(sK10(relation_rng_restriction(X0,X1),X2,X3),sK9(relation_rng_restriction(X0,X1),X2,X3))),X3)
| sP0(relation_rng_restriction(X0,X1),X2,X3)
| ~ relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_316])]) ).
fof(f1485,plain,
( spl15_153
<=> ! [X4,X0,X3,X2,X1] :
( in(sK10(X0,X1,X2),X3)
| ~ sP0(X4,X3,X0)
| in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X2)
| sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_153])]) ).
fof(f1531,plain,
( ! [X2,X3,X0,X1] :
( in(sK10(relation_rng_restriction(X0,X1),X2,X3),X0)
| in(unordered_pair(singleton(sK9(relation_rng_restriction(X0,X1),X2,X3)),unordered_pair(sK10(relation_rng_restriction(X0,X1),X2,X3),sK9(relation_rng_restriction(X0,X1),X2,X3))),X3)
| sP0(relation_rng_restriction(X0,X1),X2,X3)
| ~ relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) )
| ~ spl15_63
| ~ spl15_153 ),
inference(resolution,[],[f1486,f537]) ).
fof(f1486,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ sP0(X4,X3,X0)
| in(sK10(X0,X1,X2),X3)
| in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X2)
| sP0(X0,X1,X2) )
| ~ spl15_153 ),
inference(avatar_component_clause,[],[f1485]) ).
fof(f5040,plain,
( spl15_315
| ~ spl15_63
| ~ spl15_136 ),
inference(avatar_split_clause,[],[f1250,f1240,f536,f5038]) ).
fof(f1240,plain,
( spl15_136
<=> ! [X0,X3,X2,X1] :
( sP0(X0,X1,X0)
| in(unordered_pair(singleton(sK9(X0,X1,X0)),unordered_pair(sK10(X0,X1,X0),sK9(X0,X1,X0))),X2)
| ~ sP0(X2,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_136])]) ).
fof(f1250,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(singleton(sK9(relation_rng_restriction(X0,X1),X2,relation_rng_restriction(X0,X1))),unordered_pair(sK10(relation_rng_restriction(X0,X1),X2,relation_rng_restriction(X0,X1)),sK9(relation_rng_restriction(X0,X1),X2,relation_rng_restriction(X0,X1)))),X1)
| sP0(relation_rng_restriction(X0,X1),X2,relation_rng_restriction(X0,X1))
| ~ relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) )
| ~ spl15_63
| ~ spl15_136 ),
inference(resolution,[],[f1241,f537]) ).
fof(f1241,plain,
( ! [X2,X3,X0,X1] :
( ~ sP0(X2,X3,X0)
| in(unordered_pair(singleton(sK9(X0,X1,X0)),unordered_pair(sK10(X0,X1,X0),sK9(X0,X1,X0))),X2)
| sP0(X0,X1,X0) )
| ~ spl15_136 ),
inference(avatar_component_clause,[],[f1240]) ).
fof(f5024,plain,
( spl15_314
| ~ spl15_20
| ~ spl15_191 ),
inference(avatar_split_clause,[],[f2137,f2064,f242,f5022]) ).
fof(f2137,plain,
( ! [X0,X1] :
( relation_rng(X1) = relation_rng_restriction(X0,sK4)
| ~ empty(X0)
| ~ empty(relation_rng(X1))
| ~ empty(X1) )
| ~ spl15_20
| ~ spl15_191 ),
inference(resolution,[],[f2065,f243]) ).
fof(f5020,plain,
( spl15_313
| ~ spl15_84
| ~ spl15_149 ),
inference(avatar_split_clause,[],[f1478,f1419,f710,f5018]) ).
fof(f5018,plain,
( spl15_313
<=> ! [X0,X1] :
( ~ relation(X0)
| in(sK5(X0,X1),X1)
| relation_rng(X0) = X1
| ~ sP0(X0,relation_rng(X0),sK8(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1)))))
| empty(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_313])]) ).
fof(f710,plain,
( spl15_84
<=> ! [X0] :
( empty(X0)
| ~ in(X0,sK8(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_84])]) ).
fof(f1478,plain,
( ! [X0,X1] :
( ~ relation(X0)
| in(sK5(X0,X1),X1)
| relation_rng(X0) = X1
| ~ sP0(X0,relation_rng(X0),sK8(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1)))))
| empty(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1)))) )
| ~ spl15_84
| ~ spl15_149 ),
inference(resolution,[],[f1420,f711]) ).
fof(f711,plain,
( ! [X0] :
( ~ in(X0,sK8(X0))
| empty(X0) )
| ~ spl15_84 ),
inference(avatar_component_clause,[],[f710]) ).
fof(f4818,plain,
( spl15_312
| ~ spl15_77
| ~ spl15_148 ),
inference(avatar_split_clause,[],[f1447,f1415,f648,f4816]) ).
fof(f4816,plain,
( spl15_312
<=> ! [X4,X0,X3,X2,X1] :
( ~ relation(X0)
| in(sK10(X1,X2,X0),relation_rng(X0))
| sP0(X1,X2,X0)
| in(unordered_pair(singleton(sK9(X1,X2,X0)),unordered_pair(sK10(X1,X2,X0),sK9(X1,X2,X0))),X3)
| ~ in(sK10(X1,X2,X0),X4)
| ~ sP0(X1,X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_312])]) ).
fof(f648,plain,
( spl15_77
<=> ! [X4,X0,X3,X2,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),X2)
| in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),X3)
| ~ in(X1,X4)
| ~ sP0(X2,X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_77])]) ).
fof(f1415,plain,
( spl15_148
<=> ! [X2,X0,X1] :
( in(sK10(X0,X1,X2),relation_rng(X2))
| ~ relation(X2)
| in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X0)
| sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_148])]) ).
fof(f1447,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ relation(X0)
| in(sK10(X1,X2,X0),relation_rng(X0))
| sP0(X1,X2,X0)
| in(unordered_pair(singleton(sK9(X1,X2,X0)),unordered_pair(sK10(X1,X2,X0),sK9(X1,X2,X0))),X3)
| ~ in(sK10(X1,X2,X0),X4)
| ~ sP0(X1,X4,X3) )
| ~ spl15_77
| ~ spl15_148 ),
inference(resolution,[],[f1416,f649]) ).
fof(f649,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),X2)
| in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),X3)
| ~ in(X1,X4)
| ~ sP0(X2,X4,X3) )
| ~ spl15_77 ),
inference(avatar_component_clause,[],[f648]) ).
fof(f1416,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X0)
| ~ relation(X2)
| in(sK10(X0,X1,X2),relation_rng(X2))
| sP0(X0,X1,X2) )
| ~ spl15_148 ),
inference(avatar_component_clause,[],[f1415]) ).
fof(f4814,plain,
( spl15_311
| ~ spl15_77
| ~ spl15_147 ),
inference(avatar_split_clause,[],[f1431,f1411,f648,f4812]) ).
fof(f4812,plain,
( spl15_311
<=> ! [X4,X0,X3,X2,X1] :
( ~ relation(X0)
| in(sK10(X0,X1,X2),relation_rng(X0))
| sP0(X0,X1,X2)
| in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X3)
| ~ in(sK10(X0,X1,X2),X4)
| ~ sP0(X2,X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_311])]) ).
fof(f1411,plain,
( spl15_147
<=> ! [X2,X0,X1] :
( in(sK10(X0,X1,X2),relation_rng(X0))
| ~ relation(X0)
| in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X2)
| sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_147])]) ).
fof(f1431,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ relation(X0)
| in(sK10(X0,X1,X2),relation_rng(X0))
| sP0(X0,X1,X2)
| in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X3)
| ~ in(sK10(X0,X1,X2),X4)
| ~ sP0(X2,X4,X3) )
| ~ spl15_77
| ~ spl15_147 ),
inference(resolution,[],[f1412,f649]) ).
fof(f1412,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X2)
| ~ relation(X0)
| in(sK10(X0,X1,X2),relation_rng(X0))
| sP0(X0,X1,X2) )
| ~ spl15_147 ),
inference(avatar_component_clause,[],[f1411]) ).
fof(f4810,plain,
( spl15_310
| ~ spl15_77
| ~ spl15_144 ),
inference(avatar_split_clause,[],[f1394,f1346,f648,f4808]) ).
fof(f4808,plain,
( spl15_310
<=> ! [X4,X0,X3,X2,X1] :
( ~ empty(X0)
| ~ relation(X0)
| sP0(X1,X2,relation_rng(X0))
| in(unordered_pair(singleton(sK9(X1,X2,relation_rng(X0))),unordered_pair(sK10(X1,X2,relation_rng(X0)),sK9(X1,X2,relation_rng(X0)))),X3)
| ~ in(sK10(X1,X2,relation_rng(X0)),X4)
| ~ sP0(X1,X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_310])]) ).
fof(f1394,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ empty(X0)
| ~ relation(X0)
| sP0(X1,X2,relation_rng(X0))
| in(unordered_pair(singleton(sK9(X1,X2,relation_rng(X0))),unordered_pair(sK10(X1,X2,relation_rng(X0)),sK9(X1,X2,relation_rng(X0)))),X3)
| ~ in(sK10(X1,X2,relation_rng(X0)),X4)
| ~ sP0(X1,X4,X3) )
| ~ spl15_77
| ~ spl15_144 ),
inference(resolution,[],[f1347,f649]) ).
fof(f4806,plain,
( spl15_309
| ~ spl15_77
| ~ spl15_143 ),
inference(avatar_split_clause,[],[f1381,f1342,f648,f4804]) ).
fof(f4804,plain,
( spl15_309
<=> ! [X4,X0,X3,X2,X1] :
( ~ empty(X0)
| ~ relation(X0)
| sP0(relation_rng(X0),X1,X2)
| in(unordered_pair(singleton(sK9(relation_rng(X0),X1,X2)),unordered_pair(sK10(relation_rng(X0),X1,X2),sK9(relation_rng(X0),X1,X2))),X3)
| ~ in(sK10(relation_rng(X0),X1,X2),X4)
| ~ sP0(X2,X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_309])]) ).
fof(f1381,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ empty(X0)
| ~ relation(X0)
| sP0(relation_rng(X0),X1,X2)
| in(unordered_pair(singleton(sK9(relation_rng(X0),X1,X2)),unordered_pair(sK10(relation_rng(X0),X1,X2),sK9(relation_rng(X0),X1,X2))),X3)
| ~ in(sK10(relation_rng(X0),X1,X2),X4)
| ~ sP0(X2,X4,X3) )
| ~ spl15_77
| ~ spl15_143 ),
inference(resolution,[],[f1343,f649]) ).
fof(f4733,plain,
( spl15_308
| ~ spl15_23
| ~ spl15_166 ),
inference(avatar_split_clause,[],[f1675,f1667,f263,f4731]) ).
fof(f4731,plain,
( spl15_308
<=> ! [X2,X0,X1] :
( ~ relation(relation_rng_restriction(X0,X1))
| in(sK5(relation_rng_restriction(X0,X1),X2),X2)
| relation_rng(relation_rng_restriction(X0,X1)) = X2
| ~ relation(X1)
| ~ in(X1,unordered_pair(singleton(sK6(relation_rng_restriction(X0,X1),X2)),unordered_pair(sK6(relation_rng_restriction(X0,X1),X2),sK5(relation_rng_restriction(X0,X1),X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_308])]) ).
fof(f1675,plain,
( ! [X2,X0,X1] :
( ~ relation(relation_rng_restriction(X0,X1))
| in(sK5(relation_rng_restriction(X0,X1),X2),X2)
| relation_rng(relation_rng_restriction(X0,X1)) = X2
| ~ relation(X1)
| ~ in(X1,unordered_pair(singleton(sK6(relation_rng_restriction(X0,X1),X2)),unordered_pair(sK6(relation_rng_restriction(X0,X1),X2),sK5(relation_rng_restriction(X0,X1),X2)))) )
| ~ spl15_23
| ~ spl15_166 ),
inference(resolution,[],[f1668,f264]) ).
fof(f4729,plain,
( spl15_307
| ~ spl15_24
| ~ spl15_166 ),
inference(avatar_split_clause,[],[f1674,f1667,f267,f4727]) ).
fof(f4727,plain,
( spl15_307
<=> ! [X2,X0,X1] :
( ~ relation(relation_rng_restriction(X0,X1))
| in(sK5(relation_rng_restriction(X0,X1),X2),X2)
| relation_rng(relation_rng_restriction(X0,X1)) = X2
| ~ relation(X1)
| element(unordered_pair(singleton(sK6(relation_rng_restriction(X0,X1),X2)),unordered_pair(sK6(relation_rng_restriction(X0,X1),X2),sK5(relation_rng_restriction(X0,X1),X2))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_307])]) ).
fof(f1674,plain,
( ! [X2,X0,X1] :
( ~ relation(relation_rng_restriction(X0,X1))
| in(sK5(relation_rng_restriction(X0,X1),X2),X2)
| relation_rng(relation_rng_restriction(X0,X1)) = X2
| ~ relation(X1)
| element(unordered_pair(singleton(sK6(relation_rng_restriction(X0,X1),X2)),unordered_pair(sK6(relation_rng_restriction(X0,X1),X2),sK5(relation_rng_restriction(X0,X1),X2))),X1) )
| ~ spl15_24
| ~ spl15_166 ),
inference(resolution,[],[f1668,f268]) ).
fof(f4725,plain,
( spl15_306
| ~ spl15_42
| ~ spl15_149 ),
inference(avatar_split_clause,[],[f1458,f1419,f371,f4723]) ).
fof(f4723,plain,
( spl15_306
<=> ! [X4,X0,X3,X2,X1] :
( ~ relation(X0)
| in(sK5(X0,X1),X1)
| relation_rng(X0) = X1
| ~ sP0(X0,relation_rng(X0),X2)
| in(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X3)
| ~ in(sK5(X0,X1),X4)
| ~ sP0(X2,X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_306])]) ).
fof(f1458,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ relation(X0)
| in(sK5(X0,X1),X1)
| relation_rng(X0) = X1
| ~ sP0(X0,relation_rng(X0),X2)
| in(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X3)
| ~ in(sK5(X0,X1),X4)
| ~ sP0(X2,X4,X3) )
| ~ spl15_42
| ~ spl15_149 ),
inference(resolution,[],[f1420,f372]) ).
fof(f4677,plain,
( spl15_305
| ~ spl15_63
| ~ spl15_142 ),
inference(avatar_split_clause,[],[f1335,f1306,f536,f4675]) ).
fof(f1306,plain,
( spl15_142
<=> ! [X4,X0,X3,X2,X1] :
( sP0(X0,X1,X2)
| ~ empty(X0)
| in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X3)
| ~ sP0(X3,X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_142])]) ).
fof(f1335,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| in(unordered_pair(singleton(sK9(X0,X1,relation_rng_restriction(X2,X3))),unordered_pair(sK10(X0,X1,relation_rng_restriction(X2,X3)),sK9(X0,X1,relation_rng_restriction(X2,X3)))),X3)
| sP0(X0,X1,relation_rng_restriction(X2,X3))
| ~ relation(relation_rng_restriction(X2,X3))
| ~ relation(X3) )
| ~ spl15_63
| ~ spl15_142 ),
inference(resolution,[],[f1307,f537]) ).
fof(f1307,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ sP0(X3,X4,X2)
| ~ empty(X0)
| in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X3)
| sP0(X0,X1,X2) )
| ~ spl15_142 ),
inference(avatar_component_clause,[],[f1306]) ).
fof(f4673,plain,
( spl15_304
| ~ spl15_63
| ~ spl15_141 ),
inference(avatar_split_clause,[],[f1326,f1302,f536,f4671]) ).
fof(f1302,plain,
( spl15_141
<=> ! [X4,X0,X3,X2,X1] :
( sP0(X0,X1,X2)
| ~ empty(X2)
| in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X3)
| ~ sP0(X3,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_141])]) ).
fof(f1326,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| in(unordered_pair(singleton(sK9(relation_rng_restriction(X1,X2),X3,X0)),unordered_pair(sK10(relation_rng_restriction(X1,X2),X3,X0),sK9(relation_rng_restriction(X1,X2),X3,X0))),X2)
| sP0(relation_rng_restriction(X1,X2),X3,X0)
| ~ relation(relation_rng_restriction(X1,X2))
| ~ relation(X2) )
| ~ spl15_63
| ~ spl15_141 ),
inference(resolution,[],[f1303,f537]) ).
fof(f1303,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ sP0(X3,X4,X0)
| ~ empty(X2)
| in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X3)
| sP0(X0,X1,X2) )
| ~ spl15_141 ),
inference(avatar_component_clause,[],[f1302]) ).
fof(f4652,plain,
( spl15_303
| ~ spl15_18
| ~ spl15_292 ),
inference(avatar_split_clause,[],[f4504,f4381,f233,f4650]) ).
fof(f4381,plain,
( spl15_292
<=> ! [X0] :
( sK12 = relation_rng_restriction(relation_rng(relation_rng(relation_rng(relation_rng(X0)))),sK4)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_292])]) ).
fof(f4504,plain,
( ! [X0] :
( sK12 = relation_rng_restriction(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(X0))))),sK4)
| ~ empty(X0) )
| ~ spl15_18
| ~ spl15_292 ),
inference(resolution,[],[f4382,f234]) ).
fof(f4382,plain,
( ! [X0] :
( ~ empty(X0)
| sK12 = relation_rng_restriction(relation_rng(relation_rng(relation_rng(relation_rng(X0)))),sK4) )
| ~ spl15_292 ),
inference(avatar_component_clause,[],[f4381]) ).
fof(f4625,plain,
( spl15_302
| ~ spl15_47
| ~ spl15_101 ),
inference(avatar_split_clause,[],[f887,f868,f408,f4623]) ).
fof(f4623,plain,
( spl15_302
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| ~ relation(X0)
| ~ relation(relation_rng(X0))
| in(unordered_pair(singleton(sK9(X1,X2,relation_rng(relation_rng(X0)))),unordered_pair(sK10(X1,X2,relation_rng(relation_rng(X0))),sK9(X1,X2,relation_rng(relation_rng(X0))))),X1)
| sP0(X1,X2,relation_rng(relation_rng(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_302])]) ).
fof(f408,plain,
( spl15_47
<=> ! [X2,X0,X1] :
( in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X2)
| in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X0)
| sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_47])]) ).
fof(f887,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| ~ relation(X0)
| ~ relation(relation_rng(X0))
| in(unordered_pair(singleton(sK9(X1,X2,relation_rng(relation_rng(X0)))),unordered_pair(sK10(X1,X2,relation_rng(relation_rng(X0))),sK9(X1,X2,relation_rng(relation_rng(X0))))),X1)
| sP0(X1,X2,relation_rng(relation_rng(X0))) )
| ~ spl15_47
| ~ spl15_101 ),
inference(resolution,[],[f869,f409]) ).
fof(f409,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X2)
| in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X0)
| sP0(X0,X1,X2) )
| ~ spl15_47 ),
inference(avatar_component_clause,[],[f408]) ).
fof(f4621,plain,
( spl15_301
| ~ spl15_89
| ~ spl15_101 ),
inference(avatar_split_clause,[],[f885,f868,f738,f4619]) ).
fof(f4619,plain,
( spl15_301
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| ~ relation(X0)
| ~ relation(relation_rng(X0))
| element(unordered_pair(singleton(sK9(X1,X2,relation_rng(relation_rng(X0)))),unordered_pair(sK10(X1,X2,relation_rng(relation_rng(X0))),sK9(X1,X2,relation_rng(relation_rng(X0))))),X1)
| sP0(X1,X2,relation_rng(relation_rng(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_301])]) ).
fof(f738,plain,
( spl15_89
<=> ! [X2,X0,X1] :
( in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X2)
| sP0(X0,X1,X2)
| element(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_89])]) ).
fof(f885,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| ~ relation(X0)
| ~ relation(relation_rng(X0))
| element(unordered_pair(singleton(sK9(X1,X2,relation_rng(relation_rng(X0)))),unordered_pair(sK10(X1,X2,relation_rng(relation_rng(X0))),sK9(X1,X2,relation_rng(relation_rng(X0))))),X1)
| sP0(X1,X2,relation_rng(relation_rng(X0))) )
| ~ spl15_89
| ~ spl15_101 ),
inference(resolution,[],[f869,f739]) ).
fof(f739,plain,
( ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X0)
| in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X2)
| sP0(X0,X1,X2) )
| ~ spl15_89 ),
inference(avatar_component_clause,[],[f738]) ).
fof(f4617,plain,
( spl15_300
| ~ spl15_47
| ~ spl15_101 ),
inference(avatar_split_clause,[],[f883,f868,f408,f4615]) ).
fof(f883,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| ~ relation(X0)
| ~ relation(relation_rng(X0))
| in(unordered_pair(singleton(sK9(relation_rng(relation_rng(X0)),X1,X2)),unordered_pair(sK10(relation_rng(relation_rng(X0)),X1,X2),sK9(relation_rng(relation_rng(X0)),X1,X2))),X2)
| sP0(relation_rng(relation_rng(X0)),X1,X2) )
| ~ spl15_47
| ~ spl15_101 ),
inference(resolution,[],[f869,f409]) ).
fof(f4613,plain,
( spl15_299
| ~ spl15_87
| ~ spl15_101 ),
inference(avatar_split_clause,[],[f881,f868,f730,f4611]) ).
fof(f4611,plain,
( spl15_299
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| ~ relation(X0)
| ~ relation(relation_rng(X0))
| element(unordered_pair(singleton(sK9(relation_rng(relation_rng(X0)),X1,X2)),unordered_pair(sK10(relation_rng(relation_rng(X0)),X1,X2),sK9(relation_rng(relation_rng(X0)),X1,X2))),X2)
| sP0(relation_rng(relation_rng(X0)),X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_299])]) ).
fof(f730,plain,
( spl15_87
<=> ! [X2,X0,X1] :
( in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X0)
| sP0(X0,X1,X2)
| element(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_87])]) ).
fof(f881,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| ~ relation(X0)
| ~ relation(relation_rng(X0))
| element(unordered_pair(singleton(sK9(relation_rng(relation_rng(X0)),X1,X2)),unordered_pair(sK10(relation_rng(relation_rng(X0)),X1,X2),sK9(relation_rng(relation_rng(X0)),X1,X2))),X2)
| sP0(relation_rng(relation_rng(X0)),X1,X2) )
| ~ spl15_87
| ~ spl15_101 ),
inference(resolution,[],[f869,f731]) ).
fof(f731,plain,
( ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X2)
| in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X0)
| sP0(X0,X1,X2) )
| ~ spl15_87 ),
inference(avatar_component_clause,[],[f730]) ).
fof(f4455,plain,
( spl15_298
| ~ spl15_101
| ~ spl15_166 ),
inference(avatar_split_clause,[],[f1678,f1667,f868,f4453]) ).
fof(f4453,plain,
( spl15_298
<=> ! [X2,X0,X1] :
( ~ relation(relation_rng_restriction(X0,relation_rng(relation_rng(X1))))
| in(sK5(relation_rng_restriction(X0,relation_rng(relation_rng(X1))),X2),X2)
| relation_rng(relation_rng_restriction(X0,relation_rng(relation_rng(X1)))) = X2
| ~ relation(relation_rng(relation_rng(X1)))
| ~ empty(X1)
| ~ relation(X1)
| ~ relation(relation_rng(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_298])]) ).
fof(f1678,plain,
( ! [X2,X0,X1] :
( ~ relation(relation_rng_restriction(X0,relation_rng(relation_rng(X1))))
| in(sK5(relation_rng_restriction(X0,relation_rng(relation_rng(X1))),X2),X2)
| relation_rng(relation_rng_restriction(X0,relation_rng(relation_rng(X1)))) = X2
| ~ relation(relation_rng(relation_rng(X1)))
| ~ empty(X1)
| ~ relation(X1)
| ~ relation(relation_rng(X1)) )
| ~ spl15_101
| ~ spl15_166 ),
inference(resolution,[],[f1668,f869]) ).
fof(f4451,plain,
( spl15_297
| ~ spl15_126
| ~ spl15_162 ),
inference(avatar_split_clause,[],[f1643,f1632,f1154,f4449]) ).
fof(f1154,plain,
( spl15_126
<=> ! [X2,X0,X1] :
( in(sK10(X0,X1,X2),relation_rng(X2))
| ~ relation(X2)
| sP0(X0,X1,X2)
| in(sK10(X0,X1,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_126])]) ).
fof(f1632,plain,
( spl15_162
<=> ! [X4,X0,X3,X2,X1] :
( in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X3)
| ~ in(sK10(X0,X1,X2),X4)
| ~ sP0(X2,X4,X3)
| sP0(X0,X1,X2)
| in(sK10(X0,X1,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_162])]) ).
fof(f1643,plain,
( ! [X2,X3,X0,X1] :
( in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X3)
| ~ sP0(X2,relation_rng(X2),X3)
| sP0(X0,X1,X2)
| in(sK10(X0,X1,X2),X1)
| ~ relation(X2) )
| ~ spl15_126
| ~ spl15_162 ),
inference(duplicate_literal_removal,[],[f1640]) ).
fof(f1640,plain,
( ! [X2,X3,X0,X1] :
( in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X3)
| ~ sP0(X2,relation_rng(X2),X3)
| sP0(X0,X1,X2)
| in(sK10(X0,X1,X2),X1)
| in(sK10(X0,X1,X2),X1)
| sP0(X0,X1,X2)
| ~ relation(X2) )
| ~ spl15_126
| ~ spl15_162 ),
inference(resolution,[],[f1633,f1155]) ).
fof(f1155,plain,
( ! [X2,X0,X1] :
( in(sK10(X0,X1,X2),relation_rng(X2))
| in(sK10(X0,X1,X2),X1)
| sP0(X0,X1,X2)
| ~ relation(X2) )
| ~ spl15_126 ),
inference(avatar_component_clause,[],[f1154]) ).
fof(f1633,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ in(sK10(X0,X1,X2),X4)
| in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X3)
| ~ sP0(X2,X4,X3)
| sP0(X0,X1,X2)
| in(sK10(X0,X1,X2),X1) )
| ~ spl15_162 ),
inference(avatar_component_clause,[],[f1632]) ).
fof(f4447,plain,
( spl15_296
| ~ spl15_39
| ~ spl15_149 ),
inference(avatar_split_clause,[],[f1459,f1419,f354,f4445]) ).
fof(f4445,plain,
( spl15_296
<=> ! [X4,X0,X3,X2,X1] :
( ~ relation(X0)
| in(sK5(X0,X1),X1)
| relation_rng(X0) = X1
| ~ sP0(X0,relation_rng(X0),X2)
| in(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X3)
| ~ sP0(X3,X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_296])]) ).
fof(f1459,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ relation(X0)
| in(sK5(X0,X1),X1)
| relation_rng(X0) = X1
| ~ sP0(X0,relation_rng(X0),X2)
| in(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X3)
| ~ sP0(X3,X4,X2) )
| ~ spl15_39
| ~ spl15_149 ),
inference(resolution,[],[f1420,f355]) ).
fof(f4443,plain,
( spl15_295
| ~ spl15_72
| ~ spl15_148 ),
inference(avatar_split_clause,[],[f1448,f1415,f606,f4441]) ).
fof(f4441,plain,
( spl15_295
<=> ! [X4,X0,X3,X2,X1] :
( ~ relation(X0)
| in(sK10(X1,X2,X0),relation_rng(X0))
| sP0(X1,X2,X0)
| in(unordered_pair(singleton(sK9(X1,X2,X0)),unordered_pair(sK10(X1,X2,X0),sK9(X1,X2,X0))),X3)
| ~ sP0(X3,X4,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_295])]) ).
fof(f606,plain,
( spl15_72
<=> ! [X4,X0,X3,X2,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),X2)
| in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),X3)
| ~ sP0(X3,X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_72])]) ).
fof(f1448,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ relation(X0)
| in(sK10(X1,X2,X0),relation_rng(X0))
| sP0(X1,X2,X0)
| in(unordered_pair(singleton(sK9(X1,X2,X0)),unordered_pair(sK10(X1,X2,X0),sK9(X1,X2,X0))),X3)
| ~ sP0(X3,X4,X1) )
| ~ spl15_72
| ~ spl15_148 ),
inference(resolution,[],[f1416,f607]) ).
fof(f607,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),X2)
| in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),X3)
| ~ sP0(X3,X4,X2) )
| ~ spl15_72 ),
inference(avatar_component_clause,[],[f606]) ).
fof(f4439,plain,
( spl15_294
| ~ spl15_72
| ~ spl15_147 ),
inference(avatar_split_clause,[],[f1432,f1411,f606,f4437]) ).
fof(f4437,plain,
( spl15_294
<=> ! [X4,X0,X3,X2,X1] :
( ~ relation(X0)
| in(sK10(X0,X1,X2),relation_rng(X0))
| sP0(X0,X1,X2)
| in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X3)
| ~ sP0(X3,X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_294])]) ).
fof(f1432,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ relation(X0)
| in(sK10(X0,X1,X2),relation_rng(X0))
| sP0(X0,X1,X2)
| in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X3)
| ~ sP0(X3,X4,X2) )
| ~ spl15_72
| ~ spl15_147 ),
inference(resolution,[],[f1412,f607]) ).
fof(f4387,plain,
( spl15_293
| ~ spl15_72
| ~ spl15_144 ),
inference(avatar_split_clause,[],[f1395,f1346,f606,f4385]) ).
fof(f4385,plain,
( spl15_293
<=> ! [X4,X0,X3,X2,X1] :
( ~ empty(X0)
| ~ relation(X0)
| sP0(X1,X2,relation_rng(X0))
| in(unordered_pair(singleton(sK9(X1,X2,relation_rng(X0))),unordered_pair(sK10(X1,X2,relation_rng(X0)),sK9(X1,X2,relation_rng(X0)))),X3)
| ~ sP0(X3,X4,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_293])]) ).
fof(f1395,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ empty(X0)
| ~ relation(X0)
| sP0(X1,X2,relation_rng(X0))
| in(unordered_pair(singleton(sK9(X1,X2,relation_rng(X0))),unordered_pair(sK10(X1,X2,relation_rng(X0)),sK9(X1,X2,relation_rng(X0)))),X3)
| ~ sP0(X3,X4,X1) )
| ~ spl15_72
| ~ spl15_144 ),
inference(resolution,[],[f1347,f607]) ).
fof(f4383,plain,
( spl15_292
| ~ spl15_18
| ~ spl15_281 ),
inference(avatar_split_clause,[],[f4166,f4110,f233,f4381]) ).
fof(f4110,plain,
( spl15_281
<=> ! [X0] :
( sK12 = relation_rng_restriction(relation_rng(relation_rng(relation_rng(X0))),sK4)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_281])]) ).
fof(f4166,plain,
( ! [X0] :
( sK12 = relation_rng_restriction(relation_rng(relation_rng(relation_rng(relation_rng(X0)))),sK4)
| ~ empty(X0) )
| ~ spl15_18
| ~ spl15_281 ),
inference(resolution,[],[f4111,f234]) ).
fof(f4111,plain,
( ! [X0] :
( ~ empty(X0)
| sK12 = relation_rng_restriction(relation_rng(relation_rng(relation_rng(X0))),sK4) )
| ~ spl15_281 ),
inference(avatar_component_clause,[],[f4110]) ).
fof(f4379,plain,
( spl15_291
| ~ spl15_72
| ~ spl15_143 ),
inference(avatar_split_clause,[],[f1382,f1342,f606,f4377]) ).
fof(f4377,plain,
( spl15_291
<=> ! [X4,X0,X3,X2,X1] :
( ~ empty(X0)
| ~ relation(X0)
| sP0(relation_rng(X0),X1,X2)
| in(unordered_pair(singleton(sK9(relation_rng(X0),X1,X2)),unordered_pair(sK10(relation_rng(X0),X1,X2),sK9(relation_rng(X0),X1,X2))),X3)
| ~ sP0(X3,X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_291])]) ).
fof(f1382,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ empty(X0)
| ~ relation(X0)
| sP0(relation_rng(X0),X1,X2)
| in(unordered_pair(singleton(sK9(relation_rng(X0),X1,X2)),unordered_pair(sK10(relation_rng(X0),X1,X2),sK9(relation_rng(X0),X1,X2))),X3)
| ~ sP0(X3,X4,X2) )
| ~ spl15_72
| ~ spl15_143 ),
inference(resolution,[],[f1343,f607]) ).
fof(f4357,plain,
( spl15_290
| ~ spl15_101
| ~ spl15_138 ),
inference(avatar_split_clause,[],[f1282,f1267,f868,f4355]) ).
fof(f4355,plain,
( spl15_290
<=> ! [X2,X0,X1] :
( in(sK5(relation_rng_restriction(relation_rng(relation_rng(X0)),X1),X2),X2)
| ~ relation(relation_rng_restriction(relation_rng(relation_rng(X0)),X1))
| relation_rng(relation_rng_restriction(relation_rng(relation_rng(X0)),X1)) = X2
| ~ relation(X1)
| ~ empty(X0)
| ~ relation(X0)
| ~ relation(relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_290])]) ).
fof(f1282,plain,
( ! [X2,X0,X1] :
( in(sK5(relation_rng_restriction(relation_rng(relation_rng(X0)),X1),X2),X2)
| ~ relation(relation_rng_restriction(relation_rng(relation_rng(X0)),X1))
| relation_rng(relation_rng_restriction(relation_rng(relation_rng(X0)),X1)) = X2
| ~ relation(X1)
| ~ empty(X0)
| ~ relation(X0)
| ~ relation(relation_rng(X0)) )
| ~ spl15_101
| ~ spl15_138 ),
inference(resolution,[],[f1268,f869]) ).
fof(f4148,plain,
( spl15_289
| ~ spl15_35
| ~ spl15_166 ),
inference(avatar_split_clause,[],[f1672,f1667,f330,f4146]) ).
fof(f4146,plain,
( spl15_289
<=> ! [X4,X0,X3,X2,X1] :
( ~ relation(relation_rng_restriction(X0,X1))
| in(sK5(relation_rng_restriction(X0,X1),X2),X2)
| relation_rng(relation_rng_restriction(X0,X1)) = X2
| ~ relation(X1)
| in(sK5(relation_rng_restriction(X0,X1),X2),X3)
| ~ sP0(X4,X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_289])]) ).
fof(f330,plain,
( spl15_35
<=> ! [X5,X0,X6,X2,X1] :
( ~ in(unordered_pair(singleton(X5),unordered_pair(X5,X6)),X2)
| in(X6,X1)
| ~ sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_35])]) ).
fof(f1672,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ relation(relation_rng_restriction(X0,X1))
| in(sK5(relation_rng_restriction(X0,X1),X2),X2)
| relation_rng(relation_rng_restriction(X0,X1)) = X2
| ~ relation(X1)
| in(sK5(relation_rng_restriction(X0,X1),X2),X3)
| ~ sP0(X4,X3,X1) )
| ~ spl15_35
| ~ spl15_166 ),
inference(resolution,[],[f1668,f331]) ).
fof(f331,plain,
( ! [X2,X0,X1,X6,X5] :
( ~ in(unordered_pair(singleton(X5),unordered_pair(X5,X6)),X2)
| in(X6,X1)
| ~ sP0(X0,X1,X2) )
| ~ spl15_35 ),
inference(avatar_component_clause,[],[f330]) ).
fof(f4144,plain,
( spl15_288
| ~ spl15_114
| ~ spl15_160 ),
inference(avatar_split_clause,[],[f1620,f1596,f1005,f4142]) ).
fof(f1005,plain,
( spl15_114
<=> ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ empty(X0)
| in(sK10(X0,X1,X2),relation_rng(X2))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_114])]) ).
fof(f1596,plain,
( spl15_160
<=> ! [X4,X0,X3,X2,X1] :
( sP0(X0,X1,X2)
| ~ empty(X0)
| in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X3)
| ~ in(sK10(X0,X1,X2),X4)
| ~ sP0(X2,X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_160])]) ).
fof(f1620,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X3)
| sP0(X0,X1,X2)
| ~ sP0(X2,relation_rng(X2),X3)
| ~ relation(X2) )
| ~ spl15_114
| ~ spl15_160 ),
inference(duplicate_literal_removal,[],[f1619]) ).
fof(f1619,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X3)
| sP0(X0,X1,X2)
| ~ sP0(X2,relation_rng(X2),X3)
| ~ empty(X0)
| sP0(X0,X1,X2)
| ~ relation(X2) )
| ~ spl15_114
| ~ spl15_160 ),
inference(resolution,[],[f1597,f1006]) ).
fof(f1006,plain,
( ! [X2,X0,X1] :
( in(sK10(X0,X1,X2),relation_rng(X2))
| ~ empty(X0)
| sP0(X0,X1,X2)
| ~ relation(X2) )
| ~ spl15_114 ),
inference(avatar_component_clause,[],[f1005]) ).
fof(f1597,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ in(sK10(X0,X1,X2),X4)
| ~ empty(X0)
| in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X3)
| sP0(X0,X1,X2)
| ~ sP0(X2,X4,X3) )
| ~ spl15_160 ),
inference(avatar_component_clause,[],[f1596]) ).
fof(f4140,plain,
( spl15_287
| ~ spl15_113
| ~ spl15_159 ),
inference(avatar_split_clause,[],[f1608,f1592,f1001,f4138]) ).
fof(f1001,plain,
( spl15_113
<=> ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ empty(X2)
| in(sK10(X0,X1,X2),relation_rng(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_113])]) ).
fof(f1592,plain,
( spl15_159
<=> ! [X4,X0,X3,X2,X1] :
( sP0(X0,X1,X2)
| ~ empty(X2)
| in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X3)
| ~ in(sK10(X0,X1,X2),X4)
| ~ sP0(X0,X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_159])]) ).
fof(f1608,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| in(unordered_pair(singleton(sK9(X1,X2,X0)),unordered_pair(sK10(X1,X2,X0),sK9(X1,X2,X0))),X3)
| sP0(X1,X2,X0)
| ~ sP0(X1,relation_rng(X1),X3)
| ~ relation(X1) )
| ~ spl15_113
| ~ spl15_159 ),
inference(duplicate_literal_removal,[],[f1603]) ).
fof(f1603,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| in(unordered_pair(singleton(sK9(X1,X2,X0)),unordered_pair(sK10(X1,X2,X0),sK9(X1,X2,X0))),X3)
| sP0(X1,X2,X0)
| ~ sP0(X1,relation_rng(X1),X3)
| ~ empty(X0)
| sP0(X1,X2,X0)
| ~ relation(X1) )
| ~ spl15_113
| ~ spl15_159 ),
inference(resolution,[],[f1593,f1002]) ).
fof(f1002,plain,
( ! [X2,X0,X1] :
( in(sK10(X0,X1,X2),relation_rng(X0))
| ~ empty(X2)
| sP0(X0,X1,X2)
| ~ relation(X0) )
| ~ spl15_113 ),
inference(avatar_component_clause,[],[f1001]) ).
fof(f1593,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ in(sK10(X0,X1,X2),X4)
| ~ empty(X2)
| in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X3)
| sP0(X0,X1,X2)
| ~ sP0(X0,X4,X3) )
| ~ spl15_159 ),
inference(avatar_component_clause,[],[f1592]) ).
fof(f4136,plain,
( spl15_286
| ~ spl15_23
| ~ spl15_149 ),
inference(avatar_split_clause,[],[f1464,f1419,f263,f4134]) ).
fof(f4134,plain,
( spl15_286
<=> ! [X2,X0,X1] :
( ~ relation(X0)
| in(sK5(X0,X1),X1)
| relation_rng(X0) = X1
| ~ sP0(X0,relation_rng(X0),X2)
| ~ in(X2,unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_286])]) ).
fof(f1464,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| in(sK5(X0,X1),X1)
| relation_rng(X0) = X1
| ~ sP0(X0,relation_rng(X0),X2)
| ~ in(X2,unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1)))) )
| ~ spl15_23
| ~ spl15_149 ),
inference(resolution,[],[f1420,f264]) ).
fof(f4132,plain,
( spl15_285
| ~ spl15_24
| ~ spl15_149 ),
inference(avatar_split_clause,[],[f1463,f1419,f267,f4130]) ).
fof(f4130,plain,
( spl15_285
<=> ! [X2,X0,X1] :
( ~ relation(X0)
| in(sK5(X0,X1),X1)
| relation_rng(X0) = X1
| ~ sP0(X0,relation_rng(X0),X2)
| element(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_285])]) ).
fof(f1463,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| in(sK5(X0,X1),X1)
| relation_rng(X0) = X1
| ~ sP0(X0,relation_rng(X0),X2)
| element(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X2) )
| ~ spl15_24
| ~ spl15_149 ),
inference(resolution,[],[f1420,f268]) ).
fof(f4128,plain,
( spl15_284
| ~ spl15_23
| ~ spl15_148 ),
inference(avatar_split_clause,[],[f1452,f1415,f263,f4126]) ).
fof(f4126,plain,
( spl15_284
<=> ! [X2,X0,X1] :
( ~ relation(X0)
| in(sK10(X1,X2,X0),relation_rng(X0))
| sP0(X1,X2,X0)
| ~ in(X1,unordered_pair(singleton(sK9(X1,X2,X0)),unordered_pair(sK10(X1,X2,X0),sK9(X1,X2,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_284])]) ).
fof(f1452,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| in(sK10(X1,X2,X0),relation_rng(X0))
| sP0(X1,X2,X0)
| ~ in(X1,unordered_pair(singleton(sK9(X1,X2,X0)),unordered_pair(sK10(X1,X2,X0),sK9(X1,X2,X0)))) )
| ~ spl15_23
| ~ spl15_148 ),
inference(resolution,[],[f1416,f264]) ).
fof(f4124,plain,
( spl15_283
| ~ spl15_23
| ~ spl15_147 ),
inference(avatar_split_clause,[],[f1436,f1411,f263,f4122]) ).
fof(f4122,plain,
( spl15_283
<=> ! [X2,X0,X1] :
( ~ relation(X0)
| in(sK10(X0,X1,X2),relation_rng(X0))
| sP0(X0,X1,X2)
| ~ in(X2,unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_283])]) ).
fof(f1436,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| in(sK10(X0,X1,X2),relation_rng(X0))
| sP0(X0,X1,X2)
| ~ in(X2,unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2)))) )
| ~ spl15_23
| ~ spl15_147 ),
inference(resolution,[],[f1412,f264]) ).
fof(f4120,plain,
( spl15_282
| ~ spl15_101
| ~ spl15_138 ),
inference(avatar_split_clause,[],[f1276,f1267,f868,f4118]) ).
fof(f4118,plain,
( spl15_282
<=> ! [X2,X0,X1] :
( in(sK5(relation_rng_restriction(X0,X1),relation_rng(relation_rng(X2))),X0)
| ~ relation(relation_rng_restriction(X0,X1))
| relation_rng(relation_rng_restriction(X0,X1)) = relation_rng(relation_rng(X2))
| ~ relation(X1)
| ~ empty(X2)
| ~ relation(X2)
| ~ relation(relation_rng(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_282])]) ).
fof(f1276,plain,
( ! [X2,X0,X1] :
( in(sK5(relation_rng_restriction(X0,X1),relation_rng(relation_rng(X2))),X0)
| ~ relation(relation_rng_restriction(X0,X1))
| relation_rng(relation_rng_restriction(X0,X1)) = relation_rng(relation_rng(X2))
| ~ relation(X1)
| ~ empty(X2)
| ~ relation(X2)
| ~ relation(relation_rng(X2)) )
| ~ spl15_101
| ~ spl15_138 ),
inference(resolution,[],[f1268,f869]) ).
fof(f4112,plain,
( spl15_281
| ~ spl15_18
| ~ spl15_271 ),
inference(avatar_split_clause,[],[f3916,f3790,f233,f4110]) ).
fof(f3790,plain,
( spl15_271
<=> ! [X0] :
( sK12 = relation_rng_restriction(relation_rng(relation_rng(X0)),sK4)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_271])]) ).
fof(f3916,plain,
( ! [X0] :
( sK12 = relation_rng_restriction(relation_rng(relation_rng(relation_rng(X0))),sK4)
| ~ empty(X0) )
| ~ spl15_18
| ~ spl15_271 ),
inference(resolution,[],[f3791,f234]) ).
fof(f3791,plain,
( ! [X0] :
( ~ empty(X0)
| sK12 = relation_rng_restriction(relation_rng(relation_rng(X0)),sK4) )
| ~ spl15_271 ),
inference(avatar_component_clause,[],[f3790]) ).
fof(f4104,plain,
( spl15_280
| ~ spl15_23
| ~ spl15_144 ),
inference(avatar_split_clause,[],[f1399,f1346,f263,f4102]) ).
fof(f4102,plain,
( spl15_280
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| ~ relation(X0)
| sP0(X1,X2,relation_rng(X0))
| ~ in(X1,unordered_pair(singleton(sK9(X1,X2,relation_rng(X0))),unordered_pair(sK10(X1,X2,relation_rng(X0)),sK9(X1,X2,relation_rng(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_280])]) ).
fof(f1399,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| ~ relation(X0)
| sP0(X1,X2,relation_rng(X0))
| ~ in(X1,unordered_pair(singleton(sK9(X1,X2,relation_rng(X0))),unordered_pair(sK10(X1,X2,relation_rng(X0)),sK9(X1,X2,relation_rng(X0))))) )
| ~ spl15_23
| ~ spl15_144 ),
inference(resolution,[],[f1347,f264]) ).
fof(f4100,plain,
( spl15_279
| ~ spl15_23
| ~ spl15_143 ),
inference(avatar_split_clause,[],[f1386,f1342,f263,f4098]) ).
fof(f4098,plain,
( spl15_279
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| ~ relation(X0)
| sP0(relation_rng(X0),X1,X2)
| ~ in(X2,unordered_pair(singleton(sK9(relation_rng(X0),X1,X2)),unordered_pair(sK10(relation_rng(X0),X1,X2),sK9(relation_rng(X0),X1,X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_279])]) ).
fof(f1386,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| ~ relation(X0)
| sP0(relation_rng(X0),X1,X2)
| ~ in(X2,unordered_pair(singleton(sK9(relation_rng(X0),X1,X2)),unordered_pair(sK10(relation_rng(X0),X1,X2),sK9(relation_rng(X0),X1,X2)))) )
| ~ spl15_23
| ~ spl15_143 ),
inference(resolution,[],[f1343,f264]) ).
fof(f3979,plain,
( spl15_278
| ~ spl15_109
| ~ spl15_156 ),
inference(avatar_split_clause,[],[f1567,f1497,f919,f3977]) ).
fof(f919,plain,
( spl15_109
<=> ! [X0,X1] :
( sP0(X0,X1,X0)
| in(sK10(X0,X1,X0),relation_rng(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_109])]) ).
fof(f1497,plain,
( spl15_156
<=> ! [X0,X3,X2,X1] :
( in(unordered_pair(singleton(sK9(X0,X1,X0)),unordered_pair(sK10(X0,X1,X0),sK9(X0,X1,X0))),X2)
| ~ in(sK10(X0,X1,X0),X3)
| ~ sP0(X0,X3,X2)
| sP0(X0,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_156])]) ).
fof(f1567,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(singleton(sK9(X0,X1,X0)),unordered_pair(sK10(X0,X1,X0),sK9(X0,X1,X0))),X2)
| ~ sP0(X0,relation_rng(X0),X2)
| sP0(X0,X1,X0)
| ~ relation(X0) )
| ~ spl15_109
| ~ spl15_156 ),
inference(duplicate_literal_removal,[],[f1560]) ).
fof(f1560,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(singleton(sK9(X0,X1,X0)),unordered_pair(sK10(X0,X1,X0),sK9(X0,X1,X0))),X2)
| ~ sP0(X0,relation_rng(X0),X2)
| sP0(X0,X1,X0)
| sP0(X0,X1,X0)
| ~ relation(X0) )
| ~ spl15_109
| ~ spl15_156 ),
inference(resolution,[],[f1498,f920]) ).
fof(f920,plain,
( ! [X0,X1] :
( in(sK10(X0,X1,X0),relation_rng(X0))
| sP0(X0,X1,X0)
| ~ relation(X0) )
| ~ spl15_109 ),
inference(avatar_component_clause,[],[f919]) ).
fof(f1498,plain,
( ! [X2,X3,X0,X1] :
( ~ in(sK10(X0,X1,X0),X3)
| in(unordered_pair(singleton(sK9(X0,X1,X0)),unordered_pair(sK10(X0,X1,X0),sK9(X0,X1,X0))),X2)
| ~ sP0(X0,X3,X2)
| sP0(X0,X1,X0) )
| ~ spl15_156 ),
inference(avatar_component_clause,[],[f1497]) ).
fof(f3975,plain,
( spl15_277
| ~ spl15_63
| ~ spl15_131 ),
inference(avatar_split_clause,[],[f1208,f1197,f536,f3973]) ).
fof(f1197,plain,
( spl15_131
<=> ! [X0,X3,X2,X1] :
( in(unordered_pair(singleton(sK7(X0,X1)),unordered_pair(X1,sK7(X0,X1))),X2)
| ~ sP0(X2,X3,X0)
| ~ in(X1,relation_rng(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_131])]) ).
fof(f1208,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(singleton(sK7(relation_rng_restriction(X0,X1),X2)),unordered_pair(X2,sK7(relation_rng_restriction(X0,X1),X2))),X1)
| ~ in(X2,relation_rng(relation_rng_restriction(X0,X1)))
| ~ relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) )
| ~ spl15_63
| ~ spl15_131 ),
inference(duplicate_literal_removal,[],[f1203]) ).
fof(f1203,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(singleton(sK7(relation_rng_restriction(X0,X1),X2)),unordered_pair(X2,sK7(relation_rng_restriction(X0,X1),X2))),X1)
| ~ in(X2,relation_rng(relation_rng_restriction(X0,X1)))
| ~ relation(relation_rng_restriction(X0,X1))
| ~ relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) )
| ~ spl15_63
| ~ spl15_131 ),
inference(resolution,[],[f1198,f537]) ).
fof(f1198,plain,
( ! [X2,X3,X0,X1] :
( ~ sP0(X2,X3,X0)
| in(unordered_pair(singleton(sK7(X0,X1)),unordered_pair(X1,sK7(X0,X1))),X2)
| ~ in(X1,relation_rng(X0))
| ~ relation(X0) )
| ~ spl15_131 ),
inference(avatar_component_clause,[],[f1197]) ).
fof(f3971,plain,
( spl15_276
| ~ spl15_63
| ~ spl15_127 ),
inference(avatar_split_clause,[],[f1178,f1172,f536,f3969]) ).
fof(f1172,plain,
( spl15_127
<=> ! [X4,X0,X3,X2,X1] :
( in(sK10(X0,X1,X2),X3)
| ~ sP0(X4,X3,X2)
| sP0(X0,X1,X2)
| in(sK10(X0,X1,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_127])]) ).
fof(f1178,plain,
( ! [X2,X3,X0,X1] :
( in(sK10(X0,X1,relation_rng_restriction(X2,X3)),X2)
| sP0(X0,X1,relation_rng_restriction(X2,X3))
| in(sK10(X0,X1,relation_rng_restriction(X2,X3)),X1)
| ~ relation(relation_rng_restriction(X2,X3))
| ~ relation(X3) )
| ~ spl15_63
| ~ spl15_127 ),
inference(resolution,[],[f1173,f537]) ).
fof(f1173,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ sP0(X4,X3,X2)
| in(sK10(X0,X1,X2),X3)
| sP0(X0,X1,X2)
| in(sK10(X0,X1,X2),X1) )
| ~ spl15_127 ),
inference(avatar_component_clause,[],[f1172]) ).
fof(f3853,plain,
( spl15_275
| ~ spl15_34
| ~ spl15_166 ),
inference(avatar_split_clause,[],[f1682,f1667,f324,f3851]) ).
fof(f324,plain,
( spl15_34
<=> ! [X5,X0,X6] :
( ~ in(unordered_pair(singleton(X6),unordered_pair(X6,X5)),X0)
| in(X5,relation_rng(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_34])]) ).
fof(f1682,plain,
( ! [X2,X0,X1] :
( ~ relation(relation_rng_restriction(X0,X1))
| in(sK5(relation_rng_restriction(X0,X1),X2),X2)
| relation_rng(relation_rng_restriction(X0,X1)) = X2
| ~ relation(X1)
| in(sK5(relation_rng_restriction(X0,X1),X2),relation_rng(X1)) )
| ~ spl15_34
| ~ spl15_166 ),
inference(duplicate_literal_removal,[],[f1673]) ).
fof(f1673,plain,
( ! [X2,X0,X1] :
( ~ relation(relation_rng_restriction(X0,X1))
| in(sK5(relation_rng_restriction(X0,X1),X2),X2)
| relation_rng(relation_rng_restriction(X0,X1)) = X2
| ~ relation(X1)
| in(sK5(relation_rng_restriction(X0,X1),X2),relation_rng(X1))
| ~ relation(X1) )
| ~ spl15_34
| ~ spl15_166 ),
inference(resolution,[],[f1668,f325]) ).
fof(f325,plain,
( ! [X0,X6,X5] :
( ~ in(unordered_pair(singleton(X6),unordered_pair(X6,X5)),X0)
| in(X5,relation_rng(X0))
| ~ relation(X0) )
| ~ spl15_34 ),
inference(avatar_component_clause,[],[f324]) ).
fof(f3849,plain,
( spl15_274
| ~ spl15_61
| ~ spl15_166 ),
inference(avatar_split_clause,[],[f1677,f1667,f511,f3847]) ).
fof(f1677,plain,
( ! [X2,X0,X1] :
( ~ relation(relation_rng_restriction(X0,relation_rng(X1)))
| in(sK5(relation_rng_restriction(X0,relation_rng(X1)),X2),X2)
| relation_rng(relation_rng_restriction(X0,relation_rng(X1))) = X2
| ~ relation(relation_rng(X1))
| ~ relation(X1)
| ~ empty(X1) )
| ~ spl15_61
| ~ spl15_166 ),
inference(resolution,[],[f1668,f512]) ).
fof(f3845,plain,
( spl15_273
| ~ spl15_64
| ~ spl15_159 ),
inference(avatar_split_clause,[],[f1611,f1592,f540,f3843]) ).
fof(f1611,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| in(unordered_pair(singleton(sK9(X1,X2,X0)),unordered_pair(sK10(X1,X2,X0),sK9(X1,X2,X0))),X3)
| sP0(X1,X2,X0)
| ~ sP0(X1,X2,X3) )
| ~ spl15_64
| ~ spl15_159 ),
inference(duplicate_literal_removal,[],[f1600]) ).
fof(f1600,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| in(unordered_pair(singleton(sK9(X1,X2,X0)),unordered_pair(sK10(X1,X2,X0),sK9(X1,X2,X0))),X3)
| sP0(X1,X2,X0)
| ~ sP0(X1,X2,X3)
| sP0(X1,X2,X0)
| ~ empty(X0) )
| ~ spl15_64
| ~ spl15_159 ),
inference(resolution,[],[f1593,f541]) ).
fof(f3841,plain,
( spl15_272
| ~ spl15_63
| ~ spl15_137 ),
inference(avatar_split_clause,[],[f1265,f1244,f536,f3839]) ).
fof(f1244,plain,
( spl15_137
<=> ! [X0,X3,X2,X1] :
( in(unordered_pair(singleton(sK7(X0,X1)),unordered_pair(X1,sK7(X0,X1))),X2)
| ~ in(X1,X3)
| ~ sP0(X0,X3,X2)
| ~ in(X1,relation_rng(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_137])]) ).
fof(f1265,plain,
( ! [X2,X0,X1] :
( ~ in(X0,X1)
| in(unordered_pair(singleton(sK7(X2,X0)),unordered_pair(X0,sK7(X2,X0))),relation_rng_restriction(X1,X2))
| ~ in(X0,relation_rng(X2))
| ~ relation(X2)
| ~ relation(relation_rng_restriction(X1,X2)) )
| ~ spl15_63
| ~ spl15_137 ),
inference(duplicate_literal_removal,[],[f1259]) ).
fof(f1259,plain,
( ! [X2,X0,X1] :
( ~ in(X0,X1)
| in(unordered_pair(singleton(sK7(X2,X0)),unordered_pair(X0,sK7(X2,X0))),relation_rng_restriction(X1,X2))
| ~ in(X0,relation_rng(X2))
| ~ relation(X2)
| ~ relation(relation_rng_restriction(X1,X2))
| ~ relation(X2) )
| ~ spl15_63
| ~ spl15_137 ),
inference(resolution,[],[f1245,f537]) ).
fof(f1245,plain,
( ! [X2,X3,X0,X1] :
( ~ sP0(X0,X3,X2)
| ~ in(X1,X3)
| in(unordered_pair(singleton(sK7(X0,X1)),unordered_pair(X1,sK7(X0,X1))),X2)
| ~ in(X1,relation_rng(X0))
| ~ relation(X0) )
| ~ spl15_137 ),
inference(avatar_component_clause,[],[f1244]) ).
fof(f3792,plain,
( spl15_271
| ~ spl15_18
| ~ spl15_223 ),
inference(avatar_split_clause,[],[f2652,f2615,f233,f3790]) ).
fof(f2615,plain,
( spl15_223
<=> ! [X0] :
( sK12 = relation_rng_restriction(relation_rng(X0),sK4)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_223])]) ).
fof(f2652,plain,
( ! [X0] :
( sK12 = relation_rng_restriction(relation_rng(relation_rng(X0)),sK4)
| ~ empty(X0) )
| ~ spl15_18
| ~ spl15_223 ),
inference(resolution,[],[f2616,f234]) ).
fof(f2616,plain,
( ! [X0] :
( ~ empty(X0)
| sK12 = relation_rng_restriction(relation_rng(X0),sK4) )
| ~ spl15_223 ),
inference(avatar_component_clause,[],[f2615]) ).
fof(f3761,plain,
( spl15_270
| ~ spl15_61
| ~ spl15_138 ),
inference(avatar_split_clause,[],[f1281,f1267,f511,f3759]) ).
fof(f3759,plain,
( spl15_270
<=> ! [X2,X0,X1] :
( in(sK5(relation_rng_restriction(relation_rng(X0),X1),X2),X2)
| ~ relation(relation_rng_restriction(relation_rng(X0),X1))
| relation_rng(relation_rng_restriction(relation_rng(X0),X1)) = X2
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_270])]) ).
fof(f1281,plain,
( ! [X2,X0,X1] :
( in(sK5(relation_rng_restriction(relation_rng(X0),X1),X2),X2)
| ~ relation(relation_rng_restriction(relation_rng(X0),X1))
| relation_rng(relation_rng_restriction(relation_rng(X0),X1)) = X2
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(X0) )
| ~ spl15_61
| ~ spl15_138 ),
inference(resolution,[],[f1268,f512]) ).
fof(f3757,plain,
( spl15_269
| ~ spl15_23
| ~ spl15_138 ),
inference(avatar_split_clause,[],[f1279,f1267,f263,f3755]) ).
fof(f3755,plain,
( spl15_269
<=> ! [X2,X0,X1] :
( in(sK5(relation_rng_restriction(X0,X1),X2),X2)
| ~ relation(relation_rng_restriction(X0,X1))
| relation_rng(relation_rng_restriction(X0,X1)) = X2
| ~ relation(X1)
| ~ in(X0,sK5(relation_rng_restriction(X0,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_269])]) ).
fof(f1279,plain,
( ! [X2,X0,X1] :
( in(sK5(relation_rng_restriction(X0,X1),X2),X2)
| ~ relation(relation_rng_restriction(X0,X1))
| relation_rng(relation_rng_restriction(X0,X1)) = X2
| ~ relation(X1)
| ~ in(X0,sK5(relation_rng_restriction(X0,X1),X2)) )
| ~ spl15_23
| ~ spl15_138 ),
inference(resolution,[],[f1268,f264]) ).
fof(f3753,plain,
( spl15_268
| ~ spl15_24
| ~ spl15_138 ),
inference(avatar_split_clause,[],[f1278,f1267,f267,f3751]) ).
fof(f3751,plain,
( spl15_268
<=> ! [X2,X0,X1] :
( in(sK5(relation_rng_restriction(X0,X1),X2),X2)
| ~ relation(relation_rng_restriction(X0,X1))
| relation_rng(relation_rng_restriction(X0,X1)) = X2
| ~ relation(X1)
| element(sK5(relation_rng_restriction(X0,X1),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_268])]) ).
fof(f1278,plain,
( ! [X2,X0,X1] :
( in(sK5(relation_rng_restriction(X0,X1),X2),X2)
| ~ relation(relation_rng_restriction(X0,X1))
| relation_rng(relation_rng_restriction(X0,X1)) = X2
| ~ relation(X1)
| element(sK5(relation_rng_restriction(X0,X1),X2),X0) )
| ~ spl15_24
| ~ spl15_138 ),
inference(resolution,[],[f1268,f268]) ).
fof(f3749,plain,
( spl15_267
| ~ spl15_23
| ~ spl15_138 ),
inference(avatar_split_clause,[],[f1273,f1267,f263,f3747]) ).
fof(f3747,plain,
( spl15_267
<=> ! [X2,X0,X1] :
( in(sK5(relation_rng_restriction(X0,X1),X2),X0)
| ~ relation(relation_rng_restriction(X0,X1))
| relation_rng(relation_rng_restriction(X0,X1)) = X2
| ~ relation(X1)
| ~ in(X2,sK5(relation_rng_restriction(X0,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_267])]) ).
fof(f1273,plain,
( ! [X2,X0,X1] :
( in(sK5(relation_rng_restriction(X0,X1),X2),X0)
| ~ relation(relation_rng_restriction(X0,X1))
| relation_rng(relation_rng_restriction(X0,X1)) = X2
| ~ relation(X1)
| ~ in(X2,sK5(relation_rng_restriction(X0,X1),X2)) )
| ~ spl15_23
| ~ spl15_138 ),
inference(resolution,[],[f1268,f264]) ).
fof(f3745,plain,
( spl15_266
| ~ spl15_24
| ~ spl15_138 ),
inference(avatar_split_clause,[],[f1272,f1267,f267,f3743]) ).
fof(f3743,plain,
( spl15_266
<=> ! [X2,X0,X1] :
( in(sK5(relation_rng_restriction(X0,X1),X2),X0)
| ~ relation(relation_rng_restriction(X0,X1))
| relation_rng(relation_rng_restriction(X0,X1)) = X2
| ~ relation(X1)
| element(sK5(relation_rng_restriction(X0,X1),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_266])]) ).
fof(f1272,plain,
( ! [X2,X0,X1] :
( in(sK5(relation_rng_restriction(X0,X1),X2),X0)
| ~ relation(relation_rng_restriction(X0,X1))
| relation_rng(relation_rng_restriction(X0,X1)) = X2
| ~ relation(X1)
| element(sK5(relation_rng_restriction(X0,X1),X2),X2) )
| ~ spl15_24
| ~ spl15_138 ),
inference(resolution,[],[f1268,f268]) ).
fof(f3653,plain,
( spl15_265
| ~ spl15_101
| ~ spl15_149 ),
inference(avatar_split_clause,[],[f1475,f1419,f868,f3651]) ).
fof(f3651,plain,
( spl15_265
<=> ! [X2,X0,X1] :
( ~ relation(X0)
| in(sK5(X0,X1),X1)
| relation_rng(X0) = X1
| ~ sP0(X0,relation_rng(X0),relation_rng(relation_rng(X2)))
| ~ empty(X2)
| ~ relation(X2)
| ~ relation(relation_rng(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_265])]) ).
fof(f1475,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| in(sK5(X0,X1),X1)
| relation_rng(X0) = X1
| ~ sP0(X0,relation_rng(X0),relation_rng(relation_rng(X2)))
| ~ empty(X2)
| ~ relation(X2)
| ~ relation(relation_rng(X2)) )
| ~ spl15_101
| ~ spl15_149 ),
inference(resolution,[],[f1420,f869]) ).
fof(f3649,plain,
( spl15_264
| ~ spl15_35
| ~ spl15_149 ),
inference(avatar_split_clause,[],[f1460,f1419,f330,f3647]) ).
fof(f3647,plain,
( spl15_264
<=> ! [X4,X0,X3,X2,X1] :
( ~ relation(X0)
| in(sK5(X0,X1),X1)
| relation_rng(X0) = X1
| ~ sP0(X0,relation_rng(X0),X2)
| in(sK5(X0,X1),X3)
| ~ sP0(X4,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_264])]) ).
fof(f1460,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ relation(X0)
| in(sK5(X0,X1),X1)
| relation_rng(X0) = X1
| ~ sP0(X0,relation_rng(X0),X2)
| in(sK5(X0,X1),X3)
| ~ sP0(X4,X3,X2) )
| ~ spl15_35
| ~ spl15_149 ),
inference(resolution,[],[f1420,f331]) ).
fof(f3645,plain,
( spl15_263
| ~ spl15_61
| ~ spl15_138 ),
inference(avatar_split_clause,[],[f1275,f1267,f511,f3643]) ).
fof(f1275,plain,
( ! [X2,X0,X1] :
( in(sK5(relation_rng_restriction(X0,X1),relation_rng(X2)),X0)
| ~ relation(relation_rng_restriction(X0,X1))
| relation_rng(X2) = relation_rng(relation_rng_restriction(X0,X1))
| ~ relation(X1)
| ~ relation(X2)
| ~ empty(X2) )
| ~ spl15_61
| ~ spl15_138 ),
inference(resolution,[],[f1268,f512]) ).
fof(f3465,plain,
( spl15_262
| ~ spl15_34
| ~ spl15_149 ),
inference(avatar_split_clause,[],[f1461,f1419,f324,f3463]) ).
fof(f3463,plain,
( spl15_262
<=> ! [X2,X0,X1] :
( ~ relation(X0)
| in(sK5(X0,X1),X1)
| relation_rng(X0) = X1
| ~ sP0(X0,relation_rng(X0),X2)
| in(sK5(X0,X1),relation_rng(X2))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_262])]) ).
fof(f1461,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| in(sK5(X0,X1),X1)
| relation_rng(X0) = X1
| ~ sP0(X0,relation_rng(X0),X2)
| in(sK5(X0,X1),relation_rng(X2))
| ~ relation(X2) )
| ~ spl15_34
| ~ spl15_149 ),
inference(resolution,[],[f1420,f325]) ).
fof(f3461,plain,
( ~ spl15_1
| ~ spl15_19
| ~ spl15_29
| spl15_234 ),
inference(avatar_split_clause,[],[f3366,f2798,f300,f237,f151]) ).
fof(f2798,plain,
( spl15_234
<=> sP1(sK12,sK12,sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_234])]) ).
fof(f3366,plain,
( ~ relation(sK12)
| ~ relation(sK4)
| ~ spl15_29
| spl15_234 ),
inference(resolution,[],[f2800,f301]) ).
fof(f2800,plain,
( ~ sP1(sK12,sK12,sK4)
| spl15_234 ),
inference(avatar_component_clause,[],[f2798]) ).
fof(f3460,plain,
( spl15_261
| ~ spl15_101
| ~ spl15_148 ),
inference(avatar_split_clause,[],[f1455,f1415,f868,f3458]) ).
fof(f1455,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| in(sK10(relation_rng(relation_rng(X1)),X2,X0),relation_rng(X0))
| sP0(relation_rng(relation_rng(X1)),X2,X0)
| ~ empty(X1)
| ~ relation(X1)
| ~ relation(relation_rng(X1)) )
| ~ spl15_101
| ~ spl15_148 ),
inference(resolution,[],[f1416,f869]) ).
fof(f3456,plain,
( spl15_260
| ~ spl15_101
| ~ spl15_147 ),
inference(avatar_split_clause,[],[f1439,f1411,f868,f3454]) ).
fof(f1439,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| in(sK10(X0,X1,relation_rng(relation_rng(X2))),relation_rng(X0))
| sP0(X0,X1,relation_rng(relation_rng(X2)))
| ~ empty(X2)
| ~ relation(X2)
| ~ relation(relation_rng(X2)) )
| ~ spl15_101
| ~ spl15_147 ),
inference(resolution,[],[f1412,f869]) ).
fof(f3452,plain,
( spl15_259
| ~ spl15_101
| ~ spl15_126 ),
inference(avatar_split_clause,[],[f1166,f1154,f868,f3450]) ).
fof(f1166,plain,
( ! [X2,X0,X1] :
( in(sK10(X0,relation_rng(relation_rng(X1)),X2),relation_rng(X2))
| sP0(X0,relation_rng(relation_rng(X1)),X2)
| ~ relation(X2)
| ~ empty(X1)
| ~ relation(X1)
| ~ relation(relation_rng(X1)) )
| ~ spl15_101
| ~ spl15_126 ),
inference(resolution,[],[f1155,f869]) ).
fof(f3448,plain,
( spl15_258
| ~ spl15_63
| ~ spl15_112 ),
inference(avatar_split_clause,[],[f995,f961,f536,f3446]) ).
fof(f961,plain,
( spl15_112
<=> ! [X2,X0,X1,X3] :
( sP0(X0,X1,X0)
| in(sK10(X0,X1,X0),X2)
| ~ sP0(X3,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_112])]) ).
fof(f995,plain,
( ! [X2,X0,X1] :
( in(sK10(relation_rng_restriction(X0,X1),X2,relation_rng_restriction(X0,X1)),X0)
| sP0(relation_rng_restriction(X0,X1),X2,relation_rng_restriction(X0,X1))
| ~ relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) )
| ~ spl15_63
| ~ spl15_112 ),
inference(resolution,[],[f962,f537]) ).
fof(f962,plain,
( ! [X2,X3,X0,X1] :
( ~ sP0(X3,X2,X0)
| in(sK10(X0,X1,X0),X2)
| sP0(X0,X1,X0) )
| ~ spl15_112 ),
inference(avatar_component_clause,[],[f961]) ).
fof(f3444,plain,
( spl15_257
| ~ spl15_45
| ~ spl15_101 ),
inference(avatar_split_clause,[],[f880,f868,f387,f3442]) ).
fof(f387,plain,
( spl15_45
<=> ! [X0,X1] :
( in(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X0)
| relation_rng(X0) = X1
| in(sK5(X0,X1),X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_45])]) ).
fof(f880,plain,
( ! [X0,X1] :
( ~ empty(X0)
| ~ relation(X0)
| ~ relation(relation_rng(X0))
| relation_rng(relation_rng(relation_rng(X0))) = X1
| in(sK5(relation_rng(relation_rng(X0)),X1),X1)
| ~ relation(relation_rng(relation_rng(X0))) )
| ~ spl15_45
| ~ spl15_101 ),
inference(resolution,[],[f869,f388]) ).
fof(f388,plain,
( ! [X0,X1] :
( in(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X0)
| relation_rng(X0) = X1
| in(sK5(X0,X1),X1)
| ~ relation(X0) )
| ~ spl15_45 ),
inference(avatar_component_clause,[],[f387]) ).
fof(f3370,plain,
( spl15_256
| ~ spl15_68
| ~ spl15_148 ),
inference(avatar_split_clause,[],[f1449,f1415,f573,f3368]) ).
fof(f3368,plain,
( spl15_256
<=> ! [X4,X0,X3,X2,X1] :
( ~ relation(X0)
| in(sK10(X1,X2,X0),relation_rng(X0))
| sP0(X1,X2,X0)
| in(sK10(X1,X2,X0),X3)
| ~ sP0(X4,X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_256])]) ).
fof(f1449,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ relation(X0)
| in(sK10(X1,X2,X0),relation_rng(X0))
| sP0(X1,X2,X0)
| in(sK10(X1,X2,X0),X3)
| ~ sP0(X4,X3,X1) )
| ~ spl15_68
| ~ spl15_148 ),
inference(resolution,[],[f1416,f574]) ).
fof(f3365,plain,
( spl15_255
| ~ spl15_68
| ~ spl15_147 ),
inference(avatar_split_clause,[],[f1433,f1411,f573,f3363]) ).
fof(f3363,plain,
( spl15_255
<=> ! [X4,X0,X3,X2,X1] :
( ~ relation(X0)
| in(sK10(X0,X1,X2),relation_rng(X0))
| sP0(X0,X1,X2)
| in(sK10(X0,X1,X2),X3)
| ~ sP0(X4,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_255])]) ).
fof(f1433,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ relation(X0)
| in(sK10(X0,X1,X2),relation_rng(X0))
| sP0(X0,X1,X2)
| in(sK10(X0,X1,X2),X3)
| ~ sP0(X4,X3,X2) )
| ~ spl15_68
| ~ spl15_147 ),
inference(resolution,[],[f1412,f574]) ).
fof(f3361,plain,
( spl15_254
| ~ spl15_101
| ~ spl15_119 ),
inference(avatar_split_clause,[],[f1088,f1063,f868,f3359]) ).
fof(f3359,plain,
( spl15_254
<=> ! [X0,X1] :
( element(sK5(X0,relation_rng(relation_rng(X1))),relation_rng(X0))
| relation_rng(X0) = relation_rng(relation_rng(X1))
| ~ relation(X0)
| ~ empty(X1)
| ~ relation(X1)
| ~ relation(relation_rng(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_254])]) ).
fof(f1063,plain,
( spl15_119
<=> ! [X0,X1] :
( in(sK5(X0,X1),X1)
| ~ relation(X0)
| relation_rng(X0) = X1
| element(sK5(X0,X1),relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_119])]) ).
fof(f1088,plain,
( ! [X0,X1] :
( element(sK5(X0,relation_rng(relation_rng(X1))),relation_rng(X0))
| relation_rng(X0) = relation_rng(relation_rng(X1))
| ~ relation(X0)
| ~ empty(X1)
| ~ relation(X1)
| ~ relation(relation_rng(X1)) )
| ~ spl15_101
| ~ spl15_119 ),
inference(resolution,[],[f1064,f869]) ).
fof(f1064,plain,
( ! [X0,X1] :
( element(sK5(X0,X1),relation_rng(X0))
| in(sK5(X0,X1),X1)
| relation_rng(X0) = X1
| ~ relation(X0) )
| ~ spl15_119 ),
inference(avatar_component_clause,[],[f1063]) ).
fof(f3357,plain,
( spl15_253
| ~ spl15_69
| ~ spl15_101 ),
inference(avatar_split_clause,[],[f890,f868,f583,f3355]) ).
fof(f583,plain,
( spl15_69
<=> ! [X0,X1] :
( relation_rng(X0) = X1
| in(sK5(X0,X1),X1)
| ~ relation(X0)
| in(sK5(X0,X1),relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_69])]) ).
fof(f890,plain,
( ! [X0,X1] :
( ~ empty(X0)
| ~ relation(X0)
| ~ relation(relation_rng(X0))
| in(sK5(X1,relation_rng(relation_rng(X0))),relation_rng(X1))
| ~ relation(X1)
| relation_rng(X1) = relation_rng(relation_rng(X0)) )
| ~ spl15_69
| ~ spl15_101 ),
inference(resolution,[],[f869,f584]) ).
fof(f584,plain,
( ! [X0,X1] :
( in(sK5(X0,X1),relation_rng(X0))
| in(sK5(X0,X1),X1)
| ~ relation(X0)
| relation_rng(X0) = X1 )
| ~ spl15_69 ),
inference(avatar_component_clause,[],[f583]) ).
fof(f3237,plain,
( spl15_252
| ~ spl15_67
| ~ spl15_147 ),
inference(avatar_split_clause,[],[f1434,f1411,f562,f3235]) ).
fof(f1434,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| in(sK10(X0,X1,X2),relation_rng(X0))
| sP0(X0,X1,X2)
| in(sK10(X0,X1,X2),relation_rng(X2))
| ~ relation(X2) )
| ~ spl15_67
| ~ spl15_147 ),
inference(resolution,[],[f1412,f563]) ).
fof(f3233,plain,
( spl15_251
| ~ spl15_63
| ~ spl15_117 ),
inference(avatar_split_clause,[],[f1057,f1033,f536,f3231]) ).
fof(f1033,plain,
( spl15_117
<=> ! [X4,X0,X3,X2,X1] :
( sP0(X0,X1,X2)
| ~ empty(X0)
| in(sK10(X0,X1,X2),X3)
| ~ sP0(X4,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_117])]) ).
fof(f1057,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| in(sK10(X0,X1,relation_rng_restriction(X2,X3)),X2)
| sP0(X0,X1,relation_rng_restriction(X2,X3))
| ~ relation(relation_rng_restriction(X2,X3))
| ~ relation(X3) )
| ~ spl15_63
| ~ spl15_117 ),
inference(resolution,[],[f1034,f537]) ).
fof(f1034,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ sP0(X4,X3,X2)
| ~ empty(X0)
| in(sK10(X0,X1,X2),X3)
| sP0(X0,X1,X2) )
| ~ spl15_117 ),
inference(avatar_component_clause,[],[f1033]) ).
fof(f3229,plain,
( spl15_250
| ~ spl15_63
| ~ spl15_116 ),
inference(avatar_split_clause,[],[f1049,f1029,f536,f3227]) ).
fof(f1029,plain,
( spl15_116
<=> ! [X4,X0,X3,X2,X1] :
( sP0(X0,X1,X2)
| ~ empty(X2)
| in(sK10(X0,X1,X2),X3)
| ~ sP0(X4,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_116])]) ).
fof(f1049,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| in(sK10(relation_rng_restriction(X1,X2),X3,X0),X1)
| sP0(relation_rng_restriction(X1,X2),X3,X0)
| ~ relation(relation_rng_restriction(X1,X2))
| ~ relation(X2) )
| ~ spl15_63
| ~ spl15_116 ),
inference(resolution,[],[f1030,f537]) ).
fof(f1030,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ sP0(X4,X3,X0)
| ~ empty(X2)
| in(sK10(X0,X1,X2),X3)
| sP0(X0,X1,X2) )
| ~ spl15_116 ),
inference(avatar_component_clause,[],[f1029]) ).
fof(f3081,plain,
( spl15_249
| ~ spl15_21
| ~ spl15_166 ),
inference(avatar_split_clause,[],[f1676,f1667,f246,f3079]) ).
fof(f1676,plain,
( ! [X2,X0,X1] :
( ~ relation(relation_rng_restriction(X0,X1))
| in(sK5(relation_rng_restriction(X0,X1),X2),X2)
| relation_rng(relation_rng_restriction(X0,X1)) = X2
| ~ relation(X1)
| ~ empty(X1) )
| ~ spl15_21
| ~ spl15_166 ),
inference(resolution,[],[f1668,f247]) ).
fof(f3077,plain,
( spl15_248
| ~ spl15_61
| ~ spl15_149 ),
inference(avatar_split_clause,[],[f1474,f1419,f511,f3075]) ).
fof(f3075,plain,
( spl15_248
<=> ! [X2,X0,X1] :
( ~ relation(X0)
| in(sK5(X0,X1),X1)
| relation_rng(X0) = X1
| ~ sP0(X0,relation_rng(X0),relation_rng(X2))
| ~ relation(X2)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_248])]) ).
fof(f1474,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| in(sK5(X0,X1),X1)
| relation_rng(X0) = X1
| ~ sP0(X0,relation_rng(X0),relation_rng(X2))
| ~ relation(X2)
| ~ empty(X2) )
| ~ spl15_61
| ~ spl15_149 ),
inference(resolution,[],[f1420,f512]) ).
fof(f3073,plain,
( spl15_247
| ~ spl15_21
| ~ spl15_138 ),
inference(avatar_split_clause,[],[f1280,f1267,f246,f3071]) ).
fof(f1280,plain,
( ! [X2,X0,X1] :
( in(sK5(relation_rng_restriction(X0,X1),X2),X2)
| ~ relation(relation_rng_restriction(X0,X1))
| relation_rng(relation_rng_restriction(X0,X1)) = X2
| ~ relation(X1)
| ~ empty(X0) )
| ~ spl15_21
| ~ spl15_138 ),
inference(resolution,[],[f1268,f247]) ).
fof(f3069,plain,
( spl15_246
| ~ spl15_21
| ~ spl15_138 ),
inference(avatar_split_clause,[],[f1274,f1267,f246,f3067]) ).
fof(f1274,plain,
( ! [X2,X0,X1] :
( in(sK5(relation_rng_restriction(X0,X1),X2),X0)
| ~ relation(relation_rng_restriction(X0,X1))
| relation_rng(relation_rng_restriction(X0,X1)) = X2
| ~ relation(X1)
| ~ empty(X2) )
| ~ spl15_21
| ~ spl15_138 ),
inference(resolution,[],[f1268,f247]) ).
fof(f3065,plain,
( spl15_245
| ~ spl15_101
| ~ spl15_124 ),
inference(avatar_split_clause,[],[f1135,f1122,f868,f3063]) ).
fof(f1122,plain,
( spl15_124
<=> ! [X0,X1] :
( ~ relation(X0)
| ~ empty(X0)
| relation_rng(relation_rng(X0)) = X1
| in(sK5(relation_rng(X0),X1),X1)
| ~ relation(relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_124])]) ).
fof(f1135,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_rng(relation_rng(X0)) = relation_rng(relation_rng(X1))
| ~ relation(X0)
| ~ relation(relation_rng(X0))
| ~ empty(X1)
| ~ relation(X1)
| ~ relation(relation_rng(X1)) )
| ~ spl15_101
| ~ spl15_124 ),
inference(resolution,[],[f1123,f869]) ).
fof(f1123,plain,
( ! [X0,X1] :
( in(sK5(relation_rng(X0),X1),X1)
| ~ empty(X0)
| relation_rng(relation_rng(X0)) = X1
| ~ relation(X0)
| ~ relation(relation_rng(X0)) )
| ~ spl15_124 ),
inference(avatar_component_clause,[],[f1122]) ).
fof(f3061,plain,
( ~ spl15_5
| ~ spl15_93
| spl15_233 ),
inference(avatar_split_clause,[],[f2894,f2794,f789,f171]) ).
fof(f2794,plain,
( spl15_233
<=> sP0(sK4,sK12,sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_233])]) ).
fof(f2894,plain,
( ~ empty(sK12)
| ~ spl15_93
| spl15_233 ),
inference(duplicate_literal_removal,[],[f2893]) ).
fof(f2893,plain,
( ~ empty(sK12)
| ~ empty(sK12)
| ~ spl15_93
| spl15_233 ),
inference(resolution,[],[f2795,f790]) ).
fof(f2795,plain,
( ~ sP0(sK4,sK12,sK12)
| spl15_233 ),
inference(avatar_component_clause,[],[f2794]) ).
fof(f3060,plain,
( spl15_244
| ~ spl15_46
| ~ spl15_101 ),
inference(avatar_split_clause,[],[f888,f868,f401,f3058]) ).
fof(f401,plain,
( spl15_46
<=> ! [X2,X0,X1] :
( in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X2)
| sP0(X0,X1,X2)
| in(sK10(X0,X1,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_46])]) ).
fof(f888,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| ~ relation(X0)
| ~ relation(relation_rng(X0))
| sP0(X1,X2,relation_rng(relation_rng(X0)))
| in(sK10(X1,X2,relation_rng(relation_rng(X0))),X2) )
| ~ spl15_46
| ~ spl15_101 ),
inference(resolution,[],[f869,f402]) ).
fof(f402,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X2)
| sP0(X0,X1,X2)
| in(sK10(X0,X1,X2),X1) )
| ~ spl15_46 ),
inference(avatar_component_clause,[],[f401]) ).
fof(f3010,plain,
( spl15_243
| ~ spl15_68
| ~ spl15_144 ),
inference(avatar_split_clause,[],[f1396,f1346,f573,f3008]) ).
fof(f3008,plain,
( spl15_243
<=> ! [X4,X0,X3,X2,X1] :
( ~ empty(X0)
| ~ relation(X0)
| sP0(X1,X2,relation_rng(X0))
| in(sK10(X1,X2,relation_rng(X0)),X3)
| ~ sP0(X4,X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_243])]) ).
fof(f1396,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ empty(X0)
| ~ relation(X0)
| sP0(X1,X2,relation_rng(X0))
| in(sK10(X1,X2,relation_rng(X0)),X3)
| ~ sP0(X4,X3,X1) )
| ~ spl15_68
| ~ spl15_144 ),
inference(resolution,[],[f1347,f574]) ).
fof(f3006,plain,
( spl15_242
| ~ spl15_68
| ~ spl15_143 ),
inference(avatar_split_clause,[],[f1383,f1342,f573,f3004]) ).
fof(f3004,plain,
( spl15_242
<=> ! [X4,X0,X3,X2,X1] :
( ~ empty(X0)
| ~ relation(X0)
| sP0(relation_rng(X0),X1,X2)
| in(sK10(relation_rng(X0),X1,X2),X3)
| ~ sP0(X4,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_242])]) ).
fof(f1383,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ empty(X0)
| ~ relation(X0)
| sP0(relation_rng(X0),X1,X2)
| in(sK10(relation_rng(X0),X1,X2),X3)
| ~ sP0(X4,X3,X2) )
| ~ spl15_68
| ~ spl15_143 ),
inference(resolution,[],[f1343,f574]) ).
fof(f2829,plain,
( spl15_241
| ~ spl15_67
| ~ spl15_144 ),
inference(avatar_split_clause,[],[f1397,f1346,f562,f2827]) ).
fof(f1397,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| ~ relation(X0)
| sP0(X1,X2,relation_rng(X0))
| in(sK10(X1,X2,relation_rng(X0)),relation_rng(X1))
| ~ relation(X1) )
| ~ spl15_67
| ~ spl15_144 ),
inference(resolution,[],[f1347,f563]) ).
fof(f2825,plain,
( spl15_240
| ~ spl15_67
| ~ spl15_143 ),
inference(avatar_split_clause,[],[f1384,f1342,f562,f2823]) ).
fof(f1384,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| ~ relation(X0)
| sP0(relation_rng(X0),X1,X2)
| in(sK10(relation_rng(X0),X1,X2),relation_rng(X2))
| ~ relation(X2) )
| ~ spl15_67
| ~ spl15_143 ),
inference(resolution,[],[f1343,f563]) ).
fof(f2821,plain,
( spl15_239
| ~ spl15_138 ),
inference(avatar_split_clause,[],[f1283,f1267,f2819]) ).
fof(f1283,plain,
( ! [X0,X1] :
( in(sK5(relation_rng_restriction(X0,X1),X0),X0)
| ~ relation(relation_rng_restriction(X0,X1))
| relation_rng(relation_rng_restriction(X0,X1)) = X0
| ~ relation(X1) )
| ~ spl15_138 ),
inference(factoring,[],[f1268]) ).
fof(f2817,plain,
( spl15_238
| ~ spl15_61
| ~ spl15_126 ),
inference(avatar_split_clause,[],[f1165,f1154,f511,f2815]) ).
fof(f1165,plain,
( ! [X2,X0,X1] :
( in(sK10(X0,relation_rng(X1),X2),relation_rng(X2))
| sP0(X0,relation_rng(X1),X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ empty(X1) )
| ~ spl15_61
| ~ spl15_126 ),
inference(resolution,[],[f1155,f512]) ).
fof(f2813,plain,
( spl15_237
| ~ spl15_23
| ~ spl15_126 ),
inference(avatar_split_clause,[],[f1163,f1154,f263,f2811]) ).
fof(f2811,plain,
( spl15_237
<=> ! [X2,X0,X1] :
( in(sK10(X0,X1,X2),relation_rng(X2))
| sP0(X0,X1,X2)
| ~ relation(X2)
| ~ in(X1,sK10(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_237])]) ).
fof(f1163,plain,
( ! [X2,X0,X1] :
( in(sK10(X0,X1,X2),relation_rng(X2))
| sP0(X0,X1,X2)
| ~ relation(X2)
| ~ in(X1,sK10(X0,X1,X2)) )
| ~ spl15_23
| ~ spl15_126 ),
inference(resolution,[],[f1155,f264]) ).
fof(f2809,plain,
( spl15_236
| ~ spl15_24
| ~ spl15_126 ),
inference(avatar_split_clause,[],[f1162,f1154,f267,f2807]) ).
fof(f1162,plain,
( ! [X2,X0,X1] :
( in(sK10(X0,X1,X2),relation_rng(X2))
| sP0(X0,X1,X2)
| ~ relation(X2)
| element(sK10(X0,X1,X2),X1) )
| ~ spl15_24
| ~ spl15_126 ),
inference(resolution,[],[f1155,f268]) ).
fof(f2805,plain,
( spl15_235
| ~ spl15_23
| ~ spl15_126 ),
inference(avatar_split_clause,[],[f1160,f1154,f263,f2803]) ).
fof(f1160,plain,
( ! [X2,X0,X1] :
( in(sK10(X0,X1,X2),X1)
| sP0(X0,X1,X2)
| ~ relation(X2)
| ~ in(relation_rng(X2),sK10(X0,X1,X2)) )
| ~ spl15_23
| ~ spl15_126 ),
inference(resolution,[],[f1155,f264]) ).
fof(f2801,plain,
( spl15_233
| ~ spl15_234
| ~ spl15_31
| ~ spl15_212 ),
inference(avatar_split_clause,[],[f2518,f2400,f309,f2798,f2794]) ).
fof(f2400,plain,
( spl15_212
<=> sK12 = relation_rng_restriction(sK12,sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_212])]) ).
fof(f2518,plain,
( ~ sP1(sK12,sK12,sK4)
| sP0(sK4,sK12,sK12)
| ~ spl15_31
| ~ spl15_212 ),
inference(superposition,[],[f310,f2402]) ).
fof(f2402,plain,
( sK12 = relation_rng_restriction(sK12,sK4)
| ~ spl15_212 ),
inference(avatar_component_clause,[],[f2400]) ).
fof(f2792,plain,
( spl15_232
| ~ spl15_24
| ~ spl15_126 ),
inference(avatar_split_clause,[],[f1159,f1154,f267,f2790]) ).
fof(f1159,plain,
( ! [X2,X0,X1] :
( in(sK10(X0,X1,X2),X1)
| sP0(X0,X1,X2)
| ~ relation(X2)
| element(sK10(X0,X1,X2),relation_rng(X2)) )
| ~ spl15_24
| ~ spl15_126 ),
inference(resolution,[],[f1155,f268]) ).
fof(f2665,plain,
( spl15_231
| ~ spl15_21
| ~ spl15_149 ),
inference(avatar_split_clause,[],[f1465,f1419,f246,f2663]) ).
fof(f1465,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| in(sK5(X0,X1),X1)
| relation_rng(X0) = X1
| ~ sP0(X0,relation_rng(X0),X2)
| ~ empty(X2) )
| ~ spl15_21
| ~ spl15_149 ),
inference(resolution,[],[f1420,f247]) ).
fof(f2651,plain,
( spl15_230
| ~ spl15_101
| ~ spl15_144 ),
inference(avatar_split_clause,[],[f1402,f1346,f868,f2649]) ).
fof(f2649,plain,
( spl15_230
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| ~ relation(X0)
| sP0(relation_rng(relation_rng(X1)),X2,relation_rng(X0))
| ~ empty(X1)
| ~ relation(X1)
| ~ relation(relation_rng(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_230])]) ).
fof(f1402,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| ~ relation(X0)
| sP0(relation_rng(relation_rng(X1)),X2,relation_rng(X0))
| ~ empty(X1)
| ~ relation(X1)
| ~ relation(relation_rng(X1)) )
| ~ spl15_101
| ~ spl15_144 ),
inference(resolution,[],[f1347,f869]) ).
fof(f2647,plain,
( spl15_229
| ~ spl15_101
| ~ spl15_143 ),
inference(avatar_split_clause,[],[f1389,f1342,f868,f2645]) ).
fof(f2645,plain,
( spl15_229
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| ~ relation(X0)
| sP0(relation_rng(X0),X1,relation_rng(relation_rng(X2)))
| ~ empty(X2)
| ~ relation(X2)
| ~ relation(relation_rng(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_229])]) ).
fof(f1389,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| ~ relation(X0)
| sP0(relation_rng(X0),X1,relation_rng(relation_rng(X2)))
| ~ empty(X2)
| ~ relation(X2)
| ~ relation(relation_rng(X2)) )
| ~ spl15_101
| ~ spl15_143 ),
inference(resolution,[],[f1343,f869]) ).
fof(f2643,plain,
( spl15_228
| ~ spl15_23
| ~ spl15_125 ),
inference(avatar_split_clause,[],[f1145,f1126,f263,f2641]) ).
fof(f2641,plain,
( spl15_228
<=> ! [X0,X1] :
( ~ relation(X0)
| relation_rng(X0) = relation_rng(X1)
| ~ relation(X1)
| ~ empty(X1)
| ~ in(relation_rng(X0),sK5(X0,relation_rng(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_228])]) ).
fof(f1126,plain,
( spl15_125
<=> ! [X0,X1] :
( in(sK5(X0,relation_rng(X1)),relation_rng(X0))
| ~ relation(X0)
| relation_rng(X0) = relation_rng(X1)
| ~ relation(X1)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_125])]) ).
fof(f1145,plain,
( ! [X0,X1] :
( ~ relation(X0)
| relation_rng(X0) = relation_rng(X1)
| ~ relation(X1)
| ~ empty(X1)
| ~ in(relation_rng(X0),sK5(X0,relation_rng(X1))) )
| ~ spl15_23
| ~ spl15_125 ),
inference(resolution,[],[f1127,f264]) ).
fof(f1127,plain,
( ! [X0,X1] :
( in(sK5(X0,relation_rng(X1)),relation_rng(X0))
| ~ relation(X0)
| relation_rng(X0) = relation_rng(X1)
| ~ relation(X1)
| ~ empty(X1) )
| ~ spl15_125 ),
inference(avatar_component_clause,[],[f1126]) ).
fof(f2639,plain,
( spl15_227
| ~ spl15_23
| ~ spl15_124 ),
inference(avatar_split_clause,[],[f1132,f1122,f263,f2637]) ).
fof(f2637,plain,
( spl15_227
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_rng(relation_rng(X0)) = X1
| ~ relation(X0)
| ~ relation(relation_rng(X0))
| ~ in(X1,sK5(relation_rng(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_227])]) ).
fof(f1132,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_rng(relation_rng(X0)) = X1
| ~ relation(X0)
| ~ relation(relation_rng(X0))
| ~ in(X1,sK5(relation_rng(X0),X1)) )
| ~ spl15_23
| ~ spl15_124 ),
inference(resolution,[],[f1123,f264]) ).
fof(f2635,plain,
( spl15_226
| ~ spl15_101
| ~ spl15_121 ),
inference(avatar_split_clause,[],[f1100,f1071,f868,f2633]) ).
fof(f2633,plain,
( spl15_226
<=> ! [X0,X1] :
( element(sK5(relation_rng(X0),X1),X1)
| relation_rng(relation_rng(X0)) = X1
| ~ relation(relation_rng(X0))
| ~ empty(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_226])]) ).
fof(f1100,plain,
( ! [X0,X1] :
( element(sK5(relation_rng(X0),X1),X1)
| relation_rng(relation_rng(X0)) = X1
| ~ relation(relation_rng(X0))
| ~ empty(X0)
| ~ relation(X0) )
| ~ spl15_101
| ~ spl15_121 ),
inference(duplicate_literal_removal,[],[f1094]) ).
fof(f1094,plain,
( ! [X0,X1] :
( element(sK5(relation_rng(X0),X1),X1)
| relation_rng(relation_rng(X0)) = X1
| ~ relation(relation_rng(X0))
| ~ empty(X0)
| ~ relation(X0)
| ~ relation(relation_rng(X0)) )
| ~ spl15_101
| ~ spl15_121 ),
inference(resolution,[],[f1072,f869]) ).
fof(f2631,plain,
( spl15_225
| ~ spl15_61
| ~ spl15_119 ),
inference(avatar_split_clause,[],[f1087,f1063,f511,f2629]) ).
fof(f2629,plain,
( spl15_225
<=> ! [X0,X1] :
( element(sK5(X0,relation_rng(X1)),relation_rng(X0))
| relation_rng(X0) = relation_rng(X1)
| ~ relation(X0)
| ~ relation(X1)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_225])]) ).
fof(f1087,plain,
( ! [X0,X1] :
( element(sK5(X0,relation_rng(X1)),relation_rng(X0))
| relation_rng(X0) = relation_rng(X1)
| ~ relation(X0)
| ~ relation(X1)
| ~ empty(X1) )
| ~ spl15_61
| ~ spl15_119 ),
inference(resolution,[],[f1064,f512]) ).
fof(f2627,plain,
( spl15_224
| ~ spl15_101
| ~ spl15_115 ),
inference(avatar_split_clause,[],[f1040,f1025,f868,f2625]) ).
fof(f1040,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| sP0(X1,relation_rng(relation_rng(X2)),relation_rng(X0))
| ~ relation(X0)
| ~ empty(X2)
| ~ relation(X2)
| ~ relation(relation_rng(X2)) )
| ~ spl15_101
| ~ spl15_115 ),
inference(resolution,[],[f1026,f869]) ).
fof(f2617,plain,
( spl15_223
| ~ spl15_18
| ~ spl15_205 ),
inference(avatar_split_clause,[],[f2235,f2188,f233,f2615]) ).
fof(f2188,plain,
( spl15_205
<=> ! [X0] :
( sK12 = relation_rng_restriction(X0,sK4)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_205])]) ).
fof(f2235,plain,
( ! [X0] :
( sK12 = relation_rng_restriction(relation_rng(X0),sK4)
| ~ empty(X0) )
| ~ spl15_18
| ~ spl15_205 ),
inference(resolution,[],[f2189,f234]) ).
fof(f2189,plain,
( ! [X0] :
( ~ empty(X0)
| sK12 = relation_rng_restriction(X0,sK4) )
| ~ spl15_205 ),
inference(avatar_component_clause,[],[f2188]) ).
fof(f2551,plain,
( spl15_222
| ~ spl15_23
| ~ spl15_121 ),
inference(avatar_split_clause,[],[f1096,f1071,f263,f2549]) ).
fof(f2549,plain,
( spl15_222
<=> ! [X0,X1] :
( element(sK5(X0,X1),X1)
| relation_rng(X0) = X1
| ~ relation(X0)
| ~ in(relation_rng(X0),sK5(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_222])]) ).
fof(f1096,plain,
( ! [X0,X1] :
( element(sK5(X0,X1),X1)
| relation_rng(X0) = X1
| ~ relation(X0)
| ~ in(relation_rng(X0),sK5(X0,X1)) )
| ~ spl15_23
| ~ spl15_121 ),
inference(resolution,[],[f1072,f264]) ).
fof(f2547,plain,
( spl15_221
| ~ spl15_23
| ~ spl15_119 ),
inference(avatar_split_clause,[],[f1085,f1063,f263,f2545]) ).
fof(f2545,plain,
( spl15_221
<=> ! [X0,X1] :
( element(sK5(X0,X1),relation_rng(X0))
| relation_rng(X0) = X1
| ~ relation(X0)
| ~ in(X1,sK5(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_221])]) ).
fof(f1085,plain,
( ! [X0,X1] :
( element(sK5(X0,X1),relation_rng(X0))
| relation_rng(X0) = X1
| ~ relation(X0)
| ~ in(X1,sK5(X0,X1)) )
| ~ spl15_23
| ~ spl15_119 ),
inference(resolution,[],[f1064,f264]) ).
fof(f2543,plain,
( spl15_220
| ~ spl15_24
| ~ spl15_119 ),
inference(avatar_split_clause,[],[f1084,f1063,f267,f2541]) ).
fof(f2541,plain,
( spl15_220
<=> ! [X0,X1] :
( element(sK5(X0,X1),relation_rng(X0))
| relation_rng(X0) = X1
| ~ relation(X0)
| element(sK5(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_220])]) ).
fof(f1084,plain,
( ! [X0,X1] :
( element(sK5(X0,X1),relation_rng(X0))
| relation_rng(X0) = X1
| ~ relation(X0)
| element(sK5(X0,X1),X1) )
| ~ spl15_24
| ~ spl15_119 ),
inference(resolution,[],[f1064,f268]) ).
fof(f2539,plain,
( spl15_219
| ~ spl15_22
| ~ spl15_106 ),
inference(avatar_split_clause,[],[f923,f907,f259,f2537]) ).
fof(f2537,plain,
( spl15_219
<=> ! [X2,X0,X1] :
( ~ relation(X0)
| ~ empty(X0)
| relation_rng(X0) = relation_rng(relation_rng_restriction(X1,X2))
| ~ empty(relation_rng_restriction(X1,X2))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_219])]) ).
fof(f907,plain,
( spl15_106
<=> ! [X0,X1] :
( relation_rng(X0) = relation_rng(X1)
| ~ relation(X0)
| ~ empty(X0)
| ~ relation(X1)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_106])]) ).
fof(f923,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| ~ empty(X0)
| relation_rng(X0) = relation_rng(relation_rng_restriction(X1,X2))
| ~ empty(relation_rng_restriction(X1,X2))
| ~ relation(X2) )
| ~ spl15_22
| ~ spl15_106 ),
inference(resolution,[],[f908,f260]) ).
fof(f908,plain,
( ! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| ~ empty(X0)
| relation_rng(X0) = relation_rng(X1)
| ~ empty(X1) )
| ~ spl15_106 ),
inference(avatar_component_clause,[],[f907]) ).
fof(f2535,plain,
( spl15_218
| ~ spl15_38
| ~ spl15_101 ),
inference(avatar_split_clause,[],[f879,f868,f347,f2533]) ).
fof(f879,plain,
( ! [X0,X1] :
( ~ empty(X0)
| ~ relation(X0)
| ~ relation(relation_rng(X0))
| ~ in(X1,relation_rng(relation_rng(relation_rng(X0))))
| ~ relation(relation_rng(relation_rng(X0))) )
| ~ spl15_38
| ~ spl15_101 ),
inference(resolution,[],[f869,f348]) ).
fof(f2531,plain,
( spl15_217
| ~ spl15_65
| ~ spl15_100 ),
inference(avatar_split_clause,[],[f853,f840,f548,f2529]) ).
fof(f840,plain,
( spl15_100
<=> ! [X2,X0,X1] :
( sP0(X0,X1,relation_rng(X2))
| ~ empty(X0)
| ~ relation(X2)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_100])]) ).
fof(f853,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| ~ relation(X1)
| ~ empty(X1)
| relation_rng(X1) = relation_rng_restriction(X2,X0)
| ~ relation(relation_rng(X1))
| ~ relation(X0) )
| ~ spl15_65
| ~ spl15_100 ),
inference(resolution,[],[f841,f549]) ).
fof(f841,plain,
( ! [X2,X0,X1] :
( sP0(X0,X1,relation_rng(X2))
| ~ empty(X0)
| ~ relation(X2)
| ~ empty(X2) )
| ~ spl15_100 ),
inference(avatar_component_clause,[],[f840]) ).
fof(f2516,plain,
( spl15_216
| ~ spl15_65
| ~ spl15_99 ),
inference(avatar_split_clause,[],[f849,f836,f548,f2514]) ).
fof(f836,plain,
( spl15_99
<=> ! [X2,X0,X1] :
( sP0(relation_rng(X0),X1,X2)
| ~ empty(X2)
| ~ relation(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_99])]) ).
fof(f849,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| ~ relation(X1)
| ~ empty(X1)
| relation_rng_restriction(X2,relation_rng(X1)) = X0
| ~ relation(X0)
| ~ relation(relation_rng(X1)) )
| ~ spl15_65
| ~ spl15_99 ),
inference(resolution,[],[f837,f549]) ).
fof(f837,plain,
( ! [X2,X0,X1] :
( sP0(relation_rng(X0),X1,X2)
| ~ empty(X2)
| ~ relation(X0)
| ~ empty(X0) )
| ~ spl15_99 ),
inference(avatar_component_clause,[],[f836]) ).
fof(f2496,plain,
( spl15_215
| ~ spl15_23
| ~ spl15_115 ),
inference(avatar_split_clause,[],[f1037,f1025,f263,f2494]) ).
fof(f2494,plain,
( spl15_215
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| sP0(X1,X2,relation_rng(X0))
| ~ relation(X0)
| ~ in(X2,sK10(X1,X2,relation_rng(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_215])]) ).
fof(f1037,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| sP0(X1,X2,relation_rng(X0))
| ~ relation(X0)
| ~ in(X2,sK10(X1,X2,relation_rng(X0))) )
| ~ spl15_23
| ~ spl15_115 ),
inference(resolution,[],[f1026,f264]) ).
fof(f2492,plain,
( spl15_214
| ~ spl15_24
| ~ spl15_115 ),
inference(avatar_split_clause,[],[f1036,f1025,f267,f2490]) ).
fof(f2490,plain,
( spl15_214
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| sP0(X1,X2,relation_rng(X0))
| ~ relation(X0)
| element(sK10(X1,X2,relation_rng(X0)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_214])]) ).
fof(f1036,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| sP0(X1,X2,relation_rng(X0))
| ~ relation(X0)
| element(sK10(X1,X2,relation_rng(X0)),X2) )
| ~ spl15_24
| ~ spl15_115 ),
inference(resolution,[],[f1026,f268]) ).
fof(f2488,plain,
( spl15_213
| ~ spl15_65
| ~ spl15_98 ),
inference(avatar_split_clause,[],[f845,f832,f548,f2486]) ).
fof(f832,plain,
( spl15_98
<=> ! [X2,X0,X1] :
( sP0(X0,relation_rng(X1),X2)
| ~ empty(X2)
| ~ relation(X1)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_98])]) ).
fof(f845,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| ~ relation(X1)
| ~ empty(X1)
| relation_rng_restriction(relation_rng(X1),X2) = X0
| ~ relation(X0)
| ~ relation(X2) )
| ~ spl15_65
| ~ spl15_98 ),
inference(resolution,[],[f833,f549]) ).
fof(f833,plain,
( ! [X2,X0,X1] :
( sP0(X0,relation_rng(X1),X2)
| ~ empty(X2)
| ~ relation(X1)
| ~ empty(X1) )
| ~ spl15_98 ),
inference(avatar_component_clause,[],[f832]) ).
fof(f2403,plain,
( spl15_212
| ~ spl15_2
| ~ spl15_55
| ~ spl15_205 ),
inference(avatar_split_clause,[],[f2240,f2188,f468,f156,f2400]) ).
fof(f2240,plain,
( sK12 = relation_rng_restriction(sK12,sK4)
| ~ spl15_2
| ~ spl15_55
| ~ spl15_205 ),
inference(forward_demodulation,[],[f2237,f470]) ).
fof(f2237,plain,
( sK12 = relation_rng_restriction(empty_set,sK4)
| ~ spl15_2
| ~ spl15_205 ),
inference(resolution,[],[f2189,f158]) ).
fof(f2234,plain,
( spl15_211
| ~ spl15_126 ),
inference(avatar_split_clause,[],[f1167,f1154,f2232]) ).
fof(f1167,plain,
( ! [X0,X1] :
( in(sK10(X0,relation_rng(X1),X1),relation_rng(X1))
| sP0(X0,relation_rng(X1),X1)
| ~ relation(X1) )
| ~ spl15_126 ),
inference(factoring,[],[f1155]) ).
fof(f2230,plain,
( spl15_210
| ~ spl15_21
| ~ spl15_126 ),
inference(avatar_split_clause,[],[f1164,f1154,f246,f2228]) ).
fof(f1164,plain,
( ! [X2,X0,X1] :
( in(sK10(X0,X1,X2),relation_rng(X2))
| sP0(X0,X1,X2)
| ~ relation(X2)
| ~ empty(X1) )
| ~ spl15_21
| ~ spl15_126 ),
inference(resolution,[],[f1155,f247]) ).
fof(f2226,plain,
( spl15_209
| ~ spl15_21
| ~ spl15_126 ),
inference(avatar_split_clause,[],[f1161,f1154,f246,f2224]) ).
fof(f1161,plain,
( ! [X2,X0,X1] :
( in(sK10(X0,X1,X2),X1)
| sP0(X0,X1,X2)
| ~ relation(X2)
| ~ empty(relation_rng(X2)) )
| ~ spl15_21
| ~ spl15_126 ),
inference(resolution,[],[f1155,f247]) ).
fof(f2216,plain,
( ~ spl15_19
| spl15_208
| ~ spl15_74
| ~ spl15_123 ),
inference(avatar_split_clause,[],[f1114,f1079,f614,f2214,f237]) ).
fof(f2214,plain,
( spl15_208
<=> ! [X0] :
( ~ in(sK5(sK12,X0),sK12)
| sK12 = X0
| ~ in(sK5(sK12,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_208])]) ).
fof(f1079,plain,
( spl15_123
<=> ! [X0,X1] :
( relation_rng(X0) = X1
| ~ in(sK5(X0,X1),X1)
| ~ relation(X0)
| ~ in(sK5(X0,X1),relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_123])]) ).
fof(f1114,plain,
( ! [X0] :
( ~ in(sK5(sK12,X0),sK12)
| ~ in(sK5(sK12,X0),X0)
| ~ relation(sK12)
| sK12 = X0 )
| ~ spl15_74
| ~ spl15_123 ),
inference(superposition,[],[f1080,f616]) ).
fof(f1080,plain,
( ! [X0,X1] :
( ~ in(sK5(X0,X1),relation_rng(X0))
| ~ in(sK5(X0,X1),X1)
| ~ relation(X0)
| relation_rng(X0) = X1 )
| ~ spl15_123 ),
inference(avatar_component_clause,[],[f1079]) ).
fof(f2206,plain,
( ~ spl15_19
| spl15_207
| ~ spl15_74
| ~ spl15_121 ),
inference(avatar_split_clause,[],[f1099,f1071,f614,f2204,f237]) ).
fof(f1099,plain,
( ! [X0] :
( in(sK5(sK12,X0),sK12)
| element(sK5(sK12,X0),X0)
| sK12 = X0
| ~ relation(sK12) )
| ~ spl15_74
| ~ spl15_121 ),
inference(superposition,[],[f1072,f616]) ).
fof(f2202,plain,
( ~ spl15_19
| spl15_206
| ~ spl15_74
| ~ spl15_120 ),
inference(avatar_split_clause,[],[f1091,f1067,f614,f2200,f237]) ).
fof(f2200,plain,
( spl15_206
<=> ! [X0] :
( ~ in(sK12,sK5(sK12,X0))
| in(sK5(sK12,X0),X0)
| sK12 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_206])]) ).
fof(f1067,plain,
( spl15_120
<=> ! [X0,X1] :
( in(sK5(X0,X1),X1)
| ~ relation(X0)
| relation_rng(X0) = X1
| ~ in(relation_rng(X0),sK5(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_120])]) ).
fof(f1091,plain,
( ! [X0] :
( ~ in(sK12,sK5(sK12,X0))
| ~ relation(sK12)
| sK12 = X0
| in(sK5(sK12,X0),X0) )
| ~ spl15_74
| ~ spl15_120 ),
inference(superposition,[],[f1068,f616]) ).
fof(f1068,plain,
( ! [X0,X1] :
( ~ in(relation_rng(X0),sK5(X0,X1))
| ~ relation(X0)
| relation_rng(X0) = X1
| in(sK5(X0,X1),X1) )
| ~ spl15_120 ),
inference(avatar_component_clause,[],[f1067]) ).
fof(f2190,plain,
( spl15_205
| ~ spl15_5
| ~ spl15_3
| ~ spl15_55
| ~ spl15_191 ),
inference(avatar_split_clause,[],[f2144,f2064,f468,f161,f171,f2188]) ).
fof(f2144,plain,
( ! [X0] :
( ~ empty(sK12)
| sK12 = relation_rng_restriction(X0,sK4)
| ~ empty(X0) )
| ~ spl15_3
| ~ spl15_55
| ~ spl15_191 ),
inference(forward_demodulation,[],[f2143,f470]) ).
fof(f2143,plain,
( ! [X0] :
( sK12 = relation_rng_restriction(X0,sK4)
| ~ empty(X0)
| ~ empty(empty_set) )
| ~ spl15_3
| ~ spl15_55
| ~ spl15_191 ),
inference(forward_demodulation,[],[f2138,f470]) ).
fof(f2138,plain,
( ! [X0] :
( empty_set = relation_rng_restriction(X0,sK4)
| ~ empty(X0)
| ~ empty(empty_set) )
| ~ spl15_3
| ~ spl15_191 ),
inference(resolution,[],[f2065,f163]) ).
fof(f2186,plain,
( ~ spl15_19
| spl15_204
| ~ spl15_74
| ~ spl15_119 ),
inference(avatar_split_clause,[],[f1089,f1063,f614,f2184,f237]) ).
fof(f1089,plain,
( ! [X0] :
( element(sK5(sK12,X0),sK12)
| in(sK5(sK12,X0),X0)
| sK12 = X0
| ~ relation(sK12) )
| ~ spl15_74
| ~ spl15_119 ),
inference(superposition,[],[f1064,f616]) ).
fof(f2182,plain,
( spl15_203
| ~ spl15_23
| ~ spl15_114 ),
inference(avatar_split_clause,[],[f1019,f1005,f263,f2180]) ).
fof(f1019,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| sP0(X0,X1,X2)
| ~ relation(X2)
| ~ in(relation_rng(X2),sK10(X0,X1,X2)) )
| ~ spl15_23
| ~ spl15_114 ),
inference(resolution,[],[f1006,f264]) ).
fof(f2178,plain,
( spl15_202
| ~ spl15_24
| ~ spl15_114 ),
inference(avatar_split_clause,[],[f1018,f1005,f267,f2176]) ).
fof(f1018,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| sP0(X0,X1,X2)
| ~ relation(X2)
| element(sK10(X0,X1,X2),relation_rng(X2)) )
| ~ spl15_24
| ~ spl15_114 ),
inference(resolution,[],[f1006,f268]) ).
fof(f2174,plain,
( spl15_201
| ~ spl15_23
| ~ spl15_113 ),
inference(avatar_split_clause,[],[f1011,f1001,f263,f2172]) ).
fof(f1011,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| sP0(X1,X2,X0)
| ~ relation(X1)
| ~ in(relation_rng(X1),sK10(X1,X2,X0)) )
| ~ spl15_23
| ~ spl15_113 ),
inference(resolution,[],[f1002,f264]) ).
fof(f2170,plain,
( spl15_200
| ~ spl15_24
| ~ spl15_113 ),
inference(avatar_split_clause,[],[f1010,f1001,f267,f2168]) ).
fof(f1010,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| sP0(X1,X2,X0)
| ~ relation(X1)
| element(sK10(X1,X2,X0),relation_rng(X1)) )
| ~ spl15_24
| ~ spl15_113 ),
inference(resolution,[],[f1002,f268]) ).
fof(f2166,plain,
( spl15_199
| ~ spl15_63
| ~ spl15_107 ),
inference(avatar_split_clause,[],[f943,f911,f536,f2164]) ).
fof(f911,plain,
( spl15_107
<=> ! [X0,X3,X2,X1] :
( in(X0,X1)
| ~ sP0(X2,X1,X3)
| ~ in(X0,relation_rng(X3))
| ~ relation(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_107])]) ).
fof(f943,plain,
( ! [X2,X0,X1] :
( in(X0,X1)
| ~ in(X0,relation_rng(relation_rng_restriction(X1,X2)))
| ~ relation(relation_rng_restriction(X1,X2))
| ~ relation(X2) )
| ~ spl15_63
| ~ spl15_107 ),
inference(duplicate_literal_removal,[],[f938]) ).
fof(f938,plain,
( ! [X2,X0,X1] :
( in(X0,X1)
| ~ in(X0,relation_rng(relation_rng_restriction(X1,X2)))
| ~ relation(relation_rng_restriction(X1,X2))
| ~ relation(relation_rng_restriction(X1,X2))
| ~ relation(X2) )
| ~ spl15_63
| ~ spl15_107 ),
inference(resolution,[],[f912,f537]) ).
fof(f912,plain,
( ! [X2,X3,X0,X1] :
( ~ sP0(X2,X1,X3)
| in(X0,X1)
| ~ in(X0,relation_rng(X3))
| ~ relation(X3) )
| ~ spl15_107 ),
inference(avatar_component_clause,[],[f911]) ).
fof(f2162,plain,
( spl15_198
| ~ spl15_20
| ~ spl15_106 ),
inference(avatar_split_clause,[],[f924,f907,f242,f2160]) ).
fof(f924,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ empty(X0)
| relation_rng(X0) = relation_rng(relation_rng(X1))
| ~ empty(relation_rng(X1))
| ~ empty(X1) )
| ~ spl15_20
| ~ spl15_106 ),
inference(resolution,[],[f908,f243]) ).
fof(f2158,plain,
( spl15_197
| ~ spl15_64
| ~ spl15_101 ),
inference(avatar_split_clause,[],[f893,f868,f540,f2156]) ).
fof(f893,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| ~ relation(X0)
| ~ relation(relation_rng(X0))
| sP0(X1,relation_rng(relation_rng(X0)),X2)
| ~ empty(X2) )
| ~ spl15_64
| ~ spl15_101 ),
inference(resolution,[],[f869,f541]) ).
fof(f2154,plain,
( spl15_196
| ~ spl15_79
| ~ spl15_101 ),
inference(avatar_split_clause,[],[f886,f868,f656,f2152]) ).
fof(f886,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| ~ relation(X0)
| ~ relation(relation_rng(X0))
| sP0(X1,X2,relation_rng(relation_rng(X0)))
| ~ empty(X1) )
| ~ spl15_79
| ~ spl15_101 ),
inference(resolution,[],[f869,f657]) ).
fof(f2150,plain,
( spl15_195
| ~ spl15_76
| ~ spl15_101 ),
inference(avatar_split_clause,[],[f884,f868,f631,f2148]) ).
fof(f884,plain,
( ! [X0,X1] :
( ~ empty(X0)
| ~ relation(X0)
| ~ relation(relation_rng(X0))
| sP0(relation_rng(relation_rng(X0)),X1,relation_rng(relation_rng(X0))) )
| ~ spl15_76
| ~ spl15_101 ),
inference(resolution,[],[f869,f632]) ).
fof(f2135,plain,
( spl15_194
| ~ spl15_78
| ~ spl15_101 ),
inference(avatar_split_clause,[],[f882,f868,f652,f2133]) ).
fof(f882,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| ~ relation(X0)
| ~ relation(relation_rng(X0))
| sP0(relation_rng(relation_rng(X0)),X1,X2)
| ~ empty(X2) )
| ~ spl15_78
| ~ spl15_101 ),
inference(resolution,[],[f869,f653]) ).
fof(f2074,plain,
( spl15_193
| ~ spl15_61
| ~ spl15_143 ),
inference(avatar_split_clause,[],[f1388,f1342,f511,f2072]) ).
fof(f1388,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| ~ relation(X0)
| sP0(relation_rng(X0),X1,relation_rng(X2))
| ~ relation(X2)
| ~ empty(X2) )
| ~ spl15_61
| ~ spl15_143 ),
inference(resolution,[],[f1343,f512]) ).
fof(f2070,plain,
( spl15_192
| ~ spl15_61
| ~ spl15_115 ),
inference(avatar_split_clause,[],[f1039,f1025,f511,f2068]) ).
fof(f1039,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| sP0(X1,relation_rng(X2),relation_rng(X0))
| ~ relation(X0)
| ~ relation(X2)
| ~ empty(X2) )
| ~ spl15_61
| ~ spl15_115 ),
inference(resolution,[],[f1026,f512]) ).
fof(f2066,plain,
( spl15_191
| ~ spl15_1
| ~ spl15_182 ),
inference(avatar_split_clause,[],[f2017,f1970,f151,f2064]) ).
fof(f2017,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_rng_restriction(X0,sK4) = X1
| ~ relation(X1)
| ~ empty(X1) )
| ~ spl15_1
| ~ spl15_182 ),
inference(resolution,[],[f1971,f153]) ).
fof(f2062,plain,
( spl15_190
| ~ spl15_23
| ~ spl15_111 ),
inference(avatar_split_clause,[],[f986,f957,f263,f2060]) ).
fof(f2060,plain,
( spl15_190
<=> ! [X0,X1] :
( ~ relation(X0)
| relation_rng(X0) = X1
| ~ empty(X1)
| ~ in(relation_rng(X0),sK5(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_190])]) ).
fof(f957,plain,
( spl15_111
<=> ! [X0,X1] :
( in(sK5(X0,X1),relation_rng(X0))
| ~ relation(X0)
| relation_rng(X0) = X1
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_111])]) ).
fof(f986,plain,
( ! [X0,X1] :
( ~ relation(X0)
| relation_rng(X0) = X1
| ~ empty(X1)
| ~ in(relation_rng(X0),sK5(X0,X1)) )
| ~ spl15_23
| ~ spl15_111 ),
inference(resolution,[],[f958,f264]) ).
fof(f958,plain,
( ! [X0,X1] :
( in(sK5(X0,X1),relation_rng(X0))
| ~ relation(X0)
| relation_rng(X0) = X1
| ~ empty(X1) )
| ~ spl15_111 ),
inference(avatar_component_clause,[],[f957]) ).
fof(f2058,plain,
( spl15_189
| ~ spl15_24
| ~ spl15_111 ),
inference(avatar_split_clause,[],[f985,f957,f267,f2056]) ).
fof(f2056,plain,
( spl15_189
<=> ! [X0,X1] :
( ~ relation(X0)
| relation_rng(X0) = X1
| ~ empty(X1)
| element(sK5(X0,X1),relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_189])]) ).
fof(f985,plain,
( ! [X0,X1] :
( ~ relation(X0)
| relation_rng(X0) = X1
| ~ empty(X1)
| element(sK5(X0,X1),relation_rng(X0)) )
| ~ spl15_24
| ~ spl15_111 ),
inference(resolution,[],[f958,f268]) ).
fof(f2054,plain,
( spl15_188
| ~ spl15_23
| ~ spl15_110 ),
inference(avatar_split_clause,[],[f966,f953,f263,f2052]) ).
fof(f2052,plain,
( spl15_188
<=> ! [X0,X1] :
( ~ relation(X0)
| relation_rng(X0) = X1
| ~ empty(relation_rng(X0))
| ~ in(X1,sK5(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_188])]) ).
fof(f953,plain,
( spl15_110
<=> ! [X0,X1] :
( in(sK5(X0,X1),X1)
| ~ relation(X0)
| relation_rng(X0) = X1
| ~ empty(relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_110])]) ).
fof(f966,plain,
( ! [X0,X1] :
( ~ relation(X0)
| relation_rng(X0) = X1
| ~ empty(relation_rng(X0))
| ~ in(X1,sK5(X0,X1)) )
| ~ spl15_23
| ~ spl15_110 ),
inference(resolution,[],[f954,f264]) ).
fof(f954,plain,
( ! [X0,X1] :
( in(sK5(X0,X1),X1)
| ~ relation(X0)
| relation_rng(X0) = X1
| ~ empty(relation_rng(X0)) )
| ~ spl15_110 ),
inference(avatar_component_clause,[],[f953]) ).
fof(f2050,plain,
( spl15_187
| ~ spl15_24
| ~ spl15_110 ),
inference(avatar_split_clause,[],[f965,f953,f267,f2048]) ).
fof(f2048,plain,
( spl15_187
<=> ! [X0,X1] :
( ~ relation(X0)
| relation_rng(X0) = X1
| ~ empty(relation_rng(X0))
| element(sK5(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_187])]) ).
fof(f965,plain,
( ! [X0,X1] :
( ~ relation(X0)
| relation_rng(X0) = X1
| ~ empty(relation_rng(X0))
| element(sK5(X0,X1),X1) )
| ~ spl15_24
| ~ spl15_110 ),
inference(resolution,[],[f954,f268]) ).
fof(f2046,plain,
( spl15_186
| ~ spl15_65
| ~ spl15_97 ),
inference(avatar_split_clause,[],[f830,f823,f548,f2044]) ).
fof(f823,plain,
( spl15_97
<=> ! [X0,X1] :
( sP0(relation_rng(X0),X1,relation_rng(X0))
| ~ relation(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_97])]) ).
fof(f830,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ empty(X0)
| relation_rng(X0) = relation_rng_restriction(X1,relation_rng(X0))
| ~ relation(relation_rng(X0)) )
| ~ spl15_65
| ~ spl15_97 ),
inference(duplicate_literal_removal,[],[f828]) ).
fof(f828,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ empty(X0)
| relation_rng(X0) = relation_rng_restriction(X1,relation_rng(X0))
| ~ relation(relation_rng(X0))
| ~ relation(relation_rng(X0)) )
| ~ spl15_65
| ~ spl15_97 ),
inference(resolution,[],[f824,f549]) ).
fof(f824,plain,
( ! [X0,X1] :
( sP0(relation_rng(X0),X1,relation_rng(X0))
| ~ relation(X0)
| ~ empty(X0) )
| ~ spl15_97 ),
inference(avatar_component_clause,[],[f823]) ).
fof(f2013,plain,
( spl15_185
| ~ spl15_23
| ~ spl15_109 ),
inference(avatar_split_clause,[],[f947,f919,f263,f2011]) ).
fof(f2011,plain,
( spl15_185
<=> ! [X0,X1] :
( sP0(X0,X1,X0)
| ~ relation(X0)
| ~ in(relation_rng(X0),sK10(X0,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_185])]) ).
fof(f947,plain,
( ! [X0,X1] :
( sP0(X0,X1,X0)
| ~ relation(X0)
| ~ in(relation_rng(X0),sK10(X0,X1,X0)) )
| ~ spl15_23
| ~ spl15_109 ),
inference(resolution,[],[f920,f264]) ).
fof(f1980,plain,
( spl15_184
| ~ spl15_24
| ~ spl15_109 ),
inference(avatar_split_clause,[],[f946,f919,f267,f1978]) ).
fof(f1978,plain,
( spl15_184
<=> ! [X0,X1] :
( sP0(X0,X1,X0)
| ~ relation(X0)
| element(sK10(X0,X1,X0),relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_184])]) ).
fof(f946,plain,
( ! [X0,X1] :
( sP0(X0,X1,X0)
| ~ relation(X0)
| element(sK10(X0,X1,X0),relation_rng(X0)) )
| ~ spl15_24
| ~ spl15_109 ),
inference(resolution,[],[f920,f268]) ).
fof(f1976,plain,
( spl15_183
| ~ spl15_65
| ~ spl15_94 ),
inference(avatar_split_clause,[],[f801,f793,f548,f1974]) ).
fof(f793,plain,
( spl15_94
<=> ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ empty(X2)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_94])]) ).
fof(f801,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| ~ empty(X1)
| relation_rng_restriction(X2,X1) = X0
| ~ relation(X0)
| ~ relation(X1) )
| ~ spl15_65
| ~ spl15_94 ),
inference(resolution,[],[f794,f549]) ).
fof(f794,plain,
( ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ empty(X2)
| ~ empty(X0) )
| ~ spl15_94 ),
inference(avatar_component_clause,[],[f793]) ).
fof(f1972,plain,
( spl15_182
| ~ spl15_65
| ~ spl15_93 ),
inference(avatar_split_clause,[],[f798,f789,f548,f1970]) ).
fof(f798,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| ~ empty(X1)
| relation_rng_restriction(X1,X2) = X0
| ~ relation(X0)
| ~ relation(X2) )
| ~ spl15_65
| ~ spl15_93 ),
inference(resolution,[],[f790,f549]) ).
fof(f1878,plain,
( spl15_181
| ~ spl15_21
| ~ spl15_115 ),
inference(avatar_split_clause,[],[f1038,f1025,f246,f1876]) ).
fof(f1038,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| sP0(X1,X2,relation_rng(X0))
| ~ relation(X0)
| ~ empty(X2) )
| ~ spl15_21
| ~ spl15_115 ),
inference(resolution,[],[f1026,f247]) ).
fof(f1874,plain,
( spl15_180
| ~ spl15_21
| ~ spl15_114 ),
inference(avatar_split_clause,[],[f1020,f1005,f246,f1872]) ).
fof(f1020,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| sP0(X0,X1,X2)
| ~ relation(X2)
| ~ empty(relation_rng(X2)) )
| ~ spl15_21
| ~ spl15_114 ),
inference(resolution,[],[f1006,f247]) ).
fof(f1870,plain,
( spl15_179
| ~ spl15_21
| ~ spl15_113 ),
inference(avatar_split_clause,[],[f1012,f1001,f246,f1868]) ).
fof(f1012,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| sP0(X1,X2,X0)
| ~ relation(X1)
| ~ empty(relation_rng(X1)) )
| ~ spl15_21
| ~ spl15_113 ),
inference(resolution,[],[f1002,f247]) ).
fof(f1866,plain,
( spl15_178
| ~ spl15_109
| ~ spl15_176 ),
inference(avatar_split_clause,[],[f1855,f1837,f919,f1864]) ).
fof(f1864,plain,
( spl15_178
<=> ! [X0] :
( sP0(X0,relation_rng(X0),X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_178])]) ).
fof(f1855,plain,
( ! [X0] :
( sP0(X0,relation_rng(X0),X0)
| ~ relation(X0) )
| ~ spl15_109
| ~ spl15_176 ),
inference(duplicate_literal_removal,[],[f1849]) ).
fof(f1849,plain,
( ! [X0] :
( sP0(X0,relation_rng(X0),X0)
| sP0(X0,relation_rng(X0),X0)
| ~ relation(X0) )
| ~ spl15_109
| ~ spl15_176 ),
inference(resolution,[],[f1838,f920]) ).
fof(f1862,plain,
( spl15_177
| ~ spl15_59
| ~ spl15_101 ),
inference(avatar_split_clause,[],[f892,f868,f494,f1860]) ).
fof(f892,plain,
( ! [X0] :
( ~ empty(X0)
| ~ relation(X0)
| ~ relation(relation_rng(X0))
| empty(relation_rng(relation_rng(X0))) )
| ~ spl15_59
| ~ spl15_101 ),
inference(resolution,[],[f869,f495]) ).
fof(f1839,plain,
( spl15_176
| ~ spl15_76
| ~ spl15_140 ),
inference(avatar_split_clause,[],[f1320,f1298,f631,f1837]) ).
fof(f1298,plain,
( spl15_140
<=> ! [X0,X1] :
( sP0(X0,X1,X0)
| ~ in(unordered_pair(singleton(sK9(X0,X1,X0)),unordered_pair(sK10(X0,X1,X0),sK9(X0,X1,X0))),X0)
| ~ in(sK10(X0,X1,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_140])]) ).
fof(f1320,plain,
( ! [X0,X1] :
( sP0(X0,X1,X0)
| ~ in(sK10(X0,X1,X0),X1) )
| ~ spl15_76
| ~ spl15_140 ),
inference(duplicate_literal_removal,[],[f1312]) ).
fof(f1312,plain,
( ! [X0,X1] :
( sP0(X0,X1,X0)
| ~ in(sK10(X0,X1,X0),X1)
| sP0(X0,X1,X0) )
| ~ spl15_76
| ~ spl15_140 ),
inference(resolution,[],[f1299,f632]) ).
fof(f1299,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(sK9(X0,X1,X0)),unordered_pair(sK10(X0,X1,X0),sK9(X0,X1,X0))),X0)
| sP0(X0,X1,X0)
| ~ in(sK10(X0,X1,X0),X1) )
| ~ spl15_140 ),
inference(avatar_component_clause,[],[f1298]) ).
fof(f1779,plain,
( spl15_175
| ~ spl15_77
| ~ spl15_89 ),
inference(avatar_split_clause,[],[f762,f738,f648,f1777]) ).
fof(f1777,plain,
( spl15_175
<=> ! [X4,X0,X3,X2,X1] :
( element(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X0)
| sP0(X0,X1,X2)
| in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X3)
| ~ in(sK10(X0,X1,X2),X4)
| ~ sP0(X2,X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_175])]) ).
fof(f762,plain,
( ! [X2,X3,X0,X1,X4] :
( element(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X0)
| sP0(X0,X1,X2)
| in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X3)
| ~ in(sK10(X0,X1,X2),X4)
| ~ sP0(X2,X4,X3) )
| ~ spl15_77
| ~ spl15_89 ),
inference(resolution,[],[f739,f649]) ).
fof(f1775,plain,
( spl15_174
| ~ spl15_77
| ~ spl15_87 ),
inference(avatar_split_clause,[],[f747,f730,f648,f1773]) ).
fof(f1773,plain,
( spl15_174
<=> ! [X4,X0,X3,X2,X1] :
( element(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X2)
| sP0(X0,X1,X2)
| in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X3)
| ~ in(sK10(X0,X1,X2),X4)
| ~ sP0(X0,X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_174])]) ).
fof(f747,plain,
( ! [X2,X3,X0,X1,X4] :
( element(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X2)
| sP0(X0,X1,X2)
| in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X3)
| ~ in(sK10(X0,X1,X2),X4)
| ~ sP0(X0,X4,X3) )
| ~ spl15_77
| ~ spl15_87 ),
inference(resolution,[],[f731,f649]) ).
fof(f1771,plain,
( spl15_173
| ~ spl15_18
| ~ spl15_96 ),
inference(avatar_split_clause,[],[f810,f807,f233,f1769]) ).
fof(f810,plain,
( ! [X0,X1] :
( relation_rng(relation_rng(relation_rng(X0))) = X1
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl15_18
| ~ spl15_96 ),
inference(resolution,[],[f808,f234]) ).
fof(f1767,plain,
( spl15_172
| ~ spl15_47
| ~ spl15_77 ),
inference(avatar_split_clause,[],[f662,f648,f408,f1765]) ).
fof(f1765,plain,
( spl15_172
<=> ! [X4,X0,X3,X2,X1] :
( in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X3)
| ~ in(sK10(X0,X1,X2),X4)
| ~ sP0(X2,X4,X3)
| in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X0)
| sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_172])]) ).
fof(f662,plain,
( ! [X2,X3,X0,X1,X4] :
( in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X3)
| ~ in(sK10(X0,X1,X2),X4)
| ~ sP0(X2,X4,X3)
| in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X0)
| sP0(X0,X1,X2) )
| ~ spl15_47
| ~ spl15_77 ),
inference(resolution,[],[f649,f409]) ).
fof(f1763,plain,
( spl15_171
| ~ spl15_47
| ~ spl15_77 ),
inference(avatar_split_clause,[],[f660,f648,f408,f1761]) ).
fof(f1761,plain,
( spl15_171
<=> ! [X4,X0,X3,X2,X1] :
( in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X3)
| ~ in(sK10(X0,X1,X2),X4)
| ~ sP0(X0,X4,X3)
| in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X2)
| sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_171])]) ).
fof(f660,plain,
( ! [X2,X3,X0,X1,X4] :
( in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X3)
| ~ in(sK10(X0,X1,X2),X4)
| ~ sP0(X0,X4,X3)
| in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X2)
| sP0(X0,X1,X2) )
| ~ spl15_47
| ~ spl15_77 ),
inference(resolution,[],[f649,f409]) ).
fof(f1719,plain,
( spl15_170
| ~ spl15_72
| ~ spl15_89 ),
inference(avatar_split_clause,[],[f763,f738,f606,f1717]) ).
fof(f763,plain,
( ! [X2,X3,X0,X1,X4] :
( element(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X0)
| sP0(X0,X1,X2)
| in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X3)
| ~ sP0(X3,X4,X2) )
| ~ spl15_72
| ~ spl15_89 ),
inference(resolution,[],[f739,f607]) ).
fof(f1715,plain,
( spl15_169
| ~ spl15_72
| ~ spl15_87 ),
inference(avatar_split_clause,[],[f748,f730,f606,f1713]) ).
fof(f748,plain,
( ! [X2,X3,X0,X1,X4] :
( element(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X2)
| sP0(X0,X1,X2)
| in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X3)
| ~ sP0(X3,X4,X0) )
| ~ spl15_72
| ~ spl15_87 ),
inference(resolution,[],[f731,f607]) ).
fof(f1711,plain,
( spl15_168
| ~ spl15_47
| ~ spl15_72 ),
inference(avatar_split_clause,[],[f620,f606,f408,f1709]) ).
fof(f620,plain,
( ! [X2,X3,X0,X1,X4] :
( in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X3)
| ~ sP0(X3,X4,X2)
| in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X0)
| sP0(X0,X1,X2) )
| ~ spl15_47
| ~ spl15_72 ),
inference(resolution,[],[f607,f409]) ).
fof(f1707,plain,
( spl15_167
| ~ spl15_47
| ~ spl15_72 ),
inference(avatar_split_clause,[],[f619,f606,f408,f1705]) ).
fof(f619,plain,
( ! [X2,X3,X0,X1,X4] :
( in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X3)
| ~ sP0(X3,X4,X0)
| in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X2)
| sP0(X0,X1,X2) )
| ~ spl15_47
| ~ spl15_72 ),
inference(resolution,[],[f607,f409]) ).
fof(f1669,plain,
( spl15_166
| ~ spl15_63
| ~ spl15_85 ),
inference(avatar_split_clause,[],[f718,f714,f536,f1667]) ).
fof(f714,plain,
( spl15_85
<=> ! [X0,X3,X2,X1] :
( relation_rng(X0) = X1
| in(sK5(X0,X1),X1)
| ~ relation(X0)
| in(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X2)
| ~ sP0(X2,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_85])]) ).
fof(f718,plain,
( ! [X2,X0,X1] :
( in(sK5(relation_rng_restriction(X0,X1),X2),X2)
| ~ relation(relation_rng_restriction(X0,X1))
| in(unordered_pair(singleton(sK6(relation_rng_restriction(X0,X1),X2)),unordered_pair(sK6(relation_rng_restriction(X0,X1),X2),sK5(relation_rng_restriction(X0,X1),X2))),X1)
| relation_rng(relation_rng_restriction(X0,X1)) = X2
| ~ relation(X1) )
| ~ spl15_63
| ~ spl15_85 ),
inference(duplicate_literal_removal,[],[f717]) ).
fof(f717,plain,
( ! [X2,X0,X1] :
( in(sK5(relation_rng_restriction(X0,X1),X2),X2)
| ~ relation(relation_rng_restriction(X0,X1))
| in(unordered_pair(singleton(sK6(relation_rng_restriction(X0,X1),X2)),unordered_pair(sK6(relation_rng_restriction(X0,X1),X2),sK5(relation_rng_restriction(X0,X1),X2))),X1)
| relation_rng(relation_rng_restriction(X0,X1)) = X2
| ~ relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) )
| ~ spl15_63
| ~ spl15_85 ),
inference(resolution,[],[f715,f537]) ).
fof(f715,plain,
( ! [X2,X3,X0,X1] :
( ~ sP0(X2,X3,X0)
| in(sK5(X0,X1),X1)
| ~ relation(X0)
| in(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X2)
| relation_rng(X0) = X1 )
| ~ spl15_85 ),
inference(avatar_component_clause,[],[f714]) ).
fof(f1660,plain,
( spl15_165
| ~ spl15_23
| ~ spl15_89 ),
inference(avatar_split_clause,[],[f767,f738,f263,f1658]) ).
fof(f767,plain,
( ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X0)
| sP0(X0,X1,X2)
| ~ in(X2,unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2)))) )
| ~ spl15_23
| ~ spl15_89 ),
inference(resolution,[],[f739,f264]) ).
fof(f1656,plain,
( spl15_164
| ~ spl15_23
| ~ spl15_87 ),
inference(avatar_split_clause,[],[f752,f730,f263,f1654]) ).
fof(f752,plain,
( ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X2)
| sP0(X0,X1,X2)
| ~ in(X0,unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2)))) )
| ~ spl15_23
| ~ spl15_87 ),
inference(resolution,[],[f731,f264]) ).
fof(f1652,plain,
( spl15_163
| ~ spl15_24
| ~ spl15_87 ),
inference(avatar_split_clause,[],[f751,f730,f267,f1650]) ).
fof(f1650,plain,
( spl15_163
<=> ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X2)
| sP0(X0,X1,X2)
| element(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_163])]) ).
fof(f751,plain,
( ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X2)
| sP0(X0,X1,X2)
| element(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X0) )
| ~ spl15_24
| ~ spl15_87 ),
inference(resolution,[],[f731,f268]) ).
fof(f1634,plain,
( spl15_162
| ~ spl15_46
| ~ spl15_77 ),
inference(avatar_split_clause,[],[f663,f648,f401,f1632]) ).
fof(f663,plain,
( ! [X2,X3,X0,X1,X4] :
( in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X3)
| ~ in(sK10(X0,X1,X2),X4)
| ~ sP0(X2,X4,X3)
| sP0(X0,X1,X2)
| in(sK10(X0,X1,X2),X1) )
| ~ spl15_46
| ~ spl15_77 ),
inference(resolution,[],[f649,f402]) ).
fof(f1630,plain,
( spl15_161
| ~ spl15_18
| ~ spl15_95 ),
inference(avatar_split_clause,[],[f855,f803,f233,f1628]) ).
fof(f1628,plain,
( spl15_161
<=> ! [X0] :
( sK12 = relation_rng(relation_rng(relation_rng(relation_rng(X0))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_161])]) ).
fof(f803,plain,
( spl15_95
<=> ! [X0] :
( sK12 = relation_rng(relation_rng(relation_rng(X0)))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_95])]) ).
fof(f855,plain,
( ! [X0] :
( sK12 = relation_rng(relation_rng(relation_rng(relation_rng(X0))))
| ~ empty(X0) )
| ~ spl15_18
| ~ spl15_95 ),
inference(resolution,[],[f804,f234]) ).
fof(f804,plain,
( ! [X0] :
( ~ empty(X0)
| sK12 = relation_rng(relation_rng(relation_rng(X0))) )
| ~ spl15_95 ),
inference(avatar_component_clause,[],[f803]) ).
fof(f1598,plain,
( spl15_160
| ~ spl15_77
| ~ spl15_79 ),
inference(avatar_split_clause,[],[f682,f656,f648,f1596]) ).
fof(f682,plain,
( ! [X2,X3,X0,X1,X4] :
( sP0(X0,X1,X2)
| ~ empty(X0)
| in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X3)
| ~ in(sK10(X0,X1,X2),X4)
| ~ sP0(X2,X4,X3) )
| ~ spl15_77
| ~ spl15_79 ),
inference(resolution,[],[f657,f649]) ).
fof(f1594,plain,
( spl15_159
| ~ spl15_77
| ~ spl15_78 ),
inference(avatar_split_clause,[],[f672,f652,f648,f1592]) ).
fof(f672,plain,
( ! [X2,X3,X0,X1,X4] :
( sP0(X0,X1,X2)
| ~ empty(X2)
| in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X3)
| ~ in(sK10(X0,X1,X2),X4)
| ~ sP0(X0,X4,X3) )
| ~ spl15_77
| ~ spl15_78 ),
inference(resolution,[],[f653,f649]) ).
fof(f1507,plain,
( spl15_158
| ~ spl15_68
| ~ spl15_89 ),
inference(avatar_split_clause,[],[f764,f738,f573,f1505]) ).
fof(f764,plain,
( ! [X2,X3,X0,X1,X4] :
( element(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X0)
| sP0(X0,X1,X2)
| in(sK10(X0,X1,X2),X3)
| ~ sP0(X4,X3,X2) )
| ~ spl15_68
| ~ spl15_89 ),
inference(resolution,[],[f739,f574]) ).
fof(f1503,plain,
( spl15_157
| ~ spl15_68
| ~ spl15_87 ),
inference(avatar_split_clause,[],[f749,f730,f573,f1501]) ).
fof(f749,plain,
( ! [X2,X3,X0,X1,X4] :
( element(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X2)
| sP0(X0,X1,X2)
| in(sK10(X0,X1,X2),X3)
| ~ sP0(X4,X3,X0) )
| ~ spl15_68
| ~ spl15_87 ),
inference(resolution,[],[f731,f574]) ).
fof(f1499,plain,
( spl15_156
| ~ spl15_76
| ~ spl15_77 ),
inference(avatar_split_clause,[],[f661,f648,f631,f1497]) ).
fof(f661,plain,
( ! [X2,X3,X0,X1] :
( in(unordered_pair(singleton(sK9(X0,X1,X0)),unordered_pair(sK10(X0,X1,X0),sK9(X0,X1,X0))),X2)
| ~ in(sK10(X0,X1,X0),X3)
| ~ sP0(X0,X3,X2)
| sP0(X0,X1,X0) )
| ~ spl15_76
| ~ spl15_77 ),
inference(resolution,[],[f649,f632]) ).
fof(f1495,plain,
( spl15_155
| ~ spl15_46
| ~ spl15_72 ),
inference(avatar_split_clause,[],[f621,f606,f401,f1493]) ).
fof(f621,plain,
( ! [X2,X3,X0,X1,X4] :
( in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X3)
| ~ sP0(X3,X4,X2)
| sP0(X0,X1,X2)
| in(sK10(X0,X1,X2),X1) )
| ~ spl15_46
| ~ spl15_72 ),
inference(resolution,[],[f607,f402]) ).
fof(f1491,plain,
( spl15_154
| ~ spl15_47
| ~ spl15_68 ),
inference(avatar_split_clause,[],[f578,f573,f408,f1489]) ).
fof(f578,plain,
( ! [X2,X3,X0,X1,X4] :
( in(sK10(X0,X1,X2),X3)
| ~ sP0(X4,X3,X2)
| in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X0)
| sP0(X0,X1,X2) )
| ~ spl15_47
| ~ spl15_68 ),
inference(resolution,[],[f574,f409]) ).
fof(f1487,plain,
( spl15_153
| ~ spl15_47
| ~ spl15_68 ),
inference(avatar_split_clause,[],[f577,f573,f408,f1485]) ).
fof(f577,plain,
( ! [X2,X3,X0,X1,X4] :
( in(sK10(X0,X1,X2),X3)
| ~ sP0(X4,X3,X0)
| in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X2)
| sP0(X0,X1,X2) )
| ~ spl15_47
| ~ spl15_68 ),
inference(resolution,[],[f574,f409]) ).
fof(f1445,plain,
( spl15_152
| ~ spl15_21
| ~ spl15_109 ),
inference(avatar_split_clause,[],[f948,f919,f246,f1443]) ).
fof(f948,plain,
( ! [X0,X1] :
( sP0(X0,X1,X0)
| ~ relation(X0)
| ~ empty(relation_rng(X0)) )
| ~ spl15_21
| ~ spl15_109 ),
inference(resolution,[],[f920,f247]) ).
fof(f1429,plain,
( spl15_151
| ~ spl15_67
| ~ spl15_89 ),
inference(avatar_split_clause,[],[f765,f738,f562,f1427]) ).
fof(f1427,plain,
( spl15_151
<=> ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X0)
| sP0(X0,X1,X2)
| in(sK10(X0,X1,X2),relation_rng(X2))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_151])]) ).
fof(f765,plain,
( ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X0)
| sP0(X0,X1,X2)
| in(sK10(X0,X1,X2),relation_rng(X2))
| ~ relation(X2) )
| ~ spl15_67
| ~ spl15_89 ),
inference(resolution,[],[f739,f563]) ).
fof(f1425,plain,
( spl15_150
| ~ spl15_67
| ~ spl15_87 ),
inference(avatar_split_clause,[],[f750,f730,f562,f1423]) ).
fof(f1423,plain,
( spl15_150
<=> ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X2)
| sP0(X0,X1,X2)
| in(sK10(X0,X1,X2),relation_rng(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_150])]) ).
fof(f750,plain,
( ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X2)
| sP0(X0,X1,X2)
| in(sK10(X0,X1,X2),relation_rng(X0))
| ~ relation(X0) )
| ~ spl15_67
| ~ spl15_87 ),
inference(resolution,[],[f731,f563]) ).
fof(f1421,plain,
( spl15_149
| ~ spl15_69
| ~ spl15_86 ),
inference(avatar_split_clause,[],[f726,f720,f583,f1419]) ).
fof(f726,plain,
( ! [X2,X0,X1] :
( in(sK5(X0,X1),X1)
| ~ relation(X0)
| in(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X2)
| relation_rng(X0) = X1
| ~ sP0(X0,relation_rng(X0),X2) )
| ~ spl15_69
| ~ spl15_86 ),
inference(duplicate_literal_removal,[],[f725]) ).
fof(f725,plain,
( ! [X2,X0,X1] :
( in(sK5(X0,X1),X1)
| ~ relation(X0)
| in(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X2)
| relation_rng(X0) = X1
| ~ sP0(X0,relation_rng(X0),X2)
| in(sK5(X0,X1),X1)
| ~ relation(X0)
| relation_rng(X0) = X1 )
| ~ spl15_69
| ~ spl15_86 ),
inference(resolution,[],[f721,f584]) ).
fof(f1417,plain,
( spl15_148
| ~ spl15_47
| ~ spl15_67 ),
inference(avatar_split_clause,[],[f567,f562,f408,f1415]) ).
fof(f567,plain,
( ! [X2,X0,X1] :
( in(sK10(X0,X1,X2),relation_rng(X2))
| ~ relation(X2)
| in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X0)
| sP0(X0,X1,X2) )
| ~ spl15_47
| ~ spl15_67 ),
inference(resolution,[],[f563,f409]) ).
fof(f1413,plain,
( spl15_147
| ~ spl15_47
| ~ spl15_67 ),
inference(avatar_split_clause,[],[f566,f562,f408,f1411]) ).
fof(f566,plain,
( ! [X2,X0,X1] :
( in(sK10(X0,X1,X2),relation_rng(X0))
| ~ relation(X0)
| in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X2)
| sP0(X0,X1,X2) )
| ~ spl15_47
| ~ spl15_67 ),
inference(resolution,[],[f563,f409]) ).
fof(f1356,plain,
( spl15_146
| ~ spl15_61
| ~ spl15_89 ),
inference(avatar_split_clause,[],[f769,f738,f511,f1354]) ).
fof(f1354,plain,
( spl15_146
<=> ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK9(X0,X1,relation_rng(X2))),unordered_pair(sK10(X0,X1,relation_rng(X2)),sK9(X0,X1,relation_rng(X2)))),X0)
| sP0(X0,X1,relation_rng(X2))
| ~ relation(X2)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_146])]) ).
fof(f769,plain,
( ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK9(X0,X1,relation_rng(X2))),unordered_pair(sK10(X0,X1,relation_rng(X2)),sK9(X0,X1,relation_rng(X2)))),X0)
| sP0(X0,X1,relation_rng(X2))
| ~ relation(X2)
| ~ empty(X2) )
| ~ spl15_61
| ~ spl15_89 ),
inference(resolution,[],[f739,f512]) ).
fof(f1352,plain,
( spl15_145
| ~ spl15_61
| ~ spl15_87 ),
inference(avatar_split_clause,[],[f754,f730,f511,f1350]) ).
fof(f1350,plain,
( spl15_145
<=> ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK9(relation_rng(X0),X1,X2)),unordered_pair(sK10(relation_rng(X0),X1,X2),sK9(relation_rng(X0),X1,X2))),X2)
| sP0(relation_rng(X0),X1,X2)
| ~ relation(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_145])]) ).
fof(f754,plain,
( ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK9(relation_rng(X0),X1,X2)),unordered_pair(sK10(relation_rng(X0),X1,X2),sK9(relation_rng(X0),X1,X2))),X2)
| sP0(relation_rng(X0),X1,X2)
| ~ relation(X0)
| ~ empty(X0) )
| ~ spl15_61
| ~ spl15_87 ),
inference(resolution,[],[f731,f512]) ).
fof(f1348,plain,
( spl15_144
| ~ spl15_47
| ~ spl15_61 ),
inference(avatar_split_clause,[],[f527,f511,f408,f1346]) ).
fof(f527,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| ~ empty(X0)
| in(unordered_pair(singleton(sK9(X1,X2,relation_rng(X0))),unordered_pair(sK10(X1,X2,relation_rng(X0)),sK9(X1,X2,relation_rng(X0)))),X1)
| sP0(X1,X2,relation_rng(X0)) )
| ~ spl15_47
| ~ spl15_61 ),
inference(resolution,[],[f512,f409]) ).
fof(f1344,plain,
( spl15_143
| ~ spl15_47
| ~ spl15_61 ),
inference(avatar_split_clause,[],[f526,f511,f408,f1342]) ).
fof(f526,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| ~ empty(X0)
| in(unordered_pair(singleton(sK9(relation_rng(X0),X1,X2)),unordered_pair(sK10(relation_rng(X0),X1,X2),sK9(relation_rng(X0),X1,X2))),X2)
| sP0(relation_rng(X0),X1,X2) )
| ~ spl15_47
| ~ spl15_61 ),
inference(resolution,[],[f512,f409]) ).
fof(f1308,plain,
( spl15_142
| ~ spl15_72
| ~ spl15_79 ),
inference(avatar_split_clause,[],[f683,f656,f606,f1306]) ).
fof(f683,plain,
( ! [X2,X3,X0,X1,X4] :
( sP0(X0,X1,X2)
| ~ empty(X0)
| in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X3)
| ~ sP0(X3,X4,X2) )
| ~ spl15_72
| ~ spl15_79 ),
inference(resolution,[],[f657,f607]) ).
fof(f1304,plain,
( spl15_141
| ~ spl15_72
| ~ spl15_78 ),
inference(avatar_split_clause,[],[f673,f652,f606,f1302]) ).
fof(f673,plain,
( ! [X2,X3,X0,X1,X4] :
( sP0(X0,X1,X2)
| ~ empty(X2)
| in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X3)
| ~ sP0(X3,X4,X0) )
| ~ spl15_72
| ~ spl15_78 ),
inference(resolution,[],[f653,f607]) ).
fof(f1300,plain,
( spl15_140
| ~ spl15_48
| ~ spl15_76 ),
inference(avatar_split_clause,[],[f646,f631,f419,f1298]) ).
fof(f419,plain,
( spl15_48
<=> ! [X2,X0,X1] :
( ~ in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X2)
| ~ in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X0)
| sP0(X0,X1,X2)
| ~ in(sK10(X0,X1,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_48])]) ).
fof(f646,plain,
( ! [X0,X1] :
( sP0(X0,X1,X0)
| ~ in(unordered_pair(singleton(sK9(X0,X1,X0)),unordered_pair(sK10(X0,X1,X0),sK9(X0,X1,X0))),X0)
| ~ in(sK10(X0,X1,X0),X1) )
| ~ spl15_48
| ~ spl15_76 ),
inference(duplicate_literal_removal,[],[f638]) ).
fof(f638,plain,
( ! [X0,X1] :
( sP0(X0,X1,X0)
| ~ in(unordered_pair(singleton(sK9(X0,X1,X0)),unordered_pair(sK10(X0,X1,X0),sK9(X0,X1,X0))),X0)
| sP0(X0,X1,X0)
| ~ in(sK10(X0,X1,X0),X1) )
| ~ spl15_48
| ~ spl15_76 ),
inference(resolution,[],[f632,f420]) ).
fof(f420,plain,
( ! [X2,X0,X1] :
( ~ in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X2)
| ~ in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X0)
| sP0(X0,X1,X2)
| ~ in(sK10(X0,X1,X2),X1) )
| ~ spl15_48 ),
inference(avatar_component_clause,[],[f419]) ).
fof(f1296,plain,
( ~ spl15_19
| spl15_139
| ~ spl15_74
| ~ spl15_107
| ~ spl15_128 ),
inference(avatar_split_clause,[],[f1236,f1184,f911,f614,f1294,f237]) ).
fof(f1294,plain,
( spl15_139
<=> ! [X0,X1] :
( ~ in(X0,sK12)
| in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_139])]) ).
fof(f1184,plain,
( spl15_128
<=> ! [X0] : sP0(sK12,X0,sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_128])]) ).
fof(f1236,plain,
( ! [X0,X1] :
( ~ in(X0,sK12)
| in(X0,X1)
| ~ relation(sK12) )
| ~ spl15_74
| ~ spl15_107
| ~ spl15_128 ),
inference(forward_demodulation,[],[f1228,f616]) ).
fof(f1228,plain,
( ! [X0,X1] :
( in(X0,X1)
| ~ in(X0,relation_rng(sK12))
| ~ relation(sK12) )
| ~ spl15_107
| ~ spl15_128 ),
inference(resolution,[],[f1185,f912]) ).
fof(f1185,plain,
( ! [X0] : sP0(sK12,X0,sK12)
| ~ spl15_128 ),
inference(avatar_component_clause,[],[f1184]) ).
fof(f1269,plain,
( spl15_138
| ~ spl15_63
| ~ spl15_73 ),
inference(avatar_split_clause,[],[f625,f610,f536,f1267]) ).
fof(f610,plain,
( spl15_73
<=> ! [X2,X0,X1,X3] :
( relation_rng(X0) = X1
| in(sK5(X0,X1),X1)
| ~ relation(X0)
| in(sK5(X0,X1),X2)
| ~ sP0(X3,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_73])]) ).
fof(f625,plain,
( ! [X2,X0,X1] :
( in(sK5(relation_rng_restriction(X0,X1),X2),X2)
| ~ relation(relation_rng_restriction(X0,X1))
| in(sK5(relation_rng_restriction(X0,X1),X2),X0)
| relation_rng(relation_rng_restriction(X0,X1)) = X2
| ~ relation(X1) )
| ~ spl15_63
| ~ spl15_73 ),
inference(duplicate_literal_removal,[],[f624]) ).
fof(f624,plain,
( ! [X2,X0,X1] :
( in(sK5(relation_rng_restriction(X0,X1),X2),X2)
| ~ relation(relation_rng_restriction(X0,X1))
| in(sK5(relation_rng_restriction(X0,X1),X2),X0)
| relation_rng(relation_rng_restriction(X0,X1)) = X2
| ~ relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) )
| ~ spl15_63
| ~ spl15_73 ),
inference(resolution,[],[f611,f537]) ).
fof(f611,plain,
( ! [X2,X3,X0,X1] :
( ~ sP0(X3,X2,X0)
| in(sK5(X0,X1),X1)
| ~ relation(X0)
| in(sK5(X0,X1),X2)
| relation_rng(X0) = X1 )
| ~ spl15_73 ),
inference(avatar_component_clause,[],[f610]) ).
fof(f1246,plain,
( spl15_137
| ~ spl15_38
| ~ spl15_77 ),
inference(avatar_split_clause,[],[f659,f648,f347,f1244]) ).
fof(f659,plain,
( ! [X2,X3,X0,X1] :
( in(unordered_pair(singleton(sK7(X0,X1)),unordered_pair(X1,sK7(X0,X1))),X2)
| ~ in(X1,X3)
| ~ sP0(X0,X3,X2)
| ~ in(X1,relation_rng(X0))
| ~ relation(X0) )
| ~ spl15_38
| ~ spl15_77 ),
inference(resolution,[],[f649,f348]) ).
fof(f1242,plain,
( spl15_136
| ~ spl15_72
| ~ spl15_76 ),
inference(avatar_split_clause,[],[f639,f631,f606,f1240]) ).
fof(f639,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,X1,X0)
| in(unordered_pair(singleton(sK9(X0,X1,X0)),unordered_pair(sK10(X0,X1,X0),sK9(X0,X1,X0))),X2)
| ~ sP0(X2,X3,X0) )
| ~ spl15_72
| ~ spl15_76 ),
inference(resolution,[],[f632,f607]) ).
fof(f1224,plain,
( spl15_135
| ~ spl15_23
| ~ spl15_79 ),
inference(avatar_split_clause,[],[f687,f656,f263,f1222]) ).
fof(f687,plain,
( ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ empty(X0)
| ~ in(X2,unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2)))) )
| ~ spl15_23
| ~ spl15_79 ),
inference(resolution,[],[f657,f264]) ).
fof(f1220,plain,
( spl15_134
| ~ spl15_24
| ~ spl15_79 ),
inference(avatar_split_clause,[],[f686,f656,f267,f1218]) ).
fof(f1218,plain,
( spl15_134
<=> ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ empty(X0)
| element(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_134])]) ).
fof(f686,plain,
( ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ empty(X0)
| element(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X2) )
| ~ spl15_24
| ~ spl15_79 ),
inference(resolution,[],[f657,f268]) ).
fof(f1216,plain,
( spl15_133
| ~ spl15_23
| ~ spl15_78 ),
inference(avatar_split_clause,[],[f677,f652,f263,f1214]) ).
fof(f677,plain,
( ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ empty(X2)
| ~ in(X0,unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2)))) )
| ~ spl15_23
| ~ spl15_78 ),
inference(resolution,[],[f653,f264]) ).
fof(f1212,plain,
( spl15_132
| ~ spl15_24
| ~ spl15_78 ),
inference(avatar_split_clause,[],[f676,f652,f267,f1210]) ).
fof(f1210,plain,
( spl15_132
<=> ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ empty(X2)
| element(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_132])]) ).
fof(f676,plain,
( ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ empty(X2)
| element(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X0) )
| ~ spl15_24
| ~ spl15_78 ),
inference(resolution,[],[f653,f268]) ).
fof(f1199,plain,
( spl15_131
| ~ spl15_38
| ~ spl15_72 ),
inference(avatar_split_clause,[],[f618,f606,f347,f1197]) ).
fof(f618,plain,
( ! [X2,X3,X0,X1] :
( in(unordered_pair(singleton(sK7(X0,X1)),unordered_pair(X1,sK7(X0,X1))),X2)
| ~ sP0(X2,X3,X0)
| ~ in(X1,relation_rng(X0))
| ~ relation(X0) )
| ~ spl15_38
| ~ spl15_72 ),
inference(resolution,[],[f607,f348]) ).
fof(f1194,plain,
( spl15_130
| ~ spl15_23
| ~ spl15_76 ),
inference(avatar_split_clause,[],[f643,f631,f263,f1192]) ).
fof(f643,plain,
( ! [X0,X1] :
( sP0(X0,X1,X0)
| ~ in(X0,unordered_pair(singleton(sK9(X0,X1,X0)),unordered_pair(sK10(X0,X1,X0),sK9(X0,X1,X0)))) )
| ~ spl15_23
| ~ spl15_76 ),
inference(resolution,[],[f632,f264]) ).
fof(f1190,plain,
( spl15_129
| ~ spl15_24
| ~ spl15_76 ),
inference(avatar_split_clause,[],[f642,f631,f267,f1188]) ).
fof(f1188,plain,
( spl15_129
<=> ! [X0,X1] :
( sP0(X0,X1,X0)
| element(unordered_pair(singleton(sK9(X0,X1,X0)),unordered_pair(sK10(X0,X1,X0),sK9(X0,X1,X0))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_129])]) ).
fof(f642,plain,
( ! [X0,X1] :
( sP0(X0,X1,X0)
| element(unordered_pair(singleton(sK9(X0,X1,X0)),unordered_pair(sK10(X0,X1,X0),sK9(X0,X1,X0))),X0) )
| ~ spl15_24
| ~ spl15_76 ),
inference(resolution,[],[f632,f268]) ).
fof(f1186,plain,
( ~ spl15_19
| spl15_128
| ~ spl15_63
| ~ spl15_118 ),
inference(avatar_split_clause,[],[f1106,f1043,f536,f1184,f237]) ).
fof(f1043,plain,
( spl15_118
<=> ! [X0] : sK12 = relation_rng_restriction(X0,sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_118])]) ).
fof(f1106,plain,
( ! [X0] :
( sP0(sK12,X0,sK12)
| ~ relation(sK12) )
| ~ spl15_63
| ~ spl15_118 ),
inference(duplicate_literal_removal,[],[f1103]) ).
fof(f1103,plain,
( ! [X0] :
( sP0(sK12,X0,sK12)
| ~ relation(sK12)
| ~ relation(sK12) )
| ~ spl15_63
| ~ spl15_118 ),
inference(superposition,[],[f537,f1044]) ).
fof(f1044,plain,
( ! [X0] : sK12 = relation_rng_restriction(X0,sK12)
| ~ spl15_118 ),
inference(avatar_component_clause,[],[f1043]) ).
fof(f1174,plain,
( spl15_127
| ~ spl15_46
| ~ spl15_68 ),
inference(avatar_split_clause,[],[f579,f573,f401,f1172]) ).
fof(f579,plain,
( ! [X2,X3,X0,X1,X4] :
( in(sK10(X0,X1,X2),X3)
| ~ sP0(X4,X3,X2)
| sP0(X0,X1,X2)
| in(sK10(X0,X1,X2),X1) )
| ~ spl15_46
| ~ spl15_68 ),
inference(resolution,[],[f574,f402]) ).
fof(f1156,plain,
( spl15_126
| ~ spl15_46
| ~ spl15_67 ),
inference(avatar_split_clause,[],[f568,f562,f401,f1154]) ).
fof(f568,plain,
( ! [X2,X0,X1] :
( in(sK10(X0,X1,X2),relation_rng(X2))
| ~ relation(X2)
| sP0(X0,X1,X2)
| in(sK10(X0,X1,X2),X1) )
| ~ spl15_46
| ~ spl15_67 ),
inference(resolution,[],[f563,f402]) ).
fof(f1128,plain,
( spl15_125
| ~ spl15_61
| ~ spl15_69 ),
inference(avatar_split_clause,[],[f593,f583,f511,f1126]) ).
fof(f593,plain,
( ! [X0,X1] :
( in(sK5(X0,relation_rng(X1)),relation_rng(X0))
| ~ relation(X0)
| relation_rng(X0) = relation_rng(X1)
| ~ relation(X1)
| ~ empty(X1) )
| ~ spl15_61
| ~ spl15_69 ),
inference(resolution,[],[f584,f512]) ).
fof(f1124,plain,
( spl15_124
| ~ spl15_45
| ~ spl15_61 ),
inference(avatar_split_clause,[],[f525,f511,f387,f1122]) ).
fof(f525,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ empty(X0)
| relation_rng(relation_rng(X0)) = X1
| in(sK5(relation_rng(X0),X1),X1)
| ~ relation(relation_rng(X0)) )
| ~ spl15_45
| ~ spl15_61 ),
inference(resolution,[],[f512,f388]) ).
fof(f1081,plain,
( spl15_123
| ~ spl15_38
| ~ spl15_75 ),
inference(avatar_split_clause,[],[f637,f627,f347,f1079]) ).
fof(f637,plain,
( ! [X0,X1] :
( relation_rng(X0) = X1
| ~ in(sK5(X0,X1),X1)
| ~ relation(X0)
| ~ in(sK5(X0,X1),relation_rng(X0)) )
| ~ spl15_38
| ~ spl15_75 ),
inference(duplicate_literal_removal,[],[f634]) ).
fof(f634,plain,
( ! [X0,X1] :
( relation_rng(X0) = X1
| ~ in(sK5(X0,X1),X1)
| ~ relation(X0)
| ~ in(sK5(X0,X1),relation_rng(X0))
| ~ relation(X0) )
| ~ spl15_38
| ~ spl15_75 ),
inference(resolution,[],[f628,f348]) ).
fof(f1077,plain,
( spl15_122
| ~ spl15_23
| ~ spl15_69 ),
inference(avatar_split_clause,[],[f591,f583,f263,f1075]) ).
fof(f591,plain,
( ! [X0,X1] :
( in(sK5(X0,X1),relation_rng(X0))
| ~ relation(X0)
| relation_rng(X0) = X1
| ~ in(X1,sK5(X0,X1)) )
| ~ spl15_23
| ~ spl15_69 ),
inference(resolution,[],[f584,f264]) ).
fof(f1073,plain,
( spl15_121
| ~ spl15_24
| ~ spl15_69 ),
inference(avatar_split_clause,[],[f590,f583,f267,f1071]) ).
fof(f590,plain,
( ! [X0,X1] :
( in(sK5(X0,X1),relation_rng(X0))
| ~ relation(X0)
| relation_rng(X0) = X1
| element(sK5(X0,X1),X1) )
| ~ spl15_24
| ~ spl15_69 ),
inference(resolution,[],[f584,f268]) ).
fof(f1069,plain,
( spl15_120
| ~ spl15_23
| ~ spl15_69 ),
inference(avatar_split_clause,[],[f588,f583,f263,f1067]) ).
fof(f588,plain,
( ! [X0,X1] :
( in(sK5(X0,X1),X1)
| ~ relation(X0)
| relation_rng(X0) = X1
| ~ in(relation_rng(X0),sK5(X0,X1)) )
| ~ spl15_23
| ~ spl15_69 ),
inference(resolution,[],[f584,f264]) ).
fof(f1065,plain,
( spl15_119
| ~ spl15_24
| ~ spl15_69 ),
inference(avatar_split_clause,[],[f587,f583,f267,f1063]) ).
fof(f587,plain,
( ! [X0,X1] :
( in(sK5(X0,X1),X1)
| ~ relation(X0)
| relation_rng(X0) = X1
| element(sK5(X0,X1),relation_rng(X0)) )
| ~ spl15_24
| ~ spl15_69 ),
inference(resolution,[],[f584,f268]) ).
fof(f1045,plain,
( spl15_118
| ~ spl15_5
| ~ spl15_3
| ~ spl15_55
| ~ spl15_108 ),
inference(avatar_split_clause,[],[f979,f915,f468,f161,f171,f1043]) ).
fof(f979,plain,
( ! [X0] :
( ~ empty(sK12)
| sK12 = relation_rng_restriction(X0,sK12) )
| ~ spl15_3
| ~ spl15_55
| ~ spl15_108 ),
inference(forward_demodulation,[],[f978,f470]) ).
fof(f978,plain,
( ! [X0] :
( sK12 = relation_rng_restriction(X0,sK12)
| ~ empty(empty_set) )
| ~ spl15_3
| ~ spl15_55
| ~ spl15_108 ),
inference(forward_demodulation,[],[f973,f470]) ).
fof(f973,plain,
( ! [X0] :
( empty_set = relation_rng_restriction(X0,empty_set)
| ~ empty(empty_set) )
| ~ spl15_3
| ~ spl15_108 ),
inference(resolution,[],[f916,f163]) ).
fof(f1035,plain,
( spl15_117
| ~ spl15_68
| ~ spl15_79 ),
inference(avatar_split_clause,[],[f684,f656,f573,f1033]) ).
fof(f684,plain,
( ! [X2,X3,X0,X1,X4] :
( sP0(X0,X1,X2)
| ~ empty(X0)
| in(sK10(X0,X1,X2),X3)
| ~ sP0(X4,X3,X2) )
| ~ spl15_68
| ~ spl15_79 ),
inference(resolution,[],[f657,f574]) ).
fof(f1031,plain,
( spl15_116
| ~ spl15_68
| ~ spl15_78 ),
inference(avatar_split_clause,[],[f674,f652,f573,f1029]) ).
fof(f674,plain,
( ! [X2,X3,X0,X1,X4] :
( sP0(X0,X1,X2)
| ~ empty(X2)
| in(sK10(X0,X1,X2),X3)
| ~ sP0(X4,X3,X0) )
| ~ spl15_68
| ~ spl15_78 ),
inference(resolution,[],[f653,f574]) ).
fof(f1027,plain,
( spl15_115
| ~ spl15_46
| ~ spl15_61 ),
inference(avatar_split_clause,[],[f528,f511,f401,f1025]) ).
fof(f528,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| ~ empty(X0)
| sP0(X1,X2,relation_rng(X0))
| in(sK10(X1,X2,relation_rng(X0)),X2) )
| ~ spl15_46
| ~ spl15_61 ),
inference(resolution,[],[f512,f402]) ).
fof(f1007,plain,
( spl15_114
| ~ spl15_67
| ~ spl15_79 ),
inference(avatar_split_clause,[],[f685,f656,f562,f1005]) ).
fof(f685,plain,
( ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ empty(X0)
| in(sK10(X0,X1,X2),relation_rng(X2))
| ~ relation(X2) )
| ~ spl15_67
| ~ spl15_79 ),
inference(resolution,[],[f657,f563]) ).
fof(f1003,plain,
( spl15_113
| ~ spl15_67
| ~ spl15_78 ),
inference(avatar_split_clause,[],[f675,f652,f562,f1001]) ).
fof(f675,plain,
( ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ empty(X2)
| in(sK10(X0,X1,X2),relation_rng(X0))
| ~ relation(X0) )
| ~ spl15_67
| ~ spl15_78 ),
inference(resolution,[],[f653,f563]) ).
fof(f963,plain,
( spl15_112
| ~ spl15_68
| ~ spl15_76 ),
inference(avatar_split_clause,[],[f640,f631,f573,f961]) ).
fof(f640,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,X1,X0)
| in(sK10(X0,X1,X0),X2)
| ~ sP0(X3,X2,X0) )
| ~ spl15_68
| ~ spl15_76 ),
inference(resolution,[],[f632,f574]) ).
fof(f959,plain,
( spl15_111
| ~ spl15_21
| ~ spl15_69 ),
inference(avatar_split_clause,[],[f592,f583,f246,f957]) ).
fof(f592,plain,
( ! [X0,X1] :
( in(sK5(X0,X1),relation_rng(X0))
| ~ relation(X0)
| relation_rng(X0) = X1
| ~ empty(X1) )
| ~ spl15_21
| ~ spl15_69 ),
inference(resolution,[],[f584,f247]) ).
fof(f955,plain,
( spl15_110
| ~ spl15_21
| ~ spl15_69 ),
inference(avatar_split_clause,[],[f589,f583,f246,f953]) ).
fof(f589,plain,
( ! [X0,X1] :
( in(sK5(X0,X1),X1)
| ~ relation(X0)
| relation_rng(X0) = X1
| ~ empty(relation_rng(X0)) )
| ~ spl15_21
| ~ spl15_69 ),
inference(resolution,[],[f584,f247]) ).
fof(f921,plain,
( spl15_109
| ~ spl15_67
| ~ spl15_76 ),
inference(avatar_split_clause,[],[f641,f631,f562,f919]) ).
fof(f641,plain,
( ! [X0,X1] :
( sP0(X0,X1,X0)
| in(sK10(X0,X1,X0),relation_rng(X0))
| ~ relation(X0) )
| ~ spl15_67
| ~ spl15_76 ),
inference(resolution,[],[f632,f563]) ).
fof(f917,plain,
( spl15_108
| ~ spl15_65
| ~ spl15_91 ),
inference(avatar_split_clause,[],[f774,f757,f548,f915]) ).
fof(f757,plain,
( spl15_91
<=> ! [X0,X1] :
( sP0(X0,X1,X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_91])]) ).
fof(f774,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_rng_restriction(X1,X0) = X0
| ~ relation(X0) )
| ~ spl15_65
| ~ spl15_91 ),
inference(duplicate_literal_removal,[],[f773]) ).
fof(f773,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_rng_restriction(X1,X0) = X0
| ~ relation(X0)
| ~ relation(X0) )
| ~ spl15_65
| ~ spl15_91 ),
inference(resolution,[],[f758,f549]) ).
fof(f758,plain,
( ! [X0,X1] :
( sP0(X0,X1,X0)
| ~ empty(X0) )
| ~ spl15_91 ),
inference(avatar_component_clause,[],[f757]) ).
fof(f913,plain,
( spl15_107
| ~ spl15_38
| ~ spl15_68 ),
inference(avatar_split_clause,[],[f576,f573,f347,f911]) ).
fof(f576,plain,
( ! [X2,X3,X0,X1] :
( in(X0,X1)
| ~ sP0(X2,X1,X3)
| ~ in(X0,relation_rng(X3))
| ~ relation(X3) )
| ~ spl15_38
| ~ spl15_68 ),
inference(resolution,[],[f574,f348]) ).
fof(f909,plain,
( spl15_106
| ~ spl15_61
| ~ spl15_66 ),
inference(avatar_split_clause,[],[f560,f552,f511,f907]) ).
fof(f552,plain,
( spl15_66
<=> ! [X0,X1] :
( relation_rng(X0) = X1
| in(sK5(X0,X1),X1)
| ~ relation(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_66])]) ).
fof(f560,plain,
( ! [X0,X1] :
( relation_rng(X0) = relation_rng(X1)
| ~ relation(X0)
| ~ empty(X0)
| ~ relation(X1)
| ~ empty(X1) )
| ~ spl15_61
| ~ spl15_66 ),
inference(resolution,[],[f553,f512]) ).
fof(f553,plain,
( ! [X0,X1] :
( in(sK5(X0,X1),X1)
| relation_rng(X0) = X1
| ~ relation(X0)
| ~ empty(X0) )
| ~ spl15_66 ),
inference(avatar_component_clause,[],[f552]) ).
fof(f905,plain,
( spl15_105
| ~ spl15_23
| ~ spl15_66 ),
inference(avatar_split_clause,[],[f558,f552,f263,f903]) ).
fof(f558,plain,
( ! [X0,X1] :
( relation_rng(X0) = X1
| ~ relation(X0)
| ~ empty(X0)
| ~ in(X1,sK5(X0,X1)) )
| ~ spl15_23
| ~ spl15_66 ),
inference(resolution,[],[f553,f264]) ).
fof(f901,plain,
( spl15_104
| ~ spl15_24
| ~ spl15_66 ),
inference(avatar_split_clause,[],[f557,f552,f267,f899]) ).
fof(f899,plain,
( spl15_104
<=> ! [X0,X1] :
( relation_rng(X0) = X1
| ~ relation(X0)
| ~ empty(X0)
| element(sK5(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_104])]) ).
fof(f557,plain,
( ! [X0,X1] :
( relation_rng(X0) = X1
| ~ relation(X0)
| ~ empty(X0)
| element(sK5(X0,X1),X1) )
| ~ spl15_24
| ~ spl15_66 ),
inference(resolution,[],[f553,f268]) ).
fof(f878,plain,
( spl15_103
| ~ spl15_23
| ~ spl15_64 ),
inference(avatar_split_clause,[],[f544,f540,f263,f876]) ).
fof(f544,plain,
( ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ empty(X2)
| ~ in(X1,sK10(X0,X1,X2)) )
| ~ spl15_23
| ~ spl15_64 ),
inference(resolution,[],[f541,f264]) ).
fof(f874,plain,
( spl15_102
| ~ spl15_24
| ~ spl15_64 ),
inference(avatar_split_clause,[],[f543,f540,f267,f872]) ).
fof(f872,plain,
( spl15_102
<=> ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ empty(X2)
| element(sK10(X0,X1,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_102])]) ).
fof(f543,plain,
( ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ empty(X2)
| element(sK10(X0,X1,X2),X1) )
| ~ spl15_24
| ~ spl15_64 ),
inference(resolution,[],[f541,f268]) ).
fof(f870,plain,
( spl15_101
| ~ spl15_38
| ~ spl15_61 ),
inference(avatar_split_clause,[],[f524,f511,f347,f868]) ).
fof(f524,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ empty(X0)
| ~ in(X1,relation_rng(relation_rng(X0)))
| ~ relation(relation_rng(X0)) )
| ~ spl15_38
| ~ spl15_61 ),
inference(resolution,[],[f512,f348]) ).
fof(f842,plain,
( spl15_100
| ~ spl15_61
| ~ spl15_79 ),
inference(avatar_split_clause,[],[f689,f656,f511,f840]) ).
fof(f689,plain,
( ! [X2,X0,X1] :
( sP0(X0,X1,relation_rng(X2))
| ~ empty(X0)
| ~ relation(X2)
| ~ empty(X2) )
| ~ spl15_61
| ~ spl15_79 ),
inference(resolution,[],[f657,f512]) ).
fof(f838,plain,
( spl15_99
| ~ spl15_61
| ~ spl15_78 ),
inference(avatar_split_clause,[],[f679,f652,f511,f836]) ).
fof(f679,plain,
( ! [X2,X0,X1] :
( sP0(relation_rng(X0),X1,X2)
| ~ empty(X2)
| ~ relation(X0)
| ~ empty(X0) )
| ~ spl15_61
| ~ spl15_78 ),
inference(resolution,[],[f653,f512]) ).
fof(f834,plain,
( spl15_98
| ~ spl15_61
| ~ spl15_64 ),
inference(avatar_split_clause,[],[f546,f540,f511,f832]) ).
fof(f546,plain,
( ! [X2,X0,X1] :
( sP0(X0,relation_rng(X1),X2)
| ~ empty(X2)
| ~ relation(X1)
| ~ empty(X1) )
| ~ spl15_61
| ~ spl15_64 ),
inference(resolution,[],[f541,f512]) ).
fof(f825,plain,
( spl15_97
| ~ spl15_61
| ~ spl15_76 ),
inference(avatar_split_clause,[],[f645,f631,f511,f823]) ).
fof(f645,plain,
( ! [X0,X1] :
( sP0(relation_rng(X0),X1,relation_rng(X0))
| ~ relation(X0)
| ~ empty(X0) )
| ~ spl15_61
| ~ spl15_76 ),
inference(resolution,[],[f632,f512]) ).
fof(f809,plain,
( spl15_96
| ~ spl15_18
| ~ spl15_60 ),
inference(avatar_split_clause,[],[f514,f507,f233,f807]) ).
fof(f507,plain,
( spl15_60
<=> ! [X0,X1] :
( relation_rng(X1) = X0
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_60])]) ).
fof(f514,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_rng(relation_rng(X1)) = X0
| ~ empty(X1) )
| ~ spl15_18
| ~ spl15_60 ),
inference(resolution,[],[f508,f234]) ).
fof(f508,plain,
( ! [X0,X1] :
( ~ empty(X1)
| ~ empty(X0)
| relation_rng(X1) = X0 )
| ~ spl15_60 ),
inference(avatar_component_clause,[],[f507]) ).
fof(f805,plain,
( spl15_95
| ~ spl15_18
| ~ spl15_92 ),
inference(avatar_split_clause,[],[f779,f776,f233,f803]) ).
fof(f776,plain,
( spl15_92
<=> ! [X0] :
( sK12 = relation_rng(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_92])]) ).
fof(f779,plain,
( ! [X0] :
( sK12 = relation_rng(relation_rng(relation_rng(X0)))
| ~ empty(X0) )
| ~ spl15_18
| ~ spl15_92 ),
inference(resolution,[],[f777,f234]) ).
fof(f777,plain,
( ! [X0] :
( ~ empty(X0)
| sK12 = relation_rng(relation_rng(X0)) )
| ~ spl15_92 ),
inference(avatar_component_clause,[],[f776]) ).
fof(f795,plain,
( spl15_94
| ~ spl15_21
| ~ spl15_78 ),
inference(avatar_split_clause,[],[f678,f652,f246,f793]) ).
fof(f678,plain,
( ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ empty(X2)
| ~ empty(X0) )
| ~ spl15_21
| ~ spl15_78 ),
inference(resolution,[],[f653,f247]) ).
fof(f791,plain,
( spl15_93
| ~ spl15_21
| ~ spl15_64 ),
inference(avatar_split_clause,[],[f545,f540,f246,f789]) ).
fof(f545,plain,
( ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ empty(X2)
| ~ empty(X1) )
| ~ spl15_21
| ~ spl15_64 ),
inference(resolution,[],[f541,f247]) ).
fof(f778,plain,
( spl15_92
| ~ spl15_18
| ~ spl15_58 ),
inference(avatar_split_clause,[],[f497,f490,f233,f776]) ).
fof(f490,plain,
( spl15_58
<=> ! [X0] :
( relation_rng(X0) = sK12
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_58])]) ).
fof(f497,plain,
( ! [X0] :
( sK12 = relation_rng(relation_rng(X0))
| ~ empty(X0) )
| ~ spl15_18
| ~ spl15_58 ),
inference(resolution,[],[f491,f234]) ).
fof(f491,plain,
( ! [X0] :
( ~ empty(X0)
| relation_rng(X0) = sK12 )
| ~ spl15_58 ),
inference(avatar_component_clause,[],[f490]) ).
fof(f759,plain,
( spl15_91
| ~ spl15_21
| ~ spl15_76 ),
inference(avatar_split_clause,[],[f644,f631,f246,f757]) ).
fof(f644,plain,
( ! [X0,X1] :
( sP0(X0,X1,X0)
| ~ empty(X0) )
| ~ spl15_21
| ~ spl15_76 ),
inference(resolution,[],[f632,f247]) ).
fof(f744,plain,
( spl15_90
| ~ spl15_23
| ~ spl15_47 ),
inference(avatar_split_clause,[],[f415,f408,f263,f742]) ).
fof(f415,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X2)
| sP0(X0,X1,X2)
| ~ in(X0,unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2)))) )
| ~ spl15_23
| ~ spl15_47 ),
inference(resolution,[],[f409,f264]) ).
fof(f740,plain,
( spl15_89
| ~ spl15_24
| ~ spl15_47 ),
inference(avatar_split_clause,[],[f414,f408,f267,f738]) ).
fof(f414,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X2)
| sP0(X0,X1,X2)
| element(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X0) )
| ~ spl15_24
| ~ spl15_47 ),
inference(resolution,[],[f409,f268]) ).
fof(f736,plain,
( spl15_88
| ~ spl15_23
| ~ spl15_47 ),
inference(avatar_split_clause,[],[f412,f408,f263,f734]) ).
fof(f412,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X0)
| sP0(X0,X1,X2)
| ~ in(X2,unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2)))) )
| ~ spl15_23
| ~ spl15_47 ),
inference(resolution,[],[f409,f264]) ).
fof(f732,plain,
( spl15_87
| ~ spl15_24
| ~ spl15_47 ),
inference(avatar_split_clause,[],[f411,f408,f267,f730]) ).
fof(f411,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X0)
| sP0(X0,X1,X2)
| element(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X2) )
| ~ spl15_24
| ~ spl15_47 ),
inference(resolution,[],[f409,f268]) ).
fof(f722,plain,
( spl15_86
| ~ spl15_42
| ~ spl15_45 ),
inference(avatar_split_clause,[],[f390,f387,f371,f720]) ).
fof(f390,plain,
( ! [X2,X3,X0,X1] :
( relation_rng(X0) = X1
| in(sK5(X0,X1),X1)
| ~ relation(X0)
| in(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X2)
| ~ in(sK5(X0,X1),X3)
| ~ sP0(X0,X3,X2) )
| ~ spl15_42
| ~ spl15_45 ),
inference(resolution,[],[f388,f372]) ).
fof(f716,plain,
( spl15_85
| ~ spl15_39
| ~ spl15_45 ),
inference(avatar_split_clause,[],[f391,f387,f354,f714]) ).
fof(f391,plain,
( ! [X2,X3,X0,X1] :
( relation_rng(X0) = X1
| in(sK5(X0,X1),X1)
| ~ relation(X0)
| in(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X2)
| ~ sP0(X2,X3,X0) )
| ~ spl15_39
| ~ spl15_45 ),
inference(resolution,[],[f388,f355]) ).
fof(f712,plain,
( spl15_84
| ~ spl15_23
| ~ spl15_59 ),
inference(avatar_split_clause,[],[f504,f494,f263,f710]) ).
fof(f504,plain,
( ! [X0] :
( empty(X0)
| ~ in(X0,sK8(X0)) )
| ~ spl15_23
| ~ spl15_59 ),
inference(resolution,[],[f495,f264]) ).
fof(f707,plain,
( spl15_83
| ~ spl15_23
| ~ spl15_46 ),
inference(avatar_split_clause,[],[f405,f401,f263,f705]) ).
fof(f405,plain,
( ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| in(sK10(X0,X1,X2),X1)
| ~ in(X2,unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2)))) )
| ~ spl15_23
| ~ spl15_46 ),
inference(resolution,[],[f402,f264]) ).
fof(f703,plain,
( spl15_82
| ~ spl15_24
| ~ spl15_46 ),
inference(avatar_split_clause,[],[f404,f401,f267,f701]) ).
fof(f701,plain,
( spl15_82
<=> ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| in(sK10(X0,X1,X2),X1)
| element(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_82])]) ).
fof(f404,plain,
( ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| in(sK10(X0,X1,X2),X1)
| element(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X2) )
| ~ spl15_24
| ~ spl15_46 ),
inference(resolution,[],[f402,f268]) ).
fof(f698,plain,
( spl15_81
| ~ spl15_23
| ~ spl15_45 ),
inference(avatar_split_clause,[],[f396,f387,f263,f696]) ).
fof(f396,plain,
( ! [X0,X1] :
( relation_rng(X0) = X1
| in(sK5(X0,X1),X1)
| ~ relation(X0)
| ~ in(X0,unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1)))) )
| ~ spl15_23
| ~ spl15_45 ),
inference(resolution,[],[f388,f264]) ).
fof(f694,plain,
( spl15_80
| ~ spl15_24
| ~ spl15_45 ),
inference(avatar_split_clause,[],[f395,f387,f267,f692]) ).
fof(f692,plain,
( spl15_80
<=> ! [X0,X1] :
( relation_rng(X0) = X1
| in(sK5(X0,X1),X1)
| ~ relation(X0)
| element(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_80])]) ).
fof(f395,plain,
( ! [X0,X1] :
( relation_rng(X0) = X1
| in(sK5(X0,X1),X1)
| ~ relation(X0)
| element(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X0) )
| ~ spl15_24
| ~ spl15_45 ),
inference(resolution,[],[f388,f268]) ).
fof(f658,plain,
( spl15_79
| ~ spl15_21
| ~ spl15_47 ),
inference(avatar_split_clause,[],[f416,f408,f246,f656]) ).
fof(f416,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X2)
| sP0(X0,X1,X2)
| ~ empty(X0) )
| ~ spl15_21
| ~ spl15_47 ),
inference(resolution,[],[f409,f247]) ).
fof(f654,plain,
( spl15_78
| ~ spl15_21
| ~ spl15_47 ),
inference(avatar_split_clause,[],[f413,f408,f246,f652]) ).
fof(f413,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X0)
| sP0(X0,X1,X2)
| ~ empty(X2) )
| ~ spl15_21
| ~ spl15_47 ),
inference(resolution,[],[f409,f247]) ).
fof(f650,plain,
( spl15_77
| ~ spl15_27
| ~ spl15_42 ),
inference(avatar_split_clause,[],[f379,f371,f284,f648]) ).
fof(f284,plain,
( spl15_27
<=> ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_27])]) ).
fof(f379,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),X2)
| in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),X3)
| ~ in(X1,X4)
| ~ sP0(X2,X4,X3) )
| ~ spl15_27
| ~ spl15_42 ),
inference(superposition,[],[f372,f285]) ).
fof(f285,plain,
( ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0)
| ~ spl15_27 ),
inference(avatar_component_clause,[],[f284]) ).
fof(f633,plain,
( spl15_76
| ~ spl15_47 ),
inference(avatar_split_clause,[],[f417,f408,f631]) ).
fof(f417,plain,
( ! [X0,X1] :
( in(unordered_pair(singleton(sK9(X0,X1,X0)),unordered_pair(sK10(X0,X1,X0),sK9(X0,X1,X0))),X0)
| sP0(X0,X1,X0) )
| ~ spl15_47 ),
inference(factoring,[],[f409]) ).
fof(f629,plain,
( spl15_75
| ~ spl15_27
| ~ spl15_41 ),
inference(avatar_split_clause,[],[f368,f365,f284,f627]) ).
fof(f365,plain,
( spl15_41
<=> ! [X0,X1,X3] :
( ~ in(unordered_pair(singleton(X3),unordered_pair(X3,sK5(X0,X1))),X0)
| relation_rng(X0) = X1
| ~ in(sK5(X0,X1),X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_41])]) ).
fof(f368,plain,
( ! [X2,X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(sK5(X1,X2),X0)),X1)
| relation_rng(X1) = X2
| ~ in(sK5(X1,X2),X2)
| ~ relation(X1) )
| ~ spl15_27
| ~ spl15_41 ),
inference(superposition,[],[f366,f285]) ).
fof(f366,plain,
( ! [X3,X0,X1] :
( ~ in(unordered_pair(singleton(X3),unordered_pair(X3,sK5(X0,X1))),X0)
| relation_rng(X0) = X1
| ~ in(sK5(X0,X1),X1)
| ~ relation(X0) )
| ~ spl15_41 ),
inference(avatar_component_clause,[],[f365]) ).
fof(f617,plain,
( spl15_74
| ~ spl15_2
| ~ spl15_55
| ~ spl15_58 ),
inference(avatar_split_clause,[],[f501,f490,f468,f156,f614]) ).
fof(f501,plain,
( sK12 = relation_rng(sK12)
| ~ spl15_2
| ~ spl15_55
| ~ spl15_58 ),
inference(forward_demodulation,[],[f498,f470]) ).
fof(f498,plain,
( sK12 = relation_rng(empty_set)
| ~ spl15_2
| ~ spl15_58 ),
inference(resolution,[],[f491,f158]) ).
fof(f612,plain,
( spl15_73
| ~ spl15_35
| ~ spl15_45 ),
inference(avatar_split_clause,[],[f392,f387,f330,f610]) ).
fof(f392,plain,
( ! [X2,X3,X0,X1] :
( relation_rng(X0) = X1
| in(sK5(X0,X1),X1)
| ~ relation(X0)
| in(sK5(X0,X1),X2)
| ~ sP0(X3,X2,X0) )
| ~ spl15_35
| ~ spl15_45 ),
inference(resolution,[],[f388,f331]) ).
fof(f608,plain,
( spl15_72
| ~ spl15_27
| ~ spl15_39 ),
inference(avatar_split_clause,[],[f357,f354,f284,f606]) ).
fof(f357,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),X2)
| in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),X3)
| ~ sP0(X3,X4,X2) )
| ~ spl15_27
| ~ spl15_39 ),
inference(superposition,[],[f355,f285]) ).
fof(f603,plain,
( spl15_71
| ~ spl15_23
| ~ spl15_38 ),
inference(avatar_split_clause,[],[f351,f347,f263,f601]) ).
fof(f351,plain,
( ! [X0,X1] :
( ~ in(X0,relation_rng(X1))
| ~ relation(X1)
| ~ in(X1,unordered_pair(singleton(sK7(X1,X0)),unordered_pair(X0,sK7(X1,X0)))) )
| ~ spl15_23
| ~ spl15_38 ),
inference(resolution,[],[f348,f264]) ).
fof(f599,plain,
( spl15_70
| ~ spl15_24
| ~ spl15_38 ),
inference(avatar_split_clause,[],[f350,f347,f267,f597]) ).
fof(f597,plain,
( spl15_70
<=> ! [X0,X1] :
( ~ in(X0,relation_rng(X1))
| ~ relation(X1)
| element(unordered_pair(singleton(sK7(X1,X0)),unordered_pair(X0,sK7(X1,X0))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_70])]) ).
fof(f350,plain,
( ! [X0,X1] :
( ~ in(X0,relation_rng(X1))
| ~ relation(X1)
| element(unordered_pair(singleton(sK7(X1,X0)),unordered_pair(X0,sK7(X1,X0))),X1) )
| ~ spl15_24
| ~ spl15_38 ),
inference(resolution,[],[f348,f268]) ).
fof(f585,plain,
( spl15_69
| ~ spl15_34
| ~ spl15_45 ),
inference(avatar_split_clause,[],[f399,f387,f324,f583]) ).
fof(f399,plain,
( ! [X0,X1] :
( relation_rng(X0) = X1
| in(sK5(X0,X1),X1)
| ~ relation(X0)
| in(sK5(X0,X1),relation_rng(X0)) )
| ~ spl15_34
| ~ spl15_45 ),
inference(duplicate_literal_removal,[],[f393]) ).
fof(f393,plain,
( ! [X0,X1] :
( relation_rng(X0) = X1
| in(sK5(X0,X1),X1)
| ~ relation(X0)
| in(sK5(X0,X1),relation_rng(X0))
| ~ relation(X0) )
| ~ spl15_34
| ~ spl15_45 ),
inference(resolution,[],[f388,f325]) ).
fof(f575,plain,
( spl15_68
| ~ spl15_27
| ~ spl15_35 ),
inference(avatar_split_clause,[],[f338,f330,f284,f573]) ).
fof(f338,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),X2)
| in(X1,X3)
| ~ sP0(X4,X3,X2) )
| ~ spl15_27
| ~ spl15_35 ),
inference(superposition,[],[f331,f285]) ).
fof(f564,plain,
( spl15_67
| ~ spl15_27
| ~ spl15_34 ),
inference(avatar_split_clause,[],[f327,f324,f284,f562]) ).
fof(f327,plain,
( ! [X2,X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),X2)
| in(X1,relation_rng(X2))
| ~ relation(X2) )
| ~ spl15_27
| ~ spl15_34 ),
inference(superposition,[],[f325,f285]) ).
fof(f554,plain,
( spl15_66
| ~ spl15_21
| ~ spl15_45 ),
inference(avatar_split_clause,[],[f397,f387,f246,f552]) ).
fof(f397,plain,
( ! [X0,X1] :
( relation_rng(X0) = X1
| in(sK5(X0,X1),X1)
| ~ relation(X0)
| ~ empty(X0) )
| ~ spl15_21
| ~ spl15_45 ),
inference(resolution,[],[f388,f247]) ).
fof(f550,plain,
( spl15_65
| ~ spl15_29
| ~ spl15_32 ),
inference(avatar_split_clause,[],[f317,f314,f300,f548]) ).
fof(f314,plain,
( spl15_32
<=> ! [X2,X0,X1] :
( relation_rng_restriction(X1,X2) = X0
| ~ sP0(X2,X1,X0)
| ~ sP1(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_32])]) ).
fof(f317,plain,
( ! [X2,X0,X1] :
( ~ sP0(X0,X1,X2)
| relation_rng_restriction(X1,X0) = X2
| ~ relation(X2)
| ~ relation(X0) )
| ~ spl15_29
| ~ spl15_32 ),
inference(resolution,[],[f315,f301]) ).
fof(f315,plain,
( ! [X2,X0,X1] :
( ~ sP1(X0,X1,X2)
| ~ sP0(X2,X1,X0)
| relation_rng_restriction(X1,X2) = X0 )
| ~ spl15_32 ),
inference(avatar_component_clause,[],[f314]) ).
fof(f542,plain,
( spl15_64
| ~ spl15_21
| ~ spl15_46 ),
inference(avatar_split_clause,[],[f406,f401,f246,f540]) ).
fof(f406,plain,
( ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| in(sK10(X0,X1,X2),X1)
| ~ empty(X2) )
| ~ spl15_21
| ~ spl15_46 ),
inference(resolution,[],[f402,f247]) ).
fof(f538,plain,
( spl15_63
| ~ spl15_29
| ~ spl15_31 ),
inference(avatar_split_clause,[],[f312,f309,f300,f536]) ).
fof(f312,plain,
( ! [X0,X1] :
( sP0(X0,X1,relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ relation(X0) )
| ~ spl15_29
| ~ spl15_31 ),
inference(resolution,[],[f310,f301]) ).
fof(f534,plain,
( ~ spl15_62
| ~ spl15_18
| spl15_49 ),
inference(avatar_split_clause,[],[f433,f429,f233,f531]) ).
fof(f531,plain,
( spl15_62
<=> empty(relation_rng_restriction(sK3,sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_62])]) ).
fof(f433,plain,
( ~ empty(relation_rng_restriction(sK3,sK4))
| ~ spl15_18
| spl15_49 ),
inference(resolution,[],[f431,f234]) ).
fof(f431,plain,
( ~ empty(relation_rng(relation_rng_restriction(sK3,sK4)))
| spl15_49 ),
inference(avatar_component_clause,[],[f429]) ).
fof(f513,plain,
( spl15_61
| ~ spl15_21
| ~ spl15_38 ),
inference(avatar_split_clause,[],[f352,f347,f246,f511]) ).
fof(f352,plain,
( ! [X0,X1] :
( ~ in(X0,relation_rng(X1))
| ~ relation(X1)
| ~ empty(X1) )
| ~ spl15_21
| ~ spl15_38 ),
inference(resolution,[],[f348,f247]) ).
fof(f509,plain,
( spl15_60
| ~ spl15_18
| ~ spl15_28 ),
inference(avatar_split_clause,[],[f294,f288,f233,f507]) ).
fof(f288,plain,
( spl15_28
<=> ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_28])]) ).
fof(f294,plain,
( ! [X0,X1] :
( relation_rng(X1) = X0
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl15_18
| ~ spl15_28 ),
inference(resolution,[],[f289,f234]) ).
fof(f289,plain,
( ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) )
| ~ spl15_28 ),
inference(avatar_component_clause,[],[f288]) ).
fof(f496,plain,
( spl15_59
| ~ spl15_15
| ~ spl15_30 ),
inference(avatar_split_clause,[],[f307,f304,f218,f494]) ).
fof(f218,plain,
( spl15_15
<=> ! [X0] : element(sK8(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_15])]) ).
fof(f307,plain,
( ! [X0] :
( empty(X0)
| in(sK8(X0),X0) )
| ~ spl15_15
| ~ spl15_30 ),
inference(resolution,[],[f305,f219]) ).
fof(f219,plain,
( ! [X0] : element(sK8(X0),X0)
| ~ spl15_15 ),
inference(avatar_component_clause,[],[f218]) ).
fof(f492,plain,
( spl15_58
| ~ spl15_5
| ~ spl15_17
| ~ spl15_18 ),
inference(avatar_split_clause,[],[f255,f233,f229,f171,f490]) ).
fof(f229,plain,
( spl15_17
<=> ! [X0] :
( empty_set = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_17])]) ).
fof(f255,plain,
( ! [X0] :
( relation_rng(X0) = sK12
| ~ empty(X0) )
| ~ spl15_5
| ~ spl15_17
| ~ spl15_18 ),
inference(forward_demodulation,[],[f253,f250]) ).
fof(f250,plain,
( empty_set = sK12
| ~ spl15_5
| ~ spl15_17 ),
inference(resolution,[],[f230,f173]) ).
fof(f173,plain,
( empty(sK12)
| ~ spl15_5 ),
inference(avatar_component_clause,[],[f171]) ).
fof(f230,plain,
( ! [X0] :
( ~ empty(X0)
| empty_set = X0 )
| ~ spl15_17 ),
inference(avatar_component_clause,[],[f229]) ).
fof(f253,plain,
( ! [X0] :
( ~ empty(X0)
| relation_rng(X0) = empty_set )
| ~ spl15_17
| ~ spl15_18 ),
inference(resolution,[],[f234,f230]) ).
fof(f484,plain,
( spl15_57
| ~ spl15_5
| ~ spl15_28 ),
inference(avatar_split_clause,[],[f296,f288,f171,f482]) ).
fof(f482,plain,
( spl15_57
<=> ! [X0] :
( sK12 = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_57])]) ).
fof(f296,plain,
( ! [X0] :
( sK12 = X0
| ~ empty(X0) )
| ~ spl15_5
| ~ spl15_28 ),
inference(resolution,[],[f289,f173]) ).
fof(f476,plain,
( spl15_56
| ~ spl15_5
| ~ spl15_8
| ~ spl15_17 ),
inference(avatar_split_clause,[],[f252,f229,f186,f171,f473]) ).
fof(f473,plain,
( spl15_56
<=> sK12 = sK14 ),
introduced(avatar_definition,[new_symbols(naming,[spl15_56])]) ).
fof(f186,plain,
( spl15_8
<=> empty(sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_8])]) ).
fof(f252,plain,
( sK12 = sK14
| ~ spl15_5
| ~ spl15_8
| ~ spl15_17 ),
inference(forward_demodulation,[],[f251,f250]) ).
fof(f251,plain,
( empty_set = sK14
| ~ spl15_8
| ~ spl15_17 ),
inference(resolution,[],[f230,f188]) ).
fof(f188,plain,
( empty(sK14)
| ~ spl15_8 ),
inference(avatar_component_clause,[],[f186]) ).
fof(f471,plain,
( spl15_55
| ~ spl15_5
| ~ spl15_17 ),
inference(avatar_split_clause,[],[f250,f229,f171,f468]) ).
fof(f462,plain,
( ~ spl15_54
| ~ spl15_18
| spl15_52 ),
inference(avatar_split_clause,[],[f452,f448,f233,f459]) ).
fof(f459,plain,
( spl15_54
<=> empty(sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_54])]) ).
fof(f448,plain,
( spl15_52
<=> empty(relation_rng(sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_52])]) ).
fof(f452,plain,
( ~ empty(sK4)
| ~ spl15_18
| spl15_52 ),
inference(resolution,[],[f450,f234]) ).
fof(f450,plain,
( ~ empty(relation_rng(sK4))
| spl15_52 ),
inference(avatar_component_clause,[],[f448]) ).
fof(f457,plain,
( spl15_53
| ~ spl15_12
| ~ spl15_24 ),
inference(avatar_split_clause,[],[f444,f267,f205,f454]) ).
fof(f454,plain,
( spl15_53
<=> element(sK2,relation_rng(sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_53])]) ).
fof(f444,plain,
( element(sK2,relation_rng(sK4))
| ~ spl15_12
| ~ spl15_24 ),
inference(resolution,[],[f207,f268]) ).
fof(f451,plain,
( ~ spl15_52
| ~ spl15_12
| ~ spl15_21 ),
inference(avatar_split_clause,[],[f446,f246,f205,f448]) ).
fof(f446,plain,
( ~ empty(relation_rng(sK4))
| ~ spl15_12
| ~ spl15_21 ),
inference(resolution,[],[f207,f247]) ).
fof(f443,plain,
( spl15_51
| ~ spl15_10
| ~ spl15_24 ),
inference(avatar_split_clause,[],[f278,f267,f196,f440]) ).
fof(f278,plain,
( element(sK2,relation_rng(relation_rng_restriction(sK3,sK4)))
| ~ spl15_10
| ~ spl15_24 ),
inference(resolution,[],[f268,f198]) ).
fof(f438,plain,
( ~ spl15_50
| ~ spl15_10
| ~ spl15_23 ),
inference(avatar_split_clause,[],[f276,f263,f196,f435]) ).
fof(f435,plain,
( spl15_50
<=> in(relation_rng(relation_rng_restriction(sK3,sK4)),sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_50])]) ).
fof(f276,plain,
( ~ in(relation_rng(relation_rng_restriction(sK3,sK4)),sK2)
| ~ spl15_10
| ~ spl15_23 ),
inference(resolution,[],[f264,f198]) ).
fof(f432,plain,
( ~ spl15_49
| ~ spl15_10
| ~ spl15_21 ),
inference(avatar_split_clause,[],[f257,f246,f196,f429]) ).
fof(f257,plain,
( ~ empty(relation_rng(relation_rng_restriction(sK3,sK4)))
| ~ spl15_10
| ~ spl15_21 ),
inference(resolution,[],[f247,f198]) ).
fof(f421,plain,
spl15_48,
inference(avatar_split_clause,[],[f138,f419]) ).
fof(f138,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X2)
| ~ in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X0)
| sP0(X0,X1,X2)
| ~ in(sK10(X0,X1,X2),X1) ),
inference(forward_demodulation,[],[f137,f98]) ).
fof(f98,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f137,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK9(X0,X1,X2),sK10(X0,X1,X2))),X2)
| ~ in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X0)
| sP0(X0,X1,X2)
| ~ in(sK10(X0,X1,X2),X1) ),
inference(forward_demodulation,[],[f136,f98]) ).
fof(f136,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X0)
| sP0(X0,X1,X2)
| ~ in(sK10(X0,X1,X2),X1)
| ~ in(unordered_pair(unordered_pair(sK9(X0,X1,X2),sK10(X0,X1,X2)),singleton(sK9(X0,X1,X2))),X2) ),
inference(forward_demodulation,[],[f135,f98]) ).
fof(f135,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK9(X0,X1,X2),sK10(X0,X1,X2))),X0)
| sP0(X0,X1,X2)
| ~ in(sK10(X0,X1,X2),X1)
| ~ in(unordered_pair(unordered_pair(sK9(X0,X1,X2),sK10(X0,X1,X2)),singleton(sK9(X0,X1,X2))),X2) ),
inference(forward_demodulation,[],[f126,f98]) ).
fof(f126,plain,
! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ in(unordered_pair(unordered_pair(sK9(X0,X1,X2),sK10(X0,X1,X2)),singleton(sK9(X0,X1,X2))),X0)
| ~ in(sK10(X0,X1,X2),X1)
| ~ in(unordered_pair(unordered_pair(sK9(X0,X1,X2),sK10(X0,X1,X2)),singleton(sK9(X0,X1,X2))),X2) ),
inference(definition_unfolding,[],[f108,f99,f99]) ).
fof(f99,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(f108,plain,
! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ in(ordered_pair(sK9(X0,X1,X2),sK10(X0,X1,X2)),X0)
| ~ in(sK10(X0,X1,X2),X1)
| ~ in(ordered_pair(sK9(X0,X1,X2),sK10(X0,X1,X2)),X2) ),
inference(cnf_transformation,[],[f69]) ).
fof(f69,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ( ( ~ in(ordered_pair(sK9(X0,X1,X2),sK10(X0,X1,X2)),X0)
| ~ in(sK10(X0,X1,X2),X1)
| ~ in(ordered_pair(sK9(X0,X1,X2),sK10(X0,X1,X2)),X2) )
& ( ( in(ordered_pair(sK9(X0,X1,X2),sK10(X0,X1,X2)),X0)
& in(sK10(X0,X1,X2),X1) )
| in(ordered_pair(sK9(X0,X1,X2),sK10(X0,X1,X2)),X2) ) ) )
& ( ! [X5,X6] :
( ( in(ordered_pair(X5,X6),X2)
| ~ in(ordered_pair(X5,X6),X0)
| ~ in(X6,X1) )
& ( ( in(ordered_pair(X5,X6),X0)
& in(X6,X1) )
| ~ in(ordered_pair(X5,X6),X2) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10])],[f67,f68]) ).
fof(f68,plain,
! [X0,X1,X2] :
( ? [X3,X4] :
( ( ~ in(ordered_pair(X3,X4),X0)
| ~ in(X4,X1)
| ~ in(ordered_pair(X3,X4),X2) )
& ( ( in(ordered_pair(X3,X4),X0)
& in(X4,X1) )
| in(ordered_pair(X3,X4),X2) ) )
=> ( ( ~ in(ordered_pair(sK9(X0,X1,X2),sK10(X0,X1,X2)),X0)
| ~ in(sK10(X0,X1,X2),X1)
| ~ in(ordered_pair(sK9(X0,X1,X2),sK10(X0,X1,X2)),X2) )
& ( ( in(ordered_pair(sK9(X0,X1,X2),sK10(X0,X1,X2)),X0)
& in(sK10(X0,X1,X2),X1) )
| in(ordered_pair(sK9(X0,X1,X2),sK10(X0,X1,X2)),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f67,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ? [X3,X4] :
( ( ~ in(ordered_pair(X3,X4),X0)
| ~ in(X4,X1)
| ~ in(ordered_pair(X3,X4),X2) )
& ( ( in(ordered_pair(X3,X4),X0)
& in(X4,X1) )
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ! [X5,X6] :
( ( in(ordered_pair(X5,X6),X2)
| ~ in(ordered_pair(X5,X6),X0)
| ~ in(X6,X1) )
& ( ( in(ordered_pair(X5,X6),X0)
& in(X6,X1) )
| ~ in(ordered_pair(X5,X6),X2) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(rectify,[],[f66]) ).
fof(f66,plain,
! [X1,X0,X2] :
( ( sP0(X1,X0,X2)
| ? [X3,X4] :
( ( ~ in(ordered_pair(X3,X4),X1)
| ~ in(X4,X0)
| ~ in(ordered_pair(X3,X4),X2) )
& ( ( in(ordered_pair(X3,X4),X1)
& in(X4,X0) )
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ! [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ~ in(ordered_pair(X3,X4),X1)
| ~ in(X4,X0) )
& ( ( in(ordered_pair(X3,X4),X1)
& in(X4,X0) )
| ~ in(ordered_pair(X3,X4),X2) ) )
| ~ sP0(X1,X0,X2) ) ),
inference(flattening,[],[f65]) ).
fof(f65,plain,
! [X1,X0,X2] :
( ( sP0(X1,X0,X2)
| ? [X3,X4] :
( ( ~ in(ordered_pair(X3,X4),X1)
| ~ in(X4,X0)
| ~ in(ordered_pair(X3,X4),X2) )
& ( ( in(ordered_pair(X3,X4),X1)
& in(X4,X0) )
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ! [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ~ in(ordered_pair(X3,X4),X1)
| ~ in(X4,X0) )
& ( ( in(ordered_pair(X3,X4),X1)
& in(X4,X0) )
| ~ in(ordered_pair(X3,X4),X2) ) )
| ~ sP0(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f48]) ).
fof(f48,plain,
! [X1,X0,X2] :
( sP0(X1,X0,X2)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ( in(ordered_pair(X3,X4),X1)
& in(X4,X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f410,plain,
spl15_47,
inference(avatar_split_clause,[],[f142,f408]) ).
fof(f142,plain,
! [X2,X0,X1] :
( in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X2)
| in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X0)
| sP0(X0,X1,X2) ),
inference(forward_demodulation,[],[f141,f98]) ).
fof(f141,plain,
! [X2,X0,X1] :
( in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK9(X0,X1,X2),sK10(X0,X1,X2))),X2)
| in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X0)
| sP0(X0,X1,X2) ),
inference(forward_demodulation,[],[f140,f98]) ).
fof(f140,plain,
! [X2,X0,X1] :
( in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X0)
| sP0(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK9(X0,X1,X2),sK10(X0,X1,X2)),singleton(sK9(X0,X1,X2))),X2) ),
inference(forward_demodulation,[],[f139,f98]) ).
fof(f139,plain,
! [X2,X0,X1] :
( in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK9(X0,X1,X2),sK10(X0,X1,X2))),X0)
| sP0(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK9(X0,X1,X2),sK10(X0,X1,X2)),singleton(sK9(X0,X1,X2))),X2) ),
inference(forward_demodulation,[],[f127,f98]) ).
fof(f127,plain,
! [X2,X0,X1] :
( sP0(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK9(X0,X1,X2),sK10(X0,X1,X2)),singleton(sK9(X0,X1,X2))),X0)
| in(unordered_pair(unordered_pair(sK9(X0,X1,X2),sK10(X0,X1,X2)),singleton(sK9(X0,X1,X2))),X2) ),
inference(definition_unfolding,[],[f107,f99,f99]) ).
fof(f107,plain,
! [X2,X0,X1] :
( sP0(X0,X1,X2)
| in(ordered_pair(sK9(X0,X1,X2),sK10(X0,X1,X2)),X0)
| in(ordered_pair(sK9(X0,X1,X2),sK10(X0,X1,X2)),X2) ),
inference(cnf_transformation,[],[f69]) ).
fof(f403,plain,
spl15_46,
inference(avatar_split_clause,[],[f144,f401]) ).
fof(f144,plain,
! [X2,X0,X1] :
( in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2))),X2)
| sP0(X0,X1,X2)
| in(sK10(X0,X1,X2),X1) ),
inference(forward_demodulation,[],[f143,f98]) ).
fof(f143,plain,
! [X2,X0,X1] :
( in(unordered_pair(singleton(sK9(X0,X1,X2)),unordered_pair(sK9(X0,X1,X2),sK10(X0,X1,X2))),X2)
| sP0(X0,X1,X2)
| in(sK10(X0,X1,X2),X1) ),
inference(forward_demodulation,[],[f128,f98]) ).
fof(f128,plain,
! [X2,X0,X1] :
( sP0(X0,X1,X2)
| in(sK10(X0,X1,X2),X1)
| in(unordered_pair(unordered_pair(sK9(X0,X1,X2),sK10(X0,X1,X2)),singleton(sK9(X0,X1,X2))),X2) ),
inference(definition_unfolding,[],[f106,f99]) ).
fof(f106,plain,
! [X2,X0,X1] :
( sP0(X0,X1,X2)
| in(sK10(X0,X1,X2),X1)
| in(ordered_pair(sK9(X0,X1,X2),sK10(X0,X1,X2)),X2) ),
inference(cnf_transformation,[],[f69]) ).
fof(f389,plain,
( spl15_45
| ~ spl15_27
| ~ spl15_44 ),
inference(avatar_split_clause,[],[f385,f382,f284,f387]) ).
fof(f382,plain,
( spl15_44
<=> ! [X0,X1] :
( relation_rng(X0) = X1
| in(unordered_pair(unordered_pair(sK6(X0,X1),sK5(X0,X1)),singleton(sK6(X0,X1))),X0)
| in(sK5(X0,X1),X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_44])]) ).
fof(f385,plain,
( ! [X0,X1] :
( in(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X0)
| relation_rng(X0) = X1
| in(sK5(X0,X1),X1)
| ~ relation(X0) )
| ~ spl15_27
| ~ spl15_44 ),
inference(forward_demodulation,[],[f383,f285]) ).
fof(f383,plain,
( ! [X0,X1] :
( relation_rng(X0) = X1
| in(unordered_pair(unordered_pair(sK6(X0,X1),sK5(X0,X1)),singleton(sK6(X0,X1))),X0)
| in(sK5(X0,X1),X1)
| ~ relation(X0) )
| ~ spl15_44 ),
inference(avatar_component_clause,[],[f382]) ).
fof(f384,plain,
spl15_44,
inference(avatar_split_clause,[],[f122,f382]) ).
fof(f122,plain,
! [X0,X1] :
( relation_rng(X0) = X1
| in(unordered_pair(unordered_pair(sK6(X0,X1),sK5(X0,X1)),singleton(sK6(X0,X1))),X0)
| in(sK5(X0,X1),X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f88,f99]) ).
fof(f88,plain,
! [X0,X1] :
( relation_rng(X0) = X1
| in(ordered_pair(sK6(X0,X1),sK5(X0,X1)),X0)
| in(sK5(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f60,plain,
! [X0] :
( ! [X1] :
( ( relation_rng(X0) = X1
| ( ( ! [X3] : ~ in(ordered_pair(X3,sK5(X0,X1)),X0)
| ~ in(sK5(X0,X1),X1) )
& ( in(ordered_pair(sK6(X0,X1),sK5(X0,X1)),X0)
| in(sK5(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
& ( in(ordered_pair(sK7(X0,X5),X5),X0)
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f56,f59,f58,f57]) ).
fof(f57,plain,
! [X0,X1] :
( ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X4,X2),X0)
| in(X2,X1) ) )
=> ( ( ! [X3] : ~ in(ordered_pair(X3,sK5(X0,X1)),X0)
| ~ in(sK5(X0,X1),X1) )
& ( ? [X4] : in(ordered_pair(X4,sK5(X0,X1)),X0)
| in(sK5(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f58,plain,
! [X0,X1] :
( ? [X4] : in(ordered_pair(X4,sK5(X0,X1)),X0)
=> in(ordered_pair(sK6(X0,X1),sK5(X0,X1)),X0) ),
introduced(choice_axiom,[]) ).
fof(f59,plain,
! [X0,X5] :
( ? [X7] : in(ordered_pair(X7,X5),X0)
=> in(ordered_pair(sK7(X0,X5),X5),X0) ),
introduced(choice_axiom,[]) ).
fof(f56,plain,
! [X0] :
( ! [X1] :
( ( relation_rng(X0) = X1
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X4,X2),X0)
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
& ( ? [X7] : in(ordered_pair(X7,X5),X0)
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(rectify,[],[f55]) ).
fof(f55,plain,
! [X0] :
( ! [X1] :
( ( relation_rng(X0) = X1
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) )
& ( ? [X3] : in(ordered_pair(X3,X2),X0)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X3,X2),X0) )
& ( ? [X3] : in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f34]) ).
fof(f34,plain,
! [X0] :
( ! [X1] :
( relation_rng(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation_rng(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_relat_1) ).
fof(f378,plain,
( spl15_43
| ~ spl15_11
| ~ spl15_24 ),
inference(avatar_split_clause,[],[f277,f267,f200,f375]) ).
fof(f277,plain,
( element(sK2,sK3)
| ~ spl15_11
| ~ spl15_24 ),
inference(resolution,[],[f268,f202]) ).
fof(f202,plain,
( in(sK2,sK3)
| ~ spl15_11 ),
inference(avatar_component_clause,[],[f200]) ).
fof(f373,plain,
spl15_42,
inference(avatar_split_clause,[],[f146,f371]) ).
fof(f146,plain,
! [X2,X0,X1,X6,X5] :
( ~ in(unordered_pair(singleton(X5),unordered_pair(X5,X6)),X0)
| in(unordered_pair(singleton(X5),unordered_pair(X5,X6)),X2)
| ~ in(X6,X1)
| ~ sP0(X0,X1,X2) ),
inference(forward_demodulation,[],[f145,f98]) ).
fof(f145,plain,
! [X2,X0,X1,X6,X5] :
( in(unordered_pair(singleton(X5),unordered_pair(X5,X6)),X2)
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X0)
| ~ in(X6,X1)
| ~ sP0(X0,X1,X2) ),
inference(forward_demodulation,[],[f129,f98]) ).
fof(f129,plain,
! [X2,X0,X1,X6,X5] :
( in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X2)
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X0)
| ~ in(X6,X1)
| ~ sP0(X0,X1,X2) ),
inference(definition_unfolding,[],[f105,f99,f99]) ).
fof(f105,plain,
! [X2,X0,X1,X6,X5] :
( in(ordered_pair(X5,X6),X2)
| ~ in(ordered_pair(X5,X6),X0)
| ~ in(X6,X1)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f69]) ).
fof(f367,plain,
( spl15_41
| ~ spl15_27
| ~ spl15_40 ),
inference(avatar_split_clause,[],[f363,f360,f284,f365]) ).
fof(f360,plain,
( spl15_40
<=> ! [X0,X1,X3] :
( relation_rng(X0) = X1
| ~ in(unordered_pair(unordered_pair(X3,sK5(X0,X1)),singleton(X3)),X0)
| ~ in(sK5(X0,X1),X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_40])]) ).
fof(f363,plain,
( ! [X3,X0,X1] :
( ~ in(unordered_pair(singleton(X3),unordered_pair(X3,sK5(X0,X1))),X0)
| relation_rng(X0) = X1
| ~ in(sK5(X0,X1),X1)
| ~ relation(X0) )
| ~ spl15_27
| ~ spl15_40 ),
inference(forward_demodulation,[],[f361,f285]) ).
fof(f361,plain,
( ! [X3,X0,X1] :
( relation_rng(X0) = X1
| ~ in(unordered_pair(unordered_pair(X3,sK5(X0,X1)),singleton(X3)),X0)
| ~ in(sK5(X0,X1),X1)
| ~ relation(X0) )
| ~ spl15_40 ),
inference(avatar_component_clause,[],[f360]) ).
fof(f362,plain,
spl15_40,
inference(avatar_split_clause,[],[f121,f360]) ).
fof(f121,plain,
! [X3,X0,X1] :
( relation_rng(X0) = X1
| ~ in(unordered_pair(unordered_pair(X3,sK5(X0,X1)),singleton(X3)),X0)
| ~ in(sK5(X0,X1),X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f89,f99]) ).
fof(f89,plain,
! [X3,X0,X1] :
( relation_rng(X0) = X1
| ~ in(ordered_pair(X3,sK5(X0,X1)),X0)
| ~ in(sK5(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f356,plain,
spl15_39,
inference(avatar_split_clause,[],[f148,f354]) ).
fof(f148,plain,
! [X2,X0,X1,X6,X5] :
( ~ in(unordered_pair(singleton(X5),unordered_pair(X5,X6)),X2)
| in(unordered_pair(singleton(X5),unordered_pair(X5,X6)),X0)
| ~ sP0(X0,X1,X2) ),
inference(forward_demodulation,[],[f147,f98]) ).
fof(f147,plain,
! [X2,X0,X1,X6,X5] :
( in(unordered_pair(singleton(X5),unordered_pair(X5,X6)),X0)
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X2)
| ~ sP0(X0,X1,X2) ),
inference(forward_demodulation,[],[f130,f98]) ).
fof(f130,plain,
! [X2,X0,X1,X6,X5] :
( in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X0)
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X2)
| ~ sP0(X0,X1,X2) ),
inference(definition_unfolding,[],[f104,f99,f99]) ).
fof(f104,plain,
! [X2,X0,X1,X6,X5] :
( in(ordered_pair(X5,X6),X0)
| ~ in(ordered_pair(X5,X6),X2)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f69]) ).
fof(f349,plain,
( spl15_38
| ~ spl15_27
| ~ spl15_37 ),
inference(avatar_split_clause,[],[f345,f341,f284,f347]) ).
fof(f341,plain,
( spl15_37
<=> ! [X5,X0] :
( in(unordered_pair(unordered_pair(sK7(X0,X5),X5),singleton(sK7(X0,X5))),X0)
| ~ in(X5,relation_rng(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_37])]) ).
fof(f345,plain,
( ! [X0,X5] :
( in(unordered_pair(singleton(sK7(X0,X5)),unordered_pair(X5,sK7(X0,X5))),X0)
| ~ in(X5,relation_rng(X0))
| ~ relation(X0) )
| ~ spl15_27
| ~ spl15_37 ),
inference(forward_demodulation,[],[f344,f285]) ).
fof(f344,plain,
( ! [X0,X5] :
( in(unordered_pair(singleton(sK7(X0,X5)),unordered_pair(sK7(X0,X5),X5)),X0)
| ~ in(X5,relation_rng(X0))
| ~ relation(X0) )
| ~ spl15_27
| ~ spl15_37 ),
inference(forward_demodulation,[],[f342,f285]) ).
fof(f342,plain,
( ! [X0,X5] :
( in(unordered_pair(unordered_pair(sK7(X0,X5),X5),singleton(sK7(X0,X5))),X0)
| ~ in(X5,relation_rng(X0))
| ~ relation(X0) )
| ~ spl15_37 ),
inference(avatar_component_clause,[],[f341]) ).
fof(f343,plain,
spl15_37,
inference(avatar_split_clause,[],[f133,f341]) ).
fof(f133,plain,
! [X0,X5] :
( in(unordered_pair(unordered_pair(sK7(X0,X5),X5),singleton(sK7(X0,X5))),X0)
| ~ in(X5,relation_rng(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f124]) ).
fof(f124,plain,
! [X0,X1,X5] :
( in(unordered_pair(unordered_pair(sK7(X0,X5),X5),singleton(sK7(X0,X5))),X0)
| ~ in(X5,X1)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(definition_unfolding,[],[f86,f99]) ).
fof(f86,plain,
! [X0,X1,X5] :
( in(ordered_pair(sK7(X0,X5),X5),X0)
| ~ in(X5,X1)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f337,plain,
( ~ spl15_36
| ~ spl15_11
| ~ spl15_23 ),
inference(avatar_split_clause,[],[f275,f263,f200,f334]) ).
fof(f334,plain,
( spl15_36
<=> in(sK3,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_36])]) ).
fof(f275,plain,
( ~ in(sK3,sK2)
| ~ spl15_11
| ~ spl15_23 ),
inference(resolution,[],[f264,f202]) ).
fof(f332,plain,
spl15_35,
inference(avatar_split_clause,[],[f149,f330]) ).
fof(f149,plain,
! [X2,X0,X1,X6,X5] :
( ~ in(unordered_pair(singleton(X5),unordered_pair(X5,X6)),X2)
| in(X6,X1)
| ~ sP0(X0,X1,X2) ),
inference(forward_demodulation,[],[f131,f98]) ).
fof(f131,plain,
! [X2,X0,X1,X6,X5] :
( in(X6,X1)
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X2)
| ~ sP0(X0,X1,X2) ),
inference(definition_unfolding,[],[f103,f99]) ).
fof(f103,plain,
! [X2,X0,X1,X6,X5] :
( in(X6,X1)
| ~ in(ordered_pair(X5,X6),X2)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f69]) ).
fof(f326,plain,
( spl15_34
| ~ spl15_27
| ~ spl15_33 ),
inference(avatar_split_clause,[],[f322,f319,f284,f324]) ).
fof(f319,plain,
( spl15_33
<=> ! [X5,X0,X6] :
( in(X5,relation_rng(X0))
| ~ in(unordered_pair(unordered_pair(X6,X5),singleton(X6)),X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_33])]) ).
fof(f322,plain,
( ! [X0,X6,X5] :
( ~ in(unordered_pair(singleton(X6),unordered_pair(X6,X5)),X0)
| in(X5,relation_rng(X0))
| ~ relation(X0) )
| ~ spl15_27
| ~ spl15_33 ),
inference(forward_demodulation,[],[f320,f285]) ).
fof(f320,plain,
( ! [X0,X6,X5] :
( in(X5,relation_rng(X0))
| ~ in(unordered_pair(unordered_pair(X6,X5),singleton(X6)),X0)
| ~ relation(X0) )
| ~ spl15_33 ),
inference(avatar_component_clause,[],[f319]) ).
fof(f321,plain,
spl15_33,
inference(avatar_split_clause,[],[f132,f319]) ).
fof(f132,plain,
! [X0,X6,X5] :
( in(X5,relation_rng(X0))
| ~ in(unordered_pair(unordered_pair(X6,X5),singleton(X6)),X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f123]) ).
fof(f123,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(unordered_pair(unordered_pair(X6,X5),singleton(X6)),X0)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(definition_unfolding,[],[f87,f99]) ).
fof(f87,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(ordered_pair(X6,X5),X0)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f316,plain,
spl15_32,
inference(avatar_split_clause,[],[f102,f314]) ).
fof(f102,plain,
! [X2,X0,X1] :
( relation_rng_restriction(X1,X2) = X0
| ~ sP0(X2,X1,X0)
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f64]) ).
fof(f64,plain,
! [X0,X1,X2] :
( ( ( relation_rng_restriction(X1,X2) = X0
| ~ sP0(X2,X1,X0) )
& ( sP0(X2,X1,X0)
| relation_rng_restriction(X1,X2) != X0 ) )
| ~ sP1(X0,X1,X2) ),
inference(rectify,[],[f63]) ).
fof(f63,plain,
! [X2,X0,X1] :
( ( ( relation_rng_restriction(X0,X1) = X2
| ~ sP0(X1,X0,X2) )
& ( sP0(X1,X0,X2)
| relation_rng_restriction(X0,X1) != X2 ) )
| ~ sP1(X2,X0,X1) ),
inference(nnf_transformation,[],[f49]) ).
fof(f49,plain,
! [X2,X0,X1] :
( ( relation_rng_restriction(X0,X1) = X2
<=> sP0(X1,X0,X2) )
| ~ sP1(X2,X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f311,plain,
spl15_31,
inference(avatar_split_clause,[],[f134,f309]) ).
fof(f134,plain,
! [X2,X1] :
( sP0(X2,X1,relation_rng_restriction(X1,X2))
| ~ sP1(relation_rng_restriction(X1,X2),X1,X2) ),
inference(equality_resolution,[],[f101]) ).
fof(f101,plain,
! [X2,X0,X1] :
( sP0(X2,X1,X0)
| relation_rng_restriction(X1,X2) != X0
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f64]) ).
fof(f306,plain,
spl15_30,
inference(avatar_split_clause,[],[f112,f304]) ).
fof(f112,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f45]) ).
fof(f45,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f44]) ).
fof(f44,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f29]) ).
fof(f29,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f302,plain,
spl15_29,
inference(avatar_split_clause,[],[f109,f300]) ).
fof(f109,plain,
! [X2,X0,X1] :
( sP1(X2,X0,X1)
| ~ relation(X2)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f50]) ).
fof(f50,plain,
! [X0,X1] :
( ! [X2] :
( sP1(X2,X0,X1)
| ~ relation(X2) )
| ~ relation(X1) ),
inference(definition_folding,[],[f41,f49,f48]) ).
fof(f41,plain,
! [X0,X1] :
( ! [X2] :
( ( relation_rng_restriction(X0,X1) = X2
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ( in(ordered_pair(X3,X4),X1)
& in(X4,X0) ) ) )
| ~ relation(X2) )
| ~ relation(X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0,X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( relation_rng_restriction(X0,X1) = X2
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ( in(ordered_pair(X3,X4),X1)
& in(X4,X0) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_relat_1) ).
fof(f290,plain,
spl15_28,
inference(avatar_split_clause,[],[f113,f288]) ).
fof(f113,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f46]) ).
fof(f46,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(ennf_transformation,[],[f32]) ).
fof(f32,axiom,
! [X0,X1] :
~ ( empty(X1)
& X0 != X1
& empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
fof(f286,plain,
spl15_27,
inference(avatar_split_clause,[],[f98,f284]) ).
fof(f282,plain,
spl15_26,
inference(avatar_split_clause,[],[f94,f280]) ).
fof(f280,plain,
( spl15_26
<=> ! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_26])]) ).
fof(f94,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ),
inference(cnf_transformation,[],[f39]) ).
fof(f39,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ),
inference(flattening,[],[f38]) ).
fof(f38,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f20,axiom,
! [X0] :
( ( relation(X0)
& ~ empty(X0) )
=> ~ empty(relation_rng(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_relat_1) ).
fof(f274,plain,
( ~ spl15_25
| ~ spl15_11
| ~ spl15_21 ),
inference(avatar_split_clause,[],[f256,f246,f200,f271]) ).
fof(f256,plain,
( ~ empty(sK3)
| ~ spl15_11
| ~ spl15_21 ),
inference(resolution,[],[f247,f202]) ).
fof(f269,plain,
spl15_24,
inference(avatar_split_clause,[],[f111,f267]) ).
fof(f111,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f43]) ).
fof(f43,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f28]) ).
fof(f28,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
fof(f265,plain,
spl15_23,
inference(avatar_split_clause,[],[f110,f263]) ).
fof(f110,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f42]) ).
fof(f42,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f261,plain,
spl15_22,
inference(avatar_split_clause,[],[f100,f259]) ).
fof(f100,plain,
! [X0,X1] :
( relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) ),
inference(cnf_transformation,[],[f40]) ).
fof(f40,plain,
! [X0,X1] :
( relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0,X1] :
( relation(X1)
=> relation(relation_rng_restriction(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_relat_1) ).
fof(f248,plain,
spl15_21,
inference(avatar_split_clause,[],[f114,f246]) ).
fof(f114,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f47]) ).
fof(f47,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f244,plain,
spl15_20,
inference(avatar_split_clause,[],[f93,f242]) ).
fof(f93,plain,
! [X0] :
( relation(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f37,plain,
! [X0] :
( ( relation(relation_rng(X0))
& empty(relation_rng(X0)) )
| ~ empty(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,axiom,
! [X0] :
( empty(X0)
=> ( relation(relation_rng(X0))
& empty(relation_rng(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc8_relat_1) ).
fof(f240,plain,
( spl15_19
| ~ spl15_5
| ~ spl15_14 ),
inference(avatar_split_clause,[],[f226,f214,f171,f237]) ).
fof(f226,plain,
( relation(sK12)
| ~ spl15_5
| ~ spl15_14 ),
inference(resolution,[],[f215,f173]) ).
fof(f235,plain,
spl15_18,
inference(avatar_split_clause,[],[f92,f233]) ).
fof(f92,plain,
! [X0] :
( empty(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f231,plain,
spl15_17,
inference(avatar_split_clause,[],[f91,f229]) ).
fof(f91,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(cnf_transformation,[],[f36]) ).
fof(f36,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f30,axiom,
! [X0] :
( empty(X0)
=> empty_set = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(f224,plain,
spl15_16,
inference(avatar_split_clause,[],[f96,f222]) ).
fof(f222,plain,
( spl15_16
<=> ! [X0,X1] : ~ empty(unordered_pair(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_16])]) ).
fof(f96,plain,
! [X0,X1] : ~ empty(unordered_pair(X0,X1)),
inference(cnf_transformation,[],[f18]) ).
fof(f18,axiom,
! [X0,X1] : ~ empty(unordered_pair(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_subset_1) ).
fof(f220,plain,
spl15_15,
inference(avatar_split_clause,[],[f95,f218]) ).
fof(f95,plain,
! [X0] : element(sK8(X0),X0),
inference(cnf_transformation,[],[f62]) ).
fof(f62,plain,
! [X0] : element(sK8(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f14,f61]) ).
fof(f61,plain,
! [X0] :
( ? [X1] : element(X1,X0)
=> element(sK8(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f14,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f216,plain,
spl15_14,
inference(avatar_split_clause,[],[f90,f214]) ).
fof(f90,plain,
! [X0] :
( relation(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f35]) ).
fof(f35,plain,
! [X0] :
( relation(X0)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0] :
( empty(X0)
=> relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
fof(f212,plain,
spl15_13,
inference(avatar_split_clause,[],[f85,f210]) ).
fof(f210,plain,
( spl15_13
<=> ! [X0] : ~ empty(singleton(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_13])]) ).
fof(f85,plain,
! [X0] : ~ empty(singleton(X0)),
inference(cnf_transformation,[],[f17]) ).
fof(f17,axiom,
! [X0] : ~ empty(singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_subset_1) ).
fof(f208,plain,
( spl15_10
| spl15_12 ),
inference(avatar_split_clause,[],[f80,f205,f196]) ).
fof(f80,plain,
( in(sK2,relation_rng(sK4))
| in(sK2,relation_rng(relation_rng_restriction(sK3,sK4))) ),
inference(cnf_transformation,[],[f54]) ).
fof(f203,plain,
( spl15_10
| spl15_11 ),
inference(avatar_split_clause,[],[f79,f200,f196]) ).
fof(f79,plain,
( in(sK2,sK3)
| in(sK2,relation_rng(relation_rng_restriction(sK3,sK4))) ),
inference(cnf_transformation,[],[f54]) ).
fof(f194,plain,
spl15_9,
inference(avatar_split_clause,[],[f120,f191]) ).
fof(f191,plain,
( spl15_9
<=> relation(sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_9])]) ).
fof(f120,plain,
relation(sK14),
inference(cnf_transformation,[],[f77]) ).
fof(f77,plain,
( relation(sK14)
& empty(sK14) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f22,f76]) ).
fof(f76,plain,
( ? [X0] :
( relation(X0)
& empty(X0) )
=> ( relation(sK14)
& empty(sK14) ) ),
introduced(choice_axiom,[]) ).
fof(f22,axiom,
? [X0] :
( relation(X0)
& empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
fof(f189,plain,
spl15_8,
inference(avatar_split_clause,[],[f119,f186]) ).
fof(f119,plain,
empty(sK14),
inference(cnf_transformation,[],[f77]) ).
fof(f184,plain,
spl15_7,
inference(avatar_split_clause,[],[f118,f181]) ).
fof(f118,plain,
relation(sK13),
inference(cnf_transformation,[],[f75]) ).
fof(f75,plain,
( relation(sK13)
& ~ empty(sK13) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f24,f74]) ).
fof(f74,plain,
( ? [X0] :
( relation(X0)
& ~ empty(X0) )
=> ( relation(sK13)
& ~ empty(sK13) ) ),
introduced(choice_axiom,[]) ).
fof(f24,axiom,
? [X0] :
( relation(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
fof(f179,plain,
~ spl15_6,
inference(avatar_split_clause,[],[f117,f176]) ).
fof(f176,plain,
( spl15_6
<=> empty(sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_6])]) ).
fof(f117,plain,
~ empty(sK13),
inference(cnf_transformation,[],[f75]) ).
fof(f174,plain,
spl15_5,
inference(avatar_split_clause,[],[f116,f171]) ).
fof(f116,plain,
empty(sK12),
inference(cnf_transformation,[],[f73]) ).
fof(f73,plain,
empty(sK12),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f23,f72]) ).
fof(f72,plain,
( ? [X0] : empty(X0)
=> empty(sK12) ),
introduced(choice_axiom,[]) ).
fof(f23,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f169,plain,
~ spl15_4,
inference(avatar_split_clause,[],[f115,f166]) ).
fof(f166,plain,
( spl15_4
<=> empty(sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_4])]) ).
fof(f115,plain,
~ empty(sK11),
inference(cnf_transformation,[],[f71]) ).
fof(f71,plain,
~ empty(sK11),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f25,f70]) ).
fof(f70,plain,
( ? [X0] : ~ empty(X0)
=> ~ empty(sK11) ),
introduced(choice_axiom,[]) ).
fof(f25,axiom,
? [X0] : ~ empty(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f164,plain,
spl15_3,
inference(avatar_split_clause,[],[f84,f161]) ).
fof(f84,plain,
relation(empty_set),
inference(cnf_transformation,[],[f19]) ).
fof(f19,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(f159,plain,
spl15_2,
inference(avatar_split_clause,[],[f82,f156]) ).
fof(f82,plain,
empty(empty_set),
inference(cnf_transformation,[],[f15]) ).
fof(f15,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f154,plain,
spl15_1,
inference(avatar_split_clause,[],[f78,f151]) ).
fof(f78,plain,
relation(sK4),
inference(cnf_transformation,[],[f54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.07 % Problem : SEU197+1 : TPTP v8.1.2. Released v3.3.0.
% 0.05/0.08 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.08/0.26 % Computer : n024.cluster.edu
% 0.08/0.26 % Model : x86_64 x86_64
% 0.08/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.26 % Memory : 8042.1875MB
% 0.08/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.26 % CPULimit : 300
% 0.08/0.26 % WCLimit : 300
% 0.08/0.26 % DateTime : Mon Apr 29 20:21:51 EDT 2024
% 0.08/0.26 % CPUTime :
% 0.08/0.26 % (11688)Running in auto input_syntax mode. Trying TPTP
% 0.08/0.27 % (11692)WARNING: value z3 for option sas not known
% 0.08/0.27 % (11693)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.08/0.27 % (11694)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)
% 0.08/0.27 % (11691)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.08/0.27 % (11690)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.08/0.27 % (11692)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)
% 0.08/0.27 % (11695)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)
% 0.08/0.27 % (11696)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)
% 0.08/0.27 TRYING [1]
% 0.08/0.28 TRYING [2]
% 0.08/0.28 TRYING [3]
% 0.08/0.28 TRYING [1]
% 0.08/0.28 TRYING [2]
% 0.08/0.30 TRYING [3]
% 0.08/0.30 TRYING [4]
% 0.11/0.32 TRYING [1]
% 0.11/0.32 TRYING [2]
% 0.11/0.32 TRYING [3]
% 0.11/0.34 TRYING [4]
% 0.11/0.35 TRYING [4]
% 0.11/0.40 TRYING [5]
% 2.49/0.63 TRYING [6]
% 2.80/0.67 % (11694)First to succeed.
% 2.80/0.69 % (11694)Refutation found. Thanks to Tanya!
% 2.80/0.69 % SZS status Theorem for theBenchmark
% 2.80/0.69 % SZS output start Proof for theBenchmark
% See solution above
% 2.80/0.70 % (11694)------------------------------
% 2.80/0.70 % (11694)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 2.80/0.70 % (11694)Termination reason: Refutation
% 2.80/0.70
% 2.80/0.70 % (11694)Memory used [KB]: 8608
% 2.80/0.70 % (11694)Time elapsed: 0.416 s
% 2.80/0.70 % (11694)Instructions burned: 1203 (million)
% 2.80/0.70 % (11694)------------------------------
% 2.80/0.70 % (11694)------------------------------
% 2.80/0.70 % (11688)Success in time 0.428 s
%------------------------------------------------------------------------------